Finite Group Databasebeta

← #29695585

Subgroups — #29695585

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×D4×Dic122C211yesmaximal, characteristic
2C2×#16839772C211yesmaximal, characteristic, complemented
3C22×#14519702C211yesmaximal, characteristic, complemented
4#21448748C211yesmaximal, characteristic
5#21446741C211yesmaximal, characteristic, complemented
6#21446639C211yesmaximal, characteristic, complemented
7#21446252C211yesmaximal, characteristic, complemented
8#21446242C211yesmaximal, characteristic, complemented
9#21446129C211yesmaximal, characteristic, complemented
10#21446124C211yesmaximal, characteristic, complemented
11#21445835C211yesmaximal, characteristic, complemented
12#21445755C211yesmaximal, characteristic, complemented
13#21445755C211yesmaximal, characteristic, complemented
14#21445650C211yesmaximal, characteristic, complemented
15C2×C61×#435C211yesmaximal, characteristic
16C23×Dic122C2211yescharacteristic
17C23×Dic122C2211yescharacteristic
18D4×Dic122—24no—
19D4×Dic122C418yescomplemented
20C2×#14519777C2211yescharacteristic
21C2×#14519776—21no—
22C2×#14519756C2211yescharacteristic
23C2×#14519756C2211yescharacteristic
24C2×#14519754—21no—
25C2×#14519754—21no—
26C2×C4×Dic122C2211yescharacteristic
27C2×D4×Dic61—21no—
28C2×#14519736C2211yescharacteristic
29C22×C4⋊Dic61C2211yescharacteristic
30#16839772—24no—
31C2×#14519702—24no—
32C2×#14519702C2211yescharacteristic
33C2×#14519702C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519702C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519702C2211yescharacteristic
39C2×#14519702C2211yescharacteristic
40C2×#14519702C2211yescharacteristic
41C2×#14519702C2211yescharacteristic
42C2×#14519702C2211yescharacteristic
43C2×#14519702C2211yescharacteristic
44#16839655—21no—
45#16839648—21no—
46#16839642—21no—
47#16839628C2211yescharacteristic
48#16839622C2211yescharacteristic
49#16839622C2211yescharacteristic
50C4×C4⋊Dic61C2211yescharacteristic
51C22⋊C4×Dic61—21no—
52#16839525C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839525C2211yescharacteristic
55#16839525C2211yescharacteristic
56C22×M16×C61C2211yescharacteristic
57C23×C8×C61C2211yescharacteristic
58C2×C4×D4×C61C2211yescharacteristic
59C61×#435—24no—
60C2×C4⋊C8×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic
63C2×#97×C61C2211yescharacteristic
64C22×Dic122—22no—
65C22×Dic122—22no—
66C22×Dic122—22no—
67C22×Dic122—22no—
68C22×Dic122—21no—
69C22×Dic122—21no—
70C22×Dic122—22no—
71C22×Dic122—22no—
72C22×Dic122—41no—
73C22×Dic122—41no—
74C22×Dic122—41no—
75C22×Dic122—41no—
76C22×Dic122C2×C414yes—
77C22×Dic122C2×C414yescomplemented
78C22×Dic122C2311yescharacteristic
79C22×Dic122C2311yescharacteristic
80C22×Dic122C2311yescharacteristic
81C23×Dic61—21no—
82C23×Dic61—21no—
83C23×Dic61—21no—
84#14519777—22no—
85#14519777C2×C414yescomplemented
86#14519776—28no—
87#14519756—22no—
88#14519756—22no—
89#14519756C2×C414yes—
90#14519756C2×C414yescomplemented
91#14519754—28no—
92#14519754—28no—
93C4×Dic122—22no—
94C4×Dic122C2×C414yescomplemented
95D4×Dic61—28no—
96#14519736—22no—
97#14519736—41no—
98C2×C4⋊Dic61—21no—
99C2×C4⋊Dic61—21no—
100C2×C4⋊Dic61—22no—
101C2×C4⋊Dic61—21no—
102C2×C4⋊Dic61—41no—
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×C4⋊Dic61C2311yescharacteristic
108C2×#11758196—21no—
109C2×#11758196—21no—
110C2×#11758196—21no—
111C2×C22⋊Dic61—21no—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×C22⋊Dic61—21no—
115C2×C22⋊Dic61—21no—
116C2×C4×Dic61—21no—
117C2×C4×Dic61—21no—
118C2×C4×Dic61—21no—
119#14519702—22no—
120#14519702—22no—
121#14519702—22no—
122#14519702—22no—
123#14519702—22no—
124#14519702—22no—
125#14519702—22no—
126#14519702—41no—
127#14519702—41no—
128#14519702—41no—
129#14519702—41no—
130#14519702D414yescomplemented
131#14519684—21no—
132#14519684—21no—
133#14519684—21no—
134#14519684—21no—
135#14519684—21no—
136C22×D4×C61D411yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C2×M16×C61—22no—
140C2×M16×C61—22no—
141C2×M16×C61—41no—
142C22×C8×C61—22no—
143C22×C8×C61—22no—
144C22×C8×C61—41no—
145C22×C8×C61C2311yescharacteristic
146C22×C8×C61C2311yescharacteristic
147C22×C8×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149C4×D4×C61C2×C414yes—
150C4×D4×C61D414yes—
151C2×C4⋊C4×C61D411yescharacteristic
152C2×C22⋊C4×C61D411yescharacteristic
153C2×C22⋊C4×C61D411yescharacteristic
154C2×C42×C61C2311yescharacteristic
155C4⋊C8×C61—22no—
156C22⋊C8×C61—22no—
157C22⋊C8×C61—22no—
158#97×C61—22no—
159C24×C61C2×D411yescharacteristic
160C24×C61C2×D411yescharacteristic
161C2×D4×C61—22no—
162C2×D4×C61—22no—
163C2×D4×C61C22⋊C414yes—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61C22×C412yes—
173C22×C4×C61C22×C412yes—
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D412yes—
179C22×C4×C61C2×D412yes—
180C22×C4×C61C2411yescharacteristic
181C22×Dic61—21no—
182C22×Dic61—24no—
183C22×Dic61—24no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—42no—
192C22×Dic61—42no—
193C22×Dic61—42no—
194C22×Dic61—42no—
195C22×Dic61—42no—
196C22×Dic61—42no—
197C22×Dic61—81no—
198C2×Dic122—21no—
199C2×Dic122—21no—
200C2×Dic122—21no—
201C2×Dic122—21no—
202C2×Dic122—21no—
203C2×Dic122—21no—
204C2×Dic122—21no—
205C2×Dic122—21no—
206C2×Dic122—21no—
207C2×Dic122—21no—
208C2×Dic122—21no—
209C2×Dic122—28no—
210C2×Dic122—28no—
211C2×Dic122—24no—
212C2×Dic122—24no—
213C2×Dic122—21no—
214C2×Dic122—21no—
215C2×Dic122—44no—
216C2×Dic122—44no—
217C2×Dic122—44no—
218C2×Dic122—44no—
219C2×Dic122—44no—
220C2×Dic122—44no—
221C2×Dic122—42no—
222C2×Dic122—42no—
223C2×Dic122—42no—
224C2×Dic122—42no—
225C2×Dic122C22×C412yes—
226C2×Dic122C22×C412yes—
227C2×Dic122C22×C412yes—
228C2×Dic122C2×D412yes—
229C2×Dic122#4112yes—
230M16×C61—44no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—44no—
243C2×C8×C61C2×D412yes—
244C4⋊C4×C61C22⋊C414yes—
245C22⋊C4×C61C22⋊C414yes—
246C22⋊C4×C61C22⋊C414yes—
247C42×C61C22×C412yes—
248C42×C61C2×D412yes—
249C22⋊Dic61—24no—
250C22⋊Dic61—24no—
251C22⋊Dic61—42no—
252C22⋊Dic61—42no—
253C22⋊Dic61—81no—
254C4⋊Dic61—24no—
255C4⋊Dic61—24no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—42no—
265C4⋊Dic61C22×C412yes—
266C4⋊Dic61C2×D412yes—
267#11758196—24no—
268#11758196—24no—
269#11758196—24no—
270C4×Dic61—24no—
271C4×Dic61—42no—
272C4×Dic61—81no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61C2×C22⋊C412yes—
284C23×C61C2×C22⋊C412yes—
285C23×C61#13712yes—
286C23×C61#13712yes—
287C23×C61C22×D411yescharacteristic
288D4×C61—28no—
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×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61C2×C22⋊C412yes—
306C2×C4×C61C2×C22⋊C412yes—
307C2×C4×C61C2×C22⋊C412yes—
308C2×C4×C61C2×C22⋊C412yes—
309C2×C4×C61C23×C411yescharacteristic
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61C22×D411yescharacteristic
312C2×C4×C61C2×#4111yescharacteristic
313C2×C4×C61H(5,𝔽2)11yescharacteristic
314C2×C4×C61H(5,𝔽2)11yescharacteristic
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—48no—
323C2×Dic61—48no—
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×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—84no—
342Dic122—22no—
343Dic122—22no—
344Dic122—22no—
345Dic122—22no—
346Dic122—22no—
347Dic122—22no—
348Dic122—22no—
349Dic122—48no—
350Dic122—48no—
351Dic122—41no—
352Dic122—41no—
353Dic122—41no—
354Dic122—41no—
355Dic122C4×D414yes—
356C8×C61—22no—
357C8×C61—41no—
358C8×C61—41no—
359C8×C61—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—22no—
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61#41914yescomplemented
375C22×C61C22×C22⋊C411yescharacteristic
376C22×C61D4211yescharacteristic
377C22×C61#54611yescharacteristic
378C22×C61C2×#13711yescharacteristic
379C22×C61C2×#13711yescharacteristic
380C22×C61#57711yescharacteristic
381C22×C61#57811yescharacteristic
382C4×C61—22no—
383C4×C61—22no—
384C4×C61—22no—
385C4×C61—22no—
386C4×C61C2×C4×D411yescharacteristic
387C4×C61#51811yescharacteristic
388C4×C61D4211yescharacteristic
389C4×C61#54611yescharacteristic
390Dic61—24no—
391Dic61—42no—
392Dic61—42no—
393Dic61—42no—
394Dic61—42no—
395Dic61—81no—
396Dic61—81no—
397Dic61—81no—
398C2×D4×Q8—611no—
399C2×#435D6111yescharacteristic
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#1805—611no—
410#1787—611no—
411#1787—611no—
412#1763—611no—
413C2×C61—24no—
414C2×C61—42no—
415C2×C61D4×C22⋊C411yescharacteristic
416C2×C61C2×#41911yescharacteristic
417C2×C61#289811yescharacteristic
418C2×C61#326611yescharacteristic
419C2×C61#327011yescharacteristic
420C2×C61#331211yescharacteristic
421C2×C61#332011yescharacteristic
422C23×Q8—611no—
423C23×Q8—611no—
424C22×M16C2×D6111yescharacteristic
425C23×C8C2×D6111yescharacteristic
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×Q8—611no—
435C2×C4×D4—1221no—
436C2×C4×D4C2×D6111yescharacteristic
437C2×#117—611no—
438C22×C4⋊C4—611no—
439#435—24no—
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—611no—
453C2×#103—611no—
454C2×#103—1224no—
455C2×C22⋊C8C2×D6111yescharacteristic
456C2×C22⋊C8C2×D6111yescharacteristic
457C2×#97C2×D6111yescharacteristic
458#388—1221no—
459#387—1221no—
460#386—1221no—
461#382—611no—
462#380—611no—
463#380—611no—
464C4×C4⋊C4—611no—
465C4×C22⋊C4—1221no—
466#340—611no—
467#340—611no—
468#340—611no—
469#340—611no—
470C61#2242511yescharacteristic, complemented, Sylow
471C22×Q8—614no—
472C22×Q8—614no—
473C22×Q8—611no—
474C22×Q8—611no—
475C22×Q8—611no—
476C22×Q8—1222no—
477C22×Q8—1222no—
478C22×Q8—1222no—
479C22×Q8—1222no—
480C22×Q8—1221no—
481C22×Q8—1221no—
482C22×Q8—1222no—
483C22×Q8—1222no—
484C22×Q8—2441no—
485C22×Q8—2441no—
486C22×Q8—2441no—
487C22×Q8—2441no—
488C22×D4D24411yescharacteristic
489C23×C4—1221no—
490C23×C4—1221no—
491C23×C4—1221no—
492C23×C4C22×D6111yescharacteristic
493C23×C4C22×D6111yescharacteristic
494C2×M16—22no—
495C2×M16—22no—
496C2×M16—41no—
497C22×C8—22no—
498C22×C8—22no—
499C22×C8—41no—
500C22×C8C22×D6111yescharacteristic
501C22×C8C22×D6111yescharacteristic
502C22×C8C22×D6111yescharacteristic
503C22×C8C22×D6111yescharacteristic
504C4⋊Q8—614no—
505C4⋊Q8—1228no—
506C4⋊Q8—1222no—
507C22⋊Q8—614no—
508C22⋊Q8—614no—
509C22⋊Q8—1222no—
510C22⋊Q8—1222no—
511C22⋊Q8—1228no—
512C22⋊Q8—1228no—
513C4×Q8—614no—
514C4×Q8—1222no—
515C4×D4—1228no—
516C4×D4C4×D6114yes—
517C4×D4C22⋊D6114yes—
518#117—1222no—
519#117—2441no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—611no—
525C2×C4⋊C4—1222no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4—2441no—
533C2×C4⋊C4D24411yescharacteristic
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4D24411yescharacteristic
540C2×C22⋊C4D24411yescharacteristic
541C2×C42—1221no—
542C2×C42—1221no—
543C2×C42—1221no—
544C2×C42C22×D6111yescharacteristic
545C4⋊C8—22no—
546#103—614no—
547#103—1222no—
548#103—1222no—
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—22no—
559C22⋊C8—22no—
560#97—22no—
561#95—1221no—
562#95—1221no—
563#95—1221no—
564#95—1221no—
565#95—1221no—
566C24C2×D24411yescharacteristic
567C24C2×D24411yescharacteristic
568C2×Q8—612no—
569C2×Q8—612no—
570C2×Q8—612no—
571C2×Q8—612no—
572C2×Q8—612no—
573C2×Q8—1228no—
574C2×Q8—1228no—
575C2×Q8—1221no—
576C2×Q8—1221no—
577C2×Q8—1221no—
578C2×Q8—1221no—
579C2×Q8—1221no—
580C2×Q8—1224no—
581C2×Q8—1224no—
582C2×Q8—1221no—
583C2×Q8—1221no—
584C2×Q8—1221no—
585C2×Q8—1221no—
586C2×Q8—1221no—
587C2×Q8—1221no—
588C2×Q8—1221no—
589C2×Q8—1221no—
590C2×Q8—2442no—
591C2×Q8—2442no—
592C2×Q8—2442no—
593C2×Q8—2442no—
594C2×Q8—2444no—
595C2×Q8—2444no—
596C2×Q8—2444no—
597C2×Q8—2444no—
598C2×Q8—2444no—
599C2×Q8—2444no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4#1175819814yes—
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—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1224no—
617C22×C4—1224no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—4881no—
622C22×C4—2442no—
623C22×C4—2442no—
624C22×C4—2442no—
625C22×C4—2442no—
626C22×C4—2442no—
627C22×C4—2442no—
628C22×C4C2×C4×D6112yes—
629C22×C4C2×C4×D6112yes—
630C22×C4C2×D24411yescharacteristic
631C22×C4C2×D24411yescharacteristic
632C22×C4C2×D24411yescharacteristic
633C22×C4C2×D24411yescharacteristic
634C22×C4C2×C22⋊D6112yes—
635C22×C4C2×C22⋊D6112yes—
636C22×C4C23×D6111yescharacteristic
637M16—44no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—44no—
650C2×C8D4×D6112yes—
651C4⋊C4—612no—
652C4⋊C4—612no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1224no—
656C4⋊C4—1224no—
657C4⋊C4—1224no—
658C4⋊C4—1224no—
659C4⋊C4—1224no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4—1221no—
663C4⋊C4—1221no—
664C4⋊C4—1221no—
665C4⋊C4—1221no—
666C4⋊C4—2442no—
667C4⋊C4#1175819814yes—
668C22⋊C4—1224no—
669C22⋊C4—1224no—
670C22⋊C4—4881no—
671C22⋊C4—2442no—
672C22⋊C4—2442no—
673C22⋊C4#1175819814yes—
674C22⋊C4#1175819814yes—
675C42—1224no—
676C42—4881no—
677C42—2442no—
678C42C2×C4×D6112yes—
679C42C2×C22⋊D6112yes—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23C2×#1175819812yes—
691C23C2×#1175819812yes—
692C23#1451981012yes—
693C23#1451981012yes—
694C23C22×D24411yescharacteristic
695Q8—614no—
696Q8—1222no—
697Q8—1222no—
698Q8—1222no—
699Q8—1222no—
700Q8—1222no—
701Q8—1222no—
702Q8—1222no—
703Q8—2448no—
704Q8—2448no—
705Q8—2441no—
706Q8—2441no—
707Q8—2441no—
708Q8—2441no—
709D4—28no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—4884no—
734C2×C4—2448no—
735C2×C4—2448no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4—2441no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4C2×#1175819812yes—
754C2×C4C2×#1175819812yes—
755C2×C4C2×#1175819812yes—
756C2×C4C2×#1175819812yes—
757C2×C4C22×C4×D6111yescharacteristic
758C2×C4C2×D4×D6111yescharacteristic
759C2×C4C22×C22⋊D6111yescharacteristic
760C2×C4#41×D6111yescharacteristic
761C2×C4#1451982211yescharacteristic
762C2×C4#1451982311yescharacteristic
763C8—22no—
764C8—41no—
765C8—41no—
766C8—41no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22#1683977214yescomplemented
781C22C22×#1175819811yescharacteristic
782C22D4×D24411yescharacteristic
783C22#1684040711yescharacteristic
784C22C2×#1451981011yescharacteristic
785C22C2×#1451981011yescharacteristic
786C22#1684057411yescharacteristic
787C22#1684057911yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—1224no—
793C4—4881no—
794C4—4881no—
795C4—4881no—
796C4—2442no—
797C4—2442no—
798C4—2442no—
799C4—2442no—
800C4C4×D4×D6111yescharacteristic
801C4#1684023411yescharacteristic
802C4D4×C22⋊D6111yescharacteristic
803C4#1684040011yescharacteristic
804C2—24no—
805C2—42no—
806C2D4×#1175819811yescharacteristic
807C2C2×#1683977211yescharacteristic
808C2#2145435311yescharacteristic
809C2#2145733411yescharacteristic
810C2#2145739411yescharacteristic
811C2#2145787211yescharacteristic
812C2#2145799211yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#435C2
socleC23×C61C22×D4
prime radicalC22×D4×C61D4
cosocleC22×C4×C61C24
hypercenterC2×#435D61
hypocenterC61#22425
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×#16839772C2semidirect
3. C22×#14519702C2semidirect
5. #21446741C2semidirect
6. #21446639C2semidirect
7. #21446252C2semidirect
8. #21446242C2semidirect
9. #21446129C2semidirect
10. #21446124C2semidirect
11. #21445835C2semidirect
12. #21445755C2semidirect
13. #21445755C2semidirect
14. #21445650C2semidirect
19. D4×Dic122C4semidirect
77. C22×Dic122C2×C4semidirect
85. #14519777C2×C4semidirect
90. #14519756C2×C4semidirect
94. C4×Dic122C2×C4semidirect
130. #14519702D4semidirect
374. C22×C61#419semidirect
470. C61#22425semidirect
780. C22#16839772semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic1222
C2×#168397722
C22×#145197022
#214487482
#214467412
#214466392
#214462522
#214462422
#214461292
#214461242
#214458352
#214457552
#214456502
C2×C61×#4352
#2242561