Finite Group Databasebeta

← C2×#22589341 #32024240

Subgroups — C2×#22589341 #32024240

Order 18176.

2526 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11765852C211yesmaximal, characteristic, complemented
2C22×#14556102C211yesmaximal, characteristic
3C22×#14556052C211yesmaximal, characteristic, complemented
4C22×#14556048C211yesmaximal, characteristic, complemented
5C22×C22⋊(C71⋊C8)C211yesmaximal, characteristic, complemented
6#22589341C218yesmaximal, direct product factor
7C2×#17985761C211yesmaximal, characteristic, complemented
8C22×C22⋊Q8×C71C211yesmaximal, characteristic, complemented
9C23×D284C2211yescharacteristic
10C23×C22⋊D71—21no—
11C22×#11765852—24no—
12C22×#11765852—24no—
13C22×#11765852—24no—
14C22×#11765852C2214yescomplemented
15C23×C71⋊C8C2211yescharacteristic
16C23×C71⋊C8C2211yescharacteristic
17C2×#14556102—24no—
18C2×#14556102—22no—
19C2×#14556102—24no—
20C2×#14556102C2214yes—
21C22×C4⋊Dic71C2211yescharacteristic
22C22×(C2×D71)⋊C4—21no—
23C2×#14556052—24no—
24C2×#14556052C2214yescomplemented
25C2×#14556048—24no—
26C2×#14556048C2214yescomplemented
27C2×C22⋊(C71⋊C8)—24no—
28C2×C22⋊(C71⋊C8)C2214yescomplemented
29#17985761C2214yescomplemented
30C23×Q8×C71C2211yescharacteristic
31C24×C4×C71C2211yescharacteristic
32C2×C22⋊Q8×C71—24no—
33C2×C22⋊Q8×C71—22no—
34C2×C22⋊Q8×C71—24no—
35C2×C22⋊Q8×C71C2214yescomplemented
36C22×C4⋊C4×C71—21no—
37C22×C4⋊C4×C71C2211yescharacteristic
38C22×C22⋊C4×C71—21no—
39C24×D71—21no—
40C22×D284—22no—
41C22×D284—22no—
42C22×D284—22no—
43C22×D284—22no—
44C22×D284—21no—
45C22×D284—22no—
46C22×D284D414yes—
47C22×D284C2312yes—
48C22×C22⋊D71—28no—
49C22×C22⋊D71—24no—
50C22×C22⋊D71—44no—
51C22×C22⋊D71—44no—
52C23×Dic71—21no—
53C2×#11765852—232no—
54C2×#11765852—28no—
55C2×#11765852—28no—
56C2×#11765852—28no—
57C22×C71⋊C8—22no—
58C22×C71⋊C8—22no—
59C22×C71⋊C8—22no—
60C22×C71⋊C8—22no—
61C22×C71⋊C8—22no—
62C22×C71⋊C8D414yescomplemented
63C22×C71⋊C8C2312yes—
64C22×C71⋊C8C2312yes—
65#14556102—216no—
66#14556102—28no—
67#14556102—28no—
68C2×C4⋊Dic71—22no—
69C2×C4⋊Dic71—21no—
70C2×C4⋊Dic71D414yes—
71C2×C4⋊Dic71C2312yes—
72C2×(C2×D71)⋊C4—28no—
73C2×(C2×D71)⋊C4—24no—
74#14556052—28no—
75#14556048—28no—
76C22⋊(C71⋊C8)—28no—
77C25×C71D411yescharacteristic
78C22×Q8×C71—22no—
79C22×Q8×C71—21no—
80C22×Q8×C71—22no—
81C22×Q8×C71—22no—
82C22×Q8×C71—22no—
83C22×Q8×C71—22no—
84C22×Q8×C71D414yescomplemented
85C22×Q8×C71C2312yes—
86C23×C4×C71—21no—
87C23×C4×C71—21no—
88C23×C4×C71—22no—
89C23×C4×C71—22no—
90C23×C4×C71—22no—
91C23×C4×C71—22no—
92C23×C4×C71—22no—
93C23×C4×C71—22no—
94C23×C4×C71D411yescharacteristic
95C23×C4×C71D412yes—
96C23×C4×C71C2312yes—
97C23×C4×C71C2311yescharacteristic
98C22⋊Q8×C71—216no—
99C22⋊Q8×C71—28no—
100C22⋊Q8×C71—28no—
101C2×C4⋊C4×C71—28no—
102C2×C4⋊C4×C71—24no—
103C2×C4⋊C4×C71—21no—
104C2×C4⋊C4×C71—22no—
105C2×C4⋊C4×C71D414yescomplemented
106C2×C4⋊C4×C71C2312yes—
107C2×C22⋊C4×C71—28no—
108C2×C22⋊C4×C71—24no—
109C23×D71—24no—
110C23×D71—22no—
111C23×D71—42no—
112C23×D71—42no—
113C23×D71—42no—
114C23×D71—42no—
115C23×D71—42no—
116C23×D71—42no—
117C2×D284—28no—
118C2×D284—28no—
119C2×D284—22no—
120C2×D284—22no—
121C2×D284—22no—
122C2×D284—22no—
123C2×D284—24no—
124C2×D284—22no—
125C2×D284—42no—
126C2×D284—44no—
127C2×D284—42no—
128C2×D284—44no—
129C2×D284C2×D414yes—
130C2×C22⋊D71—216no—
131C2×C22⋊D71—48no—
132C2×C22⋊D71—432no—
133C2×C22⋊D71—48no—
134C22×Dic71—24no—
135C22×Dic71—22no—
136C22×Dic71—42no—
137C22×Dic71—42no—
138#11765852—232no—
139C2×C71⋊C8—28no—
140C2×C71⋊C8—22no—
141C2×C71⋊C8—22no—
142C2×C71⋊C8—22no—
143C2×C71⋊C8—22no—
144C2×C71⋊C8—22no—
145C2×C71⋊C8—44no—
146C2×C71⋊C8C2×D414yescomplemented
147C4⋊Dic71—24no—
148C4⋊Dic71—22no—
149C4⋊Dic71C2×D414yes—
150(C2×D71)⋊C4—216no—
151C24×C71—22no—
152C24×C71—22no—
153C24×C71—22no—
154C24×C71—22no—
155C24×C71—22no—
156C24×C71—22no—
157C24×C71SD1614yescomplemented
158C24×C71C2×D412yes—
159C24×C71C2×D411yescharacteristic
160C2×Q8×C71—24no—
161C2×Q8×C71—22no—
162C2×Q8×C71—28no—
163C2×Q8×C71—28no—
164C2×Q8×C71—22no—
165C2×Q8×C71—22no—
166C2×Q8×C71—22no—
167C2×Q8×C71—22no—
168C2×Q8×C71—42no—
169C2×Q8×C71—44no—
170C2×Q8×C71—42no—
171C2×Q8×C71—44no—
172C2×Q8×C71C2×D414yescomplemented
173C22×C4×C71—24no—
174C22×C4×C71—24no—
175C22×C4×C71—22no—
176C22×C4×C71—22no—
177C22×C4×C71—22no—
178C22×C4×C71—22no—
179C22×C4×C71—22no—
180C22×C4×C71—24no—
181C22×C4×C71—24no—
182C22×C4×C71—24no—
183C22×C4×C71—22no—
184C22×C4×C71—22no—
185C22×C4×C71—22no—
186C22×C4×C71—22no—
187C22×C4×C71—22no—
188C22×C4×C71—22no—
189C22×C4×C71—42no—
190C22×C4×C71—42no—
191C22×C4×C71—42no—
192C22×C4×C71—42no—
193C22×C4×C71—44no—
194C22×C4×C71—44no—
195C22×C4×C71—44no—
196C22×C4×C71—44no—
197C22×C4×C71C2×D412yes—
198C22×C4×C71C2×D412yes—
199C22×C4×C71C2×D412yes—
200C22×C4×C71C2×D412yes—
201C22×C4×C71C2×D411yescharacteristic
202C22×C4×C71C2×D412yes—
203C22×C4×C71C2×D412yes—
204C22×C4×C71#4112yes—
205C22×C4×C71C2411yescharacteristic
206C4⋊C4×C71—216no—
207C4⋊C4×C71—24no—
208C4⋊C4×C71—22no—
209C4⋊C4×C71C2×D414yescomplemented
210C22⋊C4×C71—216no—
211C23×C71—22no—
212C23×C71—22no—
213C23×C71—22no—
214C23×C71—22no—
215C23×C71—22no—
216C23×C71—22no—
217C23×C71—28no—
218C23×C71—28no—
219C23×C71—28no—
220C23×C71—44no—
221C23×C71—44no—
222C23×C71—44no—
223C23×C71—44no—
224C23×C71#12012yes—
225C23×C71#12012yes—
226C23×C71#12112yes—
227C23×C71C2×SD1612yes—
228C23×C71C2×SD1614yescomplemented
229C23×C71#13512yes—
230C23×C71AGL(1,ℤ/8)12yes—
231C23×C71#13712yes—
232C23×C71C22×D411yescharacteristic
233C22×D71—24no—
234C22×D71—42no—
235C22×D71—42no—
236C22×D71—42no—
237C22×D71—42no—
238C22×D71—42no—
239C22×D71—42no—
240C22×D71—48no—
241C22×D71—48no—
242C22×D71—48no—
243C22×D71—84no—
244C22×D71—84no—
245C22×D71—84no—
246C22×D71—84no—
247Q8×C71—24no—
248Q8×C71—24no—
249Q8×C71—42no—
250Q8×C71—42no—
251Q8×C71—48no—
252C2×C4×C71—24no—
253C2×C4×C71—24no—
254C2×C4×C71—22no—
255C2×C4×C71—22no—
256C2×C4×C71—22no—
257C2×C4×C71—42no—
258C2×C4×C71—42no—
259C2×C4×C71—42no—
260C2×C4×C71—42no—
261C2×C4×C71—44no—
262C2×C4×C71—48no—
263C2×C4×C71—48no—
264C2×C4×C71—42no—
265C2×C4×C71—42no—
266C2×C4×C71—42no—
267C2×C4×C71—42no—
268C2×C4×C71—48no—
269C2×C4×C71#12014yes—
270C2×C4×C71#12012yes—
271C2×C4×C71#12012yes—
272C2×C4×C71#12114yes—
273C2×C4×C71#12114yes—
274C2×C4×C71#12112yes—
275C2×C4×C71#12714yes—
276C2×C4×C71C22×D411yescharacteristic
277C2×C4×C71C22×D411yescharacteristic
278C2×C4×C71C22×D411yescharacteristic
279C2×C4×C71C22×D411yescharacteristic
280C2×C4×C71C22×D411yescharacteristic
281C2×C4×C71C2×#4111yescharacteristic
282C22⋊D71—432no—
283C2×Dic71—24no—
284C2×Dic71—42no—
285C2×Dic71—42no—
286C2×Dic71—48no—
287D284—24no—
288D284—24no—
289D284—42no—
290D284—42no—
291D284—48no—
292C71⋊C8—24no—
293C71⋊C8—42no—
294C22×C71—24no—
295C22×C71—24no—
296C22×C71—24no—
297C22×C71—42no—
298C22×C71—42no—
299C22×C71—42no—
300C22×C71—416no—
301C22×C71—42no—
302C22×C71#39214yes—
303C22×C71#44814yes—
304C22×C71#44914yes—
305C22×C71#45014yes—
306C22×C71#45214yes—
307C22×C71#46514yes—
308C22×C71#46814yes—
309C22×C71C2×#12011yescharacteristic
310C22×C71C2×#12011yescharacteristic
311C22×C71C2×#12111yescharacteristic
312C22×C71C22×SD1611yescharacteristic
313C22×C71C2×#13511yescharacteristic
314C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
315C22×C71C2×#13711yescharacteristic
316C2×D71—44no—
317C2×D71—44no—
318C2×D71—44no—
319C2×D71—82no—
320C2×D71—82no—
321C2×D71—816no—
322C2×D71—82no—
323C2×D71—82no—
324C4×C71—42no—
325C4×C71—44no—
326C4×C71—44no—
327C4×C71#39214yes—
328C4×C71C2×#12011yescharacteristic
329C4×C71C2×#12111yescharacteristic
330C4×C71C2×#12111yescharacteristic
331C4×C71C2×#12711yescharacteristic
332Dic71—44no—
333C2×#2000—711nomaximal, Sylow
334C2×C71—44no—
335C2×C71#200018yescomplemented
336C2×C71C2×#39211yescharacteristic
337C2×C71C2×#45011yescharacteristic
338C2×C71C2×#44811yescharacteristic
339C2×C71C2×#44911yescharacteristic
340C2×C71C2×#45211yescharacteristic
341C2×C71C2×#46511yescharacteristic
342C2×C71C2×#46811yescharacteristic
343D71—84no—
344C23×SD16—711no—
345C22×C22⋊Q8D7111yescharacteristic, complemented
346C22×#121—711no—
347C22×#103—711no—
348C22×#102—711no—
349C22×C22⋊C8—711no—
350#2000—718no—
351C2×#340—711no—
352C71C2×#200011yescharacteristic, complemented, Sylow
353C23×Q8C2×D7111yescharacteristic
354C23×D4—711no—
355C23×D4—1421no—
356C24×C4C2×D7111yescharacteristic
357C22×SD16—714no—
358C22×SD16—1424no—
359C22×SD16—1424no—
360C22×SD16—1424no—
361C23×C8—711no—
362C23×C8—711no—
363C2×C22⋊Q8—24no—
364C2×C22⋊Q8—22no—
365C2×C22⋊Q8—24no—
366C2×C22⋊Q8C2×D7114yescomplemented
367C2×#121—714no—
368C2×#121—1424no—
369C2×#121—1424no—
370C2×#121—1422no—
371C22×C4⋊C4—21no—
372C22×C4⋊C4—711no—
373C22×C4⋊C4C2×D7111yescharacteristic
374C22×C22⋊C4—21no—
375C22×C22⋊C4—1421no—
376C2×#103—714no—
377C2×#103—1424no—
378C2×#102—714no—
379C2×#102—1424no—
380C2×C22⋊C8—714no—
381C2×C22⋊C8—1424no—
382#340—714no—
383C25—1421no—
384C25C22⋊D7111yescharacteristic
385C22×Q8—21no—
386C22×Q8—22no—
387C22×Q8—22no—
388C22×Q8—22no—
389C22×Q8—22no—
390C22×Q8—22no—
391C22×Q8C22⋊D7114yescomplemented
392C22×Q8C22×D7112yes—
393C22×D4—2844no—
394C22×D4—2844no—
395C22×D4—714no—
396C22×D4—712no—
397C22×D4—1428no—
398C22×D4—1424no—
399C22×D4—1422no—
400C22×D4—1422no—
401C22×D4—1421no—
402C22×D4—1422no—
403C22×D4—1422no—
404C22×D4—1422no—
405C23×C4—21no—
406C23×C4—21no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—22no—
413C23×C4—1421no—
414C23×C4C22⋊D7112yes—
415C23×C4C22⋊D7111yescharacteristic
416C23×C4C22×D7112yes—
417C23×C4C22×D7111yescharacteristic
418C2×SD16—1428no—
419C2×SD16—1428no—
420C2×SD16—14232no—
421C2×SD16—1428no—
422C22×C8—714no—
423C22×C8—712no—
424C22×C8—712no—
425C22×C8—1422no—
426C22×C8—1422no—
427C22×C8—1422no—
428C22×C8—1422no—
429C22×C8—1422no—
430C22⋊Q8—216no—
431C22⋊Q8—28no—
432C22⋊Q8—28no—
433#121—1428no—
434#121—1428no—
435#121—14216no—
436C2×C4⋊C4—28no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—714no—
441C2×C4⋊C4—712no—
442C2×C4⋊C4—1422no—
443C2×C4⋊C4—1421no—
444C2×C4⋊C4C22⋊D7114yescomplemented
445C2×C4⋊C4C22×D7112yes—
446C2×C22⋊C4—28no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—1428no—
449C2×C22⋊C4—1424no—
450#103—1428no—
451#102—1428no—
452C22⋊C8—1428no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—2842no—
460C24—2842no—
461C24—2842no—
462C24—2842no—
463C24—2842no—
464C24—2842no—
465C24—1422no—
466C24—1424no—
467C24#1176585214yescomplemented
468C24C2×C22⋊D7112yes—
469C24C2×C22⋊D7111yescharacteristic
470C2×Q8—22no—
471C2×Q8—24no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—28no—
477C2×Q8—28no—
478C2×Q8—42no—
479C2×Q8—44no—
480C2×Q8—42no—
481C2×Q8—44no—
482C2×Q8C2×C22⋊D7114yescomplemented
483C2×D4—28432no—
484C2×D4—2848no—
485C2×D4—2848no—
486C2×D4—2842no—
487C2×D4—2842no—
488C2×D4—2844no—
489C2×D4—2844no—
490C2×D4—714no—
491C2×D4—14216no—
492C2×D4—1422no—
493C2×D4—1422no—
494C2×D4—1422no—
495C2×D4—1422no—
496C2×D4—1422no—
497C2×D4—1424no—
498C2×D4—1428no—
499C2×D4—1428no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—2842no—
525C22×C4—2842no—
526C22×C4—1422no—
527C22×C4—1424no—
528C22×C4D4×D7112yes—
529C22×C4D4×D7112yes—
530C22×C4D4×D7112yes—
531C22×C4C2×C22⋊D7112yes—
532C22×C4C2×C22⋊D7112yes—
533C22×C4C2×C22⋊D7112yes—
534C22×C4C2×C22⋊D7111yescharacteristic
535C22×C4#1176586412yes—
536C22×C4C23×D7111yescharacteristic
537SD16—14232no—
538C2×C8—2844no—
539C2×C8—714no—
540C2×C8—1422no—
541C2×C8—1422no—
542C2×C8—1422no—
543C2×C8—1422no—
544C2×C8—1422no—
545C2×C8—1428no—
546C4⋊C4—216no—
547C4⋊C4—22no—
548C4⋊C4—24no—
549C4⋊C4—714no—
550C4⋊C4—1422no—
551C4⋊C4—1424no—
552C4⋊C4C2×C22⋊D7114yescomplemented
553C22⋊C4—216no—
554C22⋊C4—14216no—
555C23—28no—
556C23—28no—
557C23—22no—
558C23—22no—
559C23—28no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—22no—
564C23—44no—
565C23—44no—
566C23—44no—
567C23—44no—
568C23—2848no—
569C23—2848no—
570C23—2848no—
571C23—2842no—
572C23—2842no—
573C23—2842no—
574C23—2842no—
575C23—2842no—
576C23—2842no—
577C23—5684no—
578C23—5684no—
579C23—5684no—
580C23—5684no—
581C23—1424no—
582C23#1455609612yes—
583C23#1455609712yes—
584C23#1455610012yes—
585C23C2×#1176585212yes—
586C23C2×#1176585214yescomplemented
587C23#1455614812yes—
588C23#1455615312yes—
589C23#1455615912yes—
590C23C22×C22⋊D7111yescharacteristic
591Q8—24no—
592Q8—24no—
593Q8—48no—
594Q8—42no—
595Q8—42no—
596D4—28432no—
597D4—2848no—
598D4—2842no—
599D4—2842no—
600D4—1424no—
601D4—1424no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—48no—
608C2×C4—44no—
609C2×C4—48no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—48no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—2848no—
620C2×C4—2842no—
621C2×C4—2842no—
622C2×C4—1424no—
623C2×C4#1455609612yes—
624C2×C4#1455609614yes—
625C2×C4#1455609712yes—
626C2×C4#1455609914yes—
627C2×C4#1455610012yes—
628C2×C4#1455610014yes—
629C2×C4#1455612414yes—
630C2×C4C2×D4×D7111yescharacteristic
631C2×C4C2×D4×D7111yescharacteristic
632C2×C4C2×D4×D7111yescharacteristic
633C2×C4C22×C22⋊D7111yescharacteristic
634C2×C4C22×C22⋊D7111yescharacteristic
635C2×C4C2×#1176586411yescharacteristic
636C8—2842no—
637C8—1424no—
638C22—24no—
639C22—24no—
640C22—24no—
641C22—42no—
642C22—42no—
643C22—416no—
644C22—42no—
645C22—42no—
646C22—2844no—
647C22—2844no—
648C22—2844no—
649C22—5682no—
650C22—5682no—
651C22—5682no—
652C22—56816no—
653C22—5682no—
654C22#1798590714yes—
655C22#1798613814yes—
656C22#1798614414yes—
657C22#1798614914yes—
658C22#1798615914yes—
659C22#1798623014yes—
660C22#1798624714yes—
661C22C2×#1455609611yescharacteristic
662C22C2×#1455609711yescharacteristic
663C22C2×#1455610011yescharacteristic
664C22C22×#1176585211yescharacteristic
665C22C2×#1455614811yescharacteristic
666C22C2×#1455615311yescharacteristic
667C22C2×#1455615911yescharacteristic
668C4—42no—
669C4—44no—
670C4—44no—
671C4—2844no—
672C4#1798590714yes—
673C4C2×#1455609611yescharacteristic
674C4C2×#1455609911yescharacteristic
675C4C2×#1455610011yescharacteristic
676C4C2×#1455612411yescharacteristic
677C2—44no—
678C2—5684no—
679C2#2258934118yesdirect product factor
680C2C2×#1798590711yescharacteristic
681C2C2×#1798614911yescharacteristic
682C2C2×#1798613811yescharacteristic
683C2C2×#1798614411yescharacteristic
684C2C2×#1798615911yescharacteristic
685C2C2×#1798623011yescharacteristic
686C2C2×#1798624711yescharacteristic
subgroupG/H
centerC24C2×C22⋊D71
commutator, cosocleC22×C4×C71C24
FrattiniC22×C4C23×D71
FittingC22×C22⋊Q8×C71C2
socleC24×C71C2×D4
prime radicalC22×#14556102C2
hypercenterC22×C22⋊Q8D71
hypocenterC71C2×#2000
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C23×#11765852C2semidirect
3. C22×#14556052C2semidirect
4. C22×#14556048C2semidirect
5. C22×C22⋊(C71⋊C8)C2semidirect
6. #22589341C2direct (N × H)
7. C2×#17985761C2semidirect
8. C22×C22⋊Q8×C71C2semidirect
14. C22×#11765852C22semidirect
24. C2×#14556052C22semidirect
26. C2×#14556048C22semidirect
28. C2×C22⋊(C71⋊C8)C22semidirect
29. #17985761C22semidirect
35. C2×C22⋊Q8×C71C22semidirect
62. C22×C71⋊C8D4semidirect
84. C22×Q8×C71D4semidirect
105. C2×C4⋊C4×C71D4semidirect
146. C2×C71⋊C8C2×D4semidirect
157. C24×C71SD16semidirect
172. C2×Q8×C71C2×D4semidirect
209. C4⋊C4×C71C2×D4semidirect
228. C23×C71C2×SD16semidirect
335. C2×C71#2000semidirect
345. C22×C22⋊Q8D71semidirect
352. C71C2×#2000semidirect
366. C2×C22⋊Q8C2×D71semidirect
391. C22×Q8C22⋊D71semidirect
444. C2×C4⋊C4C22⋊D71semidirect
467. C24#11765852semidirect
482. C2×Q8C2×C22⋊D71semidirect
552. C4⋊C4C2×C22⋊D71semidirect
586. C23C2×#11765852semidirect
679. C2#22589341direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#117658522
C22×#145561022
C22×#145560522
C22×#145560482
C22×C22⋊(C71⋊C8)2
#225893412
C2×#179857612
C22×C22⋊Q8×C712
C2×#200071