Finite Group Databasebeta

← C2×#22591787 #32165403

Subgroups — C2×#22591787 #32165403

Order 18176.

3830 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556104C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D71C211yesmaximal, characteristic
3C22×C4⋊C4×D71C211yesmaximal, characteristic, complemented
4#22591787C2116yesmaximal, direct product factor
5C2×#17985930C212yesmaximal, complemented
6C2×#17985922C212yesmaximal, complemented
7C2×#17985906C211yesmaximal, characteristic, complemented
8C2×#17985898C211yesmaximal, characteristic, complemented
9C2×#17985875C212yesmaximal
10C2×#17985859C211yesmaximal, characteristic, complemented
11C2×#17985856C212yesmaximal, complemented
12C22×C22⋊Q8×C71C211yesmaximal, characteristic, complemented
13C23×C22⋊D71C2211yescharacteristic
14C23×C4×D71C2212yes—
15C23×C4×D71C2211yescharacteristic
16C2×#14556104—28no—
17C2×#14556104C2218yescomplemented
18C2×C4×C22⋊D71—28no—
19C2×C4×C22⋊D71C2218yes—
20C22×C4⋊Dic71C2211yescharacteristic
21C22×C4⋊Dic71C2211yescharacteristic
22C22×C4⋊Dic71C2212yes—
23C22×Dic71⋊C4C2212yes—
24C22×Dic71⋊C4C2211yescharacteristic
25C22×Dic71⋊C4C2212yes—
26C2×C4⋊C4×D71—28no—
27C2×C4⋊C4×D71C2218yescomplemented
28C22×C22⋊Dic71C2211yescharacteristic
29C22×C22⋊Dic71C2212yes—
30C22×(C2×D71)⋊C4C2212yes—
31C22×(C2×D71)⋊C4C2211yescharacteristic
32C22×C4×Dic71C2211yescharacteristic
33#17985930C22116yescomplemented
34#17985922C22116yescomplemented
35#17985906C2218yescomplemented
36#17985898C2218yescomplemented
37#17985875C22116yes—
38#17985859C2218yescomplemented
39#17985856C22116yescomplemented
40C2×C71⋊#95C2212yes—
41C2×C71⋊#95C2212yes—
42C2×C71⋊#95C2212yes—
43C2×C71⋊#95C2212yes—
44C23×Q8×C71C2211yescharacteristic
45C24×C4×C71C2211yescharacteristic
46C2×C22⋊Q8×C71—28no—
47C2×C22⋊Q8×C71C2218yescomplemented
48C22×C4⋊C4×C71C2212yes—
49C22×C4⋊C4×C71C2211yescharacteristic
50C22×C22⋊C4×C71C2212yes—
51C24×D71C2311yescharacteristic
52C22×C22⋊D71—24no—
53C22×C22⋊D71—24no—
54C22×C22⋊D71Q818yescomplemented
55C22×C22⋊D71C2314yes—
56C23×Dic71C2312yes—
57C23×Dic71C2311yescharacteristic
58C23×Dic71C2312yes—
59C23×Dic71C2311yescharacteristic
60C23×Dic71C2311yescharacteristic
61C22×C4×D71—28no—
62C22×C4×D71—24no—
63C22×C4×D71—28no—
64C22×C4×D71—24no—
65C22×C4×D71—44no—
66C22×C4×D71D418yes—
67C22×C4×D71C2318yes—
68C22×C4×D71C2314yes—
69#14556104—232no—
70C4×C22⋊D71—232no—
71C2×C4⋊Dic71—24no—
72C2×C4⋊Dic71—24no—
73C2×C4⋊Dic71—44no—
74C2×C4⋊Dic71C2314yes—
75C2×C4⋊Dic71C2314yes—
76C2×C4⋊Dic71C2318yes—
77C2×Dic71⋊C4—24no—
78C2×Dic71⋊C4—28no—
79C2×Dic71⋊C4—28no—
80C2×Dic71⋊C4C2318yes—
81C2×Dic71⋊C4C2318yes—
82C2×Dic71⋊C4C2314yes—
83C4⋊C4×D71—232no—
84C2×C22⋊Dic71—24no—
85C2×C22⋊Dic71—44no—
86C2×C22⋊Dic71C2314yes—
87C2×C22⋊Dic71C2318yes—
88C2×(C2×D71)⋊C4—24no—
89C2×(C2×D71)⋊C4—28no—
90C2×(C2×D71)⋊C4C2314yes—
91C2×(C2×D71)⋊C4C2318yes—
92C2×C4×Dic71—24no—
93C2×C4×Dic71C2314yes—
94C71⋊#95C2318yes—
95C71⋊#95C2318yes—
96C71⋊#95C2318yes—
97C71⋊#95C2318yes—
98C25×C71C2311yescharacteristic
99C22×Q8×C71—24no—
100C22×Q8×C71—24no—
101C22×Q8×C71—24no—
102C22×Q8×C71C2314yes—
103C23×C4×C71—24no—
104C23×C4×C71—24no—
105C23×C4×C71—24no—
106C23×C4×C71C2312yes—
107C23×C4×C71C2311yescharacteristic
108C23×C4×C71C2314yes—
109C23×C4×C71C2312yes—
110C23×C4×C71C2311yescharacteristic
111C22⋊Q8×C71—232no—
112C2×C4⋊C4×C71—28no—
113C2×C4⋊C4×C71D418yescomplemented
114C2×C4⋊C4×C71C2318yes—
115C2×C4⋊C4×C71C2314yes—
116C2×C22⋊C4×C71—28no—
117C2×C22⋊C4×C71C2318yes—
118C23×D71—22no—
119C23×D71—22no—
120C23×D71—22no—
121C23×D71—22no—
122C23×D71C2×D414yes—
123C23×D71C2×Q814yes—
124C23×D71#4114yes—
125C23×D71C2412yes—
126C2×C22⋊D71—232no—
127C2×C22⋊D71—28no—
128C2×C22⋊D71—28no—
129C2×C22⋊D71C2×Q8116yescomplemented
130C22×Dic71—22no—
131C22×Dic71—22no—
132C22×Dic71—22no—
133C22×Dic71—22no—
134C22×Dic71—24no—
135C22×Dic71—22no—
136C22×Dic71—24no—
137C22×Dic71—24no—
138C22×Dic71—24no—
139C22×Dic71—24no—
140C22×Dic71—22no—
141C22×Dic71—22no—
142C22×Dic71—24no—
143C22×Dic71C2×D414yes—
144C22×Dic71C2×Q814yes—
145C22×Dic71C2414yes—
146C22×Dic71C2412yes—
147C22×Dic71C2414yes—
148C22×Dic71C2412yes—
149C22×Dic71C2412yes—
150C2×C4×D71—232no—
151C2×C4×D71—28no—
152C2×C4×D71—28no—
153C2×C4×D71—216no—
154C2×C4×D71—216no—
155C2×C4×D71—48no—
156C2×C4×D71—432no—
157C2×C4×D71C2×D4116yes—
158C4⋊Dic71—28no—
159C4⋊Dic71—28no—
160C4⋊Dic71—48no—
161Dic71⋊C4—216no—
162Dic71⋊C4—28no—
163Dic71⋊C4—216no—
164C22⋊Dic71—28no—
165C22⋊Dic71—48no—
166(C2×D71)⋊C4—28no—
167(C2×D71)⋊C4—216no—
168C4×Dic71—28no—
169C24×C71—22no—
170C24×C71—22no—
171C24×C71—22no—
172C24×C71—22no—
173C24×C71—22no—
174C24×C71—22no—
175C24×C71C2×Q814yes—
176C24×C71C2412yes—
177C24×C71C2411yescharacteristic
178C2×Q8×C71—28no—
179C2×Q8×C71—28no—
180C2×Q8×C71—28no—
181C2×Q8×C71—416no—
182C22×C4×C71—24no—
183C22×C4×C71—24no—
184C22×C4×C71—24no—
185C22×C4×C71—22no—
186C22×C4×C71—22no—
187C22×C4×C71—24no—
188C22×C4×C71—22no—
189C22×C4×C71—24no—
190C22×C4×C71—28no—
191C22×C4×C71—28no—
192C22×C4×C71—28no—
193C22×C4×C71—416no—
194C22×C4×C71C2×D414yes—
195C22×C4×C71C2×D418yes—
196C22×C4×C71C2×D414yes—
197C22×C4×C71#4114yes—
198C22×C4×C71C2414yes—
199C22×C4×C71C2412yes—
200C22×C4×C71C2414yes—
201C22×C4×C71C2412yes—
202C4⋊C4×C71—216no—
203C4⋊C4×C71C2×D4116yescomplemented
204C22⋊C4×C71—216no—
205C23×C71—28no—
206C23×C71—28no—
207C23×C71—28no—
208C23×C71—22no—
209C23×C71—22no—
210C23×C71—22no—
211C23×C71—22no—
212C23×C71—22no—
213C23×C71—22no—
214C23×C71—44no—
215C23×C71—44no—
216C23×C71—44no—
217C23×C71—44no—
218C23×C71C22×D412yes—
219C23×C71C22×D412yes—
220C23×C71C22×Q814yes—
221C23×C71C22×Q812yes—
222C23×C71C2×#4112yes—
223C23×C71C2×#4112yes—
224C23×C71H(5,𝔽2)12yes—
225C23×C712−1+412yes—
226C23×C71C2511yescharacteristic
227C22×D71—28no—
228C22×D71—28no—
229C22×D71—28no—
230C22×D71—28no—
231C22×D71—28no—
232C22×D71—28no—
233C22×D71—22no—
234C22×D71—22no—
235C22×D71—22no—
236C22×D71—22no—
237C22×D71C22⋊Q8116yescomplemented
238C22×D71C22×D414yes—
239C22×D71C22×Q814yes—
240C22×D71C2×#4114yes—
241Q8×C71—416no—
242C2×C4×C71—216no—
243C2×C4×C71—24no—
244C2×C4×C71—24no—
245C2×C4×C71—24no—
246C2×C4×C71—22no—
247C2×C4×C71—22no—
248C2×C4×C71—24no—
249C2×C4×C71—22no—
250C2×C4×C71—24no—
251C2×C4×C71—44no—
252C2×C4×C71—48no—
253C2×C4×C71—416no—
254C2×C4×C71#121116yes—
255C2×C4×C71C22×D414yes—
256C2×C4×C71C22×D418yes—
257C2×C4×C71C22×D414yes—
258C2×C4×C71C2×#4114yes—
259C22⋊D71—232no—
260C2×Dic71—28no—
261C2×Dic71—28no—
262C2×Dic71—22no—
263C2×Dic71—22no—
264C2×Dic71—22no—
265C2×Dic71—22no—
266C2×Dic71—22no—
267C2×Dic71—24no—
268C2×Dic71—24no—
269C2×Dic71—24no—
270C2×Dic71—24no—
271C2×Dic71—24no—
272C2×Dic71—22no—
273C2×Dic71—22no—
274C2×Dic71—24no—
275C2×Dic71—44no—
276C2×Dic71—48no—
277C2×Dic71—48no—
278C2×Dic71C22×D414yes—
279C2×Dic71C22×Q814yes—
280C4×D71—232no—
281C4×D71—432no—
282C22×C71—24no—
283C22×C71—24no—
284C22×C71—24no—
285C22×C71—42no—
286C22×C71—416no—
287C22×C71—42no—
288C22×C71—42no—
289C22×C71—42no—
290C22×C71C2×#12114yes—
291C22×C71C2×C22⋊Q814yes—
292C22×C71#53714yes—
293C22×C71#54614yes—
294C22×C71D4×Q814yes—
295C22×C71#55214yes—
296C22×C71#55414yes—
297C22×C71C23×D411yescharacteristic
298C22×C71C23×D411yescharacteristic
299C22×C71C23×Q811yescharacteristic
300C22×C71C22×#4111yescharacteristic
301C22×C71C22×#4111yescharacteristic
302C22×C71C2×H(5,𝔽2)11yescharacteristic
303C22×C71C2×2−1+411yescharacteristic
304C2×D71—24no—
305C2×D71—232no—
306C2×D71—24no—
307C2×D71—24no—
308C2×D71—24no—
309C2×D71—24no—
310C2×D71—24no—
311C2×D71C2×C22⋊Q818yescomplemented
312C4×C71—28no—
313C4×C71—42no—
314C4×C71—44no—
315C4×C71C2×#12118yes—
316Dic71—24no—
317Dic71—24no—
318Dic71—42no—
319Dic71—44no—
320Dic71—44no—
321C2×#2417—711nomaximal, Sylow
322C2×C71—44no—
323C2×C71#241718yescomplemented
324C2×C71C22×#12111yescharacteristic
325C2×C71C22×C22⋊Q811yescharacteristic
326C2×C71C2×#53711yescharacteristic
327C2×C71C2×#54611yescharacteristic
328C2×C71C2×D4×Q811yescharacteristic
329C2×C71C2×#55211yescharacteristic
330C2×C71C2×#55411yescharacteristic
331D71—28no—
332C22×C22⋊Q8—711no—
333C22×C22⋊Q8D7111yescharacteristic, complemented
334C22×C4×D4—711no—
335C23×C4⋊C4—711no—
336#2417—7116no—
337C2×#398—712no—
338C2×#396—712no—
339C2×#391—711no—
340C2×#389—711no—
341C2×#386—712no—
342C2×#380—711no—
343C2×#380—712no—
344C71C2×#241711yescharacteristic, complemented, Sylow
345C23×Q8C2×D7111yescharacteristic
346C23×D4—711no—
347C24×C4—712no—
348C24×C4—711no—
349C24×C4C2×D7111yescharacteristic
350C2×C22⋊Q8—28no—
351C2×C22⋊Q8—718no—
352C2×C22⋊Q8—1428no—
353C2×C22⋊Q8C2×D7118yescomplemented
354C2×C4×D4—718no—
355C2×C4×D4—1428no—
356C22×C4⋊C4—712no—
357C22×C4⋊C4—712no—
358C22×C4⋊C4—712no—
359C22×C4⋊C4—711no—
360C22×C4⋊C4—711no—
361C22×C4⋊C4—711no—
362C22×C4⋊C4—718no—
363C22×C4⋊C4—1428no—
364C22×C4⋊C4C2×D7112yes—
365C22×C4⋊C4C2×D7111yescharacteristic
366C22×C22⋊C4—712no—
367C22×C22⋊C4—711no—
368C22×C22⋊C4—711no—
369C22×C22⋊C4—712no—
370C22×C22⋊C4C2×D7112yes—
371C22×C42—711no—
372#398—7116no—
373#396—7116no—
374#391—718no—
375#389—718no—
376#386—7116no—
377#380—718no—
378#380—7116no—
379C2×#95—712no—
380C2×#95—712no—
381C2×#95—712no—
382C2×#95—712no—
383C25—711no—
384C25C22×D7111yescharacteristic
385C22×Q8—24no—
386C22×Q8—24no—
387C22×Q8—24no—
388C22×Q8C22×D7114yes—
389C22×D4—718no—
390C22×D4—714no—
391C22×D4—1424no—
392C22×D4—1424no—
393C23×C4—24no—
394C23×C4—24no—
395C23×C4—24no—
396C23×C4—2844no—
397C23×C4—718no—
398C23×C4—711no—
399C23×C4—711no—
400C23×C4—718no—
401C23×C4—714no—
402C23×C4—712no—
403C23×C4—711no—
404C23×C4—712no—
405C23×C4—1428no—
406C23×C4—1428no—
407C23×C4—1424no—
408C23×C4—1424no—
409C23×C4C22×D7114yes—
410C23×C4C22×D7112yes—
411C23×C4C22×D7111yescharacteristic
412C23×C4C22×D7112yes—
413C23×C4C22×D7111yescharacteristic
414C22⋊Q8—232no—
415C22⋊Q8—14232no—
416C4×D4—14232no—
417C2×C4⋊C4—28no—
418C2×C4⋊C4—2844no—
419C2×C4⋊C4—718no—
420C2×C4⋊C4—714no—
421C2×C4⋊C4—718no—
422C2×C4⋊C4—714no—
423C2×C4⋊C4—714no—
424C2×C4⋊C4—718no—
425C2×C4⋊C4—1424no—
426C2×C4⋊C4—1428no—
427C2×C4⋊C4—1424no—
428C2×C4⋊C4—1428no—
429C2×C4⋊C4—1424no—
430C2×C4⋊C4—14232no—
431C2×C4⋊C4C22⋊D7118yescomplemented
432C2×C4⋊C4C22×D7118yes—
433C2×C4⋊C4C22×D7114yes—
434C2×C22⋊C4—28no—
435C2×C22⋊C4—2844no—
436C2×C22⋊C4—718no—
437C2×C22⋊C4—714no—
438C2×C22⋊C4—714no—
439C2×C22⋊C4—718no—
440C2×C22⋊C4—1424no—
441C2×C22⋊C4—1428no—
442C2×C22⋊C4—1424no—
443C2×C22⋊C4C22×D7118yes—
444C2×C42—714no—
445C2×C42—1424no—
446#95—718no—
447#95—718no—
448#95—718no—
449#95—718no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—714no—
457C24—714no—
458C24—714no—
459C24—712no—
460C24—1422no—
461C24—1422no—
462C24—1422no—
463C24—1422no—
464C24Q8×D7114yes—
465C24C23×D7112yes—
466C24C23×D7111yescharacteristic
467C2×Q8—28no—
468C2×Q8—28no—
469C2×Q8—28no—
470C2×Q8—416no—
471C2×D4—7116no—
472C2×D4—1428no—
473C2×D4—1428no—
474C2×D4—14232no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—416no—
487C22×C4—28432no—
488C22×C4—2848no—
489C22×C4—714no—
490C22×C4—714no—
491C22×C4—712no—
492C22×C4—712no—
493C22×C4—7116no—
494C22×C4—714no—
495C22×C4—712no—
496C22×C4—714no—
497C22×C4—14216no—
498C22×C4—1422no—
499C22×C4—1424no—
500C22×C4—1424no—
501C22×C4—1424no—
502C22×C4—1424no—
503C22×C4—1424no—
504C22×C4—1422no—
505C22×C4—1424no—
506C22×C4—1422no—
507C22×C4—14216no—
508C22×C4—1422no—
509C22×C4—1422no—
510C22×C4—1422no—
511C22×C4—1422no—
512C22×C4—1428no—
513C22×C4—1428no—
514C22×C4—14232no—
515C22×C4D4×D7114yes—
516C22×C4C2×C22⋊D7118yes—
517C22×C4C2×C22⋊D7114yes—
518C22×C4#1176586414yes—
519C22×C4C23×D7114yes—
520C22×C4C23×D7112yes—
521C22×C4C23×D7114yes—
522C22×C4C23×D7112yes—
523C4⋊C4—216no—
524C4⋊C4—2848no—
525C4⋊C4—1428no—
526C4⋊C4—14216no—
527C4⋊C4—1428no—
528C4⋊C4—14216no—
529C4⋊C4—1428no—
530C4⋊C4C2×C22⋊D71116yescomplemented
531C22⋊C4—216no—
532C22⋊C4—2848no—
533C22⋊C4—1428no—
534C22⋊C4—14216no—
535C22⋊C4—1428no—
536C42—1428no—
537C23—22no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—28no—
544C23—28no—
545C23—28no—
546C23—44no—
547C23—44no—
548C23—44no—
549C23—44no—
550C23—714no—
551C23—714no—
552C23—714no—
553C23—7116no—
554C23—1422no—
555C23—1422no—
556C23—1422no—
557C23—1422no—
558C23—1428no—
559C23—1428no—
560C23—1428no—
561C23—1428no—
562C23—1428no—
563C23—1428no—
564C23C2×D4×D7112yes—
565C23C22×C22⋊D7112yes—
566C23C2×Q8×D7114yes—
567C23C2×Q8×D7112yes—
568C23#41×D7112yes—
569C23C2×#1176586412yes—
570C23#1455617412yes—
571C23#1455617612yes—
572C23C24×D7111yescharacteristic
573Q8—416no—
574D4—14232no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—216no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—44no—
585C2×C4—48no—
586C2×C4—416no—
587C2×C4—28432no—
588C2×C4—2844no—
589C2×C4—2848no—
590C2×C4—2848no—
591C2×C4—714no—
592C2×C4—714no—
593C2×C4—1422no—
594C2×C4—1424no—
595C2×C4—1424no—
596C2×C4—1424no—
597C2×C4—1424no—
598C2×C4—1424no—
599C2×C4—1422no—
600C2×C4—1422no—
601C2×C4—1424no—
602C2×C4—1422no—
603C2×C4—1422no—
604C2×C4—1422no—
605C2×C4—1422no—
606C2×C4—1428no—
607C2×C4—1428no—
608C2×C4—14232no—
609C2×C4#14556099116yes—
610C2×C4C2×D4×D7114yes—
611C2×C4C22×C22⋊D7118yes—
612C2×C4C22×C22⋊D7114yes—
613C2×C4C2×#1176586414yes—
614C22—24no—
615C22—24no—
616C22—24no—
617C22—416no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—718no—
623C22—14232no—
624C22—1424no—
625C22—1424no—
626C22—1424no—
627C22—1424no—
628C22—1424no—
629C22—1424no—
630C22C2×#1455609914yes—
631C22C22⋊Q8×D7114yes—
632C22#1798657914yes—
633C22#1798663714yes—
634C22Q8×C22⋊D7114yes—
635C22#1798668314yes—
636C22#1798670714yes—
637C22C22×D4×D7111yescharacteristic
638C22C23×C22⋊D7111yescharacteristic
639C22C22×Q8×D7111yescharacteristic
640C22C2×#41×D7111yescharacteristic
641C22C22×#1176586411yescharacteristic
642C22C2×#1455617411yescharacteristic
643C22C2×#1455617611yescharacteristic
644C4—28no—
645C4—42no—
646C4—44no—
647C4—2844no—
648C4—2842no—
649C4—2844no—
650C4—1424no—
651C4—1424no—
652C4C2×#1455609918yes—
653C2—44no—
654C2—1428no—
655C2#2259178718yesdirect product factor
656C2C22×#1455609911yescharacteristic
657C2C2×C22⋊Q8×D7111yescharacteristic
658C2C2×#1798657911yescharacteristic
659C2C2×#1798663711yescharacteristic
660C2C2×Q8×C22⋊D7111yescharacteristic
661C2C2×#1798668311yescharacteristic
662C2C2×#1798670711yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC22×C22⋊Q8×C71C2
socleC24×C71C24
prime radicalC23×C22⋊D71C22
hypercenterC22×C22⋊Q8D71
hypocenterC71C2×#2417
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14556104C2semidirect
3. C22×C4⋊C4×D71C2semidirect
4. #22591787C2direct (N × H)
5. C2×#17985930C2semidirect
6. C2×#17985922C2semidirect
7. C2×#17985906C2semidirect
8. C2×#17985898C2semidirect
10. C2×#17985859C2semidirect
11. C2×#17985856C2semidirect
12. C22×C22⋊Q8×C71C2semidirect
17. C2×#14556104C22semidirect
27. C2×C4⋊C4×D71C22semidirect
33. #17985930C22semidirect
34. #17985922C22semidirect
35. #17985906C22semidirect
36. #17985898C22semidirect
38. #17985859C22semidirect
39. #17985856C22semidirect
47. C2×C22⋊Q8×C71C22semidirect
54. C22×C22⋊D71Q8semidirect
113. C2×C4⋊C4×C71D4semidirect
129. C2×C22⋊D71C2×Q8semidirect
203. C4⋊C4×C71C2×D4semidirect
237. C22×D71C22⋊Q8semidirect
311. C2×D71C2×C22⋊Q8semidirect
323. C2×C71#2417semidirect
333. C22×C22⋊Q8D71semidirect
344. C71C2×#2417semidirect
353. C2×C22⋊Q8C2×D71semidirect
431. C2×C4⋊C4C22⋊D71semidirect
530. C4⋊C4C2×C22⋊D71semidirect
655. C2#22591787direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561042
C22×C4×C22⋊D712
C22×C4⋊C4×D712
#225917872
C2×#179859302
C2×#179859222
C2×#179859062
C2×#179858982
C2×#179858752
C2×#179858592
C2×#179858562
C22×C22⋊Q8×C712
C2×#241771