Finite Group Databasebeta

← #28749401

Subgroups — #28749401

Order 15104.

2826 conjugacy classes of subgroups.

The subgroup lattice has 1646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837910C211yesmaximal, characteristic
2#21427115C211yesmaximal, characteristic, complemented
3#21427109C211yesmaximal, characteristic, complemented
4#21427104C211yesmaximal, characteristic, complemented
5#21427098C211yesmaximal, characteristic, complemented
6#21427079C211yesmaximal, characteristic, complemented
7#21427077C211yesmaximal, characteristic, complemented
8#21427074C211yesmaximal, characteristic, complemented
9#21427074C211yesmaximal, characteristic, complemented
10#21427035C211yesmaximal, characteristic, complemented
11#21427031C211yesmaximal, characteristic, complemented
12#21427005C211yesmaximal, characteristic, complemented
13#21427002C211yesmaximal, characteristic, complemented
14#21426986C211yesmaximal, characteristic, complemented
15#21426978C211yesmaximal, characteristic, complemented
16#21426935C211yesmaximal, characteristic, complemented
17#21426922C211yesmaximal, characteristic, complemented
18#21426890C211yesmaximal, characteristic, complemented
19#21426886C211yesmaximal, characteristic, complemented
20#21426882C211yesmaximal, characteristic, complemented
21#21426728C211yesmaximal, characteristic, complemented
22#21426726C211yesmaximal, characteristic, complemented
23#21426630C211yesmaximal, characteristic, complemented
24C4×#14273705C211yesmaximal, characteristic, complemented
25#21426608C211yesmaximal, characteristic, complemented
26C4×#14273700C211yesmaximal, characteristic, complemented
27#380×D59C211yesmaximal, characteristic, complemented
28#21426456C211yesmaximal, characteristic, complemented
29#21426455C211yesmaximal, characteristic, complemented
30C4×C22⋊C4×D59C211yesmaximal, characteristic, complemented
31C59×#2335C211yesmaximal, characteristic, complemented
32C22×#11745687C2211yescharacteristic
33C23×C4×D59C2211yescharacteristic
34#16837910C4116yescomplemented
35C2×#14273710C2211yescharacteristic
36C2×#14273705C2211yescharacteristic
37C2×#14273705C2211yescharacteristic
38C2×#14273700C2211yescharacteristic
39C2×#14273700C2211yescharacteristic
40C2×#14273697C2211yescharacteristic
41C2×#14273695C2211yescharacteristic
42C2×C4×Dic118C2211yescharacteristic, complemented
43C2×#14273692C2211yescharacteristic, complemented
44C2×C4×D236C2211yescharacteristic
45C2×C4×D236C2211yescharacteristic
46C2×#14273689C2211yescharacteristic
47C2×#14273689C2211yescharacteristic
48C2×#14273689C2211yescharacteristic
49C2×#14273689C2211yescharacteristic
50C2×C4×C22⋊D59C2211yescharacteristic
51C2×C4×C22⋊D59C2211yescharacteristic
52C2×C4×C22⋊D59C2211yescharacteristic, complemented
53C2×(C22⋊D59)⋊C4C2211yescharacteristic
54C2×(C22⋊D59)⋊C4C2211yescharacteristic
55C2×(C22⋊D59)⋊C4C2211yescharacteristic
56C2×(C22⋊D59)⋊C4C2211yescharacteristic
57C2×(C22⋊D59)⋊C4C2211yescharacteristic, complemented
58C2×#14273683C2211yescharacteristic
59C2×C4⋊C4×D59C2211yescharacteristic
60C2×C4⋊C4×D59C2211yescharacteristic
61C2×C22⋊C4×D59C2211yescharacteristic
62C2×C22⋊C4×D59C2211yescharacteristic
63C2×C22⋊C4×D59C2211yescharacteristic
64C2×C22⋊C4×D59C2211yescharacteristic
65C2×C42×D59C2211yescharacteristic
66C2×C42×D59C2211yescharacteristic
67#16837306C2211yescharacteristic, complemented
68#16837306C2211yescharacteristic, complemented
69#16837305C2211yescharacteristic
70#16837302C2211yescharacteristic
71#16837302C2211yescharacteristic
72#16837302C2211yescharacteristic, complemented
73#16837302C2211yescharacteristic, complemented
74#16837301C2211yescharacteristic, complemented
75#16837299C2211yescharacteristic, complemented
76#16837299C2211yescharacteristic, complemented
77#16837299C2211yescharacteristic, complemented
78#16837297C2211yescharacteristic, complemented
79#16837297C2211yescharacteristic, complemented
80#16837297C2211yescharacteristic, complemented
81#16837296C2211yescharacteristic
82#16837296C2211yescharacteristic
83#16837295C2211yescharacteristic
84#16837295C2211yescharacteristic
85#16837295C2211yescharacteristic, complemented
86#16837295C2211yescharacteristic, complemented
87#16837294C2211yescharacteristic, complemented
88#16837293C2211yescharacteristic, complemented
89#16837292C2211yescharacteristic, complemented
90#16837291C2211yescharacteristic, complemented
91#16837290C2211yescharacteristic
92#16837290C2211yescharacteristic
93#16837289C2211yescharacteristic, complemented
94#16837288C2211yescharacteristic, complemented
95#16837288C2211yescharacteristic, complemented
96#16837286C2211yescharacteristic, complemented
97#16837284C2211yescharacteristic, complemented
98#16837283C2211yescharacteristic, complemented
99#16837282C2211yescharacteristic
100#16837280C2211yescharacteristic
101#16837280C2211yescharacteristic
102#16837280C2211yescharacteristic
103#16837280C2211yescharacteristic
104#16837278C2211yescharacteristic
105#16837278C2211yescharacteristic
106#16837278C2211yescharacteristic
107#16837278C2211yescharacteristic
108#16837278C2211yescharacteristic
109#16837278C2211yescharacteristic
110#16837277C2211yescharacteristic, complemented
111#16837276C2211yescharacteristic
112#16837276C2211yescharacteristic
113#16837276C2211yescharacteristic
114#16837276C2211yescharacteristic
115#16837276C2211yescharacteristic, complemented
116#16837273C2211yescharacteristic
117#16837273C2211yescharacteristic
118#16837273C2211yescharacteristic
119#16837273C2211yescharacteristic
120#16837273C2211yescharacteristic, complemented
121#16837269C2211yescharacteristic, complemented
122#16837269C2211yescharacteristic, complemented
123#16837267C2211yescharacteristic, complemented
124#16837266C2211yescharacteristic, complemented
125#16837264C2211yescharacteristic, complemented
126#16837263C2211yescharacteristic, complemented
127#16837262C2211yescharacteristic
128#16837261C2211yescharacteristic
129#16837261C2211yescharacteristic
130#16837260C2211yescharacteristic
131#16837260C2211yescharacteristic
132#16837260C2211yescharacteristic, complemented
133#16837259C2211yescharacteristic
134#16837259C2211yescharacteristic
135#16837259C2211yescharacteristic, complemented
136C4⋊C4×Dic59C2211yescharacteristic, complemented
137C4⋊C4×Dic59C2211yescharacteristic, complemented
138C4×Dic59⋊C4C2211yescharacteristic, complemented
139C4×Dic59⋊C4C2211yescharacteristic, complemented
140C4×Dic59⋊C4C2211yescharacteristic, complemented
141C4×Dic59⋊C4C2211yescharacteristic, complemented
142#16837253C2211yescharacteristic, complemented
143#16837253C2211yescharacteristic, complemented
144#16837253C2211yescharacteristic, complemented
145C22⋊C4×Dic59C2211yescharacteristic
146C22⋊C4×Dic59C2211yescharacteristic
147C22⋊C4×Dic59C2211yescharacteristic, complemented
148C22⋊C4×Dic59C2211yescharacteristic, complemented
149C4×(C2×D59)⋊C4C2211yescharacteristic
150C4×(C2×D59)⋊C4C2211yescharacteristic
151C4×(C2×D59)⋊C4C2211yescharacteristic
152C4×(C2×D59)⋊C4C2211yescharacteristic
153C4×(C2×D59)⋊C4C2211yescharacteristic
154C4×(C2×D59)⋊C4C2211yescharacteristic
155C4×(C2×D59)⋊C4C2211yescharacteristic, complemented
156C4×(C2×D59)⋊C4C2211yescharacteristic, complemented
157C4×C22⋊Dic59C2211yescharacteristic
158#16837249C2211yescharacteristic
159#16837249C2211yescharacteristic
160#16837249C2211yescharacteristic
161#16837249C2211yescharacteristic
162#16837249C2211yescharacteristic
163#16837249C2211yescharacteristic
164#16837249C2211yescharacteristic, complemented
165#16837248C2211yescharacteristic, complemented
166#16837247C2211yescharacteristic, complemented
167C2×C59⋊#95C2211yescharacteristic, complemented
168#95×D59C2211yescharacteristic
169#95×D59C2211yescharacteristic
170#95×D59C2211yescharacteristic
171#95×D59C2211yescharacteristic
172#95×D59C2211yescharacteristic, complemented
173C2×#123×C59C2211yescharacteristic
174C59×#390C2211yescharacteristic
175C59×#389C2211yescharacteristic, complemented
176C59×#388C2211yescharacteristic
177C59×#388C2211yescharacteristic
178C59×#388C2211yescharacteristic, complemented
179C59×#388C2211yescharacteristic, complemented
180C59×#387C2211yescharacteristic, complemented
181C59×#387C2211yescharacteristic, complemented
182C59×#386C2211yescharacteristic
183C59×#385C2211yescharacteristic, complemented
184C59×#380C2211yescharacteristic
185C4×C4⋊C4×C59C2211yescharacteristic, complemented
186C4×C22⋊C4×C59C2211yescharacteristic
187C4×C22⋊C4×C59C2211yescharacteristic, complemented
188C24×D59C2311yescharacteristic
189C2×#11745687—42no—
190C2×#11745687—42no—
191C2×#11745687C2×C418yescomplemented
192C22×Dic118C2311yescharacteristic
193C22×D236C2311yescharacteristic
194C22×D236C2311yescharacteristic
195C22×C22⋊D59C2311yescharacteristic
196C22×C22⋊D59C2311yescharacteristic
197C22×C22⋊D59C2311yescharacteristic
198C22×C22⋊D59C2311yescharacteristic
199C23×Dic59C2311yescharacteristic
200C23×Dic59C2311yescharacteristic
201C23×Dic59C2311yescharacteristic
202C22×C4×D59—42no—
203C22×C4×D59—42no—
204C22×C4×D59C2×C418yescomplemented
205C22×C4×D59C2311yescharacteristic
206C22×C4×D59C2311yescharacteristic
207C22×C4×D59C2311yescharacteristic
208C22×C4×D59C2311yescharacteristic
209C22×C4×D59C2311yescharacteristic
210C22×C4×D59C2311yescharacteristic
211C22×C4×D59C2311yescharacteristic
212C22×C4×D59C2311yescharacteristic
213C22×C4×D59C2311yescharacteristic
214C22×C4×D59C2311yescharacteristic
215C22×C4×D59C2311yescharacteristic
216C22×C4×D59C2311yescharacteristic
217C22×C4×D59C2311yescharacteristic
218C22×C4×D59C2311yescharacteristic
219C22×C4×D59C2311yescharacteristic
220#14273710C2×C418yescomplemented
221#14273705C2×C418yescomplemented
222#14273705C2×C418yescomplemented
223#14273700C2×C418yescomplemented
224#14273700C2×C418yescomplemented
225#14273697C2×C418yescomplemented
226#14273695C2×C418yescomplemented
227C4×Dic118—42no—
228#14273692—42no—
229C4×D236—24no—
230C4×D236—42no—
231#14273689—24no—
232#14273689—42no—
233#14273689C2×C418yescomplemented
234#14273689C2×C418yescomplemented
235C4×C22⋊D59—24no—
236C4×C22⋊D59—42no—
237C4×C22⋊D59—42no—
238(C22⋊D59)⋊C4—24no—
239(C22⋊D59)⋊C4—42no—
240(C22⋊D59)⋊C4—42no—
241(C22⋊D59)⋊C4C2×C418yescomplemented
242(C22⋊D59)⋊C4C2×C418yescomplemented
243#14273683C2×C418yescomplemented
244C2×C4⋊Dic59C2311yescharacteristic
245C2×C4⋊Dic59C2311yescharacteristic
246C2×C4⋊Dic59C2311yescharacteristic
247C2×C4⋊Dic59C2311yescharacteristic
248C2×C4⋊Dic59C2311yescharacteristic
249C2×Dic59⋊C4C2311yescharacteristic
250C2×Dic59⋊C4C2311yescharacteristic
251C2×Dic59⋊C4C2311yescharacteristic
252C2×Dic59⋊C4C2311yescharacteristic
253C2×Dic59⋊C4C2311yescharacteristic
254C2×Dic59⋊C4C2311yescharacteristic
255C2×Dic59⋊C4C2311yescharacteristic
256C2×Dic59⋊C4C2311yescharacteristic
257C2×Dic59⋊C4C2311yescharacteristic
258C2×Dic59⋊C4C2311yescharacteristic
259C2×Dic59⋊C4C2311yescharacteristic
260C2×Dic59⋊C4C2311yescharacteristic
261C2×Dic59⋊C4C2311yescharacteristic
262C2×Dic59⋊C4C2311yescharacteristic
263C4⋊C4×D59—42no—
264C4⋊C4×D59—42no—
265C2×C22⋊Dic59C2311yescharacteristic
266C2×C22⋊Dic59C2311yescharacteristic
267C2×C22⋊Dic59C2311yescharacteristic
268C2×C22⋊Dic59C2311yescharacteristic
269C2×C22⋊Dic59C2311yescharacteristic
270C2×C22⋊Dic59C2311yescharacteristic
271C2×C22⋊Dic59C2311yescharacteristic
272C2×C22⋊Dic59C2311yescharacteristic
273C2×(C2×D59)⋊C4C2311yescharacteristic
274C2×(C2×D59)⋊C4C2311yescharacteristic
275C2×(C2×D59)⋊C4C2311yescharacteristic
276C2×(C2×D59)⋊C4C2311yescharacteristic
277C2×(C2×D59)⋊C4C2311yescharacteristic
278C2×(C2×D59)⋊C4C2311yescharacteristic
279C2×(C2×D59)⋊C4C2311yescharacteristic
280C2×(C2×D59)⋊C4C2311yescharacteristic
281C2×(C2×D59)⋊C4C2311yescharacteristic
282C2×(C2×D59)⋊C4C2311yescharacteristic
283C2×(C2×D59)⋊C4C2311yescharacteristic
284C2×(C2×D59)⋊C4C2311yescharacteristic
285C2×(C2×D59)⋊C4C2311yescharacteristic
286C2×(C2×D59)⋊C4C2311yescharacteristic
287C2×(C2×D59)⋊C4C2311yescharacteristic
288C2×(C2×D59)⋊C4C2311yescharacteristic
289C2×(C2×D59)⋊C4C2311yescharacteristic
290C2×(C2×D59)⋊C4C2311yescharacteristic
291C2×(C2×D59)⋊C4C2311yescharacteristic
292C2×(C2×D59)⋊C4C2311yescharacteristic
293C22⋊C4×D59—24no—
294C22⋊C4×D59—24no—
295C22⋊C4×D59—42no—
296C22⋊C4×D59—42no—
297C2×C4×Dic59C2311yescharacteristic
298C2×C4×Dic59C2311yescharacteristic
299C2×C4×Dic59C2311yescharacteristic
300C2×C4×Dic59C2311yescharacteristic
301C2×C4×Dic59C2311yescharacteristic
302C2×C4×Dic59C2311yescharacteristic
303C2×C4×Dic59C2311yescharacteristic
304C2×C4×Dic59C2311yescharacteristic
305C2×C4×Dic59C2311yescharacteristic
306C2×C4×Dic59C2311yescharacteristic
307C2×C4×Dic59C2311yescharacteristic
308C2×C4×Dic59C2311yescharacteristic
309C2×C4×Dic59C2311yescharacteristic
310C2×C4×Dic59C2311yescharacteristic
311C2×C4×Dic59C2311yescharacteristic
312C2×C4×Dic59C2311yescharacteristic
313C2×C4×Dic59C2311yescharacteristic
314C42×D59—42no—
315C42×D59—42no—
316C59⋊#95C2311yescharacteristic
317C59⋊#95C2311yescharacteristic
318C59⋊#95C2311yescharacteristic
319C59⋊#95C2311yescharacteristic
320C59⋊#95C2311yescharacteristic
321C59⋊#95C2311yescharacteristic
322C59⋊#95C2311yescharacteristic
323C59⋊#95C2311yescharacteristic
324C59⋊#95C2311yescharacteristic
325C59⋊#95C2311yescharacteristic
326C59⋊#95C2311yescharacteristic
327C59⋊#95C2311yescharacteristic
328C59⋊#95C2311yescharacteristic
329C59⋊#95C2311yescharacteristic
330C59⋊#95C2311yescharacteristic
331C59⋊#95C2311yescharacteristic
332C59⋊#95C2311yescharacteristic
333C59⋊#95C2311yescharacteristic
334C59⋊#95C2311yescharacteristic
335C59⋊#95C2311yescharacteristic
336C59⋊#95C2311yescharacteristic
337C59⋊#95C2311yescharacteristic
338C59⋊#95C2311yescharacteristic
339C59⋊#95C2311yescharacteristic
340C59⋊#95C2311yescharacteristic
341C59⋊#95C2311yescharacteristic
342C59⋊#95C2311yescharacteristic
343C59⋊#95C2311yescharacteristic
344C59⋊#95C2311yescharacteristic
345C59⋊#95C2311yescharacteristic
346C22×D4×C59C2311yescharacteristic
347C23×C4×C59C2311yescharacteristic
348C23×C4×C59C2311yescharacteristic
349#123×C59C2×C418yescomplemented
350C2×C4⋊C4×C59C2311yescharacteristic
351C2×C4⋊C4×C59C2311yescharacteristic
352C2×C4⋊C4×C59C2311yescharacteristic
353C2×C4⋊C4×C59C2311yescharacteristic
354C2×C4⋊C4×C59C2311yescharacteristic
355C2×C4⋊C4×C59C2311yescharacteristic
356C2×C4⋊C4×C59C2311yescharacteristic
357C2×C22⋊C4×C59C2311yescharacteristic
358C2×C22⋊C4×C59C2311yescharacteristic
359C2×C22⋊C4×C59C2311yescharacteristic
360C2×C22⋊C4×C59C2311yescharacteristic
361C2×C22⋊C4×C59C2311yescharacteristic
362C2×C22⋊C4×C59C2311yescharacteristic
363C2×C22⋊C4×C59C2311yescharacteristic
364C2×C22⋊C4×C59C2311yescharacteristic
365C2×C22⋊C4×C59C2311yescharacteristic
366C2×C22⋊C4×C59C2311yescharacteristic
367C2×C42×C59C2311yescharacteristic
368C2×C42×C59C2311yescharacteristic
369C2×C42×C59C2311yescharacteristic
370C2×C42×C59C2311yescharacteristic
371C2×C42×C59C2311yescharacteristic
372#95×C59C2311yescharacteristic
373#95×C59C2311yescharacteristic
374#95×C59C2311yescharacteristic
375#95×C59C2311yescharacteristic
376#95×C59C2311yescharacteristic
377#95×C59C2311yescharacteristic
378#95×C59C2311yescharacteristic
379#95×C59C2311yescharacteristic
380#95×C59C2311yescharacteristic
381#95×C59C2311yescharacteristic
382C24×C59C2411yescharacteristic
383C24×C59C2411yescharacteristic
384C23×D59—22no—
385C23×D59—22no—
386C23×D59—22no—
387C23×D59—22no—
388C23×D59—41no—
389C23×D59—41no—
390C23×D59C22×C414yes—
391C23×D59C2411yescharacteristic
392C23×D59C2411yescharacteristic
393C23×D59C2411yescharacteristic
394C2×D4×C59—41no—
395C2×D4×C59—41no—
396C2×D4×C59C22×C414yes—
397C22×C4×C59—22no—
398C22×C4×C59—41no—
399C22×C4×C59—41no—
400C22×C4×C59—41no—
401C22×C4×C59—41no—
402C22×C4×C59C22×C414yes—
403C22×C4×C59C2411yescharacteristic
404C22×C4×C59C2411yescharacteristic
405C22×C4×C59C2411yescharacteristic
406C22×C4×C59C2411yescharacteristic
407C22×C4×C59C2411yescharacteristic
408C22×C4×C59C2411yescharacteristic
409C22×C4×C59C2411yescharacteristic
410C22×C4×C59C2411yescharacteristic
411C22×C4×C59C2411yescharacteristic
412C22×C4×C59C2411yescharacteristic
413C22×C4×C59C2411yescharacteristic
414C22×C4×C59C2411yescharacteristic
415C22×C4×C59C2411yescharacteristic
416C2×C22⋊D59—22no—
417C2×C22⋊D59—22no—
418C2×C22⋊D59—22no—
419C2×C22⋊D59—22no—
420C2×C22⋊D59—22no—
421C2×C22⋊D59—22no—
422C2×C22⋊D59—41no—
423C2×C22⋊D59—41no—
424C2×C22⋊D59C22×C414yes—
425C2×C22⋊D59C22×C414yes—
426C2×C22⋊D59C22×C414yes—
427C2×C22⋊D59C22×C414yes—
428C22×Dic59—22no—
429C22×Dic59—22no—
430C22×Dic59—22no—
431C22×Dic59—41no—
432C22×Dic59—41no—
433C22×Dic59—41no—
434C22×Dic59—41no—
435C22×Dic59C22×C414yes—
436C22×Dic59C22×C414yes—
437C22×Dic59C2411yescharacteristic
438C22×Dic59C2411yescharacteristic
439C22×Dic59C2411yescharacteristic
440C22×Dic59C2411yescharacteristic
441C22×Dic59C2411yescharacteristic
442C22×Dic59C2411yescharacteristic
443C22×Dic59C2411yescharacteristic
444C22×Dic59C2411yescharacteristic
445C22×Dic59C2411yescharacteristic
446C22×Dic59C2411yescharacteristic
447C22×Dic59C2411yescharacteristic
448C22×Dic59C2411yescharacteristic
449C22×Dic59C2411yescharacteristic
450#11745687—416no—
451C2×D236—22no—
452C2×D236—22no—
453C2×D236—22no—
454C2×D236—22no—
455C2×D236C22×C414yes—
456C2×D236C22×C414yes—
457C2×C4×D59—22no—
458C2×C4×D59—22no—
459C2×C4×D59—22no—
460C2×C4×D59—22no—
461C2×C4×D59—22no—
462C2×C4×D59—22no—
463C2×C4×D59—22no—
464C2×C4×D59—22no—
465C2×C4×D59—22no—
466C2×C4×D59—22no—
467C2×C4×D59—22no—
468C2×C4×D59—22no—
469C2×C4×D59—22no—
470C2×C4×D59—22no—
471C2×C4×D59—22no—
472C2×C4×D59—22no—
473C2×C4×D59—22no—
474C2×C4×D59—22no—
475C2×C4×D59—416no—
476C2×C4×D59—41no—
477C2×C4×D59—41no—
478C2×C4×D59—41no—
479C2×C4×D59—41no—
480C2×C4×D59—41no—
481C2×C4×D59—41no—
482C2×C4×D59—41no—
483C2×C4×D59—41no—
484C2×C4×D59—41no—
485C2×C4×D59—41no—
486C2×C4×D59—41no—
487C2×C4×D59—41no—
488C2×C4×D59—41no—
489C2×C4×D59—41no—
490C2×C4×D59—41no—
491C2×C4×D59—41no—
492C2×C4×D59—41no—
493C2×C4×D59—41no—
494C2×C4×D59—41no—
495C2×C4×D59—41no—
496C2×C4×D59—41no—
497C2×C4×D59—41no—
498C2×C4×D59C22×C414yes—
499C2×C4×D59C22×C414yes—
500C2×C4×D59C22×C414yes—
501C2×C4×D59C22×C414yes—
502C2×C4×D59C22×C414yes—
503C2×Dic118—22no—
504C2×Dic118—22no—
505C2×Dic118C22×C414yes—
506C4⋊C4×C59—22no—
507C4⋊C4×C59—41no—
508C4⋊C4×C59—41no—
509C4⋊C4×C59—41no—
510C4⋊C4×C59—41no—
511C4⋊C4×C59C22×C414yes—
512C4⋊C4×C59C22×C414yes—
513C22⋊C4×C59—22no—
514C22⋊C4×C59—22no—
515C22⋊C4×C59—22no—
516C22⋊C4×C59—41no—
517C22⋊C4×C59—41no—
518C22⋊C4×C59—41no—
519C22⋊C4×C59—41no—
520C22⋊C4×C59C22×C414yes—
521C22⋊C4×C59C22×C414yes—
522C22⋊C4×C59C22×C414yes—
523C42×C59—22no—
524C42×C59—41no—
525C42×C59—41no—
526C42×C59—41no—
527C42×C59—41no—
528C22⋊Dic59—22no—
529C22⋊Dic59—22no—
530C22⋊Dic59—22no—
531C22⋊Dic59—41no—
532C22⋊Dic59—41no—
533C22⋊Dic59—41no—
534C22⋊Dic59—41no—
535C22⋊Dic59C22×C414yes—
536(C2×D59)⋊C4—22no—
537(C2×D59)⋊C4—22no—
538(C2×D59)⋊C4—22no—
539(C2×D59)⋊C4—22no—
540(C2×D59)⋊C4—22no—
541(C2×D59)⋊C4—22no—
542(C2×D59)⋊C4—22no—
543(C2×D59)⋊C4—22no—
544(C2×D59)⋊C4—41no—
545(C2×D59)⋊C4—41no—
546(C2×D59)⋊C4—41no—
547(C2×D59)⋊C4—41no—
548(C2×D59)⋊C4C22×C414yes—
549(C2×D59)⋊C4C22×C414yes—
550(C2×D59)⋊C4C22×C414yes—
551(C2×D59)⋊C4C22×C414yes—
552(C2×D59)⋊C4C22×C414yes—
553(C2×D59)⋊C4C22×C414yes—
554(C2×D59)⋊C4#4114yescomplemented
555(C2×D59)⋊C4#4114yescomplemented
556C4⋊Dic59—22no—
557C4⋊Dic59—41no—
558C4⋊Dic59—41no—
559C4⋊Dic59—41no—
560C4⋊Dic59—41no—
561Dic59⋊C4—22no—
562Dic59⋊C4—22no—
563Dic59⋊C4—22no—
564Dic59⋊C4—22no—
565Dic59⋊C4—22no—
566Dic59⋊C4—22no—
567Dic59⋊C4—41no—
568Dic59⋊C4—41no—
569Dic59⋊C4—41no—
570Dic59⋊C4—41no—
571Dic59⋊C4C22×C414yes—
572Dic59⋊C4C22×C414yes—
573Dic59⋊C4C22×C414yes—
574Dic59⋊C4C22×C414yes—
575C4×Dic59—22no—
576C4×Dic59—22no—
577C4×Dic59—22no—
578C4×Dic59—22no—
579C4×Dic59—22no—
580C4×Dic59—22no—
581C4×Dic59—22no—
582C4×Dic59—41no—
583C4×Dic59—41no—
584C4×Dic59—41no—
585C4×Dic59—41no—
586C4×Dic59—41no—
587C4×Dic59—41no—
588C4×Dic59—41no—
589C4×Dic59—41no—
590C4×Dic59C22×C414yes—
591C4×Dic59C22×C414yes—
592C23×C59—21no—
593C23×C59—21no—
594C23×C59—21no—
595C23×C59—21no—
596C23×C59—21no—
597C23×C59—21no—
598C23×C59—21no—
599C23×C59—21no—
600C23×C59—21no—
601C23×C59—21no—
602C23×C59—21no—
603C23×C59—21no—
604C23×C59C23×C412yes—
605C23×C59C23×C412yes—
606C23×C59C2511yescharacteristic
607C22×D59—21no—
608C22×D59—21no—
609C22×D59—21no—
610C22×D59—21no—
611C22×D59—21no—
612C22×D59—21no—
613C22×D59—21no—
614C22×D59—21no—
615C22×D59—21no—
616C22×D59—21no—
617C22×D59—21no—
618C22×D59—21no—
619C22×D59—21no—
620C22×D59—21no—
621C22×D59—28no—
622C22×D59—28no—
623C22×D59—44no—
624C22×D59—44no—
625C22×D59—44no—
626C22×D59—44no—
627C22×D59—44no—
628C22×D59C23×C412yes—
629C22×D59C23×C412yes—
630C22×D59C23×C412yes—
631C22×D59C2×#4112yes—
632C22×D59C2×#4112yes—
633C22×D59H(5,𝔽2)12yes—
634C22×D592−1+412yes—
635D4×C59—44no—
636C2×C4×C59—21no—
637C2×C4×C59—21no—
638C2×C4×C59—21no—
639C2×C4×C59—21no—
640C2×C4×C59—21no—
641C2×C4×C59—21no—
642C2×C4×C59—21no—
643C2×C4×C59—21no—
644C2×C4×C59—21no—
645C2×C4×C59—21no—
646C2×C4×C59—21no—
647C2×C4×C59—21no—
648C2×C4×C59—21no—
649C2×C4×C59—21no—
650C2×C4×C59—21no—
651C2×C4×C59—21no—
652C2×C4×C59—21no—
653C2×C4×C59—21no—
654C2×C4×C59—21no—
655C2×C4×C59—21no—
656C2×C4×C59—21no—
657C2×C4×C59—21no—
658C2×C4×C59—21no—
659C2×C4×C59—21no—
660C2×C4×C59—21no—
661C2×C4×C59—21no—
662C2×C4×C59—21no—
663C2×C4×C59—21no—
664C2×C4×C59—21no—
665C2×C4×C59—21no—
666C2×C4×C59—21no—
667C2×C4×C59—21no—
668C2×C4×C59—44no—
669C2×C4×C59—82no—
670C2×C4×C59C23×C412yes—
671C2×C4×C59C23×C412yes—
672C2×C4×C59C23×C412yes—
673C2×C4×C59C23×C412yes—
674C2×C4×C59C23×C412yes—
675C2×C4×C59C2×#4112yes—
676C2×C4×C59C2×#4112yes—
677C22⋊D59—28no—
678C22⋊D59—28no—
679C22⋊D59—28no—
680C22⋊D59—44no—
681C2×Dic59—21no—
682C2×Dic59—21no—
683C2×Dic59—21no—
684C2×Dic59—21no—
685C2×Dic59—21no—
686C2×Dic59—21no—
687C2×Dic59—21no—
688C2×Dic59—21no—
689C2×Dic59—21no—
690C2×Dic59—21no—
691C2×Dic59—21no—
692C2×Dic59—21no—
693C2×Dic59—28no—
694C2×Dic59—21no—
695C2×Dic59—21no—
696C2×Dic59—21no—
697C2×Dic59—21no—
698C2×Dic59—21no—
699C2×Dic59—21no—
700C2×Dic59—21no—
701C2×Dic59—21no—
702C2×Dic59—21no—
703C2×Dic59—21no—
704C2×Dic59—21no—
705C2×Dic59—21no—
706C2×Dic59—21no—
707C2×Dic59—21no—
708C2×Dic59—21no—
709C2×Dic59—21no—
710C2×Dic59—21no—
711C2×Dic59—21no—
712C2×Dic59—44no—
713C2×Dic59—82no—
714C2×Dic59C23×C412yes—
715C2×Dic59C23×C412yes—
716C2×Dic59C23×C412yes—
717C2×Dic59C23×C412yes—
718C2×Dic59C23×C412yes—
719C2×Dic59C2×#4112yes—
720C2×Dic59C2×#4112yes—
721C2×Dic59H(5,𝔽2)12yes—
722C2×Dic59H(5,𝔽2)12yes—
723D236—28no—
724D236—28no—
725C4×D59—28no—
726C4×D59—28no—
727C4×D59—44no—
728C4×D59—44no—
729C4×D59—44no—
730C4×D59—44no—
731C4×D59—44no—
732C4×D59—44no—
733C4×D59—44no—
734C4×D59—82no—
735C4×D59—82no—
736C4×D59—82no—
737C4×D59—82no—
738C4×D59—82no—
739C4×D59—82no—
740Dic118—28no—
741#34233—591nomaximal, Sylow
742C22×C59—22no—
743C22×C59—22no—
744C22×C59—22no—
745C22×C59—22no—
746C22×C59—22no—
747C22×C59—22no—
748C22×C59—41no—
749C22×C59—41no—
750C22×C59—41no—
751C22×C59—41no—
752C22×C59—41no—
753C22×C59—41no—
754C22×C59—41no—
755C22×C59—41no—
756C22×C59C24×C411yescharacteristic
757C22×C59C22×#4111yescharacteristic
758C22×C59C22×#4111yescharacteristic
759C22×C59C2×H(5,𝔽2)11yescharacteristic
760C22×C59C2×H(5,𝔽2)11yescharacteristic
761C22×C59C2×H(5,𝔽2)11yescharacteristic
762C22×C59C2×2−1+411yescharacteristic
763C2×D59—22no—
764C2×D59—22no—
765C2×D59—22no—
766C2×D59—22no—
767C2×D59—22no—
768C2×D59—22no—
769C2×D59—22no—
770C2×D59—22no—
771C2×D59—22no—
772C2×D59—22no—
773C2×D59—22no—
774C2×D59—22no—
775C2×D59—22no—
776C2×D59—22no—
777C2×D59—22no—
778C2×D59—416no—
779C2×D59—41no—
780C2×D59—41no—
781C2×D59—41no—
782C2×D59—41no—
783C2×D59C4×#4114yes—
784C2×D59#52014yes—
785C4×C59—22no—
786C4×C59—22no—
787C4×C59—22no—
788C4×C59—22no—
789C4×C59—22no—
790C4×C59—22no—
791C4×C59—22no—
792C4×C59—41no—
793C4×C59—41no—
794C4×C59—41no—
795C4×C59—41no—
796C4×C59—41no—
797C4×C59—41no—
798Dic59—22no—
799Dic59—22no—
800Dic59—22no—
801Dic59—22no—
802Dic59—22no—
803Dic59—22no—
804Dic59—41no—
805Dic59—41no—
806Dic59—41no—
807Dic59—41no—
808Dic59—41no—
809Dic59—41no—
810Dic59#51814yes—
811C2×#525—591no—
812#2361—591no—
813#2361—591no—
814#2360—591no—
815#2360—591no—
816#2358—591no—
817#2358—591no—
818#2358—591no—
819#2358—591no—
820#2353—591no—
821#2353—591no—
822#2349—591no—
823#2349—591no—
824#2347—591no—
825#2346—591no—
826#2341—591no—
827#2339—591no—
828#2335—591no—
829#2335—591no—
830#2335—591no—
831#2335D5911yescharacteristic, complemented
832#2318—591no—
833#2318—591no—
834C4×C22⋊Q8—591no—
835C4×C22⋊Q8—591no—
836C4×#121—591no—
837C4×#121—591no—
838C2×#380—591no—
839#2275—591no—
840#2275—591no—
841C2×C4×C22⋊C4—591no—
842C2×C59—42no—
843C2×C59—42no—
844C2×C59C2×C4×#4111yescharacteristic
845C2×C59C2×#51811yescharacteristic
846C2×C59C2×#52011yescharacteristic
847C2×C59#351911yescharacteristic
848C2×C59#351911yescharacteristic
849C2×C59#352011yescharacteristic
850C2×C59#352011yescharacteristic
851D59—24no—
852D59—24no—
853D59—42no—
854C22×#41—591no—
855C24×C4—591no—
856#525—5916no—
857C2×#123—591no—
858C2×#123C2×D5911yescharacteristic
859C2×C22⋊Q8—591no—
860C2×C22⋊Q8—591no—
861C2×#121—591no—
862C2×#121—591no—
863C2×#120—591no—
864C2×#120—591no—
865C2×C4×Q8—591no—
866C2×C4×Q8—591no—
867C2×C4×D4—591no—
868C2×C4×D4—591no—
869C2×C4×D4—591no—
870C2×C4×D4—591no—
871C2×C4×D4—591no—
872C2×C4×D4—591no—
873C2×C4×D4—591no—
874C2×C4×D4—591no—
875C2×C4×D4—591no—
876C2×C4×D4—591no—
877C2×C4×D4—591no—
878C2×C4×D4—591no—
879C2×C4×D4—591no—
880C2×C4×D4—591no—
881C2×#117—591no—
882C22×C4⋊C4—591no—
883C22×C4⋊C4—591no—
884C22×C22⋊C4—591no—
885C22×C22⋊C4—591no—
886C22×C22⋊C4—591no—
887C22×C22⋊C4—591no—
888C22×C42—591no—
889C22×C42—591no—
890#391—591no—
891#391—591no—
892#390—591no—
893#390—591no—
894#390—591no—
895#390—591no—
896#390—591no—
897#390C2×D5911yescharacteristic
898#389—591no—
899#389—591no—
900#389—591no—
901#389—591no—
902#389—591no—
903#389—591no—
904#389—591no—
905#389C2×D5911yescharacteristic, complemented
906#388—591no—
907#388—591no—
908#388—591no—
909#388—591no—
910#388—591no—
911#388—591no—
912#388—591no—
913#388—591no—
914#388—591no—
915#388—591no—
916#388—591no—
917#388—591no—
918#388C2×D5911yescharacteristic
919#388C2×D5911yescharacteristic
920#388C2×D5911yescharacteristic, complemented
921#388C2×D5911yescharacteristic, complemented
922#387—591no—
923#387—591no—
924#387—591no—
925#387—591no—
926#387—591no—
927#387—591no—
928#387C2×D5911yescharacteristic, complemented
929#387C2×D5911yescharacteristic, complemented
930#386—591no—
931#386—591no—
932#386—591no—
933#386—591no—
934#386—591no—
935#386—591no—
936#386—591no—
937#386—591no—
938#386—591no—
939#386—591no—
940#386—591no—
941#386C2×D5911yescharacteristic
942#385—591no—
943#385—591no—
944#385—591no—
945#385—591no—
946#385—591no—
947#385—591no—
948#385—591no—
949#385—591no—
950#385—591no—
951#385—591no—
952#385—591no—
953#385C2×D5911yescharacteristic, complemented
954#383—591no—
955#383—591no—
956#382—591no—
957#382—591no—
958#381—591no—
959#381—591no—
960#380—591no—
961#380—591no—
962#380—591no—
963#380—591no—
964#380—591no—
965#380—591no—
966#380—591no—
967#380—591no—
968#380—591no—
969#380C2×D5911yescharacteristic
970C4×C4⋊C4—591no—
971C4×C4⋊C4—591no—
972C4×C4⋊C4—591no—
973C4×C4⋊C4—591no—
974C4×C4⋊C4—591no—
975C4×C4⋊C4—591no—
976C4×C4⋊C4—591no—
977C4×C4⋊C4—591no—
978C4×C4⋊C4—591no—
979C4×C4⋊C4C2×D5911yescharacteristic, complemented
980C4×C22⋊C4—591no—
981C4×C22⋊C4—591no—
982C4×C22⋊C4—591no—
983C4×C22⋊C4—591no—
984C4×C22⋊C4—591no—
985C4×C22⋊C4—591no—
986C4×C22⋊C4—591no—
987C4×C22⋊C4—591no—
988C4×C22⋊C4—591no—
989C4×C22⋊C4—591no—
990C4×C22⋊C4—591no—
991C4×C22⋊C4—591no—
992C4×C22⋊C4—591no—
993C4×C22⋊C4—591no—
994C4×C22⋊C4—591no—
995C4×C22⋊C4—591no—
996C4×C22⋊C4—591no—
997C4×C22⋊C4—591no—
998C4×C22⋊C4—591no—
999C4×C22⋊C4—591no—
1000C4×C22⋊C4C2×D5911yescharacteristic
1001C4×C22⋊C4C2×D5911yescharacteristic, complemented
1002#376—591no—
1003#376—591no—
1004C2×#95—591no—
1005C2×#95—591no—
1006C2×#95—591no—
1007C2×#95—591no—
1008C2×#95—591no—
1009C2×#95—591no—
1010C59#3423311yescharacteristic, complemented, Sylow
1011C25—591no—
1012C2×#41—598no—
1013C2×#41—2362no—
1014C2×#41—2362no—
1015C22×Q8—591no—
1016C22×D4—591no—
1017C22×D4—591no—
1018C22×D4—591no—
1019C22×D4—591no—
1020C22×D4—591no—
1021C22×D4—591no—
1022C22×D4C22×D5911yescharacteristic
1023C23×C4—591no—
1024C23×C4—591no—
1025C23×C4—591no—
1026C23×C4—591no—
1027C23×C4—598no—
1028C23×C4—591no—
1029C23×C4—591no—
1030C23×C4—591no—
1031C23×C4—591no—
1032C23×C4—591no—
1033C23×C4—591no—
1034C23×C4—591no—
1035C23×C4—591no—
1036C23×C4—591no—
1037C23×C4—591no—
1038C23×C4—591no—
1039C23×C4—591no—
1040C23×C4—591no—
1041C23×C4—591no—
1042C23×C4—2362no—
1043C23×C4—2362no—
1044C23×C4C22×D5911yescharacteristic
1045C23×C4C22×D5911yescharacteristic
1046#123—598no—
1047#123C4×D5918yescomplemented
1048C22⋊Q8—598no—
1049C22⋊Q8—598no—
1050#121—598no—
1051#121—598no—
1052#120—598no—
1053#120—598no—
1054C4×Q8—2362no—
1055C4×Q8—2362no—
1056C4×D4—598no—
1057C4×D4—598no—
1058C4×D4—598no—
1059C4×D4—598no—
1060C4×D4—1184no—
1061C4×D4—1184no—
1062C4×D4—1184no—
1063C4×D4—1184no—
1064C4×D4—2362no—
1065C4×D4—2362no—
1066C4×D4—2362no—
1067C4×D4—2362no—
1068C4×D4—2362no—
1069C4×D4—2362no—
1070#117—598no—
1071C2×C4⋊C4—591no—
1072C2×C4⋊C4—591no—
1073C2×C4⋊C4—591no—
1074C2×C4⋊C4—591no—
1075C2×C4⋊C4—591no—
1076C2×C4⋊C4—591no—
1077C2×C4⋊C4—591no—
1078C2×C4⋊C4—591no—
1079C2×C4⋊C4—591no—
1080C2×C4⋊C4—591no—
1081C2×C4⋊C4—591no—
1082C2×C4⋊C4—591no—
1083C2×C4⋊C4—591no—
1084C2×C4⋊C4—591no—
1085C2×C4⋊C4—591no—
1086C2×C4⋊C4—591no—
1087C2×C4⋊C4—591no—
1088C2×C4⋊C4—591no—
1089C2×C4⋊C4—591no—
1090C2×C4⋊C4—2362no—
1091C2×C4⋊C4—2362no—
1092C2×C4⋊C4C22×D5911yescharacteristic
1093C2×C4⋊C4C22×D5911yescharacteristic
1094C2×C4⋊C4C22×D5911yescharacteristic
1095C2×C4⋊C4C22×D5911yescharacteristic
1096C2×C4⋊C4C22×D5911yescharacteristic
1097C2×C4⋊C4C22×D5911yescharacteristic
1098C2×C4⋊C4C22×D5911yescharacteristic
1099C2×C22⋊C4—591no—
1100C2×C22⋊C4—591no—
1101C2×C22⋊C4—591no—
1102C2×C22⋊C4—591no—
1103C2×C22⋊C4—591no—
1104C2×C22⋊C4—591no—
1105C2×C22⋊C4—591no—
1106C2×C22⋊C4—591no—
1107C2×C22⋊C4—591no—
1108C2×C22⋊C4—591no—
1109C2×C22⋊C4—591no—
1110C2×C22⋊C4—591no—
1111C2×C22⋊C4—591no—
1112C2×C22⋊C4—591no—
1113C2×C22⋊C4—591no—
1114C2×C22⋊C4—591no—
1115C2×C22⋊C4—591no—
1116C2×C22⋊C4—591no—
1117C2×C22⋊C4—591no—
1118C2×C22⋊C4—591no—
1119C2×C22⋊C4—591no—
1120C2×C22⋊C4—591no—
1121C2×C22⋊C4—591no—
1122C2×C22⋊C4—591no—
1123C2×C22⋊C4—591no—
1124C2×C22⋊C4—591no—
1125C2×C22⋊C4—591no—
1126C2×C22⋊C4—591no—
1127C2×C22⋊C4—1184no—
1128C2×C22⋊C4—1184no—
1129C2×C22⋊C4—2362no—
1130C2×C22⋊C4—2362no—
1131C2×C22⋊C4C22×D5911yescharacteristic
1132C2×C22⋊C4C22×D5911yescharacteristic
1133C2×C22⋊C4C22×D5911yescharacteristic
1134C2×C22⋊C4C22×D5911yescharacteristic
1135C2×C22⋊C4C22×D5911yescharacteristic
1136C2×C22⋊C4C22×D5911yescharacteristic
1137C2×C22⋊C4C22×D5911yescharacteristic
1138C2×C22⋊C4C22×D5911yescharacteristic
1139C2×C22⋊C4C22×D5911yescharacteristic
1140C2×C22⋊C4C22×D5911yescharacteristic
1141C2×C42—591no—
1142C2×C42—591no—
1143C2×C42—591no—
1144C2×C42—591no—
1145C2×C42—591no—
1146C2×C42—591no—
1147C2×C42—591no—
1148C2×C42—591no—
1149C2×C42—591no—
1150C2×C42—591no—
1151C2×C42—591no—
1152C2×C42—591no—
1153C2×C42—591no—
1154C2×C42—591no—
1155C2×C42—591no—
1156C2×C42—591no—
1157C2×C42—591no—
1158C2×C42—2362no—
1159C2×C42—2362no—
1160C2×C42C22×D5911yescharacteristic
1161C2×C42C22×D5911yescharacteristic
1162C2×C42C22×D5911yescharacteristic
1163C2×C42C22×D5911yescharacteristic
1164C2×C42C22×D5911yescharacteristic
1165#95—591no—
1166#95—591no—
1167#95—591no—
1168#95—591no—
1169#95—591no—
1170#95—591no—
1171#95—591no—
1172#95—591no—
1173#95—591no—
1174#95—591no—
1175#95—591no—
1176#95—591no—
1177#95—591no—
1178#95—591no—
1179#95—591no—
1180#95—591no—
1181#95—591no—
1182#95—591no—
1183#95—591no—
1184#95—591no—
1185#95—591no—
1186#95—591no—
1187#95—591no—
1188#95—591no—
1189#95—591no—
1190#95—591no—
1191#95—591no—
1192#95—591no—
1193#95—591no—
1194#95—591no—
1195#95C22×D5911yescharacteristic
1196#95C22×D5911yescharacteristic
1197#95C22×D5911yescharacteristic
1198#95C22×D5911yescharacteristic
1199#95C22×D5911yescharacteristic
1200#95C22×D5911yescharacteristic
1201#95C22×D5911yescharacteristic
1202#95C22×D5911yescharacteristic
1203#95C22×D5911yescharacteristic
1204#95C22×D5911yescharacteristic
1205C24—591no—
1206C24—591no—
1207C24—591no—
1208C24—594no—
1209C24—1182no—
1210C24—1182no—
1211C24—1182no—
1212C24—1182no—
1213C24—2361no—
1214C24—2361no—
1215C24C23×D5911yescharacteristic
1216C24C23×D5911yescharacteristic
1217#41—23616no—
1218C2×Q8—594no—
1219C2×Q8—1182no—
1220C2×Q8—1182no—
1221C2×D4—41no—
1222C2×D4—41no—
1223C2×D4—594no—
1224C2×D4—594no—
1225C2×D4—594no—
1226C2×D4—594no—
1227C2×D4—594no—
1228C2×D4—594no—
1229C2×D4—1182no—
1230C2×D4—1182no—
1231C2×D4—1182no—
1232C2×D4—1182no—
1233C2×D4—1182no—
1234C2×D4—1182no—
1235C2×D4—1182no—
1236C2×D4—1182no—
1237C2×D4—1182no—
1238C2×D4—1182no—
1239C2×D4—2361no—
1240C2×D4—2361no—
1241C2×D4C2×C4×D5914yes—
1242C22×C4—22no—
1243C22×C4—41no—
1244C22×C4—41no—
1245C22×C4—41no—
1246C22×C4—41no—
1247C22×C4—591no—
1248C22×C4—594no—
1249C22×C4—591no—
1250C22×C4—591no—
1251C22×C4—591no—
1252C22×C4—591no—
1253C22×C4—591no—
1254C22×C4—591no—
1255C22×C4—594no—
1256C22×C4—594no—
1257C22×C4—594no—
1258C22×C4—594no—
1259C22×C4—594no—
1260C22×C4—594no—
1261C22×C4—591no—
1262C22×C4—591no—
1263C22×C4—591no—
1264C22×C4—591no—
1265C22×C4—591no—
1266C22×C4—591no—
1267C22×C4—1182no—
1268C22×C4—1182no—
1269C22×C4—1182no—
1270C22×C4—1182no—
1271C22×C4—1182no—
1272C22×C4—1182no—
1273C22×C4—1182no—
1274C22×C4—1182no—
1275C22×C4—1182no—
1276C22×C4—1182no—
1277C22×C4—1182no—
1278C22×C4—1182no—
1279C22×C4—1182no—
1280C22×C4—1182no—
1281C22×C4—1182no—
1282C22×C4—1182no—
1283C22×C4—1182no—
1284C22×C4—1182no—
1285C22×C4—1182no—
1286C22×C4—1182no—
1287C22×C4—1182no—
1288C22×C4—2361no—
1289C22×C4—2361no—
1290C22×C4—2361no—
1291C22×C4—2361no—
1292C22×C4—2361no—
1293C22×C4—2361no—
1294C22×C4—2361no—
1295C22×C4—2361no—
1296C22×C4—2361no—
1297C22×C4—2361no—
1298C22×C4—2361no—
1299C22×C4—2361no—
1300C22×C4—2361no—
1301C22×C4—2361no—
1302C22×C4—2361no—
1303C22×C4—2361no—
1304C22×C4—2361no—
1305C22×C4—2361no—
1306C22×C4—2361no—
1307C22×C4—2361no—
1308C22×C4—2361no—
1309C22×C4—2361no—
1310C22×C4—23616no—
1311C22×C4—2361no—
1312C22×C4—2361no—
1313C22×C4—2361no—
1314C22×C4—2361no—
1315C22×C4C2×C4×D5914yes—
1316C22×C4C23×D5911yescharacteristic
1317C22×C4C23×D5911yescharacteristic
1318C22×C4C23×D5911yescharacteristic
1319C22×C4C23×D5911yescharacteristic
1320C22×C4C23×D5911yescharacteristic
1321C22×C4C23×D5911yescharacteristic
1322C22×C4C23×D5911yescharacteristic
1323C22×C4C23×D5911yescharacteristic
1324C22×C4C23×D5911yescharacteristic
1325C22×C4C23×D5911yescharacteristic
1326C22×C4C23×D5911yescharacteristic
1327C22×C4C23×D5911yescharacteristic
1328C22×C4C23×D5911yescharacteristic
1329C4⋊C4—22no—
1330C4⋊C4—41no—
1331C4⋊C4—41no—
1332C4⋊C4—41no—
1333C4⋊C4—41no—
1334C4⋊C4—594no—
1335C4⋊C4—594no—
1336C4⋊C4—594no—
1337C4⋊C4—594no—
1338C4⋊C4—1182no—
1339C4⋊C4—1182no—
1340C4⋊C4—1182no—
1341C4⋊C4—1182no—
1342C4⋊C4—1182no—
1343C4⋊C4—1182no—
1344C4⋊C4—1182no—
1345C4⋊C4—2361no—
1346C4⋊C4—2361no—
1347C4⋊C4—2361no—
1348C4⋊C4—2361no—
1349C4⋊C4—2361no—
1350C4⋊C4—2361no—
1351C4⋊C4—2361no—
1352C4⋊C4—2361no—
1353C4⋊C4C2×C4×D5914yes—
1354C4⋊C4C2×C4×D5914yes—
1355C22⋊C4—22no—
1356C22⋊C4—22no—
1357C22⋊C4—22no—
1358C22⋊C4—41no—
1359C22⋊C4—41no—
1360C22⋊C4—41no—
1361C22⋊C4—41no—
1362C22⋊C4—594no—
1363C22⋊C4—594no—
1364C22⋊C4—594no—
1365C22⋊C4—594no—
1366C22⋊C4—594no—
1367C22⋊C4—594no—
1368C22⋊C4—594no—
1369C22⋊C4—594no—
1370C22⋊C4—594no—
1371C22⋊C4—1182no—
1372C22⋊C4—1182no—
1373C22⋊C4—1182no—
1374C22⋊C4—1182no—
1375C22⋊C4—1182no—
1376C22⋊C4—1182no—
1377C22⋊C4—1182no—
1378C22⋊C4—1182no—
1379C22⋊C4—1182no—
1380C22⋊C4—1182no—
1381C22⋊C4—1182no—
1382C22⋊C4—2361no—
1383C22⋊C4—2361no—
1384C22⋊C4—2361no—
1385C22⋊C4—2361no—
1386C22⋊C4—2361no—
1387C22⋊C4—2361no—
1388C22⋊C4—2361no—
1389C22⋊C4—2361no—
1390C22⋊C4C2×C4×D5914yes—
1391C22⋊C4C2×C4×D5914yes—
1392C22⋊C4C2×C4×D5914yes—
1393C42—22no—
1394C42—41no—
1395C42—41no—
1396C42—41no—
1397C42—41no—
1398C42—594no—
1399C42—594no—
1400C42—1182no—
1401C42—1182no—
1402C42—1182no—
1403C42—1182no—
1404C42—1182no—
1405C42—1182no—
1406C42—1182no—
1407C42—2361no—
1408C42—2361no—
1409C42—2361no—
1410C42—2361no—
1411C42—2361no—
1412C42—2361no—
1413C42—2361no—
1414C42—2361no—
1415C23—21no—
1416C23—21no—
1417C23—21no—
1418C23—21no—
1419C23—21no—
1420C23—21no—
1421C23—21no—
1422C23—21no—
1423C23—21no—
1424C23—21no—
1425C23—21no—
1426C23—21no—
1427C23—592no—
1428C23—592no—
1429C23—592no—
1430C23—592no—
1431C23—592no—
1432C23—592no—
1433C23—592no—
1434C23—1188no—
1435C23—1188no—
1436C23—1181no—
1437C23—1181no—
1438C23—1181no—
1439C23—1181no—
1440C23—1181no—
1441C23—1181no—
1442C23—1181no—
1443C23—1181no—
1444C23—1181no—
1445C23—1181no—
1446C23—1181no—
1447C23—1181no—
1448C23—1181no—
1449C23—1181no—
1450C23—2364no—
1451C23—2364no—
1452C23—2364no—
1453C23—2364no—
1454C23—2364no—
1455C23C22×C4×D5912yes—
1456C23C22×C4×D5912yes—
1457C23C24×D5911yescharacteristic
1458Q8—1188no—
1459D4—44no—
1460D4—1188no—
1461D4—1188no—
1462D4—1188no—
1463D4—1188no—
1464D4—1188no—
1465D4—2364no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—44no—
1499C2×C4—82no—
1500C2×C4—592no—
1501C2×C4—592no—
1502C2×C4—592no—
1503C2×C4—592no—
1504C2×C4—592no—
1505C2×C4—592no—
1506C2×C4—592no—
1507C2×C4—592no—
1508C2×C4—592no—
1509C2×C4—1188no—
1510C2×C4—1188no—
1511C2×C4—1188no—
1512C2×C4—1181no—
1513C2×C4—1181no—
1514C2×C4—1181no—
1515C2×C4—1181no—
1516C2×C4—1181no—
1517C2×C4—1181no—
1518C2×C4—1181no—
1519C2×C4—1181no—
1520C2×C4—1181no—
1521C2×C4—1181no—
1522C2×C4—1181no—
1523C2×C4—1181no—
1524C2×C4—1181no—
1525C2×C4—1181no—
1526C2×C4—1181no—
1527C2×C4—1181no—
1528C2×C4—1181no—
1529C2×C4—1181no—
1530C2×C4—1181no—
1531C2×C4—1181no—
1532C2×C4—1181no—
1533C2×C4—1181no—
1534C2×C4—1181no—
1535C2×C4—1181no—
1536C2×C4—1181no—
1537C2×C4—1181no—
1538C2×C4—1181no—
1539C2×C4—1181no—
1540C2×C4—1181no—
1541C2×C4—1181no—
1542C2×C4—4722no—
1543C2×C4—4722no—
1544C2×C4—4722no—
1545C2×C4—4722no—
1546C2×C4—4722no—
1547C2×C4—4722no—
1548C2×C4—4722no—
1549C2×C4—2364no—
1550C2×C4—2364no—
1551C2×C4—2364no—
1552C2×C4—2364no—
1553C2×C4—2364no—
1554C2×C4—2364no—
1555C2×C4—2364no—
1556C2×C4—2364no—
1557C2×C4C22×C4×D5912yes—
1558C2×C4C22×C4×D5912yes—
1559C2×C4C22×C4×D5912yes—
1560C2×C4C22×C4×D5912yes—
1561C2×C4C22×C4×D5912yes—
1562C2×C4#41×D5912yes—
1563C2×C4#41×D5912yes—
1564C22—22no—
1565C22—22no—
1566C22—22no—
1567C22—22no—
1568C22—22no—
1569C22—22no—
1570C22—41no—
1571C22—41no—
1572C22—41no—
1573C22—41no—
1574C22—41no—
1575C22—41no—
1576C22—41no—
1577C22—41no—
1578C22—594no—
1579C22—594no—
1580C22—1182no—
1581C22—1182no—
1582C22—1182no—
1583C22—1182no—
1584C22—1182no—
1585C22—1182no—
1586C22—1182no—
1587C22—1182no—
1588C22—1182no—
1589C22—1182no—
1590C22—1182no—
1591C22—1182no—
1592C22—1182no—
1593C22—1182no—
1594C22—1182no—
1595C22—23616no—
1596C22—2361no—
1597C22—2361no—
1598C22—2361no—
1599C22—2361no—
1600C22C23×C4×D5911yescharacteristic
1601C22C2×#41×D5911yescharacteristic
1602C22C2×#41×D5911yescharacteristic
1603C22H(5,𝔽2)×D5911yescharacteristic
1604C22H(5,𝔽2)×D5911yescharacteristic
1605C22H(5,𝔽2)×D5911yescharacteristic
1606C222−1+4×D5911yescharacteristic
1607C4—22no—
1608C4—22no—
1609C4—22no—
1610C4—22no—
1611C4—22no—
1612C4—22no—
1613C4—22no—
1614C4—41no—
1615C4—41no—
1616C4—41no—
1617C4—41no—
1618C4—41no—
1619C4—41no—
1620C4—594no—
1621C4—1182no—
1622C4—1182no—
1623C4—1182no—
1624C4—1182no—
1625C4—1182no—
1626C4—1182no—
1627C4—2361no—
1628C4—2361no—
1629C4—2361no—
1630C4—2361no—
1631C4—2361no—
1632C4—2361no—
1633C2—42no—
1634C2—42no—
1635C2—1184no—
1636C2—1184no—
1637C2—2362no—
1638C2C4×#41×D5911yescharacteristic
1639C2#518×D5911yescharacteristic
1640C2#520×D5911yescharacteristic
1641C2#2143812011yescharacteristic
1642C2#2143812611yescharacteristic
1643C2#2143813711yescharacteristic
1644C2#2143814311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D59
commutatorC22×C59C24×C4
FittingC59×#2335C2
socle, cosocleC23×C59C25
prime radicalC2×#16837910C2
hypercenter#2335D59
hypocenterC59#34233
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ #2335

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #21427115C2semidirect
3. #21427109C2semidirect
4. #21427104C2semidirect
5. #21427098C2semidirect
6. #21427079C2semidirect
7. #21427077C2semidirect
8. #21427074C2semidirect
9. #21427074C2semidirect
10. #21427035C2semidirect
11. #21427031C2semidirect
12. #21427005C2semidirect
13. #21427002C2semidirect
14. #21426986C2semidirect
15. #21426978C2semidirect
16. #21426935C2semidirect
17. #21426922C2semidirect
18. #21426890C2semidirect
19. #21426886C2semidirect
20. #21426882C2semidirect
21. #21426728C2semidirect
22. #21426726C2semidirect
23. #21426630C2semidirect
24. C4×#14273705C2semidirect
25. #21426608C2semidirect
26. C4×#14273700C2semidirect
27. #380×D59C2semidirect
28. #21426456C2semidirect
29. #21426455C2semidirect
30. C4×C22⋊C4×D59C2semidirect
31. C59×#2335C2semidirect
34. #16837910C4semidirect
42. C2×C4×Dic118C22semidirect
43. C2×#14273692C22semidirect
52. C2×C4×C22⋊D59C22semidirect
57. C2×(C22⋊D59)⋊C4C22semidirect
67. #16837306C22semidirect
68. #16837306C22semidirect
72. #16837302C22semidirect
73. #16837302C22semidirect
74. #16837301C22semidirect
75. #16837299C22semidirect
76. #16837299C22semidirect
77. #16837299C22semidirect
78. #16837297C22semidirect
79. #16837297C22semidirect
80. #16837297C22semidirect
85. #16837295C22semidirect
86. #16837295C22semidirect
87. #16837294C22semidirect
88. #16837293C22semidirect
89. #16837292C22semidirect
90. #16837291C22semidirect
93. #16837289C22semidirect
94. #16837288C22semidirect
95. #16837288C22semidirect
96. #16837286C22semidirect
97. #16837284C22semidirect
98. #16837283C22semidirect
110. #16837277C22semidirect
115. #16837276C22semidirect
120. #16837273C22semidirect
121. #16837269C22semidirect
122. #16837269C22semidirect
123. #16837267C22semidirect
124. #16837266C22semidirect
125. #16837264C22semidirect
126. #16837263C22semidirect
132. #16837260C22semidirect
135. #16837259C22semidirect
136. C4⋊C4×Dic59C22semidirect
137. C4⋊C4×Dic59C22semidirect
138. C4×Dic59⋊C4C22semidirect
139. C4×Dic59⋊C4C22semidirect
140. C4×Dic59⋊C4C22semidirect
141. C4×Dic59⋊C4C22semidirect
142. #16837253C22semidirect
143. #16837253C22semidirect
144. #16837253C22semidirect
147. C22⋊C4×Dic59C22semidirect
148. C22⋊C4×Dic59C22semidirect
155. C4×(C2×D59)⋊C4C22semidirect
156. C4×(C2×D59)⋊C4C22semidirect
164. #16837249C22semidirect
165. #16837248C22semidirect
166. #16837247C22semidirect
167. C2×C59⋊#95C22semidirect
172. #95×D59C22semidirect
175. C59×#389C22semidirect
178. C59×#388C22semidirect
179. C59×#388C22semidirect
180. C59×#387C22semidirect
181. C59×#387C22semidirect
183. C59×#385C22semidirect
185. C4×C4⋊C4×C59C22semidirect
187. C4×C22⋊C4×C59C22semidirect
191. C2×#11745687C2×C4semidirect
204. C22×C4×D59C2×C4semidirect
220. #14273710C2×C4semidirect
221. #14273705C2×C4semidirect
222. #14273705C2×C4semidirect
223. #14273700C2×C4semidirect
224. #14273700C2×C4semidirect
225. #14273697C2×C4semidirect
226. #14273695C2×C4semidirect
233. #14273689C2×C4semidirect
234. #14273689C2×C4semidirect
241. (C22⋊D59)⋊C4C2×C4semidirect
242. (C22⋊D59)⋊C4C2×C4semidirect
243. #14273683C2×C4semidirect
349. #123×C59C2×C4semidirect
554. (C2×D59)⋊C4#41semidirect
555. (C2×D59)⋊C4#41semidirect
831. #2335D59semidirect
905. #389C2×D59semidirect
920. #388C2×D59semidirect
921. #388C2×D59semidirect
928. #387C2×D59semidirect
929. #387C2×D59semidirect
953. #385C2×D59semidirect
979. C4×C4⋊C4C2×D59semidirect
1001. C4×C22⋊C4C2×D59semidirect
1010. C59#34233semidirect
1047. #123C4×D59semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168379102
#214271152
#214271092
#214271042
#214270982
#214270792
#214270772
#214270742
#214270352
#214270312
#214270052
#214270022
#214269862
#214269782
#214269352
#214269222
#214268902
#214268862
#214268822
#214267282
#214267262
#214266302
C4×#142737052
#214266082
C4×#142737002
#380×D592
#214264562
#214264552
C4×C22⋊C4×D592
C59×#23352
#3423359