Finite Group Databasebeta

← #32015653

Subgroups — #32015653

Order 18176.

970 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986071C211yesmaximal, characteristic
2C2×#17986042C211yesmaximal, characteristic, complemented
3C2×#17986035C211yesmaximal, characteristic, complemented
4#22591269C211yesmaximal, characteristic
5#22589108C211yesmaximal, characteristic, complemented
6#22589101C211yesmaximal, characteristic, complemented
7#22588539C211yesmaximal, characteristic, complemented
8#22588539C211yesmaximal, characteristic, complemented
9#22588537C211yesmaximal, characteristic, complemented
10#22588532C211yesmaximal, characteristic, complemented
11#22588506C211yesmaximal, characteristic, complemented
12#22588371C211yesmaximal, characteristic, complemented
13#22588363C211yesmaximal, characteristic, complemented
14#22588238C211yesmaximal, characteristic, complemented
15C71×#2354C211yesmaximal, characteristic
16C22×#11765849C2211yescharacteristic
17C23×C71⋊C8C2211yescharacteristic
18C2×#14556087C2211yescharacteristic
19C22×C4⋊Dic71C2211yescharacteristic
20#17986071C418yescomplemented
21#17986042—24no—
22#17986035—24no—
23C2×#14556061C2211yescharacteristic
24C2×#14556061C2211yescharacteristic
25C2×#14556061C2211yescharacteristic
26C2×#14556061C2211yescharacteristic
27C2×#14556059C2211yescharacteristic
28C2×#14556059C2211yescharacteristic
29C2×#14556059C2211yescharacteristic
30C2×#14556059C2211yescharacteristic
31C2×#14556059C2211yescharacteristic
32C2×#14556059C2211yescharacteristic
33C2×C4⋊(C71⋊C8)C2211yescharacteristic
34C2×C22⋊(C71⋊C8)C2211yescharacteristic
35C2×C22⋊(C71⋊C8)C2211yescharacteristic
36C2×#14556039C2211yescharacteristic
37#17985892—21no—
38#17985885—21no—
39#17985879—21no—
40#17985865C2211yescharacteristic
41#17985859C2211yescharacteristic
42#17985859C2211yescharacteristic
43C4×C4⋊Dic71C2211yescharacteristic
44C22⋊C4×Dic71—21no—
45#17985761C2211yescharacteristic
46#17985761C2211yescharacteristic
47#17985761C2211yescharacteristic
48#17985761C2211yescharacteristic
49#17985761C2211yescharacteristic
50#17985761C2211yescharacteristic
51C2×C4×D4×C71C2211yescharacteristic
52C2×#117×C71C2211yescharacteristic
53C2×#117×C71C2211yescharacteristic
54#390×C71—21no—
55#388×C71—21no—
56#388×C71—21no—
57#384×C71C2211yescharacteristic
58#380×C71C2211yescharacteristic
59#380×C71C2211yescharacteristic
60C4×C4⋊C4×C71—21no—
61C4×C4⋊C4×C71C2211yescharacteristic
62C23×Dic71—21no—
63C2×#11765849—22no—
64C2×#11765849—22no—
65C2×#11765849C2×C414yes—
66C22×C71⋊C8—22no—
67C22×C71⋊C8—22no—
68C22×C71⋊C8C2×C414yescomplemented
69C22×C71⋊C8C2311yescharacteristic
70C22×C71⋊C8C2311yescharacteristic
71C22×C71⋊C8C2311yescharacteristic
72C22×C71⋊C8C2311yescharacteristic
73#14556087—22no—
74#14556087—41no—
75C2×C4⋊Dic71—22no—
76C2×C4⋊Dic71—21no—
77C2×C4⋊Dic71—41no—
78C2×C4⋊Dic71C2311yescharacteristic
79C2×C4⋊Dic71C2311yescharacteristic
80C2×C4⋊Dic71C2311yescharacteristic
81C2×C4⋊Dic71C2311yescharacteristic
82C2×C22⋊Dic71—21no—
83C2×C22⋊Dic71—21no—
84C2×C22⋊Dic71—21no—
85C2×C4×Dic71—21no—
86C2×C4×Dic71—21no—
87#14556061—22no—
88#14556061—22no—
89#14556061—41no—
90#14556061D414yescomplemented
91#14556059—22no—
92#14556059—22no—
93#14556059—22no—
94#14556059—22no—
95#14556059—22no—
96#14556059—41no—
97C4⋊(C71⋊C8)C2×C414yescomplemented
98C22⋊(C71⋊C8)C2×C414yes—
99C22⋊(C71⋊C8)C2×C414yescomplemented
100#14556039C2×C414yescomplemented
101C71⋊#95—21no—
102C71⋊#95—21no—
103C71⋊#95—21no—
104C71⋊#95—21no—
105C71⋊#95—21no—
106C22×D4×C71D411yescharacteristic
107C23×C4×C71C2311yescharacteristic
108C23×C4×C71C2311yescharacteristic
109C4×D4×C71C2×C414yes—
110C4×D4×C71Q814yes—
111#117×C71—22no—
112#117×C71—22no—
113#117×C71—41no—
114#117×C71—41no—
115C2×C4⋊C4×C71—21no—
116C2×C4⋊C4×C71—21no—
117C2×C4⋊C4×C71D411yescharacteristic
118C2×C4⋊C4×C71C2311yescharacteristic
119C2×C4⋊C4×C71C2311yescharacteristic
120C2×C4⋊C4×C71C2311yescharacteristic
121C2×C4⋊C4×C71C2311yescharacteristic
122C2×C22⋊C4×C71—21no—
123C2×C22⋊C4×C71—21no—
124C2×C22⋊C4×C71—21no—
125C2×C22⋊C4×C71—21no—
126C2×C22⋊C4×C71D411yescharacteristic
127C2×C22⋊C4×C71D411yescharacteristic
128C2×C42×C71—21no—
129C2×C42×C71—21no—
130C2×C42×C71—21no—
131C2×C42×C71C2311yescharacteristic
132#95×C71—21no—
133#95×C71—21no—
134#95×C71—21no—
135C22×Dic71—21no—
136C22×Dic71—21no—
137C22×Dic71—21no—
138C22×Dic71—21no—
139C22×Dic71—42no—
140C22×Dic71—42no—
141C22×Dic71—81no—
142#11765849—28no—
143C2×C71⋊C8—21no—
144C2×C71⋊C8—21no—
145C2×C71⋊C8—21no—
146C2×C71⋊C8—21no—
147C2×C71⋊C8—21no—
148C2×C71⋊C8—21no—
149C2×C71⋊C8—28no—
150C2×C71⋊C8C22×C412yes—
151C2×C71⋊C8C22×C412yes—
152C2×C71⋊C8C22×C412yes—
153C2×C71⋊C8C22×C412yes—
154C2×C71⋊C8C2×D412yes—
155C2×C71⋊C8#4112yes—
156C4⋊Dic71—21no—
157C4⋊Dic71—21no—
158C4⋊Dic71—21no—
159C4⋊Dic71—21no—
160C4⋊Dic71—21no—
161C4⋊Dic71—21no—
162C4⋊Dic71—21no—
163C4⋊Dic71—42no—
164C4⋊Dic71C2×D412yes—
165C22⋊Dic71—42no—
166C22⋊Dic71—42no—
167C22⋊Dic71—81no—
168C4×Dic71—42no—
169C4×Dic71—81no—
170C24×C71C2×D411yescharacteristic
171C24×C71C2×D411yescharacteristic
172C2×D4×C71—41no—
173C2×D4×C71—41no—
174C2×D4×C71C4⋊C414yes—
175C22×C4×C71—21no—
176C22×C4×C71—21no—
177C22×C4×C71—21no—
178C22×C4×C71—21no—
179C22×C4×C71—21no—
180C22×C4×C71—21no—
181C22×C4×C71—21no—
182C22×C4×C71—21no—
183C22×C4×C71—21no—
184C22×C4×C71—21no—
185C22×C4×C71—21no—
186C22×C4×C71—21no—
187C22×C4×C71C22×C412yes—
188C22×C4×C71C22×C412yes—
189C22×C4×C71C2×D411yescharacteristic
190C22×C4×C71C2×D411yescharacteristic
191C22×C4×C71C2×D411yescharacteristic
192C22×C4×C71C2×D411yescharacteristic
193C22×C4×C71C2×Q812yes—
194C22×C4×C71C2×Q812yes—
195C22×C4×C71C2411yescharacteristic
196C4⋊C4×C71—21no—
197C4⋊C4×C71—21no—
198C4⋊C4×C71—21no—
199C4⋊C4×C71—21no—
200C4⋊C4×C71—21no—
201C4⋊C4×C71—21no—
202C4⋊C4×C71—21no—
203C4⋊C4×C71—42no—
204C4⋊C4×C71—81no—
205C4⋊C4×C71C4⋊C414yes—
206C4⋊C4×C71C2×D412yes—
207C22⋊C4×C71—42no—
208C22⋊C4×C71—42no—
209C22⋊C4×C71—81no—
210C22⋊C4×C71—81no—
211C22⋊C4×C71C4⋊C414yes—
212C22⋊C4×C71C4⋊C414yes—
213C42×C71—42no—
214C42×C71—42no—
215C42×C71—42no—
216C42×C71C22×C412yes—
217C42×C71C2×Q812yes—
218C23×C71—21no—
219C23×C71—21no—
220C23×C71—21no—
221C23×C71—21no—
222C23×C71—21no—
223C23×C71—21no—
224C23×C71—21no—
225C23×C71—21no—
226C23×C71—21no—
227C23×C71—21no—
228C23×C71—21no—
229C23×C71—21no—
230C23×C71C2×C4⋊C412yes—
231C23×C71C2×C4⋊C412yes—
232C23×C71C22×D411yescharacteristic
233D4×C71—44no—
234C2×C4×C71—21no—
235C2×C4×C71—21no—
236C2×C4×C71—21no—
237C2×C4×C71—21no—
238C2×C4×C71—21no—
239C2×C4×C71—21no—
240C2×C4×C71—21no—
241C2×C4×C71—21no—
242C2×C4×C71—22no—
243C2×C4×C71—22no—
244C2×C4×C71—22no—
245C2×C4×C71—22no—
246C2×C4×C71—22no—
247C2×C4×C71—22no—
248C2×C4×C71—22no—
249C2×C4×C71—22no—
250C2×C4×C71—22no—
251C2×C4×C71—41no—
252C2×C4×C71—41no—
253C2×C4×C71—41no—
254C2×C4×C71—41no—
255C2×C4×C71—41no—
256C2×C4×C71—41no—
257C2×C4×C71—41no—
258C2×C4×C71—41no—
259C2×C4×C71—41no—
260C2×C4×C71—41no—
261C2×C4×C71—41no—
262C2×C4×C71C2×C4⋊C412yes—
263C2×C4×C71C2×C4⋊C412yes—
264C2×C4×C71C2×C4⋊C412yes—
265C2×C4×C71C2×C4⋊C412yes—
266C2×C4×C71C23×C411yescharacteristic
267C2×C4×C71C22×D411yescharacteristic
268C2×C4×C71C22×Q811yescharacteristic
269C2×C4×C71C2×#4111yescharacteristic
270C2×C4×C71H(5,𝔽2)11yescharacteristic
271C2×C4×C712−1+411yescharacteristic
272C2×Dic71—22no—
273C2×Dic71—41no—
274C2×Dic71—41no—
275C2×Dic71—41no—
276C2×Dic71—41no—
277C2×Dic71—41no—
278C2×Dic71—41no—
279C2×Dic71—41no—
280C2×Dic71—41no—
281C2×Dic71—41no—
282C2×Dic71—41no—
283C2×Dic71—41no—
284C2×Dic71—84no—
285C71⋊C8—22no—
286C71⋊C8—22no—
287C71⋊C8—22no—
288C71⋊C8C4×D414yes—
289C22×C71—22no—
290C22×C71—22no—
291C22×C71—22no—
292C22×C71—22no—
293C22×C71—22no—
294C22×C71—22no—
295C22×C71—41no—
296C22×C71—41no—
297C22×C71—41no—
298C22×C71—41no—
299C22×C71—41no—
300C22×C71—41no—
301C22×C71—41no—
302C22×C71—41no—
303C22×C71C22×C4⋊C411yescharacteristic
304C22×C71D4211yescharacteristic
305C22×C71#54711yescharacteristic
306C22×C71#57511yescharacteristic
307C22×C71#57511yescharacteristic
308C22×C71#57711yescharacteristic
309C22×C71#57711yescharacteristic
310C4×C71—22no—
311C4×C71—22no—
312C4×C71—22no—
313C4×C71—22no—
314C4×C71—42no—
315C4×C71—81no—
316C4×C71—81no—
317C4×C71—81no—
318C4×C71C2×C4×D411yescharacteristic
319C4×C71#52011yescharacteristic
320C4×C71D4×Q811yescharacteristic
321C4×C71#55411yescharacteristic
322Dic71—42no—
323Dic71—81no—
324Dic71—81no—
325Dic71—81no—
326#22662—711nomaximal, Sylow
327C2×C71—42no—
328C2×C71—42no—
329C2×C71D4×C4⋊C411yescharacteristic
330C2×C71#291111yescharacteristic
331C2×C71#291211yescharacteristic
332C2×C71#326711yescharacteristic
333C2×C71#327111yescharacteristic
334C2×C71#334811yescharacteristic
335C2×C71#335011yescharacteristic
336C2×#435—711no—
337C2×#428—711no—
338C2×#427—711no—
339#2354D7111yescharacteristic
340#2352—711no—
341#1949—711no—
342#1948—711no—
343#1854—711no—
344#1854—711no—
345#1854—711no—
346#1853—711no—
347#1847—711no—
348#1809—711no—
349#1807—711no—
350#1776—711no—
351C71#2266211yescharacteristic, complemented, Sylow
352C22×M16—711no—
353C23×C8—711no—
354C2×C4×D4C2×D7111yescharacteristic
355C2×#117—711no—
356C2×#117C2×D7111yescharacteristic
357C2×#117C2×D7111yescharacteristic
358C22×C4⋊C4—711no—
359#435—718no—
360#428—1424no—
361#427—1424no—
362C2×#107—711no—
363C2×#107—711no—
364C2×#107—711no—
365C2×#107—711no—
366C2×#106—711no—
367C2×#106—711no—
368C2×#106—711no—
369C2×#106—711no—
370C2×#106—711no—
371C2×#106—711no—
372C2×C4⋊C8—711no—
373C2×C22⋊C8—711no—
374C2×C22⋊C8—711no—
375C2×#97—711no—
376#390—21no—
377#388—21no—
378#388—21no—
379#388—1421no—
380#387—1421no—
381#386—1421no—
382#384C2×D7111yescharacteristic
383#382—711no—
384#380—711no—
385#380—711no—
386#380C2×D7111yescharacteristic
387#380C2×D7111yescharacteristic
388C4×C4⋊C4—21no—
389C4×C4⋊C4—711no—
390C4×C4⋊C4C2×D7111yescharacteristic
391C4×C22⋊C4—1421no—
392#340—711no—
393#340—711no—
394#340—711no—
395#340—711no—
396#340—711no—
397#340—711no—
398C22×D4C22⋊D7111yescharacteristic
399C23×C4—1421no—
400C23×C4C22×D7111yescharacteristic
401C23×C4C22×D7111yescharacteristic
402C2×M16—714no—
403C2×M16—1422no—
404C2×M16—1422no—
405C22×C8—711no—
406C22×C8—714no—
407C22×C8—711no—
408C22×C8—711no—
409C22×C8—711no—
410C22×C8—1422no—
411C22×C8—1422no—
412C4×D4Dic14214yes—
413C4×D4C4×D7114yes—
414#117—22no—
415#117—22no—
416#117—41no—
417#117—41no—
418#117—2841no—
419#117—1422no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—2841no—
423C2×C4⋊C4—711no—
424C2×C4⋊C4—711no—
425C2×C4⋊C4—711no—
426C2×C4⋊C4—711no—
427C2×C4⋊C4—1421no—
428C2×C4⋊C4—1422no—
429C2×C4⋊C4C22⋊D7111yescharacteristic
430C2×C4⋊C4C22×D7111yescharacteristic
431C2×C4⋊C4C22×D7111yescharacteristic
432C2×C4⋊C4C22×D7111yescharacteristic
433C2×C4⋊C4C22×D7111yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—1421no—
439C2×C22⋊C4—1421no—
440C2×C22⋊C4—1421no—
441C2×C22⋊C4C22⋊D7111yescharacteristic
442C2×C22⋊C4C22⋊D7111yescharacteristic
443C2×C42—21no—
444C2×C42—21no—
445C2×C42—21no—
446C2×C42—1421no—
447C2×C42—1421no—
448C2×C42C22×D7111yescharacteristic
449#107—2841no—
450#107—714no—
451#107—1422no—
452#107—1422no—
453#106—2841no—
454#106—1422no—
455#106—1422no—
456#106—1422no—
457#106—1422no—
458#106—1422no—
459C4⋊C8—714no—
460C22⋊C8—714no—
461C22⋊C8—714no—
462#97—714no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—1421no—
467#95—1421no—
468#95—1421no—
469#95—1421no—
470#95—1421no—
471C24C2×C22⋊D7111yescharacteristic
472C24C2×C22⋊D7111yescharacteristic
473C2×D4—41no—
474C2×D4—41no—
475C2×D4Dic71⋊C414yes—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—2842no—
489C22×C4—2842no—
490C22×C4—5681no—
491C22×C4—1421no—
492C22×C4—1421no—
493C22×C4—1421no—
494C22×C4—1421no—
495C22×C4C2×C4×D7112yes—
496C22×C4C2×C4×D7112yes—
497C22×C4C2×C22⋊D7111yescharacteristic
498C22×C4C2×C22⋊D7111yescharacteristic
499C22×C4C2×C22⋊D7111yescharacteristic
500C22×C4C2×C22⋊D7111yescharacteristic
501C22×C4C2×Dic14212yes—
502C22×C4C2×Dic14212yes—
503C22×C4C23×D7111yescharacteristic
504M16—1428no—
505C2×C8—712no—
506C2×C8—712no—
507C2×C8—712no—
508C2×C8—712no—
509C2×C8—712no—
510C2×C8—712no—
511C2×C8—1428no—
512C2×C8—1421no—
513C2×C8—1421no—
514C2×C8—1421no—
515C2×C8—1421no—
516C2×C8—1421no—
517C2×C8—1421no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—42no—
526C4⋊C4—81no—
527C4⋊C4—2842no—
528C4⋊C4—712no—
529C4⋊C4—1421no—
530C4⋊C4—1421no—
531C4⋊C4—1421no—
532C4⋊C4—1421no—
533C4⋊C4—1421no—
534C4⋊C4—1421no—
535C4⋊C4—1421no—
536C4⋊C4Dic71⋊C414yes—
537C4⋊C4D4×D7112yes—
538C22⋊C4—42no—
539C22⋊C4—42no—
540C22⋊C4—81no—
541C22⋊C4—81no—
542C22⋊C4—2842no—
543C22⋊C4—2842no—
544C22⋊C4—5681no—
545C22⋊C4Dic71⋊C414yes—
546C22⋊C4Dic71⋊C414yes—
547C42—42no—
548C42—42no—
549C42—42no—
550C42—2842no—
551C42—5681no—
552C42C2×C4×D7112yes—
553C42C2×Dic14212yes—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23C2×Dic71⋊C412yes—
567C23C2×Dic71⋊C412yes—
568C23C22×C22⋊D7111yescharacteristic
569D4—44no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—2841no—
599C2×C4—2841no—
600C2×C4—2841no—
601C2×C4—2841no—
602C2×C4—2841no—
603C2×C4—2841no—
604C2×C4—2841no—
605C2×C4—2841no—
606C2×C4—2841no—
607C2×C4—2841no—
608C2×C4—2841no—
609C2×C4—5684no—
610C2×C4—1422no—
611C2×C4C2×Dic71⋊C412yes—
612C2×C4C2×Dic71⋊C412yes—
613C2×C4C2×Dic71⋊C412yes—
614C2×C4C2×Dic71⋊C412yes—
615C2×C4C22×C4×D7111yescharacteristic
616C2×C4C2×D4×D7111yescharacteristic
617C2×C4C22×Dic14211yescharacteristic
618C2×C4#41×D7111yescharacteristic
619C2×C4#1455617311yescharacteristic
620C2×C4#1455617511yescharacteristic
621C8—714no—
622C8—1422no—
623C8—1422no—
624C8—1422no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22C22×Dic71⋊C411yescharacteristic
640C22D4×C22⋊D7111yescharacteristic
641C22#1798664811yescharacteristic
642C22#1798679711yescharacteristic
643C22#1798679711yescharacteristic
644C22#1798680711yescharacteristic
645C22#1798681011yescharacteristic
646C4—22no—
647C4—22no—
648C4—22no—
649C4—22no—
650C4—42no—
651C4—81no—
652C4—81no—
653C4—81no—
654C4—2842no—
655C4—5681no—
656C4—5681no—
657C4—5681no—
658C4C4×D4×D7111yescharacteristic
659C4#1798647811yescharacteristic
660C4D4×Dic14211yescharacteristic
661C4#1798670811yescharacteristic
662C2—42no—
663C2—42no—
664C2D4×Dic71⋊C411yescharacteristic
665C2#2259692911yescharacteristic
666C2#2259693311yescharacteristic
667C2#2259986611yescharacteristic
668C2#2259992111yescharacteristic
669C2#2260085511yescharacteristic
670C2#2260088511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC71×#2354C2
socleC23×C71C22×D4
prime radicalC22×D4×C71D4
cosocleC22×C4×C71C24
hypercenter#2354D71
hypocenterC71#22662
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. C2×#17986042C2semidirect
3. C2×#17986035C2semidirect
5. #22589108C2semidirect
6. #22589101C2semidirect
7. #22588539C2semidirect
8. #22588539C2semidirect
9. #22588537C2semidirect
10. #22588532C2semidirect
11. #22588506C2semidirect
12. #22588371C2semidirect
13. #22588363C2semidirect
14. #22588238C2semidirect
20. #17986071C4semidirect
68. C22×C71⋊C8C2×C4semidirect
90. #14556061D4semidirect
97. C4⋊(C71⋊C8)C2×C4semidirect
99. C22⋊(C71⋊C8)C2×C4semidirect
100. #14556039C2×C4semidirect
351. C71#22662semidirect

Maximal subgroups

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

subgroupindex
C2×#179860712
C2×#179860422
C2×#179860352
#225912692
#225891082
#225891012
#225885392
#225885372
#225885322
#225885062
#225883712
#225883632
#225882382
C71×#23542
#2266271