Finite Group Databasebeta

← #29733246

Subgroups — #29733246

Order 15616.

1170 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840470C211yesmaximal, 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#21446765C211yesmaximal, characteristic, complemented
9#21446611C211yesmaximal, characteristic
10#21446127C211yesmaximal, characteristic, complemented
11#21446125C211yesmaximal, characteristic, complemented
12#21446124C211yesmaximal, characteristic, complemented
13#21446123C211yesmaximal, characteristic, complemented
14#103×Dic61C211yesmaximal, characteristic, complemented
15C61×#2001C211yesmaximal, characteristic, complemented
16C22×#11758202C2211yescharacteristic
17#16840470—24no—
18#16840470—24no—
19C2×#14519776C2211yescharacteristic
20C2×#14519775C2211yescharacteristic
21C2×#14519767—21no—
22C2×#14519757—21no—
23C2×#14519757C2211yescharacteristic
24C2×#14519756C2211yescharacteristic
25C2×#14519754—21no—
26C2×#14519753C2211yescharacteristic
27C2×#14519753C2211yescharacteristic
28C2×Q8×Dic61C2211yescharacteristic
29C2×C4×C22⋊D61C2211yescharacteristic
30C2×#14519737—21no—
31C22×C4⋊Dic61C2211yescharacteristic
32C2×C4⋊C4×D61C2211yescharacteristic
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
66C23×Dic61—21no—
67C22×C4×D61—21no—
68C22×C4×D61C2311yescharacteristic
69C2×#11758202—22no—
70C2×#11758202—41no—
71C2×#11758202—41no—
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74#14519776—22no—
75#14519776D414yes—
76#14519775—22no—
77#14519775—22no—
78#14519767—28no—
79#14519757—28no—
80#14519757—22no—
81#14519757—41no—
82#14519756—22no—
83#14519756—41no—
84#14519754—28no—
85#14519753—22no—
86#14519753—22no—
87#14519753—22no—
88#14519753—41no—
89Q8×Dic61—22no—
90Q8×Dic61D414yes—
91C4×C22⋊D61—22no—
92C4×C22⋊D61—22no—
93#14519737—28no—
94C2×C4⋊Dic61—21no—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61—22no—
97C2×C4⋊Dic61—22no—
98C2×C4⋊Dic61—21no—
99C2×C4⋊Dic61C2311yescharacteristic
100C2×C4⋊Dic61C2311yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×#11758196D411yescharacteristic
110C4⋊C4×D61—22no—
111C4⋊C4×D61—22no—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61D411yescharacteristic
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198D411yescharacteristic
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⋊D61Q1614yescomplemented
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—24no—
187C22×Dic61—21no—
188C22×Dic61—81no—
189C22×Dic61—81no—
190C22×Dic61C2×D411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192C22×Dic61C2×D411yescharacteristic
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—24no—
200C2×C4×D61—81no—
201C2×C4×D61—81no—
202C2×Dic122—21no—
203C2×Dic122—21no—
204C2×Dic122—21no—
205C2×Dic122—21no—
206C2×Dic122—21no—
207C2×Dic122—21no—
208C2×Dic122—24no—
209C2×Dic122—81no—
210C2×Dic122—81no—
211Q16×C61—44no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C4⋊C4×C61—24no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—42no—
222C4⋊C4×C61C2×D412yes—
223C4⋊C4×C61#4112yes—
224C22⋊C4×C61—24no—
225C22⋊C4×C61—42no—
226C22⋊Dic61—22no—
227C22⋊Dic61—42no—
228#11758202—44no—
229#11758198—24no—
230#11758198—22no—
231#11758198—42no—
232#11758198—42no—
233C4⋊Dic61—24no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—24no—
238C4⋊Dic61—42no—
239C4⋊Dic61C2×D412yes—
240C4⋊Dic61C2×D412yes—
241C4⋊Dic61#4112yes—
242#11758196—24no—
243#11758196—24no—
244#11758196—24no—
245#11758196—22no—
246#11758196—42no—
247#11758196—42no—
248#11758196—42no—
249#11758196—42no—
250C4×Dic61—24no—
251C4×Dic61—42no—
252C4×Dic61C2×D412yes—
253C4×Dic61C2×D412yes—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61C2×Q1612yes—
267C23×C61C22×D411yescharacteristic
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—21no—
274C22×D61C2×Q1612yes—
275Q8×C61—22no—
276Q8×C61—22no—
277Q8×C61—41no—
278Q8×C61—41no—
279Q8×C61—41no—
280Q8×C61—41no—
281Q8×C61—41no—
282Q8×C61—41no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—22no—
288C2×C4×C61—21no—
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×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61H(5,𝔽2)11yescharacteristic
307C2×C4×C61H(5,𝔽2)11yescharacteristic
308C22⋊D61—28no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—22no—
312C2×Dic61—21no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—84no—
327C2×Dic61#12012yes—
328C2×Dic61#12012yes—
329C2×Dic61C2×Q1612yes—
330C2×Dic61#13712yes—
331C4×D61—41no—
332C4×D61—41no—
333C4×D61—41no—
334C4×D61—41no—
335C4×D61—84no—
336Dic122—41no—
337Dic122—41no—
338Dic122—41no—
339Dic122—41no—
340Dic122—84no—
341C8×C61—41no—
342C8×C61—41no—
343#92418—41no—
344#92418—41no—
345#25573—611nomaximal, Sylow
346C22×C61—22no—
347C22×C61—22no—
348C22×C61—22no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61C2×#12011yescharacteristic
354C22×C61#54611yescharacteristic
355C22×C61#54611yescharacteristic
356C22×C61C22×Q1611yescharacteristic
357C22×C61C2×#13711yescharacteristic
358C22×C61#57711yescharacteristic
359C22×C61#57711yescharacteristic
360C2×D61—22no—
361C2×D61—22no—
362C2×D61—22no—
363C2×D61—41no—
364C2×D61—41no—
365C2×D61—41no—
366C2×D61—41no—
367C4×C61—42no—
368C4×C61—41no—
369C4×C61—42no—
370C4×C61—42no—
371C4×C61—81no—
372C4×C61#53211yescharacteristic
373C4×C61#53511yescharacteristic
374C4×C61#55011yescharacteristic
375C4×C61#55011yescharacteristic
376Dic61—22no—
377Dic61—42no—
378Dic61—41no—
379Dic61—42no—
380Dic61—42no—
381Dic61—81no—
382Dic61#45114yes—
383C2×#554—611no—
384C2×#487—611no—
385C2×#462—611no—
386#2542—611no—
387#2001—611no—
388#2001—611no—
389#2001—611no—
390#2001D6111yescharacteristic, complemented
391#1987—611no—
392#1954—611no—
393#1872—611no—
394#1872—611no—
395#1872—611no—
396#1872—611no—
397C4×#103—611no—
398C2×C61—42no—
399C2×C61#243111yescharacteristic
400C2×C61C2×#45111yescharacteristic
401C2×C61#300911yescharacteristic
402C2×C61#329911yescharacteristic
403C2×C61#329911yescharacteristic
404C2×C61#333111yescharacteristic
405C2×C61#333111yescharacteristic
406D61—42no—
407C22×Q16—611no—
408C22×Q16C2×D6111yescharacteristic
409#554—1224no—
410#554—1224no—
411C2×C4⋊Q8—611no—
412C2×C4⋊Q8—611no—
413C2×#125—1221no—
414C2×C22⋊Q8—611no—
415C2×C22⋊Q8—611no—
416C2×C22⋊Q8—611no—
417C2×C22⋊Q8—611no—
418C2×C22⋊Q8—1221no—
419C2×C22⋊Q8—1221no—
420C2×C22⋊Q8C2×D6111yescharacteristic
421C2×C22⋊Q8C2×D6111yescharacteristic
422C2×C4×Q8—611no—
423C2×C4×D4—611no—
424C2×C4×D4—1221no—
425C22×C4⋊C4—611no—
426C22×C4⋊C4—611no—
427#487—1224no—
428#462—1224no—
429C2×C4⋊C8—611no—
430C2×#103—611no—
431C2×#103—611no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#103—611no—
435C2×#103—611no—
436C2×#103C2×D6111yescharacteristic
437C2×#103C2×D6111yescharacteristic
438C2×C22⋊C8—611no—
439C2×C22⋊C8—611no—
440C2×C22⋊C8—611no—
441C2×C22⋊C8C2×D6111yescharacteristic
442C2×C4×C8—611no—
443#399—1221no—
444#399—1221no—
445#390—1221no—
446#384—1221no—
447C4×C4⋊C4—611no—
448#340—611no—
449#340—611no—
450#340—611no—
451#340—611no—
452#340—611no—
453#340C2×D6111yescharacteristic
454C61#2557311yescharacteristic, complemented, Sylow
455C22×Q8—611no—
456C22×Q8—1221no—
457C22×Q8C22×D6111yescharacteristic
458C22×Q8C22×D6111yescharacteristic
459C22×D4—611no—
460C23×C4—611no—
461C23×C4—1221no—
462C23×C4—1221no—
463C23×C4C22×D6111yescharacteristic
464C2×Q16—22no—
465C2×Q16—41no—
466C2×Q16—41no—
467C2×Q16—1222no—
468C2×Q16—2441no—
469C2×Q16—2441no—
470C22×C8—611no—
471C22×C8—611no—
472C22×C8C22×D6111yescharacteristic
473C22×C8C22×D6111yescharacteristic
474C4⋊Q8—614no—
475C4⋊Q8—1222no—
476C4⋊Q8—1222no—
477C4⋊Q8—1222no—
478#125—1228no—
479C22⋊Q8—22no—
480C22⋊Q8—22no—
481C22⋊Q8—22no—
482C22⋊Q8—41no—
483C22⋊Q8—1228no—
484C22⋊Q8—1228no—
485C22⋊Q8—1222no—
486C22⋊Q8—1222no—
487C22⋊Q8—1222no—
488C22⋊Q8—1222no—
489C22⋊Q8—1222no—
490C22⋊Q8—2441no—
491C22⋊Q8—2441no—
492C22⋊Q8—2441no—
493C4×Q8—614no—
494C4×Q8—1222no—
495C4×D4—1222no—
496C4×D4—1222no—
497C4×D4—1228no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—1222no—
505C2×C4⋊C4—1222no—
506C2×C4⋊C4—1222no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1222no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4C22×D6111yescharacteristic
519C2×C4⋊C4C22×D6111yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—611no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C42—611no—
529C2×C42—1221no—
530C2×C42—1221no—
531C4⋊C8—1222no—
532#103—22no—
533#103—22no—
534#103—1222no—
535#103—1222no—
536#103—1222no—
537#103—1222no—
538#103—1222no—
539#103—1222no—
540C22⋊C8—41no—
541C22⋊C8—2441no—
542C22⋊C8—2441no—
543C22⋊C8—2441no—
544C4×C8—1222no—
545#95—1221no—
546C24—611no—
547C24D4×D6111yescharacteristic
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—1224no—
560C2×Q8—1221no—
561C2×Q8—1221no—
562C2×Q8—1221no—
563C2×Q8—1221no—
564C2×Q8—1221no—
565C2×Q8—1221no—
566C2×Q8—4881no—
567C2×Q8—4881no—
568C2×Q8D4×D6112yes—
569C2×D4—614no—
570C2×D4—1222no—
571C2×D4—1222no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—1224no—
586C22×C4—1224no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—4881no—
598C22×C4—4881no—
599C22×C4—4881no—
600C22×C4—4881no—
601C22×C4D4×D6111yescharacteristic
602C22×C4C23×D6111yescharacteristic
603Q16—44no—
604Q16—2444no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—42no—
621C4⋊C4—612no—
622C4⋊C4—612no—
623C4⋊C4—612no—
624C4⋊C4—1222no—
625C4⋊C4—1224no—
626C4⋊C4—1224no—
627C4⋊C4—1224no—
628C4⋊C4—1224no—
629C4⋊C4—1224no—
630C4⋊C4—1221no—
631C4⋊C4—1221no—
632C4⋊C4—1221no—
633C4⋊C4—2442no—
634C4⋊C4—2442no—
635C4⋊C4—2442no—
636C4⋊C4—2442no—
637C4⋊C4—2442no—
638C4⋊C4D4×D6112yes—
639C4⋊C4#1175822412yes—
640C22⋊C4—24no—
641C22⋊C4—42no—
642C22⋊C4—1222no—
643C22⋊C4—1224no—
644C22⋊C4—1222no—
645C22⋊C4—2442no—
646C22⋊C4—2442no—
647C22⋊C4—2442no—
648C42—612no—
649C42—612no—
650C42—1224no—
651C42—2442no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—612no—
659C23—1221no—
660C23—1221no—
661C23—1221no—
662C23—1221no—
663C23—1221no—
664C23—1221no—
665C23Q16×D6112yes—
666C23C2×D4×D6111yescharacteristic
667Q8—22no—
668Q8—22no—
669Q8—41no—
670Q8—41no—
671Q8—41no—
672Q8—41no—
673Q8—41no—
674Q8—41no—
675Q8—4884no—
676Q8—2441no—
677Q8—2441no—
678Q8—2441no—
679Q8—2441no—
680D4—1228no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—612no—
701C2×C4—612no—
702C2×C4—612no—
703C2×C4—612no—
704C2×C4—1221no—
705C2×C4—1221no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—1221no—
709C2×C4—1221no—
710C2×C4—1222no—
711C2×C4—1221no—
712C2×C4—4884no—
713C2×C4—4884no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4C2×D4×D6111yescharacteristic
728C2×C4C2×D4×D6111yescharacteristic
729C2×C4#41×D6111yescharacteristic
730C2×C4C2×#1175822411yescharacteristic
731C2×C4#1451982211yescharacteristic
732C2×C4#1451982211yescharacteristic
733C8—41no—
734C8—41no—
735C8—2441no—
736C8—2441no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—1222no—
745C22—1222no—
746C22—1222no—
747C22—2441no—
748C22—2441no—
749C22—2441no—
750C22—2441no—
751C22#120×D6111yescharacteristic
752C22#1684039911yescharacteristic
753C22#1684040111yescharacteristic
754C22C2×Q16×D6111yescharacteristic
755C22#137×D6111yescharacteristic
756C22#1684056911yescharacteristic
757C22#1684057111yescharacteristic
758C4—42no—
759C4—41no—
760C4—42no—
761C4—42no—
762C4—81no—
763C4—614no—
764C4—1222no—
765C4—4881no—
766C4—2442no—
767C4—2441no—
768C4—2442no—
769C4—2442no—
770C4#1684030711yescharacteristic
771C4#1684032711yescharacteristic
772C4#1684043011yescharacteristic
773C4#1684043211yescharacteristic
774C2—42no—
775C2—2442no—
776C2#2144943311yescharacteristic
777C2#451×D6111yescharacteristic
778C2#2145509311yescharacteristic
779C2#2145768811yescharacteristic
780C2#2145769011yescharacteristic
781C2#2145812811yescharacteristic
782C2#2145813011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2001C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenter#2001D61
hypocenterC61#25573
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. #21446765C2semidirect
10. #21446127C2semidirect
11. #21446125C2semidirect
12. #21446124C2semidirect
13. #21446123C2semidirect
14. #103×Dic61C2semidirect
15. C61×#2001C2semidirect
182. C2×C22⋊D61Q16semidirect
390. #2001D61semidirect
454. C61#25573semidirect

Maximal subgroups

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

subgroupindex
C2×#168404702
C2×#168401112
C2×#168399702
#214507692
#214468282
#214468272
#214468262
#214467652
#214466112
#214461272
#214461252
#214461242
#214461232
#103×Dic612
C61×#20012
#2557361