Finite Group Databasebeta

← #41×#11924029 #33993098

Subgroups — #41×#11924029 #33993098

Order 18688.

7812 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623558C211yesmaximal, characteristic, complemented
2#22623552C213yesmaximal, complemented
3#22623551C213yesmaximal, complemented
4#22623542C219yesmaximal, complemented
5#22623531C213yesmaximal, complemented
6#22623526C213yesmaximal, complemented
7Q8×#11924029C211yesmaximal, characteristic, complemented
8#22623498C219yesmaximal, complemented
9#22623497C219yesmaximal, complemented
10D4×#11924029C213yesmaximal, complemented
11#41×D292C213yesmaximal, complemented
12#22623228C219yesmaximal, complemented
13C2×C4×#11924029C213yesmaximal, complemented
14C4×#41×D73C213yesmaximal, complemented
15Q8×#41×C73C211yesmaximal, characteristic, complemented
16C22×#11924029C2213yes—
17C2×#41×D73C2213yes—
18#17989322C2219yescomplemented
19#17989316C2213yescomplemented
20#17989311C2219yescomplemented
21#17989310C2219yescomplemented
22#17989303C2219yescomplemented
23#17989298C2219yescomplemented
24#17989290C22118yescomplemented
25#17989285C22118yescomplemented
26#17989279C22118yescomplemented
27#17989275C22118yescomplemented
28#17989264C22136yescomplemented
29#17989259C2213yescomplemented
30#17989259C2213yescomplemented
31Q8×D292C2213yescomplemented
32#17989249C2216yescomplemented
33#17989248C2216yescomplemented
34#17989241C2219yescomplemented
35#17989240C2219yescomplemented
36#17989232C22118yescomplemented
37#17989228C22118yescomplemented
38D4×D292C2219yescomplemented
39#17989142C2219yescomplemented
40#17989142C2219yescomplemented
41#17989138C2219yescomplemented
42#17989138C2219yescomplemented
43#17989137C2219yescomplemented
44#17989124C22118yescomplemented
45#17989124C22118yescomplemented
46#17989123C22118yescomplemented
47#17989123C22118yescomplemented
48#17989122C22118yescomplemented
49#17989122C22118yescomplemented
50#17989100C22118yescomplemented
51#17989100C22118yescomplemented
52#17989099C22118yescomplemented
53#41×Dic73C2211yescharacteristic
54C4×#11924029C2213yes—
55C4×#11924029C2211yescharacteristic
56C4×#11924029C2219yescomplemented
57C4×#11924029C2219yescomplemented
58C4×#11924029C2213yescomplemented
59C4×#11924029C2213yescomplemented
60C4×#11924029C2219yescomplemented
61C4×#11924029C2213yescomplemented
62C4×#11924029C2213yescomplemented
63C4×#11924029C2219yescomplemented
64C4×#11924029C2216yescomplemented
65C4×#11924028C2219yescomplemented
66#17989055C2219yescomplemented
67C4×#11924027C2219yescomplemented
68C4×#11924027C2219yescomplemented
69C2×Q8×Dic73C2213yescomplemented
70C4×Q8×D73C2213yescomplemented
71C4×Q8×D73C2213yescomplemented
72C2×C4×D292C2219yescomplemented
73C2×#14556553C2219yescomplemented
74C4×D4×D73C2219yescomplemented
75C4×D4×D73C2219yescomplemented
76C2×#14556549C2219yescomplemented
77#117×D73C2219yescomplemented
78C2×C42×D73C2219yescomplemented
79Q82×C73C2211yescharacteristic, complemented
80#557×C73C2213yescomplemented
81#554×C73C2219yescomplemented
82D4×Q8×C73C2213yescomplemented
83#533×C73C2219yescomplemented
84C4×#41×C73C2213yes—
85C2×C4×Q8×C73C2213yescomplemented
86C2×#11924029—224no—
87C2×#11924029C2319yes—
88C2×#11924029C2313yes—
89C2×#11924029C2319yes—
90C2×#11924029C2313yes—
91C2×#11924029C2316yes—
92C2×#11924029C2311yescharacteristic
93C2×#11924028C2319yes—
94C2×#11924027C2319yes—
95#41×D73—224no—
96C2×Q8×D73C2313yes—
97C22×D292C2319yes—
98C2×D4×D73C2319yes—
99C22×C4×D73C2319yes—
100C22×C4×D73C2319yes—
101C22×C4×D73C2319yes—
102#14556591C2319yes—
103#14556588C2319yes—
104#14556586C23136yes—
105#14556586C23136yes—
106#14556582C23118yes—
107#14556582C23118yes—
108#14556580C23118yes—
109#14556580C23118yes—
110#14556579C23118yes—
111#14556576C23136yes—
112#14556576C23136yes—
113#14556575C23136yes—
114#14556571C23118yes—
115#14556571C23118yes—
116#14556567C23118yes—
117#14556567C23118yes—
118#14556566C23118yes—
119#14556566C23118yes—
120#14556566C23118yes—
121#14556566C23118yes—
122#14556565C23118yes—
123#14556565C23118yes—
124#14556561C23136yes—
125Q8×Dic73C2316yes—
126Q8×Dic73C2319yes—
127Q8×Dic73C2313yes—
128Q8×Dic73C2319yes—
129Q8×Dic73C2311yescharacteristic
130Q8×Dic73C2311yescharacteristic
131Q8×Dic73C2311yescharacteristic
132C4×Dic146C2319yes—
133C4×Dic146C2319yes—
134#14556556C2319yes—
135#14556556C2319yes—
136C4×D292C23118yes—
137C4×D292C2319yes—
138C4×D292C23118yes—
139C4×D292C2319yes—
140C4×D292C23118yes—
141C4×D292C2319yes—
142C4×D292C2319yes—
143C4×D292C2319yes—
144C4×D292C2313yes—
145D4×Dic73C2313yes—
146D4×Dic73C2313yes—
147#14556553C23118yes—
148#14556553C2319yes—
149#14556553C2319yes—
150#14556553C23118yes—
151#14556553C2319yes—
152#14556553C2319yes—
153#14556553C23118yes—
154#14556553C2319yes—
155#14556553C2313yes—
156C4×C22⋊D73C23118yes—
157C4×C22⋊D73C23118yes—
158#14556551C23118yes—
159#14556551C23118yes—
160#14556550C2313yes—
161#14556549C23118yes—
162#14556549C23118yes—
163#14556549C2319yes—
164#14556549C23118yes—
165#14556549C2319yes—
166#14556549C2319yes—
167#14556549C2319yes—
168#14556549C2319yes—
169#14556549C2313yes—
170#14556548C23118yes—
171#14556547C23118yes—
172C2×C4⋊Dic73C2319yes—
173C4⋊C4×D73C2319yes—
174C4⋊C4×D73C2319yes—
175C2×#11924005C23118yes—
176C22⋊C4×D73C23118yes—
177C2×C4×Dic73C2319yes—
178C2×C4×Dic73C2319yes—
179C2×C4×Dic73C2313yes—
180C42×D73C2319yes—
181C42×D73C2319yes—
182C42×D73C2319yes—
183C42×D73C2319yes—
184C42×D73C2319yes—
185C42×D73C2319yes—
186C42×D73C2313yes—
187C42×D73C2319yes—
188C2×#41×C73C2311yescharacteristic
189C22×Q8×C73C2313yes—
190C4⋊Q8×C73C2319yes—
191C4⋊Q8×C73C2319yes—
192#125×C73C23118yes—
193C22⋊Q8×C73C23118yes—
194C22⋊Q8×C73C23118yes—
195C4×Q8×C73C2316yes—
196C4×Q8×C73C2319yes—
197C4×Q8×C73C2313yes—
198C4×Q8×C73C2313yes—
199C4×Q8×C73C2311yescharacteristic
200C4×Q8×C73C2313yes—
201C4×Q8×C73C2319yes—
202C4×D4×C73C2319yes—
203C4×D4×C73C2319yes—
204#117×C73C2319yes—
205C2×C4⋊C4×C73C2319yes—
206C2×C42×C73C2319yes—
207C23×D73C2419yes—
208#11924029—212no—
209#11924029—212no—
210#11924029—236no—
211#11924029—236no—
212#11924029—412no—
213#11924029#4118yesdirect product factor
214#11924028—236no—
215#11924027—236no—
216C2×Dic146C2419yes—
217Q8×D73—212no—
218C2×D292—236no—
219C2×D292C24118yes—
220C2×D292C2419yes—
221C2×D292C2419yes—
222C2×D292C24118yes—
223C2×D292C2413yes—
224C2×C22⋊D73C24118yes—
225D4×D73—236no—
226C22×Dic73C2413yes—
227C22×Dic73C2413yes—
228C22×Dic73C2419yes—
229C2×C4×D73—236no—
230C2×C4×D73—236no—
231C2×C4×D73—418no—
232C2×C4×D73C2413yes—
233C2×C4×D73C2413yes—
234C2×C4×D73C2419yes—
235C2×C4×D73C2419yes—
236C2×C4×D73C2419yes—
237C2×C4×D73C2419yes—
238C2×C4×D73C2419yes—
239C2×C4×D73C2419yes—
240C2×C4×D73C2419yes—
241C2×C4×D73C2419yes—
242C2×C4×D73C2419yes—
243C2×C4×D73C2413yes—
244C4⋊Dic73C2413yes—
245C4⋊Dic73C2413yes—
246C4⋊Dic73C2413yes—
247C4⋊Dic73C2419yes—
248C4⋊Dic73C24118yes—
249C4⋊Dic73C24118yes—
250#11924007C24118yes—
251#11924007C24118yes—
252C22⋊Dic73C2416yes—
253#11924005C24118yes—
254#11924005C24118yes—
255#11924005C2416yes—
256#11924005C24118yes—
257#11924005C24118yes—
258#11924005C24118yes—
259#11924005C24136yes—
260C4×Dic73C2411yescharacteristic
261C4×Dic73C2413yes—
262C4×Dic73C2413yes—
263C4×Dic73C2413yes—
264C4×Dic73C2413yes—
265C4×Dic73C2413yes—
266C4×Dic73C2419yes—
267C4×Dic73C2419yes—
268C4×Dic73C2419yes—
269C4×Dic73C2419yes—
270C4×Dic73C2419yes—
271C4×Dic73C2419yes—
272#41×C73#4118yescomplemented
273C2×Q8×C73—212no—
274C2×Q8×C73C2419yes—
275C2×Q8×C73C2416yes—
276C2×Q8×C73C2411yescharacteristic
277C2×Q8×C73C2411yescharacteristic
278C2×D4×C73C2413yes—
279C22×C4×C73C2419yes—
280C22×C4×C73C2419yes—
281C22×C4×C73C2413yes—
282C4⋊C4×C73C2413yes—
283C4⋊C4×C73C24118yes—
284C4⋊C4×C73C2419yes—
285C4⋊C4×C73C2419yes—
286C4⋊C4×C73C2419yes—
287C4⋊C4×C73C24118yes—
288C22⋊C4×C73C24118yes—
289C42×C73C2413yes—
290C42×C73C2419yes—
291C42×C73C2419yes—
292C42×C73C2419yes—
293C23×C73C2513yes—
294C22×D73—218no—
295C22×D73—218no—
296C22×D73—49no—
297C22×D73C2519yes—
298C22×D73C2513yes—
299Q8×C73—218no—
300Q8×C73—46no—
301Q8×C73C2×#4114yescomplemented
302Q8×C73C2×#4114yescomplemented
303D4×C73C2×#41112yescomplemented
304C2×C4×C73—218no—
305C2×C4×C73—49no—
306C2×C4×C73C2×#41112yescomplemented
307C2×C4×C73C2513yes—
308C2×C4×C73C2519yes—
309C2×C4×C73C2519yes—
310C2×C4×C73C2513yes—
311C2×C4×C73C2513yes—
312C2×C4×C73C2511yescharacteristic
313C22⋊D73—236no—
314C2×Dic73—218no—
315C2×Dic73—26no—
316C2×Dic73—26no—
317C2×Dic73C2513yes—
318C2×Dic73C2513yes—
319C2×Dic73C2513yes—
320C2×Dic73C2519yes—
321C2×Dic73C2511yescharacteristic
322C2×Dic73C2511yescharacteristic
323D292—236no—
324D292—218no—
325D292—218no—
326D292—418no—
327D292C2×#41112yescomplemented
328C4×D73—218no—
329C4×D73—26no—
330C4×D73—218no—
331C4×D73—218no—
332C4×D73—218no—
333C4×D73—218no—
334C4×D73—218no—
335C4×D73—26no—
336C4×D73—218no—
337C4×D73—49no—
338C4×D73—49no—
339C4×D73C2×#41112yescomplemented
340Dic146—218no—
341C22×C73—23no—
342C22×C73—23no—
343C22×C73C22×#4116yes—
344C22×C73C2611yescharacteristic
345C2×D73—23no—
346C2×D73—23no—
347C2×D73—29no—
348C2×D73—29no—
349C2×D73—29no—
350C2×D73—436no—
351C2×D73C22×#4116yes—
352C4×C73—29no—
353C4×C73—23no—
354C4×C73—29no—
355C4×C73C22×#4116yes—
356C4×C73C22×#4116yes—
357C4×C73C22×#4112yes—
358Dic73—29no—
359Dic73—23no—
360Dic73—23no—
361Dic73—23no—
362Dic73C22×#4112yes—
363Dic73#58512yes—
364#412—731nomaximal, Sylow
365C2×C73—26no—
366C2×C73C23×#4111yescharacteristic
367C2×C73C23×#4111yescharacteristic
368C2×C73C2×#58511yescharacteristic
369D73—26no—
370D73—49no—
371#3483—731no—
372#3482—733no—
373#3482—733no—
374#3481—739no—
375#3480—733no—
376#3480—733no—
377Q8×#41—731no—
378Q8×#41D7311yescharacteristic, complemented
379#3475—739no—
380#3475—739no—
381D4×#41—733no—
382D4×#41—733no—
383#3444—739no—
384C2×C4×#41—733no—
385C2×C4×#41—733no—
386C73#41211yescharacteristic, complemented, Sylow
387C22×#41—733no—
388C22×#41—733no—
389#559—739no—
390Q82C2×D7311yescharacteristic, complemented
391#557—733no—
392#557C2×D7313yescomplemented
393#556—739no—
394#556—739no—
395#555—739no—
396#554—739no—
397#554C2×D7319yescomplemented
398#553—7318no—
399#553—7318no—
400#552—7318no—
401#552—7318no—
402#551—7336no—
403#550—733no—
404#550—733no—
405D4×Q8—733no—
406D4×Q8C2×D7313yescomplemented
407#548—736no—
408#548—736no—
409#547—739no—
410#547—739no—
411#546—7318no—
412#546—7318no—
413D42—739no—
414#533—739no—
415#533—739no—
416#533C2×D7319yescomplemented
417#532—739no—
418#532—739no—
419#532—739no—
420#529—7318no—
421#529—7318no—
422#529—7318no—
423#529—7318no—
424#529—7318no—
425#529—7318no—
426#525—7318no—
427#525—7318no—
428#525—7318no—
429C4×#41—731no—
430C4×#41—731no—
431C4×#41—739no—
432C4×#41—733no—
433C4×#41—739no—
434C4×#41—739no—
435C4×#41—733no—
436C4×#41—733no—
437C4×#41—739no—
438C4×#41—733no—
439C4×#41—733no—
440C4×#41—736no—
441C4×#41—739no—
442C4×#41—739no—
443C4×#41—739no—
444C4×#41—739no—
445C4×#41C2×D7313yes—
446C2×C4×Q8—733no—
447C2×C4×Q8—733no—
448C2×C4×Q8—733no—
449C2×C4×Q8C2×D7313yescomplemented
450C2×C4×D4—739no—
451C2×C4×D4—739no—
452C2×C4×D4—739no—
453C2×C4×D4—739no—
454C2×#117—739no—
455C2×#117—739no—
456C22×C42—739no—
457C2×#41—736no—
458C2×#41—731no—
459C2×#41—739no—
460C2×#41—739no—
461C2×#41—733no—
462C2×#41—733no—
463C2×#41—739no—
464C2×#41—739no—
465C2×#41—14624no—
466C2×#41—14624no—
467C2×#41C22×D7311yescharacteristic
468C22×Q8—733no—
469C22×Q8C22×D7313yes—
470C22×D4—739no—
471C22×D4—739no—
472C23×C4—739no—
473C23×C4—739no—
474C23×C4—739no—
475C4⋊Q8—739no—
476C4⋊Q8C22×D7319yes—
477C4⋊Q8C22×D7319yes—
478#127—739no—
479#126—7336no—
480#126—7336no—
481#125—7318no—
482#125—7318no—
483#125C22×D73118yes—
484#124—7318no—
485#124—7318no—
486#124—7318no—
487#123—7336no—
488#123—7336no—
489#123—7336no—
490C22⋊Q8—7318no—
491C22⋊Q8—7318no—
492C22⋊Q8—7318no—
493C22⋊Q8—7318no—
494C22⋊Q8C22×D73118yes—
495C22⋊Q8C22×D73118yes—
496#121—7318no—
497#121—7318no—
498#121—7318no—
499#121—7318no—
500#121—7318no—
501#121—7318no—
502#120—7336no—
503C4×Q8—731no—
504C4×Q8—731no—
505C4×Q8—731no—
506C4×Q8—739no—
507C4×Q8—733no—
508C4×Q8—739no—
509C4×Q8—736no—
510C4×Q8—739no—
511C4×Q8—739no—
512C4×Q8—739no—
513C4×Q8—739no—
514C4×Q8C22×D7313yes—
515C4×Q8C22×D7313yes—
516C4×Q8C22×D7311yescharacteristic
517C4×Q8C22×D7319yes—
518C4×Q8C22×D7313yes—
519C4×Q8C22×D7319yes—
520C4×Q8C22×D7316yes—
521C4×D4—733no—
522C4×D4—733no—
523C4×D4—7318no—
524C4×D4—7318no—
525C4×D4—733no—
526C4×D4—7318no—
527C4×D4—739no—
528C4×D4—739no—
529C4×D4—739no—
530C4×D4—739no—
531C4×D4—7318no—
532C4×D4—739no—
533C4×D4—7318no—
534C4×D4—7318no—
535C4×D4—7318no—
536C4×D4—733no—
537C4×D4—7318no—
538C4×D4—739no—
539C4×D4—739no—
540C4×D4—7318no—
541C4×D4—739no—
542C4×D4—739no—
543C4×D4—739no—
544C4×D4—7318no—
545C4×D4C22×D7319yes—
546C4×D4C22×D7319yes—
547#117—733no—
548#117—733no—
549#117—739no—
550#117—7318no—
551#117—7318no—
552#117—739no—
553#117—739no—
554#117—739no—
555#117—739no—
556#117—7318no—
557#117—7318no—
558#117—7318no—
559#117C22×D7319yes—
560C2×C4⋊C4—739no—
561C2×C4⋊C4—739no—
562C2×C4⋊C4—739no—
563C2×C4⋊C4C22×D7319yes—
564C2×C22⋊C4—7318no—
565C2×C22⋊C4—7318no—
566C2×C42—739no—
567C2×C42—739no—
568C2×C42—733no—
569C2×C42—739no—
570C2×C42—739no—
571C2×C42—739no—
572C2×C42—739no—
573C2×C42—739no—
574C2×C42—739no—
575C2×C42—739no—
576C2×C42—733no—
577C2×C42C22×D7319yes—
578C24—739no—
579#41—29212no—
580#41—738no—
581#41—14636no—
582#41—14636no—
583#41—14612no—
584#41—14612no—
585#41—14636no—
586#41—14636no—
587#41#1192402918yesdirect product factor
588C2×Q8—212no—
589C2×Q8—739no—
590C2×Q8—14612no—
591C2×Q8C23×D7319yes—
592C2×Q8C23×D7316yes—
593C2×Q8C23×D7311yescharacteristic
594C2×Q8C23×D7311yescharacteristic
595C2×D4—7318no—
596C2×D4—7318no—
597C2×D4—733no—
598C2×D4—7318no—
599C2×D4—739no—
600C2×D4—739no—
601C2×D4—14636no—
602C2×D4—14636no—
603C2×D4C23×D7313yes—
604C22×C4—29218no—
605C22×C4—739no—
606C22×C4—739no—
607C22×C4—733no—
608C22×C4—733no—
609C22×C4—733no—
610C22×C4—739no—
611C22×C4—733no—
612C22×C4—739no—
613C22×C4—739no—
614C22×C4—739no—
615C22×C4—739no—
616C22×C4—739no—
617C22×C4—739no—
618C22×C4—733no—
619C22×C4—739no—
620C22×C4—14636no—
621C22×C4—14636no—
622C22×C4C23×D7319yes—
623C22×C4C23×D7319yes—
624C22×C4C23×D7313yes—
625C4⋊C4—7318no—
626C4⋊C4—7318no—
627C4⋊C4—733no—
628C4⋊C4—733no—
629C4⋊C4—733no—
630C4⋊C4—739no—
631C4⋊C4—7318no—
632C4⋊C4—7318no—
633C4⋊C4C23×D7319yes—
634C4⋊C4C23×D7319yes—
635C4⋊C4C23×D7313yes—
636C4⋊C4C23×D7319yes—
637C4⋊C4C23×D73118yes—
638C4⋊C4C23×D73118yes—
639C22⋊C4—736no—
640C22⋊C4—736no—
641C22⋊C4—7318no—
642C22⋊C4—7318no—
643C22⋊C4—7318no—
644C22⋊C4—7318no—
645C22⋊C4—7318no—
646C22⋊C4—7336no—
647C22⋊C4C23×D73118yes—
648C42—733no—
649C42—733no—
650C42—733no—
651C42—733no—
652C42—739no—
653C42—739no—
654C42—739no—
655C42—739no—
656C42—739no—
657C42—739no—
658C42—731no—
659C42—733no—
660C42C23×D7319yes—
661C42C23×D7319yes—
662C42C23×D7313yes—
663C42C23×D7319yes—
664C23—2929no—
665C23—733no—
666C23—739no—
667C23—14618no—
668C23—14618no—
669C23C24×D7313yes—
670Q8—218no—
671Q8—46no—
672Q8—14618no—
673Q8#41×D7314yescomplemented
674Q8C2×#1192402914yescomplemented
675D4—29218no—
676D4—7312no—
677D4—14636no—
678D4—14636no—
679D4—14618no—
680D4—14618no—
681D4C2×#11924029112yescomplemented
682C2×C4—218no—
683C2×C4—49no—
684C2×C4—2929no—
685C2×C4—2929no—
686C2×C4—731no—
687C2×C4—731no—
688C2×C4—7312no—
689C2×C4—733no—
690C2×C4—733no—
691C2×C4—733no—
692C2×C4—739no—
693C2×C4—1466no—
694C2×C4—14618no—
695C2×C4—14618no—
696C2×C4—14618no—
697C2×C4—1466no—
698C2×C4—1466no—
699C2×C4—14618no—
700C2×C4—14618no—
701C2×C4—1466no—
702C2×C4—14618no—
703C2×C4—14618no—
704C2×C4—14618no—
705C2×C4C2×#11924029112yescomplemented
706C2×C4C24×D7313yes—
707C2×C4C24×D7319yes—
708C2×C4C24×D7319yes—
709C2×C4C24×D7313yes—
710C2×C4C24×D7313yes—
711C2×C4C24×D7311yescharacteristic
712C22—23no—
713C22—23no—
714C22—29236no—
715C22—736no—
716C22—1469no—
717C22—1469no—
718C22—1469no—
719C22—1463no—
720C22—1463no—
721C22C22×#1192402916yes—
722C22C25×D7311yescharacteristic
723C4—29no—
724C4—23no—
725C4—29no—
726C4—732no—
727C4—732no—
728C4—1463no—
729C4—1463no—
730C4—1469no—
731C4—1463no—
732C4C2×#41×D7316yes—
733C4C22×#1192402912yes—
734C4C22×#1192402916yes—
735C2—26no—
736C2—2929no—
737C2—1466no—
738C2C22×#41×D7311yescharacteristic
739C2C23×#1192402911yescharacteristic
740C2#585×D7311yescharacteristic
subgroupG/H
centerC2×C4C24×D73
commutator, socle, cosocleC22×C73C26
FrattiniC22C25×D73
FittingQ8×#41×C73C2
hypercenterQ8×#41D73
hypocenterC73#412
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ Q8×#41

Complements

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

NH ≅ G/Ntype
1. #22623558C2semidirect
2. #22623552C2semidirect
3. #22623551C2semidirect
4. #22623542C2semidirect
5. #22623531C2semidirect
6. #22623526C2semidirect
7. Q8×#11924029C2semidirect
8. #22623498C2semidirect
9. #22623497C2semidirect
10. D4×#11924029C2semidirect
11. #41×D292C2semidirect
12. #22623228C2semidirect
13. C2×C4×#11924029C2semidirect
14. C4×#41×D73C2semidirect
15. Q8×#41×C73C2semidirect
18. #17989322C22semidirect
19. #17989316C22semidirect
20. #17989311C22semidirect
21. #17989310C22semidirect
22. #17989303C22semidirect
23. #17989298C22semidirect
24. #17989290C22semidirect
25. #17989285C22semidirect
26. #17989279C22semidirect
27. #17989275C22semidirect
28. #17989264C22semidirect
29. #17989259C22semidirect
30. #17989259C22semidirect
31. Q8×D292C22semidirect
32. #17989249C22semidirect
33. #17989248C22semidirect
34. #17989241C22semidirect
35. #17989240C22semidirect
36. #17989232C22semidirect
37. #17989228C22semidirect
38. D4×D292C22semidirect
39. #17989142C22semidirect
40. #17989142C22semidirect
41. #17989138C22semidirect
42. #17989138C22semidirect
43. #17989137C22semidirect
44. #17989124C22semidirect
45. #17989124C22semidirect
46. #17989123C22semidirect
47. #17989123C22semidirect
48. #17989122C22semidirect
49. #17989122C22semidirect
50. #17989100C22semidirect
51. #17989100C22semidirect
52. #17989099C22semidirect
56. C4×#11924029C22semidirect
57. C4×#11924029C22semidirect
58. C4×#11924029C22semidirect
59. C4×#11924029C22semidirect
60. C4×#11924029C22semidirect
61. C4×#11924029C22semidirect
62. C4×#11924029C22semidirect
63. C4×#11924029C22semidirect
64. C4×#11924029C22semidirect
65. C4×#11924028C22semidirect
66. #17989055C22semidirect
67. C4×#11924027C22semidirect
68. C4×#11924027C22semidirect
69. C2×Q8×Dic73C22semidirect
70. C4×Q8×D73C22semidirect
71. C4×Q8×D73C22semidirect
72. C2×C4×D292C22semidirect
73. C2×#14556553C22semidirect
74. C4×D4×D73C22semidirect
75. C4×D4×D73C22semidirect
76. C2×#14556549C22semidirect
77. #117×D73C22semidirect
78. C2×C42×D73C22semidirect
79. Q82×C73C22semidirect
80. #557×C73C22semidirect
81. #554×C73C22semidirect
82. D4×Q8×C73C22semidirect
83. #533×C73C22semidirect
85. C2×C4×Q8×C73C22semidirect
213. #11924029#41direct (N × H)
272. #41×C73#41semidirect
301. Q8×C73C2×#41semidirect
302. Q8×C73C2×#41semidirect
303. D4×C73C2×#41semidirect
306. C2×C4×C73C2×#41semidirect
327. D292C2×#41semidirect
339. C4×D73C2×#41semidirect
378. Q8×#41D73semidirect
386. C73#412semidirect
390. Q82C2×D73semidirect
392. #557C2×D73semidirect
397. #554C2×D73semidirect
406. D4×Q8C2×D73semidirect
416. #533C2×D73semidirect
449. C2×C4×Q8C2×D73semidirect
587. #41#11924029direct (N × H)
673. Q8#41×D73semidirect
674. Q8C2×#11924029semidirect
681. D4C2×#11924029semidirect
705. C2×C4C2×#11924029semidirect

Maximal subgroups

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

subgroupindex
#226235582
#226235522
#226235512
#226235422
#226235312
#226235262
Q8×#119240292
#226234982
#226234972
D4×#119240292
#41×D2922
#226232282
C2×C4×#119240292
C4×#41×D732
Q8×#41×C732
#41273