Finite Group Databasebeta

← C2×#428×D71 #32861103

Subgroups — C2×#428×D71 #32861103

Order 18176.

3182 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D71C211yesmaximal, characteristic
2C2×#117×D71C211yesmaximal, characteristic
3C22×C4⋊C4×D71C211yesmaximal, characteristic
4C2×#17986042C211yesmaximal, characteristic, complemented
5C2×#17986041C211yesmaximal, characteristic, complemented
6C2×#17986040C212yesmaximal, complemented
7C2×#17986039C211yesmaximal, characteristic, complemented
8C2×#17986038C212yesmaximal, complemented
9#428×D71C2116yesmaximal, direct product factor
10C2×#107×D71C212yesmaximal, complemented
11C2×#106×D71C212yesmaximal, complemented
12C2×#428×C71C211yesmaximal, characteristic, complemented
13C23×C4×D71—21no—
14C23×C4×D71C2211yescharacteristic
15C22×#11765849C2211yescharacteristic
16C22×#11765848C2212yes—
17C2×M16×D71C4116yescomplemented
18C2×M16×D71C2218yes—
19C22×C8×D71C2212yes—
20C2×#14556087C2211yescharacteristic
21C2×#14556086C2211yescharacteristic
22C2×#14556086C2211yescharacteristic
23C2×#14556085—21no—
24C2×#14556084—21no—
25#117×D71—24no—
26#117×D71C2218yes—
27C22×C4⋊Dic71C2211yescharacteristic
28C22×Dic71⋊C4—21no—
29C2×C4⋊C4×D71—21no—
30C2×C4⋊C4×D71—24no—
31C2×C4⋊C4×D71—21no—
32C2×C4⋊C4×D71C2212yes—
33C2×C4⋊C4×D71C2218yes—
34C2×C4⋊C4×D71C2212yes—
35C2×C4⋊C4×D71C2211yescharacteristic
36C2×C4⋊C4×D71C2211yescharacteristic
37C2×C22⋊C4×D71—21no—
38C2×C42×D71—21no—
39#17986042C2218yescomplemented
40#17986041C2218yescomplemented
41#17986040C22116yescomplemented
42#17986039C2218yescomplemented
43#17986038C22116yescomplemented
44C2×#14556062C2212yescomplemented
45C2×#14556061C2212yescomplemented
46C2×#14556061C2212yescomplemented
47#107×D71C22116yescomplemented
48C2×#14556060C2212yescomplemented
49C2×#14556059C2212yescomplemented
50C2×#14556059C2212yescomplemented
51#106×D71C22116yescomplemented
52C22×M16×C71C2211yescharacteristic
53C2×#117×C71C2211yescharacteristic
54C22×C4⋊C4×C71C2211yescharacteristic
55#428×C71C2218yescomplemented
56C2×#107×C71C2212yescomplemented
57C2×#106×C71C2212yescomplemented
58C24×D71D411yescharacteristic
59C23×Dic71—21no—
60C23×Dic71D411yescharacteristic
61C22×C4×D71—28no—
62C22×C4×D71—22no—
63C22×C4×D71—22no—
64C22×C4×D71—21no—
65C22×C4×D71—21no—
66C22×C4×D71—48no—
67C22×C4×D71C2×C418yes—
68C22×C4×D71D411yescharacteristic
69C22×C4×D71D414yes—
70C22×C4×D71D411yescharacteristic
71C22×C4×D71Q818yes—
72C22×C4×D71C2311yescharacteristic
73C22×C4×D71C2314yes—
74C22×C4×D71C2311yescharacteristic
75C2×#11765849C2×C418yescomplemented
76C2×#11765849C2314yes—
77C2×#11765848C2×C4116yescomplemented
78C2×#11765848C2318yes—
79M16×D71C2×C4164yescomplemented
80C22×C71⋊C8C2312yes—
81C2×C8×D71C2×C4116yescomplemented
82C2×C8×D71C2318yes—
83#14556087—22no—
84#14556087C2314yes—
85#14556086—22no—
86#14556086—22no—
87#14556086C2314yes—
88#14556086C2314yes—
89#14556085—28no—
90#14556084—28no—
91C2×C4⋊Dic71—21no—
92C2×C4⋊Dic71—22no—
93C2×C4⋊Dic71C2312yes—
94C2×C4⋊Dic71C2314yes—
95C2×C4⋊Dic71C2311yescharacteristic
96C2×C4⋊Dic71C2311yescharacteristic
97C2×Dic71⋊C4—22no—
98C2×Dic71⋊C4—22no—
99C2×Dic71⋊C4—28no—
100C2×Dic71⋊C4—21no—
101C2×Dic71⋊C4—21no—
102C4⋊C4×D71—28no—
103C4⋊C4×D71—24no—
104C4⋊C4×D71—28no—
105C4⋊C4×D71—24no—
106C4⋊C4×D71—22no—
107C4⋊C4×D71—22no—
108C4⋊C4×D71C2318yes—
109C4⋊C4×D71C2318yes—
110C4⋊C4×D71C2314yes—
111C4⋊C4×D71C2314yes—
112C2×C22⋊Dic71—21no—
113C2×(C2×D71)⋊C4—21no—
114C2×(C2×D71)⋊C4—21no—
115C22⋊C4×D71—28no—
116C2×C4×Dic71—21no—
117C2×C4×Dic71—21no—
118C2×C4×Dic71—21no—
119C42×D71—28no—
120#14556062C2318yescomplemented
121#14556061C2318yescomplemented
122#14556061C2318yescomplemented
123#14556060C2318yescomplemented
124#14556059C2318yescomplemented
125#14556059C2318yescomplemented
126C23×C4×C71—21no—
127C23×C4×C71C2311yescharacteristic
128C2×M16×C71C2×C418yescomplemented
129C2×M16×C71C2314yes—
130C22×C8×C71C2312yes—
131#117×C71—22no—
132#117×C71C2314yes—
133C2×C4⋊C4×C71—21no—
134C2×C4⋊C4×C71—22no—
135C2×C4⋊C4×C71C2311yescharacteristic
136C2×C4⋊C4×C71C2312yes—
137C2×C4⋊C4×C71C2311yescharacteristic
138C2×C4⋊C4×C71C2314yes—
139C2×C22⋊C4×C71—21no—
140C2×C42×C71—21no—
141#107×C71C2318yescomplemented
142#106×C71C2318yescomplemented
143C23×D71—24no—
144C23×D71—24no—
145C23×D71C4⋊C418yes—
146C23×D71C2×D414yes—
147C23×D71C2×D411yescharacteristic
148C23×D71C2×D411yescharacteristic
149C22×Dic71—24no—
150C22×Dic71—22no—
151C22×Dic71—21no—
152C22×Dic71—21no—
153C22×Dic71—44no—
154C22×Dic71C4⋊C418yes—
155C22×Dic71C2×D411yescharacteristic
156C22×Dic71C2×D411yescharacteristic
157C22×Dic71C2×D414yes—
158C2×C4×D71—28no—
159C2×C4×D71—28no—
160C2×C4×D71—24no—
161C2×C4×D71—24no—
162C2×C4×D71—48no—
163C2×C4×D71—432no—
164C2×C4×D71—44no—
165C2×C4×D71—48no—
166C2×C4×D71—44no—
167C2×C4×D71C4⋊C4132yes—
168C2×C4×D71C4⋊C418yes—
169C2×C4×D71C4⋊C418yes—
170C2×C4×D71C22×C414yes—
171C2×C4×D71C22×C4116yes—
172C2×C4×D71C22×C414yes—
173C2×C4×D71C2×D414yes—
174C2×C4×D71C2×D412yes—
175C2×C4×D71C2×D414yes—
176C2×C4×D71C2×D412yes—
177C2×C4×D71C2×Q8116yes—
178C2×C4×D71C2×Q814yes—
179C2×C4×D71C2×Q814yes—
180C2×C4×D71C2412yes—
181C2×C4×D71C2412yes—
182#11765849C22×C4116yescomplemented
183#11765848C22×C4132yescomplemented
184C2×C71⋊C8C22×C418yescomplemented
185C2×C71⋊C8C2414yes—
186C8×D71C22×C4132yescomplemented
187C4⋊Dic71—24no—
188C4⋊Dic71—22no—
189C4⋊Dic71—21no—
190C4⋊Dic71—21no—
191C4⋊Dic71C2412yes—
192C4⋊Dic71C2414yes—
193C4⋊Dic71C2412yes—
194Dic71⋊C4—28no—
195Dic71⋊C4—28no—
196Dic71⋊C4—24no—
197Dic71⋊C4—24no—
198C22⋊Dic71—24no—
199(C2×D71)⋊C4—24no—
200(C2×D71)⋊C4—24no—
201C4×Dic71—24no—
202C4×Dic71—24no—
203C4×Dic71—24no—
204C24×C71C2×D411yescharacteristic
205C22×C4×C71—24no—
206C22×C4×C71—22no—
207C22×C4×C71—21no—
208C22×C4×C71—21no—
209C22×C4×C71—44no—
210C22×C4×C71C22×C414yes—
211C22×C4×C71C2×D411yescharacteristic
212C22×C4×C71C2×D412yes—
213C22×C4×C71C2×Q814yes—
214C22×C4×C71C2411yescharacteristic
215C22×C4×C71C2412yes—
216M16×C71C22×C4116yescomplemented
217C2×C8×C71C22×C418yescomplemented
218C2×C8×C71C2414yes—
219C4⋊C4×C71—24no—
220C4⋊C4×C71—22no—
221C4⋊C4×C71—21no—
222C4⋊C4×C71—21no—
223C4⋊C4×C71C2412yes—
224C4⋊C4×C71C2414yes—
225C4⋊C4×C71C2412yes—
226C22⋊C4×C71—24no—
227C42×C71—24no—
228C23×C71—22no—
229C23×C71—22no—
230C23×C71C2×C4⋊C414yes—
231C23×C71C22×D412yes—
232C23×C71C22×D411yescharacteristic
233C22×D71—22no—
234C22×D71—22no—
235C22×D71—28no—
236C22×D71—28no—
237C22×D71—232no—
238C22×D71C2×C4⋊C414yes—
239C22×D71C2×C4⋊C4116yes—
240C22×D71C2×C4⋊C414yes—
241C22×D71AGL(1,ℤ/8)14yes—
242C22×D71#13714yes—
243C22×D71C22×D412yes—
244C22×D71C22×D412yes—
245C2×C4×C71—22no—
246C2×C4×C71—22no—
247C2×C4×C71—24no—
248C2×C4×C71—48no—
249C2×C4×C71—44no—
250C2×C4×C71—42no—
251C2×C4×C71—42no—
252C2×C4×C71C2×C4⋊C418yes—
253C2×C4×C71C2×C4⋊C414yes—
254C2×C4×C71C23×C412yes—
255C2×C4×C71C23×C414yes—
256C2×C4×C71C22×D412yes—
257C2×C4×C71C22×D411yescharacteristic
258C2×C4×C71C22×Q814yes—
259C2×C4×C71C22×Q812yes—
260C2×C4×C71C2511yescharacteristic
261C2×Dic71—22no—
262C2×Dic71—22no—
263C2×Dic71—24no—
264C2×Dic71—48no—
265C2×Dic71—44no—
266C2×Dic71—42no—
267C2×Dic71—42no—
268C2×Dic71C2×C4⋊C4116yes—
269C2×Dic71C2×C4⋊C414yes—
270C2×Dic71C2×C4⋊C414yes—
271C2×Dic71C22×D412yes—
272C2×Dic71C22×D412yes—
273C4×D71—416no—
274C4×D71—48no—
275C4×D71—416no—
276C4×D71—48no—
277C4×D71C2×C4⋊C4116yes—
278C4×D71C2×C4⋊C418yes—
279C4×D71C2×C4⋊C418yes—
280C4×D71C2×C4⋊C4116yes—
281C4×D71C23×C414yes—
282C4×D71C23×C414yes—
283C4×D71C22×Q814yes—
284C4×D71C22×Q814yes—
285C8×C71C23×C418yescomplemented
286C71⋊C8C23×C418yescomplemented
287C22×C71—28no—
288C22×C71—22no—
289C22×C71—22no—
290C22×C71C22×C4⋊C414yes—
291C22×C71C22×C4⋊C412yes—
292C22×C71C2×AGL(1,ℤ/8)12yes—
293C22×C71C2×#13712yes—
294C22×C71C23×D411yescharacteristic
295C2×D71—28no—
296C2×D71—22no—
297C2×D71—22no—
298C2×D71—232no—
299C2×D71#428116yesdirect product factor
300C2×D71C22×C4⋊C414yes—
301C2×D71C22×C4⋊C414yes—
302C2×D71C2×AGL(1,ℤ/8)14yes—
303C2×D71C2×#13714yes—
304C4×C71—44no—
305C4×C71—42no—
306C4×C71—42no—
307C4×C71C22×C4⋊C412yes—
308C4×C71C22×C4⋊C414yes—
309C4×C71C24×C411yescharacteristic
310C4×C71C23×Q811yescharacteristic
311Dic71—44no—
312Dic71—42no—
313Dic71—42no—
314Dic71C22×C4⋊C414yes—
315Dic71C22×C4⋊C414yes—
316C22×#428—711nomaximal, Sylow
317C2×C71—24no—
318C2×C71C2×#42814yescomplemented
319C2×C71C23×C4⋊C411yescharacteristic
320C2×C71C22×AGL(1,ℤ/8)11yescharacteristic
321C2×C71C22×#13711yescharacteristic
322D71—24no—
323D71C2×#42818yesdirect product factor
324C23×M16—711no—
325C22×#117—711no—
326C23×C4⋊C4—711no—
327C2×#428—7116no—
328C2×#428—712no—
329C2×#428—712no—
330C2×#428—711no—
331C2×#428—711no—
332C2×#428—711no—
333C2×#428D7111yescharacteristic, direct product factor
334C22×#107—712no—
335C22×#106—712no—
336C71C22×#42811yescharacteristic, complemented, Sylow
337C24×C4—711no—
338C24×C4—1421no—
339C22×M16—711no—
340C22×M16—7116no—
341C22×M16—718no—
342C22×M16—712no—
343C22×M16C2×D7111yescharacteristic
344C23×C8—712no—
345C2×#117—711no—
346C2×#117—718no—
347C2×#117—711no—
348C2×#117—711no—
349C2×#117—1421no—
350C2×#117—1421no—
351C2×#117—1424no—
352C2×#117C2×D7111yescharacteristic
353C22×C4⋊C4—711no—
354C22×C4⋊C4—711no—
355C22×C4⋊C4—712no—
356C22×C4⋊C4—711no—
357C22×C4⋊C4—712no—
358C22×C4⋊C4—718no—
359C22×C4⋊C4—1424no—
360C22×C4⋊C4—1421no—
361C22×C4⋊C4—1421no—
362C22×C4⋊C4—1421no—
363C22×C4⋊C4C2×D7111yescharacteristic
364C22×C22⋊C4—1421no—
365C22×C42—1421no—
366#428—718no—
367#428—718no—
368#428—718no—
369#428—7116no—
370#428—7116no—
371#428C2×D7118yesdirect product factor
372C2×#107—712no—
373C2×#107—712no—
374C2×#107—712no—
375C2×#107—7116no—
376C2×#107C2×D7112yescomplemented
377C2×#106—712no—
378C2×#106—712no—
379C2×#106—712no—
380C2×#106—7116no—
381C2×#106C2×D7112yescomplemented
382C25—711no—
383C23×C4—21no—
384C23×C4—2848no—
385C23×C4—711no—
386C23×C4—718no—
387C23×C4—714no—
388C23×C4—711no—
389C23×C4—711no—
390C23×C4—718no—
391C23×C4—711no—
392C23×C4—714no—
393C23×C4—711no—
394C23×C4—1421no—
395C23×C4—1421no—
396C23×C4—1428no—
397C23×C4—1422no—
398C23×C4—1422no—
399C23×C4—1421no—
400C23×C4C22×D7111yescharacteristic
401C2×M16—718no—
402C2×M16—714no—
403C2×M16—7164no—
404C2×M16—7116no—
405C2×M16—718no—
406C2×M16C4×D7118yescomplemented
407C2×M16C22×D7114yes—
408C22×C8—712no—
409C22×C8—7116no—
410C22×C8—718no—
411C22×C8C22×D7112yes—
412#117—22no—
413#117—714no—
414#117—714no—
415#117—714no—
416#117—1428no—
417#117—1428no—
418#117—1422no—
419#117—1422no—
420#117—1422no—
421#117C22×D7114yes—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—712no—
425C2×C4⋊C4—714no—
426C2×C4⋊C4—711no—
427C2×C4⋊C4—711no—
428C2×C4⋊C4—718no—
429C2×C4⋊C4—718no—
430C2×C4⋊C4—714no—
431C2×C4⋊C4—714no—
432C2×C4⋊C4—1428no—
433C2×C4⋊C4—1424no—
434C2×C4⋊C4—1428no—
435C2×C4⋊C4—1424no—
436C2×C4⋊C4—1422no—
437C2×C4⋊C4—1422no—
438C2×C4⋊C4—1428no—
439C2×C4⋊C4—1422no—
440C2×C4⋊C4—1422no—
441C2×C4⋊C4—1421no—
442C2×C4⋊C4—1421no—
443C2×C4⋊C4—1422no—
444C2×C4⋊C4—1421no—
445C2×C4⋊C4C22×D7112yes—
446C2×C4⋊C4C22×D7114yes—
447C2×C4⋊C4C22×D7111yescharacteristic
448C2×C4⋊C4C22×D7111yescharacteristic
449C2×C22⋊C4—21no—
450C2×C22⋊C4—1428no—
451C2×C22⋊C4—1421no—
452C2×C22⋊C4—1421no—
453C2×C22⋊C4—1421no—
454C2×C42—21no—
455C2×C42—1428no—
456C2×C42—1421no—
457C2×C42—1421no—
458C2×C42—1421no—
459#107—718no—
460#107—718no—
461#107—718no—
462#107C22×D7118yescomplemented
463#106—718no—
464#106—718no—
465#106—718no—
466#106C22×D7118yescomplemented
467C24—711no—
468C24—714no—
469C24—711no—
470C24—718no—
471C24—1424no—
472C24—1424no—
473C24D4×D7111yescharacteristic
474C22×C4—24no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—44no—
479C22×C4—2848no—
480C22×C4—2844no—
481C22×C4—2844no—
482C22×C4—28432no—
483C22×C4—2848no—
484C22×C4—2844no—
485C22×C4—714no—
486C22×C4—711no—
487C22×C4—711no—
488C22×C4—718no—
489C22×C4—714no—
490C22×C4—7116no—
491C22×C4—714no—
492C22×C4—714no—
493C22×C4—712no—
494C22×C4—712no—
495C22×C4—714no—
496C22×C4—714no—
497C22×C4—7116no—
498C22×C4—714no—
499C22×C4—712no—
500C22×C4—712no—
501C22×C4—718no—
502C22×C4—7132no—
503C22×C4—718no—
504C22×C4—1424no—
505C22×C4—1424no—
506C22×C4—1428no—
507C22×C4—1428no—
508C22×C4—1424no—
509C22×C4—1421no—
510C22×C4—1421no—
511C22×C4—1422no—
512C22×C4C2×C4×D7114yes—
513C22×C4D4×D7112yes—
514C22×C4D4×D7111yescharacteristic
515C22×C4Q8×D7114yes—
516C22×C4C23×D7112yes—
517C22×C4C23×D7111yescharacteristic
518M16—7116no—
519M16—7132no—
520M16C2×C4×D71116yescomplemented
521C2×C8—718no—
522C2×C8—714no—
523C2×C8—7132no—
524C2×C8C2×C4×D7118yescomplemented
525C2×C8C23×D7114yes—
526C4⋊C4—24no—
527C4⋊C4—22no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—712no—
531C4⋊C4—714no—
532C4⋊C4—712no—
533C4⋊C4—1428no—
534C4⋊C4—1428no—
535C4⋊C4—1424no—
536C4⋊C4—1424no—
537C4⋊C4—1424no—
538C4⋊C4—1422no—
539C4⋊C4—1421no—
540C4⋊C4—1421no—
541C4⋊C4C23×D7112yes—
542C4⋊C4C23×D7114yes—
543C4⋊C4C23×D7112yes—
544C22⋊C4—24no—
545C22⋊C4—1424no—
546C22⋊C4—1424no—
547C22⋊C4—1424no—
548C42—24no—
549C42—1424no—
550C42—1424no—
551C42—1424no—
552C23—22no—
553C23—22no—
554C23—712no—
555C23—714no—
556C23—714no—
557C23—714no—
558C23—712no—
559C23—7116no—
560C23—714no—
561C23—1428no—
562C23—14232no—
563C23—1428no—
564C23—1422no—
565C23—1422no—
566C23C4⋊C4×D7114yes—
567C23C2×D4×D7112yes—
568C23C2×D4×D7111yescharacteristic
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—48no—
573C2×C4—44no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—28416no—
577C2×C4—2848no—
578C2×C4—2848no—
579C2×C4—28416no—
580C2×C4—2848no—
581C2×C4—2844no—
582C2×C4—2842no—
583C2×C4—2842no—
584C2×C4—712no—
585C2×C4—712no—
586C2×C4—7116no—
587C2×C4—714no—
588C2×C4—714no—
589C2×C4—714no—
590C2×C4—714no—
591C2×C4—714no—
592C2×C4—714no—
593C2×C4—718no—
594C2×C4—7116no—
595C2×C4—718no—
596C2×C4—7116no—
597C2×C4—1422no—
598C2×C4—1422no—
599C2×C4—1424no—
600C2×C4C4⋊C4×D7118yes—
601C2×C4C4⋊C4×D7114yes—
602C2×C4C22×C4×D7112yes—
603C2×C4C22×C4×D7114yes—
604C2×C4C2×D4×D7112yes—
605C2×C4C2×D4×D7111yescharacteristic
606C2×C4C2×Q8×D7114yes—
607C2×C4C2×Q8×D7112yes—
608C2×C4C24×D7111yescharacteristic
609C8—718no—
610C8C22×C4×D7118yescomplemented
611C22—28no—
612C22—22no—
613C22—22no—
614C22—714no—
615C22—7116no—
616C22—714no—
617C22—714no—
618C22—714no—
619C22—14232no—
620C22—1428no—
621C22—1422no—
622C22—1422no—
623C22C2×C4⋊C4×D7114yes—
624C22C2×C4⋊C4×D7112yes—
625C22AGL(1,ℤ/8)×D7112yes—
626C22#137×D7112yes—
627C22C22×D4×D7111yescharacteristic
628C4—44no—
629C4—42no—
630C4—42no—
631C4—2844no—
632C4—2842no—
633C4—2842no—
634C4—714no—
635C4—714no—
636C4C2×C4⋊C4×D7112yes—
637C4C2×C4⋊C4×D7114yes—
638C4C23×C4×D7111yescharacteristic
639C4C22×Q8×D7111yescharacteristic
640C2—24no—
641C2—718no—
642C2—1424no—
643C2#428×D7114yesdirect product factor
644C2C22×C4⋊C4×D7111yescharacteristic
645C2C2×AGL(1,ℤ/8)×D7111yescharacteristic
646C2C2×#137×D7111yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutatorC4×C71C24×C4
FrattiniC2×C4C24×D71
FittingC2×#428×C71C2
socleC23×C71C22×D4
prime radicalC24×D71D4
cosocleC2×C4×C71C25
hypercenterC2×#428D71
hypocenterC71C22×#428
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
4. C2×#17986042C2semidirect
5. C2×#17986041C2semidirect
6. C2×#17986040C2semidirect
7. C2×#17986039C2semidirect
8. C2×#17986038C2semidirect
9. #428×D71C2direct (N × H)
10. C2×#107×D71C2semidirect
11. C2×#106×D71C2semidirect
12. C2×#428×C71C2semidirect
17. C2×M16×D71C4semidirect
39. #17986042C22semidirect
40. #17986041C22semidirect
41. #17986040C22semidirect
42. #17986039C22semidirect
43. #17986038C22semidirect
44. C2×#14556062C22semidirect
45. C2×#14556061C22semidirect
46. C2×#14556061C22semidirect
47. #107×D71C22semidirect
48. C2×#14556060C22semidirect
49. C2×#14556059C22semidirect
50. C2×#14556059C22semidirect
51. #106×D71C22semidirect
55. #428×C71C22semidirect
56. C2×#107×C71C22semidirect
57. C2×#106×C71C22semidirect
75. C2×#11765849C2×C4semidirect
77. C2×#11765848C2×C4semidirect
79. M16×D71C2×C4semidirect
81. C2×C8×D71C2×C4semidirect
120. #14556062C23semidirect
121. #14556061C23semidirect
122. #14556061C23semidirect
123. #14556060C23semidirect
124. #14556059C23semidirect
125. #14556059C23semidirect
128. C2×M16×C71C2×C4semidirect
141. #107×C71C23semidirect
142. #106×C71C23semidirect
182. #11765849C22×C4semidirect
183. #11765848C22×C4semidirect
184. C2×C71⋊C8C22×C4semidirect
186. C8×D71C22×C4semidirect
216. M16×C71C22×C4semidirect
217. C2×C8×C71C22×C4semidirect
285. C8×C71C23×C4semidirect
286. C71⋊C8C23×C4semidirect
299. C2×D71#428direct (N × H)
318. C2×C71C2×#428semidirect
323. D71C2×#428direct (N × H)
333. C2×#428D71direct (N × H)
336. C71C22×#428semidirect
371. #428C2×D71direct (N × H)
376. C2×#107C2×D71semidirect
381. C2×#106C2×D71semidirect
406. C2×M16C4×D71semidirect
462. #107C22×D71semidirect
466. #106C22×D71semidirect
520. M16C2×C4×D71semidirect
524. C2×C8C2×C4×D71semidirect
610. C8C22×C4×D71semidirect
643. C2#428×D71direct (N × H)

Maximal subgroups

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

subgroupindex
C22×M16×D712
C2×#117×D712
C22×C4⋊C4×D712
C2×#179860422
C2×#179860412
C2×#179860402
C2×#179860392
C2×#179860382
#428×D712
C2×#107×D712
C2×#106×D712
C2×#428×C712
C22×#42871