Finite Group Databasebeta

← Q8×(C22⋊D71)⋊C4 #32157311

Subgroups — Q8×(C22⋊D71)⋊C4 #32157311

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
2C22×Q8×Dic71C211yesmaximal, characteristic, complemented
3C2×C4×Q8×D71C211yesmaximal, characteristic, complemented
4#22591397C213yesmaximal, complemented
5#22591350C213yesmaximal, complemented
6#22591343C213yesmaximal, complemented
7Q8×Dic71⋊C4C211yesmaximal, characteristic, complemented
8#22591236C213yesmaximal
9Q8×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
10#22590909C213yesmaximal, complemented
11#22590878C213yesmaximal, complemented
12#22590868C213yesmaximal, complemented
13C4×Q8×Dic71C211yesmaximal, characteristic, complemented
14C4×(C22⋊D71)⋊C4C213yesmaximal
15Q8×C22⋊C4×C71C211yesmaximal, characteristic, complemented
16C22×Q8×D71C2211yescharacteristic
17Q8×C22⋊D71C4116yescomplemented
18C2×#14556126C2213yes—
19C2×#14556107C2213yes—
20C2×#14556104C2213yes—
21C2×Q8×Dic71—28no—
22C2×Q8×Dic71C2211yescharacteristic
23C2×Q8×Dic71C2213yes—
24C2×Q8×Dic71C2213yes—
25C2×Q8×Dic71C2211yescharacteristic
26C2×Q8×Dic71C2211yescharacteristic
27C2×C4×Dic142C2213yes—
28C2×#14556093C2213yes—
29C4×Q8×D71—28no—
30C2×C4×C22⋊D71C2213yes—
31C2×(C22⋊D71)⋊C4C2213yes—
32C2×(C22⋊D71)⋊C4C2211yescharacteristic
33C22×C4⋊Dic71C2213yes—
34C2×C4⋊C4×D71C2213yes—
35C22×C4×Dic71C2213yes—
36C2×C42×D71C2213yes—
37#17985905C2213yes—
38#17985904C2213yes—
39#17985897C2213yes—
40#17985896C2216yes—
41#17985896C2216yes—
42#17985895C2213yes—
43#17985886C2216yes—
44#17985881C2216yes—
45#17985873C2216yes—
46#17985871C2216yes—
47#17985868C2213yes—
48#17985856C2213yes—
49C4⋊C4×Dic71C2213yes—
50C4⋊C4×Dic71C2213yes—
51C4×Dic71⋊C4C2213yes—
52C4×C4⋊Dic71C2213yes—
53#17985850C2216yes—
54#17985850C2213yes—
55#17985850C2213yes—
56C22⋊C4×Dic71C2213yes—
57C22⋊C4×Dic71C2213yes—
58C4×(C2×D71)⋊C4C2213yes—
59#17985846C2213yes—
60#17985846C2213yes—
61C42×Dic71C2213yes—
62C23×Q8×C71C2211yescharacteristic
63C2×C4×Q8×C71C2211yescharacteristic
64C2×C4×Q8×C71C2211yescharacteristic
65#391×C71C2213yes—
66#391×C71C2213yes—
67#380×C71C2213yes—
68C4×C22⋊C4×C71C2213yes—
69C22×Dic142C2313yes—
70C2×Q8×D71—24no—
71C2×Q8×D71—24no—
72C2×Q8×D71C2×C418yescomplemented
73C22×C22⋊D71C2311yescharacteristic
74C23×Dic71C2313yes—
75C23×Dic71C2311yescharacteristic
76C22×C4×D71C2313yes—
77C22×C4×D71C2313yes—
78C22×C4×D71C2311yescharacteristic
79#14556126C2×C4124yescomplemented
80#14556107C2×C4124yescomplemented
81#14556104C2×C4124yescomplemented
82Q8×Dic71—212no—
83Q8×Dic71—212no—
84Q8×Dic71—24no—
85Q8×Dic71C2×C418yescomplemented
86Q8×Dic71D418yescomplemented
87C4×Dic142—212no—
88#14556093—212no—
89C4×C22⋊D71C2×C4124yes—
90(C22⋊D71)⋊C4—212no—
91(C22⋊D71)⋊C4Q818yesdirect product factor
92C2×C4⋊Dic71—212no—
93C2×C4⋊Dic71C2313yes—
94C2×C4⋊Dic71C2316yes—
95C2×C4⋊Dic71C2313yes—
96C2×C4⋊Dic71C2313yes—
97C2×Dic71⋊C4C2313yes—
98C2×Dic71⋊C4C2316yes—
99C2×Dic71⋊C4C2316yes—
100C2×Dic71⋊C4C2313yes—
101C2×Dic71⋊C4C2316yes—
102C2×Dic71⋊C4C2311yescharacteristic
103C4⋊C4×D71—212no—
104C2×C22⋊Dic71C2313yes—
105C2×(C2×D71)⋊C4C2313yes—
106C2×(C2×D71)⋊C4C2313yes—
107C2×(C2×D71)⋊C4C2311yescharacteristic
108C2×C4×Dic71—212no—
109C2×C4×Dic71C2313yes—
110C2×C4×Dic71C2313yes—
111C2×C4×Dic71C2313yes—
112C2×C4×Dic71C2313yes—
113C2×C4×Dic71C2313yes—
114C2×C4×Dic71C2313yes—
115C2×C4×Dic71C2313yes—
116C2×C4×Dic71C2313yes—
117C2×C4×Dic71C2313yes—
118C2×C4×Dic71C2313yes—
119C2×C4×Dic71C2311yescharacteristic
120C42×D71—212no—
121C71⋊#95C2313yes—
122C71⋊#95C2313yes—
123C71⋊#95C2313yes—
124C71⋊#95C2313yes—
125C71⋊#95C2316yes—
126C71⋊#95C2316yes—
127C22×Q8×C71—24no—
128C22×Q8×C71—24no—
129C22×Q8×C71C2×C418yescomplemented
130C22×Q8×C71C2313yes—
131C22×Q8×C71C2311yescharacteristic
132C23×C4×C71C2313yes—
133C4×Q8×C71—24no—
134C4×Q8×C71—24no—
135C2×C4⋊C4×C71C2313yes—
136C2×C4⋊C4×C71C2313yes—
137C2×C22⋊C4×C71C2313yes—
138C2×C22⋊C4×C71C2311yescharacteristic
139C2×C42×C71C2313yes—
140C2×C42×C71C2313yes—
141#95×C71C2313yes—
142#95×C71C2313yes—
143#95×C71C2316yes—
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×Dic71—22no—
153C22×Dic71—22no—
154C22×Dic71—26no—
155C22×Dic71—26no—
156C22×Dic71—43no—
157C22×Dic71C2×Q814yescomplemented
158C22×Dic71C2413yes—
159C22×Dic71C2413yes—
160C22×Dic71C2413yes—
161C22×Dic71C2413yes—
162C22×Dic71C2411yescharacteristic
163C22×Dic71C2411yescharacteristic
164C22×Dic71C2411yescharacteristic
165C2×C4×D71—26no—
166C2×C4×D71—26no—
167C2×C4×D71—22no—
168C2×C4×D71—22no—
169C2×C4×D71—26no—
170C2×C4×D71—26no—
171C2×C4×D71—43no—
172C2×C4×D71C22×C4112yes—
173C2×C4×D71C2×Q814yescomplemented
174C4⋊Dic71—26no—
175C4⋊Dic71—212no—
176C4⋊Dic71C22×C4112yes—
177C4⋊Dic71C2×D4112yes—
178Dic71⋊C4—212no—
179Dic71⋊C4—26no—
180Dic71⋊C4—46no—
181Dic71⋊C4C22×C4112yes—
182Dic71⋊C4C22×C4124yes—
183Dic71⋊C4C2×Q814yescomplemented
184C22⋊Dic71C22×C4112yes—
185(C2×D71)⋊C4—26no—
186(C2×D71)⋊C4C22×C4112yes—
187(C2×D71)⋊C4C2×Q814yescomplemented
188C4×Dic71—26no—
189C4×Dic71—26no—
190C4×Dic71—26no—
191C4×Dic71—26no—
192C4×Dic71—26no—
193C4×Dic71—26no—
194C4×Dic71—26no—
195C4×Dic71—43no—
196C4×Dic71C22×C4112yes—
197C4×Dic71C2×D4112yes—
198C4×Dic71C2×Q814yescomplemented
199C24×C71C2411yescharacteristic
200C2×Q8×C71—232no—
201C2×Q8×C71—26no—
202C2×Q8×C71—26no—
203C2×Q8×C71C22×C4112yes—
204C2×Q8×C71C22×C414yes—
205C2×Q8×C71C2×D414yes—
206C2×Q8×C71#4114yes—
207C22×C4×C71—26no—
208C22×C4×C71—26no—
209C22×C4×C71C22×C4112yes—
210C22×C4×C71C2413yes—
211C22×C4×C71C2413yes—
212C22×C4×C71C2413yes—
213C22×C4×C71C2411yescharacteristic
214C22×C4×C71C2411yescharacteristic
215C22×C4×C71C2413yes—
216C4⋊C4×C71—26no—
217C4⋊C4×C71—26no—
218C22⋊C4×C71—26no—
219C22⋊C4×C71C2×Q814yescomplemented
220C42×C71—26no—
221C42×C71—26no—
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—21no—
242C2×C4×C71—23no—
243C2×C4×C71—21no—
244C2×C4×C71—21no—
245C2×C4×C71—224no—
246C2×C4×C71—23no—
247C2×C4×C71—23no—
248C2×C4×C71—23no—
249C2×C4×C71—23no—
250C2×C4×C71—23no—
251C2×C4×C71—23no—
252C2×C4×C71C23×C416yes—
253C2×C4×C71C23×C416yes—
254C2×C4×C71C22×D416yes—
255C2×C4×C71C22×Q812yes—
256C2×C4×C71C22×Q812yes—
257C2×C4×C71C2×#4116yes—
258C22⋊D71C4×Q8116yescomplemented
259C2×Dic71—21no—
260C2×Dic71—23no—
261C2×Dic71—23no—
262C2×Dic71—23no—
263C2×Dic71—23no—
264C2×Dic71—21no—
265C2×Dic71—23no—
266C2×Dic71—23no—
267C2×Dic71—28no—
268C2×Dic71—23no—
269C2×Dic71—23no—
270C2×Dic71—23no—
271C2×Dic71—412no—
272C2×Dic71C23×C416yes—
273C2×Dic71C23×C416yes—
274C2×Dic71C23×C412yes—
275C2×Dic71C22×D416yes—
276C2×Dic71C22×D412yes—
277C2×Dic71C22×Q812yes—
278C2×Dic71C22×Q812yes—
279C2×Dic71C22×Q812yes—
280C2×Dic71C2×#4112yes—
281C2×Dic712−1+412yes—
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—22no—
310C4×C71—43no—
311C4×C71—43no—
312C4×C71C2×C4×D4112yes—
313Dic71—26no—
314Dic71—26no—
315Dic71—22no—
316Dic71—26no—
317Dic71—43no—
318Dic71C2×C4×Q814yescomplemented
319Dic71D4×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×Q8—711no—
333#2365—713no—
334#2360—713no—
335#2360—713no—
336Q8×C4⋊C4—711no—
337D4×C4⋊C4—713no—
338Q8×C22⋊C4—711no—
339Q8×C22⋊C4D7111yescharacteristic, complemented
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—711no—
353C2×C4×Q8—711no—
354C2×C4×Q8—713no—
355C2×C4×Q8—711no—
356C2×C4×Q8—713no—
357C2×C4×Q8—713no—
358C2×C4×Q8—713no—
359C2×C4×Q8—1428no—
360C2×C4×Q8—1428no—
361C2×C4×Q8C2×D7111yescharacteristic
362C2×C4×Q8C2×D7111yescharacteristic
363C2×C4×D4—713no—
364C2×C4×D4—711no—
365C2×C4×D4—713no—
366C22×C4⋊C4—713no—
367C22×C4⋊C4—713no—
368C22×C42—713no—
369C22×C42—713no—
370#391—713no—
371#391—713no—
372#391C2×D7113yes—
373#391C2×D7113yes—
374#389—713no—
375#389—713no—
376#389—716no—
377#389—716no—
378#387—716no—
379#387—716no—
380#385—716no—
381#385—716no—
382#384—713no—
383#380—713no—
384#380C2×D7113yes—
385C4×C4⋊C4—713no—
386C4×C4⋊C4—713no—
387C4×C4⋊C4—713no—
388C4×C4⋊C4—713no—
389C4×C4⋊C4—713no—
390C4×C4⋊C4—716no—
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⋊C4C2×D7113yes—
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×C4—713no—
413C23×C4—711no—
414C23×C4C22×D7113yes—
415C4⋊Q8—7124no—
416C22⋊Q8—7124no—
417C22⋊Q8—7124no—
418C4×Q8—24no—
419C4×Q8—24no—
420C4×Q8—718no—
421C4×Q8—718no—
422C4×Q8—14212no—
423C4×Q8—14212no—
424C4×Q8—14212no—
425C4×Q8—14212no—
426C4×Q8—1424no—
427C4×D4—7124no—
428C4×D4—718no—
429C4×D4—14212no—
430C2×C4⋊C4—716no—
431C2×C4⋊C4—713no—
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—716no—
439C2×C4⋊C4—713no—
440C2×C4⋊C4—14212no—
441C2×C4⋊C4—14212no—
442C2×C4⋊C4C22×D7113yes—
443C2×C4⋊C4C22×D7113yes—
444C2×C22⋊C4—713no—
445C2×C22⋊C4—713no—
446C2×C22⋊C4—711no—
447C2×C22⋊C4—713no—
448C2×C22⋊C4C22×D7113yes—
449C2×C22⋊C4C22×D7111yescharacteristic
450C2×C42—713no—
451C2×C42—713no—
452C2×C42—711no—
453C2×C42—713no—
454C2×C42—713no—
455C2×C42—713no—
456C2×C42—713no—
457C2×C42—713no—
458C2×C42—713no—
459C2×C42—713no—
460C2×C42—713no—
461C2×C42—14212no—
462C2×C42—14212no—
463C2×C42C22×D7113yes—
464C2×C42C22×D7113yes—
465#95—713no—
466#95—713no—
467#95—713no—
468#95—713no—
469#95—716no—
470#95—716no—
471#95C22×D7113yes—
472#95C22×D7113yes—
473#95C22×D7116yes—
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×Q8D4×D7114yes—
486C2×Q8#1176586414yes—
487C2×D4—714no—
488C2×D4—714no—
489C2×D4—714no—
490C22×C4—26no—
491C22×C4—26no—
492C22×C4—2843no—
493C22×C4—2843no—
494C22×C4—711no—
495C22×C4—711no—
496C22×C4—714no—
497C22×C4—711no—
498C22×C4—713no—
499C22×C4—713no—
500C22×C4—713no—
501C22×C4—7112no—
502C22×C4—714no—
503C22×C4—713no—
504C22×C4—1426no—
505C22×C4—1426no—
506C22×C4—1422no—
507C22×C4—1422no—
508C22×C4—1426no—
509C22×C4—1426no—
510C22×C4—1422no—
511C22×C4—1422no—
512C22×C4—1426no—
513C22×C4—1426no—
514C22×C4C2×C4×D71112yes—
515C22×C4C23×D7113yes—
516C22×C4C23×D7113yes—
517C22×C4C23×D7113yes—
518C22×C4C23×D7111yescharacteristic
519C22×C4C23×D7111yescharacteristic
520C22×C4C23×D7113yes—
521C4⋊C4—26no—
522C4⋊C4—26no—
523C4⋊C4—2846no—
524C4⋊C4—7112no—
525C4⋊C4—7124no—
526C4⋊C4—7112no—
527C4⋊C4—7112no—
528C4⋊C4—714no—
529C4⋊C4—14212no—
530C4⋊C4—1426no—
531C4⋊C4—14212no—
532C4⋊C4—1426no—
533C22⋊C4—26no—
534C22⋊C4—7112no—
535C22⋊C4—7112no—
536C22⋊C4—714no—
537C22⋊C4—1426no—
538C22⋊C4Q8×D7114yescomplemented
539C42—26no—
540C42—26no—
541C42—2843no—
542C42—7112no—
543C42—7112no—
544C42—714no—
545C42—1426no—
546C42—1426no—
547C42—1426no—
548C42—1426no—
549C42—1426no—
550C42—1426no—
551C42—1426no—
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—
569Q8(C22⋊D71)⋊C4116yesdirect product factor
570D4—7116no—
571C2×C4—21no—
572C2×C4—23no—
573C2×C4—21no—
574C2×C4—23no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—224no—
578C2×C4—23no—
579C2×C4—23no—
580C2×C4—23no—
581C2×C4—23no—
582C2×C4—23no—
583C2×C4—23no—
584C2×C4—28412no—
585C2×C4—28412no—
586C2×C4—712no—
587C2×C4—712no—
588C2×C4—712no—
589C2×C4—712no—
590C2×C4—712no—
591C2×C4—712no—
592C2×C4—716no—
593C2×C4—716no—
594C2×C4—716no—
595C2×C4—712no—
596C2×C4—1428no—
597C2×C4—1423no—
598C2×C4—1423no—
599C2×C4—1423no—
600C2×C4—1428no—
601C2×C4—1421no—
602C2×C4—1423no—
603C2×C4—1423no—
604C2×C4—1423no—
605C2×C4—1423no—
606C2×C4—1421no—
607C2×C4—1423no—
608C2×C4—1423no—
609C2×C4—14224no—
610C2×C4C22×C4×D7116yes—
611C2×C4C22×C4×D7116yes—
612C2×C4C2×D4×D7116yes—
613C2×C4C2×Q8×D7112yes—
614C2×C4C2×Q8×D7112yes—
615C2×C4C2×#1176586416yes—
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
631C22C22×D4×D7111yescharacteristic
632C22C22×Q8×D7111yescharacteristic
633C22C2×#41×D7111yescharacteristic
634C22C22×#1176586411yescharacteristic
635C222−1+4×D7111yescharacteristic
636C22#1798683611yescharacteristic
637C4—26no—
638C4—22no—
639C4—22no—
640C4—43no—
641C4—43no—
642C4—2843no—
643C4—714no—
644C4—714no—
645C4—1426no—
646C4—1426no—
647C4—1422no—
648C4—1426no—
649C4C2×(C22⋊D71)⋊C4112yes—
650C2—24no—
651C2—1424no—
652C2C22×(C22⋊D71)⋊C411yescharacteristic
653C2C2×C4×Q8×D7111yescharacteristic
654C2#2260154911yescharacteristic
655C2D4×Q8×D7111yescharacteristic
656C2#2260182911yescharacteristic
657C2Q8×#1176586411yescharacteristic
658C2#2260195611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingQ8×C22⋊C4×C71C2
socle, cosocleC23×C71C25
prime radicalC22×C22⋊D71C23
hypercenterQ8×C22⋊C4D71
hypocenterC71C4×D4×Q8
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×Q8×Dic71C2semidirect
3. C2×C4×Q8×D71C2semidirect
4. #22591397C2semidirect
5. #22591350C2semidirect
6. #22591343C2semidirect
7. Q8×Dic71⋊C4C2semidirect
9. Q8×(C2×D71)⋊C4C2semidirect
10. #22590909C2semidirect
11. #22590878C2semidirect
12. #22590868C2semidirect
13. C4×Q8×Dic71C2semidirect
15. Q8×C22⋊C4×C71C2semidirect
17. Q8×C22⋊D71C4semidirect
72. C2×Q8×D71C2×C4semidirect
79. #14556126C2×C4semidirect
80. #14556107C2×C4semidirect
81. #14556104C2×C4semidirect
85. Q8×Dic71C2×C4semidirect
86. Q8×Dic71D4semidirect
91. (C22⋊D71)⋊C4Q8direct (N × H)
129. C22×Q8×C71C2×C4semidirect
157. C22×Dic71C2×Q8semidirect
173. C2×C4×D71C2×Q8semidirect
183. Dic71⋊C4C2×Q8semidirect
187. (C2×D71)⋊C4C2×Q8semidirect
198. C4×Dic71C2×Q8semidirect
219. C22⋊C4×C71C2×Q8semidirect
238. Q8×C71C4×D4semidirect
258. C22⋊D71C4×Q8semidirect
292. C22×C71C2×C4×Q8semidirect
306. C2×D71C2×C4×Q8semidirect
318. Dic71C2×C4×Q8semidirect
319. Dic71D4×Q8semidirect
339. Q8×C22⋊C4D71semidirect
345. C71C4×D4×Q8semidirect
405. C22×Q8C4×D71semidirect
538. C22⋊C4Q8×D71semidirect
569. Q8(C22⋊D71)⋊C4direct (N × H)
629. C22C4×Q8×D71semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D712
C22×Q8×Dic712
C2×C4×Q8×D712
#225913972
#225913502
#225913432
Q8×Dic71⋊C42
#225912362
Q8×(C2×D71)⋊C42
#225909092
#225908782
#225908682
C4×Q8×Dic712
C4×(C22⋊D71)⋊C42
Q8×C22⋊C4×C712
C4×D4×Q871