Finite Group Databasebeta

← D3×#3499 #11703595

Subgroups — D3×#3499 #11703595

Order 768.

11126 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×2−1+4C212yesmaximal, complemented
2C3×#3499C211yesmaximal, characteristic, complemented
3#87292C212yesmaximal, complemented
4D3×D4×Q8C214yesmaximal, complemented
5#86746C214yesmaximal, complemented
6D3×#547C2112yesmaximal, complemented
7#86679C2112yesmaximal, complemented
8D3×#536C216yesmaximal, complemented
9#86340C216yesmaximal, complemented
10#86243C213yesmaximal, complemented
11D3×#532C213yesmaximal, complemented
12#86214C213yesmaximal, complemented
13C2×D3×C4⋊Q8C213yesmaximal, complemented
14C4×D3×#41C211yesmaximal, characteristic, complemented
15#85827C211yesmaximal, characteristic, complemented
16C2×#3499—31nomaximal, Sylow
17C2×C3×2−1+4C2212yescomplemented
18D3×2−1+4—232no—
19C2×#1010C2212yescomplemented
20C2×#1010C2216yescomplemented
21C2×#1010C22112yescomplemented
22C2×D3×#41C2216yes—
23C2×D3×#41C22112yes—
24C2×D3×#41C2211yescharacteristic
25C2×#1007C2216yescomplemented
26C2×#1007C2214yescomplemented
27C22×D3×Q8C2216yes—
28C22×D3×Q8C2214yes—
29C3×D4×Q8C2214yescomplemented
30C3×#547C22112yescomplemented
31C3×#536C2216yescomplemented
32C3×#532C2213yescomplemented
33C2×C3×C4⋊Q8C2213yescomplemented
34C3×C4×#41C2211yescharacteristic, complemented
35#5832C2216yescomplemented
36Dic3×#41C2211yescharacteristic, complemented
37#5825C2216yescomplemented
38#5824C22124yescomplemented
39#5816C2216yescomplemented
40Q8×#67C2218yescomplemented
41C2×#944C2216yescomplemented
42#5727C22112yescomplemented
43#5726C22112yescomplemented
44#5725C2213yescomplemented
45#5724C22112yescomplemented
46D3×C4⋊Q8C2216yes—
47D3×C4⋊Q8C22112yes—
48D3×C4⋊Q8C2213yes—
49D3×C4⋊Q8C2216yescomplemented
50D3×C4⋊Q8C22112yescomplemented
51D3×C4⋊Q8C2216yescomplemented
52#5716C2213yescomplemented
53D3×#127C2211yescharacteristic
54#5675C22112yescomplemented
55D3×#124C2216yes—
56#5668C2216yescomplemented
57#5655C22148yescomplemented
58D3×#123C22124yes—
59#5648C22124yescomplemented
60#5632C22124yescomplemented
61#5631C22124yescomplemented
62#5628C22124yescomplemented
63D3×C22⋊Q8C22124yes—
64#5611C22124yescomplemented
65D3×#121C22112yes—
66#5596C22112yescomplemented
67Q8×D12C2214yescomplemented
68C4×#239C2212yescomplemented
69C4×D3×Q8C2212yes—
70#5555C22112yescomplemented
71#5551C22112yescomplemented
72#5548C22112yescomplemented
73C4×D3×D4C2216yes—
74C4×D3×D4C22112yes—
75D4×Dic6C22112yescomplemented
76C4×#237C2216yescomplemented
77#5526C2216yescomplemented
78#5522C2213yescomplemented
79D3×#117C2213yes—
80#5507C22124yescomplemented
81C2×D3×C4⋊C4C22112yes—
82C2×#888C22112yescomplemented
83#5477C2213yescomplemented
84C4×#235C2213yescomplemented
85C2×C42×D3C2213yes—
86C2×#869C2213yescomplemented
87C22×2−1+4—32no—
88#3499—32no—
89#3499—34no—
90#3499—312no—
91#3499—36no—
92#3499—33no—
93#3499—33no—
94#3499—31no—
95#3499D311yescharacteristic, direct product factor
96C2×D4×Q8—34no—
97C2×#547—312no—
98C2×#536—36no—
99C2×#532—33no—
100C22×C4⋊Q8—33no—
101C2×C4×#41—31no—
102C3×2−1+4—216no—
103C2×C3×#41C23112yes—
104C2×C3×#41C2316yes—
105C2×C3×#41C2311yescharacteristic
106C22×C3×Q8C2316yes—
107C22×C3×Q8C2314yes—
108#1010—216no—
109#1010—296no—
110#1010—248no—
111D3×#41—296no—
112D3×#41—248no—
113D3×#41D4116yescomplemented
114#1007—232no—
115#1007—248no—
116C2×#239C2316yes—
117C2×#239C23112yes—
118C2×#239C2311yescharacteristic
119C2×D3×Q8—232no—
120C2×D3×Q8—248no—
121C2×D3×Q8C23112yes—
122C2×D3×Q8C2316yes—
123C2×D3×Q8C23112yes—
124C2×D3×Q8C23112yes—
125C2×D3×Q8C23112yes—
126C2×D3×Q8C2314yes—
127C2×D3×Q8C2311yescharacteristic
128C2×#237C23112yes—
129C2×#237C23124yes—
130C2×#237C2316yes—
131C2×#237C23112yes—
132C2×#237C2313yes—
133C2×D3×D4C23112yes—
134C2×D3×D4C2312yes—
135C2×D3×D4C2314yes—
136C2×D3×D4C2313yes—
137C2×#235C23124yes—
138C2×#235C2316yes—
139C2×#235C23112yes—
140C2×#235C23112yes—
141C2×#235C2313yes—
142C22×C4×D3C23112yes—
143C22×C4×D3C23112yes—
144C22×C4×D3C2316yes—
145C22×C4×D3C2313yes—
146C22×Dic6C23112yes—
147C22×Dic6C23112yes—
148C22×Dic6C2316yes—
149C3×C4⋊Q8C2313yes—
150C3×C4⋊Q8C2316yes—
151C3×C4⋊Q8C23112yes—
152C3×#127C2311yescharacteristic
153C3×#124C2316yes—
154C3×#123C23124yes—
155C3×C22⋊Q8C23124yes—
156C3×#121C23112yes—
157C3×C4×Q8C2312yes—
158C3×C4×D4C2316yes—
159C3×C4×D4C23112yes—
160C3×#117C2313yes—
161C2×C3×C4⋊C4C23112yes—
162C2×C3×C42C2313yes—
163#947C2316yes—
164#946C23124yes—
165Q8×Dic3C2312yes—
166#944C23124yes—
167#944C2316yes—
168#944C23112yes—
169#940C2312yes—
170#940C2314yes—
171#939C23124yes—
172#938C23112yes—
173#936C2316yes—
174#935C23124yes—
175D4×Dic3C23112yes—
176D4×Dic3C2316yes—
177#930C23112yes—
178#929C23124yes—
179C4×#67C23124yes—
180C4×#67C23112yes—
181#926C2313yes—
182C2×C4⋊Dic3C23112yes—
183#924C23124yes—
184C2×Dic3⋊C4C23124yes—
185C2×C4×Dic3C2316yes—
186C2×C4×Dic3C2313yes—
187#897C23124yes—
188#896C23148yes—
189#895C23112yes—
190#894C23148yes—
191#893C23112yes—
192#893C2316yes—
193#892C2316yes—
194D3×C4⋊C4C23124yes—
195D3×C4⋊C4C23124yes—
196D3×C4⋊C4C23112yes—
197D3×C4⋊C4C23124yes—
198D3×C4⋊C4C2316yes—
199#888C23124yes—
200#888C23124yes—
201#888C23112yes—
202#888C23124yes—
203#887C2316yes—
204#886C23124yes—
205#885C23124yes—
206#884C23124yes—
207#883C23148yes—
208#67⋊C4C23124yes—
209#67⋊C4C23112yes—
210D3×C22⋊C4C2316yes—
211D3×C22⋊C4C23124yes—
212#878C23148yes—
213#877C2316yes—
214#875C2316yes—
215#874C2311yescharacteristic
216C4×D12C2316yes—
217C4×D12C23112yes—
218#872C2316yes—
219C42×D3C2313yes—
220C42×D3C2313yes—
221C42×D3C2311yescharacteristic
222C42×D3C2313yes—
223C42×D3C2316yes—
224C42×D3C2316yes—
225#869C2316yes—
226#869C2313yes—
227#869C23112yes—
228C4×Dic6C2316yes—
229C2×2−1+4—36no—
230C2×2−1+4—312no—
231C2×2−1+4—32no—
232C2×2−1+4—34no—
233C2×2−1+4—36no—
234C2×2−1+4—632no—
235C2×2−1+4C2×D312yescomplemented
236C22×#41—31no—
237C22×#41—36no—
238C22×#41—312no—
239C23×Q8—36no—
240C23×Q8—34no—
241D4×Q8—38no—
242D4×Q8—312no—
243D4×Q8—324no—
244D4×Q8—34no—
245D4×Q8—312no—
246D4×Q8C2×D314yescomplemented
247#547—324no—
248#547—312no—
249#547—348no—
250#547—324no—
251#547—324no—
252#547—312no—
253#547—312no—
254#547—324no—
255#547C2×D3112yescomplemented
256#536—36no—
257#536—36no—
258#536—312no—
259#536—312no—
260#536—324no—
261#536—324no—
262#536—36no—
263#536C2×D316yescomplemented
264#532—36no—
265#532—33no—
266#532—33no—
267#532—36no—
268#532—312no—
269#532—312no—
270#532—33no—
271#532C2×D313yescomplemented
272C2×C4⋊Q8—36no—
273C2×C4⋊Q8—33no—
274C2×C4⋊Q8—36no—
275C2×C4⋊Q8—312no—
276C2×C4⋊Q8—36no—
277C2×C4⋊Q8—36no—
278C2×C4⋊Q8—312no—
279C2×C4⋊Q8—312no—
280C2×C4⋊Q8—33no—
281C2×C4⋊Q8C2×D313yescomplemented
282C2×#127—31no—
283C2×#124—36no—
284C2×#123—324no—
285C2×C22⋊Q8—324no—
286C2×#121—312no—
287C4×#41—31no—
288C4×#41—32no—
289C4×#41—36no—
290C4×#41—33no—
291C4×#41—33no—
292C4×#41C2×D311yescharacteristic, complemented
293C2×C4×Q8—32no—
294C2×C4×D4—36no—
295C2×C4×D4—312no—
296C2×#117—33no—
297C22×C4⋊C4—312no—
298C22×C42—33no—
299C23×D3C2414yes—
300C23×D3C2413yes—
301C3×#41—248no—
302C3×#41—224no—
303C3×#41C2×D418yescomplemented
304C2×C3×Q8—216no—
305C2×C3×Q8—224no—
306C2×C3×Q8C2416yes—
307C2×C3×Q8C24112yes—
308C2×C3×Q8C2411yescharacteristic
309C2×C3×D4C2414yes—
310C2×C3×D4C24112yes—
311C2×C3×D4C2412yes—
312C2×C3×D4C2413yes—
313C22×C3×C4C2416yes—
314C22×C3×C4C24112yes—
315C22×C3×C4C24112yes—
316C22×C3×C4C2413yes—
317C2×#67C2418yes—
318C2×#67C24112yes—
319C2×#67C2414yes—
320C2×#67C24112yes—
321C2×#67C2416yes—
322C22×Dic3C24112yes—
323C22×Dic3C2416yes—
324C22×Dic3C24112yes—
325C22×Dic3C2413yes—
326#239—248no—
327#239—224no—
328#239C2×D418yescomplemented
329D3×Q8—216no—
330D3×Q8—248no—
331D3×Q8—224no—
332D3×Q8—248no—
333D3×Q8—248no—
334D3×Q8—248no—
335D3×Q8C2×D418yes—
336#237—248no—
337#237—296no—
338#237—248no—
339#237—224no—
340#237C2×D4124yescomplemented
341D3×D4—248no—
342D3×D4—28no—
343D3×D4—216no—
344D3×D4C2×D4124yes—
345#235—224no—
346#235—296no—
347#235—248no—
348#235—248no—
349#235C2×D4124yescomplemented
350C2×D12C2414yes—
351C2×D12C2412yes—
352C2×D12C24112yes—
353C2×D12C2413yes—
354C2×C4×D3—248no—
355C2×C4×D3—248no—
356C2×C4×D3—224no—
357C2×C4×D3C2×D4124yes—
358C2×C4×D3C2416yes—
359C2×C4×D3C2416yes—
360C2×C4×D3C2416yes—
361C2×C4×D3C24112yes—
362C2×C4×D3C24112yes—
363C2×C4×D3C24112yes—
364C2×C4×D3C24124yes—
365C2×C4×D3C2411yescharacteristic
366C2×C4×D3C2413yes—
367C2×C4×D3C2413yes—
368C2×C4×D3C2413yes—
369C2×C4×D3C2412yes—
370C2×Dic6—224no—
371C2×Dic6—248no—
372C2×Dic6—248no—
373C2×Dic6C2416yes—
374C2×Dic6C24112yes—
375C2×Dic6C24124yes—
376C2×Dic6C24112yes—
377C2×Dic6C2413yes—
378C3×C4⋊C4C2416yes—
379C3×C4⋊C4C24112yes—
380C3×C4⋊C4C24124yes—
381C3×C22⋊C4C2416yes—
382C3×C22⋊C4C24124yes—
383C3×C42C2416yes—
384C3×C42C2411yescharacteristic
385C3×C42C2413yes—
386#217C2416yes—
387#217C24124yes—
388(C2×D3)⋊C4C24112yes—
389(C2×D3)⋊C4C24124yes—
390(C2×D3)⋊C4C24124yes—
391C4⋊Dic3C2416yes—
392C4⋊Dic3C24112yes—
393C4⋊Dic3C24124yes—
394Dic3⋊C4C24112yes—
395Dic3⋊C4C24148yes—
396Dic3⋊C4C24124yes—
397C4×Dic3C2416yes—
398C4×Dic3C2412yes—
399C4×Dic3C2411yescharacteristic
400C4×Dic3C2413yes—
401C4×Dic3C2416yes—
402C4×Dic3C2416yes—
403C4×Dic3C2416yes—
4042−1+4—216no—
4052−1+4—632no—
4062−1+4—648no—
4072−1+4—696no—
4082−1+4—648no—
4092−1+4—616no—
410C2×#41—316no—
411C2×#41—31no—
412C2×#41—36no—
413C2×#41—312no—
414C2×#41—33no—
415C2×#41—312no—
416C2×#41—36no—
417C2×#41—312no—
418C2×#41—324no—
419C2×#41—33no—
420C2×#41—312no—
421C2×#41—36no—
422C2×#41—312no—
423C2×#41—324no—
424C2×#41—648no—
425C2×#41—696no—
426C2×#41C22×D316yes—
427C2×#41C22×D3112yes—
428C2×#41C22×D311yescharacteristic
429C22×Q8—31no—
430C22×Q8—312no—
431C22×Q8—36no—
432C22×Q8—312no—
433C22×Q8—312no—
434C22×Q8—312no—
435C22×Q8—34no—
436C22×Q8—312no—
437C22×Q8—36no—
438C22×Q8—312no—
439C22×Q8—648no—
440C22×Q8—632no—
441C22×Q8C22×D316yes—
442C22×Q8C22×D314yes—
443C22×D4—33no—
444C22×D4—34no—
445C22×D4—312no—
446C22×D4—32no—
447C23×C4—33no—
448C23×C4—36no—
449C23×C4—312no—
450C23×C4—312no—
451C4⋊Q8—36no—
452C4⋊Q8—312no—
453C4⋊Q8—324no—
454C4⋊Q8—312no—
455C4⋊Q8—324no—
456C4⋊Q8—324no—
457C4⋊Q8—324no—
458C4⋊Q8—33no—
459C4⋊Q8—36no—
460C4⋊Q8—312no—
461C4⋊Q8C22×D313yes—
462C4⋊Q8C22×D316yes—
463C4⋊Q8C22×D3112yes—
464#127—32no—
465#127—34no—
466#127—31no—
467#127C22×D311yescharacteristic
468#124—36no—
469#124—36no—
470#124—324no—
471#124—36no—
472#124C22×D316yes—
473#123—324no—
474#123—324no—
475#123—348no—
476#123—348no—
477#123—324no—
478#123C22×D3124yes—
479C22⋊Q8—324no—
480C22⋊Q8—324no—
481C22⋊Q8—348no—
482C22⋊Q8—324no—
483C22⋊Q8—348no—
484C22⋊Q8C22×D3124yes—
485#121—312no—
486#121—324no—
487#121—312no—
488#121—312no—
489#121—324no—
490#121C22×D3112yes—
491C4×Q8—32no—
492C4×Q8—36no—
493C4×Q8—36no—
494C4×Q8C22×D312yes—
495C4×D4—36no—
496C4×D4—312no—
497C4×D4—312no—
498C4×D4—324no—
499C4×D4—36no—
500C4×D4—312no—
501C4×D4—312no—
502C4×D4—324no—
503C4×D4—36no—
504C4×D4—312no—
505C4×D4C22×D316yes—
506C4×D4C22×D3112yes—
507#117—33no—
508#117—36no—
509#117—36no—
510#117—36no—
511#117C22×D313yes—
512C2×C4⋊C4—324no—
513C2×C4⋊C4—312no—
514C2×C4⋊C4—312no—
515C2×C4⋊C4—324no—
516C2×C4⋊C4—324no—
517C2×C4⋊C4—324no—
518C2×C4⋊C4—36no—
519C2×C4⋊C4C22×D3112yes—
520C2×C22⋊C4—36no—
521C2×C22⋊C4—324no—
522C2×C42—36no—
523C2×C42—33no—
524C2×C42—33no—
525C2×C42—36no—
526C2×C42—36no—
527C2×C42—33no—
528C2×C42—33no—
529C2×C42—31no—
530C2×C42C22×D313yes—
531C23×C3C2514yes—
532C23×C3C2513yes—
533C22×D3—212no—
534C22×D3—28no—
535C22×D3—216no—
536C22×D3C22×D4112yes—
537C22×D3C2514yes—
538C22×D3C2513yes—
539C22×D3C2511yescharacteristic
540C3×Q8—212no—
541C3×Q8—224no—
542C3×Q8C22×D414yes—
543C3×D4—224no—
544C3×D4—24no—
545C3×D4—28no—
546C3×D4C22×D4112yes—
547C2×C3×C4—224no—
548C2×C3×C4—224no—
549C2×C3×C4—212no—
550C2×C3×C4C22×D4112yes—
551C2×C3×C4C2516yes—
552C2×C3×C4C25112yes—
553C2×C3×C4C2511yescharacteristic
554C2×C3×C4C2513yes—
555C2×C3×C4C2512yes—
556#67—224no—
557#67—224no—
558#67—28no—
559#67—216no—
560#67C22×D4124yes—
561C2×Dic3—224no—
562C2×Dic3—224no—
563C2×Dic3—212no—
564C2×Dic3C22×D4112yes—
565C2×Dic3C2516yes—
566C2×Dic3C25112yes—
567C2×Dic3C2511yescharacteristic
568C2×Dic3C2513yes—
569C2×Dic3C2512yes—
570D12—224no—
571D12—24no—
572D12—28no—
573D12C22×D4112yes—
574C4×D3—224no—
575C4×D3—248no—
576C4×D3—212no—
577C4×D3—224no—
578C4×D3—212no—
579C4×D3—224no—
580C4×D3—212no—
581C4×D3C22×D4112yes—
582C4×D3C22×D414yes—
583C4×D3C22×D4112yes—
584C4×D3C22×D4112yes—
585C4×D32−1+418yescomplemented
586Dic6—212no—
587Dic6—224no—
588Dic6—224no—
589Dic6—248no—
590Dic6C22×D4112yes—
591C24—33no—
592C24—34no—
593#41—248no—
594#41—224no—
595#41—38no—
596#41—324no—
597#41—324no—
598#41—648no—
599#41—696no—
600#41—648no—
601#41—648no—
602#41—624no—
603#41—624no—
604#41—696no—
605#41—648no—
606#41—648no—
607#41—624no—
608#41D3×D418yescomplemented
609C2×Q8—216no—
610C2×Q8—224no—
611C2×Q8—38no—
612C2×Q8—33no—
613C2×Q8—324no—
614C2×Q8—312no—
615C2×Q8—312no—
616C2×Q8—36no—
617C2×Q8—648no—
618C2×Q8—648no—
619C2×Q8—624no—
620C2×Q8—648no—
621C2×Q8—648no—
622C2×Q8—648no—
623C2×Q8—648no—
624C2×Q8—616no—
625C2×Q8—624no—
626C2×Q8C23×D3112yes—
627C2×Q8C23×D316yes—
628C2×Q8C23×D311yescharacteristic
629C2×D4—36no—
630C2×D4—324no—
631C2×D4—38no—
632C2×D4—312no—
633C2×D4—312no—
634C2×D4—34no—
635C2×D4—33no—
636C2×D4—34no—
637C2×D4—312no—
638C2×D4—32no—
639C2×D4—68no—
640C2×D4—616no—
641C2×D4—648no—
642C2×D4C23×D314yes—
643C2×D4C23×D3112yes—
644C2×D4C23×D312yes—
645C2×D4C23×D313yes—
646C22×C4—33no—
647C22×C4—324no—
648C22×C4—32no—
649C22×C4—31no—
650C22×C4—33no—
651C22×C4—33no—
652C22×C4—33no—
653C22×C4—36no—
654C22×C4—312no—
655C22×C4—312no—
656C22×C4—36no—
657C22×C4—36no—
658C22×C4—36no—
659C22×C4—312no—
660C22×C4—324no—
661C22×C4—312no—
662C22×C4—312no—
663C22×C4—648no—
664C22×C4—624no—
665C22×C4—648no—
666C22×C4C23×D316yes—
667C22×C4C23×D3112yes—
668C22×C4C23×D3112yes—
669C22×C4C23×D313yes—
670C4⋊C4—324no—
671C4⋊C4—312no—
672C4⋊C4—348no—
673C4⋊C4—324no—
674C4⋊C4—312no—
675C4⋊C4—36no—
676C4⋊C4C23×D3112yes—
677C4⋊C4C23×D3124yes—
678C4⋊C4C23×D316yes—
679C22⋊C4—36no—
680C22⋊C4—324no—
681C22⋊C4—312no—
682C22⋊C4—324no—
683C22⋊C4—324no—
684C22⋊C4C23×D316yes—
685C22⋊C4C23×D3124yes—
686C42—31no—
687C42—32no—
688C42—36no—
689C42—33no—
690C42—36no—
691C42—36no—
692C42—36no—
693C42C23×D311yescharacteristic
694C42C23×D313yes—
695C42C23×D316yes—
696C22×C3—26no—
697C22×C3—24no—
698C22×C3—28no—
699C22×C3C23×D416yes—
700C22×C3C2611yescharacteristic
701C2×D3—26no—
702C2×D3—224no—
703C2×D3—24no—
704C2×D3—28no—
705C2×D3—416no—
706C2×D3C23×D416yes—
707C2×D3C23×D412yes—
708C2×D3C2×2−1+414yes—
709C3×C4—212no—
710C3×C4—26no—
711C3×C4C23×D412yes—
712C3×C4C23×D416yes—
713C3×C4C2×2−1+414yescomplemented
714Dic3—212no—
715Dic3—26no—
716Dic3C23×D412yes—
717Dic3C23×D416yes—
718Dic3C2×2−1+414yescomplemented
719C23—31no—
720C23—312no—
721C23—33no—
722C23—34no—
723C23—612no—
724C23—68no—
725C23—616no—
726C23C24×D314yes—
727C23C24×D313yes—
728Q8—224no—
729Q8—212no—
730Q8—312no—
731Q8—624no—
732Q8—648no—
733Q8—624no—
734Q8—612no—
735Q8C2×D3×D414yes—
736D4—224no—
737D4—24no—
738D4—28no—
739D4—324no—
740D4—312no—
741D4—624no—
742D4—68no—
743D4—616no—
744D4—624no—
745D4—624no—
746D4—64no—
747D4—68no—
748D4C2×D3×D4112yes—
749C2×C4—224no—
750C2×C4—224no—
751C2×C4—212no—
752C2×C4—312no—
753C2×C4—32no—
754C2×C4—31no—
755C2×C4—33no—
756C2×C4—34no—
757C2×C4—312no—
758C2×C4—312no—
759C2×C4—312no—
760C2×C4—38no—
761C2×C4—36no—
762C2×C4—312no—
763C2×C4—624no—
764C2×C4—612no—
765C2×C4—624no—
766C2×C4—648no—
767C2×C4—612no—
768C2×C4—624no—
769C2×C4—612no—
770C2×C4—624no—
771C2×C4—624no—
772C2×C4—612no—
773C2×C4C2×D3×D4112yes—
774C2×C4C24×D316yes—
775C2×C4C24×D3112yes—
776C2×C4C24×D311yescharacteristic
777C2×C4C24×D313yes—
778C2×C4C24×D312yes—
779C2×C3—26no—
780C2×C3—44no—
781C2×C3C24×D411yescharacteristic
782C2×C3C22×2−1+412yes—
783D3—26no—
784D3—44no—
785D3#349914yesdirect product factor
786C22—26no—
787C22—24no—
788C22—28no—
789C22—32no—
790C22—34no—
791C22—36no—
792C22—624no—
793C22—66no—
794C22—64no—
795C22—68no—
796C22—1216no—
797C22C22×D3×D416yes—
798C22C25×D311yescharacteristic
799C4—212no—
800C4—26no—
801C4—32no—
802C4—36no—
803C4—34no—
804C4—612no—
805C4—66no—
806C4C22×D3×D416yes—
807C4C22×D3×D412yes—
808C4D3×2−1+414yescomplemented
809C3C2×#349911yescharacteristic, complemented, Sylow
810C2—26no—
811C2—34no—
812C2—44no—
813C2—66no—
814C2—124no—
815C2C23×D3×D411yescharacteristic
816C2C2×D3×2−1+412yes—
subgroupG/H
center, FrattiniC22C25×D3
commutator, socle, cosocleC22×C3C26
FittingC3×#3499C2
hypercenter#3499D3
hypocenterC3C2×#3499
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. C2×D3×2−1+4C2semidirect
2. C3×#3499C2semidirect
3. #87292C2semidirect
4. D3×D4×Q8C2semidirect
5. #86746C2semidirect
6. D3×#547C2semidirect
7. #86679C2semidirect
8. D3×#536C2semidirect
9. #86340C2semidirect
10. #86243C2semidirect
11. D3×#532C2semidirect
12. #86214C2semidirect
13. C2×D3×C4⋊Q8C2semidirect
14. C4×D3×#41C2semidirect
15. #85827C2semidirect
17. C2×C3×2−1+4C22semidirect
19. C2×#1010C22semidirect
20. C2×#1010C22semidirect
21. C2×#1010C22semidirect
25. C2×#1007C22semidirect
26. C2×#1007C22semidirect
29. C3×D4×Q8C22semidirect
30. C3×#547C22semidirect
31. C3×#536C22semidirect
32. C3×#532C22semidirect
33. C2×C3×C4⋊Q8C22semidirect
34. C3×C4×#41C22semidirect
35. #5832C22semidirect
36. Dic3×#41C22semidirect
37. #5825C22semidirect
38. #5824C22semidirect
39. #5816C22semidirect
40. Q8×#67C22semidirect
41. C2×#944C22semidirect
42. #5727C22semidirect
43. #5726C22semidirect
44. #5725C22semidirect
45. #5724C22semidirect
49. D3×C4⋊Q8C22semidirect
50. D3×C4⋊Q8C22semidirect
51. D3×C4⋊Q8C22semidirect
52. #5716C22semidirect
54. #5675C22semidirect
56. #5668C22semidirect
57. #5655C22semidirect
59. #5648C22semidirect
60. #5632C22semidirect
61. #5631C22semidirect
62. #5628C22semidirect
64. #5611C22semidirect
66. #5596C22semidirect
67. Q8×D12C22semidirect
68. C4×#239C22semidirect
70. #5555C22semidirect
71. #5551C22semidirect
72. #5548C22semidirect
75. D4×Dic6C22semidirect
76. C4×#237C22semidirect
77. #5526C22semidirect
78. #5522C22semidirect
80. #5507C22semidirect
82. C2×#888C22semidirect
83. #5477C22semidirect
84. C4×#235C22semidirect
86. C2×#869C22semidirect
95. #3499D3direct (N × H)
113. D3×#41D4semidirect
235. C2×2−1+4C2×D3semidirect
246. D4×Q8C2×D3semidirect
255. #547C2×D3semidirect
263. #536C2×D3semidirect
271. #532C2×D3semidirect
281. C2×C4⋊Q8C2×D3semidirect
292. C4×#41C2×D3semidirect
303. C3×#41C2×D4semidirect
328. #239C2×D4semidirect
340. #237C2×D4semidirect
349. #235C2×D4semidirect
585. C4×D32−1+4semidirect
608. #41D3×D4semidirect
713. C3×C4C2×2−1+4semidirect
718. Dic3C2×2−1+4semidirect
785. D3#3499direct (N × H)
808. C4D3×2−1+4semidirect
809. C3C2×#3499semidirect

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×#34992
#872922
D3×D4×Q82
#867462
D3×#5472
#866792
D3×#5362
#863402
#862432
D3×#5322
#862142
C2×D3×C4⋊Q82
C4×D3×#412
#858272
C2×#34993