Finite Group Databasebeta

← #29696750

Subgroups — #29696750

Order 15616.

1108 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840299C211yesmaximal, characteristic
2C2×#16839893C211yesmaximal, characteristic, complemented
3#21446617C211yesmaximal, characteristic, complemented
4#21446617C211yesmaximal, characteristic, complemented
5#21446616C211yesmaximal, characteristic, complemented
6#21446616C211yesmaximal, characteristic, complemented
7#21446613C211yesmaximal, characteristic, complemented
8#21446612C211yesmaximal, characteristic, complemented
9#21445800C211yesmaximal, characteristic, complemented
10#21445800C211yesmaximal, characteristic, complemented
11#21445796C211yesmaximal, characteristic, complemented
12#21445588C211yesmaximal, characteristic, complemented
13#21445586C211yesmaximal, characteristic, complemented
14#21445582C211yesmaximal, characteristic, complemented
15C2×C61×#446C211yesmaximal, characteristic, complemented
16#16840299—24no—
17#16840299—24no—
18C2×#14519772C411yescharacteristic
19C2×#14519772C411yescharacteristic
20C2×#14519768C411yescharacteristic
21C2×#14519766C411yescharacteristic
22C2×#14519762C411yescharacteristic
23C2×#14519762C411yescharacteristic
24C2×#14519753C411yescharacteristic
25C2×#14519752C411yescharacteristic
26C2×C4×D244C2211yescharacteristic
27C2×C4×D244C2211yescharacteristic
28C2×C4×D244C2211yescharacteristic
29C2×#14519734C2211yescharacteristic
30C2×#14519734C2211yescharacteristic
31C2×C42×D61C2211yescharacteristic
32#16839893—24no—
33C2×C4⋊#92418C2211yescharacteristic
34C2×C4⋊#92418C2211yescharacteristic
35C2×C4⋊#92418C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C2×#14519689C2211yescharacteristic
38C2×#14519689C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41C2×#14519689C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47C2×#14519689C2211yescharacteristic
48C2×#14519688C2211yescharacteristic
49C2×#14519688C2211yescharacteristic
50C2×C4×#92418C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55C2×C4×Q8×C61C2211yescharacteristic
56C61×#446—24no—
57C2×C4⋊C8×C61C2211yescharacteristic
58C2×C4⋊C8×C61C2211yescharacteristic
59C2×C4⋊C8×C61C2211yescharacteristic
60C2×#97×C61C2211yescharacteristic
61C2×#97×C61C2211yescharacteristic
62C2×C4×C8×C61C2211yescharacteristic
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
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75#14519772—24no—
76#14519772—24no—
77#14519768—24no—
78#14519766—24no—
79#14519762—24no—
80#14519762—24no—
81#14519753—24no—
82#14519752—24no—
83C4×D244—22no—
84C4×D244—22no—
85C4×D244—22no—
86C4×D244—22no—
87C4×D244—22no—
88C4×D244—22no—
89#14519734—22no—
90#14519734—22no—
91#14519734—22no—
92#14519734—22no—
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×C4⋊Dic61C2×C411yescharacteristic
95C2×C4⋊Dic61C2×C411yescharacteristic
96C2×#11758196C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×#11758196C2×C411yescharacteristic
99C2×#11758196C2×C411yescharacteristic
100C2×#11758198C2×C411yescharacteristic
101C2×#11758198C2×C411yescharacteristic
102C2×#11758198C2×C411yescharacteristic
103C2×#11758198C2×C411yescharacteristic
104C2×#11758198C2×C411yescharacteristic
105C2×#11758198C2×C411yescharacteristic
106C2×#11758198C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×#11758198C2×C411yescharacteristic
109C2×#11758198C2×C411yescharacteristic
110C2×C4×Dic61C2×C411yescharacteristic
111C2×C4×Dic61C2×C411yescharacteristic
112C2×C4×Dic61C2311yescharacteristic
113C42×D61—22no—
114C42×D61—22no—
115C4⋊#92418—22no—
116C4⋊#92418—22no—
117C4⋊#92418—22no—
118#14519689—22no—
119#14519689—22no—
120#14519689—22no—
121#14519689—22no—
122#14519689—22no—
123#14519689—22no—
124#14519689—41no—
125#14519689—41no—
126#14519689—41no—
127#14519689—41no—
128#14519689—41no—
129#14519689—41no—
130#14519688—22no—
131#14519688—22no—
132C4×#92418—22no—
133C22×Q8×C61C2×C411yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C22×C8×C61C2311yescharacteristic
136C22×C8×C61C2311yescharacteristic
137C22×C8×C61C2311yescharacteristic
138C4×Q8×C61D414yes—
139C4×Q8×C61D414yes—
140C2×C4⋊C4×C61C2×C411yescharacteristic
141C2×C4⋊C4×C61C2×C411yescharacteristic
142C2×C4⋊C4×C61C2×C411yescharacteristic
143C2×C42×C61C2311yescharacteristic
144C2×C42×C61C2311yescharacteristic
145C2×C42×C61C2311yescharacteristic
146C4⋊C8×C61—22no—
147C4⋊C8×C61—22no—
148C4⋊C8×C61—22no—
149#97×C61—22no—
150#97×C61—22no—
151C4×C8×C61—22no—
152C23×D61C22×C411yescharacteristic
153C23×D61C22×C411yescharacteristic
154C23×D61C22×C411yescharacteristic
155C2×Q8×C61—41no—
156C2×Q8×C61—41no—
157C2×Q8×C61C22⋊C414yes—
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—22no—
175C2×D244—41no—
176C2×D244—41no—
177C2×D244—41no—
178C2×D244—41no—
179C2×C4×D61—22no—
180C2×C4×D61—22no—
181C2×C4×D61—22no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
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×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—21no—
200C2×C4×D61—41no—
201C2×C4×D61—41no—
202C2×C4×D61—41no—
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×C61C22⋊C414yes—
216C4⋊C4×C61C22⋊C414yes—
217C4⋊C4×C61C22⋊C414yes—
218C42×C61C2×D412yes—
219C42×C61C2×D412yes—
220C42×C61C2×D412yes—
221C42×C61C2×D412yes—
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#11758198—22no—
233#11758198—22no—
234C4⋊Dic61—22no—
235C4⋊Dic61—22no—
236C4⋊Dic61—22no—
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—
257C23×C61C23×C411yescharacteristic
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
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#13112yes—
279Q8×C61—44no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
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×C61C2×C22⋊C412yes—
293C2×C4×C61C2×C22⋊C412yes—
294C2×C4×C61C2×C22⋊C412yes—
295C2×C4×C61C2×C22⋊C412yes—
296C2×C4×C61C2×C22⋊C412yes—
297C2×C4×C61C2×C22⋊C412yes—
298C2×C4×C61C22×D411yescharacteristic
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C2×#4111yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61H(5,𝔽2)11yescharacteristic
303C2×C4×C612−1+411yescharacteristic
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
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—
319D244—44no—
320D244—44no—
321D244—44no—
322C4×D61—44no—
323C4×D61—44no—
324C4×D61—41no—
325C4×D61—41no—
326C4×D61—41no—
327C4×D61—41no—
328C4×D61—41no—
329C4×D61—41no—
330C4×D61—41no—
331C4×D61—41no—
332C4×D61—41no—
333C4×D61—41no—
334C4×D61—41no—
335C4×D61—41no—
336C8×C61—22no—
337C8×C61—41no—
338C8×C61—41no—
339C8×C61—41no—
340#92418—22no—
341#92418—41no—
342#92418—41no—
343#92418—41no—
344#22533—611nomaximal, Sylow
345C22×C61C22×C22⋊C411yescharacteristic
346C22×C61C4×#4111yescharacteristic
347C22×C61#52011yescharacteristic
348C22×C61C2×#13111yescharacteristic
349C22×C61#56811yescharacteristic
350C22×C61#56811yescharacteristic
351C22×C61#56811yescharacteristic
352C2×D61—22no—
353C2×D61—22no—
354C2×D61—22no—
355C2×D61—41no—
356C2×D61—41no—
357C2×D61—41no—
358C2×D61—41no—
359C2×D61—41no—
360C2×D61—41no—
361C2×D61—41no—
362C2×D61—41no—
363C2×D61—41no—
364C2×D61—41no—
365C2×D61—41no—
366C2×D61—41no—
367C2×D61—41no—
368C2×D61—41no—
369C2×D61—41no—
370C2×D61—41no—
371C2×D61—41no—
372C2×D61—41no—
373C4×C61—22no—
374C4×C61—22no—
375C4×C61—22no—
376C4×C61—22no—
377C4×C61—22no—
378C4×C61—22no—
379C4×C61#54811yescharacteristic
380C4×C61#54811yescharacteristic
381C4×C61#55011yescharacteristic
382C4×C61#55011yescharacteristic
383Dic61—41no—
384Dic61—41no—
385Dic61—41no—
386Dic61—41no—
387Dic61—41no—
388C2×#529—611no—
389C2×#446—611no—
390C2×#446D6111yescharacteristic, complemented
391#1955—611no—
392#1955—611no—
393#1955—611no—
394#1955—611no—
395#1954—611no—
396#1954—611no—
397#1798—611no—
398#1798—611no—
399#1797—611no—
400#1750—611no—
401#1750—611no—
402#1749—611no—
403C2×C61#234111yescharacteristic
404C2×C61#287911yescharacteristic
405C2×C61#288011yescharacteristic
406C2×C61#296711yescharacteristic
407C2×C61#296811yescharacteristic
408C2×C61#299211yescharacteristic
409C2×C61#299511yescharacteristic
410D61—42no—
411D61—81no—
412D61—81no—
413#529—1224no—
414#529—1224no—
415C2×#126—611no—
416C2×#126—611no—
417C2×#125—611no—
418C2×#124—611no—
419C2×#123—611no—
420C2×#123—611no—
421C2×C22⋊Q8—611no—
422C2×#121—611no—
423C2×C4×Q8C2×D6111yescharacteristic
424C2×C4×D4—611no—
425C2×C4×D4—611no—
426C2×C4×D4—611no—
427C2×#117—611no—
428C2×#117—611no—
429C22×C42—611no—
430#446—24no—
431#446—1224no—
432C2×C4⋊C8—611no—
433C2×C4⋊C8—611no—
434C2×C4⋊C8—611no—
435C2×C4⋊C8C2×D6111yescharacteristic
436C2×C4⋊C8C2×D6111yescharacteristic
437C2×C4⋊C8C2×D6111yescharacteristic
438C2×C22⋊C8—611no—
439C2×C22⋊C8—611no—
440C2×C22⋊C8—611no—
441C2×C22⋊C8—611no—
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×#97—611no—
452C2×#97C2×D6111yescharacteristic
453C2×#97C2×D6111yescharacteristic
454C2×C4×C8—611no—
455C2×C4×C8C2×D6111yescharacteristic
456#336—611no—
457#336—611no—
458#336—611no—
459#336—611no—
460C61#2253311yescharacteristic, complemented, Sylow
461C22×Q8C4×D6111yescharacteristic
462C22×D4—611no—
463C22×D4—611no—
464C22×D4—611no—
465C23×C4—611no—
466C23×C4—611no—
467C23×C4—611no—
468C23×C4—611no—
469C23×C4—611no—
470C22×C8—611no—
471C22×C8—611no—
472C22×C8—611no—
473C22×C8—611no—
474C22×C8C22×D6111yescharacteristic
475C22×C8C22×D6111yescharacteristic
476C22×C8C22×D6111yescharacteristic
477C22×C8C22×D6111yescharacteristic
478#126—1224no—
479#126—1224no—
480#125—1224no—
481#124—1224no—
482#123—1224no—
483#123—1224no—
484C22⋊Q8—1224no—
485#121—1224no—
486C4×Q8D24414yes—
487C4×Q8C22⋊D6114yes—
488C4×D4—1222no—
489C4×D4—1222no—
490C4×D4—1222no—
491C4×D4—1222no—
492C4×D4—1222no—
493C4×D4—1222no—
494#117—1222no—
495#117—1222no—
496#117—1222no—
497#117—1222no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4C4×D6111yescharacteristic
506C2×C4⋊C4C4×D6111yescharacteristic
507C2×C4⋊C4C4×D6111yescharacteristic
508C2×C22⋊C4—611no—
509C2×C22⋊C4—611no—
510C2×C22⋊C4—611no—
511C2×C22⋊C4—611no—
512C2×C22⋊C4—611no—
513C2×C22⋊C4—611no—
514C2×C22⋊C4—611no—
515C2×C22⋊C4—611no—
516C2×C22⋊C4—611no—
517C2×C22⋊C4—611no—
518C2×C42—611no—
519C2×C42—611no—
520C2×C42—611no—
521C2×C42—1222no—
522C2×C42—1222no—
523C2×C42C22×D6111yescharacteristic
524C2×C42C22×D6111yescharacteristic
525C2×C42C22×D6111yescharacteristic
526C4⋊C8—22no—
527C4⋊C8—22no—
528C4⋊C8—22no—
529C4⋊C8—1222no—
530C4⋊C8—1222no—
531C4⋊C8—1222no—
532C22⋊C8—1222no—
533C22⋊C8—1222no—
534C22⋊C8—1222no—
535C22⋊C8—1222no—
536C22⋊C8—1222no—
537C22⋊C8—1222no—
538C22⋊C8—2441no—
539C22⋊C8—2441no—
540C22⋊C8—2441no—
541C22⋊C8—2441no—
542C22⋊C8—2441no—
543C22⋊C8—2441no—
544#97—22no—
545#97—22no—
546#97—1222no—
547#97—1222no—
548C4×C8—22no—
549C4×C8—1222no—
550C24—611no—
551C24—611no—
552C24—611no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8#1175819814yes—
556C2×D4—1222no—
557C2×D4—1222no—
558C2×D4—1222no—
559C2×D4—1222no—
560C2×D4—1222no—
561C2×D4—2441no—
562C2×D4—2441no—
563C2×D4—2441no—
564C2×D4—2441no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—611no—
570C22×C4—1222no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—1221no—
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—1222no—
590C22×C4—1222no—
591C22×C4—2441no—
592C22×C4—2441no—
593C22×C4—2441no—
594C22×C4C2×C4×D6111yescharacteristic
595C22×C4C2×C4×D6111yescharacteristic
596C22×C4C2×C4×D6111yescharacteristic
597C22×C4C2×C4×D6111yescharacteristic
598C22×C4C2×C4×D6111yescharacteristic
599C22×C4C2×C4×D6111yescharacteristic
600C22×C4C23×D6111yescharacteristic
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—612no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8#1175822612yes—
625C4⋊C4—1222no—
626C4⋊C4—1222no—
627C4⋊C4—1222no—
628C4⋊C4—1222no—
629C4⋊C4—1222no—
630C4⋊C4—1222no—
631C4⋊C4—1222no—
632C4⋊C4#1175819814yes—
633C4⋊C4#1175819814yes—
634C4⋊C4#1175819814yes—
635C22⋊C4—1222no—
636C22⋊C4—1222no—
637C22⋊C4—1222no—
638C22⋊C4—1222no—
639C22⋊C4—1222no—
640C22⋊C4—1222no—
641C22⋊C4—1222no—
642C22⋊C4—1222no—
643C22⋊C4—1222no—
644C22⋊C4—1222no—
645C42—1221no—
646C42—1221no—
647C42—1222no—
648C42—1222no—
649C42C2×D24412yes—
650C42C2×D24412yes—
651C42C2×D24412yes—
652C42C2×C22⋊D6112yes—
653C42C2×C22⋊D6112yes—
654C42C2×C22⋊D6112yes—
655C23—612no—
656C23—1221no—
657C23—1221no—
658C23—1221no—
659C23—1221no—
660C23—1221no—
661C23—1221no—
662C23—1221no—
663C23—1221no—
664C23—1221no—
665C23—1221no—
666C23—1221no—
667C23—1221no—
668C23—1221no—
669C23—1221no—
670C23—1221no—
671C23—1221no—
672C23—1221no—
673C23—1221no—
674C23—1221no—
675C23—1221no—
676C23C22×C4×D6111yescharacteristic
677Q8—44no—
678D4—2444no—
679D4—2444no—
680D4—2444no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—1221no—
703C2×C4—1221no—
704C2×C4—1221no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—2444no—
709C2×C4—2444no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
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×C4C2×#1175819812yes—
723C2×C4C2×#1175819812yes—
724C2×C4C2×#1175819812yes—
725C2×C4C2×#1175819812yes—
726C2×C4C2×#1175819812yes—
727C2×C4C2×#1175819812yes—
728C2×C4C22×C22⋊D6111yescharacteristic
729C2×C4C22×D24411yescharacteristic
730C2×C4#41×D6111yescharacteristic
731C2×C4C2×#1175822611yescharacteristic
732C2×C4#1451982311yescharacteristic
733C2×C4#1451982511yescharacteristic
734C8—22no—
735C8—41no—
736C8—41no—
737C8—41no—
738C8—1222no—
739C8—2441no—
740C8—2441no—
741C8—2441no—
742C22—1222no—
743C22—1222no—
744C22—1222no—
745C22—2441no—
746C22—2441no—
747C22—2441no—
748C22—2441no—
749C22—2441no—
750C22—2441no—
751C22—2441no—
752C22—2441no—
753C22—2441no—
754C22—2441no—
755C22—2441no—
756C22—2441no—
757C22—2441no—
758C22—2441no—
759C22—2441no—
760C22—2441no—
761C22—2441no—
762C22—2441no—
763C22C22×#1175819811yescharacteristic
764C22C4×#1175822611yescharacteristic
765C22#1684024411yescharacteristic
766C22#131×D6111yescharacteristic
767C22#1684052711yescharacteristic
768C22#1684052811yescharacteristic
769C22#1684052811yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—22no—
776C4—2441no—
777C4—2441no—
778C4—2441no—
779C4—2441no—
780C4—2441no—
781C4#1684042311yescharacteristic
782C4#1684042411yescharacteristic
783C4#1684043111yescharacteristic
784C4#1684043411yescharacteristic
785C2—4881no—
786C2—4881no—
787C2—2442no—
788C2#2144865711yescharacteristic
789C2#2145426311yescharacteristic
790C2#2145426611yescharacteristic
791C2#2145480311yescharacteristic
792C2#2145481211yescharacteristic
793C2#2145495711yescharacteristic
794C2#2145498811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC2×C61×#446C2
prime radicalC2×#14519752C4
cosocleC22×C4×C61C24
hypercenterC2×#446D61
hypocenterC61#22533
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. C2×#16839893C2semidirect
3. #21446617C2semidirect
4. #21446617C2semidirect
5. #21446616C2semidirect
6. #21446616C2semidirect
7. #21446613C2semidirect
8. #21446612C2semidirect
9. #21445800C2semidirect
10. #21445800C2semidirect
11. #21445796C2semidirect
12. #21445588C2semidirect
13. #21445586C2semidirect
14. #21445582C2semidirect
15. C2×C61×#446C2semidirect
390. C2×#446D61semidirect
460. C61#22533semidirect

Maximal subgroups

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

subgroupindex
C2×#168402992
C2×#168398932
#214466172
#214466162
#214466132
#214466122
#214458002
#214457962
#214455882
#214455862
#214455822
C2×C61×#4462
#2253361