Finite Group Databasebeta

← #29696135

Subgroups — #29696135

Order 15616.

1168 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840299C211yesmaximal, characteristic
2C2×#16839835C211yesmaximal, characteristic, complemented
3C2×#16839832C211yesmaximal, characteristic, complemented
4#21446760C211yesmaximal, characteristic, complemented
5#21446115C211yesmaximal, characteristic, complemented
6#21446115C211yesmaximal, characteristic, complemented
7#21446110C211yesmaximal, characteristic, complemented
8#21446110C211yesmaximal, characteristic, complemented
9#21445889C211yesmaximal, characteristic, complemented
10#21445889C211yesmaximal, characteristic, complemented
11#21445796C211yesmaximal, characteristic, complemented
12#21445582C211yesmaximal, characteristic, complemented
13#21445514C211yesmaximal, characteristic, complemented
14#21445514C211yesmaximal, characteristic, complemented
15C61×#1985C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840299—24no—
21#16840299—24no—
22C2×#14519772C411yescharacteristic
23C2×#14519772C411yescharacteristic
24C2×#14519768C411yescharacteristic
25C2×#14519766C411yescharacteristic
26C2×#14519762C411yescharacteristic
27C2×#14519762C411yescharacteristic
28C2×#14519753C411yescharacteristic
29C2×#14519752C411yescharacteristic
30C2×C4×D244C2211yescharacteristic
31C2×C4×D244C2211yescharacteristic
32C2×C4×D244C2211yescharacteristic
33C2×#14519734C2211yescharacteristic
34C2×#14519734C2211yescharacteristic
35C2×C42×D61C2211yescharacteristic
36#16839835—24no—
37#16839832—24no—
38C2×C4⋊#92418C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41C2×#14519689C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47C2×#14519688C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C2×C4×Q8×C61C2211yescharacteristic
57C2×C4⋊C8×C61C2211yescharacteristic
58C2×#97×C61C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C22×D244C2×C411yescharacteristic
64C22×D244C2×C411yescharacteristic
65C22×D244C2×C411yescharacteristic
66C22×C4×D61C2×C411yescharacteristic
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61C2311yescharacteristic
69C22×C4×D61C2311yescharacteristic
70C22×C4×D61C2311yescharacteristic
71C2×#11758189—22no—
72C2×#11758189—22no—
73C2×#11758189—22no—
74C2×#11758189—22no—
75C2×#11758189—41no—
76C2×#11758189—41no—
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C2×C8×D61—22no—
82C2×C8×D61—22no—
83C2×C8×D61—22no—
84C2×C8×D61—22no—
85C2×C8×D61—41no—
86C2×C8×D61—41no—
87#14519772—24no—
88#14519772—24no—
89#14519768—24no—
90#14519766—24no—
91#14519762—24no—
92#14519762—24no—
93#14519753—24no—
94#14519752—24no—
95C4×D244—22no—
96C4×D244—22no—
97C4×D244—22no—
98C4×D244—22no—
99C4×D244D414yes—
100C4×D244D414yes—
101#14519734—22no—
102#14519734—22no—
103#14519734—22no—
104#14519734—22no—
105C2×C4⋊Dic61C2×C411yescharacteristic
106C2×C4⋊Dic61C2×C411yescharacteristic
107C2×C4⋊Dic61C2×C411yescharacteristic
108C2×#11758196C2×C411yescharacteristic
109C2×#11758196C2×C411yescharacteristic
110C2×#11758196C2×C411yescharacteristic
111C2×#11758196C2×C411yescharacteristic
112C2×#11758198C2×C411yescharacteristic
113C2×#11758198C2×C411yescharacteristic
114C2×#11758198C2×C411yescharacteristic
115C2×#11758198C2×C411yescharacteristic
116C2×#11758198C2×C411yescharacteristic
117C2×#11758198C2×C411yescharacteristic
118C2×#11758198C2×C411yescharacteristic
119C2×#11758198C2×C411yescharacteristic
120C2×#11758198C2×C411yescharacteristic
121C2×#11758198C2×C411yescharacteristic
122C2×C4×Dic61C2×C411yescharacteristic
123C2×C4×Dic61C2×C411yescharacteristic
124C2×C4×Dic61C2311yescharacteristic
125C42×D61—22no—
126C42×D61—22no—
127C4⋊#92418—22no—
128#14519689—22no—
129#14519689—22no—
130#14519689—22no—
131#14519689—22no—
132#14519689—22no—
133#14519689—22no—
134#14519689—41no—
135#14519689—41no—
136#14519688—22no—
137C22×Q8×C61C2×C411yescharacteristic
138C22×C8×C61C2311yescharacteristic
139C22×C8×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141C22×C8×C61C2311yescharacteristic
142C4×Q8×C61—22no—
143C4×Q8×C61—22no—
144C2×C4⋊C4×C61C2×C411yescharacteristic
145C2×C4⋊C4×C61C2×C411yescharacteristic
146C2×C4⋊C4×C61C2×C411yescharacteristic
147C2×C42×C61C2311yescharacteristic
148C2×C42×C61C2311yescharacteristic
149C2×C42×C61C2311yescharacteristic
150C4⋊C8×C61—22no—
151#97×C61—22no—
152C23×D61C22×C411yescharacteristic
153C23×D61C22×C411yescharacteristic
154C23×D61C22×C411yescharacteristic
155C2×Q8×C61—22no—
156C2×Q8×C61—41no—
157C2×Q8×C61—41no—
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C2411yescharacteristic
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C22×C411yescharacteristic
168C22×Dic61C22×C411yescharacteristic
169C22×Dic61C22×C411yescharacteristic
170C2×D244—22no—
171C2×D244—22no—
172C2×D244—22no—
173C2×D244—22no—
174C2×D244—41no—
175C2×D244—41no—
176C2×D244—41no—
177C2×D244—41no—
178C2×D244C22⋊C414yes—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—22no—
188C2×C4×D61—22no—
189C2×C4×D61—22no—
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×C4×D61—41no—
197C2×C4×D61—41no—
198C2×C4×D61—41no—
199C2×C4×D61C2×D412yes—
200C2×C4×D61C2×D412yes—
201C2×C4×D61C2×D412yes—
202C2×C4×D61C2×D412yes—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61#4112yes—
215C4⋊C4×C61—22no—
216C4⋊C4×C61—22no—
217C4⋊C4×C61—22no—
218C42×C61—21no—
219C42×C61—21no—
220C42×C61—21no—
221C42×C61—21no—
222C42×C61C2×D412yes—
223C42×C61C2×D412yes—
224#11758198—22no—
225#11758198—22no—
226#11758198—22no—
227#11758198—22no—
228#11758198—22no—
229#11758198—22no—
230#11758198—22no—
231#11758198—22no—
232#11758198C22⋊C414yes—
233#11758198C22⋊C414yes—
234C4⋊Dic61—22no—
235C4⋊Dic61—22no—
236C4⋊Dic61C22⋊C414yes—
237#11758196—22no—
238#11758196—22no—
239#11758196—22no—
240#11758196—22no—
241C4×Dic61—22no—
242C4×Dic61—22no—
243C4×Dic61—21no—
244C4×Dic61—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418#4112yes—
257#11758189—44no—
258#11758189—44no—
259C8×D61—44no—
260C8×D61—44no—
261C23×C61C23×C411yescharacteristic
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61C2×C22⋊C412yes—
281C22×D61C2×C22⋊C412yes—
282C22×D61#13112yes—
283Q8×C61—44no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61C2×C22⋊C412yes—
301C2×C4×C61C2×C22⋊C412yes—
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61H(5,𝔽2)11yescharacteristic
307C2×C4×C612−1+411yescharacteristic
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61C2×C22⋊C412yes—
322C2×Dic61C2×C22⋊C412yes—
323D244—44no—
324D244—44no—
325D244—44no—
326C4×D61—22no—
327C4×D61—22no—
328C4×D61—22no—
329C4×D61—22no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—22no—
333C4×D61—22no—
334C4×D61—44no—
335C4×D61—44no—
336C4×D61—41no—
337C4×D61—41no—
338C4×D61—41no—
339C4×D61—41no—
340C8×C61—22no—
341C8×C61—41no—
342C8×C61—41no—
343C8×C61—41no—
344#92418—22no—
345#92418—41no—
346#92418—41no—
347#92418—41no—
348#22475—611nomaximal, Sylow
349C22×C61C22×C22⋊C411yescharacteristic
350C22×C61C4×#4111yescharacteristic
351C22×C61#52011yescharacteristic
352C22×C61C2×#13111yescharacteristic
353C22×C61#56811yescharacteristic
354C22×C61#56811yescharacteristic
355C22×C61#56811yescharacteristic
356C2×D61—22no—
357C2×D61—22no—
358C2×D61—22no—
359C2×D61—22no—
360C2×D61—22no—
361C2×D61—22no—
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—22no—
365C2×D61—41no—
366C2×D61—41no—
367C2×D61—41no—
368C2×D61—41no—
369C2×D61—41no—
370C2×D61—41no—
371C2×D61—41no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61—41no—
375C2×D61—41no—
376C2×D61—41no—
377C4×C61—22no—
378C4×C61—22no—
379C4×C61—41no—
380C4×C61—41no—
381C4×C61—41no—
382C4×C61—41no—
383C4×C61#54611yescharacteristic
384C4×C61#54611yescharacteristic
385C4×C61#54711yescharacteristic
386C4×C61#54711yescharacteristic
387Dic61—22no—
388Dic61—22no—
389Dic61—41no—
390Dic61—41no—
391Dic61—41no—
392C2×#529—611no—
393C2×#435—611no—
394C2×#435—611no—
395#1985—611no—
396#1985D6111yescharacteristic, complemented
397#1870—611no—
398#1870—611no—
399#1869—611no—
400#1869—611no—
401#1818—611no—
402#1818—611no—
403#1797—611no—
404#1749—611no—
405#1729—611no—
406#1729—611no—
407C2×C61#233911yescharacteristic
408C2×C61#287911yescharacteristic
409C2×C61#288011yescharacteristic
410C2×C61#296711yescharacteristic
411C2×C61#296811yescharacteristic
412C2×C61#299211yescharacteristic
413C2×C61#299511yescharacteristic
414D61—42no—
415D61—42no—
416D61—42no—
417C22×M16—611no—
418C22×M16—611no—
419C23×C8—611no—
420C23×C8—611no—
421#529—1224no—
422#529—1224no—
423C2×#126—611no—
424C2×#126—611no—
425C2×#125—611no—
426C2×#124—611no—
427C2×#123—611no—
428C2×#123—611no—
429C2×C22⋊Q8—611no—
430C2×#121—611no—
431C2×C4×Q8C2×D6111yescharacteristic
432C2×C4×D4—611no—
433C2×C4×D4—611no—
434C2×C4×D4—611no—
435C2×#117—611no—
436C2×#117—611no—
437C22×C42—611no—
438#435—1224no—
439#435—1224no—
440C2×C4⋊C8—611no—
441C2×C4⋊C8C2×D6111yescharacteristic
442C2×C22⋊C8—611no—
443C2×C22⋊C8—611no—
444C2×C22⋊C8—611no—
445C2×C22⋊C8—611no—
446C2×C22⋊C8—611no—
447C2×C22⋊C8—611no—
448C2×C22⋊C8—611no—
449C2×C22⋊C8—611no—
450C2×#97—611no—
451C2×#97C2×D6111yescharacteristic
452#336—611no—
453#336—611no—
454#336—611no—
455#336—611no—
456#336—611no—
457#336—611no—
458#336—611no—
459#336—611no—
460#336C2×D6111yescharacteristic
461#336C2×D6111yescharacteristic
462#336C2×D6111yescharacteristic
463#336C2×D6111yescharacteristic
464C61#2247511yescharacteristic, complemented, Sylow
465C22×Q8C4×D6111yescharacteristic
466C22×D4—611no—
467C22×D4—611no—
468C22×D4—611no—
469C23×C4—611no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—611no—
473C23×C4—611no—
474C2×M16—1222no—
475C2×M16—1222no—
476C2×M16—1222no—
477C2×M16—1222no—
478C2×M16—2441no—
479C2×M16—2441no—
480C22×C8—611no—
481C22×C8—611no—
482C22×C8—611no—
483C22×C8—611no—
484C22×C8—1222no—
485C22×C8—1222no—
486C22×C8—1222no—
487C22×C8—1222no—
488C22×C8—2441no—
489C22×C8—2441no—
490C22×C8C22×D6111yescharacteristic
491C22×C8C22×D6111yescharacteristic
492C22×C8C22×D6111yescharacteristic
493C22×C8C22×D6111yescharacteristic
494#126—1224no—
495#126—1224no—
496#125—1224no—
497#124—1224no—
498#123—1224no—
499#123—1224no—
500C22⋊Q8—1224no—
501#121—1224no—
502C4×Q8—22no—
503C4×Q8—22no—
504C4×D4—614no—
505C4×D4—614no—
506C4×D4—1222no—
507C4×D4—1222no—
508C4×D4—1222no—
509C4×D4—1222no—
510#117—1222no—
511#117—1222no—
512#117—1222no—
513#117—1222no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—611no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4C4×D6111yescharacteristic
522C2×C4⋊C4C4×D6111yescharacteristic
523C2×C4⋊C4C4×D6111yescharacteristic
524C2×C22⋊C4—611no—
525C2×C22⋊C4—611no—
526C2×C22⋊C4—611no—
527C2×C22⋊C4—611no—
528C2×C22⋊C4—611no—
529C2×C22⋊C4—611no—
530C2×C22⋊C4—611no—
531C2×C22⋊C4—611no—
532C2×C22⋊C4—611no—
533C2×C22⋊C4—611no—
534C2×C42—611no—
535C2×C42—611no—
536C2×C42—611no—
537C2×C42—1222no—
538C2×C42—1222no—
539C2×C42C22×D6111yescharacteristic
540C2×C42C22×D6111yescharacteristic
541C2×C42C22×D6111yescharacteristic
542C4⋊C8—22no—
543C4⋊C8—1222no—
544C22⋊C8—1222no—
545C22⋊C8—1222no—
546C22⋊C8—1222no—
547C22⋊C8—1222no—
548C22⋊C8—1222no—
549C22⋊C8—1222no—
550C22⋊C8—2441no—
551C22⋊C8—2441no—
552#97—22no—
553#97—1222no—
554C24—611no—
555C24—611no—
556C24—611no—
557C2×Q8—22no—
558C2×Q8—41no—
559C2×Q8—41no—
560C2×D4—614no—
561C2×D4—1222no—
562C2×D4—1222no—
563C2×D4—1222no—
564C2×D4—1222no—
565C2×D4—2441no—
566C2×D4—2441no—
567C2×D4—2441no—
568C2×D4—2441no—
569C22×C4—611no—
570C22×C4—611no—
571C22×C4—612no—
572C22×C4—612no—
573C22×C4—612no—
574C22×C4—612no—
575C22×C4—611no—
576C22×C4—611no—
577C22×C4—611no—
578C22×C4—1222no—
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×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—2441no—
596C22×C4—2441no—
597C22×C4—2441no—
598C22×C4C2×C4×D6111yescharacteristic
599C22×C4C2×C4×D6111yescharacteristic
600C22×C4C2×C4×D6111yescharacteristic
601C22×C4C2×C4×D6111yescharacteristic
602C22×C4C2×C4×D6111yescharacteristic
603C22×C4C2×C4×D6111yescharacteristic
604C22×C4C23×D6111yescharacteristic
605M16—2444no—
606M16—2444no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—612no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1221no—
628C2×C8—1221no—
629C2×C8—1221no—
630C2×C8—2444no—
631C2×C8—2444no—
632C2×C8#1175822612yes—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—614no—
637C4⋊C4—1222no—
638C4⋊C4—1222no—
639C4⋊C4—1222no—
640C4⋊C4—1222no—
641C4⋊C4—1222no—
642C4⋊C4—1222no—
643C22⋊C4—614no—
644C22⋊C4—614no—
645C22⋊C4—1222no—
646C22⋊C4—1222no—
647C22⋊C4—1222no—
648C22⋊C4—1222no—
649C22⋊C4—1222no—
650C22⋊C4—1222no—
651C22⋊C4—1222no—
652C22⋊C4—1222no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—1221no—
658C42—1221no—
659C42—1222no—
660C42—1222no—
661C42D4×D6112yes—
662C42D4×D6112yes—
663C23—612no—
664C23—612no—
665C23—612no—
666C23—1221no—
667C23—1221no—
668C23—1221no—
669C23—1221no—
670C23—1221no—
671C23—1221no—
672C23—1221no—
673C23—1221no—
674C23—1221no—
675C23—1221no—
676C23—1221no—
677C23—1221no—
678C23—1221no—
679C23—1221no—
680C23—1221no—
681C23—1221no—
682C23—1221no—
683C23—1221no—
684C23C22×C4×D6111yescharacteristic
685Q8—44no—
686D4—2444no—
687D4—2444no—
688D4—2444no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—612no—
706C2×C4—612no—
707C2×C4—1221no—
708C2×C4—1221no—
709C2×C4—1221no—
710C2×C4—1221no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—1221no—
726C2×C4—1221no—
727C2×C4—1221no—
728C2×C4—2444no—
729C2×C4—2444no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4C22⋊C4×D6112yes—
735C2×C4C22⋊C4×D6112yes—
736C2×C4C2×D4×D6111yescharacteristic
737C2×C4C2×D4×D6111yescharacteristic
738C2×C4#41×D6111yescharacteristic
739C2×C4C2×#1175822611yescharacteristic
740C2×C4#1451982311yescharacteristic
741C2×C4#1451982511yescharacteristic
742C8—22no—
743C8—41no—
744C8—41no—
745C8—41no—
746C8—1222no—
747C8—2441no—
748C8—2441no—
749C8—2441no—
750C22—1222no—
751C22—1222no—
752C22—1222no—
753C22—1222no—
754C22—1222no—
755C22—1222no—
756C22—1222no—
757C22—1222no—
758C22—1222no—
759C22—2441no—
760C22—2441no—
761C22—2441no—
762C22—2441no—
763C22—2441no—
764C22—2441no—
765C22—2441no—
766C22—2441no—
767C22—2441no—
768C22—2441no—
769C22—2441no—
770C22—2441no—
771C22C2×C22⋊C4×D6111yescharacteristic
772C22C4×#1175822611yescharacteristic
773C22#1684024411yescharacteristic
774C22#131×D6111yescharacteristic
775C22#1684052711yescharacteristic
776C22#1684052811yescharacteristic
777C22#1684052811yescharacteristic
778C4—22no—
779C4—22no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—1222no—
785C4—1222no—
786C4—2441no—
787C4—2441no—
788C4—2441no—
789C4#1684040311yescharacteristic
790C4#1684040511yescharacteristic
791C4#1684041411yescharacteristic
792C4#1684041511yescharacteristic
793C2—2442no—
794C2—2442no—
795C2—2442no—
796C2#2144864811yescharacteristic
797C2#2145426211yescharacteristic
798C2#2145426711yescharacteristic
799C2#2145480311yescharacteristic
800C2#2145481211yescharacteristic
801C2#2145495711yescharacteristic
802C2#2145498811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1985C2
prime radicalC2×#14519752C4
cosocleC22×C4×C61C24
hypercenter#1985D61
hypocenterC61#22475
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1985

Complements

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

NH ≅ G/Ntype
2. C2×#16839835C2semidirect
3. C2×#16839832C2semidirect
4. #21446760C2semidirect
5. #21446115C2semidirect
6. #21446115C2semidirect
7. #21446110C2semidirect
8. #21446110C2semidirect
9. #21445889C2semidirect
10. #21445889C2semidirect
11. #21445796C2semidirect
12. #21445582C2semidirect
13. #21445514C2semidirect
14. #21445514C2semidirect
15. C61×#1985C2semidirect
396. #1985D61semidirect
464. C61#22475semidirect

Maximal subgroups

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

subgroupindex
C2×#168402992
C2×#168398352
C2×#168398322
#214467602
#214461152
#214461102
#214458892
#214457962
#214455822
#214455142
C61×#19852
#2247561