Finite Group Databasebeta

← #11681997

Subgroups — #11681997

Order 768.

2064 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#87293C211yesmaximal, characteristic, complemented
2#86350C211yesmaximal, characteristic, complemented
3C3×#3011C211yesmaximal, characteristic, complemented
4#84113C211yesmaximal, characteristic, complemented
5#83991C212yesmaximal, complemented
6#83889C212yesmaximal, complemented
7#83407C211yesmaximal, characteristic, complemented
8#80246C212yesmaximal, complemented
9#80243C212yesmaximal, complemented
10#80231C212yesmaximal, complemented
11#80212C212yesmaximal, complemented
12#80207C212yesmaximal, complemented
13#80201C212yesmaximal, complemented
14#80199C212yesmaximal, complemented
15#80191C212yesmaximal, complemented
16#78970C212yesmaximal, complemented
17#78846C212yesmaximal, complemented
18#78674C211yesmaximal, characteristic, complemented
19#78667C211yesmaximal, characteristic, complemented
20#61666—31nomaximal, Sylow
21C2×C3×2−1+4C2211yescharacteristic
22C2×#1009C2211yescharacteristic, complemented
23C2×C3×#137C2211yescharacteristic, complemented
24C22×C3×Q16C2211yescharacteristic, complemented
25C3×#536C2211yescharacteristic, complemented
26#5832—21no—
27#5832C2211yescharacteristic
28#5830—21no—
29#5830C2211yescharacteristic
30#5830C2211yescharacteristic, complemented
31#5829—22no—
32#5829—22no—
33#5829C2212yes—
34#5829C2212yescomplemented
35Dic3×#41C2211yescharacteristic, complemented
36C2×#949C2211yescharacteristic, complemented
37#5817C2212yes—
38#5817C2212yescomplemented
39#5817C2212yescomplemented
40#5816—21no—
41#5816C2211yescharacteristic, complemented
42C2×#947—21no—
43C2×#947C2211yescharacteristic, complemented
44C22×#215C2211yescharacteristic, complemented
45C2×#919C2212yes—
46C2×#914C2212yes—
47#5735—21no—
48#5734—21no—
49#5678—22no—
50#5666—21no—
51#5663—22no—
52#5659—21no—
53#5639C2212yescomplemented
54#5630C2212yescomplemented
55#5629C2212yes—
56#5624C2212yescomplemented
57#5530C2212yescomplemented
58C3×#452C2212yescomplemented
59C3×#452C2212yescomplemented
60C3×#451C2212yescomplemented
61C3×#451C2212yescomplemented
62C3×#419C2211yescharacteristic, complemented
63C3×#416C2211yescharacteristic, complemented
64C3×#408C2211yescharacteristic, complemented
65#5238C2212yes—
66#5238C2212yescomplemented
67#5234C2211yescharacteristic, complemented
68#5233C2211yescharacteristic, complemented
69#5227C2212yescomplemented
70#5227C2212yescomplemented
71#5227C2212yescomplemented
72#5225C2211yescharacteristic, complemented
73#5191C2212yescomplemented
74#5191C2212yescomplemented
75#5189C2212yescomplemented
76#5188C2212yescomplemented
77#5187C2212yescomplemented
78#5187C2212yescomplemented
79#5187C2212yescomplemented
80#5185C2212yescomplemented
81#5185C2212yescomplemented
82#5185C2212yescomplemented
83Dic3×Q16C2212yescomplemented
84#5169C2212yescomplemented
85#5165C2212yescomplemented
86Dic3×SD16C2212yescomplemented
87#5135C2212yescomplemented
88#5128C2212yescomplemented
89#5115C2212yescomplemented
90C8×#67C2212yescomplemented
91#5049C2212yescomplemented
92#5048C2212yescomplemented
93#5046C2212yescomplemented
94#5045C2212yescomplemented
95#5003C2212yescomplemented
96#4819C2212yescomplemented
97#4819C2212yescomplemented
98#4812C2212yescomplemented
99#4811C2212yescomplemented
100#4810C2212yes—
101#4807C2212yescomplemented
102#4805C2212yescomplemented
103#4803C2212yescomplemented
104#4800C2212yescomplemented
105#4800C2212yescomplemented
106#4799C2212yescomplemented
107#4788C2212yescomplemented
108#4773C2212yes—
109D3×#102C2212yescomplemented
110#4766C2212yescomplemented
111#4756C2212yescomplemented
112#4737C2212yescomplemented
113#4737C2212yescomplemented
114#4732C2212yes—
115#4732C2212yescomplemented
116#4729C2212yescomplemented
117#4727C2212yescomplemented
118#67⋊C8C2212yescomplemented
119#4718C2212yescomplemented
120#3551—31no—
121#3500—31no—
122#3327—32no—
123#3326—32no—
124#3297—32no—
125#3296—32no—
126#3285—32no—
127#3282—32no—
128#3275—32no—
129#3273—32no—
130#3211—32no—
131#3201—32no—
132#3200—31no—
133#3199—31no—
134#3102—32no—
135#3012—32no—
136#3011D311yescharacteristic, complemented
137#3010—31no—
138#2979—31no—
139C3×2−1+4—42no—
140C3×2−1+4—42no—
141C2×C3×#41—21no—
142C2×C3×#41—21no—
143C2×C3×#41—21no—
144C2×C3×#41C2311yescharacteristic
145C2×C3×#41C2311yescharacteristic
146C2×C3×#41C2311yescharacteristic
147C2×C3×#41C2311yescharacteristic
148C22×C3×Q8—21no—
149C22×C3×Q8C2311yescharacteristic
150C22×C3×Q8C2311yescharacteristic
151C22×C3×Q8C2311yescharacteristic
152C22×C3×Q8C2311yescharacteristic
153#1009—42no—
154#1009—42no—
155C2×#239C2312yes—
156C2×#239C2312yes—
157C2×D3×D4—22no—
158C2×D3×D4C2312yes—
159C2×#235—21no—
160C2×#235C2311yescharacteristic
161C22×D12—21no—
162C22×D12C2311yescharacteristic
163C22×D12C2311yescharacteristic
164C3×#137—42no—
165C2×C3×Q16—42no—
166C2×C3×Q16C2312yes—
167C2×C3×Q16C2312yes—
168C2×C3×Q16C2312yes—
169C2×C3×SD16C2312yes—
170C2×C3×M16C2311yescharacteristic
171C22×C3×C8C2311yescharacteristic
172C3×C4⋊Q8—21no—
173C3×#124—21no—
174C3×#123—21no—
175C3×#123—21no—
176C3×C22⋊Q8C2312yes—
177C3×C22⋊Q8C2312yes—
178C3×#117C2311yescharacteristic
179#949—42no—
180#947—21no—
181#947—21no—
182#947—21no—
183#947—22no—
184#947—22no—
185#947—22no—
186#947—21no—
187#947—21no—
188#947D411yescharacteristic
189#947C2312yes—
190#947C2312yes—
191#947C2312yes—
192#946—22no—
193#946—22no—
194#946—22no—
195#946C2312yes—
196#946C2312yes—
197#946C2312yes—
198Q8×Dic3C2312yes—
199Q8×Dic3C2312yes—
200#944—21no—
201#944D411yescharacteristic
202C2×#215—42no—
203C2×#215C2312yes—
204C2×#215C2312yes—
205C2×#215C2312yes—
206C2×#215C2312yes—
207C2×#215C2312yes—
208#940—21no—
209#940—21no—
210#940D411yescharacteristic
211#939—22no—
212#939—22no—
213#939D412yes—
214#939D412yes—
215#937—21no—
216#937—21no—
217#937—21no—
218#937—21no—
219#937—22no—
220#937—22no—
221#936D411yescharacteristic
222D4×Dic3—22no—
223D4×Dic3C2312yes—
224C2×#213C2312yes—
225#930—22no—
226#930—22no—
227#930—22no—
228#930C2312yes—
229#930C2312yes—
230#930C2312yes—
231#930C2312yes—
232#929—22no—
233#929—22no—
234#929—22no—
235C4×#67—22no—
236C4×#67—22no—
237C4×#67—22no—
238C4×#67C2312yes—
239C4×#67C2312yes—
240C2×(C2×D3)⋊C4—22no—
241C2×(C2×D3)⋊C4—22no—
242C2×(C2×D3)⋊C4—22no—
243#926—21no—
244#926C2311yescharacteristic
245#926C2311yescharacteristic
246C2×C4×Dic3—21no—
247C2×C4×Dic3C2311yescharacteristic
248C2×#208C2311yescharacteristic
249C22×C3⋊C8C2311yescharacteristic
250#919—44no—
251#914—44no—
252C2×D24C2312yes—
253C2×D24C2312yes—
254C2×ΓL(1,𝔽25)C2312yes—
255C2×D3×C8C2312yes—
256#898—22no—
257#896—22no—
258#895—22no—
259#895—22no—
260#895C2312yes—
261#894—22no—
262#893C2312yes—
263#892—22no—
264#892—22no—
265D3×C4⋊C4C2312yes—
266#890C2312yes—
267#889—22no—
268#886—22no—
269#884—22no—
270#884—22no—
271#884—22no—
272#883—22no—
273#883—22no—
274#882—22no—
275#67⋊C4—22no—
276D3×C22⋊C4—22no—
277#879—22no—
278#876—22no—
279C4×D12—22no—
280C3×#103C2312yes—
281C3×#103C2312yes—
282C3×#103C2312yes—
283C3×#102C2312yes—
284C3×C22⋊C8C2312yes—
285C3×C22⋊C8C2312yes—
286#835C2312yes—
287#835C2312yes—
288#835C2312yes—
289#835C2312yes—
290#835C2312yes—
291#832C2312yes—
292#830C2312yes—
293#830C2312yes—
294#821C2312yes—
295#821C2312yes—
296#821C2312yes—
297#821C2312yes—
298(C2×D3)⋊C8C2312yes—
299(C2×D3)⋊C8C2312yes—
300#818C2312yes—
301#817C2312yes—
302Dic3⋊C8C2312yes—
303Dic3⋊C8C2312yes—
304C8×Dic3C2312yes—
305C8×Dic3C2312yes—
306#809C2312yes—
307#809C2312yes—
308#808C2312yes—
309#807C2312yes—
310C2×2−1+4C2×D311yescharacteristic
311C2×H(5,𝔽2)—31no—
312C2×#137C2×D311yescharacteristic, complemented
313C2×AGL(1,ℤ/8)—31no—
314C2×AGL(1,ℤ/8)—32no—
315C2×#135—32no—
316C22×Q16C2×D311yescharacteristic, complemented
317C22×SD16—31no—
318#563—61no—
319#560—61no—
320#555—61no—
321#553—32no—
322#552—32no—
323#551—61no—
324#548—32no—
325#548—32no—
326#548—32no—
327#546—32no—
328#546—32no—
329#546—32no—
330#546—62no—
331#546—62no—
332#540—62no—
333#538—62no—
334#537—32no—
335#536—31no—
336#536—61no—
337#536C2×D311yescharacteristic, complemented
338#535—31no—
339#535—31no—
340#535—61no—
341#532—31no—
342#532—61no—
343#529—32no—
344C2×#124—31no—
345C2×#124—61no—
346C4×#41—31no—
347#495—32no—
348#495—32no—
349#488—32no—
350#488—32no—
351#485—32no—
352#484—32no—
353#483—32no—
354#482—32no—
355#482—32no—
356#482—32no—
357#479—32no—
358#478—32no—
359#470—32no—
360#469—32no—
361#468—32no—
362#468—32no—
363#467—32no—
364#466—32no—
365#465—32no—
366#465—32no—
367#464—32no—
368#464—32no—
369#464—32no—
370#463—32no—
371#463—32no—
372#463—32no—
373#452—32no—
374#452—32no—
375#452—32no—
376#452C2×D312yescomplemented
377#452C2×D312yescomplemented
378#451C2×D312yescomplemented
379#451C2×D312yescomplemented
380#450—32no—
381#450—32no—
382#449—32no—
383#449—32no—
384#449—32no—
385#448—32no—
386#448—32no—
387#448—32no—
388#447—32no—
389#447—32no—
390#447—32no—
391C4×Q16—32no—
392C4×SD16—32no—
393C4×SD16—32no—
394C4×D8—32no—
395#436—32no—
396#436—32no—
397C8×D4—32no—
398C8×D4—32no—
399#431—32no—
400#419—31no—
401#419C2×D311yescharacteristic, complemented
402#417—32no—
403#416—31no—
404#416C2×D311yescharacteristic, complemented
405C2×#102—32no—
406#408—31no—
407#408—32no—
408#408C2×D311yescharacteristic, complemented
409C23×D3—21no—
410C23×D3—21no—
411C23×D3—22no—
412C3×#41—22no—
413C3×#41—22no—
414C3×#41—22no—
415C3×#41—22no—
416C3×#41—41no—
417C3×#41—41no—
418C3×#41—41no—
419C3×#41—41no—
420C3×#41—44no—
421C3×#41—44no—
422C3×#41—44no—
423C2×C3×Q8—21no—
424C2×C3×Q8—21no—
425C2×C3×Q8—21no—
426C2×C3×Q8—21no—
427C2×C3×Q8—22no—
428C2×C3×Q8—22no—
429C2×C3×Q8—41no—
430C2×C3×Q8—41no—
431C2×C3×Q8—41no—
432C2×C3×Q8—41no—
433C2×C3×Q8—44no—
434C2×C3×Q8—41no—
435C2×C3×Q8—41no—
436C2×C3×Q8C2×D411yescharacteristic
437C2×C3×Q8C2411yescharacteristic
438C2×C3×Q8C2411yescharacteristic
439C2×C3×Q8C2412yes—
440C2×C3×Q8C2411yescharacteristic
441C2×C3×D4—21no—
442C2×C3×D4—21no—
443C2×C3×D4—21no—
444C2×C3×D4C2×D411yescharacteristic
445C2×C3×D4C2×D411yescharacteristic
446C2×C3×D4C2×D411yescharacteristic
447C2×C3×D4C2411yescharacteristic
448C22×C3×C4—21no—
449C22×C3×C4—21no—
450C22×C3×C4—21no—
451C22×C3×C4—21no—
452C22×C3×C4—21no—
453C22×C3×C4—21no—
454C22×C3×C4—21no—
455C22×C3×C4C2411yescharacteristic
456C22×C3×C4C2411yescharacteristic
457C22×C3×C4C2411yescharacteristic
458C2×#67—22no—
459C2×#67—22no—
460C2×#67—22no—
461C2×#67—22no—
462C2×#67—22no—
463C2×#67C2×D412yes—
464C2×#67C2×D412yes—
465C2×#67C2×D412yes—
466C22×Dic3—22no—
467C22×Dic3C2×D412yes—
468#239—24no—
469#239—42no—
470#239—42no—
471#239—42no—
472D3×D4—24no—
473D3×D4—42no—
474D3×D4—48no—
475#235—41no—
476#235—41no—
477#235—44no—
478C2×D12—22no—
479C2×D12—21no—
480C2×D12—22no—
481C2×D12—22no—
482C2×D12—21no—
483C2×D12—41no—
484C2×D12—41no—
485C2×D12—41no—
486C2×D12—41no—
487C2×D12—44no—
488C2×D12C2×D411yescharacteristic
489C2×D12C2412yes—
490C2×D12C2412yes—
491C2×C4×D3—22no—
492C2×C4×D3—22no—
493C2×C4×D3—22no—
494C2×C4×D3—22no—
495C2×C4×D3C2412yes—
496C2×Dic6C2×D411yescharacteristic
497C3×Q16—24no—
498C3×Q16—42no—
499C3×Q16—42no—
500C3×SD16—24no—
501C3×M16—41no—
502C2×C3×C8—41no—
503C2×C3×C8C2412yes—
504C2×C3×C8C2412yes—
505C3×C4⋊C4—22no—
506C3×C4⋊C4—22no—
507C3×C4⋊C4C2412yes—
508C3×C22⋊C4—22no—
509C3×C22⋊C4—22no—
510C3×C22⋊C4—21no—
511C3×C42—21no—
512#217—21no—
513#217—21no—
514#217—22no—
515#217C2×D412yes—
516#217C2×D412yes—
517#215—24no—
518#215—42no—
519#215—42no—
520#215—42no—
521#215—42no—
522#213—24no—
523(C2×D3)⋊C4—22no—
524(C2×D3)⋊C4—22no—
525(C2×D3)⋊C4—22no—
526(C2×D3)⋊C4—22no—
527(C2×D3)⋊C4—22no—
528(C2×D3)⋊C4—22no—
529(C2×D3)⋊C4—22no—
530(C2×D3)⋊C4—22no—
531(C2×D3)⋊C4—22no—
532(C2×D3)⋊C4—22no—
533(C2×D3)⋊C4—22no—
534(C2×D3)⋊C4—22no—
535(C2×D3)⋊C4—22no—
536(C2×D3)⋊C4—22no—
537(C2×D3)⋊C4—22no—
538(C2×D3)⋊C4C2×D412yes—
539(C2×D3)⋊C4C2×D412yes—
540C4⋊Dic3—22no—
541C4⋊Dic3—22no—
542C4⋊Dic3—22no—
543C4⋊Dic3C2412yes—
544C4⋊Dic3C2412yes—
545Dic3⋊C4—22no—
546Dic3⋊C4—22no—
547Dic3⋊C4—22no—
548Dic3⋊C4—22no—
549Dic3⋊C4—22no—
550Dic3⋊C4C2×D412yes—
551Dic3⋊C4C2×D412yes—
552C4×Dic3—21no—
553C4×Dic3—21no—
554C4×Dic3—22no—
555C4×Dic3—22no—
556C4×Dic3C2×D411yescharacteristic
557C4×Dic3C2×D411yescharacteristic
558C4×Dic3C2412yes—
559#208—41no—
560C2×C3⋊C8—41no—
561C2×C3⋊C8C2412yes—
562C2×C3⋊C8C2412yes—
563D24—42no—
564D24—42no—
565ΓL(1,𝔽25)—42no—
566D3×C8—42no—
5672−1+4—42no—
5682−1+4—42no—
569H(5,𝔽2)—122no—
570H(5,𝔽2)—122no—
571C2×#41—21no—
572C2×#41—21no—
573C2×#41—21no—
574C2×#41—31no—
575C2×#41—32no—
576C2×#41—32no—
577C2×#41—61no—
578C2×#41C22×D311yescharacteristic
579C2×#41C22×D311yescharacteristic
580C2×#41C22×D311yescharacteristic
581C2×#41C22×D311yescharacteristic
582C22×Q8—21no—
583C22×Q8C22×D311yescharacteristic
584C22×Q8C22×D311yescharacteristic
585C22×Q8C22×D311yescharacteristic
586C22×Q8C22×D311yescharacteristic
587C22×D4—32no—
588C22×D4—31no—
589C22×D4—31no—
590C22×D4—61no—
591C22×D4—62no—
592#137—42no—
593AGL(1,ℤ/8)—122no—
594AGL(1,ℤ/8)—124no—
595#135—124no—
596C2×Q16—42no—
597C2×Q16C22×D312yes—
598C2×Q16C22×D312yes—
599C2×Q16C22×D312yes—
600C2×SD16—32no—
601C2×SD16—32no—
602C2×SD16—32no—
603C2×SD16—32no—
604C2×SD16—32no—
605C2×SD16—122no—
606C2×SD16C22×D312yes—
607C2×D8—32no—
608C2×D8—32no—
609C2×D8—32no—
610C2×M16—31no—
611C2×M16—32no—
612C2×M16C22×D311yescharacteristic
613C22×C8—31no—
614C22×C8—32no—
615C22×C8C22×D311yescharacteristic
616C4⋊Q8—21no—
617C4⋊Q8—31no—
618C4⋊Q8—61no—
619#127—31no—
620#127—61no—
621#127—61no—
622#126—62no—
623#126—62no—
624#126—62no—
625#125—32no—
626#125—62no—
627#124—21no—
628#124—31no—
629#124—31no—
630#124—32no—
631#124—32no—
632#124—32no—
633#124—61no—
634#124—61no—
635#124—62no—
636#124—62no—
637#124—62no—
638#124—61no—
639#124—61no—
640#124—61no—
641#123—21no—
642#123—21no—
643#123—62no—
644#123—62no—
645#123—62no—
646#123—62no—
647#123—62no—
648#123—62no—
649#123—62no—
650C22⋊Q8—32no—
651C22⋊Q8—32no—
652C22⋊Q8—32no—
653C22⋊Q8—62no—
654C22⋊Q8—62no—
655C22⋊Q8—62no—
656C22⋊Q8—62no—
657C22⋊Q8C22×D312yes—
658C22⋊Q8C22×D312yes—
659#121—32no—
660#121—32no—
661#121—32no—
662#121—32no—
663#121—32no—
664#121—32no—
665#121—32no—
666#121—62no—
667#121—62no—
668#121—62no—
669#121—62no—
670#121—62no—
671#121—62no—
672#121—62no—
673#121—62no—
674#121—62no—
675#121—62no—
676#120—62no—
677#120—62no—
678#120—62no—
679#120—61no—
680#120—61no—
681#120—61no—
682#120—61no—
683C4×Q8—32no—
684C4×Q8—32no—
685C4×D4—32no—
686C4×D4—32no—
687C4×D4—32no—
688C4×D4—32no—
689C4×D4—62no—
690C4×D4—62no—
691C4×D4—62no—
692C4×D4—62no—
693C4×D4—62no—
694C4×D4—62no—
695#117—31no—
696#117—31no—
697#117—62no—
698#117—61no—
699#117—62no—
700#117C22×D311yescharacteristic
701C2×C4⋊C4—32no—
702C2×C22⋊C4—62no—
703C2×C22⋊C4—62no—
704C2×C22⋊C4—62no—
705C2×C22⋊C4—62no—
706C2×C42—31no—
707C2×C42—61no—
708#107—32no—
709#107—32no—
710#106—32no—
711#106—32no—
712C4⋊C8—32no—
713C4⋊C8—32no—
714#103—32no—
715#103—32no—
716#103—32no—
717#103—32no—
718#103—32no—
719#103C22×D312yes—
720#103C22×D312yes—
721#103C22×D312yes—
722#102—32no—
723#102—32no—
724#102—32no—
725#102—32no—
726#102—32no—
727#102—32no—
728#102—32no—
729#102C22×D312yes—
730C22⋊C8—32no—
731C22⋊C8—32no—
732C22⋊C8—32no—
733C22⋊C8—32no—
734C22⋊C8C22×D312yes—
735C22⋊C8C22×D312yes—
736C4×C8—32no—
737C4×C8—32no—
738C23×C3—21no—
739C23×C3C22×D411yescharacteristic
740C23×C3C22×D411yescharacteristic
741C23×C3C22×D411yescharacteristic
742C22×D3—22no—
743C22×D3—22no—
744C22×D3—44no—
745C22×D3—42no—
746C22×D3—82no—
747C22×D3—82no—
748C22×D3—81no—
749C22×D3—82no—
750C22×D3—82no—
751C22×D3C22×D412yes—
752C3×Q8—21no—
753C3×Q8—21no—
754C3×Q8—21no—
755C3×Q8—22no—
756C3×Q8—22no—
757C3×Q8—21no—
758C3×Q8—21no—
759C3×Q8—41no—
760C3×Q8—42no—
761C3×Q8—42no—
762C3×Q8—42no—
763C3×Q8—81no—
764C3×Q8H(5,𝔽2)12yes—
765C3×D4—24no—
766C3×D4—21no—
767C3×D4—41no—
768C3×D4—41no—
769C3×D4—41no—
770C3×D4—42no—
771C3×D4—42no—
772C3×D4H(5,𝔽2)12yes—
773C2×C3×C4—24no—
774C2×C3×C4—21no—
775C2×C3×C4—21no—
776C2×C3×C4—21no—
777C2×C3×C4—21no—
778C2×C3×C4—21no—
779C2×C3×C4—21no—
780C2×C3×C4—21no—
781C2×C3×C4—22no—
782C2×C3×C4—22no—
783C2×C3×C4—21no—
784C2×C3×C4—21no—
785C2×C3×C4—42no—
786C2×C3×C4—42no—
787C2×C3×C4—42no—
788C2×C3×C4—42no—
789C2×C3×C4—42no—
790C2×C3×C4—81no—
791C2×C3×C4C22×D411yescharacteristic
792C2×C3×C4C22×D411yescharacteristic
793C2×C3×C4C22×D411yescharacteristic
794C2×C3×C4C2511yescharacteristic
795#67—42no—
796#67—42no—
797#67—42no—
798#67—44no—
799#67—82no—
800#67—82no—
801#67—82no—
802#67—82no—
803C2×Dic3—22no—
804C2×Dic3—22no—
805C2×Dic3—42no—
806C2×Dic3—82no—
807C2×Dic3C22×D412yes—
808C2×Dic3C22×D412yes—
809C2×Dic3C22×D412yes—
810D12—22no—
811D12—22no—
812D12—22no—
813D12—22no—
814D12—41no—
815D12—44no—
816D12—42no—
817D12—81no—
818D12—82no—
819D12—82no—
820C4×D3—22no—
821C4×D3—22no—
822C4×D3—44no—
823C4×D3—82no—
824C4×D3—82no—
825C4×D3—82no—
826Dic6—41no—
827C3×C8—22no—
828C3×C8—22no—
829C3⋊C8—22no—
830C3⋊C8—22no—
831C24—62no—
832C24—61no—
833C24—61no—
834#41—22no—
835#41—22no—
836#41—22no—
837#41—22no—
838#41—41no—
839#41—41no—
840#41—41no—
841#41—41no—
842#41—44no—
843#41—44no—
844#41—44no—
845#41—64no—
846#41—121no—
847#41—121no—
848#41—124no—
849#41—122no—
850#41—122no—
851#41—122no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—22no—
857C2×Q8—22no—
858C2×Q8—31no—
859C2×Q8—41no—
860C2×Q8—41no—
861C2×Q8—41no—
862C2×Q8—41no—
863C2×Q8—44no—
864C2×Q8—41no—
865C2×Q8—41no—
866C2×Q8D3×D411yescharacteristic
867C2×Q8C23×D311yescharacteristic
868C2×Q8C23×D311yescharacteristic
869C2×Q8C23×D312yes—
870C2×Q8C23×D311yescharacteristic
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—32no—
875C2×D4—32no—
876C2×D4—32no—
877C2×D4—31no—
878C2×D4—32no—
879C2×D4—32no—
880C2×D4—62no—
881C2×D4—62no—
882C2×D4—62no—
883C2×D4—62no—
884C2×D4—64no—
885C2×D4—62no—
886C2×D4—62no—
887C2×D4—62no—
888C2×D4—62no—
889C2×D4—61no—
890C2×D4—61no—
891C2×D4—121no—
892C2×D4—121no—
893C2×D4—121no—
894C2×D4—121no—
895C2×D4—124no—
896C2×D4—122no—
897C2×D4—128no—
898C2×D4D3×D411yescharacteristic
899C2×D4D3×D411yescharacteristic
900C2×D4D3×D411yescharacteristic
901C2×D4C23×D311yescharacteristic
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—32no—
910C22×C4—32no—
911C22×C4—62no—
912C22×C4—62no—
913C22×C4—62no—
914C22×C4—62no—
915C22×C4—62no—
916C22×C4C23×D311yescharacteristic
917C22×C4C23×D311yescharacteristic
918C22×C4C23×D311yescharacteristic
919Q16—24no—
920Q16—42no—
921Q16—42no—
922SD16—24no—
923SD16—64no—
924SD16—122no—
925SD16—122no—
926SD16—122no—
927SD16—122no—
928D8—64no—
929D8—122no—
930D8—122no—
931M16—41no—
932M16—122no—
933M16—121no—
934C2×C8—32no—
935C2×C8—32no—
936C2×C8—41no—
937C2×C8—122no—
938C2×C8—121no—
939C2×C8C23×D312yes—
940C2×C8C23×D312yes—
941C4⋊C4—22no—
942C4⋊C4—22no—
943C4⋊C4—32no—
944C4⋊C4—32no—
945C4⋊C4—32no—
946C4⋊C4—32no—
947C4⋊C4—62no—
948C4⋊C4—62no—
949C4⋊C4—62no—
950C4⋊C4—62no—
951C4⋊C4—62no—
952C4⋊C4—62no—
953C4⋊C4—62no—
954C4⋊C4—62no—
955C4⋊C4C23×D312yes—
956C22⋊C4—22no—
957C22⋊C4—21no—
958C22⋊C4—22no—
959C22⋊C4—32no—
960C22⋊C4—32no—
961C22⋊C4—32no—
962C22⋊C4—32no—
963C22⋊C4—62no—
964C22⋊C4—62no—
965C22⋊C4—62no—
966C22⋊C4—62no—
967C22⋊C4—62no—
968C22⋊C4—62no—
969C22⋊C4—62no—
970C22⋊C4—62no—
971C22⋊C4—62no—
972C22⋊C4—62no—
973C22⋊C4—62no—
974C22⋊C4—62no—
975C22⋊C4—61no—
976C22⋊C4—61no—
977C22⋊C4—62no—
978C22⋊C4—62no—
979C22⋊C4—62no—
980C22⋊C4—62no—
981C42—21no—
982C42—31no—
983C42—31no—
984C42—32no—
985C42—62no—
986C42—62no—
987C42—61no—
988C42—61no—
989C22×C3—22no—
990C22×C3—22no—
991C22×C3—22no—
992C22×C3—21no—
993C22×C3—22no—
994C22×C3—21no—
995C22×C3—21no—
996C22×C3—42no—
997C22×C3C23×D411yescharacteristic
998C2×D3—22no—
999C2×D3—22no—
1000C2×D3—22no—
1001C2×D3—42no—
1002C2×D3—42no—
1003C2×D3—42no—
1004C2×D3—42no—
1005C2×D3—42no—
1006C2×D3—42no—
1007C2×D3—164no—
1008C2×D3—162no—
1009C2×D3—162no—
1010C3×C4—21no—
1011C3×C4—22no—
1012C3×C4—21no—
1013C3×C4—21no—
1014C3×C4—42no—
1015C3×C4—42no—
1016C3×C4—41no—
1017C3×C4—41no—
1018C3×C4C2×H(5,𝔽2)11yescharacteristic
1019C3×C4C2×H(5,𝔽2)11yescharacteristic
1020Dic3—22no—
1021Dic3—22no—
1022Dic3—22no—
1023Dic3—42no—
1024Dic3—42no—
1025C23—21no—
1026C23—32no—
1027C23—62no—
1028C23—62no—
1029C23—124no—
1030C23—122no—
1031C23—241no—
1032C23—242no—
1033C23—242no—
1034C23—242no—
1035C23—242no—
1036C23C2×D3×D411yescharacteristic
1037C23C2×D3×D411yescharacteristic
1038C23C2×D3×D411yescharacteristic
1039Q8—21no—
1040Q8—22no—
1041Q8—21no—
1042Q8—21no—
1043Q8—22no—
1044Q8—21no—
1045Q8—21no—
1046Q8—41no—
1047Q8—42no—
1048Q8—42no—
1049Q8—42no—
1050Q8—81no—
1051Q8—121no—
1052Q8#100412yes—
1053D4—24no—
1054D4—21no—
1055D4—41no—
1056D4—41no—
1057D4—41no—
1058D4—42no—
1059D4—42no—
1060D4—62no—
1061D4—62no—
1062D4—62no—
1063D4—62no—
1064D4—121no—
1065D4—124no—
1066D4—122no—
1067D4—122no—
1068D4—122no—
1069D4—122no—
1070D4—124no—
1071D4—241no—
1072D4—242no—
1073D4—242no—
1074D4—242no—
1075D4—242no—
1076D4—242no—
1077D4—242no—
1078D4#100412yes—
1079C2×C4—24no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—32no—
1092C2×C4—32no—
1093C2×C4—32no—
1094C2×C4—42no—
1095C2×C4—42no—
1096C2×C4—42no—
1097C2×C4—42no—
1098C2×C4—42no—
1099C2×C4—62no—
1100C2×C4—62no—
1101C2×C4—62no—
1102C2×C4—62no—
1103C2×C4—81no—
1104C2×C4—124no—
1105C2×C4—122no—
1106C2×C4—242no—
1107C2×C4—242no—
1108C2×C4—242no—
1109C2×C4—242no—
1110C2×C4C2×D3×D411yescharacteristic
1111C2×C4C2×D3×D411yescharacteristic
1112C2×C4C2×D3×D411yescharacteristic
1113C2×C4C24×D311yescharacteristic
1114C8—22no—
1115C8—22no—
1116C8—62no—
1117C8—62no—
1118C2×C3—41no—
1119C2×C3—41no—
1120C2×C3—42no—
1121C2×C3—41no—
1122C2×C3#348411yescharacteristic
1123C2×C3#358412yes—
1124D3—42no—
1125D3—82no—
1126D3—82no—
1127C22—21no—
1128C22—21no—
1129C22—22no—
1130C22—21no—
1131C22—22no—
1132C22—22no—
1133C22—22no—
1134C22—42no—
1135C22—62no—
1136C22—62no—
1137C22—62no—
1138C22—122no—
1139C22—122no—
1140C22—122no—
1141C22—122no—
1142C22—122no—
1143C22—122no—
1144C22—484no—
1145C22—482no—
1146C22—482no—
1147C22C22×D3×D411yescharacteristic
1148C4—21no—
1149C4—22no—
1150C4—21no—
1151C4—21no—
1152C4—41no—
1153C4—41no—
1154C4—42no—
1155C4—42no—
1156C4—62no—
1157C4—62no—
1158C4—62no—
1159C4—122no—
1160C4—122no—
1161C4C2×#100411yescharacteristic
1162C4C2×#100411yescharacteristic
1163C3#6166611yescharacteristic, complemented, Sylow
1164C2—41no—
1165C2—41no—
1166C2—41no—
1167C2—42no—
1168C2—122no—
1169C2—242no—
1170C2—242no—
1171C2#8591911yescharacteristic
1172C2#8721012yes—
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3011C2
socleC22×C3C23×D4
hypercenter#3011D3
hypocenterC3#61666
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3011

Complements

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

NH ≅ G/Ntype
1. #87293C2semidirect
2. #86350C2semidirect
3. C3×#3011C2semidirect
4. #84113C2semidirect
5. #83991C2semidirect
6. #83889C2semidirect
7. #83407C2semidirect
8. #80246C2semidirect
9. #80243C2semidirect
10. #80231C2semidirect
11. #80212C2semidirect
12. #80207C2semidirect
13. #80201C2semidirect
14. #80199C2semidirect
15. #80191C2semidirect
16. #78970C2semidirect
17. #78846C2semidirect
18. #78674C2semidirect
19. #78667C2semidirect
22. C2×#1009C22semidirect
23. C2×C3×#137C22semidirect
24. C22×C3×Q16C22semidirect
25. C3×#536C22semidirect
30. #5830C22semidirect
34. #5829C22semidirect
35. Dic3×#41C22semidirect
36. C2×#949C22semidirect
38. #5817C22semidirect
39. #5817C22semidirect
41. #5816C22semidirect
43. C2×#947C22semidirect
44. C22×#215C22semidirect
53. #5639C22semidirect
54. #5630C22semidirect
56. #5624C22semidirect
57. #5530C22semidirect
58. C3×#452C22semidirect
59. C3×#452C22semidirect
60. C3×#451C22semidirect
61. C3×#451C22semidirect
62. C3×#419C22semidirect
63. C3×#416C22semidirect
64. C3×#408C22semidirect
66. #5238C22semidirect
67. #5234C22semidirect
68. #5233C22semidirect
69. #5227C22semidirect
70. #5227C22semidirect
71. #5227C22semidirect
72. #5225C22semidirect
73. #5191C22semidirect
74. #5191C22semidirect
75. #5189C22semidirect
76. #5188C22semidirect
77. #5187C22semidirect
78. #5187C22semidirect
79. #5187C22semidirect
80. #5185C22semidirect
81. #5185C22semidirect
82. #5185C22semidirect
83. Dic3×Q16C22semidirect
84. #5169C22semidirect
85. #5165C22semidirect
86. Dic3×SD16C22semidirect
87. #5135C22semidirect
88. #5128C22semidirect
89. #5115C22semidirect
90. C8×#67C22semidirect
91. #5049C22semidirect
92. #5048C22semidirect
93. #5046C22semidirect
94. #5045C22semidirect
95. #5003C22semidirect
96. #4819C22semidirect
97. #4819C22semidirect
98. #4812C22semidirect
99. #4811C22semidirect
101. #4807C22semidirect
102. #4805C22semidirect
103. #4803C22semidirect
104. #4800C22semidirect
105. #4800C22semidirect
106. #4799C22semidirect
107. #4788C22semidirect
109. D3×#102C22semidirect
110. #4766C22semidirect
111. #4756C22semidirect
112. #4737C22semidirect
113. #4737C22semidirect
115. #4732C22semidirect
116. #4729C22semidirect
117. #4727C22semidirect
118. #67⋊C8C22semidirect
119. #4718C22semidirect
136. #3011D3semidirect
312. C2×#137C2×D3semidirect
316. C22×Q16C2×D3semidirect
337. #536C2×D3semidirect
376. #452C2×D3semidirect
377. #452C2×D3semidirect
378. #451C2×D3semidirect
379. #451C2×D3semidirect
401. #419C2×D3semidirect
404. #416C2×D3semidirect
408. #408C2×D3semidirect
1163. C3#61666semidirect

Maximal subgroups

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

subgroupindex
#872932
#863502
C3×#30112
#841132
#839912
#838892
#834072
#802462
#802432
#802312
#802122
#802072
#802012
#801992
#801912
#789702
#788462
#786742
#786672
#616663