Finite Group Databasebeta

← #32865089

Subgroups — #32865089

Order 18176.

2030 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22601541C211yesmaximal, characteristic
2#22598198C214yesmaximal, complemented
3#22598187C214yesmaximal, complemented
4#22598176C214yesmaximal, complemented
5#22598165C214yesmaximal, complemented
6#22598158C214yesmaximal, complemented
7#22598149C214yesmaximal, complemented
8#22596929C211yesmaximal, characteristic, complemented
9C2×#17986039C211yesmaximal, characteristic, complemented
10#22596904C211yesmaximal, characteristic, complemented
11#22596857C211yesmaximal, characteristic
12C2×#17985998C211yesmaximal, characteristic
13C2×#544×C71C211yesmaximal, characteristic, complemented
14C22×#11765865C2211yescharacteristic
15C22×#11765849C2211yescharacteristic
16C22×#11765849C2211yescharacteristic
17#17986480—21no—
18#17986480—21no—
19#17986479C2212yes—
20#17986479C2212yes—
21#17986476C2212yes—
22#17986473C2212yes—
23#17986472—22no—
24C4×#11765865C2214yes—
25#17986467—22no—
26C2×#14556087C2211yescharacteristic
27#117×D71—22no—
28#17986303C2218yescomplemented
29#17986303C2218yescomplemented
30#17986296C2218yescomplemented
31#17986296C2218yescomplemented
32#17986291C2218yescomplemented
33#17986286C2218yescomplemented
34#17986281C2218yescomplemented
35#17986276C2218yescomplemented
36#17986042C2212yescomplemented
37#17986042C2212yescomplemented
38#17986039C2214yes—
39#17986039C2212yescomplemented
40#17986039C2214yescomplemented
41#17986039C2212yescomplemented
42#17986035C2214yes—
43C2×#14556061C2212yescomplemented
44C2×#14556059C2212yescomplemented
45#17986026C2214yes—
46#17986026C2214yescomplemented
47#17986023C2214yescomplemented
48#17986007C2212yes—
49#17986003C2212yes—
50#17985998C2212yes—
51#17985998C2214yes—
52#17985998C2212yes—
53#17985998C2214yes—
54#17985993C2214yes—
55C2×#14556051C2212yes—
56C2×#14556048C2212yes—
57#544×C71—22no—
58#544×C71—22no—
59#544×C71C2214yes—
60#544×C71C2214yescomplemented
61C2×C4⋊Q8×C71—21no—
62C2×C4⋊Q8×C71C2212yescomplemented
63C2×#125×C71—21no—
64C2×#125×C71C2212yescomplemented
65C2×C22⋊Q8×C71—22no—
66C2×#117×C71C2211yescharacteristic
67C2×#117×C71C2211yescharacteristic
68C22×C4⋊C4×C71C2211yescharacteristic
69C2×#11765865—21no—
70C2×#11765865—21no—
71C2×#11765865—24no—
72C2×#11765865Q818yescomplemented
73C2×#11765865C2312yes—
74C2×#11765865C2312yes—
75C22×Dic142C2311yescharacteristic
76C22×D284C2311yescharacteristic
77C22×C22⋊D71—21no—
78C22×C4×D71—21no—
79C2×#11765849—24no—
80C2×#11765849—24no—
81C2×#11765849C2312yes—
82C2×#11765849C2312yes—
83C2×#11765849C2312yes—
84C2×#11765849C2312yes—
85C22×C71⋊C8C2312yes—
86C22×C71⋊C8C2312yes—
87C4×Dic142C2314yes—
88C4×Dic142C2314yes—
89#14556093—22no—
90#14556093—22no—
91C4×D284C2314yes—
92C4×D284C2314yes—
93#14556090—22no—
94#14556090—22no—
95C4×C22⋊D71—24no—
96C4×C22⋊D71—24no—
97(C22⋊D71)⋊C4—24no—
98(C22⋊D71)⋊C4—24no—
99#14556087—21no—
100#14556087—21no—
101#14556087C2312yes—
102#14556087C2312yes—
103#14556086—22no—
104#14556086—22no—
105#14556085—24no—
106#14556084—24no—
107C2×C4⋊Dic71C2311yescharacteristic
108C2×C4⋊Dic71C2311yescharacteristic
109C4⋊C4×D71—22no—
110C4⋊C4×D71—22no—
111C2×C22⋊Dic71—21no—
112C22⋊C4×D71—24no—
113C2×C4×Dic71—21no—
114C42×D71—24no—
115#14556061C2314yes—
116#14556061C2318yes—
117#14556061C2314yes—
118#14556059C2314yes—
119#14556059C2318yes—
120#14556059C2314yes—
121C4⋊(C71⋊C8)C2318yes—
122C4⋊(C71⋊C8)C2318yes—
123#14556051C2318yes—
124#14556051C2314yes—
125#14556051C2314yes—
126#14556048C2318yes—
127#14556048C2314yes—
128#14556048C2314yes—
129C22×Q8×C71—22no—
130C23×C4×C71—21no—
131C23×C4×C71C2311yescharacteristic
132C4⋊Q8×C71—24no—
133C4⋊Q8×C71—24no—
134C4⋊Q8×C71—24no—
135C4⋊Q8×C71C2318yes—
136#125×C71—24no—
137#125×C71—24no—
138#125×C71—24no—
139#125×C71C2318yes—
140C22⋊Q8×C71—28no—
141C22⋊Q8×C71—28no—
142#117×C71—21no—
143#117×C71—21no—
144#117×C71D412yes—
145#117×C71D412yes—
146#117×C71C2312yes—
147#117×C71C2312yes—
148#117×C71C2312yes—
149#117×C71C2312yes—
150C2×C4⋊C4×C71—21no—
151C2×C4⋊C4×C71—21no—
152C2×C4⋊C4×C71—21no—
153C2×C4⋊C4×C71—22no—
154C2×C4⋊C4×C71—22no—
155C2×C4⋊C4×C71—22no—
156C2×C4⋊C4×C71D411yescharacteristic
157C2×C4⋊C4×C71D411yescharacteristic
158C2×C4⋊C4×C71C2312yes—
159C2×C4⋊C4×C71C2312yes—
160C2×C4⋊C4×C71C2312yes—
161C2×C4⋊C4×C71C2311yescharacteristic
162C2×C4⋊C4×C71C2311yescharacteristic
163C2×C22⋊C4×C71—21no—
164C2×C22⋊C4×C71D412yes—
165C2×C42×C71—21no—
166C2×C42×C71C2312yes—
167C23×D71—21no—
168#11765865—28no—
169#11765865—28no—
170#11765865—24no—
171#11765865—24no—
172#11765865C2×Q818yes—
173#11765865C2×Q818yescomplemented
174C2×Dic142—21no—
175C2×Dic142—22no—
176C2×Dic142C2×Q814yescomplemented
177C2×Dic142C2412yes—
178C2×D284—21no—
179C2×D284—22no—
180C2×D284C2×Q814yescomplemented
181C2×D284C2412yes—
182C2×C22⋊D71—28no—
183C2×C22⋊D71—22no—
184C2×C22⋊D71—22no—
185C22×Dic71—21no—
186C22×Dic71—21no—
187C22×Dic71—21no—
188C2×C4×D71—28no—
189C2×C4×D71—22no—
190C2×C4×D71—22no—
191C2×C4×D71—24no—
192C2×C4×D71—24no—
193#11765849—24no—
194#11765849—24no—
195#11765849—24no—
196#11765849—24no—
197C2×C71⋊C8—24no—
198C2×C71⋊C8—24no—
199C2×C71⋊C8C2414yes—
200C2×C71⋊C8C2414yes—
201C4⋊Dic71—21no—
202C4⋊Dic71—21no—
203C4⋊Dic71C2412yes—
204C4⋊Dic71C2412yes—
205Dic71⋊C4—24no—
206Dic71⋊C4—24no—
207C22⋊Dic71—22no—
208C22⋊Dic71—22no—
209(C2×D71)⋊C4—24no—
210(C2×D71)⋊C4—24no—
211C4×Dic71—22no—
212C4×Dic71—24no—
213C4×Dic71—24no—
214C4×Dic71—22no—
215C24×C71C2×D411yescharacteristic
216C2×Q8×C71—28no—
217C2×Q8×C71—84no—
218C22×C4×C71—21no—
219C22×C4×C71—21no—
220C22×C4×C71—22no—
221C22×C4×C71—22no—
222C22×C4×C71—22no—
223C22×C4×C71—82no—
224C22×C4×C71C2×D412yes—
225C22×C4×C71C2×D412yes—
226C22×C4×C71C2×D411yescharacteristic
227C22×C4×C71C2×D411yescharacteristic
228C22×C4×C71C2×D411yescharacteristic
229C22×C4×C71C2×Q814yes—
230C22×C4×C71#4114yes—
231C22×C4×C71C2411yescharacteristic
232C22×C4×C71C2411yescharacteristic
233C22×C4×C71C2411yescharacteristic
234C4⋊C4×C71—22no—
235C4⋊C4×C71—22no—
236C4⋊C4×C71—22no—
237C4⋊C4×C71—28no—
238C4⋊C4×C71—28no—
239C4⋊C4×C71—28no—
240C4⋊C4×C71—21no—
241C4⋊C4×C71—21no—
242C4⋊C4×C71C2×D412yes—
243C4⋊C4×C71C2×D412yes—
244C4⋊C4×C71C2×D412yes—
245C4⋊C4×C71C2×D412yes—
246C4⋊C4×C71C2414yes—
247C4⋊C4×C71C2412yes—
248C4⋊C4×C71C2412yes—
249C22⋊C4×C71—22no—
250C22⋊C4×C71—22no—
251C22⋊C4×C71C2×D414yes—
252C22⋊C4×C71C2×D414yes—
253C42×C71—22no—
254C42×C71—22no—
255C42×C71C2×D414yes—
256C42×C71C2414yes—
257C23×C71—41no—
258C23×C71—41no—
259C23×C71C22⋊Q814yes—
260C23×C71C22×D411yescharacteristic
261C23×C71C22×D411yescharacteristic
262C23×C71C22×D411yescharacteristic
263C22×D71—22no—
264C22×D71—24no—
265C22×D71—81no—
266C22×D71—81no—
267Q8×C71—88no—
268C2×C4×C71—22no—
269C2×C4×C71—22no—
270C2×C4×C71—24no—
271C2×C4×C71—42no—
272C2×C4×C71—42no—
273C2×C4×C71—42no—
274C2×C4×C71—44no—
275C2×C4×C71—42no—
276C2×C4×C71—82no—
277C2×C4×C71—82no—
278C2×C4×C71C22⋊Q814yes—
279C2×C4×C71C22⋊Q814yes—
280C2×C4×C71C22⋊Q814yes—
281C2×C4×C71C22×D414yes—
282C2×C4×C71C22×D414yes—
283C2×C4×C71C22×D411yescharacteristic
284C2×C4×C71C22×D411yescharacteristic
285C2×C4×C71C22×D411yescharacteristic
286C2×C4×C71C22×Q812yes—
287C2×C4×C71C22×Q812yes—
288C2×C4×C71C22×Q812yes—
289C2×C4×C71C2×#4112yes—
290C2×C4×C71C2×#4112yes—
291C2×C4×C71C2×#4112yes—
292C2×C4×C71C2511yescharacteristic
293C22⋊D71—28no—
294C22⋊D71—28no—
295C2×Dic71—24no—
296C2×Dic71—22no—
297C2×Dic71—22no—
298C2×Dic71—22no—
299C2×Dic71—81no—
300C2×Dic71—81no—
301D284—24no—
302D284—22no—
303D284C22×Q814yes—
304C4×D71—28no—
305C4×D71—28no—
306C4×D71—84no—
307C4×D71—84no—
308Dic142—24no—
309Dic142—22no—
310Dic142C22×Q814yes—
311C71⋊C8—24no—
312C71⋊C8—24no—
313C22×C71—21no—
314C22×C71—21no—
315C22×C71—21no—
316C22×C71—21no—
317C22×C71—21no—
318C22×C71—21no—
319C22×C71—44no—
320C22×C71C2×C22⋊Q812yes—
321C22×C71C2×C22⋊Q812yes—
322C22×C71C2×C22⋊Q812yes—
323C22×C71C23×D411yescharacteristic
324C2×D71—24no—
325C2×D71—42no—
326C2×D71—42no—
327C2×D71—84no—
328C4×C71—24no—
329C4×C71—24no—
330C4×C71—44no—
331C4×C71—42no—
332C4×C71—42no—
333C4×C71C2×C22⋊Q812yes—
334C4×C71C2×C22⋊Q812yes—
335C4×C71C2×C22⋊Q812yes—
336C4×C71C23×Q811yescharacteristic
337C4×C71C22×#4111yescharacteristic
338Dic71—24no—
339Dic71—42no—
340Dic71—42no—
341#60493—711nomaximal, Sylow
342C2×C71—22no—
343C2×C71—22no—
344C2×C71—22no—
345C2×C71C22×C22⋊Q811yescharacteristic
346C2×C71#358511yescharacteristic
347C2×C71#358611yescharacteristic
348D71—44no—
349C2×#544D7111yescharacteristic, complemented
350#3428—711no—
351#3084—714no—
352#3083—714no—
353#3082—714no—
354#3081—714no—
355#3080—714no—
356#3079—714no—
357#2911—711no—
358C2×#428—711no—
359#2905—711no—
360#2896—711no—
361C2×#417—711no—
362C71#6049311yescharacteristic, complemented, Sylow
363C22×#41—711no—
364C22×M16—711no—
365C22×M16—711no—
366#544—22no—
367#544—22no—
368#544C2×D7114yes—
369#544C2×D7114yescomplemented
370C2×C4⋊Q8—21no—
371C2×C4⋊Q8C2×D7112yescomplemented
372C2×#125—21no—
373C2×#125C2×D7112yescomplemented
374C2×C22⋊Q8—22no—
375#520—712no—
376#520—712no—
377#520—1421no—
378#520—1421no—
379#519—712no—
380#518—712no—
381#518—1422no—
382C4×#41—714no—
383C4×#41—1422no—
384C2×#117—711no—
385C2×#117—1422no—
386C2×#117C2×D7111yescharacteristic
387C2×#117C2×D7111yescharacteristic
388C22×C4⋊C4C2×D7111yescharacteristic
389#479—718no—
390#479—718no—
391#478—718no—
392#478—718no—
393#477—718no—
394#476—718no—
395#475—718no—
396#474—718no—
397#428—712no—
398#428—712no—
399#428—712no—
400#428—714no—
401#428—712no—
402#428—714no—
403#427—714no—
404C2×#107—712no—
405C2×#106—712no—
406#424—714no—
407#424—714no—
408#423—714no—
409#419—712no—
410#418—712no—
411#417—712no—
412#417—714no—
413#417—712no—
414#417—714no—
415#416—714no—
416C2×#103—712no—
417C2×#102—712no—
418C2×#41—718no—
419C2×#41—712no—
420C2×#41—712no—
421C2×#41—1421no—
422C2×#41—1421no—
423C2×#41—1424no—
424C22×Q8—22no—
425C22×Q8—711no—
426C22×D4—711no—
427C22×D4—1421no—
428C23×C4—21no—
429C23×C4—1421no—
430C23×C4C22×D7111yescharacteristic
431C2×M16—712no—
432C2×M16—712no—
433C2×M16—712no—
434C2×M16—712no—
435C2×M16—1424no—
436C2×M16—1424no—
437C22×C8—712no—
438C22×C8—712no—
439C4⋊Q8—24no—
440C4⋊Q8—24no—
441C4⋊Q8—24no—
442C4⋊Q8C22×D7118yes—
443#125—24no—
444#125—24no—
445#125—24no—
446#125C22×D7118yes—
447C22⋊Q8—28no—
448C22⋊Q8—28no—
449C4×Q8—714no—
450C4×Q8—714no—
451C4×Q8—1422no—
452C4×Q8—1422no—
453C4×D4—714no—
454C4×D4—714no—
455C4×D4—1424no—
456C4×D4—1424no—
457C4×D4—1422no—
458C4×D4—1422no—
459C4×D4—1424no—
460C4×D4—1424no—
461#117—21no—
462#117—21no—
463#117—712no—
464#117—712no—
465#117—1421no—
466#117—1421no—
467#117—1422no—
468#117—1422no—
469#117—1424no—
470#117—1424no—
471#117C22⋊D7112yes—
472#117C22⋊D7112yes—
473#117C22×D7112yes—
474#117C22×D7112yes—
475#117C22×D7112yes—
476#117C22×D7112yes—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—711no—
484C2×C4⋊C4—711no—
485C2×C4⋊C4—1422no—
486C2×C4⋊C4—1422no—
487C2×C4⋊C4C22⋊D7111yescharacteristic
488C2×C4⋊C4C22⋊D7111yescharacteristic
489C2×C4⋊C4C22×D7112yes—
490C2×C4⋊C4C22×D7112yes—
491C2×C4⋊C4C22×D7112yes—
492C2×C4⋊C4C22×D7111yescharacteristic
493C2×C4⋊C4C22×D7111yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—1421no—
496C2×C22⋊C4—1424no—
497C2×C22⋊C4C22⋊D7112yes—
498C2×C42—21no—
499C2×C42—1421no—
500C2×C42—1424no—
501C2×C42C22×D7112yes—
502#107—718no—
503#107—714no—
504#107—714no—
505#106—718no—
506#106—714no—
507#106—714no—
508C4⋊C8—718no—
509C4⋊C8—718no—
510#103—718no—
511#103—714no—
512#103—714no—
513#102—718no—
514#102—714no—
515#102—714no—
516C24—1421no—
517C24C2×C22⋊D7111yescharacteristic
518#41—718no—
519#41—718no—
520#41—1424no—
521#41—1424no—
522#41—1428no—
523#41—1428no—
524C2×Q8—28no—
525C2×Q8—84no—
526C2×Q8—714no—
527C2×Q8—712no—
528C2×Q8—1421no—
529C2×Q8—1422no—
530C2×D4—714no—
531C2×D4—712no—
532C2×D4—1422no—
533C2×D4—1422no—
534C2×D4—1428no—
535C2×D4—1421no—
536C2×D4—1422no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—82no—
543C22×C4—1421no—
544C22×C4—1421no—
545C22×C4—1424no—
546C22×C4—1424no—
547C22×C4—1421no—
548C22×C4—1422no—
549C22×C4—1422no—
550C22×C4—1428no—
551C22×C4C2×C22⋊D7112yes—
552C22×C4C2×C22⋊D7112yes—
553C22×C4C2×C22⋊D7111yescharacteristic
554C22×C4C2×C22⋊D7111yescharacteristic
555C22×C4C2×C22⋊D7111yescharacteristic
556C22×C4Q8×D7114yes—
557C22×C4#1176586614yes—
558C22×C4C23×D7111yescharacteristic
559C22×C4C23×D7111yescharacteristic
560C22×C4C23×D7111yescharacteristic
561M16—1424no—
562M16—1424no—
563M16—1424no—
564M16—1424no—
565C2×C8—714no—
566C2×C8—714no—
567C2×C8—1424no—
568C2×C8—1424no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—28no—
573C4⋊C4—28no—
574C4⋊C4—28no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—712no—
578C4⋊C4—712no—
579C4⋊C4—1424no—
580C4⋊C4—1424no—
581C4⋊C4—1421no—
582C4⋊C4—1421no—
583C4⋊C4C2×C22⋊D7112yes—
584C4⋊C4C2×C22⋊D7112yes—
585C4⋊C4C2×C22⋊D7112yes—
586C4⋊C4C2×C22⋊D7112yes—
587C4⋊C4C23×D7114yes—
588C4⋊C4C23×D7112yes—
589C4⋊C4C23×D7112yes—
590C22⋊C4—22no—
591C22⋊C4—22no—
592C22⋊C4—1422no—
593C22⋊C4—1422no—
594C22⋊C4—1424no—
595C22⋊C4—1424no—
596C22⋊C4C2×C22⋊D7114yes—
597C22⋊C4C2×C22⋊D7114yes—
598C42—22no—
599C42—22no—
600C42—1422no—
601C42—1422no—
602C42—1424no—
603C42—1424no—
604C42C2×C22⋊D7114yes—
605C42C23×D7114yes—
606C23—41no—
607C23—41no—
608C23—5681no—
609C23—5681no—
610C23—1422no—
611C23—1424no—
612C23#1455610414yes—
613C23C22×C22⋊D7111yescharacteristic
614C23C22×C22⋊D7111yescharacteristic
615C23C22×C22⋊D7111yescharacteristic
616Q8—88no—
617Q8—714no—
618Q8—1422no—
619Q8—1424no—
620D4—714no—
621D4—1428no—
622D4—1428no—
623D4—1422no—
624D4—1424no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—24no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—44no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—82no—
634C2×C4—82no—
635C2×C4—5684no—
636C2×C4—5684no—
637C2×C4—5681no—
638C2×C4—5681no—
639C2×C4—1422no—
640C2×C4—1422no—
641C2×C4—1422no—
642C2×C4—1424no—
643C2×C4—1428no—
644C2×C4—1428no—
645C2×C4#1455610414yes—
646C2×C4#1455610414yes—
647C2×C4#1455610414yes—
648C2×C4C22×C22⋊D7114yes—
649C2×C4C22×C22⋊D7114yes—
650C2×C4C22×C22⋊D7111yescharacteristic
651C2×C4C22×C22⋊D7111yescharacteristic
652C2×C4C22×C22⋊D7111yescharacteristic
653C2×C4C2×Q8×D7112yes—
654C2×C4C2×Q8×D7112yes—
655C2×C4C2×Q8×D7112yes—
656C2×C4C2×#1176586612yes—
657C2×C4C2×#1176586612yes—
658C2×C4C2×#1176586612yes—
659C2×C4C24×D7111yescharacteristic
660C8—1424no—
661C8—1424no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—44no—
669C22—2842no—
670C22—2842no—
671C22—5684no—
672C22—1424no—
673C22C2×#1455610412yes—
674C22C2×#1455610412yes—
675C22C2×#1455610412yes—
676C22C23×C22⋊D7111yescharacteristic
677C4—24no—
678C4—24no—
679C4—44no—
680C4—42no—
681C4—42no—
682C4—2842no—
683C4—2842no—
684C4—1424no—
685C4C2×#1455610412yes—
686C4C2×#1455610412yes—
687C4C2×#1455610412yes—
688C4C22×Q8×D7111yescharacteristic
689C4C22×#1176586611yescharacteristic
690C2—22no—
691C2—22no—
692C2—22no—
693C2—2844no—
694C2C22×#1455610411yescharacteristic
695C2#2260312011yescharacteristic
696C2#2260312711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#544×C71C2
socleC22×C71C23×D4
prime radicalC22×#11765865C22
hypercenterC2×#544D71
hypocenterC71#60493
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #22598198C2semidirect
3. #22598187C2semidirect
4. #22598176C2semidirect
5. #22598165C2semidirect
6. #22598158C2semidirect
7. #22598149C2semidirect
8. #22596929C2semidirect
9. C2×#17986039C2semidirect
10. #22596904C2semidirect
13. C2×#544×C71C2semidirect
28. #17986303C22semidirect
29. #17986303C22semidirect
30. #17986296C22semidirect
31. #17986296C22semidirect
32. #17986291C22semidirect
33. #17986286C22semidirect
34. #17986281C22semidirect
35. #17986276C22semidirect
36. #17986042C22semidirect
37. #17986042C22semidirect
39. #17986039C22semidirect
40. #17986039C22semidirect
41. #17986039C22semidirect
43. C2×#14556061C22semidirect
44. C2×#14556059C22semidirect
46. #17986026C22semidirect
47. #17986023C22semidirect
60. #544×C71C22semidirect
62. C2×C4⋊Q8×C71C22semidirect
64. C2×#125×C71C22semidirect
72. C2×#11765865Q8semidirect
173. #11765865C2×Q8semidirect
176. C2×Dic142C2×Q8semidirect
180. C2×D284C2×Q8semidirect
349. C2×#544D71semidirect
362. C71#60493semidirect
369. #544C2×D71semidirect
371. C2×C4⋊Q8C2×D71semidirect
373. C2×#125C2×D71semidirect

Maximal subgroups

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

subgroupindex
#226015412
#225981982
#225981872
#225981762
#225981652
#225981582
#225981492
#225969292
C2×#179860392
#225969042
#225968572
C2×#179859982
C2×#544×C712
#6049371