Finite Group Databasebeta

← #28803650

Subgroups — #28803650

Order 15104.

1442 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432484C211yesmaximal, characteristic, complemented
2#21432484C211yesmaximal, characteristic, complemented
3#21431918C211yesmaximal, characteristic, complemented
4#21431915C211yesmaximal, characteristic, complemented
5#21431817C211yesmaximal, characteristic, complemented
6#21431812C211yesmaximal, characteristic, complemented
7#21431502C211yesmaximal, characteristic, complemented
8#21431498C211yesmaximal, characteristic, complemented
9#21431354C211yesmaximal, characteristic, complemented
10#21431348C211yesmaximal, characteristic, complemented
11#21431343C211yesmaximal, characteristic, complemented
12#21431287C211yesmaximal, characteristic, complemented
13#21431277C211yesmaximal, characteristic, complemented
14#21431235C211yesmaximal, characteristic, complemented
15#21431229C211yesmaximal, characteristic, complemented
16#21431154C211yesmaximal, characteristic, complemented
17#21431144C211yesmaximal, characteristic, complemented
18#21430119C211yesmaximal, characteristic, complemented
19#21430111C211yesmaximal, characteristic, complemented
20#21429759C211yesmaximal, characteristic, complemented
21#21429570C211yesmaximal, characteristic
22#21429419C211yesmaximal, characteristic, complemented
23#21429416C211yesmaximal, characteristic, complemented
24#21428879C211yesmaximal, characteristic, complemented
25#21428876C211yesmaximal, characteristic, complemented
26#21428557C211yesmaximal, characteristic
27#21428384C211yesmaximal, characteristic, complemented
28#21426857C211yesmaximal, characteristic
29#21426695C211yesmaximal, characteristic, complemented
30#21426588C211yesmaximal, characteristic, complemented
31C59×#2751C211yesmaximal, characteristic, complemented
32C2×#14273698C2211yescharacteristic
33C2×#14273685C2211yescharacteristic
34C2×C4⋊C4×D59C2211yescharacteristic
35C59⋊#401C2211yescharacteristic
36C59⋊#401C2211yescharacteristic
37#16837344C2211yescharacteristic
38#16837344C2211yescharacteristic
39#16837344C2211yescharacteristic
40#16837344C2211yescharacteristic
41#16837343C2211yescharacteristic
42#16837343C2211yescharacteristic
43#16837343C2211yescharacteristic
44#16837343C2211yescharacteristic
45#16837343C2211yescharacteristic
46#16837342C2211yescharacteristic
47#16837341C2211yescharacteristic
48#16837341C2211yescharacteristic
49#16837340C2211yescharacteristic
50#16837339C2211yescharacteristic
51#16837337C2211yescharacteristic
52#16837334C2211yescharacteristic
53#16837334C2211yescharacteristic
54#16837333C2211yescharacteristic
55#16837332C2211yescharacteristic
56#16837330C2211yescharacteristic
57#16837330C2211yescharacteristic
58#16837330C2211yescharacteristic
59#16837330C2211yescharacteristic
60#16837330C2211yescharacteristic
61#16837327C2211yescharacteristic
62#16837327C2211yescharacteristic
63#16837327C2211yescharacteristic
64#16837325C2211yescharacteristic
65#16837325C2211yescharacteristic
66#16837322C2211yescharacteristic
67#16837321C2211yescharacteristic
68#16837317C2211yescharacteristic
69#16837317C2211yescharacteristic
70#16837317C2211yescharacteristic
71#16837317C2211yescharacteristic
72#16837316C2211yescharacteristic
73#16837315C2211yescharacteristic
74#16837314C2211yescharacteristic
75#16837314C2211yescharacteristic
76#16837313C2211yescharacteristic
77#16837309C2211yescharacteristic
78#16837309C2211yescharacteristic
79#16837308C2211yescharacteristic
80#16837306C2211yescharacteristic
81#16837306C2211yescharacteristic
82#16837305C2211yescharacteristic
83#16837302C2211yescharacteristic
84#16837302C2211yescharacteristic
85#16837296C2211yescharacteristic
86#16837296C2211yescharacteristic
87#16837296C2211yescharacteristic
88#16837296C2211yescharacteristic
89#16837296C2211yescharacteristic
90#16837296C2211yescharacteristic
91#16837295C2211yescharacteristic
92#16837295C2211yescharacteristic
93#16837295C2211yescharacteristic
94#16837295C2211yescharacteristic
95#16837295C2211yescharacteristic
96#16837294C2211yescharacteristic
97#16837293C2211yescharacteristic
98#16837292C2211yescharacteristic
99#16837291C2211yescharacteristic
100#16837290C2211yescharacteristic
101#16837290C2211yescharacteristic
102#16837290C2211yescharacteristic
103#16837290C2211yescharacteristic
104#16837290C2211yescharacteristic
105#16837289C2211yescharacteristic
106#16837289C2211yescharacteristic
107#16837289C2211yescharacteristic
108#16837289C2211yescharacteristic
109#16837289C2211yescharacteristic
110#16837289C2211yescharacteristic
111#16837288C2211yescharacteristic
112#16837288C2211yescharacteristic
113#16837288C2211yescharacteristic
114#16837288C2211yescharacteristic
115#16837287C2211yescharacteristic
116#16837287C2211yescharacteristic
117#16837287C2211yescharacteristic
118#16837287C2211yescharacteristic
119#16837287C2211yescharacteristic
120#16837286C2211yescharacteristic
121#16837286C2211yescharacteristic
122#16837286C2211yescharacteristic
123#16837285C2211yescharacteristic
124#16837285C2211yescharacteristic
125#16837285C2211yescharacteristic
126#16837285C2211yescharacteristic
127#16837285C2211yescharacteristic
128#16837285C2211yescharacteristic
129#16837285C2211yescharacteristic
130#16837284C2211yescharacteristic
131#16837284C2211yescharacteristic
132#16837284C2211yescharacteristic
133#16837284C2211yescharacteristic
134#16837283C2211yescharacteristic
135#16837283C2211yescharacteristic
136#16837283C2211yescharacteristic
137#16837282C2211yescharacteristic
138#16837281C2211yescharacteristic
139#16837279C2211yescharacteristic
140#16837278C2211yescharacteristic
141#16837278C2211yescharacteristic
142#16837278C2211yescharacteristic
143#16837278C2211yescharacteristic
144#16837277C2211yescharacteristic
145#16837277C2211yescharacteristic
146#16837276C2211yescharacteristic
147#16837276C2211yescharacteristic
148#16837275C2211yescharacteristic
149#16837271C2211yescharacteristic
150#16837269C2211yescharacteristic
151#16837269C2211yescharacteristic
152#16837268C2211yescharacteristic
153#16837264C2211yescharacteristic
154#16837264C2211yescharacteristic
155#16837264C2211yescharacteristic
156#16837264C2211yescharacteristic
157#16837264C2211yescharacteristic
158#16837263C2211yescharacteristic
159#16837262C2211yescharacteristic
160#16837261C2211yescharacteristic
161#16837260C2211yescharacteristic
162#16837259C2211yescharacteristic
163C4⋊C4×Dic59C2211yescharacteristic
164#16837253C2211yescharacteristic
165C22⋊C4×Dic59C2211yescharacteristic
166C4×(C2×D59)⋊C4C2211yescharacteristic
167C4×C22⋊Dic59C2211yescharacteristic
168#16837249C2211yescharacteristic
169#16837249C2211yescharacteristic
170#16837247C2211yescharacteristic
171C42×Dic59C2211yescharacteristic
172C59×#400C2211yescharacteristic
173C59×#397C2211yescharacteristic
174C59×#397C2211yescharacteristic
175C59×#394C2211yescharacteristic
176C59×#393C2211yescharacteristic
177C59×#393C2211yescharacteristic
178C59×#391C2211yescharacteristic
179C59×#390C2211yescharacteristic
180C59×#388C2211yescharacteristic
181C59×#388C2211yescharacteristic
182C59×#387C2211yescharacteristic
183C59×#387C2211yescharacteristic
184C59×#386C2211yescharacteristic
185C59×#385C2211yescharacteristic
186C59×#381C2211yescharacteristic
187C22×Dic118C2311yescharacteristic
188C22×C22⋊D59C2311yescharacteristic
189C22×C22⋊D59C2311yescharacteristic
190C23×Dic59C2311yescharacteristic
191C22×C4×D59C2311yescharacteristic
192C22×C4×D59C2311yescharacteristic
193C22×C4×D59C2311yescharacteristic
194#14273698—24no—
195#14273685—24no—
196C2×C4⋊Dic59C2311yescharacteristic
197C2×C4⋊Dic59C2311yescharacteristic
198C2×C4⋊Dic59C2311yescharacteristic
199C2×C4⋊Dic59C2311yescharacteristic
200C2×C4⋊Dic59C2311yescharacteristic
201C2×C4⋊Dic59C2311yescharacteristic
202C2×C4⋊Dic59C2311yescharacteristic
203C2×C4⋊Dic59C2311yescharacteristic
204C2×C4⋊Dic59C2311yescharacteristic
205C2×C4⋊Dic59C2311yescharacteristic
206C2×Dic59⋊C4C2311yescharacteristic
207C2×Dic59⋊C4C2311yescharacteristic
208C2×Dic59⋊C4C2311yescharacteristic
209C2×Dic59⋊C4C2311yescharacteristic
210C2×Dic59⋊C4C2311yescharacteristic
211C2×Dic59⋊C4C2311yescharacteristic
212C2×Dic59⋊C4C2311yescharacteristic
213C2×Dic59⋊C4C2311yescharacteristic
214C2×Dic59⋊C4C2311yescharacteristic
215C2×Dic59⋊C4C2311yescharacteristic
216C2×Dic59⋊C4C2311yescharacteristic
217C2×Dic59⋊C4C2311yescharacteristic
218C2×Dic59⋊C4C2311yescharacteristic
219C2×Dic59⋊C4C2311yescharacteristic
220C2×Dic59⋊C4C2311yescharacteristic
221C2×Dic59⋊C4C2311yescharacteristic
222C4⋊C4×D59—24no—
223C2×C22⋊Dic59C2311yescharacteristic
224C2×C22⋊Dic59C2311yescharacteristic
225C2×C22⋊Dic59C2311yescharacteristic
226C2×C22⋊Dic59C2311yescharacteristic
227C2×C22⋊Dic59C2311yescharacteristic
228C2×C22⋊Dic59C2311yescharacteristic
229C2×C22⋊Dic59C2311yescharacteristic
230C2×C22⋊Dic59C2311yescharacteristic
231C2×C22⋊Dic59C2311yescharacteristic
232C2×C22⋊Dic59C2311yescharacteristic
233C2×C22⋊Dic59C2311yescharacteristic
234C2×C22⋊Dic59C2311yescharacteristic
235C2×C22⋊Dic59C2311yescharacteristic
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×C4×Dic59C2311yescharacteristic
247C2×C4×Dic59C2311yescharacteristic
248C2×C4×Dic59C2311yescharacteristic
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
310C22×Q8×C59C2311yescharacteristic
311C22×D4×C59C2311yescharacteristic
312C23×C4×C59C2311yescharacteristic
313C2×C4⋊C4×C59C2311yescharacteristic
314C2×C4⋊C4×C59C2311yescharacteristic
315C2×C4⋊C4×C59C2311yescharacteristic
316C2×C4⋊C4×C59C2311yescharacteristic
317C2×C4⋊C4×C59C2311yescharacteristic
318C2×C22⋊C4×C59C2311yescharacteristic
319C2×C22⋊C4×C59C2311yescharacteristic
320C2×C22⋊C4×C59C2311yescharacteristic
321C2×C22⋊C4×C59C2311yescharacteristic
322C2×C22⋊C4×C59C2311yescharacteristic
323C2×C22⋊C4×C59C2311yescharacteristic
324C2×C22⋊C4×C59C2311yescharacteristic
325C2×C22⋊C4×C59C2311yescharacteristic
326C2×C22⋊C4×C59C2311yescharacteristic
327C2×C22⋊C4×C59C2311yescharacteristic
328C2×C22⋊C4×C59C2311yescharacteristic
329C2×C42×C59C2311yescharacteristic
330C2×C42×C59C2311yescharacteristic
331#95×C59C2311yescharacteristic
332#95×C59C2311yescharacteristic
333#95×C59C2311yescharacteristic
334#95×C59C2311yescharacteristic
335#95×C59C2311yescharacteristic
336#95×C59C2311yescharacteristic
337#95×C59C2311yescharacteristic
338#95×C59C2311yescharacteristic
339#95×C59C2311yescharacteristic
340#95×C59C2311yescharacteristic
341#95×C59C2311yescharacteristic
342#95×C59C2311yescharacteristic
343#95×C59C2311yescharacteristic
344#95×C59C2311yescharacteristic
345C24×C59C2411yescharacteristic
346C24×C59C2411yescharacteristic
347C23×D59C2411yescharacteristic
348C2×Q8×C59—41no—
349C2×Q8×C59—41no—
350C2×Q8×C59—41no—
351C2×D4×C59—22no—
352C2×D4×C59—41no—
353C2×D4×C59—41no—
354C22×C4×C59—41no—
355C22×C4×C59—41no—
356C22×C4×C59—41no—
357C22×C4×C59C2411yescharacteristic
358C22×C4×C59C2411yescharacteristic
359C22×C4×C59C2411yescharacteristic
360C22×C4×C59C2411yescharacteristic
361C22×C4×C59C2411yescharacteristic
362C22×C4×C59C2411yescharacteristic
363C22×C4×C59C2411yescharacteristic
364C22×C4×C59C2411yescharacteristic
365C22×C4×C59C2411yescharacteristic
366C22×C4×C59C2411yescharacteristic
367C22×C4×C59C2411yescharacteristic
368C22×C4×C59C2411yescharacteristic
369C22×C4×C59C2411yescharacteristic
370C2×C22⋊D59—22no—
371C2×C22⋊D59—22no—
372C2×C22⋊D59—41no—
373C2×C22⋊D59—41no—
374C2×C22⋊D59—41no—
375C2×C22⋊D59—41no—
376C22×Dic59—41no—
377C22×Dic59—41no—
378C22×Dic59—41no—
379C22×Dic59C2411yescharacteristic
380C22×Dic59C2411yescharacteristic
381C22×Dic59C2411yescharacteristic
382C22×Dic59C2411yescharacteristic
383C22×Dic59C2411yescharacteristic
384C22×Dic59C2411yescharacteristic
385C22×Dic59C2411yescharacteristic
386C22×Dic59C2411yescharacteristic
387C22×Dic59C2411yescharacteristic
388C22×Dic59C2411yescharacteristic
389C22×Dic59C2411yescharacteristic
390C22×Dic59C2411yescharacteristic
391C22×Dic59C2411yescharacteristic
392C22×Dic59C2411yescharacteristic
393C22×Dic59C2411yescharacteristic
394C2×C4×D59—22no—
395C2×C4×D59—22no—
396C2×C4×D59—41no—
397C2×C4×D59—41no—
398C2×C4×D59—41no—
399C2×C4×D59—41no—
400C2×C4×D59—41no—
401C2×C4×D59—41no—
402C2×C4×D59#4114yes—
403C2×Dic118—41no—
404C2×Dic118—41no—
405C2×Dic118—41no—
406C4⋊C4×C59—22no—
407C4⋊C4×C59—22no—
408C4⋊C4×C59—41no—
409C4⋊C4×C59—41no—
410C4⋊C4×C59—41no—
411C22⋊C4×C59—41no—
412C22⋊C4×C59—41no—
413C22⋊C4×C59—41no—
414C22⋊C4×C59—41no—
415C22⋊C4×C59—41no—
416C22⋊C4×C59—41no—
417C22⋊C4×C59—41no—
418C22⋊C4×C59—41no—
419C22⋊C4×C59—41no—
420C22⋊C4×C59—41no—
421C22⋊C4×C59—41no—
422C42×C59—41no—
423C42×C59—41no—
424C22⋊Dic59—22no—
425C22⋊Dic59—22no—
426C22⋊Dic59—41no—
427C22⋊Dic59—41no—
428C22⋊Dic59—41no—
429C22⋊Dic59—41no—
430C22⋊Dic59—41no—
431C22⋊Dic59—41no—
432C22⋊Dic59—41no—
433C22⋊Dic59—41no—
434C22⋊Dic59—41no—
435C22⋊Dic59—41no—
436C22⋊Dic59—41no—
437(C2×D59)⋊C4—22no—
438(C2×D59)⋊C4—22no—
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—
447C4⋊Dic59—22no—
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—
457Dic59⋊C4—22no—
458Dic59⋊C4—22no—
459Dic59⋊C4—41no—
460Dic59⋊C4—41no—
461Dic59⋊C4—41no—
462Dic59⋊C4—41no—
463Dic59⋊C4—41no—
464Dic59⋊C4—41no—
465Dic59⋊C4—41no—
466Dic59⋊C4—41no—
467Dic59⋊C4—41no—
468Dic59⋊C4—41no—
469Dic59⋊C4—41no—
470Dic59⋊C4—41no—
471Dic59⋊C4—41no—
472Dic59⋊C4—41no—
473C4×Dic59—22no—
474C4×Dic59—22no—
475C4×Dic59—41no—
476C4×Dic59—41no—
477C4×Dic59—41no—
478C4×Dic59—41no—
479C4×Dic59—41no—
480C4×Dic59—41no—
481C4×Dic59—41no—
482C4×Dic59—41no—
483C4×Dic59—41no—
484C4×Dic59—41no—
485C23×C59—21no—
486C23×C59—21no—
487C23×C59—21no—
488C23×C59—21no—
489C23×C59—21no—
490C23×C59—21no—
491C23×C59—21no—
492C23×C59—21no—
493C23×C59—21no—
494C23×C59—21no—
495C23×C59—21no—
496C23×C59—21no—
497C23×C59—21no—
498C23×C59—21no—
499C23×C59C2511yescharacteristic
500C22×D59—21no—
501C22×D59—21no—
502C22×D59—21no—
503C22×D59—21no—
504C22×D59—21no—
505C22×D59—21no—
506C22×D59C2×#4112yes—
507Q8×C59—82no—
508D4×C59—82no—
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—21no—
544C2×C4×C59—21no—
545C2×C4×C59—21no—
546C2×C4×C59—21no—
547C2×C4×C59—82no—
548C2×C4×C59C2×#4112yes—
549C22⋊D59—82no—
550C22⋊D59—82no—
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—82no—
596C2×Dic59C2×#4112yes—
597C4×D59—44no—
598C4×D59—44no—
599C4×D59—82no—
600Dic118—82no—
601#37013—591nomaximal, Sylow
602C22×C59—41no—
603C22×C59—41no—
604C22×C59—41no—
605C22×C59—41no—
606C22×C59—41no—
607C22×C59—41no—
608C22×C59—41no—
609C22×C59—41no—
610C22×C59—41no—
611C22×C59—41no—
612C22×C59—41no—
613C22×C59—41no—
614C22×C59—41no—
615C22×C59—41no—
616C22×C59C22×#4111yescharacteristic
617C22×C59#58511yescharacteristic
618C22×C59#58511yescharacteristic
619C22×C59#58511yescharacteristic
620C22×C59#58511yescharacteristic
621C22×C59#58511yescharacteristic
622C22×C59#58511yescharacteristic
623C2×D59—22no—
624C2×D59—22no—
625C2×D59—22no—
626C2×D59—41no—
627C2×D59—41no—
628C2×D59—41no—
629C2×D59—41no—
630C4×C59—22no—
631C4×C59—41no—
632C4×C59—41no—
633C4×C59—41no—
634C4×C59—41no—
635C4×C59—41no—
636C4×C59—41no—
637C4×C59—41no—
638C4×C59—41no—
639C4×C59—41no—
640C4×C59—41no—
641C4×C59—41no—
642C4×C59—41no—
643Dic59—22no—
644Dic59—41no—
645Dic59—41no—
646Dic59—41no—
647Dic59—41no—
648Dic59—41no—
649Dic59—41no—
650Dic59—41no—
651Dic59—41no—
652Dic59—41no—
653Dic59—41no—
654Dic59—41no—
655Dic59—41no—
656Dic59—41no—
657Dic59—41no—
658#2865—591no—
659#2865—591no—
660#2794—591no—
661#2794—591no—
662#2786—591no—
663#2786—591no—
664#2762—591no—
665#2762—591no—
666#2751—591no—
667#2751—591no—
668#2751—591no—
669#2751D5911yescharacteristic, complemented
670#2746—591no—
671#2746—591no—
672#2743—591no—
673#2743—591no—
674#2737—591no—
675#2737—591no—
676#2650—591no—
677#2650—591no—
678#2607—591no—
679#2591—591no—
680#2577—591no—
681#2577—591no—
682#2527—591no—
683#2527—591no—
684#2500—591no—
685#2484—591no—
686#2333—591no—
687#2313—591no—
688#2298—591no—
689C2×C59—81no—
690C2×C59—81no—
691C2×C59#345511yescharacteristic
692C2×C59#349111yescharacteristic
693C2×C59#351011yescharacteristic
694C2×C59#356611yescharacteristic
695C2×C59#356611yescharacteristic
696C2×C59#356611yescharacteristic
697C2×C59#356611yescharacteristic
698D59—42no—
699C2×#121—591no—
700C2×#117—591no—
701C22×C4⋊C4—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#400C2×D5911yescharacteristic
718#399—591no—
719#399—591no—
720#398—591no—
721#398—591no—
722#398—591no—
723#398—591no—
724#397—591no—
725#397—591no—
726#397—591no—
727#397—591no—
728#397—591no—
729#397—591no—
730#397—591no—
731#397—591no—
732#397C2×D5911yescharacteristic
733#397C2×D5911yescharacteristic
734#396—591no—
735#396—591no—
736#395—591no—
737#395—591no—
738#394—591no—
739#394—591no—
740#394—591no—
741#394—591no—
742#394—591no—
743#394C2×D5911yescharacteristic
744#393—591no—
745#393—591no—
746#393—591no—
747#393—591no—
748#393C2×D5911yescharacteristic
749#393C2×D5911yescharacteristic
750#391—591no—
751#391—591no—
752#391—591no—
753#391—591no—
754#391—591no—
755#391C2×D5911yescharacteristic
756#390—591no—
757#390—591no—
758#390—591no—
759#390C2×D5911yescharacteristic
760#388—591no—
761#388—591no—
762#388—591no—
763#388—591no—
764#388—591no—
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#388—591no—
775#388—591no—
776#388—591no—
777#388—591no—
778#388—591no—
779#388—591no—
780#388C2×D5911yescharacteristic
781#388C2×D5911yescharacteristic
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#387—591no—
804#387—591no—
805#387—591no—
806#387—591no—
807#387—591no—
808#387—591no—
809#387—591no—
810#387—591no—
811#387—591no—
812#387—591no—
813#387—591no—
814#387C2×D5911yescharacteristic
815#387C2×D5911yescharacteristic
816#386—591no—
817#386—591no—
818#386—591no—
819#386—591no—
820#386—591no—
821#386—591no—
822#386—591no—
823#386C2×D5911yescharacteristic
824#385—591no—
825#385—591no—
826#385—591no—
827#385—591no—
828#385—591no—
829#385C2×D5911yescharacteristic
830#384—591no—
831#383—591no—
832#383—591no—
833#382—591no—
834#381—591no—
835#381—591no—
836#381—591no—
837#381—591no—
838#381—591no—
839#381—591no—
840#381C2×D5911yescharacteristic
841#380—591no—
842#380—591no—
843#380—591no—
844#380—591no—
845C4×C4⋊C4—591no—
846C4×C4⋊C4—591no—
847C4×C22⋊C4—591no—
848C4×C22⋊C4—591no—
849C4×C22⋊C4—591no—
850C4×C22⋊C4—591no—
851C4×C22⋊C4—591no—
852#376—591no—
853C43—591no—
854C59#3701311yescharacteristic, complemented, Sylow
855C22×Q8—591no—
856C22×Q8C22×D5911yescharacteristic
857C22×D4—591no—
858C22×D4—591no—
859C22×D4C22×D5911yescharacteristic
860C23×C4—591no—
861C23×C4—591no—
862C23×C4—591no—
863C23×C4—591no—
864C23×C4C22×D5911yescharacteristic
865#121—1184no—
866#117—1184no—
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—1184no—
894C2×C4⋊C4C22×D5911yescharacteristic
895C2×C4⋊C4C22×D5911yescharacteristic
896C2×C4⋊C4C22×D5911yescharacteristic
897C2×C4⋊C4C22×D5911yescharacteristic
898C2×C4⋊C4C22×D5911yescharacteristic
899C2×C22⋊C4—591no—
900C2×C22⋊C4—591no—
901C2×C22⋊C4—591no—
902C2×C22⋊C4—591no—
903C2×C22⋊C4—591no—
904C2×C22⋊C4—591no—
905C2×C22⋊C4—591no—
906C2×C22⋊C4—591no—
907C2×C22⋊C4—591no—
908C2×C22⋊C4—591no—
909C2×C22⋊C4—591no—
910C2×C22⋊C4—591no—
911C2×C22⋊C4—591no—
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⋊C4C22×D5911yescharacteristic
923C2×C22⋊C4C22×D5911yescharacteristic
924C2×C22⋊C4C22×D5911yescharacteristic
925C2×C22⋊C4C22×D5911yescharacteristic
926C2×C22⋊C4C22×D5911yescharacteristic
927C2×C22⋊C4C22×D5911yescharacteristic
928C2×C22⋊C4C22×D5911yescharacteristic
929C2×C22⋊C4C22×D5911yescharacteristic
930C2×C22⋊C4C22×D5911yescharacteristic
931C2×C22⋊C4C22×D5911yescharacteristic
932C2×C22⋊C4C22×D5911yescharacteristic
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—591no—
942C2×C42—591no—
943C2×C42—591no—
944C2×C42—591no—
945C2×C42C22×D5911yescharacteristic
946C2×C42C22×D5911yescharacteristic
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#95C22×D5911yescharacteristic
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
1012#95C22×D5911yescharacteristic
1013C24—591no—
1014C24C23×D5911yescharacteristic
1015C24C23×D5911yescharacteristic
1016C2×Q8—41no—
1017C2×Q8—41no—
1018C2×Q8—41no—
1019C2×Q8—2361no—
1020C2×Q8—2361no—
1021C2×Q8—2361no—
1022C2×D4—22no—
1023C2×D4—41no—
1024C2×D4—41no—
1025C2×D4—1182no—
1026C2×D4—1182no—
1027C2×D4—2361no—
1028C2×D4—2361no—
1029C2×D4—2361no—
1030C2×D4—2361no—
1031C22×C4—41no—
1032C22×C4—41no—
1033C22×C4—41no—
1034C22×C4—591no—
1035C22×C4—594no—
1036C22×C4—591no—
1037C22×C4—591no—
1038C22×C4—591no—
1039C22×C4—591no—
1040C22×C4—591no—
1041C22×C4—591no—
1042C22×C4—591no—
1043C22×C4—591no—
1044C22×C4—591no—
1045C22×C4—591no—
1046C22×C4—591no—
1047C22×C4—591no—
1048C22×C4—591no—
1049C22×C4—591no—
1050C22×C4—1182no—
1051C22×C4—1182no—
1052C22×C4—2361no—
1053C22×C4—2361no—
1054C22×C4—2361no—
1055C22×C4—2361no—
1056C22×C4—2361no—
1057C22×C4—2361no—
1058C22×C4—2361no—
1059C22×C4—2361no—
1060C22×C4—2361no—
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
1073C22×C4C23×D5911yescharacteristic
1074C4⋊C4—22no—
1075C4⋊C4—22no—
1076C4⋊C4—41no—
1077C4⋊C4—41no—
1078C4⋊C4—41no—
1079C4⋊C4—1182no—
1080C4⋊C4—1182no—
1081C4⋊C4—1182no—
1082C4⋊C4—1182no—
1083C4⋊C4—1182no—
1084C4⋊C4—2361no—
1085C4⋊C4—2361no—
1086C4⋊C4—2361no—
1087C4⋊C4—2361no—
1088C4⋊C4—2361no—
1089C4⋊C4—2361no—
1090C4⋊C4—2361no—
1091C4⋊C4—2361no—
1092C4⋊C4—2361no—
1093C4⋊C4—2361no—
1094C4⋊C4—2361no—
1095C4⋊C4—2361no—
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—
1105C22⋊C4—41no—
1106C22⋊C4—41no—
1107C22⋊C4—41no—
1108C22⋊C4—41no—
1109C22⋊C4—41no—
1110C22⋊C4—41no—
1111C22⋊C4—41no—
1112C22⋊C4—41no—
1113C22⋊C4—41no—
1114C22⋊C4—41no—
1115C22⋊C4—41no—
1116C22⋊C4—1182no—
1117C22⋊C4—1182no—
1118C22⋊C4—1182no—
1119C22⋊C4—1182no—
1120C22⋊C4—2361no—
1121C22⋊C4—2361no—
1122C22⋊C4—2361no—
1123C22⋊C4—2361no—
1124C22⋊C4—2361no—
1125C22⋊C4—2361no—
1126C22⋊C4—2361no—
1127C22⋊C4—2361no—
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—2361no—
1144C42—2361no—
1145C42—2361no—
1146C42—2361no—
1147C42—2361no—
1148C42—2361no—
1149C42—2361no—
1150C42—2361no—
1151C42—2361no—
1152C42—2361no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—592no—
1168C23—1181no—
1169C23—1181no—
1170C23—1181no—
1171C23—1181no—
1172C23—1181no—
1173C23—1181no—
1174C23C24×D5911yescharacteristic
1175Q8—82no—
1176Q8—4722no—
1177D4—82no—
1178D4—4722no—
1179D4—4722no—
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—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—82no—
1219C2×C4—592no—
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—1181no—
1255C2×C4—1181no—
1256C2×C4—1181no—
1257C2×C4—1181no—
1258C2×C4—1181no—
1259C2×C4—1181no—
1260C2×C4—1181no—
1261C2×C4—1181no—
1262C2×C4—1181no—
1263C2×C4—1181no—
1264C2×C4—4722no—
1265C2×C4—4722no—
1266C2×C4—2364no—
1267C2×C4—2364no—
1268C2×C4#41×D5912yes—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—1182no—
1284C22—1182no—
1285C22—1182no—
1286C22—2361no—
1287C22—2361no—
1288C22—2361no—
1289C22—2361no—
1290C22C2×#41×D5911yescharacteristic
1291C22#1683823711yescharacteristic
1292C22#1683823711yescharacteristic
1293C22#1683823711yescharacteristic
1294C22#1683823811yescharacteristic
1295C22#1683823811yescharacteristic
1296C22#1683823911yescharacteristic
1297C4—22no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—1182no—
1311C4—2361no—
1312C4—2361no—
1313C4—2361no—
1314C4—2361no—
1315C4—2361no—
1316C4—2361no—
1317C4—2361no—
1318C4—2361no—
1319C4—2361no—
1320C4—2361no—
1321C4—2361no—
1322C4—2361no—
1323C4—2361no—
1324C4—2361no—
1325C2—81no—
1326C2—81no—
1327C2—2362no—
1328C2#2143748311yescharacteristic
1329C2#2143778711yescharacteristic
1330C2#2143798911yescharacteristic
1331C2#2143876011yescharacteristic
1332C2#2143876111yescharacteristic
1333C2#2143876311yescharacteristic
1334C2#2143877411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D59
commutator, socle, cosocleC23×C59C25
FittingC59×#2751C2
prime radicalC2×#14273698C22
hypercenter#2751D59
hypocenterC59#37013
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #2751

Complements

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

NH ≅ G/Ntype
1. #21432484C2semidirect
2. #21432484C2semidirect
3. #21431918C2semidirect
4. #21431915C2semidirect
5. #21431817C2semidirect
6. #21431812C2semidirect
7. #21431502C2semidirect
8. #21431498C2semidirect
9. #21431354C2semidirect
10. #21431348C2semidirect
11. #21431343C2semidirect
12. #21431287C2semidirect
13. #21431277C2semidirect
14. #21431235C2semidirect
15. #21431229C2semidirect
16. #21431154C2semidirect
17. #21431144C2semidirect
18. #21430119C2semidirect
19. #21430111C2semidirect
20. #21429759C2semidirect
22. #21429419C2semidirect
23. #21429416C2semidirect
24. #21428879C2semidirect
25. #21428876C2semidirect
27. #21428384C2semidirect
29. #21426695C2semidirect
30. #21426588C2semidirect
31. C59×#2751C2semidirect
669. #2751D59semidirect
854. C59#37013semidirect

Maximal subgroups

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

subgroupindex
#214324842
#214319182
#214319152
#214318172
#214318122
#214315022
#214314982
#214313542
#214313482
#214313432
#214312872
#214312772
#214312352
#214312292
#214311542
#214311442
#214301192
#214301112
#214297592
#214295702
#214294192
#214294162
#214288792
#214288762
#214285572
#214283842
#214268572
#214266952
#214265882
C59×#27512
#3701359