Finite Group Databasebeta

← C2×#24912413 #35576182

Subgroups — C2×#24912413 #35576182

Order 21248.

4006 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581790C211yesmaximal, characteristic, complemented
2C22×#14581772C211yesmaximal, characteristic, complemented
3C22×#14581771C211yesmaximal, characteristic, complemented
4C22×#14581768C211yesmaximal, characteristic, complemented
5C22×C4×C22⋊D83C211yesmaximal, characteristic
6#24912413C2116yesmaximal, direct product factor
7C2×#19127637C212yesmaximal, complemented
8C2×#19127636C212yesmaximal, complemented
9C2×#19127601C212yesmaximal
10C2×#19127570C212yesmaximal, complemented
11C2×C4⋊C4×Dic83C211yesmaximal, characteristic, complemented
12C22×C22⋊Q8×C83C211yesmaximal, characteristic, complemented
13C23×Dic166C2211yescharacteristic
14C23×C22⋊D83C2211yescharacteristic
15C23×C4×D83C2211yescharacteristic
16C2×#14581790—28no—
17C2×#14581790C2218yescomplemented
18C2×#14581772—28no—
19C2×#14581772C2218yescomplemented
20C2×#14581771—28no—
21C2×#14581771C2218yescomplemented
22C2×#14581768—28no—
23C2×#14581768C2218yescomplemented
24C2×C4×C22⋊D83—28no—
25C2×C4×C22⋊D83C2218yes—
26C22×C4⋊Dic83C2212yes—
27C22×C4⋊Dic83C2211yescharacteristic
28C22×Dic83⋊C4C2211yescharacteristic
29C22×Dic83⋊C4C2212yes—
30C22×Dic83⋊C4C2212yes—
31C22×Dic83⋊C4C2212yes—
32C22×Dic83⋊C4C2212yes—
33C22×C22⋊Dic83C2211yescharacteristic
34C22×C22⋊Dic83C2212yes—
35C22×(C2×D83)⋊C4C2211yescharacteristic
36C22×(C2×D83)⋊C4C2212yes—
37C22×(C2×D83)⋊C4C2212yes—
38C22×C4×Dic83C2212yes—
39C22×C4×Dic83C2211yescharacteristic
40#19127637C22116yescomplemented
41#19127636C22116yescomplemented
42#19127601C22116yes—
43#19127570C22116yescomplemented
44C4⋊C4×Dic83C2218yescomplemented
45C2×C83⋊#95C2212yes—
46C23×Q8×C83C2211yescharacteristic
47C24×C4×C83C2211yescharacteristic
48C2×C22⋊Q8×C83—28no—
49C2×C22⋊Q8×C83C2218yescomplemented
50C22×C4⋊C4×C83C2212yes—
51C22×C4⋊C4×C83C2211yescharacteristic
52C22×C22⋊C4×C83C2212yes—
53C24×D83C2311yescharacteristic
54C22×Dic166—24no—
55C22×Dic166—24no—
56C22×Dic166—24no—
57C22×Dic166C2314yes—
58C22×C22⋊D83—24no—
59C22×C22⋊D83—24no—
60C22×C22⋊D83Q818yescomplemented
61C22×C22⋊D83C2314yes—
62C23×Dic83C2312yes—
63C23×Dic83C2311yescharacteristic
64C23×Dic83C2312yes—
65C23×Dic83C2311yescharacteristic
66C23×Dic83C2311yescharacteristic
67C22×C4×D83—24no—
68C22×C4×D83—24no—
69C22×C4×D83—24no—
70C22×C4×D83C2314yes—
71#14581790—232no—
72#14581772—232no—
73#14581771—232no—
74#14581768—232no—
75C4×C22⋊D83—232no—
76C2×C4⋊Dic83—28no—
77C2×C4⋊Dic83D418yescomplemented
78C2×C4⋊Dic83C2318yes—
79C2×C4⋊Dic83C2314yes—
80C2×Dic83⋊C4—24no—
81C2×Dic83⋊C4—28no—
82C2×Dic83⋊C4—28no—
83C2×Dic83⋊C4—28no—
84C2×Dic83⋊C4—28no—
85C2×Dic83⋊C4C2314yes—
86C2×Dic83⋊C4C2318yes—
87C2×Dic83⋊C4C2318yes—
88C2×Dic83⋊C4C2318yes—
89C2×Dic83⋊C4C2318yes—
90C2×C22⋊Dic83—24no—
91C2×C22⋊Dic83—28no—
92C2×C22⋊Dic83C2318yes—
93C2×C22⋊Dic83C2314yes—
94C2×(C2×D83)⋊C4—24no—
95C2×(C2×D83)⋊C4—28no—
96C2×(C2×D83)⋊C4—28no—
97C2×(C2×D83)⋊C4C2318yes—
98C2×(C2×D83)⋊C4C2318yes—
99C2×(C2×D83)⋊C4C2314yes—
100C2×C4×Dic83—28no—
101C2×C4×Dic83D418yes—
102C2×C4×Dic83C2318yes—
103C2×C4×Dic83C2314yes—
104C83⋊#95C2318yes—
105C25×C83C2311yescharacteristic
106C22×Q8×C83—24no—
107C22×Q8×C83—24no—
108C22×Q8×C83—24no—
109C22×Q8×C83C2314yes—
110C23×C4×C83—24no—
111C23×C4×C83—24no—
112C23×C4×C83—24no—
113C23×C4×C83C2312yes—
114C23×C4×C83C2311yescharacteristic
115C23×C4×C83C2314yes—
116C23×C4×C83C2312yes—
117C23×C4×C83C2311yescharacteristic
118C22⋊Q8×C83—232no—
119C2×C4⋊C4×C83—28no—
120C2×C4⋊C4×C83D418yescomplemented
121C2×C4⋊C4×C83C2318yes—
122C2×C4⋊C4×C83C2314yes—
123C2×C22⋊C4×C83—28no—
124C2×C22⋊C4×C83C2318yes—
125C23×D83—22no—
126C23×D83—22no—
127C23×D83—22no—
128C23×D83—22no—
129C23×D83—22no—
130C23×D83—22no—
131C23×D83C2×Q814yes—
132C23×D83C2412yes—
133C2×Dic166—28no—
134C2×Dic166—28no—
135C2×Dic166—28no—
136C2×Dic166—416no—
137C2×C22⋊D83—232no—
138C2×C22⋊D83—28no—
139C2×C22⋊D83—28no—
140C2×C22⋊D83C2×Q8116yescomplemented
141C22×Dic83—24no—
142C22×Dic83—22no—
143C22×Dic83—22no—
144C22×Dic83—24no—
145C22×Dic83—22no—
146C22×Dic83—22no—
147C22×Dic83—22no—
148C22×Dic83—24no—
149C22×Dic83—24no—
150C22×Dic83—24no—
151C22×Dic83C2×D414yes—
152C22×Dic83C2×D418yes—
153C22×Dic83C2×D414yes—
154C22×Dic83C2×Q814yes—
155C22×Dic83#4114yes—
156C22×Dic83C2412yes—
157C22×Dic83C2414yes—
158C22×Dic83C2412yes—
159C22×Dic83C2414yes—
160C22×Dic83C2412yes—
161C2×C4×D83—28no—
162C2×C4×D83—28no—
163C2×C4×D83—28no—
164C2×C4×D83—416no—
165C4⋊Dic83—216no—
166C4⋊Dic83C2×D4116yescomplemented
167Dic83⋊C4—216no—
168Dic83⋊C4—216no—
169Dic83⋊C4—216no—
170Dic83⋊C4—216no—
171Dic83⋊C4—28no—
172C22⋊Dic83—216no—
173C22⋊Dic83—28no—
174(C2×D83)⋊C4—216no—
175(C2×D83)⋊C4—216no—
176(C2×D83)⋊C4—28no—
177C4×Dic83—216no—
178C4×Dic83C2×D4116yes—
179C24×C83—22no—
180C24×C83—22no—
181C24×C83—22no—
182C24×C83—22no—
183C24×C83—22no—
184C24×C83—22no—
185C24×C83C2×Q814yes—
186C24×C83C2412yes—
187C24×C83C2411yescharacteristic
188C2×Q8×C83—28no—
189C2×Q8×C83—28no—
190C2×Q8×C83—28no—
191C2×Q8×C83—416no—
192C22×C4×C83—24no—
193C22×C4×C83—24no—
194C22×C4×C83—24no—
195C22×C4×C83—22no—
196C22×C4×C83—22no—
197C22×C4×C83—22no—
198C22×C4×C83—24no—
199C22×C4×C83—24no—
200C22×C4×C83—28no—
201C22×C4×C83—28no—
202C22×C4×C83—28no—
203C22×C4×C83—416no—
204C22×C4×C83C2×D414yes—
205C22×C4×C83C2×D414yes—
206C22×C4×C83C2×D418yes—
207C22×C4×C83C2×D414yes—
208C22×C4×C83C2414yes—
209C22×C4×C83C2412yes—
210C22×C4×C83C2414yes—
211C22×C4×C83C2412yes—
212C4⋊C4×C83—216no—
213C4⋊C4×C83C2×D4116yescomplemented
214C22⋊C4×C83—216no—
215C23×C83—28no—
216C23×C83—28no—
217C23×C83—28no—
218C23×C83—22no—
219C23×C83—22no—
220C23×C83—22no—
221C23×C83—22no—
222C23×C83—22no—
223C23×C83—22no—
224C23×C83—44no—
225C23×C83—44no—
226C23×C83—44no—
227C23×C83—44no—
228C23×C83C22×D412yes—
229C23×C83C22×D412yes—
230C23×C83C22×D412yes—
231C23×C83C22×Q814yes—
232C23×C83C22×Q812yes—
233C23×C83C2×#4112yes—
234C23×C832−1+412yes—
235C23×C832−1+412yes—
236C23×C83C2511yescharacteristic
237C22×D83—28no—
238C22×D83—28no—
239C22×D83—28no—
240C22×D83—22no—
241C22×D83—22no—
242C22×D83—22no—
243C22×D83—22no—
244C22×D83—22no—
245C22×D83—22no—
246C22×D83—44no—
247C22×D83—44no—
248C22×D83—44no—
249C22×D83—44no—
250C22×D83C22×Q814yes—
251Q8×C83—416no—
252C2×C4×C83—216no—
253C2×C4×C83—24no—
254C2×C4×C83—24no—
255C2×C4×C83—24no—
256C2×C4×C83—22no—
257C2×C4×C83—22no—
258C2×C4×C83—22no—
259C2×C4×C83—24no—
260C2×C4×C83—24no—
261C2×C4×C83—44no—
262C2×C4×C83—48no—
263C2×C4×C83—416no—
264C2×C4×C83#127116yes—
265C2×C4×C83C22×D414yes—
266C2×C4×C83C22×D414yes—
267C2×C4×C83C22×D418yes—
268C2×C4×C83C22×D414yes—
269C22⋊D83—232no—
270C2×Dic83—28no—
271C2×Dic83—216no—
272C2×Dic83—24no—
273C2×Dic83—22no—
274C2×Dic83—22no—
275C2×Dic83—24no—
276C2×Dic83—24no—
277C2×Dic83—22no—
278C2×Dic83—24no—
279C2×Dic83—22no—
280C2×Dic83—24no—
281C2×Dic83—22no—
282C2×Dic83—44no—
283C2×Dic83—48no—
284C2×Dic83C22⋊Q8116yescomplemented
285C2×Dic83C22×D414yes—
286C2×Dic83C22×D418yes—
287C2×Dic83C22×D414yes—
288C2×Dic83C22×Q814yes—
289C2×Dic83C2×#4114yes—
290C4×D83—416no—
291Dic166—416no—
292C22×C83—24no—
293C22×C83—24no—
294C22×C83—24no—
295C22×C83—42no—
296C22×C83—42no—
297C22×C83—42no—
298C22×C83—42no—
299C22×C83—416no—
300C22×C83C2×C22⋊Q814yes—
301C22×C83C2×#12714yes—
302C22×C83#53614yes—
303C22×C83#54714yes—
304C22×C83#54714yes—
305C22×C83D4×Q814yes—
306C22×C83D4×Q814yes—
307C22×C83C23×D411yescharacteristic
308C22×C83C23×D411yescharacteristic
309C22×C83C23×D411yescharacteristic
310C22×C83C23×Q811yescharacteristic
311C22×C83C22×#4111yescharacteristic
312C22×C83C2×2−1+411yescharacteristic
313C22×C83C2×2−1+411yescharacteristic
314C2×D83—24no—
315C2×D83—24no—
316C2×D83—24no—
317C2×D83—42no—
318C2×D83—42no—
319C2×D83—42no—
320C2×D83—42no—
321C2×D83—416no—
322C4×C83—28no—
323C4×C83—42no—
324C4×C83—44no—
325C4×C83C2×#12718yes—
326Dic83—24no—
327Dic83—28no—
328Dic83—44no—
329Dic83—42no—
330Dic83C2×C22⋊Q818yescomplemented
331C2×#2542—831nomaximal, Sylow
332C2×C83—44no—
333C2×C83#254218yescomplemented
334C2×C83C22×C22⋊Q811yescharacteristic
335C2×C83C22×#12711yescharacteristic
336C2×C83C2×#53611yescharacteristic
337C2×C83C2×#54711yescharacteristic
338C2×C83C2×#54711yescharacteristic
339C2×C83C2×D4×Q811yescharacteristic
340C2×C83C2×D4×Q811yescharacteristic
341D83—44no—
342C22×C4⋊Q8—831no—
343C22×C22⋊Q8—831no—
344C22×C22⋊Q8—831no—
345C22×C22⋊Q8—831no—
346C22×C22⋊Q8D8311yescharacteristic, complemented
347C22×C4×D4—831no—
348#2542—8316no—
349C2×#399—832no—
350C2×#399—832no—
351C2×#390—832no—
352C2×#384—832no—
353C2×C4×C4⋊C4—831no—
354C83C2×#254211yescharacteristic, complemented, Sylow
355C23×Q8—831no—
356C23×Q8C2×D8311yescharacteristic
357C23×D4—831no—
358C24×C4—831no—
359C24×C4C2×D8311yescharacteristic
360C2×C4⋊Q8—838no—
361C2×C4⋊Q8—1668no—
362C2×C22⋊Q8—28no—
363C2×C22⋊Q8—838no—
364C2×C22⋊Q8—838no—
365C2×C22⋊Q8—838no—
366C2×C22⋊Q8—1668no—
367C2×C22⋊Q8—1668no—
368C2×C22⋊Q8—1668no—
369C2×C22⋊Q8C2×D8318yescomplemented
370C2×C4×D4—838no—
371C2×C4×D4—1668no—
372C22×C4⋊C4—831no—
373C22×C4⋊C4—832no—
374C22×C4⋊C4—832no—
375C22×C4⋊C4—832no—
376C22×C4⋊C4—831no—
377C22×C4⋊C4—832no—
378C22×C4⋊C4—832no—
379C22×C4⋊C4C2×D8312yes—
380C22×C4⋊C4C2×D8311yescharacteristic
381C22×C22⋊C4—831no—
382C22×C22⋊C4—832no—
383C22×C22⋊C4—831no—
384C22×C22⋊C4—832no—
385C22×C22⋊C4—832no—
386C22×C22⋊C4C2×D8312yes—
387C22×C42—831no—
388C22×C42—832no—
389#399—8316no—
390#399—8316no—
391#390—8316no—
392#384—8316no—
393C4×C4⋊C4—838no—
394C2×#95—832no—
395C25—831no—
396C25C22×D8311yescharacteristic
397C22×Q8—24no—
398C22×Q8—24no—
399C22×Q8—24no—
400C22×Q8—834no—
401C22×Q8—1664no—
402C22×Q8—1664no—
403C22×Q8—1664no—
404C22×Q8C22×D8314yes—
405C22×D4—838no—
406C22×D4—834no—
407C22×D4—1664no—
408C22×D4—1664no—
409C23×C4—24no—
410C23×C4—24no—
411C23×C4—24no—
412C23×C4—831no—
413C23×C4—832no—
414C23×C4—831no—
415C23×C4—832no—
416C23×C4—831no—
417C23×C4—834no—
418C23×C4—1664no—
419C23×C4—1664no—
420C23×C4—1664no—
421C23×C4C22×D8314yes—
422C23×C4C22×D8312yes—
423C23×C4C22×D8311yescharacteristic
424C23×C4C22×D8312yes—
425C23×C4C22×D8311yescharacteristic
426C4⋊Q8—16632no—
427C22⋊Q8—232no—
428C22⋊Q8—16632no—
429C22⋊Q8—16632no—
430C22⋊Q8—16632no—
431C4×D4—16632no—
432C2×C4⋊C4—28no—
433C2×C4⋊C4—838no—
434C2×C4⋊C4—834no—
435C2×C4⋊C4—834no—
436C2×C4⋊C4—838no—
437C2×C4⋊C4—838no—
438C2×C4⋊C4—838no—
439C2×C4⋊C4—838no—
440C2×C4⋊C4—838no—
441C2×C4⋊C4—1664no—
442C2×C4⋊C4—1668no—
443C2×C4⋊C4—1668no—
444C2×C4⋊C4—1668no—
445C2×C4⋊C4—1668no—
446C2×C4⋊C4—1668no—
447C2×C4⋊C4C22⋊D8318yescomplemented
448C2×C4⋊C4C22×D8318yes—
449C2×C4⋊C4C22×D8314yes—
450C2×C22⋊C4—28no—
451C2×C22⋊C4—834no—
452C2×C22⋊C4—838no—
453C2×C22⋊C4—834no—
454C2×C22⋊C4—838no—
455C2×C22⋊C4—838no—
456C2×C22⋊C4—1664no—
457C2×C22⋊C4—1668no—
458C2×C22⋊C4—1664no—
459C2×C22⋊C4—1668no—
460C2×C22⋊C4—1668no—
461C2×C22⋊C4C22×D8318yes—
462C2×C42—838no—
463C2×C42—834no—
464C2×C42—838no—
465C2×C42—1668no—
466#95—838no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—834no—
474C24—832no—
475C24—1662no—
476C24—1662no—
477C24—1662no—
478C24—1662no—
479C24—1662no—
480C24—1662no—
481C24Q8×D8314yes—
482C24C23×D8312yes—
483C24C23×D8311yescharacteristic
484C2×Q8—28no—
485C2×Q8—28no—
486C2×Q8—28no—
487C2×Q8—416no—
488C2×Q8—33216no—
489C2×Q8—1668no—
490C2×Q8—1668no—
491C2×Q8—1668no—
492C2×D4—8316no—
493C2×D4—1668no—
494C2×D4—16632no—
495C2×D4—1668no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—416no—
508C22×C4—33216no—
509C22×C4—834no—
510C22×C4—834no—
511C22×C4—834no—
512C22×C4—832no—
513C22×C4—834no—
514C22×C4—838no—
515C22×C4—832no—
516C22×C4—834no—
517C22×C4—834no—
518C22×C4—832no—
519C22×C4—1662no—
520C22×C4—1664no—
521C22×C4—1662no—
522C22×C4—1664no—
523C22×C4—1664no—
524C22×C4—1662no—
525C22×C4—1668no—
526C22×C4—1668no—
527C22×C4—1668no—
528C22×C4—1664no—
529C22×C4—1662no—
530C22×C4—1664no—
531C22×C4—1662no—
532C22×C4D4×D8314yes—
533C22×C4D4×D8314yes—
534C22×C4C2×C22⋊D8318yes—
535C22×C4C2×C22⋊D8314yes—
536C22×C4C23×D8314yes—
537C22×C4C23×D8312yes—
538C22×C4C23×D8314yes—
539C22×C4C23×D8312yes—
540C4⋊C4—216no—
541C4⋊C4—8316no—
542C4⋊C4—1668no—
543C4⋊C4—16616no—
544C4⋊C4—16616no—
545C4⋊C4—16616no—
546C4⋊C4—16616no—
547C4⋊C4—16616no—
548C4⋊C4C2×C22⋊D83116yescomplemented
549C22⋊C4—216no—
550C22⋊C4—1668no—
551C22⋊C4—16616no—
552C22⋊C4—1668no—
553C22⋊C4—16616no—
554C22⋊C4—16616no—
555C42—8316no—
556C42—16616no—
557C23—28no—
558C23—28no—
559C23—28no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—22no—
564C23—22no—
565C23—22no—
566C23—44no—
567C23—44no—
568C23—44no—
569C23—44no—
570C23—3324no—
571C23—3324no—
572C23—3324no—
573C23—3324no—
574C23—834no—
575C23—1668no—
576C23—1668no—
577C23—1668no—
578C23—1662no—
579C23—1662no—
580C23—1662no—
581C23—1662no—
582C23—1662no—
583C23—1662no—
584C23C2×D4×D8312yes—
585C23C2×D4×D8312yes—
586C23C22×C22⋊D8312yes—
587C23C2×Q8×D8314yes—
588C23C2×Q8×D8312yes—
589C23#41×D8312yes—
590C23#1458183912yes—
591C23#1458184012yes—
592C23C24×D8311yescharacteristic
593Q8—416no—
594Q8—33216no—
595D4—16632no—
596C2×C4—216no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—22no—
600C2×C4—24no—
601C2×C4—22no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—22no—
605C2×C4—44no—
606C2×C4—48no—
607C2×C4—416no—
608C2×C4—3324no—
609C2×C4—3328no—
610C2×C4—33216no—
611C2×C4—8316no—
612C2×C4—834no—
613C2×C4—834no—
614C2×C4—834no—
615C2×C4—834no—
616C2×C4—838no—
617C2×C4—1662no—
618C2×C4—1664no—
619C2×C4—1662no—
620C2×C4—1664no—
621C2×C4—1664no—
622C2×C4—1662no—
623C2×C4—16616no—
624C2×C4—1664no—
625C2×C4—1668no—
626C2×C4—1662no—
627C2×C4—1664no—
628C2×C4—1662no—
629C2×C4#14581788116yes—
630C2×C4C2×D4×D8314yes—
631C2×C4C2×D4×D8314yes—
632C2×C4C22×C22⋊D8318yes—
633C2×C4C22×C22⋊D8314yes—
634C22—24no—
635C22—24no—
636C22—24no—
637C22—416no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—33216no—
643C22—3322no—
644C22—3322no—
645C22—3322no—
646C22—3322no—
647C22—1664no—
648C22—1664no—
649C22—1664no—
650C22C22⋊Q8×D8314yes—
651C22C2×#1458178814yes—
652C22#1912827414yes—
653C22#1912835014yes—
654C22#1912835314yes—
655C22#1912836414yes—
656C22Q8×C22⋊D8314yes—
657C22C22×D4×D8311yescharacteristic
658C22C22×D4×D8311yescharacteristic
659C22C23×C22⋊D8311yescharacteristic
660C22C22×Q8×D8311yescharacteristic
661C22C2×#41×D8311yescharacteristic
662C22C2×#1458183911yescharacteristic
663C22C2×#1458184011yescharacteristic
664C4—28no—
665C4—42no—
666C4—44no—
667C4—3322no—
668C4—3324no—
669C4—838no—
670C4—1668no—
671C4—1664no—
672C4C2×#1458178818yes—
673C2—44no—
674C2—3324no—
675C2#2491241318yesdirect product factor
676C2C2×C22⋊Q8×D8311yescharacteristic
677C2C22×#1458178811yescharacteristic
678C2C2×#1912827411yescharacteristic
679C2C2×#1912835011yescharacteristic
680C2C2×#1912835311yescharacteristic
681C2C2×#1912836411yescharacteristic
682C2C2×Q8×C22⋊D8311yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC22×C22⋊Q8×C83C2
socleC24×C83C24
prime radicalC23×C22⋊D83C22
hypercenterC22×C22⋊Q8D83
hypocenterC83C2×#2542
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14581790C2semidirect
2. C22×#14581772C2semidirect
3. C22×#14581771C2semidirect
4. C22×#14581768C2semidirect
6. #24912413C2direct (N × H)
7. C2×#19127637C2semidirect
8. C2×#19127636C2semidirect
10. C2×#19127570C2semidirect
11. C2×C4⋊C4×Dic83C2semidirect
12. C22×C22⋊Q8×C83C2semidirect
17. C2×#14581790C22semidirect
19. C2×#14581772C22semidirect
21. C2×#14581771C22semidirect
23. C2×#14581768C22semidirect
40. #19127637C22semidirect
41. #19127636C22semidirect
43. #19127570C22semidirect
44. C4⋊C4×Dic83C22semidirect
49. C2×C22⋊Q8×C83C22semidirect
60. C22×C22⋊D83Q8semidirect
77. C2×C4⋊Dic83D4semidirect
120. C2×C4⋊C4×C83D4semidirect
140. C2×C22⋊D83C2×Q8semidirect
166. C4⋊Dic83C2×D4semidirect
213. C4⋊C4×C83C2×D4semidirect
284. C2×Dic83C22⋊Q8semidirect
330. Dic83C2×C22⋊Q8semidirect
333. C2×C83#2542semidirect
346. C22×C22⋊Q8D83semidirect
354. C83C2×#2542semidirect
369. C2×C22⋊Q8C2×D83semidirect
447. C2×C4⋊C4C22⋊D83semidirect
548. C4⋊C4C2×C22⋊D83semidirect
675. C2#24912413direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817902
C22×#145817722
C22×#145817712
C22×#145817682
C22×C4×C22⋊D832
#249124132
C2×#191276372
C2×#191276362
C2×#191276012
C2×#191275702
C2×C4⋊C4×Dic832
C22×C22⋊Q8×C832
C2×#254283