Finite Group Databasebeta

← #29684103

Subgroups — #29684103

Order 15616.

1534 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840337C211yesmaximal, characteristic
2C2×#16839787C211yesmaximal, characteristic, complemented
3C2×#16839762C211yesmaximal, characteristic
4C2×#16839769C211yesmaximal, characteristic, complemented
5C2×#16839757C211yesmaximal, characteristic
6C2×#103×D61C211yesmaximal, characteristic, complemented
7#21448173C211yesmaximal, characteristic, complemented
8#21446751C211yesmaximal, characteristic, complemented
9#21446749C211yesmaximal, characteristic, complemented
10#21446748C211yesmaximal, characteristic, complemented
11#21446748C211yesmaximal, characteristic, complemented
12#21446743C211yesmaximal, characteristic, complemented
13#21446740C211yesmaximal, characteristic, complemented
14#21446740C211yesmaximal, characteristic, complemented
15C61×#1981C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840337—24no—
21#16840337C418yescomplemented
22C2×#14519775C2211yescharacteristic
23C2×#14519766C2211yescharacteristic
24C2×#14519765C2211yescharacteristic
25C2×#14519762—21no—
26C2×#14519762—21no—
27C2×#14519755—21no—
28C2×#14519755—21no—
29C2×#14519735C2211yescharacteristic
30C2×#14519734C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32#16839787—24no—
33C2×C4⋊#92418C2211yescharacteristic
34C2×#14519706C2211yescharacteristic
35C2×#14519706C2211yescharacteristic
36#16839769—24no—
37#16839762—24no—
38#16839757—24no—
39C2×#14519702C2211yescharacteristic
40C2×#14519702C2211yescharacteristic
41C2×#14519701C2211yescharacteristic
42C2×#14519701C2211yescharacteristic
43C2×#14519701C2211yescharacteristic
44C2×#14519701C2211yescharacteristic
45C2×#14519700C2211yescharacteristic
46C2×#14519700C2211yescharacteristic
47#103×D61—24no—
48C2×#14519699C2211yescharacteristic
49C2×#14519699C2211yescharacteristic
50C2×#14519697C2211yescharacteristic
51C2×#14519697C2211yescharacteristic
52C4⋊C4×Dic61C2211yescharacteristic
53C4⋊C4×Dic61C2211yescharacteristic
54C4×#11758196—21no—
55C4×C4⋊Dic61C2211yescharacteristic
56#16839613—21no—
57C4×#11758198—21no—
58#16839609—21no—
59C2×C4⋊Q8×C61C2211yescharacteristic
60C2×C4⋊C8×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×#103×C61C2211yescharacteristic
63C2×#103×C61C2211yescharacteristic
64C2×#103×C61C2211yescharacteristic
65C4×C4⋊C4×C61C2211yescharacteristic
66C2×#11758226—22no—
67C2×#11758226—22no—
68C2×#11758226—22no—
69C2×#11758226—22no—
70C2×#11758226—22no—
71C2×#11758226C2×C414yes—
72C22×Dic122—21no—
73C22×Dic122C2311yescharacteristic
74C2×Q8×D61—22no—
75C2×Q8×D61—22no—
76C2×Q8×D61—22no—
77C2×Q8×D61—22no—
78C2×Q8×D61—22no—
79C2×Q8×D61C2×C414yes—
80C22×D244—21no—
81C22×D244C2311yescharacteristic
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61C2311yescharacteristic
86C2×#11758189—22no—
87C2×#11758189—22no—
88C2×#11758189—22no—
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C2×C8×D61—22no—
92C2×C8×D61—22no—
93C2×C8×D61—22no—
94#14519775—22no—
95#14519775C2×C414yescomplemented
96#14519766—22no—
97#14519766C2×C414yescomplemented
98#14519765—22no—
99#14519765C2×C414yescomplemented
100#14519762—28no—
101#14519762—28no—
102#14519755—28no—
103#14519755—28no—
104#14519735—22no—
105#14519735D414yes—
106#14519734C2×C414yes—
107#14519734D414yes—
108C2×C4⋊Dic61C2311yescharacteristic
109C2×C4⋊Dic61C2311yescharacteristic
110C2×#11758196—21no—
111C2×#11758196—21no—
112C2×#11758196—21no—
113C2×#11758196D411yescharacteristic
114C2×#11758196D411yescharacteristic
115C4⋊C4×D61—22no—
116C4⋊C4×D61D414yes—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×#11758198D411yescharacteristic
123C2×#11758198D411yescharacteristic
124C2×C4×Dic61—21no—
125C2×C4×Dic61—21no—
126C2×C4×Dic61—21no—
127C2×C4×Dic61—21no—
128C2×C4×Dic61C2311yescharacteristic
129C4⋊#92418—22no—
130#14519706—22no—
131#14519706—22no—
132#14519702—22no—
133#14519702—22no—
134#14519701—22no—
135#14519701—22no—
136#14519701—22no—
137#14519701—22no—
138#14519700—22no—
139#14519700—22no—
140#14519699—22no—
141#14519699—22no—
142#14519697—22no—
143#14519697—22no—
144#14519684—21no—
145#14519684—21no—
146#14519684—21no—
147C22×Q8×C61C2311yescharacteristic
148C22×Q8×C61C2311yescharacteristic
149C22×C8×C61C2311yescharacteristic
150C22×C8×C61C2311yescharacteristic
151C4⋊Q8×C61—22no—
152C4⋊Q8×C61C2×C414yescomplemented
153C2×C4⋊C4×C61—21no—
154C2×C4⋊C4×C61—21no—
155C2×C4⋊C4×C61C2311yescharacteristic
156C2×C4⋊C4×C61C2311yescharacteristic
157C2×C42×C61—21no—
158C2×C42×C61C2311yescharacteristic
159C4⋊C8×C61—22no—
160#103×C61—22no—
161#103×C61—22no—
162#103×C61—22no—
163#103×C61—22no—
164#95×C61—21no—
165C23×D61—21no—
166C23×D61C2×D411yescharacteristic
167C2×Q8×C61—21no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—21no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61—21no—
175C2×Q8×C61—21no—
176C2×Q8×C61—21no—
177C2×Q8×C61C22×C412yes—
178C2×Q8×C61C22×C412yes—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2411yescharacteristic
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61C2×D411yescharacteristic
190C22×Dic61C2×D411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192#11758226—28no—
193#11758226—28no—
194#11758226—44no—
195#11758226—44no—
196Q8×D61—28no—
197Q8×D61—28no—
198Q8×D61—44no—
199Q8×D61—44no—
200C2×D244—21no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—24no—
205C2×D244—21no—
206C2×D244—42no—
207C2×D244—42no—
208C2×D244C22×C412yes—
209C2×C4×D61—24no—
210C2×C4×D61—24no—
211C2×C4×D61—24no—
212C2×C4×D61—42no—
213C2×C4×D61—42no—
214C2×C4×D61—42no—
215C2×C4×D61—42no—
216C2×C4×D61—81no—
217C2×C4×D61—81no—
218C2×C4×D61C22×C412yes—
219C2×C4×D61C2×D412yes—
220C2×C4×D61C2×D412yes—
221C2×C4×D61C2×D412yes—
222C2×C4×D61#4112yes—
223C2×C4×D61#4112yes—
224C2×Dic122—21no—
225C2×Dic122—21no—
226C2×Dic122—21no—
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122—24no—
230C2×Dic122—42no—
231C2×Dic122—42no—
232C2×Dic122C22×C412yes—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C4⋊C4×C61—24no—
240C4⋊C4×C61—24no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61C2×D412yes—
244C4⋊C4×C61C2×D412yes—
245C42×C61—81no—
246C42×C61C22×C412yes—
247C42×C61C2×D412yes—
248#11758198—24no—
249#11758198—24no—
250#11758198—24no—
251#11758198—24no—
252#11758198—24no—
253#11758198C22⋊C414yes—
254#11758198C22⋊C414yes—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61C2×D412yes—
258C4⋊Dic61C2×D412yes—
259#11758196—24no—
260#11758196—24no—
261#11758196—24no—
262#11758196C22⋊C414yes—
263#11758196C22⋊C414yes—
264C4×Dic61—24no—
265C4×Dic61—81no—
266C4×Dic61—81no—
267C4×Dic61—81no—
268C4×Dic61C22×C412yes—
269C4×Dic61C2×D412yes—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276#11758189—44no—
277C8×D61—44no—
278C23×C61C22×D411yescharacteristic
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—22no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61C2×C22⋊C412yes—
291C22×D61#12112yes—
292C22×D61#12112yes—
293Q8×C61—22no—
294Q8×C61—22no—
295Q8×C61—22no—
296Q8×C61—22no—
297Q8×C61—41no—
298Q8×C61—41no—
299Q8×C61—41no—
300Q8×C61—41no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61C2×C22⋊C412yes—
318C2×C4×C61C2×C22⋊C412yes—
319C2×C4×C61C23×C411yescharacteristic
320C2×C4×C61C22×D411yescharacteristic
321C2×C4×C61C22×D411yescharacteristic
322C2×C4×C61C22×D411yescharacteristic
323C2×C4×C61C2×#4111yescharacteristic
324C2×C4×C61C2×#4111yescharacteristic
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61C2×C22⋊C412yes—
339C2×Dic61C2×C22⋊C412yes—
340C2×Dic61C2×C22⋊C412yes—
341C2×Dic61#12112yes—
342C2×Dic61#12112yes—
343D244—22no—
344D244—22no—
345D244—48no—
346D244—41no—
347D244—41no—
348C4×D61—48no—
349C4×D61—48no—
350C4×D61—84no—
351C4×D61C4×D414yes—
352C4×D61C4×D414yes—
353C4×D61#12414yes—
354C4×D61#12714yes—
355Dic122—22no—
356Dic122—22no—
357Dic122—41no—
358Dic122—41no—
359Dic122—48no—
360C8×C61—41no—
361C8×C61—41no—
362#92418—41no—
363#92418—41no—
364#21262—611nomaximal, Sylow
365C22×C61C22×C22⋊C411yescharacteristic
366C22×C61C2×#12111yescharacteristic
367C22×C61C2×#12111yescharacteristic
368C22×C61#57711yescharacteristic
369C22×C61#57711yescharacteristic
370C22×C61#57811yescharacteristic
371C22×C61#57811yescharacteristic
372C2×D61—22no—
373C2×D61—22no—
374C2×D61—22no—
375C2×D61—22no—
376C2×D61—22no—
377C2×D61—22no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—42no—
381C2×D61—81no—
382C2×D61—81no—
383C2×D61—81no—
384C2×D61—81no—
385C2×D61#39014yes—
386C4×C61—22no—
387C4×C61—22no—
388C4×C61—42no—
389C4×C61—42no—
390C4×C61—42no—
391C4×C61—42no—
392C4×C61C2×C4×D411yescharacteristic
393C4×C61C2×C4×D411yescharacteristic
394C4×C61C2×#12411yescharacteristic
395C4×C61C2×#12711yescharacteristic
396Dic61—22no—
397Dic61—22no—
398Dic61—42no—
399Dic61—42no—
400Dic61—42no—
401Dic61#39014yes—
402C2×#536—611no—
403C2×#424—611no—
404C2×#417—611no—
405C2×#419—611no—
406C2×#416—611no—
407C22×#103—611no—
408#2274—611no—
409#1983—611no—
410#1983—611no—
411#1983—611no—
412#1983—611no—
413#1981—611no—
414#1981—611no—
415#1981—611no—
416#1981D6111yescharacteristic, complemented
417C2×C61C2×#39011yescharacteristic
418C2×C61#289811yescharacteristic
419C2×C61#289811yescharacteristic
420C2×C61#304211yescharacteristic
421C2×C61#304411yescharacteristic
422C2×C61#304611yescharacteristic
423C2×C61#304611yescharacteristic
424D61—24no—
425D61—82no—
426C22×#41—611no—
427C23×Q8—611no—
428C22×M16—611no—
429C23×C8—611no—
430#536—618no—
431#536—1224no—
432C2×C4⋊Q8—611no—
433C2×C4⋊Q8C2×D6111yescharacteristic
434C2×#124—611no—
435C2×#124—611no—
436C2×#123—1221no—
437C2×#123—1221no—
438C2×C22⋊Q8—1221no—
439C2×C22⋊Q8—1221no—
440C2×#117—611no—
441C2×#117—611no—
442C22×C4⋊C4—611no—
443#424—1224no—
444C2×C4⋊C8—611no—
445C2×C4⋊C8—611no—
446C2×C4⋊C8—611no—
447C2×C4⋊C8C2×D6111yescharacteristic
448#419—1224no—
449#417—1224no—
450#416—1224no—
451C2×#103—611no—
452C2×#103—611no—
453C2×#103—611no—
454C2×#103—611no—
455C2×#103—611no—
456C2×#103—611no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—1224no—
460C2×#103C2×D6111yescharacteristic
461C2×#103C2×D6111yescharacteristic
462C2×#103C2×D6111yescharacteristic
463C2×#103C2×D6111yescharacteristic
464C2×#102—611no—
465C2×#102—611no—
466C2×#102—611no—
467C2×#102—611no—
468C4×C4⋊C4—611no—
469C4×C4⋊C4—611no—
470C4×C4⋊C4—611no—
471C4×C4⋊C4—1221no—
472C4×C4⋊C4—1221no—
473C4×C4⋊C4C2×D6111yescharacteristic
474C4×C22⋊C4—1221no—
475C4×C22⋊C4—1221no—
476C61#2126211yescharacteristic, complemented, Sylow
477C2×#41—614no—
478C2×#41—1222no—
479C2×#41—1222no—
480C2×#41—1222no—
481C2×#41—1222no—
482C2×#41—1222no—
483C22×Q8—614no—
484C22×Q8—611no—
485C22×Q8—1221no—
486C22×Q8—1222no—
487C22×Q8—1222no—
488C22×Q8—1222no—
489C22×Q8—1222no—
490C22×Q8—1222no—
491C22×Q8C22×D6111yescharacteristic
492C22×Q8C22×D6111yescharacteristic
493C22×D4—611no—
494C22×D4—1221no—
495C23×C4—611no—
496C23×C4—1221no—
497C23×C4—1221no—
498C23×C4—1221no—
499C2×M16—1222no—
500C2×M16—1222no—
501C2×M16—1222no—
502C22×C8—611no—
503C22×C8—611no—
504C22×C8—1222no—
505C22×C8—1222no—
506C22×C8—1222no—
507C22×C8C22×D6111yescharacteristic
508C22×C8C22×D6111yescharacteristic
509C4⋊Q8—22no—
510C4⋊Q8—614no—
511C4⋊Q8—1222no—
512C4⋊Q8C4×D6114yescomplemented
513#124—614no—
514#124—614no—
515#124—1222no—
516#124—1222no—
517#123—1228no—
518#123—1228no—
519C22⋊Q8—1228no—
520C22⋊Q8—1228no—
521#117—614no—
522#117—614no—
523#117—614no—
524#117—1222no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—611no—
528C2×C4⋊C4—611no—
529C2×C4⋊C4—611no—
530C2×C4⋊C4—611no—
531C2×C4⋊C4—614no—
532C2×C4⋊C4—1222no—
533C2×C4⋊C4—1221no—
534C2×C4⋊C4—1221no—
535C2×C4⋊C4—1221no—
536C2×C4⋊C4C22×D6111yescharacteristic
537C2×C4⋊C4C22×D6111yescharacteristic
538C2×C22⋊C4—611no—
539C2×C22⋊C4—611no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1221no—
545C2×C42—21no—
546C2×C42—611no—
547C2×C42—1221no—
548C2×C42—1221no—
549C2×C42—1221no—
550C2×C42—1221no—
551C2×C42C22×D6111yescharacteristic
552C4⋊C8—22no—
553C4⋊C8—1222no—
554C4⋊C8—1222no—
555C4⋊C8—1222no—
556#103—22no—
557#103—22no—
558#103—22no—
559#103—22no—
560#103—1222no—
561#103—1222no—
562#103—1222no—
563#103—1222no—
564#103—1222no—
565#103—1222no—
566#103—1222no—
567#103—1222no—
568#102—1222no—
569#102—1222no—
570#102—1222no—
571#102—1222no—
572#95—21no—
573#95—1221no—
574#95—1221no—
575#95—1221no—
576C24—611no—
577C24—1221no—
578#41—1228no—
579#41—1228no—
580#41—2444no—
581#41—2444no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—612no—
593C2×Q8—1224no—
594C2×Q8—1228no—
595C2×Q8—1228no—
596C2×Q8—1221no—
597C2×Q8—1221no—
598C2×Q8—1221no—
599C2×Q8—1221no—
600C2×Q8—1221no—
601C2×Q8—2442no—
602C2×Q8—2442no—
603C2×Q8—2444no—
604C2×Q8—2444no—
605C2×Q8C2×C4×D6112yes—
606C2×Q8C2×C4×D6112yes—
607C2×D4—612no—
608C2×D4—1224no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4—1221no—
613C2×D4—1221no—
614C2×D4—2442no—
615C2×D4—2442no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—611no—
621C22×C4—612no—
622C22×C4—612no—
623C22×C4—612no—
624C22×C4—612no—
625C22×C4—612no—
626C22×C4—612no—
627C22×C4—611no—
628C22×C4—611no—
629C22×C4—1224no—
630C22×C4—1224no—
631C22×C4—1224no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—4881no—
636C22×C4—4881no—
637C22×C4—2442no—
638C22×C4—2442no—
639C22×C4—2442no—
640C22×C4—2442no—
641C22×C4D4×D6111yescharacteristic
642C22×C4D4×D6111yescharacteristic
643C22×C4C23×D6111yescharacteristic
644M16—2444no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—1221no—
652C2×C8—1221no—
653C2×C8—1221no—
654C2×C8—1221no—
655C2×C8—1221no—
656C2×C8—1221no—
657C2×C8—2444no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—614no—
663C4⋊C4—614no—
664C4⋊C4—612no—
665C4⋊C4—612no—
666C4⋊C4—1224no—
667C4⋊C4—1224no—
668C4⋊C4—1224no—
669C4⋊C4—1221no—
670C4⋊C4—1221no—
671C4⋊C4D4×D6112yes—
672C4⋊C4D4×D6112yes—
673C22⋊C4—614no—
674C22⋊C4—614no—
675C22⋊C4—1224no—
676C22⋊C4—1224no—
677C22⋊C4—1224no—
678C22⋊C4—1224no—
679C22⋊C4—1224no—
680C42—81no—
681C42—612no—
682C42—612no—
683C42—1224no—
684C42—4881no—
685C42—4881no—
686C42—4881no—
687C42C2×C4×D6112yes—
688C42D4×D6112yes—
689C23—612no—
690C23—612no—
691C23—612no—
692C23—1221no—
693C23—1221no—
694C23—1221no—
695C23—1221no—
696C23—1222no—
697C23—2441no—
698C23—2441no—
699C23—2441no—
700C23—2441no—
701C23—2441no—
702C23—2441no—
703C23C2×D4×D6111yescharacteristic
704Q8—22no—
705Q8—22no—
706Q8—22no—
707Q8—22no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711Q8—41no—
712Q8—1222no—
713Q8—1222no—
714Q8—2448no—
715Q8—2441no—
716Q8—2441no—
717D4—1222no—
718D4—1222no—
719D4—2448no—
720D4—2441no—
721D4—2441no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—612no—
739C2×C4—612no—
740C2×C4—612no—
741C2×C4—614no—
742C2×C4—614no—
743C2×C4—614no—
744C2×C4—614no—
745C2×C4—612no—
746C2×C4—612no—
747C2×C4—1221no—
748C2×C4—1221no—
749C2×C4—1221no—
750C2×C4—1221no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—4884no—
755C2×C4—2448no—
756C2×C4—2448no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4C22⋊C4×D6112yes—
764C2×C4C22⋊C4×D6112yes—
765C2×C4C22×C4×D6111yescharacteristic
766C2×C4C2×D4×D6111yescharacteristic
767C2×C4C2×D4×D6111yescharacteristic
768C2×C4C2×D4×D6111yescharacteristic
769C2×C4#41×D6111yescharacteristic
770C2×C4#41×D6111yescharacteristic
771C8—41no—
772C8—41no—
773C8—2441no—
774C8—2441no—
775C22—614no—
776C22—1222no—
777C22—1222no—
778C22—1222no—
779C22—1222no—
780C22—1222no—
781C22—1222no—
782C22—4881no—
783C22—4881no—
784C22—4881no—
785C22—4881no—
786C22—2442no—
787C22—2442no—
788C22—2442no—
789C22C2×C22⋊C4×D6111yescharacteristic
790C22#121×D6111yescharacteristic
791C22#121×D6111yescharacteristic
792C22#1684056811yescharacteristic
793C22#1684057111yescharacteristic
794C22#1684057511yescharacteristic
795C22#1684057811yescharacteristic
796C4—22no—
797C4—22no—
798C4—42no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—614no—
803C4—1222no—
804C4—1222no—
805C4—2442no—
806C4—2442no—
807C4—2442no—
808C4C4×D4×D6111yescharacteristic
809C4C4×D4×D6111yescharacteristic
810C4#124×D6111yescharacteristic
811C4#127×D6111yescharacteristic
812C2—1224no—
813C2—4882no—
814C2#390×D6111yescharacteristic
815C2#2145434711yescharacteristic
816C2#2145435111yescharacteristic
817C2#2145532611yescharacteristic
818C2#2145534411yescharacteristic
819C2#2145536411yescharacteristic
820C2#2145536611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1981C2
socleC23×C61C22×D4
prime radicalC22×#11758226C22
cosocleC22×C4×C61C24
hypercenter#1981D61
hypocenterC61#21262
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
2. C2×#16839787C2semidirect
4. C2×#16839769C2semidirect
6. C2×#103×D61C2semidirect
7. #21448173C2semidirect
8. #21446751C2semidirect
9. #21446749C2semidirect
10. #21446748C2semidirect
11. #21446748C2semidirect
12. #21446743C2semidirect
13. #21446740C2semidirect
14. #21446740C2semidirect
15. C61×#1981C2semidirect
21. #16840337C4semidirect
95. #14519775C2×C4semidirect
97. #14519766C2×C4semidirect
99. #14519765C2×C4semidirect
152. C4⋊Q8×C61C2×C4semidirect
416. #1981D61semidirect
476. C61#21262semidirect
512. C4⋊Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403372
C2×#168397872
C2×#168397622
C2×#168397692
C2×#168397572
C2×#103×D612
#214481732
#214467512
#214467492
#214467482
#214467432
#214467402
C61×#19812
#2126261