Finite Group Databasebeta

← C2×#21455928 #30548193

Subgroups — C2×#21455928 #30548193

Order 15616.

2182 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840296C211yesmaximal, characteristic, complemented
2#21455928C2116yesmaximal, direct product factor
3C2×#16840103C211yesmaximal, characteristic, complemented
4C2×#16840086C211yesmaximal, characteristic, complemented
5C2×#16840069C211yesmaximal, characteristic, complemented
6C2×#16840062C211yesmaximal, characteristic, complemented
7C2×#16839984C211yesmaximal, characteristic, complemented
8C2×#16839977C211yesmaximal, characteristic, complemented
9C2×#16839924C211yesmaximal, characteristic, complemented
10C2×#16839907C211yesmaximal, characteristic
11C2×#16839872C211yesmaximal, characteristic, complemented
12C2×#16839867C211yesmaximal, characteristic, complemented
13C2×#16839862C211yesmaximal, characteristic, complemented
14C2×#16839860C211yesmaximal, characteristic, complemented
15C2×#16839819C211yesmaximal, characteristic, complemented
16C2×C4×#41×C61C211yesmaximal, characteristic, complemented
17C22×#11758202C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C22×#11758201C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21#16840296—24no—
22#16840296C2218yescomplemented
23C2×#14519771—21no—
24C2×#14519769C2211yescharacteristic
25C2×#14519765C2211yescharacteristic
26C2×#14519760—21no—
27C2×#14519756C2211yescharacteristic
28C2×#14519751C2211yescharacteristic
29C2×C4×Dic122C2211yescharacteristic
30C2×C4×D244C2211yescharacteristic
31C2×C4×C22⋊D61—21no—
32C2×#14519734—21no—
33#16840103C2218yescomplemented
34#16840086C2218yescomplemented
35#16840069C2218yescomplemented
36#16840062C2218yescomplemented
37#16839984C2218yescomplemented
38#16839977C2218yescomplemented
39#16839924C2218yescomplemented
40#16839907C2218yes—
41#16839872C2218yescomplemented
42#16839867C2218yescomplemented
43#16839862C2218yescomplemented
44#16839860C2218yescomplemented
45#16839819C2218yescomplemented
46C2×#14519710C2211yescharacteristic
47C2×#14519710C2211yescharacteristic
48C2×#14519708C2211yescharacteristic
49C2×#14519708C2211yescharacteristic
50C2×C4⋊#92418C2211yescharacteristic
51C2×C4⋊#92418C2211yescharacteristic
52C2×#14519701C2211yescharacteristic
53C2×#14519701C2211yescharacteristic
54C2×#14519700C2211yescharacteristic
55C2×#14519700C2211yescharacteristic
56C2×#14519698C2211yescharacteristic
57C2×#14519698C2211yescharacteristic
58C2×#14519697C2211yescharacteristic
59C2×#14519697C2211yescharacteristic
60C2×C22⋊#92418C2211yescharacteristic
61C2×C22⋊#92418C2211yescharacteristic
62C2×#14519688C2211yescharacteristic
63C2×#14519688C2211yescharacteristic
64C22×#41×C61C2211yescharacteristic
65C4×#41×C61—24no—
66C4×#41×C61C2218yescomplemented
67C2×C4×Q8×C61C2211yescharacteristic
68C2×C4×Q8×C61C2211yescharacteristic
69C2×C4×D4×C61—21no—
70C2×C4×D4×C61—21no—
71C2×C4×D4×C61C2211yescharacteristic
72C2×C4×D4×C61C2211yescharacteristic
73C2×#117×C61—21no—
74C2×#117×C61C2211yescharacteristic
75C22×C42×C61—21no—
76C22×C42×C61C2211yescharacteristic
77C22×Dic122C2311yescharacteristic
78C22×D244C2311yescharacteristic
79C22×C22⋊D61—21no—
80C22×C4×D61—21no—
81C2×#11758202—24no—
82C2×#11758202C2314yes—
83C2×#11758200—24no—
84C2×#11758200C2314yes—
85C2×#11758201—24no—
86C2×#11758201C2314yes—
87C2×#11758199—24no—
88C2×#11758199C2314yes—
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93#14519771—28no—
94#14519769—22no—
95#14519769C2314yes—
96#14519765—22no—
97#14519765C2314yes—
98#14519760—28no—
99#14519756—22no—
100#14519756C2314yes—
101#14519751—22no—
102#14519751C2314yes—
103C4×Dic122—22no—
104C4×Dic122C2314yes—
105C4×D244—22no—
106C4×D244C2314yes—
107C4×C22⋊D61—28no—
108#14519734—28no—
109C2×C4⋊Dic61C2311yescharacteristic
110C2×C4⋊Dic61C2311yescharacteristic
111C2×#11758196—21no—
112C2×#11758196—21no—
113C2×#11758196—21no—
114C2×#11758196—21no—
115C2×C22⋊Dic61—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×C4×Dic61—21no—
121#14519710C2314yes—
122#14519710C2314yes—
123#14519708C2314yes—
124#14519708C2314yes—
125C4⋊#92418C2314yes—
126C4⋊#92418C2314yes—
127#14519701C2314yes—
128#14519701C2314yes—
129#14519700C2314yes—
130#14519700C2314yes—
131#14519698C2314yes—
132#14519698C2314yes—
133#14519697C2314yes—
134#14519697C2314yes—
135C22⋊#92418C2314yes—
136C22⋊#92418C2314yes—
137#14519688C2314yes—
138#14519688C2314yes—
139C2×#41×C61—24no—
140C2×#41×C61—24no—
141C2×#41×C61—22no—
142C2×#41×C61C2314yes—
143C22×Q8×C61C2311yescharacteristic
144C22×D4×C61—21no—
145C22×D4×C61C2311yescharacteristic
146C23×C4×C61—21no—
147C23×C4×C61—21no—
148C23×C4×C61—21no—
149C23×C4×C61D411yescharacteristic
150C23×C4×C61D411yescharacteristic
151C23×C4×C61C2311yescharacteristic
152C4×Q8×C61—22no—
153C4×Q8×C61—22no—
154C4×Q8×C61C2314yes—
155C4×Q8×C61C2314yes—
156C4×D4×C61—28no—
157C4×D4×C61—28no—
158C4×D4×C61—22no—
159C4×D4×C61—22no—
160C4×D4×C61C2314yes—
161C4×D4×C61C2314yes—
162#117×C61—22no—
163#117×C61—28no—
164#117×C61C2314yes—
165C2×C4⋊C4×C61—21no—
166C2×C4⋊C4×C61—21no—
167C2×C4⋊C4×C61C2311yescharacteristic
168C2×C4⋊C4×C61C2311yescharacteristic
169C2×C22⋊C4×C61—21no—
170C2×C22⋊C4×C61—21no—
171C2×C22⋊C4×C61—21no—
172C2×C42×C61—21no—
173C2×C42×C61—21no—
174C2×C42×C61—21no—
175C2×C42×C61—28no—
176C2×C42×C61D411yescharacteristic
177C2×C42×C61D411yescharacteristic
178C2×C42×C61D414yes—
179C2×C42×C61C2311yescharacteristic
180C2×C42×C61C2311yescharacteristic
181C2×C42×C61C2314yes—
182C24×C61—21no—
183C24×C61C2×D411yescharacteristic
184C23×D61—21no—
185#41×C61—216no—
186#41×C61—28no—
187#41×C61—28no—
188C2×Q8×C61—21no—
189C2×Q8×C61—22no—
190C2×Q8×C61#4114yes—
191C2×Q8×C61C2412yes—
192C2×D4×C61—28no—
193C2×D4×C61—24no—
194C2×D4×C61—21no—
195C2×D4×C61—22no—
196C2×D4×C61#4114yes—
197C2×D4×C61C2412yes—
198C22×C4×C61—28no—
199C22×C4×C61—21no—
200C22×C4×C61—24no—
201C22×C4×C61—22no—
202C22×C4×C61—22no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—24no—
206C22×C4×C61—24no—
207C22×C4×C61—42no—
208C22×C4×C61—42no—
209C22×C4×C61—44no—
210C22×C4×C61—44no—
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D412yes—
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D414yes—
218C22×C4×C61C2×D414yes—
219C22×C4×C61C2412yes—
220C22×C4×C61C2411yescharacteristic
221C2×C22⋊D61—24no—
222C2×C22⋊D61—44no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C2×D244—22no—
227C2×D244—22no—
228C2×D244—21no—
229C2×D244C2412yes—
230C2×C4×D61—24no—
231C2×C4×D61—44no—
232C2×Dic122—22no—
233C2×Dic122—22no—
234C2×Dic122—21no—
235C2×Dic122C2412yes—
236C4⋊C4×C61—24no—
237C4⋊C4×C61—24no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61C2412yes—
241C4⋊C4×C61C2412yes—
242C22⋊C4×C61—24no—
243C22⋊C4×C61—24no—
244C22⋊C4×C61—24no—
245C42×C61—24no—
246C42×C61—24no—
247C42×C61—24no—
248C42×C61C2×D414yes—
249C42×C61C2×D414yes—
250C42×C61C2×D412yes—
251C42×C61C2×D412yes—
252C42×C61C2412yes—
253C42×C61C2412yes—
254C22⋊Dic61—24no—
255#11758202—28no—
256#11758201—28no—
257#11758200—28no—
258#11758199—28no—
259#11758198—24no—
260#11758198—24no—
261#11758198—24no—
262#11758198—24no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61C2412yes—
266C4⋊Dic61C2412yes—
267#11758196—24no—
268#11758196—24no—
269#11758196—24no—
270#11758196—24no—
271C4×Dic61—24no—
272C2×#92418—22no—
273C2×#92418—22no—
274C2×#92418—22no—
275C2×#92418—22no—
276C2×#92418C2412yes—
277C2×#92418C2412yes—
278C2×#92418C2412yes—
279C2×#92418C2412yes—
280C23×C61—22no—
281C23×C61—24no—
282C23×C61—22no—
283C23×C61—22no—
284C23×C61—22no—
285C23×C61—42no—
286C23×C61—42no—
287C23×C61C22×D412yes—
288C23×C61C22×D411yescharacteristic
289C22×D61—22no—
290C22×D61—42no—
291C22×D61—42no—
292C22×D61—42no—
293Q8×C61—24no—
294Q8×C61—22no—
295Q8×C61C2×#4114yes—
296D4×C61—216no—
297D4×C61—24no—
298D4×C61—22no—
299D4×C61C2×#4114yes—
300C2×C4×C61—216no—
301C2×C4×C61—22no—
302C2×C4×C61—24no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—24no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—44no—
314C2×C4×C61—44no—
315C2×C4×C61—48no—
316C2×C4×C61—48no—
317C2×C4×C61—42no—
318C2×C4×C61—42no—
319C2×C4×C61C22×D412yes—
320C2×C4×C61C22×D412yes—
321C2×C4×C61C22×D412yes—
322C2×C4×C61C22×D412yes—
323C2×C4×C61C22×D412yes—
324C2×C4×C61C22×D411yescharacteristic
325C2×C4×C61C2×#4112yes—
326C2×C4×C61C2×#4112yes—
327C2×C4×C61C2511yescharacteristic
328C22⋊D61—48no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335D244—22no—
336D244—22no—
337D244—42no—
338C4×D61—48no—
339Dic122—22no—
340Dic122—22no—
341Dic122—42no—
342#92418—22no—
343#92418—22no—
344#92418—22no—
345#92418—22no—
346C2×#3111—611nomaximal, Sylow
347C22×C61—22no—
348C22×C61—24no—
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—44no—
352C22×C61—48no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61#52512yes—
356C22×C61#57512yes—
357C22×C61#57512yes—
358C22×C61C23×D411yescharacteristic
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—84no—
363C4×C61—22no—
364C4×C61—24no—
365C4×C61—22no—
366C4×C61—22no—
367C4×C61—22no—
368C4×C61—22no—
369C4×C61—42no—
370C4×C61—42no—
371C4×C61#52512yes—
372C4×C61C22×#4111yescharacteristic
373C4×C61C22×#4111yescharacteristic
374Dic61—42no—
375Dic61—42no—
376Dic61—42no—
377C2×#529—611no—
378C2×C4×#41D6111yescharacteristic, complemented
379#3111—6116no—
380C2×#485—611no—
381C2×#482—611no—
382C2×#479—611no—
383C2×#478—611no—
384C2×#464—611no—
385C2×#463—611no—
386C2×#452—611no—
387C2×#449—611no—
388C2×#442—611no—
389C2×#441—611no—
390C2×#440—611no—
391C2×#440—611no—
392C2×#432—611no—
393C2×C61—42no—
394C2×C61—44no—
395C2×C61#311114yescomplemented
396C2×C61C2×#52511yescharacteristic
397C2×C61C2×#57511yescharacteristic
398C2×C61C2×#57511yescharacteristic
399D61—82no—
400C22×#41C2×D6111yescharacteristic
401C22×Q16—611no—
402C22×SD16—611no—
403C22×SD16—611no—
404C22×D8—611no—
405#529—618no—
406#529—1224no—
407C2×#126—1221no—
408C2×#125—611no—
409C2×#124—611no—
410C2×#123—1221no—
411C2×C22⋊Q8—611no—
412C2×#121—611no—
413C4×#41—24no—
414C4×#41C2×D6118yescomplemented
415C2×C4×Q8—611no—
416C2×C4×Q8C2×D6111yescharacteristic
417C2×C4×Q8C2×D6111yescharacteristic
418C2×C4×D4—21no—
419C2×C4×D4—21no—
420C2×C4×D4—611no—
421C2×C4×D4—1221no—
422C2×C4×D4C2×D6111yescharacteristic
423C2×C4×D4C2×D6111yescharacteristic
424C2×#117—21no—
425C2×#117—1221no—
426C2×#117C2×D6111yescharacteristic
427C22×C42—21no—
428C22×C42C2×D6111yescharacteristic
429#485—618no—
430#482—618no—
431#479—618no—
432#478—618no—
433#464—618no—
434#463—618no—
435#452—618no—
436#449—618no—
437#442—618no—
438#441—618no—
439#440—618no—
440#440—618no—
441#432—618no—
442C2×#107—611no—
443C2×#107—611no—
444C2×#106—611no—
445C2×#106—611no—
446C2×C4⋊C8—611no—
447C2×C4⋊C8—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#103—611no—
451C2×#103—611no—
452C2×#102—611no—
453C2×#102—611no—
454C2×#102—611no—
455C2×#102—611no—
456C2×C22⋊C8—611no—
457C2×C22⋊C8—611no—
458C2×#97—611no—
459C2×#97—611no—
460C61C2×#311111yescharacteristic, complemented, Sylow
461C2×#41—24no—
462C2×#41—24no—
463C2×#41—22no—
464C2×#41C22×D6114yes—
465C22×Q8—611no—
466C22×Q8C22×D6111yescharacteristic
467C22×D4—21no—
468C22×D4—611no—
469C22×D4—1221no—
470C22×D4C22×D6111yescharacteristic
471C23×C4—21no—
472C23×C4—21no—
473C23×C4—21no—
474C23×C4—1221no—
475C23×C4C22⋊D6111yescharacteristic
476C23×C4C22⋊D6111yescharacteristic
477C23×C4C22×D6111yescharacteristic
478C2×Q16—614no—
479C2×Q16—1224no—
480C2×SD16—614no—
481C2×SD16—614no—
482C2×SD16—1224no—
483C2×SD16—1224no—
484C2×D8—614no—
485C2×D8—1224no—
486C22×C8—611no—
487C22×C8—611no—
488C22×C8—611no—
489C22×C8—611no—
490#126—1228no—
491#125—614no—
492#125—1222no—
493#124—614no—
494#124—1222no—
495#123—1228no—
496C22⋊Q8—614no—
497C22⋊Q8—1222no—
498#121—614no—
499#121—1222no—
500C4×Q8—22no—
501C4×Q8—22no—
502C4×Q8—614no—
503C4×Q8—1222no—
504C4×Q8C22×D6114yes—
505C4×Q8C22×D6114yes—
506C4×D4—28no—
507C4×D4—28no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—614no—
511C4×D4—1228no—
512C4×D4—1222no—
513C4×D4C22×D6114yes—
514C4×D4C22×D6114yes—
515#117—22no—
516#117—28no—
517#117—1228no—
518#117C22×D6114yes—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4C22×D6111yescharacteristic
528C2×C4⋊C4C22×D6111yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C42—21no—
538C2×C42—21no—
539C2×C42—21no—
540C2×C42—28no—
541C2×C42—1221no—
542C2×C42C22⋊D6111yescharacteristic
543C2×C42C22⋊D6114yes—
544C2×C42C22⋊D6111yescharacteristic
545C2×C42C22×D6111yescharacteristic
546C2×C42C22×D6111yescharacteristic
547C2×C42C22×D6114yes—
548#107—614no—
549#107—614no—
550#106—614no—
551#106—614no—
552C4⋊C8—614no—
553C4⋊C8—614no—
554#103—614no—
555#103—614no—
556#103—614no—
557#103—614no—
558#102—614no—
559#102—614no—
560#102—614no—
561#102—614no—
562C22⋊C8—614no—
563C22⋊C8—614no—
564#97—614no—
565#97—614no—
566C24—21no—
567C24—1221no—
568C24C2×C22⋊D6111yescharacteristic
569#41—216no—
570#41—28no—
571#41—28no—
572C2×Q8—21no—
573C2×Q8—22no—
574C2×Q8—612no—
575C2×Q8—1221no—
576C2×Q8—1222no—
577C2×Q8—1222no—
578C2×Q8#1175822214yes—
579C2×Q8C23×D6112yes—
580C2×D4—28no—
581C2×D4—24no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—612no—
585C2×D4—1224no—
586C2×D4—1221no—
587C2×D4—1222no—
588C2×D4—1222no—
589C2×D4—2444no—
590C2×D4#1175822214yes—
591C2×D4C23×D6112yes—
592C22×C4—28no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1224no—
609C22×C4—2444no—
610C22×C4C2×C22⋊D6112yes—
611C22×C4C2×C22⋊D6111yescharacteristic
612C22×C4C2×C22⋊D6111yescharacteristic
613C22×C4C2×C22⋊D6111yescharacteristic
614C22×C4C2×C22⋊D6111yescharacteristic
615C22×C4C2×C22⋊D6111yescharacteristic
616C22×C4C2×C22⋊D6114yes—
617C22×C4C2×C22⋊D6114yes—
618C22×C4C23×D6112yes—
619C22×C4C23×D6111yescharacteristic
620Q16—1228no—
621SD16—1228no—
622SD16—1228no—
623D8—1228no—
624C2×C8—612no—
625C2×C8—612no—
626C2×C8—612no—
627C2×C8—612no—
628C2×C8—1222no—
629C2×C8—1222no—
630C2×C8—1222no—
631C2×C8—1222no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—612no—
637C4⋊C4—612no—
638C4⋊C4—1221no—
639C4⋊C4—1221no—
640C4⋊C4—1224no—
641C4⋊C4—1224no—
642C4⋊C4—1224no—
643C4⋊C4—1224no—
644C4⋊C4C23×D6112yes—
645C4⋊C4C23×D6112yes—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—1224no—
650C22⋊C4—1224no—
651C22⋊C4—1224no—
652C22⋊C4—1224no—
653C22⋊C4—1224no—
654C42—24no—
655C42—24no—
656C42—24no—
657C42—1224no—
658C42C2×C22⋊D6114yes—
659C42C2×C22⋊D6114yes—
660C42C2×C22⋊D6112yes—
661C42C2×C22⋊D6112yes—
662C42C23×D6112yes—
663C42C23×D6112yes—
664C23—22no—
665C23—24no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—42no—
670C23—42no—
671C23—1222no—
672C23—2442no—
673C23—2442no—
674C23—2442no—
675C23C22×C22⋊D6112yes—
676C23C22×C22⋊D6111yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—1222no—
680Q8—1222no—
681Q8—2442no—
682Q8C2×#1175822214yes—
683D4—216no—
684D4—24no—
685D4—22no—
686D4—1222no—
687D4—1222no—
688D4—2448no—
689D4—2442no—
690D4C2×#1175822214yes—
691C2×C4—216no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—48no—
707C2×C4—48no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—2448no—
714C2×C4—2442no—
715C2×C4—2442no—
716C2×C4—2442no—
717C2×C4C22×C22⋊D6112yes—
718C2×C4C22×C22⋊D6112yes—
719C2×C4C22×C22⋊D6112yes—
720C2×C4C22×C22⋊D6112yes—
721C2×C4C22×C22⋊D6112yes—
722C2×C4C22×C22⋊D6111yescharacteristic
723C2×C4C2×#1175822212yes—
724C2×C4C2×#1175822212yes—
725C2×C4C24×D6111yescharacteristic
726C8—1222no—
727C8—1222no—
728C8—1222no—
729C8—1222no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—24no—
734C22—44no—
735C22—48no—
736C22—42no—
737C22—42no—
738C22—4884no—
739C22—2442no—
740C22—2442no—
741C22—2442no—
742C22#1684027312yes—
743C22#1684056012yes—
744C22#1684056012yes—
745C22C23×C22⋊D6111yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—2442no—
755C4—2442no—
756C4—2442no—
757C4#1684027312yes—
758C4C22×#1175822211yescharacteristic
759C4C22×#1175822211yescharacteristic
760C2—42no—
761C2—44no—
762C2—4882no—
763C2#2145592814yesdirect product factor
764C2C2×#1684027311yescharacteristic
765C2C2×#1684056011yescharacteristic
766C2C2×#1684056011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C4×#41×C61C2
socleC23×C61C22×D4
prime radicalC2×#16839907C2
hypercenterC2×C4×#41D61
hypocenterC61C2×#3111
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#16840296C2semidirect
2. #21455928C2direct (N × H)
3. C2×#16840103C2semidirect
4. C2×#16840086C2semidirect
5. C2×#16840069C2semidirect
6. C2×#16840062C2semidirect
7. C2×#16839984C2semidirect
8. C2×#16839977C2semidirect
9. C2×#16839924C2semidirect
11. C2×#16839872C2semidirect
12. C2×#16839867C2semidirect
13. C2×#16839862C2semidirect
14. C2×#16839860C2semidirect
15. C2×#16839819C2semidirect
16. C2×C4×#41×C61C2semidirect
22. #16840296C22semidirect
33. #16840103C22semidirect
34. #16840086C22semidirect
35. #16840069C22semidirect
36. #16840062C22semidirect
37. #16839984C22semidirect
38. #16839977C22semidirect
39. #16839924C22semidirect
41. #16839872C22semidirect
42. #16839867C22semidirect
43. #16839862C22semidirect
44. #16839860C22semidirect
45. #16839819C22semidirect
66. C4×#41×C61C22semidirect
378. C2×C4×#41D61semidirect
395. C2×C61#3111semidirect
414. C4×#41C2×D61semidirect
460. C61C2×#3111semidirect
763. C2#21455928direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402962
#214559282
C2×#168401032
C2×#168400862
C2×#168400692
C2×#168400622
C2×#168399842
C2×#168399772
C2×#168399242
C2×#168399072
C2×#168398722
C2×#168398672
C2×#168398622
C2×#168398602
C2×#168398192
C2×C4×#41×C612
C2×#311161