Finite Group Databasebeta

← C4×Q8×C22⋊D83 #35564266

Subgroups — C4×Q8×C22⋊D83 #35564266

Order 21248.

3148 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D83C211yesmaximal, characteristic
2C2×C4×Q8×D83C211yesmaximal, characteristic, complemented
3#24910517C213yesmaximal, complemented
4#24910468C213yesmaximal, complemented
5#24910464C213yesmaximal, complemented
6Q8×Dic83⋊C4C211yesmaximal, characteristic, complemented
7C4⋊C4×C22⋊D83C213yesmaximal
8Q8×C22⋊Dic83C211yesmaximal, characteristic, complemented
9Q8×(C2×D83)⋊C4C211yesmaximal, characteristic, complemented
10C4×#14581790C213yesmaximal, complemented
11C4×#14581771C213yesmaximal, complemented
12C4×#14581768C213yesmaximal, complemented
13C4×Q8×Dic83C211yesmaximal, characteristic, complemented
14C42×C22⋊D83C213yesmaximal
15C22×C4×Q8×C83C211yesmaximal, characteristic, complemented
16C22×Q8×D83C2211yescharacteristic
17Q8×C22⋊D83C4116yesdirect product factor
18C2×#14581790C2213yes—
19C2×#14581771C2213yes—
20C2×#14581768C2213yes—
21C2×Q8×Dic83C2211yescharacteristic
22C2×Q8×Dic83C2211yescharacteristic
23C2×Q8×Dic83C2211yescharacteristic
24C2×C4×Dic166C2213yes—
25C2×#14581757C2213yes—
26C4×Q8×D83—28no—
27C2×C4×C22⋊D83C2213yes—
28C2×C4×C22⋊D83C2213yes—
29C2×C4×C22⋊D83C2211yescharacteristic
30C2×C4⋊C4×D83C2213yes—
31C2×C42×D83C2213yes—
32#19127608C2213yes—
33#19127608C2213yes—
34#19127607C2213yes—
35#19127606C2213yes—
36#19127599C2213yes—
37#19127597C2213yes—
38#19127596C2216yes—
39#19127596C2216yes—
40#19127585C2216yes—
41#19127582C2216yes—
42#19127574C2216yes—
43#19127572C2216yes—
44#19127570C2213yes—
45#19127561C2213yes—
46#19127558C2213yes—
47C4⋊C4×Dic83C2213yes—
48C4⋊C4×Dic83C2213yes—
49C4×Dic83⋊C4C2213yes—
50C4×Dic83⋊C4C2216yes—
51C4×Dic83⋊C4C2213yes—
52C4×Dic83⋊C4C2213yes—
53C4×C4⋊Dic83C2213yes—
54C4×(C2×D83)⋊C4C2213yes—
55C4×(C2×D83)⋊C4C2213yes—
56C4×(C2×D83)⋊C4C2213yes—
57C4×C22⋊Dic83C2213yes—
58C4×C22⋊Dic83C2213yes—
59C4×C22⋊Dic83C2213yes—
60C42×Dic83C2213yes—
61C23×Q8×C83C2211yescharacteristic
62C2×C4×Q8×C83—28no—
63C2×C4×Q8×C83C2211yescharacteristic
64C2×C4×Q8×C83C2213yes—
65C2×C4×Q8×C83C2213yes—
66C2×C4×Q8×C83C2211yescharacteristic
67C22×C4⋊C4×C83C2213yes—
68C22×C42×C83C2213yes—
69C22×Dic166C2313yes—
70C2×Q8×D83—24no—
71C2×Q8×D83—24no—
72C2×Q8×D83C2×C418yescomplemented
73C22×C22⋊D83C2311yescharacteristic
74C22×C4×D83C2313yes—
75C22×C4×D83C2313yes—
76C22×C4×D83C2311yescharacteristic
77#14581790C2×C4124yescomplemented
78#14581771C2×C4124yescomplemented
79#14581768C2×C4124yescomplemented
80Q8×Dic83—24no—
81Q8×Dic83—24no—
82Q8×Dic83C2×C418yescomplemented
83C4×Dic166—212no—
84#14581757—212no—
85C4×C22⋊D83—212no—
86C4×C22⋊D83C2×C4124yes—
87C4×C22⋊D83Q818yesdirect product factor
88C2×C4⋊Dic83C2313yes—
89C2×C4⋊Dic83C2313yes—
90C2×C4⋊Dic83C2313yes—
91C2×Dic83⋊C4C2313yes—
92C2×Dic83⋊C4C2316yes—
93C2×Dic83⋊C4C2316yes—
94C2×Dic83⋊C4C2313yes—
95C2×Dic83⋊C4C2316yes—
96C2×Dic83⋊C4C2311yescharacteristic
97C4⋊C4×D83—212no—
98C2×C22⋊Dic83C2313yes—
99C2×C22⋊Dic83C2313yes—
100C2×C22⋊Dic83C2311yescharacteristic
101C2×(C2×D83)⋊C4C2313yes—
102C2×(C2×D83)⋊C4C2313yes—
103C2×(C2×D83)⋊C4C2311yescharacteristic
104C2×C4×Dic83C2313yes—
105C2×C4×Dic83C2313yes—
106C2×C4×Dic83C2313yes—
107C2×C4×Dic83C2313yes—
108C2×C4×Dic83C2313yes—
109C2×C4×Dic83C2313yes—
110C2×C4×Dic83C2313yes—
111C2×C4×Dic83C2313yes—
112C2×C4×Dic83C2311yescharacteristic
113C42×D83—212no—
114C83⋊#95C2316yes—
115C83⋊#95C2316yes—
116C83⋊#95C2316yes—
117C83⋊#95C2313yes—
118C83⋊#95C2313yes—
119C83⋊#95C2313yes—
120C83⋊#95C2313yes—
121C83⋊#95C2313yes—
122C83⋊#95C2313yes—
123C22×Q8×C83—24no—
124C22×Q8×C83—24no—
125C22×Q8×C83C2×C418yescomplemented
126C22×Q8×C83C2313yes—
127C22×Q8×C83C2311yescharacteristic
128C23×C4×C83C2313yes—
129C23×C4×C83C2313yes—
130C23×C4×C83C2311yescharacteristic
131C4×Q8×C83—24no—
132C4×Q8×C83—212no—
133C4×Q8×C83—212no—
134C4×Q8×C83D418yescomplemented
135C2×C4⋊C4×C83—212no—
136C2×C4⋊C4×C83C2313yes—
137C2×C4⋊C4×C83C2316yes—
138C2×C4⋊C4×C83C2313yes—
139C2×C42×C83—212no—
140C2×C42×C83C2313yes—
141C2×C42×C83C2313yes—
142C2×C42×C83C2313yes—
143C2×C42×C83C2313yes—
144C23×D83C2411yescharacteristic
145C2×Dic166—26no—
146C2×Dic166—26no—
147C2×Dic166C22×C4112yes—
148Q8×D83—232no—
149C2×C22⋊D83C22×C414yes—
150C2×C22⋊D83C2×Q814yes—
151C2×C22⋊D83#4114yes—
152C22×Dic83C2413yes—
153C22×Dic83C2413yes—
154C22×Dic83C2413yes—
155C22×Dic83C2413yes—
156C22×Dic83C2411yescharacteristic
157C22×Dic83C2411yescharacteristic
158C22×Dic83C2411yescharacteristic
159C2×C4×D83—26no—
160C2×C4×D83—22no—
161C2×C4×D83—26no—
162C2×C4×D83—22no—
163C2×C4×D83—26no—
164C2×C4×D83—26no—
165C2×C4×D83—43no—
166C2×C4×D83C22×C4112yes—
167C2×C4×D83C2×Q814yescomplemented
168C4⋊Dic83—26no—
169C4⋊Dic83—26no—
170C4⋊Dic83C22×C4112yes—
171Dic83⋊C4—212no—
172Dic83⋊C4—26no—
173Dic83⋊C4—46no—
174Dic83⋊C4C22×C4124yes—
175Dic83⋊C4C22×C4112yes—
176Dic83⋊C4C2×Q814yescomplemented
177C22⋊Dic83—26no—
178C22⋊Dic83C22×C4112yes—
179C22⋊Dic83C2×Q814yescomplemented
180(C2×D83)⋊C4—26no—
181(C2×D83)⋊C4C22×C4112yes—
182(C2×D83)⋊C4C2×Q814yescomplemented
183C4×Dic83—26no—
184C4×Dic83—26no—
185C4×Dic83—26no—
186C4×Dic83—26no—
187C4×Dic83—26no—
188C4×Dic83—26no—
189C4×Dic83—43no—
190C4×Dic83C22×C4112yes—
191C4×Dic83C2×Q814yescomplemented
192C24×C83C2411yescharacteristic
193C2×Q8×C83—232no—
194C2×Q8×C83—26no—
195C2×Q8×C83—26no—
196C2×Q8×C83C22×C4112yes—
197C2×Q8×C83C22×C414yes—
198C2×Q8×C83C2×D414yes—
199C2×Q8×C83#4114yes—
200C22×C4×C83—22no—
201C22×C4×C83—26no—
202C22×C4×C83—26no—
203C22×C4×C83—22no—
204C22×C4×C83—26no—
205C22×C4×C83—26no—
206C22×C4×C83—43no—
207C22×C4×C83C22×C4112yes—
208C22×C4×C83C2×Q814yescomplemented
209C22×C4×C83C2413yes—
210C22×C4×C83C2413yes—
211C22×C4×C83C2413yes—
212C22×C4×C83C2411yescharacteristic
213C22×C4×C83C2413yes—
214C22×C4×C83C2411yescharacteristic
215C4⋊C4×C83—212no—
216C4⋊C4×C83—26no—
217C4⋊C4×C83C2×D4112yes—
218C42×C83—26no—
219C42×C83—26no—
220C42×C83—26no—
221C42×C83C2×D4112yes—
222C23×C83—21no—
223C23×C83—21no—
224C23×C83—21no—
225C23×C83—21no—
226C23×C83C23×C412yes—
227C23×C83C22×Q812yes—
228C23×C83C2×#4112yes—
229C23×C83C2511yescharacteristic
230C22×D83—21no—
231C22×D83—21no—
232C22×D83—21no—
233C22×D83—21no—
234C22×D83C23×C412yes—
235C22×D83C22×Q812yes—
236C22×D83C2×#4112yes—
237Q8×C83—224no—
238Q8×C83C4×D4116yescomplemented
239C2×C4×C83—21no—
240C2×C4×C83—23no—
241C2×C4×C83—23no—
242C2×C4×C83—23no—
243C2×C4×C83—21no—
244C2×C4×C83—23no—
245C2×C4×C83—224no—
246C2×C4×C83—28no—
247C2×C4×C83—23no—
248C2×C4×C83—23no—
249C2×C4×C83—23no—
250C2×C4×C83—412no—
251C2×C4×C83C23×C416yes—
252C2×C4×C83C23×C416yes—
253C2×C4×C83C22×D416yes—
254C2×C4×C83C22×D416yes—
255C2×C4×C83C22×D412yes—
256C2×C4×C83C22×Q812yes—
257C2×C4×C83C22×Q812yes—
258C2×C4×C83C2×#4116yes—
259C2×C4×C832−1+412yes—
260C22⋊D83C4×Q8116yesdirect product factor
261C2×Dic83—21no—
262C2×Dic83—23no—
263C2×Dic83—21no—
264C2×Dic83—23no—
265C2×Dic83—23no—
266C2×Dic83—21no—
267C2×Dic83—21no—
268C2×Dic83—23no—
269C2×Dic83—23no—
270C2×Dic83—23no—
271C2×Dic83—23no—
272C2×Dic83—23no—
273C2×Dic83—23no—
274C2×Dic83—23no—
275C2×Dic83C23×C416yes—
276C2×Dic83C23×C416yes—
277C2×Dic83C23×C412yes—
278C2×Dic83C22×Q812yes—
279C2×Dic83C22×Q812yes—
280C2×Dic83C22×Q812yes—
281C2×Dic83C2×#4112yes—
282C4×D83—224no—
283C4×D83—28no—
284C4×D83—412no—
285Dic166—224no—
286C22×C83—22no—
287C22×C83—22no—
288C22×C83—22no—
289C22×C83—22no—
290C22×C83—22no—
291C22×C83—22no—
292C22×C83C2×C4×Q814yescomplemented
293C22×C83C24×C411yescharacteristic
294C22×C83C23×D411yescharacteristic
295C22×C83C23×Q811yescharacteristic
296C22×C83C22×#4111yescharacteristic
297C22×C83C22×#4111yescharacteristic
298C22×C83C2×2−1+411yescharacteristic
299C22×C83#58511yescharacteristic
300C2×D83—22no—
301C2×D83—22no—
302C2×D83—22no—
303C2×D83—22no—
304C2×D83—22no—
305C2×D83—22no—
306C2×D83C2×C4×Q814yescomplemented
307C4×C83—26no—
308C4×C83—22no—
309C4×C83—26no—
310C4×C83—43no—
311C4×C83C2×C4×D4112yes—
312C4×C83D4×Q814yescomplemented
313Dic83—26no—
314Dic83—26no—
315Dic83—22no—
316Dic83—22no—
317Dic83—43no—
318Dic83—43no—
319Dic83C2×C4×Q814yescomplemented
320C4×D4×Q8—831nomaximal, Sylow
321C2×C83—24no—
322C2×C83C22×C4×D411yescharacteristic
323C2×C83C22×C4×Q811yescharacteristic
324C2×C83C4×2−1+411yescharacteristic
325C2×C83C2×D4×Q811yescharacteristic
326C2×C83D4×#4111yescharacteristic
327C2×C83Q8×#4111yescharacteristic
328C2×C83#348211yescharacteristic
329D83—24no—
330C2×D4×Q8—831no—
331C22×C4×Q8—831no—
332C22×C4×Q8D8311yescharacteristic, complemented
333#2365—833no—
334#2360—833no—
335#2360—833no—
336Q8×C4⋊C4—831no—
337D4×C4⋊C4—833no—
338Q8×C22⋊C4—831no—
339Q8×C22⋊C4—831no—
340C4×C4⋊Q8—833no—
341C4×C22⋊Q8—833no—
342C4×C22⋊Q8—833no—
343C42×Q8—831no—
344C42×D4—833no—
345C83C4×D4×Q811yescharacteristic, complemented, Sylow
346C23×Q8—831no—
347C23×Q8C2×D8311yescharacteristic
348D4×Q8—8316no—
349C2×C4⋊Q8—833no—
350C2×C22⋊Q8—833no—
351C2×C22⋊Q8—833no—
352C2×C4×Q8—28no—
353C2×C4×Q8—831no—
354C2×C4×Q8—831no—
355C2×C4×Q8—831no—
356C2×C4×Q8—833no—
357C2×C4×Q8—833no—
358C2×C4×Q8—1668no—
359C2×C4×Q8C2×D8313yes—
360C2×C4×Q8C2×D8311yescharacteristic
361C2×C4×Q8C2×D8313yes—
362C2×C4×Q8C2×D8311yescharacteristic
363C2×C4×D4—833no—
364C2×C4×D4—831no—
365C2×C4×D4—833no—
366C22×C4⋊C4—833no—
367C22×C4⋊C4C2×D8313yes—
368C22×C42—833no—
369C22×C42C2×D8313yes—
370#391—833no—
371#391—833no—
372#391—833no—
373#391—833no—
374#389—836no—
375#389—836no—
376#389—833no—
377#389—833no—
378#387—836no—
379#387—836no—
380#385—836no—
381#385—836no—
382#384—833no—
383#380—833no—
384#380—833no—
385C4×C4⋊C4—833no—
386C4×C4⋊C4—833no—
387C4×C4⋊C4—833no—
388C4×C4⋊C4—833no—
389C4×C4⋊C4—836no—
390C4×C4⋊C4—833no—
391C4×C4⋊C4—833no—
392C4×C22⋊C4—833no—
393C4×C22⋊C4—833no—
394C4×C22⋊C4—833no—
395C4×C22⋊C4—833no—
396C4×C22⋊C4—833no—
397C4×C22⋊C4—833no—
398C43—833no—
399C22×Q8—24no—
400C22×Q8—24no—
401C22×Q8—838no—
402C22×Q8—833no—
403C22×Q8—1664no—
404C22×Q8—1664no—
405C22×Q8C4×D8318yescomplemented
406C22×Q8C22×D8313yes—
407C22×Q8C22×D8311yescharacteristic
408C22×D4—831no—
409C23×C4—833no—
410C23×C4—833no—
411C23×C4—831no—
412C23×C4C22×D8313yes—
413C23×C4C22×D8313yes—
414C23×C4C22×D8311yescharacteristic
415C4⋊Q8—8324no—
416C22⋊Q8—8324no—
417C22⋊Q8—8324no—
418C4×Q8—24no—
419C4×Q8—212no—
420C4×Q8—212no—
421C4×Q8—838no—
422C4×Q8—1664no—
423C4×Q8—1664no—
424C4×Q8—16612no—
425C4×Q8—16612no—
426C4×Q8C22⋊D8318yesdirect product factor
427C4×D4—8324no—
428C4×D4—838no—
429C4×D4—16612no—
430C2×C4⋊C4—212no—
431C2×C4⋊C4—836no—
432C2×C4⋊C4—833no—
433C2×C4⋊C4—831no—
434C2×C4⋊C4—833no—
435C2×C4⋊C4—836no—
436C2×C4⋊C4—833no—
437C2×C4⋊C4—836no—
438C2×C4⋊C4—833no—
439C2×C4⋊C4—833no—
440C2×C4⋊C4—16612no—
441C2×C4⋊C4C22×D8313yes—
442C2×C4⋊C4C22×D8316yes—
443C2×C4⋊C4C22×D8313yes—
444C2×C22⋊C4—833no—
445C2×C22⋊C4—831no—
446C2×C22⋊C4—833no—
447C2×C22⋊C4—831no—
448C2×C22⋊C4—833no—
449C2×C22⋊C4—833no—
450C2×C42—212no—
451C2×C42—833no—
452C2×C42—833no—
453C2×C42—831no—
454C2×C42—833no—
455C2×C42—833no—
456C2×C42—833no—
457C2×C42—833no—
458C2×C42—833no—
459C2×C42—833no—
460C2×C42—16612no—
461C2×C42C22×D8313yes—
462C2×C42C22×D8313yes—
463C2×C42C22×D8313yes—
464C2×C42C22×D8313yes—
465#95—833no—
466#95—833no—
467#95—833no—
468#95—833no—
469#95—833no—
470#95—833no—
471#95—836no—
472#95—836no—
473#95—836no—
474C24—831no—
475C24C23×D8311yescharacteristic
476C2×Q8—232no—
477C2×Q8—26no—
478C2×Q8—26no—
479C2×Q8—8312no—
480C2×Q8—16632no—
481C2×Q8—1666no—
482C2×Q8—1666no—
483C2×Q8C2×C4×D83112yes—
484C2×Q8C2×C4×D8314yes—
485C2×Q8C2×C22⋊D8314yes—
486C2×Q8#1305059014yes—
487C2×D4—834no—
488C2×D4—834no—
489C2×D4—834no—
490C22×C4—22no—
491C22×C4—26no—
492C22×C4—26no—
493C22×C4—22no—
494C22×C4—26no—
495C22×C4—26no—
496C22×C4—43no—
497C22×C4—3323no—
498C22×C4—831no—
499C22×C4—831no—
500C22×C4—831no—
501C22×C4—833no—
502C22×C4—833no—
503C22×C4—8312no—
504C22×C4—834no—
505C22×C4—833no—
506C22×C4—833no—
507C22×C4—1666no—
508C22×C4—1666no—
509C22×C4—1662no—
510C22×C4—1666no—
511C22×C4—1666no—
512C22×C4—1662no—
513C22×C4C2×C4×D83112yes—
514C22×C4Q8×D8314yescomplemented
515C22×C4C23×D8313yes—
516C22×C4C23×D8313yes—
517C22×C4C23×D8313yes—
518C22×C4C23×D8311yescharacteristic
519C22×C4C23×D8313yes—
520C22×C4C23×D8311yescharacteristic
521C4⋊C4—212no—
522C4⋊C4—26no—
523C4⋊C4—3326no—
524C4⋊C4—8312no—
525C4⋊C4—8312no—
526C4⋊C4—8324no—
527C4⋊C4—834no—
528C4⋊C4—1666no—
529C4⋊C4—16612no—
530C4⋊C4—1666no—
531C4⋊C4—1666no—
532C4⋊C4C2×C22⋊D83112yes—
533C22⋊C4—8312no—
534C22⋊C4—834no—
535C22⋊C4—8312no—
536C22⋊C4—834no—
537C22⋊C4—1666no—
538C22⋊C4—1666no—
539C42—26no—
540C42—26no—
541C42—26no—
542C42—3323no—
543C42—8312no—
544C42—834no—
545C42—1666no—
546C42—1666no—
547C42—1666no—
548C42—1666no—
549C42—1666no—
550C42—1666no—
551C42C2×C22⋊D83112yes—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—832no—
557C23—832no—
558C23—832no—
559C23—1661no—
560C23—1661no—
561C23—1661no—
562C23—1661no—
563C23C22×C4×D8312yes—
564C23C2×Q8×D8312yes—
565C23#41×D8312yes—
566C23C24×D8311yescharacteristic
567Q8—224no—
568Q8—16624no—
569Q8C4×C22⋊D83116yesdirect product factor
570D4—8316no—
571C2×C4—21no—
572C2×C4—23no—
573C2×C4—23no—
574C2×C4—23no—
575C2×C4—21no—
576C2×C4—23no—
577C2×C4—28no—
578C2×C4—224no—
579C2×C4—23no—
580C2×C4—23no—
581C2×C4—23no—
582C2×C4—412no—
583C2×C4—33212no—
584C2×C4—832no—
585C2×C4—832no—
586C2×C4—832no—
587C2×C4—836no—
588C2×C4—836no—
589C2×C4—832no—
590C2×C4—832no—
591C2×C4—1663no—
592C2×C4—1663no—
593C2×C4—1663no—
594C2×C4—1663no—
595C2×C4—1663no—
596C2×C4—1663no—
597C2×C4—1661no—
598C2×C4—1663no—
599C2×C4—1661no—
600C2×C4—1663no—
601C2×C4—1663no—
602C2×C4—1661no—
603C2×C4—1661no—
604C2×C4—1663no—
605C2×C4—1668no—
606C2×C4—16624no—
607C2×C4C22×C4×D8316yes—
608C2×C4C22×C4×D8316yes—
609C2×C4C22×C22⋊D8316yes—
610C2×C4C22×C22⋊D8312yes—
611C2×C4C22×C22⋊D8316yes—
612C2×C4C2×Q8×D8312yes—
613C2×C4C2×Q8×D8312yes—
614C2×C4C2×#1305059016yes—
615C2×C4#1458184012yes—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—834no—
623C22—1662no—
624C22—1662no—
625C22—1662no—
626C22—1662no—
627C22—1662no—
628C22—1662no—
629C22C4×Q8×D8314yescomplemented
630C22C23×C4×D8311yescharacteristic
631C22C23×C22⋊D8311yescharacteristic
632C22C22×Q8×D8311yescharacteristic
633C22C2×#41×D8311yescharacteristic
634C22C22×#1305059011yescharacteristic
635C22C2×#1458184011yescharacteristic
636C22#1912853711yescharacteristic
637C4—26no—
638C4—22no—
639C4—26no—
640C4—43no—
641C4—3323no—
642C4—3323no—
643C4—834no—
644C4—1666no—
645C4—1666no—
646C4—1662no—
647C4—1662no—
648C4C2×C4×C22⋊D83112yes—
649C4Q8×C22⋊D8314yesdirect product factor
650C2—24no—
651C2—1664no—
652C2C22×C4×C22⋊D8311yescharacteristic
653C2C2×C4×Q8×D8311yescharacteristic
654C2C4×#1458184011yescharacteristic
655C2C2×Q8×C22⋊D8311yescharacteristic
656C2#41×C22⋊D8311yescharacteristic
657C2Q8×#1305059011yescharacteristic
658C2#2492108011yescharacteristic
subgroupG/H
centerC22×C4C23×D83
commutatorC22×C83C24×C4
FrattiniC23C24×D83
FittingC22×C4×Q8×C83C2
socle, cosocleC23×C83C25
prime radicalC22×C22⋊D83C23
hypercenterC22×C4×Q8D83
hypocenterC83C4×D4×Q8
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D83C2semidirect
3. #24910517C2semidirect
4. #24910468C2semidirect
5. #24910464C2semidirect
6. Q8×Dic83⋊C4C2semidirect
8. Q8×C22⋊Dic83C2semidirect
9. Q8×(C2×D83)⋊C4C2semidirect
10. C4×#14581790C2semidirect
11. C4×#14581771C2semidirect
12. C4×#14581768C2semidirect
13. C4×Q8×Dic83C2semidirect
15. C22×C4×Q8×C83C2semidirect
17. Q8×C22⋊D83C4direct (N × H)
72. C2×Q8×D83C2×C4semidirect
77. #14581790C2×C4semidirect
78. #14581771C2×C4semidirect
79. #14581768C2×C4semidirect
82. Q8×Dic83C2×C4semidirect
87. C4×C22⋊D83Q8direct (N × H)
125. C22×Q8×C83C2×C4semidirect
134. C4×Q8×C83D4semidirect
167. C2×C4×D83C2×Q8semidirect
176. Dic83⋊C4C2×Q8semidirect
179. C22⋊Dic83C2×Q8semidirect
182. (C2×D83)⋊C4C2×Q8semidirect
191. C4×Dic83C2×Q8semidirect
208. C22×C4×C83C2×Q8semidirect
238. Q8×C83C4×D4semidirect
260. C22⋊D83C4×Q8direct (N × H)
292. C22×C83C2×C4×Q8semidirect
306. C2×D83C2×C4×Q8semidirect
312. C4×C83D4×Q8semidirect
319. Dic83C2×C4×Q8semidirect
332. C22×C4×Q8D83semidirect
345. C83C4×D4×Q8semidirect
405. C22×Q8C4×D83semidirect
426. C4×Q8C22⋊D83direct (N × H)
514. C22×C4Q8×D83semidirect
569. Q8C4×C22⋊D83direct (N × H)
629. C22C4×Q8×D83semidirect
649. C4Q8×C22⋊D83direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D832
C2×C4×Q8×D832
#249105172
#249104682
#249104642
Q8×Dic83⋊C42
C4⋊C4×C22⋊D832
Q8×C22⋊Dic832
Q8×(C2×D83)⋊C42
C4×#145817902
C4×#145817712
C4×#145817682
C4×Q8×Dic832
C42×C22⋊D832
C22×C4×Q8×C832
C4×D4×Q883