Finite Group Databasebeta

← #29733380

Subgroups — #29733380

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×#16840447C211yesmaximal, characteristic
2C2×#16840129C211yesmaximal, characteristic, complemented
3C2×#16839971C211yesmaximal, characteristic, complemented
4#21450769C211yesmaximal, characteristic
5#21446830C211yesmaximal, characteristic, complemented
6#21446829C211yesmaximal, characteristic, complemented
7#21446828C211yesmaximal, characteristic, complemented
8#21446827C211yesmaximal, characteristic, complemented
9#21446773C211yesmaximal, characteristic, complemented
10#21446615C211yesmaximal, characteristic
11#21446130C211yesmaximal, characteristic, complemented
12#21446128C211yesmaximal, characteristic, complemented
13#21446126C211yesmaximal, characteristic, complemented
14#21445648C211yesmaximal, characteristic, complemented
15C61×#1872C211yesmaximal, characteristic, complemented
16C22×Dic244C2211yescharacteristic
17C22×#11758202C2211yescharacteristic
18#16840447—24no—
19#16840447—24no—
20C2×#14519775C2211yescharacteristic
21C2×#14519772—21no—
22C2×#14519768C2211yescharacteristic
23C2×#14519767—21no—
24C2×#14519760—21no—
25C2×#14519757C2211yescharacteristic
26C2×#14519757C2211yescharacteristic
27C2×#14519756C2211yescharacteristic
28C2×#14519756C2211yescharacteristic
29C2×#14519753C2211yescharacteristic
30C2×#14519742C2211yescharacteristic
31C2×C4×C22⋊D61C2211yescharacteristic
32C2×#14519736—21no—
33C2×#14519735C2211yescharacteristic
34#16840129—24no—
35#16839971—24no—
36C2×#14519706C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519702C2211yescharacteristic
39C2×#14519701C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41C2×#14519700C2211yescharacteristic
42C2×#14519700C2211yescharacteristic
43C2×C22⋊#92418C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46C2×#14519687C2211yescharacteristic
47#16839698—21no—
48#16839697—21no—
49#16839662—21no—
50#16839631—21no—
51C4⋊C4×Dic61C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56C2×C22⋊Q8×C61C2211yescharacteristic
57C22×C4⋊C4×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C22×Dic122C2311yescharacteristic
65C22×C22⋊D61D411yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C2×Dic244—22no—
68C2×Dic244—41no—
69C2×Dic244—41no—
70C2×#11758202—22no—
71C2×#11758202—41no—
72C2×#11758202—41no—
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75#14519775—22no—
76#14519775—22no—
77#14519772—28no—
78#14519768—22no—
79#14519768D414yes—
80#14519767—28no—
81#14519760—28no—
82#14519757—22no—
83#14519757—22no—
84#14519757—22no—
85#14519757—41no—
86#14519756—22no—
87#14519756—22no—
88#14519756—22no—
89#14519756—41no—
90#14519753—22no—
91#14519753—41no—
92#14519742—22no—
93#14519742D414yes—
94C4×C22⋊D61—22no—
95C4×C22⋊D61—22no—
96#14519736—28no—
97#14519735—22no—
98#14519735—22no—
99C2×C4⋊Dic61—21no—
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61—21no—
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2311yescharacteristic
104C2×#11758196—21no—
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×#11758196—21no—
110C2×#11758196—21no—
111C2×#11758196D411yescharacteristic
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×C22⋊Dic61D411yescharacteristic
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198D411yescharacteristic
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61—21no—
123C2×C4×Dic61C2311yescharacteristic
124#14519706—22no—
125#14519702—22no—
126#14519702—22no—
127#14519701—22no—
128#14519700—22no—
129#14519700—22no—
130#14519700—22no—
131C22⋊#92418—41no—
132#14519689—41no—
133#14519689—41no—
134#14519687—22no—
135#14519684—21no—
136C22×Q8×C61C2311yescharacteristic
137C23×C4×C61—21no—
138C23×C4×C61C2311yescharacteristic
139C22×C8×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141C22⋊Q8×C61—22no—
142C22⋊Q8×C61—41no—
143C2×C4⋊C4×C61—21no—
144C2×C4⋊C4×C61—22no—
145C2×C4⋊C4×C61—22no—
146C2×C4⋊C4×C61—21no—
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C4⋊C4×C61C2311yescharacteristic
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—
162C22×C4×C61—24no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
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—42no—
174C22×C4×C61—42no—
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2411yescharacteristic
177C2×C22⋊D61—22no—
178C2×C22⋊D61—22no—
179C2×C22⋊D61—41no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61C2×D411yescharacteristic
185C22×Dic61C2×D411yescharacteristic
186C22×Dic61C2×D411yescharacteristic
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122—21no—
196C2×Dic122—21no—
197C2×Dic122—21no—
198C2×Dic122—21no—
199C2×Dic122—21no—
200C2×Dic122—21no—
201C2×Dic122—21no—
202C2×Dic122—21no—
203C2×Dic122—21no—
204C2×Dic122C2×D412yes—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C4⋊C4×C61—24no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—42no—
216C4⋊C4×C61C2×D412yes—
217C4⋊C4×C61C2×D412yes—
218C4⋊C4×C61#4112yes—
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—24no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—24no—
233C4⋊Dic61—42no—
234C4⋊Dic61C2×D412yes—
235C4⋊Dic61#4112yes—
236#11758196—24no—
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—42no—
247C4×Dic61C2×D412yes—
248C4×Dic61C2×D412yes—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255Dic244—44no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61#13712yes—
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—41no—
272Q8×C61—41no—
273Q8×C61—41no—
274Q8×C61—41no—
275C2×C4×C61—22no—
276C2×C4×C61—21no—
277C2×C4×C61—22no—
278C2×C4×C61—21no—
279C2×C4×C61—22no—
280C2×C4×C61—21no—
281C2×C4×C61—48no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
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×C61C22×D411yescharacteristic
296C2×C4×C61C22×D411yescharacteristic
297C2×C4×C61C2×#4111yescharacteristic
298C2×C4×C61C2×#4111yescharacteristic
299C2×C4×C61H(5,𝔽2)11yescharacteristic
300C2×C4×C61H(5,𝔽2)11yescharacteristic
301C22⋊D61—44no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—41no—
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#12012yes—
322C2×Dic61#12012yes—
323C4×D61—41no—
324C4×D61—41no—
325C4×D61—41no—
326C4×D61—41no—
327Dic122—22no—
328Dic122—22no—
329Dic122—41no—
330Dic122—41no—
331Dic122—41no—
332Dic122—41no—
333Dic122—41no—
334Dic122—41no—
335C8×C61—41no—
336C8×C61—41no—
337#92418—41no—
338#92418—41no—
339#25584—611nomaximal, Sylow
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61C2×#12011yescharacteristic
348C22×C61#54611yescharacteristic
349C22×C61#54611yescharacteristic
350C22×C61C2×#13711yescharacteristic
351C22×C61#57511yescharacteristic
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—22no—
372Dic61—42no—
373Dic61—41no—
374Dic61—42no—
375Dic61—42no—
376Dic61—81no—
377C2×#552—611no—
378C2×#491—611no—
379C2×#462—611no—
380#2542—611no—
381#2001—611no—
382#2001—611no—
383#2001—611no—
384#2001—611no—
385#1989—611no—
386#1955—611no—
387#1873—611no—
388#1873—611no—
389#1872—611no—
390#1872D6111yescharacteristic, complemented
391#1763—611no—
392C2×C61—42no—
393C2×C61#243111yescharacteristic
394C2×C61#300711yescharacteristic
395C2×C61#301111yescharacteristic
396C2×C61#331211yescharacteristic
397C2×C61#331211yescharacteristic
398C2×C61#331511yescharacteristic
399C2×C61#331511yescharacteristic
400D61—81no—
401C22×Q16—611no—
402C22×Q16—611no—
403#552—1224no—
404#552—1224no—
405C2×C4⋊Q8—611no—
406C2×#126—1221no—
407C2×#125—611no—
408C2×#125—1221no—
409C2×#123—1221no—
410C2×C22⋊Q8—611no—
411C2×C22⋊Q8—611no—
412C2×C22⋊Q8—611no—
413C2×C22⋊Q8—611no—
414C2×C22⋊Q8—611no—
415C2×C22⋊Q8C2×D6111yescharacteristic
416C2×C4×Q8—611no—
417C2×C4×D4—611no—
418C2×#117—611no—
419C2×#117—1221no—
420C22×C4⋊C4C2×D6111yescharacteristic
421#491—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×#97—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#340C2×D6111yescharacteristic
447#340C2×D6111yescharacteristic
448C61#2558411yescharacteristic, complemented, Sylow
449C22×Q8—611no—
450C22×Q8—611no—
451C22×Q8C22×D6111yescharacteristic
452C22×D4—611no—
453C23×C4—21no—
454C23×C4—611no—
455C23×C4C22×D6111yescharacteristic
456C2×Q16—1222no—
457C2×Q16—1222no—
458C2×Q16—2441no—
459C2×Q16—2441no—
460C2×Q16—2441no—
461C2×Q16—2441no—
462C22×C8—611no—
463C22×C8—611no—
464C22×C8C22×D6111yescharacteristic
465C22×C8C22×D6111yescharacteristic
466C4⋊Q8—1222no—
467C4⋊Q8—1222no—
468#126—1228no—
469#125—614no—
470#125—1222no—
471#125—1228no—
472#123—1228no—
473C22⋊Q8—22no—
474C22⋊Q8—41no—
475C22⋊Q8—1222no—
476C22⋊Q8—1222no—
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×D4—1222no—
488C4×D4—1222no—
489#117—1222no—
490#117—1228no—
491#117—1222no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—1221no—
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⋊C4—1221no—
509C2×C4⋊C4C22×D6111yescharacteristic
510C2×C4⋊C4C22×D6111yescharacteristic
511C2×C4⋊C4C22×D6111yescharacteristic
512C2×C22⋊C4—21no—
513C2×C22⋊C4—611no—
514C2×C22⋊C4—611no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C42—611no—
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—
538#97—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—612no—
549C2×Q8—1221no—
550C2×Q8—1221no—
551C2×Q8—1221no—
552C2×Q8—1221no—
553C2×Q8—1221no—
554C2×Q8—1221no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×Q8—1221no—
558C2×Q8—1221no—
559C2×Q8—1221no—
560C2×D4—1222no—
561C2×D4—1222no—
562C2×D4—2441no—
563C22×C4—24no—
564C22×C4—21no—
565C22×C4—21no—
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—42no—
575C22×C4—42no—
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—2444no—
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—21no—
609C4⋊C4—42no—
610C4⋊C4—612no—
611C4⋊C4—612no—
612C4⋊C4—1222no—
613C4⋊C4—1224no—
614C4⋊C4—1224no—
615C4⋊C4—1224no—
616C4⋊C4—1224no—
617C4⋊C4—1224no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—2442no—
621C4⋊C4—2442no—
622C4⋊C4—2442no—
623C4⋊C4—2442no—
624C4⋊C4—2442no—
625C4⋊C4#1175822212yes—
626C4⋊C4D4×D6112yes—
627C4⋊C4D4×D6112yes—
628C22⋊C4—42no—
629C22⋊C4—1222no—
630C22⋊C4—1224no—
631C22⋊C4—1224no—
632C22⋊C4—1222no—
633C22⋊C4—1224no—
634C22⋊C4—2442no—
635C22⋊C4—2442no—
636C22⋊C4—2442no—
637C42—612no—
638C42—612no—
639C42—1224no—
640C42—1224no—
641C42—2442no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—1221no—
649C23—1221no—
650C23—1221no—
651C23—1221no—
652C23—1221no—
653C23—1221no—
654C23—1221no—
655C23#1451980612yes—
656C23C2×D4×D6111yescharacteristic
657Q8—41no—
658Q8—41no—
659Q8—41no—
660Q8—41no—
661Q8—1222no—
662Q8—1222no—
663Q8—2441no—
664Q8—2441no—
665Q8—2441no—
666Q8—2441no—
667Q8—2441no—
668Q8—2441no—
669D4—2444no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—48no—
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—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1221no—
697C2×C4—1222no—
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×#1175822211yescharacteristic
719C2×C4#1451982211yescharacteristic
720C2×C4#1451982311yescharacteristic
721C8—41no—
722C8—41no—
723C8—2441no—
724C8—2441no—
725C22—22no—
726C22—22no—
727C22—22no—
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#1684040211yescharacteristic
741C22#1684040411yescharacteristic
742C22C2×#1451980611yescharacteristic
743C22#1684055811yescharacteristic
744C22#1684057511yescharacteristic
745C22#1684057811yescharacteristic
746C4—41no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—81no—
751C4—1222no—
752C4—1222no—
753C4—4881no—
754C4—2442no—
755C4—2441no—
756C4—2442no—
757C4—2442no—
758C4#1684030911yescharacteristic
759C4#1684032811yescharacteristic
760C4#1684043011yescharacteristic
761C4#1684043311yescharacteristic
762C2—42no—
763C2—4881no—
764C2#2144943611yescharacteristic
765C2#2145507411yescharacteristic
766C2#2145510911yescharacteristic
767C2#2145786611yescharacteristic
768C2#2145786811yescharacteristic
769C2#2145791611yescharacteristic
770C2#2145791811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1872C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenter#1872D61
hypocenterC61#25584
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
2. C2×#16840129C2semidirect
3. C2×#16839971C2semidirect
5. #21446830C2semidirect
6. #21446829C2semidirect
7. #21446828C2semidirect
8. #21446827C2semidirect
9. #21446773C2semidirect
11. #21446130C2semidirect
12. #21446128C2semidirect
13. #21446126C2semidirect
14. #21445648C2semidirect
15. C61×#1872C2semidirect
390. #1872D61semidirect
448. C61#25584semidirect

Maximal subgroups

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

subgroupindex
C2×#168404472
C2×#168401292
C2×#168399712
#214507692
#214468302
#214468292
#214468282
#214468272
#214467732
#214466152
#214461302
#214461282
#214461262
#214456482
C61×#18722
#2558461