Finite Group Databasebeta

← #29696132

Subgroups — #29696132

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×#16840292C211yesmaximal, characteristic
2C2×#16839831C211yesmaximal, characteristic, complemented
3C2×#16839830C211yesmaximal, characteristic, complemented
4#21446757C211yesmaximal, characteristic, complemented
5#21446757C211yesmaximal, characteristic, complemented
6#21446113C211yesmaximal, characteristic, complemented
7#21446112C211yesmaximal, characteristic, complemented
8#21446108C211yesmaximal, characteristic, complemented
9#21445889C211yesmaximal, characteristic, complemented
10#21445888C211yesmaximal, characteristic, complemented
11#21445797C211yesmaximal, characteristic, complemented
12#21445583C211yesmaximal, characteristic, complemented
13#21445517C211yesmaximal, characteristic, complemented
14#21445514C211yesmaximal, characteristic, complemented
15C61×#1870C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C23×#92418C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840292—24no—
20#16840292—24no—
21C2×#14519772C411yescharacteristic
22C2×#14519770C411yescharacteristic
23C2×#14519767C411yescharacteristic
24C2×#14519763C411yescharacteristic
25C2×#14519761C411yescharacteristic
26C2×#14519758C411yescharacteristic
27C2×#14519754C411yescharacteristic
28C2×#14519749C411yescharacteristic
29C2×C4×Dic122C2211yescharacteristic
30C2×C4×C22⋊D61C2211yescharacteristic
31C2×C4×C22⋊D61C2211yescharacteristic
32C2×#14519736C2211yescharacteristic
33C2×#14519734C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35#16839831—24no—
36#16839830—24no—
37C2×#14519706C2211yescharacteristic
38C2×#14519706C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519687C2211yescharacteristic
45C2×#14519687C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C22×M16×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C22×Dic122C2×C411yescharacteristic
64C22×C22⋊D61C2×C411yescharacteristic
65C22×C22⋊D61C2×C411yescharacteristic
66C23×Dic61C2×C411yescharacteristic
67C23×Dic61C2×C411yescharacteristic
68C22×C4×D61C2311yescharacteristic
69C2×#11758189—22no—
70C2×#11758189—22no—
71C2×#11758189—41no—
72C22×#92418—22no—
73C22×#92418—22no—
74C22×#92418—41no—
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C2×C8×D61—22no—
80C2×C8×D61—22no—
81C2×C8×D61—41no—
82#14519772—24no—
83#14519770—24no—
84#14519767—24no—
85#14519763—24no—
86#14519761—24no—
87#14519758—24no—
88#14519754—24no—
89#14519749—24no—
90C4×Dic122—22no—
91C4×Dic122—22no—
92C4×C22⋊D61—22no—
93C4×C22⋊D61—22no—
94C4×C22⋊D61D414yes—
95C4×C22⋊D61D414yes—
96#14519736—22no—
97#14519736—22no—
98#14519734—22no—
99#14519734—22no—
100C2×C4⋊Dic61C2×C411yescharacteristic
101C2×C4⋊Dic61C2×C411yescharacteristic
102C2×C4⋊Dic61C2×C411yescharacteristic
103C2×#11758196C2×C411yescharacteristic
104C2×#11758196C2×C411yescharacteristic
105C2×#11758196C2×C411yescharacteristic
106C2×#11758196C2×C411yescharacteristic
107C2×#11758196C2×C411yescharacteristic
108C2×#11758196C2×C411yescharacteristic
109C2×C22⋊Dic61C2×C411yescharacteristic
110C2×C22⋊Dic61C2×C411yescharacteristic
111C2×C22⋊Dic61C2×C411yescharacteristic
112C2×C22⋊Dic61C2×C411yescharacteristic
113C2×#11758198C2×C411yescharacteristic
114C2×#11758198C2×C411yescharacteristic
115C2×#11758198C2×C411yescharacteristic
116C2×#11758198C2×C411yescharacteristic
117C2×C4×Dic61—22no—
118C2×C4×Dic61—22no—
119C2×C4×Dic61C2×C411yescharacteristic
120C2×C4×Dic61C2×C411yescharacteristic
121C2×C4×Dic61C2311yescharacteristic
122C2×C4×Dic61C2311yescharacteristic
123C2×C4×Dic61C2311yescharacteristic
124#14519706—22no—
125#14519706—22no—
126C22⋊#92418—22no—
127C22⋊#92418—22no—
128C22⋊#92418—41no—
129#14519689—22no—
130#14519689—22no—
131#14519687—22no—
132#14519687—22no—
133C22×D4×C61C2×C411yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C2×M16×C61—22no—
137C2×M16×C61—22no—
138C2×M16×C61—41no—
139C22×C8×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141C22×C8×C61C2311yescharacteristic
142C22×C8×C61C2311yescharacteristic
143C4×D4×C61—22no—
144C4×D4×C61—22no—
145C2×C4⋊C4×C61C2×C411yescharacteristic
146C2×C22⋊C4×C61C2×C411yescharacteristic
147C2×C22⋊C4×C61C2×C411yescharacteristic
148C2×C42×C61C2311yescharacteristic
149C22⋊C8×C61—22no—
150C22⋊C8×C61—22no—
151C22⋊C8×C61—41no—
152C24×C61C22×C411yescharacteristic
153C24×C61C22×C411yescharacteristic
154C23×D61C22×C411yescharacteristic
155C2×D4×C61—22no—
156C2×D4×C61—22no—
157C2×D4×C61—41no—
158C22×C4×C61—21no—
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×C61C22×C411yescharacteristic
169C22×C4×C61C22×C411yescharacteristic
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C2×D412yes—
173C22×C4×C61C2×D412yes—
174C22×C4×C61C2411yescharacteristic
175C2×C22⋊D61—22no—
176C2×C22⋊D61—22no—
177C2×C22⋊D61—41no—
178C2×C22⋊D61—41no—
179C2×C22⋊D61—41no—
180C2×C22⋊D61C22⋊C414yes—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—41no—
185C22×Dic61—41no—
186C22×Dic61—41no—
187C22×Dic61C22×C411yescharacteristic
188C22×Dic61C22×C411yescharacteristic
189C22×Dic61C22×C411yescharacteristic
190C22×Dic61C22×C411yescharacteristic
191C22×Dic61C22×C411yescharacteristic
192C22×Dic61C22×C411yescharacteristic
193C22×Dic61C22×C411yescharacteristic
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61C2×D412yes—
199C2×C4×D61C2×D412yes—
200C2×Dic122—22no—
201C2×Dic122—41no—
202C2×Dic122—41no—
203M16×C61—44no—
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—
215C2×C8×C61#4112yes—
216C4⋊C4×C61—22no—
217C22⋊C4×C61—22no—
218C22⋊C4×C61—22no—
219C42×C61—21no—
220C42×C61—21no—
221C22⋊Dic61—22no—
222C22⋊Dic61—22no—
223C22⋊Dic61—22no—
224C22⋊Dic61C22⋊C414yes—
225#11758198—22no—
226#11758198—22no—
227#11758198—22no—
228#11758198C22⋊C414yes—
229C4⋊Dic61—22no—
230C4⋊Dic61—22no—
231C4⋊Dic61—22no—
232#11758196—22no—
233#11758196—22no—
234#11758196—22no—
235#11758196—22no—
236#11758196—22no—
237#11758196C22⋊C414yes—
238C4×Dic61—21no—
239C4×Dic61—21no—
240C4×Dic61—21no—
241C4×Dic61—21no—
242C4×Dic61—22no—
243C4×Dic61—22no—
244C4×Dic61C2×D412yes—
245C4×Dic61C2×D412yes—
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—
257C2×#92418—44no—
258C2×#92418#4112yes—
259#11758189—44no—
260C8×D61—44no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61C2×C22⋊C412yes—
274C23×C61#13112yes—
275C23×C61C23×C411yescharacteristic
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61C2×C22⋊C412yes—
283D4×C61—44no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
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—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61C2×C22⋊C412yes—
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C22×D411yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C2×C4×C61H(5,𝔽2)11yescharacteristic
309C2×C4×C612−1+411yescharacteristic
310C22⋊D61—44no—
311C22⋊D61—44no—
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×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—44no—
331C2×Dic61—44no—
332C2×Dic61C2×C22⋊C412yes—
333C2×Dic61C2×C22⋊C412yes—
334C2×Dic61C2×C22⋊C412yes—
335C4×D61—22no—
336C4×D61—22no—
337C4×D61—22no—
338C4×D61—22no—
339Dic122—44no—
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×C61—22no—
350C22×C61—22no—
351C22×C61—22no—
352C22×C61—22no—
353C22×C61—22no—
354C22×C61—22no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61C22×C22⋊C411yescharacteristic
364C22×C61C4×#4111yescharacteristic
365C22×C61#52011yescharacteristic
366C22×C61C2×#13111yescharacteristic
367C22×C61#56811yescharacteristic
368C22×C61#56811yescharacteristic
369C22×C61#56811yescharacteristic
370C2×D61—22no—
371C2×D61—22no—
372C2×D61—22no—
373C2×D61—41no—
374C2×D61—41no—
375C2×D61—41no—
376C2×D61—41no—
377C4×C61—22no—
378C4×C61—41no—
379C4×C61—41no—
380C4×C61—41no—
381C4×C61#54611yescharacteristic
382C4×C61#54611yescharacteristic
383C4×C61#54711yescharacteristic
384C4×C61#54711yescharacteristic
385Dic61—22no—
386Dic61—22no—
387Dic61—22no—
388Dic61—41no—
389Dic61—41no—
390Dic61—41no—
391Dic61—41no—
392C2×#529—611no—
393C2×#435—611no—
394C2×#435—611no—
395#1985—611no—
396#1985—611no—
397#1870—611no—
398#1870D6111yescharacteristic, complemented
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—42no—
408C2×C61—42no—
409C2×C61#233911yescharacteristic
410C2×C61#287911yescharacteristic
411C2×C61#288011yescharacteristic
412C2×C61#296711yescharacteristic
413C2×C61#296811yescharacteristic
414C2×C61#299211yescharacteristic
415C2×C61#299511yescharacteristic
416D61—42no—
417C22×M16—611no—
418C22×M16C2×D6111yescharacteristic
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×Q8—611no—
432C2×C4×D4—611no—
433C2×C4×D4—611no—
434C2×C4×D4C2×D6111yescharacteristic
435C2×#117—611no—
436C2×#117—611no—
437C22×C42—611no—
438#435—1224no—
439#435—1224no—
440C2×C4⋊C8—611no—
441C2×C4⋊C8—611no—
442C2×C22⋊C8—611no—
443C2×C22⋊C8—611no—
444C2×C22⋊C8—611no—
445C2×C22⋊C8—611no—
446C2×C22⋊C8—611no—
447C2×C22⋊C8C2×D6111yescharacteristic
448C2×C22⋊C8C2×D6111yescharacteristic
449C2×C22⋊C8C2×D6111yescharacteristic
450C2×#97—611no—
451C2×#97—611no—
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#336—611no—
461#336—611no—
462#336C2×D6111yescharacteristic
463#336C2×D6111yescharacteristic
464C61#2247511yescharacteristic, complemented, Sylow
465C22×Q8—611no—
466C22×D4—611no—
467C22×D4—611no—
468C22×D4C4×D6111yescharacteristic
469C23×C4—611no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4C22×D6111yescharacteristic
473C23×C4C22×D6111yescharacteristic
474C2×M16—22no—
475C2×M16—22no—
476C2×M16—41no—
477C2×M16—1222no—
478C2×M16—1222no—
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—1222no—
503C4×Q8—1222no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—614no—
507C4×D4—614no—
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⋊C4—611no—
522C2×C4⋊C4—611no—
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⋊C4C4×D6111yescharacteristic
533C2×C22⋊C4C4×D6111yescharacteristic
534C2×C42—611no—
535C2×C42—611no—
536C2×C42—611no—
537C2×C42—611no—
538C2×C42—611no—
539C2×C42—1222no—
540C2×C42—1222no—
541C2×C42C22×D6111yescharacteristic
542C4⋊C8—1222no—
543C4⋊C8—1222no—
544C22⋊C8—22no—
545C22⋊C8—22no—
546C22⋊C8—41no—
547C22⋊C8—1222no—
548C22⋊C8—1222no—
549C22⋊C8—1222no—
550C22⋊C8—1222no—
551C22⋊C8—2441no—
552#97—1222no—
553#97—1222no—
554C24—611no—
555C24C2×C4×D6111yescharacteristic
556C24C2×C4×D6111yescharacteristic
557C2×Q8—1222no—
558C2×Q8—2441no—
559C2×Q8—2441no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—41no—
563C2×D4—614no—
564C2×D4—1222no—
565C2×D4—1222no—
566C2×D4—2441no—
567C2×D4—2441no—
568C2×D4—2441no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—612no—
583C22×C4—612no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
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×C4D4×D6112yes—
603C22×C4D4×D6112yes—
604C22×C4C23×D6111yescharacteristic
605M16—44no—
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#1175822412yes—
633C4⋊C4—22no—
634C4⋊C4—614no—
635C4⋊C4—1222no—
636C4⋊C4—1222no—
637C4⋊C4—1222no—
638C4⋊C4—1222no—
639C4⋊C4—1222no—
640C4⋊C4—1222no—
641C4⋊C4—1222no—
642C4⋊C4—1222no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—614no—
646C22⋊C4—614no—
647C22⋊C4—1222no—
648C22⋊C4—1222no—
649C22⋊C4—1222no—
650C22⋊C4—1222no—
651C22⋊C4—1222no—
652C22⋊C4—1222no—
653C42—21no—
654C42—21no—
655C42—612no—
656C42—612no—
657C42—1222no—
658C42—1222no—
659C42—1221no—
660C42—1221no—
661C42—1221no—
662C42—1221no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—612no—
676C23—1221no—
677C23—1221no—
678C23—1221no—
679C23—1221no—
680C23—1221no—
681C23—1221no—
682C23C22⋊C4×D6112yes—
683C23#1451978512yes—
684C23C22×C4×D6111yescharacteristic
685Q8—2444no—
686D4—44no—
687D4—2444no—
688D4—2444no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
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—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—612no—
709C2×C4—612no—
710C2×C4—612no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—1221no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—1221no—
726C2×C4—1221no—
727C2×C4—1221no—
728C2×C4—1221no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—1221no—
733C2×C4—2444no—
734C2×C4—2444no—
735C2×C4C22⋊C4×D6112yes—
736C2×C4C2×D4×D6111yescharacteristic
737C2×C4C2×D4×D6111yescharacteristic
738C2×C4#41×D6111yescharacteristic
739C2×C4C2×#1175822411yescharacteristic
740C2×C4#1451982211yescharacteristic
741C2×C4#1451982411yescharacteristic
742C8—22no—
743C8—41no—
744C8—41no—
745C8—41no—
746C8—1222no—
747C8—2441no—
748C8—2441no—
749C8—2441no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—1222no—
765C22—1222no—
766C22—1222no—
767C22—2441no—
768C22—2441no—
769C22—2441no—
770C22—2441no—
771C22C2×C22⋊C4×D6111yescharacteristic
772C22C4×#1175822411yescharacteristic
773C22#1684024111yescharacteristic
774C22C2×#1451978511yescharacteristic
775C22#1684052711yescharacteristic
776C22#1684052711yescharacteristic
777C22#1684052811yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—1222no—
783C4—1222no—
784C4—1222no—
785C4—2441no—
786C4—2441no—
787C4—2441no—
788C4—2441no—
789C4#1684039911yescharacteristic
790C4#1684040111yescharacteristic
791C4#1684041011yescharacteristic
792C4#1684041211yescharacteristic
793C2—42no—
794C2—42no—
795C2—2442no—
796C2#2144864511yescharacteristic
797C2#2145426111yescharacteristic
798C2#2145426911yescharacteristic
799C2#2145480511yescharacteristic
800C2#2145481411yescharacteristic
801C2#2145495911yescharacteristic
802C2#2145498311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1870C2
prime radicalC2×#14519749C4
cosocleC22×C4×C61C24
hypercenter#1870D61
hypocenterC61#22475
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. C2×#16839831C2semidirect
3. C2×#16839830C2semidirect
4. #21446757C2semidirect
5. #21446757C2semidirect
6. #21446113C2semidirect
7. #21446112C2semidirect
8. #21446108C2semidirect
9. #21445889C2semidirect
10. #21445888C2semidirect
11. #21445797C2semidirect
12. #21445583C2semidirect
13. #21445517C2semidirect
14. #21445514C2semidirect
15. C61×#1870C2semidirect
398. #1870D61semidirect
464. C61#22475semidirect

Maximal subgroups

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

subgroupindex
C2×#168402922
C2×#168398312
C2×#168398302
#214467572
#214461132
#214461122
#214461082
#214458892
#214458882
#214457972
#214455832
#214455172
#214455142
C61×#18702
#2247561