Finite Group Databasebeta

← #29736732

Subgroups — #29736732

Order 15616.

1052 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840124C211yesmaximal, characteristic, complemented
2C2×#16840119C211yesmaximal, characteristic, complemented
3#21451576C211yesmaximal, characteristic
4#21446967C211yesmaximal, characteristic, complemented
5#21446962C211yesmaximal, characteristic, complemented
6#21446957C211yesmaximal, characteristic, complemented
7#21446952C211yesmaximal, characteristic, complemented
8#21446789C211yesmaximal, characteristic, complemented
9#21446781C211yesmaximal, characteristic, complemented
10#21446141C211yesmaximal, characteristic
11#21446136C211yesmaximal, characteristic
12#21446131C211yesmaximal, characteristic, complemented
13#21446126C211yesmaximal, characteristic, complemented
14#21445585C211yesmaximal, characteristic, complemented
15C2×C61×#544C211yesmaximal, characteristic, complemented
16C2×#14519765C2211yescharacteristic
17C2×#14519756C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19#16840124—24no—
20#16840119—24no—
21C2×#14519700C2211yescharacteristic
22C2×#14519700C2211yescharacteristic
23C2×#14519700C2211yescharacteristic
24C2×#14519700C2211yescharacteristic
25C2×#14519697C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×C22⋊#92418C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×#14519688C2211yescharacteristic
32C2×C4×#92418C2211yescharacteristic
33#16839684—21no—
34#16839684—21no—
35#16839678—21no—
36#16839678—21no—
37#16839668C2211yescharacteristic
38#16839664C2211yescharacteristic
39#16839632C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C61×#544—24no—
51C61×#544—24no—
52C2×C4⋊Q8×C61—21no—
53C2×C4⋊Q8×C61C2211yescharacteristic
54C2×C4⋊Q8×C61C2211yescharacteristic
55C2×#125×C61—21no—
56C2×#125×C61C2211yescharacteristic
57C2×#125×C61C2211yescharacteristic
58C2×C22⋊Q8×C61—21no—
59C2×C22⋊Q8×C61—21no—
60C2×#117×C61C2211yescharacteristic
61C2×#117×C61C2211yescharacteristic
62C22×C4⋊C4×C61C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C22×D244C2311yescharacteristic
65C22×C22⋊D61—21no—
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70#14519765—22no—
71#14519765—22no—
72#14519756—22no—
73#14519756—22no—
74#14519751—22no—
75#14519751—22no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×#11758196—21no—
81C2×C22⋊Dic61—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87#14519700—22no—
88#14519700—22no—
89#14519700—22no—
90#14519700—22no—
91#14519697—22no—
92#14519697—22no—
93#14519697—22no—
94#14519697—22no—
95C22⋊#92418—22no—
96C22⋊#92418—22no—
97#14519688—22no—
98C4×#92418—22no—
99#14519684—21no—
100#14519684—21no—
101C22×Q8×C61—21no—
102C22×Q8×C61—21no—
103C23×C4×C61—21no—
104C23×C4×C61C2311yescharacteristic
105C4⋊Q8×C61—28no—
106C4⋊Q8×C61—22no—
107C4⋊Q8×C61—22no—
108C4⋊Q8×C61—22no—
109C4⋊Q8×C61D414yescomplemented
110#125×C61—28no—
111#125×C61—22no—
112#125×C61—22no—
113#125×C61—22no—
114#125×C61D414yescomplemented
115C22⋊Q8×C61—28no—
116C22⋊Q8×C61—28no—
117#117×C61—22no—
118#117×C61—22no—
119#117×C61—22no—
120#117×C61—22no—
121C2×C4⋊C4×C61—21no—
122C2×C4⋊C4×C61—21no—
123C2×C4⋊C4×C61—21no—
124C2×C4⋊C4×C61—21no—
125C2×C4⋊C4×C61—21no—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61—22no—
129C2×C4⋊C4×C61—22no—
130C2×C4⋊C4×C61D411yescharacteristic
131C2×C4⋊C4×C61D411yescharacteristic
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61D411yescharacteristic
138C2×C22⋊C4×C61D411yescharacteristic
139C2×C42×C61—21no—
140C2×C42×C61C2311yescharacteristic
141C2×C42×C61C2311yescharacteristic
142C24×C61C2×D411yescharacteristic
143C23×D61—21no—
144C2×Q8×C61—24no—
145C2×Q8×C61—24no—
146C2×Q8×C61—81no—
147C2×Q8×C61—81no—
148C2×Q8×C61—81no—
149C2×Q8×C61—81no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—24no—
159C22×C4×C61—81no—
160C22×C4×C61—81no—
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61#4112yes—
167C22×C4×C61#4112yes—
168C22×C4×C61C2411yescharacteristic
169C2×C22⋊D61—42no—
170C2×C22⋊D61—81no—
171C2×C22⋊D61—81no—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244—21no—
181C2×Dic122—21no—
182C2×Dic122—21no—
183C2×Dic122—21no—
184C2×Dic122—21no—
185C2×Dic122—21no—
186C2×Dic122—21no—
187C4⋊C4×C61—24no—
188C4⋊C4×C61—24no—
189C4⋊C4×C61—24no—
190C4⋊C4×C61—24no—
191C4⋊C4×C61—24no—
192C4⋊C4×C61—24no—
193C4⋊C4×C61—24no—
194C4⋊C4×C61—22no—
195C4⋊C4×C61—22no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61C2×D412yes—
201C4⋊C4×C61C2×D412yes—
202C4⋊C4×C61C2×D412yes—
203C4⋊C4×C61C2×D412yes—
204C22⋊C4×C61—24no—
205C22⋊C4×C61—22no—
206C22⋊C4×C61—22no—
207C42×C61—24no—
208C42×C61—21no—
209C42×C61—21no—
210C42×C61C2×D412yes—
211C42×C61C2×D412yes—
212C22⋊Dic61—42no—
213#11758198—42no—
214#11758198—42no—
215#11758198—42no—
216#11758198—81no—
217#11758198—81no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—81no—
223C4⋊Dic61—81no—
224#11758196—42no—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61#12412yes—
244C23×C61C22×D411yescharacteristic
245C22×D61—41no—
246C22×D61—41no—
247C22×D61—41no—
248C22×D61—41no—
249C22×D61—41no—
250C22×D61—41no—
251C22×D61—41no—
252Q8×C61—84no—
253Q8×C61—84no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—22no—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—21no—
265C2×C4×C61—22no—
266C2×C4×C61—21no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—84no—
283C2×C4×C61#12012yes—
284C2×C4×C61#12012yes—
285C2×C4×C61#12412yes—
286C2×C4×C61C22×D411yescharacteristic
287C2×C4×C61C22×D411yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C612−1+411yescharacteristic
291C2×C4×C612−1+411yescharacteristic
292C22⋊D61—84no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302D244—41no—
303D244—41no—
304D244—41no—
305D244—41no—
306Dic122—41no—
307Dic122—41no—
308Dic122—41no—
309Dic122—41no—
310#92418—41no—
311#92418—41no—
312#92418—41no—
313#92418—41no—
314#25916—611nomaximal, Sylow
315C22×C61—22no—
316C22×C61—22no—
317C22×C61—22no—
318C22×C61—41no—
319C22×C61—41no—
320C22×C61—41no—
321C22×C61—41no—
322C22×C61C2×#12011yescharacteristic
323C22×C61C2×#12411yescharacteristic
324C22×C61#53611yescharacteristic
325C22×C61#57611yescharacteristic
326C22×C61#57711yescharacteristic
327C22×C61#57711yescharacteristic
328C22×C61#57811yescharacteristic
329C2×D61—81no—
330C2×D61—81no—
331C2×D61—81no—
332C2×D61—81no—
333C2×D61—81no—
334C2×D61—81no—
335C2×D61—81no—
336C4×C61—22no—
337C4×C61—22no—
338C4×C61—22no—
339C4×C61—41no—
340C4×C61—42no—
341C4×C61—42no—
342C4×C61—42no—
343C4×C61—41no—
344C4×C61—42no—
345C4×C61#54811yescharacteristic
346C4×C61#54811yescharacteristic
347C4×C61#54811yescharacteristic
348C4×C61#54811yescharacteristic
349Dic61—81no—
350Dic61—81no—
351Dic61—81no—
352C2×#544D6111yescharacteristic, complemented
353C2×#489—611no—
354C2×#488—611no—
355#2620—611no—
356#2026—611no—
357#2025—611no—
358#2024—611no—
359#2023—611no—
360#1992—611no—
361#1990—611no—
362#1875—611no—
363#1874—611no—
364#1873—611no—
365#1872—611no—
366#1750—611no—
367C2×C61—42no—
368C2×C61#243611yescharacteristic
369C2×C61#301211yescharacteristic
370C2×C61#301311yescharacteristic
371C2×C61#313611yescharacteristic
372C2×C61#313711yescharacteristic
373C2×C61#324311yescharacteristic
374C2×C61#324411yescharacteristic
375D61—161no—
376#544—24no—
377#544—24no—
378C2×C4⋊Q8—21no—
379C2×C4⋊Q8C2×D6111yescharacteristic
380C2×C4⋊Q8C2×D6111yescharacteristic
381C2×#125—21no—
382C2×#125C2×D6111yescharacteristic
383C2×#125C2×D6111yescharacteristic
384C2×#124—611no—
385C2×C22⋊Q8—21no—
386C2×C22⋊Q8—21no—
387C2×C22⋊Q8—611no—
388C2×#121—611no—
389C2×#117C2×D6111yescharacteristic
390C2×#117C2×D6111yescharacteristic
391C22×C4⋊C4C2×D6111yescharacteristic
392#489—1224no—
393#488—1224no—
394C2×#103—611no—
395C2×#103—611no—
396C2×#103—611no—
397C2×#103—611no—
398C2×#102—611no—
399C2×#102—611no—
400C2×#102—611no—
401C2×#102—611no—
402C2×C22⋊C8—611no—
403C2×C22⋊C8—611no—
404C2×#97—611no—
405C2×C4×C8—611no—
406#396—1221no—
407#396—1221no—
408#394—1221no—
409#394—1221no—
410#391—611no—
411#390—611no—
412#384—611no—
413#340—611no—
414#340—611no—
415#340—611no—
416#340—611no—
417#340—611no—
418#340—611no—
419#340—611no—
420#340—611no—
421#336—611no—
422#336—611no—
423C61#2591611yescharacteristic, complemented, Sylow
424C22×Q8—21no—
425C22×Q8—21no—
426C22×Q8—611no—
427C22×D4—611no—
428C22×D4—1221no—
429C23×C4—21no—
430C23×C4C22×D6111yescharacteristic
431C22×C8—611no—
432C22×C8—611no—
433C22×C8—611no—
434C22×C8—611no—
435C4⋊Q8—28no—
436C4⋊Q8—22no—
437C4⋊Q8—22no—
438C4⋊Q8—22no—
439C4⋊Q8C22⋊D6114yescomplemented
440#125—28no—
441#125—22no—
442#125—22no—
443#125—22no—
444#125C22⋊D6114yescomplemented
445#124—1222no—
446#124—1222no—
447C22⋊Q8—28no—
448C22⋊Q8—28no—
449C22⋊Q8—1222no—
450C22⋊Q8—1222no—
451#121—1222no—
452#121—1222no—
453#117—22no—
454#117—22no—
455#117—22no—
456#117—22no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—611no—
467C2×C4⋊C4—611no—
468C2×C4⋊C4—1221no—
469C2×C4⋊C4—1221no—
470C2×C4⋊C4—1221no—
471C2×C4⋊C4C22⋊D6111yescharacteristic
472C2×C4⋊C4C22⋊D6111yescharacteristic
473C2×C4⋊C4C22×D6111yescharacteristic
474C2×C4⋊C4C22×D6111yescharacteristic
475C2×C4⋊C4C22×D6111yescharacteristic
476C2×C4⋊C4C22×D6111yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—1221no—
479C2×C22⋊C4—1221no—
480C2×C22⋊C4—1221no—
481C2×C22⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
484C2×C22⋊C4C22⋊D6111yescharacteristic
485C2×C22⋊C4C22⋊D6111yescharacteristic
486C2×C42—21no—
487C2×C42C22×D6111yescharacteristic
488C2×C42C22×D6111yescharacteristic
489#103—1222no—
490#103—1222no—
491#103—1222no—
492#103—1222no—
493#102—1222no—
494#102—1222no—
495#102—1222no—
496#102—1222no—
497C22⋊C8—1222no—
498C22⋊C8—1222no—
499#97—1222no—
500C4×C8—1222no—
501#95—1221no—
502#95—1221no—
503C24—1221no—
504C24C2×C22⋊D6111yescharacteristic
505C2×Q8—24no—
506C2×Q8—24no—
507C2×Q8—81no—
508C2×Q8—81no—
509C2×Q8—81no—
510C2×Q8—81no—
511C2×Q8—1221no—
512C2×Q8—1221no—
513C2×Q8—1221no—
514C2×Q8—1221no—
515C2×Q8—1221no—
516C2×Q8—1221no—
517C2×D4—1221no—
518C2×D4—1221no—
519C2×D4—1221no—
520C2×D4—1221no—
521C2×D4—1221no—
522C2×D4—1221no—
523C2×D4—4881no—
524C2×D4—4881no—
525C2×D4—2442no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—24no—
535C22×C4—81no—
536C22×C4—81no—
537C22×C4—1221no—
538C22×C4—1221no—
539C22×C4—1221no—
540C22×C4#1175822612yes—
541C22×C4#1175822612yes—
542C22×C4C2×C22⋊D6111yescharacteristic
543C22×C4C2×C22⋊D6111yescharacteristic
544C22×C4C2×C22⋊D6111yescharacteristic
545C22×C4C2×C22⋊D6111yescharacteristic
546C22×C4C2×C22⋊D6111yescharacteristic
547C22×C4C23×D6111yescharacteristic
548C2×C8—1221no—
549C2×C8—1221no—
550C2×C8—1221no—
551C2×C8—1221no—
552C2×C8—1221no—
553C2×C8—1221no—
554C2×C8—1221no—
555C2×C8—1221no—
556C2×C8—1221no—
557C2×C8—1221no—
558C2×C8—1221no—
559C2×C8—1221no—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—1221no—
574C4⋊C4—1221no—
575C4⋊C4—1221no—
576C4⋊C4—1221no—
577C4⋊C4—4881no—
578C4⋊C4—4881no—
579C4⋊C4—2442no—
580C4⋊C4C2×C22⋊D6112yes—
581C4⋊C4C2×C22⋊D6112yes—
582C4⋊C4C2×C22⋊D6112yes—
583C4⋊C4C2×C22⋊D6112yes—
584C22⋊C4—24no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—4881no—
588C22⋊C4—4881no—
589C22⋊C4—2442no—
590C22⋊C4—2442no—
591C22⋊C4—2442no—
592C22⋊C4—2442no—
593C42—24no—
594C42—21no—
595C42—21no—
596C42C2×C22⋊D6112yes—
597C42C2×C22⋊D6112yes—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—2441no—
605C23—2441no—
606C23—2441no—
607C23—2441no—
608C23—2441no—
609C23—2441no—
610C23—2441no—
611C23#1451976612yes—
612C23C22×C22⋊D6111yescharacteristic
613Q8—84no—
614Q8—84no—
615Q8—2441no—
616Q8—2441no—
617Q8—2441no—
618Q8—2441no—
619D4—4884no—
620D4—2441no—
621D4—2441no—
622D4—2441no—
623D4—2441no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—22no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—84no—
653C2×C4—2441no—
654C2×C4—2441no—
655C2×C4—2441no—
656C2×C4—2441no—
657C2×C4—2441no—
658C2×C4—2441no—
659C2×C4—2441no—
660C2×C4—2441no—
661C2×C4—2441no—
662C2×C4#1451974612yes—
663C2×C4#1451974612yes—
664C2×C4#1451976612yes—
665C2×C4C22×C22⋊D6111yescharacteristic
666C2×C4C22×C22⋊D6111yescharacteristic
667C2×C4C2×#1175822611yescharacteristic
668C2×C4C2×#1175822611yescharacteristic
669C2×C4#1451982511yescharacteristic
670C2×C4#1451982511yescharacteristic
671C8—2441no—
672C8—2441no—
673C8—2441no—
674C8—2441no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—4881no—
683C22—4881no—
684C22—4881no—
685C22—4881no—
686C22—4881no—
687C22—4881no—
688C22—4881no—
689C22C2×#1451974611yescharacteristic
690C22C2×#1451976611yescharacteristic
691C22#1684033611yescharacteristic
692C22#1684056511yescharacteristic
693C22#1684057011yescharacteristic
694C22#1684057311yescharacteristic
695C22#1684057711yescharacteristic
696C4—22no—
697C4—22no—
698C4—22no—
699C4—41no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—41no—
704C4—42no—
705C4—4881no—
706C4—4881no—
707C4—4881no—
708C4#1684042311yescharacteristic
709C4#1684042311yescharacteristic
710C4#1684042311yescharacteristic
711C4#1684042311yescharacteristic
712C2—42no—
713C2—9761no—
714C2#2144947311yescharacteristic
715C2#2145512311yescharacteristic
716C2#2145513411yescharacteristic
717C2#2145617811yescharacteristic
718C2#2145618911yescharacteristic
719C2#2145710211yescharacteristic
720C2#2145711711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#544C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenterC2×#544D61
hypocenterC61#25916
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. C2×#16840124C2semidirect
2. C2×#16840119C2semidirect
4. #21446967C2semidirect
5. #21446962C2semidirect
6. #21446957C2semidirect
7. #21446952C2semidirect
8. #21446789C2semidirect
9. #21446781C2semidirect
12. #21446131C2semidirect
13. #21446126C2semidirect
14. #21445585C2semidirect
15. C2×C61×#544C2semidirect
109. C4⋊Q8×C61D4semidirect
114. #125×C61D4semidirect
352. C2×#544D61semidirect
423. C61#25916semidirect
439. C4⋊Q8C22⋊D61semidirect
444. #125C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168401242
C2×#168401192
#214515762
#214469672
#214469622
#214469572
#214469522
#214467892
#214467812
#214461412
#214461362
#214461312
#214461262
#214455852
C2×C61×#5442
#2591661