Finite Group Databasebeta

← C2×#21458878 #30561012

Subgroups — C2×#21458878 #30561012

Order 15616.

2002 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×#16840498C211yesmaximal, characteristic, complemented
2C2×#16840484C211yesmaximal, characteristic, complemented
3#21458878C2116yesmaximal, direct product factor
4C2×#16840153C211yesmaximal, characteristic, complemented
5C2×#16840149C211yesmaximal, characteristic
6C2×#16840143C211yesmaximal, characteristic, complemented
7C2×#16839985C211yesmaximal, characteristic, complemented
8C2×#16839983C211yesmaximal, characteristic, complemented
9C2×#16839979C211yesmaximal, characteristic, complemented
10C2×#16839976C211yesmaximal, characteristic, complemented
11C2×#16839965C211yesmaximal, characteristic, complemented
12C2×#16839891C211yesmaximal, characteristic, complemented
13C2×#16839871C211yesmaximal, characteristic, complemented
14C2×#16839867C211yesmaximal, characteristic, complemented
15C2×#16839853C211yesmaximal, characteristic, complemented
16C2×C61×#460C211yesmaximal, characteristic, complemented
17C22×Dic244C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758190C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×#11758200C2211yescharacteristic
22C22×#11758199C2211yescharacteristic
23C22×#11758199C2211yescharacteristic
24#16840498—24no—
25#16840498C2218yescomplemented
26#16840484—24no—
27#16840484C2218yescomplemented
28C2×#14519775C2211yescharacteristic
29C2×#14519772—21no—
30C2×#14519771—21no—
31C2×#14519766C2211yescharacteristic
32C2×#14519765C2211yescharacteristic
33C2×#14519764—21no—
34C2×#14519764C2211yescharacteristic
35C2×#14519764C2211yescharacteristic
36C2×#14519758—21no—
37C2×#14519758—21no—
38C2×#14519755—21no—
39C2×C4×Dic122C2211yescharacteristic
40C2×C4×Dic122C2211yescharacteristic
41C2×#14519742C2211yescharacteristic
42C2×D4×Dic61—21no—
43C2×D4×Dic61C2211yescharacteristic
44C2×D4×Dic61C2211yescharacteristic
45C2×#14519739C2211yescharacteristic
46C2×#14519734—21no—
47#16840153C2218yescomplemented
48#16840149C2218yes—
49#16840143C2218yescomplemented
50#16839985C2218yescomplemented
51#16839983C2218yescomplemented
52#16839979C2218yescomplemented
53#16839976C2218yescomplemented
54#16839965C2218yescomplemented
55#16839891C2218yescomplemented
56#16839871C2218yescomplemented
57#16839867C2218yescomplemented
58#16839853C2218yescomplemented
59C2×#14519708C2211yescharacteristic
60C2×#14519706C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519702C2211yescharacteristic
63C2×#14519701C2211yescharacteristic
64C2×#14519700C2211yescharacteristic
65C2×#14519699C2211yescharacteristic
66C2×#14519688C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C2×#127×C61C2211yescharacteristic
72C2×C4×Q8×C61C2211yescharacteristic
73C61×#460C2218yescomplemented
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C22×Dic122D411yescharacteristic
78C22×Dic122C2311yescharacteristic
79C22×Dic122C2311yescharacteristic
80C22×D244C2311yescharacteristic
81C23×Dic61—21no—
82C23×Dic61—21no—
83C22×C4×D61—21no—
84C2×Dic244—42no—
85C2×Dic244C2314yes—
86C2×#11758202—24no—
87C2×#11758202C2314yes—
88C2×#11758190—42no—
89C2×#11758190C2314yes—
90C2×#11758200—24no—
91C2×#11758200—42no—
92C2×#11758200C2314yes—
93C2×#11758200C2314yes—
94C2×#11758199—24no—
95C2×#11758199—42no—
96C2×#11758199C2314yes—
97C2×#11758199C2314yes—
98C22×#92418C2311yescharacteristic
99C22×#92418C2311yescharacteristic
100#14519775—22no—
101#14519775C2314yes—
102#14519772—28no—
103#14519771—28no—
104#14519766—22no—
105#14519766C2314yes—
106#14519765—22no—
107#14519765C2314yes—
108#14519764—28no—
109#14519764—22no—
110#14519764—22no—
111#14519764C2314yes—
112#14519764C2314yes—
113#14519758—28no—
114#14519758—28no—
115#14519755—28no—
116C4×Dic122—22no—
117C4×Dic122D414yes—
118C4×Dic122C2314yes—
119C4×Dic122C2314yes—
120#14519742—22no—
121#14519742C2314yes—
122D4×Dic61—28no—
123D4×Dic61—22no—
124D4×Dic61—22no—
125D4×Dic61C2314yes—
126D4×Dic61C2314yes—
127#14519739—22no—
128#14519739C2314yes—
129#14519734—28no—
130C2×C4⋊Dic61D411yescharacteristic
131C2×C4⋊Dic61C2311yescharacteristic
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196D411yescharacteristic
137C2×#11758196D411yescharacteristic
138C2×C22⋊Dic61—21no—
139C2×C22⋊Dic61—21no—
140C2×C22⋊Dic61—21no—
141C2×C22⋊Dic61—21no—
142C2×C22⋊Dic61—21no—
143C2×C22⋊Dic61—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×C4×Dic61—21no—
150C2×C4×Dic61—21no—
151C2×C4×Dic61C2311yescharacteristic
152C2×C4×Dic61C2311yescharacteristic
153#14519708C2314yes—
154#14519706C2314yes—
155#14519706C2314yes—
156#14519702C2314yes—
157#14519701C2314yes—
158#14519700C2314yes—
159#14519699C2314yes—
160#14519688C2314yes—
161#14519687C2314yes—
162C8×Dic61C2314yes—
163C22×Q8×C61C2311yescharacteristic
164C22×D4×C61—21no—
165C22×D4×C61—21no—
166C22×D4×C61C2311yescharacteristic
167C22×D4×C61C2311yescharacteristic
168C2×SD16×C61—42no—
169C2×SD16×C61—42no—
170C2×SD16×C61C2314yes—
171C2×SD16×C61C2314yes—
172C22×C8×C61C2311yescharacteristic
173C22×C8×C61C2311yescharacteristic
174#127×C61—22no—
175#127×C61C2314yes—
176C4×Q8×C61—22no—
177C4×Q8×C61C2314yes—
178C2×C4⋊C4×C61—21no—
179C2×C4⋊C4×C61C2311yescharacteristic
180C2×C42×C61—21no—
181C2×C42×C61C2311yescharacteristic
182C4⋊C8×C61C2314yes—
183#102×C61C2314yes—
184#102×C61C2314yes—
185C24×C61—21no—
186C24×C61—21no—
187C23×D61—21no—
188C2×Q8×C61—21no—
189C2×Q8×C61—22no—
190C2×Q8×C61—22no—
191C2×Q8×C61C2412yes—
192C2×D4×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61—24no—
195C2×D4×C61—24no—
196C2×D4×C61—22no—
197C2×D4×C61—22no—
198C2×D4×C61—22no—
199C2×D4×C61—22no—
200C2×D4×C61—44no—
201C2×D4×C61—82no—
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
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—24no—
213C22×Dic61—24no—
214C22×Dic61—82no—
215C22×Dic61—82no—
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220C2×D244—22no—
221C2×D244—22no—
222C2×D244—21no—
223C2×D244C2412yes—
224C2×C4×D61—24no—
225C2×C4×D61—44no—
226C2×Dic122—22no—
227C2×Dic122—22no—
228C2×Dic122—22no—
229C2×Dic122—22no—
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122—42no—
233C2×Dic122C2×D414yes—
234C2×Dic122C2412yes—
235C2×Dic122C2412yes—
236SD16×C61—44no—
237SD16×C61—44no—
238C2×C8×C61—22no—
239C2×C8×C61—22no—
240C2×C8×C61C2412yes—
241C2×C8×C61C2412yes—
242C4⋊C4×C61—24no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61C2412yes—
245C42×C61—24no—
246C42×C61C2×D412yes—
247C42×C61C2412yes—
248C22⋊Dic61—24no—
249C22⋊Dic61—24no—
250C22⋊Dic61—24no—
251C22⋊Dic61—24no—
252C22⋊Dic61—24no—
253C22⋊Dic61—24no—
254#11758202—28no—
255#11758200—28no—
256#11758200—44no—
257#11758199—28no—
258#11758199—44no—
259#11758198—24no—
260#11758198—24no—
261#11758198—24no—
262#11758198—24no—
263#11758198—24no—
264C4⋊Dic61—21no—
265C4⋊Dic61C2×D414yes—
266C4⋊Dic61C2412yes—
267#11758196—24no—
268#11758196—24no—
269#11758196—24no—
270#11758196—24no—
271#11758196C2×D414yes—
272#11758196C2×D414yes—
273C4×Dic61—24no—
274C4×Dic61—24no—
275C4×Dic61C2×D412yes—
276C4×Dic61C2×D412yes—
277C4×Dic61C2412yes—
278C4×Dic61C2412yes—
279C2×#92418—22no—
280C2×#92418#4114yes—
281C2×#92418C2412yes—
282C2×#92418C2412yes—
283Dic244—44no—
284#11758190—44no—
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—42no—
301D4×C61—22no—
302D4×C61—22no—
303D4×C61—22no—
304D4×C61—22no—
305D4×C61—48no—
306D4×C61—42no—
307D4×C61—42no—
308D4×C61—84no—
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×D412yes—
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C2×#4112yes—
319C2×C4×C61H(5,𝔽2)12yes—
320C2×C4×C61C2511yescharacteristic
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—84no—
332C2×Dic61—84no—
333C2×Dic61C22×D412yes—
334C2×Dic61C22×D412yes—
335C2×Dic61C22×D412yes—
336C2×Dic61C22×D412yes—
337D244—22no—
338D244—22no—
339D244—42no—
340C4×D61—48no—
341Dic122—22no—
342Dic122—22no—
343Dic122—22no—
344Dic122—22no—
345Dic122—44no—
346Dic122—42no—
347Dic122—42no—
348C8×C61—22no—
349C8×C61—22no—
350#92418—22no—
351#92418C2×#4114yes—
352C2×#3401—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×C61#57512yes—
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—22no—
380Dic61—42no—
381Dic61—42no—
382Dic61—42no—
383C2×#559—611no—
384C2×#556—611no—
385#3401—6116no—
386C2×#497—611no—
387C2×#496—611no—
388C2×#495—611no—
389C2×#464—611no—
390C2×#464—611no—
391C2×#460D6111yescharacteristic, complemented
392C2×#463—611no—
393C2×#463—611no—
394C2×#461—611no—
395C2×#446—611no—
396C2×#442—611no—
397C2×#441—611no—
398C2×C4×SD16—611no—
399C2×C61—82no—
400C2×C61—82no—
401C2×C61#340114yescomplemented
402C2×C61C2×#55011yescharacteristic
403C2×C61C2×#57511yescharacteristic
404C2×C61C2×#57711yescharacteristic
405D61—82no—
406C22×Q16—611no—
407C22×Q16—611no—
408C22×SD16—611no—
409C22×SD16—611no—
410C22×SD16—611no—
411C22×SD16C2×D6111yescharacteristic
412C22×SD16C2×D6111yescharacteristic
413C22×D8—611no—
414C22×D8—611no—
415#559—618no—
416#559—1224no—
417#556—618no—
418#556—1224no—
419C2×C4⋊Q8—611no—
420C2×#127C2×D6111yescharacteristic
421C2×#126—1221no—
422C2×#126—1221no—
423C2×#124—611no—
424C2×#124—611no—
425C2×#124—611no—
426C2×#124—611no—
427C2×#124—1221no—
428C2×#123—1221no—
429C2×#123—1221no—
430C2×C22⋊Q8—1221no—
431C2×C4×Q8—611no—
432C2×C4×Q8—611no—
433C2×C4×Q8—611no—
434C2×C4×Q8C2×D6111yescharacteristic
435C2×C4×D4—611no—
436C2×C4×D4—611no—
437C2×C4×D4—611no—
438C2×C4×D4—1221no—
439C2×#117—1221no—
440#497—618no—
441#496—618no—
442#495—618no—
443#464—618no—
444#464—618no—
445#463—618no—
446#463—618no—
447#461—618no—
448#460C2×D6118yescomplemented
449#446—618no—
450#442—618no—
451#441—618no—
452C4×SD16—618no—
453C2×#106—611no—
454C2×C4⋊C8—611no—
455C2×C4⋊C8—611no—
456C2×C4⋊C8C2×D6111yescharacteristic
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#102—611no—
461C2×#102C2×D6111yescharacteristic
462C2×#102C2×D6111yescharacteristic
463C2×#97—611no—
464C2×#97—611no—
465C2×C4×C8—611no—
466C61C2×#340111yescharacteristic, complemented, Sylow
467C22×Q8—611no—
468C22×Q8—611no—
469C22×Q8—611no—
470C22×Q8C22×D6111yescharacteristic
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—611no—
474C22×D4C22×D6111yescharacteristic
475C22×D4C22×D6111yescharacteristic
476C23×C4—1221no—
477C23×C4—1221no—
478C23×C4—1221no—
479C2×Q16—614no—
480C2×Q16—614no—
481C2×Q16—1224no—
482C2×Q16—2442no—
483C2×SD16—42no—
484C2×SD16—42no—
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—614no—
494C2×D8—614no—
495C2×D8—1224no—
496C2×D8—2442no—
497C22×C8—611no—
498C22×C8—611no—
499C22×C8C22×D6111yescharacteristic
500C22×C8C22×D6111yescharacteristic
501C4⋊Q8—614no—
502C4⋊Q8—1222no—
503#127—22no—
504#127C22×D6114yes—
505#126—1228no—
506#126—1228no—
507#124—614no—
508#124—614no—
509#124—614no—
510#124—614no—
511#124—1222no—
512#124—1222no—
513#124—1222no—
514#124—1228no—
515#124—1222no—
516#123—1228no—
517#123—1228no—
518C22⋊Q8—1228no—
519C4×Q8—22no—
520C4×Q8—614no—
521C4×Q8—614no—
522C4×Q8—614no—
523C4×Q8—614no—
524C4×Q8—1222no—
525C4×Q8—1222no—
526C4×Q8C22×D6114yes—
527C4×D4—614no—
528C4×D4—614no—
529C4×D4—614no—
530C4×D4—1222no—
531C4×D4—1222no—
532C4×D4—1222no—
533C4×D4—1228no—
534#117—1228no—
535C2×C4⋊C4—21no—
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⋊C4C22×D6111yescharacteristic
545C2×C22⋊C4—1221no—
546C2×C22⋊C4—1221no—
547C2×C22⋊C4—1221no—
548C2×C22⋊C4—1221no—
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—21no—
557C2×C42—611no—
558C2×C42—611no—
559C2×C42—1221no—
560C2×C42—1221no—
561C2×C42C22×D6111yescharacteristic
562#106—614no—
563C4⋊C8—614no—
564C4⋊C8—614no—
565C4⋊C8C22×D6114yes—
566#103—614no—
567#103—614no—
568#103—614no—
569#102—614no—
570#102C22×D6114yes—
571#102C22×D6114yes—
572#97—614no—
573#97—614no—
574C4×C8—614no—
575C24—21no—
576C24—21no—
577C24—1221no—
578C2×Q8—21no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—614no—
582C2×Q8—612no—
583C2×Q8—612no—
584C2×Q8—1221no—
585C2×Q8—1221no—
586C2×Q8—1222no—
587C2×Q8—1222no—
588C2×Q8—1222no—
589C2×Q8—1222no—
590C2×Q8—2442no—
591C2×Q8C23×D6112yes—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—24no—
595C2×D4—24no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—44no—
601C2×D4—82no—
602C2×D4—612no—
603C2×D4—1221no—
604C2×D4—1222no—
605C2×D4—1222no—
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—1224no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—4882no—
621C22×C4—4882no—
622C22×C4—2444no—
623C22×C4D4×D6111yescharacteristic
624C22×C4D4×D6111yescharacteristic
625C22×C4C23×D6111yescharacteristic
626Q16—1228no—
627Q16—2444no—
628SD16—44no—
629SD16—44no—
630SD16—1228no—
631SD16—2444no—
632SD16—2444no—
633D8—1228no—
634D8—2444no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—614no—
638C2×C8—612no—
639C2×C8—612no—
640C2×C8—1222no—
641C2×C8C23×D6112yes—
642C2×C8C23×D6112yes—
643C4⋊C4—24no—
644C4⋊C4—21no—
645C4⋊C4—614no—
646C4⋊C4—614no—
647C4⋊C4—614no—
648C4⋊C4—612no—
649C4⋊C4—1224no—
650C4⋊C4—1224no—
651C4⋊C4—1224no—
652C4⋊C4—1221no—
653C4⋊C4—1224no—
654C4⋊C4C23×D6112yes—
655C22⋊C4—1224no—
656C22⋊C4—1224no—
657C22⋊C4—1224no—
658C22⋊C4—1224no—
659C22⋊C4—1224no—
660C22⋊C4—1224no—
661C22⋊C4—1224no—
662C22⋊C4—1224no—
663C22⋊C4—1224no—
664C22⋊C4—1224no—
665C22⋊C4—1224no—
666C42—24no—
667C42—612no—
668C42—612no—
669C42—612no—
670C42—612no—
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—42no—
691Q8—1222no—
692Q8—1222no—
693Q8—1222no—
694Q8—1222no—
695Q8—2444no—
696Q8—2442no—
697Q8—2442no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—48no—
703D4—42no—
704D4—42no—
705D4—84no—
706D4—1222no—
707D4—1222no—
708D4—2442no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—612no—
716C2×C4—612no—
717C2×C4—612no—
718C2×C4—612no—
719C2×C4—1222no—
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×C4#41×D6112yes—
736C2×C4#1451982212yes—
737C2×C4C24×D6111yescharacteristic
738C8—22no—
739C8—22no—
740C8—614no—
741C8—1222no—
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#1684043012yes—
755C22#1684055812yes—
756C22#1684056812yes—
757C22C22×D4×D6111yescharacteristic
758C4—22no—
759C4—22no—
760C4—42no—
761C4—42no—
762C4—1222no—
763C4—1222no—
764C4—1222no—
765C4—1222no—
766C4—2442no—
767C4—2442no—
768C4—2442no—
769C4#1684043012yes—
770C4C2×#41×D6111yescharacteristic
771C4C2×#1451982211yescharacteristic
772C2—82no—
773C2—82no—
774C2—4882no—
775C2#2145887814yesdirect product factor
776C2C2×#1684043011yescharacteristic
777C2C2×#1684055811yescharacteristic
778C2C2×#1684056811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#460C2
socleC23×C61C22×D4
prime radicalC2×#16840149C2
hypercenterC2×#460D61
hypocenterC61C2×#3401
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C2×#16840498C2semidirect
2. C2×#16840484C2semidirect
3. #21458878C2direct (N × H)
4. C2×#16840153C2semidirect
6. C2×#16840143C2semidirect
7. C2×#16839985C2semidirect
8. C2×#16839983C2semidirect
9. C2×#16839979C2semidirect
10. C2×#16839976C2semidirect
11. C2×#16839965C2semidirect
12. C2×#16839891C2semidirect
13. C2×#16839871C2semidirect
14. C2×#16839867C2semidirect
15. C2×#16839853C2semidirect
16. C2×C61×#460C2semidirect
25. #16840498C22semidirect
27. #16840484C22semidirect
47. #16840153C22semidirect
49. #16840143C22semidirect
50. #16839985C22semidirect
51. #16839983C22semidirect
52. #16839979C22semidirect
53. #16839976C22semidirect
54. #16839965C22semidirect
55. #16839891C22semidirect
56. #16839871C22semidirect
57. #16839867C22semidirect
58. #16839853C22semidirect
73. C61×#460C22semidirect
391. C2×#460D61semidirect
401. C2×C61#3401semidirect
448. #460C2×D61semidirect
466. C61C2×#3401semidirect
775. C2#21458878direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404982
C2×#168404842
#214588782
C2×#168401532
C2×#168401492
C2×#168401432
C2×#168399852
C2×#168399832
C2×#168399792
C2×#168399762
C2×#168399652
C2×#168398912
C2×#168398712
C2×#168398672
C2×#168398532
C2×C61×#4602
C2×#340161