Finite Group Databasebeta

← #28605097

Subgroups — #28605097

Order 15104.

1130 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837480C211yesmaximal, characteristic
2#21427025C211yesmaximal, characteristic
3#21425062C211yesmaximal, characteristic, complemented
4#21425054C211yesmaximal, characteristic, complemented
5#21424530C211yesmaximal, characteristic, complemented
6#21424530C211yesmaximal, characteristic, complemented
7#21424409C211yesmaximal, characteristic, complemented
8#21424404C211yesmaximal, characteristic, complemented
9#21424191C211yesmaximal, characteristic, complemented
10#21424186C211yesmaximal, characteristic, complemented
11#21424111C211yesmaximal, characteristic, complemented
12C4×#14273651C211yesmaximal, characteristic, complemented
13#21423817C211yesmaximal, characteristic, complemented
14#21423815C211yesmaximal, characteristic, complemented
15C2×C59×#552C211yesmaximal, characteristic
16C22×#11745664C2211yescharacteristic
17C22×#11745664C2211yescharacteristic
18C2×#14273686C2211yescharacteristic
19C22×C4⋊Dic59C2211yescharacteristic
20#16837480—24no—
21C2×C4⋊(C59⋊C8)C2211yescharacteristic
22C2×#14273651C2211yescharacteristic
23C2×#14273651C2211yescharacteristic
24C2×#14273651C2211yescharacteristic
25C2×#14273651C2211yescharacteristic
26C2×C22⋊(C59⋊C8)C2211yescharacteristic
27C2×C22⋊(C59⋊C8)C2211yescharacteristic
28C2×C4×C59⋊C8C2211yescharacteristic
29#16837295—21no—
30#16837288—21no—
31#16837282—21no—
32#16837268C2211yescharacteristic
33#16837262C2211yescharacteristic
34#16837262C2211yescharacteristic
35C4×C4⋊Dic59C2211yescharacteristic
36C22⋊C4×Dic59—21no—
37#16837164C2211yescharacteristic
38#16837164C2211yescharacteristic
39#16837164C2211yescharacteristic
40#16837164C2211yescharacteristic
41#16837164C2211yescharacteristic
42#16837164C2211yescharacteristic
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49C59×#552—24no—
50C59×#552C418yescomplemented
51C2×#126×C59—21no—
52C2×#125×C59—21no—
53C2×#125×C59C2211yescharacteristic
54C2×#123×C59—21no—
55C2×C22⋊Q8×C59C2211yescharacteristic
56C2×C22⋊Q8×C59C2211yescharacteristic
57C2×C4×Q8×C59C2211yescharacteristic
58C2×C4×D4×C59C2211yescharacteristic
59C2×#117×C59—21no—
60C2×#117×C59C2211yescharacteristic
61C22×C4⋊C4×C59C2211yescharacteristic
62C23×Dic59—21no—
63C2×#11745664—22no—
64C2×#11745664—22no—
65C2×#11745664—22no—
66C2×#11745664—22no—
67C2×#11745664—41no—
68C2×#11745664—41no—
69C22×C59⋊C8C2311yescharacteristic
70C22×C59⋊C8C2311yescharacteristic
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73#14273686—22no—
74#14273686—41no—
75C2×C4⋊Dic59—22no—
76C2×C4⋊Dic59—21no—
77C2×C4⋊Dic59—41no—
78C2×C4⋊Dic59C2311yescharacteristic
79C2×C4⋊Dic59C2311yescharacteristic
80C2×C4⋊Dic59C2311yescharacteristic
81C2×C4⋊Dic59C2311yescharacteristic
82C2×C22⋊Dic59—21no—
83C2×C22⋊Dic59—21no—
84C2×C22⋊Dic59—21no—
85C2×C4×Dic59—21no—
86C2×C4×Dic59—21no—
87C4⋊(C59⋊C8)—22no—
88#14273651—22no—
89#14273651—22no—
90#14273651—41no—
91#14273651—41no—
92C22⋊(C59⋊C8)—22no—
93C22⋊(C59⋊C8)—22no—
94C4×C59⋊C8—22no—
95C59⋊#95—21no—
96C59⋊#95—21no—
97C59⋊#95—21no—
98C59⋊#95—21no—
99C59⋊#95—21no—
100C22×Q8×C59C2311yescharacteristic
101C22×D4×C59D411yescharacteristic
102C23×C4×C59—21no—
103C23×C4×C59C2311yescharacteristic
104C23×C4×C59C2311yescharacteristic
105#126×C59—28no—
106#125×C59—28no—
107#125×C59—22no—
108#125×C59C2×C414yescomplemented
109#123×C59—28no—
110C22⋊Q8×C59—22no—
111C22⋊Q8×C59—22no—
112C22⋊Q8×C59C2×C414yes—
113C22⋊Q8×C59C2×C414yescomplemented
114C4×Q8×C59—22no—
115C4×Q8×C59C2×C414yescomplemented
116C4×D4×C59C2×C414yes—
117C4×D4×C59D414yes—
118#117×C59—22no—
119#117×C59—28no—
120#117×C59C2×C414yes—
121C2×C4⋊C4×C59—21no—
122C2×C4⋊C4×C59—22no—
123C2×C4⋊C4×C59—21no—
124C2×C4⋊C4×C59—21no—
125C2×C4⋊C4×C59—21no—
126C2×C4⋊C4×C59—21no—
127C2×C4⋊C4×C59—21no—
128C2×C4⋊C4×C59C2×C414yescomplemented
129C2×C4⋊C4×C59D411yescharacteristic
130C2×C4⋊C4×C59C2311yescharacteristic
131C2×C4⋊C4×C59C2311yescharacteristic
132C2×C4⋊C4×C59C2311yescharacteristic
133C2×C22⋊C4×C59—21no—
134C2×C22⋊C4×C59—21no—
135C2×C22⋊C4×C59—21no—
136C2×C22⋊C4×C59D411yescharacteristic
137C2×C22⋊C4×C59D411yescharacteristic
138C2×C42×C59—21no—
139C2×C42×C59—21no—
140C2×C42×C59C2311yescharacteristic
141C24×C59C2×D411yescharacteristic
142C24×C59C2×D411yescharacteristic
143C2×Q8×C59—21no—
144C2×Q8×C59—21no—
145C2×Q8×C59—21no—
146C2×Q8×C59—21no—
147C2×Q8×C59—21no—
148C2×Q8×C59C22×C412yes—
149C2×D4×C59—41no—
150C2×D4×C59—41no—
151C2×D4×C59C22⋊C414yes—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—21no—
159C22×C4×C59—21no—
160C22×C4×C59—24no—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59—21no—
164C22×C4×C59—21no—
165C22×C4×C59—42no—
166C22×C4×C59—42no—
167C22×C4×C59C22×C412yes—
168C22×C4×C59C22×C412yes—
169C22×C4×C59C2×D411yescharacteristic
170C22×C4×C59C2×D411yescharacteristic
171C22×C4×C59C2×D411yescharacteristic
172C22×C4×C59C2×D411yescharacteristic
173C22×C4×C59C2×D412yes—
174C22×C4×C59C2×D412yes—
175C22×C4×C59C2411yescharacteristic
176C22×Dic59—21no—
177C22×Dic59—21no—
178C22×Dic59—21no—
179C22×Dic59—21no—
180C22×Dic59—42no—
181C22×Dic59—42no—
182C22×Dic59—81no—
183C4⋊C4×C59—24no—
184C4⋊C4×C59—24no—
185C4⋊C4×C59—24no—
186C4⋊C4×C59—24no—
187C4⋊C4×C59—24no—
188C4⋊C4×C59—24no—
189C4⋊C4×C59—21no—
190C4⋊C4×C59—21no—
191C4⋊C4×C59—21no—
192C4⋊C4×C59C22⋊C414yes—
193C4⋊C4×C59C22×C412yes—
194C4⋊C4×C59C22×C412yes—
195C4⋊C4×C59C22×C412yes—
196C22⋊C4×C59—24no—
197C22⋊C4×C59—24no—
198C22⋊C4×C59—24no—
199C22⋊C4×C59C22⋊C414yes—
200C22⋊C4×C59C22⋊C414yes—
201C42×C59—24no—
202C42×C59—24no—
203C42×C59C22×C412yes—
204C42×C59C2×D412yes—
205C22⋊Dic59—42no—
206C22⋊Dic59—42no—
207C22⋊Dic59—81no—
208C4⋊Dic59—21no—
209C4⋊Dic59—21no—
210C4⋊Dic59—21no—
211C4⋊Dic59—21no—
212C4⋊Dic59—21no—
213C4⋊Dic59—21no—
214C4⋊Dic59—21no—
215C4⋊Dic59—42no—
216C4⋊Dic59#4112yes—
217C4×Dic59—42no—
218C4×Dic59—81no—
219#11745664—44no—
220#11745664—44no—
221C2×C59⋊C8—21no—
222C2×C59⋊C8—21no—
223C2×C59⋊C8—21no—
224C2×C59⋊C8—21no—
225C2×C59⋊C8—21no—
226C2×C59⋊C8—21no—
227C2×C59⋊C8—21no—
228C2×C59⋊C8—21no—
229C2×C59⋊C8—21no—
230C2×C59⋊C8—21no—
231C2×C59⋊C8—21no—
232C2×C59⋊C8#4112yes—
233C23×C59—21no—
234C23×C59—21no—
235C23×C59—21no—
236C23×C59—21no—
237C23×C59—21no—
238C23×C59—21no—
239C23×C59—21no—
240C23×C59—21no—
241C23×C59—21no—
242C23×C59—21no—
243C23×C59—21no—
244C23×C59—21no—
245C23×C59C2×C22⋊C412yes—
246C23×C59C2×C22⋊C412yes—
247C23×C59C22×D411yescharacteristic
248Q8×C59—22no—
249Q8×C59—22no—
250Q8×C59—41no—
251Q8×C59—41no—
252D4×C59—44no—
253C2×C4×C59—21no—
254C2×C4×C59—21no—
255C2×C4×C59—21no—
256C2×C4×C59—21no—
257C2×C4×C59—21no—
258C2×C4×C59—21no—
259C2×C4×C59—21no—
260C2×C4×C59—21no—
261C2×C4×C59—22no—
262C2×C4×C59—22no—
263C2×C4×C59—22no—
264C2×C4×C59—22no—
265C2×C4×C59—22no—
266C2×C4×C59—22no—
267C2×C4×C59—22no—
268C2×C4×C59—22no—
269C2×C4×C59—22no—
270C2×C4×C59—22no—
271C2×C4×C59—22no—
272C2×C4×C59—22no—
273C2×C4×C59—48no—
274C2×C4×C59—41no—
275C2×C4×C59—41no—
276C2×C4×C59—41no—
277C2×C4×C59—41no—
278C2×C4×C59—41no—
279C2×C4×C59—41no—
280C2×C4×C59—41no—
281C2×C4×C59—41no—
282C2×C4×C59C2×C22⋊C412yes—
283C2×C4×C59C2×C22⋊C412yes—
284C2×C4×C59C2×C22⋊C412yes—
285C2×C4×C59C2×C22⋊C412yes—
286C2×C4×C59C23×C411yescharacteristic
287C2×C4×C59C22×D411yescharacteristic
288C2×C4×C59C2×#4111yescharacteristic
289C2×C4×C59C2×#4111yescharacteristic
290C2×C4×C59H(5,𝔽2)11yescharacteristic
291C2×C4×C592−1+411yescharacteristic
292C2×Dic59—22no—
293C2×Dic59—41no—
294C2×Dic59—41no—
295C2×Dic59—41no—
296C2×Dic59—41no—
297C2×Dic59—41no—
298C2×Dic59—41no—
299C2×Dic59—41no—
300C2×Dic59—41no—
301C2×Dic59—41no—
302C2×Dic59—41no—
303C2×Dic59—41no—
304C2×Dic59—84no—
305C59⋊C8—22no—
306C59⋊C8—41no—
307C59⋊C8—41no—
308C59⋊C8—41no—
309#22499—591nomaximal, Sylow
310C22×C59—22no—
311C22×C59—22no—
312C22×C59—22no—
313C22×C59—22no—
314C22×C59—22no—
315C22×C59—22no—
316C22×C59—41no—
317C22×C59—41no—
318C22×C59—41no—
319C22×C59—41no—
320C22×C59—41no—
321C22×C59—41no—
322C22×C59—41no—
323C22×C59—41no—
324C22×C59C22×C22⋊C411yescharacteristic
325C22×C59#54611yescharacteristic
326C22×C59#54711yescharacteristic
327C22×C59#57511yescharacteristic
328C22×C59#57511yescharacteristic
329C22×C59#57711yescharacteristic
330C22×C59#57811yescharacteristic
331C4×C59—22no—
332C4×C59—22no—
333C4×C59—22no—
334C4×C59—22no—
335C4×C59—42no—
336C4×C59—42no—
337C4×C59—42no—
338C4×C59—42no—
339C4×C59C4×#4111yescharacteristic
340C4×C59#52011yescharacteristic
341C4×C59#54611yescharacteristic
342C4×C59#54711yescharacteristic
343Dic59—42no—
344Dic59—81no—
345Dic59—81no—
346Dic59—81no—
347C2×#552D5911yescharacteristic
348C2×#436—591no—
349#2352—591no—
350#1991—591no—
351#1989—591no—
352#1894—591no—
353#1894—591no—
354#1873—591no—
355#1872—591no—
356#1825—591no—
357#1824—591no—
358#1805—591no—
359C4×#103—591no—
360#1736—591no—
361#1736—591no—
362C2×C59—42no—
363C2×C59—42no—
364C2×C59#233911yescharacteristic
365C2×C59#289611yescharacteristic
366C2×C59#289811yescharacteristic
367C2×C59#332311yescharacteristic
368C2×C59#332711yescharacteristic
369C2×C59#335111yescharacteristic
370C2×C59#335211yescharacteristic
371C22×M16—591no—
372C22×M16—591no—
373#552—24no—
374#552Dic5918yescomplemented
375C2×#126—21no—
376C2×#125—21no—
377C2×#125C2×D5911yescharacteristic
378C2×#123—21no—
379C2×C22⋊Q8C2×D5911yescharacteristic
380C2×C22⋊Q8C2×D5911yescharacteristic
381C2×C4×Q8C2×D5911yescharacteristic
382C2×C4×D4C2×D5911yescharacteristic
383C2×#117—21no—
384C2×#117—591no—
385C2×#117C2×D5911yescharacteristic
386C22×C4⋊C4—591no—
387C22×C4⋊C4C2×D5911yescharacteristic
388#436—1184no—
389C2×C4⋊C8—591no—
390C2×#103—591no—
391C2×#103—591no—
392C2×#103—591no—
393C2×#103—591no—
394C2×C22⋊C8—591no—
395C2×C22⋊C8—591no—
396C2×C4×C8—591no—
397#388—1181no—
398#387—1181no—
399#386—1181no—
400#382—591no—
401#380—591no—
402#380—591no—
403C4×C4⋊C4—591no—
404C4×C22⋊C4—1181no—
405#340—591no—
406#340—591no—
407#340—591no—
408#340—591no—
409#340—591no—
410#340—591no—
411#340—591no—
412#340—591no—
413#340—591no—
414#340—591no—
415#340—591no—
416#340—591no—
417C59#2249911yescharacteristic, complemented, Sylow
418C22×Q8C22×D5911yescharacteristic
419C22×D4C22⋊D5911yescharacteristic
420C23×C4—21no—
421C23×C4—1181no—
422C23×C4C22×D5911yescharacteristic
423C23×C4C22×D5911yescharacteristic
424C2×M16—1182no—
425C2×M16—1182no—
426C2×M16—1182no—
427C2×M16—1182no—
428C2×M16—2361no—
429C2×M16—2361no—
430C22×C8—591no—
431C22×C8—591no—
432C22×C8—591no—
433C22×C8—591no—
434#126—28no—
435#125—28no—
436#125—22no—
437#125C2×Dic5914yescomplemented
438#123—28no—
439C22⋊Q8—22no—
440C22⋊Q8—22no—
441C22⋊Q8C2×Dic5914yes—
442C22⋊Q8C2×Dic5914yescomplemented
443C4×Q8—22no—
444C4×Q8C2×Dic5914yescomplemented
445C4×D4C2×Dic5914yes—
446C4×D4C22⋊D5914yes—
447#117—22no—
448#117—28no—
449#117—1182no—
450#117—2361no—
451#117C2×Dic5914yes—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—591no—
460C2×C4⋊C4—591no—
461C2×C4⋊C4—591no—
462C2×C4⋊C4—591no—
463C2×C4⋊C4—1182no—
464C2×C4⋊C4—1181no—
465C2×C4⋊C4—2361no—
466C2×C4⋊C4C2×Dic5914yescomplemented
467C2×C4⋊C4C22⋊D5911yescharacteristic
468C2×C4⋊C4C22×D5911yescharacteristic
469C2×C4⋊C4C22×D5911yescharacteristic
470C2×C4⋊C4C22×D5911yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—1181no—
475C2×C22⋊C4—1181no—
476C2×C22⋊C4—1181no—
477C2×C22⋊C4C22⋊D5911yescharacteristic
478C2×C22⋊C4C22⋊D5911yescharacteristic
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—1181no—
482C2×C42—1181no—
483C2×C42C22×D5911yescharacteristic
484C4⋊C8—1182no—
485#103—1182no—
486#103—1182no—
487#103—2361no—
488#103—2361no—
489C22⋊C8—1182no—
490C22⋊C8—1182no—
491C4×C8—1182no—
492#95—1181no—
493#95—1181no—
494#95—1181no—
495#95—1181no—
496#95—1181no—
497C24C2×C22⋊D5911yescharacteristic
498C24C2×C22⋊D5911yescharacteristic
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8C22×Dic5912yes—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4C22⋊Dic5914yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—24no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—1181no—
524C22×C4—1181no—
525C22×C4—1181no—
526C22×C4—1181no—
527C22×C4—4721no—
528C22×C4—2362no—
529C22×C4—2362no—
530C22×C4C22×Dic5912yes—
531C22×C4C22×Dic5912yes—
532C22×C4C2×C22⋊D5911yescharacteristic
533C22×C4C2×C22⋊D5911yescharacteristic
534C22×C4C2×C22⋊D5911yescharacteristic
535C22×C4C2×C22⋊D5911yescharacteristic
536C22×C4C2×C22⋊D5912yes—
537C22×C4C2×C22⋊D5912yes—
538C22×C4C23×D5911yescharacteristic
539M16—2364no—
540M16—2364no—
541C2×C8—592no—
542C2×C8—1181no—
543C2×C8—1181no—
544C2×C8—1181no—
545C2×C8—1181no—
546C2×C8—1181no—
547C2×C8—1181no—
548C2×C8—1181no—
549C2×C8—1181no—
550C2×C8—1181no—
551C2×C8—1181no—
552C2×C8—1181no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—592no—
563C4⋊C4—1181no—
564C4⋊C4—1181no—
565C4⋊C4—1181no—
566C4⋊C4—1181no—
567C4⋊C4—1181no—
568C4⋊C4—1181no—
569C4⋊C4—1181no—
570C4⋊C4—2362no—
571C4⋊C4C22⋊Dic5914yes—
572C4⋊C4C22×Dic5912yes—
573C4⋊C4C22×Dic5912yes—
574C4⋊C4C22×Dic5912yes—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—4721no—
579C22⋊C4—2362no—
580C22⋊C4—2362no—
581C22⋊C4C22⋊Dic5914yes—
582C22⋊C4C22⋊Dic5914yes—
583C42—24no—
584C42—24no—
585C42—4721no—
586C42—2362no—
587C42C22×Dic5912yes—
588C42C2×C22⋊D5912yes—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23C2×C22⋊Dic5912yes—
602C23C2×C22⋊Dic5912yes—
603C23C22×C22⋊D5911yescharacteristic
604Q8—22no—
605Q8—22no—
606Q8—41no—
607Q8—41no—
608D4—44no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—48no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—1182no—
639C2×C4—4724no—
640C2×C4—2361no—
641C2×C4—2361no—
642C2×C4—2361no—
643C2×C4—2361no—
644C2×C4—2361no—
645C2×C4—2361no—
646C2×C4—2361no—
647C2×C4—2361no—
648C2×C4—2361no—
649C2×C4—2361no—
650C2×C4—2361no—
651C2×C4C2×C22⋊Dic5912yes—
652C2×C4C2×C22⋊Dic5912yes—
653C2×C4C2×C22⋊Dic5912yes—
654C2×C4C2×C22⋊Dic5912yes—
655C2×C4C23×Dic5911yescharacteristic
656C2×C4C22×C22⋊D5911yescharacteristic
657C2×C4#41×D5911yescharacteristic
658C2×C4#41×D5911yescharacteristic
659C2×C4#1427377311yescharacteristic
660C2×C4#1427377411yescharacteristic
661C8—1182no—
662C8—2361no—
663C8—2361no—
664C8—2361no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22C22×C22⋊Dic5911yescharacteristic
680C22#1683804011yescharacteristic
681C22#1683805111yescharacteristic
682C22#1683820011yescharacteristic
683C22#1683820011yescharacteristic
684C22#1683821011yescharacteristic
685C22#1683821711yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—42no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—4721no—
695C4—4721no—
696C4—4721no—
697C4—2362no—
698C4#41×Dic5911yescharacteristic
699C4#1683788511yescharacteristic
700C4#1683804011yescharacteristic
701C4#1683805111yescharacteristic
702C2—42no—
703C2—42no—
704C2#2142692611yescharacteristic
705C2#2143261511yescharacteristic
706C2#2143262911yescharacteristic
707C2#2143630611yescharacteristic
708C2#2143635811yescharacteristic
709C2#2143665611yescharacteristic
710C2#2143666511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C59×#552C2
socleC23×C59C22×D4
prime radicalC22×D4×C59D4
cosocleC22×C4×C59C24
hypercenterC2×#552D59
hypocenterC59#22499
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
3. #21425062C2semidirect
4. #21425054C2semidirect
5. #21424530C2semidirect
6. #21424530C2semidirect
7. #21424409C2semidirect
8. #21424404C2semidirect
9. #21424191C2semidirect
10. #21424186C2semidirect
11. #21424111C2semidirect
12. C4×#14273651C2semidirect
13. #21423817C2semidirect
14. #21423815C2semidirect
50. C59×#552C4semidirect
108. #125×C59C2×C4semidirect
113. C22⋊Q8×C59C2×C4semidirect
115. C4×Q8×C59C2×C4semidirect
128. C2×C4⋊C4×C59C2×C4semidirect
374. #552Dic59semidirect
417. C59#22499semidirect
437. #125C2×Dic59semidirect
442. C22⋊Q8C2×Dic59semidirect
444. C4×Q8C2×Dic59semidirect
466. C2×C4⋊C4C2×Dic59semidirect

Maximal subgroups

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

subgroupindex
C2×#168374802
#214270252
#214250622
#214250542
#214245302
#214244092
#214244042
#214241912
#214241862
#214241112
C4×#142736512
#214238172
#214238152
C2×C59×#5522
#2249959