Finite Group Databasebeta

← #29695589

Subgroups — #29695589

Order 15616.

1446 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840425C211yesmaximal, characteristic
2C2×#16839833C211yesmaximal, characteristic
3C2×#16839769C211yesmaximal, characteristic, complemented
4C22×#14519702C211yesmaximal, characteristic, complemented
5#21448750C211yesmaximal, characteristic
6#21446740C211yesmaximal, characteristic, complemented
7#21446637C211yesmaximal, characteristic, complemented
8#21446251C211yesmaximal, characteristic, complemented
9#21446130C211yesmaximal, characteristic, complemented
10#21446127C211yesmaximal, characteristic, complemented
11#21445833C211yesmaximal, characteristic, complemented
12#21445753C211yesmaximal, characteristic, complemented
13#21445752C211yesmaximal, characteristic, complemented
14#21445648C211yesmaximal, characteristic, complemented
15C61×#1892C211yesmaximal, characteristic, complemented
16C23×Dic122C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19#16840425—24no—
20#16840425C418yescomplemented
21C2×#14519776—21no—
22C2×#14519775C2211yescharacteristic
23C2×#14519757C2211yescharacteristic
24C2×#14519755—21no—
25C2×#14519754—21no—
26C2×#14519742C2211yescharacteristic
27C2×C4×C22⋊D61C2211yescharacteristic
28C2×#14519737—21no—
29C2×#14519735C2211yescharacteristic
30C22×C4⋊Dic61C2211yescharacteristic
31#16839833—24no—
32C2×#14519706C2211yescharacteristic
33#16839769—24no—
34C2×#14519702—24no—
35C2×#14519702C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519702C2211yescharacteristic
39C2×#14519701C2211yescharacteristic
40C2×#14519701C2211yescharacteristic
41C2×#14519700C2211yescharacteristic
42C2×#14519700C2211yescharacteristic
43C2×#14519700C2211yescharacteristic
44C2×#14519700C2211yescharacteristic
45C2×C22⋊#92418C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47C2×#14519687C2211yescharacteristic
48#16839654—21no—
49#16839649—21no—
50#16839639—21no—
51#16839627C2211yescharacteristic
52#16839619C2211yescharacteristic
53C4⋊C4×Dic61C2211yescharacteristic
54C22⋊C4×Dic61—21no—
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57C23×C8×C61C2211yescharacteristic
58C2×C22⋊Q8×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#340C2211yescharacteristic
64C22×Dic122—22no—
65C22×Dic122—22no—
66C22×Dic122—21no—
67C22×Dic122—22no—
68C22×Dic122—21no—
69C22×Dic122—41no—
70C22×Dic122—41no—
71C22×Dic122C2×C414yes—
72C22×Dic122C2311yescharacteristic
73C22×Dic122C2311yescharacteristic
74C2×Q8×D61—22no—
75C2×Q8×D61—22no—
76C2×Q8×D61—22no—
77C2×Q8×D61—41no—
78C2×Q8×D61—41no—
79C2×Q8×D61C2×C414yescomplemented
80C22×C22⋊D61D411yescharacteristic
81C23×Dic61—21no—
82C23×Dic61—21no—
83C22×C4×D61—21no—
84C22×C4×D61C2311yescharacteristic
85C2×#11758189—22no—
86C2×#11758189—22no—
87C2×#11758189—41no—
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90#14519776—28no—
91#14519775—22no—
92#14519775C2×C414yescomplemented
93#14519757—22no—
94#14519757C2×C414yescomplemented
95#14519755—28no—
96#14519754—28no—
97#14519742—22no—
98#14519742C2×C414yescomplemented
99C4×C22⋊D61C2×C414yes—
100C4×C22⋊D61D414yes—
101#14519737—28no—
102#14519735—22no—
103#14519735—41no—
104C2×C4⋊Dic61—21no—
105C2×C4⋊Dic61—22no—
106C2×C4⋊Dic61—21no—
107C2×C4⋊Dic61—41no—
108C2×C4⋊Dic61C2311yescharacteristic
109C2×C4⋊Dic61C2311yescharacteristic
110C2×#11758196—21no—
111C2×#11758196—21no—
112C2×#11758196—21no—
113C2×#11758196D411yescharacteristic
114C2×C22⋊Dic61D411yescharacteristic
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198D411yescharacteristic
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61C2311yescharacteristic
123#14519706—22no—
124#14519702—22no—
125#14519702—22no—
126#14519702—22no—
127#14519702D414yescomplemented
128#14519701—22no—
129#14519701—41no—
130#14519700—22no—
131#14519700—22no—
132#14519700—41no—
133#14519700—41no—
134C22⋊#92418—22no—
135#14519689—22no—
136#14519687—22no—
137#14519684—21no—
138#14519684—21no—
139#14519684—21no—
140#14519684—21no—
141C22×Q8×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C22×C8×C61—22no—
144C22×C8×C61—22no—
145C22×C8×C61—41no—
146C22×C8×C61C2311yescharacteristic
147C22×C8×C61C2311yescharacteristic
148C22⋊Q8×C61—22no—
149C22⋊Q8×C61C2×C414yes—
150C2×C4⋊C4×C61—21no—
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C22⋊C4×C61—21no—
155C2×C22⋊C4×C61—21no—
156#103×C61—22no—
157#103×C61—41no—
158#95×C61—21no—
159C24×C61C2×D411yescharacteristic
160C23×D61C2×D411yescharacteristic
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61C22×C412yes—
167C22×C4×C61—21no—
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×C61C22×C412yes—
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D412yes—
178C22×C4×C61C2411yescharacteristic
179C2×C22⋊D61—22no—
180C2×C22⋊D61—22no—
181C2×C22⋊D61C22⋊C414yes—
182C22×Dic61—21no—
183C22×Dic61—24no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—42no—
188C22×Dic61—42no—
189C22×Dic61—42no—
190C22×Dic61—42no—
191C22×Dic61—81no—
192C22×Dic61C2×D411yescharacteristic
193C22×Dic61C2×D411yescharacteristic
194C22×Dic61C2×D411yescharacteristic
195Q8×D61—28no—
196Q8×D61—44no—
197Q8×D61—44no—
198Q8×D61—44no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—24no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61C22×C412yes—
207C2×C4×D61C2×D412yes—
208C2×Dic122—21no—
209C2×Dic122—21no—
210C2×Dic122—21no—
211C2×Dic122—21no—
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122—21no—
215C2×Dic122—28no—
216C2×Dic122—24no—
217C2×Dic122—21no—
218C2×Dic122—24no—
219C2×Dic122—44no—
220C2×Dic122—44no—
221C2×Dic122—44no—
222C2×Dic122—42no—
223C2×Dic122—42no—
224C2×Dic122—42no—
225C2×Dic122—42no—
226C2×Dic122C22×C412yes—
227C2×Dic122C22×C412yes—
228C2×Dic122C2×D412yes—
229C2×Dic122#4112yes—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61—44no—
236C2×C8×C61C2×D412yes—
237C4⋊C4×C61—24no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61C22×C412yes—
244C22⋊C4×C61—24no—
245C22⋊C4×C61—42no—
246C22⋊Dic61C22⋊C414yes—
247#11758198—24no—
248#11758198—42no—
249#11758198—81no—
250#11758198C22⋊C414yes—
251C4⋊Dic61—21no—
252C4⋊Dic61—24no—
253C4⋊Dic61—21no—
254C4⋊Dic61—21no—
255C4⋊Dic61—42no—
256C4⋊Dic61C2×D412yes—
257#11758196—24no—
258#11758196—24no—
259#11758196—24no—
260#11758196C22⋊C414yes—
261C4×Dic61—24no—
262C4×Dic61—42no—
263C4×Dic61—81no—
264C4×Dic61C22×C412yes—
265C4×Dic61C2×D412yes—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272#11758189—44no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61C2×C22⋊C412yes—
278C23×C61#13712yes—
279C23×C61#13712yes—
280C23×C61C22×D411yescharacteristic
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61C2×C22⋊C412yes—
288Q8×C61—22no—
289Q8×C61—22no—
290Q8×C61—41no—
291Q8×C61—41no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61C2×C22⋊C412yes—
311C2×C4×C61C23×C411yescharacteristic
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C22×D411yescharacteristic
314C2×C4×C61C2×#4111yescharacteristic
315C2×C4×C61H(5,𝔽2)11yescharacteristic
316C2×C4×C61H(5,𝔽2)11yescharacteristic
317C22⋊D61—28no—
318C2×Dic61—22no—
319C2×Dic61—21no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—48no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—84no—
338C2×Dic61C2×C22⋊C412yes—
339C2×Dic61C2×C22⋊C412yes—
340C2×Dic61C2×C22⋊C412yes—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—48no—
346Dic122—22no—
347Dic122—22no—
348Dic122—22no—
349Dic122—22no—
350Dic122—22no—
351Dic122—48no—
352Dic122—48no—
353Dic122—41no—
354Dic122—41no—
355Dic122C4×D414yes—
356C8×C61—22no—
357C8×C61—41no—
358#92418—41no—
359#92418—41no—
360#22425—611nomaximal, Sylow
361C22×C61—22no—
362C22×C61—22no—
363C22×C61—22no—
364C22×C61—22no—
365C22×C61—22no—
366C22×C61—22no—
367C22×C61#41914yescomplemented
368C22×C61C22×C22⋊C411yescharacteristic
369C22×C61D4211yescharacteristic
370C22×C61#54611yescharacteristic
371C22×C61C2×#13711yescharacteristic
372C22×C61C2×#13711yescharacteristic
373C22×C61#57711yescharacteristic
374C22×C61#57811yescharacteristic
375C2×D61—22no—
376C2×D61—22no—
377C2×D61—22no—
378C2×D61—41no—
379C2×D61—41no—
380C2×D61—41no—
381C2×D61—41no—
382C4×C61—22no—
383C4×C61—42no—
384C4×C61—42no—
385C4×C61—81no—
386C4×C61—81no—
387C4×C61C2×C4×D411yescharacteristic
388C4×C61#51811yescharacteristic
389C4×C61D4211yescharacteristic
390C4×C61#54611yescharacteristic
391Dic61—24no—
392Dic61—22no—
393Dic61—22no—
394Dic61—22no—
395Dic61—42no—
396Dic61—42no—
397Dic61—81no—
398C2×D4×Q8—611no—
399C2×#435—611no—
400C2×#419—611no—
401C22×#103—611no—
402#2352—611no—
403#1981—611no—
404#1960—611no—
405#1894—611no—
406#1892D6111yescharacteristic, complemented
407#1873—611no—
408#1872—611no—
409#1805—611no—
410#1787—611no—
411#1787—611no—
412#1763—611no—
413C2×C61—24no—
414C2×C61D4×C22⋊C411yescharacteristic
415C2×C61C2×#41911yescharacteristic
416C2×C61#289811yescharacteristic
417C2×C61#326611yescharacteristic
418C2×C61#327011yescharacteristic
419C2×C61#331211yescharacteristic
420C2×C61#332011yescharacteristic
421D61—42no—
422C23×Q8—611no—
423C23×Q8—611no—
424C22×M16—611no—
425C23×C8C2×D6111yescharacteristic
426D4×Q8—618no—
427D4×Q8—1224no—
428C2×C4⋊Q8—611no—
429C2×C4⋊Q8—1221no—
430C2×C22⋊Q8—611no—
431C2×C22⋊Q8—1221no—
432C2×C22⋊Q8—1221no—
433C2×C22⋊Q8C2×D6111yescharacteristic
434C2×C4×Q8—611no—
435C2×C4×D4—611no—
436C2×C4×D4—1221no—
437C2×#117—611no—
438C22×C4⋊C4—611no—
439#435—1224no—
440C2×C4⋊C8—611no—
441#419—1224no—
442C2×#103—611no—
443C2×#103—611no—
444C2×#103—611no—
445C2×#103—611no—
446C2×#103—611no—
447C2×#103—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#103—611no—
451C2×#103—611no—
452C2×#103—1224no—
453C2×#103C2×D6111yescharacteristic
454C2×#103C2×D6111yescharacteristic
455C2×C22⋊C8—611no—
456C2×C22⋊C8—611no—
457C2×#97—611no—
458#388—1221no—
459#387—1221no—
460#386—1221no—
461#382—611no—
462#380—611no—
463#380C2×D6111yescharacteristic
464C4×C4⋊C4—611no—
465C4×C22⋊C4—1221no—
466#340—611no—
467#340—611no—
468#340C2×D6111yescharacteristic
469#340C2×D6111yescharacteristic
470C61#2242511yescharacteristic, complemented, Sylow
471C22×Q8—614no—
472C22×Q8—614no—
473C22×Q8—611no—
474C22×Q8—611no—
475C22×Q8—1221no—
476C22×Q8—1222no—
477C22×Q8—1222no—
478C22×Q8—1222no—
479C22×Q8—1221no—
480C22×Q8—1222no—
481C22×Q8—1222no—
482C22×Q8—1222no—
483C22×Q8—2441no—
484C22×Q8—2441no—
485C22×Q8—2441no—
486C22×Q8—2441no—
487C22×Q8C22×D6111yescharacteristic
488C22×D4—611no—
489C23×C4—611no—
490C23×C4—1221no—
491C23×C4—1221no—
492C23×C4—1221no—
493C23×C4C22×D6111yescharacteristic
494C2×M16—1222no—
495C2×M16—1222no—
496C2×M16—2441no—
497C22×C8—22no—
498C22×C8—22no—
499C22×C8—41no—
500C22×C8—611no—
501C22×C8—611no—
502C22×C8C22×D6111yescharacteristic
503C22×C8C22×D6111yescharacteristic
504C4⋊Q8—614no—
505C4⋊Q8—1222no—
506C4⋊Q8—1228no—
507C22⋊Q8—22no—
508C22⋊Q8—614no—
509C22⋊Q8—1228no—
510C22⋊Q8—1228no—
511C22⋊Q8—1222no—
512C22⋊Q8C4×D6114yes—
513C4×Q8—614no—
514C4×Q8—1222no—
515C4×D4—614no—
516C4×D4—614no—
517C4×D4—1228no—
518#117—1222no—
519#117—2441no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—1222no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—2441no—
531C2×C4⋊C4C22×D6111yescharacteristic
532C2×C4⋊C4C22×D6111yescharacteristic
533C2×C4⋊C4C22×D6111yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—611no—
537C2×C22⋊C4—611no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C42—611no—
542C2×C42—1221no—
543C2×C42—1221no—
544C2×C42—1221no—
545C4⋊C8—1222no—
546#103—22no—
547#103—41no—
548#103—614no—
549#103—1222no—
550#103—1222no—
551#103—1222no—
552#103—1222no—
553#103—1222no—
554#103—1222no—
555#103—2441no—
556#103—2441no—
557#103—2441no—
558C22⋊C8—1222no—
559C22⋊C8—1222no—
560#97—1222no—
561#95—21no—
562#95—1221no—
563#95—1221no—
564#95—1221no—
565#95—1221no—
566C24—611no—
567C24D4×D6111yescharacteristic
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—612no—
574C2×Q8—612no—
575C2×Q8—612no—
576C2×Q8—612no—
577C2×Q8—1224no—
578C2×Q8—1228no—
579C2×Q8—1221no—
580C2×Q8—1221no—
581C2×Q8—1221no—
582C2×Q8—1221no—
583C2×Q8—1224no—
584C2×Q8—1228no—
585C2×Q8—1221no—
586C2×Q8—1221no—
587C2×Q8—1221no—
588C2×Q8—1221no—
589C2×Q8—2442no—
590C2×Q8—2442no—
591C2×Q8—2444no—
592C2×Q8—2444no—
593C2×Q8—2444no—
594C2×Q8—2442no—
595C2×Q8—2442no—
596C2×Q8—2444no—
597C2×Q8—2444no—
598C2×Q8—2444no—
599C2×Q8C2×C4×D6112yes—
600C2×D4—614no—
601C2×D4—1222no—
602C2×D4—1222no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—612no—
615C22×C4—612no—
616C22×C4—1224no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1224no—
625C22×C4—1221no—
626C22×C4—4881no—
627C22×C4—2442no—
628C22×C4—2442no—
629C22×C4—2442no—
630C22×C4—2442no—
631C22×C4—2442no—
632C22×C4—2442no—
633C22×C4C2×C4×D6112yes—
634C22×C4D4×D6112yes—
635C22×C4D4×D6111yescharacteristic
636C22×C4C23×D6111yescharacteristic
637M16—2444no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—44no—
644C2×C8—1221no—
645C2×C8—1221no—
646C2×C8—1221no—
647C2×C8—1221no—
648C2×C8—1221no—
649C2×C8—1221no—
650C2×C8D4×D6112yes—
651C4⋊C4—21no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—614no—
658C4⋊C4—612no—
659C4⋊C4—1224no—
660C4⋊C4—1224no—
661C4⋊C4—1224no—
662C4⋊C4—1224no—
663C4⋊C4—1221no—
664C4⋊C4—1221no—
665C4⋊C4—1221no—
666C4⋊C4—2442no—
667C4⋊C4C2×C4×D6112yes—
668C22⋊C4—24no—
669C22⋊C4—42no—
670C22⋊C4—614no—
671C22⋊C4—614no—
672C22⋊C4—1224no—
673C22⋊C4—4881no—
674C22⋊C4—2442no—
675C42—612no—
676C42—612no—
677C42—1224no—
678C42—4881no—
679C42—2442no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—612no—
685C23—1221no—
686C23—1221no—
687C23—1221no—
688C23—1221no—
689C23—1221no—
690C23—1221no—
691C23C22⋊C4×D6112yes—
692C23#1451980612yes—
693C23#1451980912yes—
694C23C2×D4×D6111yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—41no—
698Q8—41no—
699Q8—614no—
700Q8—1222no—
701Q8—1222no—
702Q8—1222no—
703Q8—1222no—
704Q8—1222no—
705Q8—2448no—
706Q8—2448no—
707Q8—2441no—
708Q8—2441no—
709D4—1228no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—612no—
729C2×C4—612no—
730C2×C4—612no—
731C2×C4—1222no—
732C2×C4—1221no—
733C2×C4—1221no—
734C2×C4—1221no—
735C2×C4—1221no—
736C2×C4—1221no—
737C2×C4—1222no—
738C2×C4—1221no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—4884no—
747C2×C4—2448no—
748C2×C4—2448no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4C22⋊C4×D6112yes—
757C2×C4C22×C4×D6111yescharacteristic
758C2×C4C2×D4×D6111yescharacteristic
759C2×C4C2×D4×D6111yescharacteristic
760C2×C4#41×D6111yescharacteristic
761C2×C4#1451982211yescharacteristic
762C2×C4#1451982311yescharacteristic
763C8—22no—
764C8—41no—
765C8—2441no—
766C8—2441no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—1222no—
774C22—1222no—
775C22—1222no—
776C22—2441no—
777C22—2441no—
778C22—2441no—
779C22—2441no—
780C22#1683976914yescomplemented
781C22C2×C22⋊C4×D6111yescharacteristic
782C22#1684039611yescharacteristic
783C22#1684040111yescharacteristic
784C22C2×#1451980611yescharacteristic
785C22C2×#1451980911yescharacteristic
786C22#1684056911yescharacteristic
787C22#1684057611yescharacteristic
788C4—22no—
789C4—42no—
790C4—42no—
791C4—81no—
792C4—81no—
793C4—1222no—
794C4—1222no—
795C4—1224no—
796C4—1222no—
797C4—4881no—
798C4—2442no—
799C4—2442no—
800C4C4×D4×D6111yescharacteristic
801C4#1684023411yescharacteristic
802C4#1684039411yescharacteristic
803C4#1684040411yescharacteristic
804C2—24no—
805C2—2442no—
806C2#2144863711yescharacteristic
807C2C2×#1683976911yescharacteristic
808C2#2145434811yescharacteristic
809C2#2145732611yescharacteristic
810C2#2145738611yescharacteristic
811C2#2145787611yescharacteristic
812C2#2145799611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1892C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
cosocleC22×C4×C61C24
hypercenter#1892D61
hypocenterC61#22425
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
3. C2×#16839769C2semidirect
4. C22×#14519702C2semidirect
6. #21446740C2semidirect
7. #21446637C2semidirect
8. #21446251C2semidirect
9. #21446130C2semidirect
10. #21446127C2semidirect
11. #21445833C2semidirect
12. #21445753C2semidirect
13. #21445752C2semidirect
14. #21445648C2semidirect
15. C61×#1892C2semidirect
20. #16840425C4semidirect
79. C2×Q8×D61C2×C4semidirect
92. #14519775C2×C4semidirect
94. #14519757C2×C4semidirect
98. #14519742C2×C4semidirect
127. #14519702D4semidirect
367. C22×C61#419semidirect
406. #1892D61semidirect
470. C61#22425semidirect
780. C22#16839769semidirect

Maximal subgroups

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

subgroupindex
C2×#168404252
C2×#168398332
C2×#168397692
C22×#145197022
#214487502
#214467402
#214466372
#214462512
#214461302
#214461272
#214458332
#214457532
#214457522
#214456482
C61×#18922
#2242561