Finite Group Databasebeta

← #32861133

Subgroups — #32861133

Order 18176.

2694 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
1C2×#17986765C211yesmaximal, characteristic
2#22601541C211yesmaximal, characteristic
3C2×#17986480C211yesmaximal, characteristic
4#22596939C214yesmaximal, complemented
5#22596936C214yesmaximal, complemented
6#22596934C214yesmaximal, complemented
7#22596931C214yesmaximal, complemented
8#22596930C211yesmaximal, characteristic, complemented
9#22596929C211yesmaximal, characteristic, complemented
10#22596927C214yesmaximal, complemented
11C2×#17986039C211yesmaximal, characteristic, complemented
12#428×D71C214yesmaximal, complemented
13C2×#428×C71C211yesmaximal, characteristic, complemented
14C22×#11765865C2211yescharacteristic
15#17986765C4116yescomplemented
16C2×#14556136C2214yes—
17C2×#14556134C2214yes—
18C22×#11765849C2211yescharacteristic
19C2×M16×D71C2214yes—
20#17986480—22no—
21#17986480—22no—
22#17986480C2214yes—
23#17986480C2214yes—
24#17986480C2212yes—
25#17986480C2212yes—
26#17986479C2212yes—
27#17986479C2212yes—
28#17986476—21no—
29#17986473—21no—
30#17986472—22no—
31C4×#11765865—22no—
32#17986467—22no—
33C2×#14556093—21no—
34C2×#14556090—21no—
35C2×C4×C22⋊D71—22no—
36C2×#14556087C2211yescharacteristic
37C2×#14556087C2211yescharacteristic
38C2×#14556086C2212yes—
39#117×D71C2214yes—
40C2×C4⋊C4×D71C2212yes—
41#17986042C2212yes—
42#17986042C2212yes—
43#17986041C2212yes—
44#17986041C2212yes—
45#17986041C2212yescomplemented
46#17986041C2212yescomplemented
47#17986040C2218yescomplemented
48#17986040C2218yescomplemented
49#17986039C2214yes—
50#17986039C2214yescomplemented
51#17986039C2212yescomplemented
52#17986039C2212yescomplemented
53#17986038C2218yescomplemented
54#17986038C2218yescomplemented
55#17986037C2214yescomplemented
56#17986036C2218yescomplemented
57#17986035C2214yescomplemented
58#17986034C2218yescomplemented
59C2×#14556061C2212yescomplemented
60#107×D71C2218yescomplemented
61C2×#14556059C2212yescomplemented
62#106×D71C2218yescomplemented
63C22×M16×C71C2211yescharacteristic
64C2×#117×C71C2211yescharacteristic
65C22×C4⋊C4×C71C2211yescharacteristic
66#428×C71C2214yes—
67#428×C71C2214yescomplemented
68C2×#107×C71C2212yescomplemented
69C2×#106×C71C2212yescomplemented
70C2×#11765865C2×C418yes—
71C2×#11765865D412yes—
72C2×#11765865D412yes—
73C2×#11765865Q818yes—
74C2×#11765865C2312yes—
75C2×#11765865C2312yes—
76C22×Dic142D411yescharacteristic
77C22×D284D411yescharacteristic
78C22×C22⋊D71D412yes—
79C22×C4×D71—22no—
80C22×C4×D71C2312yes—
81#14556136C2×C4132yescomplemented
82#14556134C2×C4132yescomplemented
83C2×#11765849C2×C418yescomplemented
84C2×#11765849C2312yes—
85C2×#11765849C2312yes—
86C2×#11765848C2318yes—
87M16×D71C2×C4132yescomplemented
88C22×C71⋊C8C2312yes—
89C2×C8×D71C2318yes—
90C4×Dic142—22no—
91C4×Dic142—22no—
92#14556093—24no—
93#14556093—24no—
94#14556093—22no—
95#14556093—22no—
96C4×D284—22no—
97C4×D284—22no—
98#14556090—24no—
99#14556090—24no—
100#14556090—22no—
101#14556090—22no—
102C4×C22⋊D71—28no—
103C4×C22⋊D71—28no—
104C4×C22⋊D71—24no—
105C4×C22⋊D71—24no—
106(C22⋊D71)⋊C4—24no—
107(C22⋊D71)⋊C4—24no—
108#14556087—21no—
109#14556087—21no—
110#14556087—21no—
111#14556087—21no—
112#14556087C2312yes—
113#14556087C2312yes—
114#14556087C2312yes—
115#14556087C2312yes—
116#14556086—24no—
117#14556086C2314yes—
118#14556086C2314yes—
119#14556086C2318yes—
120#14556085—24no—
121#14556084—24no—
122C2×C4⋊Dic71C2311yescharacteristic
123C2×C4⋊Dic71C2311yescharacteristic
124C2×C4⋊Dic71C2311yescharacteristic
125C2×C4⋊Dic71C2311yescharacteristic
126C2×Dic71⋊C4—22no—
127C4⋊C4×D71—24no—
128C4⋊C4×D71C2318yes—
129C4⋊C4×D71C2314yes—
130C4⋊C4×D71C2314yes—
131C2×C22⋊Dic71—21no—
132C2×C22⋊Dic71—21no—
133C2×(C2×D71)⋊C4—22no—
134C22⋊C4×D71—24no—
135C2×C4×Dic71—22no—
136C2×C4×Dic71—21no—
137C2×C4×Dic71—21no—
138C42×D71—24no—
139#14556062C2314yes—
140#14556062C2314yes—
141#14556061C2314yes—
142#14556061C2318yes—
143#14556061C2314yes—
144#14556060C2314yes—
145#14556060C2314yes—
146#14556059C2314yes—
147#14556059C2318yes—
148#14556059C2314yes—
149C23×C4×C71—21no—
150C23×C4×C71C2311yescharacteristic
151C2×M16×C71C2×C418yescomplemented
152C2×M16×C71C2312yes—
153C2×M16×C71C2312yes—
154C22×C8×C71C2312yes—
155#117×C71—21no—
156#117×C71—21no—
157#117×C71C2312yes—
158#117×C71C2312yes—
159C2×C4⋊C4×C71—21no—
160C2×C4⋊C4×C71—21no—
161C2×C4⋊C4×C71—21no—
162C2×C4⋊C4×C71C2311yescharacteristic
163C2×C4⋊C4×C71C2312yes—
164C2×C4⋊C4×C71C2311yescharacteristic
165C2×C4⋊C4×C71C2312yes—
166C2×C4⋊C4×C71C2312yes—
167C2×C22⋊C4×C71—21no—
168C2×C42×C71—21no—
169#107×C71C2318yes—
170#106×C71C2318yes—
171C23×D71C2×D412yes—
172#11765865C4⋊C4116yes—
173#11765865C4⋊C4116yes—
174#11765865C22×C418yes—
175#11765865C22×C418yes—
176#11765865C2×Q818yes—
177#11765865C2×Q818yes—
178C2×Dic142C4⋊C418yes—
179C2×Dic142C2×D412yes—
180C2×Dic142C2×D412yes—
181C2×D284C4⋊C418yes—
182C2×D284C2×D412yes—
183C2×D284C2×D412yes—
184C2×C22⋊D71C4⋊C4116yes—
185C2×C22⋊D71C2×D414yes—
186C2×C22⋊D71C2×D414yes—
187C22×Dic71—21no—
188C22×Dic71—21no—
189C22×Dic71—21no—
190C22×Dic71—21no—
191C22×Dic71C2×D412yes—
192C2×C4×D71—28no—
193C2×C4×D71—24no—
194C2×C4×D71—24no—
195C2×C4×D71—84no—
196C2×C4×D71C22×C418yes—
197C2×C4×D71C2×D414yes—
198C2×C4×D71C2×Q818yes—
199C2×C4×D71C2414yes—
200#11765849C22×C418yes—
201#11765849C22×C418yescomplemented
202#11765848C22×C4132yescomplemented
203C2×C71⋊C8C22×C418yescomplemented
204C2×C71⋊C8C2414yes—
205C8×D71C22×C4132yescomplemented
206C4⋊Dic71—21no—
207C4⋊Dic71—21no—
208C4⋊Dic71—21no—
209C4⋊Dic71—21no—
210C4⋊Dic71C2412yes—
211C4⋊Dic71C2412yes—
212C4⋊Dic71C2412yes—
213C4⋊Dic71C2412yes—
214Dic71⋊C4—28no—
215Dic71⋊C4—24no—
216Dic71⋊C4—24no—
217C22⋊Dic71—22no—
218C22⋊Dic71—22no—
219C22⋊Dic71—22no—
220C22⋊Dic71—22no—
221(C2×D71)⋊C4—24no—
222(C2×D71)⋊C4—24no—
223(C2×D71)⋊C4—28no—
224C4×Dic71—22no—
225C4×Dic71—22no—
226C4×Dic71—22no—
227C4×Dic71—22no—
228C4×Dic71—24no—
229C4×Dic71—24no—
230C4×Dic71—28no—
231C24×C71C2×D411yescharacteristic
232C22×C4×C71—22no—
233C22×C4×C71—21no—
234C22×C4×C71—21no—
235C22×C4×C71—22no—
236C22×C4×C71—22no—
237C22×C4×C71—82no—
238C22×C4×C71C22×C414yes—
239C22×C4×C71C2×D411yescharacteristic
240C22×C4×C71C2×D411yescharacteristic
241C22×C4×C71C2×D411yescharacteristic
242C22×C4×C71C2×Q814yes—
243C22×C4×C71C2411yescharacteristic
244C22×C4×C71C2411yescharacteristic
245C22×C4×C71C2411yescharacteristic
246M16×C71C22×C418yes—
247M16×C71C22×C418yescomplemented
248C2×C8×C71C22×C418yescomplemented
249C2×C8×C71C2414yes—
250C4⋊C4×C71—22no—
251C4⋊C4×C71—22no—
252C4⋊C4×C71—22no—
253C4⋊C4×C71—21no—
254C4⋊C4×C71—21no—
255C4⋊C4×C71C2412yes—
256C4⋊C4×C71C2414yes—
257C4⋊C4×C71C2412yes—
258C22⋊C4×C71—22no—
259C22⋊C4×C71—22no—
260C42×C71—22no—
261C42×C71—22no—
262C23×C71—41no—
263C23×C71—41no—
264C23×C71C2×C4⋊C414yes—
265C23×C71C22×D411yescharacteristic
266C23×C71C22×D411yescharacteristic
267C23×C71C22×D411yescharacteristic
268C22×D71—42no—
269C22×D71—42no—
270C22×D71C2×C4⋊C418yes—
271C22×D71C22×D414yes—
272C2×C4×C71—22no—
273C2×C4×C71—22no—
274C2×C4×C71—24no—
275C2×C4×C71—44no—
276C2×C4×C71—81no—
277C2×C4×C71—81no—
278C2×C4×C71—82no—
279C2×C4×C71—82no—
280C2×C4×C71C2×C4⋊C414yes—
281C2×C4×C71C2×C4⋊C414yes—
282C2×C4×C71C2×C4⋊C414yes—
283C2×C4×C71C23×C412yes—
284C2×C4×C71C23×C412yes—
285C2×C4×C71C23×C412yes—
286C2×C4×C71C22×D411yescharacteristic
287C2×C4×C71C22×D411yescharacteristic
288C2×C4×C71C22×D411yescharacteristic
289C2×C4×C71C22×Q812yes—
290C2×C4×C71C22×Q812yes—
291C2×C4×C71C22×Q812yes—
292C2×C4×C71C2511yescharacteristic
293C22⋊D71C2×C4⋊C4116yes—
294C22⋊D71C2×C4⋊C4116yes—
295C2×Dic71—22no—
296C2×Dic71—22no—
297C2×Dic71—22no—
298C2×Dic71—22no—
299C2×Dic71—42no—
300C2×Dic71—42no—
301C2×Dic71—81no—
302C2×Dic71—81no—
303C2×Dic71C2×C4⋊C418yes—
304C2×Dic71C22×D414yes—
305D284C2×C4⋊C418yes—
306D284C2×C4⋊C418yes—
307C4×D71—84no—
308C4×D71—84no—
309C4×D71—88no—
310C4×D71C2×C4⋊C4116yes—
311C4×D71C23×C418yes—
312C4×D71C22×Q818yes—
313Dic142C2×C4⋊C418yes—
314Dic142C2×C4⋊C418yes—
315C8×C71C23×C418yes—
316C71⋊C8C23×C418yes—
317C22×C71—21no—
318C22×C71—21no—
319C22×C71—21no—
320C22×C71—21no—
321C22×C71—21no—
322C22×C71—21no—
323C22×C71—44no—
324C22×C71C22×C4⋊C412yes—
325C22×C71C22×C4⋊C412yes—
326C22×C71C22×C4⋊C412yes—
327C22×C71C23×D411yescharacteristic
328C2×D71—24no—
329C2×D71—24no—
330C2×D71—48no—
331C2×D71C22×C4⋊C418yes—
332C4×C71—44no—
333C4×C71—42no—
334C4×C71—42no—
335C4×C71C22×C4⋊C412yes—
336C4×C71C22×C4⋊C412yes—
337C4×C71C22×C4⋊C412yes—
338C4×C71C24×C411yescharacteristic
339C4×C71C23×Q811yescharacteristic
340Dic71—42no—
341Dic71—42no—
342Dic71—42no—
343Dic71—42no—
344Dic71C22×C4⋊C418yes—
345#60109—711nomaximal, Sylow
346C2×C71—22no—
347C2×C71—22no—
348C2×C71—22no—
349C2×C71C23×C4⋊C411yescharacteristic
350C2×C71#358511yescharacteristic
351C2×C71#358611yescharacteristic
352D71—28no—
353C2×#568—711no—
354#3428—711no—
355C2×#520—711no—
356#2913—714no—
357#2913—714no—
358#2912—714no—
359#2912—714no—
360#2911—714no—
361#2911—711no—
362#2911—711no—
363C2×#428—714no—
364C2×#428—711no—
365C2×#428D7111yescharacteristic, complemented
366C71#6010911yescharacteristic, complemented, Sylow
367C22×#41—711no—
368#568—7116no—
369C2×#131—714no—
370C2×#131—714no—
371C22×M16—711no—
372C22×M16—714no—
373C22×M16C2×D7111yescharacteristic
374#520—712no—
375#520—712no—
376#520—712no—
377#520—714no—
378#520—714no—
379#520—712no—
380#520—1422no—
381#520—1422no—
382#519—1421no—
383#518—1422no—
384#518—1421no—
385C4×#41—1422no—
386C4×#41—1422no—
387C2×C4×Q8—1421no—
388C2×C4×D4—1421no—
389C2×C4×D4—1422no—
390C2×#117—711no—
391C2×#117—711no—
392C2×#117—714no—
393C2×#117—712no—
394C2×#117C2×D7111yescharacteristic
395C22×C4⋊C4—712no—
396C22×C4⋊C4C2×D7111yescharacteristic
397#428—712no—
398#428—712no—
399#428—712no—
400#428—712no—
401#428—712no—
402#428—712no—
403#428—714no—
404#428—714no—
405#428—712no—
406#428—712no—
407#428—718no—
408#428—718no—
409#428—718no—
410#428—718no—
411#428C2×D7114yes—
412#428C2×D7114yescomplemented
413#427—714no—
414#427—714no—
415#427—718no—
416#427—718no—
417C2×#107—712no—
418C2×#107—718no—
419C2×#107C2×D7112yescomplemented
420C2×#106—712no—
421C2×#106—718no—
422C2×#106C2×D7112yescomplemented
423C2×#41—718no—
424C2×#41—712no—
425C2×#41—712no—
426C2×#41—718no—
427C2×#41—712no—
428C2×#41—712no—
429C22×Q8—711no—
430C22×D4—712no—
431C22×D4—711no—
432C23×C4—21no—
433C23×C4—712no—
434C23×C4—1422no—
435C23×C4C22×D7111yescharacteristic
436#131—7132no—
437#131—7132no—
438C2×M16—718no—
439C2×M16—712no—
440C2×M16—712no—
441C2×M16—7132no—
442C2×M16—718no—
443C2×M16C4×D7118yescomplemented
444C2×M16C22×D7112yes—
445C2×M16C22×D7112yes—
446C22×C8—712no—
447C22×C8—718no—
448C22×C8C22×D7112yes—
449C4×Q8—1422no—
450C4×Q8—1422no—
451C4×Q8—1424no—
452C4×Q8—1424no—
453C4×Q8—1422no—
454C4×Q8—1422no—
455C4×D4—1422no—
456C4×D4—1422no—
457C4×D4—1424no—
458C4×D4—1424no—
459C4×D4—1424no—
460C4×D4—1424no—
461C4×D4—1422no—
462C4×D4—1422no—
463C4×D4—1428no—
464C4×D4—1428no—
465C4×D4—1424no—
466C4×D4—1424no—
467#117—21no—
468#117—21no—
469#117—712no—
470#117—712no—
471#117—712no—
472#117—712no—
473#117—714no—
474#117—718no—
475#117—714no—
476#117—1424no—
477#117—1424no—
478#117—1424no—
479#117—1421no—
480#117—1421no—
481#117—1421no—
482#117—1421no—
483#117C22×D7112yes—
484#117C22×D7112yes—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—711no—
489C2×C4⋊C4—711no—
490C2×C4⋊C4—711no—
491C2×C4⋊C4—711no—
492C2×C4⋊C4—718no—
493C2×C4⋊C4—714no—
494C2×C4⋊C4—714no—
495C2×C4⋊C4—1424no—
496C2×C4⋊C4—1422no—
497C2×C4⋊C4C22×D7112yes—
498C2×C4⋊C4C22×D7112yes—
499C2×C4⋊C4C22×D7112yes—
500C2×C4⋊C4C22×D7111yescharacteristic
501C2×C4⋊C4C22×D7111yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—1424no—
504C2×C22⋊C4—1422no—
505C2×C22⋊C4—1421no—
506C2×C22⋊C4—1421no—
507C2×C42—21no—
508C2×C42—1424no—
509C2×C42—1422no—
510C2×C42—1421no—
511C2×C42—1421no—
512#107—714no—
513#107—714no—
514#107—714no—
515#107—718no—
516#107—714no—
517#107C22×D7118yes—
518#106—714no—
519#106—714no—
520#106—718no—
521#106—714no—
522#106—714no—
523#106C22×D7118yes—
524C24—712no—
525C24D4×D7111yescharacteristic
526#41—718no—
527#41—718no—
528#41—718no—
529#41—718no—
530#41—7116no—
531#41—7116no—
532C2×Q8—712no—
533C2×Q8—712no—
534C2×Q8—718no—
535C2×D4—714no—
536C2×D4—714no—
537C2×D4—7116no—
538C2×D4—712no—
539C2×D4—712no—
540C2×D4—718no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—82no—
547C22×C4—5684no—
548C22×C4—712no—
549C22×C4—718no—
550C22×C4—714no—
551C22×C4—718no—
552C22×C4—714no—
553C22×C4—1424no—
554C22×C4—1424no—
555C22×C4—1428no—
556C22×C4—1421no—
557C22×C4—1421no—
558C22×C4—1421no—
559C22×C4—1421no—
560C22×C4C2×C4×D7114yes—
561C22×C4D4×D7111yescharacteristic
562C22×C4D4×D7111yescharacteristic
563C22×C4D4×D7111yescharacteristic
564C22×C4Q8×D7114yes—
565C22×C4C23×D7111yescharacteristic
566C22×C4C23×D7111yescharacteristic
567C22×C4C23×D7111yescharacteristic
568M16—718no—
569M16—718no—
570M16—7132no—
571M16C2×C4×D7118yes—
572M16C2×C4×D7118yescomplemented
573C2×C8—718no—
574C2×C8—714no—
575C2×C8—7132no—
576C2×C8C2×C4×D7118yescomplemented
577C2×C8C23×D7114yes—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—712no—
584C4⋊C4—712no—
585C4⋊C4—712no—
586C4⋊C4—712no—
587C4⋊C4—1428no—
588C4⋊C4—1424no—
589C4⋊C4—1424no—
590C4⋊C4—1421no—
591C4⋊C4—1421no—
592C4⋊C4—1421no—
593C4⋊C4—1421no—
594C4⋊C4C23×D7112yes—
595C4⋊C4C23×D7114yes—
596C4⋊C4C23×D7112yes—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—1424no—
600C22⋊C4—1424no—
601C22⋊C4—1428no—
602C22⋊C4—1422no—
603C22⋊C4—1422no—
604C22⋊C4—1422no—
605C22⋊C4—1422no—
606C42—22no—
607C42—22no—
608C42—1424no—
609C42—1424no—
610C42—1428no—
611C42—1422no—
612C42—1422no—
613C42—1422no—
614C42—1422no—
615C23—41no—
616C23—41no—
617C23—2842no—
618C23—2842no—
619C23—718no—
620C23—714no—
621C23C4⋊C4×D7114yes—
622C23C2×D4×D7111yescharacteristic
623C23C2×D4×D7111yescharacteristic
624C23C2×D4×D7111yescharacteristic
625Q8—718no—
626Q8—718no—
627D4—7116no—
628D4—7116no—
629D4—718no—
630D4—718no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—24no—
634C2×C4—44no—
635C2×C4—82no—
636C2×C4—82no—
637C2×C4—81no—
638C2×C4—81no—
639C2×C4—2842no—
640C2×C4—2842no—
641C2×C4—5688no—
642C2×C4—5684no—
643C2×C4—5684no—
644C2×C4—5681no—
645C2×C4—5681no—
646C2×C4—714no—
647C2×C4—718no—
648C2×C4—718no—
649C2×C4—718no—
650C2×C4—7116no—
651C2×C4—1422no—
652C2×C4—1422no—
653C2×C4—1422no—
654C2×C4—1422no—
655C2×C4C4⋊C4×D7114yes—
656C2×C4C4⋊C4×D7114yes—
657C2×C4C4⋊C4×D7114yes—
658C2×C4C22×C4×D7112yes—
659C2×C4C22×C4×D7112yes—
660C2×C4C22×C4×D7112yes—
661C2×C4C2×D4×D7111yescharacteristic
662C2×C4C2×D4×D7111yescharacteristic
663C2×C4C2×D4×D7111yescharacteristic
664C2×C4C2×Q8×D7112yes—
665C2×C4C2×Q8×D7112yes—
666C2×C4C2×Q8×D7112yes—
667C2×C4C24×D7111yescharacteristic
668C8—718no—
669C8C22×C4×D7118yes—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—44no—
677C22—2848no—
678C22—718no—
679C22—1424no—
680C22—1424no—
681C22C2×C4⋊C4×D7112yes—
682C22C2×C4⋊C4×D7112yes—
683C22C2×C4⋊C4×D7112yes—
684C22C22×D4×D7111yescharacteristic
685C4—44no—
686C4—42no—
687C4—42no—
688C4—2842no—
689C4—2842no—
690C4—2842no—
691C4—2842no—
692C4—718no—
693C4C2×C4⋊C4×D7112yes—
694C4C2×C4⋊C4×D7112yes—
695C4C2×C4⋊C4×D7112yes—
696C4C23×C4×D7111yescharacteristic
697C4C22×Q8×D7111yescharacteristic
698C2—22no—
699C2—22no—
700C2—22no—
701C2—1428no—
702C2C22×C4⋊C4×D7111yescharacteristic
703C2#2260311611yescharacteristic
704C2#2260312311yescharacteristic
subgroupG/H
centerC22C22×D4×D71
commutatorC4×C71C24×C4
FrattiniC2×C4C24×D71
FittingC2×#428×C71C2
socleC22×C71C23×D4
prime radicalC22×#11765865C22
cosocleC2×C4×C71C25
hypercenterC2×#428D71
hypocenterC71#60109
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
4. #22596939C2semidirect
5. #22596936C2semidirect
6. #22596934C2semidirect
7. #22596931C2semidirect
8. #22596930C2semidirect
9. #22596929C2semidirect
10. #22596927C2semidirect
11. C2×#17986039C2semidirect
12. #428×D71C2semidirect
13. C2×#428×C71C2semidirect
15. #17986765C4semidirect
45. #17986041C22semidirect
46. #17986041C22semidirect
47. #17986040C22semidirect
48. #17986040C22semidirect
50. #17986039C22semidirect
51. #17986039C22semidirect
52. #17986039C22semidirect
53. #17986038C22semidirect
54. #17986038C22semidirect
55. #17986037C22semidirect
56. #17986036C22semidirect
57. #17986035C22semidirect
58. #17986034C22semidirect
59. C2×#14556061C22semidirect
60. #107×D71C22semidirect
61. C2×#14556059C22semidirect
62. #106×D71C22semidirect
67. #428×C71C22semidirect
68. C2×#107×C71C22semidirect
69. C2×#106×C71C22semidirect
81. #14556136C2×C4semidirect
82. #14556134C2×C4semidirect
83. C2×#11765849C2×C4semidirect
87. M16×D71C2×C4semidirect
151. C2×M16×C71C2×C4semidirect
201. #11765849C22×C4semidirect
202. #11765848C22×C4semidirect
203. C2×C71⋊C8C22×C4semidirect
205. C8×D71C22×C4semidirect
247. M16×C71C22×C4semidirect
248. C2×C8×C71C22×C4semidirect
365. C2×#428D71semidirect
366. C71#60109semidirect
412. #428C2×D71semidirect
419. C2×#107C2×D71semidirect
422. C2×#106C2×D71semidirect
443. C2×M16C4×D71semidirect
572. M16C2×C4×D71semidirect
576. C2×C8C2×C4×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179867652
#226015412
C2×#179864802
#225969392
#225969362
#225969342
#225969312
#225969302
#225969292
#225969272
C2×#179860392
#428×D712
C2×#428×C712
#6010971