Finite Group Databasebeta

← C2×#21456507 #30549902

Subgroups — C2×#21456507 #30549902

Order 15616.

2034 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840386C211yesmaximal, characteristic, complemented
2C2×#16840368C211yesmaximal, characteristic, complemented
3#21456507C2116yesmaximal, direct product factor
4C2×#16840151C211yesmaximal, characteristic, complemented
5C2×#16840119C211yesmaximal, characteristic, complemented
6C2×#16840110C211yesmaximal, characteristic, complemented
7C2×#16840016C211yesmaximal, characteristic, complemented
8C2×#16840009C211yesmaximal, characteristic, complemented
9C2×#16839999C211yesmaximal, characteristic, complemented
10C2×#16839992C211yesmaximal, characteristic, complemented
11C2×#16839873C211yesmaximal, characteristic, complemented
12C2×#16839861C211yesmaximal, characteristic, complemented
13C2×#16839849C211yesmaximal, characteristic, complemented
14C2×#16839844C211yesmaximal, characteristic, complemented
15C2×#16839719C211yesmaximal, characteristic, complemented
16C2×C61×#501C211yesmaximal, characteristic, complemented
17C22×#11758190C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C22×D488C2211yescharacteristic
20C22×D488C2211yescharacteristic
21C22×#11758189C2211yescharacteristic
22C22×C8×D61C2211yescharacteristic
23#16840386—24no—
24#16840386C2218yescomplemented
25#16840368—24no—
26#16840368C2218yescomplemented
27C2×#14519774C2211yescharacteristic
28C2×#14519772—21no—
29C2×#14519766—21no—
30C2×#14519765C2211yescharacteristic
31C2×#14519762—21no—
32C2×#14519762—21no—
33C2×#14519762—21no—
34C2×#14519757C2211yescharacteristic
35C2×#14519753—21no—
36C2×#14519752—21no—
37C2×#14519752—21no—
38C2×#14519752C2211yescharacteristic
39C2×#14519752C2211yescharacteristic
40C2×#14519752C2211yescharacteristic
41C2×#14519742C2211yescharacteristic
42C2×#14519739C2211yescharacteristic
43C2×#14519739C2211yescharacteristic
44C2×#14519739C2211yescharacteristic
45C2×#14519734C2211yescharacteristic
46#16840151C2218yescomplemented
47#16840119C2218yescomplemented
48#16840110C2218yescomplemented
49#16840016C2218yescomplemented
50#16840009C2218yescomplemented
51#16839999C2218yescomplemented
52#16839992C2218yescomplemented
53#16839873C2218yescomplemented
54#16839861C2218yescomplemented
55#16839849C2218yescomplemented
56#16839844C2218yescomplemented
57C2×#14519700C2211yescharacteristic
58C2×#14519700C2211yescharacteristic
59C2×#14519697C2211yescharacteristic
60C2×#14519697C2211yescharacteristic
61C2×#14519697C2211yescharacteristic
62C2×#14519697C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65#16839719C2218yescomplemented
66C2×#14519687C2211yescharacteristic
67C2×C4×#92418C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C2×C4⋊Q8×C61C2211yescharacteristic
70C2×#125×C61C2211yescharacteristic
71C61×#501C2218yescomplemented
72C2×#107×C61C2211yescharacteristic
73C2×#107×C61C2211yescharacteristic
74C2×#106×C61C2211yescharacteristic
75C2×#106×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C22×Dic122C2311yescharacteristic
78C22×D244—21no—
79C22×D244—21no—
80C22×D244—21no—
81C22×D244—21no—
82C22×D244—21no—
83C22×D244C2311yescharacteristic
84C22×D244C2311yescharacteristic
85C22×D244C2311yescharacteristic
86C22×C4×D61—21no—
87C22×C4×D61—21no—
88C22×C4×D61—21no—
89C22×C4×D61C2311yescharacteristic
90C2×#11758190—24no—
91C2×#11758190—24no—
92C2×#11758190C2314yes—
93C2×#11758190C2314yes—
94C2×D488—24no—
95C2×D488—24no—
96C2×D488C2314yes—
97C2×D488C2314yes—
98C2×#11758189—24no—
99C2×#11758189C2314yes—
100C22×#92418C2311yescharacteristic
101C22×#92418C2311yescharacteristic
102C2×C8×D61—24no—
103C2×C8×D61C2314yes—
104#14519774—22no—
105#14519774C2314yes—
106#14519772—28no—
107#14519766—28no—
108#14519765—22no—
109#14519765C2314yes—
110#14519762—28no—
111#14519762—28no—
112#14519762—28no—
113#14519757—22no—
114#14519757C2314yes—
115#14519753—28no—
116#14519752—22no—
117#14519752—22no—
118#14519752—22no—
119#14519752—28no—
120#14519752—28no—
121#14519752C2314yes—
122#14519752C2314yes—
123#14519752C2314yes—
124#14519742—22no—
125#14519742C2314yes—
126#14519739—22no—
127#14519739—22no—
128#14519739—22no—
129#14519739C2314yes—
130#14519739C2314yes—
131#14519739C2314yes—
132#14519734D414yes—
133#14519734C2314yes—
134C2×C4⋊Dic61—21no—
135C2×#11758196—21no—
136C2×#11758196D411yescharacteristic
137C2×#11758196D411yescharacteristic
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198D411yescharacteristic
148C2×#11758198D411yescharacteristic
149C2×C4×Dic61—21no—
150C2×C4×Dic61C2311yescharacteristic
151#14519700C2314yes—
152#14519700C2314yes—
153#14519697C2314yes—
154#14519697C2314yes—
155#14519697C2314yes—
156#14519697C2314yes—
157#14519697C2314yes—
158#14519697C2314yes—
159#14519687C2314yes—
160C4×#92418C2314yes—
161C8×Dic61C2314yes—
162C22×Q8×C61—21no—
163C22×C8×C61C2311yescharacteristic
164C22×C8×C61C2311yescharacteristic
165C4⋊Q8×C61—22no—
166C4⋊Q8×C61C2314yes—
167#125×C61—22no—
168#125×C61C2314yes—
169C2×C4⋊C4×C61—21no—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C42×C61C2311yescharacteristic
177#107×C61C2314yes—
178#107×C61C2314yes—
179#106×C61C2314yes—
180#106×C61C2314yes—
181#97×C61C2314yes—
182C23×D61—21no—
183C23×D61—21no—
184C23×D61—21no—
185C23×D61C2×D411yescharacteristic
186C2×Q8×C61—24no—
187C2×Q8×C61—82no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2411yescharacteristic
195C22×Dic61—21no—
196C22×Dic61C2×D411yescharacteristic
197C22×Dic61C2×D411yescharacteristic
198C22×Dic61C2×D411yescharacteristic
199C2×D244—22no—
200C2×D244—22no—
201C2×D244—22no—
202C2×D244—22no—
203C2×D244—22no—
204C2×D244—22no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—24no—
209C2×D244—24no—
210C2×D244—24no—
211C2×D244—24no—
212C2×D244—24no—
213C2×D244—82no—
214C2×D244—82no—
215C2×D244—82no—
216C2×D244—82no—
217C2×D244—82no—
218C2×D244C2412yes—
219C2×D244C2412yes—
220C2×D244C2412yes—
221C2×C4×D61—22no—
222C2×C4×D61—22no—
223C2×C4×D61—24no—
224C2×C4×D61—24no—
225C2×C4×D61—24no—
226C2×C4×D61—82no—
227C2×C4×D61—82no—
228C2×C4×D61—82no—
229C2×C4×D61C2×D412yes—
230C2×C4×D61C2412yes—
231C2×Dic122—22no—
232C2×Dic122—22no—
233C2×Dic122—21no—
234C2×Dic122C2412yes—
235C2×C8×C61#4114yes—
236C2×C8×C61#4114yes—
237C2×C8×C61C2412yes—
238C2×C8×C61C2412yes—
239C4⋊C4×C61—24no—
240C4⋊C4×C61—24no—
241C4⋊C4×C61—24no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61C2412yes—
247C4⋊C4×C61C2412yes—
248C4⋊C4×C61C2412yes—
249C4⋊C4×C61C2412yes—
250C42×C61C2×D412yes—
251C42×C61C2412yes—
252#11758198—24no—
253#11758198—24no—
254#11758198—24no—
255#11758198—24no—
256#11758198—24no—
257#11758198—24no—
258#11758198—24no—
259#11758198—24no—
260#11758198—24no—
261#11758198C2×D414yes—
262#11758198C2×D414yes—
263C4⋊Dic61—24no—
264#11758196—24no—
265#11758196C2×D414yes—
266#11758196C2×D414yes—
267C4×Dic61—24no—
268C4×Dic61C2×D412yes—
269C4×Dic61C2412yes—
270C2×#92418—22no—
271C2×#92418—22no—
272C2×#92418C2412yes—
273C2×#92418C2412yes—
274D488—28no—
275D488—28no—
276#11758190—28no—
277#11758190—28no—
278#11758189—28no—
279C8×D61—28no—
280C23×C61C22×D411yescharacteristic
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—22no—
287C22×D61—42no—
288C22×D61—42no—
289C22×D61—42no—
290C22×D61—42no—
291C22×D61—42no—
292C22×D61—42no—
293C22×D61—42no—
294C22×D61—42no—
295C22×D61—42no—
296C22×D61C22×D412yes—
297Q8×C61—84no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61C22×D412yes—
309C2×C4×C61C22×D412yes—
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61C2×#4112yes—
312C2×C4×C61C2×#4112yes—
313C2×C4×C61C2511yescharacteristic
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—42no—
319C2×Dic61C22×D412yes—
320C2×Dic61C22×D412yes—
321C2×Dic61C22×D412yes—
322D244—22no—
323D244—22no—
324D244—22no—
325D244—22no—
326D244—22no—
327D244—22no—
328D244—42no—
329D244—42no—
330D244—42no—
331D244—84no—
332D244—84no—
333D244—84no—
334D244—84no—
335D244—84no—
336C4×D61—24no—
337C4×D61—22no—
338C4×D61—22no—
339C4×D61—84no—
340C4×D61—84no—
341C4×D61—84no—
342Dic122—22no—
343Dic122—22no—
344Dic122—42no—
345C8×C61C2×#4114yes—
346C8×C61C2×#4114yes—
347#92418—22no—
348#92418—22no—
349C2×#3179—611nomaximal, Sylow
350C22×C61#53212yes—
351C22×C61#57612yes—
352C22×C61#57712yes—
353C22×C61C23×D411yescharacteristic
354C2×D61—22no—
355C2×D61—22no—
356C2×D61—22no—
357C2×D61—44no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—42no—
365C2×D61—42no—
366C2×D61—42no—
367C2×D61—84no—
368C2×D61—84no—
369C2×D61—84no—
370C4×C61—22no—
371C4×C61—22no—
372C4×C61—42no—
373C4×C61—42no—
374C4×C61—42no—
375C4×C61—42no—
376C4×C61#53212yes—
377C4×C61C22×#4111yescharacteristic
378C4×C61C22×#4111yescharacteristic
379Dic61—22no—
380Dic61—22no—
381Dic61—22no—
382Dic61—42no—
383C2×#542—611no—
384C2×#540—611no—
385#3179—6116no—
386C2×#501D6111yescharacteristic, complemented
387C2×#496—611no—
388C2×#488—611no—
389C2×#486—611no—
390C2×#469—611no—
391C2×#468—611no—
392C2×#466—611no—
393C2×#465—611no—
394C2×#442—611no—
395C2×#440—611no—
396C2×C4×SD16—611no—
397C2×C4×D8—611no—
398C2×#405—611no—
399C2×C61#317914yescomplemented
400C2×C61C2×#53211yescharacteristic
401C2×C61C2×#57611yescharacteristic
402C2×C61C2×#57711yescharacteristic
403D61—42no—
404D61—82no—
405D61—82no—
406D61—82no—
407C22×SD16—611no—
408C22×SD16—611no—
409C22×D8—611no—
410C22×D8—611no—
411C22×M16—611no—
412C23×C8—611no—
413#542—618no—
414#542—1224no—
415#540—618no—
416#540—1224no—
417C2×C4⋊Q8C2×D6111yescharacteristic
418C2×#127—611no—
419C2×#126—1221no—
420C2×#125C2×D6111yescharacteristic
421C2×#124—611no—
422C2×#124—1221no—
423C2×#123—1221no—
424C2×#123—1221no—
425C2×#123—1221no—
426C2×C22⋊Q8—611no—
427C2×C22⋊Q8—1221no—
428C2×#121—611no—
429C2×#121—611no—
430C2×#121—611no—
431C2×#121—1221no—
432C2×#121—1221no—
433C2×C4×Q8—611no—
434C2×C4×D4—611no—
435C2×C4×D4—611no—
436C2×C4×D4—611no—
437C2×#117—611no—
438#501C2×D6118yescomplemented
439#496—618no—
440#488—618no—
441#486—618no—
442#469—618no—
443#468—618no—
444#466—618no—
445#465—618no—
446#442—618no—
447#440—618no—
448C4×SD16—618no—
449C4×D8—618no—
450C2×#107C2×D6111yescharacteristic
451C2×#107C2×D6111yescharacteristic
452C2×#106C2×D6111yescharacteristic
453C2×#106C2×D6111yescharacteristic
454C2×#103—611no—
455C2×#103—611no—
456C2×#102—611no—
457C2×#102—611no—
458C2×#102—611no—
459C2×#102—611no—
460C2×#102—611no—
461C2×#102—611no—
462#405—618no—
463C2×#97—611no—
464C2×#97C2×D6111yescharacteristic
465C2×C4×C8—611no—
466C2×C4×C8—611no—
467C61C2×#317911yescharacteristic, complemented, Sylow
468C22×Q8—21no—
469C22×Q8—611no—
470C22×D4—611no—
471C22×D4—611no—
472C22×D4—611no—
473C22×D4—1221no—
474C22×D4—1221no—
475C22×D4—1221no—
476C22×D4—1221no—
477C22×D4—1221no—
478C23×C4—611no—
479C23×C4—1221no—
480C23×C4—1221no—
481C23×C4—1221no—
482C2×SD16—614no—
483C2×SD16—614no—
484C2×SD16—1224no—
485C2×SD16—1224no—
486C2×D8—614no—
487C2×D8—614no—
488C2×D8—1224no—
489C2×D8—1224no—
490C2×M16—614no—
491C2×M16—1224no—
492C22×C8—611no—
493C22×C8—611no—
494C22×C8—614no—
495C22×C8—1224no—
496C22×C8C22×D6111yescharacteristic
497C22×C8C22×D6111yescharacteristic
498C4⋊Q8—22no—
499C4⋊Q8C22×D6114yes—
500#127—614no—
501#127—1222no—
502#126—1228no—
503#125—22no—
504#125C22×D6114yes—
505#124—614no—
506#124—1228no—
507#124—1222no—
508#123—1228no—
509#123—1228no—
510#123—1228no—
511C22⋊Q8—614no—
512C22⋊Q8—1222no—
513C22⋊Q8—1228no—
514#121—614no—
515#121—614no—
516#121—614no—
517#121—1228no—
518#121—1228no—
519#121—1222no—
520#121—1222no—
521#121—1222no—
522C4×Q8—614no—
523C4×Q8—1222no—
524C4×D4—614no—
525C4×D4—614no—
526C4×D4—614no—
527C4×D4—1222no—
528C4×D4—1222no—
529C4×D4—1222no—
530#117—614no—
531#117—614no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—1221no—
538C2×C4⋊C4—1221no—
539C2×C4⋊C4C22×D6111yescharacteristic
540C2×C4⋊C4C22×D6111yescharacteristic
541C2×C4⋊C4C22×D6111yescharacteristic
542C2×C4⋊C4C22×D6111yescharacteristic
543C2×C22⋊C4—611no—
544C2×C22⋊C4—611no—
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×C42—611no—
555C2×C42—1221no—
556C2×C42C22×D6111yescharacteristic
557#107C22×D6114yes—
558#107C22×D6114yes—
559#106C22×D6114yes—
560#106C22×D6114yes—
561#103—614no—
562#103—614no—
563#102—614no—
564#102—614no—
565#102—614no—
566#102—614no—
567#102—614no—
568#102—614no—
569#97—614no—
570#97C22×D6114yes—
571C4×C8—614no—
572C4×C8—614no—
573C24—611no—
574C24—1221no—
575C24—1221no—
576C24—1221no—
577C2×Q8—24no—
578C2×Q8—82no—
579C2×Q8—612no—
580C2×Q8—1221no—
581C2×Q8—1222no—
582C2×Q8—1222no—
583C2×D4—612no—
584C2×D4—612no—
585C2×D4—612no—
586C2×D4—1224no—
587C2×D4—1224no—
588C2×D4—1224no—
589C2×D4—1224no—
590C2×D4—1224no—
591C2×D4—1221no—
592C2×D4—1221no—
593C2×D4—1221no—
594C2×D4—1222no—
595C2×D4—1222no—
596C2×D4—1222no—
597C2×D4—1222no—
598C2×D4—1222no—
599C2×D4—1222no—
600C2×D4—4882no—
601C2×D4—4882no—
602C2×D4—4882no—
603C2×D4—4882no—
604C2×D4—4882no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—612no—
613C22×C4—612no—
614C22×C4—1224no—
615C22×C4—1224no—
616C22×C4—1224no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—1221no—
620C22×C4—4882no—
621C22×C4—4882no—
622C22×C4—4882no—
623C22×C4D4×D6111yescharacteristic
624C22×C4D4×D6111yescharacteristic
625C22×C4C23×D6111yescharacteristic
626SD16—1228no—
627SD16—1228no—
628D8—1228no—
629D8—1228no—
630M16—1228no—
631C2×C8—612no—
632C2×C8—612no—
633C2×C8—1222no—
634C2×C8—1222no—
635C2×C8—1228no—
636C2×C8#1175822614yes—
637C2×C8#1175822614yes—
638C2×C8C23×D6112yes—
639C2×C8C23×D6112yes—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—614no—
648C4⋊C4—614no—
649C4⋊C4—1224no—
650C4⋊C4—1224no—
651C4⋊C4C23×D6112yes—
652C4⋊C4C23×D6112yes—
653C4⋊C4C23×D6112yes—
654C4⋊C4C23×D6112yes—
655C22⋊C4—614no—
656C22⋊C4—614no—
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—612no—
667C42—612no—
668C42—1224no—
669C42D4×D6112yes—
670C42C23×D6112yes—
671C23—612no—
672C23—1222no—
673C23—1222no—
674C23—1222no—
675C23—1222no—
676C23—1222no—
677C23—1222no—
678C23—2442no—
679C23—2442no—
680C23—2442no—
681C23—2442no—
682C23—2442no—
683C23—2442no—
684C23—2442no—
685C23—2442no—
686C23—2442no—
687C23C2×D4×D6111yescharacteristic
688Q8—84no—
689Q8—1222no—
690Q8—1222no—
691Q8—2442no—
692D4—1222no—
693D4—1222no—
694D4—1222no—
695D4—1222no—
696D4—1222no—
697D4—1222no—
698D4—4884no—
699D4—4884no—
700D4—4884no—
701D4—4884no—
702D4—4884no—
703D4—2442no—
704D4—2442no—
705D4—2442no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—612no—
717C2×C4—612no—
718C2×C4—612no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1224no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—4884no—
727C2×C4—4884no—
728C2×C4—4884no—
729C2×C4—2442no—
730C2×C4C2×D4×D6112yes—
731C2×C4C2×D4×D6112yes—
732C2×C4C2×D4×D6111yescharacteristic
733C2×C4C2×#1175822612yes—
734C2×C4C2×#1175822612yes—
735C2×C4C24×D6111yescharacteristic
736C8—1222no—
737C8—1222no—
738C8C2×#1175822614yes—
739C8C2×#1175822614yes—
740C22—1222no—
741C22—1222no—
742C22—1222no—
743C22—4884no—
744C22—4884no—
745C22—4884no—
746C22—2442no—
747C22—2442no—
748C22—2442no—
749C22—2442no—
750C22—2442no—
751C22—2442no—
752C22—2442no—
753C22—2442no—
754C22—2442no—
755C22—2444no—
756C22#1684031312yes—
757C22#1684056612yes—
758C22#1684057112yes—
759C22C22×D4×D6111yescharacteristic
760C4—22no—
761C4—22no—
762C4—42no—
763C4—42no—
764C4—42no—
765C4—42no—
766C4—1222no—
767C4—1222no—
768C4—1222no—
769C4—2442no—
770C4#1684031312yes—
771C4C22×#1175822611yescharacteristic
772C4C22×#1175822611yescharacteristic
773C2—4882no—
774C2—4882no—
775C2—4882no—
776C2—2442no—
777C2#2145650714yesdirect product factor
778C2C2×#1684031311yescharacteristic
779C2C2×#1684056611yescharacteristic
780C2C2×#1684057111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#501C2
socleC23×C61C22×D4
hypercenterC2×#501D61
hypocenterC61C2×#3179
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#16840386C2semidirect
2. C2×#16840368C2semidirect
3. #21456507C2direct (N × H)
4. C2×#16840151C2semidirect
5. C2×#16840119C2semidirect
6. C2×#16840110C2semidirect
7. C2×#16840016C2semidirect
8. C2×#16840009C2semidirect
9. C2×#16839999C2semidirect
10. C2×#16839992C2semidirect
11. C2×#16839873C2semidirect
12. C2×#16839861C2semidirect
13. C2×#16839849C2semidirect
14. C2×#16839844C2semidirect
15. C2×#16839719C2semidirect
16. C2×C61×#501C2semidirect
24. #16840386C22semidirect
26. #16840368C22semidirect
46. #16840151C22semidirect
47. #16840119C22semidirect
48. #16840110C22semidirect
49. #16840016C22semidirect
50. #16840009C22semidirect
51. #16839999C22semidirect
52. #16839992C22semidirect
53. #16839873C22semidirect
54. #16839861C22semidirect
55. #16839849C22semidirect
56. #16839844C22semidirect
65. #16839719C22semidirect
71. C61×#501C22semidirect
386. C2×#501D61semidirect
399. C2×C61#3179semidirect
438. #501C2×D61semidirect
467. C61C2×#3179semidirect
777. C2#21456507direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403862
C2×#168403682
#214565072
C2×#168401512
C2×#168401192
C2×#168401102
C2×#168400162
C2×#168400092
C2×#168399992
C2×#168399922
C2×#168398732
C2×#168398612
C2×#168398492
C2×#168398442
C2×#168397192
C2×C61×#5012
C2×#317961