Finite Group Databasebeta

← C2×#22597968 #32864608

Subgroups — C2×#22597968 #32864608

Order 18176.

2898 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556159C211yesmaximal, characteristic, complemented
2C22×M16×D71C211yesmaximal, characteristic, complemented
3C2×#17986511C211yesmaximal, characteristic
4C22×#14556104C211yesmaximal, characteristic, complemented
5#22597968C2116yesmaximal, direct product factor
6C2×#17986256C212yesmaximal, complemented
7C2×#17986248C212yesmaximal, complemented
8C2×#17986239C212yesmaximal, complemented
9C2×#17986231C212yesmaximal, complemented
10C2×#17986042C211yesmaximal, characteristic, complemented
11C2×#17986001C211yesmaximal, characteristic, complemented
12C2×#419×C71C211yesmaximal, characteristic, complemented
13C22×#11765865C2211yescharacteristic
14C23×C4×D71C2211yescharacteristic
15C2×#14556159—28no—
16C2×#14556159C2218yescomplemented
17C22×#11765855C2212yescomplemented
18C22×#11765852C2212yescomplemented
19C22×#11765849C2211yescharacteristic
20C22×#11765848C2212yes—
21C2×M16×D71—28no—
22C2×M16×D71C2218yescomplemented
23C22×C8×D71C2212yes—
24#17986511—24no—
25#17986511C2218yes—
26C2×#14556112—21no—
27C2×#14556108C2211yescharacteristic
28C2×#14556108C2211yescharacteristic
29C2×#14556104—21no—
30C2×#14556104—21no—
31C2×#14556104—24no—
32C2×#14556104C2212yes—
33C2×#14556104C2212yes—
34C2×#14556104C2218yescomplemented
35C2×#14556103C2211yescharacteristic
36C2×#14556103C2211yescharacteristic
37C2×#14556098—21no—
38C2×C4×D284—21no—
39C2×C4×D284—21no—
40C22×C4⋊Dic71C2211yescharacteristic
41C22×Dic71⋊C4—21no—
42C22×(C2×D71)⋊C4—21no—
43#17986256C22116yescomplemented
44#17986248C22116yescomplemented
45#17986239C22116yescomplemented
46#17986231C22116yescomplemented
47#17986042C2218yescomplemented
48C2×#14556061C2212yescomplemented
49C2×#14556059C2212yescomplemented
50#17986001C2218yescomplemented
51C2×#14556053C2212yescomplemented
52C2×#14556050C2212yescomplemented
53C23×Q8×C71C2211yescharacteristic
54C22×M16×C71C2211yescharacteristic
55C2×#117×C71C2211yescharacteristic
56#419×C71C2218yescomplemented
57C2×#103×C71C2212yescomplemented
58C2×#103×C71C2212yescomplemented
59C24×D71D411yescharacteristic
60C2×#11765865—22no—
61C2×#11765865—24no—
62C2×#11765865—24no—
63C2×#11765865C2314yes—
64C22×Dic142C2311yescharacteristic
65C22×D284—21no—
66C22×D284—21no—
67C22×D284C2311yescharacteristic
68C22×C22⋊D71—21no—
69C23×Dic71—21no—
70C23×Dic71D411yescharacteristic
71C22×C4×D71—24no—
72C22×C4×D71—21no—
73C22×C4×D71—24no—
74C22×C4×D71D411yescharacteristic
75C22×C4×D71D411yescharacteristic
76C22×C4×D71D414yes—
77C22×C4×D71C2311yescharacteristic
78C22×C4×D71C2311yescharacteristic
79C22×C4×D71C2314yes—
80#14556159—232no—
81C2×#11765855—28no—
82C2×#11765855C2318yescomplemented
83C2×#11765852—28no—
84C2×#11765852C2318yescomplemented
85C2×#11765849D418yescomplemented
86C2×#11765849C2314yes—
87C2×#11765848—28no—
88C2×#11765848C2318yes—
89M16×D71—232no—
90C22×C71⋊C8C2312yes—
91C2×C8×D71—28no—
92C2×C8×D71C2318yes—
93#14556112—28no—
94#14556108—22no—
95#14556108—22no—
96#14556108C2314yes—
97#14556108C2314yes—
98#14556104—24no—
99#14556104—24no—
100#14556104—28no—
101#14556104—28no—
102#14556104C2318yes—
103#14556104C2318yes—
104#14556103—22no—
105#14556103—22no—
106#14556103C2314yes—
107#14556103C2314yes—
108#14556098—28no—
109C4×D284—28no—
110C4×D284—28no—
111C2×C4⋊Dic71—21no—
112C2×C4⋊Dic71—21no—
113C2×C4⋊Dic71—21no—
114C2×C4⋊Dic71—22no—
115C2×C4⋊Dic71C2312yes—
116C2×C4⋊Dic71C2314yes—
117C2×Dic71⋊C4—22no—
118C2×Dic71⋊C4—22no—
119C2×Dic71⋊C4—28no—
120C2×(C2×D71)⋊C4—22no—
121C2×(C2×D71)⋊C4—22no—
122C2×(C2×D71)⋊C4—28no—
123C2×(C2×D71)⋊C4—21no—
124C2×(C2×D71)⋊C4—21no—
125C2×(C2×D71)⋊C4—21no—
126C2×(C2×D71)⋊C4—21no—
127#14556061C2318yescomplemented
128#14556059C2318yescomplemented
129#14556053C2318yescomplemented
130#14556050C2318yescomplemented
131C22×Q8×C71—21no—
132C22×Q8×C71—22no—
133C22×Q8×C71—24no—
134C22×Q8×C71—24no—
135C22×Q8×C71C2312yes—
136C22×Q8×C71C2314yes—
137C23×C4×C71—21no—
138C23×C4×C71C2311yescharacteristic
139C2×M16×C71—24no—
140C2×M16×C71C2314yes—
141C22×C8×C71C2312yes—
142#117×C71—22no—
143#117×C71C2314yes—
144C2×C4⋊C4×C71C2311yescharacteristic
145C2×C4⋊C4×C71C2311yescharacteristic
146C2×C22⋊C4×C71—21no—
147C2×C42×C71—21no—
148#103×C71C2318yescomplemented
149#103×C71C2318yescomplemented
150C23×D71—24no—
151C23×D71—24no—
152C23×D71—21no—
153C23×D71—42no—
154C23×D71C2×D411yescharacteristic
155C23×D71C2×D414yes—
156C23×D71C2×D411yescharacteristic
157#11765865—28no—
158#11765865—28no—
159#11765865—48no—
160C2×Dic142—22no—
161C2×Dic142—22no—
162C2×Dic142—21no—
163C2×Dic142C2412yes—
164C2×D284—22no—
165C2×D284—22no—
166C2×D284—24no—
167C2×D284—24no—
168C2×D284—21no—
169C2×D284—44no—
170C2×D284—44no—
171C2×D284C2412yes—
172C2×C22⋊D71—24no—
173C2×C22⋊D71—44no—
174C22×Dic71—24no—
175C22×Dic71—21no—
176C22×Dic71—24no—
177C22×Dic71—22no—
178C22×Dic71—44no—
179C22×Dic71C2×D411yescharacteristic
180C22×Dic71C2×D411yescharacteristic
181C22×Dic71C2×D414yes—
182C2×C4×D71—24no—
183C2×C4×D71—24no—
184C2×C4×D71—216no—
185C2×C4×D71—22no—
186C2×C4×D71—28no—
187C2×C4×D71—22no—
188C2×C4×D71—22no—
189C2×C4×D71—22no—
190C2×C4×D71—28no—
191C2×C4×D71—24no—
192C2×C4×D71—44no—
193C2×C4×D71C2×D414yes—
194C2×C4×D71C2×D414yes—
195C2×C4×D71C2×D412yes—
196C2×C4×D71C2×D412yes—
197C2×C4×D71C2412yes—
198C2×C4×D71C2412yes—
199#11765855—216no—
200#11765852—216no—
201#11765849C2×D4116yescomplemented
202#11765848—216no—
203C2×C71⋊C8C2×D418yes—
204C2×C71⋊C8C2414yes—
205C8×D71—216no—
206C4⋊Dic71—24no—
207C4⋊Dic71—22no—
208C4⋊Dic71—24no—
209C4⋊Dic71—24no—
210C4⋊Dic71C2414yes—
211Dic71⋊C4—28no—
212Dic71⋊C4—28no—
213(C2×D71)⋊C4—28no—
214(C2×D71)⋊C4—28no—
215(C2×D71)⋊C4—24no—
216(C2×D71)⋊C4—24no—
217(C2×D71)⋊C4—24no—
218(C2×D71)⋊C4—24no—
219C24×C71C2×D411yescharacteristic
220C2×Q8×C71—24no—
221C2×Q8×C71—22no—
222C2×Q8×C71—24no—
223C2×Q8×C71—28no—
224C2×Q8×C71—24no—
225C2×Q8×C71—28no—
226C2×Q8×C71—44no—
227C2×Q8×C71—48no—
228C2×Q8×C71C2414yes—
229C22×C4×C71—21no—
230C22×C4×C71—21no—
231C22×C4×C71—24no—
232C22×C4×C71—22no—
233C22×C4×C71—44no—
234C22×C4×C71C2×D411yescharacteristic
235C22×C4×C71C2×D412yes—
236C22×C4×C71C2×D414yes—
237C22×C4×C71#4114yes—
238C22×C4×C71C2411yescharacteristic
239C22×C4×C71C2412yes—
240M16×C71—28no—
241C2×C8×C71—24no—
242C2×C8×C71C2414yes—
243C4⋊C4×C71—21no—
244C4⋊C4×C71—21no—
245C4⋊C4×C71C2412yes—
246C4⋊C4×C71C2412yes—
247C22⋊C4×C71—24no—
248C42×C71—24no—
249C23×C71—22no—
250C23×C71—22no—
251C23×C71#12114yes—
252C23×C71C22×D412yes—
253C23×C71C22×D411yescharacteristic
254C22×D71—22no—
255C22×D71—22no—
256C22×D71—28no—
257C22×D71—22no—
258C22×D71—22no—
259C22×D71—22no—
260C22×D71—28no—
261C22×D71—22no—
262C22×D71—44no—
263C22×D71—416no—
264C22×D71—42no—
265C22×D71—42no—
266C22×D71—42no—
267C22×D71#13714yescomplemented
268C22×D71C22×D412yes—
269C22×D71C22×D412yes—
270Q8×C71—24no—
271Q8×C71—24no—
272Q8×C71—44no—
273Q8×C71—48no—
274C2×C4×C71—22no—
275C2×C4×C71—22no—
276C2×C4×C71—24no—
277C2×C4×C71—48no—
278C2×C4×C71—44no—
279C2×C4×C71—42no—
280C2×C4×C71—42no—
281C2×C4×C71#12114yes—
282C2×C4×C71#12118yes—
283C2×C4×C71C22×D412yes—
284C2×C4×C71C22×D411yescharacteristic
285C2×C4×C71C22×D412yes—
286C2×C4×C71C22×D414yes—
287C2×C4×C71C2×#4112yes—
288C2×C4×C71C2×#4114yes—
289C2×C4×C71C2511yescharacteristic
290C22⋊D71—48no—
291C2×Dic71—28no—
292C2×Dic71—22no—
293C2×Dic71—22no—
294C2×Dic71—24no—
295C2×Dic71—22no—
296C2×Dic71—48no—
297C2×Dic71—42no—
298C2×Dic71—44no—
299C2×Dic71C22×D412yes—
300C2×Dic71C22×D412yes—
301D284—22no—
302D284—22no—
303D284—48no—
304D284—48no—
305D284—42no—
306C4×D71—24no—
307C4×D71—24no—
308C4×D71—28no—
309C4×D71—28no—
310C4×D71—22no—
311C4×D71—22no—
312C4×D71—22no—
313C4×D71—22no—
314C4×D71—48no—
315Dic142—22no—
316Dic142—22no—
317Dic142—42no—
318C8×C71—24no—
319C71⋊C8C22×D418yes—
320C22×C71—28no—
321C22×C71—22no—
322C22×C71—22no—
323C22×C71C2×#12114yes—
324C22×C71C2×#12112yes—
325C22×C71C2×#13712yes—
326C22×C71#57512yes—
327C22×C71C23×D411yescharacteristic
328C2×D71—22no—
329C2×D71—28no—
330C2×D71—22no—
331C2×D71—22no—
332C2×D71—22no—
333C2×D71—22no—
334C2×D71—416no—
335C2×D71—44no—
336C2×D71—42no—
337C2×D71—42no—
338C2×D71—42no—
339C2×D71—84no—
340C2×D71C2×#13714yescomplemented
341C4×C71—44no—
342C4×C71—42no—
343C4×C71—42no—
344C4×C71C2×#12112yes—
345C4×C71C2×#12114yes—
346C4×C71C23×D411yescharacteristic
347C4×C71C22×#4111yescharacteristic
348Dic71—22no—
349Dic71—22no—
350Dic71—42no—
351Dic71—44no—
352C2×#3056—711nomaximal, Sylow
353C2×C71—24no—
354C2×C71#305614yescomplemented
355C2×C71C22×#12111yescharacteristic
356C2×C71C22×#13711yescharacteristic
357C2×C71C2×#57511yescharacteristic
358D71—24no—
359D71—42no—
360D71—82no—
361C22×#137—711no—
362C23×M16—711no—
363C2×#525—711no—
364C22×C22⋊Q8—711no—
365#3056—7116no—
366C2×#470—712no—
367C2×#468—712no—
368C2×#467—712no—
369C2×#465—712no—
370C2×#428—711no—
371C2×#417—711no—
372C2×#419D7111yescharacteristic, complemented
373C71C2×#305611yescharacteristic, complemented, Sylow
374C22×#41—711no—
375C23×Q8C2×D7111yescharacteristic
376C24×C4—711no—
377C2×#137—718no—
378C2×#137—1428no—
379C22×Q16—712no—
380C22×SD16—712no—
381C22×M16—711no—
382C22×M16—718no—
383C22×M16—712no—
384C22×M16—1428no—
385C22×M16C2×D7111yescharacteristic
386C23×C8—712no—
387#525—718no—
388#525—1424no—
389C2×#123—1421no—
390C2×C22⋊Q8—712no—
391C2×C22⋊Q8—712no—
392C2×C22⋊Q8—718no—
393C2×C22⋊Q8—711no—
394C2×C22⋊Q8—711no—
395C2×C22⋊Q8—1421no—
396C2×C22⋊Q8—1421no—
397C2×C22⋊Q8—1424no—
398C2×#121—711no—
399C2×#121—711no—
400C2×#120—1421no—
401C2×C4×D4—1421no—
402C2×C4×D4—1421no—
403C2×#117C2×D7111yescharacteristic
404C22×C4⋊C4—711no—
405C22×C4⋊C4—1421no—
406C22×C22⋊C4—1421no—
407#470—7116no—
408#468—7116no—
409#467—7116no—
410#465—7116no—
411#428—718no—
412C2×#107—712no—
413C2×#106—712no—
414#419C2×D7118yescomplemented
415#417—718no—
416C2×#103—712no—
417C2×#103C2×D7112yescomplemented
418C2×#103C2×D7112yescomplemented
419C2×#102—712no—
420C25—711no—
421C2×#41—714no—
422C2×#41—1424no—
423C2×#41—1424no—
424C2×#41—1422no—
425C22×Q8—22no—
426C22×Q8—21no—
427C22×Q8—24no—
428C22×Q8—24no—
429C22×Q8—711no—
430C22×Q8C22×D7112yes—
431C22×Q8C22×D7114yes—
432C22×D4—711no—
433C22×D4—1421no—
434C22×D4—1421no—
435C22×D4—1421no—
436C23×C4—21no—
437C23×C4—711no—
438C23×C4—711no—
439C23×C4—711no—
440C23×C4—714no—
441C23×C4—711no—
442C23×C4—711no—
443C23×C4—714no—
444C23×C4—1421no—
445C23×C4—1421no—
446C23×C4—1424no—
447C23×C4—1424no—
448C23×C4C22×D7111yescharacteristic
449#137—14232no—
450C2×Q16—718no—
451C2×Q16—1428no—
452C2×SD16—718no—
453C2×SD16—1428no—
454C2×M16—24no—
455C2×M16—718no—
456C2×M16—714no—
457C2×M16—718no—
458C2×M16—1428no—
459C2×M16—14232no—
460C2×M16C22×D7114yes—
461C22×C8—712no—
462C22×C8—718no—
463C22×C8—1428no—
464C22×C8C22×D7112yes—
465#123—1428no—
466C22⋊Q8—718no—
467C22⋊Q8—718no—
468C22⋊Q8—714no—
469C22⋊Q8—714no—
470C22⋊Q8—1422no—
471C22⋊Q8—1422no—
472C22⋊Q8—1428no—
473C22⋊Q8—1428no—
474C22⋊Q8—1424no—
475C22⋊Q8—1424no—
476#121—714no—
477#121—714no—
478#121—1422no—
479#121—1422no—
480#120—1428no—
481C4×D4—1428no—
482C4×D4—1428no—
483#117—22no—
484#117C22×D7114yes—
485C2×C4⋊C4—712no—
486C2×C4⋊C4—714no—
487C2×C4⋊C4—1428no—
488C2×C4⋊C4—1422no—
489C2×C4⋊C4—1422no—
490C2×C4⋊C4—1421no—
491C2×C4⋊C4—1421no—
492C2×C4⋊C4—1422no—
493C2×C4⋊C4—1421no—
494C2×C4⋊C4C22×D7111yescharacteristic
495C2×C4⋊C4C22×D7111yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—1421no—
498C2×C22⋊C4—1421no—
499C2×C22⋊C4—1428no—
500C2×C22⋊C4—1422no—
501C2×C22⋊C4—1422no—
502C2×C22⋊C4—1421no—
503C2×C22⋊C4—1421no—
504C2×C42—21no—
505#107—718no—
506#106—718no—
507#103—718no—
508#103C22×D7118yescomplemented
509#103C22×D7118yescomplemented
510#102—718no—
511C24—2842no—
512C24—714no—
513C24—711no—
514C24—711no—
515C24—1424no—
516C24—1421no—
517C24—1424no—
518C24D4×D7111yescharacteristic
519#41—2848no—
520#41—1428no—
521#41—1428no—
522C2×Q8—24no—
523C2×Q8—22no—
524C2×Q8—24no—
525C2×Q8—28no—
526C2×Q8—24no—
527C2×Q8—28no—
528C2×Q8—44no—
529C2×Q8—48no—
530C2×Q8—712no—
531C2×Q8—1422no—
532C2×Q8—1422no—
533C2×Q8—1421no—
534C2×Q8C23×D7114yes—
535C2×D4—2844no—
536C2×D4—2844no—
537C2×D4—2844no—
538C2×D4—712no—
539C2×D4—1424no—
540C2×D4—1424no—
541C2×D4—1424no—
542C2×D4—1421no—
543C2×D4—1422no—
544C2×D4—1422no—
545C22×C4—24no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—44no—
550C22×C4—2844no—
551C22×C4—2844no—
552C22×C4—714no—
553C22×C4—711no—
554C22×C4—711no—
555C22×C4—714no—
556C22×C4—714no—
557C22×C4—712no—
558C22×C4—712no—
559C22×C4—712no—
560C22×C4—712no—
561C22×C4—1424no—
562C22×C4—1422no—
563C22×C4—1421no—
564C22×C4—1424no—
565C22×C4—1424no—
566C22×C4—1422no—
567C22×C4—1428no—
568C22×C4—1422no—
569C22×C4—1422no—
570C22×C4—1422no—
571C22×C4—1428no—
572C22×C4—1424no—
573C22×C4—1424no—
574C22×C4—14216no—
575C22×C4D4×D7114yes—
576C22×C4D4×D7112yes—
577C22×C4D4×D7111yescharacteristic
578C22×C4#1176586514yes—
579C22×C4C23×D7112yes—
580C22×C4C23×D7111yescharacteristic
581Q16—14216no—
582SD16—14216no—
583M16—28no—
584M16—7116no—
585M16—14216no—
586C2×C8—24no—
587C2×C8—718no—
588C2×C8—714no—
589C2×C8—14216no—
590C2×C8C23×D7114yes—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—714no—
594C4⋊C4—1428no—
595C4⋊C4—1428no—
596C4⋊C4—1424no—
597C4⋊C4—1424no—
598C4⋊C4—1424no—
599C4⋊C4—1422no—
600C4⋊C4C23×D7112yes—
601C4⋊C4C23×D7112yes—
602C22⋊C4—24no—
603C22⋊C4—1424no—
604C22⋊C4—1424no—
605C22⋊C4—1428no—
606C22⋊C4—1428no—
607C22⋊C4—1424no—
608C22⋊C4—1424no—
609C42—24no—
610C23—22no—
611C23—22no—
612C23—28416no—
613C23—2844no—
614C23—2842no—
615C23—2842no—
616C23—2842no—
617C23—712no—
618C23—714no—
619C23—712no—
620C23—1428no—
621C23—1422no—
622C23—1428no—
623C23—1422no—
624C23—1422no—
625C23—1422no—
626C23—1422no—
627C23—1422no—
628C23#1455610114yes—
629C23C2×D4×D7112yes—
630C23C2×D4×D7111yescharacteristic
631Q8—24no—
632Q8—24no—
633Q8—48no—
634Q8—44no—
635Q8—2842no—
636Q8—1422no—
637Q8—1422no—
638D4—2848no—
639D4—2848no—
640D4—2848no—
641D4—2842no—
642D4—1422no—
643D4—1422no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—48no—
648C2×C4—44no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—2848no—
652C2×C4—2842no—
653C2×C4—2844no—
654C2×C4—2848no—
655C2×C4—712no—
656C2×C4—712no—
657C2×C4—1424no—
658C2×C4—1422no—
659C2×C4—1428no—
660C2×C4—1422no—
661C2×C4—1422no—
662C2×C4—1422no—
663C2×C4—1422no—
664C2×C4—1422no—
665C2×C4—1422no—
666C2×C4—1428no—
667C2×C4—1428no—
668C2×C4—1424no—
669C2×C4—1424no—
670C2×C4#1455610114yes—
671C2×C4#1455610118yes—
672C2×C4C2×D4×D7112yes—
673C2×C4C2×D4×D7114yes—
674C2×C4C2×D4×D7112yes—
675C2×C4C2×D4×D7111yescharacteristic
676C2×C4C2×#1176586512yes—
677C2×C4C2×#1176586514yes—
678C2×C4C24×D7111yescharacteristic
679C8—24no—
680C8—718no—
681C22—22no—
682C22—22no—
683C22—28no—
684C22—28416no—
685C22—2844no—
686C22—2842no—
687C22—2842no—
688C22—2842no—
689C22—5684no—
690C22—714no—
691C22—1422no—
692C22—1422no—
693C22—1422no—
694C22—1422no—
695C22—1428no—
696C22—1422no—
697C22C2×#1455610114yes—
698C22C2×#1455610112yes—
699C22#137×D7112yes—
700C22#1798679812yes—
701C22C22×D4×D7111yescharacteristic
702C4—42no—
703C4—42no—
704C4—44no—
705C4—2844no—
706C4—2842no—
707C4—1422no—
708C4—1422no—
709C4C2×#1455610114yes—
710C4C2×#1455610112yes—
711C4C22×D4×D7111yescharacteristic
712C4C22×#1176586511yescharacteristic
713C2—24no—
714C2—2842no—
715C2—5682no—
716C2—1424no—
717C2#2259796814yesdirect product factor
718C2C22×#1455610111yescharacteristic
719C2C2×#137×D7111yescharacteristic
720C2C2×#1798679811yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#419×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986511C2
hypercenterC2×#419D71
hypocenterC71C2×#3056
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
1. C22×#14556159C2semidirect
2. C22×M16×D71C2semidirect
4. C22×#14556104C2semidirect
5. #22597968C2direct (N × H)
6. C2×#17986256C2semidirect
7. C2×#17986248C2semidirect
8. C2×#17986239C2semidirect
9. C2×#17986231C2semidirect
10. C2×#17986042C2semidirect
11. C2×#17986001C2semidirect
12. C2×#419×C71C2semidirect
16. C2×#14556159C22semidirect
17. C22×#11765855C22semidirect
18. C22×#11765852C22semidirect
22. C2×M16×D71C22semidirect
34. C2×#14556104C22semidirect
43. #17986256C22semidirect
44. #17986248C22semidirect
45. #17986239C22semidirect
46. #17986231C22semidirect
47. #17986042C22semidirect
48. C2×#14556061C22semidirect
49. C2×#14556059C22semidirect
50. #17986001C22semidirect
51. C2×#14556053C22semidirect
52. C2×#14556050C22semidirect
56. #419×C71C22semidirect
57. C2×#103×C71C22semidirect
58. C2×#103×C71C22semidirect
82. C2×#11765855C23semidirect
84. C2×#11765852C23semidirect
85. C2×#11765849D4semidirect
127. #14556061C23semidirect
128. #14556059C23semidirect
129. #14556053C23semidirect
130. #14556050C23semidirect
148. #103×C71C23semidirect
149. #103×C71C23semidirect
201. #11765849C2×D4semidirect
267. C22×D71#137semidirect
340. C2×D71C2×#137semidirect
354. C2×C71#3056semidirect
372. C2×#419D71semidirect
373. C71C2×#3056semidirect
414. #419C2×D71semidirect
417. C2×#103C2×D71semidirect
418. C2×#103C2×D71semidirect
508. #103C22×D71semidirect
509. #103C22×D71semidirect
717. C2#22597968direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561592
C22×M16×D712
C2×#179865112
C22×#145561042
#225979682
C2×#179862562
C2×#179862482
C2×#179862392
C2×#179862312
C2×#179860422
C2×#179860012
C2×#419×C712
C2×#305671