Finite Group Databasebeta

← C2×#21456083 #30548330

Subgroups — C2×#21456083 #30548330

Order 15616.

2134 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×#16840383C211yesmaximal, characteristic, complemented
2C2×#16840242C211yesmaximal, characteristic, complemented
3#21456083C2116yesmaximal, direct product factor
4C2×#16840098C211yesmaximal, characteristic, complemented
5C2×#16840076C211yesmaximal, characteristic, complemented
6C2×#16840058C211yesmaximal, characteristic, complemented
7C2×#16840043C211yesmaximal, characteristic, complemented
8C2×#16839985C211yesmaximal, characteristic, complemented
9C2×#16839978C211yesmaximal, characteristic, complemented
10C2×#16839926C211yesmaximal, characteristic, complemented
11C2×#16839909C211yesmaximal, characteristic
12C2×#16839864C211yesmaximal, characteristic, complemented
13C2×#16839864C211yesmaximal, characteristic, complemented
14C2×C4×Dic244C211yesmaximal, characteristic, complemented
15C2×C4×D488C211yesmaximal, characteristic, complemented
16C2×C61×#433C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×Dic244C2211yescharacteristic
19C22×#11758190C2211yescharacteristic
20C22×#11758190C2211yescharacteristic
21C22×D488C2211yescharacteristic
22#16840383—24no—
23#16840383C2218yescomplemented
24C2×#14519777C2211yescharacteristic
25C2×#14519772—21no—
26C2×#14519765C2211yescharacteristic
27C2×#14519763—21no—
28C2×#14519759—21no—
29C2×#14519756C2211yescharacteristic
30C2×#14519755—21no—
31C2×#14519751C2211yescharacteristic
32#16840242—24no—
33#16840242C2218yescomplemented
34C2×C4×Dic122C2211yescharacteristic
35C2×C4×Dic122C2211yescharacteristic
36C2×C4×Dic122C2211yescharacteristic
37C2×C4×D244C2211yescharacteristic
38C2×C4×D244C2211yescharacteristic
39C2×C4×D244C2211yescharacteristic
40C2×#14519737—21no—
41C2×#14519737—21no—
42C2×#14519735—21no—
43C22×C4⋊Dic61C2211yescharacteristic
44C2×C4⋊C4×D61—21no—
45#16840098C2218yescomplemented
46#16840076C2218yescomplemented
47#16840058C2218yescomplemented
48#16840043C2218yescomplemented
49#16839985C2218yescomplemented
50#16839978C2218yescomplemented
51#16839926C2218yescomplemented
52#16839909C2218yes—
53#16839864C2218yescomplemented
54#16839864C2218yescomplemented
55C4×Dic244C2218yescomplemented
56C4×D488C2218yescomplemented
57C2×#14519711C2211yescharacteristic
58C2×#14519711C2211yescharacteristic
59C2×#14519711C2211yescharacteristic
60C2×#14519711C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519702C2211yescharacteristic
63C2×#14519702C2211yescharacteristic
64C2×#14519702C2211yescharacteristic
65C2×#14519699C2211yescharacteristic
66C2×#14519699C2211yescharacteristic
67C2×#14519699C2211yescharacteristic
68C2×#14519699C2211yescharacteristic
69C2×#117×C61C2211yescharacteristic
70C61×#433C2218yescomplemented
71C2×C4⋊C8×C61C2211yescharacteristic
72C2×C4⋊C8×C61C2211yescharacteristic
73C2×C22⋊C8×C61C2211yescharacteristic
74C2×C22⋊C8×C61C2211yescharacteristic
75C2×#97×C61C2211yescharacteristic
76C2×C4×C8×C61C2211yescharacteristic
77C2×#11758222—22no—
78C2×#11758222—24no—
79C2×#11758222—24no—
80C2×#11758222C2314yes—
81C22×Dic122—21no—
82C22×Dic122C2311yescharacteristic
83C22×Dic122C2311yescharacteristic
84C22×D244C2311yescharacteristic
85C22×D244C2311yescharacteristic
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C23×Dic61—21no—
89C22×C4×D61—21no—
90C22×C4×D61—21no—
91C22×C4×D61—21no—
92C22×C4×D61—21no—
93C2×Dic244—24no—
94C2×Dic244C2314yes—
95C2×#11758190—24no—
96C2×#11758190—24no—
97C2×#11758190C2314yes—
98C2×#11758190C2314yes—
99C2×D488—24no—
100C2×D488C2314yes—
101#14519777—22no—
102#14519777C2314yes—
103#14519772—28no—
104#14519765—22no—
105#14519765C2314yes—
106#14519763—28no—
107#14519759—28no—
108#14519756—22no—
109#14519756C2314yes—
110#14519755—28no—
111#14519751—22no—
112#14519751C2314yes—
113C4×Dic122—22no—
114C4×Dic122—22no—
115C4×Dic122—22no—
116C4×Dic122C2314yes—
117C4×Dic122C2314yes—
118C4×Dic122C2314yes—
119C4×D244—22no—
120C4×D244—22no—
121C4×D244—22no—
122C4×D244C2314yes—
123C4×D244C2314yes—
124C4×D244C2314yes—
125#14519737—28no—
126#14519737—28no—
127#14519735—28no—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61—22no—
130C2×C4⋊Dic61—21no—
131C2×C4⋊Dic61C2311yescharacteristic
132C2×C4⋊Dic61C2311yescharacteristic
133C2×C4⋊Dic61C2314yes—
134C2×C4⋊Dic61C2311yescharacteristic
135C2×C4⋊Dic61C2311yescharacteristic
136C2×#11758196—21no—
137C2×#11758196—21no—
138C2×#11758196—21no—
139C2×#11758196—21no—
140C4⋊C4×D61—28no—
141C2×C22⋊Dic61—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×C4×Dic61—21no—
149C2×C4×Dic61—21no—
150C2×C4×Dic61—21no—
151#14519711C2314yes—
152#14519711C2314yes—
153#14519711C2314yes—
154#14519711C2314yes—
155#14519702C2314yes—
156#14519702C2314yes—
157#14519702C2314yes—
158#14519702C2314yes—
159#14519699C2314yes—
160#14519699C2314yes—
161#14519699C2314yes—
162#14519699C2314yes—
163C23×C4×C61C2311yescharacteristic
164C22×C8×C61C2311yescharacteristic
165C22×C8×C61C2311yescharacteristic
166C22×C8×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168#117×C61D414yes—
169#117×C61C2314yes—
170C2×C4⋊C4×C61D411yescharacteristic
171C2×C4⋊C4×C61D411yescharacteristic
172C2×C22⋊C4×C61D411yescharacteristic
173C2×C22⋊C4×C61D411yescharacteristic
174C2×C42×C61C2311yescharacteristic
175C2×C42×C61C2311yescharacteristic
176C4⋊C8×C61C2314yes—
177C4⋊C8×C61C2314yes—
178C22⋊C8×C61C2314yes—
179C22⋊C8×C61C2314yes—
180#97×C61C2314yes—
181C4×C8×C61C2314yes—
182C24×C61C2×D411yescharacteristic
183C23×D61—21no—
184C23×D61—21no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D412yes—
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2412yes—
194C22×C4×C61C2411yescharacteristic
195C2×C22⋊D61—28no—
196C2×C22⋊D61—24no—
197C2×C22⋊D61—24no—
198C2×C22⋊D61—82no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—24no—
206C22×Dic61—82no—
207#11758222—216no—
208#11758222—28no—
209#11758222—28no—
210C2×D244—21no—
211C2×D244—22no—
212C2×D244—22no—
213C2×D244—22no—
214C2×D244—21no—
215C2×D244#4114yes—
216C2×D244C2412yes—
217C2×D244C2412yes—
218C2×C4×D61—28no—
219C2×C4×D61—24no—
220C2×C4×D61—24no—
221C2×C4×D61—24no—
222C2×C4×D61—24no—
223C2×C4×D61—82no—
224C2×C4×D61—82no—
225C2×C4×D61—82no—
226C2×Dic122—21no—
227C2×Dic122—22no—
228C2×Dic122—22no—
229C2×Dic122—22no—
230C2×Dic122—21no—
231C2×Dic122—24no—
232C2×Dic122—82no—
233C2×Dic122#4114yes—
234C2×Dic122C2412yes—
235C2×Dic122C2412yes—
236C2×C8×C61—22no—
237C2×C8×C61—22no—
238C2×C8×C61—22no—
239C2×C8×C61—22no—
240C2×C8×C61C2412yes—
241C2×C8×C61C2412yes—
242C2×C8×C61C2412yes—
243C2×C8×C61C2412yes—
244C4⋊C4×C61C2×D414yes—
245C4⋊C4×C61C2×D414yes—
246C22⋊C4×C61C2×D414yes—
247C22⋊C4×C61C2×D414yes—
248C42×C61C2×D412yes—
249C42×C61C2×D412yes—
250C42×C61C2412yes—
251C42×C61C2412yes—
252C22⋊Dic61—24no—
253#11758198—24no—
254#11758198—24no—
255#11758198—24no—
256#11758198—24no—
257#11758198—24no—
258#11758198—24no—
259C4⋊Dic61—24no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—24no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61C2412yes—
266C4⋊Dic61C2412yes—
267C4⋊Dic61C2412yes—
268C4⋊Dic61C2412yes—
269#11758196—24no—
270#11758196—24no—
271#11758196—24no—
272#11758196—24no—
273C4×Dic61—24no—
274C4×Dic61—24no—
275C4×Dic61—24no—
276Dic244—28no—
277D488—28no—
278#11758190—28no—
279#11758190—28no—
280C23×C61—22no—
281C23×C61—22no—
282C23×C61—22no—
283C23×C61C22×D412yes—
284C23×C61C22×D411yescharacteristic
285C22×D61—24no—
286C22×D61—22no—
287C22×D61—22no—
288C22×D61—42no—
289C22×D61—42no—
290C22×D61—42no—
291C22×D61—42no—
292C22×D61—42no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—24no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61C22×D412yes—
302C2×C4×C61C22×D412yes—
303C2×C4×C61C22×D412yes—
304C2×C4×C61C22×D412yes—
305C2×C4×C61C22×D412yes—
306C2×C4×C61C22×D411yescharacteristic
307C2×C4×C61C2×#4112yes—
308C2×C4×C61C2×#4112yes—
309C2×C4×C61C2511yescharacteristic
310C22⋊D61—216no—
311C22⋊D61—84no—
312C2×Dic61—24no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—84no—
325D244—24no—
326D244—22no—
327D244—22no—
328D244—22no—
329D244—42no—
330D244C2×#4114yes—
331C4×D61—216no—
332C4×D61—84no—
333C4×D61—84no—
334C4×D61—84no—
335Dic122—24no—
336Dic122—22no—
337Dic122—22no—
338Dic122—22no—
339Dic122—42no—
340Dic122—84no—
341Dic122C2×#4114yes—
342C8×C61—22no—
343C8×C61—22no—
344C8×C61—22no—
345C8×C61—22no—
346C2×#3124—611nomaximal, Sylow
347C22×C61—22no—
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—44no—
351C22×C61#52512yes—
352C22×C61#57612yes—
353C22×C61#57812yes—
354C22×C61C23×D411yescharacteristic
355C2×D61—24no—
356C2×D61—48no—
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—84no—
363C4×C61—22no—
364C4×C61—22no—
365C4×C61—22no—
366C4×C61—22no—
367C4×C61—22no—
368C4×C61#52512yes—
369C4×C61C22×#4111yescharacteristic
370C4×C61C22×#4111yescharacteristic
371Dic61—24no—
372Dic61—42no—
373Dic61—42no—
374Dic61—42no—
375Dic61—42no—
376Dic61—42no—
377C2×#542—611no—
378C2×#520—611no—
379#3124—6116no—
380C2×#484—611no—
381C2×#480—611no—
382C2×#477—611no—
383C2×#474—611no—
384C2×#464—611no—
385C2×#463—611no—
386C2×#452—611no—
387C2×#449—611no—
388C2×#440—611no—
389C2×#440—611no—
390C2×C4×Q16—611no—
391C2×C4×D8—611no—
392C2×#433D6111yescharacteristic, complemented
393C2×C61—42no—
394C2×C61#312414yescomplemented
395C2×C61C2×#52511yescharacteristic
396C2×C61C2×#57611yescharacteristic
397C2×C61C2×#57811yescharacteristic
398D61—44no—
399D61—82no—
400C22×#41—611no—
401C22×Q16—611no—
402C22×SD16—611no—
403C22×SD16—611no—
404C22×D8—611no—
405#542—618no—
406#542—1224no—
407C2×C4⋊Q8—611no—
408C2×#126—1221no—
409C2×#124—611no—
410C2×#124—1221no—
411C2×#123—1221no—
412C2×C22⋊Q8—611no—
413C2×C22⋊Q8—1221no—
414C2×#121—611no—
415#520—618no—
416#520—1224no—
417C2×C4×Q8—611no—
418C2×C4×Q8—611no—
419C2×C4×Q8—611no—
420C2×C4×D4—611no—
421C2×C4×D4—611no—
422C2×C4×D4—611no—
423C2×C4×D4—1221no—
424C2×C4×D4—1221no—
425C2×#117—1221no—
426C2×#117C2×D6111yescharacteristic
427C22×C4⋊C4—611no—
428C22×C4⋊C4—1221no—
429#484—618no—
430#480—618no—
431#477—618no—
432#474—618no—
433#464—618no—
434#463—618no—
435#452—618no—
436#449—618no—
437#440—618no—
438#440—618no—
439C4×Q16—618no—
440C4×D8—618no—
441#433C2×D6118yescomplemented
442C2×#107—611no—
443C2×#107—611no—
444C2×#107—611no—
445C2×#107—611no—
446C2×C4⋊C8C2×D6111yescharacteristic
447C2×C4⋊C8C2×D6111yescharacteristic
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⋊C8C2×D6111yescharacteristic
457C2×C22⋊C8C2×D6111yescharacteristic
458C2×#97C2×D6111yescharacteristic
459C2×C4×C8C2×D6111yescharacteristic
460C61C2×#312411yescharacteristic, complemented, Sylow
461C2×#41—614no—
462C2×#41—1224no—
463C2×#41—1224no—
464C2×#41—1222no—
465C22×Q8—611no—
466C22×Q8—611no—
467C22×Q8—1221no—
468C22×D4—611no—
469C22×D4—611no—
470C22×D4—1221no—
471C22×D4—1221no—
472C23×C4—1221no—
473C23×C4—1221no—
474C23×C4—1221no—
475C23×C4—1221no—
476C23×C4—1221no—
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×C8C22×D6111yescharacteristic
487C22×C8C22×D6111yescharacteristic
488C22×C8C22×D6111yescharacteristic
489C22×C8C22×D6111yescharacteristic
490C4⋊Q8—614no—
491C4⋊Q8—1222no—
492#126—1228no—
493#124—614no—
494#124—1228no—
495#124—1222no—
496#123—1228no—
497C22⋊Q8—614no—
498C22⋊Q8—1222no—
499C22⋊Q8—1228no—
500#121—614no—
501#121—1222no—
502C4×Q8—614no—
503C4×Q8—614no—
504C4×Q8—614no—
505C4×Q8—1222no—
506C4×Q8—1222no—
507C4×Q8—1222no—
508C4×D4—614no—
509C4×D4—614no—
510C4×D4—614no—
511C4×D4—1228no—
512C4×D4—1228no—
513C4×D4—1222no—
514C4×D4—1222no—
515C4×D4—1222no—
516#117—1228no—
517#117D24414yes—
518#117C22×D6114yes—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—614no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—1222no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1228no—
532C2×C4⋊C4D24411yescharacteristic
533C2×C4⋊C4D24411yescharacteristic
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4D24411yescharacteristic
542C2×C22⋊C4D24411yescharacteristic
543C2×C42—1221no—
544C2×C42—1221no—
545C2×C42—1221no—
546C2×C42C22×D6111yescharacteristic
547C2×C42C22×D6111yescharacteristic
548#107—614no—
549#107—614no—
550#107—614no—
551#107—614no—
552C4⋊C8C22×D6114yes—
553C4⋊C8C22×D6114yes—
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⋊C8C22×D6114yes—
563C22⋊C8C22×D6114yes—
564#97C22×D6114yes—
565C4×C8C22×D6114yes—
566C24—1221no—
567C24—1221no—
568C24C2×D24411yescharacteristic
569#41—1228no—
570#41—1228no—
571#41—12216no—
572C2×Q8—614no—
573C2×Q8—612no—
574C2×Q8—612no—
575C2×Q8—1221no—
576C2×Q8—1224no—
577C2×Q8—1221no—
578C2×Q8—1222no—
579C2×Q8—1222no—
580C2×Q8—1222no—
581C2×Q8—4882no—
582C2×D4—614no—
583C2×D4—612no—
584C2×D4—612no—
585C2×D4—1228no—
586C2×D4—1224no—
587C2×D4—1224no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4—1222no—
591C2×D4—1222no—
592C2×D4—1222no—
593C2×D4—4882no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—1228no—
597C22×C4—1221no—
598C22×C4—1224no—
599C22×C4—1224no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1224no—
606C22×C4—1224no—
607C22×C4—1224no—
608C22×C4—4882no—
609C22×C4—4882no—
610C22×C4—4882no—
611C22×C4—4882no—
612C22×C4C2×D24412yes—
613C22×C4C2×D24411yescharacteristic
614C22×C4C2×D24411yescharacteristic
615C22×C4C2×D24411yescharacteristic
616C22×C4C2×D24411yescharacteristic
617C22×C4C2×D24411yescharacteristic
618C22×C4C23×D6112yes—
619C22×C4C23×D6111yescharacteristic
620Q16—1228no—
621SD16—1228no—
622SD16—1228no—
623D8—1228no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8C23×D6112yes—
629C2×C8C23×D6112yes—
630C2×C8C23×D6112yes—
631C2×C8C23×D6112yes—
632C4⋊C4—612no—
633C4⋊C4—612no—
634C4⋊C4—612no—
635C4⋊C4—612no—
636C4⋊C4—1224no—
637C4⋊C4—1221no—
638C4⋊C4—1221no—
639C4⋊C4—1221no—
640C4⋊C4—1221no—
641C4⋊C4—1224no—
642C4⋊C4—1224no—
643C4⋊C4—1224no—
644C4⋊C4—1224no—
645C4⋊C4—1224no—
646C4⋊C4C2×D24414yes—
647C4⋊C4C2×D24414yes—
648C22⋊C4—1224no—
649C22⋊C4—1224no—
650C22⋊C4—1224no—
651C22⋊C4—1224no—
652C22⋊C4—1224no—
653C22⋊C4—1224no—
654C22⋊C4—1224no—
655C22⋊C4C2×D24414yes—
656C22⋊C4C2×D24414yes—
657C42—1224no—
658C42—1224no—
659C42—1224no—
660C42C2×D24412yes—
661C42C2×D24412yes—
662C42C23×D6112yes—
663C42C23×D6112yes—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—1224no—
668C23—1222no—
669C23—1222no—
670C23—2442no—
671C23—2442no—
672C23—2442no—
673C23—2442no—
674C23—2442no—
675C23C22×D24412yes—
676C23C22×D24411yescharacteristic
677Q8—614no—
678Q8—1224no—
679Q8—1222no—
680Q8—1222no—
681Q8—1222no—
682Q8—4884no—
683Q8—2442no—
684D4—614no—
685D4—12216no—
686D4—1224no—
687D4—1222no—
688D4—1222no—
689D4—1222no—
690D4—4884no—
691D4—2442no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—12216no—
701C2×C4—1224no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—4884no—
709C2×C4—4884no—
710C2×C4—4884no—
711C2×C4—4884no—
712C2×C4—2442no—
713C2×C4—2442no—
714C2×C4—2442no—
715C2×C4—2442no—
716C2×C4—2442no—
717C2×C4C22×D24412yes—
718C2×C4C22×D24412yes—
719C2×C4C22×D24412yes—
720C2×C4C22×D24412yes—
721C2×C4C22×D24412yes—
722C2×C4C22×D24411yescharacteristic
723C2×C4#41×D6112yes—
724C2×C4#41×D6112yes—
725C2×C4C24×D6111yescharacteristic
726C8—22no—
727C8—22no—
728C8—22no—
729C8—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—1224no—
735C22—4884no—
736C22—2442no—
737C22—2442no—
738C22—2442no—
739C22—2442no—
740C22—2442no—
741C22—2448no—
742C22#1684027412yes—
743C22#1684056712yes—
744C22#1684057912yes—
745C22C23×D24411yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—1224no—
752C4—2442no—
753C4—2442no—
754C4—2442no—
755C4—2442no—
756C4—2442no—
757C4#1684027412yes—
758C4C2×#41×D6111yescharacteristic
759C4C2×#41×D6111yescharacteristic
760C2—42no—
761C2—4882no—
762C2—2444no—
763C2#2145608314yesdirect product factor
764C2C2×#1684027411yescharacteristic
765C2C2×#1684056711yescharacteristic
766C2C2×#1684057911yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#433C2
socleC23×C61C22×D4
prime radicalC2×#16839909C2
hypercenterC2×#433D61
hypocenterC61C2×#3124
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#16840383C2semidirect
2. C2×#16840242C2semidirect
3. #21456083C2direct (N × H)
4. C2×#16840098C2semidirect
5. C2×#16840076C2semidirect
6. C2×#16840058C2semidirect
7. C2×#16840043C2semidirect
8. C2×#16839985C2semidirect
9. C2×#16839978C2semidirect
10. C2×#16839926C2semidirect
12. C2×#16839864C2semidirect
13. C2×#16839864C2semidirect
14. C2×C4×Dic244C2semidirect
15. C2×C4×D488C2semidirect
16. C2×C61×#433C2semidirect
23. #16840383C22semidirect
33. #16840242C22semidirect
45. #16840098C22semidirect
46. #16840076C22semidirect
47. #16840058C22semidirect
48. #16840043C22semidirect
49. #16839985C22semidirect
50. #16839978C22semidirect
51. #16839926C22semidirect
53. #16839864C22semidirect
54. #16839864C22semidirect
55. C4×Dic244C22semidirect
56. C4×D488C22semidirect
70. C61×#433C22semidirect
392. C2×#433D61semidirect
394. C2×C61#3124semidirect
441. #433C2×D61semidirect
460. C61C2×#3124semidirect
763. C2#21456083direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403832
C2×#168402422
#214560832
C2×#168400982
C2×#168400762
C2×#168400582
C2×#168400432
C2×#168399852
C2×#168399782
C2×#168399262
C2×#168399092
C2×#168398642
C2×C4×Dic2442
C2×C4×D4882
C2×C61×#4332
C2×#312461