Finite Group Databasebeta

← #11681995

Subgroups — #11681995

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#86253C211yesmaximal, characteristic, complemented
2#86244C211yesmaximal, characteristic, complemented
3C3×#2979C211yesmaximal, characteristic, complemented
4#79562C212yesmaximal, complemented
5#79561C212yesmaximal, complemented
6#79551C212yesmaximal, complemented
7#79549C212yesmaximal, complemented
8#79444C212yesmaximal, complemented
9#79441C212yesmaximal, complemented
10#79440C212yesmaximal, complemented
11#79435C212yesmaximal, complemented
12#79307C212yesmaximal, complemented
13#79299C212yesmaximal, complemented
14#78681C212yesmaximal, complemented
15#78679C211yesmaximal, characteristic, complemented
16#78678C211yesmaximal, characteristic, complemented
17#78675C211yesmaximal, characteristic, complemented
18#78674C211yesmaximal, characteristic, complemented
19#78672C212yesmaximal, complemented
20#61666—31nomaximal, Sylow
21C2×#1010C2211yescharacteristic
22C2×#1009C2211yescharacteristic, complemented
23C3×#532C2211yescharacteristic
24#5833C2212yes—
25#5830C2211yescharacteristic
26#5830C2211yescharacteristic, complemented
27#5825C2211yescharacteristic, complemented
28#5825C2211yescharacteristic, complemented
29C2×#909C2211yescharacteristic, complemented
30C2×#908C2212yes—
31C2×#908C2211yescharacteristic, complemented
32C22×Dic12C2211yescharacteristic, complemented
33C2×#904C2212yes—
34C22×#204C2211yescharacteristic, complemented
35#5735—21no—
36#5724—21no—
37#5720—21no—
38#5715—21no—
39#5679—21no—
40D3×#124—21no—
41#5670—21no—
42#5668—21no—
43#5615—22no—
44#5613—22no—
45#5610—22no—
46#5610—22no—
47#5565C2212yescomplemented
48#5552C2212yes—
49#5552C2212yescomplemented
50#5552C2212yescomplemented
51#5550C2212yes—
52#5550C2212yescomplemented
53#5550C2212yescomplemented
54#5541C2212yescomplemented
55#5479C2212yescomplemented
56C2×#875C2211yescharacteristic, complemented
57C4×#235C2211yescharacteristic, complemented
58C3×#436C2212yescomplemented
59C3×#436C2212yescomplemented
60C3×C8×D4C2212yescomplemented
61C3×C8×D4C2212yescomplemented
62C3×#431C2212yescomplemented
63C3×#408C2212yescomplemented
64C3×#408C2211yescharacteristic, complemented
65C3×#408C2211yescharacteristic, complemented
66#5137C2212yescomplemented
67#5135C2212yescomplemented
68#5134C2212yescomplemented
69#5134C2212yescomplemented
70#5133C2212yescomplemented
71#5120C2211yescharacteristic, complemented
72#5120C2211yescharacteristic, complemented
73#5116C2212yescomplemented
74#5115C2212yescomplemented
75#5114C2212yescomplemented
76#5114C2212yescomplemented
77#5113C2211yescharacteristic, complemented
78#5113C2211yescharacteristic, complemented
79C2×#821C2212yescomplemented
80#4847C2212yescomplemented
81#4845C2212yescomplemented
82#4845C2212yescomplemented
83#4845C2212yescomplemented
84#4844C2212yescomplemented
85#4844C2212yescomplemented
86#4844C2212yescomplemented
87#4829C2212yescomplemented
88#4739C2212yescomplemented
89#4739C2212yescomplemented
90#4738C2212yescomplemented
91#4738C2212yescomplemented
92#4738C2212yescomplemented
93#4737C2212yescomplemented
94#4737C2212yescomplemented
95#4737C2212yescomplemented
96#4734C2212yes—
97#4734C2212yes—
98#4734C2212yescomplemented
99#4733C2212yescomplemented
100#4733C2212yescomplemented
101#4733C2212yescomplemented
102#4733C2212yescomplemented
103#4733C2212yescomplemented
104#4732C2212yes—
105#4732C2212yes—
106#4732C2212yescomplemented
107#4731C2212yescomplemented
108#4731C2212yescomplemented
109#4723C2212yescomplemented
110#4722C2212yescomplemented
111#4721C2212yescomplemented
112C4×Dic12C2212yescomplemented
113#4697C2212yescomplemented
114#4697C2212yescomplemented
115#4696C2212yescomplemented
116#4696C2212yescomplemented
117C4×D24C2212yescomplemented
118C4×#204C2212yescomplemented
119C4×#204C2212yescomplemented
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#3011—31no—
137#3010—31no—
138#2979D311yescharacteristic, complemented
139C2×C3×#41C2311yescharacteristic
140C2×C3×#41C2311yescharacteristic
141#1010—42no—
142#1010—42no—
143#1009—42no—
144#1009—42no—
145C2×#239—21no—
146C2×D3×Q8—21no—
147C2×#237—21no—
148C2×#237—21no—
149C2×#237—21no—
150C2×D3×D4—21no—
151C2×D3×D4—22no—
152C2×#235C2311yescharacteristic
153C2×#235C2312yes—
154C2×#235C2311yescharacteristic
155C2×#235C2311yescharacteristic
156C2×#235C2312yes—
157C22×D12C2312yes—
158C22×D12C2311yescharacteristic
159C22×D12C2311yescharacteristic
160C22×Dic6C2311yescharacteristic
161C22×Dic6C2311yescharacteristic
162C22×Dic6C2311yescharacteristic
163C22×Dic6C2311yescharacteristic
164C2×C3×M16C2311yescharacteristic
165C2×C3×M16C2311yescharacteristic
166C2×C3×M16C2312yes—
167C22×C3×C8C2311yescharacteristic
168C22×C3×C8C2312yes—
169C22×C3×C8C2311yescharacteristic
170C3×C4⋊Q8D411yescharacteristic
171C3×#127D411yescharacteristic
172C3×#124D411yescharacteristic
173C3×#124D411yescharacteristic
174C3×#121D412yes—
175C3×#121D412yes—
176C3×C4×D4C2312yes—
177C3×C4×D4C2312yes—
178C2×C3×C42C2311yescharacteristic
179#947—21no—
180#947—21no—
181#946—22no—
182#944—21no—
183#944—21no—
184#940—21no—
185#940—21no—
186#939—22no—
187#939—22no—
188#939—22no—
189#939—22no—
190#939—22no—
191#939—22no—
192#938—22no—
193#937—21no—
194#937—22no—
195#937—22no—
196#937—22no—
197#937—21no—
198#937—21no—
199#937—21no—
200#936—21no—
201#936—21no—
202#935—21no—
203#935—22no—
204#935—22no—
205#935—21no—
206#930C2312yes—
207#930C2312yes—
208#930C2312yes—
209#930C2312yes—
210#930C2312yes—
211#929—22no—
212C4×#67—22no—
213C4×#67—22no—
214C2×(C2×D3)⋊C4—22no—
215#926C2311yescharacteristic
216#926C2311yescharacteristic
217#926C2311yescharacteristic
218C2×C4⋊Dic3C2312yes—
219#924C2312yes—
220#924C2312yes—
221#924C2312yes—
222#924C2312yes—
223#924C2312yes—
224#909—42no—
225#908—44no—
226#908—42no—
227C2×Dic12—42no—
228C2×Dic12C2312yes—
229C2×Dic12C2312yes—
230C2×Dic12C2312yes—
231#904—44no—
232C2×D24C2312yes—
233C2×D24C2312yes—
234C2×D24C2312yes—
235C2×#204—42no—
236C2×#204C2312yes—
237C2×#204C2312yes—
238C2×#204C2312yes—
239C2×#204C2312yes—
240C2×#204C2312yes—
241C2×#204C2312yes—
242#898—22no—
243#896—22no—
244#896—22no—
245#896—22no—
246#894—22no—
247#894—22no—
248#894—22no—
249#889—22no—
250#885—22no—
251#885—22no—
252#885—22no—
253#884—22no—
254#884—22no—
255#884—22no—
256#883—22no—
257#67⋊C4—22no—
258#67⋊C4—22no—
259#67⋊C4—22no—
260#67⋊C4—22no—
261D3×C22⋊C4—22no—
262D3×C22⋊C4—22no—
263D3×C22⋊C4—22no—
264#879—22no—
265#877—22no—
266#876—22no—
267#875—21no—
268#875—21no—
269#875C2312yes—
270#875C2312yes—
271#875C2312yes—
272C4×D12C2312yes—
273C4×D12C2312yes—
274#872—22no—
275#872—21no—
276C42×D3—21no—
277#870C2312yes—
278C4×Dic6C2312yes—
279C4×Dic6C2312yes—
280C3×C4⋊C8C2312yes—
281C3×C4⋊C8C2312yes—
282C3×C22⋊C8C2312yes—
283C3×C22⋊C8C2312yes—
284C3×C22⋊C8C2312yes—
285C3×C22⋊C8C2312yes—
286C3×C22⋊C8C2312yes—
287C3×C22⋊C8C2312yes—
288C3×C4×C8C2312yes—
289C3×C4×C8C2312yes—
290#821C2312yes—
291#821C2312yes—
292#821C2312yes—
293#821C2312yes—
294#821C2312yes—
295#821C2312yes—
296#821C2312yes—
297#821C2312yes—
298#818C2312yes—
299#818C2312yes—
300#817C2312yes—
301#817C2312yes—
302#816C2312yes—
303#816C2312yes—
304#816C2312yes—
305#816C2312yes—
306#816C2312yes—
307#816C2312yes—
308#816C2312yes—
309#816C2312yes—
310C2×2−1+4—31no—
311C2×H(5,𝔽2)—31no—
312C2×#137—31no—
313C2×AGL(1,ℤ/8)—32no—
314C2×AGL(1,ℤ/8)—31no—
315C2×#135—32no—
316C22×Q16—31no—
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—31no—
337#536—61no—
338#535—31no—
339#535—31no—
340#535—61no—
341#532—61no—
342#532C2×D311yescharacteristic
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#452—32no—
377#452—32no—
378#451—32no—
379#451—32no—
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#436C2×D312yescomplemented
396#436C2×D312yescomplemented
397C8×D4C2×D312yescomplemented
398C8×D4C2×D312yescomplemented
399#431C2×D312yescomplemented
400#419—31no—
401#419—31no—
402#417—32no—
403#416—31no—
404#416—31no—
405C2×#102—32no—
406#408C2×D311yescharacteristic, complemented
407#408C2×D311yescharacteristic, complemented
408#408C2×D312yescomplemented
409C23×D3—22no—
410C23×D3—21no—
411C23×D3—21no—
412C3×#41—41no—
413C3×#41—41no—
414C3×#41—41no—
415C3×#41—41no—
416C2×C3×Q8C2×D411yescharacteristic
417C2×C3×Q8C2×D411yescharacteristic
418C2×C3×D4C2×D412yes—
419C2×C3×D4C2×D411yescharacteristic
420C2×C3×D4C2×D411yescharacteristic
421C2×C3×D4C2×D412yes—
422C2×C3×D4C2×D411yescharacteristic
423C2×C3×D4C2×D411yescharacteristic
424C2×C3×D4C2×D412yes—
425C22×C3×C4C2×D412yes—
426C22×C3×C4C2411yescharacteristic
427C22×C3×C4C2412yes—
428C22×C3×C4C2411yescharacteristic
429C22×C3×C4C2411yescharacteristic
430C2×#67—21no—
431C2×#67—21no—
432C2×#67—21no—
433C2×#67—22no—
434C2×#67—22no—
435C2×#67—22no—
436C2×#67—22no—
437C2×#67—22no—
438C2×#67—22no—
439C2×#67—22no—
440C22×Dic3—21no—
441C22×Dic3—21no—
442C22×Dic3—21no—
443C22×Dic3—22no—
444C22×Dic3—21no—
445#239—44no—
446D3×Q8—44no—
447#237—44no—
448#237—44no—
449#237—44no—
450D3×D4—44no—
451D3×D4—48no—
452#235—22no—
453#235—22no—
454#235—22no—
455#235—22no—
456#235—24no—
457#235—42no—
458#235—41no—
459#235—41no—
460#235—42no—
461#235—42no—
462C2×D12—24no—
463C2×D12—21no—
464C2×D12—22no—
465C2×D12—21no—
466C2×D12—42no—
467C2×D12—41no—
468C2×D12—41no—
469C2×D12—41no—
470C2×D12—41no—
471C2×D12C2412yes—
472C2×D12C2412yes—
473C2×D12C2411yescharacteristic
474C2×C4×D3—21no—
475C2×C4×D3—21no—
476C2×C4×D3—21no—
477C2×C4×D3—22no—
478C2×C4×D3—22no—
479C2×C4×D3—22no—
480C2×C4×D3—22no—
481C2×Dic6—22no—
482C2×Dic6—22no—
483C2×Dic6—21no—
484C2×Dic6—21no—
485C2×Dic6—21no—
486C2×Dic6—21no—
487C2×Dic6—41no—
488C2×Dic6—41no—
489C2×Dic6—41no—
490C2×Dic6—41no—
491C2×Dic6—41no—
492C2×Dic6—41no—
493C2×Dic6C2411yescharacteristic
494C2×Dic6C2411yescharacteristic
495C2×Dic6C2412yes—
496C2×Dic6C2411yescharacteristic
497C3×M16—42no—
498C3×M16—41no—
499C3×M16—41no—
500C2×C3×C8—41no—
501C2×C3×C8—42no—
502C2×C3×C8—41no—
503C2×C3×C8C2412yes—
504C2×C3×C8C2412yes—
505C2×C3×C8C2412yes—
506C2×C3×C8C2412yes—
507C3×C4⋊C4C2×D412yes—
508C3×C4⋊C4C2×D412yes—
509C3×C22⋊C4C2×D412yes—
510C3×C22⋊C4C2×D412yes—
511C3×C22⋊C4C2×D412yes—
512C3×C22⋊C4C2×D412yes—
513C3×C42C2×D411yescharacteristic
514C3×C42C2×D411yescharacteristic
515C3×C42C2412yes—
516#217—22no—
517#217—21no—
518#217—22no—
519#217—22no—
520#217—22no—
521#217—21no—
522#217—22no—
523#217—21no—
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—
537C4⋊Dic3—22no—
538C4⋊Dic3C2412yes—
539C4⋊Dic3C2412yes—
540C4⋊Dic3C2412yes—
541Dic3⋊C4—22no—
542Dic3⋊C4—22no—
543Dic3⋊C4—22no—
544Dic3⋊C4—22no—
545Dic3⋊C4—22no—
546Dic3⋊C4—22no—
547Dic3⋊C4—22no—
548Dic3⋊C4—22no—
549Dic3⋊C4—22no—
550C4×Dic3—22no—
551C4×Dic3—22no—
552C4×Dic3—21no—
553C4×Dic3—21no—
554C4×Dic3—21no—
555Dic12—24no—
556Dic12—42no—
557Dic12—42no—
558D24—24no—
559D24—42no—
560D24—42no—
561#204—24no—
562#204—24no—
563#204—42no—
564#204—42no—
565#204—42no—
566#204—42no—
5672−1+4—122no—
5682−1+4—122no—
569H(5,𝔽2)—122no—
570H(5,𝔽2)—122no—
571C2×#41—31no—
572C2×#41—31no—
573C2×#41—31no—
574C2×#41—32no—
575C2×#41—32no—
576C2×#41—61no—
577C2×#41—61no—
578C2×#41—61no—
579C2×#41—61no—
580C2×#41C22×D311yescharacteristic
581C2×#41C22×D311yescharacteristic
582C22×Q8—31no—
583C22×Q8—31no—
584C22×Q8—31no—
585C22×Q8—31no—
586C22×Q8—61no—
587C22×D4—32no—
588C22×D4—31no—
589C22×D4—31no—
590C22×D4—61no—
591C22×D4—62no—
592#137—122no—
593AGL(1,ℤ/8)—122no—
594AGL(1,ℤ/8)—124no—
595#135—124no—
596C2×Q16—32no—
597C2×Q16—32no—
598C2×Q16—32no—
599C2×Q16—122no—
600C2×SD16—32no—
601C2×SD16—32no—
602C2×SD16—32no—
603C2×SD16—32no—
604C2×SD16—32no—
605C2×SD16—32no—
606C2×SD16—122no—
607C2×D8—32no—
608C2×D8—32no—
609C2×D8—32no—
610C2×M16C22×D312yes—
611C2×M16C22×D311yescharacteristic
612C2×M16C22×D311yescharacteristic
613C22×C8C22×D311yescharacteristic
614C22×C8C22×D311yescharacteristic
615C22×C8C22×D312yes—
616C4⋊Q8—61no—
617C4⋊Q8—61no—
618C4⋊Q8D1211yescharacteristic
619#127—61no—
620#127—61no—
621#127D1211yescharacteristic
622#126—62no—
623#126—62no—
624#126—62no—
625#125—32no—
626#125—62no—
627#124—32no—
628#124—32no—
629#124—32no—
630#124—61no—
631#124—61no—
632#124—61no—
633#124—61no—
634#124—62no—
635#124—62no—
636#124—62no—
637#124—61no—
638#124—61no—
639#124D1211yescharacteristic
640#124D1211yescharacteristic
641#123—61no—
642#123—62no—
643#123—61no—
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—32no—
654C22⋊Q8—32no—
655C22⋊Q8—62no—
656C22⋊Q8—62no—
657C22⋊Q8—62no—
658C22⋊Q8—62no—
659#121—32no—
660#121—32no—
661#121—32no—
662#121—32no—
663#121—32no—
664#121—62no—
665#121—62no—
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#121D1212yes—
675#121D1212yes—
676#120—61no—
677#120—61no—
678#120—61no—
679#120—61no—
680#120—62no—
681#120—62no—
682#120—62no—
683C4×Q8—32no—
684C4×Q8—32no—
685C4×D4—32no—
686C4×D4—32no—
687C4×D4—62no—
688C4×D4—62no—
689C4×D4—62no—
690C4×D4—62no—
691C4×D4—62no—
692C4×D4—62no—
693C4×D4C22×D312yes—
694C4×D4C22×D312yes—
695#117—31no—
696#117—31no—
697#117—31no—
698#117—62no—
699#117—61no—
700#117—62no—
701C2×C4⋊C4—32no—
702C2×C22⋊C4—62no—
703C2×C22⋊C4—62no—
704C2×C22⋊C4—62no—
705C2×C22⋊C4—62no—
706C2×C42—61no—
707C2×C42C22×D311yescharacteristic
708#107—32no—
709#107—32no—
710#106—32no—
711#106—32no—
712C4⋊C8C22×D312yes—
713C4⋊C8C22×D312yes—
714#103—32no—
715#103—32no—
716#103—32no—
717#103—32no—
718#103—32no—
719#103—32no—
720#103—32no—
721#103—32no—
722#102—32no—
723#102—32no—
724#102—32no—
725#102—32no—
726#102—32no—
727#102—32no—
728#102—32no—
729#102—32no—
730C22⋊C8C22×D312yes—
731C22⋊C8C22×D312yes—
732C22⋊C8C22×D312yes—
733C22⋊C8C22×D312yes—
734C22⋊C8C22×D312yes—
735C22⋊C8C22×D312yes—
736C4×C8C22×D312yes—
737C4×C8C22×D312yes—
738C23×C3C22×D412yes—
739C23×C3C22×D411yescharacteristic
740C23×C3C22×D411yescharacteristic
741C23×C3C22×D411yescharacteristic
742C22×D3—21no—
743C22×D3—22no—
744C22×D3—22no—
745C22×D3—44no—
746C22×D3—42no—
747C22×D3—81no—
748C22×D3—82no—
749C22×D3—82no—
750C22×D3—82no—
751C22×D3—82no—
752C3×Q8—41no—
753C3×Q8—41no—
754C3×D4—41no—
755C3×D4—42no—
756C3×D4—41no—
757C3×D4—41no—
758C3×D4—41no—
759C3×D4—42no—
760C3×D4—42no—
761C2×C3×C4—21no—
762C2×C3×C4—21no—
763C2×C3×C4—22no—
764C2×C3×C4—21no—
765C2×C3×C4—21no—
766C2×C3×C4—22no—
767C2×C3×C4—21no—
768C2×C3×C4—21no—
769C2×C3×C4—42no—
770C2×C3×C4C22×D412yes—
771C2×C3×C4C22×D411yescharacteristic
772C2×C3×C4C22×D411yescharacteristic
773C2×C3×C4C22×D411yescharacteristic
774C2×C3×C4C22×D412yes—
775C2×C3×C4C22×D412yes—
776C2×C3×C4C2511yescharacteristic
777#67—24no—
778#67—44no—
779#67—42no—
780#67—42no—
781#67—82no—
782#67—82no—
783#67—82no—
784#67—82no—
785#67—82no—
786#67—82no—
787C2×Dic3—21no—
788C2×Dic3—22no—
789C2×Dic3—22no—
790C2×Dic3—22no—
791C2×Dic3—22no—
792C2×Dic3—21no—
793C2×Dic3—21no—
794C2×Dic3—42no—
795C2×Dic3—42no—
796C2×Dic3—42no—
797C2×Dic3—81no—
798C2×Dic3—82no—
799D12—21no—
800D12—22no—
801D12—22no—
802D12—22no—
803D12—22no—
804D12—44no—
805D12—42no—
806D12—81no—
807D12H(5,𝔽2)12yes—
808C4×D3—24no—
809C4×D3—44no—
810C4×D3—42no—
811C4×D3—42no—
812C4×D3—82no—
813C4×D3—82no—
814C4×D3—82no—
815Dic6—21no—
816Dic6—22no—
817Dic6—21no—
818Dic6—21no—
819Dic6—22no—
820Dic6—21no—
821Dic6—21no—
822Dic6—42no—
823Dic6—42no—
824Dic6—42no—
825Dic6—81no—
826Dic6H(5,𝔽2)12yes—
827C3×C8—22no—
828C3×C8—22no—
829C3×C8—22no—
830C3×C8—22no—
831C24—62no—
832C24—61no—
833C24—61no—
834#41—41no—
835#41—41no—
836#41—41no—
837#41—41no—
838#41—62no—
839#41—62no—
840#41—62no—
841#41—62no—
842#41—64no—
843#41—122no—
844#41—121no—
845#41—121no—
846#41—122no—
847#41—122no—
848#41—124no—
849#41—124no—
850#41—124no—
851#41—124no—
852C2×Q8—31no—
853C2×Q8—31no—
854C2×Q8—31no—
855C2×Q8—32no—
856C2×Q8—62no—
857C2×Q8—62no—
858C2×Q8—61no—
859C2×Q8—61no—
860C2×Q8—61no—
861C2×Q8—61no—
862C2×Q8—121no—
863C2×Q8—121no—
864C2×Q8—121no—
865C2×Q8—121no—
866C2×Q8—121no—
867C2×Q8—121no—
868C2×Q8—124no—
869C2×Q8C2×D1211yescharacteristic
870C2×Q8C2×D1211yescharacteristic
871C2×D4—31no—
872C2×D4—32no—
873C2×D4—32no—
874C2×D4—64no—
875C2×D4—61no—
876C2×D4—61no—
877C2×D4—61no—
878C2×D4—62no—
879C2×D4—62no—
880C2×D4—62no—
881C2×D4—62no—
882C2×D4—62no—
883C2×D4—62no—
884C2×D4—62no—
885C2×D4—62no—
886C2×D4—61no—
887C2×D4—61no—
888C2×D4—122no—
889C2×D4—121no—
890C2×D4—121no—
891C2×D4—121no—
892C2×D4—121no—
893C2×D4—124no—
894C2×D4—128no—
895C2×D4C2×D1212yes—
896C2×D4C2×D1212yes—
897C2×D4C2×D1211yescharacteristic
898C2×D4C2×D1211yescharacteristic
899C2×D4C2×D1211yescharacteristic
900C2×D4C2×D1212yes—
901C2×D4C2×D1211yescharacteristic
902C22×C4—61no—
903C22×C4—61no—
904C22×C4—61no—
905C22×C4—61no—
906C22×C4—62no—
907C22×C4—61no—
908C22×C4—61no—
909C22×C4—61no—
910C22×C4—62no—
911C22×C4—62no—
912C22×C4—62no—
913C22×C4—62no—
914C22×C4C2×D1212yes—
915C22×C4C23×D311yescharacteristic
916C22×C4C23×D312yes—
917C22×C4C23×D311yescharacteristic
918C22×C4C23×D311yescharacteristic
919Q16—64no—
920Q16—122no—
921Q16—122no—
922SD16—64no—
923SD16—64no—
924SD16—122no—
925SD16—122no—
926SD16—122no—
927SD16—122no—
928D8—64no—
929D8—122no—
930D8—122no—
931M16—41no—
932M16—42no—
933M16—41no—
934C2×C8—41no—
935C2×C8—41no—
936C2×C8—42no—
937C2×C8C23×D312yes—
938C2×C8C23×D312yes—
939C2×C8C23×D312yes—
940C2×C8C23×D312yes—
941C4⋊C4—32no—
942C4⋊C4—32no—
943C4⋊C4—32no—
944C4⋊C4—62no—
945C4⋊C4—62no—
946C4⋊C4—62no—
947C4⋊C4—62no—
948C4⋊C4—62no—
949C4⋊C4—62no—
950C4⋊C4—62no—
951C4⋊C4—62no—
952C4⋊C4—62no—
953C4⋊C4—62no—
954C4⋊C4C2×D1212yes—
955C4⋊C4C2×D1212yes—
956C22⋊C4—62no—
957C22⋊C4—62no—
958C22⋊C4—62no—
959C22⋊C4—61no—
960C22⋊C4—61no—
961C22⋊C4—61no—
962C22⋊C4—62no—
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—62no—
976C22⋊C4—62no—
977C22⋊C4C2×D1212yes—
978C22⋊C4C2×D1212yes—
979C22⋊C4C2×D1212yes—
980C22⋊C4C2×D1212yes—
981C42—61no—
982C42—62no—
983C42—61no—
984C42—61no—
985C42—62no—
986C42C2×D1211yescharacteristic
987C42C2×D1211yescharacteristic
988C42C23×D312yes—
989C22×C3—22no—
990C22×C3—22no—
991C22×C3—22no—
992C22×C3—22no—
993C22×C3—22no—
994C22×C3—21no—
995C22×C3—21no—
996C22×C3—21no—
997C22×C3—22no—
998C22×C3C23×D411yescharacteristic
999C2×D3—22no—
1000C2×D3—42no—
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—22no—
1011C3×C4—22no—
1012C3×C4—21no—
1013C3×C4—21no—
1014C3×C4—21no—
1015C3×C4—22no—
1016C3×C4C2×H(5,𝔽2)11yescharacteristic
1017C3×C4C2×H(5,𝔽2)11yescharacteristic
1018Dic3—22no—
1019Dic3—42no—
1020Dic3—42no—
1021Dic3—42no—
1022Dic3—41no—
1023Dic3—41no—
1024Dic3—42no—
1025C23—61no—
1026C23—62no—
1027C23—62no—
1028C23—124no—
1029C23—122no—
1030C23—241no—
1031C23—242no—
1032C23—242no—
1033C23—242no—
1034C23—242no—
1035C23C22×D1211yescharacteristic
1036C23C22×D1212yes—
1037C23C22×D1211yescharacteristic
1038C23C22×D1211yescharacteristic
1039Q8—32no—
1040Q8—41no—
1041Q8—41no—
1042Q8—61no—
1043Q8—62no—
1044Q8—61no—
1045Q8—61no—
1046Q8—62no—
1047Q8—61no—
1048Q8—61no—
1049Q8—122no—
1050Q8—122no—
1051Q8—122no—
1052Q8—241no—
1053D4—32no—
1054D4—41no—
1055D4—42no—
1056D4—41no—
1057D4—41no—
1058D4—41no—
1059D4—42no—
1060D4—42no—
1061D4—64no—
1062D4—61no—
1063D4—62no—
1064D4—62no—
1065D4—62no—
1066D4—62no—
1067D4—124no—
1068D4—122no—
1069D4—124no—
1070D4—122no—
1071D4—122no—
1072D4—241no—
1073D4—242no—
1074D4—242no—
1075D4—242no—
1076D4—242no—
1077D4—242no—
1078D4—242no—
1079C2×C4—21no—
1080C2×C4—22no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—42no—
1088C2×C4—64no—
1089C2×C4—61no—
1090C2×C4—62no—
1091C2×C4—62no—
1092C2×C4—62no—
1093C2×C4—62no—
1094C2×C4—61no—
1095C2×C4—61no—
1096C2×C4—124no—
1097C2×C4—122no—
1098C2×C4—122no—
1099C2×C4—122no—
1100C2×C4—122no—
1101C2×C4—122no—
1102C2×C4—242no—
1103C2×C4—242no—
1104C2×C4—242no—
1105C2×C4—241no—
1106C2×C4—242no—
1107C2×C4C22×D1212yes—
1108C2×C4C22×D1211yescharacteristic
1109C2×C4C22×D1211yescharacteristic
1110C2×C4C22×D1211yescharacteristic
1111C2×C4C22×D1212yes—
1112C2×C4C22×D1212yes—
1113C2×C4C24×D311yescharacteristic
1114C8—22no—
1115C8—22no—
1116C8—22no—
1117C8—22no—
1118C2×C3—42no—
1119C2×C3—41no—
1120C2×C3—41no—
1121C2×C3—41no—
1122C2×C3#348411yescharacteristic
1123C2×C3#358412yes—
1124D3—42no—
1125D3—82no—
1126D3—82no—
1127C22—21no—
1128C22—21no—
1129C22—21no—
1130C22—22no—
1131C22—22no—
1132C22—22no—
1133C22—22no—
1134C22—22no—
1135C22—22no—
1136C22—62no—
1137C22—122no—
1138C22—122no—
1139C22—122no—
1140C22—122no—
1141C22—122no—
1142C22—122no—
1143C22—122no—
1144C22—484no—
1145C22—482no—
1146C22—482no—
1147C22C23×D1211yescharacteristic
1148C4—21no—
1149C4—22no—
1150C4—21no—
1151C4—21no—
1152C4—22no—
1153C4—22no—
1154C4—62no—
1155C4—121no—
1156C4—121no—
1157C4—122no—
1158C4—122no—
1159C4—122no—
1160C4—122no—
1161C4D3×H(5,𝔽2)11yescharacteristic
1162C4D3×H(5,𝔽2)11yescharacteristic
1163C3#6166611yescharacteristic, complemented, Sylow
1164C2—41no—
1165C2—41no—
1166C2—42no—
1167C2—41no—
1168C2—122no—
1169C2—242no—
1170C2—242no—
1171C2#8586711yescharacteristic
1172C2#8716312yes—
subgroupG/H
centerC22C23×D12
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#2979C2
socleC22×C3C23×D4
hypercenter#2979D3
hypocenterC3#61666
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #532 ◁ #2979

Complements

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

NH ≅ G/Ntype
1. #86253C2semidirect
2. #86244C2semidirect
3. C3×#2979C2semidirect
4. #79562C2semidirect
5. #79561C2semidirect
6. #79551C2semidirect
7. #79549C2semidirect
8. #79444C2semidirect
9. #79441C2semidirect
10. #79440C2semidirect
11. #79435C2semidirect
12. #79307C2semidirect
13. #79299C2semidirect
14. #78681C2semidirect
15. #78679C2semidirect
16. #78678C2semidirect
17. #78675C2semidirect
18. #78674C2semidirect
19. #78672C2semidirect
22. C2×#1009C22semidirect
26. #5830C22semidirect
27. #5825C22semidirect
28. #5825C22semidirect
29. C2×#909C22semidirect
31. C2×#908C22semidirect
32. C22×Dic12C22semidirect
34. C22×#204C22semidirect
47. #5565C22semidirect
49. #5552C22semidirect
50. #5552C22semidirect
52. #5550C22semidirect
53. #5550C22semidirect
54. #5541C22semidirect
55. #5479C22semidirect
56. C2×#875C22semidirect
57. C4×#235C22semidirect
58. C3×#436C22semidirect
59. C3×#436C22semidirect
60. C3×C8×D4C22semidirect
61. C3×C8×D4C22semidirect
62. C3×#431C22semidirect
63. C3×#408C22semidirect
64. C3×#408C22semidirect
65. C3×#408C22semidirect
66. #5137C22semidirect
67. #5135C22semidirect
68. #5134C22semidirect
69. #5134C22semidirect
70. #5133C22semidirect
71. #5120C22semidirect
72. #5120C22semidirect
73. #5116C22semidirect
74. #5115C22semidirect
75. #5114C22semidirect
76. #5114C22semidirect
77. #5113C22semidirect
78. #5113C22semidirect
79. C2×#821C22semidirect
80. #4847C22semidirect
81. #4845C22semidirect
82. #4845C22semidirect
83. #4845C22semidirect
84. #4844C22semidirect
85. #4844C22semidirect
86. #4844C22semidirect
87. #4829C22semidirect
88. #4739C22semidirect
89. #4739C22semidirect
90. #4738C22semidirect
91. #4738C22semidirect
92. #4738C22semidirect
93. #4737C22semidirect
94. #4737C22semidirect
95. #4737C22semidirect
98. #4734C22semidirect
99. #4733C22semidirect
100. #4733C22semidirect
101. #4733C22semidirect
102. #4733C22semidirect
103. #4733C22semidirect
106. #4732C22semidirect
107. #4731C22semidirect
108. #4731C22semidirect
109. #4723C22semidirect
110. #4722C22semidirect
111. #4721C22semidirect
112. C4×Dic12C22semidirect
113. #4697C22semidirect
114. #4697C22semidirect
115. #4696C22semidirect
116. #4696C22semidirect
117. C4×D24C22semidirect
118. C4×#204C22semidirect
119. C4×#204C22semidirect
138. #2979D3semidirect
395. #436C2×D3semidirect
396. #436C2×D3semidirect
397. C8×D4C2×D3semidirect
398. C8×D4C2×D3semidirect
399. #431C2×D3semidirect
406. #408C2×D3semidirect
407. #408C2×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
#862532
#862442
C3×#29792
#795622
#795612
#795512
#795492
#794442
#794412
#794402
#794352
#793072
#792992
#786812
#786792
#786782
#786752
#786742
#786722
#616663