Finite Group Databasebeta

← #11886867

Subgroups — #11886867

Order 1152.

1049 conjugacy classes of subgroups.

The subgroup lattice has 1003 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596308C211yesmaximal, characteristic, complemented
2C3×#5837C211yesmaximal, characteristic, complemented
3#10595473C211yesmaximal, characteristic, complemented
4#10595464C211yesmaximal, characteristic, complemented
5C3×#5246C211yesmaximal, characteristic, complemented
6#10591681C211yesmaximal, characteristic, complemented
7#10591680C211yesmaximal, characteristic, complemented
8#10591675C211yesmaximal, characteristic, complemented
9#10591667C211yesmaximal, characteristic, complemented
10#10591666C211yesmaximal, characteristic, complemented
11#10591662C211yesmaximal, characteristic, complemented
12#10591661C211yesmaximal, characteristic, complemented
13#10591643C211yesmaximal, characteristic, complemented
14#10591618C211yesmaximal, characteristic, complemented
15#10591542C211yesmaximal, characteristic, complemented
16#84014—31nomaximal
17#80302—31nomaximal
18C32×2−1+4C2211yescharacteristic
19#64366C2211yescharacteristic, complemented
20C3×#1009C2211yescharacteristic, complemented
21#64297C2211yescharacteristic
22#64159—21no—
23#64159C2211yescharacteristic
24#64158—21no—
25#64158C2211yescharacteristic
26#64157C2211yescharacteristic, complemented
27#64151—21no—
28#64151C2211yescharacteristic, complemented
29C2×#3755—21no—
30C2×#3755C2211yescharacteristic, complemented
31C3×#951C2211yescharacteristic, complemented
32C3×#951C2211yescharacteristic, complemented
33C3×#950—21no—
34C3×#950C2211yescharacteristic
35C3×#949—21no—
36C3×#949C2211yescharacteristic
37C3×#948C2211yescharacteristic, complemented
38C3×#944C2211yescharacteristic, complemented
39C3×#942—21no—
40C3×#942C2211yescharacteristic, complemented
41C2×C3×#215—21no—
42C2×C3×#215C2211yescharacteristic, complemented
43#63950—21no—
44#63949—21no—
45#63945—21no—
46#63943—21no—
47#63937—21no—
48#63934—21no—
49#63930—21no—
50D3×#214—21no—
51#63911C2211yescharacteristic
52C2×#3717C2211yescharacteristic, complemented
53#63830C2211yescharacteristic
54C2×#3715C2211yescharacteristic, complemented
55#63825C2211yescharacteristic
56#63817C2211yescharacteristic, complemented
57#63815C2211yescharacteristic, complemented
58C3×#837C2211yescharacteristic, complemented
59C3×#837C2211yescharacteristic, complemented
60C3×#836C2211yescharacteristic, complemented
61#63578C2211yescharacteristic, complemented
62#63577C2211yescharacteristic, complemented
63#63570C2211yescharacteristic, complemented
64#63569C2211yescharacteristic, complemented
65#63560C2211yescharacteristic, complemented
66#63559C2211yescharacteristic, complemented
67#63558C2211yescharacteristic, complemented
68Dic3×C3⋊C8C2211yescharacteristic, complemented
69C3×#577—31no—
70#5837—31no—
71#5837—31no—
72#5837—61no—
73#5837D311yescharacteristic, complemented
74#5836—31no—
75#5778—31no—
76#5778—31no—
77#5770—31no—
78C3×#456—31no—
79#5246D311yescharacteristic, complemented
80#5241—31no—
81#5205—31no—
82#5203—31no—
83#5203—31no—
84#5203—31no—
85#5200—31no—
86#5198—31no—
87#5196—31no—
88#5177—31no—
89#5175—31no—
90#5144—31no—
91#5141—31no—
92#5095—31no—
93#5085—31no—
94#4824—31no—
95#4824—31no—
96#4822—31no—
97#4822—31no—
98#4754—31no—
99#4754—31no—
100C32×#41—21no—
101C32×#41—21no—
102C32×#41—41no—
103C32×#41C2311yescharacteristic
104C32×#41C2311yescharacteristic
105C2×C32×Q8—21no—
106C2×C32×Q8—21no—
107C2×C32×Q8C2311yescharacteristic
108#3832—21no—
109D4×C3⋊D3—21no—
110D4×C3⋊D3—41no—
111#3828—21no—
112#3828C2311yescharacteristic
113C2×C4⋊(C3⋊D3)—21no—
114C2×C4⋊(C3⋊D3)C2311yescharacteristic
115C3×#239—21no—
116C3×D3×D4—21no—
117C3×D3×D4—41no—
118C3×#235—21no—
119C3×#235C2311yescharacteristic
120C2×C3×D12—21no—
121C2×C3×D12C2311yescharacteristic
122C2×C3×Dic6C2311yescharacteristic
123C2×#626—41no—
124#3804—41no—
125#3799—21no—
126#3797—21no—
127#3796—21no—
128D3×Dic6—21no—
129#3756—21no—
130#3756D411yescharacteristic, complemented
131#3755—21no—
132#3755—21no—
133#3755—21no—
134#3755—21no—
135#3755D411yescharacteristic, complemented
136#3754D411yescharacteristic, complemented
137#3753—21no—
138#3753D411yescharacteristic, complemented
139#3748—21no—
140#3748C2311yescharacteristic
141C2×C3⋊(C3⋊C8)—21no—
142C2×C3⋊(C3⋊C8)C2311yescharacteristic
143C3×#216—21no—
144C3×#216—21no—
145C3×#216—21no—
146C3×#216D411yescharacteristic, complemented
147C3×#215—21no—
148C3×#215—21no—
149C3×#215—21no—
150C3×#215—21no—
151C3×#215D411yescharacteristic, complemented
152C3×#214—21no—
153C3×#214—21no—
154C3×#214D411yescharacteristic, complemented
155C3×#213—21no—
156C3×#213D411yescharacteristic, complemented
157C3×Dic3⋊C4—41no—
158C3×C4×Dic3C2311yescharacteristic
159C3×#208—21no—
160C3×#208C2311yescharacteristic
161C3×#208C2311yescharacteristic
162C3×#208C2311yescharacteristic
163C2×C3×C3⋊C8—21no—
164C2×C3×C3⋊C8C2311yescharacteristic
165#3717—21no—
166#3717—21no—
167#3717—21no—
168#3716—21no—
169#3715—21no—
170#3715—21no—
171#3714—21no—
172#3714—21no—
173#3712—21no—
174#3711—21no—
175#3710—21no—
176D3×C3⋊C8—21no—
177#3291—91noSylow
178C3×2−1+4—21no—
179C3×2−1+4C2×D311yescharacteristic
180C3×2−1+4C2×D311yescharacteristic
181C3×H(5,𝔽2)—31no—
182#1010—31no—
183#1009—31no—
184#1009—31no—
185#1009—61no—
186#1009C2×D311yescharacteristic, complemented
187#1007—31no—
188C3×#137—31no—
189C3×#137—31no—
190C3×#137—31no—
191C3×#137—61no—
192C3×AGL(1,ℤ/8)—31no—
193C3×AGL(1,ℤ/8)—61no—
194C3×#135—31no—
195C3×#135—61no—
196C2×C3×SD16—31no—
197C2×C3×SD16—61no—
198C3×#131—31no—
199C3×C4⋊Q8—31no—
200#951—61no—
201#951C2×D311yescharacteristic, complemented
202#951C2×D311yescharacteristic, complemented
203#950—21no—
204#950—31no—
205#950—31no—
206#950—61no—
207#950—61no—
208#950—61no—
209#950—61no—
210#950—62no—
211#950C2×D311yescharacteristic
212#949—21no—
213#949—31no—
214#949—31no—
215#949—31no—
216#949—61no—
217#949—61no—
218#949—61no—
219#949—62no—
220#949C2×D311yescharacteristic
221#948—31no—
222#948—31no—
223#948—31no—
224#948—61no—
225#948C2×D311yescharacteristic, complemented
226#944C2×D311yescharacteristic, complemented
227#942—21no—
228#942—31no—
229#942—31no—
230#942—61no—
231#942—61no—
232#942—61no—
233#942—62no—
234#942C2×D311yescharacteristic, complemented
235C2×#215—21no—
236C2×#215—31no—
237C2×#215—31no—
238C2×#215—31no—
239C2×#215—31no—
240C2×#215—61no—
241C2×#215—61no—
242C2×#215—61no—
243C2×#215—62no—
244C2×#215C2×D311yescharacteristic, complemented
245#940—31no—
246C2×#214—31no—
247C2×#214—61no—
248#932—31no—
249#932—61no—
250#919—61no—
251#919—61no—
252#918—61no—
253#918—61no—
254#918—61no—
255#916—61no—
256#914—61no—
257#914—61no—
258D3×SD16—61no—
259D3×SD16—61no—
260D3×SD16—61no—
261#911—61no—
262#908—31no—
263#908—31no—
264#907—31no—
265#907—31no—
266C2×#204—31no—
267#901—31no—
268#874—31no—
269C3×#104—31no—
270C3×#104—31no—
271C3×#101—31no—
272#837—31no—
273#837C2×D311yescharacteristic, complemented
274#837C2×D311yescharacteristic, complemented
275#836—31no—
276#836C2×D311yescharacteristic, complemented
277#833—31no—
278#825—31no—
279#824—31no—
280#823—31no—
281#823—31no—
282#823—31no—
283#822—31no—
284#822—31no—
285#822—31no—
286#819—31no—
287C8×Dic3—31no—
288#805—31no—
289#805—31no—
290C4×C3⋊C8—31no—
291C22×C3⋊D3—21no—
292C22×C3⋊D3—41no—
293C22×C3×D3—21no—
294C22×C3×D3—41no—
295C32×Q8—21no—
296C32×Q8—21no—
297C32×Q8—41no—
298C32×Q8C2×D411yescharacteristic
299C32×Q8C2×D411yescharacteristic
300C32×D4—21no—
301C32×D4—21no—
302C32×D4—41no—
303C32×D4C2×D411yescharacteristic
304C32×D4C2×D411yescharacteristic
305C2×C32×C4—21no—
306C2×C32×C4—21no—
307C2×C32×C4—21no—
308C2×C32×C4—41no—
309C2×C32×C4—41no—
310C2×C32×C4C2411yescharacteristic
311#638—21no—
312#638—41no—
313C4⋊(C3⋊D3)—21no—
314C4⋊(C3⋊D3)—21no—
315C4⋊(C3⋊D3)—41no—
316C4⋊(C3⋊D3)C2×D411yescharacteristic
317C4×C3⋊D3—21no—
318C4×C3⋊D3—41no—
319#634C2×D411yescharacteristic
320C3×#67—21no—
321C3×#67—41no—
322C2×C3×Dic3—21no—
323C2×C3×Dic3—21no—
324C3×D12—21no—
325C3×D12—21no—
326C3×D12—41no—
327C3×D12C2×D411yescharacteristic
328C3×C4×D3—21no—
329C3×C4×D3—41no—
330C3×Dic6—21no—
331C3×Dic6—21no—
332C3×Dic6C2×D411yescharacteristic
333#627—41no—
334#626—41no—
335#626—82no—
336#624—41no—
337D3×Dic3—41no—
338C3⋊(C3⋊C8)—21no—
339C3⋊(C3⋊C8)C2×D411yescharacteristic
340C3⋊(C3⋊C8)C2×D411yescharacteristic
341C3×C3⋊C8—21no—
342C3×C3⋊C8—21no—
343C3×C3⋊C8—21no—
344C3×C3⋊C8C2×D411yescharacteristic
345C3×C3⋊C8C2×D411yescharacteristic
346#577—31no—
347#577—91no—
348#577—91no—
349#577—91no—
350#492—91no—
351#471—91no—
352#471—91no—
353#471—91no—
354#471—91no—
355#456—31no—
356#456—91no—
357#453—91no—
358#453—91no—
359#443—91no—
360#443—91no—
361C3×#41—22no—
362C3×#41—21no—
363C3×#41—21no—
364C3×#41—21no—
365C3×#41—21no—
366C3×#41—21no—
367C3×#41—21no—
368C3×#41—31no—
369C3×#41—41no—
370C3×#41—41no—
371C3×#41—41no—
372C3×#41—42no—
373C3×#41—61no—
374C3×#41—61no—
375C3×#41C22×D311yescharacteristic
376C3×#41C22×D311yescharacteristic
377C3×#41C22×D311yescharacteristic
378C3×#41C22×D311yescharacteristic
379C2×C3×Q8—22no—
380C2×C3×Q8—21no—
381C2×C3×Q8—21no—
382C2×C3×Q8—21no—
383C2×C3×Q8—21no—
384C2×C3×Q8—21no—
385C2×C3×Q8—31no—
386C2×C3×Q8—41no—
387C2×C3×Q8C22×D311yescharacteristic
388C2×C3×Q8C22×D311yescharacteristic
389C2×C3×D4—31no—
390C2×C3×D4—61no—
391C2×C3×D4—61no—
392C2×C3×D4—121no—
393C2×#67—121no—
394#239—21no—
395#239—61no—
396#239—61no—
397#239—61no—
398#239—61no—
399#239—121no—
400D3×Q8—61no—
401D3×Q8—61no—
402D3×Q8—61no—
403#237—61no—
404#237—121no—
405D3×D4—21no—
406D3×D4—41no—
407D3×D4—61no—
408D3×D4—61no—
409D3×D4—121no—
410D3×D4—121no—
411D3×D4—121no—
412D3×D4—122no—
413#235—21no—
414#235—31no—
415#235—31no—
416#235—61no—
417#235—61no—
418#235—61no—
419#235—61no—
420#235—62no—
421#235—121no—
422#235C22×D311yescharacteristic
423C2×D12—21no—
424C2×D12—31no—
425C2×D12—31no—
426C2×D12—61no—
427C2×D12—61no—
428C2×D12—61no—
429C2×D12—62no—
430C2×D12—121no—
431C2×D12C22×D311yescharacteristic
432C2×Dic6—61no—
433C2×Dic6C22×D311yescharacteristic
434C3×Q16—31no—
435C3×Q16—61no—
436C3×Q16—61no—
437C3×Q16—61no—
438C3×SD16—31no—
439C3×SD16—31no—
440C3×SD16—61no—
441C3×SD16—61no—
442C3×SD16—61no—
443C3×SD16—61no—
444C3×SD16—61no—
445C3×SD16—61no—
446C3×D8—31no—
447C3×D8—61no—
448C3×M16—31no—
449C3×M16—31no—
450C3×M16—31no—
451C3×M16—61no—
452C2×C3×C8—31no—
453C2×C3×C8—61no—
454C3×C4⋊C4—121no—
455C3×C42—31no—
456#216—21no—
457#216—21no—
458#216—21no—
459#216—31no—
460#216—31no—
461#216—61no—
462#216—61no—
463#216—61no—
464#216—62no—
465#216#6711yescharacteristic, complemented
466#215—21no—
467#215—21no—
468#215—21no—
469#215—21no—
470#215—31no—
471#215—31no—
472#215—61no—
473#215—61no—
474#215—61no—
475#215—61no—
476#215—61no—
477#215—61no—
478#215—61no—
479#215—61no—
480#215—61no—
481#215—61no—
482#215—62no—
483#215—62no—
484#215—62no—
485#215—62no—
486#215—61no—
487#215—61no—
488#215—61no—
489#215—61no—
490#215#6711yescharacteristic, complemented
491#214—21no—
492#214—21no—
493#214—31no—
494#214—31no—
495#214—61no—
496#214—61no—
497#214—61no—
498#214—61no—
499#214#6711yescharacteristic, complemented
500#213—21no—
501#213—31no—
502#213—31no—
503#213—61no—
504#213—61no—
505#213—61no—
506#213—62no—
507#213—61no—
508#213—61no—
509#213#6711yescharacteristic, complemented
510Dic3⋊C4—41no—
511C4×Dic3C22×D311yescharacteristic
512#208—21no—
513#208—31no—
514#208—31no—
515#208—61no—
516#208—61no—
517#208—61no—
518#208—61no—
519#208—62no—
520#208C22×D311yescharacteristic
521#208C22×D311yescharacteristic
522#208C22×D311yescharacteristic
523C2×C3⋊C8—21no—
524C2×C3⋊C8—31no—
525C2×C3⋊C8—31no—
526C2×C3⋊C8—61no—
527C2×C3⋊C8—61no—
528C2×C3⋊C8—61no—
529C2×C3⋊C8—61no—
530C2×C3⋊C8—62no—
531C2×C3⋊C8C22×D311yescharacteristic
532D24—61no—
533D24—61no—
534#204—61no—
535#204—61no—
536#204—61no—
537#204—61no—
538ΓL(1,𝔽25)—61no—
539ΓL(1,𝔽25)—61no—
540ΓL(1,𝔽25)—61no—
541D3×C8—61no—
542D3×C8—61no—
543D3×C8—61no—
544C22×C32—21no—
545C22×C32—21no—
546C22×C32H(5,𝔽2)11yescharacteristic
547C2×C3⋊D3—21no—
548C2×C3⋊D3—41no—
549C2×C3⋊D3—81no—
550C2×C3⋊D3—161no—
551C2×C3×D3—21no—
552C2×C3×D3—41no—
553C2×C3×D3—81no—
554C2×C3×D3—161no—
555C32×C4—21no—
556C32×C4—21no—
557C32×C4—41no—
558C32×C4C22×D411yescharacteristic
559C32×C4C22×D411yescharacteristic
560C3⋊Dic3—21no—
561C3×Dic3—22no—
562C3×Dic3—21no—
563C3×Dic3—41no—
5642−1+4—91no—
5652−1+4D3211yescharacteristic
566H(5,𝔽2)—31no—
567H(5,𝔽2)—91no—
568#137—31no—
569#137—31no—
570#137—31no—
571#137—61no—
572#137—91no—
573#137—181no—
574#137—181no—
575#137—181no—
576AGL(1,ℤ/8)—31no—
577AGL(1,ℤ/8)—61no—
578AGL(1,ℤ/8)—91no—
579AGL(1,ℤ/8)—91no—
580AGL(1,ℤ/8)—91no—
581AGL(1,ℤ/8)—181no—
582AGL(1,ℤ/8)—181no—
583AGL(1,ℤ/8)—181no—
584#135—31no—
585#135—61no—
586#135—91no—
587#135—181no—
588#135—181no—
589#135—181no—
590C2×SD16—31no—
591C2×SD16—61no—
592C2×SD16—91no—
593C2×SD16—91no—
594C2×SD16—91no—
595C2×SD16—181no—
596C2×SD16—181no—
597C2×SD16—181no—
598#131—31no—
599#131—91no—
600#131—91no—
601#131—91no—
602C4⋊Q8—31no—
603#127—91no—
604#108—91no—
605#108—91no—
606#104—31no—
607#104—31no—
608#104—91no—
609#104—91no—
610#101—31no—
611#101—91no—
612#100—91no—
613#100—91no—
614C4×C8—91no—
615C23×C3—61no—
616C23×C3—121no—
617C22×D3—21no—
618C22×D3—41no—
619C22×D3—61no—
620C22×D3—61no—
621C22×D3—121no—
622C22×D3—121no—
623C22×D3—121no—
624C22×D3—122no—
625C3×Q8—22no—
626C3×Q8—21no—
627C3×Q8—21no—
628C3×Q8—21no—
629C3×Q8—21no—
630C3×Q8—21no—
631C3×Q8—21no—
632C3×Q8—31no—
633C3×Q8—41no—
634C3×Q8—41no—
635C3×Q8—41no—
636C3×Q8—42no—
637C3×Q8—61no—
638C3×Q8—61no—
639C3×Q8D3×D411yescharacteristic
640C3×Q8D3×D411yescharacteristic
641C3×Q8D3×D411yescharacteristic
642C3×Q8C2×#6711yescharacteristic
643C3×D4—22no—
644C3×D4—21no—
645C3×D4—21no—
646C3×D4—21no—
647C3×D4—21no—
648C3×D4—21no—
649C3×D4—21no—
650C3×D4—31no—
651C3×D4—41no—
652C3×D4—41no—
653C3×D4—41no—
654C3×D4—42no—
655C3×D4—61no—
656C3×D4—61no—
657C3×D4—61no—
658C3×D4—121no—
659C3×D4—121no—
660C3×D4D3×D411yescharacteristic
661C3×D4D3×D411yescharacteristic
662C3×D4D3×D411yescharacteristic
663C3×D4C2×#6711yescharacteristic
664C2×C3×C4—22no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—21no—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—41no—
673C2×C3×C4—41no—
674C2×C3×C4—41no—
675C2×C3×C4—41no—
676C2×C3×C4—41no—
677C2×C3×C4—41no—
678C2×C3×C4—42no—
679C2×C3×C4—42no—
680C2×C3×C4—61no—
681C2×C3×C4—61no—
682C2×C3×C4—61no—
683C2×C3×C4—121no—
684C2×C3×C4C23×D311yescharacteristic
685C2×C3×C4C23×D311yescharacteristic
686#67—21no—
687#67—41no—
688#67—61no—
689#67—61no—
690#67—121no—
691#67—121no—
692#67—121no—
693#67—121no—
694#67—122no—
695#67—242no—
696C2×Dic3—21no—
697C2×Dic3—21no—
698C2×Dic3—121no—
699D12—21no—
700D12—21no—
701D12—31no—
702D12—31no—
703D12—41no—
704D12—61no—
705D12—62no—
706D12—61no—
707D12—61no—
708D12—61no—
709D12—61no—
710D12—121no—
711D12—121no—
712D12—121no—
713D12—122no—
714D12—121no—
715D12—242no—
716D12C2×#6711yescharacteristic
717C4×D3—21no—
718C4×D3—41no—
719C4×D3—61no—
720C4×D3—61no—
721C4×D3—121no—
722C4×D3—121no—
723C4×D3—121no—
724C4×D3—121no—
725C4×D3—121no—
726C4×D3—121no—
727C4×D3—122no—
728Dic6—21no—
729Dic6—21no—
730Dic6—31no—
731Dic6—31no—
732Dic6—61no—
733Dic6—121no—
734Dic6—121no—
735Dic6C2×#6711yescharacteristic
736C3×C8—31no—
737C3×C8—31no—
738C3×C8—61no—
739C3×C8—61no—
740C3×C8—61no—
741C3⋊C8—21no—
742C3⋊C8—21no—
743C3⋊C8—21no—
744C3⋊C8—31no—
745C3⋊C8—31no—
746C3⋊C8—31no—
747C3⋊C8—31no—
748C3⋊C8—61no—
749C3⋊C8—61no—
750C3⋊C8—62no—
751C3⋊C8—61no—
752C3⋊C8—61no—
753C3⋊C8C2×#6711yescharacteristic
754C3⋊C8C2×#6711yescharacteristic
755C2×C32—21no—
756C2×C32—41no—
757C2×C32—41no—
758C2×C32D4211yescharacteristic
759C3⋊D3—41no—
760C3⋊D3—81no—
761C3×D3—41no—
762C3×D3—81no—
763#41—21no—
764#41—21no—
765#41—31no—
766#41—41no—
767#41—61no—
768#41—61no—
769#41—91no—
770#41—181no—
771#41—181no—
772#41—181no—
773#41—181no—
774#41—361no—
775#41C2×D3211yescharacteristic
776#41C2×D3211yescharacteristic
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—31no—
780C2×Q8—181no—
781C2×Q8—181no—
782C2×Q8C2×D3211yescharacteristic
783C2×D4—31no—
784C2×D4—61no—
785C2×D4—61no—
786C2×D4—91no—
787C2×D4—121no—
788C2×D4—181no—
789C2×D4—181no—
790C2×D4—361no—
791C2×D4—361no—
792Q16—31no—
793Q16—61no—
794Q16—61no—
795Q16—61no—
796Q16—91no—
797Q16—181no—
798SD16—31no—
799SD16—31no—
800SD16—61no—
801SD16—61no—
802SD16—61no—
803SD16—61no—
804SD16—61no—
805SD16—61no—
806SD16—91no—
807SD16—91no—
808SD16—181no—
809SD16—181no—
810SD16—181no—
811SD16—181no—
812SD16—181no—
813SD16—181no—
814SD16—181no—
815SD16—181no—
816SD16—181no—
817SD16—181no—
818D8—31no—
819D8—61no—
820D8—91no—
821D8—181no—
822D8—181no—
823D8—181no—
824M16—31no—
825M16—31no—
826M16—31no—
827M16—61no—
828M16—91no—
829M16—181no—
830M16—181no—
831M16—181no—
832C2×C8—31no—
833C2×C8—61no—
834C2×C8—91no—
835C2×C8—181no—
836C2×C8—181no—
837C2×C8—181no—
838C4⋊C4—121no—
839C42—31no—
840C22×C3—22no—
841C22×C3—21no—
842C22×C3—21no—
843C22×C3—21no—
844C22×C3—21no—
845C22×C3—21no—
846C22×C3—41no—
847C22×C3—61no—
848C22×C3—121no—
849C22×C3—241no—
850C22×C3—481no—
851C22×C3#100411yescharacteristic
852C22×C3#100411yescharacteristic
853C2×D3—21no—
854C2×D3—41no—
855C2×D3—61no—
856C2×D3—61no—
857C2×D3—81no—
858C2×D3—121no—
859C2×D3—122no—
860C2×D3—121no—
861C2×D3—121no—
862C2×D3—161no—
863C2×D3—241no—
864C2×D3—241no—
865C2×D3—481no—
866C2×D3—481no—
867C2×D3—481no—
868C2×D3—482no—
869C3×C4—22no—
870C3×C4—21no—
871C3×C4—21no—
872C3×C4—21no—
873C3×C4—21no—
874C3×C4—21no—
875C3×C4—21no—
876C3×C4—41no—
877C3×C4—42no—
878C3×C4—41no—
879C3×C4—41no—
880C3×C4—62no—
881C3×C4—61no—
882C3×C4—121no—
883C3×C4C2×D3×D411yescharacteristic
884C3×C4C2×D3×D411yescharacteristic
885C3×C4C2×D3×D411yescharacteristic
886C3×C4C22×#6711yescharacteristic
887Dic3—22no—
888Dic3—21no—
889Dic3—41no—
890Dic3—61no—
891Dic3—61no—
892Dic3—121no—
893C32#329111yescharacteristic, complemented, Sylow
894C23—61no—
895C23—121no—
896C23—181no—
897C23—361no—
898Q8—21no—
899Q8—21no—
900Q8—31no—
901Q8—41no—
902Q8—61no—
903Q8—61no—
904Q8—91no—
905Q8—361no—
906Q8D3×#6711yescharacteristic
907Q8#381111yescharacteristic
908D4—21no—
909D4—21no—
910D4—31no—
911D4—41no—
912D4—61no—
913D4—61no—
914D4—61no—
915D4—91no—
916D4—121no—
917D4—121no—
918D4—181no—
919D4—181no—
920D4—181no—
921D4—361no—
922D4—361no—
923D4—361no—
924D4—722no—
925D4D3×#6711yescharacteristic
926D4#381111yescharacteristic
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—61no—
933C2×C4—61no—
934C2×C4—61no—
935C2×C4—121no—
936C2×C4—181no—
937C2×C4—361no—
938C2×C4—361no—
939C2×C4—361no—
940C2×C4C22×D3211yescharacteristic
941C8—31no—
942C8—31no—
943C8—61no—
944C8—61no—
945C8—61no—
946C8—91no—
947C8—91no—
948C8—181no—
949C2×C3—21no—
950C2×C3—21no—
951C2×C3—21no—
952C2×C3—41no—
953C2×C3—42no—
954C2×C3—41no—
955C2×C3—41no—
956C2×C3—41no—
957C2×C3—41no—
958C2×C3—81no—
959C2×C3—121no—
960C2×C3—241no—
961C2×C3#559011yescharacteristic
962C2×C3D4×#6711yescharacteristic
963D3—41no—
964D3—81no—
965D3—121no—
966D3—121no—
967D3—241no—
968D3—242no—
969D3—241no—
970D3—241no—
971C22—21no—
972C22—21no—
973C22—61no—
974C22—121no—
975C22—181no—
976C22—241no—
977C22—361no—
978C22—481no—
979C22—721no—
980C22—1441no—
981C22#6433011yescharacteristic
982C4—21no—
983C4—21no—
984C4—41no—
985C4—62no—
986C4—61no—
987C4—121no—
988C4—181no—
989C4C2×D3×#6711yescharacteristic
990C4C2×#381111yescharacteristic
991C3—21no—
992C3#8030211yescharacteristic, complemented
993C3#8401411yescharacteristic, complemented
994C2—21no—
995C2—41no—
996C2—41no—
997C2—121no—
998C2—241no—
999C2—361no—
1000C2—721no—
1001C2#1059552611yescharacteristic
subgroupG/H
centerC2#10595526
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×2−1+4C22
socleC2×C32D42
hypercenter2−1+4D32
hypocenterC32#3291
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ 2−1+4

Complements

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

NH ≅ G/Ntype
1. #10596308C2semidirect
2. C3×#5837C2semidirect
3. #10595473C2semidirect
4. #10595464C2semidirect
5. C3×#5246C2semidirect
6. #10591681C2semidirect
7. #10591680C2semidirect
8. #10591675C2semidirect
9. #10591667C2semidirect
10. #10591666C2semidirect
11. #10591662C2semidirect
12. #10591661C2semidirect
13. #10591643C2semidirect
14. #10591618C2semidirect
15. #10591542C2semidirect
19. #64366C22semidirect
20. C3×#1009C22semidirect
26. #64157C22semidirect
28. #64151C22semidirect
30. C2×#3755C22semidirect
31. C3×#951C22semidirect
32. C3×#951C22semidirect
37. C3×#948C22semidirect
38. C3×#944C22semidirect
40. C3×#942C22semidirect
42. C2×C3×#215C22semidirect
52. C2×#3717C22semidirect
54. C2×#3715C22semidirect
56. #63817C22semidirect
57. #63815C22semidirect
58. C3×#837C22semidirect
59. C3×#837C22semidirect
60. C3×#836C22semidirect
61. #63578C22semidirect
62. #63577C22semidirect
63. #63570C22semidirect
64. #63569C22semidirect
65. #63560C22semidirect
66. #63559C22semidirect
67. #63558C22semidirect
68. Dic3×C3⋊C8C22semidirect
73. #5837D3semidirect
79. #5246D3semidirect
130. #3756D4semidirect
135. #3755D4semidirect
136. #3754D4semidirect
138. #3753D4semidirect
146. C3×#216D4semidirect
151. C3×#215D4semidirect
154. C3×#214D4semidirect
156. C3×#213D4semidirect
186. #1009C2×D3semidirect
201. #951C2×D3semidirect
202. #951C2×D3semidirect
225. #948C2×D3semidirect
226. #944C2×D3semidirect
234. #942C2×D3semidirect
244. C2×#215C2×D3semidirect
273. #837C2×D3semidirect
274. #837C2×D3semidirect
276. #836C2×D3semidirect
465. #216#67semidirect
490. #215#67semidirect
499. #214#67semidirect
509. #213#67semidirect
893. C32#3291semidirect
992. C3#80302semidirect
993. C3#84014semidirect

Maximal subgroups

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

subgroupindex
#105963082
C3×#58372
#105954732
#105954642
C3×#52462
#105916812
#105916802
#105916752
#105916672
#105916662
#105916622
#105916612
#105916432
#105916182
#105915422
#840143
#803023