Finite Group Databasebeta

← C2×#21456107 #30548356

Subgroups — C2×#21456107 #30548356

Order 15616.

2122 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×#16840363C211yesmaximal, characteristic
2C2×#16840238C211yesmaximal, characteristic, complemented
3#21456107C2116yesmaximal, direct product factor
4C2×#16840088C211yesmaximal, characteristic, complemented
5C2×#16840085C211yesmaximal, characteristic, complemented
6C2×#16840072C211yesmaximal, characteristic, complemented
7C2×#16840067C211yesmaximal, characteristic, complemented
8C2×#16839961C211yesmaximal, characteristic, complemented
9C2×#16839960C211yesmaximal, characteristic, complemented
10C2×#16839902C211yesmaximal, characteristic, complemented
11C2×#16839899C211yesmaximal, characteristic, complemented
12C2×#16839862C211yesmaximal, characteristic, complemented
13C2×#16839860C211yesmaximal, characteristic, complemented
14C2×C4×#11758190C211yesmaximal, characteristic, complemented
15C2×#16839821C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C61C211yesmaximal, characteristic, complemented
17C22×Q8×D61C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21#16840363—24no—
22#16840363C2218yes—
23C2×#14519773C2211yescharacteristic
24C2×#14519768C2211yescharacteristic
25C2×#14519760—21no—
26C2×#14519759—21no—
27C2×#14519752C2211yescharacteristic
28C2×#14519751—21no—
29C2×#14519750—21no—
30C2×#14519748C2211yescharacteristic
31#16840238—24no—
32#16840238C2218yescomplemented
33C2×Q8×Dic61C2211yescharacteristic
34C2×C4×Dic122—21no—
35C2×C4×Dic122C2211yescharacteristic
36C2×#14519742—21no—
37C2×#14519742C2211yescharacteristic
38C2×C4×D244C2211yescharacteristic
39C2×#14519735—21no—
40C2×#14519735C2211yescharacteristic
41C2×#14519734—21no—
42C2×#14519734C2211yescharacteristic
43#16840088C2218yescomplemented
44#16840085C2218yescomplemented
45#16840072C2218yescomplemented
46#16840067C2218yescomplemented
47#16839961C2218yescomplemented
48#16839960C2218yescomplemented
49#16839902C2218yescomplemented
50#16839899C2218yescomplemented
51#16839862C2218yescomplemented
52#16839860C2218yescomplemented
53C4×#11758190C2218yescomplemented
54#16839821C2218yescomplemented
55C2×#14519710C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519709C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519688C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C2×C4×Q8×C61C2211yescharacteristic
71C2×C4×D4×C61C2211yescharacteristic
72C4×SD16×C61C2218yescomplemented
73C2×#106×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C4×C8×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122C2311yescharacteristic
79C2×Q8×D61—24no—
80C2×Q8×D61—22no—
81C2×Q8×D61—24no—
82C2×Q8×D61C2314yes—
83C22×D244—21no—
84C22×D244C2311yescharacteristic
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C22×C4×D61—21no—
89C22×C4×D61—21no—
90C22×C4×D61C2311yescharacteristic
91C2×#11758190—24no—
92C2×#11758190C2314yes—
93C2×#11758200—24no—
94C2×#11758200C2314yes—
95C2×#11758201—24no—
96C2×#11758201C2314yes—
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99#14519773—22no—
100#14519773C2314yes—
101#14519768—22no—
102#14519768C2314yes—
103#14519760—28no—
104#14519759—28no—
105#14519752—22no—
106#14519752C2314yes—
107#14519751—28no—
108#14519750—28no—
109#14519748—22no—
110#14519748C2314yes—
111Q8×Dic61—22no—
112Q8×Dic61C2314yes—
113C4×Dic122—22no—
114C4×Dic122—28no—
115C4×Dic122C2314yes—
116#14519742—28no—
117#14519742—22no—
118#14519742C2314yes—
119C4×D244—22no—
120C4×D244C2314yes—
121#14519735—22no—
122#14519735—28no—
123#14519735C2314yes—
124#14519734—28no—
125#14519734D414yes—
126#14519734C2314yes—
127C2×C4⋊Dic61—21no—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61C2311yescharacteristic
130C2×C4⋊Dic61C2311yescharacteristic
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196D411yescharacteristic
135C2×#11758196D411yescharacteristic
136C2×C22⋊Dic61—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198D411yescharacteristic
141C2×#11758198D411yescharacteristic
142C2×C4×Dic61—21no—
143C2×C4×Dic61—21no—
144C2×C4×Dic61—21no—
145C2×C4×Dic61—21no—
146C2×C4×Dic61C2311yescharacteristic
147#14519710C2314yes—
148#14519710C2314yes—
149#14519709C2314yes—
150#14519706C2314yes—
151#14519706C2314yes—
152#14519702C2314yes—
153#14519701C2314yes—
154#14519700C2314yes—
155#14519699C2314yes—
156#14519698C2314yes—
157#14519697C2314yes—
158#14519689C2314yes—
159#14519689C2314yes—
160#14519688C2314yes—
161C22×Q8×C61C2311yescharacteristic
162C22×D4×C61C2311yescharacteristic
163C23×C4×C61—21no—
164C2×SD16×C61—24no—
165C2×SD16×C61C2314yes—
166C22×C8×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168C4×Q8×C61—22no—
169C4×Q8×C61C2314yes—
170C4×D4×C61—22no—
171C4×D4×C61C2314yes—
172C2×C4⋊C4×C61—21no—
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C22⋊C4×C61—21no—
176C2×C42×C61—21no—
177C2×C42×C61C2311yescharacteristic
178#106×C61C2314yes—
179#103×C61C2314yes—
180#102×C61C2314yes—
181C4×C8×C61C2314yes—
182C24×C61—21no—
183C23×D61—21no—
184C23×D61C2×D411yescharacteristic
185C2×Q8×C61—21no—
186C2×Q8×C61—22no—
187C2×Q8×C61#4114yes—
188C2×Q8×C61C2412yes—
189C2×D4×C61—21no—
190C2×D4×C61—22no—
191C2×D4×C61—22no—
192C2×D4×C61C2412yes—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—24no—
197C22×C4×C61—82no—
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2411yescharacteristic
201C2×C22⋊D61—24no—
202C2×C22⋊D61—24no—
203C2×C22⋊D61—24no—
204C2×C22⋊D61—82no—
205C2×C22⋊D61—82no—
206C2×C22⋊D61—82no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61C2×D411yescharacteristic
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213Q8×D61—216no—
214Q8×D61—28no—
215Q8×D61—28no—
216C2×D244—22no—
217C2×D244—22no—
218C2×D244—21no—
219C2×D244—24no—
220C2×D244—82no—
221C2×D244C2412yes—
222C2×C4×D61—28no—
223C2×C4×D61—24no—
224C2×C4×D61—22no—
225C2×C4×D61—22no—
226C2×C4×D61—24no—
227C2×C4×D61—82no—
228C2×C4×D61C2×D412yes—
229C2×C4×D61C2412yes—
230C2×Dic122—28no—
231C2×Dic122—21no—
232C2×Dic122—22no—
233C2×Dic122—24no—
234C2×Dic122#4114yes—
235C2×Dic122C2412yes—
236SD16×C61—28no—
237C2×C8×C61—22no—
238C2×C8×C61—22no—
239C2×C8×C61C2412yes—
240C2×C8×C61C2412yes—
241C4⋊C4×C61—24no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61C2412yes—
245C4⋊C4×C61C2412yes—
246C22⋊C4×C61—24no—
247C42×C61—24no—
248C42×C61C2×D412yes—
249C42×C61C2412yes—
250C22⋊Dic61—24no—
251#11758201—28no—
252#11758200—28no—
253#11758198—24no—
254#11758198—24no—
255#11758198—24no—
256#11758198C2×D414yes—
257#11758198C2×D414yes—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—24no—
261C4⋊Dic61—24no—
262C4⋊Dic61C2412yes—
263C4⋊Dic61C2412yes—
264#11758196—24no—
265#11758196—24no—
266#11758196—24no—
267#11758196C2×D414yes—
268#11758196C2×D414yes—
269C4×Dic61—24no—
270C4×Dic61—24no—
271C4×Dic61—24no—
272C4×Dic61—24no—
273C4×Dic61C2×D412yes—
274C4×Dic61C2412yes—
275C2×#92418—22no—
276C2×#92418—22no—
277C2×#92418C2412yes—
278C2×#92418C2412yes—
279#11758190—28no—
280C23×C61—22no—
281C23×C61—42no—
282C23×C61—42no—
283C23×C61—42no—
284C23×C61C22×D411yescharacteristic
285C22×D61—22no—
286C22×D61—22no—
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—42no—
290C22×D61—42no—
291C22×D61—42no—
292C22×D61C22×D412yes—
293Q8×C61—24no—
294Q8×C61—22no—
295Q8×C61C2×#4114yes—
296D4×C61—22no—
297D4×C61—22no—
298D4×C61—42no—
299C2×C4×C61—24no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—84no—
308C2×C4×C61C22×D412yes—
309C2×C4×C61C22×D412yes—
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61C2×#4112yes—
312C2×C4×C61C2×#4112yes—
313C2×C4×C61C2511yescharacteristic
314C22⋊D61—84no—
315C22⋊D61—84no—
316C22⋊D61—84no—
317C2×Dic61—22no—
318C2×Dic61—24no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61C22×D412yes—
327C2×Dic61C22×D412yes—
328C2×Dic61C22×D412yes—
329D244—22no—
330D244—22no—
331D244—42no—
332D244—84no—
333C4×D61—216no—
334C4×D61—24no—
335C4×D61—22no—
336C4×D61—22no—
337C4×D61—84no—
338Dic122—216no—
339Dic122—24no—
340Dic122—22no—
341Dic122C2×#4114yes—
342C8×C61—22no—
343C8×C61—22no—
344#92418—22no—
345#92418—22no—
346C2×#3126—611nomaximal, Sylow
347C22×C61—42no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—84no—
351C22×C61#52512yes—
352C22×C61#57712yes—
353C22×C61#57712yes—
354C22×C61C23×D411yescharacteristic
355C2×D61—22no—
356C2×D61—22no—
357C2×D61—22no—
358C2×D61—44no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—84no—
363C4×C61—24no—
364C4×C61—22no—
365C4×C61—22no—
366C4×C61—42no—
367C4×C61—42no—
368C4×C61#52512yes—
369C4×C61C22×#4111yescharacteristic
370C4×C61C22×#4111yescharacteristic
371Dic61—22no—
372Dic61—24no—
373Dic61—22no—
374Dic61—22no—
375Dic61—42no—
376Dic61—42no—
377C2×#540—611no—
378C2×#519—611no—
379#3126—6116no—
380C2×#482—611no—
381C2×#482—611no—
382C2×#479—611no—
383C2×#479—611no—
384C2×#460—611no—
385C2×#460—611no—
386C2×#448—611no—
387C2×#448—611no—
388C2×#440—611no—
389C2×#440—611no—
390C2×C4×SD16—611no—
391C2×C4×SD16D6111yescharacteristic, complemented
392C2×#433—611no—
393C2×C61—82no—
394C2×C61#312614yescomplemented
395C2×C61C2×#52511yescharacteristic
396C2×C61C2×#57711yescharacteristic
397C2×C61C2×#57711yescharacteristic
398D61—42no—
399D61—82no—
400C23×Q8—611no—
401C22×SD16—611no—
402C22×SD16—611no—
403C22×SD16—611no—
404C22×SD16C2×D6111yescharacteristic
405#540—618no—
406#540—1224no—
407C2×#127—611no—
408C2×#125—611no—
409C2×#123—1221no—
410C2×#123—1221no—
411C2×#121—611no—
412C2×#121—611no—
413C2×#121—1221no—
414C2×#121—1221no—
415#519—618no—
416#519—1224no—
417C2×C4×Q8—611no—
418C2×C4×Q8—611no—
419C2×C4×Q8—611no—
420C2×C4×Q8—1221no—
421C2×C4×Q8—1221no—
422C2×C4×Q8C2×D6111yescharacteristic
423C2×C4×D4—611no—
424C2×C4×D4C2×D6111yescharacteristic
425C2×#117—611no—
426C2×#117—611no—
427C2×#117—1221no—
428C2×#117—1221no—
429#482—618no—
430#482—618no—
431#479—618no—
432#479—618no—
433#460—618no—
434#460—618no—
435#448—618no—
436#448—618no—
437#440—618no—
438#440—618no—
439C4×SD16—618no—
440C4×SD16C2×D6118yescomplemented
441#433—618no—
442C2×#107—611no—
443C2×#107—611no—
444C2×#106—611no—
445C2×#106C2×D6111yescharacteristic
446C2×C4⋊C8—611no—
447C2×C4⋊C8—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#103—611no—
451C2×#103C2×D6111yescharacteristic
452C2×#102—611no—
453C2×#102—611no—
454C2×#102—611no—
455C2×#102C2×D6111yescharacteristic
456C2×C22⋊C8—611no—
457C2×C22⋊C8—611no—
458C2×#97—611no—
459C2×C4×C8C2×D6111yescharacteristic
460C61C2×#312611yescharacteristic, complemented, Sylow
461C22×Q8—614no—
462C22×Q8—611no—
463C22×Q8—1221no—
464C22×Q8—1222no—
465C22×Q8—1224no—
466C22×Q8—1224no—
467C22×Q8C22×D6111yescharacteristic
468C22×D4—611no—
469C22×D4—1221no—
470C22×D4—1221no—
471C22×D4—1221no—
472C22×D4—1221no—
473C22×D4C22×D6111yescharacteristic
474C23×C4—21no—
475C23×C4—611no—
476C23×C4—1221no—
477C23×C4—1221no—
478C2×SD16—24no—
479C2×SD16—614no—
480C2×SD16—614no—
481C2×SD16—614no—
482C2×SD16—1224no—
483C2×SD16—1224no—
484C2×SD16—1224no—
485C2×SD16C22×D6114yes—
486C22×C8—611no—
487C22×C8—611no—
488C22×C8C22×D6111yescharacteristic
489C22×C8C22×D6111yescharacteristic
490#127—614no—
491#127—1222no—
492#125—614no—
493#125—1222no—
494#123—1228no—
495#123—1228no—
496#121—614no—
497#121—614no—
498#121—1228no—
499#121—1228no—
500#121—1222no—
501#121—1222no—
502C4×Q8—22no—
503C4×Q8—614no—
504C4×Q8—614no—
505C4×Q8—614no—
506C4×Q8—1228no—
507C4×Q8—1222no—
508C4×Q8—1222no—
509C4×Q8—1228no—
510C4×Q8—1222no—
511C4×Q8C22×D6114yes—
512C4×D4—22no—
513C4×D4—614no—
514C4×D4—1222no—
515C4×D4C22×D6114yes—
516#117—614no—
517#117—614no—
518#117—614no—
519#117—1228no—
520#117—1228no—
521#117—1222no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—611no—
525C2×C4⋊C4—611no—
526C2×C4⋊C4—611no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4C22×D6111yescharacteristic
533C2×C4⋊C4C22×D6111yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—611no—
536C2×C22⋊C4—611no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C42—21no—
542C2×C42—611no—
543C2×C42—1221no—
544C2×C42—1221no—
545C2×C42—1221no—
546C2×C42—1221no—
547C2×C42C22×D6111yescharacteristic
548#107—614no—
549#107—614no—
550#106—614no—
551#106C22×D6114yes—
552C4⋊C8—614no—
553C4⋊C8—614no—
554#103—614no—
555#103—614no—
556#103—614no—
557#103C22×D6114yes—
558#102—614no—
559#102—614no—
560#102—614no—
561#102C22×D6114yes—
562C22⋊C8—614no—
563C22⋊C8—614no—
564#97—614no—
565C4×C8C22×D6114yes—
566C24—21no—
567C24—611no—
568C24—1221no—
569C2×Q8—21no—
570C2×Q8—22no—
571C2×Q8—614no—
572C2×Q8—612no—
573C2×Q8—1224no—
574C2×Q8—1228no—
575C2×Q8—1228no—
576C2×Q8—12216no—
577C2×Q8—1228no—
578C2×Q8—1221no—
579C2×Q8—1222no—
580C2×Q8#1175822214yes—
581C2×Q8C23×D6112yes—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—612no—
586C2×D4—1224no—
587C2×D4—1224no—
588C2×D4—1224no—
589C2×D4—1224no—
590C2×D4—1221no—
591C2×D4—1222no—
592C2×D4—1222no—
593C2×D4—4882no—
594C2×D4—4882no—
595C2×D4—4882no—
596C2×D4—4882no—
597C2×D4C23×D6112yes—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—82no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—612no—
607C22×C4—612no—
608C22×C4—1224no—
609C22×C4—1228no—
610C22×C4—1221no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1224no—
616C22×C4—4882no—
617C22×C4D4×D6111yescharacteristic
618C22×C4D4×D6111yescharacteristic
619C22×C4C23×D6111yescharacteristic
620SD16—28no—
621SD16—1228no—
622SD16—1228no—
623SD16—1228no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—612no—
627C2×C8—612no—
628C2×C8—1222no—
629C2×C8—1222no—
630C2×C8C23×D6112yes—
631C2×C8C23×D6112yes—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—614no—
636C4⋊C4—614no—
637C4⋊C4—612no—
638C4⋊C4—612no—
639C4⋊C4—1224no—
640C4⋊C4—1224no—
641C4⋊C4—1224no—
642C4⋊C4—1224no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—1224no—
646C4⋊C4C23×D6112yes—
647C4⋊C4C23×D6112yes—
648C22⋊C4—24no—
649C22⋊C4—614no—
650C22⋊C4—614no—
651C22⋊C4—1224no—
652C22⋊C4—1224no—
653C22⋊C4—1224no—
654C22⋊C4—1224no—
655C42—24no—
656C42—612no—
657C42—612no—
658C42—1224no—
659C42—1224no—
660C42—1224no—
661C42—1224no—
662C42D4×D6112yes—
663C42C23×D6112yes—
664C23—22no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—612no—
669C23—1222no—
670C23—1222no—
671C23—1222no—
672C23—1222no—
673C23—2442no—
674C23—2442no—
675C23—2442no—
676C23C2×D4×D6111yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—614no—
680Q8—12216no—
681Q8—1224no—
682Q8—1222no—
683Q8C2×#1175822214yes—
684D4—22no—
685D4—22no—
686D4—42no—
687D4—1222no—
688D4—1222no—
689D4—4884no—
690D4—4884no—
691D4—4884no—
692D4—4884no—
693D4—2442no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—84no—
703C2×C4—612no—
704C2×C4—612no—
705C2×C4—612no—
706C2×C4—12216no—
707C2×C4—1222no—
708C2×C4—1224no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1224no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—4884no—
718C2×C4—2442no—
719C2×C4—2442no—
720C2×C4C2×D4×D6112yes—
721C2×C4C2×D4×D6112yes—
722C2×C4C2×D4×D6111yescharacteristic
723C2×C4#41×D6112yes—
724C2×C4C2×#1175822212yes—
725C2×C4C24×D6111yescharacteristic
726C8—22no—
727C8—22no—
728C8—1222no—
729C8—1222no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—84no—
734C22—1222no—
735C22—1222no—
736C22—1222no—
737C22—4884no—
738C22—2442no—
739C22—2442no—
740C22—2442no—
741C22—2444no—
742C22#1684027112yes—
743C22#1684056812yes—
744C22#1684056912yes—
745C22C22×D4×D6111yescharacteristic
746C4—22no—
747C4—22no—
748C4—24no—
749C4—42no—
750C4—42no—
751C4—1222no—
752C4—1222no—
753C4—1222no—
754C4—1224no—
755C4—2442no—
756C4—2442no—
757C4#1684027112yes—
758C4C2×#41×D6111yescharacteristic
759C4C22×#1175822211yescharacteristic
760C2—82no—
761C2—4882no—
762C2—2442no—
763C2#2145610714yesdirect product factor
764C2C2×#1684027111yescharacteristic
765C2C2×#1684056811yescharacteristic
766C2C2×#1684056911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C4×SD16×C61C2
socleC23×C61C22×D4
prime radicalC2×#16840363C2
hypercenterC2×C4×SD16D61
hypocenterC61C2×#3126
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#16840238C2semidirect
3. #21456107C2direct (N × H)
4. C2×#16840088C2semidirect
5. C2×#16840085C2semidirect
6. C2×#16840072C2semidirect
7. C2×#16840067C2semidirect
8. C2×#16839961C2semidirect
9. C2×#16839960C2semidirect
10. C2×#16839902C2semidirect
11. C2×#16839899C2semidirect
12. C2×#16839862C2semidirect
13. C2×#16839860C2semidirect
14. C2×C4×#11758190C2semidirect
15. C2×#16839821C2semidirect
16. C2×C4×SD16×C61C2semidirect
32. #16840238C22semidirect
43. #16840088C22semidirect
44. #16840085C22semidirect
45. #16840072C22semidirect
46. #16840067C22semidirect
47. #16839961C22semidirect
48. #16839960C22semidirect
49. #16839902C22semidirect
50. #16839899C22semidirect
51. #16839862C22semidirect
52. #16839860C22semidirect
53. C4×#11758190C22semidirect
54. #16839821C22semidirect
72. C4×SD16×C61C22semidirect
391. C2×C4×SD16D61semidirect
394. C2×C61#3126semidirect
440. C4×SD16C2×D61semidirect
460. C61C2×#3126semidirect
763. C2#21456107direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403632
C2×#168402382
#214561072
C2×#168400882
C2×#168400852
C2×#168400722
C2×#168400672
C2×#168399612
C2×#168399602
C2×#168399022
C2×#168398992
C2×#168398622
C2×#168398602
C2×C4×#117581902
C2×#168398212
C2×C4×SD16×C612
C2×#312661