Finite Group Databasebeta

← #11886627

Subgroups — #11886627

Order 1152.

982 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5757C211yesmaximal, characteristic, complemented
2#10595105C211yesmaximal, characteristic, complemented
3#10595096C211yesmaximal, characteristic, complemented
4#10594686C211yesmaximal, characteristic, complemented
5#10592859C211yesmaximal, characteristic, complemented
6C3×#5154C211yesmaximal, characteristic, complemented
7#10591525C211yesmaximal, characteristic, complemented
8#10591523C211yesmaximal, characteristic, complemented
9#10591512C211yesmaximal, characteristic, complemented
10#10591509C211yesmaximal, characteristic, complemented
11#10591506C211yesmaximal, characteristic, complemented
12#10591505C211yesmaximal, characteristic, complemented
13#10590925C211yesmaximal, characteristic, complemented
14#10590924C211yesmaximal, characteristic, complemented
15#10590916C211yesmaximal, characteristic, complemented
16#84009—31nomaximal
17#81860—31nomaximal
18C3×#1004C2211yescharacteristic
19C3×#1004C2211yescharacteristic, complemented
20#64307C2211yescharacteristic, complemented
21#64297C2211yescharacteristic, complemented
22C2×C32×D8C2211yescharacteristic, complemented
23#64141C2211yescharacteristic, complemented
24#64141C2211yescharacteristic, complemented
25#64110C2211yescharacteristic, complemented
26C3×#940C2211yescharacteristic, complemented
27C3×#936C2211yescharacteristic, complemented
28C2×C3×#214C2211yescharacteristic, complemented
29C3×#932C2211yescharacteristic
30C3×#932C2211yescharacteristic, complemented
31C2×C3×#213C2211yescharacteristic, complemented
32C3×#912—21no—
33C3×#911—21no—
34C3×#911—21no—
35C3×D3×D8—21no—
36C3×#904C2211yescharacteristic
37C2×C3×#204C2211yescharacteristic, complemented
38C3×#901C2211yescharacteristic, complemented
39#63935—21no—
40#63934—21no—
41#63933—21no—
42#63932—21no—
43#63929—21no—
44D3×#214—21no—
45#63925—21no—
46D3×#213—21no—
47#63829C2211yescharacteristic
48#63827C2211yescharacteristic, complemented
49#63827C2211yescharacteristic, complemented
50#63823C2211yescharacteristic
51#63823C2211yescharacteristic, complemented
52#63814C2211yescharacteristic, complemented
53#63814C2211yescharacteristic, complemented
54#63811—21no—
55#63809—21no—
56#63798—21no—
57#63796—21no—
58#63660C2211yescharacteristic, complemented
59#63660C2211yescharacteristic, complemented
60#63646C2211yescharacteristic, complemented
61C3×#815C2211yescharacteristic, complemented
62#63577C2211yescharacteristic, complemented
63#63570C2211yescharacteristic, complemented
64#63569C2211yescharacteristic, complemented
65#63569C2211yescharacteristic, complemented
66#63569C2211yescharacteristic, complemented
67#63560C2211yescharacteristic, complemented
68#63558C2211yescharacteristic, complemented
69C3×#576—31no—
70#5836—31no—
71#5835—31no—
72#5770—31no—
73#5762—31no—
74#5762—31no—
75#5757—31no—
76#5757D311yescharacteristic, complemented
77C3×#496—31no—
78#5242—31no—
79#5241—31no—
80#5201—31no—
81#5200—31no—
82#5199—31no—
83#5198—31no—
84#5197—31no—
85#5177—31no—
86#5177—31no—
87#5160—31no—
88#5160—31no—
89#5160—31no—
90#5160—61no—
91#5154D311yescharacteristic, complemented
92#5145—31no—
93#5141—31no—
94#5077—31no—
95#5077—31no—
96#5062—31no—
97#5061—31no—
98#4717—31no—
99#4717—31no—
100C2×C32×D4C2311yescharacteristic
101C2×C32×D4C2311yescharacteristic
102#3828C2311yescharacteristic
103C2×C3×#67—41no—
104C2×C3×#67—41no—
105C2×C3×#67—41no—
106C3×#237—21no—
107C3×#237—21no—
108C3×#237—21no—
109C3×#237—21no—
110C3×D3×D4—21no—
111C3×D3×D4—21no—
112C3×D3×D4—21no—
113C3×D3×D4—21no—
114C3×#235C2311yescharacteristic
115C3×#235C2311yescharacteristic
116C3×#235C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119D3×#67—41no—
120#3804—41no—
121#3802—21no—
122D3×D12—21no—
123#3799—21no—
124#3797—21no—
125#3796—21no—
126#3796—21no—
127#3795—21no—
128D3×Dic6—21no—
129C32×D8—21no—
130C32×D8—21no—
131C2×C32×C8C2311yescharacteristic
132#3754—21no—
133#3754—21no—
134#3753—21no—
135#3753—21no—
136#3748C2311yescharacteristic
137#3748C2311yescharacteristic
138#3748C2311yescharacteristic
139#3743—21no—
140C8×C3⋊D3—21no—
141C3×#217—41no—
142C3×#214—21no—
143C3×#214—21no—
144C3×#214—21no—
145C3×#214—21no—
146C3×#213—21no—
147C3×#213—21no—
148C3×#213—21no—
149C3×#213—21no—
150C3×C4×Dic3C2311yescharacteristic
151C3×#208C2311yescharacteristic
152C2×C3×C3⋊C8C2311yescharacteristic
153C3×Dic12D411yescharacteristic, complemented
154C3×D24D411yescharacteristic, complemented
155C3×#204—21no—
156C3×#204—21no—
157C3×#204D411yescharacteristic, complemented
158C3×#204D411yescharacteristic, complemented
159C3×ΓL(1,𝔽25)—21no—
160C3×D3×C8—21no—
161#3719D411yescharacteristic, complemented
162#3718—21no—
163#3718—21no—
164#3717D411yescharacteristic, complemented
165#3716D411yescharacteristic, complemented
166#3715—21no—
167#3715—21no—
168#3715—21no—
169#3715—21no—
170#3714D411yescharacteristic, complemented
171#3713—21no—
172#3713—21no—
173#3711—21no—
174#3711—21no—
175D3×C3⋊C8—21no—
176D3×C3⋊C8—21no—
177#3288—91noSylow
178C3×H(5,𝔽2)—31no—
179C3×H(5,𝔽2)—31no—
180#1010—31no—
181#1009—31no—
182#1007—31no—
183#1004—31no—
184#1004C2×D311yescharacteristic
185#1004C2×D311yescharacteristic, complemented
186C3×AGL(1,ℤ/8)—31no—
187C3×AGL(1,ℤ/8)—31no—
188C3×AGL(1,ℤ/8)—61no—
189C3×AGL(1,ℤ/8)—61no—
190C3×#135—31no—
191C3×#135—61no—
192C2×C3×SD16—31no—
193C2×C3×SD16—31no—
194C2×C3×D8—21no—
195C2×C3×D8—31no—
196C2×C3×D8—61no—
197C2×C3×D8C2×D311yescharacteristic, complemented
198C2×C3×D8C2×D311yescharacteristic, complemented
199C3×#131—31no—
200C3×#127—31no—
201C3×#124—31no—
202#951—31no—
203#951—31no—
204#951—61no—
205#950—31no—
206#950—61no—
207#950—61no—
208#949—31no—
209#949—31no—
210#949—61no—
211#948—31no—
212#948—31no—
213#942—31no—
214#942—31no—
215#940C2×D311yescharacteristic, complemented
216#936C2×D311yescharacteristic, complemented
217C2×#214—61no—
218C2×#214C2×D311yescharacteristic, complemented
219#932—31no—
220#932—31no—
221#932—31no—
222#932—31no—
223#932—31no—
224#932—31no—
225#932—61no—
226#932—61no—
227#932—61no—
228#932—61no—
229#932C2×D311yescharacteristic
230#932C2×D311yescharacteristic, complemented
231C2×#213—61no—
232C2×#213C2×D311yescharacteristic, complemented
233#918—61no—
234#916—61no—
235#916—61no—
236#916—61no—
237#915—61no—
238#915—61no—
239#914—61no—
240#914—61no—
241D3×SD16—61no—
242D3×SD16—61no—
243D3×SD16—61no—
244#912—21no—
245#912—61no—
246#911—21no—
247#911—21no—
248#911—61no—
249#911—61no—
250#911—61no—
251D3×D8—21no—
252D3×D8—61no—
253#904—31no—
254#904C2×D311yescharacteristic
255C2×#204C2×D311yescharacteristic, complemented
256#901—31no—
257#901—31no—
258#901—31no—
259#901—31no—
260#901—61no—
261#901C2×D311yescharacteristic, complemented
262C3×#97—31no—
263#837—31no—
264#837—31no—
265#837—31no—
266#836—31no—
267#833—31no—
268#833—31no—
269#833—31no—
270#833—31no—
271#833—31no—
272#833—61no—
273#833—61no—
274#825—31no—
275#824—31no—
276#823—31no—
277#822—31no—
278#819—31no—
279#819—31no—
280#819—31no—
281#819—61no—
282#815C2×D311yescharacteristic, complemented
283#805—31no—
284#805—31no—
285#805—31no—
286#805—31no—
287C23×C32—21no—
288C23×C32—21no—
289C22×C3×D3—21no—
290C22×C3×D3—41no—
291C22×C3×D3—41no—
292C2×D32—41no—
293C32×D4—21no—
294C32×D4—21no—
295C32×D4—21no—
296C32×D4—21no—
297C2×C32×C4C2411yescharacteristic
298#638—21no—
299C4⋊(C3⋊D3)C2×D411yescharacteristic
300C4×C3⋊D3—21no—
301#634C2×D411yescharacteristic
302C3×#67—21no—
303C3×#67—21no—
304C3×#67—21no—
305C3×#67—41no—
306C3×#67—41no—
307C3×#67—41no—
308C3×#67—41no—
309C3×#67—82no—
310C2×C3×Dic3—21no—
311C2×C3×Dic3—21no—
312C2×C3×Dic3—41no—
313C2×C3×Dic3—41no—
314C3×D12—21no—
315C3×D12—21no—
316C3×D12C2×D411yescharacteristic
317C3×D12C2×D411yescharacteristic
318C3×D12C2×D411yescharacteristic
319C3×C4×D3—21no—
320C3×C4×D3—21no—
321C3×C4×D3—21no—
322C3×Dic6—21no—
323C3×Dic6—21no—
324C3×Dic6C2×D411yescharacteristic
325C3×Dic6C2×D411yescharacteristic
326C3×Dic6C2×D411yescharacteristic
327#627—41no—
328#626—41no—
329#626—41no—
330#625—41no—
331#624—41no—
332D3×Dic3—41no—
333D3×Dic3—41no—
334C32×C8C2×D411yescharacteristic
335C32×C8C2×D411yescharacteristic
336C3⋊(C3⋊C8)—21no—
337C3⋊(C3⋊C8)—21no—
338C3⋊(C3⋊C8)—21no—
339C3×C3⋊C8—21no—
340C3×C3⋊C8C2×D411yescharacteristic
341C3×C3⋊C8C2×D411yescharacteristic
342#577—91no—
343#577—91no—
344#576—31no—
345#576—91no—
346#496—31no—
347#472—91no—
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—31no—
358C3×#41—31no—
359C3×#41—31no—
360C3×#41—61no—
361C3×#41—61no—
362C3×#41—61no—
363C3×#41—61no—
364C2×C3×Q8—31no—
365C2×C3×D4—21no—
366C2×C3×D4—21no—
367C2×C3×D4—31no—
368C2×C3×D4—61no—
369C2×C3×D4—61no—
370C2×C3×D4—61no—
371C2×C3×D4—61no—
372C2×C3×D4—121no—
373C2×C3×D4—121no—
374C2×C3×D4—121no—
375C2×C3×D4C22×D311yescharacteristic
376C2×C3×D4C22×D311yescharacteristic
377C2×C3×D4C22×D311yescharacteristic
378C2×C3×D4C22×D311yescharacteristic
379C2×#67—41no—
380C2×#67—41no—
381C2×#67—41no—
382C2×#67—121no—
383#239—61no—
384#239—61no—
385#239—61no—
386D3×Q8—61no—
387D3×Q8—61no—
388D3×Q8—61no—
389#237—21no—
390#237—21no—
391#237—21no—
392#237—21no—
393#237—61no—
394#237—61no—
395#237—61no—
396#237—121no—
397D3×D4—21no—
398D3×D4—21no—
399D3×D4—21no—
400D3×D4—21no—
401D3×D4—61no—
402D3×D4—61no—
403D3×D4—61no—
404D3×D4—121no—
405#235—31no—
406#235—31no—
407#235—61no—
408#235—61no—
409#235—61no—
410#235—121no—
411#235C22×D311yescharacteristic
412#235C22×D311yescharacteristic
413#235C22×D311yescharacteristic
414C2×D12—61no—
415C2×D12C22×D311yescharacteristic
416C2×Dic6—61no—
417C2×Dic6C22×D311yescharacteristic
418C3×Q16—31no—
419C3×SD16—31no—
420C3×SD16—31no—
421C3×SD16—61no—
422C3×SD16—61no—
423C3×SD16—61no—
424C3×SD16—61no—
425C3×SD16—61no—
426C3×SD16—61no—
427C3×D8—21no—
428C3×D8—21no—
429C3×D8—21no—
430C3×D8—21no—
431C3×D8—31no—
432C3×D8—41no—
433C3×D8—41no—
434C3×D8—61no—
435C3×D8—61no—
436C3×D8—61no—
437C3×D8—61no—
438C3×M16—31no—
439C3×M16—61no—
440C2×C3×C8—21no—
441C2×C3×C8—31no—
442C2×C3×C8—61no—
443C2×C3×C8C22×D311yescharacteristic
444C2×C3×C8C22×D311yescharacteristic
445C3×C22⋊C4—121no—
446C3×C42—31no—
447#217—41no—
448#216—31no—
449#216—61no—
450#216—61no—
451#216—61no—
452#216—61no—
453#215—31no—
454#215—61no—
455#215—61no—
456#215—61no—
457#215—61no—
458#214—21no—
459#214—21no—
460#214—21no—
461#214—21no—
462#214—31no—
463#214—61no—
464#214—61no—
465#214—61no—
466#214—61no—
467#214—61no—
468#214—61no—
469#214—61no—
470#214—61no—
471#214—121no—
472#214—121no—
473#213—21no—
474#213—21no—
475#213—21no—
476#213—21no—
477#213—31no—
478#213—61no—
479#213—61no—
480#213—61no—
481#213—61no—
482#213—61no—
483#213—61no—
484#213—61no—
485#213—61no—
486#213—121no—
487#213—121no—
488C4×Dic3C22×D311yescharacteristic
489#208—31no—
490#208—31no—
491#208—31no—
492#208—31no—
493#208—31no—
494#208—31no—
495#208—61no—
496#208—61no—
497#208—61no—
498#208—61no—
499#208—61no—
500#208C22×D311yescharacteristic
501C2×C3⋊C8—61no—
502C2×C3⋊C8—61no—
503C2×C3⋊C8C22×D311yescharacteristic
504Dic12—31no—
505Dic12#6711yescharacteristic, complemented
506D24—31no—
507D24#6711yescharacteristic, complemented
508#204—21no—
509#204—21no—
510#204—31no—
511#204—31no—
512#204#6711yescharacteristic, complemented
513#204#6711yescharacteristic, complemented
514ΓL(1,𝔽25)—21no—
515ΓL(1,𝔽25)—61no—
516ΓL(1,𝔽25)—61no—
517ΓL(1,𝔽25)—61no—
518ΓL(1,𝔽25)—61no—
519ΓL(1,𝔽25)—121no—
520D3×C8—21no—
521D3×C8—61no—
522D3×C8—61no—
523D3×C8—61no—
524D3×C8—61no—
525D3×C8—121no—
526C22×C32—41no—
527C22×C32—41no—
528C22×C32—81no—
529C22×C32—81no—
530C22×C32H(5,𝔽2)11yescharacteristic
531C2×C3⋊D3—21no—
532C2×C3×D3—21no—
533C2×C3×D3—21no—
534C2×C3×D3—21no—
535C2×C3×D3—41no—
536C2×C3×D3—81no—
537C2×C3×D3—161no—
538C2×C3×D3—161no—
539D32—161no—
540C32×C4C22×D411yescharacteristic
541C32×C4C22×D411yescharacteristic
542C3⋊Dic3—21no—
543C3×Dic3—21no—
544C3×Dic3—21no—
545C3×Dic3—21no—
546C3×Dic3—41no—
547C3×Dic3—41no—
5482−1+4—91no—
549H(5,𝔽2)—31no—
550H(5,𝔽2)—31no—
551H(5,𝔽2)—91no—
552#137—91no—
553#137—91no—
554#137—181no—
555#137—181no—
556AGL(1,ℤ/8)—31no—
557AGL(1,ℤ/8)—31no—
558AGL(1,ℤ/8)—61no—
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—
568#135—31no—
569#135—61no—
570#135—91no—
571#135—181no—
572#135—181no—
573#135—181no—
574C2×SD16—31no—
575C2×SD16—31no—
576C2×SD16—181no—
577C2×SD16—181no—
578C2×D8—31no—
579C2×D8—61no—
580C2×D8—181no—
581C2×D8D3211yescharacteristic, complemented
582#131—31no—
583#131—91no—
584#131—91no—
585#131—91no—
586#127—31no—
587#124—31no—
588#108—91no—
589#108—91no—
590#104—91no—
591#104—91no—
592#104—91no—
593#104—91no—
594#101—91no—
595#100—91no—
596#100—91no—
597#100—91no—
598#97—31no—
599C23×C3—21no—
600C23×C3—21no—
601C23×C3—21no—
602C23×C3—21no—
603C23×C3—41no—
604C23×C3—41no—
605C23×C3—61no—
606C23×C3—121no—
607C23×C3—121no—
608C22×D3—21no—
609C22×D3—41no—
610C22×D3—41no—
611C22×D3—121no—
612C22×D3—121no—
613C3×Q8—31no—
614C3×Q8—31no—
615C3×Q8—31no—
616C3×Q8—61no—
617C3×Q8—61no—
618C3×D4—21no—
619C3×D4—21no—
620C3×D4—21no—
621C3×D4—21no—
622C3×D4—21no—
623C3×D4—21no—
624C3×D4—21no—
625C3×D4—21no—
626C3×D4—31no—
627C3×D4—31no—
628C3×D4—31no—
629C3×D4—41no—
630C3×D4—41no—
631C3×D4—41no—
632C3×D4—41no—
633C3×D4—61no—
634C3×D4—61no—
635C3×D4—61no—
636C3×D4—61no—
637C3×D4—61no—
638C3×D4—121no—
639C3×D4—121no—
640C3×D4—121no—
641C3×D4—121no—
642C3×D4—242no—
643C2×C3×C4—21no—
644C2×C3×C4—61no—
645C2×C3×C4—61no—
646C2×C3×C4—61no—
647C2×C3×C4—61no—
648C2×C3×C4—61no—
649C2×C3×C4—121no—
650C2×C3×C4—121no—
651C2×C3×C4C23×D311yescharacteristic
652C2×C3×C4C23×D311yescharacteristic
653#67—21no—
654#67—21no—
655#67—21no—
656#67—41no—
657#67—41no—
658#67—41no—
659#67—41no—
660#67—61no—
661#67—61no—
662#67—82no—
663#67—121no—
664#67—121no—
665#67—121no—
666#67—121no—
667#67—121no—
668C2×Dic3—21no—
669C2×Dic3—21no—
670C2×Dic3—41no—
671C2×Dic3—41no—
672C2×Dic3—121no—
673C2×Dic3—121no—
674D12—21no—
675D12—21no—
676D12—31no—
677D12—31no—
678D12—61no—
679D12—121no—
680D12—121no—
681D12D3×D411yescharacteristic
682D12C2×#6711yescharacteristic
683D12C2×#6711yescharacteristic
684C4×D3—21no—
685C4×D3—21no—
686C4×D3—21no—
687C4×D3—61no—
688C4×D3—61no—
689C4×D3—121no—
690C4×D3—121no—
691C4×D3—121no—
692C4×D3—121no—
693C4×D3—121no—
694Dic6—21no—
695Dic6—21no—
696Dic6—31no—
697Dic6—31no—
698Dic6—61no—
699Dic6—121no—
700Dic6—121no—
701Dic6D3×D411yescharacteristic
702Dic6C2×#6711yescharacteristic
703Dic6C2×#6711yescharacteristic
704C3×C8—21no—
705C3×C8—21no—
706C3×C8—31no—
707C3×C8—31no—
708C3×C8—61no—
709C3×C8D3×D411yescharacteristic
710C3×C8D3×D411yescharacteristic
711C3×C8C2×#6711yescharacteristic
712C3×C8C2×#6711yescharacteristic
713C3⋊C8—21no—
714C3⋊C8—61no—
715C3⋊C8—61no—
716C3⋊C8—61no—
717C3⋊C8—61no—
718C3⋊C8—61no—
719C3⋊C8—61no—
720C3⋊C8—121no—
721C3⋊C8—121no—
722C3⋊C8—121no—
723C3⋊C8D3×D411yescharacteristic
724C3⋊C8D3×D411yescharacteristic
725C2×C32—21no—
726C2×C32—81no—
727C2×C32—81no—
728C2×C32D4211yescharacteristic
729C3⋊D3—41no—
730C3×D3—41no—
731C3×D3—41no—
732C3×D3—41no—
733C3×D3—81no—
734#41—31no—
735#41—31no—
736#41—31no—
737#41—61no—
738#41—61no—
739#41—61no—
740#41—61no—
741#41—91no—
742#41—181no—
743#41—181no—
744#41—181no—
745#41—181no—
746#41—361no—
747C2×Q8—31no—
748C2×Q8—181no—
749C2×Q8—181no—
750C2×D4—31no—
751C2×D4—61no—
752C2×D4—61no—
753C2×D4—61no—
754C2×D4—61no—
755C2×D4—121no—
756C2×D4—121no—
757C2×D4—121no—
758C2×D4—181no—
759C2×D4—181no—
760C2×D4—361no—
761C2×D4C2×D3211yescharacteristic
762C2×D4C2×D3211yescharacteristic
763Q16—31no—
764Q16—91no—
765Q16—181no—
766Q16—181no—
767SD16—31no—
768SD16—31no—
769SD16—61no—
770SD16—61no—
771SD16—61no—
772SD16—61no—
773SD16—61no—
774SD16—61no—
775SD16—91no—
776SD16—91no—
777SD16—181no—
778SD16—181no—
779SD16—181no—
780SD16—181no—
781SD16—181no—
782SD16—181no—
783D8—21no—
784D8—21no—
785D8—31no—
786D8—61no—
787D8—61no—
788D8—61no—
789D8—61no—
790D8—91no—
791D8—181no—
792D8—181no—
793D8—181no—
794D8—181no—
795M16—31no—
796M16—61no—
797M16—91no—
798M16—91no—
799M16—91no—
800M16—181no—
801M16—181no—
802M16—181no—
803C2×C8—31no—
804C2×C8—61no—
805C2×C8—181no—
806C2×C8—181no—
807C2×C8—181no—
808C2×C8C2×D3211yescharacteristic
809C22⋊C4—121no—
810C42—31no—
811C22×C3—21no—
812C22×C3—41no—
813C22×C3—41no—
814C22×C3—41no—
815C22×C3—41no—
816C22×C3—61no—
817C22×C3—61no—
818C22×C3—61no—
819C22×C3—81no—
820C22×C3—81no—
821C22×C3—81no—
822C22×C3—81no—
823C22×C3—81no—
824C22×C3—81no—
825C22×C3—121no—
826C22×C3—161no—
827C22×C3—161no—
828C22×C3—241no—
829C22×C3—481no—
830C22×C3—481no—
831C22×C3#100411yescharacteristic
832C22×C3#100411yescharacteristic
833C2×D3—21no—
834C2×D3—21no—
835C2×D3—21no—
836C2×D3—41no—
837C2×D3—61no—
838C2×D3—61no—
839C2×D3—81no—
840C2×D3—121no—
841C2×D3—161no—
842C2×D3—161no—
843C2×D3—481no—
844C2×D3—481no—
845C3×C4—21no—
846C3×C4—21no—
847C3×C4—61no—
848C3×C4—61no—
849C3×C4—61no—
850C3×C4—121no—
851C3×C4—121no—
852C3×C4C2×D3×D411yescharacteristic
853C3×C4C2×D3×D411yescharacteristic
854C3×C4C2×D3×D411yescharacteristic
855C3×C4C22×#6711yescharacteristic
856Dic3—21no—
857Dic3—21no—
858Dic3—21no—
859Dic3—41no—
860Dic3—41no—
861Dic3—61no—
862Dic3—61no—
863Dic3—121no—
864C32#328811yescharacteristic, complemented, Sylow
865C23—21no—
866C23—21no—
867C23—61no—
868C23—121no—
869C23—121no—
870C23—361no—
871Q8—31no—
872Q8—31no—
873Q8—31no—
874Q8—61no—
875Q8—61no—
876Q8—91no—
877Q8—361no—
878D4—21no—
879D4—21no—
880D4—21no—
881D4—21no—
882D4—31no—
883D4—31no—
884D4—31no—
885D4—61no—
886D4—61no—
887D4—61no—
888D4—61no—
889D4—61no—
890D4—91no—
891D4—121no—
892D4—121no—
893D4—121no—
894D4—121no—
895D4—181no—
896D4—242no—
897D4—361no—
898D4—361no—
899D4—361no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—61no—
904C2×C4—61no—
905C2×C4—121no—
906C2×C4—121no—
907C2×C4—181no—
908C2×C4—361no—
909C2×C4—361no—
910C2×C4—361no—
911C2×C4C22×D3211yescharacteristic
912C8—31no—
913C8—31no—
914C8—61no—
915C8—181no—
916C8—181no—
917C8—181no—
918C8D3×#6711yescharacteristic
919C8D3×#6711yescharacteristic
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—21no—
923C2×C3—41no—
924C2×C3—81no—
925C2×C3—81no—
926C2×C3—81no—
927C2×C3—81no—
928C2×C3—121no—
929C2×C3—121no—
930C2×C3—121no—
931C2×C3—161no—
932C2×C3—161no—
933C2×C3—241no—
934C2×C3#571711yescharacteristic
935C2×C3D4×#6711yescharacteristic
936D3—41no—
937D3—41no—
938D3—41no—
939D3—81no—
940D3—121no—
941D3—121no—
942D3—241no—
943C22—41no—
944C22—41no—
945C22—61no—
946C22—61no—
947C22—61no—
948C22—81no—
949C22—81no—
950C22—121no—
951C22—181no—
952C22—241no—
953C22—481no—
954C22—481no—
955C22—1441no—
956C22#6431311yescharacteristic
957C4—61no—
958C4—61no—
959C4—61no—
960C4—121no—
961C4—121no—
962C4—181no—
963C4D32×D411yescharacteristic
964C4C2×D3×#6711yescharacteristic
965C3—21no—
966C3#8186011yescharacteristic, complemented
967C3#8400911yescharacteristic, complemented
968C2—21no—
969C2—81no—
970C2—81no—
971C2—121no—
972C2—121no—
973C2—121no—
974C2—241no—
975C2—361no—
976C2#1059529311yescharacteristic
subgroupG/H
centerC2#10595293
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC2×C32D42
hypercenterC2×D8D32
hypocenterC32#3288
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C3×#5757C2semidirect
2. #10595105C2semidirect
3. #10595096C2semidirect
4. #10594686C2semidirect
5. #10592859C2semidirect
6. C3×#5154C2semidirect
7. #10591525C2semidirect
8. #10591523C2semidirect
9. #10591512C2semidirect
10. #10591509C2semidirect
11. #10591506C2semidirect
12. #10591505C2semidirect
13. #10590925C2semidirect
14. #10590924C2semidirect
15. #10590916C2semidirect
19. C3×#1004C22semidirect
20. #64307C22semidirect
21. #64297C22semidirect
22. C2×C32×D8C22semidirect
23. #64141C22semidirect
24. #64141C22semidirect
25. #64110C22semidirect
26. C3×#940C22semidirect
27. C3×#936C22semidirect
28. C2×C3×#214C22semidirect
30. C3×#932C22semidirect
31. C2×C3×#213C22semidirect
37. C2×C3×#204C22semidirect
38. C3×#901C22semidirect
48. #63827C22semidirect
49. #63827C22semidirect
51. #63823C22semidirect
52. #63814C22semidirect
53. #63814C22semidirect
58. #63660C22semidirect
59. #63660C22semidirect
60. #63646C22semidirect
61. C3×#815C22semidirect
62. #63577C22semidirect
63. #63570C22semidirect
64. #63569C22semidirect
65. #63569C22semidirect
66. #63569C22semidirect
67. #63560C22semidirect
68. #63558C22semidirect
76. #5757D3semidirect
91. #5154D3semidirect
153. C3×Dic12D4semidirect
154. C3×D24D4semidirect
157. C3×#204D4semidirect
158. C3×#204D4semidirect
161. #3719D4semidirect
164. #3717D4semidirect
165. #3716D4semidirect
170. #3714D4semidirect
185. #1004C2×D3semidirect
197. C2×C3×D8C2×D3semidirect
198. C2×C3×D8C2×D3semidirect
215. #940C2×D3semidirect
216. #936C2×D3semidirect
218. C2×#214C2×D3semidirect
230. #932C2×D3semidirect
232. C2×#213C2×D3semidirect
255. C2×#204C2×D3semidirect
261. #901C2×D3semidirect
282. #815C2×D3semidirect
505. Dic12#67semidirect
507. D24#67semidirect
512. #204#67semidirect
513. #204#67semidirect
581. C2×D8D32semidirect
864. C32#3288semidirect
966. C3#81860semidirect
967. C3#84009semidirect

Maximal subgroups

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

subgroupindex
C3×#57572
#105951052
#105950962
#105946862
#105928592
C3×#51542
#105915252
#105915232
#105915122
#105915092
#105915062
#105915052
#105909252
#105909242
#105909162
#840093
#818603