Finite Group Databasebeta

← #29714183

Subgroups — #29714183

Order 15616.

1090 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840452C211yesmaximal, characteristic
2C2×#16840069C211yesmaximal, characteristic, complemented
3C2×#16839867C211yesmaximal, characteristic, complemented
4#21447022C211yesmaximal, characteristic, complemented
5#21447015C211yesmaximal, characteristic, complemented
6#21446827C211yesmaximal, characteristic, complemented
7#21446827C211yesmaximal, characteristic, complemented
8#21446787C211yesmaximal, characteristic, complemented
9#21446618C211yesmaximal, characteristic
10#21446132C211yesmaximal, characteristic, complemented
11#21446127C211yesmaximal, characteristic, complemented
12#21446016C211yesmaximal, characteristic, complemented
13#21446011C211yesmaximal, characteristic, complemented
14#21445821C211yesmaximal, characteristic, complemented
15C61×#2538C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17#16840452—24no—
18#16840452—24no—
19C2×#14519770—21no—
20C2×#14519769C2211yescharacteristic
21C2×#14519767—21no—
22C2×#14519758—21no—
23C2×#14519756C2211yescharacteristic
24C2×#14519756C2211yescharacteristic
25C2×C4×Dic122C2211yescharacteristic
26C2×#14519736C2211yescharacteristic
27C2×#14519733—21no—
28C22×C4⋊Dic61C2211yescharacteristic
29#16840069—24no—
30#16839867—24no—
31C2×#14519710C2211yescharacteristic
32C2×#14519708C2211yescharacteristic
33C2×#14519708C2211yescharacteristic
34C2×C4⋊#92418C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×C22⋊#92418C2211yescharacteristic
43C2×C22⋊#92418C2211yescharacteristic
44C2×C22⋊#92418C2211yescharacteristic
45C2×#14519688C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52C2×C22⋊Q8×C61C2211yescharacteristic
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×C4×Q8×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C61×#396—21no—
57C61×#396—21no—
58C61×#390—21no—
59C61×#389—21no—
60C61×#384C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C61×#380C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C23×Dic61—21no—
65C2×#11758202—22no—
66C2×#11758202—22no—
67C2×#11758202—22no—
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72#14519770—28no—
73#14519769—22no—
74#14519769D414yes—
75#14519767—28no—
76#14519758—28no—
77#14519756—22no—
78#14519756—22no—
79#14519756—22no—
80#14519756—22no—
81C4×Dic122—22no—
82C4×Dic122D414yes—
83#14519736—22no—
84#14519736—22no—
85#14519733—28no—
86C2×C4⋊Dic61—21no—
87C2×C4⋊Dic61—22no—
88C2×C4⋊Dic61—22no—
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×#11758196—21no—
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×C4×Dic61—21no—
101C2×C4×Dic61—21no—
102#14519710—22no—
103#14519708—22no—
104#14519708—22no—
105C4⋊#92418—22no—
106#14519701—22no—
107#14519701—22no—
108#14519701—22no—
109#14519700—22no—
110#14519700—41no—
111#14519700—41no—
112C22⋊#92418—22no—
113C22⋊#92418—22no—
114C22⋊#92418—41no—
115C22⋊#92418—41no—
116#14519688—22no—
117C22×Q8×C61C2311yescharacteristic
118C22×D4×C61D411yescharacteristic
119C23×C4×C61C2311yescharacteristic
120C23×C4×C61C2311yescharacteristic
121C22⋊Q8×C61—22no—
122C22⋊Q8×C61—22no—
123C22⋊Q8×C61—41no—
124C22⋊Q8×C61—41no—
125C4×Q8×C61—22no—
126C4×Q8×C61—22no—
127C4×D4×C61—22no—
128C4×D4×C61—22no—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61D411yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61D411yescharacteristic
143C2×C22⋊C4×C61D411yescharacteristic
144C2×C42×C61—21no—
145C2×C42×C61C2311yescharacteristic
146#95×C61—21no—
147#95×C61—21no—
148C24×C61C2×D411yescharacteristic
149C24×C61C2×D411yescharacteristic
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61#4112yes—
156C2×D4×C61—22no—
157C2×D4×C61—22no—
158C2×D4×C61—41no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
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—21no—
174C22×C4×C61—21no—
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2411yescharacteristic
180C22×Dic61—24no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—42no—
186C22×Dic61—42no—
187C2×Dic122—21no—
188C2×Dic122—21no—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122C2×D412yes—
193C4⋊C4×C61—22no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—42no—
201C4⋊C4×C61—42no—
202C4⋊C4×C61—42no—
203C4⋊C4×C61—42no—
204C4⋊C4×C61—81no—
205C22⋊C4×C61—22no—
206C22⋊C4×C61—22no—
207C22⋊C4×C61—42no—
208C22⋊C4×C61—42no—
209C22⋊C4×C61—81no—
210C22⋊C4×C61—81no—
211C42×C61—42no—
212C42×C61C2×D412yes—
213C42×C61C2×D412yes—
214C22⋊Dic61—24no—
215C22⋊Dic61—24no—
216C22⋊Dic61—24no—
217#11758202—28no—
218C4⋊Dic61—24no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61C2×D412yes—
223C4⋊Dic61C2×D412yes—
224C4⋊Dic61C2×D412yes—
225#11758196—24no—
226#11758196—24no—
227#11758196—24no—
228#11758196—24no—
229#11758196—24no—
230C4×Dic61—24no—
231C4×Dic61—24no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418#4112yes—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61#13712yes—
258C23×C61C22×D411yescharacteristic
259Q8×C61—22no—
260Q8×C61—22no—
261Q8×C61—41no—
262Q8×C61—41no—
263D4×C61—44no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—22no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
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#12012yes—
295C2×C4×C61#12012yes—
296C2×C4×C61C22×D411yescharacteristic
297C2×C4×C61C22×D411yescharacteristic
298C2×C4×C61C2×#4111yescharacteristic
299C2×C4×C61C2×#4111yescharacteristic
300C2×C4×C61H(5,𝔽2)11yescharacteristic
301C2×C4×C612−1+411yescharacteristic
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—48no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315Dic122—22no—
316Dic122—22no—
317Dic122—41no—
318Dic122—41no—
319#92418—22no—
320#92418—41no—
321#92418—41no—
322#92418—41no—
323#24139—611nomaximal, Sylow
324C22×C61—22no—
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61C2×#12011yescharacteristic
339C22×C61#54611yescharacteristic
340C22×C61#54711yescharacteristic
341C22×C61C2×#13711yescharacteristic
342C22×C61#57511yescharacteristic
343C22×C61#57711yescharacteristic
344C22×C61#57811yescharacteristic
345C4×C61—22no—
346C4×C61—22no—
347C4×C61—41no—
348C4×C61—41no—
349C4×C61—42no—
350C4×C61—81no—
351C4×C61—81no—
352C4×C61—81no—
353C4×C61#52511yescharacteristic
354C4×C61#53711yescharacteristic
355C4×C61#54811yescharacteristic
356C4×C61#55011yescharacteristic
357Dic61—42no—
358Dic61—42no—
359Dic61—42no—
360Dic61—42no—
361C2×#552—611no—
362C2×#479—611no—
363C2×#441—611no—
364#2538D6111yescharacteristic
365#2036—611no—
366#2035—611no—
367#2001—611no—
368#2001—611no—
369#1992—611no—
370#1955—611no—
371#1873—611no—
372#1872—611no—
373#1854—611no—
374#1853—611no—
375#1803—611no—
376C2×C61—42no—
377C2×C61—81no—
378C2×C61#240711yescharacteristic
379C2×C61#300711yescharacteristic
380C2×C61#301311yescharacteristic
381C2×C61#331211yescharacteristic
382C2×C61#331711yescharacteristic
383C2×C61#334411yescharacteristic
384C2×C61#334911yescharacteristic
385C22×Q16—611no—
386#552—1224no—
387#552—1224no—
388C2×#126—1221no—
389C2×#125—611no—
390C2×#125—1221no—
391C2×#123—1221no—
392C2×C22⋊Q8—611no—
393C2×C22⋊Q8—611no—
394C2×C22⋊Q8C2×D6111yescharacteristic
395C2×C22⋊Q8C2×D6111yescharacteristic
396C2×C4×Q8—611no—
397C2×C4×Q8C2×D6111yescharacteristic
398C2×C4×D4C2×D6111yescharacteristic
399C2×#117—611no—
400C2×#117—1221no—
401C22×C4⋊C4—611no—
402#479—1224no—
403#441—1224no—
404C2×#107—611no—
405C2×#106—611no—
406C2×#106—611no—
407C2×C4⋊C8—611no—
408C2×#103—611no—
409C2×#103—611no—
410C2×#103—611no—
411C2×#103—611no—
412C2×#103—611no—
413C2×#103—611no—
414C2×C22⋊C8—611no—
415C2×C22⋊C8—611no—
416C2×C22⋊C8—611no—
417C2×C22⋊C8—611no—
418C2×#97—611no—
419#396—21no—
420#396—21no—
421#390—21no—
422#389—21no—
423#384C2×D6111yescharacteristic
424#380C2×D6111yescharacteristic
425#380C2×D6111yescharacteristic
426#340—611no—
427#340—611no—
428#340—611no—
429#340—611no—
430#340—611no—
431#340—611no—
432C61#2413911yescharacteristic, complemented, Sylow
433C22×Q8—611no—
434C22×Q8C22×D6111yescharacteristic
435C22×D4C22⋊D6111yescharacteristic
436C23×C4—1221no—
437C23×C4C22×D6111yescharacteristic
438C23×C4C22×D6111yescharacteristic
439C2×Q16—1222no—
440C2×Q16—1222no—
441C2×Q16—1222no—
442C22×C8—611no—
443C22×C8—611no—
444C22×C8—611no—
445C22×C8—611no—
446#126—1228no—
447#125—614no—
448#125—1228no—
449#125—1222no—
450#123—1228no—
451C22⋊Q8—22no—
452C22⋊Q8—22no—
453C22⋊Q8—41no—
454C22⋊Q8—41no—
455C22⋊Q8—1222no—
456C22⋊Q8—1222no—
457C22⋊Q8—1222no—
458C22⋊Q8—1222no—
459C4×Q8—22no—
460C4×Q8—22no—
461C4×Q8—614no—
462C4×Q8—1222no—
463C4×D4—22no—
464C4×D4—22no—
465#117—1228no—
466#117—1222no—
467#117—1222no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—1222no—
477C2×C4⋊C4—1222no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4—1221no—
484C2×C4⋊C4C22⋊D6111yescharacteristic
485C2×C4⋊C4C22×D6111yescharacteristic
486C2×C4⋊C4C22×D6111yescharacteristic
487C2×C4⋊C4C22×D6111yescharacteristic
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4C22⋊D6111yescharacteristic
496C2×C22⋊C4C22⋊D6111yescharacteristic
497C2×C42—21no—
498C2×C42—1221no—
499C2×C42—1221no—
500C2×C42C22×D6111yescharacteristic
501#107—1222no—
502#106—1222no—
503#106—1222no—
504C4⋊C8—1222no—
505#103—1222no—
506#103—1222no—
507#103—1222no—
508#103—1222no—
509#103—2441no—
510#103—2441no—
511C22⋊C8—1222no—
512C22⋊C8—1222no—
513C22⋊C8—2441no—
514C22⋊C8—2441no—
515#97—1222no—
516#95—21no—
517#95—21no—
518C24C2×C22⋊D6111yescharacteristic
519C24C2×C22⋊D6111yescharacteristic
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—612no—
526C2×Q8—1221no—
527C2×Q8—1221no—
528C2×Q8—1221no—
529C2×Q8—1221no—
530C2×Q8—1221no—
531C2×Q8#1175822412yes—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—41no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—1224no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—2442no—
557C22×C4—2442no—
558C22×C4C2×C22⋊D6111yescharacteristic
559C22×C4C2×C22⋊D6111yescharacteristic
560C22×C4C2×C22⋊D6111yescharacteristic
561C22×C4C2×C22⋊D6111yescharacteristic
562C22×C4C23×D6111yescharacteristic
563Q16—1228no—
564C2×C8—612no—
565C2×C8—1221no—
566C2×C8—1221no—
567C2×C8—1221no—
568C2×C8—1221no—
569C2×C8—1221no—
570C2×C8—1221no—
571C2×C8—1221no—
572C2×C8—1221no—
573C2×C8—1221no—
574C2×C8—1221no—
575C2×C8—1221no—
576C4⋊C4—22no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—81no—
588C4⋊C4—612no—
589C4⋊C4—612no—
590C4⋊C4—612no—
591C4⋊C4—1224no—
592C4⋊C4—1224no—
593C4⋊C4—1224no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1224no—
598C4⋊C4—1224no—
599C4⋊C4—1224no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C22⋊C4—1224no—
607C22⋊C4—1224no—
608C22⋊C4—1224no—
609C42—42no—
610C42—1224no—
611C42—1224no—
612C42D4×D6112yes—
613C42D4×D6112yes—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23#1451980812yes—
628C23C22×C22⋊D6111yescharacteristic
629Q8—22no—
630Q8—22no—
631Q8—41no—
632Q8—41no—
633Q8—1222no—
634Q8—1222no—
635Q8—2441no—
636Q8—2441no—
637D4—44no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—2448no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4#1451974512yes—
682C2×C4#1451974512yes—
683C2×C4C2×D4×D6111yescharacteristic
684C2×C4C2×D4×D6111yescharacteristic
685C2×C4#41×D6111yescharacteristic
686C2×C4C2×#1175822411yescharacteristic
687C2×C4#1451982211yescharacteristic
688C2×C4#1451982411yescharacteristic
689C8—1222no—
690C8—2441no—
691C8—2441no—
692C8—2441no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22C2×#1451974511yescharacteristic
708C22#1684040611yescharacteristic
709C22#1684041111yescharacteristic
710C22C2×#1451980811yescharacteristic
711C22#1684056011yescharacteristic
712C22#1684057311yescharacteristic
713C22#1684057711yescharacteristic
714C4—22no—
715C4—22no—
716C4—41no—
717C4—41no—
718C4—42no—
719C4—81no—
720C4—81no—
721C4—81no—
722C4—2442no—
723C4—2442no—
724C4—2442no—
725C4—2442no—
726C4#1684027211yescharacteristic
727C4#1684034111yescharacteristic
728C4#1684041811yescharacteristic
729C4#1684043011yescharacteristic
730C2—42no—
731C2—81no—
732C2#2144916011yescharacteristic
733C2#2145507711yescharacteristic
734C2#2145513111yescharacteristic
735C2#2145787011yescharacteristic
736C2#2145794511yescharacteristic
737C2#2145826811yescharacteristic
738C2#2145834311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2538C2
socleC23×C61C22×D4
prime radicalC22×D4×C61D4
hypercenter#2538D61
hypocenterC61#24139
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2538

Complements

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

NH ≅ G/Ntype
2. C2×#16840069C2semidirect
3. C2×#16839867C2semidirect
4. #21447022C2semidirect
5. #21447015C2semidirect
6. #21446827C2semidirect
7. #21446827C2semidirect
8. #21446787C2semidirect
10. #21446132C2semidirect
11. #21446127C2semidirect
12. #21446016C2semidirect
13. #21446011C2semidirect
14. #21445821C2semidirect
432. C61#24139semidirect

Maximal subgroups

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

subgroupindex
C2×#168404522
C2×#168400692
C2×#168398672
#214470222
#214470152
#214468272
#214467872
#214466182
#214461322
#214461272
#214460162
#214460112
#214458212
C61×#25382
#2413961