Finite Group Databasebeta

← #28797216

Subgroups — #28797216

Order 15104.

1518 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432413C211yesmaximal, characteristic
2#21432404C211yesmaximal, characteristic, complemented
3#21431777C211yesmaximal, characteristic, complemented
4#21431777C211yesmaximal, characteristic, complemented
5#21431682C211yesmaximal, characteristic, complemented
6#21431682C211yesmaximal, characteristic, complemented
7#21431620C211yesmaximal, characteristic, complemented
8#21431592C211yesmaximal, characteristic, complemented
9#21431552C211yesmaximal, characteristic, complemented
10#21431542C211yesmaximal, characteristic, complemented
11#21431504C211yesmaximal, characteristic, complemented
12#21431491C211yesmaximal, characteristic, complemented
13#21431301C211yesmaximal, characteristic, complemented
14#21431249C211yesmaximal, characteristic, complemented
15#21431032C211yesmaximal, characteristic, complemented
16#21430957C211yesmaximal, characteristic, complemented
17#21430569C211yesmaximal, characteristic, complemented
18#21430554C211yesmaximal, characteristic, complemented
19#21430069C211yesmaximal, characteristic, complemented
20#21430052C211yesmaximal, characteristic
21#21429471C211yesmaximal, characteristic, complemented
22#21429445C211yesmaximal, characteristic
23#21428652C211yesmaximal, characteristic
24#21428652C211yesmaximal, characteristic
25#21428601C211yesmaximal, characteristic, complemented
26#21428601C211yesmaximal, characteristic, complemented
27#21427541C211yesmaximal, characteristic
28#21426826C211yesmaximal, characteristic, complemented
29#21426723C211yesmaximal, characteristic
30C2×#16837283C211yesmaximal, characteristic, complemented
31C59×#2442C211yesmaximal, characteristic, complemented
32C2×#14273722C2211yescharacteristic
33C2×#14273718C2211yescharacteristic
34C2×#14273707C2211yescharacteristic
35C2×#14273706C2211yescharacteristic
36C2×C4×C22⋊D59C2211yescharacteristic
37C22×Dic59⋊C4C2211yescharacteristic
38C22×C4×Dic59C2211yescharacteristic
39C59⋊#401C2211yescharacteristic
40C59⋊#401C2211yescharacteristic
41C59⋊#401C2211yescharacteristic
42#16837344C2211yescharacteristic
43#16837344C2211yescharacteristic
44#16837344C2211yescharacteristic
45#16837344C2211yescharacteristic
46#16837344C2211yescharacteristic
47#16837341C2211yescharacteristic
48#16837341C2211yescharacteristic
49#16837341C2211yescharacteristic
50#16837341C2211yescharacteristic
51#16837341C2211yescharacteristic
52#16837341C2211yescharacteristic
53#16837341C2211yescharacteristic
54#16837341C2211yescharacteristic
55#16837341C2211yescharacteristic
56#16837340C2211yescharacteristic
57#16837335C2211yescharacteristic
58#16837335C2211yescharacteristic
59#16837334C2211yescharacteristic
60#16837334C2211yescharacteristic
61#16837334C2211yescharacteristic
62#16837334C2211yescharacteristic
63#16837334C2211yescharacteristic
64#16837334C2211yescharacteristic
65#16837332C2211yescharacteristic
66#16837332C2211yescharacteristic
67#16837332C2211yescharacteristic
68#16837332C2211yescharacteristic
69#16837331C2211yescharacteristic
70#16837329C2211yescharacteristic
71#16837329C2211yescharacteristic
72#16837329C2211yescharacteristic
73#16837328C2211yescharacteristic
74#16837328C2211yescharacteristic
75#16837328C2211yescharacteristic
76#16837324C2211yescharacteristic
77#16837324C2211yescharacteristic
78#16837324C2211yescharacteristic
79#16837324C2211yescharacteristic
80#16837324C2211yescharacteristic
81#16837323C2211yescharacteristic
82#16837323C2211yescharacteristic
83#16837307C2211yescharacteristic
84#16837306C2211yescharacteristic
85#16837306C2211yescharacteristic
86#16837301C2211yescharacteristic
87#16837301C2211yescharacteristic
88#16837301C2211yescharacteristic
89#16837301C2211yescharacteristic
90#16837300C2211yescharacteristic
91#16837300C2211yescharacteristic
92#16837300C2211yescharacteristic
93#16837300C2211yescharacteristic
94#16837298C2211yescharacteristic
95#16837297C2211yescharacteristic
96#16837297C2211yescharacteristic
97#16837294C2211yescharacteristic
98#16837294C2211yescharacteristic
99#16837294C2211yescharacteristic
100#16837293C2211yescharacteristic
101#16837293C2211yescharacteristic
102#16837292C2211yescharacteristic
103#16837292C2211yescharacteristic
104#16837292C2211yescharacteristic
105#16837291C2211yescharacteristic
106#16837289C2211yescharacteristic
107#16837289C2211yescharacteristic
108#16837289C2211yescharacteristic
109#16837289C2211yescharacteristic
110#16837288C2211yescharacteristic
111#16837288C2211yescharacteristic
112#16837288C2211yescharacteristic
113#16837287C2211yescharacteristic
114#16837287C2211yescharacteristic
115#16837287C2211yescharacteristic
116#16837287C2211yescharacteristic
117#16837286C2211yescharacteristic
118#16837286C2211yescharacteristic
119#16837285C2211yescharacteristic
120#16837285C2211yescharacteristic
121#16837285C2211yescharacteristic
122#16837285C2211yescharacteristic
123#16837285C2211yescharacteristic
124#16837283C2211yescharacteristic
125#16837283C2211yescharacteristic
126#16837283C2211yescharacteristic
127#16837283C2211yescharacteristic
128#16837283C2211yescharacteristic
129#16837283C2211yescharacteristic
130#16837283C2211yescharacteristic
131#16837283C2211yescharacteristic
132#16837283C2211yescharacteristic
133#16837283C2211yescharacteristic
134#16837283C2211yescharacteristic
135#16837281C2211yescharacteristic
136#16837281C2211yescharacteristic
137#16837279C2211yescharacteristic
138#16837279C2211yescharacteristic
139#16837279C2211yescharacteristic
140#16837279C2211yescharacteristic
141#16837277C2211yescharacteristic
142#16837277C2211yescharacteristic
143#16837277C2211yescharacteristic
144#16837277C2211yescharacteristic
145#16837277C2211yescharacteristic
146#16837277C2211yescharacteristic
147#16837276C2211yescharacteristic
148#16837276C2211yescharacteristic
149#16837274C2211yescharacteristic
150#16837274C2211yescharacteristic
151#16837274C2211yescharacteristic
152#16837274C2211yescharacteristic
153#16837269C2211yescharacteristic
154#16837269C2211yescharacteristic
155#16837269C2211yescharacteristic
156#16837269C2211yescharacteristic
157#16837267C2211yescharacteristic
158#16837267C2211yescharacteristic
159#16837267C2211yescharacteristic
160#16837266C2211yescharacteristic
161#16837264C2211yescharacteristic
162#16837262C2211yescharacteristic
163#16837262C2211yescharacteristic
164#16837261C2211yescharacteristic
165#16837259C2211yescharacteristic
166C22⋊C4×Dic59C2211yescharacteristic
167C22⋊C4×Dic59C2211yescharacteristic
168C2×C59⋊#95C2211yescharacteristic
169C2×C59⋊#95C2211yescharacteristic
170C2×C59⋊#95C2211yescharacteristic
171C2×C59⋊#95C2211yescharacteristic
172C2×#125×C59C2211yescharacteristic
173C22×C4⋊C4×C59C2211yescharacteristic
174C59×#400C2211yescharacteristic
175C59×#400C2211yescharacteristic
176C59×#398C2211yescharacteristic
177C59×#398C2211yescharacteristic
178C59×#389C2211yescharacteristic
179C59×#389C2211yescharacteristic
180C59×#385C2211yescharacteristic
181C59×#385C2211yescharacteristic
182C59×#382C2211yescharacteristic
183C59×#380C2211yescharacteristic
184C59×#380C2211yescharacteristic
185C59×#380C2211yescharacteristic
186C4×C22⋊C4×C59C2211yescharacteristic
187C22×Dic118C2311yescharacteristic
188C22×C22⋊D59C2311yescharacteristic
189C23×Dic59C2311yescharacteristic
190C23×Dic59C2311yescharacteristic
191C23×Dic59C2311yescharacteristic
192C23×Dic59C2311yescharacteristic
193C22×C4×D59C2311yescharacteristic
194#14273722—42no—
195#14273718—42no—
196#14273707—42no—
197#14273706—24no—
198C4×C22⋊D59—24no—
199C2×C4⋊Dic59C2311yescharacteristic
200C2×C4⋊Dic59C2311yescharacteristic
201C2×C4⋊Dic59C2311yescharacteristic
202C2×C4⋊Dic59C2311yescharacteristic
203C2×C4⋊Dic59C2311yescharacteristic
204C2×C4⋊Dic59C2311yescharacteristic
205C2×C4⋊Dic59C2311yescharacteristic
206C2×C4⋊Dic59C2311yescharacteristic
207C2×C4⋊Dic59C2311yescharacteristic
208C2×C4⋊Dic59C2311yescharacteristic
209C2×C4⋊Dic59C2311yescharacteristic
210C2×C4⋊Dic59C2311yescharacteristic
211C2×C4⋊Dic59C2311yescharacteristic
212C2×C4⋊Dic59C2311yescharacteristic
213C2×C4⋊Dic59C2311yescharacteristic
214C2×C4⋊Dic59C2311yescharacteristic
215C2×C4⋊Dic59C2311yescharacteristic
216C2×Dic59⋊C4—24no—
217C2×Dic59⋊C4C2311yescharacteristic
218C2×Dic59⋊C4C2311yescharacteristic
219C2×Dic59⋊C4C2311yescharacteristic
220C2×Dic59⋊C4C2311yescharacteristic
221C2×Dic59⋊C4C2311yescharacteristic
222C2×Dic59⋊C4C2311yescharacteristic
223C2×Dic59⋊C4C2311yescharacteristic
224C2×Dic59⋊C4C2311yescharacteristic
225C2×Dic59⋊C4C2311yescharacteristic
226C2×Dic59⋊C4C2311yescharacteristic
227C2×Dic59⋊C4C2311yescharacteristic
228C2×Dic59⋊C4C2311yescharacteristic
229C2×Dic59⋊C4C2311yescharacteristic
230C2×Dic59⋊C4C2311yescharacteristic
231C2×Dic59⋊C4C2311yescharacteristic
232C2×C22⋊Dic59C2311yescharacteristic
233C2×C22⋊Dic59C2311yescharacteristic
234C2×C22⋊Dic59C2311yescharacteristic
235C2×(C2×D59)⋊C4C2311yescharacteristic
236C2×(C2×D59)⋊C4C2311yescharacteristic
237C2×(C2×D59)⋊C4C2311yescharacteristic
238C2×(C2×D59)⋊C4C2311yescharacteristic
239C2×(C2×D59)⋊C4C2311yescharacteristic
240C2×(C2×D59)⋊C4C2311yescharacteristic
241C2×(C2×D59)⋊C4C2311yescharacteristic
242C2×(C2×D59)⋊C4C2311yescharacteristic
243C2×(C2×D59)⋊C4C2311yescharacteristic
244C2×(C2×D59)⋊C4C2311yescharacteristic
245C2×(C2×D59)⋊C4C2311yescharacteristic
246C2×(C2×D59)⋊C4C2311yescharacteristic
247C2×(C2×D59)⋊C4C2311yescharacteristic
248C2×C4×Dic59—42no—
249C2×C4×Dic59C2311yescharacteristic
250C2×C4×Dic59C2311yescharacteristic
251C2×C4×Dic59C2311yescharacteristic
252C2×C4×Dic59C2311yescharacteristic
253C2×C4×Dic59C2311yescharacteristic
254C2×C4×Dic59C2311yescharacteristic
255C2×C4×Dic59C2311yescharacteristic
256C2×C4×Dic59C2311yescharacteristic
257C2×C4×Dic59C2311yescharacteristic
258C59⋊#95C2311yescharacteristic
259C59⋊#95C2311yescharacteristic
260C59⋊#95C2311yescharacteristic
261C59⋊#95C2311yescharacteristic
262C59⋊#95C2311yescharacteristic
263C59⋊#95C2311yescharacteristic
264C59⋊#95C2311yescharacteristic
265C59⋊#95C2311yescharacteristic
266C59⋊#95C2311yescharacteristic
267C59⋊#95C2311yescharacteristic
268C59⋊#95C2311yescharacteristic
269C59⋊#95C2311yescharacteristic
270C59⋊#95C2311yescharacteristic
271C59⋊#95C2311yescharacteristic
272C59⋊#95C2311yescharacteristic
273C59⋊#95C2311yescharacteristic
274C59⋊#95C2311yescharacteristic
275C59⋊#95C2311yescharacteristic
276C59⋊#95C2311yescharacteristic
277C59⋊#95C2311yescharacteristic
278C59⋊#95C2311yescharacteristic
279C59⋊#95C2311yescharacteristic
280C59⋊#95C2311yescharacteristic
281C59⋊#95C2311yescharacteristic
282C59⋊#95C2311yescharacteristic
283C59⋊#95C2311yescharacteristic
284C59⋊#95C2311yescharacteristic
285C59⋊#95C2311yescharacteristic
286C59⋊#95C2311yescharacteristic
287C59⋊#95C2311yescharacteristic
288C59⋊#95C2311yescharacteristic
289C59⋊#95C2311yescharacteristic
290C59⋊#95C2311yescharacteristic
291C59⋊#95C2311yescharacteristic
292C59⋊#95C2311yescharacteristic
293C59⋊#95C2311yescharacteristic
294C59⋊#95C2311yescharacteristic
295C59⋊#95C2311yescharacteristic
296C59⋊#95C2311yescharacteristic
297C59⋊#95C2311yescharacteristic
298C59⋊#95C2311yescharacteristic
299C59⋊#95C2311yescharacteristic
300C59⋊#95C2311yescharacteristic
301C59⋊#95C2311yescharacteristic
302C59⋊#95C2311yescharacteristic
303C59⋊#95C2311yescharacteristic
304C59⋊#95C2311yescharacteristic
305C59⋊#95C2311yescharacteristic
306C59⋊#95C2311yescharacteristic
307C59⋊#95C2311yescharacteristic
308C59⋊#95C2311yescharacteristic
309C59⋊#95C2311yescharacteristic
310C59⋊#95C2311yescharacteristic
311C59⋊#95C2311yescharacteristic
312C59⋊#95C2311yescharacteristic
313C59⋊#95C2311yescharacteristic
314C23×C4×C59C2311yescharacteristic
315C23×C4×C59C2311yescharacteristic
316C23×C4×C59C2311yescharacteristic
317#125×C59—42no—
318C2×C4⋊C4×C59—42no—
319C2×C4⋊C4×C59C2311yescharacteristic
320C2×C4⋊C4×C59C2311yescharacteristic
321C2×C4⋊C4×C59C2311yescharacteristic
322C2×C4⋊C4×C59C2311yescharacteristic
323C2×C4⋊C4×C59C2311yescharacteristic
324C2×C4⋊C4×C59C2311yescharacteristic
325C2×C4⋊C4×C59C2311yescharacteristic
326C2×C4⋊C4×C59C2311yescharacteristic
327C2×C4⋊C4×C59C2311yescharacteristic
328C2×C4⋊C4×C59C2311yescharacteristic
329C2×C4⋊C4×C59C2311yescharacteristic
330C2×C4⋊C4×C59C2311yescharacteristic
331C2×C4⋊C4×C59C2311yescharacteristic
332C2×C4⋊C4×C59C2311yescharacteristic
333C2×C22⋊C4×C59C2311yescharacteristic
334C2×C22⋊C4×C59C2311yescharacteristic
335C2×C22⋊C4×C59C2311yescharacteristic
336C2×C22⋊C4×C59C2311yescharacteristic
337C2×C42×C59C2311yescharacteristic
338C2×C42×C59C2311yescharacteristic
339#95×C59C2311yescharacteristic
340#95×C59C2311yescharacteristic
341#95×C59C2311yescharacteristic
342#95×C59C2311yescharacteristic
343#95×C59C2311yescharacteristic
344#95×C59C2311yescharacteristic
345#95×C59C2311yescharacteristic
346#95×C59C2311yescharacteristic
347#95×C59C2311yescharacteristic
348#95×C59C2311yescharacteristic
349#95×C59C2311yescharacteristic
350#95×C59C2311yescharacteristic
351C24×C59C2411yescharacteristic
352C23×D59C2411yescharacteristic
353C22×C4×C59—22no—
354C22×C4×C59—22no—
355C22×C4×C59—22no—
356C22×C4×C59—41no—
357C22×C4×C59—41no—
358C22×C4×C59—41no—
359C22×C4×C59—41no—
360C22×C4×C59—41no—
361C22×C4×C59#4114yes—
362C22×C4×C59C2411yescharacteristic
363C22×C4×C59C2411yescharacteristic
364C22×C4×C59C2411yescharacteristic
365C22×C4×C59C2411yescharacteristic
366C22×C4×C59C2411yescharacteristic
367C22×C4×C59C2411yescharacteristic
368C22×C4×C59C2411yescharacteristic
369C22×C4×C59C2411yescharacteristic
370C22×C4×C59C2411yescharacteristic
371C22×C4×C59C2411yescharacteristic
372C22×C4×C59C2411yescharacteristic
373C22×C4×C59C2411yescharacteristic
374C22×C4×C59C2411yescharacteristic
375C22×C4×C59C2411yescharacteristic
376C2×C22⋊D59—22no—
377C2×C22⋊D59—22no—
378C2×C22⋊D59—22no—
379C22×Dic59—22no—
380C22×Dic59—22no—
381C22×Dic59—22no—
382C22×Dic59—22no—
383C22×Dic59—41no—
384C22×Dic59—41no—
385C22×Dic59—41no—
386C22×Dic59—41no—
387C22×Dic59—41no—
388C22×Dic59—41no—
389C22×Dic59—41no—
390C22×Dic59—41no—
391C22×Dic59C2411yescharacteristic
392C22×Dic59C2411yescharacteristic
393C22×Dic59C2411yescharacteristic
394C22×Dic59C2411yescharacteristic
395C22×Dic59C2411yescharacteristic
396C22×Dic59C2411yescharacteristic
397C22×Dic59C2411yescharacteristic
398C22×Dic59C2411yescharacteristic
399C22×Dic59C2411yescharacteristic
400C22×Dic59C2411yescharacteristic
401C22×Dic59C2411yescharacteristic
402C22×Dic59C2411yescharacteristic
403C22×Dic59C2411yescharacteristic
404C22×Dic59C2411yescharacteristic
405C22×Dic59C2411yescharacteristic
406C2×C4×D59—22no—
407C2×C4×D59—41no—
408C2×C4×D59—41no—
409C2×Dic118—22no—
410C2×Dic118—41no—
411C2×Dic118—41no—
412C4⋊C4×C59—22no—
413C4⋊C4×C59—22no—
414C4⋊C4×C59—22no—
415C4⋊C4×C59—22no—
416C4⋊C4×C59—41no—
417C4⋊C4×C59—41no—
418C4⋊C4×C59—41no—
419C4⋊C4×C59—41no—
420C4⋊C4×C59—41no—
421C4⋊C4×C59—41no—
422C4⋊C4×C59—41no—
423C4⋊C4×C59—41no—
424C4⋊C4×C59—41no—
425C4⋊C4×C59—41no—
426C22⋊C4×C59—22no—
427C22⋊C4×C59—22no—
428C22⋊C4×C59—22no—
429C22⋊C4×C59—22no—
430C42×C59—41no—
431C42×C59—41no—
432C22⋊Dic59—22no—
433C22⋊Dic59—22no—
434C22⋊Dic59—22no—
435(C2×D59)⋊C4—22no—
436(C2×D59)⋊C4—22no—
437(C2×D59)⋊C4—41no—
438(C2×D59)⋊C4—41no—
439(C2×D59)⋊C4—41no—
440(C2×D59)⋊C4—41no—
441(C2×D59)⋊C4—41no—
442(C2×D59)⋊C4—41no—
443(C2×D59)⋊C4—41no—
444(C2×D59)⋊C4—41no—
445(C2×D59)⋊C4—41no—
446(C2×D59)⋊C4—41no—
447(C2×D59)⋊C4—41no—
448C4⋊Dic59—22no—
449C4⋊Dic59—22no—
450C4⋊Dic59—41no—
451C4⋊Dic59—41no—
452C4⋊Dic59—41no—
453C4⋊Dic59—41no—
454C4⋊Dic59—41no—
455C4⋊Dic59—41no—
456C4⋊Dic59—41no—
457C4⋊Dic59—41no—
458C4⋊Dic59—41no—
459C4⋊Dic59—41no—
460C4⋊Dic59—41no—
461C4⋊Dic59—41no—
462C4⋊Dic59—41no—
463C4⋊Dic59—41no—
464C4⋊Dic59—41no—
465Dic59⋊C4—22no—
466Dic59⋊C4—22no—
467Dic59⋊C4—22no—
468Dic59⋊C4—22no—
469Dic59⋊C4—22no—
470Dic59⋊C4—22no—
471Dic59⋊C4—22no—
472Dic59⋊C4—41no—
473Dic59⋊C4—41no—
474Dic59⋊C4—41no—
475Dic59⋊C4—41no—
476Dic59⋊C4—41no—
477Dic59⋊C4—41no—
478Dic59⋊C4—41no—
479Dic59⋊C4—41no—
480C4×Dic59—22no—
481C4×Dic59—22no—
482C4×Dic59—22no—
483C4×Dic59—41no—
484C4×Dic59—41no—
485C4×Dic59—41no—
486C4×Dic59—41no—
487C4×Dic59—41no—
488C4×Dic59—41no—
489C23×C59—21no—
490C23×C59—21no—
491C23×C59—21no—
492C23×C59—21no—
493C23×C59C2×#4112yes—
494C23×C592−1+412yes—
495C23×C592−1+412yes—
496C23×C59C2511yescharacteristic
497C22×D59—21no—
498C22×D59—21no—
499C22×D59—21no—
500C22×D59—21no—
501C22×D59—21no—
502C22×D59—21no—
503C22×D59—21no—
504C2×C4×C59—21no—
505C2×C4×C59—21no—
506C2×C4×C59—21no—
507C2×C4×C59—21no—
508C2×C4×C59—21no—
509C2×C4×C59—21no—
510C2×C4×C59—21no—
511C2×C4×C59—21no—
512C2×C4×C59—21no—
513C2×C4×C59—21no—
514C2×C4×C59—21no—
515C2×C4×C59—21no—
516C2×C4×C59—21no—
517C2×C4×C59—21no—
518C2×C4×C59—21no—
519C2×C4×C59—21no—
520C2×C4×C59—21no—
521C2×C4×C59—21no—
522C2×C4×C59—21no—
523C2×C4×C59—21no—
524C2×C4×C59—21no—
525C2×C4×C59—21no—
526C2×C4×C59—21no—
527C2×C4×C59—21no—
528C2×C4×C59—21no—
529C2×C4×C59—21no—
530C2×C4×C59—21no—
531C2×C4×C59—21no—
532C2×C4×C59—21no—
533C2×C4×C59—21no—
534C2×C4×C59—21no—
535C2×C4×C59—21no—
536C2×C4×C59—21no—
537C2×C4×C59—21no—
538C2×C4×C59—21no—
539C2×C4×C59—21no—
540C2×C4×C59—21no—
541C2×C4×C59—21no—
542C2×C4×C59—21no—
543C2×C4×C59—44no—
544C2×C4×C59—44no—
545C2×C4×C59—82no—
546C2×C4×C59C2×#4112yes—
547C2×C4×C59C2×#4112yes—
548C2×C4×C59H(5,𝔽2)12yes—
549C22⋊D59—44no—
550C2×Dic59—21no—
551C2×Dic59—21no—
552C2×Dic59—21no—
553C2×Dic59—21no—
554C2×Dic59—21no—
555C2×Dic59—21no—
556C2×Dic59—21no—
557C2×Dic59—21no—
558C2×Dic59—21no—
559C2×Dic59—21no—
560C2×Dic59—21no—
561C2×Dic59—21no—
562C2×Dic59—21no—
563C2×Dic59—21no—
564C2×Dic59—21no—
565C2×Dic59—21no—
566C2×Dic59—21no—
567C2×Dic59—21no—
568C2×Dic59—21no—
569C2×Dic59—21no—
570C2×Dic59—21no—
571C2×Dic59—21no—
572C2×Dic59—21no—
573C2×Dic59—21no—
574C2×Dic59—21no—
575C2×Dic59—21no—
576C2×Dic59—21no—
577C2×Dic59—21no—
578C2×Dic59—21no—
579C2×Dic59—21no—
580C2×Dic59—21no—
581C2×Dic59—21no—
582C2×Dic59—21no—
583C2×Dic59—21no—
584C2×Dic59—21no—
585C2×Dic59—21no—
586C2×Dic59—21no—
587C2×Dic59—21no—
588C2×Dic59—21no—
589C2×Dic59—21no—
590C2×Dic59—21no—
591C2×Dic59—21no—
592C2×Dic59—21no—
593C2×Dic59—21no—
594C2×Dic59—21no—
595C2×Dic59—44no—
596C2×Dic59—44no—
597C2×Dic59—44no—
598C2×Dic59—82no—
599C4×D59—82no—
600Dic118—82no—
601#36782—591nomaximal, Sylow
602C22×C59—22no—
603C22×C59—22no—
604C22×C59—22no—
605C22×C59—22no—
606C22×C59—22no—
607C22×C59—22no—
608C22×C59#54114yes—
609C22×C59C22×#4111yescharacteristic
610C22×C59C2×H(5,𝔽2)11yescharacteristic
611C22×C59C2×2−1+411yescharacteristic
612C22×C59C2×2−1+411yescharacteristic
613C22×C59#58511yescharacteristic
614C22×C59#58511yescharacteristic
615C22×C59#58511yescharacteristic
616C2×D59—41no—
617C2×D59—41no—
618C2×D59—41no—
619C2×D59—41no—
620C2×D59—41no—
621C2×D59—41no—
622C2×D59—41no—
623C4×C59—22no—
624C4×C59—22no—
625C4×C59—22no—
626C4×C59—41no—
627C4×C59—41no—
628C4×C59—41no—
629C4×C59—41no—
630C4×C59—41no—
631C4×C59—41no—
632C4×C59—41no—
633C4×C59—41no—
634C4×C59—41no—
635C4×C59—41no—
636C4×C59—41no—
637Dic59—41no—
638Dic59—41no—
639Dic59—41no—
640Dic59—41no—
641Dic59—41no—
642Dic59—41no—
643Dic59—41no—
644Dic59—41no—
645Dic59—41no—
646Dic59—41no—
647Dic59—41no—
648Dic59—41no—
649Dic59—41no—
650Dic59—41no—
651Dic59—41no—
652#2852—591no—
653#2851—591no—
654#2783—591no—
655#2783—591no—
656#2776—591no—
657#2776—591no—
658#2772—591no—
659#2769—591no—
660#2766—591no—
661#2766—591no—
662#2762—591no—
663#2762—591no—
664#2747—591no—
665#2744—591no—
666#2725—591no—
667#2719—591no—
668#2690—591no—
669#2689—591no—
670#2646—591no—
671#2643—591no—
672#2583—591no—
673#2579—591no—
674#2510—591no—
675#2510—591no—
676#2505—591no—
677#2505—591no—
678#2442D5911yescharacteristic, complemented
679#2417—591no—
680#2329—591no—
681#2318—591no—
682C2×#387—591no—
683C2×C59—24no—
684C2×C59C2×#54111yescharacteristic
685C2×C59#349311yescharacteristic
686C2×C59#350511yescharacteristic
687C2×C59#353511yescharacteristic
688C2×C59#354111yescharacteristic
689C2×C59#355311yescharacteristic
690C2×C59#356411yescharacteristic
691D59—81no—
692C2×#126—591no—
693C2×#125—591no—
694C2×#125C2×D5911yescharacteristic
695C2×C22⋊Q8—591no—
696C2×C22⋊Q8—591no—
697C2×C4×D4—591no—
698C22×C4⋊C4—591no—
699C22×C4⋊C4C2×D5911yescharacteristic
700C22×C42—591no—
701#401—591no—
702#401—591no—
703#401—591no—
704#400—591no—
705#400—591no—
706#400—591no—
707#400—591no—
708#400—591no—
709#400—591no—
710#400—591no—
711#400—591no—
712#400—591no—
713#400—591no—
714#400—591no—
715#400—591no—
716#400—591no—
717#400—591no—
718#400—591no—
719#400C2×D5911yescharacteristic
720#400C2×D5911yescharacteristic
721#398—591no—
722#398—591no—
723#398—591no—
724#398—591no—
725#398—591no—
726#398—591no—
727#398—591no—
728#398—591no—
729#398—591no—
730#398—591no—
731#398—591no—
732#398—591no—
733#398C2×D5911yescharacteristic
734#398C2×D5911yescharacteristic
735#397—591no—
736#397—591no—
737#397—591no—
738#397—591no—
739#397—591no—
740#397—591no—
741#397—591no—
742#396—591no—
743#396—591no—
744#396—591no—
745#396—591no—
746#396—591no—
747#395—591no—
748#395—591no—
749#391—591no—
750#391—591no—
751#391—591no—
752#389—591no—
753#389—591no—
754#389—591no—
755#389—591no—
756#389—591no—
757#389—591no—
758#389—591no—
759#389—591no—
760#389—591no—
761#389—591no—
762#389—591no—
763#389C2×D5911yescharacteristic
764#389C2×D5911yescharacteristic
765#388—591no—
766#388—591no—
767#388—591no—
768#388—591no—
769#388—591no—
770#388—591no—
771#388—591no—
772#388—591no—
773#388—591no—
774#387—591no—
775#387—591no—
776#387—591no—
777#387—591no—
778#387—591no—
779#387—591no—
780#387—591no—
781#387—591no—
782#387—591no—
783#387—591no—
784#387—591no—
785#387—591no—
786#387—591no—
787#387—591no—
788#387—591no—
789#387—591no—
790#387—591no—
791#387—591no—
792#387—591no—
793#387—591no—
794#387—591no—
795#387—591no—
796#387—591no—
797#387—591no—
798#387—591no—
799#387—591no—
800#387—591no—
801#387—591no—
802#387—591no—
803#386—591no—
804#386—591no—
805#386—591no—
806#386—591no—
807#386—591no—
808#386—591no—
809#385—591no—
810#385—591no—
811#385—591no—
812#385—591no—
813#385—591no—
814#385—591no—
815#385—591no—
816#385—591no—
817#385—591no—
818#385—591no—
819#385—591no—
820#385—591no—
821#385C2×D5911yescharacteristic
822#385C2×D5911yescharacteristic
823#383—591no—
824#383—591no—
825#383—591no—
826#383—591no—
827#382—591no—
828#382—591no—
829#382—591no—
830#382—591no—
831#382C2×D5911yescharacteristic
832#381—591no—
833#380—591no—
834#380—591no—
835#380—591no—
836#380—591no—
837#380C2×D5911yescharacteristic
838#380C2×D5911yescharacteristic
839#380C2×D5911yescharacteristic
840C4×C22⋊C4—591no—
841C4×C22⋊C4—591no—
842C4×C22⋊C4C2×D5911yescharacteristic
843C2×#95—591no—
844C2×#95—591no—
845C2×#95—591no—
846C2×#95—591no—
847C59#3678211yescharacteristic, complemented, Sylow
848C22×Q8—591no—
849C22×D4—591no—
850C23×C4—591no—
851C23×C4—591no—
852C23×C4—591no—
853C23×C4—591no—
854C23×C4—591no—
855C23×C4C22×D5911yescharacteristic
856C23×C4C22×D5911yescharacteristic
857C23×C4C22×D5911yescharacteristic
858#126—2362no—
859#125—42no—
860#125—2362no—
861C22⋊Q8—1184no—
862C22⋊Q8—2362no—
863C4×D4—1184no—
864C2×C4⋊C4—42no—
865C2×C4⋊C4—591no—
866C2×C4⋊C4—591no—
867C2×C4⋊C4—591no—
868C2×C4⋊C4—591no—
869C2×C4⋊C4—591no—
870C2×C4⋊C4—591no—
871C2×C4⋊C4—591no—
872C2×C4⋊C4—591no—
873C2×C4⋊C4—591no—
874C2×C4⋊C4—591no—
875C2×C4⋊C4—591no—
876C2×C4⋊C4—591no—
877C2×C4⋊C4—591no—
878C2×C4⋊C4—591no—
879C2×C4⋊C4—591no—
880C2×C4⋊C4—591no—
881C2×C4⋊C4—591no—
882C2×C4⋊C4—591no—
883C2×C4⋊C4—591no—
884C2×C4⋊C4—591no—
885C2×C4⋊C4—591no—
886C2×C4⋊C4—591no—
887C2×C4⋊C4—591no—
888C2×C4⋊C4—591no—
889C2×C4⋊C4—591no—
890C2×C4⋊C4—591no—
891C2×C4⋊C4—591no—
892C2×C4⋊C4—591no—
893C2×C4⋊C4—591no—
894C2×C4⋊C4—591no—
895C2×C4⋊C4—591no—
896C2×C4⋊C4—591no—
897C2×C4⋊C4—1184no—
898C2×C4⋊C4C22×D5911yescharacteristic
899C2×C4⋊C4C22×D5911yescharacteristic
900C2×C4⋊C4C22×D5911yescharacteristic
901C2×C4⋊C4C22×D5911yescharacteristic
902C2×C4⋊C4C22×D5911yescharacteristic
903C2×C4⋊C4C22×D5911yescharacteristic
904C2×C4⋊C4C22×D5911yescharacteristic
905C2×C4⋊C4C22×D5911yescharacteristic
906C2×C4⋊C4C22×D5911yescharacteristic
907C2×C4⋊C4C22×D5911yescharacteristic
908C2×C4⋊C4C22×D5911yescharacteristic
909C2×C4⋊C4C22×D5911yescharacteristic
910C2×C4⋊C4C22×D5911yescharacteristic
911C2×C4⋊C4C22×D5911yescharacteristic
912C2×C22⋊C4—591no—
913C2×C22⋊C4—591no—
914C2×C22⋊C4—591no—
915C2×C22⋊C4—591no—
916C2×C22⋊C4—591no—
917C2×C22⋊C4—591no—
918C2×C22⋊C4—591no—
919C2×C22⋊C4—591no—
920C2×C22⋊C4—591no—
921C2×C22⋊C4—591no—
922C2×C22⋊C4—591no—
923C2×C22⋊C4—591no—
924C2×C22⋊C4—591no—
925C2×C22⋊C4—591no—
926C2×C22⋊C4—591no—
927C2×C22⋊C4—591no—
928C2×C22⋊C4C22×D5911yescharacteristic
929C2×C22⋊C4C22×D5911yescharacteristic
930C2×C22⋊C4C22×D5911yescharacteristic
931C2×C22⋊C4C22×D5911yescharacteristic
932C2×C42—591no—
933C2×C42—591no—
934C2×C42—591no—
935C2×C42—591no—
936C2×C42—591no—
937C2×C42—591no—
938C2×C42—591no—
939C2×C42—591no—
940C2×C42—591no—
941C2×C42—2362no—
942C2×C42C22×D5911yescharacteristic
943C2×C42C22×D5911yescharacteristic
944#95—591no—
945#95—591no—
946#95—591no—
947#95—591no—
948#95—591no—
949#95—591no—
950#95—591no—
951#95—591no—
952#95—591no—
953#95—591no—
954#95—591no—
955#95—591no—
956#95—591no—
957#95—591no—
958#95—591no—
959#95—591no—
960#95—591no—
961#95—591no—
962#95—591no—
963#95—591no—
964#95—591no—
965#95—591no—
966#95—591no—
967#95—591no—
968#95—591no—
969#95—591no—
970#95—591no—
971#95—591no—
972#95—591no—
973#95—591no—
974#95—591no—
975#95—591no—
976#95—591no—
977#95—591no—
978#95—591no—
979#95—591no—
980#95—591no—
981#95—591no—
982#95—591no—
983#95—591no—
984#95—591no—
985#95—591no—
986#95—591no—
987#95—591no—
988#95—591no—
989#95—591no—
990#95—591no—
991#95—591no—
992#95—591no—
993#95—591no—
994#95—591no—
995#95—591no—
996#95—591no—
997#95—591no—
998#95—591no—
999#95—591no—
1000#95C22×D5911yescharacteristic
1001#95C22×D5911yescharacteristic
1002#95C22×D5911yescharacteristic
1003#95C22×D5911yescharacteristic
1004#95C22×D5911yescharacteristic
1005#95C22×D5911yescharacteristic
1006#95C22×D5911yescharacteristic
1007#95C22×D5911yescharacteristic
1008#95C22×D5911yescharacteristic
1009#95C22×D5911yescharacteristic
1010#95C22×D5911yescharacteristic
1011#95C22×D5911yescharacteristic
1012C24—591no—
1013C24C23×D5911yescharacteristic
1014C2×Q8—1182no—
1015C2×Q8—2361no—
1016C2×Q8—2361no—
1017C2×D4—1182no—
1018C2×D4—1182no—
1019C2×D4—1182no—
1020C22×C4—22no—
1021C22×C4—22no—
1022C22×C4—22no—
1023C22×C4—41no—
1024C22×C4—41no—
1025C22×C4—41no—
1026C22×C4—41no—
1027C22×C4—41no—
1028C22×C4—591no—
1029C22×C4—591no—
1030C22×C4—591no—
1031C22×C4—591no—
1032C22×C4—591no—
1033C22×C4—591no—
1034C22×C4—591no—
1035C22×C4—591no—
1036C22×C4—591no—
1037C22×C4—591no—
1038C22×C4—591no—
1039C22×C4—591no—
1040C22×C4—591no—
1041C22×C4—591no—
1042C22×C4—591no—
1043C22×C4—1182no—
1044C22×C4—1182no—
1045C22×C4—1182no—
1046C22×C4—1182no—
1047C22×C4—1182no—
1048C22×C4—2361no—
1049C22×C4—2361no—
1050C22×C4—2361no—
1051C22×C4—2361no—
1052C22×C4—2361no—
1053C22×C4—2361no—
1054C22×C4—2361no—
1055C22×C4—2361no—
1056C22×C4—2361no—
1057C22×C4—2361no—
1058C22×C4#1174568914yes—
1059C22×C4C23×D5911yescharacteristic
1060C22×C4C23×D5911yescharacteristic
1061C22×C4C23×D5911yescharacteristic
1062C22×C4C23×D5911yescharacteristic
1063C22×C4C23×D5911yescharacteristic
1064C22×C4C23×D5911yescharacteristic
1065C22×C4C23×D5911yescharacteristic
1066C22×C4C23×D5911yescharacteristic
1067C22×C4C23×D5911yescharacteristic
1068C22×C4C23×D5911yescharacteristic
1069C22×C4C23×D5911yescharacteristic
1070C22×C4C23×D5911yescharacteristic
1071C22×C4C23×D5911yescharacteristic
1072C22×C4C23×D5911yescharacteristic
1073C4⋊C4—22no—
1074C4⋊C4—22no—
1075C4⋊C4—22no—
1076C4⋊C4—22no—
1077C4⋊C4—41no—
1078C4⋊C4—41no—
1079C4⋊C4—41no—
1080C4⋊C4—41no—
1081C4⋊C4—41no—
1082C4⋊C4—41no—
1083C4⋊C4—41no—
1084C4⋊C4—41no—
1085C4⋊C4—41no—
1086C4⋊C4—41no—
1087C4⋊C4—1182no—
1088C4⋊C4—1182no—
1089C4⋊C4—1182no—
1090C4⋊C4—1182no—
1091C4⋊C4—1182no—
1092C4⋊C4—1182no—
1093C4⋊C4—1182no—
1094C4⋊C4—1182no—
1095C4⋊C4—1182no—
1096C4⋊C4—2361no—
1097C4⋊C4—2361no—
1098C4⋊C4—2361no—
1099C4⋊C4—2361no—
1100C4⋊C4—2361no—
1101C4⋊C4—2361no—
1102C4⋊C4—2361no—
1103C4⋊C4—2361no—
1104C4⋊C4—2361no—
1105C4⋊C4—2361no—
1106C4⋊C4—2361no—
1107C4⋊C4—2361no—
1108C4⋊C4—2361no—
1109C4⋊C4—2361no—
1110C4⋊C4—2361no—
1111C4⋊C4—2361no—
1112C4⋊C4—2361no—
1113C4⋊C4—2361no—
1114C4⋊C4—2361no—
1115C4⋊C4—2361no—
1116C4⋊C4—2361no—
1117C4⋊C4—2361no—
1118C4⋊C4—2361no—
1119C22⋊C4—22no—
1120C22⋊C4—22no—
1121C22⋊C4—22no—
1122C22⋊C4—22no—
1123C22⋊C4—1182no—
1124C22⋊C4—1182no—
1125C22⋊C4—1182no—
1126C22⋊C4—1182no—
1127C22⋊C4—1182no—
1128C22⋊C4—2361no—
1129C22⋊C4—2361no—
1130C22⋊C4—2361no—
1131C22⋊C4—2361no—
1132C22⋊C4—2361no—
1133C22⋊C4—2361no—
1134C22⋊C4—2361no—
1135C22⋊C4—2361no—
1136C22⋊C4—2361no—
1137C22⋊C4—2361no—
1138C22⋊C4—2361no—
1139C42—41no—
1140C42—41no—
1141C42—1182no—
1142C42—1182no—
1143C42—1182no—
1144C42—2361no—
1145C42—2361no—
1146C42—2361no—
1147C42—2361no—
1148C42—2361no—
1149C42—2361no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—1181no—
1155C23—1181no—
1156C23—1181no—
1157C23—1181no—
1158C23—1181no—
1159C23—1181no—
1160C23—1181no—
1161C23C2×#1174568912yes—
1162C23#1427377412yes—
1163C23#1427377412yes—
1164C23C24×D5911yescharacteristic
1165Q8—4722no—
1166D4—2364no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—44no—
1207C2×C4—44no—
1208C2×C4—82no—
1209C2×C4—1181no—
1210C2×C4—1181no—
1211C2×C4—1181no—
1212C2×C4—1181no—
1213C2×C4—1181no—
1214C2×C4—1181no—
1215C2×C4—1181no—
1216C2×C4—1181no—
1217C2×C4—1181no—
1218C2×C4—1181no—
1219C2×C4—1181no—
1220C2×C4—1181no—
1221C2×C4—1181no—
1222C2×C4—1181no—
1223C2×C4—1181no—
1224C2×C4—1181no—
1225C2×C4—1181no—
1226C2×C4—1181no—
1227C2×C4—1181no—
1228C2×C4—1181no—
1229C2×C4—1181no—
1230C2×C4—1181no—
1231C2×C4—1181no—
1232C2×C4—1181no—
1233C2×C4—1181no—
1234C2×C4—1181no—
1235C2×C4—1181no—
1236C2×C4—1181no—
1237C2×C4—1181no—
1238C2×C4—1181no—
1239C2×C4—1181no—
1240C2×C4—1181no—
1241C2×C4—1181no—
1242C2×C4—1181no—
1243C2×C4—1181no—
1244C2×C4—1181no—
1245C2×C4—1181no—
1246C2×C4—1181no—
1247C2×C4—1181no—
1248C2×C4—1181no—
1249C2×C4—1181no—
1250C2×C4—1181no—
1251C2×C4—1181no—
1252C2×C4—1181no—
1253C2×C4—1181no—
1254C2×C4—4722no—
1255C2×C4—4722no—
1256C2×C4—2364no—
1257C2×C4—2364no—
1258C2×C4—2364no—
1259C2×C4C2×#1174568912yes—
1260C2×C4C2×#1174568912yes—
1261C2×C4#1427377212yes—
1262C22—22no—
1263C22—22no—
1264C22—22no—
1265C22—22no—
1266C22—22no—
1267C22—22no—
1268C22—2361no—
1269C22—2361no—
1270C22—2361no—
1271C22—2361no—
1272C22—2361no—
1273C22—2361no—
1274C22—2361no—
1275C22#1683801514yes—
1276C22C22×#1174568911yescharacteristic
1277C22C2×#1427377211yescharacteristic
1278C22C2×#1427377411yescharacteristic
1279C22C2×#1427377411yescharacteristic
1280C22#1683823711yescharacteristic
1281C22#1683823811yescharacteristic
1282C22#1683823911yescharacteristic
1283C4—22no—
1284C4—22no—
1285C4—22no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—2361no—
1298C4—2361no—
1299C4—2361no—
1300C4—2361no—
1301C4—2361no—
1302C4—2361no—
1303C4—2361no—
1304C4—2361no—
1305C4—2361no—
1306C4—2361no—
1307C4—2361no—
1308C4—2361no—
1309C4—2361no—
1310C4—2361no—
1311C4—2361no—
1312C2—24no—
1313C2—4721no—
1314C2C2×#1683801511yescharacteristic
1315C2#2143781711yescharacteristic
1316C2#2143793711yescharacteristic
1317C2#2143829311yescharacteristic
1318C2#2143837511yescharacteristic
1319C2#2143854411yescharacteristic
1320C2#2143871611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D59
commutator, socle, cosocleC23×C59C25
FittingC59×#2442C2
prime radicalC22×C22⋊D59C23
hypercenter#2442D59
hypocenterC59#36782
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #2442

Complements

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

NH ≅ G/Ntype
2. #21432404C2semidirect
3. #21431777C2semidirect
4. #21431777C2semidirect
5. #21431682C2semidirect
6. #21431682C2semidirect
7. #21431620C2semidirect
8. #21431592C2semidirect
9. #21431552C2semidirect
10. #21431542C2semidirect
11. #21431504C2semidirect
12. #21431491C2semidirect
13. #21431301C2semidirect
14. #21431249C2semidirect
15. #21431032C2semidirect
16. #21430957C2semidirect
17. #21430569C2semidirect
18. #21430554C2semidirect
19. #21430069C2semidirect
21. #21429471C2semidirect
25. #21428601C2semidirect
26. #21428601C2semidirect
28. #21426826C2semidirect
30. C2×#16837283C2semidirect
31. C59×#2442C2semidirect
678. #2442D59semidirect
847. C59#36782semidirect

Maximal subgroups

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

subgroupindex
#214324132
#214324042
#214317772
#214316822
#214316202
#214315922
#214315522
#214315422
#214315042
#214314912
#214313012
#214312492
#214310322
#214309572
#214305692
#214305542
#214300692
#214300522
#214294712
#214294452
#214286522
#214286012
#214275412
#214268262
#214267232
C2×#168372832
C59×#24422
#3678259