Finite Group Databasebeta

← #29695592

Subgroups — #29695592

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×#16840421C211yesmaximal, characteristic
2C2×#16839834C211yesmaximal, characteristic, complemented
3C2×#16839770C211yesmaximal, characteristic, complemented
4C2×#16839756C211yesmaximal, characteristic, complemented
5#21446751C211yesmaximal, characteristic, complemented
6#21446633C211yesmaximal, characteristic, complemented
7#21446255C211yesmaximal, characteristic, complemented
8#21446240C211yesmaximal, characteristic, complemented
9#21446141C211yesmaximal, characteristic, complemented
10#21446131C211yesmaximal, characteristic, complemented
11#21445821C211yesmaximal, characteristic, complemented
12#21445757C211yesmaximal, characteristic, complemented
13#21445753C211yesmaximal, characteristic, complemented
14#21445652C211yesmaximal, characteristic, complemented
15C61×#2354C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C23×Dic122C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20#16840421—24no—
21#16840421C418yescomplemented
22C2×#14519765C2211yescharacteristic
23C2×#14519763—21no—
24C2×#14519756C2211yescharacteristic
25C2×#14519755—21no—
26C2×#14519751C2211yescharacteristic
27C2×#14519749—21no—
28C2×C4×Dic122C2211yescharacteristic
29C2×#14519737—21no—
30#16839834—24no—
31C2×C4⋊#92418C2211yescharacteristic
32#16839770—24no—
33#16839756—24no—
34C2×#14519700C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41C2×#14519700C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×#14519697C2211yescharacteristic
46C2×C22⋊#92418C2211yescharacteristic
47C2×C22⋊#92418C2211yescharacteristic
48C2×#14519688C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C2×#117×C61C2211yescharacteristic
55C2×#117×C61C2211yescharacteristic
56C61×#390—21no—
57C61×#388—21no—
58C61×#388—21no—
59C61×#384C2211yescharacteristic
60C61×#380C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C4×C4⋊C4×C61—21no—
63C4×C4⋊C4×C61C2211yescharacteristic
64C2×#11758222—22no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—41no—
68C2×#11758222—41no—
69C2×#11758222C2×C414yes—
70C22×Dic122—22no—
71C22×Dic122—22no—
72C22×Dic122—21no—
73C22×Dic122—22no—
74C22×Dic122—41no—
75C22×Dic122—41no—
76C22×Dic122C2×C414yes—
77C22×Dic122C2311yescharacteristic
78C22×Dic122C2311yescharacteristic
79C22×D244C2311yescharacteristic
80C22×C22⋊D61—21no—
81C22×C22⋊D61—21no—
82C23×Dic61—21no—
83C22×C4×D61—21no—
84C2×#11758194—22no—
85C2×#11758194—22no—
86C2×#11758194—41no—
87C22×#92418—22no—
88C22×#92418—22no—
89C22×#92418—41no—
90C22×#92418C2311yescharacteristic
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93C22×#92418C2311yescharacteristic
94#14519765—22no—
95#14519765C2×C414yes—
96#14519763—28no—
97#14519756—22no—
98#14519756C2×C414yes—
99#14519755—28no—
100#14519751—22no—
101#14519751C2×C414yes—
102#14519749—28no—
103C4×Dic122—22no—
104C4×Dic122C2×C414yes—
105#14519737—28no—
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×C22⋊Dic61—21no—
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×C4×Dic61—21no—
114C4⋊#92418—22no—
115#14519700—22no—
116#14519700—22no—
117#14519700—22no—
118#14519700—22no—
119#14519700—22no—
120#14519700—41no—
121#14519700—41no—
122#14519700D414yescomplemented
123#14519697—22no—
124#14519697—22no—
125#14519697—41no—
126#14519697—41no—
127C22⋊#92418—22no—
128C22⋊#92418—22no—
129#14519688—22no—
130C22×D4×C61D411yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C4×D4×C61C2×C414yes—
134C4×D4×C61D414yes—
135#117×C61—22no—
136#117×C61—22no—
137#117×C61—41no—
138#117×C61—41no—
139C2×C4⋊C4×C61—21no—
140C2×C4⋊C4×C61—21no—
141C2×C4⋊C4×C61D411yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61—21no—
147C2×C22⋊C4×C61—21no—
148C2×C22⋊C4×C61—21no—
149C2×C22⋊C4×C61—21no—
150C2×C22⋊C4×C61D411yescharacteristic
151C2×C22⋊C4×C61D411yescharacteristic
152C2×C42×C61—21no—
153C2×C42×C61—21no—
154C2×C42×C61—21no—
155C2×C42×C61C2311yescharacteristic
156#95×C61—21no—
157#95×C61—21no—
158#95×C61—21no—
159C24×C61C2×D411yescharacteristic
160C24×C61C2×D411yescharacteristic
161C23×D61—21no—
162C2×D4×C61—41no—
163C2×D4×C61—41no—
164C2×D4×C61C22⋊C414yes—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61C22×C412yes—
178C22×C4×C61C22×C412yes—
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D412yes—
184C22×C4×C61C2×D412yes—
185C22×C4×C61C2411yescharacteristic
186C2×C22⋊D61—24no—
187C2×C22⋊D61—24no—
188C2×C22⋊D61—42no—
189C2×C22⋊D61—42no—
190C2×C22⋊D61—42no—
191C2×C22⋊D61—42no—
192C22×Dic61—21no—
193C22×Dic61—24no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—42no—
197C22×Dic61—42no—
198#11758222—28no—
199#11758222—44no—
200#11758222—44no—
201#11758222—44no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244C22×C412yes—
208C2×C4×D61—24no—
209C2×C4×D61—42no—
210C2×C4×D61—42no—
211C2×Dic122—21no—
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122—21no—
215C2×Dic122—21no—
216C2×Dic122—21no—
217C2×Dic122—21no—
218C2×Dic122—28no—
219C2×Dic122—24no—
220C2×Dic122—21no—
221C2×Dic122—44no—
222C2×Dic122—44no—
223C2×Dic122—44no—
224C2×Dic122—42no—
225C2×Dic122—42no—
226C2×Dic122C22×C412yes—
227C2×Dic122C22×C412yes—
228C2×Dic122C2×D412yes—
229C2×Dic122#4112yes—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—42no—
238C4⋊C4×C61—81no—
239C4⋊C4×C61C22⋊C414yes—
240C4⋊C4×C61C2×D412yes—
241C22⋊C4×C61—42no—
242C22⋊C4×C61—42no—
243C22⋊C4×C61—81no—
244C22⋊C4×C61—81no—
245C22⋊C4×C61C22⋊C414yes—
246C22⋊C4×C61C22⋊C414yes—
247C42×C61—42no—
248C42×C61—42no—
249C42×C61—42no—
250C42×C61C22×C412yes—
251C42×C61C2×D412yes—
252C22⋊Dic61—24no—
253#11758198—24no—
254#11758198—24no—
255#11758198—24no—
256C4⋊Dic61—21no—
257C4⋊Dic61C22×C412yes—
258#11758196—24no—
259#11758196—24no—
260C4×Dic61—24no—
261#11758194—44no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273C2×#92418—44no—
274C2×#92418C2×D412yes—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61C2×C22⋊C412yes—
288C23×C61C2×C22⋊C412yes—
289C23×C61C22×D411yescharacteristic
290C22×D61—22no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297D4×C61—44no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61C2×C22⋊C412yes—
327C2×C4×C61C2×C22⋊C412yes—
328C2×C4×C61C2×C22⋊C412yes—
329C2×C4×C61C2×C22⋊C412yes—
330C2×C4×C61C23×C411yescharacteristic
331C2×C4×C61C22×D411yescharacteristic
332C2×C4×C61C22×D411yescharacteristic
333C2×C4×C61C2×#4111yescharacteristic
334C2×C4×C61H(5,𝔽2)11yescharacteristic
335C2×C4×C61H(5,𝔽2)11yescharacteristic
336C22⋊D61—48no—
337C22⋊D61—48no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—48no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348D244—22no—
349D244—22no—
350D244—41no—
351D244—41no—
352C4×D61—48no—
353Dic122—22no—
354Dic122—22no—
355Dic122—22no—
356Dic122—22no—
357Dic122—22no—
358Dic122—48no—
359Dic122—41no—
360Dic122—41no—
361Dic122C4×D414yes—
362#92418—22no—
363#92418—41no—
364#92418—41no—
365#92418—41no—
366#22426—611nomaximal, Sylow
367C22×C61—22no—
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—22no—
371C22×C61—22no—
372C22×C61—22no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—41no—
380C22×C61—41no—
381C22×C61C22×C22⋊C411yescharacteristic
382C22×C61D4211yescharacteristic
383C22×C61#54611yescharacteristic
384C22×C61#57511yescharacteristic
385C22×C61#57511yescharacteristic
386C22×C61#57711yescharacteristic
387C22×C61#57811yescharacteristic
388C2×D61—42no—
389C2×D61—42no—
390C2×D61—42no—
391C2×D61—81no—
392C2×D61—81no—
393C2×D61—81no—
394C2×D61—81no—
395C4×C61—22no—
396C4×C61—22no—
397C4×C61—22no—
398C4×C61—22no—
399C4×C61—42no—
400C4×C61—81no—
401C4×C61—81no—
402C4×C61—81no—
403C4×C61C2×C4×D411yescharacteristic
404C4×C61#51811yescharacteristic
405C4×C61D4211yescharacteristic
406C4×C61#54611yescharacteristic
407Dic61—24no—
408Dic61—42no—
409Dic61—42no—
410C2×#548—611no—
411C2×#435—611no—
412C2×#419—611no—
413C2×#416—611no—
414#2354D6111yescharacteristic, complemented
415#1983—611no—
416#1959—611no—
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—42no—
426C2×C61—42no—
427C2×C61D4×C22⋊C411yescharacteristic
428C2×C61#289611yescharacteristic
429C2×C61#289811yescharacteristic
430C2×C61#326911yescharacteristic
431C2×C61#327111yescharacteristic
432C2×C61#331311yescharacteristic
433C2×C61#332111yescharacteristic
434D61—82no—
435C22×#41—611no—
436C23×Q8—611no—
437C22×M16—611no—
438C23×C8—611no—
439#548—618no—
440#548—1224no—
441C2×#124—611no—
442C2×#124—1221no—
443C2×C22⋊Q8—611no—
444C2×C22⋊Q8—1221no—
445C2×#121—611no—
446C2×#121—1221no—
447C2×C4×Q8—611no—
448C2×C4×D4—1221no—
449C2×C4×D4C2×D6111yescharacteristic
450C2×#117C2×D6111yescharacteristic
451C2×#117C2×D6111yescharacteristic
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×#103—611no—
463C2×#103—611no—
464C2×#102—611no—
465C2×#102—611no—
466C2×#102—611no—
467C2×#102—611no—
468C2×C22⋊C8—611no—
469C2×C22⋊C8—611no—
470C2×#97—611no—
471#390—21no—
472#388—21no—
473#388—21no—
474#384C2×D6111yescharacteristic
475#380C2×D6111yescharacteristic
476#380C2×D6111yescharacteristic
477C4×C4⋊C4—21no—
478C4×C4⋊C4C2×D6111yescharacteristic
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—611no—
493C22×Q8—1222no—
494C22×Q8—1222no—
495C22×Q8—1222no—
496C22×Q8—1221no—
497C22×Q8—2441no—
498C22×Q8—2441no—
499C22×D4—611no—
500C22×D4—1221no—
501C22×D4—1221no—
502C22×D4C22⋊D6111yescharacteristic
503C23×C4—1221no—
504C23×C4—1221no—
505C23×C4C22×D6111yescharacteristic
506C23×C4C22×D6111yescharacteristic
507C2×M16—1222no—
508C2×M16—1222no—
509C2×M16—2441no—
510C22×C8—611no—
511C22×C8—611no—
512C22×C8—611no—
513C22×C8—611no—
514C22×C8—1222no—
515C22×C8—1222no—
516C22×C8—2441no—
517#124—614no—
518#124—1228no—
519#124—1222no—
520C22⋊Q8—614no—
521C22⋊Q8—1222no—
522C22⋊Q8—1228no—
523#121—614no—
524#121—1228no—
525#121—1222no—
526C4×Q8—614no—
527C4×Q8—1222no—
528C4×D4—1228no—
529C4×D4C4×D6114yes—
530C4×D4D24414yes—
531#117—22no—
532#117—22no—
533#117—41no—
534#117—41no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—1221no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4C22⋊D6111yescharacteristic
541C2×C4⋊C4C22×D6111yescharacteristic
542C2×C4⋊C4C22×D6111yescharacteristic
543C2×C4⋊C4C22×D6111yescharacteristic
544C2×C4⋊C4C22×D6111yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4C22⋊D6111yescharacteristic
554C2×C22⋊C4C22⋊D6111yescharacteristic
555C2×C42—21no—
556C2×C42—21no—
557C2×C42—21no—
558C2×C42—1221no—
559C2×C42C22×D6111yescharacteristic
560C4⋊C8—1222no—
561#103—614no—
562#103—1222no—
563#103—1222no—
564#103—1222no—
565#103—1222no—
566#103—1222no—
567#103—2441no—
568#103—2441no—
569#102—1222no—
570#102—1222no—
571#102—2441no—
572#102—2441no—
573C22⋊C8—1222no—
574C22⋊C8—1222no—
575#97—1222no—
576#95—21no—
577#95—21no—
578#95—21no—
579C24—1221no—
580C24C2×C22⋊D6111yescharacteristic
581C24C2×C22⋊D6111yescharacteristic
582#41—1228no—
583#41—2444no—
584#41—2444no—
585#41—2444no—
586C2×Q8—612no—
587C2×Q8—612no—
588C2×Q8—612no—
589C2×Q8—612no—
590C2×Q8—1228no—
591C2×Q8—1221no—
592C2×Q8—1221no—
593C2×Q8—1221no—
594C2×Q8—1221no—
595C2×Q8—1224no—
596C2×Q8—1221no—
597C2×Q8—1221no—
598C2×Q8—1221no—
599C2×Q8—1221no—
600C2×Q8—2442no—
601C2×Q8—2442no—
602C2×Q8—2444no—
603C2×Q8—2444no—
604C2×Q8—2444no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—612no—
608C2×D4—1224no—
609C2×D4—1224no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4—1221no—
613C2×D4—1221no—
614C2×D4—1221no—
615C2×D4—2442no—
616C2×D4—2442no—
617C2×D4—2442no—
618C2×D4—2442no—
619C2×D4#1175819814yes—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—1224no—
636C22×C4—1224no—
637C22×C4—2442no—
638C22×C4—2442no—
639C22×C4—2442no—
640C22×C4—2442no—
641C22×C4C2×C4×D6112yes—
642C22×C4C2×C4×D6112yes—
643C22×C4C2×D24412yes—
644C22×C4C2×D24412yes—
645C22×C4C2×C22⋊D6111yescharacteristic
646C22×C4C2×C22⋊D6111yescharacteristic
647C22×C4C2×C22⋊D6111yescharacteristic
648C22×C4C2×C22⋊D6111yescharacteristic
649C22×C4C23×D6111yescharacteristic
650M16—2444no—
651C2×C8—612no—
652C2×C8—1221no—
653C2×C8—1221no—
654C2×C8—1221no—
655C2×C8—1221no—
656C2×C8—1221no—
657C2×C8—1221no—
658C2×C8—1221no—
659C2×C8—1221no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—1221no—
663C2×C8—2444no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—42no—
672C4⋊C4—81no—
673C4⋊C4—612no—
674C4⋊C4—1221no—
675C4⋊C4—1224no—
676C4⋊C4—1224no—
677C4⋊C4#1175819814yes—
678C4⋊C4D4×D6112yes—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—81no—
682C22⋊C4—81no—
683C22⋊C4—1224no—
684C22⋊C4—1224no—
685C22⋊C4—1224no—
686C22⋊C4—1224no—
687C22⋊C4#1175819814yes—
688C22⋊C4#1175819814yes—
689C42—42no—
690C42—42no—
691C42—42no—
692C42—1224no—
693C42C2×C4×D6112yes—
694C42C2×D24412yes—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—1222no—
708C23—2441no—
709C23—2441no—
710C23—2441no—
711C23—2441no—
712C23—2441no—
713C23—2441no—
714C23C2×#1175819812yes—
715C23C2×#1175819812yes—
716C23C22×C22⋊D6111yescharacteristic
717Q8—614no—
718Q8—1222no—
719Q8—1222no—
720Q8—1222no—
721Q8—1222no—
722Q8—1222no—
723Q8—2448no—
724Q8—2441no—
725Q8—2441no—
726D4—44no—
727D4—1222no—
728D4—1222no—
729D4—2448no—
730D4—2448no—
731D4—2441no—
732D4—2441no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—2448no—
767C2×C4—2448no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4C2×#1175819812yes—
773C2×C4C2×#1175819812yes—
774C2×C4C2×#1175819812yes—
775C2×C4C2×#1175819812yes—
776C2×C4C22×C4×D6111yescharacteristic
777C2×C4C2×D4×D6111yescharacteristic
778C2×C4C22×D24411yescharacteristic
779C2×C4#41×D6111yescharacteristic
780C2×C4#1451982211yescharacteristic
781C2×C4#1451982311yescharacteristic
782C8—1222no—
783C8—2441no—
784C8—2441no—
785C8—2441no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—4881no—
801C22—4881no—
802C22—4881no—
803C22—4881no—
804C22—2442no—
805C22—2442no—
806C22—2442no—
807C22C22×#1175819811yescharacteristic
808C22D4×C22⋊D6111yescharacteristic
809C22#1684040011yescharacteristic
810C22#1684056011yescharacteristic
811C22#1684056011yescharacteristic
812C22#1684057311yescharacteristic
813C22#1684057711yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—42no—
819C4—81no—
820C4—81no—
821C4—81no—
822C4—1224no—
823C4—2442no—
824C4—2442no—
825C4C4×D4×D6111yescharacteristic
826C4#1684023411yescharacteristic
827C4D4×D24411yescharacteristic
828C4#1684040711yescharacteristic
829C2—42no—
830C2—42no—
831C2—4882no—
832C2D4×#1175819811yescharacteristic
833C2#2145433611yescharacteristic
834C2#2145434911yescharacteristic
835C2#2145737011yescharacteristic
836C2#2145740011yescharacteristic
837C2#2145787911yescharacteristic
838C2#2145799911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2354C2
socleC23×C61C22×D4
prime radicalC2×#16840421C2
cosocleC22×C4×C61C24
hypercenter#2354D61
hypocenterC61#22426
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. C2×#16839834C2semidirect
3. C2×#16839770C2semidirect
4. C2×#16839756C2semidirect
5. #21446751C2semidirect
6. #21446633C2semidirect
7. #21446255C2semidirect
8. #21446240C2semidirect
9. #21446141C2semidirect
10. #21446131C2semidirect
11. #21445821C2semidirect
12. #21445757C2semidirect
13. #21445753C2semidirect
14. #21445652C2semidirect
15. C61×#2354C2semidirect
21. #16840421C4semidirect
122. #14519700D4semidirect
414. #2354D61semidirect
483. C61#22426semidirect

Maximal subgroups

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

subgroupindex
C2×#168404212
C2×#168398342
C2×#168397702
C2×#168397562
#214467512
#214466332
#214462552
#214462402
#214461412
#214461312
#214458212
#214457572
#214457532
#214456522
C61×#23542
#2242661