Finite Group Databasebeta

← #11886604

Subgroups — #11886604

Order 1152.

1062 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596240C211yesmaximal, characteristic, complemented
2C3×#5770C211yesmaximal, characteristic, complemented
3#10595449C211yesmaximal, characteristic, complemented
4#10595448C211yesmaximal, characteristic, complemented
5C3×#5197C211yesmaximal, characteristic, complemented
6#10591690C211yesmaximal, characteristic, complemented
7#10591685C211yesmaximal, characteristic, complemented
8#10591680C211yesmaximal, characteristic, complemented
9#10591677C211yesmaximal, characteristic, complemented
10#10591667C211yesmaximal, characteristic, complemented
11#10591666C211yesmaximal, characteristic, complemented
12#10590928C211yesmaximal, characteristic, complemented
13#10590927C211yesmaximal, characteristic, complemented
14#10590924C211yesmaximal, characteristic, complemented
15#10590881C211yesmaximal, characteristic, complemented
16#84015—31nomaximal
17#79900—31nomaximal
18#64366C2211yescharacteristic
19#64366C2211yescharacteristic, complemented
20C3×#1010C2211yescharacteristic, complemented
21C3×#1009C2211yescharacteristic, complemented
22C32×#135C2211yescharacteristic
23#64158C2211yescharacteristic
24#64158C2211yescharacteristic, complemented
25#64128—21no—
26#64123—21no—
27#64123—21no—
28D8×C3⋊D3—21no—
29C2×#3745C2211yescharacteristic, complemented
30#64110C2211yescharacteristic, complemented
31C3×#951C2211yescharacteristic, complemented
32C3×#949C2211yescharacteristic, complemented
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, complemented
42#63864C2211yescharacteristic, complemented
43#63833—21no—
44#63833C2211yescharacteristic, complemented
45C2×#3717—21no—
46C2×#3717C2211yescharacteristic, complemented
47#63830—21no—
48#63830C2211yescharacteristic
49#63829—21no—
50#63829—21no—
51#63829C2211yescharacteristic
52#63825—21no—
53#63825—21no—
54#63825C2211yescharacteristic, complemented
55#63825C2211yescharacteristic, complemented
56C2×#3714—21no—
57C2×#3714C2211yescharacteristic, complemented
58C3×#837C2211yescharacteristic, complemented
59C3×#837C2211yescharacteristic, complemented
60C3×#819C2211yescharacteristic, complemented
61C3×#815C2211yescharacteristic, complemented
62#63577C2211yescharacteristic, complemented
63#63570C2211yescharacteristic, complemented
64#63569C2211yescharacteristic, complemented
65#63560C2211yescharacteristic, complemented
66#63559C2211yescharacteristic, complemented
67#63559C2211yescharacteristic, complemented
68#63558C2211yescharacteristic, complemented
69C3×#577—31no—
70#5837—31no—
71#5835—31no—
72#5770D311yescharacteristic, complemented
73#5769—31no—
74#5769—31no—
75#5769—61no—
76#5752—31no—
77#5751—31no—
78C3×#444—31no—
79#5245—31no—
80#5241—31no—
81#5203—31no—
82#5202—31no—
83#5199—31no—
84#5198—31no—
85#5197D311yescharacteristic, complemented
86#5177—31no—
87#5176—31no—
88#5145—31no—
89#5142—31no—
90#5142—31no—
91#5141—31no—
92#4898—31no—
93#4897—31no—
94#4827—31no—
95#4825—31no—
96#4822—31no—
97#4822—31no—
98#4717—31no—
99#4712—31no—
100C32×#41C2311yescharacteristic
101C32×#41C2311yescharacteristic
102#3832—21no—
103#3832—21no—
104D4×C3⋊D3—21no—
105D4×C3⋊D3—21no—
106D4×C3⋊D3—41no—
107D4×C3⋊D3—41no—
108#3828—21no—
109#3828—21no—
110#3828C2311yescharacteristic
111C2×C4⋊(C3⋊D3)—21no—
112C2×C4⋊(C3⋊D3)—21no—
113C2×C4⋊(C3⋊D3)C2311yescharacteristic
114C2×C4⋊(C3⋊D3)C2311yescharacteristic
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#3755—21no—
135#3755—21no—
136#3753—21no—
137#3753—21no—
138#3748C2311yescharacteristic
139#3745—21no—
140#3745—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—
160#3722—41no—
161#3719—21no—
162#3719D411yescharacteristic, complemented
163#3717—21no—
164#3717—21no—
165#3717—21no—
166#3717—21no—
167#3717—21no—
168#3717D411yescharacteristic, complemented
169#3716—21no—
170#3716D411yescharacteristic, complemented
171#3714—21no—
172#3714—21no—
173#3714—21no—
174#3714—21no—
175#3714—21no—
176#3714D411yescharacteristic, complemented
177#3288—91noSylow
178C3×2−1+4—31no—
179C3×H(5,𝔽2)—31no—
180#1010C2×D311yescharacteristic, complemented
181#1009—31no—
182#1009—31no—
183#1009—31no—
184#1009—31no—
185#1009—61no—
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#951C2×D311yescharacteristic, complemented
202#950—31no—
203#950—61no—
204#950—61no—
205#949—31no—
206#949—31no—
207#949—31no—
208#949—31no—
209#949—31no—
210#949—31no—
211#949—61no—
212#949—61no—
213#949—61no—
214#949—61no—
215#949C2×D311yescharacteristic, complemented
216#948C2×D311yescharacteristic, complemented
217#948C2×D311yescharacteristic, complemented
218#947—31no—
219#942—31no—
220#942—61no—
221C2×#215—31no—
222C2×#215—61no—
223#940—31no—
224#932—31no—
225#932—61no—
226C2×#213—31no—
227C2×#213—61no—
228#919—62no—
229#919—61no—
230#919—61no—
231#918—21no—
232#916—21no—
233#914—62no—
234#914—62no—
235#914—61no—
236#914—61no—
237#914—61no—
238#914—61no—
239D3×SD16—21no—
240#911—21no—
241D3×D8—62no—
242D3×D8—61no—
243D3×D8—61no—
244#909—31no—
245#909—61no—
246#908—31no—
247#908—31no—
248#908—31no—
249#908—61no—
250#908—61no—
251#908—61no—
252#904—31no—
253#904—61no—
254#904—61no—
255C2×D24—31no—
256C2×D24—31no—
257C2×D24—31no—
258C2×D24—61no—
259C2×D24—61no—
260C2×#204—31no—
261C2×#204—61no—
262C2×#204C2×D311yescharacteristic, complemented
263#901—31no—
264#901—31no—
265#901—61no—
266#901C2×D311yescharacteristic, complemented
267#875—31no—
268#874—31no—
269C3×#108—31no—
270C3×#104—31no—
271C3×#104—31no—
272C3×#97—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#823—31no—
281#823—31no—
282#823—31no—
283#823—31no—
284#823—31no—
285#822—31no—
286#819—31no—
287#819C2×D311yescharacteristic, complemented
288#815C2×D311yescharacteristic, complemented
289#805—31no—
290#805—31no—
291C22×C3⋊D3—21no—
292C22×C3⋊D3—21no—
293C22×C3⋊D3—41no—
294C22×C3⋊D3—41no—
295C22×C3×D3—21no—
296C22×C3×D3—41no—
297C32×Q8C2×D411yescharacteristic
298C32×Q8C2×D411yescharacteristic
299C32×D4—21no—
300C32×D4—21no—
301C32×D4C2×D411yescharacteristic
302C32×D4C2×D411yescharacteristic
303C2×C32×C4—21no—
304C2×C32×C4—21no—
305C2×C32×C4C2411yescharacteristic
306#638—21no—
307#638—41no—
308#638—41no—
309C4⋊(C3⋊D3)—21no—
310C4⋊(C3⋊D3)—21no—
311C4⋊(C3⋊D3)—21no—
312C4⋊(C3⋊D3)—21no—
313C4⋊(C3⋊D3)—41no—
314C4⋊(C3⋊D3)—41no—
315C4⋊(C3⋊D3)C2×D411yescharacteristic
316C4×C3⋊D3—21no—
317C4×C3⋊D3—41no—
318C4×C3⋊D3—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#576—91no—
349#576—91no—
350#496—91no—
351#472—91no—
352#472—91no—
353#471—91no—
354#471—91no—
355#455—91no—
356#454—91no—
357#453—91no—
358#453—91no—
359#444—31no—
360#444—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—62no—
384#239—61no—
385#239—61no—
386#239—61no—
387#239—61no—
388D3×Q8—21no—
389#237—21no—
390#237—41no—
391D3×D4—21no—
392D3×D4—41no—
393D3×D4—62no—
394D3×D4—62no—
395D3×D4—61no—
396D3×D4—61no—
397D3×D4—61no—
398D3×D4—61no—
399D3×D4—121no—
400D3×D4—121no—
401D3×D4—121no—
402D3×D4—121no—
403D3×D4—122no—
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—31no—
421C2×D12—31no—
422C2×D12—61no—
423C2×D12—61no—
424C2×D12—61no—
425C2×D12—61no—
426C2×D12—61no—
427C2×D12—61no—
428C2×D12—121no—
429C2×D12—121no—
430C2×D12—121no—
431C2×D12C22×D311yescharacteristic
432C2×Dic6—21no—
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#215—21no—
470#215—31no—
471#215—61no—
472#215—61no—
473#215—61no—
474#215—62no—
475#215—62no—
476#215—61no—
477#215—61no—
478#215—61no—
479#215—61no—
480#215—61no—
481#215—61no—
482#214—21no—
483#214—31no—
484#214—61no—
485#213—21no—
486#213—31no—
487#213—61no—
488#213—61no—
489#213—61no—
490#213—62no—
491#213—62no—
492#213—61no—
493#213—61no—
494#213—61no—
495#213—61no—
496#213—61no—
497#213—61no—
498(C2×D3)⋊C4—121no—
499(C2×D3)⋊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—
514D24—31no—
515D24—62no—
516D24—62no—
517D24—61no—
518D24—61no—
519D24—61no—
520D24—61no—
521D24—61no—
522D24—61no—
523D24—61no—
524D24—61no—
525D24—61no—
526#204—21no—
527#204—21no—
528#204—31no—
529#204—31no—
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—41no—
550C2×C3⋊D3—81no—
551C2×C3⋊D3—81no—
552C2×C3⋊D3—161no—
553C2×C3⋊D3—161no—
554C2×C3×D3—21no—
555C2×C3×D3—41no—
556C2×C3×D3—81no—
557C2×C3×D3—161no—
558C32×C4—21no—
559C32×C4—21no—
560C32×C4C22×D411yescharacteristic
561C32×C4C22×D411yescharacteristic
562C3⋊Dic3—21no—
563C3×Dic3—21no—
564C3×Dic3—41no—
565C3×Dic3—41no—
5662−1+4—31no—
567H(5,𝔽2)—31no—
568H(5,𝔽2)—91no—
569H(5,𝔽2)—91no—
570#137—31no—
571#137—61no—
572#137—91no—
573#137—181no—
574AGL(1,ℤ/8)—31no—
575AGL(1,ℤ/8)—61no—
576AGL(1,ℤ/8)—91no—
577AGL(1,ℤ/8)—91no—
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—
584AGL(1,ℤ/8)—181no—
585AGL(1,ℤ/8)—181no—
586#135—61no—
587#135—91no—
588#135—181no—
589#135—181no—
590#135—181no—
591#135D3211yescharacteristic
592C2×SD16—31no—
593C2×SD16—61no—
594C2×SD16—91no—
595C2×SD16—181no—
596C2×D8—91no—
597C2×D8—91no—
598C2×D8—181no—
599C2×D8—181no—
600#131—31no—
601#131—31no—
602#131—31no—
603#131—91no—
604#127—91no—
605#124—91no—
606#108—31no—
607#108—91no—
608#104—31no—
609#104—31no—
610#104—91no—
611#104—91no—
612#101—91no—
613#100—91no—
614#100—91no—
615#100—91no—
616#97—31no—
617C23×C3—61no—
618C23×C3—121no—
619C22×D3—21no—
620C22×D3—41no—
621C22×D3—61no—
622C22×D3—61no—
623C22×D3—61no—
624C22×D3—61no—
625C22×D3—121no—
626C22×D3—121no—
627C22×D3—121no—
628C22×D3—121no—
629C22×D3—121no—
630C22×D3—121no—
631C22×D3—122no—
632C22×D3—122no—
633C3×Q8—21no—
634C3×Q8—21no—
635C3×Q8—31no—
636C3×Q8—61no—
637C3×Q8—61no—
638C3×Q8—121no—
639C3×Q8C2×D1211yescharacteristic
640C3×Q8C2×D1211yescharacteristic
641C3×Q8C2×#6711yescharacteristic
642C3×Q8C2×#6711yescharacteristic
643C3×D4—21no—
644C3×D4—21no—
645C3×D4—21no—
646C3×D4—21no—
647C3×D4—21no—
648C3×D4—21no—
649C3×D4—31no—
650C3×D4—41no—
651C3×D4—41no—
652C3×D4—61no—
653C3×D4—61no—
654C3×D4—61no—
655C3×D4—121no—
656C3×D4—121no—
657C3×D4—121no—
658C3×D4C2×D1211yescharacteristic
659C3×D4C2×D1211yescharacteristic
660C3×D4C2×#6711yescharacteristic
661C3×D4C2×#6711yescharacteristic
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—41no—
668C2×C3×C4—41no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—121no—
673C2×C3×C4—121no—
674C2×C3×C4—121no—
675C2×C3×C4C23×D311yescharacteristic
676C2×C3×C4C23×D311yescharacteristic
677#67—21no—
678#67—41no—
679#67—41no—
680#67—62no—
681#67—61no—
682#67—61no—
683#67—121no—
684#67—121no—
685#67—121no—
686#67—121no—
687#67—122no—
688#67—122no—
689#67—242no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—41no—
693D12—21no—
694D12—21no—
695D12—31no—
696D12—31no—
697D12—41no—
698D12—61no—
699D12—62no—
700D12—62no—
701D12—61no—
702D12—61no—
703D12—61no—
704D12—61no—
705D12—61no—
706D12—61no—
707D12—61no—
708D12—61no—
709D12—121no—
710D12—121no—
711D12—121no—
712D12—121no—
713D12—121no—
714D12—121no—
715D12—122no—
716D12—122no—
717D12—242no—
718D12D3×D411yescharacteristic
719C4×D3—21no—
720C4×D3—41no—
721C4×D3—41no—
722C4×D3—62no—
723C4×D3—61no—
724C4×D3—61no—
725C4×D3—121no—
726C4×D3—121no—
727C4×D3—121no—
728C4×D3—121no—
729C4×D3—122no—
730C4×D3—122no—
731Dic6—21no—
732Dic6—21no—
733Dic6—31no—
734Dic6—31no—
735Dic6—41no—
736Dic6—61no—
737Dic6D3×D411yescharacteristic
738C3×C8—21no—
739C3×C8—21no—
740C3×C8—31no—
741C3×C8—31no—
742C3×C8—61no—
743C3×C8—61no—
744C3×C8—61no—
745C3×C8C2×D1211yescharacteristic
746C3×C8C2×D1211yescharacteristic
747C3×C8C2×#6711yescharacteristic
748C3×C8C2×#6711yescharacteristic
749C3⋊C8—21no—
750C3⋊C8—21no—
751C3⋊C8—21no—
752C3⋊C8—62no—
753C3⋊C8—61no—
754C3⋊C8—61no—
755C3⋊C8D3×D411yescharacteristic
756C3⋊C8D3×D411yescharacteristic
757C2×C32—21no—
758C2×C32—41no—
759C2×C32—41no—
760C2×C32D4211yescharacteristic
761C3⋊D3—41no—
762C3⋊D3—81no—
763C3⋊D3—81no—
764C3×D3—41no—
765C3×D3—81no—
766#41—31no—
767#41—61no—
768#41—61no—
769#41—61no—
770#41—61no—
771#41—91no—
772#41—121no—
773#41—181no—
774#41—181no—
775#41—181no—
776#41—181no—
777#41C2×D3211yescharacteristic
778#41C2×D3211yescharacteristic
779C2×Q8—31no—
780C2×Q8—61no—
781C2×Q8—61no—
782C2×D4—31no—
783C2×D4—61no—
784C2×D4—61no—
785C2×D4—91no—
786C2×D4—91no—
787C2×D4—121no—
788C2×D4—181no—
789C2×D4—181no—
790C2×D4—181no—
791C2×D4—181no—
792C2×D4—361no—
793C2×D4—361no—
794C2×D4—361no—
795Q16—61no—
796Q16—91no—
797Q16—181no—
798Q16#62611yescharacteristic, complemented
799SD16—61no—
800SD16—61no—
801SD16—61no—
802SD16—61no—
803SD16—91no—
804SD16—91no—
805SD16—181no—
806SD16—181no—
807SD16—181no—
808SD16—181no—
809SD16—181no—
810SD16—181no—
811SD16—181no—
812SD16—181no—
813SD16#62611yescharacteristic, complemented
814SD16#62611yescharacteristic, complemented
815D8—61no—
816D8—91no—
817D8—181no—
818D8—181no—
819D8—181no—
820D8—181no—
821D8—181no—
822D8—181no—
823D8—181no—
824D8—181no—
825D8—181no—
826D8#62611yescharacteristic, complemented
827M16—31no—
828M16—31no—
829M16—31no—
830M16—61no—
831M16—61no—
832M16—61no—
833M16—91no—
834M16—181no—
835C2×C8—31no—
836C2×C8—61no—
837C2×C8—61no—
838C2×C8—61no—
839C2×C8—181no—
840C2×C8C2×D3211yescharacteristic
841C22⋊C4—361no—
842C42—31no—
843C22×C3—21no—
844C22×C3—21no—
845C22×C3—21no—
846C22×C3—21no—
847C22×C3—21no—
848C22×C3—41no—
849C22×C3—41no—
850C22×C3—61no—
851C22×C3—121no—
852C22×C3—241no—
853C22×C3—481no—
854C22×C3#100411yescharacteristic
855C22×C3#100911yescharacteristic
856C2×D3—21no—
857C2×D3—41no—
858C2×D3—62no—
859C2×D3—61no—
860C2×D3—61no—
861C2×D3—81no—
862C2×D3—122no—
863C2×D3—122no—
864C2×D3—121no—
865C2×D3—121no—
866C2×D3—121no—
867C2×D3—121no—
868C2×D3—161no—
869C2×D3—241no—
870C2×D3—241no—
871C2×D3—241no—
872C2×D3—241no—
873C2×D3—481no—
874C2×D3—481no—
875C2×D3—481no—
876C2×D3—481no—
877C2×D3—481no—
878C2×D3—481no—
879C2×D3—482no—
880C2×D3—482no—
881C3×C4—21no—
882C3×C4—21no—
883C3×C4—21no—
884C3×C4—21no—
885C3×C4—21no—
886C3×C4—21no—
887C3×C4—41no—
888C3×C4—41no—
889C3×C4—61no—
890C3×C4—121no—
891C3×C4—121no—
892C3×C4C22×D1211yescharacteristic
893C3×C4C2×D3×D411yescharacteristic
894C3×C4C2×D3×D411yescharacteristic
895C3×C4C22×#6711yescharacteristic
896Dic3—21no—
897Dic3—41no—
898Dic3—41no—
899Dic3—62no—
900Dic3—61no—
901Dic3—61no—
902C32#328811yescharacteristic, complemented, Sylow
903C23—61no—
904C23—121no—
905C23—181no—
906C23—181no—
907C23—361no—
908C23—361no—
909Q8—31no—
910Q8—61no—
911Q8—61no—
912Q8—91no—
913Q8—121no—
914Q8C2×#62611yescharacteristic
915Q8C2×#62611yescharacteristic
916D4—21no—
917D4—21no—
918D4—31no—
919D4—61no—
920D4—61no—
921D4—61no—
922D4—91no—
923D4—121no—
924D4—121no—
925D4—121no—
926D4—181no—
927D4—181no—
928D4—181no—
929D4—181no—
930D4—181no—
931D4—361no—
932D4—361no—
933D4—361no—
934D4—361no—
935D4—722no—
936D4C2×#62611yescharacteristic
937D4C2×#62611yescharacteristic
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—61no—
941C2×C4—61no—
942C2×C4—61no—
943C2×C4—121no—
944C2×C4—121no—
945C2×C4—121no—
946C2×C4—181no—
947C2×C4—361no—
948C2×C4—361no—
949C2×C4C22×D3211yescharacteristic
950C8—31no—
951C8—31no—
952C8—61no—
953C8—61no—
954C8—61no—
955C8—181no—
956C8C2×#62611yescharacteristic
957C8C2×#62611yescharacteristic
958C2×C3—21no—
959C2×C3—21no—
960C2×C3—21no—
961C2×C3—41no—
962C2×C3—41no—
963C2×C3—41no—
964C2×C3—41no—
965C2×C3—41no—
966C2×C3—81no—
967C2×C3—81no—
968C2×C3—121no—
969C2×C3—241no—
970C2×C3D4×D1211yescharacteristic
971C2×C3D4×#6711yescharacteristic
972D3—41no—
973D3—81no—
974D3—122no—
975D3—121no—
976D3—121no—
977D3—242no—
978D3—242no—
979D3—241no—
980D3—241no—
981D3—241no—
982D3—241no—
983C22—21no—
984C22—21no—
985C22—61no—
986C22—121no—
987C22—181no—
988C22—241no—
989C22—361no—
990C22—361no—
991C22—481no—
992C22—721no—
993C22—721no—
994C22—1441no—
995C22—1441no—
996C22#6431411yescharacteristic
997C4—21no—
998C4—21no—
999C4—61no—
1000C4—121no—
1001C4—121no—
1002C4—181no—
1003C4D32×D411yescharacteristic
1004C4C22×#62611yescharacteristic
1005C3—21no—
1006C3#7990011yescharacteristic, complemented
1007C3#8401511yescharacteristic, complemented
1008C2—21no—
1009C2—41no—
1010C2—41no—
1011C2—121no—
1012C2—241no—
1013C2—361no—
1014C2—721no—
1015C2—721no—
1016C2D4×#62611yescharacteristic
subgroupG/H
centerC2D4×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#135C22
socleC2×C32D42
hypercenter#135D32
hypocenterC32#3288
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. #10596240C2semidirect
2. C3×#5770C2semidirect
3. #10595449C2semidirect
4. #10595448C2semidirect
5. C3×#5197C2semidirect
6. #10591690C2semidirect
7. #10591685C2semidirect
8. #10591680C2semidirect
9. #10591677C2semidirect
10. #10591667C2semidirect
11. #10591666C2semidirect
12. #10590928C2semidirect
13. #10590927C2semidirect
14. #10590924C2semidirect
15. #10590881C2semidirect
19. #64366C22semidirect
20. C3×#1010C22semidirect
21. C3×#1009C22semidirect
24. #64158C22semidirect
29. C2×#3745C22semidirect
30. #64110C22semidirect
31. C3×#951C22semidirect
32. C3×#949C22semidirect
33. C3×#948C22semidirect
34. C3×#948C22semidirect
39. C2×C3×#204C22semidirect
40. C3×#901C22semidirect
41. #63911C22semidirect
42. #63864C22semidirect
44. #63833C22semidirect
46. C2×#3717C22semidirect
54. #63825C22semidirect
55. #63825C22semidirect
57. C2×#3714C22semidirect
58. C3×#837C22semidirect
59. C3×#837C22semidirect
60. C3×#819C22semidirect
61. C3×#815C22semidirect
62. #63577C22semidirect
63. #63570C22semidirect
64. #63569C22semidirect
65. #63560C22semidirect
66. #63559C22semidirect
67. #63559C22semidirect
68. #63558C22semidirect
72. #5770D3semidirect
85. #5197D3semidirect
129. C32×Q16D4semidirect
130. C32×SD16D4semidirect
131. C32×SD16D4semidirect
132. C32×D8D4semidirect
162. #3719D4semidirect
168. #3717D4semidirect
170. #3716D4semidirect
176. #3714D4semidirect
180. #1010C2×D3semidirect
187. #1009C2×D3semidirect
201. #951C2×D3semidirect
215. #949C2×D3semidirect
216. #948C2×D3semidirect
217. #948C2×D3semidirect
262. C2×#204C2×D3semidirect
266. #901C2×D3semidirect
274. #837C2×D3semidirect
275. #837C2×D3semidirect
287. #819C2×D3semidirect
288. #815C2×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
798. Q16#626semidirect
813. SD16#626semidirect
814. SD16#626semidirect
826. D8#626semidirect
902. C32#3288semidirect
1006. C3#79900semidirect
1007. C3#84015semidirect

Maximal subgroups

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

subgroupindex
#105962402
C3×#57702
#105954492
#105954482
C3×#51972
#105916902
#105916852
#105916802
#105916772
#105916672
#105916662
#105909282
#105909272
#105909242
#105908812
#840153
#799003