Finite Group Databasebeta

← C2×#22588629 #31998567

Subgroups — C2×#22588629 #31998567

Order 18176.

2438 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C8×D71C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D71C211yesmaximal, characteristic
3C22×C22⋊(C71⋊C8)C211yesmaximal, characteristic, complemented
4C22×(C2×D71)⋊C8C211yesmaximal, characteristic, complemented
5#22588629C218yesmaximal, direct product factor
6C2×#17985753C211yesmaximal, characteristic, complemented
7C2×#17985753C211yesmaximal, characteristic, complemented
8C22×C22⋊C8×C71C211yesmaximal, characteristic, complemented
9C23×C22⋊D71C411yescharacteristic
10C23×C4×D71C2211yescharacteristic
11C23×C71⋊C8C2211yescharacteristic
12C23×C71⋊C8C2211yescharacteristic
13C22×C8×D71—24no—
14C22×C8×D71—24no—
15C22×C8×D71—24no—
16C22×C8×D71C2214yescomplemented
17C2×C4×C22⋊D71—24no—
18C2×C4×C22⋊D71—24no—
19C2×C4×C22⋊D71C414yes—
20C2×C4×C22⋊D71C2214yes—
21C22×Dic71⋊C4C411yescharacteristic
22C22×C22⋊Dic71C411yescharacteristic
23C22×(C2×D71)⋊C4C411yescharacteristic
24C22×C4×Dic71C2211yescharacteristic
25C2×C22⋊(C71⋊C8)—24no—
26C2×C22⋊(C71⋊C8)C2214yescomplemented
27C2×(C2×D71)⋊C8—24no—
28C2×(C2×D71)⋊C8C2214yescomplemented
29#17985753C2214yescomplemented
30#17985753C2214yescomplemented
31C24×C4×C71C2211yescharacteristic
32C23×C8×C71C2211yescharacteristic
33C23×C8×C71C2211yescharacteristic
34C2×C22⋊C8×C71—24no—
35C2×C22⋊C8×C71C2214yescomplemented
36C24×D71C2×C411yescharacteristic
37C22×C22⋊D71—24no—
38C22×C22⋊D71—24no—
39C22×C22⋊D71C818yescomplemented
40C22×C22⋊D71C2×C414yes—
41C23×Dic71C2×C411yescharacteristic
42C23×Dic71C2×C411yescharacteristic
43C23×Dic71C2×C411yescharacteristic
44C22×C4×D71—22no—
45C22×C4×D71—22no—
46C22×C4×D71—22no—
47C22×C4×D71—22no—
48C22×C4×D71C2×C412yes—
49C22×C4×D71D414yes—
50C22×C4×D71D414yes—
51C22×C4×D71C2312yes—
52C22×C71⋊C8—22no—
53C22×C71⋊C8—22no—
54C22×C71⋊C8—22no—
55C22×C71⋊C8—22no—
56C22×C71⋊C8—22no—
57C22×C71⋊C8D414yescomplemented
58C22×C71⋊C8C2312yes—
59C22×C71⋊C8C2312yes—
60C2×C8×D71—232no—
61C2×C8×D71—28no—
62C2×C8×D71—28no—
63C2×C8×D71—28no—
64C4×C22⋊D71—216no—
65C4×C22⋊D71—28no—
66C4×C22⋊D71—28no—
67C2×Dic71⋊C4—24no—
68C2×Dic71⋊C4C2×C414yes—
69C2×C22⋊Dic71—24no—
70C2×C22⋊Dic71C2×C414yes—
71C2×(C2×D71)⋊C4—24no—
72C2×(C2×D71)⋊C4C2×C414yes—
73C2×C4×Dic71—22no—
74C2×C4×Dic71—22no—
75C2×C4×Dic71C2×C412yes—
76C2×C4×Dic71C2312yes—
77C22⋊(C71⋊C8)—28no—
78(C2×D71)⋊C8—28no—
79C25×C71C2×C411yescharacteristic
80C23×C4×C71—22no—
81C23×C4×C71—22no—
82C23×C4×C71—22no—
83C23×C4×C71—22no—
84C23×C4×C71—22no—
85C23×C4×C71—22no—
86C23×C4×C71C2×C411yescharacteristic
87C23×C4×C71C2×C412yes—
88C23×C4×C71C2312yes—
89C23×C4×C71C2311yescharacteristic
90C22×C8×C71—22no—
91C22×C8×C71—22no—
92C22×C8×C71—22no—
93C22×C8×C71—22no—
94C22×C8×C71—22no—
95C22×C8×C71D414yescomplemented
96C22×C8×C71C2312yes—
97C22×C8×C71C2312yes—
98C22⋊C8×C71—28no—
99C23×D71—22no—
100C23×D71—22no—
101C23×D71—22no—
102C23×D71—22no—
103C23×D71C22⋊C414yes—
104C23×D71C2×C814yes—
105C23×D71M1614yes—
106C23×D71C22×C412yes—
107C2×C22⋊D71—232no—
108C2×C22⋊D71—28no—
109C2×C22⋊D71—28no—
110C2×C22⋊D71C2×C8116yescomplemented
111C22×Dic71—22no—
112C22×Dic71—22no—
113C22×Dic71—22no—
114C22×Dic71—22no—
115C22×Dic71—22no—
116C22×Dic71—22no—
117C22×Dic71—22no—
118C22×Dic71C22⋊C414yes—
119C22×Dic71C2×C814yescomplemented
120C22×Dic71C22×C412yes—
121C22×Dic71C22×C412yes—
122C22×Dic71C22×C412yes—
123C2×C4×D71—24no—
124C2×C4×D71—24no—
125C2×C4×D71—28no—
126C2×C4×D71—28no—
127C2×C4×D71—28no—
128C2×C4×D71—28no—
129C2×C4×D71—22no—
130C2×C4×D71—22no—
131C2×C4×D71—22no—
132C2×C4×D71—22no—
133C2×C4×D71C22⋊C418yes—
134C2×C4×D71C2×D414yes—
135C2×C4×D71C2×D414yes—
136C2×C71⋊C8—28no—
137C2×C71⋊C8—22no—
138C2×C71⋊C8—22no—
139C2×C71⋊C8—22no—
140C2×C71⋊C8—22no—
141C2×C71⋊C8—22no—
142C2×C71⋊C8—44no—
143C2×C71⋊C8C2×D414yescomplemented
144C8×D71—232no—
145Dic71⋊C4—28no—
146C22⋊Dic71—28no—
147(C2×D71)⋊C4—28no—
148C4×Dic71—24no—
149C4×Dic71—22no—
150C4×Dic71—22no—
151C24×C71—22no—
152C24×C71—22no—
153C24×C71—22no—
154C24×C71—22no—
155C24×C71—22no—
156C24×C71—22no—
157C24×C71C2×C814yescomplemented
158C24×C71C22×C412yes—
159C24×C71C22×C411yescharacteristic
160C22×C4×C71—22no—
161C22×C4×C71—22no—
162C22×C4×C71—22no—
163C22×C4×C71—24no—
164C22×C4×C71—24no—
165C22×C4×C71—24no—
166C22×C4×C71—22no—
167C22×C4×C71—22no—
168C22×C4×C71—22no—
169C22×C4×C71—22no—
170C22×C4×C71—22no—
171C22×C4×C71—22no—
172C22×C4×C71—44no—
173C22×C4×C71—44no—
174C22×C4×C71—44no—
175C22×C4×C71—44no—
176C22×C4×C71C22×C412yes—
177C22×C4×C71C22×C411yescharacteristic
178C22×C4×C71C2×D412yes—
179C22×C4×C71C2×D412yes—
180C22×C4×C71C2×D412yes—
181C22×C4×C71C2×D412yes—
182C22×C4×C71#4112yes—
183C22×C4×C71#4112yes—
184C22×C4×C71C2411yescharacteristic
185C2×C8×C71—28no—
186C2×C8×C71—22no—
187C2×C8×C71—22no—
188C2×C8×C71—22no—
189C2×C8×C71—22no—
190C2×C8×C71—22no—
191C2×C8×C71—44no—
192C2×C8×C71C2×D414yescomplemented
193C23×C71—22no—
194C23×C71—22no—
195C23×C71—22no—
196C23×C71—22no—
197C23×C71—22no—
198C23×C71—22no—
199C23×C71—28no—
200C23×C71—28no—
201C23×C71—28no—
202C23×C71—44no—
203C23×C71—44no—
204C23×C71—44no—
205C23×C71—44no—
206C23×C71C2×C22⋊C412yes—
207C23×C71C4×D412yes—
208C23×C71C4×D412yes—
209C23×C71C22×C812yes—
210C23×C71C22×C814yescomplemented
211C23×C71C2×M1612yes—
212C23×C71#13112yes—
213C23×C71#13112yes—
214C23×C71C23×C411yescharacteristic
215C22×D71—22no—
216C22×D71—22no—
217C22×D71—22no—
218C22×D71—22no—
219C22×D71—28no—
220C22×D71—28no—
221C22×D71—28no—
222C22×D71—28no—
223C22×D71—28no—
224C22×D71—28no—
225C22×D71C22⋊C8116yescomplemented
226C22×D71C2×C22⋊C414yes—
227C22×D71C22×C814yes—
228C22×D71C2×M1614yes—
229C2×C4×C71—22no—
230C2×C4×C71—22no—
231C2×C4×C71—22no—
232C2×C4×C71—44no—
233C2×C4×C71—42no—
234C2×C4×C71—42no—
235C2×C4×C71—42no—
236C2×C4×C71—42no—
237C2×C4×C71—48no—
238C2×C4×C71C2×C22⋊C412yes—
239C2×C4×C71C4×D412yes—
240C2×C4×C71C4×D412yes—
241C2×C4×C71#12014yes—
242C2×C4×C71#12114yes—
243C2×C4×C71#12114yes—
244C2×C4×C71#12314yes—
245C2×C4×C71C22×D411yescharacteristic
246C2×C4×C71C22×D411yescharacteristic
247C2×C4×C71C22×D411yescharacteristic
248C2×C4×C71C22×D411yescharacteristic
249C2×C4×C71C2×#4111yescharacteristic
250C2×C4×C71C2×#4111yescharacteristic
251C22⋊D71—232no—
252C2×Dic71—22no—
253C2×Dic71—22no—
254C2×Dic71—22no—
255C2×Dic71—22no—
256C2×Dic71—28no—
257C2×Dic71—28no—
258C2×Dic71—22no—
259C2×Dic71—22no—
260C2×Dic71—22no—
261C2×Dic71—44no—
262C2×Dic71C2×C22⋊C414yes—
263C2×Dic71C22×C814yescomplemented
264C4×D71—24no—
265C4×D71—24no—
266C4×D71—24no—
267C4×D71—24no—
268C4×D71—216no—
269C8×C71—24no—
270C8×C71—42no—
271C71⋊C8—24no—
272C71⋊C8—42no—
273C22×C71—24no—
274C22×C71—24no—
275C22×C71—24no—
276C22×C71—42no—
277C22×C71—416no—
278C22×C71—42no—
279C22×C71—42no—
280C22×C71—42no—
281C22×C71#38614yes—
282C22×C71C2×C22⋊C814yes—
283C22×C71#40814yes—
284C22×C71C8×D414yes—
285C22×C71C8×D414yes—
286C22×C71#43514yes—
287C22×C71#43514yes—
288C22×C71C22×C22⋊C411yescharacteristic
289C22×C71C2×C4×D411yescharacteristic
290C22×C71C2×C4×D411yescharacteristic
291C22×C71C23×C811yescharacteristic
292C22×C71C22×M1611yescharacteristic
293C22×C71C2×#13111yescharacteristic
294C22×C71C2×#13111yescharacteristic
295C2×D71—24no—
296C2×D71—232no—
297C2×D71—24no—
298C2×D71—24no—
299C2×D71—24no—
300C2×D71—24no—
301C2×D71—24no—
302C2×D71C2×C22⋊C818yescomplemented
303C4×C71—42no—
304C4×C71#38614yes—
305C4×C71C2×#12011yescharacteristic
306C4×C71C2×#12111yescharacteristic
307C4×C71C2×#12111yescharacteristic
308C4×C71C2×#12311yescharacteristic
309Dic71—24no—
310Dic71—24no—
311Dic71—42no—
312C2×#1869—711nomaximal, Sylow
313C2×C71—44no—
314C2×C71#186918yescomplemented
315C2×C71C2×#38611yescharacteristic
316C2×C71C22×C22⋊C811yescharacteristic
317C2×C71C2×#40811yescharacteristic
318C2×C71C2×C8×D411yescharacteristic
319C2×C71C2×C8×D411yescharacteristic
320C2×C71C2×#43511yescharacteristic
321C2×C71C2×#43511yescharacteristic
322D71—28no—
323C24×C8—711no—
324C22×C4×D4—711no—
325C22×C22⋊C8—711no—
326C22×C22⋊C8—711no—
327C22×C22⋊C8D7111yescharacteristic, complemented
328#1869—718no—
329C2×#336—711no—
330C2×#336—711no—
331C71C2×#186911yescharacteristic, complemented, Sylow
332C23×D4—711no—
333C24×C4—711no—
334C24×C4C2×D7111yescharacteristic
335C23×C8—711no—
336C23×C8—711no—
337C23×C8—714no—
338C23×C8—1424no—
339C23×C8—1424no—
340C23×C8—1424no—
341C23×C8C2×D7111yescharacteristic
342C23×C8C2×D7111yescharacteristic
343C2×C4×D4—714no—
344C2×C4×D4—714no—
345C2×C4×D4—1424no—
346C2×C4×D4—1424no—
347C22×C4⋊C4—711no—
348C22×C22⋊C4—711no—
349C22×C22⋊C4—711no—
350C22×C42—711no—
351C2×C22⋊C8—24no—
352C2×C22⋊C8—714no—
353C2×C22⋊C8—714no—
354C2×C22⋊C8—1424no—
355C2×C22⋊C8—1424no—
356C2×C22⋊C8C2×D7114yescomplemented
357#336—714no—
358#336—714no—
359C25—711no—
360C25C4×D7111yescharacteristic
361C22×D4—718no—
362C22×D4—714no—
363C22×D4—1424no—
364C22×D4—1424no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—711no—
372C23×C4—711no—
373C23×C4—712no—
374C23×C4—714no—
375C23×C4—714no—
376C23×C4—712no—
377C23×C4—711no—
378C23×C4—1422no—
379C23×C4—1422no—
380C23×C4—1422no—
381C23×C4—1422no—
382C23×C4C4×D7111yescharacteristic
383C23×C4C4×D7112yes—
384C23×C4C22×D7112yes—
385C23×C4C22×D7111yescharacteristic
386C22×C8—22no—
387C22×C8—22no—
388C22×C8—22no—
389C22×C8—22no—
390C22×C8—22no—
391C22×C8—714no—
392C22×C8—712no—
393C22×C8—712no—
394C22×C8—1428no—
395C22×C8—1428no—
396C22×C8—14232no—
397C22×C8—1422no—
398C22×C8—1422no—
399C22×C8—1422no—
400C22×C8—1422no—
401C22×C8—1422no—
402C22×C8—1428no—
403C22×C8C22⋊D7114yescomplemented
404C22×C8C22×D7112yes—
405C22×C8C22×D7112yes—
406C4×D4—1428no—
407C4×D4—1428no—
408C4×D4—14216no—
409C2×C4⋊C4—714no—
410C2×C4⋊C4—1424no—
411C2×C22⋊C4—714no—
412C2×C22⋊C4—714no—
413C2×C22⋊C4—1424no—
414C2×C22⋊C4—1424no—
415C2×C42—712no—
416C2×C42—712no—
417C2×C42—1422no—
418C2×C42—1422no—
419C22⋊C8—28no—
420C22⋊C8—1428no—
421C22⋊C8—1428no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—712no—
429C24—714no—
430C24—714no—
431C24—714no—
432C24—1422no—
433C24—1422no—
434C24—1422no—
435C24—1422no—
436C24C8×D7114yescomplemented
437C24C2×C4×D7112yes—
438C24C2×C4×D7111yescharacteristic
439C2×D4—7116no—
440C2×D4—1428no—
441C2×D4—14232no—
442C2×D4—1428no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—44no—
456C22×C4—44no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4—712no—
460C22×C4—712no—
461C22×C4—714no—
462C22×C4—714no—
463C22×C4—714no—
464C22×C4—714no—
465C22×C4—718no—
466C22×C4—712no—
467C22×C4—1422no—
468C22×C4—1422no—
469C22×C4—1422no—
470C22×C4—1422no—
471C22×C4—1422no—
472C22×C4—1422no—
473C22×C4—1422no—
474C22×C4—1422no—
475C22×C4—1422no—
476C22×C4—1422no—
477C22×C4—1422no—
478C22×C4—1424no—
479C22×C4—1424no—
480C22×C4—1428no—
481C22×C4—1428no—
482C22×C4—1428no—
483C22×C4—1428no—
484C22×C4C2×C4×D7112yes—
485C22×C4C2×C4×D7111yescharacteristic
486C22×C4D4×D7112yes—
487C22×C4D4×D7112yes—
488C22×C4D4×D7112yes—
489C22×C4C2×C22⋊D7112yes—
490C22×C4#1176586412yes—
491C22×C4#1176586512yes—
492C22×C4C23×D7111yescharacteristic
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—28no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—44no—
500C2×C8—2844no—
501C2×C8—714no—
502C2×C8—14232no—
503C2×C8—1422no—
504C2×C8—1422no—
505C2×C8—1422no—
506C2×C8—1422no—
507C2×C8—1422no—
508C2×C8—1428no—
509C2×C8C2×C22⋊D7114yescomplemented
510C4⋊C4—1428no—
511C22⋊C4—1428no—
512C22⋊C4—1428no—
513C42—1422no—
514C42—1422no—
515C42—1424no—
516C23—28no—
517C23—28no—
518C23—22no—
519C23—22no—
520C23—22no—
521C23—28no—
522C23—22no—
523C23—22no—
524C23—22no—
525C23—44no—
526C23—44no—
527C23—44no—
528C23—44no—
529C23—714no—
530C23—7116no—
531C23—714no—
532C23—714no—
533C23—1428no—
534C23—1428no—
535C23—1428no—
536C23—1428no—
537C23—1428no—
538C23—1422no—
539C23—1422no—
540C23—1428no—
541C23—1422no—
542C23—1422no—
543C23C22⋊C4×D7112yes—
544C23(C22⋊D71)⋊C412yes—
545C23C4×C22⋊D7112yes—
546C23C2×C8×D7112yes—
547C23C2×C8×D7114yescomplemented
548C23M16×D7112yes—
549C23#1455613412yes—
550C23#1455613612yes—
551C23C22×C4×D7111yescharacteristic
552D4—14232no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—44no—
557C2×C4—48no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—2844no—
563C2×C4—714no—
564C2×C4—714no—
565C2×C4—1422no—
566C2×C4—1422no—
567C2×C4—1422no—
568C2×C4—1428no—
569C2×C4—1422no—
570C2×C4—1422no—
571C2×C4—1422no—
572C2×C4—1428no—
573C2×C4—1422no—
574C2×C4—14216no—
575C2×C4—1424no—
576C2×C4—1424no—
577C2×C4—1424no—
578C2×C4—1424no—
579C2×C4C22⋊C4×D7112yes—
580C2×C4(C22⋊D71)⋊C412yes—
581C2×C4C4×C22⋊D7112yes—
582C2×C4#1455609614yes—
583C2×C4#1455609914yes—
584C2×C4#1455610114yes—
585C2×C4#1455611014yes—
586C2×C4C2×D4×D7111yescharacteristic
587C2×C4C2×D4×D7111yescharacteristic
588C2×C4C2×D4×D7111yescharacteristic
589C2×C4C22×C22⋊D7111yescharacteristic
590C2×C4C2×#1176586411yescharacteristic
591C2×C4C2×#1176586511yescharacteristic
592C8—24no—
593C8—42no—
594C8—2842no—
595C8—1424no—
596C22—24no—
597C22—24no—
598C22—24no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22—416no—
604C22—718no—
605C22—1424no—
606C22—1424no—
607C22—1424no—
608C22—1424no—
609C22—1424no—
610C22—1424no—
611C22—14232no—
612C22#1798587514yes—
613C22C22⋊C8×D7114yes—
614C22#1798596414yes—
615C22(C22⋊D71)⋊C814yes—
616C22C8×C22⋊D7114yes—
617C22#1798606814yes—
618C22#1798607314yes—
619C22C2×C22⋊C4×D7111yescharacteristic
620C22C2×(C22⋊D71)⋊C411yescharacteristic
621C22C2×C4×C22⋊D7111yescharacteristic
622C22C22×C8×D7111yescharacteristic
623C22C2×M16×D7111yescharacteristic
624C22C2×#1455613411yescharacteristic
625C22C2×#1455613611yescharacteristic
626C4—42no—
627C4—2842no—
628C4—1424no—
629C4—1424no—
630C4#1798587514yes—
631C4C2×#1455609611yescharacteristic
632C4C2×#1455609911yescharacteristic
633C4C2×#1455610111yescharacteristic
634C4C2×#1455611011yescharacteristic
635C2—44no—
636C2—1428no—
637C2#2258862918yesdirect product factor
638C2C2×#1798587511yescharacteristic
639C2C2×C22⋊C8×D7111yescharacteristic
640C2C2×#1798596411yescharacteristic
641C2C2×(C22⋊D71)⋊C811yescharacteristic
642C2C2×C8×C22⋊D7111yescharacteristic
643C2C2×#1798606811yescharacteristic
644C2C2×#1798607311yescharacteristic
subgroupG/H
centerC23×C4C22×D71
commutatorC22×C71C23×C8
FrattiniC22×C4C23×D71
FittingC22×C22⋊C8×C71C2
socleC24×C71C22×C4
prime radicalC23×C22⋊D71C4
cosocleC22×C4×C71C24
hypercenterC22×C22⋊C8D71
hypocenterC71C2×#1869
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C23×C8×D71C2semidirect
3. C22×C22⋊(C71⋊C8)C2semidirect
4. C22×(C2×D71)⋊C8C2semidirect
5. #22588629C2direct (N × H)
6. C2×#17985753C2semidirect
7. C2×#17985753C2semidirect
8. C22×C22⋊C8×C71C2semidirect
16. C22×C8×D71C22semidirect
26. C2×C22⋊(C71⋊C8)C22semidirect
28. C2×(C2×D71)⋊C8C22semidirect
29. #17985753C22semidirect
30. #17985753C22semidirect
35. C2×C22⋊C8×C71C22semidirect
39. C22×C22⋊D71C8semidirect
57. C22×C71⋊C8D4semidirect
95. C22×C8×C71D4semidirect
110. C2×C22⋊D71C2×C8semidirect
119. C22×Dic71C2×C8semidirect
143. C2×C71⋊C8C2×D4semidirect
157. C24×C71C2×C8semidirect
192. C2×C8×C71C2×D4semidirect
210. C23×C71C22×C8semidirect
225. C22×D71C22⋊C8semidirect
263. C2×Dic71C22×C8semidirect
302. C2×D71C2×C22⋊C8semidirect
314. C2×C71#1869semidirect
327. C22×C22⋊C8D71semidirect
331. C71C2×#1869semidirect
356. C2×C22⋊C8C2×D71semidirect
403. C22×C8C22⋊D71semidirect
436. C24C8×D71semidirect
509. C2×C8C2×C22⋊D71semidirect
547. C23C2×C8×D71semidirect
637. C2#22588629direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C8×D712
C22×C4×C22⋊D712
C22×C22⋊(C71⋊C8)2
C22×(C2×D71)⋊C82
#225886292
C2×#179857532
C22×C22⋊C8×C712
C2×#186971