Finite Group Databasebeta

← C2×#21454661 #30544121

Subgroups — C2×#21454661 #30544121

Order 15616.

2730 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519809C211yesmaximal, characteristic
2C2×#16840244C211yesmaximal, characteristic
3C2×#16840238C211yesmaximal, characteristic, complemented
4#21454661C2116yesmaximal, direct product factor
5C2×#16839866C211yesmaximal, characteristic, complemented
6C2×#16839865C211yesmaximal, characteristic, complemented
7C2×#16839864C211yesmaximal, characteristic, complemented
8C2×Q16×Dic61C211yesmaximal, characteristic, complemented
9C2×C4×#11758202C211yesmaximal, characteristic, complemented
10C2×C4×#11758201C211yesmaximal, characteristic, complemented
11C2×#16839849C211yesmaximal, characteristic, complemented
12C2×#16839801C211yesmaximal, characteristic, complemented
13C2×#16839757C211yesmaximal, characteristic
14C2×#103×D61C211yesmaximal, characteristic, complemented
15C2×#16839719C211yesmaximal, characteristic, complemented
16C2×C61×#441C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic
19C2×#14519809C4116yescomplemented
20C2×#14519809C2218yes—
21C22×#11758202C2211yescharacteristic
22C22×#11758190C2211yescharacteristic
23C22×#11758201C2211yescharacteristic
24C22×#11758189C2211yescharacteristic
25C22×C8×D61C2211yescharacteristic
26#16840244—24no—
27#16840244C2218yes—
28#16840238—24no—
29#16840238C2218yescomplemented
30C2×Q8×Dic61C2211yescharacteristic
31C2×Q8×Dic61C2211yescharacteristic
32C2×C4×Dic122—21no—
33C2×C4×Dic122C2211yescharacteristic
34C2×#14519742—21no—
35C2×#14519742C2211yescharacteristic
36C2×C4×D244—21no—
37C2×C4×D244C2211yescharacteristic
38C2×#14519739—21no—
39C2×#14519739C2211yescharacteristic
40C2×#14519735—21no—
41C2×#14519735C2211yescharacteristic
42C2×#14519734—21no—
43C2×#14519734—21no—
44C2×#14519734C2211yescharacteristic
45C2×C4⋊C4×D61—21no—
46C2×C4⋊C4×D61C2211yescharacteristic
47#16839866C2218yescomplemented
48#16839865C2218yescomplemented
49#16839864C2218yescomplemented
50Q16×Dic61C2218yescomplemented
51C4×#11758202C2218yescomplemented
52C4×#11758201C2218yescomplemented
53#16839849C2218yescomplemented
54#16839801C2218yescomplemented
55C2×#14519711C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58#16839757C2218yes—
59C2×#14519702C2211yescharacteristic
60C2×#14519701C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63#103×D61C2218yescomplemented
64C2×#14519699C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66#16839719C2218yescomplemented
67C2×#14519687C2211yescharacteristic
68C2×C4×#92418C2211yescharacteristic
69C2×C8×Dic61C2211yescharacteristic
70C22×Q16×C61C2211yescharacteristic
71C2×C4×Q8×C61C2211yescharacteristic
72C2×C4×Q8×C61C2211yescharacteristic
73C61×#441C2218yescomplemented
74C2×#106×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#103×C61C2211yescharacteristic
77C2×#97×C61C2211yescharacteristic
78C2×#11758226—22no—
79C2×#11758226—24no—
80C2×#11758226C2×C418yes—
81C2×#11758226C2314yes—
82C22×Dic122—21no—
83C22×Dic122C2311yescharacteristic
84C2×Q8×D61—22no—
85C2×Q8×D61—24no—
86C2×Q8×D61C2×C418yescomplemented
87C2×Q8×D61C2314yes—
88C22×D244—21no—
89C22×D244C2311yescharacteristic
90C22×C4×D61—21no—
91C22×C4×D61—21no—
92C22×C4×D61—21no—
93C22×C4×D61—21no—
94C22×C4×D61—21no—
95C22×C4×D61C2311yescharacteristic
96#14519809C2×C4164yescomplemented
97C2×#11758202C2×C418yescomplemented
98C2×#11758202C2314yes—
99C2×#11758190C2×C418yescomplemented
100C2×#11758190C2314yes—
101C2×#11758201C2×C418yescomplemented
102C2×#11758201C2314yes—
103C2×#11758189C2×C418yescomplemented
104C2×#11758189C2314yes—
105C22×#92418C2311yescharacteristic
106C22×#92418C2311yescharacteristic
107C2×C8×D61—24no—
108C2×C8×D61C2314yes—
109Q8×Dic61—22no—
110Q8×Dic61—22no—
111Q8×Dic61C2314yes—
112Q8×Dic61C2314yes—
113C4×Dic122—22no—
114C4×Dic122—28no—
115C4×Dic122C2314yes—
116#14519742—28no—
117#14519742—22no—
118#14519742C2314yes—
119C4×D244—22no—
120C4×D244—28no—
121C4×D244C2314yes—
122#14519739—28no—
123#14519739—22no—
124#14519739C2314yes—
125#14519735—22no—
126#14519735—28no—
127#14519735C2314yes—
128#14519734—28no—
129#14519734—28no—
130#14519734D414yes—
131#14519734C2314yes—
132C2×C4⋊Dic61—21no—
133C2×C4⋊Dic61—21no—
134C2×C4⋊Dic61C2311yescharacteristic
135C2×C4⋊Dic61C2311yescharacteristic
136C2×#11758196—21no—
137C2×#11758196—21no—
138C2×#11758196—21no—
139C2×#11758196D411yescharacteristic
140C2×#11758196D411yescharacteristic
141C4⋊C4×D61—22no—
142C4⋊C4×D61—28no—
143C4⋊C4×D61C2314yes—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198D411yescharacteristic
148C2×#11758198D411yescharacteristic
149C2×C4×Dic61—21no—
150C2×C4×Dic61—21no—
151C2×C4×Dic61—21no—
152C2×C4×Dic61—21no—
153C2×C4×Dic61—21no—
154C2×C4×Dic61C2311yescharacteristic
155#14519711C2314yes—
156#14519710C2314yes—
157#14519708C2314yes—
158#14519702C2314yes—
159#14519701C2314yes—
160#14519701C2314yes—
161#14519700C2314yes—
162#14519699C2314yes—
163#14519697C2314yes—
164#14519687C2314yes—
165C4×#92418C2314yes—
166C8×Dic61C2314yes—
167C22×Q8×C61C2311yescharacteristic
168C22×Q8×C61C2311yescharacteristic
169C2×Q16×C61C2×C418yescomplemented
170C2×Q16×C61C2314yes—
171C22×C8×C61C2311yescharacteristic
172C22×C8×C61C2311yescharacteristic
173C4×Q8×C61—22no—
174C4×Q8×C61—22no—
175C4×Q8×C61C2314yes—
176C4×Q8×C61C2314yes—
177C2×C4⋊C4×C61—21no—
178C2×C4⋊C4×C61—21no—
179C2×C4⋊C4×C61C2311yescharacteristic
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C42×C61—21no—
182C2×C42×C61—21no—
183C2×C42×C61C2311yescharacteristic
184#106×C61C2314yes—
185#103×C61C2314yes—
186#103×C61C2314yes—
187#97×C61C2314yes—
188C23×D61—21no—
189C23×D61C2×D411yescharacteristic
190C2×Q8×C61—21no—
191C2×Q8×C61—21no—
192C2×Q8×C61—22no—
193C2×Q8×C61—22no—
194C2×Q8×C61C22×C414yes—
195C2×Q8×C61C22×C414yes—
196C2×Q8×C61C2412yes—
197C2×Q8×C61C2412yes—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2411yescharacteristic
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61C2×D411yescharacteristic
209C22×Dic61C2×D411yescharacteristic
210C22×Dic61C2×D411yescharacteristic
211#11758226—216no—
212#11758226—28no—
213#11758226C22×C4116yes—
214Q8×D61—216no—
215Q8×D61—28no—
216Q8×D61C22×C4116yescomplemented
217C2×D244—28no—
218C2×D244—24no—
219C2×D244—21no—
220C2×D244—22no—
221C2×D244C22×C414yes—
222C2×D244C2412yes—
223C2×C4×D61—28no—
224C2×C4×D61—24no—
225C2×C4×D61—28no—
226C2×C4×D61—24no—
227C2×C4×D61—24no—
228C2×C4×D61—24no—
229C2×C4×D61—24no—
230C2×C4×D61—82no—
231C2×C4×D61—82no—
232C2×C4×D61—82no—
233C2×C4×D61C22×C414yes—
234C2×C4×D61C2×D412yes—
235C2×C4×D61#4114yes—
236C2×C4×D61C2412yes—
237C2×Dic122—21no—
238C2×Dic122—22no—
239C2×Dic122—28no—
240C2×Dic122—24no—
241C2×Dic122C22×C414yes—
242C2×Dic122C2412yes—
243Q16×C61C22×C4116yescomplemented
244C2×C8×C61—22no—
245C2×C8×C61C22×C414yes—
246C2×C8×C61C2412yes—
247C2×C8×C61C2412yes—
248C4⋊C4×C61—24no—
249C4⋊C4×C61—24no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61C2412yes—
253C4⋊C4×C61C2412yes—
254C42×C61—24no—
255C42×C61—24no—
256C42×C61C2×D412yes—
257C42×C61C2412yes—
258#11758202C22×C4116yescomplemented
259#11758201C22×C4116yescomplemented
260#11758198—24no—
261#11758198—24no—
262#11758198—24no—
263#11758198C2×D414yes—
264#11758198C2×D414yes—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—24no—
268C4⋊Dic61—24no—
269C4⋊Dic61C2412yes—
270C4⋊Dic61C2412yes—
271#11758196—24no—
272#11758196—24no—
273#11758196—24no—
274#11758196C2×D414yes—
275#11758196C2×D414yes—
276C4×Dic61—24no—
277C4×Dic61—24no—
278C4×Dic61—24no—
279C4×Dic61—24no—
280C4×Dic61—24no—
281C4×Dic61C2×D412yes—
282C4×Dic61C2412yes—
283C2×#92418—22no—
284C2×#92418C22×C414yes—
285C2×#92418C2412yes—
286C2×#92418C2412yes—
287#11758190C22×C4116yescomplemented
288#11758189C22×C4116yescomplemented
289C8×D61—28no—
290C23×C61C22×D411yescharacteristic
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—24no—
294C22×D61—22no—
295C22×D61—42no—
296C22×D61—42no—
297C22×D61C4×D414yes—
298C22×D61C22×D412yes—
299Q8×C61—24no—
300Q8×C61—24no—
301Q8×C61—22no—
302Q8×C61—22no—
303Q8×C61C23×C414yes—
304Q8×C61C23×C414yes—
305C2×C4×C61—24no—
306C2×C4×C61—24no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61C23×C412yes—
316C2×C4×C61C22×D412yes—
317C2×C4×C61C22×D412yes—
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C2×#4112yes—
320C2×C4×C61C2511yescharacteristic
321C2×Dic61—24no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61C4×D414yes—
330C2×Dic61C22×D412yes—
331C2×Dic61C22×D412yes—
332C2×Dic61C22×D412yes—
333D244—216no—
334D244—24no—
335D244—22no—
336D244C23×C414yes—
337C4×D61—216no—
338C4×D61—216no—
339C4×D61—84no—
340C4×D61—84no—
341C4×D61—84no—
342C4×D61C4×D418yes—
343C4×D61C23×C414yes—
344C4×D61C2×#4114yes—
345Dic122—24no—
346Dic122—22no—
347Dic122—216no—
348Dic122C23×C414yes—
349C8×C61—22no—
350C8×C61C23×C414yes—
351#92418—22no—
352#92418C23×C414yes—
353C2×#2947—611nomaximal, Sylow
354C22×C61C2×C4×D412yes—
355C22×C61#57712yes—
356C22×C61#57812yes—
357C22×C61C23×D411yescharacteristic
358C2×D61—28no—
359C2×D61—22no—
360C2×D61—22no—
361C2×D61—24no—
362C2×D61—48no—
363C2×D61—42no—
364C2×D61—42no—
365C2×D61C2×C4×D414yes—
366C4×C61—24no—
367C4×C61—24no—
368C4×C61—22no—
369C4×C61—22no—
370C4×C61—42no—
371C4×C61—42no—
372C4×C61C2×C4×D412yes—
373C4×C61C24×C411yescharacteristic
374C4×C61C22×#4111yescharacteristic
375Dic61—24no—
376Dic61—22no—
377Dic61—22no—
378Dic61—42no—
379Dic61—42no—
380Dic61C2×C4×D414yes—
381C22×#137—611no—
382C2×#520—611no—
383C2×#519—611no—
384#2947—6116no—
385C2×#441—611no—
386C2×#441D6111yescharacteristic, complemented
387C2×#440—611no—
388C2×#440—611no—
389C2×C4×Q16—611no—
390C2×C4×Q16—611no—
391C2×C4×SD16—611no—
392C2×C4×SD16—611no—
393C2×#428—611no—
394C2×#416—611no—
395C22×#103—611no—
396C2×#405—611no—
397C2×C61#294714yescomplemented
398C2×C61C22×C4×D411yescharacteristic
399C2×C61C2×#57711yescharacteristic
400C2×C61C2×#57811yescharacteristic
401D61—24no—
402D61—44no—
403C22×#41—611no—
404C23×Q8—611no—
405C2×#137—6116no—
406C2×#137—618no—
407C22×Q16—611no—
408C22×Q16C2×D6111yescharacteristic
409C22×SD16—611no—
410C22×SD16—611no—
411C22×M16—611no—
412C23×C8—611no—
413#520—618no—
414#520—1224no—
415#519—618no—
416#519—1224no—
417C2×C4×Q8—611no—
418C2×C4×Q8—611no—
419C2×C4×Q8—611no—
420C2×C4×Q8—611no—
421C2×C4×Q8—1221no—
422C2×C4×Q8—1221no—
423C2×C4×Q8C2×D6111yescharacteristic
424C2×C4×Q8C2×D6111yescharacteristic
425C2×C4×D4—611no—
426C2×C4×D4—611no—
427C2×C4×D4—1221no—
428C2×C4×D4—1221no—
429C2×#117—611no—
430C2×#117—611no—
431C2×#117—1221no—
432C2×#117—1221no—
433C2×#117—1221no—
434C22×C4⋊C4—611no—
435C22×C4⋊C4—1221no—
436#441—618no—
437#441C2×D6118yescomplemented
438#440—618no—
439#440—618no—
440C4×Q16—618no—
441C4×Q16—618no—
442C4×SD16—618no—
443C4×SD16—618no—
444#428—618no—
445C2×#107—611no—
446C2×#107—611no—
447C2×#106—611no—
448C2×#106C2×D6111yescharacteristic
449#416—618no—
450C2×#103—611no—
451C2×#103—611no—
452C2×#103—611no—
453C2×#103—611no—
454C2×#103—618no—
455C2×#103C2×D6111yescharacteristic
456C2×#103C2×D6111yescharacteristic
457C2×#102—611no—
458C2×#102—611no—
459#405—618no—
460C2×#97—611no—
461C2×#97C2×D6111yescharacteristic
462C2×C4×C8—611no—
463C2×C4×C8—611no—
464C61C2×#294711yescharacteristic, complemented, Sylow
465C2×#41—618no—
466C2×#41—614no—
467C2×#41—1222no—
468C2×#41—1224no—
469C22×Q8—618no—
470C22×Q8—614no—
471C22×Q8—611no—
472C22×Q8—1221no—
473C22×Q8—1222no—
474C22×Q8—1224no—
475C22×Q8C22×D6111yescharacteristic
476C22×Q8C22×D6111yescharacteristic
477C22×D4—611no—
478C22×D4—1221no—
479C23×C4—611no—
480C23×C4—1221no—
481C23×C4—1221no—
482C23×C4—1221no—
483C23×C4—1221no—
484C23×C4—1221no—
485#137—6164no—
486C2×Q16—618no—
487C2×Q16—614no—
488C2×Q16C4×D6118yescomplemented
489C2×Q16C22×D6114yes—
490C2×SD16—618no—
491C2×SD16—614no—
492C2×SD16—618no—
493C2×SD16—614no—
494C2×M16—618no—
495C2×M16—614no—
496C22×C8—611no—
497C22×C8—611no—
498C22×C8—614no—
499C22×C8—1224no—
500C22×C8C22×D6111yescharacteristic
501C22×C8C22×D6111yescharacteristic
502C4×Q8—22no—
503C4×Q8—22no—
504C4×Q8—614no—
505C4×Q8—614no—
506C4×Q8—614no—
507C4×Q8—614no—
508C4×Q8—1228no—
509C4×Q8—1222no—
510C4×Q8—1222no—
511C4×Q8—1222no—
512C4×Q8—1228no—
513C4×Q8—1222no—
514C4×Q8C22×D6114yes—
515C4×Q8C22×D6114yes—
516C4×D4—614no—
517C4×D4—614no—
518C4×D4—1228no—
519C4×D4—1222no—
520C4×D4—1228no—
521C4×D4—1222no—
522#117—614no—
523#117—614no—
524#117—614no—
525#117—1228no—
526#117—1228no—
527#117—1228no—
528#117—1222no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—611no—
532C2×C4⋊C4—611no—
533C2×C4⋊C4—611no—
534C2×C4⋊C4—611no—
535C2×C4⋊C4—614no—
536C2×C4⋊C4—1228no—
537C2×C4⋊C4—1222no—
538C2×C4⋊C4—1221no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4C22×D6111yescharacteristic
544C2×C4⋊C4C22×D6111yescharacteristic
545C2×C22⋊C4—611no—
546C2×C22⋊C4—611no—
547C2×C22⋊C4—1221no—
548C2×C22⋊C4—1221no—
549C2×C22⋊C4—1221no—
550C2×C42—21no—
551C2×C42—21no—
552C2×C42—611no—
553C2×C42—1221no—
554C2×C42—1221no—
555C2×C42—1221no—
556C2×C42—1221no—
557C2×C42—1221no—
558C2×C42C22×D6111yescharacteristic
559#107—614no—
560#107—614no—
561#106—614no—
562#106C22×D6114yes—
563#103—614no—
564#103—614no—
565#103—614no—
566#103—614no—
567#103C22×D6114yes—
568#103C22×D6114yes—
569#102—614no—
570#102—614no—
571#97—614no—
572#97C22×D6114yes—
573C4×C8—614no—
574C4×C8—614no—
575C24—611no—
576C24—1221no—
577#41—6116no—
578#41—12216no—
579#41—1228no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—6116no—
585C2×Q8—614no—
586C2×Q8—612no—
587C2×Q8—1224no—
588C2×Q8—1228no—
589C2×Q8—12216no—
590C2×Q8—1228no—
591C2×Q8—1221no—
592C2×Q8—1222no—
593C2×Q8C2×C4×D6114yes—
594C2×Q8C2×C4×D6114yes—
595C2×Q8C23×D6112yes—
596C2×Q8C23×D6112yes—
597C2×D4—614no—
598C2×D4—612no—
599C2×D4—1224no—
600C2×D4—1228no—
601C2×D4—1221no—
602C2×D4—1222no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—611no—
608C22×C4—614no—
609C22×C4—612no—
610C22×C4—614no—
611C22×C4—612no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—1224no—
615C22×C4—1228no—
616C22×C4—1224no—
617C22×C4—1224no—
618C22×C4—1228no—
619C22×C4—1224no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1224no—
624C22×C4—4882no—
625C22×C4—4882no—
626C22×C4—4882no—
627C22×C4D4×D6111yescharacteristic
628C22×C4D4×D6111yescharacteristic
629C22×C4C23×D6111yescharacteristic
630Q16—6116no—
631Q16C2×C4×D61116yescomplemented
632SD16—6116no—
633SD16—6116no—
634M16—6116no—
635C2×C8—22no—
636C2×C8—614no—
637C2×C8—612no—
638C2×C8—612no—
639C2×C8—1228no—
640C2×C8—1222no—
641C2×C8C2×C4×D6114yes—
642C2×C8C23×D6112yes—
643C2×C8C23×D6112yes—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—614no—
649C4⋊C4—614no—
650C4⋊C4—612no—
651C4⋊C4—612no—
652C4⋊C4—1224no—
653C4⋊C4—1224no—
654C4⋊C4—1224no—
655C4⋊C4—1224no—
656C4⋊C4—1221no—
657C4⋊C4—1221no—
658C4⋊C4—1224no—
659C4⋊C4C23×D6112yes—
660C4⋊C4C23×D6112yes—
661C22⋊C4—614no—
662C22⋊C4—614no—
663C22⋊C4—1224no—
664C22⋊C4—1224no—
665C22⋊C4—1224no—
666C42—24no—
667C42—24no—
668C42—612no—
669C42—612no—
670C42—1224no—
671C42—1224no—
672C42—1224no—
673C42—1224no—
674C42—1224no—
675C42D4×D6112yes—
676C42C23×D6112yes—
677C23—614no—
678C23—612no—
679C23—1222no—
680C23—1222no—
681C23—1224no—
682C23—1222no—
683C23—2442no—
684C23—2442no—
685C23C2×D4×D6111yescharacteristic
686Q8—24no—
687Q8—24no—
688Q8—22no—
689Q8—22no—
690Q8—614no—
691Q8—12216no—
692Q8—1224no—
693Q8—1222no—
694Q8C22×C4×D6114yes—
695Q8C22×C4×D6114yes—
696D4—614no—
697D4—12216no—
698D4—1224no—
699D4—1222no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—614no—
711C2×C4—612no—
712C2×C4—618no—
713C2×C4—614no—
714C2×C4—614no—
715C2×C4—612no—
716C2×C4—612no—
717C2×C4—12216no—
718C2×C4—12216no—
719C2×C4—1224no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—4884no—
726C2×C4—4884no—
727C2×C4—4884no—
728C2×C4—2442no—
729C2×C4—2442no—
730C2×C4C22×C4×D6112yes—
731C2×C4C2×D4×D6112yes—
732C2×C4C2×D4×D6112yes—
733C2×C4C2×D4×D6111yescharacteristic
734C2×C4#41×D6112yes—
735C2×C4C24×D6111yescharacteristic
736C8—22no—
737C8—614no—
738C8—1222no—
739C8C22×C4×D6114yes—
740C22—614no—
741C22—1228no—
742C22—1222no—
743C22—1222no—
744C22—1224no—
745C22—2448no—
746C22—2442no—
747C22—2442no—
748C22C4×D4×D6112yes—
749C22#1684057112yes—
750C22#1684057812yes—
751C22C22×D4×D6111yescharacteristic
752C4—24no—
753C4—24no—
754C4—22no—
755C4—22no—
756C4—42no—
757C4—42no—
758C4—614no—
759C4—1224no—
760C4—1222no—
761C4—1222no—
762C4—2442no—
763C4—2442no—
764C4C4×D4×D6112yes—
765C4C23×C4×D6111yescharacteristic
766C4C2×#41×D6111yescharacteristic
767C2—1224no—
768C2—2444no—
769C2#2145466114yesdirect product factor
770C2C2×C4×D4×D6111yescharacteristic
771C2C2×#1684057111yescharacteristic
772C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC4×C61C24×C4
FrattiniC2×C4C24×D61
FittingC2×C61×#441C2
socleC23×C61C22×D4
prime radicalC22×#11758226C22
cosocleC2×C4×C61C25
hypercenterC2×#441D61
hypocenterC61C2×#2947
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
3. C2×#16840238C2semidirect
4. #21454661C2direct (N × H)
5. C2×#16839866C2semidirect
6. C2×#16839865C2semidirect
7. C2×#16839864C2semidirect
8. C2×Q16×Dic61C2semidirect
9. C2×C4×#11758202C2semidirect
10. C2×C4×#11758201C2semidirect
11. C2×#16839849C2semidirect
12. C2×#16839801C2semidirect
14. C2×#103×D61C2semidirect
15. C2×#16839719C2semidirect
16. C2×C61×#441C2semidirect
19. C2×#14519809C4semidirect
29. #16840238C22semidirect
47. #16839866C22semidirect
48. #16839865C22semidirect
49. #16839864C22semidirect
50. Q16×Dic61C22semidirect
51. C4×#11758202C22semidirect
52. C4×#11758201C22semidirect
53. #16839849C22semidirect
54. #16839801C22semidirect
63. #103×D61C22semidirect
66. #16839719C22semidirect
73. C61×#441C22semidirect
86. C2×Q8×D61C2×C4semidirect
96. #14519809C2×C4semidirect
97. C2×#11758202C2×C4semidirect
99. C2×#11758190C2×C4semidirect
101. C2×#11758201C2×C4semidirect
103. C2×#11758189C2×C4semidirect
169. C2×Q16×C61C2×C4semidirect
216. Q8×D61C22×C4semidirect
243. Q16×C61C22×C4semidirect
258. #11758202C22×C4semidirect
259. #11758201C22×C4semidirect
287. #11758190C22×C4semidirect
288. #11758189C22×C4semidirect
386. C2×#441D61semidirect
397. C2×C61#2947semidirect
437. #441C2×D61semidirect
464. C61C2×#2947semidirect
488. C2×Q16C4×D61semidirect
631. Q16C2×C4×D61semidirect
769. C2#21454661direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198092
C2×#168402442
C2×#168402382
#214546612
C2×#168398662
C2×#168398652
C2×#168398642
C2×Q16×Dic612
C2×C4×#117582022
C2×C4×#117582012
C2×#168398492
C2×#168398012
C2×#168397572
C2×#103×D612
C2×#168397192
C2×C61×#4412
C2×#294761