Finite Group Databasebeta

← C2×#21458812 #30560928

Subgroups — C2×#21458812 #30560928

Order 15616.

2022 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840494C211yesmaximal, characteristic, complemented
2C2×#16840481C211yesmaximal, characteristic, complemented
3#21458812C2116yesmaximal, direct product factor
4C2×#16840143C211yesmaximal, characteristic, complemented
5C2×#16840133C211yesmaximal, characteristic, complemented
6C2×#16839986C211yesmaximal, characteristic, complemented
7C2×#16839981C211yesmaximal, characteristic, complemented
8C2×#16839970C211yesmaximal, characteristic, complemented
9C2×#16839975C211yesmaximal, characteristic, complemented
10C2×#16839974C211yesmaximal, characteristic, complemented
11C2×#16839955C211yesmaximal, characteristic
12C2×C8×Dic122C211yesmaximal, characteristic, complemented
13C2×C4×#11758190C211yesmaximal, characteristic, complemented
14C2×SD16×Dic61C211yesmaximal, characteristic, complemented
15C2×SD16×Dic61C211yesmaximal, characteristic, complemented
16C2×C61×#495C211yesmaximal, characteristic, complemented
17C22×#11758202C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C22×#11758199C2211yescharacteristic
22#16840494—24no—
23#16840494C2218yescomplemented
24#16840481—24no—
25#16840481C2218yescomplemented
26C2×#14519775C2211yescharacteristic
27C2×#14519773C2211yescharacteristic
28C2×#14519770—21no—
29C2×#14519770—21no—
30C2×#14519766C2211yescharacteristic
31C2×#14519764C2211yescharacteristic
32C2×#14519763—21no—
33C2×#14519761—21no—
34C2×#14519759—21no—
35C2×#14519754—21no—
36C2×Q8×Dic61C2211yescharacteristic
37C2×Q8×Dic61C2211yescharacteristic
38C2×C4×Dic122C2211yescharacteristic
39C2×C4×Dic122C2211yescharacteristic
40C2×C4×D244C2211yescharacteristic
41C2×D4×Dic61C2211yescharacteristic
42C2×D4×Dic61C2211yescharacteristic
43C2×#14519737—21no—
44C2×#14519733—21no—
45#16840143C2218yescomplemented
46#16840133C2218yescomplemented
47#16839986C2218yescomplemented
48#16839981C2218yescomplemented
49#16839975C2218yescomplemented
50#16839974C2218yescomplemented
51#16839970C2218yescomplemented
52#16839955C2218yes—
53C8×Dic122C2218yescomplemented
54C4×#11758190C2218yescomplemented
55SD16×Dic61C2218yescomplemented
56SD16×Dic61C2218yescomplemented
57C2×#14519709C2211yescharacteristic
58C2×C4⋊#92418C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519706C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519701C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×#14519698C2211yescharacteristic
67C2×C8×Dic61C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×Q16×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C22×SD16×C61C2211yescharacteristic
72C22×D8×C61C2211yescharacteristic
73C2×#124×C61C2211yescharacteristic
74C2×#124×C61C2211yescharacteristic
75C61×#495C2218yescomplemented
76C2×C4×C8×C61C2211yescharacteristic
77C22×Dic122D411yescharacteristic
78C22×Dic122C2311yescharacteristic
79C22×D244C2311yescharacteristic
80C22×C22⋊D61—21no—
81C22×C22⋊D61—21no—
82C23×Dic61—21no—
83C23×Dic61—21no—
84C22×C4×D61—21no—
85C2×#11758202—42no—
86C2×#11758202C2314yes—
87C2×#11758190—24no—
88C2×#11758190C2314yes—
89C2×#11758200—42no—
90C2×#11758200C2314yes—
91C2×#11758201—42no—
92C2×#11758201C2314yes—
93C2×#11758199—42no—
94C2×#11758199C2314yes—
95C22×#92418C2311yescharacteristic
96C22×#92418C2311yescharacteristic
97#14519775—22no—
98#14519775C2314yes—
99#14519773—22no—
100#14519773C2314yes—
101#14519770—28no—
102#14519770—28no—
103#14519766—22no—
104#14519766C2314yes—
105#14519764—22no—
106#14519764C2314yes—
107#14519763—28no—
108#14519761—28no—
109#14519759—28no—
110#14519754—28no—
111Q8×Dic61—22no—
112Q8×Dic61—22no—
113Q8×Dic61C2314yes—
114Q8×Dic61C2314yes—
115C4×Dic122—22no—
116C4×Dic122D414yes—
117C4×Dic122C2314yes—
118C4×Dic122C2314yes—
119C4×D244—22no—
120C4×D244C2314yes—
121D4×Dic61—22no—
122D4×Dic61—22no—
123D4×Dic61C2314yes—
124D4×Dic61C2314yes—
125#14519737—28no—
126#14519733—28no—
127C2×C4⋊Dic61—21no—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61D411yescharacteristic
130C2×C4⋊Dic61C2311yescharacteristic
131C2×C4⋊Dic61C2311yescharacteristic
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196D411yescharacteristic
136C2×#11758196D411yescharacteristic
137C2×C22⋊Dic61—21no—
138C2×C22⋊Dic61—21no—
139C2×C22⋊Dic61—21no—
140C2×C22⋊Dic61—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×C4×Dic61—21no—
145C2×C4×Dic61—21no—
146C2×C4×Dic61—21no—
147C2×C4×Dic61C2311yescharacteristic
148C2×C4×Dic61C2311yescharacteristic
149#14519709C2314yes—
150C4⋊#92418C2314yes—
151#14519706C2314yes—
152#14519706C2314yes—
153#14519702C2314yes—
154#14519701C2314yes—
155#14519701C2314yes—
156#14519699C2314yes—
157#14519698C2314yes—
158#14519698C2314yes—
159C8×Dic61C2314yes—
160C8×Dic61C2314yes—
161C22×Q8×C61C2311yescharacteristic
162C22×Q8×C61C2311yescharacteristic
163C22×D4×C61C2311yescharacteristic
164C22×D4×C61C2311yescharacteristic
165C2×Q16×C61—42no—
166C2×Q16×C61C2314yes—
167C2×SD16×C61—24no—
168C2×SD16×C61—24no—
169C2×SD16×C61C2314yes—
170C2×SD16×C61C2314yes—
171C2×D8×C61—42no—
172C2×D8×C61C2314yes—
173C22×C8×C61C2311yescharacteristic
174C22×C8×C61C2311yescharacteristic
175#124×C61—22no—
176#124×C61—22no—
177#124×C61C2314yes—
178#124×C61C2314yes—
179C2×C22⋊C4×C61—21no—
180C2×C22⋊C4×C61—21no—
181C2×C22⋊C4×C61—21no—
182C2×C22⋊C4×C61—21no—
183C2×C42×C61C2311yescharacteristic
184C4×C8×C61C2314yes—
185C24×C61—21no—
186C24×C61—21no—
187C23×D61—21no—
188C2×Q8×C61—21no—
189C2×Q8×C61—21no—
190C2×Q8×C61—22no—
191C2×Q8×C61—22no—
192C2×Q8×C61—22no—
193C2×Q8×C61—22no—
194C2×Q8×C61C2412yes—
195C2×Q8×C61C2412yes—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—22no—
199C2×D4×C61—22no—
200C2×D4×C61—22no—
201C2×D4×C61—22no—
202C2×D4×C61C2412yes—
203C2×D4×C61C2412yes—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2411yescharacteristic
209C2×C22⋊D61—24no—
210C2×C22⋊D61—24no—
211C2×C22⋊D61—44no—
212C2×C22⋊D61—82no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—24no—
217C22×Dic61—24no—
218C22×Dic61—44no—
219C22×Dic61—82no—
220C22×Dic61C2×D411yescharacteristic
221C22×Dic61C2×D411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224C2×D244—22no—
225C2×D244—22no—
226C2×D244—21no—
227C2×D244C2412yes—
228C2×C4×D61—24no—
229C2×C4×D61—82no—
230C2×Dic122—24no—
231C2×Dic122—22no—
232C2×Dic122—22no—
233C2×Dic122—21no—
234C2×Dic122C2×D414yes—
235C2×Dic122C2412yes—
236Q16×C61—44no—
237SD16×C61—28no—
238SD16×C61—28no—
239D8×C61—44no—
240C2×C8×C61—22no—
241C2×C8×C61#4114yes—
242C2×C8×C61C2412yes—
243C2×C8×C61C2412yes—
244C22⋊C4×C61—24no—
245C22⋊C4×C61—24no—
246C22⋊C4×C61—24no—
247C22⋊C4×C61—24no—
248C42×C61C2×D412yes—
249C42×C61C2412yes—
250C22⋊Dic61—24no—
251C22⋊Dic61—24no—
252C22⋊Dic61—24no—
253C22⋊Dic61—24no—
254#11758202—44no—
255#11758201—44no—
256#11758200—44no—
257#11758199—44no—
258#11758198—24no—
259#11758198—24no—
260#11758198—24no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—24no—
264C4⋊Dic61—24no—
265C4⋊Dic61C2×D414yes—
266C4⋊Dic61C2412yes—
267C4⋊Dic61C2412yes—
268#11758196—24no—
269#11758196—24no—
270#11758196—24no—
271#11758196C2×D414yes—
272#11758196C2×D414yes—
273C4×Dic61—24no—
274C4×Dic61—24no—
275C4×Dic61—24no—
276C4×Dic61C2×D412yes—
277C4×Dic61C2×D412yes—
278C4×Dic61C2412yes—
279C4×Dic61C2412yes—
280C2×#92418—22no—
281C2×#92418—22no—
282C2×#92418C2412yes—
283C2×#92418C2412yes—
284#11758190—28no—
285C23×C61—22no—
286C23×C61—22no—
287C23×C61—42no—
288C23×C61—42no—
289C23×C61—42no—
290C23×C61—42no—
291C23×C61—42no—
292C23×C61—42no—
293C23×C61C22×D411yescharacteristic
294C22×D61—22no—
295C22×D61—42no—
296C22×D61—42no—
297C22×D61—42no—
298Q8×C61—22no—
299Q8×C61—22no—
300Q8×C61—22no—
301Q8×C61—22no—
302Q8×C61—42no—
303Q8×C61—42no—
304D4×C61—22no—
305D4×C61—22no—
306D4×C61—22no—
307D4×C61—22no—
308D4×C61—42no—
309D4×C61—42no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61C22×D412yes—
317C2×C4×C61C22×D412yes—
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C2×#4112yes—
320C2×C4×C61H(5,𝔽2)12yes—
321C2×C4×C61C2511yescharacteristic
322C22⋊D61—48no—
323C22⋊D61—84no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—42no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61—48no—
334C2×Dic61—84no—
335C2×Dic61#13514yes—
336C2×Dic61C22×D412yes—
337C2×Dic61C22×D412yes—
338C2×Dic61C22×D412yes—
339C2×Dic61C22×D412yes—
340D244—22no—
341D244—22no—
342D244—42no—
343C4×D61—84no—
344Dic122—28no—
345Dic122—22no—
346Dic122—22no—
347Dic122—42no—
348C8×C61—22no—
349C8×C61C2×#4114yes—
350#92418—22no—
351#92418—22no—
352C2×#3394—611nomaximal, Sylow
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—84no—
360C22×C61—84no—
361C22×C61#55012yes—
362C22×C61C2×#13512yes—
363C22×C61#57712yes—
364C22×C61C23×D411yescharacteristic
365C2×D61—42no—
366C2×D61—42no—
367C2×D61—42no—
368C2×D61—84no—
369C4×C61—22no—
370C4×C61—22no—
371C4×C61—42no—
372C4×C61—42no—
373C4×C61#55012yes—
374C4×C61C22×#4111yescharacteristic
375C4×C61C2×H(5,𝔽2)11yescharacteristic
376Dic61—22no—
377Dic61—22no—
378Dic61—22no—
379Dic61—42no—
380Dic61—42no—
381Dic61—42no—
382Dic61C2×#13514yes—
383C2×#559—611no—
384C2×#556—611no—
385#3394—6116no—
386C2×#495—611no—
387C2×#495D6111yescharacteristic, complemented
388C2×#492—611no—
389C2×#464—611no—
390C2×#464—611no—
391C2×#462—611no—
392C2×#463—611no—
393C2×#463—611no—
394C2×#459—611no—
395C2×C8×Q8—611no—
396C2×C4×SD16—611no—
397C2×C4×SD16—611no—
398C2×C4×SD16—611no—
399C2×C61—82no—
400C2×C61—82no—
401C2×C61#339414yescomplemented
402C2×C61C2×#55011yescharacteristic
403C2×C61C22×#13511yescharacteristic
404C2×C61C2×#57711yescharacteristic
405D61—82no—
406C22×Q16—611no—
407C22×Q16C2×D6111yescharacteristic
408C22×SD16—611no—
409C22×SD16—611no—
410C22×SD16—611no—
411C22×SD16C2×D6111yescharacteristic
412C22×SD16C2×D6111yescharacteristic
413C22×D8—611no—
414C22×D8C2×D6111yescharacteristic
415#559—618no—
416#559—1224no—
417#556—618no—
418#556—1224no—
419C2×C4⋊Q8—611no—
420C2×#127—611no—
421C2×#126—1221no—
422C2×#126—1221no—
423C2×#124—611no—
424C2×#124—611no—
425C2×#124—1221no—
426C2×#124C2×D6111yescharacteristic
427C2×#124C2×D6111yescharacteristic
428C2×#123—1221no—
429C2×#123—1221no—
430C2×C22⋊Q8—1221no—
431C2×C4×Q8—611no—
432C2×C4×Q8—611no—
433C2×C4×Q8—611no—
434C2×C4×Q8—611no—
435C2×C4×D4—611no—
436C2×C4×D4—611no—
437C2×C4×D4—611no—
438C2×C4×D4—1221no—
439C2×#117—1221no—
440#495—618no—
441#495C2×D6118yescomplemented
442#492—618no—
443#464—618no—
444#464—618no—
445#463—618no—
446#463—618no—
447#462—618no—
448#459—618no—
449C8×Q8—618no—
450C4×SD16—618no—
451C4×SD16—618no—
452C4×SD16—618no—
453C2×#106—611no—
454C2×C4⋊C8—611no—
455C2×C4⋊C8—611no—
456C2×C4⋊C8—611no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#102—611no—
461C2×#102—611no—
462C2×#102—611no—
463C2×C4×C8—611no—
464C2×C4×C8—611no—
465C2×C4×C8C2×D6111yescharacteristic
466C61C2×#339411yescharacteristic, complemented, Sylow
467C22×Q8—611no—
468C22×Q8—611no—
469C22×Q8C22×D6111yescharacteristic
470C22×Q8C22×D6111yescharacteristic
471C22×D4—611no—
472C22×D4—1221no—
473C22×D4—1221no—
474C22×D4C22×D6111yescharacteristic
475C22×D4C22×D6111yescharacteristic
476C23×C4—1221no—
477C23×C4—1221no—
478C23×C4—1221no—
479C2×Q16—42no—
480C2×Q16—614no—
481C2×Q16—2442no—
482C2×Q16C22×D6114yes—
483C2×SD16—24no—
484C2×SD16—24no—
485C2×SD16—614no—
486C2×SD16—614no—
487C2×SD16—614no—
488C2×SD16—1224no—
489C2×SD16—2442no—
490C2×SD16—2442no—
491C2×SD16C22×D6114yes—
492C2×SD16C22×D6114yes—
493C2×D8—42no—
494C2×D8—614no—
495C2×D8—2442no—
496C2×D8C22×D6114yes—
497C22×C8—611no—
498C22×C8—611no—
499C22×C8C22×D6111yescharacteristic
500C22×C8C22×D6111yescharacteristic
501C4⋊Q8—614no—
502C4⋊Q8—1222no—
503#127—614no—
504#127—1222no—
505#126—1228no—
506#126—1228no—
507#124—22no—
508#124—22no—
509#124—614no—
510#124—614no—
511#124—1222no—
512#124—1222no—
513#124—1228no—
514#124C22×D6114yes—
515#124C22×D6114yes—
516#123—1228no—
517#123—1228no—
518C22⋊Q8—1228no—
519C4×Q8—614no—
520C4×Q8—614no—
521C4×Q8—614no—
522C4×Q8—614no—
523C4×Q8—614no—
524C4×Q8—1222no—
525C4×Q8—1222no—
526C4×Q8—1222no—
527C4×D4—614no—
528C4×D4—614no—
529C4×D4—614no—
530C4×D4—1222no—
531C4×D4—1222no—
532C4×D4—1228no—
533C4×D4—1222no—
534#117—1228no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—611no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4—1221no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C42—611no—
557C2×C42—611no—
558C2×C42—1221no—
559C2×C42—1221no—
560C2×C42—1221no—
561C2×C42C22×D6111yescharacteristic
562#106—614no—
563C4⋊C8—614no—
564C4⋊C8—614no—
565C4⋊C8—614no—
566#103—614no—
567#103—614no—
568#103—614no—
569#102—614no—
570#102—614no—
571#102—614no—
572C4×C8—614no—
573C4×C8—614no—
574C4×C8C22×D6114yes—
575C24—21no—
576C24—21no—
577C24—1221no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—614no—
585C2×Q8—612no—
586C2×Q8—1224no—
587C2×Q8—1221no—
588C2×Q8—1222no—
589C2×Q8—1222no—
590C2×Q8C23×D6112yes—
591C2×Q8C23×D6112yes—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—612no—
599C2×D4—1224no—
600C2×D4—1224no—
601C2×D4—1221no—
602C2×D4—1222no—
603C2×D4—1222no—
604C2×D4—4882no—
605C2×D4—2444no—
606C2×D4C23×D6112yes—
607C2×D4C23×D6112yes—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—1224no—
615C22×C4—1224no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1224no—
620C22×C4—4882no—
621C22×C4—4882no—
622C22×C4—2444no—
623C22×C4D4×D6111yescharacteristic
624C22×C4D4×D6111yescharacteristic
625C22×C4C23×D6111yescharacteristic
626Q16—44no—
627Q16—2444no—
628SD16—28no—
629SD16—28no—
630SD16—1228no—
631SD16—2444no—
632SD16—2444no—
633D8—44no—
634D8—2444no—
635C2×C8—22no—
636C2×C8—612no—
637C2×C8—612no—
638C2×C8—1222no—
639C2×C8—1222no—
640C2×C8#1175822414yes—
641C2×C8C23×D6112yes—
642C2×C8C23×D6112yes—
643C4⋊C4—614no—
644C4⋊C4—614no—
645C4⋊C4—614no—
646C4⋊C4—612no—
647C4⋊C4—612no—
648C4⋊C4—1224no—
649C4⋊C4—1224no—
650C4⋊C4—1224no—
651C4⋊C4—1224no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1224no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—1224no—
660C22⋊C4—1224no—
661C22⋊C4—1224no—
662C22⋊C4—1224no—
663C22⋊C4—1224no—
664C22⋊C4—1224no—
665C22⋊C4—1224no—
666C42—612no—
667C42—612no—
668C42—612no—
669C42—612no—
670C42—1224no—
671C42—1224no—
672C42—1224no—
673C42D4×D6112yes—
674C42C23×D6112yes—
675C23—22no—
676C23—22no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—1222no—
684C23—2442no—
685C23—2442no—
686C23—2442no—
687C23C2×D4×D6111yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—22no—
691Q8—22no—
692Q8—42no—
693Q8—42no—
694Q8—1228no—
695Q8—1222no—
696Q8—1222no—
697Q8—2442no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—42no—
703D4—42no—
704D4—1222no—
705D4—1222no—
706D4—4884no—
707D4—2448no—
708D4—2442no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—614no—
716C2×C4—612no—
717C2×C4—612no—
718C2×C4—612no—
719C2×C4—612no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—4884no—
727C2×C4—4884no—
728C2×C4—2448no—
729C2×C4—2442no—
730C2×C4—2442no—
731C2×C4—2442no—
732C2×C4C2×D4×D6112yes—
733C2×C4C2×D4×D6112yes—
734C2×C4C2×D4×D6111yescharacteristic
735C2×C4C2×#1175822412yes—
736C2×C4#1451982212yes—
737C2×C4C24×D6111yescharacteristic
738C8—22no—
739C8—1222no—
740C8—1222no—
741C8C2×#1175822414yes—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—84no—
749C22—84no—
750C22—4884no—
751C22—2442no—
752C22—2442no—
753C22—2442no—
754C22#1684043212yes—
755C22#135×D6112yes—
756C22#1684056912yes—
757C22C22×D4×D6111yescharacteristic
758C4—22no—
759C4—22no—
760C4—42no—
761C4—42no—
762C4—614no—
763C4—1222no—
764C4—1222no—
765C4—1222no—
766C4—2442no—
767C4—2442no—
768C4—2442no—
769C4#1684043212yes—
770C4C22×#1175822411yescharacteristic
771C4C2×#1451982211yescharacteristic
772C2—82no—
773C2—82no—
774C2—4882no—
775C2#2145881214yesdirect product factor
776C2C2×#1684043211yescharacteristic
777C2C2×#135×D6111yescharacteristic
778C2C2×#1684056911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#495C2
socleC23×C61C22×D4
prime radicalC2×#16839955C2
hypercenterC2×#495D61
hypocenterC61C2×#3394
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#495

Complements

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

NH ≅ G/Ntype
1. C2×#16840494C2semidirect
2. C2×#16840481C2semidirect
3. #21458812C2direct (N × H)
4. C2×#16840143C2semidirect
5. C2×#16840133C2semidirect
6. C2×#16839986C2semidirect
7. C2×#16839981C2semidirect
8. C2×#16839970C2semidirect
9. C2×#16839975C2semidirect
10. C2×#16839974C2semidirect
12. C2×C8×Dic122C2semidirect
13. C2×C4×#11758190C2semidirect
14. C2×SD16×Dic61C2semidirect
15. C2×SD16×Dic61C2semidirect
16. C2×C61×#495C2semidirect
23. #16840494C22semidirect
25. #16840481C22semidirect
45. #16840143C22semidirect
46. #16840133C22semidirect
47. #16839986C22semidirect
48. #16839981C22semidirect
49. #16839975C22semidirect
50. #16839974C22semidirect
51. #16839970C22semidirect
53. C8×Dic122C22semidirect
54. C4×#11758190C22semidirect
55. SD16×Dic61C22semidirect
56. SD16×Dic61C22semidirect
75. C61×#495C22semidirect
387. C2×#495D61semidirect
401. C2×C61#3394semidirect
441. #495C2×D61semidirect
466. C61C2×#3394semidirect
775. C2#21458812direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404942
C2×#168404812
#214588122
C2×#168401432
C2×#168401332
C2×#168399862
C2×#168399812
C2×#168399702
C2×#168399752
C2×#168399742
C2×#168399552
C2×C8×Dic1222
C2×C4×#117581902
C2×SD16×Dic612
C2×C61×#4952
C2×#339461