Finite Group Databasebeta

← #29695580

Subgroups — #29695580

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×Q8×D244C211yesmaximal, characteristic
2C2×#16839832C211yesmaximal, characteristic
3C2×#16839769C211yesmaximal, characteristic, complemented
4C2×#103×D61C211yesmaximal, characteristic, complemented
5#21448745C211yesmaximal, characteristic
6#21446741C211yesmaximal, characteristic, complemented
7#21446638C211yesmaximal, characteristic, complemented
8#21446251C211yesmaximal, characteristic, complemented
9#21446241C211yesmaximal, characteristic, complemented
10#21446130C211yesmaximal, characteristic, complemented
11#21446125C211yesmaximal, characteristic, complemented
12#21445752C211yesmaximal, characteristic, complemented
13#21445752C211yesmaximal, characteristic, complemented
14#21445649C211yesmaximal, characteristic, complemented
15C61×#1805C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20Q8×D244—24no—
21Q8×D244C418yescomplemented
22C2×#14519777—21no—
23C2×#14519777C2211yescharacteristic
24C2×#14519757—21no—
25C2×#14519757—21no—
26C2×#14519757C2211yescharacteristic
27C2×#14519757C2211yescharacteristic
28C2×C4×D244—21no—
29C2×C4×D244C2211yescharacteristic
30C2×#14519735C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32#16839832—24no—
33#16839769—24no—
34C2×#14519702C2211yescharacteristic
35C2×#14519702C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519701C2211yescharacteristic
39C2×#14519701C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41C2×#14519700C2211yescharacteristic
42C2×#14519700C2211yescharacteristic
43C2×#14519700C2211yescharacteristic
44#103×D61—24no—
45C2×#14519689C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47C2×#14519688C2211yescharacteristic
48#16839651—21no—
49#16839645—21no—
50#16839640—21no—
51#16839619C2211yescharacteristic
52#16839619C2211yescharacteristic
53C4×C4⋊Dic61C2211yescharacteristic
54#16839609—21no—
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57C2×C4×Q8×C61C2211yescharacteristic
58C2×C4⋊C8×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C61×#382C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#340C2211yescharacteristic
64C22×Dic122—21no—
65C22×Dic122—21no—
66C22×Dic122C2311yescharacteristic
67C22×Dic122C2311yescharacteristic
68C2×Q8×D61—22no—
69C2×Q8×D61—22no—
70C2×Q8×D61—22no—
71C2×Q8×D61—22no—
72C2×Q8×D61—22no—
73C2×Q8×D61—22no—
74C2×Q8×D61—41no—
75C2×Q8×D61—41no—
76C2×Q8×D61—41no—
77C2×Q8×D61—41no—
78C2×Q8×D61C2×C414yes—
79C2×Q8×D61C2×C414yescomplemented
80C22×D244D411yescharacteristic
81C22×C4×D61—21no—
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61C2311yescharacteristic
85C22×C4×D61C2311yescharacteristic
86C2×#11758189—22no—
87C2×#11758189—22no—
88C2×#11758189—41no—
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C2×C8×D61—22no—
92C2×C8×D61—22no—
93C2×C8×D61—41no—
94#14519777—22no—
95#14519777—28no—
96#14519777C2×C414yescomplemented
97#14519757—22no—
98#14519757—22no—
99#14519757—28no—
100#14519757—28no—
101#14519757C2×C414yes—
102#14519757C2×C414yescomplemented
103C4×D244—28no—
104C4×D244C2×C414yes—
105C4×D244D414yes—
106#14519735—22no—
107#14519735—41no—
108C2×C4⋊Dic61—21no—
109C2×C4⋊Dic61—21no—
110C2×C4⋊Dic61—21no—
111C2×C4⋊Dic61—21no—
112C2×C4⋊Dic61D411yescharacteristic
113C2×C4⋊Dic61C2311yescharacteristic
114C2×C4⋊Dic61C2311yescharacteristic
115C2×#11758196—21no—
116C4⋊C4×D61—22no—
117C4⋊C4×D61—41no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×#11758198—21no—
123C2×#11758198D411yescharacteristic
124C2×#11758198D411yescharacteristic
125C2×C4×Dic61—21no—
126C2×C4×Dic61—21no—
127#14519702—22no—
128#14519702—22no—
129#14519702—41no—
130#14519702—41no—
131#14519701—22no—
132#14519701D414yescomplemented
133#14519700—22no—
134#14519700—22no—
135#14519700—41no—
136#14519700—41no—
137#14519689—22no—
138#14519689—22no—
139#14519688—22no—
140#14519684—21no—
141#14519684—21no—
142#14519684—21no—
143C22×Q8×C61C2311yescharacteristic
144C22×C8×C61C2311yescharacteristic
145C22×C8×C61C2311yescharacteristic
146C4×Q8×C61—22no—
147C4×Q8×C61C2×C414yescomplemented
148C2×C4⋊C4×C61—21no—
149C2×C4⋊C4×C61C2311yescharacteristic
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C42×C61—21no—
153C2×C42×C61C2311yescharacteristic
154C4⋊C8×C61—22no—
155#103×C61—22no—
156#103×C61—22no—
157#95×C61—21no—
158#95×C61—21no—
159C23×D61C2×D411yescharacteristic
160C23×D61C2×D411yescharacteristic
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61C22×C412yes—
165C2×Q8×C61C2×D412yes—
166C2×Q8×C61#4112yes—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2411yescharacteristic
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61C2×D411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180Q8×D61—28no—
181Q8×D61—28no—
182Q8×D61—44no—
183Q8×D61—44no—
184Q8×D61—44no—
185Q8×D61—44no—
186Q8×D61—44no—
187Q8×D61—44no—
188C2×D244—22no—
189C2×D244—22no—
190C2×D244C22⋊C414yes—
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—24no—
200C2×C4×D61—24no—
201C2×C4×D61—42no—
202C2×C4×D61—42no—
203C2×C4×D61—42no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61—42no—
207C2×C4×D61—81no—
208C2×C4×D61C22×C412yes—
209C2×C4×D61C22×C412yes—
210C2×C4×D61C2×D412yes—
211C2×C4×D61C2×D412yes—
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122—21no—
215C2×Dic122—21no—
216C2×Dic122—21no—
217C2×Dic122—21no—
218C2×Dic122—21no—
219C2×Dic122—21no—
220C2×Dic122—21no—
221C2×Dic122—21no—
222C2×Dic122—24no—
223C2×Dic122—24no—
224C2×Dic122—42no—
225C2×Dic122—42no—
226C2×Dic122—42no—
227C2×Dic122—42no—
228C2×Dic122C22×C412yes—
229C2×Dic122C22×C412yes—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C4⋊C4×C61—24no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61C22×C412yes—
243C42×C61—24no—
244C42×C61C22×C412yes—
245C42×C61C2×D412yes—
246#11758198—24no—
247#11758198—24no—
248#11758198—42no—
249#11758198—42no—
250#11758198—81no—
251#11758198C22⋊C414yes—
252#11758198C22⋊C414yes—
253C4⋊Dic61—24no—
254C4⋊Dic61—24no—
255C4⋊Dic61—21no—
256C4⋊Dic61—24no—
257C4⋊Dic61—24no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61C22⋊C414yes—
261C4⋊Dic61C2×D412yes—
262#11758196—42no—
263C4×Dic61—42no—
264C4×Dic61—81no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418C2×D412yes—
271#11758189—44no—
272C8×D61—44no—
273C23×C61C22×D411yescharacteristic
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61C2×C22⋊C412yes—
285C22×D61C2×C22⋊C412yes—
286C22×D61#13712yes—
287C22×D61#13712yes—
288Q8×C61—22no—
289Q8×C61—22no—
290Q8×C61—22no—
291Q8×C61C4×D414yes—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
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×C61C2×C22⋊C412yes—
309C2×C4×C61C2×C22⋊C412yes—
310C2×C4×C61C23×C411yescharacteristic
311C2×C4×C61C22×D411yescharacteristic
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C2×#4111yescharacteristic
314C2×C4×C61H(5,𝔽2)11yescharacteristic
315C2×C4×C61H(5,𝔽2)11yescharacteristic
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61C2×C22⋊C412yes—
333C2×Dic61C2×C22⋊C412yes—
334D244—28no—
335C4×D61—22no—
336C4×D61—22no—
337C4×D61—22no—
338C4×D61—22no—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—48no—
344C4×D61—48no—
345C4×D61—84no—
346Dic122—22no—
347Dic122—22no—
348Dic122—22no—
349Dic122—22no—
350Dic122—48no—
351Dic122—48no—
352Dic122—41no—
353Dic122—41no—
354Dic122—41no—
355Dic122—41no—
356C8×C61—41no—
357C8×C61—41no—
358#92418—22no—
359#92418—41no—
360#22425—611nomaximal, Sylow
361C22×C61C22×C22⋊C411yescharacteristic
362C22×C61D4211yescharacteristic
363C22×C61#54611yescharacteristic
364C22×C61C2×#13711yescharacteristic
365C22×C61C2×#13711yescharacteristic
366C22×C61#57711yescharacteristic
367C22×C61#57811yescharacteristic
368C2×D61—22no—
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—22no—
372C2×D61—22no—
373C2×D61—22no—
374C2×D61—22no—
375C2×D61—22no—
376C2×D61—22no—
377C2×D61—41no—
378C2×D61—41no—
379C2×D61—41no—
380C2×D61—41no—
381C2×D61#41914yescomplemented
382C4×C61—24no—
383C4×C61—22no—
384C4×C61—22no—
385C4×C61—42no—
386C4×C61—81no—
387C4×C61—81no—
388C4×C61C2×C4×D411yescharacteristic
389C4×C61#51811yescharacteristic
390C4×C61D4211yescharacteristic
391C4×C61#54611yescharacteristic
392Dic61—22no—
393Dic61—22no—
394Dic61—42no—
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#1892—611no—
407#1873—611no—
408#1872—611no—
409#1805D6111yescharacteristic, complemented
410#1787—611no—
411#1787—611no—
412#1763—611no—
413C2×C61D4×C22⋊C411yescharacteristic
414C2×C61C2×#41911yescharacteristic
415C2×C61#289811yescharacteristic
416C2×C61#326611yescharacteristic
417C2×C61#327011yescharacteristic
418C2×C61#331211yescharacteristic
419C2×C61#332011yescharacteristic
420D61—24no—
421D61—42no—
422C23×Q8—611no—
423C23×Q8—611no—
424C22×M16—611no—
425C23×C8—611no—
426D4×Q8—618no—
427D4×Q8—1224no—
428C2×C4⋊Q8—611no—
429C2×C4⋊Q8—1221no—
430C2×C22⋊Q8—611no—
431C2×C22⋊Q8—611no—
432C2×C22⋊Q8—1221no—
433C2×C22⋊Q8—1221no—
434C2×C4×Q8C2×D6111yescharacteristic
435C2×C4×D4—611no—
436C2×C4×D4—1221no—
437C2×#117—611no—
438C22×C4⋊C4—611no—
439#435—1224no—
440C2×C4⋊C8C2×D6111yescharacteristic
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#382C2×D6111yescharacteristic
462#380—611no—
463#380—611no—
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—1221no—
477C22×Q8—1222no—
478C22×Q8—1222no—
479C22×Q8—1222no—
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—611no—
491C23×C4—1221no—
492C23×C4—1221no—
493C23×C4—1221no—
494C2×M16—1222no—
495C2×M16—1222no—
496C2×M16—2441no—
497C22×C8—611no—
498C22×C8—611no—
499C22×C8—1222no—
500C22×C8—1222no—
501C22×C8—2441no—
502C22×C8C22×D6111yescharacteristic
503C22×C8C22×D6111yescharacteristic
504C4⋊Q8—614no—
505C4⋊Q8—1228no—
506C4⋊Q8—1222no—
507C22⋊Q8—614no—
508C22⋊Q8—614no—
509C22⋊Q8—1228no—
510C22⋊Q8—1228no—
511C22⋊Q8—1222no—
512C22⋊Q8—1222no—
513C4×Q8—22no—
514C4×Q8C4×D6114yescomplemented
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—611no—
535C2×C22⋊C4—611no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C42—21no—
542C2×C42—1221no—
543C2×C42—1221no—
544C2×C42C22×D6111yescharacteristic
545C4⋊C8—22no—
546#103—22no—
547#103—22no—
548#103—614no—
549#103—1222no—
550#103—1222no—
551#103—1222no—
552#103—1222no—
553#103—1222no—
554#103—2441no—
555#103—2441no—
556#103—2441no—
557#103—2441no—
558C22⋊C8—1222no—
559C22⋊C8—1222no—
560#97—1222no—
561#95—21no—
562#95—21no—
563#95—1221no—
564#95—1221no—
565#95—1221no—
566C24—611no—
567C24—611no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—612no—
572C2×Q8—612no—
573C2×Q8—1224no—
574C2×Q8—1224no—
575C2×Q8—1221no—
576C2×Q8—1221no—
577C2×Q8—1228no—
578C2×Q8—1228no—
579C2×Q8—1221no—
580C2×Q8—1221no—
581C2×Q8—1221no—
582C2×Q8—1221no—
583C2×Q8—1221no—
584C2×Q8—1221no—
585C2×Q8—1221no—
586C2×Q8—1221no—
587C2×Q8—2442no—
588C2×Q8—2442no—
589C2×Q8—2442no—
590C2×Q8—2442no—
591C2×Q8—2444no—
592C2×Q8—2444no—
593C2×Q8—2444no—
594C2×Q8—2444no—
595C2×Q8—2444no—
596C2×Q8—2444no—
597C2×Q8C2×C4×D6112yes—
598C2×Q8D4×D6112yes—
599C2×Q8#1175822612yes—
600C2×D4—614no—
601C2×D4—1222no—
602C2×D4—1222no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—612no—
610C22×C4—612no—
611C22×C4—612no—
612C22×C4—612no—
613C22×C4—1224no—
614C22×C4—1224no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—4881no—
628C22×C4—2442no—
629C22×C4—2442no—
630C22×C4—2442no—
631C22×C4—2442no—
632C22×C4—2442no—
633C22×C4—2442no—
634C22×C4D4×D6111yescharacteristic
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—21no—
644C2×C8—612no—
645C2×C8—1221no—
646C2×C8—1221no—
647C2×C8—1221no—
648C2×C8—1221no—
649C2×C8—1221no—
650C2×C8—2444no—
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—1221no—
662C4⋊C4—1224no—
663C4⋊C4—1224no—
664C4⋊C4—1221no—
665C4⋊C4—1221no—
666C4⋊C4—2442no—
667C4⋊C4C2×C4×D6112yes—
668C22⋊C4—614no—
669C22⋊C4—614no—
670C22⋊C4—1224no—
671C22⋊C4—1224no—
672C22⋊C4—4881no—
673C22⋊C4—2442no—
674C22⋊C4—2442no—
675C42—24no—
676C42—4881no—
677C42—2442no—
678C42C2×C4×D6112yes—
679C42D4×D6112yes—
680C23—612no—
681C23—612no—
682C23—612no—
683C23—612no—
684C23—1221no—
685C23—1221no—
686C23—1221no—
687C23—1221no—
688C23—1221no—
689C23—1221no—
690C23—1221no—
691C23—1221no—
692C23—1221no—
693C23—1221no—
694C23C2×D4×D6111yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—1222no—
699Q8—1222no—
700Q8—1222no—
701Q8—1222no—
702Q8—2448no—
703Q8—2448no—
704Q8—2441no—
705Q8—2441no—
706Q8—2441no—
707Q8—2441no—
708Q8#1451973914yes—
709D4—1228no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
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—612no—
727C2×C4—612no—
728C2×C4—1221no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—4884no—
744C2×C4—2448no—
745C2×C4—2448no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4C22⋊C4×D6112yes—
756C2×C4C22⋊C4×D6112yes—
757C2×C4C22×C4×D6111yescharacteristic
758C2×C4C2×D4×D6111yescharacteristic
759C2×C4C2×D4×D6111yescharacteristic
760C2×C4C2×#1175822611yescharacteristic
761C2×C4#1451982311yescharacteristic
762C2×C4#1451982311yescharacteristic
763C8—41no—
764C8—41no—
765C8—1222no—
766C8—2441no—
767C22—614no—
768C22—1222no—
769C22—1222no—
770C22—1222no—
771C22—1222no—
772C22—1222no—
773C22—1222no—
774C22—1222no—
775C22—1222no—
776C22—1222no—
777C22—2441no—
778C22—2441no—
779C22—2441no—
780C22—2441no—
781C22C2×C22⋊C4×D6111yescharacteristic
782C22#1684039611yescharacteristic
783C22#1684040311yescharacteristic
784C22#137×D6111yescharacteristic
785C22#137×D6111yescharacteristic
786C22#1684056911yescharacteristic
787C22#1684057611yescharacteristic
788C4—22no—
789C4—24no—
790C4—22no—
791C4—42no—
792C4—81no—
793C4—81no—
794C4—1222no—
795C4—1222no—
796C4—4881no—
797C4—2442no—
798C4—2442no—
799C4—2442no—
800C4C2×#1451973911yescharacteristic
801C4#1684023611yescharacteristic
802C4#1684039611yescharacteristic
803C4#1684040311yescharacteristic
804C2—1224no—
805C2—2442no—
806C2#2144863911yescharacteristic
807C2#419×D6111yescharacteristic
808C2#2145434811yescharacteristic
809C2#2145732411yescharacteristic
810C2#2145738411yescharacteristic
811C2#2145786711yescharacteristic
812C2#2145798711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1805C2
socleC23×C61C22×D4
prime radicalC22×D244D4
cosocleC22×C4×C61C24
hypercenter#1805D61
hypocenterC61#22425
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
3. C2×#16839769C2semidirect
4. C2×#103×D61C2semidirect
6. #21446741C2semidirect
7. #21446638C2semidirect
8. #21446251C2semidirect
9. #21446241C2semidirect
10. #21446130C2semidirect
11. #21446125C2semidirect
12. #21445752C2semidirect
13. #21445752C2semidirect
14. #21445649C2semidirect
15. C61×#1805C2semidirect
21. Q8×D244C4semidirect
79. C2×Q8×D61C2×C4semidirect
96. #14519777C2×C4semidirect
102. #14519757C2×C4semidirect
132. #14519701D4semidirect
147. C4×Q8×C61C2×C4semidirect
381. C2×D61#419semidirect
409. #1805D61semidirect
470. C61#22425semidirect
514. C4×Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×D2442
C2×#168398322
C2×#168397692
C2×#103×D612
#214487452
#214467412
#214466382
#214462512
#214462412
#214461302
#214461252
#214457522
#214456492
C61×#18052
#2242561