Finite Group Databasebeta

← #29733219

Subgroups — #29733219

Order 15616.

1126 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840483C211yesmaximal, characteristic
2C2×#16840111C211yesmaximal, characteristic, complemented
3C2×#16839970C211yesmaximal, characteristic, complemented
4#21450769C211yesmaximal, characteristic
5#21446828C211yesmaximal, characteristic, complemented
6#21446827C211yesmaximal, characteristic, complemented
7#21446826C211yesmaximal, characteristic, complemented
8#21446769C211yesmaximal, characteristic, complemented
9#21446611C211yesmaximal, characteristic
10#21446132C211yesmaximal, characteristic, complemented
11#21446130C211yesmaximal, characteristic, complemented
12#21446129C211yesmaximal, characteristic, complemented
13#21446128C211yesmaximal, characteristic, complemented
14#103×Dic61C211yesmaximal, characteristic, complemented
15C61×#2001C211yesmaximal, characteristic, complemented
16C22×#11758202C2211yescharacteristic
17#16840483—24no—
18#16840483—24no—
19C2×#14519776C2211yescharacteristic
20C2×#14519775C2211yescharacteristic
21C2×#14519772—21no—
22C2×#14519770—21no—
23C2×#14519763—21no—
24C2×#14519757C2211yescharacteristic
25C2×#14519756C2211yescharacteristic
26C2×#14519753C2211yescharacteristic
27C2×#14519753C2211yescharacteristic
28C2×Q8×Dic61C2211yescharacteristic
29C2×#14519742—21no—
30C2×C4×C22⋊D61C2211yescharacteristic
31C2×#14519736C2211yescharacteristic
32C2×#14519735C2211yescharacteristic
33#16840111—24no—
34#16839970—24no—
35C2×#14519706C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519701C2211yescharacteristic
39C2×#14519701C2211yescharacteristic
40C2×#14519701C2211yescharacteristic
41C2×#14519700C2211yescharacteristic
42C2×C22⋊#92418C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×C8×Dic61C2211yescharacteristic
46#16839698—21no—
47#16839697—21no—
48#16839662—21no—
49#16839631—21no—
50C4⋊C4×Dic61C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56C22×Q16×C61C2211yescharacteristic
57C2×C22⋊Q8×C61C2211yescharacteristic
58C2×C22⋊Q8×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C22×Dic122—21no—
64C22×Dic122C2311yescharacteristic
65C22×C22⋊D61D411yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C2×#11758202—22no—
68C2×#11758202—41no—
69C2×#11758202—41no—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72#14519776—22no—
73#14519776D414yes—
74#14519775—22no—
75#14519775—22no—
76#14519772—28no—
77#14519770—28no—
78#14519763—28no—
79#14519757—22no—
80#14519757—41no—
81#14519756—22no—
82#14519756—41no—
83#14519753—22no—
84#14519753—22no—
85#14519753—22no—
86#14519753—41no—
87Q8×Dic61—22no—
88Q8×Dic61D414yes—
89#14519742—28no—
90C4×C22⋊D61—22no—
91C4×C22⋊D61—22no—
92#14519736—22no—
93#14519736—22no—
94#14519735—22no—
95#14519735—22no—
96C2×C4⋊Dic61—21no—
97C2×C4⋊Dic61—21no—
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×C4⋊Dic61C2311yescharacteristic
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×#11758196D411yescharacteristic
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61D411yescharacteristic
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198D411yescharacteristic
116C2×C4×Dic61—21no—
117C2×C4×Dic61—21no—
118C2×C4×Dic61—21no—
119C2×C4×Dic61—21no—
120C2×C4×Dic61C2311yescharacteristic
121#14519706—22no—
122#14519702—22no—
123#14519702—22no—
124#14519701—22no—
125#14519701—22no—
126#14519701—22no—
127#14519700—22no—
128C22⋊#92418—41no—
129#14519689—41no—
130#14519689—41no—
131C8×Dic61—22no—
132#14519684—21no—
133C22×Q8×C61C2311yescharacteristic
134C22×Q8×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C2×Q16×C61—22no—
137C2×Q16×C61—41no—
138C2×Q16×C61—41no—
139C22×C8×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141C22⋊Q8×C61—22no—
142C22⋊Q8×C61—22no—
143C22⋊Q8×C61—22no—
144C22⋊Q8×C61—41no—
145C2×C4⋊C4×C61—21no—
146C2×C4⋊C4×C61—21no—
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C22⋊C4×C61—21no—
150C2×C22⋊C4×C61—21no—
151#103×C61—22no—
152#103×C61—22no—
153C22⋊C8×C61—41no—
154C24×C61C2×D411yescharacteristic
155C23×D61C2×D411yescharacteristic
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61C2×D412yes—
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×C61—21no—
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2411yescharacteristic
180C2×C22⋊D61—22no—
181C2×C22⋊D61—22no—
182C2×C22⋊D61—22no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61C2×D411yescharacteristic
188C22×Dic61C2×D411yescharacteristic
189C22×Dic61C2×D411yescharacteristic
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×Dic122—24no—
197C2×Dic122—21no—
198C2×Dic122—21no—
199C2×Dic122—21no—
200C2×Dic122—21no—
201C2×Dic122—21no—
202C2×Dic122—21no—
203C2×Dic122—42no—
204C2×Dic122—42no—
205Q16×C61—44no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C4⋊C4×C61—24no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—42no—
216C4⋊C4×C61C2×D412yes—
217C4⋊C4×C61#4112yes—
218C22⋊C4×C61—24no—
219C22⋊C4×C61—42no—
220C22⋊Dic61—24no—
221C22⋊Dic61—22no—
222C22⋊Dic61—42no—
223#11758202—44no—
224#11758198—24no—
225#11758198—24no—
226#11758198—22no—
227#11758198—42no—
228#11758198—42no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—24no—
233C4⋊Dic61—42no—
234C4⋊Dic61C2×D412yes—
235C4⋊Dic61C2×D412yes—
236C4⋊Dic61#4112yes—
237#11758196—24no—
238#11758196—24no—
239#11758196—22no—
240#11758196—42no—
241#11758196—42no—
242#11758196—42no—
243#11758196—42no—
244C4×Dic61—24no—
245C4×Dic61—24no—
246C4×Dic61—24no—
247C4×Dic61—42no—
248C4×Dic61C2×D412yes—
249C4×Dic61C2×D412yes—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61C22×D411yescharacteristic
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271Q8×C61—22no—
272Q8×C61—22no—
273Q8×C61—41no—
274Q8×C61—41no—
275Q8×C61—41no—
276Q8×C61—41no—
277Q8×C61—41no—
278Q8×C61—41no—
279C2×C4×C61—21no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—21no—
283C2×C4×C61—22no—
284C2×C4×C61—21no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61C22×D411yescharacteristic
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C2×#4111yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61H(5,𝔽2)11yescharacteristic
303C2×C4×C61H(5,𝔽2)11yescharacteristic
304C22⋊D61—44no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—22no—
308C2×Dic61—21no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61#12012yes—
323C2×Dic61#12012yes—
324C2×Dic61#13512yes—
325C2×Dic61#13712yes—
326C4×D61—41no—
327C4×D61—41no—
328C4×D61—41no—
329C4×D61—41no—
330Dic122—48no—
331Dic122—41no—
332Dic122—41no—
333Dic122—41no—
334Dic122—41no—
335C8×C61—41no—
336C8×C61—41no—
337#92418—41no—
338#92418—41no—
339#25570—611nomaximal, Sylow
340C22×C61—41no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61C2×#12011yescharacteristic
348C22×C61#54611yescharacteristic
349C22×C61#54611yescharacteristic
350C22×C61C2×#13511yescharacteristic
351C22×C61C2×#13711yescharacteristic
352C22×C61#57811yescharacteristic
353C22×C61#57811yescharacteristic
354C2×D61—41no—
355C2×D61—41no—
356C2×D61—41no—
357C2×D61—41no—
358C2×D61—41no—
359C2×D61—41no—
360C2×D61—41no—
361C4×C61—41no—
362C4×C61—42no—
363C4×C61—42no—
364C4×C61—42no—
365C4×C61—81no—
366C4×C61#53211yescharacteristic
367C4×C61#53511yescharacteristic
368C4×C61#55011yescharacteristic
369C4×C61#55011yescharacteristic
370Dic61—22no—
371Dic61—41no—
372Dic61—42no—
373Dic61—42no—
374Dic61—42no—
375Dic61—81no—
376Dic61#45214yes—
377C2×#556—611no—
378C2×#487—611no—
379C2×#462—611no—
380#2542—611no—
381#2001—611no—
382#2001—611no—
383#2001—611no—
384#2001D6111yescharacteristic, complemented
385#1988—611no—
386#1954—611no—
387#1873—611no—
388#1873—611no—
389#1873—611no—
390#1873—611no—
391C4×#103—611no—
392C2×C61—81no—
393C2×C61#243111yescharacteristic
394C2×C61C2×#45211yescharacteristic
395C2×C61#301111yescharacteristic
396C2×C61#330211yescharacteristic
397C2×C61#330211yescharacteristic
398C2×C61#332811yescharacteristic
399C2×C61#332811yescharacteristic
400D61—81no—
401C22×Q16—611no—
402C22×Q16C2×D6111yescharacteristic
403#556—1224no—
404#556—1224no—
405C2×C4⋊Q8—611no—
406C2×C4⋊Q8—611no—
407C2×#126—1221no—
408C2×#126—1221no—
409C2×#124—1221no—
410C2×C22⋊Q8—611no—
411C2×C22⋊Q8—611no—
412C2×C22⋊Q8—611no—
413C2×C22⋊Q8—611no—
414C2×C22⋊Q8C2×D6111yescharacteristic
415C2×C22⋊Q8C2×D6111yescharacteristic
416C2×C4×Q8—611no—
417C2×C4×Q8—1221no—
418C2×C4×D4—611no—
419C2×#117—611no—
420C2×#117—611no—
421#487—1224no—
422#462—1224no—
423C2×C4⋊C8—611no—
424C2×#103—611no—
425C2×#103—611no—
426C2×#103—611no—
427C2×#103—611no—
428C2×#103—611no—
429C2×#103—611no—
430C2×#103C2×D6111yescharacteristic
431C2×#103C2×D6111yescharacteristic
432C2×C22⋊C8—611no—
433C2×C22⋊C8—611no—
434C2×C22⋊C8—611no—
435C2×C22⋊C8C2×D6111yescharacteristic
436C2×C4×C8—611no—
437#399—1221no—
438#399—1221no—
439#390—1221no—
440#384—1221no—
441C4×C4⋊C4—611no—
442#340—611no—
443#340—611no—
444#340—611no—
445#340—611no—
446#340—611no—
447#340C2×D6111yescharacteristic
448C61#2557011yescharacteristic, complemented, Sylow
449C22×Q8—611no—
450C22×Q8—1221no—
451C22×Q8C22×D6111yescharacteristic
452C22×Q8C22×D6111yescharacteristic
453C22×D4—611no—
454C23×C4—611no—
455C23×C4C22×D6111yescharacteristic
456C2×Q16—22no—
457C2×Q16—41no—
458C2×Q16—41no—
459C2×Q16—1222no—
460C2×Q16—2441no—
461C2×Q16—2441no—
462C22×C8—611no—
463C22×C8—611no—
464C22×C8C22×D6111yescharacteristic
465C22×C8C22×D6111yescharacteristic
466C4⋊Q8—614no—
467C4⋊Q8—1222no—
468C4⋊Q8—1222no—
469C4⋊Q8—1222no—
470#126—1228no—
471#126—1228no—
472#124—1228no—
473C22⋊Q8—22no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476C22⋊Q8—41no—
477C22⋊Q8—1222no—
478C22⋊Q8—1222no—
479C22⋊Q8—1222no—
480C22⋊Q8—1222no—
481C22⋊Q8—1222no—
482C22⋊Q8—2441no—
483C22⋊Q8—2441no—
484C22⋊Q8—2441no—
485C4×Q8—614no—
486C4×Q8—1222no—
487C4×Q8—1228no—
488C4×D4—1222no—
489C4×D4—1222no—
490#117—1222no—
491#117—1222no—
492#117—1222no—
493#117—1222no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4C22×D6111yescharacteristic
509C2×C4⋊C4C22×D6111yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—611no—
513C2×C22⋊C4—611no—
514C2×C22⋊C4—1221no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C42—611no—
521C2×C42—1221no—
522C2×C42—1221no—
523C2×C42—1221no—
524C2×C42—1221no—
525C4⋊C8—1222no—
526#103—22no—
527#103—22no—
528#103—1222no—
529#103—1222no—
530#103—1222no—
531#103—1222no—
532#103—1222no—
533#103—1222no—
534C22⋊C8—41no—
535C22⋊C8—2441no—
536C22⋊C8—2441no—
537C22⋊C8—2441no—
538C4×C8—1222no—
539#95—1221no—
540C24—611no—
541C24D4×D6111yescharacteristic
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—1224no—
554C2×Q8—1221no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×Q8—1221no—
558C2×Q8—1221no—
559C2×Q8—1221no—
560C2×Q8—2442no—
561C2×Q8—2442no—
562C2×Q8D4×D6112yes—
563C2×D4—1222no—
564C2×D4—1222no—
565C2×D4—1222no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—611no—
577C22×C4—611no—
578C22×C4—611no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4D4×D6111yescharacteristic
590C22×C4C23×D6111yescharacteristic
591Q16—44no—
592Q16—2444no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—1221no—
600C2×C8—1221no—
601C2×C8—1221no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8—1221no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—42no—
609C4⋊C4—612no—
610C4⋊C4—612no—
611C4⋊C4—612no—
612C4⋊C4—1222no—
613C4⋊C4—1224no—
614C4⋊C4—1224no—
615C4⋊C4—1224no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C4⋊C4—2442no—
620C4⋊C4—2442no—
621C4⋊C4—2442no—
622C4⋊C4—2442no—
623C4⋊C4—2442no—
624C4⋊C4D4×D6112yes—
625C4⋊C4#1175822412yes—
626C22⋊C4—24no—
627C22⋊C4—42no—
628C22⋊C4—1222no—
629C22⋊C4—1224no—
630C22⋊C4—1224no—
631C22⋊C4—1222no—
632C22⋊C4—1224no—
633C22⋊C4—2442no—
634C22⋊C4—2442no—
635C22⋊C4—2442no—
636C42—612no—
637C42—612no—
638C42—1224no—
639C42—1224no—
640C42—1224no—
641C42—2442no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—1221no—
650C23—1221no—
651C23—1221no—
652C23—1221no—
653C23—1221no—
654C23—1221no—
655C23—1221no—
656C23C2×D4×D6111yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—41no—
660Q8—41no—
661Q8—41no—
662Q8—41no—
663Q8—41no—
664Q8—41no—
665Q8—2448no—
666Q8—2441no—
667Q8—2441no—
668Q8—2441no—
669Q8—2441no—
670D4—2444no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—612no—
691C2×C4—612no—
692C2×C4—612no—
693C2×C4—612no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1222no—
697C2×C4—1221no—
698C2×C4—1222no—
699C2×C4—1221no—
700C2×C4—1222no—
701C2×C4—1221no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4C2×D4×D6111yescharacteristic
716C2×C4C2×D4×D6111yescharacteristic
717C2×C4#41×D6111yescharacteristic
718C2×C4C2×#1175822411yescharacteristic
719C2×C4#1451982211yescharacteristic
720C2×C4#1451982211yescharacteristic
721C8—41no—
722C8—41no—
723C8—2441no—
724C8—2441no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—2441no—
733C22—2441no—
734C22—2441no—
735C22—2441no—
736C22—2441no—
737C22—2441no—
738C22—2441no—
739C22#120×D6111yescharacteristic
740C22#1684039911yescharacteristic
741C22#1684040111yescharacteristic
742C22#135×D6111yescharacteristic
743C22#137×D6111yescharacteristic
744C22#1684057511yescharacteristic
745C22#1684057811yescharacteristic
746C4—42no—
747C4—42no—
748C4—41no—
749C4—42no—
750C4—81no—
751C4—614no—
752C4—1222no—
753C4—4881no—
754C4—2442no—
755C4—2442no—
756C4—2442no—
757C4—2441no—
758C4#1684030711yescharacteristic
759C4#1684032711yescharacteristic
760C4#1684043011yescharacteristic
761C4#1684043211yescharacteristic
762C2—81no—
763C2—4881no—
764C2#2144943311yescharacteristic
765C2#452×D6111yescharacteristic
766C2#2145510911yescharacteristic
767C2#2145772911yescharacteristic
768C2#2145773111yescharacteristic
769C2#2145809511yescharacteristic
770C2#2145809711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2001C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenter#2001D61
hypocenterC61#25570
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2001

Complements

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

NH ≅ G/Ntype
2. C2×#16840111C2semidirect
3. C2×#16839970C2semidirect
5. #21446828C2semidirect
6. #21446827C2semidirect
7. #21446826C2semidirect
8. #21446769C2semidirect
10. #21446132C2semidirect
11. #21446130C2semidirect
12. #21446129C2semidirect
13. #21446128C2semidirect
14. #103×Dic61C2semidirect
15. C61×#2001C2semidirect
384. #2001D61semidirect
448. C61#25570semidirect

Maximal subgroups

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

subgroupindex
C2×#168404832
C2×#168401112
C2×#168399702
#214507692
#214468282
#214468272
#214468262
#214467692
#214466112
#214461322
#214461302
#214461292
#214461282
#103×Dic612
C61×#20012
#2557061