Finite Group Databasebeta

← D3×#3497 #11703356

Subgroups — D3×#3497 #11703356

Order 768.

11210 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×2−1+4C212yesmaximal, complemented
2C3×#3497C211yesmaximal, characteristic, complemented
3#87291C212yesmaximal, complemented
4#86784C214yesmaximal, complemented
5D3×#550C214yesmaximal, complemented
6#86760C214yesmaximal, complemented
7D3×D4×Q8C214yesmaximal, complemented
8#86737C218yesmaximal, complemented
9D3×#548C218yesmaximal, complemented
10D3×#537C216yesmaximal, complemented
11#86367C216yesmaximal, complemented
12D3×#532C216yesmaximal, complemented
13#86222C216yesmaximal, complemented
14#85818C211yesmaximal, characteristic, complemented
15C2×C4×D3×Q8C211yesmaximal, characteristic, complemented
16C2×#3497—31nomaximal, Sylow
17C2×C3×2−1+4C2212yescomplemented
18D3×2−1+4—232no—
19C2×#1010C2218yescomplemented
20C2×#1010C22112yescomplemented
21C2×D3×#41C22112yes—
22C2×D3×#41C2218yes—
23C2×#1007C2212yescomplemented
24C2×#1007C2218yescomplemented
25C22×D3×Q8C2218yes—
26C22×D3×Q8C2211yescharacteristic
27C3×#550C2214yescomplemented
28C3×D4×Q8C2214yescomplemented
29C3×#548C2218yescomplemented
30C3×#537C2216yescomplemented
31C3×#532C2216yescomplemented
32C2×C3×C4×Q8C2211yescharacteristic, complemented
33#5834C2218yescomplemented
34#5833C22112yescomplemented
35#5832C22112yescomplemented
36#5831C2218yescomplemented
37#5817C2218yescomplemented
38Q8×#67C2218yescomplemented
39C2×Q8×Dic3C2211yescharacteristic, complemented
40#5727C22112yescomplemented
41#5725C2216yescomplemented
42D3×C4⋊Q8C2216yes—
43#5718C22112yescomplemented
44#5716C2216yescomplemented
45D3×#127C2216yes—
46#5677C22124yescomplemented
47D3×#124C22112yes—
48#5668C22112yescomplemented
49#5633C22124yescomplemented
50#5632C22124yescomplemented
51#5629C22124yescomplemented
52D3×C22⋊Q8C22124yes—
53#5608C22124yescomplemented
54D3×#121C22112yes—
55D3×#121C22124yes—
56D3×#121C2214yes—
57#5599C22124yescomplemented
58#5598C22124yescomplemented
59#5597C22124yescomplemented
60#5596C22112yescomplemented
61#5596C22112yescomplemented
62#5577C2214yescomplemented
63#5576C2218yescomplemented
64Q8×D12C2214yescomplemented
65C4×D3×Q8C2214yes—
66C4×D3×Q8C2214yes—
67C4×D3×Q8C2214yescomplemented
68C4×D3×Q8C2214yescomplemented
69#5553C22112yescomplemented
70#5552C22124yescomplemented
71#5548C22112yescomplemented
72#5548C22112yescomplemented
73C4×D3×D4C22112yes—
74C4×D3×D4C22112yes—
75D4×Dic6C22112yescomplemented
76#5510C2216yescomplemented
77C2×D3×C4⋊C4C2213yes—
78C2×#887C2213yescomplemented
79#5477C2216yescomplemented
80C2×C42×D3C2213yes—
81C2×C4×Dic6C2213yescomplemented
82C22×2−1+4—32no—
83#3497—32no—
84#3497—34no—
85#3497—34no—
86#3497—38no—
87#3497—36no—
88#3497—36no—
89#3497—31no—
90#3497D311yescharacteristic, direct product factor
91C2×#550—34no—
92C2×D4×Q8—34no—
93C2×#548—38no—
94C2×#537—36no—
95C2×#532—36no—
96C22×C4×Q8—31no—
97C3×2−1+4—216no—
98C2×C3×#41C2318yes—
99C2×C3×#41C23112yes—
100C22×C3×Q8C2318yes—
101C22×C3×Q8C2311yescharacteristic
102#1010—264no—
103#1010—296no—
104D3×#41—264no—
105D3×#41—296no—
106#1007—216no—
107#1007—264no—
108C2×#239C23112yes—
109C2×#239C2318yes—
110C2×D3×Q8—264no—
111C2×D3×Q8D4116yescomplemented
112C2×D3×Q8C23124yes—
113C2×D3×Q8C23112yes—
114C2×D3×Q8C2318yes—
115C2×D3×Q8C2314yes—
116C2×D3×Q8C2314yes—
117C2×#237C23112yes—
118C2×#237C23124yes—
119C2×#237C23124yes—
120C2×D3×D4C23112yes—
121C2×D3×D4C2318yes—
122C2×D3×D4C2314yes—
123C2×D3×D4C23112yes—
124C2×#235C23124yes—
125C2×#235C23112yes—
126C2×#235C23124yes—
127C22×C4×D3C23124yes—
128C22×C4×D3C2311yescharacteristic
129C22×C4×D3C2313yes—
130C22×C4×D3C2313yes—
131C22×Dic6C23124yes—
132C22×Dic6C2313yes—
133C3×C4⋊Q8C2316yes—
134C3×#127C2316yes—
135C3×#124C23112yes—
136C3×C22⋊Q8C23124yes—
137C3×#121C2314yes—
138C3×#121C23112yes—
139C3×#121C23124yes—
140C3×C4×Q8C2314yes—
141C3×C4×Q8C2314yes—
142C3×C4×D4C23112yes—
143C3×C4×D4C23112yes—
144C2×C3×C4⋊C4C2313yes—
145C2×C3×C42C2313yes—
146#947C23112yes—
147#946C23124yes—
148Q8×Dic3C2314yes—
149Q8×Dic3C2314yes—
150#944C23112yes—
151#940C23112yes—
152#940C23112yes—
153#940C23112yes—
154#939C23148yes—
155#939C2318yes—
156#939C23124yes—
157#938C23124yes—
158#938C2314yes—
159#938C23112yes—
160#936C23112yes—
161D4×Dic3C23112yes—
162D4×Dic3C23112yes—
163#930C2314yes—
164#930C23112yes—
165#930C23124yes—
166C4×#67C23124yes—
167C4×#67C23124yes—
168C2×C4⋊Dic3C2313yes—
169#924C23124yes—
170C2×Dic3⋊C4C2316yes—
171C2×C4×Dic3C2313yes—
172C2×C4×Dic3C2313yes—
173C2×C4×Dic3C2313yes—
174#897C23124yes—
175#896C23148yes—
176#895C23124yes—
177#895C2314yes—
178#895C23112yes—
179#893C23112yes—
180#893C23112yes—
181D3×C4⋊C4C2314yes—
182D3×C4⋊C4C23112yes—
183D3×C4⋊C4C23112yes—
184D3×C4⋊C4C23112yes—
185#888C23112yes—
186#888C23112yes—
187#887C23112yes—
188#887C23112yes—
189#885C23124yes—
190#885C23124yes—
191#884C23148yes—
192#884C2318yes—
193#884C23124yes—
194#67⋊C4C23124yes—
195#67⋊C4C23124yes—
196D3×C22⋊C4C2318yes—
197D3×C22⋊C4C23124yes—
198#878C23148yes—
199#875C23112yes—
200#874C2316yes—
201C4×D12C23112yes—
202C4×D12C23112yes—
203C42×D3C2316yes—
204C42×D3C2316yes—
205C42×D3C2316yes—
206C42×D3C2316yes—
207#869C2316yes—
208C4×Dic6C23112yes—
209C4×Dic6C23112yes—
210C2×2−1+4—38no—
211C2×2−1+4—312no—
212C2×2−1+4—38no—
213C2×2−1+4—32no—
214C2×2−1+4—632no—
215C2×2−1+4C2×D312yescomplemented
216C22×#41—312no—
217C22×#41—38no—
218C23×Q8—31no—
219C23×Q8—38no—
220#550—38no—
221#550—312no—
222#550—324no—
223#550—34no—
224#550—312no—
225#550C2×D314yescomplemented
226D4×Q8—38no—
227D4×Q8—312no—
228D4×Q8—324no—
229D4×Q8—34no—
230D4×Q8—312no—
231D4×Q8C2×D314yescomplemented
232#548—38no—
233#548—38no—
234#548—324no—
235#548—324no—
236#548—324no—
237#548—38no—
238#548—324no—
239#548C2×D318yescomplemented
240#537—312no—
241#537—324no—
242#537—324no—
243#537—324no—
244#537—36no—
245#537C2×D316yescomplemented
246#532—312no—
247#532—36no—
248#532—36no—
249#532—312no—
250#532—312no—
251#532—312no—
252#532—312no—
253#532—312no—
254#532—36no—
255#532C2×D316yescomplemented
256C2×C4⋊Q8—36no—
257C2×#127—36no—
258C2×#124—312no—
259C2×C22⋊Q8—324no—
260C2×#121—34no—
261C2×#121—312no—
262C2×#121—324no—
263C2×C4×Q8—31no—
264C2×C4×Q8—34no—
265C2×C4×Q8—34no—
266C2×C4×Q8—34no—
267C2×C4×Q8—34no—
268C2×C4×Q8—33no—
269C2×C4×Q8—33no—
270C2×C4×Q8C2×D311yescharacteristic, complemented
271C2×C4×D4—312no—
272C2×C4×D4—312no—
273C22×C4⋊C4—33no—
274C22×C42—33no—
275C23×D3C2418yes—
276C23×D3C2411yescharacteristic
277C3×#41—232no—
278C3×#41—248no—
279C2×C3×Q8—232no—
280C2×C3×Q8C2×D418yescomplemented
281C2×C3×Q8C24112yes—
282C2×C3×Q8C2414yes—
283C2×C3×D4C2414yes—
284C2×C3×D4C24112yes—
285C2×C3×D4C2418yes—
286C2×C3×D4C24112yes—
287C22×C3×C4C2411yescharacteristic
288C22×C3×C4C24124yes—
289C22×C3×C4C2413yes—
290C22×C3×C4C2413yes—
291C2×#67C2418yes—
292C2×#67C2418yes—
293C2×#67C24124yes—
294C2×#67C2418yes—
295C2×#67C24124yes—
296C22×Dic3C24124yes—
297C22×Dic3C2411yescharacteristic
298C22×Dic3C2413yes—
299C22×Dic3C2413yes—
300#239—232no—
301#239—248no—
302D3×Q8—232no—
303D3×Q8—248no—
304D3×Q8—296no—
305D3×Q8C2×D4132yes—
306D3×Q8C2×D4132yescomplemented
307#237—296no—
308#237—248no—
309#237—296no—
310D3×D4—232no—
311D3×D4—248no—
312D3×D4—216no—
313D3×D4—424no—
314#235—248no—
315#235—296no—
316#235—296no—
317C2×D12C2414yes—
318C2×D12C24112yes—
319C2×D12C2418yes—
320C2×D12C24112yes—
321C2×C4×D3—296no—
322C2×C4×D3—24no—
323C2×C4×D3—46no—
324C2×C4×D3C2×D4124yes—
325C2×C4×D3C2411yescharacteristic
326C2×C4×D3C2411yescharacteristic
327C2×C4×D3C2411yescharacteristic
328C2×C4×D3C2416yes—
329C2×C4×D3C24124yes—
330C2×C4×D3C2418yes—
331C2×C4×D3C24124yes—
332C2×C4×D3C2416yes—
333C2×C4×D3C2416yes—
334C2×C4×D3C2416yes—
335C2×C4×D3C2411yescharacteristic
336C2×Dic6—296no—
337C2×Dic6C2×D4124yescomplemented
338C2×Dic6C24112yes—
339C2×Dic6C24124yes—
340C2×Dic6C24112yes—
341C3×C4⋊C4C24112yes—
342C3×C4⋊C4C2414yes—
343C3×C4⋊C4C24112yes—
344C3×C22⋊C4C24124yes—
345C3×C22⋊C4C2418yes—
346C3×C42C2416yes—
347C3×C42C2416yes—
348#217C24124yes—
349#217C2418yes—
350(C2×D3)⋊C4C2418yes—
351(C2×D3)⋊C4C24124yes—
352(C2×D3)⋊C4C24124yes—
353(C2×D3)⋊C4C2418yes—
354C4⋊Dic3C24112yes—
355C4⋊Dic3C2414yes—
356C4⋊Dic3C24112yes—
357Dic3⋊C4C24124yes—
358Dic3⋊C4C24124yes—
359Dic3⋊C4C2418yes—
360C4×Dic3C2416yes—
361C4×Dic3C2416yes—
362C4×Dic3C2416yes—
363C4×Dic3C2416yes—
364C4×Dic3C2416yes—
365C4×Dic3C2416yes—
3662−1+4—216no—
3672−1+4—664no—
3682−1+4—664no—
3692−1+4—696no—
3702−1+4—616no—
371C2×#41—312no—
372C2×#41—38no—
373C2×#41—324no—
374C2×#41—312no—
375C2×#41—324no—
376C2×#41—324no—
377C2×#41—312no—
378C2×#41—324no—
379C2×#41—696no—
380C2×#41—664no—
381C2×#41C22×D3112yes—
382C2×#41C22×D318yes—
383C22×Q8—316no—
384C22×Q8—34no—
385C22×Q8—34no—
386C22×Q8—312no—
387C22×Q8—324no—
388C22×Q8—38no—
389C22×Q8—33no—
390C22×Q8—324no—
391C22×Q8—664no—
392C22×Q8C22×D318yes—
393C22×Q8C22×D311yescharacteristic
394C22×D4—34no—
395C22×D4—38no—
396C22×D4—312no—
397C22×D4—312no—
398C23×C4—33no—
399C23×C4—324no—
400C23×C4—31no—
401C23×C4—33no—
402C4⋊Q8—312no—
403C4⋊Q8—312no—
404C4⋊Q8—312no—
405C4⋊Q8—36no—
406C4⋊Q8C22×D316yes—
407#127—312no—
408#127—312no—
409#127—312no—
410#127—36no—
411#127C22×D316yes—
412#124—312no—
413#124—312no—
414#124—324no—
415#124—324no—
416#124—312no—
417#124C22×D3112yes—
418C22⋊Q8—324no—
419C22⋊Q8—324no—
420C22⋊Q8—348no—
421C22⋊Q8—324no—
422C22⋊Q8—348no—
423C22⋊Q8C22×D3124yes—
424#121—34no—
425#121—38no—
426#121—312no—
427#121—324no—
428#121—324no—
429#121—348no—
430#121—34no—
431#121—312no—
432#121—324no—
433#121—34no—
434#121—312no—
435#121—324no—
436#121—38no—
437#121—324no—
438#121—348no—
439#121C22×D314yes—
440#121C22×D3112yes—
441#121C22×D3124yes—
442C4×Q8—34no—
443C4×Q8—34no—
444C4×Q8—312no—
445C4×Q8—312no—
446C4×Q8—312no—
447C4×Q8—312no—
448C4×Q8C22×D314yes—
449C4×Q8C22×D314yes—
450C4×D4—312no—
451C4×D4—312no—
452C4×D4—324no—
453C4×D4—324no—
454C4×D4—312no—
455C4×D4—312no—
456C4×D4—324no—
457C4×D4—324no—
458C4×D4—312no—
459C4×D4—312no—
460C4×D4C22×D3112yes—
461C4×D4C22×D3112yes—
462C2×C4⋊C4—36no—
463C2×C4⋊C4—33no—
464C2×C4⋊C4—312no—
465C2×C4⋊C4—312no—
466C2×C4⋊C4—34no—
467C2×C4⋊C4—312no—
468C2×C4⋊C4C22×D313yes—
469C2×C22⋊C4—38no—
470C2×C22⋊C4—324no—
471C2×C42—33no—
472C2×C42—33no—
473C2×C42—33no—
474C2×C42—36no—
475C2×C42—36no—
476C2×C42—36no—
477C2×C42—36no—
478C2×C42C22×D313yes—
479C23×C3C2518yes—
480C23×C3C2511yescharacteristic
481C22×D3—22no—
482C22×D3—22no—
483C22×D3—216no—
484C22×D3—216no—
485C22×D3—216no—
486C22×D3C22×D414yes—
487C22×D3C2518yes—
488C22×D3C2511yescharacteristic
489C22×D3C2511yescharacteristic
490C3×Q8—224no—
491C3×Q8C22×D4116yes—
492C3×D4—216no—
493C3×D4—224no—
494C3×D4—28no—
495C3×D4—412no—
496C2×C3×C4—248no—
497C2×C3×C4—22no—
498C2×C3×C4—43no—
499C2×C3×C4C22×D4112yes—
500C2×C3×C4C2511yescharacteristic
501C2×C3×C4C2516yes—
502C2×C3×C4C2518yes—
503C2×C3×C4C2516yes—
504C2×C3×C4C2511yescharacteristic
505#67—216no—
506#67—216no—
507#67—248no—
508#67—216no—
509#67—424no—
510C2×Dic3—248no—
511C2×Dic3—22no—
512C2×Dic3—43no—
513C2×Dic3C22×D4112yes—
514C2×Dic3C2511yescharacteristic
515C2×Dic3C2516yes—
516C2×Dic3C2518yes—
517C2×Dic3C2516yes—
518C2×Dic3C2511yescharacteristic
519D12—216no—
520D12—224no—
521D12—28no—
522D12—412no—
523C4×D3—216no—
524C4×D3—22no—
525C4×D3—212no—
526C4×D3—248no—
527C4×D3—22no—
528C4×D3—248no—
529C4×D3—22no—
530C4×D3—46no—
531C4×D3C22×D4124yes—
532C4×D3C22×D4124yes—
533C4×D32−1+414yescomplemented
534Dic6—224no—
535Dic6—248no—
536Dic6C22×D4148yes—
537C24—31no—
538C24—38no—
539#41—232no—
540#41—248no—
541#41—696no—
542#41—696no—
543#41—696no—
544#41—648no—
545#41—648no—
546#41—696no—
547#41—632no—
548#41—648no—
549C2×Q8—232no—
550C2×Q8—332no—
551C2×Q8—332no—
552C2×Q8—324no—
553C2×Q8—312no—
554C2×Q8—324no—
555C2×Q8—312no—
556C2×Q8—696no—
557C2×Q8—648no—
558C2×Q8—696no—
559C2×Q8—632no—
560C2×Q8D3×D418yescomplemented
561C2×Q8C23×D3112yes—
562C2×Q8C23×D314yes—
563C2×D4—38no—
564C2×D4—38no—
565C2×D4—38no—
566C2×D4—324no—
567C2×D4—324no—
568C2×D4—34no—
569C2×D4—38no—
570C2×D4—312no—
571C2×D4—312no—
572C2×D4—648no—
573C2×D4—616no—
574C2×D4—632no—
575C2×D4—1224no—
576C2×D4C23×D314yes—
577C2×D4C23×D318yes—
578C2×D4C23×D3112yes—
579C2×D4C23×D3112yes—
580C22×C4—33no—
581C22×C4—324no—
582C22×C4—31no—
583C22×C4—36no—
584C22×C4—36no—
585C22×C4—31no—
586C22×C4—324no—
587C22×C4—33no—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—31no—
591C22×C4—36no—
592C22×C4—38no—
593C22×C4—324no—
594C22×C4—324no—
595C22×C4—36no—
596C22×C4—696no—
597C22×C4—64no—
598C22×C4—126no—
599C22×C4C23×D311yescharacteristic
600C22×C4C23×D3124yes—
601C22×C4C23×D313yes—
602C22×C4C23×D313yes—
603C4⋊C4—324no—
604C4⋊C4—312no—
605C4⋊C4—38no—
606C4⋊C4—34no—
607C4⋊C4—324no—
608C4⋊C4—312no—
609C4⋊C4C23×D3112yes—
610C4⋊C4C23×D314yes—
611C4⋊C4C23×D3112yes—
612C22⋊C4—38no—
613C22⋊C4—324no—
614C22⋊C4—38no—
615C22⋊C4—38no—
616C22⋊C4—324no—
617C22⋊C4—324no—
618C22⋊C4C23×D318yes—
619C22⋊C4C23×D3124yes—
620C42—36no—
621C42—36no—
622C42—36no—
623C42—36no—
624C42—36no—
625C42—36no—
626C42C23×D316yes—
627C42C23×D316yes—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—28no—
631C22×C3—28no—
632C22×C3—28no—
633C22×C3C23×D412yes—
634C22×C3C2611yescharacteristic
635C2×D3—21no—
636C2×D3—21no—
637C2×D3—28no—
638C2×D3—28no—
639C2×D3—28no—
640C2×D3—28no—
641C2×D3—432no—
642C2×D3C23×D412yes—
643C2×D3C23×D412yes—
644C2×D3C2×2−1+412yes—
645C2×D3#58512yes—
646C3×C4—28no—
647C3×C4—21no—
648C3×C4—26no—
649C3×C4C23×D4112yes—
650C3×C4C2×2−1+412yescomplemented
651Dic3—28no—
652Dic3—21no—
653Dic3—26no—
654Dic3C23×D4112yes—
655Dic3C2×2−1+412yescomplemented
656C23—31no—
657C23—34no—
658C23—31no—
659C23—38no—
660C23—62no—
661C23—62no—
662C23—616no—
663C23—616no—
664C23—616no—
665C23C24×D318yes—
666C23C24×D311yescharacteristic
667Q8—224no—
668Q8—348no—
669Q8—648no—
670Q8—624no—
671Q8C2×D3×D4116yes—
672D4—216no—
673D4—224no—
674D4—28no—
675D4—412no—
676D4—616no—
677D4—648no—
678D4—616no—
679D4—616no—
680D4—616no—
681D4—624no—
682D4—68no—
683D4—1212no—
684D4—1224no—
685C2×C4—248no—
686C2×C4—22no—
687C2×C4—312no—
688C2×C4—31no—
689C2×C4—36no—
690C2×C4—324no—
691C2×C4—324no—
692C2×C4—34no—
693C2×C4—31no—
694C2×C4—36no—
695C2×C4—38no—
696C2×C4—43no—
697C2×C4—648no—
698C2×C4—62no—
699C2×C4—616no—
700C2×C4—62no—
701C2×C4—612no—
702C2×C4—648no—
703C2×C4—62no—
704C2×C4—648no—
705C2×C4—62no—
706C2×C4—126no—
707C2×C4—123no—
708C2×C4C2×D3×D4112yes—
709C2×C4C24×D311yescharacteristic
710C2×C4C24×D316yes—
711C2×C4C24×D318yes—
712C2×C4C24×D316yes—
713C2×C4C24×D311yescharacteristic
714C2×C3—22no—
715C2×C3—48no—
716C2×C3C24×D411yescharacteristic
717C2×C3C22×2−1+411yescharacteristic
718C2×C3C2×#58511yescharacteristic
719D3—22no—
720D3—48no—
721D3#349714yesdirect product factor
722C22—21no—
723C22—21no—
724C22—28no—
725C22—28no—
726C22—28no—
727C22—32no—
728C22—32no—
729C22—32no—
730C22—32no—
731C22—68no—
732C22—61no—
733C22—61no—
734C22—68no—
735C22—68no—
736C22—68no—
737C22—1232no—
738C22C22×D3×D412yes—
739C22C25×D311yescharacteristic
740C4—28no—
741C4—21no—
742C4—26no—
743C4—312no—
744C4—32no—
745C4—68no—
746C4—61no—
747C4—66no—
748C4C22×D3×D4112yes—
749C4D3×2−1+412yescomplemented
750C3C2×#349711yescharacteristic, complemented, Sylow
751C2—22no—
752C2—34no—
753C2—48no—
754C2—62no—
755C2—128no—
756C2C23×D3×D411yescharacteristic
757C2C2×D3×2−1+411yescharacteristic
758C2D3×#58511yescharacteristic
subgroupG/H
center, FrattiniC22C25×D3
commutator, socle, cosocleC22×C3C26
FittingC3×#3497C2
hypercenter#3497D3
hypocenterC3C2×#3497
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #3497

Complements

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

NH ≅ G/Ntype
1. C2×D3×2−1+4C2semidirect
2. C3×#3497C2semidirect
3. #87291C2semidirect
4. #86784C2semidirect
5. D3×#550C2semidirect
6. #86760C2semidirect
7. D3×D4×Q8C2semidirect
8. #86737C2semidirect
9. D3×#548C2semidirect
10. D3×#537C2semidirect
11. #86367C2semidirect
12. D3×#532C2semidirect
13. #86222C2semidirect
14. #85818C2semidirect
15. C2×C4×D3×Q8C2semidirect
17. C2×C3×2−1+4C22semidirect
19. C2×#1010C22semidirect
20. C2×#1010C22semidirect
23. C2×#1007C22semidirect
24. C2×#1007C22semidirect
27. C3×#550C22semidirect
28. C3×D4×Q8C22semidirect
29. C3×#548C22semidirect
30. C3×#537C22semidirect
31. C3×#532C22semidirect
32. C2×C3×C4×Q8C22semidirect
33. #5834C22semidirect
34. #5833C22semidirect
35. #5832C22semidirect
36. #5831C22semidirect
37. #5817C22semidirect
38. Q8×#67C22semidirect
39. C2×Q8×Dic3C22semidirect
40. #5727C22semidirect
41. #5725C22semidirect
43. #5718C22semidirect
44. #5716C22semidirect
46. #5677C22semidirect
48. #5668C22semidirect
49. #5633C22semidirect
50. #5632C22semidirect
51. #5629C22semidirect
53. #5608C22semidirect
57. #5599C22semidirect
58. #5598C22semidirect
59. #5597C22semidirect
60. #5596C22semidirect
61. #5596C22semidirect
62. #5577C22semidirect
63. #5576C22semidirect
64. Q8×D12C22semidirect
67. C4×D3×Q8C22semidirect
68. C4×D3×Q8C22semidirect
69. #5553C22semidirect
70. #5552C22semidirect
71. #5548C22semidirect
72. #5548C22semidirect
75. D4×Dic6C22semidirect
76. #5510C22semidirect
78. C2×#887C22semidirect
79. #5477C22semidirect
81. C2×C4×Dic6C22semidirect
90. #3497D3direct (N × H)
111. C2×D3×Q8D4semidirect
215. C2×2−1+4C2×D3semidirect
225. #550C2×D3semidirect
231. D4×Q8C2×D3semidirect
239. #548C2×D3semidirect
245. #537C2×D3semidirect
255. #532C2×D3semidirect
270. C2×C4×Q8C2×D3semidirect
280. C2×C3×Q8C2×D4semidirect
306. D3×Q8C2×D4semidirect
337. C2×Dic6C2×D4semidirect
533. C4×D32−1+4semidirect
560. C2×Q8D3×D4semidirect
650. C3×C4C2×2−1+4semidirect
655. Dic3C2×2−1+4semidirect
721. D3#3497direct (N × H)
749. C4D3×2−1+4semidirect
750. C3C2×#3497semidirect

Maximal subgroups

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

subgroupindex
C2×D3×2−1+42
C3×#34972
#872912
#867842
D3×#5502
#867602
D3×D4×Q82
#867372
D3×#5482
D3×#5372
#863672
D3×#5322
#862222
#858182
C2×C4×D3×Q82
C2×#34973