Finite Group Databasebeta

← #29724008

Subgroups — #29724008

Order 15616.

1010 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839901C211yesmaximal, characteristic
2C2×#16839860C211yesmaximal, characteristic, complemented
3#21449333C211yesmaximal, characteristic
4#21447357C211yesmaximal, characteristic, complemented
5#21447245C211yesmaximal, characteristic, complemented
6#21447134C211yesmaximal, characteristic, complemented
7#21447001C211yesmaximal, characteristic
8#21446512C211yesmaximal, characteristic, complemented
9#21446434C211yesmaximal, characteristic, complemented
10#21446174C211yesmaximal, characteristic, complemented
11#21446156C211yesmaximal, characteristic, complemented
12#21446073C211yesmaximal, characteristic, complemented
13#21445824C211yesmaximal, characteristic, complemented
14#21445754C211yesmaximal, characteristic, complemented
15Q8×C22⋊C4×C61C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C2×#14519759—21no—
19C2×#14519751C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21#16839901—24no—
22#16839860—24no—
23C2×#14519710C2211yescharacteristic
24C2×#14519710C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×#14519688C2211yescharacteristic
37#16839689—21no—
38#16839678—21no—
39#16839664C2211yescharacteristic
40#16839660C2211yescharacteristic
41#16839636—21no—
42#16839632C2211yescharacteristic
43#16839622C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C23×Q8×C61C2211yescharacteristic
51C2×C4×Q8×C61C2211yescharacteristic
52C2×C4×Q8×C61C2211yescharacteristic
53C61×#391—21no—
54C61×#391—21no—
55C61×#391C2211yescharacteristic
56C61×#391C2211yescharacteristic
57C61×#380—21no—
58C61×#380C2211yescharacteristic
59C4×C22⋊C4×C61—21no—
60C4×C22⋊C4×C61C2211yescharacteristic
61C22×D244C2311yescharacteristic
62C22×C22⋊D61—21no—
63C22×C4×D61—21no—
64C2×#11758201—22no—
65C2×#11758201—22no—
66C2×#11758201—22no—
67C2×#11758201—22no—
68C2×#11758201—41no—
69C2×#11758201D414yes—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74#14519759—44no—
75#14519751—22no—
76#14519751—41no—
77C4×D244—22no—
78C4×D244—41no—
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61—21no—
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×#11758196—21no—
85C2×C22⋊Dic61—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90#14519710—22no—
91#14519710—41no—
92C4⋊#92418—41no—
93#14519701—22no—
94#14519701—22no—
95#14519701—22no—
96#14519701—22no—
97#14519701—22no—
98#14519701—41no—
99#14519697—22no—
100#14519697—41no—
101C22⋊#92418—22no—
102C22⋊#92418—41no—
103#14519688—22no—
104#14519684—21no—
105#14519684—21no—
106C22×Q8×C61—22no—
107C22×Q8×C61—22no—
108C22×Q8×C61—21no—
109C22×Q8×C61—22no—
110C22×Q8×C61—22no—
111C22×Q8×C61—41no—
112C22×Q8×C61—41no—
113C22×Q8×C61C2311yescharacteristic
114C22×Q8×C61C2311yescharacteristic
115C23×C4×C61—21no—
116C23×C4×C61C2311yescharacteristic
117C4×Q8×C61—22no—
118C4×Q8×C61—22no—
119C4×Q8×C61—41no—
120C4×Q8×C61—41no—
121C2×C4⋊C4×C61—21no—
122C2×C4⋊C4×C61—21no—
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61D411yescharacteristic
127C2×C22⋊C4×C61D411yescharacteristic
128C2×C42×C61—21no—
129C2×C42×C61—21no—
130C2×C42×C61C2311yescharacteristic
131C2×C42×C61C2311yescharacteristic
132#95×C61—21no—
133#95×C61—21no—
134#95×C61—21no—
135#95×C61—21no—
136#95×C61—21no—
137#95×C61D411yescharacteristic
138#95×C61D411yescharacteristic
139C24×C61C2×D411yescharacteristic
140C23×D61—21no—
141C2×Q8×C61—24no—
142C2×Q8×C61—21no—
143C2×Q8×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—42no—
151C2×Q8×C61—42no—
152C2×Q8×C61—44no—
153C2×Q8×C61—44no—
154C2×Q8×C61—44no—
155C2×Q8×C61—44no—
156C2×Q8×C61C2×D412yes—
157C2×Q8×C61#4112yes—
158C2×Q8×C61#4112yes—
159C2×Q8×C61#4112yes—
160C22×C4×C61—21no—
161C22×C4×C61—24no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—42no—
172C22×C4×C61—42no—
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2411yescharacteristic
179C2×C22⋊D61—42no—
180C2×C22⋊D61—42no—
181C2×C22⋊D61—81no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C2×D244—21no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244C2×D412yes—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×C4×D61—81no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—42no—
199C4⋊C4×C61—42no—
200C22⋊C4×C61—22no—
201C22⋊C4×C61—22no—
202C22⋊C4×C61—42no—
203C42×C61—21no—
204C42×C61—21no—
205C42×C61—21no—
206C42×C61—21no—
207C42×C61—42no—
208C42×C61—42no—
209C22⋊Dic61—42no—
210#11758201—28no—
211#11758201—44no—
212#11758198—42no—
213#11758198—42no—
214#11758198—42no—
215#11758198—42no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—42no—
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×#92418C2×D412yes—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61AGL(1,ℤ/8)12yes—
244C23×C61C22×D411yescharacteristic
245C22×D61—22no—
246C22×D61—41no—
247C22×D61—41no—
248C22×D61—41no—
249C22×D61—41no—
250C22×D61—41no—
251C22×D61—41no—
252Q8×C61—22no—
253Q8×C61—22no—
254Q8×C61—22no—
255Q8×C61—22no—
256Q8×C61—22no—
257Q8×C61—48no—
258Q8×C61—41no—
259Q8×C61—41no—
260Q8×C61#12314yescomplemented
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—21no—
264C2×C4×C61—22no—
265C2×C4×C61—21no—
266C2×C4×C61—22no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—48no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61#13712yes—
293C2×C4×C61C22×D411yescharacteristic
294C2×C4×C61C2×#4111yescharacteristic
295C2×C4×C61C2×#4111yescharacteristic
296C2×C4×C61C2×#4111yescharacteristic
297C2×C4×C61H(5,𝔽2)11yescharacteristic
298C2×C4×C61H(5,𝔽2)11yescharacteristic
299C22⋊D61—84no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309D244—22no—
310D244—22no—
311D244—41no—
312D244—41no—
313C4×D61—84no—
314#92418—22no—
315#92418—41no—
316#92418—41no—
317#92418—41no—
318#24910—611nomaximal, Sylow
319C22×C61—22no—
320C22×C61—22no—
321C22×C61—22no—
322C22×C61—41no—
323C22×C61—41no—
324C22×C61—41no—
325C22×C61—41no—
326C22×C61#52511yescharacteristic
327C22×C61D4211yescharacteristic
328C22×C61#54611yescharacteristic
329C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
330C22×C61C2×#13711yescharacteristic
331C22×C61#57711yescharacteristic
332C22×C61#57811yescharacteristic
333C2×D61—42no—
334C2×D61—42no—
335C2×D61—42no—
336C2×D61—81no—
337C2×D61—81no—
338C2×D61—81no—
339C2×D61—81no—
340C4×C61—24no—
341C4×C61—22no—
342C4×C61—41no—
343C4×C61—42no—
344C4×C61—41no—
345C4×C61—41no—
346C4×C61—41no—
347C4×C61—81no—
348C4×C61—81no—
349C4×C61C2×#12311yescharacteristic
350C4×C61#53811yescharacteristic
351C4×C61#54611yescharacteristic
352C4×C61#55111yescharacteristic
353Dic61—81no—
354Dic61—81no—
355Dic61—81no—
356C2×#448—611no—
357C2×#440—611no—
358#2422—611no—
359Q8×C22⋊C4D6111yescharacteristic, complemented
360#2095—611no—
361#2075—611no—
362#2055—611no—
363#2033—611no—
364#1935—611no—
365#1924—611no—
366#1880—611no—
367#1877—611no—
368#1863—611no—
369#1803—611no—
370#1787—611no—
371C2×C61—42no—
372C2×C61#241811yescharacteristic
373C2×C61#311211yescharacteristic
374C2×C61#312111yescharacteristic
375C2×C61#326511yescharacteristic
376C2×C61#327611yescharacteristic
377C2×C61#330811yescharacteristic
378C2×C61#332011yescharacteristic
379D61—82no—
380C23×Q8C2×D6111yescharacteristic
381C22×SD16—611no—
382C22×SD16—611no—
383C2×#123—1221no—
384C2×#121—611no—
385C2×C4×Q8C2×D6111yescharacteristic
386C2×C4×Q8C2×D6111yescharacteristic
387C2×C4×D4—611no—
388#448—1224no—
389#440—1224no—
390C2×#107—611no—
391C2×#107—611no—
392C2×C4⋊C8—611no—
393C2×#103—611no—
394C2×#103—611no—
395C2×#103—611no—
396C2×#103—611no—
397C2×#103—611no—
398C2×#103—611no—
399C2×#102—611no—
400C2×#102—611no—
401C2×C22⋊C8—611no—
402C2×C22⋊C8—611no—
403C2×#97—611no—
404#397—1221no—
405#394—1221no—
406#391—21no—
407#391—21no—
408#391C2×D6111yescharacteristic
409#391C2×D6111yescharacteristic
410#390—611no—
411#389—611no—
412#385—1221no—
413#384—611no—
414#380—21no—
415#380—611no—
416#380C2×D6111yescharacteristic
417C4×C22⋊C4—21no—
418C4×C22⋊C4C2×D6111yescharacteristic
419#340—611no—
420#340—611no—
421#340—611no—
422#340—611no—
423#336—611no—
424#336—611no—
425C61#2491011yescharacteristic, complemented, Sylow
426C22×Q8—22no—
427C22×Q8—22no—
428C22×Q8—21no—
429C22×Q8—22no—
430C22×Q8—22no—
431C22×Q8—41no—
432C22×Q8—41no—
433C22×Q8C22×D6111yescharacteristic
434C22×Q8C22×D6111yescharacteristic
435C22×D4—611no—
436C22×D4—1221no—
437C23×C4—21no—
438C23×C4—1221no—
439C23×C4C22×D6111yescharacteristic
440C2×SD16—614no—
441C2×SD16—1222no—
442C2×SD16—1222no—
443C2×SD16—1222no—
444C2×SD16—1222no—
445C2×SD16—2441no—
446C22×C8—611no—
447C22×C8—611no—
448C22×C8—611no—
449C22×C8—611no—
450#123—2444no—
451#121—1222no—
452#121—2441no—
453C4×Q8—22no—
454C4×Q8—22no—
455C4×Q8—41no—
456C4×Q8—41no—
457C4×D4—1222no—
458C4×D4—2441no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—611no—
462C2×C4⋊C4—611no—
463C2×C4⋊C4—611no—
464C2×C4⋊C4—1221no—
465C2×C4⋊C4—1221no—
466C2×C4⋊C4—1221no—
467C2×C4⋊C4C22×D6111yescharacteristic
468C2×C4⋊C4C22×D6111yescharacteristic
469C2×C22⋊C4—21no—
470C2×C22⋊C4—1221no—
471C2×C22⋊C4—1221no—
472C2×C22⋊C4—1221no—
473C2×C22⋊C4—1221no—
474C2×C22⋊C4—1221no—
475C2×C22⋊C4C22⋊D6111yescharacteristic
476C2×C22⋊C4C22⋊D6111yescharacteristic
477C2×C42—21no—
478C2×C42—21no—
479C2×C42C22×D6111yescharacteristic
480C2×C42C22×D6111yescharacteristic
481#107—1222no—
482#107—2441no—
483C4⋊C8—2441no—
484#103—1222no—
485#103—1222no—
486#103—1222no—
487#103—1222no—
488#103—1222no—
489#103—2441no—
490#102—1222no—
491#102—2441no—
492C22⋊C8—1222no—
493C22⋊C8—2441no—
494#97—1222no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—1221no—
501#95—1221no—
502#95C22⋊D6111yescharacteristic
503#95C22⋊D6111yescharacteristic
504C24—1221no—
505C24C2×C22⋊D6111yescharacteristic
506C2×Q8—24no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—42no—
516C2×Q8—42no—
517C2×Q8—44no—
518C2×Q8—44no—
519C2×Q8—44no—
520C2×Q8—44no—
521C2×Q8#1175822212yes—
522C2×Q8#1175822212yes—
523C2×Q8D4×D6112yes—
524C2×Q8#1175822412yes—
525C2×D4—612no—
526C2×D4—1221no—
527C2×D4—1221no—
528C2×D4—1221no—
529C2×D4—1221no—
530C2×D4—1221no—
531C2×D4—4881no—
532C2×D4—2442no—
533C2×D4—2442no—
534C22×C4—21no—
535C22×C4—24no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—4881no—
551C22×C4—2442no—
552C22×C4—2442no—
553C22×C4C2×C22⋊D6111yescharacteristic
554C22×C4C2×C22⋊D6111yescharacteristic
555C22×C4C2×C22⋊D6111yescharacteristic
556C22×C4C2×C22⋊D6111yescharacteristic
557C22×C4C2×C22⋊D6111yescharacteristic
558C22×C4C23×D6111yescharacteristic
559SD16—1228no—
560SD16—2444no—
561C2×C8—612no—
562C2×C8—1221no—
563C2×C8—1221no—
564C2×C8—1221no—
565C2×C8—1221no—
566C2×C8—1221no—
567C2×C8—1221no—
568C2×C8—1221no—
569C2×C8—1221no—
570C2×C8—1221no—
571C2×C8—1221no—
572C2×C8—1221no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—1221no—
580C4⋊C4—1221no—
581C4⋊C4—1221no—
582C4⋊C4—1221no—
583C4⋊C4—1221no—
584C4⋊C4—1221no—
585C4⋊C4—4881no—
586C4⋊C4—2442no—
587C4⋊C4—2442no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—42no—
591C22⋊C4—2442no—
592C22⋊C4—2442no—
593C22⋊C4—2442no—
594C22⋊C4—2442no—
595C22⋊C4—2442no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—42no—
601C42—42no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—1222no—
609C23—2441no—
610C23—2441no—
611C23—2441no—
612C23—2441no—
613C23—2441no—
614C23—2441no—
615C23#1451980212yes—
616C23C22×C22⋊D6111yescharacteristic
617Q8—22no—
618Q8—22no—
619Q8—22no—
620Q8—22no—
621Q8—22no—
622Q8—48no—
623Q8—41no—
624Q8—41no—
625Q8#1451975914yescomplemented
626D4—1222no—
627D4—1222no—
628D4—4884no—
629D4—2441no—
630D4—2441no—
631C2×C4—22no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—48no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—4884no—
663C2×C4—2441no—
664C2×C4—2441no—
665C2×C4—2441no—
666C2×C4—2441no—
667C2×C4—2441no—
668C2×C4—2441no—
669C2×C4—2441no—
670C2×C4—2441no—
671C2×C4—2441no—
672C2×C4#1451980812yes—
673C2×C4C2×D4×D6111yescharacteristic
674C2×C4C2×#1175822411yescharacteristic
675C2×C4C2×#1175822211yescharacteristic
676C2×C4C2×#1175822211yescharacteristic
677C2×C4#1451982211yescharacteristic
678C2×C4#1451982211yescharacteristic
679C8—1222no—
680C8—2441no—
681C8—2441no—
682C8—2441no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—4881no—
691C22—4881no—
692C22—4881no—
693C22—4881no—
694C22—2442no—
695C22—2442no—
696C22—2442no—
697C22#1684027311yescharacteristic
698C22D4×C22⋊D6111yescharacteristic
699C22#1684040611yescharacteristic
700C22C2×#1451980211yescharacteristic
701C22C2×#1451980811yescharacteristic
702C22#1684057011yescharacteristic
703C22#1684057711yescharacteristic
704C4—24no—
705C4—22no—
706C4—41no—
707C4—41no—
708C4—42no—
709C4—41no—
710C4—41no—
711C4—81no—
712C4—81no—
713C4—4881no—
714C4—4881no—
715C4—4881no—
716C4C2×#1451975911yescharacteristic
717C4#1684035011yescharacteristic
718C4#1684040211yescharacteristic
719C4#1684043811yescharacteristic
720C2—42no—
721C2—4882no—
722C2#2144928111yescharacteristic
723C2#2145594111yescharacteristic
724C2#2145604811yescharacteristic
725C2#2145731511yescharacteristic
726C2#2145746511yescharacteristic
727C2#2145781011yescharacteristic
728C2#2145799011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingQ8×C22⋊C4×C61C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenterQ8×C22⋊C4D61
hypocenterC61#24910
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16839860C2semidirect
4. #21447357C2semidirect
5. #21447245C2semidirect
6. #21447134C2semidirect
8. #21446512C2semidirect
9. #21446434C2semidirect
10. #21446174C2semidirect
11. #21446156C2semidirect
12. #21446073C2semidirect
13. #21445824C2semidirect
14. #21445754C2semidirect
15. Q8×C22⋊C4×C61C2semidirect
260. Q8×C61#123semidirect
359. Q8×C22⋊C4D61semidirect
425. C61#24910semidirect
625. Q8#14519759semidirect

Maximal subgroups

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

subgroupindex
C2×#168399012
C2×#168398602
#214493332
#214473572
#214472452
#214471342
#214470012
#214465122
#214464342
#214461742
#214461562
#214460732
#214458242
#214457542
Q8×C22⋊C4×C612
#2491061