Finite Group Databasebeta

← #29689661

Subgroups — #29689661

Order 15616.

1128 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840299C211yesmaximal, characteristic
2C2×#16839824C211yesmaximal, characteristic, complemented
3C2×#16839787C211yesmaximal, characteristic, complemented
4#21446756C211yesmaximal, characteristic, complemented
5#21446617C211yesmaximal, characteristic, complemented
6#21446612C211yesmaximal, characteristic, complemented
7#21446115C211yesmaximal, characteristic, complemented
8#21446115C211yesmaximal, characteristic, complemented
9#21446110C211yesmaximal, characteristic, complemented
10#21446110C211yesmaximal, characteristic, complemented
11#21445802C211yesmaximal, characteristic, complemented
12#21445802C211yesmaximal, characteristic, complemented
13#21445798C211yesmaximal, characteristic, complemented
14#21445798C211yesmaximal, characteristic, complemented
15C61×#1985C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18#16840299—24no—
19#16840299—24no—
20C2×#14519772C411yescharacteristic
21C2×#14519772C411yescharacteristic
22C2×#14519768C411yescharacteristic
23C2×#14519766C411yescharacteristic
24C2×#14519762C411yescharacteristic
25C2×#14519762C411yescharacteristic
26C2×#14519753C411yescharacteristic
27C2×#14519752C411yescharacteristic
28C2×C4×D244C2211yescharacteristic
29C2×C4×D244C2211yescharacteristic
30C2×C4×D244C2211yescharacteristic
31C2×#14519734C2211yescharacteristic
32C2×#14519734C2211yescharacteristic
33C2×C42×D61C2211yescharacteristic
34#16839824—24no—
35#16839787—24no—
36C2×C4⋊#92418C2211yescharacteristic
37C2×#14519706C2211yescharacteristic
38C2×#14519706C2211yescharacteristic
39C2×#14519706C2211yescharacteristic
40C2×#14519706C2211yescharacteristic
41C2×#14519689C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47C2×#14519689C2211yescharacteristic
48C2×#14519689C2211yescharacteristic
49C2×#14519689C2211yescharacteristic
50C2×#14519689C2211yescharacteristic
51C2×C4×#92418C2211yescharacteristic
52#16839517C2211yescharacteristic
53#16839517C2211yescharacteristic
54#16839517C2211yescharacteristic
55#16839517C2211yescharacteristic
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—41no—
73C2×#11758189—41no—
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C2×C8×D61—22no—
79C2×C8×D61—41no—
80C2×C8×D61—41no—
81#14519772—24no—
82#14519772—24no—
83#14519768—24no—
84#14519766—24no—
85#14519762—24no—
86#14519762—24no—
87#14519753—24no—
88#14519752—24no—
89C4×D244—22no—
90C4×D244—22no—
91C4×D244—22no—
92C4×D244—22no—
93C4×D244—22no—
94C4×D244—22no—
95#14519734—22no—
96#14519734—22no—
97#14519734D414yes—
98#14519734D414yes—
99C2×C4⋊Dic61C2×C411yescharacteristic
100C2×C4⋊Dic61C2×C411yescharacteristic
101C2×C4⋊Dic61C2×C411yescharacteristic
102C2×#11758196C2×C411yescharacteristic
103C2×#11758196C2×C411yescharacteristic
104C2×#11758196C2×C411yescharacteristic
105C2×#11758196C2×C411yescharacteristic
106C2×#11758198C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×#11758198C2×C411yescharacteristic
109C2×#11758198C2×C411yescharacteristic
110C2×#11758198C2×C411yescharacteristic
111C2×#11758198C2×C411yescharacteristic
112C2×#11758198C2×C411yescharacteristic
113C2×#11758198C2×C411yescharacteristic
114C2×#11758198C2×C411yescharacteristic
115C2×#11758198C2×C411yescharacteristic
116C2×C4×Dic61C2×C411yescharacteristic
117C2×C4×Dic61C2×C411yescharacteristic
118C2×C4×Dic61C2311yescharacteristic
119C42×D61—22no—
120C42×D61—22no—
121C4⋊#92418—22no—
122#14519706—22no—
123#14519706—22no—
124#14519706—22no—
125#14519706—22no—
126#14519689—22no—
127#14519689—22no—
128#14519689—41no—
129#14519689—41no—
130#14519689—41no—
131#14519689—41no—
132#14519689—41no—
133#14519689—41no—
134#14519689—41no—
135#14519689—41no—
136C4×#92418—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—22no—
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—22no—
175C2×D244—22no—
176C2×D244—41no—
177C2×D244—41no—
178C2×D244—41no—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—22no—
184C2×C4×D61—22no—
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—22no—
198C2×C4×D61—22no—
199C2×C4×D61—41no—
200C2×C4×D61—41no—
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—21no—
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⋊Dic61—22no—
237#11758196—22no—
238#11758196—22no—
239#11758196C22⋊C414yes—
240#11758196C22⋊C414yes—
241C4×Dic61—22no—
242C4×Dic61—22no—
243C4×Dic61C2×D412yes—
244C4×Dic61C2×D412yes—
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—21no—
257#11758189—44no—
258C8×D61—44no—
259C23×C61C23×C411yescharacteristic
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—21no—
279C22×D61C2×C22⋊C412yes—
280C22×D61#13112yes—
281Q8×C61—44no—
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×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61C2×C22⋊C412yes—
298C2×C4×C61C2×C22⋊C412yes—
299C2×C4×C61#13112yes—
300C2×C4×C61C22×D411yescharacteristic
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61H(5,𝔽2)11yescharacteristic
303C2×C4×C61H(5,𝔽2)11yescharacteristic
304C2×C4×C612−1+411yescharacteristic
305C2×C4×C612−1+411yescharacteristic
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×Dic61C2×C22⋊C412yes—
319C2×Dic61C2×C22⋊C412yes—
320C2×Dic61C2×C22⋊C412yes—
321D244—44no—
322D244—44no—
323D244—44no—
324C4×D61—22no—
325C4×D61—22no—
326C4×D61—22no—
327C4×D61—22no—
328C4×D61—44no—
329C4×D61—44no—
330C4×D61—41no—
331C4×D61—41no—
332C4×D61—41no—
333C4×D61—41no—
334C4×D61—41no—
335C4×D61—41no—
336C4×D61—41no—
337C4×D61—41no—
338C8×C61—41no—
339C8×C61—41no—
340C8×C61—41no—
341C8×C61—41no—
342#92418—41no—
343#92418—41no—
344#92418—41no—
345#92418—41no—
346#21855—611nomaximal, Sylow
347C22×C61C22×C22⋊C411yescharacteristic
348C22×C61#52011yescharacteristic
349C22×C61#52011yescharacteristic
350C22×C61C2×#13111yescharacteristic
351C22×C61C2×#13111yescharacteristic
352C22×C61#56811yescharacteristic
353C22×C61#56811yescharacteristic
354C2×D61—22no—
355C2×D61—22no—
356C2×D61—22no—
357C2×D61—22no—
358C2×D61—22no—
359C2×D61—22no—
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—
373C2×D61—41no—
374C2×D61—41no—
375C4×C61—22no—
376C4×C61—22no—
377C4×C61—22no—
378C4×C61—41no—
379C4×C61—41no—
380C4×C61—41no—
381C4×C61#53511yescharacteristic
382C4×C61#53611yescharacteristic
383C4×C61#53711yescharacteristic
384C4×C61#53711yescharacteristic
385Dic61—22no—
386Dic61—22no—
387Dic61—22no—
388Dic61—41no—
389Dic61—41no—
390C2×#529—611no—
391C2×#433—611no—
392C2×#424—611no—
393#1985D6111yescharacteristic, complemented
394#1984—611no—
395#1955—611no—
396#1954—611no—
397#1870—611no—
398#1870—611no—
399#1869—611no—
400#1869—611no—
401#1798—611no—
402#1798—611no—
403#1797—611no—
404#1797—611no—
405C2×C61#231111yescharacteristic
406C2×C61#288011yescharacteristic
407C2×C61#288011yescharacteristic
408C2×C61#299211yescharacteristic
409C2×C61#299311yescharacteristic
410C2×C61#299411yescharacteristic
411C2×C61#299511yescharacteristic
412D61—42no—
413D61—42no—
414D61—81no—
415C22×M16—611no—
416C23×C8—611no—
417#529—1224no—
418#529—1224no—
419C2×#126—611no—
420C2×#126—611no—
421C2×#125—611no—
422C2×#124—611no—
423C2×#123—611no—
424C2×#123—611no—
425C2×C22⋊Q8—611no—
426C2×#121—611no—
427C2×C4×Q8C2×D6111yescharacteristic
428C2×C4×D4—611no—
429C2×C4×D4—611no—
430C2×C4×D4—611no—
431C2×#117—611no—
432C2×#117—611no—
433C22×C42—611no—
434#433—1224no—
435#424—1224no—
436C2×C4⋊C8—611no—
437C2×C4⋊C8—611no—
438C2×C4⋊C8—611no—
439C2×C4⋊C8—611no—
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×C22⋊C8—611no—
451C2×C22⋊C8—611no—
452C2×#97C2×D6111yescharacteristic
453C2×C4×C8—611no—
454#336—611no—
455#336—611no—
456#336—611no—
457#336—611no—
458#336C2×D6111yescharacteristic
459#336C2×D6111yescharacteristic
460#336C2×D6111yescharacteristic
461#336C2×D6111yescharacteristic
462C61#2185511yescharacteristic, complemented, Sylow
463C22×Q8C4×D6111yescharacteristic
464C22×D4—611no—
465C22×D4—611no—
466C22×D4—611no—
467C23×C4—611no—
468C23×C4—611no—
469C23×C4—611no—
470C23×C4—611no—
471C23×C4—611no—
472C2×M16—1222no—
473C2×M16—2441no—
474C2×M16—2441no—
475C22×C8—611no—
476C22×C8—611no—
477C22×C8—611no—
478C22×C8—611no—
479C22×C8—1222no—
480C22×C8—2441no—
481C22×C8—2441no—
482C22×C8C22×D6111yescharacteristic
483C22×C8C22×D6111yescharacteristic
484C22×C8C22×D6111yescharacteristic
485C22×C8C22×D6111yescharacteristic
486#126—1224no—
487#126—1224no—
488#125—1224no—
489#124—1224no—
490#123—1224no—
491#123—1224no—
492C22⋊Q8—1224no—
493#121—1224no—
494C4×Q8—22no—
495C4×Q8—22no—
496C4×D4—1222no—
497C4×D4—1222no—
498C4×D4—1222no—
499C4×D4—1222no—
500C4×D4—1222no—
501C4×D4—1222no—
502#117—614no—
503#117—614no—
504#117—1222no—
505#117—1222no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4C4×D6111yescharacteristic
514C2×C4⋊C4C4×D6111yescharacteristic
515C2×C4⋊C4C4×D6111yescharacteristic
516C2×C22⋊C4—611no—
517C2×C22⋊C4—611no—
518C2×C22⋊C4—611no—
519C2×C22⋊C4—611no—
520C2×C22⋊C4—611no—
521C2×C22⋊C4—611no—
522C2×C22⋊C4—611no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4—611no—
525C2×C22⋊C4—611no—
526C2×C42—611no—
527C2×C42—611no—
528C2×C42—611no—
529C2×C42—1222no—
530C2×C42—1222no—
531C2×C42C22×D6111yescharacteristic
532C2×C42C22×D6111yescharacteristic
533C2×C42C22×D6111yescharacteristic
534C4⋊C8—22no—
535C4⋊C8—1222no—
536C4⋊C8—1222no—
537C4⋊C8—1222no—
538C4⋊C8—1222no—
539C4⋊C8—1222no—
540C22⋊C8—1222no—
541C22⋊C8—1222no—
542C22⋊C8—2441no—
543C22⋊C8—2441no—
544C22⋊C8—2441no—
545C22⋊C8—2441no—
546C22⋊C8—2441no—
547C22⋊C8—2441no—
548C22⋊C8—2441no—
549C22⋊C8—2441no—
550#97—22no—
551C4×C8—1222no—
552C24—611no—
553C24—611no—
554C24—611no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—41no—
558C2×D4—1222no—
559C2×D4—1222no—
560C2×D4—1222no—
561C2×D4—1222no—
562C2×D4—1222no—
563C2×D4—1222no—
564C2×D4—2441no—
565C2×D4—2441no—
566C2×D4—2441no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—611no—
570C22×C4—612no—
571C22×C4—612no—
572C22×C4—611no—
573C22×C4—611no—
574C22×C4—1222no—
575C22×C4—1222no—
576C22×C4—1222no—
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—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1222no—
594C22×C4—2441no—
595C22×C4—2441no—
596C22×C4C2×C4×D6111yescharacteristic
597C22×C4C2×C4×D6111yescharacteristic
598C22×C4C2×C4×D6111yescharacteristic
599C22×C4C2×C4×D6111yescharacteristic
600C22×C4C2×C4×D6111yescharacteristic
601C22×C4C2×C4×D6111yescharacteristic
602C22×C4C23×D6111yescharacteristic
603M16—2444no—
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—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
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—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1221no—
628C2×C8—2444no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—614no—
633C4⋊C4—614no—
634C4⋊C4—1222no—
635C4⋊C4—1222no—
636C4⋊C4—1222no—
637C4⋊C4—1222no—
638C4⋊C4—1222no—
639C22⋊C4—614no—
640C22⋊C4—614no—
641C22⋊C4—1222no—
642C22⋊C4—1222no—
643C22⋊C4—1222no—
644C22⋊C4—1222no—
645C22⋊C4—1222no—
646C22⋊C4—1222no—
647C22⋊C4—1222no—
648C22⋊C4—1222no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—612no—
654C42—612no—
655C42—1222no—
656C42—1222no—
657C42D4×D6112yes—
658C42D4×D6112yes—
659C23—612no—
660C23—612no—
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—
676C23—1221no—
677C23—1221no—
678C23—1221no—
679C23—1221no—
680C23C22×C4×D6111yescharacteristic
681Q8—44no—
682D4—2444no—
683D4—2444no—
684D4—2444no—
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—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—612no—
701C2×C4—612no—
702C2×C4—612no—
703C2×C4—1221no—
704C2×C4—1221no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—1221no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—2444no—
720C2×C4—2444no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4C22⋊C4×D6112yes—
730C2×C4C22⋊C4×D6112yes—
731C2×C4#1451978512yes—
732C2×C4C2×D4×D6111yescharacteristic
733C2×C4C2×D4×D6111yescharacteristic
734C2×C4#1451982311yescharacteristic
735C2×C4#1451982311yescharacteristic
736C2×C4#1451982511yescharacteristic
737C2×C4#1451982511yescharacteristic
738C8—41no—
739C8—41no—
740C8—41no—
741C8—41no—
742C8—2441no—
743C8—2441no—
744C8—2441no—
745C8—2441no—
746C22—1222no—
747C22—1222no—
748C22—1222no—
749C22—1222no—
750C22—1222no—
751C22—1222no—
752C22—2441no—
753C22—2441no—
754C22—2441no—
755C22—2441no—
756C22—2441no—
757C22—2441no—
758C22—2441no—
759C22—2441no—
760C22—2441no—
761C22—2441no—
762C22—2441no—
763C22—2441no—
764C22—2441no—
765C22—2441no—
766C22—2441no—
767C22C2×C22⋊C4×D6111yescharacteristic
768C22#1684024411yescharacteristic
769C22#1684024411yescharacteristic
770C22#131×D6111yescharacteristic
771C22C2×#1451978511yescharacteristic
772C22#1684052711yescharacteristic
773C22#1684052811yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—1222no—
781C4—1222no—
782C4—1222no—
783C4—2441no—
784C4—2441no—
785C4#1684033011yescharacteristic
786C4#1684033711yescharacteristic
787C4#1684034211yescharacteristic
788C4#1684034211yescharacteristic
789C2—4881no—
790C2—2442no—
791C2—2442no—
792C2#2144841011yescharacteristic
793C2#2145426711yescharacteristic
794C2#2145426911yescharacteristic
795C2#2145495711yescharacteristic
796C2#2145497111yescharacteristic
797C2#2145498211yescharacteristic
798C2#2145498811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1985C2
prime radicalC2×#14519752C4
cosocleC22×C4×C61C24
hypercenter#1985D61
hypocenterC61#21855
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1985

Complements

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

NH ≅ G/Ntype
2. C2×#16839824C2semidirect
3. C2×#16839787C2semidirect
4. #21446756C2semidirect
5. #21446617C2semidirect
6. #21446612C2semidirect
7. #21446115C2semidirect
8. #21446115C2semidirect
9. #21446110C2semidirect
10. #21446110C2semidirect
11. #21445802C2semidirect
12. #21445802C2semidirect
13. #21445798C2semidirect
14. #21445798C2semidirect
15. C61×#1985C2semidirect
393. #1985D61semidirect
462. C61#21855semidirect

Maximal subgroups

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

subgroupindex
C2×#168402992
C2×#168398242
C2×#168397872
#214467562
#214466172
#214466122
#214461152
#214461102
#214458022
#214457982
C61×#19852
#2185561