Finite Group Databasebeta

← C4×Q8×C22⋊D71 #32157314

Subgroups — C4×Q8×C22⋊D71 #32157314

Order 18176.

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⋊D71C211yesmaximal, characteristic
2C2×C4×Q8×D71C211yesmaximal, characteristic, complemented
3#22591394C213yesmaximal, complemented
4#22591345C213yesmaximal, complemented
5#22591341C213yesmaximal, complemented
6Q8×Dic71⋊C4C211yesmaximal, characteristic, complemented
7C4⋊C4×C22⋊D71C213yesmaximal
8Q8×C22⋊Dic71C211yesmaximal, characteristic, complemented
9Q8×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
10C4×#14556126C213yesmaximal, complemented
11C4×#14556107C213yesmaximal, complemented
12C4×#14556104C213yesmaximal, complemented
13C4×Q8×Dic71C211yesmaximal, characteristic, complemented
14C42×C22⋊D71C213yesmaximal
15C22×C4×Q8×C71C211yesmaximal, characteristic, complemented
16C22×Q8×D71C2211yescharacteristic
17Q8×C22⋊D71C4116yesdirect product factor
18C2×#14556126C2213yes—
19C2×#14556107C2213yes—
20C2×#14556104C2213yes—
21C2×Q8×Dic71C2211yescharacteristic
22C2×Q8×Dic71C2211yescharacteristic
23C2×Q8×Dic71C2211yescharacteristic
24C2×C4×Dic142C2213yes—
25C2×#14556093C2213yes—
26C4×Q8×D71—28no—
27C2×C4×C22⋊D71C2213yes—
28C2×C4×C22⋊D71C2213yes—
29C2×C4×C22⋊D71C2211yescharacteristic
30C2×C4⋊C4×D71C2213yes—
31C2×C42×D71C2213yes—
32#17985906C2213yes—
33#17985906C2213yes—
34#17985905C2213yes—
35#17985904C2213yes—
36#17985897C2213yes—
37#17985895C2213yes—
38#17985894C2216yes—
39#17985894C2216yes—
40#17985883C2216yes—
41#17985880C2216yes—
42#17985872C2216yes—
43#17985870C2216yes—
44#17985868C2213yes—
45#17985859C2213yes—
46#17985856C2213yes—
47C4⋊C4×Dic71C2213yes—
48C4⋊C4×Dic71C2213yes—
49C4×Dic71⋊C4C2213yes—
50C4×Dic71⋊C4C2216yes—
51C4×Dic71⋊C4C2213yes—
52C4×Dic71⋊C4C2213yes—
53C4×C4⋊Dic71C2213yes—
54C4×(C2×D71)⋊C4C2213yes—
55C4×(C2×D71)⋊C4C2213yes—
56C4×(C2×D71)⋊C4C2213yes—
57C4×C22⋊Dic71C2213yes—
58C4×C22⋊Dic71C2213yes—
59C4×C22⋊Dic71C2213yes—
60C42×Dic71C2213yes—
61C23×Q8×C71C2211yescharacteristic
62C2×C4×Q8×C71—28no—
63C2×C4×Q8×C71C2211yescharacteristic
64C2×C4×Q8×C71C2213yes—
65C2×C4×Q8×C71C2213yes—
66C2×C4×Q8×C71C2211yescharacteristic
67C22×C4⋊C4×C71C2213yes—
68C22×C42×C71C2213yes—
69C22×Dic142C2313yes—
70C2×Q8×D71—24no—
71C2×Q8×D71—24no—
72C2×Q8×D71C2×C418yescomplemented
73C22×C22⋊D71C2311yescharacteristic
74C22×C4×D71C2313yes—
75C22×C4×D71C2313yes—
76C22×C4×D71C2311yescharacteristic
77#14556126C2×C4124yescomplemented
78#14556107C2×C4124yescomplemented
79#14556104C2×C4124yescomplemented
80Q8×Dic71—24no—
81Q8×Dic71—24no—
82Q8×Dic71C2×C418yescomplemented
83C4×Dic142—212no—
84#14556093—212no—
85C4×C22⋊D71—212no—
86C4×C22⋊D71C2×C4124yes—
87C4×C22⋊D71Q818yesdirect product factor
88C2×C4⋊Dic71C2313yes—
89C2×C4⋊Dic71C2313yes—
90C2×C4⋊Dic71C2313yes—
91C2×Dic71⋊C4C2313yes—
92C2×Dic71⋊C4C2316yes—
93C2×Dic71⋊C4C2316yes—
94C2×Dic71⋊C4C2313yes—
95C2×Dic71⋊C4C2316yes—
96C2×Dic71⋊C4C2311yescharacteristic
97C4⋊C4×D71—212no—
98C2×C22⋊Dic71C2313yes—
99C2×C22⋊Dic71C2313yes—
100C2×C22⋊Dic71C2311yescharacteristic
101C2×(C2×D71)⋊C4C2313yes—
102C2×(C2×D71)⋊C4C2313yes—
103C2×(C2×D71)⋊C4C2311yescharacteristic
104C2×C4×Dic71C2313yes—
105C2×C4×Dic71C2313yes—
106C2×C4×Dic71C2313yes—
107C2×C4×Dic71C2313yes—
108C2×C4×Dic71C2313yes—
109C2×C4×Dic71C2313yes—
110C2×C4×Dic71C2313yes—
111C2×C4×Dic71C2313yes—
112C2×C4×Dic71C2311yescharacteristic
113C42×D71—212no—
114C71⋊#95C2313yes—
115C71⋊#95C2313yes—
116C71⋊#95C2313yes—
117C71⋊#95C2313yes—
118C71⋊#95C2313yes—
119C71⋊#95C2313yes—
120C71⋊#95C2316yes—
121C71⋊#95C2316yes—
122C71⋊#95C2316yes—
123C22×Q8×C71—24no—
124C22×Q8×C71—24no—
125C22×Q8×C71C2×C418yescomplemented
126C22×Q8×C71C2313yes—
127C22×Q8×C71C2311yescharacteristic
128C23×C4×C71C2313yes—
129C23×C4×C71C2313yes—
130C23×C4×C71C2311yescharacteristic
131C4×Q8×C71—24no—
132C4×Q8×C71—212no—
133C4×Q8×C71—212no—
134C4×Q8×C71D418yescomplemented
135C2×C4⋊C4×C71—212no—
136C2×C4⋊C4×C71C2313yes—
137C2×C4⋊C4×C71C2316yes—
138C2×C4⋊C4×C71C2313yes—
139C2×C42×C71—212no—
140C2×C42×C71C2313yes—
141C2×C42×C71C2313yes—
142C2×C42×C71C2313yes—
143C2×C42×C71C2313yes—
144C23×D71C2411yescharacteristic
145C2×Dic142—26no—
146C2×Dic142—26no—
147C2×Dic142C22×C4112yes—
148Q8×D71—232no—
149C2×C22⋊D71C22×C414yes—
150C2×C22⋊D71C2×Q814yes—
151C2×C22⋊D71#4114yes—
152C22×Dic71C2413yes—
153C22×Dic71C2413yes—
154C22×Dic71C2413yes—
155C22×Dic71C2413yes—
156C22×Dic71C2411yescharacteristic
157C22×Dic71C2411yescharacteristic
158C22×Dic71C2411yescharacteristic
159C2×C4×D71—26no—
160C2×C4×D71—22no—
161C2×C4×D71—26no—
162C2×C4×D71—22no—
163C2×C4×D71—26no—
164C2×C4×D71—26no—
165C2×C4×D71—43no—
166C2×C4×D71C22×C4112yes—
167C2×C4×D71C2×Q814yescomplemented
168C4⋊Dic71—26no—
169C4⋊Dic71—26no—
170C4⋊Dic71C22×C4112yes—
171Dic71⋊C4—212no—
172Dic71⋊C4—26no—
173Dic71⋊C4—46no—
174Dic71⋊C4C22×C4112yes—
175Dic71⋊C4C22×C4124yes—
176Dic71⋊C4C2×Q814yescomplemented
177C22⋊Dic71—26no—
178C22⋊Dic71C22×C4112yes—
179C22⋊Dic71C2×Q814yescomplemented
180(C2×D71)⋊C4—26no—
181(C2×D71)⋊C4C22×C4112yes—
182(C2×D71)⋊C4C2×Q814yescomplemented
183C4×Dic71—26no—
184C4×Dic71—26no—
185C4×Dic71—26no—
186C4×Dic71—26no—
187C4×Dic71—26no—
188C4×Dic71—26no—
189C4×Dic71—43no—
190C4×Dic71C22×C4112yes—
191C4×Dic71C2×Q814yescomplemented
192C24×C71C2411yescharacteristic
193C2×Q8×C71—232no—
194C2×Q8×C71—26no—
195C2×Q8×C71—26no—
196C2×Q8×C71C22×C4112yes—
197C2×Q8×C71C22×C414yes—
198C2×Q8×C71C2×D414yes—
199C2×Q8×C71#4114yes—
200C22×C4×C71—22no—
201C22×C4×C71—26no—
202C22×C4×C71—26no—
203C22×C4×C71—22no—
204C22×C4×C71—26no—
205C22×C4×C71—26no—
206C22×C4×C71—43no—
207C22×C4×C71C22×C4112yes—
208C22×C4×C71C2×Q814yescomplemented
209C22×C4×C71C2413yes—
210C22×C4×C71C2413yes—
211C22×C4×C71C2413yes—
212C22×C4×C71C2411yescharacteristic
213C22×C4×C71C2413yes—
214C22×C4×C71C2411yescharacteristic
215C4⋊C4×C71—212no—
216C4⋊C4×C71—26no—
217C4⋊C4×C71C2×D4112yes—
218C42×C71—26no—
219C42×C71—26no—
220C42×C71—26no—
221C42×C71C2×D4112yes—
222C23×C71—21no—
223C23×C71—21no—
224C23×C71—21no—
225C23×C71—21no—
226C23×C71C23×C412yes—
227C23×C71C22×Q812yes—
228C23×C71C2×#4112yes—
229C23×C71C2511yescharacteristic
230C22×D71—21no—
231C22×D71—21no—
232C22×D71—21no—
233C22×D71—21no—
234C22×D71C23×C412yes—
235C22×D71C22×Q812yes—
236C22×D71C2×#4112yes—
237Q8×C71—224no—
238Q8×C71C4×D4116yescomplemented
239C2×C4×C71—21no—
240C2×C4×C71—23no—
241C2×C4×C71—23no—
242C2×C4×C71—23no—
243C2×C4×C71—21no—
244C2×C4×C71—23no—
245C2×C4×C71—224no—
246C2×C4×C71—28no—
247C2×C4×C71—23no—
248C2×C4×C71—23no—
249C2×C4×C71—23no—
250C2×C4×C71—412no—
251C2×C4×C71C23×C416yes—
252C2×C4×C71C23×C416yes—
253C2×C4×C71C22×D416yes—
254C2×C4×C71C22×D416yes—
255C2×C4×C71C22×D412yes—
256C2×C4×C71C22×Q812yes—
257C2×C4×C71C22×Q812yes—
258C2×C4×C71C2×#4116yes—
259C2×C4×C712−1+412yes—
260C22⋊D71C4×Q8116yesdirect product factor
261C2×Dic71—21no—
262C2×Dic71—23no—
263C2×Dic71—21no—
264C2×Dic71—23no—
265C2×Dic71—23no—
266C2×Dic71—21no—
267C2×Dic71—21no—
268C2×Dic71—23no—
269C2×Dic71—23no—
270C2×Dic71—23no—
271C2×Dic71—23no—
272C2×Dic71—23no—
273C2×Dic71—23no—
274C2×Dic71—23no—
275C2×Dic71C23×C416yes—
276C2×Dic71C23×C416yes—
277C2×Dic71C23×C412yes—
278C2×Dic71C22×Q812yes—
279C2×Dic71C22×Q812yes—
280C2×Dic71C22×Q812yes—
281C2×Dic71C2×#4112yes—
282C4×D71—224no—
283C4×D71—28no—
284C4×D71—412no—
285Dic142—224no—
286C22×C71—22no—
287C22×C71—22no—
288C22×C71—22no—
289C22×C71—22no—
290C22×C71—22no—
291C22×C71—22no—
292C22×C71C2×C4×Q814yescomplemented
293C22×C71C24×C411yescharacteristic
294C22×C71C23×D411yescharacteristic
295C22×C71C23×Q811yescharacteristic
296C22×C71C22×#4111yescharacteristic
297C22×C71C22×#4111yescharacteristic
298C22×C71C2×2−1+411yescharacteristic
299C22×C71#58511yescharacteristic
300C2×D71—22no—
301C2×D71—22no—
302C2×D71—22no—
303C2×D71—22no—
304C2×D71—22no—
305C2×D71—22no—
306C2×D71C2×C4×Q814yescomplemented
307C4×C71—26no—
308C4×C71—22no—
309C4×C71—26no—
310C4×C71—43no—
311C4×C71C2×C4×D4112yes—
312C4×C71D4×Q814yescomplemented
313Dic71—26no—
314Dic71—26no—
315Dic71—22no—
316Dic71—22no—
317Dic71—43no—
318Dic71—43no—
319Dic71C2×C4×Q814yescomplemented
320C4×D4×Q8—711nomaximal, Sylow
321C2×C71—24no—
322C2×C71C22×C4×D411yescharacteristic
323C2×C71C22×C4×Q811yescharacteristic
324C2×C71C4×2−1+411yescharacteristic
325C2×C71C2×D4×Q811yescharacteristic
326C2×C71D4×#4111yescharacteristic
327C2×C71Q8×#4111yescharacteristic
328C2×C71#348211yescharacteristic
329D71—24no—
330C2×D4×Q8—711no—
331C22×C4×Q8—711no—
332C22×C4×Q8D7111yescharacteristic, complemented
333#2365—713no—
334#2360—713no—
335#2360—713no—
336Q8×C4⋊C4—711no—
337D4×C4⋊C4—713no—
338Q8×C22⋊C4—711no—
339Q8×C22⋊C4—711no—
340C4×C4⋊Q8—713no—
341C4×C22⋊Q8—713no—
342C4×C22⋊Q8—713no—
343C42×Q8—711no—
344C42×D4—713no—
345C71C4×D4×Q811yescharacteristic, complemented, Sylow
346C23×Q8—711no—
347C23×Q8C2×D7111yescharacteristic
348D4×Q8—7116no—
349C2×C4⋊Q8—713no—
350C2×C22⋊Q8—713no—
351C2×C22⋊Q8—713no—
352C2×C4×Q8—28no—
353C2×C4×Q8—711no—
354C2×C4×Q8—711no—
355C2×C4×Q8—711no—
356C2×C4×Q8—713no—
357C2×C4×Q8—713no—
358C2×C4×Q8—1428no—
359C2×C4×Q8C2×D7113yes—
360C2×C4×Q8C2×D7111yescharacteristic
361C2×C4×Q8C2×D7113yes—
362C2×C4×Q8C2×D7111yescharacteristic
363C2×C4×D4—713no—
364C2×C4×D4—711no—
365C2×C4×D4—713no—
366C22×C4⋊C4—713no—
367C22×C4⋊C4C2×D7113yes—
368C22×C42—713no—
369C22×C42C2×D7113yes—
370#391—713no—
371#391—713no—
372#391—713no—
373#391—713no—
374#389—716no—
375#389—716no—
376#389—713no—
377#389—713no—
378#387—716no—
379#387—716no—
380#385—716no—
381#385—716no—
382#384—713no—
383#380—713no—
384#380—713no—
385C4×C4⋊C4—713no—
386C4×C4⋊C4—713no—
387C4×C4⋊C4—713no—
388C4×C4⋊C4—716no—
389C4×C4⋊C4—713no—
390C4×C4⋊C4—713no—
391C4×C4⋊C4—713no—
392C4×C22⋊C4—713no—
393C4×C22⋊C4—713no—
394C4×C22⋊C4—713no—
395C4×C22⋊C4—713no—
396C4×C22⋊C4—713no—
397C4×C22⋊C4—713no—
398C43—713no—
399C22×Q8—24no—
400C22×Q8—24no—
401C22×Q8—718no—
402C22×Q8—713no—
403C22×Q8—1424no—
404C22×Q8—1424no—
405C22×Q8C4×D7118yescomplemented
406C22×Q8C22×D7113yes—
407C22×Q8C22×D7111yescharacteristic
408C22×D4—711no—
409C23×C4—713no—
410C23×C4—713no—
411C23×C4—711no—
412C23×C4C22×D7113yes—
413C23×C4C22×D7113yes—
414C23×C4C22×D7111yescharacteristic
415C4⋊Q8—7124no—
416C22⋊Q8—7124no—
417C22⋊Q8—7124no—
418C4×Q8—24no—
419C4×Q8—212no—
420C4×Q8—212no—
421C4×Q8—718no—
422C4×Q8—1424no—
423C4×Q8—1424no—
424C4×Q8—14212no—
425C4×Q8—14212no—
426C4×Q8C22⋊D7118yesdirect product factor
427C4×D4—7124no—
428C4×D4—718no—
429C4×D4—14212no—
430C2×C4⋊C4—212no—
431C2×C4⋊C4—716no—
432C2×C4⋊C4—713no—
433C2×C4⋊C4—711no—
434C2×C4⋊C4—713no—
435C2×C4⋊C4—716no—
436C2×C4⋊C4—713no—
437C2×C4⋊C4—716no—
438C2×C4⋊C4—713no—
439C2×C4⋊C4—713no—
440C2×C4⋊C4—14212no—
441C2×C4⋊C4C22×D7113yes—
442C2×C4⋊C4C22×D7116yes—
443C2×C4⋊C4C22×D7113yes—
444C2×C22⋊C4—713no—
445C2×C22⋊C4—711no—
446C2×C22⋊C4—713no—
447C2×C22⋊C4—711no—
448C2×C22⋊C4—713no—
449C2×C22⋊C4—713no—
450C2×C42—212no—
451C2×C42—713no—
452C2×C42—713no—
453C2×C42—711no—
454C2×C42—713no—
455C2×C42—713no—
456C2×C42—713no—
457C2×C42—713no—
458C2×C42—713no—
459C2×C42—713no—
460C2×C42—14212no—
461C2×C42C22×D7113yes—
462C2×C42C22×D7113yes—
463C2×C42C22×D7113yes—
464C2×C42C22×D7113yes—
465#95—713no—
466#95—713no—
467#95—713no—
468#95—713no—
469#95—713no—
470#95—713no—
471#95—716no—
472#95—716no—
473#95—716no—
474C24—711no—
475C24C23×D7111yescharacteristic
476C2×Q8—232no—
477C2×Q8—26no—
478C2×Q8—26no—
479C2×Q8—7112no—
480C2×Q8—14232no—
481C2×Q8—1426no—
482C2×Q8—1426no—
483C2×Q8C2×C4×D71112yes—
484C2×Q8C2×C4×D7114yes—
485C2×Q8C2×C22⋊D7114yes—
486C2×Q8#1176586514yes—
487C2×D4—714no—
488C2×D4—714no—
489C2×D4—714no—
490C22×C4—22no—
491C22×C4—26no—
492C22×C4—26no—
493C22×C4—22no—
494C22×C4—26no—
495C22×C4—26no—
496C22×C4—43no—
497C22×C4—2843no—
498C22×C4—711no—
499C22×C4—711no—
500C22×C4—711no—
501C22×C4—713no—
502C22×C4—713no—
503C22×C4—7112no—
504C22×C4—714no—
505C22×C4—713no—
506C22×C4—713no—
507C22×C4—1426no—
508C22×C4—1426no—
509C22×C4—1422no—
510C22×C4—1426no—
511C22×C4—1426no—
512C22×C4—1422no—
513C22×C4C2×C4×D71112yes—
514C22×C4Q8×D7114yescomplemented
515C22×C4C23×D7113yes—
516C22×C4C23×D7113yes—
517C22×C4C23×D7113yes—
518C22×C4C23×D7111yescharacteristic
519C22×C4C23×D7113yes—
520C22×C4C23×D7111yescharacteristic
521C4⋊C4—212no—
522C4⋊C4—26no—
523C4⋊C4—2846no—
524C4⋊C4—7112no—
525C4⋊C4—7124no—
526C4⋊C4—7112no—
527C4⋊C4—714no—
528C4⋊C4—1426no—
529C4⋊C4—14212no—
530C4⋊C4—1426no—
531C4⋊C4—1426no—
532C4⋊C4C2×C22⋊D71112yes—
533C22⋊C4—7112no—
534C22⋊C4—714no—
535C22⋊C4—7112no—
536C22⋊C4—714no—
537C22⋊C4—1426no—
538C22⋊C4—1426no—
539C42—26no—
540C42—26no—
541C42—26no—
542C42—2843no—
543C42—7112no—
544C42—714no—
545C42—1426no—
546C42—1426no—
547C42—1426no—
548C42—1426no—
549C42—1426no—
550C42—1426no—
551C42C2×C22⋊D71112yes—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—712no—
557C23—712no—
558C23—712no—
559C23—1421no—
560C23—1421no—
561C23—1421no—
562C23—1421no—
563C23C22×C4×D7112yes—
564C23C2×Q8×D7112yes—
565C23#41×D7112yes—
566C23C24×D7111yescharacteristic
567Q8—224no—
568Q8—14224no—
569Q8C4×C22⋊D71116yesdirect product factor
570D4—7116no—
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—28412no—
584C2×C4—712no—
585C2×C4—712no—
586C2×C4—712no—
587C2×C4—716no—
588C2×C4—716no—
589C2×C4—712no—
590C2×C4—712no—
591C2×C4—1423no—
592C2×C4—1423no—
593C2×C4—1423no—
594C2×C4—1423no—
595C2×C4—1423no—
596C2×C4—1423no—
597C2×C4—1421no—
598C2×C4—1423no—
599C2×C4—1421no—
600C2×C4—1423no—
601C2×C4—1423no—
602C2×C4—1421no—
603C2×C4—1421no—
604C2×C4—1423no—
605C2×C4—1428no—
606C2×C4—14224no—
607C2×C4C22×C4×D7116yes—
608C2×C4C22×C4×D7116yes—
609C2×C4C22×C22⋊D7116yes—
610C2×C4C22×C22⋊D7112yes—
611C2×C4C22×C22⋊D7116yes—
612C2×C4C2×Q8×D7112yes—
613C2×C4C2×Q8×D7112yes—
614C2×C4C2×#1176586516yes—
615C2×C4#1455617612yes—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—714no—
623C22—1422no—
624C22—1422no—
625C22—1422no—
626C22—1422no—
627C22—1422no—
628C22—1422no—
629C22C4×Q8×D7114yescomplemented
630C22C23×C4×D7111yescharacteristic
631C22C23×C22⋊D7111yescharacteristic
632C22C22×Q8×D7111yescharacteristic
633C22C2×#41×D7111yescharacteristic
634C22C22×#1176586511yescharacteristic
635C22C2×#1455617611yescharacteristic
636C22#1798683511yescharacteristic
637C4—26no—
638C4—22no—
639C4—26no—
640C4—43no—
641C4—2843no—
642C4—2843no—
643C4—714no—
644C4—1426no—
645C4—1426no—
646C4—1422no—
647C4—1422no—
648C4C2×C4×C22⋊D71112yes—
649C4Q8×C22⋊D7114yesdirect product factor
650C2—24no—
651C2—1424no—
652C2C22×C4×C22⋊D7111yescharacteristic
653C2C2×C4×Q8×D7111yescharacteristic
654C2C4×#1455617611yescharacteristic
655C2C2×Q8×C22⋊D7111yescharacteristic
656C2#41×C22⋊D7111yescharacteristic
657C2Q8×#1176586511yescharacteristic
658C2#2260195711yescharacteristic
subgroupG/H
centerC22×C4C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC22×C4×Q8×C71C2
socle, cosocleC23×C71C25
prime radicalC22×C22⋊D71C23
hypercenterC22×C4×Q8D71
hypocenterC71C4×D4×Q8
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D71C2semidirect
3. #22591394C2semidirect
4. #22591345C2semidirect
5. #22591341C2semidirect
6. Q8×Dic71⋊C4C2semidirect
8. Q8×C22⋊Dic71C2semidirect
9. Q8×(C2×D71)⋊C4C2semidirect
10. C4×#14556126C2semidirect
11. C4×#14556107C2semidirect
12. C4×#14556104C2semidirect
13. C4×Q8×Dic71C2semidirect
15. C22×C4×Q8×C71C2semidirect
17. Q8×C22⋊D71C4direct (N × H)
72. C2×Q8×D71C2×C4semidirect
77. #14556126C2×C4semidirect
78. #14556107C2×C4semidirect
79. #14556104C2×C4semidirect
82. Q8×Dic71C2×C4semidirect
87. C4×C22⋊D71Q8direct (N × H)
125. C22×Q8×C71C2×C4semidirect
134. C4×Q8×C71D4semidirect
167. C2×C4×D71C2×Q8semidirect
176. Dic71⋊C4C2×Q8semidirect
179. C22⋊Dic71C2×Q8semidirect
182. (C2×D71)⋊C4C2×Q8semidirect
191. C4×Dic71C2×Q8semidirect
208. C22×C4×C71C2×Q8semidirect
238. Q8×C71C4×D4semidirect
260. C22⋊D71C4×Q8direct (N × H)
292. C22×C71C2×C4×Q8semidirect
306. C2×D71C2×C4×Q8semidirect
312. C4×C71D4×Q8semidirect
319. Dic71C2×C4×Q8semidirect
332. C22×C4×Q8D71semidirect
345. C71C4×D4×Q8semidirect
405. C22×Q8C4×D71semidirect
426. C4×Q8C22⋊D71direct (N × H)
514. C22×C4Q8×D71semidirect
569. Q8C4×C22⋊D71direct (N × H)
629. C22C4×Q8×D71semidirect
649. C4Q8×C22⋊D71direct (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⋊D712
C2×C4×Q8×D712
#225913942
#225913452
#225913412
Q8×Dic71⋊C42
C4⋊C4×C22⋊D712
Q8×C22⋊Dic712
Q8×(C2×D71)⋊C42
C4×#145561262
C4×#145561072
C4×#145561042
C4×Q8×Dic712
C42×C22⋊D712
C22×C4×Q8×C712
C4×D4×Q871