Finite Group Databasebeta

← #29695597

Subgroups — #29695597

Order 15616.

1458 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840420C211yesmaximal, characteristic
2C2×#16839835C211yesmaximal, characteristic, complemented
3C2×#16839769C211yesmaximal, characteristic, complemented
4C2×#16839755C211yesmaximal, characteristic, complemented
5#21448770C211yesmaximal, characteristic, complemented
6#21446752C211yesmaximal, characteristic, complemented
7#21446254C211yesmaximal, characteristic, complemented
8#21446239C211yesmaximal, characteristic, complemented
9#21446138C211yesmaximal, characteristic, complemented
10#21446128C211yesmaximal, characteristic, complemented
11#21445821C211yesmaximal, characteristic, complemented
12#21445756C211yesmaximal, characteristic, complemented
13#21445752C211yesmaximal, characteristic, complemented
14#21445650C211yesmaximal, characteristic, complemented
15C61×#1959C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840420—24no—
21#16840420C418yescomplemented
22C2×#14519763—21no—
23C2×#14519754—21no—
24C2×#14519753C2211yescharacteristic
25C2×#14519750—21no—
26C2×#14519748C2211yescharacteristic
27C2×C4×Dic122C2211yescharacteristic
28C2×C4×D244C2211yescharacteristic
29C2×#14519737—21no—
30C2×#14519735C2211yescharacteristic
31C2×#14519735C2211yescharacteristic
32#16839835—24no—
33C2×C4⋊#92418C2211yescharacteristic
34#16839769—24no—
35#16839755—24no—
36C2×#14519702C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519701C2211yescharacteristic
39C2×#14519701C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41C2×#14519700C2211yescharacteristic
42C2×#14519698C2211yescharacteristic
43C2×#14519698C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46#16839663—21no—
47#16839652—21no—
48#16839652—21no—
49#16839619C2211yescharacteristic
50#16839619C2211yescharacteristic
51C4⋊C4×Dic61—21no—
52C4×C4⋊Dic61C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839525C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57C2×#124×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×#97×C61C2211yescharacteristic
63C61×#384C2211yescharacteristic
64C2×#11758224—22no—
65C2×#11758224—22no—
66C2×#11758224—22no—
67C2×#11758224—41no—
68C2×#11758224—41no—
69C2×#11758224C2×C414yes—
70C22×Dic122—21no—
71C22×Dic122C2311yescharacteristic
72C2×Q8×D61—22no—
73C2×Q8×D61—22no—
74C2×Q8×D61—22no—
75C2×Q8×D61—41no—
76C2×Q8×D61—41no—
77C2×Q8×D61C2×C414yes—
78C22×D244D411yescharacteristic
79C22×C22⋊D61—21no—
80C22×C22⋊D61—21no—
81C23×Dic61—21no—
82C22×C4×D61—21no—
83C22×C4×D61C2311yescharacteristic
84C22×C4×D61C2311yescharacteristic
85C2×#11758189—22no—
86C2×#11758189—22no—
87C2×#11758189—41no—
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90C2×C8×D61—22no—
91C2×C8×D61—22no—
92C2×C8×D61—41no—
93#14519763—28no—
94#14519754—28no—
95#14519753—22no—
96#14519753C2×C414yes—
97#14519750—28no—
98#14519748—22no—
99#14519748C2×C414yes—
100C4×Dic122—22no—
101C4×Dic122C2×C414yes—
102C4×D244C2×C414yes—
103C4×D244D414yes—
104#14519737—28no—
105#14519735—22no—
106#14519735—22no—
107#14519735—41no—
108#14519735—41no—
109C2×C4⋊Dic61D411yescharacteristic
110C2×C4⋊Dic61C2311yescharacteristic
111C2×C4⋊Dic61C2311yescharacteristic
112C2×C4⋊Dic61C2311yescharacteristic
113C2×#11758196—21no—
114C2×#11758196—21no—
115C2×C22⋊Dic61—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×#11758198D411yescharacteristic
122C2×#11758198D411yescharacteristic
123C2×C4×Dic61—21no—
124C2×C4×Dic61—21no—
125C2×C4×Dic61—21no—
126C2×C4×Dic61—21no—
127C4⋊#92418—22no—
128#14519702—22no—
129#14519702D414yescomplemented
130#14519701—22no—
131#14519701—41no—
132#14519700—22no—
133#14519700—22no—
134#14519698—22no—
135#14519698—41no—
136#14519689—22no—
137#14519689—22no—
138#14519684—21no—
139#14519684—21no—
140#14519684—21no—
141C22×Q8×C61C2311yescharacteristic
142C22×D4×C61C2311yescharacteristic
143C22×C8×C61C2311yescharacteristic
144C22×C8×C61C2311yescharacteristic
145#124×C61—22no—
146#124×C61C2×C414yes—
147C2×C4⋊C4×C61—21no—
148C2×C4⋊C4×C61—21no—
149C2×C4⋊C4×C61C2311yescharacteristic
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C22⋊C4×C61—21no—
152C2×C22⋊C4×C61—21no—
153C2×C42×C61C2311yescharacteristic
154#103×C61—22no—
155#103×C61—41no—
156#102×C61—22no—
157#102×C61—41no—
158#97×C61—22no—
159C24×C61—21no—
160C23×D61C2×D411yescharacteristic
161C23×D61C2×D411yescharacteristic
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61C22×C412yes—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61C22×C412yes—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2411yescharacteristic
180C2×C22⋊D61—24no—
181C2×C22⋊D61—24no—
182C2×C22⋊D61—42no—
183C2×C22⋊D61—42no—
184C2×C22⋊D61—42no—
185C2×C22⋊D61—42no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—24no—
190C22×Dic61—21no—
191C22×Dic61—42no—
192C22×Dic61—42no—
193C22×Dic61C2×D411yescharacteristic
194C22×Dic61C2×D411yescharacteristic
195Q8×D61—28no—
196Q8×D61—44no—
197Q8×D61—44no—
198Q8×D61—44no—
199#11758224—28no—
200#11758224—44no—
201#11758224—44no—
202#11758224—44no—
203C2×D244—41no—
204C2×D244—41no—
205C2×D244C22⋊C414yes—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—21no—
212C2×C4×D61—21no—
213C2×C4×D61—21no—
214C2×C4×D61—24no—
215C2×C4×D61—42no—
216C2×C4×D61—42no—
217C2×C4×D61C22×C412yes—
218C2×C4×D61C22×C412yes—
219C2×C4×D61C2×D412yes—
220C2×C4×D61C2×D412yes—
221C2×Dic122—21no—
222C2×Dic122—21no—
223C2×Dic122—21no—
224C2×Dic122—24no—
225C2×Dic122—42no—
226C2×Dic122—42no—
227C2×Dic122C22×C412yes—
228C2×Dic122C2×D412yes—
229C2×Dic122#4112yes—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61C2×D412yes—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—42no—
241C4⋊C4×C61—81no—
242C22⋊C4×C61—24no—
243C22⋊C4×C61—24no—
244C42×C61C22×C412yes—
245C42×C61C2×D412yes—
246C22⋊Dic61—24no—
247#11758198—24no—
248#11758198—42no—
249#11758198—42no—
250#11758198—81no—
251#11758198—81no—
252#11758198C22⋊C414yes—
253#11758198C22⋊C414yes—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61C22⋊C414yes—
259C4⋊Dic61C22×C412yes—
260C4⋊Dic61C2×D412yes—
261#11758196—24no—
262#11758196—24no—
263C4×Dic61—24no—
264C4×Dic61—42no—
265C4×Dic61—42no—
266C4×Dic61—42no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273#11758189—44no—
274C8×D61—44no—
275C23×C61—22no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61C22×D411yescharacteristic
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—21no—
294C22×D61—21no—
295C22×D61C2×C22⋊C412yes—
296C22×D61C2×C22⋊C412yes—
297Q8×C61—22no—
298Q8×C61—22no—
299Q8×C61—41no—
300Q8×C61—41no—
301D4×C61—22no—
302D4×C61—22no—
303D4×C61—41no—
304D4×C61—41no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—22no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61C2×C22⋊C412yes—
319C2×C4×C61C2×C22⋊C412yes—
320C2×C4×C61C23×C411yescharacteristic
321C2×C4×C61C22×D411yescharacteristic
322C2×C4×C61C22×D411yescharacteristic
323C2×C4×C61C2×#4111yescharacteristic
324C2×C4×C61H(5,𝔽2)11yescharacteristic
325C2×C4×C61H(5,𝔽2)11yescharacteristic
326C22⋊D61—48no—
327C22⋊D61—48no—
328C2×Dic61—22no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—21no—
334C2×Dic61—21no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—48no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61C2×C22⋊C412yes—
346C2×Dic61C2×C22⋊C412yes—
347D244—44no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—22no—
352C4×D61—22no—
353C4×D61—22no—
354C4×D61—22no—
355C4×D61—22no—
356C4×D61—48no—
357Dic122—22no—
358Dic122—22no—
359Dic122—22no—
360Dic122—48no—
361Dic122C4×D414yes—
362C8×C61—22no—
363C8×C61—41no—
364#92418—41no—
365#92418—41no—
366#22426—611nomaximal, Sylow
367C22×C61—42no—
368C22×C61—42no—
369C22×C61—42no—
370C22×C61—81no—
371C22×C61—81no—
372C22×C61—81no—
373C22×C61—81no—
374C22×C61C22×C22⋊C411yescharacteristic
375C22×C61D4211yescharacteristic
376C22×C61#54611yescharacteristic
377C22×C61#57511yescharacteristic
378C22×C61#57511yescharacteristic
379C22×C61#57711yescharacteristic
380C22×C61#57811yescharacteristic
381C2×D61—22no—
382C2×D61—22no—
383C2×D61—22no—
384C2×D61—22no—
385C2×D61—22no—
386C2×D61—22no—
387C2×D61—41no—
388C2×D61—41no—
389C2×D61—41no—
390C2×D61—41no—
391C2×D61—41no—
392C2×D61—41no—
393C2×D61—41no—
394C2×D61—41no—
395C4×C61—22no—
396C4×C61—22no—
397C4×C61—42no—
398C4×C61—81no—
399C4×C61—81no—
400C4×C61C2×C4×D411yescharacteristic
401C4×C61#51811yescharacteristic
402C4×C61D4211yescharacteristic
403C4×C61#54611yescharacteristic
404Dic61—24no—
405Dic61—22no—
406Dic61—22no—
407Dic61—42no—
408Dic61—42no—
409Dic61—81no—
410C2×#548—611no—
411C2×#435—611no—
412C2×#419—611no—
413C2×#416—611no—
414#2354—611no—
415#1983—611no—
416#1959D6111yescharacteristic, complemented
417#1895—611no—
418#1892—611no—
419#1875—611no—
420#1873—611no—
421#1803—611no—
422#1788—611no—
423#1787—611no—
424#1763—611no—
425C2×C61—82no—
426C2×C61D4×C22⋊C411yescharacteristic
427C2×C61#289611yescharacteristic
428C2×C61#289811yescharacteristic
429C2×C61#326911yescharacteristic
430C2×C61#327111yescharacteristic
431C2×C61#331311yescharacteristic
432C2×C61#332111yescharacteristic
433D61—42no—
434D61—42no—
435C22×#41—611no—
436C23×Q8—611no—
437C22×M16—611no—
438C23×C8—611no—
439#548—618no—
440#548—1224no—
441C2×#124—1221no—
442C2×#124C2×D6111yescharacteristic
443C2×C22⋊Q8—611no—
444C2×C22⋊Q8—1221no—
445C2×#121—611no—
446C2×#121—1221no—
447C2×C4×Q8—611no—
448C2×C4×D4—611no—
449C2×C4×D4—1221no—
450C2×#117—611no—
451C2×#117—611no—
452#435—1224no—
453C2×C4⋊C8—611no—
454#419—1224no—
455#416—1224no—
456C2×#103—611no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#103—611no—
461C2×#103—611no—
462C2×#103C2×D6111yescharacteristic
463C2×#103C2×D6111yescharacteristic
464C2×#102—611no—
465C2×#102—611no—
466C2×#102C2×D6111yescharacteristic
467C2×#102C2×D6111yescharacteristic
468C2×C22⋊C8—611no—
469C2×C22⋊C8—611no—
470C2×#97C2×D6111yescharacteristic
471#390—1221no—
472#388—1221no—
473#388—1221no—
474#384C2×D6111yescharacteristic
475#380—611no—
476#380—611no—
477C4×C4⋊C4—611no—
478C4×C4⋊C4—1221no—
479#340—611no—
480#340—611no—
481#340—611no—
482#340—611no—
483C61#2242611yescharacteristic, complemented, Sylow
484C2×#41—614no—
485C2×#41—1222no—
486C2×#41—1222no—
487C2×#41—1222no—
488C2×#41—2441no—
489C2×#41—2441no—
490C22×Q8—614no—
491C22×Q8—611no—
492C22×Q8—1221no—
493C22×Q8—1222no—
494C22×Q8—1222no—
495C22×Q8—1222no—
496C22×Q8—2441no—
497C22×Q8—2441no—
498C22×Q8C22×D6111yescharacteristic
499C22×D4—611no—
500C22×D4—1221no—
501C22×D4—1221no—
502C22×D4C22×D6111yescharacteristic
503C23×C4—611no—
504C23×C4—611no—
505C23×C4—1221no—
506C23×C4—1221no—
507C2×M16—1222no—
508C2×M16—1222no—
509C2×M16—2441no—
510C22×C8—611no—
511C22×C8—611no—
512C22×C8—1222no—
513C22×C8—1222no—
514C22×C8—2441no—
515C22×C8C22×D6111yescharacteristic
516C22×C8C22×D6111yescharacteristic
517#124—22no—
518#124—1228no—
519#124C4×D6114yes—
520C22⋊Q8—614no—
521C22⋊Q8—1228no—
522C22⋊Q8—1222no—
523#121—614no—
524#121—1228no—
525#121—1222no—
526C4×Q8—614no—
527C4×Q8—1222no—
528C4×D4—614no—
529C4×D4—614no—
530C4×D4—1228no—
531#117—1222no—
532#117—1222no—
533#117—2441no—
534#117—2441no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—611no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4C22×D6111yescharacteristic
544C2×C4⋊C4C22×D6111yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—611no—
548C2×C22⋊C4—611no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C42—1221no—
556C2×C42—1221no—
557C2×C42—1221no—
558C2×C42—1221no—
559C2×C42C22×D6111yescharacteristic
560C4⋊C8—1222no—
561#103—22no—
562#103—41no—
563#103—614no—
564#103—1222no—
565#103—1222no—
566#103—1222no—
567#103—1222no—
568#103—2441no—
569#102—22no—
570#102—41no—
571#102—1222no—
572#102—2441no—
573C22⋊C8—1222no—
574C22⋊C8—1222no—
575#97—22no—
576#95—1221no—
577#95—1221no—
578#95—1221no—
579C24—21no—
580C24—611no—
581C24—611no—
582#41—1228no—
583#41—2444no—
584#41—2444no—
585#41—2444no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—612no—
592C2×Q8—612no—
593C2×Q8—612no—
594C2×Q8—1224no—
595C2×Q8—1221no—
596C2×Q8—1221no—
597C2×Q8—1221no—
598C2×Q8—1228no—
599C2×Q8—2442no—
600C2×Q8—2442no—
601C2×Q8—2444no—
602C2×Q8—2444no—
603C2×Q8—2444no—
604C2×Q8C2×C4×D6112yes—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—614no—
611C2×D4—1224no—
612C2×D4—1224no—
613C2×D4—2441no—
614C2×D4—2441no—
615C2×D4—2442no—
616C2×D4—2442no—
617C2×D4—2442no—
618C2×D4—2442no—
619C2×D4C2×C4×D6112yes—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—611no—
624C22×C4—611no—
625C22×C4—612no—
626C22×C4—612no—
627C22×C4—612no—
628C22×C4—612no—
629C22×C4—1224no—
630C22×C4—1224no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—2442no—
644C22×C4—2442no—
645C22×C4—2442no—
646C22×C4—2442no—
647C22×C4D4×D6111yescharacteristic
648C22×C4D4×D6111yescharacteristic
649C22×C4C23×D6111yescharacteristic
650M16—2444no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—1221no—
657C2×C8—1221no—
658C2×C8—1221no—
659C2×C8—1221no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—2444no—
663C2×C8D4×D6112yes—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—42no—
669C4⋊C4—81no—
670C4⋊C4—614no—
671C4⋊C4—612no—
672C4⋊C4—612no—
673C4⋊C4—1224no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4—1224no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C22⋊C4—24no—
680C22⋊C4—24no—
681C22⋊C4—614no—
682C22⋊C4—614no—
683C22⋊C4—1224no—
684C22⋊C4—1224no—
685C22⋊C4—4881no—
686C22⋊C4—4881no—
687C22⋊C4—2442no—
688C22⋊C4—2442no—
689C42—1224no—
690C42—2442no—
691C42—2442no—
692C42—2442no—
693C42C2×C4×D6112yes—
694C42D4×D6112yes—
695C23—22no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—612no—
703C23—612no—
704C23—1221no—
705C23—1221no—
706C23—1221no—
707C23—1221no—
708C23—1221no—
709C23—1221no—
710C23—1221no—
711C23—1221no—
712C23—1221no—
713C23—1221no—
714C23—1221no—
715C23—1221no—
716C23C2×D4×D6111yescharacteristic
717Q8—22no—
718Q8—22no—
719Q8—41no—
720Q8—41no—
721Q8—614no—
722Q8—1222no—
723Q8—1222no—
724Q8—1222no—
725Q8—2448no—
726D4—22no—
727D4—22no—
728D4—41no—
729D4—41no—
730D4—2444no—
731D4—2448no—
732D4—2448no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—612no—
747C2×C4—612no—
748C2×C4—1222no—
749C2×C4—1221no—
750C2×C4—1221no—
751C2×C4—1222no—
752C2×C4—1221no—
753C2×C4—1221no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—2448no—
766C2×C4—2448no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4C22⋊C4×D6112yes—
775C2×C4C22⋊C4×D6112yes—
776C2×C4C22×C4×D6111yescharacteristic
777C2×C4C2×D4×D6111yescharacteristic
778C2×C4C2×D4×D6111yescharacteristic
779C2×C4#41×D6111yescharacteristic
780C2×C4#1451982211yescharacteristic
781C2×C4#1451982311yescharacteristic
782C8—22no—
783C8—41no—
784C8—2441no—
785C8—2441no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—1222no—
794C22—1222no—
795C22—1222no—
796C22—1222no—
797C22—1222no—
798C22—1222no—
799C22—2441no—
800C22—2441no—
801C22—2441no—
802C22—2441no—
803C22—2441no—
804C22—2441no—
805C22—2441no—
806C22—2441no—
807C22C2×C22⋊C4×D6111yescharacteristic
808C22#1684039711yescharacteristic
809C22#1684040511yescharacteristic
810C22#1684055811yescharacteristic
811C22#1684056111yescharacteristic
812C22#1684057211yescharacteristic
813C22#1684057811yescharacteristic
814C4—22no—
815C4—22no—
816C4—42no—
817C4—81no—
818C4—81no—
819C4—1222no—
820C4—1222no—
821C4—1224no—
822C4—4881no—
823C4—2442no—
824C4—2442no—
825C4C4×D4×D6111yescharacteristic
826C4#1684023411yescharacteristic
827C4#1684039611yescharacteristic
828C4#1684040911yescharacteristic
829C2—82no—
830C2—2442no—
831C2—2442no—
832C2#2144864011yescharacteristic
833C2#2145433511yescharacteristic
834C2#2145435011yescharacteristic
835C2#2145737311yescharacteristic
836C2#2145740311yescharacteristic
837C2#2145788411yescharacteristic
838C2#2145800411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1959C2
socleC23×C61C22×D4
prime radicalC2×#16840420C2
cosocleC22×C4×C61C24
hypercenter#1959D61
hypocenterC61#22426
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1959

Complements

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

NH ≅ G/Ntype
2. C2×#16839835C2semidirect
3. C2×#16839769C2semidirect
4. C2×#16839755C2semidirect
5. #21448770C2semidirect
6. #21446752C2semidirect
7. #21446254C2semidirect
8. #21446239C2semidirect
9. #21446138C2semidirect
10. #21446128C2semidirect
11. #21445821C2semidirect
12. #21445756C2semidirect
13. #21445752C2semidirect
14. #21445650C2semidirect
15. C61×#1959C2semidirect
21. #16840420C4semidirect
129. #14519702D4semidirect
416. #1959D61semidirect
483. C61#22426semidirect

Maximal subgroups

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

subgroupindex
C2×#168404202
C2×#168398352
C2×#168397692
C2×#168397552
#214487702
#214467522
#214462542
#214462392
#214461382
#214461282
#214458212
#214457562
#214457522
#214456502
C61×#19592
#2242661