Finite Group Databasebeta

← #11886583

Subgroups — #11886583

Order 1152.

1012 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5775C211yesmaximal, characteristic, complemented
2#10595461C211yesmaximal, characteristic, complemented
3#10595448C211yesmaximal, characteristic, complemented
4#10595096C211yesmaximal, characteristic, complemented
5#10592897C211yesmaximal, characteristic, complemented
6C3×#5199C211yesmaximal, characteristic, complemented
7#10591684C211yesmaximal, characteristic, complemented
8#10591674C211yesmaximal, characteristic, complemented
9#10591510C211yesmaximal, characteristic, complemented
10#10591475C211yesmaximal, characteristic, complemented
11#10591407C211yesmaximal, characteristic, complemented
12#10591012C211yesmaximal, characteristic, complemented
13#10590997C211yesmaximal, characteristic, complemented
14#10590994C211yesmaximal, characteristic, complemented
15#10590985C211yesmaximal, characteristic, complemented
16#84015—31nomaximal
17#80939—31nomaximal
18#64366C2211yescharacteristic, complemented
19C3×#1010C2211yescharacteristic, complemented
20C3×#1004C2211yescharacteristic, complemented
21#64307C2211yescharacteristic
22C32×AGL(1,ℤ/8)C2211yescharacteristic, complemented
23#64149C2211yescharacteristic, complemented
24#64141C2211yescharacteristic
25C3×#950C2211yescharacteristic
26C3×#949C2211yescharacteristic, complemented
27C3×#948C2211yescharacteristic, complemented
28C2×C3×#214C2211yescharacteristic, complemented
29C2×C3×#213C2211yescharacteristic, complemented
30C3×#915—21no—
31C3×D3×SD16—21no—
32C3×#912—21no—
33C3×#911—21no—
34C3×#909C2211yescharacteristic, complemented
35C3×#907C2211yescharacteristic, complemented
36#63950—21no—
37#63941—21no—
38#63937—21no—
39#63933—21no—
40#63932—21no—
41#63926—21no—
42#63925—21no—
43D3×#213—21no—
44#63863C2211yescharacteristic, complemented
45#63833—21no—
46#63833C2211yescharacteristic, complemented
47C2×#3717—21no—
48C2×#3717C2211yescharacteristic, complemented
49#63829—21no—
50#63829C2211yescharacteristic
51#63825—21no—
52#63825C2211yescharacteristic
53#63825C2211yescharacteristic, complemented
54C2×#3714C2211yescharacteristic, complemented
55#63823C2211yescharacteristic, complemented
56#63817C2211yescharacteristic, complemented
57#63814C2211yescharacteristic, complemented
58#63664C2211yescharacteristic, complemented
59#63652C2211yescharacteristic, complemented
60#63650C2211yescharacteristic, complemented
61C3×#833C2211yescharacteristic, complemented
62C3×#823C2211yescharacteristic, complemented
63C3×#822C2211yescharacteristic, complemented
64#63577C2211yescharacteristic, complemented
65#63568C2211yescharacteristic, complemented
66#63568C2211yescharacteristic, complemented
67#63560C2211yescharacteristic, complemented
68#63555C2211yescharacteristic, complemented
69C3×#577—31no—
70#5837—31no—
71#5835—31no—
72#5775D311yescharacteristic, complemented
73#5774—31no—
74#5769—31no—
75#5757—31no—
76#5751—31no—
77C3×#472—31no—
78#5245—31no—
79#5241—31no—
80#5203—31no—
81#5202—31no—
82#5201—31no—
83#5199D311yescharacteristic, complemented
84#5198—31no—
85#5198—31no—
86#5198—61no—
87#5197—31no—
88#5177—31no—
89#5176—31no—
90#5154—31no—
91#5145—31no—
92#5145—31no—
93#5142—31no—
94#4898—31no—
95#4894—31no—
96#4749—31no—
97#4748—31no—
98#4747—31no—
99#4746—31no—
100C32×#41C2311yescharacteristic
101C2×C32×D4C2311yescharacteristic
102C2×#638—41no—
103#3832—21no—
104D4×C3⋊D3—21no—
105D4×C3⋊D3—41no—
106#3828—21no—
107#3828C2311yescharacteristic
108C2×C4⋊(C3⋊D3)—21no—
109C2×C4⋊(C3⋊D3)C2311yescharacteristic
110C2×C3×#67—41no—
111C3×D3×Q8—21no—
112C3×#237—21no—
113C3×#237—21no—
114C3×#237—21no—
115C3×#237—41no—
116C3×D3×D4—21no—
117C3×D3×D4—21no—
118C3×#235—21no—
119C3×#235C2311yescharacteristic
120C3×#235C2311yescharacteristic
121C2×C3×D12C2311yescharacteristic
122C2×C3×Dic6—21no—
123C2×C3×Dic6C2311yescharacteristic
124D3×#67—41no—
125#3802—21no—
126D3×D12—21no—
127#3796—21no—
128#3795—21no—
129C32×SD16—21no—
130C32×D8—21no—
131C32×M16C2311yescharacteristic
132#3754—21no—
133#3753—21no—
134C4×C3⋊Dic3C2311yescharacteristic
135#3748C2311yescharacteristic
136C3×#216D411yescharacteristic, complemented
137C3×#215—21no—
138C3×#215D411yescharacteristic, complemented
139C3×#214—21no—
140C3×#214—21no—
141C3×#214D411yescharacteristic, complemented
142C3×#213—21no—
143C3×#213—21no—
144C3×#213—21no—
145C3×#213D411yescharacteristic, complemented
146C3×#208—21no—
147C3×#208C2311yescharacteristic
148C3×#208C2311yescharacteristic
149C2×C3×C3⋊C8—21no—
150C2×C3×C3⋊C8C2311yescharacteristic
151C2×C3×C3⋊C8C2311yescharacteristic
152C3×Dic12—21no—
153C3×#204—21no—
154C3×ΓL(1,𝔽25)—21no—
155C3×D3×C8—21no—
156(C2×D3)⋊Dic3—41no—
157#3719—21no—
158#3719D411yescharacteristic, complemented
159#3717—21no—
160#3717—21no—
161#3717—21no—
162#3717—21no—
163#3717—21no—
164#3717D411yescharacteristic, complemented
165#3716D411yescharacteristic, complemented
166#3715—21no—
167#3714—21no—
168#3714—21no—
169#3714—21no—
170#3714—21no—
171#3714D411yescharacteristic, complemented
172#3713—21no—
173#3712—21no—
174#3711—21no—
175#3710—21no—
176D3×C3⋊C8—21no—
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—61no—
185#1004—31no—
186#1004C2×D311yescharacteristic, complemented
187C3×#137—31no—
188C3×#137—61no—
189C3×AGL(1,ℤ/8)—21no—
190C3×AGL(1,ℤ/8)—31no—
191C3×AGL(1,ℤ/8)—61no—
192C3×AGL(1,ℤ/8)C2×D311yescharacteristic, complemented
193C3×AGL(1,ℤ/8)C2×D311yescharacteristic, complemented
194C3×#135—31no—
195C3×#135—61no—
196C2×C3×SD16—31no—
197C2×C3×SD16—61no—
198C2×C3×D8—31no—
199C3×#131—31no—
200C3×#131—31no—
201#950—31no—
202#950—61no—
203#950—61no—
204#950C2×D311yescharacteristic
205#949—31no—
206#949—31no—
207#949—31no—
208#949—61no—
209#949—61no—
210#949C2×D311yescharacteristic, complemented
211#948—31no—
212#948C2×D311yescharacteristic, complemented
213#947—31no—
214#942—31no—
215#942—61no—
216C2×#215—31no—
217C2×#215—61no—
218#940—31no—
219#940—31no—
220#940—61no—
221#936—31no—
222C2×#214C2×D311yescharacteristic, complemented
223#932—31no—
224#932—31no—
225#932—31no—
226#932—61no—
227#932—61no—
228C2×#213—31no—
229C2×#213—61no—
230C2×#213C2×D311yescharacteristic, complemented
231#919—61no—
232#916—61no—
233#915—21no—
234#914—61no—
235#914—61no—
236#914—61no—
237D3×SD16—21no—
238#912—21no—
239#912—61no—
240#911—21no—
241#911—61no—
242#911—61no—
243#911—61no—
244D3×D8—61no—
245D3×D8—61no—
246D3×D8—61no—
247#909—31no—
248#909—61no—
249#909C2×D311yescharacteristic, complemented
250#908—31no—
251#908—31no—
252#908—61no—
253#907—31no—
254#907C2×D311yescharacteristic, complemented
255#904—31no—
256#904—61no—
257C2×D24—31no—
258C2×#204—31no—
259C2×#204—61no—
260#901—31no—
261#901—31no—
262C3×#108—31no—
263C3×#100—31no—
264C3×#100—31no—
265#837—31no—
266#837—31no—
267#837—31no—
268#837—31no—
269#837—61no—
270#836—31no—
271#833C2×D311yescharacteristic, complemented
272#825—31no—
273#825—31no—
274#825—31no—
275#825—31no—
276#825—61no—
277#824—31no—
278#823—31no—
279#823—31no—
280#823—61no—
281#823C2×D311yescharacteristic, complemented
282#822—31no—
283#822C2×D311yescharacteristic, complemented
284#819—31no—
285#815—31no—
286#815—31no—
287C23×C32—21no—
288C22×C3⋊D3—21no—
289C22×C3⋊D3—41no—
290C22×C3×D3—21no—
291C22×C3×D3—41no—
292C2×D32—41no—
293C32×Q8C2×D411yescharacteristic
294C32×D4—21no—
295C32×D4—21no—
296C32×D4—21no—
297C32×D4C2×D411yescharacteristic
298C2×C32×C4—21no—
299C2×C32×C4C2411yescharacteristic
300#638—21no—
301#638—41no—
302#638—82no—
303C2×C3⋊Dic3—21no—
304C4⋊(C3⋊D3)—21no—
305C4⋊(C3⋊D3)—21no—
306C4⋊(C3⋊D3)—41no—
307C4⋊(C3⋊D3)C2×D411yescharacteristic
308C4×C3⋊D3—21no—
309C4×C3⋊D3—41no—
310#634C2×D411yescharacteristic
311C3×#67—21no—
312C3×#67—21no—
313C3×#67—41no—
314C3×#67—41no—
315C3×#67—41no—
316C2×C3×Dic3—21no—
317C2×C3×Dic3—41no—
318C2×C3×Dic3—41no—
319C3×D12—21no—
320C3×D12—21no—
321C3×D12C2×D411yescharacteristic
322C3×D12C2×D411yescharacteristic
323C3×C4×D3—21no—
324C3×C4×D3—21no—
325C3×C4×D3—41no—
326C3×Dic6—21no—
327C3×Dic6—21no—
328C3×Dic6—41no—
329C3×Dic6C2×D411yescharacteristic
330C3×Dic6C2×D411yescharacteristic
331#626—41no—
332#625—41no—
333D3×Dic3—41no—
334C32×C8—21no—
335C3⋊(C3⋊C8)—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C3×C3⋊C8C2×D411yescharacteristic
339C3×C3⋊C8C2×D411yescharacteristic
340C3×C3⋊C8C2×D411yescharacteristic
341C3×C3⋊C8C2×D411yescharacteristic
342#577—31no—
343#577—91no—
344#576—91no—
345#576—91no—
346#496—91no—
347#472—31no—
348#472—91no—
349#471—91no—
350#471—91no—
351#455—91no—
352#454—91no—
353#453—91no—
354#453—91no—
355#444—91no—
356#444—91no—
357C3×#41—21no—
358C3×#41—31no—
359C3×#41—31no—
360C3×#41—61no—
361C3×#41—61no—
362C3×#41—61no—
363C3×#41—61no—
364C3×#41—121no—
365C3×#41C22×D311yescharacteristic
366C3×#41C22×D311yescharacteristic
367C2×C3×Q8—31no—
368C2×C3×Q8—61no—
369C2×C3×Q8—61no—
370C2×C3×D4—21no—
371C2×C3×D4—31no—
372C2×C3×D4—61no—
373C2×C3×D4—61no—
374C2×C3×D4—121no—
375C2×C3×D4C22×D311yescharacteristic
376C2×C3×D4C22×D311yescharacteristic
377C2×#67—41no—
378C2×#67—121no—
379C2×#67—121no—
380C2×#67—121no—
381C2×#67—122no—
382#239—61no—
383#239—61no—
384#239—61no—
385#239—121no—
386D3×Q8—21no—
387#237—21no—
388#237—21no—
389#237—21no—
390#237—41no—
391#237—61no—
392#237—61no—
393D3×D4—21no—
394D3×D4—21no—
395D3×D4—61no—
396D3×D4—61no—
397D3×D4—61no—
398D3×D4—61no—
399D3×D4—61no—
400D3×D4—121no—
401D3×D4—121no—
402D3×D4—121no—
403D3×D4—121no—
404D3×D4—122no—
405#235—21no—
406#235—31no—
407#235—31no—
408#235—61no—
409#235—61no—
410#235—61no—
411#235—61no—
412#235—121no—
413#235C22×D311yescharacteristic
414#235C22×D311yescharacteristic
415C2×D12—31no—
416C2×D12—31no—
417C2×D12—61no—
418C2×D12—61no—
419C2×D12—61no—
420C2×D12—61no—
421C2×D12—121no—
422C2×D12C22×D311yescharacteristic
423C2×Dic6—21no—
424C2×Dic6C22×D311yescharacteristic
425C3×Q16—31no—
426C3×Q16—61no—
427C3×SD16—21no—
428C3×SD16—21no—
429C3×SD16—31no—
430C3×SD16—31no—
431C3×SD16—41no—
432C3×SD16—61no—
433C3×SD16—61no—
434C3×SD16—61no—
435C3×SD16—61no—
436C3×D8—21no—
437C3×D8—21no—
438C3×D8—31no—
439C3×D8—41no—
440C3×D8—61no—
441C3×D8—61no—
442C3×D8—61no—
443C3×M16—21no—
444C3×M16—31no—
445C3×M16—31no—
446C3×M16—61no—
447C3×M16—61no—
448C3×M16C22×D311yescharacteristic
449C3×M16C22×D311yescharacteristic
450C2×C3×C8—31no—
451C2×C3×C8—31no—
452C2×C3×C8—61no—
453C2×C3×C8—61no—
454#217—121no—
455#216—31no—
456#216—61no—
457#216#6711yescharacteristic, complemented
458#215—21no—
459#215—31no—
460#215—61no—
461#215—61no—
462#215—61no—
463#215—61no—
464#215—61no—
465#215—61no—
466#215#6711yescharacteristic, complemented
467#214—21no—
468#214—21no—
469#214—31no—
470#214—61no—
471#214—61no—
472#214—61no—
473#214—121no—
474#214#6711yescharacteristic, complemented
475#213—21no—
476#213—21no—
477#213—21no—
478#213—31no—
479#213—61no—
480#213—61no—
481#213—61no—
482#213—61no—
483#213—61no—
484#213—61no—
485#213—61no—
486#213—61no—
487#213—121no—
488#213#6711yescharacteristic, complemented
489(C2×D3)⋊C4—121no—
490C4×Dic3—31no—
491C4×Dic3—31no—
492C4×Dic3—61no—
493#208—21no—
494#208—31no—
495#208—31no—
496#208—61no—
497#208—61no—
498#208C22×D311yescharacteristic
499#208C22×D311yescharacteristic
500C2×C3⋊C8—21no—
501C2×C3⋊C8—61no—
502C2×C3⋊C8C22×D311yescharacteristic
503C2×C3⋊C8C22×D311yescharacteristic
504Dic12—21no—
505Dic12—31no—
506Dic12—61no—
507D24—31no—
508D24—61no—
509D24—61no—
510D24—61no—
511D24—61no—
512#204—21no—
513#204—31no—
514#204—31no—
515#204—61no—
516#204—61no—
517#204—61no—
518#204—61no—
519#204—61no—
520ΓL(1,𝔽25)—21no—
521ΓL(1,𝔽25)—61no—
522ΓL(1,𝔽25)—61no—
523ΓL(1,𝔽25)—61no—
524D3×C8—21no—
525D3×C8—61no—
526D3×C8—61no—
527D3×C8—61no—
528C22×C32—21no—
529C22×C32—41no—
530C22×C32—81no—
531C22×C32H(5,𝔽2)11yescharacteristic
532C2×C3⋊D3—21no—
533C2×C3⋊D3—41no—
534C2×C3⋊D3—81no—
535C2×C3⋊D3—161no—
536C2×C3×D3—21no—
537C2×C3×D3—21no—
538C2×C3×D3—41no—
539C2×C3×D3—81no—
540C2×C3×D3—161no—
541D32—161no—
542C32×C4—21no—
543C32×C4C22×D411yescharacteristic
544C32×C4C22×D411yescharacteristic
545C3⋊Dic3—21no—
546C3⋊Dic3—41no—
547C3×Dic3—21no—
548C3×Dic3—21no—
549C3×Dic3—41no—
5502−1+4—31no—
551H(5,𝔽2)—31no—
552H(5,𝔽2)—91no—
553H(5,𝔽2)—91no—
554#137—31no—
555#137—61no—
556#137—91no—
557#137—181no—
558AGL(1,ℤ/8)—31no—
559AGL(1,ℤ/8)—61no—
560AGL(1,ℤ/8)—91no—
561AGL(1,ℤ/8)—91no—
562AGL(1,ℤ/8)—91no—
563AGL(1,ℤ/8)—91no—
564AGL(1,ℤ/8)—181no—
565AGL(1,ℤ/8)—181no—
566AGL(1,ℤ/8)—181no—
567AGL(1,ℤ/8)—181no—
568AGL(1,ℤ/8)—181no—
569AGL(1,ℤ/8)D3211yescharacteristic, complemented
570#135—31no—
571#135—61no—
572#135—91no—
573#135—181no—
574#135—181no—
575#135—181no—
576C2×SD16—31no—
577C2×SD16—61no—
578C2×SD16—91no—
579C2×SD16—181no—
580C2×D8—31no—
581C2×D8—91no—
582C2×D8—181no—
583C2×D8—181no—
584#131—31no—
585#131—31no—
586#131—91no—
587#131—91no—
588#127—91no—
589#124—91no—
590#108—31no—
591#108—91no—
592#104—91no—
593#104—91no—
594#104—91no—
595#104—91no—
596#101—91no—
597#100—31no—
598#100—31no—
599#100—91no—
600#97—91no—
601C23×C3—21no—
602C23×C3—21no—
603C23×C3—41no—
604C23×C3—61no—
605C23×C3—121no—
606C22×D3—21no—
607C22×D3—41no—
608C22×D3—62no—
609C22×D3—61no—
610C22×D3—61no—
611C22×D3—121no—
612C22×D3—121no—
613C22×D3—121no—
614C22×D3—121no—
615C22×D3—122no—
616C3×Q8—21no—
617C3×Q8—31no—
618C3×Q8—31no—
619C3×Q8—61no—
620C3×Q8—61no—
621C3×Q8—121no—
622C3×Q8D3×D411yescharacteristic
623C3×Q8C2×#6711yescharacteristic
624C3×D4—21no—
625C3×D4—21no—
626C3×D4—21no—
627C3×D4—21no—
628C3×D4—21no—
629C3×D4—21no—
630C3×D4—21no—
631C3×D4—31no—
632C3×D4—31no—
633C3×D4—41no—
634C3×D4—41no—
635C3×D4—41no—
636C3×D4—61no—
637C3×D4—61no—
638C3×D4—61no—
639C3×D4—61no—
640C3×D4—121no—
641C3×D4—121no—
642C3×D4—121no—
643C3×D4D3×D411yescharacteristic
644C3×D4C2×#6711yescharacteristic
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—41no—
649C2×C3×C4—61no—
650C2×C3×C4—61no—
651C2×C3×C4—61no—
652C2×C3×C4—121no—
653C2×C3×C4—121no—
654C2×C3×C4—121no—
655C2×C3×C4C23×D311yescharacteristic
656C2×C3×C4C23×D311yescharacteristic
657#67—21no—
658#67—21no—
659#67—41no—
660#67—41no—
661#67—41no—
662#67—61no—
663#67—61no—
664#67—121no—
665#67—121no—
666#67—121no—
667#67—121no—
668#67—121no—
669#67—121no—
670#67—122no—
671#67—242no—
672#67—242no—
673#67—244no—
674C2×Dic3—21no—
675C2×Dic3—41no—
676C2×Dic3—41no—
677C2×Dic3—61no—
678C2×Dic3—61no—
679C2×Dic3—121no—
680C2×Dic3—121no—
681D12—21no—
682D12—21no—
683D12—31no—
684D12—31no—
685D12—61no—
686D12—61no—
687D12—61no—
688D12—61no—
689D12—61no—
690D12—121no—
691D12—121no—
692D12—121no—
693D12—121no—
694D12—122no—
695D12—121no—
696D12D3×D411yescharacteristic
697D12C2×#6711yescharacteristic
698C4×D3—21no—
699C4×D3—21no—
700C4×D3—41no—
701C4×D3—61no—
702C4×D3—61no—
703C4×D3—121no—
704C4×D3—121no—
705C4×D3—121no—
706C4×D3—121no—
707C4×D3—122no—
708Dic6—21no—
709Dic6—21no—
710Dic6—31no—
711Dic6—31no—
712Dic6—41no—
713Dic6—61no—
714Dic6D3×D411yescharacteristic
715Dic6C2×#6711yescharacteristic
716C3×C8—21no—
717C3×C8—21no—
718C3×C8—31no—
719C3×C8—31no—
720C3×C8—31no—
721C3×C8—31no—
722C3×C8—41no—
723C3×C8—61no—
724C3×C8—61no—
725C3⋊C8—21no—
726C3⋊C8—21no—
727C3⋊C8—61no—
728C3⋊C8—61no—
729C3⋊C8—121no—
730C3⋊C8D3×D411yescharacteristic
731C3⋊C8D3×D411yescharacteristic
732C3⋊C8C2×#6711yescharacteristic
733C3⋊C8C2×#6711yescharacteristic
734C2×C32—21no—
735C2×C32—41no—
736C2×C32—81no—
737C2×C32D4211yescharacteristic
738C3⋊D3—41no—
739C3⋊D3—81no—
740C3×D3—41no—
741C3×D3—41no—
742C3×D3—81no—
743#41—31no—
744#41—31no—
745#41—61no—
746#41—61no—
747#41—61no—
748#41—61no—
749#41—91no—
750#41—121no—
751#41—181no—
752#41—181no—
753#41—181no—
754#41—181no—
755#41C2×D3211yescharacteristic
756C2×Q8—31no—
757C2×Q8—61no—
758C2×Q8—61no—
759C2×D4—31no—
760C2×D4—61no—
761C2×D4—61no—
762C2×D4—91no—
763C2×D4—121no—
764C2×D4—181no—
765C2×D4—181no—
766C2×D4—181no—
767C2×D4—181no—
768C2×D4—361no—
769C2×D4—361no—
770C2×D4—361no—
771C2×D4C2×D3211yescharacteristic
772Q16—31no—
773Q16—61no—
774Q16—91no—
775Q16—181no—
776SD16—21no—
777SD16—31no—
778SD16—31no—
779SD16—61no—
780SD16—61no—
781SD16—61no—
782SD16—61no—
783SD16—91no—
784SD16—91no—
785SD16—181no—
786SD16—181no—
787SD16—181no—
788SD16—181no—
789SD16—181no—
790SD16—181no—
791SD16—181no—
792D8—21no—
793D8—31no—
794D8—61no—
795D8—61no—
796D8—61no—
797D8—91no—
798D8—181no—
799D8—181no—
800D8—181no—
801D8—181no—
802D8—181no—
803D8—181no—
804M16—31no—
805M16—31no—
806M16—61no—
807M16—61no—
808M16—91no—
809M16—181no—
810M16—181no—
811M16C2×D3211yescharacteristic
812C2×C8—31no—
813C2×C8—31no—
814C2×C8—61no—
815C2×C8—61no—
816C2×C8—181no—
817C2×C8—181no—
818C22⋊C4—361no—
819C42—91no—
820C22×C3—21no—
821C22×C3—21no—
822C22×C3—21no—
823C22×C3—41no—
824C22×C3—41no—
825C22×C3—41no—
826C22×C3—61no—
827C22×C3—61no—
828C22×C3—81no—
829C22×C3—81no—
830C22×C3—81no—
831C22×C3—82no—
832C22×C3—121no—
833C22×C3—241no—
834C22×C3—481no—
835C22×C3#100411yescharacteristic
836C22×C3#100911yescharacteristic
837C2×D3—21no—
838C2×D3—21no—
839C2×D3—41no—
840C2×D3—61no—
841C2×D3—61no—
842C2×D3—81no—
843C2×D3—121no—
844C2×D3—122no—
845C2×D3—121no—
846C2×D3—121no—
847C2×D3—161no—
848C2×D3—241no—
849C2×D3—241no—
850C2×D3—242no—
851C2×D3—481no—
852C2×D3—481no—
853C2×D3—481no—
854C2×D3—481no—
855C2×D3—482no—
856C3×C4—21no—
857C3×C4—21no—
858C3×C4—21no—
859C3×C4—21no—
860C3×C4—41no—
861C3×C4—61no—
862C3×C4—61no—
863C3×C4—121no—
864C3×C4C2×D3×D411yescharacteristic
865C3×C4C2×D3×D411yescharacteristic
866C3×C4C2×D3×D411yescharacteristic
867C3×C4C22×#6711yescharacteristic
868Dic3—21no—
869Dic3—21no—
870Dic3—41no—
871Dic3—61no—
872Dic3—61no—
873Dic3—121no—
874Dic3—121no—
875Dic3—121no—
876Dic3—122no—
877C32#328811yescharacteristic, complemented, Sylow
878C23—21no—
879C23—61no—
880C23—121no—
881C23—181no—
882C23—361no—
883C23—361no—
884Q8—31no—
885Q8—31no—
886Q8—61no—
887Q8—61no—
888Q8—91no—
889Q8—121no—
890Q8D3×#6711yescharacteristic
891D4—21no—
892D4—21no—
893D4—21no—
894D4—31no—
895D4—31no—
896D4—61no—
897D4—61no—
898D4—61no—
899D4—61no—
900D4—91no—
901D4—121no—
902D4—121no—
903D4—121no—
904D4—181no—
905D4—181no—
906D4—181no—
907D4—361no—
908D4—361no—
909D4—361no—
910D4—361no—
911D4—722no—
912D4D3×#6711yescharacteristic
913C2×C4—21no—
914C2×C4—61no—
915C2×C4—61no—
916C2×C4—61no—
917C2×C4—121no—
918C2×C4—121no—
919C2×C4—121no—
920C2×C4—181no—
921C2×C4—181no—
922C2×C4—361no—
923C2×C4—361no—
924C2×C4C22×D3211yescharacteristic
925C8—21no—
926C8—31no—
927C8—31no—
928C8—31no—
929C8—31no—
930C8—61no—
931C8—61no—
932C8—181no—
933C2×C3—21no—
934C2×C3—21no—
935C2×C3—21no—
936C2×C3—41no—
937C2×C3—41no—
938C2×C3—41no—
939C2×C3—81no—
940C2×C3—81no—
941C2×C3—81no—
942C2×C3—121no—
943C2×C3—121no—
944C2×C3—161no—
945C2×C3—241no—
946C2×C3#560911yescharacteristic
947C2×C3D4×#6711yescharacteristic
948D3—41no—
949D3—41no—
950D3—81no—
951D3—121no—
952D3—121no—
953D3—241no—
954D3—242no—
955D3—241no—
956D3—241no—
957C22—21no—
958C22—41no—
959C22—61no—
960C22—61no—
961C22—81no—
962C22—121no—
963C22—181no—
964C22—241no—
965C22—361no—
966C22—481no—
967C22—721no—
968C22—1441no—
969C22—1441no—
970C22#6431411yescharacteristic
971C4—21no—
972C4—61no—
973C4—61no—
974C4—121no—
975C4—181no—
976C4—361no—
977C4D32×D411yescharacteristic
978C4C2×D3×#6711yescharacteristic
979C3—21no—
980C3#8093911yescharacteristic, complemented
981C3#8401511yescharacteristic, complemented
982C2—21no—
983C2—41no—
984C2—81no—
985C2—121no—
986C2—121no—
987C2—241no—
988C2—361no—
989C2—721no—
990C2#1059529111yescharacteristic
subgroupG/H
centerC2#10595291
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×AGL(1,ℤ/8)C22
socleC2×C32D42
hypercenterAGL(1,ℤ/8)D32
hypocenterC32#3288
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C3×#5775C2semidirect
2. #10595461C2semidirect
3. #10595448C2semidirect
4. #10595096C2semidirect
5. #10592897C2semidirect
6. C3×#5199C2semidirect
7. #10591684C2semidirect
8. #10591674C2semidirect
9. #10591510C2semidirect
10. #10591475C2semidirect
11. #10591407C2semidirect
12. #10591012C2semidirect
13. #10590997C2semidirect
14. #10590994C2semidirect
15. #10590985C2semidirect
18. #64366C22semidirect
19. C3×#1010C22semidirect
20. C3×#1004C22semidirect
22. C32×AGL(1,ℤ/8)C22semidirect
23. #64149C22semidirect
26. C3×#949C22semidirect
27. C3×#948C22semidirect
28. C2×C3×#214C22semidirect
29. C2×C3×#213C22semidirect
34. C3×#909C22semidirect
35. C3×#907C22semidirect
44. #63863C22semidirect
46. #63833C22semidirect
48. C2×#3717C22semidirect
53. #63825C22semidirect
54. C2×#3714C22semidirect
55. #63823C22semidirect
56. #63817C22semidirect
57. #63814C22semidirect
58. #63664C22semidirect
59. #63652C22semidirect
60. #63650C22semidirect
61. C3×#833C22semidirect
62. C3×#823C22semidirect
63. C3×#822C22semidirect
64. #63577C22semidirect
65. #63568C22semidirect
66. #63568C22semidirect
67. #63560C22semidirect
68. #63555C22semidirect
72. #5775D3semidirect
83. #5199D3semidirect
136. C3×#216D4semidirect
138. C3×#215D4semidirect
141. C3×#214D4semidirect
145. C3×#213D4semidirect
158. #3719D4semidirect
164. #3717D4semidirect
165. #3716D4semidirect
171. #3714D4semidirect
180. #1010C2×D3semidirect
186. #1004C2×D3semidirect
192. C3×AGL(1,ℤ/8)C2×D3semidirect
193. C3×AGL(1,ℤ/8)C2×D3semidirect
210. #949C2×D3semidirect
212. #948C2×D3semidirect
222. C2×#214C2×D3semidirect
230. C2×#213C2×D3semidirect
249. #909C2×D3semidirect
254. #907C2×D3semidirect
271. #833C2×D3semidirect
281. #823C2×D3semidirect
283. #822C2×D3semidirect
457. #216#67semidirect
466. #215#67semidirect
474. #214#67semidirect
488. #213#67semidirect
569. AGL(1,ℤ/8)D32semidirect
877. C32#3288semidirect
980. C3#80939semidirect
981. C3#84015semidirect

Maximal subgroups

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

subgroupindex
C3×#57752
#105954612
#105954482
#105950962
#105928972
C3×#51992
#105916842
#105916742
#105915102
#105914752
#105914072
#105910122
#105909972
#105909942
#105909852
#840153
#809393