Finite Group Databasebeta

← C2×#21456065 #30548311

Subgroups — C2×#21456065 #30548311

Order 15616.

2210 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840372C211yesmaximal, characteristic, complemented
2C2×#16840237C211yesmaximal, characteristic
3#21456065C2116yesmaximal, direct product factor
4C2×#16840104C211yesmaximal, characteristic, complemented
5C2×#16840100C211yesmaximal, characteristic, complemented
6C2×#16840064C211yesmaximal, characteristic, complemented
7C2×#16840060C211yesmaximal, characteristic, complemented
8C2×#16839965C211yesmaximal, characteristic, complemented
9C2×#16839965C211yesmaximal, characteristic, complemented
10C2×#16839913C211yesmaximal, characteristic
11C2×#16839863C211yesmaximal, characteristic, complemented
12C2×#16839859C211yesmaximal, characteristic, complemented
13C2×#16839853C211yesmaximal, characteristic, complemented
14C2×SD16×Dic61C211yesmaximal, characteristic, complemented
15C2×#16839820C211yesmaximal, characteristic, complemented
16C2×C61×#450C211yesmaximal, characteristic
17C22×#11758200C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19#16840372—24no—
20#16840372C2218yescomplemented
21C2×#14519775C2211yescharacteristic, complemented
22C2×#14519770—21no—
23C2×#14519770—21no—
24C2×#14519768—21no—
25C2×#14519768C2211yescharacteristic, complemented
26C2×#14519767—21no—
27C2×#14519756C2211yescharacteristic
28#16840237—24no—
29#16840237C2218yes—
30C2×Q8×Dic61C2211yescharacteristic, complemented
31C2×#14519742C2211yescharacteristic, complemented
32C2×D4×Dic61—21no—
33C2×D4×Dic61—21no—
34C2×D4×Dic61C2211yescharacteristic
35C2×D4×Dic61C2211yescharacteristic
36C2×D4×Dic61C2211yescharacteristic
37C2×D4×Dic61C2211yescharacteristic
38C2×#14519736C2211yescharacteristic
39C2×#14519736C2211yescharacteristic
40C22×C22⋊Dic61—21no—
41C22×C22⋊Dic61—21no—
42#16840104C2218yescomplemented
43#16840100C2218yescomplemented
44#16840064C2218yescomplemented
45#16840060C2218yescomplemented
46#16839965C2218yescomplemented
47#16839965C2218yescomplemented
48#16839913C2218yes—
49#16839863C2218yescomplemented
50#16839859C2218yescomplemented
51#16839853C2218yescomplemented
52SD16×Dic61C2218yescomplemented
53#16839820C2218yescomplemented
54C2×#14519711C2211yescharacteristic, complemented
55C2×#14519710C2211yescharacteristic, complemented
56C2×#14519709C2211yescharacteristic, complemented
57C2×#14519708C2211yescharacteristic, complemented
58C2×#14519706C2211yescharacteristic, complemented
59C2×#14519706C2211yescharacteristic, complemented
60C2×#14519702C2211yescharacteristic, complemented
61C2×#14519702C2211yescharacteristic, complemented
62C2×#14519701C2211yescharacteristic, complemented
63C2×#14519701C2211yescharacteristic, complemented
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519687C2211yescharacteristic, complemented
68C2×C8×Dic61C2211yescharacteristic, complemented
69C23×D4×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C22×SD16×C61C2211yescharacteristic
72C2×C22⋊Q8×C61C2211yescharacteristic
73C61×#450C2218yes—
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C22×Dic122C2311yescharacteristic
78C23×Dic61—21no—
79C23×Dic61—21no—
80C23×Dic61—21no—
81C23×Dic61—21no—
82C2×#11758200—24no—
83C2×#11758200—24no—
84C2×#11758200C2314yes—
85C2×#11758200C2314yes—
86C22×#92418C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88#14519775—22no—
89#14519775C2314yescomplemented
90#14519770—28no—
91#14519770—28no—
92#14519768—28no—
93#14519768—22no—
94#14519768C2314yescomplemented
95#14519767—28no—
96#14519756—22no—
97#14519756C2314yes—
98Q8×Dic61—22no—
99Q8×Dic61C2314yescomplemented
100#14519742—22no—
101#14519742C2314yescomplemented
102D4×Dic61—28no—
103D4×Dic61—28no—
104D4×Dic61—22no—
105D4×Dic61—22no—
106D4×Dic61—22no—
107D4×Dic61—22no—
108D4×Dic61C2314yes—
109D4×Dic61C2314yes—
110D4×Dic61C2314yes—
111D4×Dic61C2314yes—
112#14519736—22no—
113#14519736D414yes—
114#14519736C2314yes—
115#14519736C2314yes—
116C2×C4⋊Dic61—21no—
117C2×C4⋊Dic61—21no—
118C2×C4⋊Dic61D411yescharacteristic
119C2×C4⋊Dic61D411yescharacteristic
120C2×C4⋊Dic61C2311yescharacteristic
121C2×C4⋊Dic61C2311yescharacteristic
122C2×C4⋊Dic61C2311yescharacteristic
123C2×#11758196—21no—
124C2×#11758196—21no—
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×C22⋊Dic61—21no—
129C2×C22⋊Dic61—21no—
130C2×C22⋊Dic61—21no—
131C2×C22⋊Dic61—21no—
132C2×C22⋊Dic61—21no—
133C2×C22⋊Dic61—21no—
134C2×C22⋊Dic61—28no—
135C2×C22⋊Dic61—28no—
136C2×C22⋊Dic61D411yescharacteristic
137C2×C22⋊Dic61D411yescharacteristic
138C2×C4×Dic61—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61C2311yescharacteristic
142C2×C4×Dic61C2311yescharacteristic
143#14519711C2314yescomplemented
144#14519710C2314yescomplemented
145#14519709C2314yescomplemented
146#14519708C2314yescomplemented
147#14519706C2314yescomplemented
148#14519706C2314yescomplemented
149#14519702C2314yescomplemented
150#14519702C2314yescomplemented
151#14519701C2314yescomplemented
152#14519701C2314yescomplemented
153#14519698C2314yes—
154#14519698C2314yes—
155C22⋊#92418C2314yes—
156#14519687C2314yescomplemented
157C8×Dic61C2314yescomplemented
158C25×C61—21no—
159C22×Q8×C61C2311yescharacteristic
160C22×D4×C61—24no—
161C22×D4×C61—24no—
162C22×D4×C61—21no—
163C22×D4×C61—22no—
164C22×D4×C61C2314yes—
165C22×D4×C61C2311yescharacteristic
166C22×D4×C61C2311yescharacteristic
167C23×C4×C61C2311yescharacteristic
168C2×SD16×C61—24no—
169C2×SD16×C61—24no—
170C2×SD16×C61C2314yes—
171C2×SD16×C61C2314yes—
172C22×C8×C61C2311yescharacteristic
173C22×C8×C61C2311yescharacteristic
174C22⋊Q8×C61—22no—
175C22⋊Q8×C61C2314yes—
176C2×C4⋊C4×C61—21no—
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C22⋊C4×C61—21no—
179#102×C61C2314yes—
180#102×C61C2314yes—
181C22⋊C8×C61C2314yes—
182C24×C61—28no—
183C24×C61—21no—
184C24×C61—21no—
185C24×C61—24no—
186C24×C61—82no—
187C24×C61—82no—
188C24×C61C2×D411yescharacteristic
189C2×Q8×C61—21no—
190C2×Q8×C61—22no—
191C2×Q8×C61—22no—
192C2×Q8×C61C2412yes—
193C2×D4×C61—28no—
194C2×D4×C61—216no—
195C2×D4×C61—28no—
196C2×D4×C61—28no—
197C2×D4×C61—24no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—22no—
201C2×D4×C61—22no—
202C2×D4×C61#4114yes—
203C2×D4×C61#4114yes—
204C2×D4×C61C2412yes—
205C2×D4×C61C2412yes—
206C22×C4×C61—22no—
207C22×C4×C61—22no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D412yes—
212C22×C4×C61C2412yes—
213C22×C4×C61C2411yescharacteristic
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—24no—
219C22×Dic61—24no—
220C22×Dic61—24no—
221C22×Dic61—24no—
222C22×Dic61—82no—
223C22×Dic61—82no—
224C22×Dic61—82no—
225C22×Dic61—82no—
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229C22×Dic61C2×D411yescharacteristic
230C2×Dic122—22no—
231C2×Dic122—22no—
232C2×Dic122—21no—
233C2×Dic122C2412yes—
234SD16×C61—28no—
235SD16×C61—28no—
236C2×C8×C61—22no—
237C2×C8×C61—22no—
238C2×C8×C61C2412yes—
239C2×C8×C61C2412yes—
240C4⋊C4×C61—24no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61C2412yes—
243C22⋊C4×C61—24no—
244C22⋊Dic61—24no—
245C22⋊Dic61—24no—
246C22⋊Dic61—24no—
247C22⋊Dic61—24no—
248C22⋊Dic61—24no—
249C22⋊Dic61—24no—
250C22⋊Dic61C2×D414yes—
251C22⋊Dic61C2×D414yes—
252#11758200—28no—
253#11758200—28no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61—24no—
258C4⋊Dic61—24no—
259C4⋊Dic61C2×D414yes—
260C4⋊Dic61C2×D414yes—
261C4⋊Dic61C2412yes—
262C4⋊Dic61C2412yes—
263C4⋊Dic61C2412yes—
264#11758196—24no—
265#11758196—24no—
266#11758196—24no—
267#11758196—24no—
268#11758196—24no—
269C4×Dic61—24no—
270C4×Dic61—24no—
271C4×Dic61—24no—
272C4×Dic61C2×D412yes—
273C4×Dic61C2×D412yes—
274C4×Dic61C2412yes—
275C4×Dic61C2412yes—
276C2×#92418—22no—
277C2×#92418—22no—
278C2×#92418C2412yes—
279C2×#92418C2412yes—
280C23×C61—216no—
281C23×C61—22no—
282C23×C61—24no—
283C23×C61—24no—
284C23×C61—22no—
285C23×C61—22no—
286C23×C61—22no—
287C23×C61—22no—
288C23×C61—42no—
289C23×C61—42no—
290C23×C61—42no—
291C23×C61—42no—
292C23×C61—84no—
293C23×C61—84no—
294C23×C61—816no—
295C23×C61C22×D412yes—
296C23×C61C22×D411yescharacteristic
297Q8×C61—22no—
298Q8×C61—22no—
299Q8×C61—42no—
300D4×C61—216no—
301D4×C61—24no—
302D4×C61—24no—
303D4×C61—22no—
304D4×C61—22no—
305D4×C61C2×#4114yes—
306D4×C61C2×#4114yes—
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—42no—
314C2×C4×C61—42no—
315C2×C4×C61C22×D412yes—
316C2×C4×C61C22×D411yescharacteristic
317C2×C4×C61C2×#4112yes—
318C2×C4×C61C2×#4112yes—
319C2×C4×C61C2511yescharacteristic
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61—42no—
332C2×Dic61—84no—
333C2×Dic61—84no—
334C2×Dic61—84no—
335C2×Dic61—84no—
336C2×Dic61C22×D412yes—
337C2×Dic61C22×D412yes—
338C2×Dic61C22×D412yes—
339C2×Dic61C22×D412yes—
340Dic122—22no—
341Dic122—22no—
342Dic122—42no—
343C8×C61—22no—
344C8×C61—22no—
345#92418—22no—
346#92418—22no—
347C2×#3123—611nomaximal, Sylow
348C22×C61—22no—
349C22×C61—24no—
350C22×C61—24no—
351C22×C61—22no—
352C22×C61—22no—
353C22×C61—44no—
354C22×C61—48no—
355C22×C61—48no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61—816no—
361C22×C61#52512yes—
362C22×C61#57712yes—
363C22×C61#57712yes—
364C22×C61C23×D411yescharacteristic
365C4×C61—22no—
366C4×C61—42no—
367C4×C61—42no—
368C4×C61#52512yes—
369C4×C61C22×#4111yescharacteristic
370C4×C61C22×#4111yescharacteristic
371Dic61—22no—
372Dic61—22no—
373Dic61—22no—
374Dic61—22no—
375Dic61—42no—
376Dic61—42no—
377Dic61—42no—
378Dic61—42no—
379C2×#541—611no—
380C2×#518—611no—
381#3123—6116no—
382C2×#485—611no—
383C2×#485—611no—
384C2×#478—611no—
385C2×#478—611no—
386C2×#461—611no—
387C2×#461—611no—
388C2×#450—611no—
389C2×#450D6111yescharacteristic
390C2×#440—611no—
391C2×#440—611no—
392C2×C4×SD16—611no—
393C2×C4×SD16—611no—
394C2×#433—611no—
395C2×C61—42no—
396C2×C61—44no—
397C2×C61—44no—
398C2×C61#312314yescomplemented
399C2×C61C2×#52511yescharacteristic
400C2×C61C2×#57711yescharacteristic
401C2×C61C2×#57711yescharacteristic
402C23×D4C2×D6111yescharacteristic
403C22×SD16—611no—
404C22×SD16—611no—
405C22×SD16C2×D6111yescharacteristic
406C22×SD16C2×D6111yescharacteristic
407#541—618no—
408#541—1224no—
409C2×C4⋊Q8—611no—
410C2×#126—1221no—
411C2×#126—1221no—
412C2×#125—611no—
413C2×#125—1221no—
414C2×#125—1221no—
415C2×C22⋊Q8—611no—
416C2×C22⋊Q8C2×D6111yescharacteristic
417#518—618no—
418#518—1224no—
419C2×C4×Q8—611no—
420C2×C4×Q8—611no—
421C2×C4×D4—611no—
422C2×C4×D4—611no—
423C2×C4×D4—611no—
424C2×C4×D4—611no—
425C2×C4×D4—1221no—
426C2×C4×D4—1221no—
427C2×#117—611no—
428C2×#117—611no—
429C22×C22⋊C4—1221no—
430C22×C22⋊C4—1221no—
431#485—618no—
432#485—618no—
433#478—618no—
434#478—618no—
435#461—618no—
436#461—618no—
437#450—618no—
438#450C2×D6118yes—
439#440—618no—
440#440—618no—
441C4×SD16—618no—
442C4×SD16—618no—
443#433—618no—
444C2×#107—611no—
445C2×#107—611no—
446C2×#106—611no—
447C2×#106—611no—
448C2×C4⋊C8—611no—
449C2×C4⋊C8—611no—
450C2×#103—611no—
451C2×#103—611no—
452C2×#103—611no—
453C2×#103—611no—
454C2×#102—611no—
455C2×#102—611no—
456C2×#102C2×D6111yescharacteristic
457C2×#102C2×D6111yescharacteristic
458C2×C22⋊C8—611no—
459C2×C22⋊C8C2×D6111yescharacteristic
460C2×#97—611no—
461C2×C4×C8—611no—
462C61C2×#312311yescharacteristic, complemented, Sylow
463C25—21no—
464C22×Q8—611no—
465C22×Q8C22×D6111yescharacteristic
466C22×D4—24no—
467C22×D4—24no—
468C22×D4—21no—
469C22×D4—22no—
470C22×D4C22×D6114yes—
471C22×D4C22×D6111yescharacteristic
472C22×D4C22×D6111yescharacteristic
473C23×C4—1221no—
474C23×C4—1221no—
475C23×C4—1221no—
476C23×C4—1221no—
477C23×C4C22×D6111yescharacteristic
478C2×SD16—24no—
479C2×SD16—24no—
480C2×SD16—614no—
481C2×SD16—614no—
482C2×SD16—1224no—
483C2×SD16—1224no—
484C2×SD16C22×D6114yes—
485C2×SD16C22×D6114yes—
486C22×C8—611no—
487C22×C8—611no—
488C22×C8C22×D6111yescharacteristic
489C22×C8C22×D6111yescharacteristic
490C4⋊Q8—614no—
491C4⋊Q8—1222no—
492#126—1228no—
493#126—1228no—
494#125—614no—
495#125—1222no—
496#125—1228no—
497#125—1228no—
498C22⋊Q8—22no—
499C22⋊Q8—614no—
500C22⋊Q8—1222no—
501C22⋊Q8C22×D6114yes—
502C4×Q8—614no—
503C4×Q8—614no—
504C4×Q8—1222no—
505C4×Q8—1222no—
506C4×D4—614no—
507C4×D4—614no—
508C4×D4—614no—
509C4×D4—614no—
510C4×D4—1222no—
511C4×D4—1222no—
512C4×D4—1222no—
513C4×D4—1222no—
514C4×D4—1228no—
515C4×D4—1228no—
516#117—614no—
517#117—614no—
518#117—614no—
519#117—1222no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—611no—
525C2×C4⋊C4—611no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4—1221no—
533C2×C4⋊C4C22×D6111yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—611no—
536C2×C22⋊C4—611no—
537C2×C22⋊C4—1228no—
538C2×C22⋊C4—1228no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1221no—
545C2×C42—611no—
546C2×C42—611no—
547C2×C42—1221no—
548C2×C42—1221no—
549C2×C42—1221no—
550#107—614no—
551#107—614no—
552#106—614no—
553#106—614no—
554C4⋊C8—614no—
555C4⋊C8—614no—
556#103—614no—
557#103—614no—
558#103—614no—
559#103—614no—
560#102—614no—
561#102—614no—
562#102C22×D6114yes—
563#102C22×D6114yes—
564C22⋊C8—614no—
565C22⋊C8C22×D6114yes—
566#97—614no—
567C4×C8—614no—
568C24—28no—
569C24—21no—
570C24—21no—
571C24—24no—
572C24—82no—
573C24—82no—
574C24D4×D6111yescharacteristic
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—612no—
579C2×Q8—1221no—
580C2×Q8—1222no—
581C2×Q8—1222no—
582C2×Q8C23×D6112yes—
583C2×D4—28no—
584C2×D4—216no—
585C2×D4—28no—
586C2×D4—28no—
587C2×D4—24no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4#1175822414yes—
593C2×D4#1175822414yes—
594C2×D4C23×D6112yes—
595C2×D4C23×D6112yes—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—1224no—
605C22×C4—1224no—
606C22×C4—1224no—
607C22×C4—1224no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—4882no—
613C22×C4—4882no—
614C22×C4—4882no—
615C22×C4—4882no—
616C22×C4D4×D6112yes—
617C22×C4D4×D6111yescharacteristic
618C22×C4C23×D6112yes—
619C22×C4C23×D6111yescharacteristic
620SD16—28no—
621SD16—28no—
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—614no—
635C4⋊C4—614no—
636C4⋊C4—612no—
637C4⋊C4—612no—
638C4⋊C4—612no—
639C4⋊C4—1224no—
640C4⋊C4—1224no—
641C4⋊C4—1224no—
642C4⋊C4—1224no—
643C4⋊C4—1224no—
644C4⋊C4—1224no—
645C4⋊C4—1221no—
646C4⋊C4—1221no—
647C4⋊C4—1221no—
648C4⋊C4—1224no—
649C4⋊C4C23×D6112yes—
650C22⋊C4—24no—
651C22⋊C4—614no—
652C22⋊C4—614no—
653C22⋊C4—1224no—
654C22⋊C4—1224no—
655C22⋊C4—1224no—
656C22⋊C4—1224no—
657C22⋊C4—1224no—
658C22⋊C4—1224no—
659C42—612no—
660C42—612no—
661C42—612no—
662C42—612no—
663C42—1224no—
664C42—1224no—
665C42—1224no—
666C23—216no—
667C23—22no—
668C23—24no—
669C23—24no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—84no—
679C23—84no—
680C23—816no—
681C23C2×D4×D6112yes—
682C23C2×D4×D6111yescharacteristic
683Q8—22no—
684Q8—22no—
685Q8—42no—
686Q8—1222no—
687Q8—1222no—
688Q8—2442no—
689D4—216no—
690D4—24no—
691D4—24no—
692D4—22no—
693D4—22no—
694D4C2×#1175822414yes—
695D4C2×#1175822414yes—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—612no—
705C2×C4—612no—
706C2×C4—612no—
707C2×C4—612no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—4884no—
717C2×C4—4884no—
718C2×C4—4884no—
719C2×C4—4884no—
720C2×C4—2442no—
721C2×C4—2442no—
722C2×C4—2442no—
723C2×C4—2442no—
724C2×C4C2×D4×D6112yes—
725C2×C4C2×D4×D6111yescharacteristic
726C2×C4C2×#1175822412yes—
727C2×C4C2×#1175822412yes—
728C2×C4C24×D6111yescharacteristic
729C8—22no—
730C8—22no—
731C8—1222no—
732C8—1222no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—24no—
737C22—24no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—44no—
743C22—48no—
744C22—48no—
745C22—816no—
746C22#1684026812yes—
747C22#1684056812yes—
748C22#1684057212yes—
749C22C22×D4×D6111yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—1222no—
754C4—1222no—
755C4—1222no—
756C4—1222no—
757C4—2442no—
758C4—2442no—
759C4—2442no—
760C4—2442no—
761C4#1684026812yes—
762C4C22×#1175822411yescharacteristic
763C4C22×#1175822411yescharacteristic
764C2—42no—
765C2—44no—
766C2—44no—
767C2#2145606514yesdirect product factor
768C2C2×#1684026811yescharacteristic
769C2C2×#1684056811yescharacteristic
770C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#450C2
socleC23×C61C22×D4
prime radicalC23×D4×C61C22
hypercenterC2×#450D61
hypocenterC61C2×#3123
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C2×#16840372C2semidirect
3. #21456065C2direct (N × H)
4. C2×#16840104C2semidirect
5. C2×#16840100C2semidirect
6. C2×#16840064C2semidirect
7. C2×#16840060C2semidirect
8. C2×#16839965C2semidirect
9. C2×#16839965C2semidirect
11. C2×#16839863C2semidirect
12. C2×#16839859C2semidirect
13. C2×#16839853C2semidirect
14. C2×SD16×Dic61C2semidirect
15. C2×#16839820C2semidirect
20. #16840372C22semidirect
21. C2×#14519775C22semidirect
25. C2×#14519768C22semidirect
30. C2×Q8×Dic61C22semidirect
31. C2×#14519742C22semidirect
42. #16840104C22semidirect
43. #16840100C22semidirect
44. #16840064C22semidirect
45. #16840060C22semidirect
46. #16839965C22semidirect
47. #16839965C22semidirect
49. #16839863C22semidirect
50. #16839859C22semidirect
51. #16839853C22semidirect
52. SD16×Dic61C22semidirect
53. #16839820C22semidirect
54. C2×#14519711C22semidirect
55. C2×#14519710C22semidirect
56. C2×#14519709C22semidirect
57. C2×#14519708C22semidirect
58. C2×#14519706C22semidirect
59. C2×#14519706C22semidirect
60. C2×#14519702C22semidirect
61. C2×#14519702C22semidirect
62. C2×#14519701C22semidirect
63. C2×#14519701C22semidirect
67. C2×#14519687C22semidirect
68. C2×C8×Dic61C22semidirect
89. #14519775C23semidirect
94. #14519768C23semidirect
99. Q8×Dic61C23semidirect
101. #14519742C23semidirect
143. #14519711C23semidirect
144. #14519710C23semidirect
145. #14519709C23semidirect
146. #14519708C23semidirect
147. #14519706C23semidirect
148. #14519706C23semidirect
149. #14519702C23semidirect
150. #14519702C23semidirect
151. #14519701C23semidirect
152. #14519701C23semidirect
156. #14519687C23semidirect
157. C8×Dic61C23semidirect
398. C2×C61#3123semidirect
462. C61C2×#3123semidirect
767. C2#21456065direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403722
C2×#168402372
#214560652
C2×#168401042
C2×#168401002
C2×#168400642
C2×#168400602
C2×#168399652
C2×#168399132
C2×#168398632
C2×#168398592
C2×#168398532
C2×SD16×Dic612
C2×#168398202
C2×C61×#4502
C2×#312361