Finite Group Databasebeta

← C2×#21457111 #30552244

Subgroups — C2×#21457111 #30552244

Order 15616.

1742 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840390C211yesmaximal, characteristic, complemented
2#21457111C2116yesmaximal, direct product factor
3C2×#16840168C211yesmaximal, characteristic, complemented
4C2×#16840158C211yesmaximal, characteristic, complemented
5C2×#16840121C211yesmaximal, characteristic, complemented
6C2×#16840116C211yesmaximal, characteristic, complemented
7C2×#16840078C211yesmaximal, characteristic
8C2×#16840100C211yesmaximal, characteristic, complemented
9C2×#16840083C211yesmaximal, characteristic
10C2×#16840090C211yesmaximal, characteristic, complemented
11C2×#16840069C211yesmaximal, characteristic, complemented
12C2×#16840047C211yesmaximal, characteristic, complemented
13C2×#16840062C211yesmaximal, characteristic, complemented
14C2×#16840052C211yesmaximal, characteristic, complemented
15C2×#16839823C211yesmaximal, characteristic, complemented
16C2×C61×#542C211yesmaximal, characteristic
17#16840390—24no—
18#16840390C2218yescomplemented
19C2×#14519777C2211yescharacteristic
20C2×#14519777C2211yescharacteristic
21C2×#14519776—21no—
22C2×#14519769C2211yescharacteristic
23C2×#14519769C2211yescharacteristic
24C2×#14519768—21no—
25C2×#14519754—21no—
26C2×#14519754—21no—
27C2×#14519736C2211yescharacteristic
28C22×C4⋊Dic61C2211yescharacteristic
29#16840168C2218yescomplemented
30#16840158C2218yescomplemented
31#16840121C2218yescomplemented
32#16840116C2218yescomplemented
33#16840100C2218yescomplemented
34#16840090C2218yescomplemented
35#16840083C2218yes—
36#16840078C2218yes—
37#16840069C2218yescomplemented
38#16840062C2218yescomplemented
39#16840052C2218yescomplemented
40#16840047C2218yescomplemented
41#16839823C2218yescomplemented
42C2×#14519710C2211yescharacteristic
43C2×#14519710C2211yescharacteristic
44C2×#14519708C2211yescharacteristic
45C2×#14519708C2211yescharacteristic
46C2×#14519708C2211yescharacteristic
47C2×#14519708C2211yescharacteristic
48C2×#14519708C2211yescharacteristic
49C2×#14519708C2211yescharacteristic
50C2×C4⋊#92418C2211yescharacteristic
51C2×C4⋊#92418C2211yescharacteristic
52C2×#14519701C2211yescharacteristic
53C2×#14519701C2211yescharacteristic
54C2×#14519701C2211yescharacteristic
55C2×#14519701C2211yescharacteristic
56C2×#14519698C2211yescharacteristic
57C2×#14519698C2211yescharacteristic
58C2×#14519698C2211yescharacteristic
59C2×#14519698C2211yescharacteristic
60C2×C22⋊#92418C2211yescharacteristic
61C2×C22⋊#92418C2211yescharacteristic
62C2×#14519688C2211yescharacteristic
63C2×C4×#92418C2211yescharacteristic
64C61×#542—24no—
65C61×#542C2218yes—
66C2×C4⋊Q8×C61C2211yescharacteristic
67C2×#126×C61—21no—
68C2×#124×C61—21no—
69C2×#124×C61C2211yescharacteristic
70C2×#123×C61—21no—
71C2×C22⋊Q8×C61—21no—
72C2×C22⋊Q8×C61C2211yescharacteristic
73C2×#121×C61C2211yescharacteristic
74C2×C4×Q8×C61C2211yescharacteristic
75C2×C4×D4×C61C2211yescharacteristic
76C2×#117×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122—21no—
79C23×Dic61—21no—
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84#14519777—22no—
85#14519777—22no—
86#14519777C2314yes—
87#14519777C2314yes—
88#14519776—28no—
89#14519769—22no—
90#14519769—22no—
91#14519769C2314yes—
92#14519769C2314yes—
93#14519768—28no—
94#14519754—28no—
95#14519754—28no—
96#14519736—22no—
97#14519736C2314yes—
98C2×C4⋊Dic61—21no—
99C2×C4⋊Dic61—22no—
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61—21no—
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2314yes—
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×#11758196—21no—
110C2×#11758196—21no—
111C2×C22⋊Dic61—21no—
112C2×C4×Dic61—21no—
113#14519710C2314yes—
114#14519710C2314yes—
115#14519708C2314yes—
116#14519708C2314yes—
117#14519708C2314yes—
118#14519708C2314yes—
119#14519708C2314yes—
120#14519708C2314yes—
121C4⋊#92418C2314yes—
122C4⋊#92418C2314yes—
123#14519701C2314yes—
124#14519701C2314yes—
125#14519701C2314yes—
126#14519701C2314yes—
127#14519698C2314yes—
128#14519698C2314yes—
129#14519698C2314yes—
130#14519698C2314yes—
131C22⋊#92418C2314yes—
132C22⋊#92418C2314yes—
133#14519688C2314yes—
134C4×#92418C2314yes—
135C22×Q8×C61—21no—
136C22×Q8×C61C2311yescharacteristic
137C22×D4×C61—21no—
138C22×D4×C61C2311yescharacteristic
139C23×C4×C61—21no—
140C23×C4×C61C2311yescharacteristic
141C4⋊Q8×C61—22no—
142C4⋊Q8×C61C2314yes—
143#126×C61—28no—
144#124×C61—28no—
145#124×C61—22no—
146#124×C61C2314yes—
147#123×C61—28no—
148C22⋊Q8×C61—22no—
149C22⋊Q8×C61—28no—
150C22⋊Q8×C61C2314yes—
151#121×C61—22no—
152#121×C61C2314yes—
153C4×Q8×C61—22no—
154C4×Q8×C61C2314yes—
155C4×D4×C61—22no—
156C4×D4×C61C2314yes—
157#117×C61D414yes—
158#117×C61C2314yes—
159C2×C4⋊C4×C61—21no—
160C2×C4⋊C4×C61—21no—
161C2×C4⋊C4×C61—21no—
162C2×C4⋊C4×C61D411yescharacteristic
163C2×C4⋊C4×C61D411yescharacteristic
164C2×C4⋊C4×C61C2311yescharacteristic
165C2×C4⋊C4×C61C2311yescharacteristic
166C2×C22⋊C4×C61—21no—
167C2×C22⋊C4×C61—21no—
168C2×C22⋊C4×C61—21no—
169C2×C22⋊C4×C61—21no—
170C2×C22⋊C4×C61—21no—
171C2×C22⋊C4×C61D411yescharacteristic
172C2×C22⋊C4×C61D411yescharacteristic
173C2×C42×C61—21no—
174C2×C42×C61C2311yescharacteristic
175C2×C42×C61C2311yescharacteristic
176C24×C61—21no—
177C24×C61C2×D411yescharacteristic
178C2×Q8×C61—21no—
179C2×Q8×C61—24no—
180C2×Q8×C61—22no—
181C2×Q8×C61—22no—
182C2×Q8×C61—82no—
183C2×Q8×C61C2412yes—
184C2×D4×C61—24no—
185C2×D4×C61—21no—
186C2×D4×C61—22no—
187C2×D4×C61—22no—
188C2×D4×C61—82no—
189C2×D4×C61C2412yes—
190C22×C4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—24no—
196C22×C4×C61—82no—
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D412yes—
203C22×C4×C61C2412yes—
204C22×C4×C61C2411yescharacteristic
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—24no—
210C22×Dic61—82no—
211C2×Dic122—24no—
212C2×Dic122—24no—
213C2×Dic122—82no—
214C2×Dic122—82no—
215C4⋊C4×C61—24no—
216C4⋊C4×C61—24no—
217C4⋊C4×C61—24no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61C2×D414yes—
221C4⋊C4×C61C2×D414yes—
222C4⋊C4×C61C2412yes—
223C4⋊C4×C61C2412yes—
224C22⋊C4×C61—24no—
225C22⋊C4×C61—24no—
226C22⋊C4×C61—24no—
227C22⋊C4×C61—24no—
228C22⋊C4×C61—24no—
229C22⋊C4×C61C2×D414yes—
230C22⋊C4×C61C2×D414yes—
231C42×C61—24no—
232C42×C61C2×D412yes—
233C42×C61C2×D412yes—
234C42×C61C2412yes—
235C42×C61C2412yes—
236C22⋊Dic61—24no—
237C4⋊Dic61—24no—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240C4⋊Dic61—24no—
241C4⋊Dic61—24no—
242C4⋊Dic61—21no—
243C4⋊Dic61—21no—
244C4⋊Dic61C2412yes—
245C4⋊Dic61C2412yes—
246C4⋊Dic61C2412yes—
247C4⋊Dic61C2412yes—
248#11758196—24no—
249#11758196—24no—
250#11758196—24no—
251#11758196—24no—
252C4×Dic61—24no—
253C2×#92418—22no—
254C2×#92418—22no—
255C2×#92418—22no—
256C2×#92418—22no—
257C2×#92418C2412yes—
258C2×#92418C2412yes—
259C2×#92418C2412yes—
260C2×#92418C2412yes—
261C23×C61—22no—
262C23×C61—22no—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61—42no—
266C23×C61—42no—
267C23×C61—42no—
268C23×C61C22×D412yes—
269C23×C61C22×D411yescharacteristic
270Q8×C61—22no—
271Q8×C61—22no—
272Q8×C61—42no—
273Q8×C61—84no—
274D4×C61—22no—
275D4×C61—22no—
276D4×C61—42no—
277D4×C61—84no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—24no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—42no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61—84no—
293C2×C4×C61C22×D412yes—
294C2×C4×C61C22×D412yes—
295C2×C4×C61C22×D412yes—
296C2×C4×C61C22×D412yes—
297C2×C4×C61C22×D412yes—
298C2×C4×C61C22×D411yescharacteristic
299C2×C4×C612−1+412yes—
300C2×C4×C612−1+412yes—
301C2×C4×C61C2511yescharacteristic
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—42no—
307C2×Dic61—42no—
308C2×Dic61—42no—
309C2×Dic61—42no—
310C2×Dic61—84no—
311Dic122—84no—
312Dic122—84no—
313#92418—22no—
314#92418—22no—
315#92418—22no—
316#92418—22no—
317C2×#3244—611nomaximal, Sylow
318C22×C61—22no—
319C22×C61—22no—
320C22×C61—22no—
321C22×C61—44no—
322C22×C61—42no—
323C22×C61—42no—
324C22×C61—42no—
325C22×C61—84no—
326C22×C61#53612yes—
327C22×C61#57712yes—
328C22×C61#57712yes—
329C22×C61C23×D411yescharacteristic
330C4×C61—22no—
331C4×C61—22no—
332C4×C61—22no—
333C4×C61—22no—
334C4×C61—22no—
335C4×C61—42no—
336C4×C61—42no—
337C4×C61—42no—
338C4×C61#53612yes—
339C4×C61C2×2−1+411yescharacteristic
340C4×C61C2×2−1+411yescharacteristic
341Dic61—42no—
342Dic61—42no—
343Dic61—42no—
344Dic61—42no—
345C2×#544—611no—
346C2×#542D6111yescharacteristic
347#3244—6116no—
348C2×#501—611no—
349C2×#498—611no—
350C2×#489—611no—
351C2×#488—611no—
352C2×#481—611no—
353C2×#485—611no—
354C2×#482—611no—
355C2×#483—611no—
356C2×#479—611no—
357C2×#475—611no—
358C2×#478—611no—
359C2×#476—611no—
360C2×#433—611no—
361C2×C61—42no—
362C2×C61—82no—
363C2×C61#324414yescomplemented
364C2×C61C2×#53611yescharacteristic
365C2×C61C2×#57711yescharacteristic
366C2×C61C2×#57711yescharacteristic
367#544—618no—
368#544—1224no—
369#542—24no—
370#542C2×D6118yes—
371C2×C4⋊Q8—611no—
372C2×C4⋊Q8—611no—
373C2×C4⋊Q8—1221no—
374C2×C4⋊Q8C2×D6111yescharacteristic
375C2×#126—21no—
376C2×#125—611no—
377C2×#125—611no—
378C2×#125—1221no—
379C2×#124—21no—
380C2×#124C2×D6111yescharacteristic
381C2×#123—21no—
382C2×C22⋊Q8—21no—
383C2×C22⋊Q8—1221no—
384C2×C22⋊Q8—1221no—
385C2×C22⋊Q8C2×D6111yescharacteristic
386C2×#121C2×D6111yescharacteristic
387C2×C4×Q8C2×D6111yescharacteristic
388C2×C4×D4C2×D6111yescharacteristic
389C2×#117—611no—
390C2×#117C2×D6111yescharacteristic
391C22×C4⋊C4—611no—
392#501—618no—
393#498—618no—
394#489—618no—
395#488—618no—
396#485—618no—
397#483—618no—
398#482—618no—
399#481—618no—
400#479—618no—
401#478—618no—
402#476—618no—
403#475—618no—
404#433—618no—
405C2×#107—611no—
406C2×#107—611no—
407C2×#106—611no—
408C2×#106—611no—
409C2×#106—611no—
410C2×#106—611no—
411C2×#106—611no—
412C2×#106—611no—
413C2×C4⋊C8—611no—
414C2×C4⋊C8—611no—
415C2×#103—611no—
416C2×#103—611no—
417C2×#103—611no—
418C2×#103—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×#102—611no—
422C2×#102—611no—
423C2×C22⋊C8—611no—
424C2×C22⋊C8—611no—
425C2×#97—611no—
426C2×C4×C8—611no—
427C61C2×#324411yescharacteristic, complemented, Sylow
428C22×Q8—21no—
429C22×Q8—1221no—
430C22×Q8—1221no—
431C22×Q8C22×D6111yescharacteristic
432C22×D4—21no—
433C22×D4C22×D6111yescharacteristic
434C23×C4—21no—
435C23×C4—1221no—
436C23×C4C22×D6111yescharacteristic
437C22×C8—611no—
438C22×C8—611no—
439C22×C8—611no—
440C22×C8—611no—
441C4⋊Q8—22no—
442C4⋊Q8—614no—
443C4⋊Q8—614no—
444C4⋊Q8—1228no—
445C4⋊Q8—1222no—
446C4⋊Q8—1222no—
447C4⋊Q8C22×D6114yes—
448#126—28no—
449#125—614no—
450#125—614no—
451#125—1228no—
452#125—1222no—
453#125—1222no—
454#124—28no—
455#124—22no—
456#124C22×D6114yes—
457#123—28no—
458C22⋊Q8—22no—
459C22⋊Q8—28no—
460C22⋊Q8—1228no—
461C22⋊Q8—1228no—
462C22⋊Q8C22×D6114yes—
463#121—22no—
464#121C22×D6114yes—
465C4×Q8—22no—
466C4×Q8C22×D6114yes—
467C4×D4—22no—
468C4×D4C22×D6114yes—
469#117—614no—
470#117—1222no—
471#117C22⋊D6114yes—
472#117C22×D6114yes—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—614no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—1222no—
483C2×C4⋊C4—1221no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4C22⋊D6111yescharacteristic
490C2×C4⋊C4C22⋊D6111yescharacteristic
491C2×C4⋊C4C22×D6111yescharacteristic
492C2×C4⋊C4C22×D6111yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4C22⋊D6111yescharacteristic
500C2×C22⋊C4C22⋊D6111yescharacteristic
501C2×C42—21no—
502C2×C42—1221no—
503C2×C42C22×D6111yescharacteristic
504C2×C42C22×D6111yescharacteristic
505#107—614no—
506#107—614no—
507#106—614no—
508#106—614no—
509#106—614no—
510#106—614no—
511#106—614no—
512#106—614no—
513C4⋊C8—614no—
514C4⋊C8—614no—
515#103—614no—
516#103—614no—
517#103—614no—
518#103—614no—
519#102—614no—
520#102—614no—
521#102—614no—
522#102—614no—
523C22⋊C8—614no—
524C22⋊C8—614no—
525#97—614no—
526C4×C8—614no—
527C24—21no—
528C24C2×C22⋊D6111yescharacteristic
529C2×Q8—21no—
530C2×Q8—24no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—82no—
534C2×Q8—1224no—
535C2×Q8—1224no—
536C2×Q8—4882no—
537C2×Q8—4882no—
538C2×Q8C23×D6112yes—
539C2×D4—24no—
540C2×D4—21no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—82no—
544C2×D4C23×D6112yes—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—82no—
552C22×C4—1224no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—4882no—
558C22×C4C2×C22⋊D6112yes—
559C22×C4C2×C22⋊D6111yescharacteristic
560C22×C4C2×C22⋊D6111yescharacteristic
561C22×C4C2×C22⋊D6111yescharacteristic
562C22×C4C2×C22⋊D6111yescharacteristic
563C22×C4C2×C22⋊D6111yescharacteristic
564C22×C4C23×D6112yes—
565C22×C4C23×D6111yescharacteristic
566C2×C8—612no—
567C2×C8—612no—
568C2×C8—612no—
569C2×C8—612no—
570C2×C8—1222no—
571C2×C8—1222no—
572C2×C8—1222no—
573C2×C8—1222no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—612no—
580C4⋊C4—612no—
581C4⋊C4—612no—
582C4⋊C4—612no—
583C4⋊C4—1224no—
584C4⋊C4—1221no—
585C4⋊C4—1221no—
586C4⋊C4—1221no—
587C4⋊C4—1221no—
588C4⋊C4—1224no—
589C4⋊C4—1224no—
590C4⋊C4—1224no—
591C4⋊C4—1224no—
592C4⋊C4—1224no—
593C4⋊C4—1224no—
594C4⋊C4C2×C22⋊D6114yes—
595C4⋊C4C2×C22⋊D6114yes—
596C4⋊C4C23×D6112yes—
597C4⋊C4C23×D6112yes—
598C22⋊C4—24no—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—1224no—
604C22⋊C4C2×C22⋊D6114yes—
605C22⋊C4C2×C22⋊D6114yes—
606C42—24no—
607C42—1224no—
608C42C2×C22⋊D6112yes—
609C42C2×C22⋊D6112yes—
610C42C23×D6112yes—
611C42C23×D6112yes—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23C22×C22⋊D6112yes—
620C23C22×C22⋊D6111yescharacteristic
621Q8—22no—
622Q8—22no—
623Q8—42no—
624Q8—84no—
625Q8—4884no—
626Q8—4884no—
627D4—22no—
628D4—22no—
629D4—42no—
630D4—84no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—84no—
646C2×C4—1222no—
647C2×C4—1222no—
648C2×C4—1222no—
649C2×C4—1222no—
650C2×C4—4884no—
651C2×C4—2442no—
652C2×C4—2442no—
653C2×C4—2442no—
654C2×C4—2442no—
655C2×C4C22×C22⋊D6112yes—
656C2×C4C22×C22⋊D6112yes—
657C2×C4C22×C22⋊D6112yes—
658C2×C4C22×C22⋊D6112yes—
659C2×C4C22×C22⋊D6112yes—
660C2×C4C22×C22⋊D6111yescharacteristic
661C2×C4#1451982412yes—
662C2×C4#1451982412yes—
663C2×C4C24×D6111yescharacteristic
664C8—1222no—
665C8—1222no—
666C8—1222no—
667C8—1222no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—44no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—84no—
676C22#1684033312yes—
677C22#1684057012yes—
678C22#1684057312yes—
679C22C23×C22⋊D6111yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—2442no—
689C4—2442no—
690C4—2442no—
691C4—2442no—
692C4#1684033312yes—
693C4C2×#1451982411yescharacteristic
694C4C2×#1451982411yescharacteristic
695C2—42no—
696C2—82no—
697C2#2145711114yesdirect product factor
698C2C2×#1684033311yescharacteristic
699C2C2×#1684057011yescharacteristic
700C2C2×#1684057311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#542C2
socleC23×C61C22×D4
prime radicalC2×#121×C61C22
hypercenterC2×#542D61
hypocenterC61C2×#3244
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#16840390C2semidirect
2. #21457111C2direct (N × H)
3. C2×#16840168C2semidirect
4. C2×#16840158C2semidirect
5. C2×#16840121C2semidirect
6. C2×#16840116C2semidirect
8. C2×#16840100C2semidirect
10. C2×#16840090C2semidirect
11. C2×#16840069C2semidirect
12. C2×#16840047C2semidirect
13. C2×#16840062C2semidirect
14. C2×#16840052C2semidirect
15. C2×#16839823C2semidirect
18. #16840390C22semidirect
29. #16840168C22semidirect
30. #16840158C22semidirect
31. #16840121C22semidirect
32. #16840116C22semidirect
33. #16840100C22semidirect
34. #16840090C22semidirect
37. #16840069C22semidirect
38. #16840062C22semidirect
39. #16840052C22semidirect
40. #16840047C22semidirect
41. #16839823C22semidirect
363. C2×C61#3244semidirect
427. C61C2×#3244semidirect
697. C2#21457111direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403902
#214571112
C2×#168401682
C2×#168401582
C2×#168401212
C2×#168401162
C2×#168400782
C2×#168401002
C2×#168400832
C2×#168400902
C2×#168400692
C2×#168400472
C2×#168400622
C2×#168400522
C2×#168398232
C2×C61×#5422
C2×#324461