Finite Group Databasebeta

← #2388×D71 #32163644

Subgroups — #2388×D71 #32163644

Order 18176.

6238 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#41×D71C211yesmaximal, characteristic, complemented
2C2×C4×D4×D71C213yesmaximal, complemented
3#22591558C211yesmaximal, characteristic, complemented
4#22591557C211yesmaximal, characteristic, complemented
5#22591556C213yesmaximal, complemented
6#22591555C213yesmaximal, complemented
7#22591554C213yesmaximal, complemented
8#22591553C211yesmaximal, characteristic, complemented
9#22591552C213yesmaximal, complemented
10#395×D71C211yesmaximal, characteristic, complemented
11#394×D71C213yesmaximal, complemented
12#393×D71C211yesmaximal, characteristic, complemented
13#392×D71C213yesmaximal, complemented
14C4×C22⋊C4×D71C213yesmaximal, complemented
15C71×#2388C211yesmaximal, characteristic, complemented
16C22×#11765866C2211yescharacteristic, complemented
17C22×#11765865C2213yescomplemented
18C22×#11765864C2213yescomplemented
19C2×#41×D71—224no—
20C22×Q8×D71C2211yescharacteristic
21C22×D4×D71C2213yes—
22C22×D4×D71C2213yes—
23C23×C4×D71C2211yescharacteristic
24C23×C4×D71C2213yes—
25C2×C4×D284C2213yescomplemented
26C2×D4×Dic71C2213yescomplemented
27C2×#14556090C2213yescomplemented
28C2×C4×C22⋊D71C2213yescomplemented
29C2×C4×C22⋊D71C2213yescomplemented
30C2×(C22⋊D71)⋊C4C2213yescomplemented
31C2×(C22⋊D71)⋊C4C2213yescomplemented
32C4×D4×D71—224no—
33C2×C4⋊C4×D71C2213yes—
34C2×C22⋊C4×D71C2213yes—
35C2×C22⋊C4×D71C2213yes—
36C2×C22⋊C4×D71C2216yes—
37C2×C42×D71C2213yes—
38#17985920C2213yescomplemented
39#17985919C2213yescomplemented
40#17985918C2211yescharacteristic, complemented
41#17985917C2213yescomplemented
42#17985916C2213yescomplemented
43#17985915C2216yescomplemented
44#17985914C2216yescomplemented
45#17985913C2213yescomplemented
46#17985912C2213yescomplemented
47#17985911C2213yescomplemented
48#17985910C2211yescharacteristic, complemented
49#17985909C2213yescomplemented
50#17985908C2216yescomplemented
51#17985908C2213yescomplemented
52#17985907C2216yescomplemented
53#17985907C2213yescomplemented
54C22⋊C4×Dic71C2216yescomplemented
55C4×(C2×D71)⋊C4C2216yescomplemented
56C4×C22⋊Dic71C2213yescomplemented
57#17985846C2213yescomplemented
58#17985846C2213yescomplemented
59#95×D71C2213yes—
60#95×D71C2213yes—
61C22×#41×C71C2211yescharacteristic, complemented
62C2×C4×D4×C71C2213yescomplemented
63#395×C71C2211yescharacteristic, complemented
64#394×C71C2213yescomplemented
65#393×C71C2211yescharacteristic, complemented
66#392×C71C2213yescomplemented
67C4×C22⋊C4×C71C2213yescomplemented
68C24×D71C2313yes—
69C24×D71C2311yescharacteristic
70C2×#11765866—212no—
71C2×#11765865—224no—
72C2×#11765865—212no—
73C2×#11765864—224no—
74C2×#11765864—212no—
75#41×D71—2128no—
76C22×Dic142C2313yes—
77C2×Q8×D71—212no—
78C22×D284C2313yes—
79C22×D284C2313yes—
80C22×C22⋊D71C2316yes—
81C22×C22⋊D71C2313yes—
82C22×C22⋊D71C2313yes—
83C2×D4×D71—224no—
84C2×D4×D71—212no—
85C2×D4×D71—212no—
86C2×D4×D71—212no—
87C2×D4×D71—212no—
88C23×Dic71C2311yescharacteristic
89C23×Dic71C2313yes—
90C22×C4×D71—224no—
91C22×C4×D71—212no—
92C22×C4×D71D4124yescomplemented
93C22×C4×D71C2311yescharacteristic
94C22×C4×D71C2311yescharacteristic
95C22×C4×D71C2311yescharacteristic
96C22×C4×D71C2313yes—
97C22×C4×D71C2313yes—
98C22×C4×D71C2313yes—
99C22×C4×D71C2313yes—
100C22×C4×D71C2313yes—
101C22×C4×D71C2311yescharacteristic
102C4×D284—212no—
103D4×Dic71—212no—
104#14556090—212no—
105C4×C22⋊D71—212no—
106C4×C22⋊D71—212no—
107(C22⋊D71)⋊C4—212no—
108(C22⋊D71)⋊C4—212no—
109C2×C4⋊Dic71C2313yes—
110C2×Dic71⋊C4C2313yes—
111C2×Dic71⋊C4C2313yes—
112C4⋊C4×D71—212no—
113C2×C22⋊Dic71C2316yes—
114C2×C22⋊Dic71C2313yes—
115C2×C22⋊Dic71C2313yes—
116C2×(C2×D71)⋊C4C2316yes—
117C2×(C2×D71)⋊C4C2316yes—
118C2×(C2×D71)⋊C4C2313yes—
119C2×(C2×D71)⋊C4C2313yes—
120C2×(C2×D71)⋊C4C2313yes—
121C2×(C2×D71)⋊C4C2313yes—
122C22⋊C4×D71—212no—
123C22⋊C4×D71—212no—
124C22⋊C4×D71—224no—
125C2×C4×Dic71C2313yes—
126C2×C4×Dic71C2313yes—
127C2×C4×Dic71C2313yes—
128C42×D71—212no—
129C71⋊#95C2313yes—
130C71⋊#95C2313yes—
131C71⋊#95C2316yes—
132C71⋊#95C2316yes—
133C2×#41×C71—212no—
134C22×Q8×C71C2311yescharacteristic
135C22×D4×C71C2313yes—
136C22×D4×C71C2313yes—
137C23×C4×C71C2311yescharacteristic
138C23×C4×C71C2313yes—
139C4×D4×C71—212no—
140C2×C4⋊C4×C71C2313yes—
141C2×C22⋊C4×C71C2316yes—
142C2×C22⋊C4×C71C2313yes—
143C2×C22⋊C4×C71C2313yes—
144C2×C42×C71C2313yes—
145#95×C71C2313yes—
146#95×C71C2313yes—
147C23×D71—212no—
148C23×D71—26no—
149C23×D71—26no—
150C23×D71—26no—
151C23×D71—26no—
152C23×D71—212no—
153C23×D71C2×D4112yes—
154C23×D71#4114yescomplemented
155C23×D71C2413yes—
156C23×D71C2411yescharacteristic
157C23×D71C2411yescharacteristic
158#11765866—232no—
159#11765865—296no—
160#11765864—296no—
161C2×Dic142—26no—
162C2×Dic142—212no—
163Q8×D71—232no—
164C2×D284—212no—
165C2×D284—26no—
166C2×D284—26no—
167C2×D284—26no—
168C2×D284—26no—
169C2×C22⋊D71—212no—
170C2×C22⋊D71—26no—
171C2×C22⋊D71—26no—
172C2×C22⋊D71—212no—
173C2×C22⋊D71—26no—
174C2×C22⋊D71—26no—
175C2×C22⋊D71—212no—
176C2×C22⋊D71—26no—
177C2×C22⋊D71—26no—
178D4×D71—296no—
179D4×D71—296no—
180C22×Dic71—212no—
181C22×Dic71—26no—
182C22×Dic71C2×D4112yescomplemented
183C22×Dic71C2411yescharacteristic
184C22×Dic71C2413yes—
185C22×Dic71C2413yes—
186C22×Dic71C2413yes—
187C22×Dic71C2411yescharacteristic
188C2×C4×D71—212no—
189C2×C4×D71—26no—
190C2×C4×D71—26no—
191C2×C4×D71—212no—
192C2×C4×D71—212no—
193C2×C4×D71—296no—
194C2×C4×D71—26no—
195C2×C4×D71—26no—
196C2×C4×D71—212no—
197C2×C4×D71—26no—
198C2×C4×D71—26no—
199C2×C4×D71—416no—
200C2×C4×D71C2×D4112yes—
201C2×C4×D71C2×D4112yes—
202C2×C4×D71C2×D4112yescomplemented
203C2×C4×D71C2×D4112yescomplemented
204C2×C4×D71#41112yescomplemented
205C4⋊Dic71—26no—
206Dic71⋊C4—26no—
207Dic71⋊C4—26no—
208C22⋊Dic71—26no—
209C22⋊Dic71—26no—
210C22⋊Dic71—212no—
211(C2×D71)⋊C4—26no—
212(C2×D71)⋊C4—26no—
213(C2×D71)⋊C4—26no—
214(C2×D71)⋊C4—212no—
215(C2×D71)⋊C4—26no—
216(C2×D71)⋊C4—212no—
217C4×Dic71—26no—
218C4×Dic71—26no—
219C4×Dic71—26no—
220C24×C71C2413yes—
221C24×C71C2411yescharacteristic
222#41×C71—232no—
223C2×Q8×C71—26no—
224C2×D4×C71—212no—
225C2×D4×C71—26no—
226C2×D4×C71—26no—
227C2×D4×C71—26no—
228C2×D4×C71—26no—
229C22×C4×C71—212no—
230C22×C4×C71—26no—
231C22×C4×C71C2×D4112yescomplemented
232C22×C4×C71C2411yescharacteristic
233C22×C4×C71C2413yes—
234C22×C4×C71C2413yes—
235C22×C4×C71C2413yes—
236C22×C4×C71C2411yescharacteristic
237C4⋊C4×C71—26no—
238C22⋊C4×C71—26no—
239C22⋊C4×C71—26no—
240C22⋊C4×C71—212no—
241C42×C71—26no—
242C23×C71—23no—
243C23×C71—26no—
244C23×C71—26no—
245C23×C71—23no—
246C23×C71—23no—
247C23×C71—23no—
248C23×C71C22×D416yes—
249C23×C71C2×#4112yescomplemented
250C23×C71C2511yescharacteristic
251C22×D71—23no—
252C22×D71—26no—
253C22×D71—26no—
254C22×D71—23no—
255C22×D71—23no—
256C22×D71—23no—
257C22×D71—224no—
258C22×D71—224no—
259C22×D71—224no—
260C22×D71—224no—
261C22×D71—44no—
262C22×D71—424no—
263C22×D71—424no—
264C22×D71—412no—
265C22×D71C22×D416yes—
266C22×D71C22×D416yes—
267C22×D71C2×#4112yes—
268C22×D71C2×#4116yes—
269C22×D71C2×#4112yescomplemented
270Q8×C71—28no—
271D4×C71—224no—
272D4×C71—224no—
273C2×C4×C71—23no—
274C2×C4×C71—26no—
275C2×C4×C71—23no—
276C2×C4×C71—224no—
277C2×C4×C71—23no—
278C2×C4×C71—23no—
279C2×C4×C71—26no—
280C2×C4×C71—44no—
281C2×C4×C71C22×D416yes—
282C2×C4×C71C22×D416yes—
283C2×C4×C71C2×#4116yescomplemented
284C22⋊D71—224no—
285C22⋊D71—224no—
286C22⋊D71—248no—
287C2×Dic71—23no—
288C2×Dic71—26no—
289C2×Dic71—23no—
290C2×Dic71—224no—
291C2×Dic71—23no—
292C2×Dic71—23no—
293C2×Dic71—26no—
294C2×Dic71—44no—
295C2×Dic71C22×D416yes—
296C2×Dic71C22×D416yes—
297C2×Dic71C2×#4116yescomplemented
298D284—224no—
299D284—224no—
300C4×D71—224no—
301C4×D71—224no—
302C4×D71—224no—
303C4×D71—224no—
304C4×D71—44no—
305C4×D71—412no—
306C4×D71—44no—
307C4×D71—44no—
308C4×D71#120116yes—
309Dic142—224no—
310C22×C71—26no—
311C22×C71—26no—
312C22×C71—26no—
313C22×C71—26no—
314C22×C71—41no—
315C22×C71—46no—
316C22×C71—43no—
317C22×C71—46no—
318C22×C71C23×D413yes—
319C22×C71C22×#4111yescharacteristic
320C22×C71C22×#4113yes—
321C2×D71—26no—
322C2×D71—26no—
323C2×D71—26no—
324C2×D71—26no—
325C2×D71—41no—
326C2×D71—46no—
327C2×D71—43no—
328C2×D71—46no—
329C2×D71—448no—
330C2×D71—416no—
331C2×D71C2×#12014yes—
332C2×D71#525112yes—
333C2×D71#532112yes—
334C4×C71—26no—
335C4×C71—26no—
336C4×C71—41no—
337C4×C71—43no—
338C4×C71C2×#12014yes—
339Dic71—26no—
340Dic71—26no—
341Dic71—41no—
342Dic71—43no—
343Dic71C2×#12014yes—
344C2×#2388—711nomaximal, Sylow
345C2×C71—46no—
346C2×C71—42no—
347C2×C71C22×#12011yescharacteristic
348C2×C71C2×#52513yes—
349C2×C71C2×#53213yes—
350D71—46no—
351D71—42no—
352D71#238818yesdirect product factor
353C23×#41—711no—
354C22×C4×D4—713no—
355#2388—711no—
356#2388—713no—
357#2388—711no—
358#2388—713no—
359#2388—713no—
360#2388—711no—
361#2388—713no—
362#2388D7111yescharacteristic, direct product factor
363C2×#395—711no—
364C2×#394—713no—
365C2×#393—711no—
366C2×#392—713no—
367C2×C4×C22⋊C4—713no—
368C71C2×#238811yescharacteristic, complemented, Sylow
369C22×#41—711no—
370C22×#41—713no—
371C22×#41—713no—
372C22×#41—14224no—
373C22×#41C2×D7111yescharacteristic, complemented
374C23×Q8—711no—
375C23×D4—713no—
376C23×D4—713no—
377C24×C4—713no—
378C24×C4—711no—
379C2×C4×D4—713no—
380C2×C4×D4—713no—
381C2×C4×D4—713no—
382C2×C4×D4—713no—
383C2×C4×D4—713no—
384C2×C4×D4—713no—
385C2×C4×D4—713no—
386C2×C4×D4—14224no—
387C2×C4×D4C2×D7113yescomplemented
388C22×C4⋊C4—713no—
389C22×C22⋊C4—713no—
390C22×C22⋊C4—716no—
391C22×C22⋊C4—713no—
392C22×C42—713no—
393#395—711no—
394#395—713no—
395#395—713no—
396#395C2×D7111yescharacteristic, complemented
397#394—713no—
398#394—713no—
399#394—716no—
400#394—716no—
401#394—713no—
402#394C2×D7113yescomplemented
403#393—711no—
404#393—713no—
405#393—713no—
406#393C2×D7111yescharacteristic, complemented
407#392—716no—
408#392—713no—
409#392—716no—
410#392—713no—
411#392—713no—
412#392C2×D7113yescomplemented
413C4×C22⋊C4—713no—
414C4×C22⋊C4—716no—
415C4×C22⋊C4—716no—
416C4×C22⋊C4—713no—
417C4×C22⋊C4—713no—
418C4×C22⋊C4C2×D7113yescomplemented
419C2×#95—713no—
420C2×#95—713no—
421C25—713no—
422C25—711no—
423C2×#41—212no—
424C2×#41—14224no—
425C2×#41—14224no—
426C2×#41—14212no—
427C2×#41—14212no—
428C2×#41—142128no—
429C2×#41—14212no—
430C22×Q8—713no—
431C22×Q8—14212no—
432C22×Q8C22×D7111yescharacteristic
433C22×D4—713no—
434C22×D4—713no—
435C22×D4—716no—
436C22×D4—713no—
437C22×D4—713no—
438C22×D4—14212no—
439C22×D4—14212no—
440C22×D4—14212no—
441C22×D4—14212no—
442C22×D4—14224no—
443C22×D4C22×D7113yes—
444C22×D4C22×D7113yes—
445C23×C4—711no—
446C23×C4—713no—
447C23×C4—7124no—
448C23×C4—713no—
449C23×C4—713no—
450C23×C4—713no—
451C23×C4—713no—
452C23×C4—711no—
453C23×C4—713no—
454C23×C4—711no—
455C23×C4—711no—
456C23×C4—711no—
457C23×C4—14212no—
458C23×C4—14224no—
459C23×C4C22×D7111yescharacteristic
460C23×C4C22×D7113yes—
461C4×D4—212no—
462C4×D4—14212no—
463C4×D4—14212no—
464C4×D4—14212no—
465C4×D4—14212no—
466C4×D4—14212no—
467C4×D4—14212no—
468C4×D4—14212no—
469C2×C4⋊C4—713no—
470C2×C4⋊C4—713no—
471C2×C4⋊C4—713no—
472C2×C4⋊C4—14212no—
473C2×C4⋊C4C22×D7113yes—
474C2×C22⋊C4—713no—
475C2×C22⋊C4—713no—
476C2×C22⋊C4—716no—
477C2×C22⋊C4—713no—
478C2×C22⋊C4—713no—
479C2×C22⋊C4—713no—
480C2×C22⋊C4—713no—
481C2×C22⋊C4—716no—
482C2×C22⋊C4—716no—
483C2×C22⋊C4—14212no—
484C2×C22⋊C4—14224no—
485C2×C22⋊C4—14212no—
486C2×C22⋊C4C22×D7113yes—
487C2×C22⋊C4C22×D7113yes—
488C2×C22⋊C4C22×D7116yes—
489C2×C42—713no—
490C2×C42—713no—
491C2×C42—713no—
492C2×C42—14212no—
493C2×C42C22×D7113yes—
494#95—713no—
495#95—716no—
496#95—716no—
497#95—713no—
498#95C22×D7113yes—
499#95C22×D7113yes—
500C24—711no—
501C24—7112no—
502C24—714no—
503C24—713no—
504C24—711no—
505C24—1426no—
506C24—14212no—
507C24—14212no—
508C24—1426no—
509C24—1426no—
510C24—1426no—
511C24C23×D7113yes—
512C24C23×D7111yescharacteristic
513#41—232no—
514#41—14296no—
515#41—14296no—
516#41—14232no—
517C2×Q8—26no—
518C2×Q8—14212no—
519C2×Q8—14232no—
520C2×Q8—1426no—
521C2×D4—26no—
522C2×D4—212no—
523C2×D4—26no—
524C2×D4—26no—
525C2×D4—26no—
526C2×D4—1426no—
527C2×D4—1426no—
528C2×D4—14212no—
529C2×D4—1426no—
530C2×D4—1426no—
531C2×D4—14212no—
532C2×D4—14296no—
533C2×D4—14296no—
534C2×D4—1426no—
535C2×D4—1426no—
536C2×D4—14212no—
537C2×D4—1426no—
538C2×D4—14212no—
539C2×D4—1426no—
540C2×D4—1426no—
541C2×D4—1426no—
542C22×C4—212no—
543C22×C4—26no—
544C22×C4—28416no—
545C22×C4—711no—
546C22×C4—7112no—
547C22×C4—7112no—
548C22×C4—713no—
549C22×C4—713no—
550C22×C4—7112no—
551C22×C4—7112no—
552C22×C4—7112no—
553C22×C4—7112no—
554C22×C4—713no—
555C22×C4—711no—
556C22×C4—1426no—
557C22×C4—1426no—
558C22×C4—1426no—
559C22×C4—14212no—
560C22×C4—14212no—
561C22×C4—14296no—
562C22×C4—1426no—
563C22×C4—14212no—
564C22×C4—1426no—
565C22×C4—1426no—
566C22×C4—1426no—
567C22×C4—14212no—
568C22×C4—14212no—
569C22×C4D4×D71112yescomplemented
570C22×C4C23×D7113yes—
571C22×C4C23×D7111yescharacteristic
572C22×C4C23×D7113yes—
573C22×C4C23×D7113yes—
574C22×C4C23×D7111yescharacteristic
575C4⋊C4—26no—
576C4⋊C4—1426no—
577C4⋊C4—1426no—
578C4⋊C4—1426no—
579C22⋊C4—26no—
580C22⋊C4—26no—
581C22⋊C4—212no—
582C22⋊C4—14212no—
583C22⋊C4—1426no—
584C22⋊C4—1426no—
585C22⋊C4—1426no—
586C22⋊C4—14212no—
587C22⋊C4—1426no—
588C22⋊C4—1426no—
589C22⋊C4—1426no—
590C22⋊C4—14212no—
591C42—26no—
592C42—1426no—
593C42—1426no—
594C42—1426no—
595C23—23no—
596C23—26no—
597C23—26no—
598C23—23no—
599C23—23no—
600C23—23no—
601C23—2844no—
602C23—28424no—
603C23—28412no—
604C23—28424no—
605C23—716no—
606C23—716no—
607C23—712no—
608C23—716no—
609C23—712no—
610C23—14224no—
611C23—14224no—
612C23—14224no—
613C23—14224no—
614C23—1423no—
615C23—1426no—
616C23—1426no—
617C23—1423no—
618C23—1423no—
619C23—1423no—
620C23C2×D4×D7116yes—
621C23#41×D7112yescomplemented
622C23C24×D7111yescharacteristic
623Q8—28no—
624Q8—14224no—
625D4—224no—
626D4—224no—
627D4—14224no—
628D4—14224no—
629D4—14248no—
630D4—14224no—
631D4—14224no—
632C2×C4—23no—
633C2×C4—26no—
634C2×C4—23no—
635C2×C4—224no—
636C2×C4—23no—
637C2×C4—23no—
638C2×C4—26no—
639C2×C4—44no—
640C2×C4—2844no—
641C2×C4—28412no—
642C2×C4—2844no—
643C2×C4—2844no—
644C2×C4—2844no—
645C2×C4—716no—
646C2×C4—7116no—
647C2×C4—716no—
648C2×C4—716no—
649C2×C4—14224no—
650C2×C4—14224no—
651C2×C4—14224no—
652C2×C4—1423no—
653C2×C4—1423no—
654C2×C4—1426no—
655C2×C4—14224no—
656C2×C4—1423no—
657C2×C4—1426no—
658C2×C4—1423no—
659C2×C4—14224no—
660C2×C4C2×D4×D7116yes—
661C2×C4C2×D4×D7116yes—
662C2×C4#41×D7116yescomplemented
663C22—26no—
664C22—26no—
665C22—26no—
666C22—26no—
667C22—41no—
668C22—46no—
669C22—43no—
670C22—46no—
671C22—28416no—
672C22—28448no—
673C22—2841no—
674C22—2846no—
675C22—2843no—
676C22—2846no—
677C22—714no—
678C22—7112no—
679C22—7112no—
680C22—1426no—
681C22—1426no—
682C22—1426no—
683C22—1426no—
684C22C22×D4×D7113yes—
685C22C2×#41×D7111yescharacteristic
686C22C2×#41×D7113yes—
687C4—26no—
688C4—26no—
689C4—41no—
690C4—43no—
691C4—2841no—
692C4—2843no—
693C4—714no—
694C4—1426no—
695C4—1426no—
696C4#120×D7114yes—
697C2—46no—
698C2—42no—
699C2—2842no—
700C2—2846no—
701C2—718no—
702C2C2×#120×D7111yescharacteristic
703C2#525×D7113yes—
704C2#532×D7113yes—
subgroupG/H
centerC22×C4C23×D71
commutator, socle, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC71×#2388C2
hypercenter#2388D71
hypocenterC71C2×#2388
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ #2388

Complements

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

NH ≅ G/Ntype
1. C22×#41×D71C2semidirect
2. C2×C4×D4×D71C2semidirect
3. #22591558C2semidirect
4. #22591557C2semidirect
5. #22591556C2semidirect
6. #22591555C2semidirect
7. #22591554C2semidirect
8. #22591553C2semidirect
9. #22591552C2semidirect
10. #395×D71C2semidirect
11. #394×D71C2semidirect
12. #393×D71C2semidirect
13. #392×D71C2semidirect
14. C4×C22⋊C4×D71C2semidirect
15. C71×#2388C2semidirect
16. C22×#11765866C22semidirect
17. C22×#11765865C22semidirect
18. C22×#11765864C22semidirect
25. C2×C4×D284C22semidirect
26. C2×D4×Dic71C22semidirect
27. C2×#14556090C22semidirect
28. C2×C4×C22⋊D71C22semidirect
29. C2×C4×C22⋊D71C22semidirect
30. C2×(C22⋊D71)⋊C4C22semidirect
31. C2×(C22⋊D71)⋊C4C22semidirect
38. #17985920C22semidirect
39. #17985919C22semidirect
40. #17985918C22semidirect
41. #17985917C22semidirect
42. #17985916C22semidirect
43. #17985915C22semidirect
44. #17985914C22semidirect
45. #17985913C22semidirect
46. #17985912C22semidirect
47. #17985911C22semidirect
48. #17985910C22semidirect
49. #17985909C22semidirect
50. #17985908C22semidirect
51. #17985908C22semidirect
52. #17985907C22semidirect
53. #17985907C22semidirect
54. C22⋊C4×Dic71C22semidirect
55. C4×(C2×D71)⋊C4C22semidirect
56. C4×C22⋊Dic71C22semidirect
57. #17985846C22semidirect
58. #17985846C22semidirect
61. C22×#41×C71C22semidirect
62. C2×C4×D4×C71C22semidirect
63. #395×C71C22semidirect
64. #394×C71C22semidirect
65. #393×C71C22semidirect
66. #392×C71C22semidirect
67. C4×C22⋊C4×C71C22semidirect
92. C22×C4×D71D4semidirect
154. C23×D71#41semidirect
182. C22×Dic71C2×D4semidirect
202. C2×C4×D71C2×D4semidirect
203. C2×C4×D71C2×D4semidirect
204. C2×C4×D71#41semidirect
231. C22×C4×C71C2×D4semidirect
249. C23×C71C2×#41semidirect
269. C22×D71C2×#41semidirect
283. C2×C4×C71C2×#41semidirect
297. C2×Dic71C2×#41semidirect
352. D71#2388direct (N × H)
362. #2388D71direct (N × H)
368. C71C2×#2388semidirect
373. C22×#41C2×D71semidirect
387. C2×C4×D4C2×D71semidirect
396. #395C2×D71semidirect
402. #394C2×D71semidirect
406. #393C2×D71semidirect
412. #392C2×D71semidirect
418. C4×C22⋊C4C2×D71semidirect
569. C22×C4D4×D71semidirect
621. C23#41×D71semidirect
662. C2×C4#41×D71semidirect

Maximal subgroups

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

subgroupindex
C22×#41×D712
C2×C4×D4×D712
#225915582
#225915572
#225915562
#225915552
#225915542
#225915532
#225915522
#395×D712
#394×D712
#393×D712
#392×D712
C4×C22⋊C4×D712
C71×#23882
C2×#238871