Finite Group Databasebeta

← #11662161

Subgroups — #11662161

Order 768.

2750 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5773C212yesmaximal, complemented
2#86235C211yesmaximal, characteristic, complemented
3C2×#5546C211yesmaximal, characteristic, complemented
4C3×#3036C211yesmaximal, characteristic, complemented
5#83931C212yesmaximal, complemented
6#83314C211yesmaximal, characteristic, complemented
7#82307C211yesmaximal, characteristic, complemented
8#80539C214yesmaximal, complemented
9#80538C214yesmaximal, complemented
10#80431C214yesmaximal, complemented
11#80335C214yesmaximal, complemented
12#79067C211yesmaximal, characteristic, complemented
13#79048C211yesmaximal, characteristic, complemented
14#78913C212yesmaximal, complemented
15D3×#417C212yesmaximal, complemented
16#60425—31nomaximal, Sylow
17C2×D3×#41C2212yes—
18C22×#237C2211yescharacteristic
19C2×C3×AGL(1,ℤ/8)C2212yescomplemented
20C3×#532C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic, complemented
22#5832C2212yes—
23C2×#951C2212yescomplemented
24C2×D4×Dic3C2211yescharacteristic, complemented
25C2×#932C2212yescomplemented
26C2×C4×#67—21no—
27C22×Dic3⋊C4—21no—
28#5773—216no—
29C2×#916C2214yes—
30C2×#915C2214yescomplemented
31C2×#912C2214yes—
32C2×#911C2214yescomplemented
33C2×#909C2212yescomplemented
34C2×D3×M16C2212yes—
35#5724C2212yescomplemented
36#5715C2212yescomplemented
37#5675C2212yescomplemented
38#5674C2212yescomplemented
39#5605—21no—
40#5605—21no—
41#5597—21no—
42#5597—21no—
43#5547—22no—
44#5547—22no—
45#5546—22no—
46#5546—22no—
47#5546C2214yescomplemented
48#5546C2214yescomplemented
49C2×D3×C4⋊C4C2211yescharacteristic
50C2×#887C2211yescharacteristic, complemented
51C2×#67⋊C4—21no—
52C2×#877—21no—
53#5477C2211yescharacteristic
54C2×#872C2211yescharacteristic
55C2×C4×Dic6C2211yescharacteristic, complemented
56C3×#463C2214yescomplemented
57C3×#461C2212yescomplemented
58C3×#459C2212yescomplemented
59C3×#423C2211yescharacteristic, complemented
60C3×#417C2212yescomplemented
61#5232C2212yescomplemented
62#5165C2214yescomplemented
63#5162C2214yescomplemented
64#5153C2214yescomplemented
65#5150C2214yescomplemented
66#5133C2212yescomplemented
67#5118C2212yescomplemented
68#5090C2212yescomplemented
69#5075C2212yescomplemented
70#5054C2214yescomplemented
71#5019C2212yescomplemented
72#5016C2214yescomplemented
73#5015C2212yescomplemented
74#4966C2212yescomplemented
75#4924C2211yescharacteristic, complemented
76#4849C2212yescomplemented
77#4848C2212yescomplemented
78#4845C2214yescomplemented
79#4839C2214yescomplemented
80#4839C2214yescomplemented
81#4803C2214yescomplemented
82D3×#103C2214yescomplemented
83#4798C2214yescomplemented
84#4795C2214yescomplemented
85#4771C2214yescomplemented
86D3×#102C2214yescomplemented
87#4767C2214yescomplemented
88#4762C2214yescomplemented
89C2×#575—32no—
90#3449—31no—
91C2×#520—31no—
92#3046—34no—
93#3046—34no—
94#3045—34no—
95#3045—34no—
96#3037—31no—
97#3037—32no—
98#3037—31no—
99#3036—32no—
100#3036—31no—
101#3036D311yescharacteristic, complemented
102#2905—31no—
103C2×#417—32no—
104C2×C3×#41C2312yes—
105C22×C3×D4C2311yescharacteristic
106C23×C3×C4—21no—
107C22×#67—21no—
108C23×Dic3—21no—
109C23×Dic3—21no—
110D3×#41—28no—
111D3×#41—28no—
112C2×#239C2312yes—
113C2×D3×Q8C2312yes—
114C2×#237—22no—
115C2×#237—22no—
116C2×#237—24no—
117C2×#237D418yescomplemented
118C2×#237C2312yes—
119C2×#237C2314yes—
120C2×D3×D4—22no—
121C2×D3×D4C2312yes—
122C2×#235—22no—
123C2×#235C2312yes—
124C22×C4×D3—21no—
125C22×C4×D3—22no—
126C22×C4×D3C2311yescharacteristic
127C22×Dic6C2311yescharacteristic
128C3×AGL(1,ℤ/8)—28no—
129C2×C3×SD16C2314yes—
130C2×C3×D8C2314yes—
131C2×C3×M16C2312yes—
132C3×C4⋊Q8C2311yescharacteristic
133C3×#127C2311yescharacteristic
134C3×#124C2312yes—
135C3×#121—21no—
136C3×#121—21no—
137C3×C4×D4—21no—
138C3×C4×D4—21no—
139C3×C4×D4—21no—
140C3×C4×D4—21no—
141C3×C4×D4C2312yes—
142C3×C4×D4C2312yes—
143C2×C3×C4⋊C4C2311yescharacteristic
144C2×C3×C22⋊C4—21no—
145C2×C3×C42C2311yescharacteristic
146C2×#217—21no—
147#951—28no—
148#947C2312yes—
149#944C2312yes—
150C2×#216C2314yes—
151#940C2312yes—
152#939—22no—
153#939—22no—
154#939—22no—
155#939—22no—
156#937—22no—
157#937—22no—
158#936C2312yes—
159D4×Dic3—22no—
160D4×Dic3C2314yes—
161C2×#214C2314yes—
162C2×#214C2314yes—
163#932—28no—
164C2×#213C2314yes—
165#930—21no—
166#930—21no—
167C4×#67—24no—
168C4×#67—24no—
169C4×#67—22no—
170C4×#67—22no—
171C2×(C2×D3)⋊C4D411yescharacteristic
172C2×(C2×D3)⋊C4D411yescharacteristic
173C2×C4⋊Dic3C2311yescharacteristic
174C2×Dic3⋊C4—21no—
175C2×Dic3⋊C4—21no—
176C2×Dic3⋊C4—21no—
177C2×Dic3⋊C4—24no—
178C2×Dic3⋊C4—24no—
179C2×Dic3⋊C4D411yescharacteristic
180C2×Dic3⋊C4D411yescharacteristic
181C2×C4×Dic3—21no—
182C2×C4×Dic3—21no—
183C2×C4×Dic3C2311yescharacteristic
184C2×#208C2312yes—
185#916—216no—
186#915—216no—
187#912—216no—
188#911—216no—
189#909—28no—
190D3×M16—28no—
191C2×Dic12C2314yes—
192C2×#204C2314yes—
193C2×ΓL(1,𝔽25)C2314yes—
194C2×D3×C8C2314yes—
195#896—22no—
196#896—22no—
197#894—22no—
198#894—22no—
199D3×C4⋊C4—22no—
200D3×C4⋊C4C2314yes—
201#887—22no—
202#887C2314yes—
203#884—22no—
204#884—22no—
205#883—22no—
206#883—22no—
207#882—22no—
208#882—22no—
209#67⋊C4—24no—
210#67⋊C4—24no—
211#878—22no—
212#878—22no—
213#877—24no—
214#877—24no—
215#875C2312yes—
216#874C2311yescharacteristic
217C4×D12—21no—
218C4×D12—21no—
219#872D412yes—
220#872D412yes—
221#872C2312yes—
222#872C2312yes—
223#869C2311yescharacteristic
224C4×Dic6—21no—
225C4×Dic6—21no—
226C4×Dic6C2312yes—
227C4×Dic6C2312yes—
228C3×C4⋊C8C2312yes—
229C3×C4⋊C8C2312yes—
230C3×#103C2314yes—
231C3×#102C2314yes—
232#835C2314yes—
233#832C2314yes—
234#821C2314yes—
235#816C2314yes—
236Dic3⋊C8C2314yes—
237Dic3⋊C8C2314yes—
238#810C2314yes—
239#809C2314yes—
240C4⋊(C3⋊C8)C2312yes—
241C4⋊(C3⋊C8)C2312yes—
242C22×#41—32no—
243C22×#41—31no—
244#575—616no—
245C2×#137—32no—
246C2×#137—34no—
247C2×#137—32no—
248C2×AGL(1,ℤ/8)—32no—
249C2×AGL(1,ℤ/8)—34no—
250C2×AGL(1,ℤ/8)C2×D312yescomplemented
251C2×#135—34no—
252C2×#135—34no—
253C22×M16—32no—
254#537—61no—
255#537—61no—
256#536—32no—
257#536—32no—
258#535—32no—
259#535—32no—
260#534—61no—
261#534—61no—
262#532—32no—
263#532—31no—
264#532C2×D311yescharacteristic
265#525—62no—
266#525—62no—
267#520—34no—
268#520—34no—
269#520—62no—
270#520—62no—
271C2×C4×Q8—31no—
272C2×C4×Q8—31no—
273C2×C4×D4—31no—
274C2×C4×D4—61no—
275C2×C4×D4—61no—
276C2×C4×D4C2×D311yescharacteristic, complemented
277C2×#117—31no—
278C2×#117—61no—
279C22×C4⋊C4—31no—
280C22×C4⋊C4—61no—
281#464—34no—
282#464—34no—
283#464—34no—
284#464—34no—
285#463—34no—
286#463—34no—
287#463—34no—
288#463C2×D314yescomplemented
289#462—32no—
290#462—32no—
291#462—34no—
292#461—34no—
293#461—32no—
294#461C2×D312yescomplemented
295#460—32no—
296#460—32no—
297#460—34no—
298#459—34no—
299#459—32no—
300#459C2×D312yescomplemented
301#424—34no—
302#424—34no—
303#423—32no—
304#423—31no—
305#423C2×D311yescharacteristic, complemented
306#417—32no—
307#417—32no—
308#417—32no—
309#417—34no—
310#417—34no—
311#417C2×D312yescomplemented
312C2×#103—34no—
313C2×#102—34no—
314C24×C3—21no—
315C23×D3—22no—
316C23×D3C2×D411yescharacteristic
317C3×#41—24no—
318C3×#41—24no—
319C2×C3×Q8C2412yes—
320C2×C3×D4—22no—
321C2×C3×D4—21no—
322C2×C3×D4—21no—
323C2×C3×D4—21no—
324C2×C3×D4—22no—
325C2×C3×D4C2×D414yes—
326C2×C3×D4C2412yes—
327C2×C3×D4C2412yes—
328C22×C3×C4—21no—
329C22×C3×C4—22no—
330C22×C3×C4—22no—
331C22×C3×C4—22no—
332C22×C3×C4—82no—
333C22×C3×C4C2×D411yescharacteristic
334C22×C3×C4C2×D411yescharacteristic
335C22×C3×C4C2411yescharacteristic
336C2×#67—28no—
337C2×#67—24no—
338C2×#67—22no—
339C2×#67—22no—
340C2×#67—22no—
341C2×#67—22no—
342C2×#67—22no—
343C22×Dic3—21no—
344C22×Dic3—28no—
345C22×Dic3—24no—
346C22×Dic3—21no—
347C22×Dic3—22no—
348C22×Dic3—24no—
349C22×Dic3—82no—
350C22×Dic3C2×D411yescharacteristic
351C22×Dic3C2×D411yescharacteristic
352C22×Dic3C2×D411yescharacteristic
353#239—24no—
354#239—24no—
355D3×Q8—24no—
356D3×Q8—24no—
357#237—216no—
358#237—24no—
359#237—28no—
360#237—24no—
361#237—48no—
362#237C2×D4116yes—
363D3×D4—24no—
364D3×D4—24no—
365D3×D4—48no—
366#235—24no—
367#235—24no—
368#235—48no—
369C2×D12—22no—
370C2×D12—21no—
371C2×D12—21no—
372C2×D12C2412yes—
373C2×C4×D3—22no—
374C2×C4×D3—22no—
375C2×C4×D3—22no—
376C2×C4×D3—24no—
377C2×C4×D3—48no—
378C2×C4×D3—82no—
379C2×C4×D3C2×D412yes—
380C2×C4×D3C2×D414yes—
381C2×C4×D3#4114yes—
382C2×C4×D3C2412yes—
383C2×Dic6—21no—
384C2×Dic6—22no—
385C2×Dic6—22no—
386C2×Dic6C2×D414yes—
387C2×Dic6C2412yes—
388C2×Dic6C2412yes—
389C3×SD16—28no—
390C3×D8—28no—
391C3×M16—24no—
392C2×C3×C8C2414yes—
393C3×C4⋊C4—21no—
394C3×C4⋊C4—21no—
395C3×C4⋊C4—21no—
396C3×C4⋊C4C2412yes—
397C3×C22⋊C4—22no—
398C3×C22⋊C4—22no—
399C3×C22⋊C4—22no—
400C3×C22⋊C4—22no—
401C3×C42C2×D411yescharacteristic
402C3×C42C2×D411yescharacteristic
403C3×C42C2411yescharacteristic
404C3×C42C2411yescharacteristic
405#217—24no—
406#217—22no—
407#217—22no—
408#216—28no—
409#214—28no—
410#214—28no—
411#213—28no—
412(C2×D3)⋊C4—22no—
413(C2×D3)⋊C4—22no—
414(C2×D3)⋊C4—22no—
415(C2×D3)⋊C4—22no—
416(C2×D3)⋊C4C2×D412yes—
417(C2×D3)⋊C4C2×D412yes—
418(C2×D3)⋊C4C2×D412yes—
419(C2×D3)⋊C4C2×D412yes—
420C4⋊Dic3—21no—
421C4⋊Dic3—21no—
422C4⋊Dic3—21no—
423C4⋊Dic3C2412yes—
424Dic3⋊C4—22no—
425Dic3⋊C4—22no—
426Dic3⋊C4—24no—
427Dic3⋊C4—22no—
428Dic3⋊C4—22no—
429Dic3⋊C4—24no—
430Dic3⋊C4C2×D412yes—
431Dic3⋊C4C2×D412yes—
432Dic3⋊C4C2×D412yes—
433Dic3⋊C4C2×D412yes—
434C4×Dic3—22no—
435C4×Dic3—22no—
436C4×Dic3—24no—
437C4×Dic3C2×D412yes—
438C4×Dic3C2412yes—
439#208—24no—
440C2×C3⋊C8C2414yes—
441Dic12—28no—
442#204—28no—
443ΓL(1,𝔽25)—28no—
444D3×C8—28no—
445C2×#41—32no—
446C2×#41—38no—
447C2×#41—34no—
448C2×#41—32no—
449C2×#41—32no—
450C2×#41—62no—
451C2×#41—62no—
452C2×#41—64no—
453C2×#41—62no—
454C2×#41—68no—
455C2×#41—68no—
456C2×#41C22×D312yes—
457C22×Q8—32no—
458C22×Q8—31no—
459C22×D4—32no—
460C22×D4—62no—
461C22×D4—61no—
462C22×D4C22×D311yescharacteristic
463C23×C4—21no—
464C23×C4—31no—
465C23×C4—62no—
466C23×C4—61no—
467C23×C4—61no—
468C23×C4—61no—
469#137—68no—
470#137—616no—
471#137—68no—
472AGL(1,ℤ/8)—28no—
473AGL(1,ℤ/8)—616no—
474AGL(1,ℤ/8)—68no—
475#135—616no—
476#135—616no—
477C2×Q16—34no—
478C2×Q16—34no—
479C2×SD16—34no—
480C2×SD16—34no—
481C2×SD16—34no—
482C2×SD16C22×D314yes—
483C2×D8—34no—
484C2×D8C22×D314yes—
485C2×M16—32no—
486C2×M16—34no—
487C2×M16—68no—
488C2×M16C22×D312yes—
489C22×C8—34no—
490C4⋊Q8—32no—
491C4⋊Q8—31no—
492C4⋊Q8C22×D311yescharacteristic
493#127—32no—
494#127—31no—
495#127C22×D311yescharacteristic
496#124—32no—
497#124—32no—
498#124—32no—
499#124C22×D312yes—
500#123—62no—
501#123—62no—
502#123—62no—
503#123—62no—
504C22⋊Q8—62no—
505C22⋊Q8—62no—
506C22⋊Q8—62no—
507C22⋊Q8—62no—
508#121—21no—
509#121—21no—
510#121—62no—
511#121—62no—
512#121—62no—
513#121—62no—
514#121—62no—
515#121—62no—
516#121—61no—
517#121—61no—
518#120—62no—
519#120—62no—
520#120—62no—
521#120—62no—
522C4×Q8—34no—
523C4×Q8—32no—
524C4×Q8—32no—
525C4×Q8—62no—
526C4×Q8—61no—
527C4×Q8—61no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—34no—
533C4×D4—62no—
534C4×D4—62no—
535C4×D4—62no—
536C4×D4—64no—
537C4×D4—64no—
538C4×D4—64no—
539C4×D4—64no—
540C4×D4—61no—
541C4×D4—61no—
542C4×D4C22×D312yes—
543C4×D4C22×D312yes—
544#117—32no—
545#117—32no—
546#117—32no—
547#117—32no—
548#117—64no—
549#117—64no—
550C2×C4⋊C4—31no—
551C2×C4⋊C4—31no—
552C2×C4⋊C4—31no—
553C2×C4⋊C4—34no—
554C2×C4⋊C4—62no—
555C2×C4⋊C4—64no—
556C2×C4⋊C4—64no—
557C2×C4⋊C4—61no—
558C2×C4⋊C4—61no—
559C2×C4⋊C4—61no—
560C2×C4⋊C4C22×D311yescharacteristic
561C2×C22⋊C4—21no—
562C2×C22⋊C4—31no—
563C2×C22⋊C4—31no—
564C2×C22⋊C4—61no—
565C2×C42—31no—
566C2×C42—61no—
567C2×C42—61no—
568C2×C42C22×D311yescharacteristic
569C4⋊C8—34no—
570C4⋊C8—34no—
571C4⋊C8—32no—
572C4⋊C8—32no—
573C4⋊C8C22×D312yes—
574C4⋊C8C22×D312yes—
575#103—34no—
576#103—34no—
577#103—34no—
578#103C22×D314yes—
579#102—34no—
580#102—34no—
581#102—34no—
582#102C22×D314yes—
583C23×C3—24no—
584C23×C3—22no—
585C23×C3—22no—
586C23×C3—42no—
587C23×C3—42no—
588C23×C3C22×D411yescharacteristic
589C22×D3—22no—
590C22×D3—41no—
591C22×D3—41no—
592C22×D3—44no—
593C22×D3—82no—
594C22×D3—82no—
595C22×D3#12114yes—
596C22×D3C22×D412yes—
597C3×Q8—22no—
598C3×Q8—22no—
599C3×D4—24no—
600C3×D4—22no—
601C3×D4—22no—
602C3×D4—22no—
603C3×D4—44no—
604C3×D4—81no—
605C3×D4—81no—
606C3×D4C22×D414yes—
607C2×C3×C4—22no—
608C2×C3×C4—22no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—42no—
612C2×C3×C4—44no—
613C2×C3×C4—82no—
614C2×C3×C4—82no—
615C2×C3×C4C22×D411yescharacteristic
616C2×C3×C4C22×D411yescharacteristic
617C2×C3×C4C22×D411yescharacteristic
618C2×C3×C4C22×D411yescharacteristic
619C2×C3×C4C22×D411yescharacteristic
620C2×C3×C4C22×D412yes—
621C2×C3×C4C2×#4112yes—
622C2×C3×C4C2511yescharacteristic
623#67—216no—
624#67—44no—
625#67—44no—
626#67—44no—
627#67—82no—
628#67—82no—
629C2×Dic3—24no—
630C2×Dic3—22no—
631C2×Dic3—216no—
632C2×Dic3—22no—
633C2×Dic3—22no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3—42no—
637C2×Dic3—44no—
638C2×Dic3—84no—
639C2×Dic3#12114yes—
640C2×Dic3C22×D412yes—
641C2×Dic3C22×D412yes—
642C2×Dic3C22×D412yes—
643D12—22no—
644D12—22no—
645D12—44no—
646D12—81no—
647D12—81no—
648C4×D3—44no—
649C4×D3—44no—
650C4×D3—44no—
651C4×D3—84no—
652C4×D3#12118yes—
653C4×D3C22×D414yes—
654C4×D3C2×#4114yes—
655Dic6—24no—
656Dic6—22no—
657Dic6—22no—
658Dic6—22no—
659Dic6—44no—
660Dic6C22×D414yes—
661C3×C8—24no—
662C3⋊C8—24no—
663C24—21no—
664C24—31no—
665C24—62no—
666#41—24no—
667#41—24no—
668#41—316no—
669#41—68no—
670#41—616no—
671#41—64no—
672#41—64no—
673#41—64no—
674#41—64no—
675#41—64no—
676#41—64no—
677#41—128no—
678#41—128no—
679C2×Q8—34no—
680C2×Q8—32no—
681C2×Q8—32no—
682C2×Q8—62no—
683C2×Q8—64no—
684C2×Q8—64no—
685C2×Q8—61no—
686C2×Q8—62no—
687C2×Q8C23×D312yes—
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—22no—
693C2×D4—32no—
694C2×D4—62no—
695C2×D4—64no—
696C2×D4—64no—
697C2×D4—62no—
698C2×D4—62no—
699C2×D4—62no—
700C2×D4—64no—
701C2×D4—68no—
702C2×D4—62no—
703C2×D4—62no—
704C2×D4—61no—
705C2×D4—61no—
706C2×D4—128no—
707C2×D4D3×D414yes—
708C2×D4C23×D312yes—
709C2×D4C23×D312yes—
710C22×C4—21no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—31no—
715C22×C4—32no—
716C22×C4—34no—
717C22×C4—34no—
718C22×C4—32no—
719C22×C4—31no—
720C22×C4—31no—
721C22×C4—62no—
722C22×C4—62no—
723C22×C4—64no—
724C22×C4—64no—
725C22×C4—68no—
726C22×C4—62no—
727C22×C4—64no—
728C22×C4—61no—
729C22×C4—61no—
730C22×C4—62no—
731C22×C4—82no—
732C22×C4—128no—
733C22×C4—242no—
734C22×C4—242no—
735C22×C4D3×D411yescharacteristic
736C22×C4D3×D411yescharacteristic
737C22×C4C23×D311yescharacteristic
738Q16—68no—
739Q16—68no—
740SD16—28no—
741SD16—68no—
742SD16—68no—
743SD16—68no—
744D8—28no—
745D8—68no—
746M16—24no—
747M16—68no—
748M16—64no—
749C2×C8—34no—
750C2×C8—68no—
751C2×C8C23×D314yes—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—32no—
756C4⋊C4—32no—
757C4⋊C4—32no—
758C4⋊C4—32no—
759C4⋊C4—32no—
760C4⋊C4—64no—
761C4⋊C4—64no—
762C4⋊C4—62no—
763C4⋊C4—62no—
764C4⋊C4—61no—
765C4⋊C4—62no—
766C4⋊C4—62no—
767C4⋊C4—61no—
768C4⋊C4—61no—
769C4⋊C4C23×D312yes—
770C22⋊C4—22no—
771C22⋊C4—22no—
772C22⋊C4—22no—
773C22⋊C4—22no—
774C22⋊C4—32no—
775C22⋊C4—32no—
776C22⋊C4—32no—
777C22⋊C4—32no—
778C22⋊C4—62no—
779C22⋊C4—62no—
780C22⋊C4—64no—
781C22⋊C4—62no—
782C22⋊C4—62no—
783C22⋊C4—62no—
784C22⋊C4—62no—
785C42—32no—
786C42—32no—
787C42—64no—
788C42—62no—
789C42—62no—
790C42D3×D411yescharacteristic
791C42D3×D411yescharacteristic
792C42C23×D311yescharacteristic
793C42C23×D311yescharacteristic
794C22×C3—21no—
795C22×C3—21no—
796C22×C3—24no—
797C22×C3—48no—
798C22×C3—42no—
799C22×C3—42no—
800C22×C3—42no—
801C22×C3—42no—
802C22×C3—42no—
803C22×C3C2×#12112yes—
804C22×C3C23×D411yescharacteristic
805C2×D3—22no—
806C2×D3—22no—
807C2×D3—44no—
808C2×D3—42no—
809C2×D3—42no—
810C2×D3—42no—
811C2×D3—88no—
812C2×D3C2×#12114yes—
813C3×C4—21no—
814C3×C4—21no—
815C3×C4—21no—
816C3×C4—21no—
817C3×C4—42no—
818C3×C4—42no—
819C3×C4C2×#12112yes—
820C3×C4C23×D411yescharacteristic
821C3×C4C22×#4111yescharacteristic
822Dic3—22no—
823Dic3—22no—
824Dic3—24no—
825Dic3—42no—
826Dic3—42no—
827Dic3C2×#12114yes—
828C23—22no—
829C23—24no—
830C23—22no—
831C23—32no—
832C23—34no—
833C23—42no—
834C23—42no—
835C23—62no—
836C23—121no—
837C23—121no—
838C23—124no—
839C23—242no—
840C23—242no—
841C23C2×D3×D411yescharacteristic
842Q8—22no—
843Q8—22no—
844Q8—34no—
845Q8—62no—
846Q8—64no—
847Q8—62no—
848Q8—62no—
849Q8—124no—
850D4—22no—
851D4—22no—
852D4—22no—
853D4—24no—
854D4—44no—
855D4—616no—
856D4—62no—
857D4—62no—
858D4—81no—
859D4—81no—
860D4—124no—
861D4—124no—
862D4—124no—
863D4—124no—
864D4—241no—
865D4—241no—
866D4—242no—
867D4—242no—
868D4C2×D3×D414yes—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—32no—
872C2×C4—34no—
873C2×C4—34no—
874C2×C4—34no—
875C2×C4—38no—
876C2×C4—32no—
877C2×C4—32no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—42no—
881C2×C4—44no—
882C2×C4—616no—
883C2×C4—62no—
884C2×C4—64no—
885C2×C4—62no—
886C2×C4—62no—
887C2×C4—82no—
888C2×C4—82no—
889C2×C4—124no—
890C2×C4—124no—
891C2×C4—124no—
892C2×C4—121no—
893C2×C4—121no—
894C2×C4—122no—
895C2×C4—124no—
896C2×C4—244no—
897C2×C4—244no—
898C2×C4C2×D3×D411yescharacteristic
899C2×C4C2×D3×D411yescharacteristic
900C2×C4C2×D3×D411yescharacteristic
901C2×C4C2×D3×D411yescharacteristic
902C2×C4C2×D3×D412yes—
903C2×C4C2×D3×D411yescharacteristic
904C2×C4D3×#4112yes—
905C2×C4C24×D311yescharacteristic
906C8—24no—
907C8—64no—
908C2×C3—22no—
909C2×C3—44no—
910C2×C3—82no—
911C2×C3C22×#12111yescharacteristic
912C2×C3#358511yescharacteristic
913C2×C3#358611yescharacteristic
914D3—24no—
915D3—82no—
916C22—21no—
917C22—21no—
918C22—24no—
919C22—34no—
920C22—48no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—62no—
927C22—62no—
928C22—124no—
929C22—122no—
930C22—122no—
931C22—122no—
932C22—248no—
933C22D3×#12112yes—
934C22C22×D3×D411yescharacteristic
935C4—21no—
936C4—21no—
937C4—21no—
938C4—21no—
939C4—34no—
940C4—42no—
941C4—42no—
942C4—62no—
943C4—62no—
944C4—64no—
945C4—122no—
946C4—122no—
947C4D3×#12112yes—
948C4C22×D3×D411yescharacteristic
949C4C2×D3×#4111yescharacteristic
950C3#6042511yescharacteristic, complemented, Sylow
951C2—22no—
952C2—44no—
953C2—64no—
954C2—82no—
955C2—242no—
956C2C2×D3×#12111yescharacteristic
957C2#8719211yescharacteristic
958C2#8720111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3036C2
socleC22×C3C23×D4
hypercenter#3036D3
hypocenterC3#60425
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. C2×#5773C2semidirect
2. #86235C2semidirect
3. C2×#5546C2semidirect
4. C3×#3036C2semidirect
5. #83931C2semidirect
6. #83314C2semidirect
7. #82307C2semidirect
8. #80539C2semidirect
9. #80538C2semidirect
10. #80431C2semidirect
11. #80335C2semidirect
12. #79067C2semidirect
13. #79048C2semidirect
14. #78913C2semidirect
15. D3×#417C2semidirect
19. C2×C3×AGL(1,ℤ/8)C22semidirect
21. C2×C3×C4×D4C22semidirect
23. C2×#951C22semidirect
24. C2×D4×Dic3C22semidirect
25. C2×#932C22semidirect
30. C2×#915C22semidirect
32. C2×#911C22semidirect
33. C2×#909C22semidirect
35. #5724C22semidirect
36. #5715C22semidirect
37. #5675C22semidirect
38. #5674C22semidirect
47. #5546C22semidirect
48. #5546C22semidirect
50. C2×#887C22semidirect
55. C2×C4×Dic6C22semidirect
56. C3×#463C22semidirect
57. C3×#461C22semidirect
58. C3×#459C22semidirect
59. C3×#423C22semidirect
60. C3×#417C22semidirect
61. #5232C22semidirect
62. #5165C22semidirect
63. #5162C22semidirect
64. #5153C22semidirect
65. #5150C22semidirect
66. #5133C22semidirect
67. #5118C22semidirect
68. #5090C22semidirect
69. #5075C22semidirect
70. #5054C22semidirect
71. #5019C22semidirect
72. #5016C22semidirect
73. #5015C22semidirect
74. #4966C22semidirect
75. #4924C22semidirect
76. #4849C22semidirect
77. #4848C22semidirect
78. #4845C22semidirect
79. #4839C22semidirect
80. #4839C22semidirect
81. #4803C22semidirect
82. D3×#103C22semidirect
83. #4798C22semidirect
84. #4795C22semidirect
85. #4771C22semidirect
86. D3×#102C22semidirect
87. #4767C22semidirect
88. #4762C22semidirect
101. #3036D3semidirect
117. C2×#237D4semidirect
250. C2×AGL(1,ℤ/8)C2×D3semidirect
276. C2×C4×D4C2×D3semidirect
288. #463C2×D3semidirect
294. #461C2×D3semidirect
300. #459C2×D3semidirect
305. #423C2×D3semidirect
311. #417C2×D3semidirect
950. C3#60425semidirect

Maximal subgroups

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

subgroupindex
C2×#57732
#862352
C2×#55462
C3×#30362
#839312
#833142
#823072
#805392
#805382
#804312
#803352
#790672
#790482
#789132
D3×#4172
#604253