Finite Group Databasebeta

← #11886868

Subgroups — #11886868

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#10596241C211yesmaximal, characteristic, complemented
2C3×#5770C211yesmaximal, characteristic, complemented
3#10595448C211yesmaximal, characteristic, complemented
4#10595447C211yesmaximal, characteristic, complemented
5C3×#5196C211yesmaximal, characteristic, complemented
6#10591689C211yesmaximal, characteristic, complemented
7#10591680C211yesmaximal, characteristic, complemented
8#10591679C211yesmaximal, characteristic, complemented
9#10591668C211yesmaximal, characteristic, complemented
10#10591667C211yesmaximal, characteristic, complemented
11#10591666C211yesmaximal, characteristic, complemented
12#10590931C211yesmaximal, characteristic, complemented
13#10590928C211yesmaximal, characteristic, complemented
14#10590923C211yesmaximal, characteristic, complemented
15#10590877C211yesmaximal, characteristic, complemented
16#84014—31nomaximal
17#79893—31nomaximal
18#64367C2211yescharacteristic
19#64366C2211yescharacteristic, complemented
20C3×#1010C2211yescharacteristic
21C3×#1009C2211yescharacteristic, complemented
22C32×#135C2211yescharacteristic
23#64160C2211yescharacteristic, complemented
24#64158C2211yescharacteristic
25#64127—21no—
26#64125—21no—
27SD16×C3⋊D3—21no—
28#64120—21no—
29C2×#3744C2211yescharacteristic, complemented
30#64110C2211yescharacteristic, complemented
31C3×#951C2211yescharacteristic, complemented
32C3×#949C2211yescharacteristic
33C3×#948C2211yescharacteristic, complemented
34C3×#948C2211yescharacteristic, complemented
35C3×#918—21no—
36C3×#916—21no—
37C3×D3×SD16—21no—
38C3×#911—21no—
39C2×C3×#204C2211yescharacteristic, complemented
40C3×#901C2211yescharacteristic, complemented
41#63911C2211yescharacteristic
42#63866C2211yescharacteristic, complemented
43#63833—21no—
44#63833C2211yescharacteristic, complemented
45C2×#3717—21no—
46C2×#3717C2211yescharacteristic, complemented
47#63831—21no—
48#63831C2211yescharacteristic, complemented
49#63830—21no—
50#63830C2211yescharacteristic
51#63829—21no—
52#63829—21no—
53#63829C2211yescharacteristic
54C2×#3716—21no—
55C2×#3716C2211yescharacteristic, complemented
56#63825—21no—
57#63825C2211yescharacteristic
58C3×#837C2211yescharacteristic, complemented
59C3×#837C2211yescharacteristic, complemented
60C3×#819C2211yescharacteristic, complemented
61C3×C8×Dic3C2211yescharacteristic, complemented
62#63577C2211yescharacteristic, complemented
63#63570C2211yescharacteristic, complemented
64#63569C2211yescharacteristic, complemented
65#63561C2211yescharacteristic, complemented
66#63560C2211yescharacteristic, complemented
67#63559C2211yescharacteristic, complemented
68#63558C2211yescharacteristic, complemented
69C3×#577—31no—
70#5837—31no—
71#5836—31no—
72#5770—31no—
73#5770—31no—
74#5770—61no—
75#5770D311yescharacteristic, complemented
76#5751—31no—
77#5751—31no—
78C3×#443—31no—
79#5246—31no—
80#5241—31no—
81#5205—31no—
82#5203—31no—
83#5200—31no—
84#5198—31no—
85#5196D311yescharacteristic, complemented
86#5177—31no—
87#5175—31no—
88#5144—31no—
89#5141—31no—
90#5141—31no—
91#5141—31no—
92#4898—31no—
93#4898—31no—
94#4826—31no—
95#4826—31no—
96#4822—31no—
97#4822—31no—
98#4700—31no—
99#4693—31no—
100C32×#41C2311yescharacteristic
101C32×#41C2311yescharacteristic
102#3832—21no—
103Q8×C3⋊D3—21no—
104#3830—21no—
105#3830—41no—
106D4×C3⋊D3—21no—
107D4×C3⋊D3—41no—
108#3828—21no—
109#3828—21no—
110#3828C2311yescharacteristic
111C2×C4⋊(C3⋊D3)—21no—
112C2×C4⋊(C3⋊D3)C2311yescharacteristic
113C2×#634—21no—
114C2×#634C2311yescharacteristic
115C3×#239—21no—
116C3×D3×Q8—21no—
117C3×#237—21no—
118C3×#237—41no—
119C3×D3×D4—21no—
120C3×D3×D4—41no—
121C3×#235—21no—
122C3×#235—21no—
123C3×#235C2311yescharacteristic
124C2×C3×D12—21no—
125C2×C3×D12C2311yescharacteristic
126C2×C3×Dic6—21no—
127C2×C3×Dic6C2311yescharacteristic
128C2×#626—41no—
129C32×Q16D411yescharacteristic, complemented
130C32×SD16D411yescharacteristic, complemented
131C32×SD16D411yescharacteristic, complemented
132C32×D8D411yescharacteristic, complemented
133C2×C32×C8C2311yescharacteristic
134#3756—21no—
135#3755—21no—
136#3754—21no—
137#3753—21no—
138#3748C2311yescharacteristic
139#3744—21no—
140#3744—21no—
141#3743—21no—
142C8×C3⋊D3—21no—
143C3×#216—21no—
144C3×#215—21no—
145C3×#214—21no—
146C3×#213—21no—
147C3×C4×Dic3C2311yescharacteristic
148C3×#208—21no—
149C3×#208—21no—
150C3×#208C2311yescharacteristic
151C3×#208C2311yescharacteristic
152C3×#208C2311yescharacteristic
153C2×C3×C3⋊C8—21no—
154C2×C3×C3⋊C8—21no—
155C2×C3×C3⋊C8C2311yescharacteristic
156C3×#204—21no—
157C3×#204—21no—
158C3×ΓL(1,𝔽25)—21no—
159C3×D3×C8—21no—
160Dic3⋊Dic3—41no—
161#3719—21no—
162#3719—21no—
163#3719D411yescharacteristic, complemented
164#3717—21no—
165#3717—21no—
166#3717—21no—
167#3717—21no—
168#3717D411yescharacteristic, complemented
169#3716—21no—
170#3716—21no—
171#3716—21no—
172#3716—21no—
173#3716D411yescharacteristic, complemented
174#3714—21no—
175#3714—21no—
176#3714D411yescharacteristic, complemented
177#3291—91noSylow
178C3×2−1+4—31no—
179C3×H(5,𝔽2)—31no—
180#1010—31no—
181#1010—31no—
182#1010—61no—
183#1010C2×D311yescharacteristic
184#1009—31no—
185#1009—31no—
186#1009—61no—
187#1009C2×D311yescharacteristic, complemented
188C3×#137—31no—
189C3×#137—61no—
190C3×AGL(1,ℤ/8)—31no—
191C3×AGL(1,ℤ/8)—61no—
192C3×#135—21no—
193C3×#135—61no—
194C3×#135C2×D311yescharacteristic
195C3×#135C2×D311yescharacteristic
196C2×C3×SD16—31no—
197C2×C3×SD16—61no—
198C3×#131—31no—
199C3×#131—31no—
200C3×#131—31no—
201#951—31no—
202#951—31no—
203#951—31no—
204#951—61no—
205#951—61no—
206#951C2×D311yescharacteristic, complemented
207#950—31no—
208#950—61no—
209#950—61no—
210#949—31no—
211#949—31no—
212#949—31no—
213#949—61no—
214#949—61no—
215#949C2×D311yescharacteristic
216#948C2×D311yescharacteristic, complemented
217#948C2×D311yescharacteristic, complemented
218#944—31no—
219#942—31no—
220#942—61no—
221C2×#215—31no—
222C2×#215—61no—
223#940—31no—
224C2×#214—31no—
225C2×#214—61no—
226#932—31no—
227#932—61no—
228#918—21no—
229#918—62no—
230#918—61no—
231#918—61no—
232#916—21no—
233#916—62no—
234#916—61no—
235#916—61no—
236D3×SD16—21no—
237D3×SD16—62no—
238D3×SD16—61no—
239D3×SD16—61no—
240#911—21no—
241#911—62no—
242#911—61no—
243#911—61no—
244#909—31no—
245#909—31no—
246#909—61no—
247#909—61no—
248#908—31no—
249#908—31no—
250#908—61no—
251#908—61no—
252#904—31no—
253#904—61no—
254#904—61no—
255C2×#204—31no—
256C2×#204—31no—
257C2×#204—31no—
258C2×#204—31no—
259C2×#204—61no—
260C2×#204—61no—
261C2×#204—61no—
262C2×#204C2×D311yescharacteristic, complemented
263#901—31no—
264#901—31no—
265#901—61no—
266#901C2×D311yescharacteristic, complemented
267#874—31no—
268#869—31no—
269C3×#108—31no—
270C3×#104—31no—
271C3×#104—31no—
272C3×C4×C8—31no—
273#837—31no—
274#837C2×D311yescharacteristic, complemented
275#837C2×D311yescharacteristic, complemented
276#836—31no—
277#833—31no—
278#825—31no—
279#824—31no—
280#824—31no—
281#824—31no—
282#823—31no—
283#823—31no—
284#823—31no—
285#822—31no—
286#819—31no—
287#819C2×D311yescharacteristic, complemented
288C8×Dic3C2×D311yescharacteristic, complemented
289#805—31no—
290#805—31no—
291C22×C3⋊D3—21no—
292C22×C3⋊D3—41no—
293C22×C3×D3—21no—
294C22×C3×D3—41no—
295C32×Q8C2×D411yescharacteristic
296C32×Q8C2×D411yescharacteristic
297C32×D4—21no—
298C32×D4—21no—
299C32×D4C2×D411yescharacteristic
300C32×D4C2×D411yescharacteristic
301C2×C32×C4—21no—
302C2×C32×C4—21no—
303C2×C32×C4C2411yescharacteristic
304#638—21no—
305#638—41no—
306#638—41no—
307C2×C3⋊Dic3—21no—
308C2×C3⋊Dic3—41no—
309C4⋊(C3⋊D3)—21no—
310C4⋊(C3⋊D3)—21no—
311C4⋊(C3⋊D3)—41no—
312C4⋊(C3⋊D3)C2×D411yescharacteristic
313C4×C3⋊D3—21no—
314C4×C3⋊D3—41no—
315C4×C3⋊D3—41no—
316#634—21no—
317#634—21no—
318#634—41no—
319#634C2×D411yescharacteristic
320C3×#67—21no—
321C3×#67—41no—
322C3×#67—41no—
323C2×C3×Dic3—21no—
324C2×C3×Dic3—21no—
325C2×C3×Dic3—41no—
326C3×D12—21no—
327C3×D12—21no—
328C3×D12—41no—
329C3×D12C2×D411yescharacteristic
330C3×C4×D3—21no—
331C3×C4×D3—41no—
332C3×C4×D3—41no—
333C3×Dic6—21no—
334C3×Dic6—21no—
335C3×Dic6—41no—
336C3×Dic6C2×D411yescharacteristic
337#626—82no—
338C32×C8C2×D411yescharacteristic
339C32×C8C2×D411yescharacteristic
340C3⋊(C3⋊C8)—21no—
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—91no—
356#456—91no—
357#453—91no—
358#453—91no—
359#443—31no—
360#443—91no—
361C3×#41—21no—
362C3×#41—21no—
363C3×#41—31no—
364C3×#41—61no—
365C3×#41—61no—
366C3×#41—61no—
367C3×#41—61no—
368C3×#41—121no—
369C3×#41C22×D311yescharacteristic
370C3×#41C22×D311yescharacteristic
371C3×#41C22×D311yescharacteristic
372C3×#41C22×D311yescharacteristic
373C2×C3×Q8—31no—
374C2×C3×Q8—61no—
375C2×C3×Q8—61no—
376C2×C3×D4—31no—
377C2×C3×D4—61no—
378C2×C3×D4—61no—
379C2×C3×D4—121no—
380C2×#67—121no—
381#239—21no—
382#239—62no—
383#239—61no—
384#239—61no—
385D3×Q8—21no—
386D3×Q8—62no—
387D3×Q8—61no—
388D3×Q8—61no—
389#237—21no—
390#237—41no—
391#237—62no—
392#237—61no—
393#237—61no—
394#237—121no—
395#237—121no—
396#237—122no—
397D3×D4—21no—
398D3×D4—41no—
399D3×D4—62no—
400D3×D4—61no—
401D3×D4—61no—
402D3×D4—121no—
403D3×D4—121no—
404D3×D4—122no—
405#235—21no—
406#235—21no—
407#235—31no—
408#235—31no—
409#235—61no—
410#235—61no—
411#235—61no—
412#235—61no—
413#235—61no—
414#235—121no—
415#235—121no—
416#235C22×D311yescharacteristic
417C2×D12—21no—
418C2×D12—31no—
419C2×D12—31no—
420C2×D12—61no—
421C2×D12—61no—
422C2×D12—61no—
423C2×D12—121no—
424C2×D12—121no—
425C2×D12C22×D311yescharacteristic
426C2×Dic6—21no—
427C2×Dic6—31no—
428C2×Dic6—31no—
429C2×Dic6—61no—
430C2×Dic6—61no—
431C2×Dic6—61no—
432C2×Dic6—121no—
433C2×Dic6C22×D311yescharacteristic
434C3×Q16—21no—
435C3×Q16—61no—
436C3×Q16D1211yescharacteristic, complemented
437C3×Q16#6711yescharacteristic, complemented
438C3×SD16—21no—
439C3×SD16—21no—
440C3×SD16—61no—
441C3×SD16—61no—
442C3×SD16—61no—
443C3×SD16—61no—
444C3×SD16D1211yescharacteristic, complemented
445C3×SD16D1211yescharacteristic, complemented
446C3×SD16#6711yescharacteristic, complemented
447C3×SD16#6711yescharacteristic, complemented
448C3×D8—21no—
449C3×D8—61no—
450C3×D8D1211yescharacteristic, complemented
451C3×D8#6711yescharacteristic, complemented
452C3×M16—31no—
453C3×M16—31no—
454C3×M16—31no—
455C3×M16—61no—
456C3×M16—61no—
457C3×M16—61no—
458C2×C3×C8—21no—
459C2×C3×C8—31no—
460C2×C3×C8—61no—
461C2×C3×C8—61no—
462C2×C3×C8—61no—
463C2×C3×C8C22×D311yescharacteristic
464C2×C3×C8C22×D311yescharacteristic
465C3×C42—31no—
466#216—21no—
467#216—31no—
468#216—61no—
469#216—61no—
470#216—62no—
471#216—61no—
472#216—61no—
473#215—21no—
474#215—31no—
475#215—61no—
476#215—61no—
477#215—62no—
478#215—61no—
479#215—61no—
480#215—61no—
481#215—61no—
482#214—21no—
483#214—31no—
484#214—61no—
485#214—61no—
486#214—62no—
487#214—61no—
488#214—61no—
489#214—61no—
490#214—61no—
491#213—21no—
492#213—31no—
493#213—61no—
494#213—61no—
495#213—62no—
496#213—61no—
497#213—61no—
498C4⋊Dic3—121no—
499Dic3⋊C4—121no—
500C4×Dic3C22×D311yescharacteristic
501#208—21no—
502#208—21no—
503#208—31no—
504#208—31no—
505#208—61no—
506#208C22×D311yescharacteristic
507#208C22×D311yescharacteristic
508#208C22×D311yescharacteristic
509C2×C3⋊C8—21no—
510C2×C3⋊C8—21no—
511C2×C3⋊C8C22×D311yescharacteristic
512Dic12—31no—
513Dic12—61no—
514Dic12—61no—
515D24—31no—
516D24—61no—
517D24—61no—
518#204—21no—
519#204—21no—
520#204—31no—
521#204—31no—
522#204—62no—
523#204—62no—
524#204—61no—
525#204—61no—
526#204—61no—
527#204—61no—
528#204—61no—
529#204—61no—
530#204—61no—
531#204—61no—
532#204—61no—
533#204—61no—
534#204—61no—
535#204—61no—
536ΓL(1,𝔽25)—21no—
537ΓL(1,𝔽25)—62no—
538ΓL(1,𝔽25)—61no—
539ΓL(1,𝔽25)—61no—
540D3×C8—21no—
541D3×C8—62no—
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×C4C22×D411yescharacteristic
558C32×C4C22×D411yescharacteristic
559C3⋊Dic3—21no—
560C3⋊Dic3—41no—
561C3×Dic3—22no—
562C3×Dic3—21no—
563C3×Dic3—41no—
5642−1+4—31no—
5652−1+4—91no—
566H(5,𝔽2)—31no—
567H(5,𝔽2)—91no—
568#137—31no—
569#137—61no—
570#137—91no—
571#137—91no—
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—61no—
585#135—91no—
586#135—181no—
587#135—181no—
588#135—181no—
589#135D3211yescharacteristic
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—31no—
600#131—31no—
601#131—91no—
602C4⋊Q8—91no—
603#127—91no—
604#108—31no—
605#108—91no—
606#104—31no—
607#104—31no—
608#104—91no—
609#104—91no—
610#101—91no—
611#101—91no—
612#100—91no—
613#100—91no—
614C4×C8—31no—
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—21no—
626C3×Q8—21no—
627C3×Q8—31no—
628C3×Q8—61no—
629C3×Q8—61no—
630C3×Q8—121no—
631C3×Q8C2×D1211yescharacteristic
632C3×Q8C2×D1211yescharacteristic
633C3×Q8C2×#6711yescharacteristic
634C3×Q8C2×#6711yescharacteristic
635C3×D4—21no—
636C3×D4—21no—
637C3×D4—21no—
638C3×D4—21no—
639C3×D4—21no—
640C3×D4—21no—
641C3×D4—31no—
642C3×D4—41no—
643C3×D4—41no—
644C3×D4—61no—
645C3×D4—61no—
646C3×D4—61no—
647C3×D4—121no—
648C3×D4—121no—
649C3×D4—121no—
650C3×D4C2×D1211yescharacteristic
651C3×D4C2×D1211yescharacteristic
652C3×D4C2×#6711yescharacteristic
653C3×D4C2×#6711yescharacteristic
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—41no—
660C2×C3×C4—41no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—121no—
665C2×C3×C4—121no—
666C2×C3×C4—121no—
667C2×C3×C4C23×D311yescharacteristic
668C2×C3×C4C23×D311yescharacteristic
669#67—21no—
670#67—41no—
671#67—41no—
672#67—62no—
673#67—61no—
674#67—61no—
675#67—121no—
676#67—121no—
677#67—122no—
678#67—121no—
679#67—121no—
680#67—122no—
681#67—242no—
682C2×Dic3—21no—
683C2×Dic3—21no—
684C2×Dic3—41no—
685C2×Dic3—61no—
686C2×Dic3—61no—
687C2×Dic3—121no—
688C2×Dic3—121no—
689C2×Dic3—121no—
690C2×Dic3—122no—
691D12—21no—
692D12—21no—
693D12—31no—
694D12—31no—
695D12—41no—
696D12—61no—
697D12—62no—
698D12—61no—
699D12—61no—
700D12—61no—
701D12—61no—
702D12—121no—
703D12—121no—
704D12—121no—
705D12—122no—
706D12—242no—
707D12D3×D411yescharacteristic
708C4×D3—21no—
709C4×D3—41no—
710C4×D3—41no—
711C4×D3—62no—
712C4×D3—61no—
713C4×D3—61no—
714C4×D3—121no—
715C4×D3—121no—
716C4×D3—122no—
717C4×D3—121no—
718C4×D3—121no—
719C4×D3—122no—
720Dic6—21no—
721Dic6—21no—
722Dic6—31no—
723Dic6—31no—
724Dic6—41no—
725Dic6—61no—
726Dic6—62no—
727Dic6—61no—
728Dic6—61no—
729Dic6—61no—
730Dic6—61no—
731Dic6—121no—
732Dic6—121no—
733Dic6—121no—
734Dic6—122no—
735Dic6D3×D411yescharacteristic
736C3×C8—21no—
737C3×C8—21no—
738C3×C8—31no—
739C3×C8—31no—
740C3×C8—61no—
741C3×C8—61no—
742C3×C8—61no—
743C3×C8C2×D1211yescharacteristic
744C3×C8C2×D1211yescharacteristic
745C3×C8C2×#6711yescharacteristic
746C3×C8C2×#6711yescharacteristic
747C3⋊C8—21no—
748C3⋊C8—21no—
749C3⋊C8—21no—
750C3⋊C8—62no—
751C3⋊C8—61no—
752C3⋊C8—61no—
753C3⋊C8D3×D411yescharacteristic
754C3⋊C8D3×D411yescharacteristic
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—31no—
764#41—61no—
765#41—61no—
766#41—61no—
767#41—61no—
768#41—91no—
769#41—121no—
770#41—181no—
771#41—181no—
772#41—181no—
773#41—181no—
774#41—361no—
775#41C2×D3211yescharacteristic
776#41C2×D3211yescharacteristic
777C2×Q8—31no—
778C2×Q8—61no—
779C2×Q8—61no—
780C2×Q8—91no—
781C2×Q8—181no—
782C2×Q8—181no—
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—61no—
793Q16—91no—
794Q16—181no—
795Q16—181no—
796Q16—181no—
797Q16#62611yescharacteristic, complemented
798SD16—61no—
799SD16—61no—
800SD16—61no—
801SD16—61no—
802SD16—91no—
803SD16—91no—
804SD16—181no—
805SD16—181no—
806SD16—181no—
807SD16—181no—
808SD16—181no—
809SD16—181no—
810SD16—181no—
811SD16—181no—
812SD16—181no—
813SD16—181no—
814SD16—181no—
815SD16—181no—
816SD16#62611yescharacteristic, complemented
817SD16#62611yescharacteristic, complemented
818D8—61no—
819D8—91no—
820D8—181no—
821D8—181no—
822D8—181no—
823D8#62611yescharacteristic, complemented
824M16—31no—
825M16—31no—
826M16—31no—
827M16—61no—
828M16—61no—
829M16—61no—
830M16—91no—
831M16—181no—
832C2×C8—31no—
833C2×C8—61no—
834C2×C8—61no—
835C2×C8—61no—
836C2×C8—181no—
837C2×C8C2×D3211yescharacteristic
838C4⋊C4—361no—
839C42—31no—
840C22×C3—21no—
841C22×C3—21no—
842C22×C3—21no—
843C22×C3—21no—
844C22×C3—21no—
845C22×C3—41no—
846C22×C3—41no—
847C22×C3—61no—
848C22×C3—121no—
849C22×C3—241no—
850C22×C3—481no—
851C22×C3#100411yescharacteristic
852C22×C3#100911yescharacteristic
853C2×D3—21no—
854C2×D3—41no—
855C2×D3—62no—
856C2×D3—61no—
857C2×D3—61no—
858C2×D3—81no—
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—21no—
870C3×C4—21no—
871C3×C4—21no—
872C3×C4—21no—
873C3×C4—21no—
874C3×C4—21no—
875C3×C4—41no—
876C3×C4—41no—
877C3×C4—62no—
878C3×C4—61no—
879C3×C4—121no—
880C3×C4C22×D1211yescharacteristic
881C3×C4C2×D3×D411yescharacteristic
882C3×C4C2×D3×D411yescharacteristic
883C3×C4C22×#6711yescharacteristic
884Dic3—22no—
885Dic3—21no—
886Dic3—41no—
887Dic3—62no—
888Dic3—61no—
889Dic3—61no—
890Dic3—122no—
891Dic3—121no—
892Dic3—121no—
893C32#329111yescharacteristic, complemented, Sylow
894C23—61no—
895C23—121no—
896C23—181no—
897C23—361no—
898Q8—31no—
899Q8—61no—
900Q8—61no—
901Q8—91no—
902Q8—121no—
903Q8—181no—
904Q8—181no—
905Q8—361no—
906Q8C2×#62611yescharacteristic
907Q8C2×#62611yescharacteristic
908D4—21no—
909D4—21no—
910D4—31no—
911D4—61no—
912D4—61no—
913D4—61no—
914D4—91no—
915D4—121no—
916D4—121no—
917D4—121no—
918D4—181no—
919D4—181no—
920D4—181no—
921D4—361no—
922D4—361no—
923D4—361no—
924D4—722no—
925D4C2×#62611yescharacteristic
926D4C2×#62611yescharacteristic
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—61no—
930C2×C4—61no—
931C2×C4—61no—
932C2×C4—121no—
933C2×C4—121no—
934C2×C4—121no—
935C2×C4—181no—
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—181no—
947C8C2×#62611yescharacteristic
948C8C2×#62611yescharacteristic
949C2×C3—21no—
950C2×C3—21no—
951C2×C3—21no—
952C2×C3—41no—
953C2×C3—41no—
954C2×C3—41no—
955C2×C3—41no—
956C2×C3—41no—
957C2×C3—81no—
958C2×C3—81no—
959C2×C3—121no—
960C2×C3—241no—
961C2×C3D4×D1211yescharacteristic
962C2×C3D4×#6711yescharacteristic
963D3—41no—
964D3—81no—
965D3—122no—
966D3—121no—
967D3—121no—
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#6431411yescharacteristic
982C4—21no—
983C4—21no—
984C4—62no—
985C4—61no—
986C4—121no—
987C4—181no—
988C4—361no—
989C4D32×D411yescharacteristic
990C4C22×#62611yescharacteristic
991C3—21no—
992C3#7989311yescharacteristic, complemented
993C3#8401411yescharacteristic, complemented
994C2—21no—
995C2—41no—
996C2—41no—
997C2—121no—
998C2—241no—
999C2—361no—
1000C2—721no—
1001C2D4×#62611yescharacteristic
subgroupG/H
centerC2D4×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#135C22
socleC2×C32D42
hypercenter#135D32
hypocenterC32#3291
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #10596241C2semidirect
2. C3×#5770C2semidirect
3. #10595448C2semidirect
4. #10595447C2semidirect
5. C3×#5196C2semidirect
6. #10591689C2semidirect
7. #10591680C2semidirect
8. #10591679C2semidirect
9. #10591668C2semidirect
10. #10591667C2semidirect
11. #10591666C2semidirect
12. #10590931C2semidirect
13. #10590928C2semidirect
14. #10590923C2semidirect
15. #10590877C2semidirect
19. #64366C22semidirect
21. C3×#1009C22semidirect
23. #64160C22semidirect
29. C2×#3744C22semidirect
30. #64110C22semidirect
31. C3×#951C22semidirect
33. C3×#948C22semidirect
34. C3×#948C22semidirect
39. C2×C3×#204C22semidirect
40. C3×#901C22semidirect
42. #63866C22semidirect
44. #63833C22semidirect
46. C2×#3717C22semidirect
48. #63831C22semidirect
55. C2×#3716C22semidirect
58. C3×#837C22semidirect
59. C3×#837C22semidirect
60. C3×#819C22semidirect
61. C3×C8×Dic3C22semidirect
62. #63577C22semidirect
63. #63570C22semidirect
64. #63569C22semidirect
65. #63561C22semidirect
66. #63560C22semidirect
67. #63559C22semidirect
68. #63558C22semidirect
75. #5770D3semidirect
85. #5196D3semidirect
129. C32×Q16D4semidirect
130. C32×SD16D4semidirect
131. C32×SD16D4semidirect
132. C32×D8D4semidirect
163. #3719D4semidirect
168. #3717D4semidirect
173. #3716D4semidirect
176. #3714D4semidirect
187. #1009C2×D3semidirect
206. #951C2×D3semidirect
216. #948C2×D3semidirect
217. #948C2×D3semidirect
262. C2×#204C2×D3semidirect
266. #901C2×D3semidirect
274. #837C2×D3semidirect
275. #837C2×D3semidirect
287. #819C2×D3semidirect
288. C8×Dic3C2×D3semidirect
436. C3×Q16D12semidirect
437. C3×Q16#67semidirect
444. C3×SD16D12semidirect
445. C3×SD16D12semidirect
446. C3×SD16#67semidirect
447. C3×SD16#67semidirect
450. C3×D8D12semidirect
451. C3×D8#67semidirect
797. Q16#626semidirect
816. SD16#626semidirect
817. SD16#626semidirect
823. D8#626semidirect
893. C32#3291semidirect
992. C3#79893semidirect
993. C3#84014semidirect

Maximal subgroups

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

subgroupindex
#105962412
C3×#57702
#105954482
#105954472
C3×#51962
#105916892
#105916802
#105916792
#105916682
#105916672
#105916662
#105909312
#105909282
#105909232
#105908772
#840143
#798933