Finite Group Databasebeta

← #11707353

Subgroups — #11707353

Order 768.

7894 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
1C3×#3483C211yesmaximal, characteristic, complemented
2#87040C211yesmaximal, characteristic, complemented
3Q8×#239C211yesmaximal, characteristic, complemented
4#86973C219yesmaximal, complemented
5#86964C219yesmaximal, complemented
6D3×#550C213yesmaximal, complemented
7#86773C213yesmaximal, complemented
8#86770C213yesmaximal, complemented
9#86766C213yesmaximal, complemented
10#86247C219yesmaximal, complemented
11#86245C219yesmaximal, complemented
12#85853C213yesmaximal, complemented
13#85842C213yesmaximal, complemented
14#41×D12C213yesmaximal, complemented
15C4×#1009C213yesmaximal, complemented
16#62986—31nomaximal, Sylow
17C2×#1009C2213yes—
18C2×D3×#41C2216yescomplemented
19C3×Q82C2211yescharacteristic, complemented
20C3×#555C2219yescomplemented
21C3×#550C2213yescomplemented
22C3×#550C2213yescomplemented
23C3×#532C2219yescomplemented
24C3×C4×#41C2213yescomplemented
25C3×C4×#41C2213yescomplemented
26#5834C2213yescomplemented
27#5834C2216yescomplemented
28#5834C2216yescomplemented
29#5831C2213yescomplemented
30#5829C22118yescomplemented
31#5827C2213yescomplemented
32#5734C2219yescomplemented
33#5730C2219yescomplemented
34#5728C2219yescomplemented
35#5725C2219yescomplemented
36#5718C2219yescomplemented
37#5717C2219yescomplemented
38#5716C2219yescomplemented
39D3×#127C2219yescomplemented
40#5681C22118yescomplemented
41#5678C22136yescomplemented
42#5676C22118yescomplemented
43#5619C22118yescomplemented
44#5618C22118yescomplemented
45#5612C22118yescomplemented
46#5609C22118yescomplemented
47#5607C22118yescomplemented
48#5606C22118yescomplemented
49D3×#121C22118yescomplemented
50#5599C22118yescomplemented
51#5577C2213yescomplemented
52#5577C2213yescomplemented
53#5576C2213yescomplemented
54Q8×D12C2213yescomplemented
55#5574C2211yescharacteristic
56#5574C2213yescomplemented
57C4×#239C2213yes—
58C4×#239C2213yescomplemented
59C4×#239C2213yescomplemented
60C4×D3×Q8C2213yescomplemented
61#5570C2213yescomplemented
62#5569C2211yescharacteristic, complemented
63#5562C22118yescomplemented
64#5559C2219yescomplemented
65#5558C2219yescomplemented
66#5557C2219yescomplemented
67#5555C2219yescomplemented
68#5554C22118yescomplemented
69#5553C2219yescomplemented
70#5551C2219yescomplemented
71D4×D12C2219yescomplemented
72#5548C2219yescomplemented
73#5545C2219yescomplemented
74#5545C2219yescomplemented
75C4×D3×D4C2219yescomplemented
76C4×D3×D4C2219yescomplemented
77#5533C2219yescomplemented
78#5530C2219yescomplemented
79#5530C22118yescomplemented
80#5524C22118yescomplemented
81#5523C2219yescomplemented
82#5521C2219yescomplemented
83#5479C2219yescomplemented
84#5477C2219yescomplemented
85C4×#235C2219yescomplemented
86C2×C4×D12C2219yescomplemented
87#3519—39no—
88#3519—39no—
89#3517—33no—
90#3517—33no—
91#3508—39no—
92#3506—39no—
93#3498—33no—
94#3483—31no—
95#3483D311yescharacteristic, complemented
96#3480—33no—
97Q8×#41—31no—
98D4×#41—33no—
99D4×#41—33no—
100C2×#550—33no—
101C4×H(5,𝔽2)—33no—
102C2×C3×#41C2313yes—
103C2×C3×#41C2313yes—
104C2×C3×#41C2316yes—
105#1009—224no—
106D3×#41—424no—
107C2×#239C2313yes—
108C2×#239C2313yes—
109C2×#239C2316yes—
110C2×#239C2311yescharacteristic
111C2×D3×Q8C2313yes—
112C2×#237C23118yes—
113C2×D3×D4C2319yes—
114C2×D3×D4C2319yes—
115C2×D3×D4C23118yes—
116C2×D3×D4C23118yes—
117C2×#235C2319yes—
118C2×#235C23118yes—
119C22×D12C2319yes—
120C22×C4×D3C23118yes—
121C3×C4⋊Q8C2319yes—
122C3×#127C2319yes—
123C3×#124C23118yes—
124C3×#121C23118yes—
125C3×#121C23118yes—
126C3×C4×Q8C2313yes—
127C3×C4×Q8C2313yes—
128C3×C4×Q8C2311yescharacteristic
129C3×C4×Q8C2311yescharacteristic
130C3×C4×D4C2319yes—
131C3×C4×D4C2319yes—
132C3×C4×D4C2319yes—
133C3×C4×D4C2319yes—
134C3×#117C2319yes—
135C3×#117C2319yes—
136C2×C3×C42C2319yes—
137#947C23118yes—
138#946C23118yes—
139Q8×Dic3C2316yes—
140Q8×Dic3C2311yescharacteristic
141Q8×Dic3C2311yescharacteristic
142Q8×Dic3C2313yes—
143Q8×Dic3C2311yescharacteristic
144#940C23118yes—
145#940C2319yes—
146#940C23118yes—
147#939C23136yes—
148#938C23118yes—
149#938C23118yes—
150#938C2319yes—
151#938C2319yes—
152#937C23136yes—
153#936C2319yes—
154D4×Dic3C23118yes—
155D4×Dic3C2319yes—
156D4×Dic3C2319yes—
157#930C23118yes—
158#930C23118yes—
159#930C2319yes—
160#929C23118yes—
161C4×#67C2319yes—
162C4×#67C2319yes—
163C4×#67C2319yes—
164C4×#67C2319yes—
165C4×#67C23118yes—
166C2×(C2×D3)⋊C4C23118yes—
167#926C2319yes—
168C2×C4⋊Dic3C2319yes—
169#924C2319yes—
170#897C23118yes—
171#897C2319yes—
172#895C23118yes—
173#895C23118yes—
174#895C2319yes—
175#893C2319yes—
176#893C2319yes—
177#893C2319yes—
178#893C2313yes—
179#893C2319yes—
180#892C2319yes—
181#892C2319yes—
182#892C2319yes—
183D3×C4⋊C4C2319yes—
184D3×C4⋊C4C2313yes—
185D3×C4⋊C4C2319yes—
186#890C23118yes—
187#890C2313yes—
188#888C2313yes—
189#887C2319yes—
190#886C23136yes—
191#885C23118yes—
192#884C23136yes—
193#884C23118yes—
194#883C23118yes—
195#883C23136yes—
196#882C23136yes—
197#67⋊C4C23118yes—
198#67⋊C4C23118yes—
199D3×C22⋊C4C23118yes—
200D3×C22⋊C4C23118yes—
201#879C23118yes—
202#876C23118yes—
203#875C2319yes—
204#874C2319yes—
205C4×D12C2319yes—
206C4×D12C23118yes—
207C4×D12C23118yes—
208C4×D12C2319yes—
209C4×D12C2319yes—
210C4×D12C2319yes—
211C4×D12C2313yes—
212C4×D12C2319yes—
213C4×D12C2319yes—
214#872C2313yes—
215#872C2319yes—
216C42×D3C2319yes—
217C42×D3C2319yes—
218#870C2313yes—
219#869C2319yes—
220C4×Dic6C2319yes—
221C4×Dic6C2319yes—
222C4×Dic6C2313yes—
223C2×H(5,𝔽2)—33no—
224C22×#41—36no—
225#559—318no—
226#559—39no—
227Q82C2×D311yescharacteristic, complemented
228#557—33no—
229#557—31no—
230#556—39no—
231#555—39no—
232#555C2×D319yescomplemented
233#554—39no—
234#553—318no—
235#553—39no—
236#553—39no—
237#553—318no—
238#550—33no—
239#550—36no—
240#550—36no—
241#550—39no—
242#550—318no—
243#550—33no—
244#550—33no—
245#550—39no—
246#550C2×D313yescomplemented
247#550C2×D313yescomplemented
248D4×Q8—33no—
249#548—33no—
250#548—33no—
251#547—39no—
252#547—39no—
253#546—318no—
254#546—318no—
255#546—318no—
256#546—318no—
257D42—39no—
258D42—318no—
259D42—39no—
260#540—318no—
261#540—318no—
262#538—336no—
263#535—318no—
264#533—39no—
265#532—39no—
266#532—39no—
267#532—39no—
268#532—39no—
269#532C2×D319yescomplemented
270C2×#127—39no—
271#529—39no—
272#529—39no—
273#525—318no—
274#525—318no—
275C2×#121—318no—
276#520—33no—
277#520—31no—
278#520—33no—
279#520—39no—
280#518—39no—
281#518—39no—
282#518—39no—
283C4×#41—33no—
284C4×#41—33no—
285C4×#41—33no—
286C4×#41—39no—
287C4×#41C2×D313yescomplemented
288C4×#41C2×D313yescomplemented
289C2×C4×Q8—33no—
290C2×C4×D4—39no—
291C2×C4×D4—39no—
292C2×C4×D4—39no—
293C23×D3C24118yes—
294C3×#41—212no—
295C3×#41—212no—
296C3×#41—86no—
297C2×C3×Q8C2416yes—
298C2×C3×Q8C2411yescharacteristic
299C2×C3×Q8C2411yescharacteristic
300C2×C3×D4C2419yes—
301C2×C3×D4C2419yes—
302C2×C3×D4C24118yes—
303C22×C3×C4C2419yes—
304C22×C3×C4C2419yes—
305C22×C3×C4C2419yes—
306C2×#67C2419yes—
307C2×#67C2419yes—
308C2×#67C24136yes—
309C2×#67C24118yes—
310C22×Dic3C24118yes—
311#239—212no—
312#239—212no—
313#239—86no—
314#239#4118yescomplemented
315D3×Q8—212no—
316#237—436no—
317D3×D4—236no—
318D3×D4—236no—
319D3×D4—436no—
320D3×D4—818no—
321#235—236no—
322#235—436no—
323C2×D12—236no—
324C2×D12C2419yes—
325C2×D12C2419yes—
326C2×D12C2419yes—
327C2×D12C24118yes—
328C2×D12C2413yes—
329C2×C4×D3—436no—
330C2×C4×D3C2419yes—
331C2×C4×D3C2419yes—
332C2×C4×D3C2419yes—
333C2×C4×D3C2419yes—
334C2×C4×D3C2419yes—
335C2×C4×D3C2416yes—
336C2×C4×D3C24118yes—
337C2×C4×D3C2413yes—
338C2×Dic6C2413yes—
339C2×Dic6C2419yes—
340C3×C4⋊C4C2419yes—
341C3×C4⋊C4C2413yes—
342C3×C4⋊C4C2419yes—
343C3×C4⋊C4C2413yes—
344C3×C22⋊C4C24118yes—
345C3×C22⋊C4C24118yes—
346C3×C42C2419yes—
347C3×C42C2413yes—
348C3×C42C2419yes—
349C3×C42C2413yes—
350#217C2419yes—
351#217C24118yes—
352#217C2419yes—
353(C2×D3)⋊C4C2413yes—
354(C2×D3)⋊C4C2419yes—
355(C2×D3)⋊C4C2413yes—
356(C2×D3)⋊C4C2419yes—
357(C2×D3)⋊C4C24118yes—
358(C2×D3)⋊C4C24118yes—
359(C2×D3)⋊C4C24118yes—
360(C2×D3)⋊C4C24118yes—
361C4⋊Dic3C2413yes—
362C4⋊Dic3C2419yes—
363C4⋊Dic3C2413yes—
364C4⋊Dic3C2419yes—
365C4⋊Dic3C24118yes—
366C4⋊Dic3C2413yes—
367C4⋊Dic3C2413yes—
368Dic3⋊C4C2411yescharacteristic
369Dic3⋊C4C2413yes—
370Dic3⋊C4C2413yes—
371Dic3⋊C4C2419yes—
372Dic3⋊C4C24118yes—
373Dic3⋊C4C2416yes—
374C4×Dic3C2419yes—
375C4×Dic3C2413yes—
376C4×Dic3C2413yes—
377C4×Dic3C2419yes—
378C4×Dic3C2419yes—
379C4×Dic3C2413yes—
380H(5,𝔽2)—624no—
381C2×#41—31no—
382C2×#41—33no—
383C2×#41—33no—
384C2×#41—36no—
385C2×#41—318no—
386C2×#41—39no—
387C2×#41—318no—
388C2×#41—1224no—
389C2×#41C22×D313yes—
390C2×#41C22×D313yes—
391C2×#41C22×D316yes—
392C22×Q8—33no—
393C22×D4—39no—
394C22×D4—39no—
395C22×D4—318no—
396C22×D4—318no—
397C22×D4—39no—
398C23×C4—318no—
399C4⋊Q8—33no—
400C4⋊Q8—39no—
401C4⋊Q8C22×D319yes—
402#127—39no—
403#127—318no—
404#127—318no—
405#127—39no—
406#127C22×D319yes—
407#126—318no—
408#126—318no—
409#125—33no—
410#125—318no—
411#125—33no—
412#124—318no—
413#124—39no—
414#124—318no—
415#124—39no—
416#124C22×D3118yes—
417#123—318no—
418#123—336no—
419#123—336no—
420#123—318no—
421C22⋊Q8—318no—
422C22⋊Q8—39no—
423C22⋊Q8—39no—
424C22⋊Q8—318no—
425#121—39no—
426#121—336no—
427#121—39no—
428#121—318no—
429#121—318no—
430#121—39no—
431#121—318no—
432#121—318no—
433#121—318no—
434#121—39no—
435#121—318no—
436#121—336no—
437#121—318no—
438#121C22×D3118yes—
439#121C22×D3118yes—
440#120—336no—
441#120—336no—
442C4×Q8—31no—
443C4×Q8—31no—
444C4×Q8—31no—
445C4×Q8—33no—
446C4×Q8—36no—
447C4×Q8—39no—
448C4×Q8—39no—
449C4×Q8—33no—
450C4×Q8—39no—
451C4×Q8C22×D313yes—
452C4×Q8C22×D313yes—
453C4×Q8C22×D311yescharacteristic
454C4×Q8C22×D311yescharacteristic
455C4×D4—39no—
456C4×D4—39no—
457C4×D4—318no—
458C4×D4—39no—
459C4×D4—39no—
460C4×D4—39no—
461C4×D4—39no—
462C4×D4—318no—
463C4×D4—33no—
464C4×D4—39no—
465C4×D4—39no—
466C4×D4—39no—
467C4×D4—39no—
468C4×D4—318no—
469C4×D4—318no—
470C4×D4—33no—
471C4×D4—39no—
472C4×D4—39no—
473C4×D4—39no—
474C4×D4—318no—
475C4×D4—39no—
476C4×D4—39no—
477C4×D4—39no—
478C4×D4—318no—
479C4×D4C22×D319yes—
480C4×D4C22×D319yes—
481C4×D4C22×D319yes—
482C4×D4C22×D319yes—
483#117—39no—
484#117—39no—
485#117—39no—
486#117—39no—
487#117—33no—
488#117—39no—
489#117C22×D319yes—
490#117C22×D319yes—
491C2×C4⋊C4—39no—
492C2×C4⋊C4—33no—
493C2×C4⋊C4—39no—
494C2×C4⋊C4—39no—
495C2×C22⋊C4—318no—
496C2×C22⋊C4—318no—
497C2×C22⋊C4—318no—
498C2×C42—39no—
499C2×C42—39no—
500C2×C42C22×D319yes—
501C23×C3C2519yes—
502C22×D3—236no—
503C22×D3—418no—
504C22×D3—418no—
505C22×D3C2519yes—
506C22×D3C2513yes—
507C3×Q8—46no—
508C3×Q8C2×#4114yescomplemented
509C3×Q8H(5,𝔽2)14yescomplemented
510C3×D4—218no—
511C3×D4—218no—
512C3×D4—418no—
513C2×C3×C4—218no—
514C2×C3×C4—218no—
515C2×C3×C4—49no—
516C2×C3×C4C2519yes—
517C2×C3×C4C2511yescharacteristic
518C2×C3×C4C2513yes—
519C2×C3×C4C2513yes—
520C2×C3×C4C2513yes—
521C2×C3×C4C2513yes—
522#67—218no—
523#67—218no—
524#67—436no—
525#67—418no—
526C2×Dic3—418no—
527C2×Dic3C2511yescharacteristic
528C2×Dic3C2513yes—
529C2×Dic3C2513yes—
530C2×Dic3C2513yes—
531C2×Dic3C2519yes—
532C2×Dic3C2511yescharacteristic
533D12—218no—
534D12—218no—
535D12—218no—
536D12—418no—
537D12C2×#41112yescomplemented
538C4×D3—218no—
539C4×D3—218no—
540C4×D3—218no—
541C4×D3—46no—
542C4×D3—418no—
543C4×D3—49no—
544C4×D3—49no—
545C4×D3C2×#41112yescomplemented
546Dic6—218no—
547Dic6—26no—
548C24—318no—
549#41—212no—
550#41—212no—
551#41—38no—
552#41—636no—
553#41—612no—
554#41—612no—
555#41—86no—
556#41—1236no—
557#41—1236no—
558#41—246no—
559C2×Q8—33no—
560C2×Q8—39no—
561C2×Q8—612no—
562C2×Q8C23×D316yes—
563C2×Q8C23×D311yescharacteristic
564C2×Q8C23×D311yescharacteristic
565C2×D4—39no—
566C2×D4—39no—
567C2×D4—318no—
568C2×D4—336no—
569C2×D4—33no—
570C2×D4—39no—
571C2×D4—39no—
572C2×D4—39no—
573C2×D4—318no—
574C2×D4—636no—
575C2×D4—636no—
576C2×D4—636no—
577C2×D4—1236no—
578C2×D4—2418no—
579C2×D4C23×D319yes—
580C2×D4C23×D319yes—
581C2×D4C23×D3118yes—
582C22×C4—33no—
583C22×C4—318no—
584C22×C4—39no—
585C22×C4—39no—
586C22×C4—39no—
587C22×C4—39no—
588C22×C4—39no—
589C22×C4—36no—
590C22×C4—318no—
591C22×C4—1236no—
592C22×C4C23×D319yes—
593C22×C4C23×D319yes—
594C22×C4C23×D319yes—
595C4⋊C4—33no—
596C4⋊C4—33no—
597C4⋊C4—33no—
598C4⋊C4—39no—
599C4⋊C4—39no—
600C4⋊C4—39no—
601C4⋊C4—318no—
602C4⋊C4—31no—
603C4⋊C4—33no—
604C4⋊C4—33no—
605C4⋊C4—33no—
606C4⋊C4—36no—
607C4⋊C4—318no—
608C4⋊C4C23×D313yes—
609C4⋊C4C23×D319yes—
610C4⋊C4C23×D319yes—
611C4⋊C4C23×D313yes—
612C22⋊C4—39no—
613C22⋊C4—39no—
614C22⋊C4—318no—
615C22⋊C4—33no—
616C22⋊C4—33no—
617C22⋊C4—318no—
618C22⋊C4—39no—
619C22⋊C4—318no—
620C22⋊C4—39no—
621C22⋊C4—318no—
622C22⋊C4—318no—
623C22⋊C4C23×D3118yes—
624C22⋊C4C23×D3118yes—
625C42—33no—
626C42—33no—
627C42—33no—
628C42—39no—
629C42—39no—
630C42—39no—
631C42C23×D319yes—
632C42C23×D313yes—
633C42C23×D313yes—
634C42C23×D319yes—
635C22×C3—29no—
636C22×C3—29no—
637C22×C3—29no—
638C22×C3C2611yescharacteristic
639C2×D3—23no—
640C2×D3—23no—
641C2×D3—29no—
642C2×D3—29no—
643C2×D3—29no—
644C2×D3—836no—
645C2×D3C22×#4116yes—
646C3×C4—23no—
647C3×C4—23no—
648C3×C4—29no—
649C3×C4—21no—
650C3×C4C22×#4116yes—
651C3×C4C2×H(5,𝔽2)16yes—
652Dic3—23no—
653Dic3—29no—
654Dic3—23no—
655Dic3—21no—
656Dic3—23no—
657Dic3C22×#4112yes—
658C23—33no—
659C23—39no—
660C23—636no—
661C23—1218no—
662C23—1218no—
663C23C24×D319yes—
664Q8—46no—
665Q8—66no—
666Q8—618no—
667Q8D3×#4114yescomplemented
668Q8#100914yescomplemented
669D4—218no—
670D4—218no—
671D4—312no—
672D4—418no—
673D4—618no—
674D4—618no—
675D4—618no—
676D4—618no—
677D4—618no—
678D4—1218no—
679D4—1236no—
680D4—1218no—
681C2×C4—218no—
682C2×C4—218no—
683C2×C4—31no—
684C2×C4—312no—
685C2×C4—31no—
686C2×C4—33no—
687C2×C4—33no—
688C2×C4—33no—
689C2×C4—39no—
690C2×C4—49no—
691C2×C4—618no—
692C2×C4—618no—
693C2×C4—618no—
694C2×C4—126no—
695C2×C4—1218no—
696C2×C4—129no—
697C2×C4—129no—
698C2×C4—1218no—
699C2×C4C24×D319yes—
700C2×C4C24×D311yescharacteristic
701C2×C4C24×D313yes—
702C2×C4C24×D313yes—
703C2×C4C24×D313yes—
704C2×C4C24×D313yes—
705C2×C3—49no—
706C2×C3C23×#4111yescharacteristic
707C2×C3C22×H(5,𝔽2)11yescharacteristic
708C2×C3H(7,𝔽2)11yescharacteristic
709D3—26no—
710D3—49no—
711C22—29no—
712C22—29no—
713C22—29no—
714C22—36no—
715C22—63no—
716C22—63no—
717C22—69no—
718C22—69no—
719C22—69no—
720C22—2436no—
721C22C25×D311yescharacteristic
722C4—23no—
723C4—23no—
724C4—21no—
725C4—29no—
726C4—32no—
727C4—63no—
728C4—63no—
729C4—69no—
730C4—61no—
731C4—63no—
732C4C2×D3×#4116yes—
733C4C2×#100916yes—
734C3#6298611yescharacteristic, complemented, Sylow
735C2—49no—
736C2—66no—
737C2—129no—
738C2C22×D3×#4111yescharacteristic
739C2C22×#100911yescharacteristic
740C2#8756811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D3
commutator, socle, cosocleC22×C3C26
FittingC3×#3483C2
hypercenter#3483D3
hypocenterC3#62986
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #3483

Complements

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

NH ≅ G/Ntype
1. C3×#3483C2semidirect
2. #87040C2semidirect
3. Q8×#239C2semidirect
4. #86973C2semidirect
5. #86964C2semidirect
6. D3×#550C2semidirect
7. #86773C2semidirect
8. #86770C2semidirect
9. #86766C2semidirect
10. #86247C2semidirect
11. #86245C2semidirect
12. #85853C2semidirect
13. #85842C2semidirect
14. #41×D12C2semidirect
15. C4×#1009C2semidirect
18. C2×D3×#41C22semidirect
19. C3×Q82C22semidirect
20. C3×#555C22semidirect
21. C3×#550C22semidirect
22. C3×#550C22semidirect
23. C3×#532C22semidirect
24. C3×C4×#41C22semidirect
25. C3×C4×#41C22semidirect
26. #5834C22semidirect
27. #5834C22semidirect
28. #5834C22semidirect
29. #5831C22semidirect
30. #5829C22semidirect
31. #5827C22semidirect
32. #5734C22semidirect
33. #5730C22semidirect
34. #5728C22semidirect
35. #5725C22semidirect
36. #5718C22semidirect
37. #5717C22semidirect
38. #5716C22semidirect
39. D3×#127C22semidirect
40. #5681C22semidirect
41. #5678C22semidirect
42. #5676C22semidirect
43. #5619C22semidirect
44. #5618C22semidirect
45. #5612C22semidirect
46. #5609C22semidirect
47. #5607C22semidirect
48. #5606C22semidirect
49. D3×#121C22semidirect
50. #5599C22semidirect
51. #5577C22semidirect
52. #5577C22semidirect
53. #5576C22semidirect
54. Q8×D12C22semidirect
56. #5574C22semidirect
58. C4×#239C22semidirect
59. C4×#239C22semidirect
60. C4×D3×Q8C22semidirect
61. #5570C22semidirect
62. #5569C22semidirect
63. #5562C22semidirect
64. #5559C22semidirect
65. #5558C22semidirect
66. #5557C22semidirect
67. #5555C22semidirect
68. #5554C22semidirect
69. #5553C22semidirect
70. #5551C22semidirect
71. D4×D12C22semidirect
72. #5548C22semidirect
73. #5545C22semidirect
74. #5545C22semidirect
75. C4×D3×D4C22semidirect
76. C4×D3×D4C22semidirect
77. #5533C22semidirect
78. #5530C22semidirect
79. #5530C22semidirect
80. #5524C22semidirect
81. #5523C22semidirect
82. #5521C22semidirect
83. #5479C22semidirect
84. #5477C22semidirect
85. C4×#235C22semidirect
86. C2×C4×D12C22semidirect
95. #3483D3semidirect
227. Q82C2×D3semidirect
232. #555C2×D3semidirect
246. #550C2×D3semidirect
247. #550C2×D3semidirect
269. #532C2×D3semidirect
287. C4×#41C2×D3semidirect
288. C4×#41C2×D3semidirect
314. #239#41semidirect
508. C3×Q8C2×#41semidirect
509. C3×Q8H(5,𝔽2)semidirect
537. D12C2×#41semidirect
545. C4×D3C2×#41semidirect
667. Q8D3×#41semidirect
668. Q8#1009semidirect
734. C3#62986semidirect

Maximal subgroups

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

subgroupindex
C3×#34832
#870402
Q8×#2392
#869732
#869642
D3×#5502
#867732
#867702
#867662
#862472
#862452
#858532
#858422
#41×D122
C4×#10092
#629863