Finite Group Databasebeta

← C2×#21455997 #30548238

Subgroups — C2×#21455997 #30548238

Order 15616.

2274 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840236C211yesmaximal, characteristic, complemented
2#21455997C2116yesmaximal, direct product factor
3C2×#16840100C211yesmaximal, characteristic, complemented
4C2×#16840083C211yesmaximal, characteristic, complemented
5C2×#16840049C211yesmaximal, characteristic, complemented
6C2×#16840039C211yesmaximal, characteristic, complemented
7C2×#16839974C211yesmaximal, characteristic, complemented
8C2×#16839974C211yesmaximal, characteristic, complemented
9C2×#16839912C211yesmaximal, characteristic, complemented
10C2×#16839895C211yesmaximal, characteristic
11C2×#16839872C211yesmaximal, characteristic, complemented
12C2×#16839860C211yesmaximal, characteristic, complemented
13C2×C4×#11758201C211yesmaximal, characteristic, complemented
14C2×C4×#11758199C211yesmaximal, characteristic, complemented
15C2×#16839823C211yesmaximal, characteristic, complemented
16C2×C61×#542C211yesmaximal, characteristic, complemented
17C23×D244C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C22×#11758201C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21C22×#11758199C2211yescharacteristic
22#16840236—24no—
23#16840236C2218yescomplemented
24C2×C4×D244C2211yescharacteristic
25C2×C4×D244C2211yescharacteristic
26C2×C4×D244C2211yescharacteristic
27C2×C4×D244C2211yescharacteristic
28C2×#14519739—21no—
29C2×#14519739—21no—
30C2×#14519736C2211yescharacteristic
31C2×C22⋊C4×D61—21no—
32C2×C22⋊C4×D61—21no—
33#16840100C2218yescomplemented
34#16840083C2218yescomplemented
35#16840049C2218yescomplemented
36#16840039C2218yescomplemented
37#16839974C2218yescomplemented
38#16839974C2218yescomplemented
39#16839912C2218yescomplemented
40#16839895C2218yes—
41#16839872C2218yescomplemented
42#16839860C2218yescomplemented
43C4×#11758201C2218yescomplemented
44C4×#11758199C2218yescomplemented
45#16839823C2218yescomplemented
46C2×#14519710C2211yescharacteristic, complemented
47C2×#14519710C2211yescharacteristic, complemented
48C2×#14519708C2211yescharacteristic, complemented
49C2×#14519708C2211yescharacteristic, complemented
50C2×C4⋊#92418C2211yescharacteristic, complemented
51C2×C4⋊#92418C2211yescharacteristic, complemented
52C2×#14519701C2211yescharacteristic, complemented
53C2×#14519701C2211yescharacteristic, complemented
54C2×#14519698C2211yescharacteristic, complemented
55C2×#14519698C2211yescharacteristic, complemented
56C2×#14519697C2211yescharacteristic
57C2×#14519697C2211yescharacteristic
58C2×#14519697C2211yescharacteristic
59C2×#14519697C2211yescharacteristic
60C2×C22⋊#92418C2211yescharacteristic
61C2×C22⋊#92418C2211yescharacteristic
62C2×#14519688C2211yescharacteristic, complemented
63C2×C4×#92418C2211yescharacteristic, complemented
64C61×#542—24no—
65C61×#542C2218yescomplemented
66C2×C4⋊Q8×C61C2211yescharacteristic, complemented
67C2×#126×C61—21no—
68C2×#124×C61—21no—
69C2×#124×C61C2211yescharacteristic, complemented
70C2×#123×C61—21no—
71C2×C22⋊Q8×C61—21no—
72C2×C22⋊Q8×C61C2211yescharacteristic
73C2×#121×C61C2211yescharacteristic
74C2×C4×Q8×C61C2211yescharacteristic, complemented
75C2×C4×D4×C61C2211yescharacteristic, complemented
76C2×#117×C61C2211yescharacteristic
77C24×D61—21no—
78C22×D244—21no—
79C22×D244—22no—
80C22×D244—24no—
81C22×D244—24no—
82C22×D244C2314yes—
83C22×D244C2311yescharacteristic
84C22×D244C2311yescharacteristic
85C22×C4×D61—21no—
86C22×C4×D61—21no—
87C22×C4×D61—21no—
88C22×C4×D61—21no—
89C2×#11758201—24no—
90C2×#11758201—24no—
91C2×#11758201C2314yes—
92C2×#11758201C2314yes—
93C2×#11758199—24no—
94C2×#11758199—24no—
95C2×#11758199C2314yes—
96C2×#11758199C2314yes—
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101C4×D244—22no—
102C4×D244—22no—
103C4×D244—22no—
104C4×D244—22no—
105C4×D244C2314yes—
106C4×D244C2314yes—
107C4×D244C2314yes—
108C4×D244C2314yes—
109#14519739—28no—
110#14519739—28no—
111#14519736—22no—
112#14519736C2314yes—
113C2×C4⋊Dic61C2311yescharacteristic
114C2×C4⋊Dic61C2311yescharacteristic
115C2×C22⋊Dic61—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C22⋊C4×D61—28no—
121C22⋊C4×D61—28no—
122C2×C4×Dic61—21no—
123#14519710C2314yescomplemented
124#14519710C2314yescomplemented
125#14519708C2314yescomplemented
126#14519708C2314yescomplemented
127C4⋊#92418C2314yescomplemented
128C4⋊#92418C2314yescomplemented
129#14519701C2314yescomplemented
130#14519701C2314yescomplemented
131#14519698C2314yescomplemented
132#14519698C2314yescomplemented
133#14519697C2314yes—
134#14519697C2314yes—
135#14519697C2314yes—
136#14519697C2314yes—
137C22⋊#92418C2314yes—
138C22⋊#92418C2314yes—
139#14519688C2314yescomplemented
140C4×#92418C2314yescomplemented
141C22×Q8×C61—21no—
142C22×Q8×C61C2311yescharacteristic
143C22×D4×C61—21no—
144C22×D4×C61C2311yescharacteristic
145C23×C4×C61—21no—
146C23×C4×C61C2311yescharacteristic
147C4⋊Q8×C61—22no—
148C4⋊Q8×C61C2314yescomplemented
149#126×C61—28no—
150#124×C61—28no—
151#124×C61—22no—
152#124×C61C2314yescomplemented
153#123×C61—28no—
154C22⋊Q8×C61—22no—
155C22⋊Q8×C61—28no—
156C22⋊Q8×C61C2314yes—
157#121×C61—22no—
158#121×C61C2314yes—
159C4×Q8×C61—22no—
160C4×Q8×C61C2314yescomplemented
161C4×D4×C61—22no—
162C4×D4×C61C2314yescomplemented
163#117×C61D414yes—
164#117×C61C2314yes—
165C2×C4⋊C4×C61—21no—
166C2×C4⋊C4×C61—21no—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61D411yescharacteristic
169C2×C4⋊C4×C61D411yescharacteristic
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C22⋊C4×C61—21no—
173C2×C22⋊C4×C61—21no—
174C2×C22⋊C4×C61—21no—
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61—21no—
177C2×C22⋊C4×C61D411yescharacteristic
178C2×C22⋊C4×C61D411yescharacteristic
179C2×C42×C61—21no—
180C2×C42×C61C2311yescharacteristic
181C2×C42×C61C2311yescharacteristic
182C24×C61—21no—
183C24×C61C2×D411yescharacteristic
184C23×D61—21no—
185C23×D61—21no—
186C23×D61—28no—
187C23×D61—24no—
188C23×D61—82no—
189C23×D61—82no—
190C2×Q8×C61—21no—
191C2×Q8×C61—24no—
192C2×Q8×C61—22no—
193C2×Q8×C61—22no—
194C2×Q8×C61—82no—
195C2×Q8×C61C2412yes—
196C2×D4×C61—24no—
197C2×D4×C61—21no—
198C2×D4×C61—22no—
199C2×D4×C61—22no—
200C2×D4×C61—82no—
201C2×D4×C61C2412yes—
202C22×C4×C61—22no—
203C22×C4×C61—22no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—24no—
208C22×C4×C61—82no—
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2×D412yes—
215C22×C4×C61C2412yes—
216C22×C4×C61C2411yescharacteristic
217C22×Dic61—21no—
218C22×Dic61—21no—
219C2×D244—28no—
220C2×D244—216no—
221C2×D244—24no—
222C2×D244—21no—
223C2×D244—21no—
224C2×D244—22no—
225C2×D244—22no—
226C2×D244—28no—
227C2×D244—28no—
228C2×D244#4114yes—
229C2×D244#4114yes—
230C2×D244C2412yes—
231C2×D244C2412yes—
232C2×C4×D61—24no—
233C2×C4×D61—24no—
234C2×C4×D61—24no—
235C2×C4×D61—24no—
236C2×C4×D61—82no—
237C2×C4×D61—82no—
238C2×C4×D61—82no—
239C2×C4×D61—82no—
240C4⋊C4×C61—24no—
241C4⋊C4×C61—24no—
242C4⋊C4×C61—24no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61C2×D414yes—
246C4⋊C4×C61C2×D414yes—
247C4⋊C4×C61C2412yes—
248C4⋊C4×C61C2412yes—
249C22⋊C4×C61—24no—
250C22⋊C4×C61—24no—
251C22⋊C4×C61—24no—
252C22⋊C4×C61—24no—
253C22⋊C4×C61—24no—
254C22⋊C4×C61C2×D414yes—
255C22⋊C4×C61C2×D414yes—
256C42×C61—24no—
257C42×C61C2×D412yes—
258C42×C61C2×D412yes—
259C42×C61C2412yes—
260C42×C61C2412yes—
261C22⋊Dic61—24no—
262#11758201—28no—
263#11758201—28no—
264#11758199—28no—
265#11758199—28no—
266#11758198—24no—
267#11758198—24no—
268#11758198—24no—
269#11758198—24no—
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61C2412yes—
273C4⋊Dic61C2412yes—
274C4×Dic61—24no—
275C2×#92418—22no—
276C2×#92418—22no—
277C2×#92418—22no—
278C2×#92418—22no—
279C2×#92418C2412yes—
280C2×#92418C2412yes—
281C2×#92418C2412yes—
282C2×#92418C2412yes—
283C23×C61—22no—
284C23×C61—22no—
285C23×C61—22no—
286C23×C61—22no—
287C23×C61—42no—
288C23×C61—42no—
289C23×C61—42no—
290C23×C61C22×D412yes—
291C23×C61C22×D411yescharacteristic
292C22×D61—24no—
293C22×D61—24no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—216no—
297C22×D61—42no—
298C22×D61—42no—
299C22×D61—42no—
300C22×D61—42no—
301C22×D61—84no—
302C22×D61—84no—
303C22×D61—816no—
304Q8×C61—22no—
305Q8×C61—22no—
306Q8×C61—42no—
307Q8×C61—84no—
308D4×C61—22no—
309D4×C61—22no—
310D4×C61—42no—
311D4×C61—84no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—24no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—42no—
324C2×C4×C61—42no—
325C2×C4×C61—42no—
326C2×C4×C61—84no—
327C2×C4×C61C22×D412yes—
328C2×C4×C61C22×D412yes—
329C2×C4×C61C22×D412yes—
330C2×C4×C61C22×D412yes—
331C2×C4×C61C22×D412yes—
332C2×C4×C61C22×D411yescharacteristic
333C2×C4×C61C2×#4112yes—
334C2×C4×C61C2×#4112yes—
335C2×C4×C61C2511yescharacteristic
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340D244—216no—
341D244—24no—
342D244—24no—
343D244—22no—
344D244—22no—
345D244C2×#4114yes—
346D244C2×#4114yes—
347C4×D61—84no—
348C4×D61—84no—
349C4×D61—84no—
350C4×D61—84no—
351#92418—22no—
352#92418—22no—
353#92418—22no—
354#92418—22no—
355C2×#3118—611nomaximal, Sylow
356C22×C61—22no—
357C22×C61—22no—
358C22×C61—22no—
359C22×C61—44no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—84no—
364C22×C61#52512yes—
365C22×C61#57612yes—
366C22×C61#57712yes—
367C22×C61C23×D411yescharacteristic
368C2×D61—24no—
369C2×D61—24no—
370C2×D61—48no—
371C2×D61—48no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—816no—
377C4×C61—22no—
378C4×C61—22no—
379C4×C61—22no—
380C4×C61—22no—
381C4×C61—22no—
382C4×C61—42no—
383C4×C61—42no—
384C4×C61—42no—
385C4×C61#52512yes—
386C4×C61C22×#4111yescharacteristic
387C4×C61C22×#4111yescharacteristic
388Dic61—42no—
389Dic61—42no—
390C2×#542D6111yescharacteristic, complemented
391C2×#518—611no—
392#3118—6116no—
393C2×#485—611no—
394C2×#482—611no—
395C2×#476—611no—
396C2×#474—611no—
397C2×#463—611no—
398C2×#463—611no—
399C2×#450—611no—
400C2×#447—611no—
401C2×#442—611no—
402C2×#440—611no—
403C2×C4×SD16—611no—
404C2×C4×D8—611no—
405C2×#433—611no—
406C2×C61—42no—
407C2×C61—82no—
408C2×C61#311814yescomplemented
409C2×C61C2×#52511yescharacteristic
410C2×C61C2×#57611yescharacteristic
411C2×C61C2×#57711yescharacteristic
412D61—44no—
413D61—44no—
414C23×D4—611no—
415C22×SD16—611no—
416C22×SD16—611no—
417C22×D8—611no—
418C22×D8—611no—
419#542—24no—
420#542C2×D6118yescomplemented
421C2×C4⋊Q8C2×D6111yescharacteristic, complemented
422C2×#126—21no—
423C2×#124—21no—
424C2×#124C2×D6111yescharacteristic, complemented
425C2×#123—21no—
426C2×C22⋊Q8—21no—
427C2×C22⋊Q8C2×D6111yescharacteristic
428C2×#121C2×D6111yescharacteristic
429#518—618no—
430#518—1224no—
431C2×C4×Q8C2×D6111yescharacteristic, complemented
432C2×C4×D4—611no—
433C2×C4×D4—611no—
434C2×C4×D4—611no—
435C2×C4×D4—611no—
436C2×C4×D4—1221no—
437C2×C4×D4—1221no—
438C2×C4×D4C2×D6111yescharacteristic, complemented
439C2×#117—611no—
440C2×#117C2×D6111yescharacteristic
441C22×C22⋊C4—1221no—
442C22×C22⋊C4—1221no—
443#485—618no—
444#482—618no—
445#476—618no—
446#474—618no—
447#463—618no—
448#463—618no—
449#450—618no—
450#447—618no—
451#442—618no—
452#440—618no—
453C4×SD16—618no—
454C4×D8—618no—
455#433—618no—
456C2×#107—611no—
457C2×#107—611no—
458C2×#106—611no—
459C2×#106—611no—
460C2×C4⋊C8—611no—
461C2×C4⋊C8—611no—
462C2×#103—611no—
463C2×#103—611no—
464C2×#102—611no—
465C2×#102—611no—
466C2×#102—611no—
467C2×#102—611no—
468C2×#102—611no—
469C2×#102—611no—
470C2×C22⋊C8—611no—
471C2×C22⋊C8—611no—
472C2×#97—611no—
473C2×C4×C8—611no—
474C61C2×#311811yescharacteristic, complemented, Sylow
475C25—1221no—
476C22×Q8—21no—
477C22×Q8C22×D6111yescharacteristic
478C22×D4—21no—
479C22×D4—611no—
480C22×D4—611no—
481C22×D4—614no—
482C22×D4—1224no—
483C22×D4—1224no—
484C22×D4—1221no—
485C22×D4—1222no—
486C22×D4C22×D6111yescharacteristic
487C23×C4—21no—
488C23×C4—1221no—
489C23×C4—1221no—
490C23×C4—1221no—
491C23×C4—1221no—
492C23×C4C22×D6111yescharacteristic
493C2×SD16—614no—
494C2×SD16—614no—
495C2×SD16—1224no—
496C2×SD16—1224no—
497C2×D8—614no—
498C2×D8—614no—
499C2×D8—1224no—
500C2×D8—1224no—
501C22×C8—611no—
502C22×C8—611no—
503C22×C8—611no—
504C22×C8—611no—
505C4⋊Q8—22no—
506C4⋊Q8C22×D6114yescomplemented
507#126—28no—
508#124—28no—
509#124—22no—
510#124C22×D6114yescomplemented
511#123—28no—
512C22⋊Q8—22no—
513C22⋊Q8—28no—
514C22⋊Q8C22×D6114yes—
515#121—22no—
516#121C22×D6114yes—
517C4×Q8—22no—
518C4×Q8C22×D6114yescomplemented
519C4×D4—22no—
520C4×D4—614no—
521C4×D4—614no—
522C4×D4—614no—
523C4×D4—614no—
524C4×D4—1228no—
525C4×D4—1228no—
526C4×D4—1222no—
527C4×D4—1222no—
528C4×D4—1222no—
529C4×D4—1222no—
530C4×D4C22×D6114yescomplemented
531#117—614no—
532#117—1222no—
533#117C22⋊D6114yes—
534#117C22×D6114yes—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—611no—
540C2×C4⋊C4C22⋊D6111yescharacteristic
541C2×C4⋊C4C22⋊D6111yescharacteristic
542C2×C4⋊C4C22×D6111yescharacteristic
543C2×C4⋊C4C22×D6111yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1228no—
555C2×C22⋊C4—1228no—
556C2×C22⋊C4C22⋊D6111yescharacteristic
557C2×C22⋊C4C22⋊D6111yescharacteristic
558C2×C42—21no—
559C2×C42—1221no—
560C2×C42C22×D6111yescharacteristic
561C2×C42C22×D6111yescharacteristic
562#107—614no—
563#107—614no—
564#106—614no—
565#106—614no—
566C4⋊C8—614no—
567C4⋊C8—614no—
568#103—614no—
569#103—614no—
570#102—614no—
571#102—614no—
572#102—614no—
573#102—614no—
574#102—614no—
575#102—614no—
576C22⋊C8—614no—
577C22⋊C8—614no—
578#97—614no—
579C4×C8—614no—
580C24—21no—
581C24—1228no—
582C24—1224no—
583C24—1221no—
584C24—1221no—
585C24—4882no—
586C24—4882no—
587C24C2×C22⋊D6111yescharacteristic
588C2×Q8—21no—
589C2×Q8—24no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—82no—
593C2×Q8C23×D6112yes—
594C2×D4—24no—
595C2×D4—21no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—82no—
599C2×D4—614no—
600C2×D4—614no—
601C2×D4—612no—
602C2×D4—612no—
603C2×D4—1228no—
604C2×D4—1228no—
605C2×D4—1228no—
606C2×D4—12216no—
607C2×D4—1224no—
608C2×D4—1221no—
609C2×D4—1221no—
610C2×D4—1222no—
611C2×D4—1222no—
612C2×D4C23×D6112yes—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—24no—
619C22×C4—82no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1224no—
623C22×C4—1224no—
624C22×C4—1224no—
625C22×C4—1224no—
626C22×C4—4882no—
627C22×C4—4882no—
628C22×C4—4882no—
629C22×C4—4882no—
630C22×C4C2×C22⋊D6112yes—
631C22×C4C2×C22⋊D6111yescharacteristic
632C22×C4C2×C22⋊D6111yescharacteristic
633C22×C4C2×C22⋊D6111yescharacteristic
634C22×C4C2×C22⋊D6111yescharacteristic
635C22×C4C2×C22⋊D6111yescharacteristic
636C22×C4C23×D6112yes—
637C22×C4C23×D6111yescharacteristic
638SD16—1228no—
639SD16—1228no—
640D8—1228no—
641D8—1228no—
642C2×C8—612no—
643C2×C8—612no—
644C2×C8—612no—
645C2×C8—612no—
646C2×C8—1222no—
647C2×C8—1222no—
648C2×C8—1222no—
649C2×C8—1222no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—612no—
656C4⋊C4—612no—
657C4⋊C4—1221no—
658C4⋊C4—1221no—
659C4⋊C4C2×C22⋊D6114yes—
660C4⋊C4C2×C22⋊D6114yes—
661C4⋊C4C23×D6112yes—
662C4⋊C4C23×D6112yes—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—1224no—
669C22⋊C4—1224no—
670C22⋊C4—1224no—
671C22⋊C4—1224no—
672C22⋊C4—1224no—
673C22⋊C4C2×C22⋊D6114yes—
674C22⋊C4C2×C22⋊D6114yes—
675C42—24no—
676C42—1224no—
677C42C2×C22⋊D6112yes—
678C42C2×C22⋊D6112yes—
679C42C23×D6112yes—
680C42C23×D6112yes—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—12216no—
689C23—1224no—
690C23—1224no—
691C23—1222no—
692C23—1222no—
693C23—4884no—
694C23—4884no—
695C23—48816no—
696C23—2442no—
697C23—2442no—
698C23—2442no—
699C23—2442no—
700C23C22×C22⋊D6112yes—
701C23C22×C22⋊D6111yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—42no—
705Q8—84no—
706D4—22no—
707D4—22no—
708D4—42no—
709D4—84no—
710D4—614no—
711D4—614no—
712D4—12216no—
713D4—1224no—
714D4—1224no—
715D4—1222no—
716D4—1222no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—84no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—4884no—
735C2×C4—4884no—
736C2×C4—4884no—
737C2×C4—4884no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4C22×C22⋊D6112yes—
741C2×C4C22×C22⋊D6112yes—
742C2×C4C22×C22⋊D6112yes—
743C2×C4C22×C22⋊D6112yes—
744C2×C4C22×C22⋊D6112yes—
745C2×C4C22×C22⋊D6111yescharacteristic
746C2×C4#41×D6112yes—
747C2×C4#41×D6112yes—
748C2×C4C24×D6111yescharacteristic
749C8—1222no—
750C8—1222no—
751C8—1222no—
752C8—1222no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—84no—
761C22—1224no—
762C22—1224no—
763C22—48816no—
764C22—2442no—
765C22—2442no—
766C22—2442no—
767C22—2442no—
768C22—2448no—
769C22—2448no—
770C22#1684026912yes—
771C22#1684056512yes—
772C22#1684057012yes—
773C22C23×C22⋊D6111yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—2442no—
783C4—2442no—
784C4#1684026912yes—
785C4C2×#41×D6111yescharacteristic
786C4C2×#41×D6111yescharacteristic
787C2—42no—
788C2—82no—
789C2—2444no—
790C2—2444no—
791C2#2145599714yesdirect product factor
792C2C2×#1684026911yescharacteristic
793C2C2×#1684056511yescharacteristic
794C2C2×#1684057011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#542C2
socleC23×C61C22×D4
prime radicalC2×#16839895C2
hypercenterC2×#542D61
hypocenterC61C2×#3118
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#16840236C2semidirect
2. #21455997C2direct (N × H)
3. C2×#16840100C2semidirect
4. C2×#16840083C2semidirect
5. C2×#16840049C2semidirect
6. C2×#16840039C2semidirect
7. C2×#16839974C2semidirect
8. C2×#16839974C2semidirect
9. C2×#16839912C2semidirect
11. C2×#16839872C2semidirect
12. C2×#16839860C2semidirect
13. C2×C4×#11758201C2semidirect
14. C2×C4×#11758199C2semidirect
15. C2×#16839823C2semidirect
16. C2×C61×#542C2semidirect
23. #16840236C22semidirect
33. #16840100C22semidirect
34. #16840083C22semidirect
35. #16840049C22semidirect
36. #16840039C22semidirect
37. #16839974C22semidirect
38. #16839974C22semidirect
39. #16839912C22semidirect
41. #16839872C22semidirect
42. #16839860C22semidirect
43. C4×#11758201C22semidirect
44. C4×#11758199C22semidirect
45. #16839823C22semidirect
46. C2×#14519710C22semidirect
47. C2×#14519710C22semidirect
48. C2×#14519708C22semidirect
49. C2×#14519708C22semidirect
50. C2×C4⋊#92418C22semidirect
51. C2×C4⋊#92418C22semidirect
52. C2×#14519701C22semidirect
53. C2×#14519701C22semidirect
54. C2×#14519698C22semidirect
55. C2×#14519698C22semidirect
62. C2×#14519688C22semidirect
63. C2×C4×#92418C22semidirect
65. C61×#542C22semidirect
66. C2×C4⋊Q8×C61C22semidirect
69. C2×#124×C61C22semidirect
74. C2×C4×Q8×C61C22semidirect
75. C2×C4×D4×C61C22semidirect
123. #14519710C23semidirect
124. #14519710C23semidirect
125. #14519708C23semidirect
126. #14519708C23semidirect
127. C4⋊#92418C23semidirect
128. C4⋊#92418C23semidirect
129. #14519701C23semidirect
130. #14519701C23semidirect
131. #14519698C23semidirect
132. #14519698C23semidirect
139. #14519688C23semidirect
140. C4×#92418C23semidirect
148. C4⋊Q8×C61C23semidirect
152. #124×C61C23semidirect
160. C4×Q8×C61C23semidirect
162. C4×D4×C61C23semidirect
390. C2×#542D61semidirect
408. C2×C61#3118semidirect
420. #542C2×D61semidirect
421. C2×C4⋊Q8C2×D61semidirect
424. C2×#124C2×D61semidirect
431. C2×C4×Q8C2×D61semidirect
438. C2×C4×D4C2×D61semidirect
474. C61C2×#3118semidirect
506. C4⋊Q8C22×D61semidirect
510. #124C22×D61semidirect
518. C4×Q8C22×D61semidirect
530. C4×D4C22×D61semidirect
791. C2#21455997direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402362
#214559972
C2×#168401002
C2×#168400832
C2×#168400492
C2×#168400392
C2×#168399742
C2×#168399122
C2×#168398952
C2×#168398722
C2×#168398602
C2×C4×#117582012
C2×C4×#117581992
C2×#168398232
C2×C61×#5422
C2×#311861