Finite Group Databasebeta

← #11886620

Subgroups — #11886620

Order 1152.

980 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5762C211yesmaximal, characteristic, complemented
2#10595318C211yesmaximal, characteristic, complemented
3#10595096C211yesmaximal, characteristic, complemented
4#10594687C211yesmaximal, characteristic, complemented
5#10592876C211yesmaximal, characteristic, complemented
6C3×#5176C211yesmaximal, characteristic, complemented
7#10591659C211yesmaximal, characteristic, complemented
8#10591645C211yesmaximal, characteristic, complemented
9#10591642C211yesmaximal, characteristic, complemented
10#10591523C211yesmaximal, characteristic, complemented
11#10591509C211yesmaximal, characteristic, complemented
12#10591505C211yesmaximal, characteristic, complemented
13#10590926C211yesmaximal, characteristic, complemented
14#10590924C211yesmaximal, characteristic, complemented
15#10590916C211yesmaximal, characteristic, complemented
16#84015—31nomaximal
17#81860—31nomaximal
18C3×#1007C2211yescharacteristic, complemented
19C3×#1004C2211yescharacteristic, complemented
20#64307C2211yescharacteristic
21#64307C2211yescharacteristic, complemented
22C2×C32×SD16C2211yescharacteristic, complemented
23#64151C2211yescharacteristic, complemented
24#64141C2211yescharacteristic
25#64110C2211yescharacteristic, complemented
26C3×#947C2211yescharacteristic, complemented
27C3×#942C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic, complemented
29C3×#940C2211yescharacteristic, complemented
30C3×#932C2211yescharacteristic, complemented
31C2×C3×#213C2211yescharacteristic, complemented
32C3×#916—21no—
33C3×#915—21no—
34C3×#914—21no—
35C3×D3×SD16—21no—
36C3×#904C2211yescharacteristic
37C2×C3×D24C2211yescharacteristic, complemented
38C3×#901C2211yescharacteristic, complemented
39#63947—21no—
40#63946—21no—
41#63939—21no—
42D3×#215—21no—
43#63933—21no—
44#63932—21no—
45#63925—21no—
46D3×#213—21no—
47#63829C2211yescharacteristic
48#63823C2211yescharacteristic
49#63823C2211yescharacteristic, complemented
50#63823C2211yescharacteristic, complemented
51#63823C2211yescharacteristic, complemented
52#63814C2211yescharacteristic, complemented
53#63814C2211yescharacteristic, complemented
54#63810—21no—
55#63798—21no—
56#63798—21no—
57#63797—21no—
58#63663C2211yescharacteristic, 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#63558C2211yescharacteristic, complemented
68#63558C2211yescharacteristic, complemented
69C3×#577—31no—
70#5837—31no—
71#5835—31no—
72#5769—31no—
73#5762—31no—
74#5762D311yescharacteristic, complemented
75#5757—31no—
76#5757—31no—
77C3×#496—31no—
78#5245—31no—
79#5241—31no—
80#5203—31no—
81#5202—31no—
82#5199—31no—
83#5198—31no—
84#5197—31no—
85#5177—31no—
86#5177—31no—
87#5177—31no—
88#5177—61no—
89#5176D311yescharacteristic, complemented
90#5160—31no—
91#5160—31no—
92#5145—31no—
93#5142—31no—
94#5077—31no—
95#5077—31no—
96#5062—31no—
97#5061—31no—
98#4717—31no—
99#4717—31no—
100C2×C32×Q8C2311yescharacteristic
101C2×C32×D4C2311yescharacteristic
102#3828C2311yescharacteristic
103C2×C3×#67—41no—
104C2×C3×#67—41no—
105C3×#239—21no—
106C3×#239—21no—
107C3×D3×Q8—21no—
108C3×D3×Q8—21no—
109C3×#237—21no—
110C3×#237—21no—
111C3×D3×D4—21no—
112C3×D3×D4—21no—
113C3×#235—41no—
114C3×#235C2311yescharacteristic
115C3×#235C2311yescharacteristic
116C3×#235C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×D12C2311yescharacteristic
119D3×#67—41no—
120D3×#67—41no—
121#3802—21no—
122#3802—21no—
123D3×D12—21no—
124D3×D12—21no—
125#3796—21no—
126#3796—21no—
127#3795—21no—
128#3795—21no—
129C32×SD16—21no—
130C32×SD16—21no—
131C2×C32×C8C2311yescharacteristic
132#3756—21no—
133#3755—21no—
134#3754—21no—
135#3753—21no—
136#3748C2311yescharacteristic
137#3748C2311yescharacteristic
138#3748C2311yescharacteristic
139#3743—21no—
140C8×C3⋊D3—21no—
141C3×#216—21no—
142C3×#215—21no—
143C3×#215—21no—
144C3×#215—21no—
145C3×#214—21no—
146C3×#213—21no—
147C3×#213—21no—
148C3×#213—21no—
149C3×(C2×D3)⋊C4—41no—
150C3×C4×Dic3C2311yescharacteristic
151C3×#208C2311yescharacteristic
152C2×C3×C3⋊C8C2311yescharacteristic
153C3×Dic12D411yescharacteristic, complemented
154C3×D24—21no—
155C3×D24—21no—
156C3×D24D411yescharacteristic, complemented
157C3×#204D411yescharacteristic, complemented
158C3×#204D411yescharacteristic, complemented
159C3×ΓL(1,𝔽25)—21no—
160C3×D3×C8—21no—
161#3719D411yescharacteristic, complemented
162#3717D411yescharacteristic, complemented
163#3716D411yescharacteristic, complemented
164#3715—21no—
165#3715—21no—
166#3715—21no—
167#3715—21no—
168#3714D411yescharacteristic, complemented
169#3713—21no—
170#3713—21no—
171#3713—21no—
172#3713—21no—
173#3711—21no—
174#3711—21no—
175D3×C3⋊C8—21no—
176D3×C3⋊C8—21no—
177#3288—91noSylow
178C3×2−1+4—31no—
179C3×H(5,𝔽2)—31no—
180#1009—31no—
181#1009—31no—
182#1007C2×D311yescharacteristic, complemented
183#1004—31no—
184#1004—31no—
185#1004C2×D311yescharacteristic, complemented
186C3×#137—31no—
187C3×#137—61no—
188C3×AGL(1,ℤ/8)—31no—
189C3×AGL(1,ℤ/8)—61no—
190C3×#135—31no—
191C3×#135—61no—
192C2×C3×SD16—21no—
193C2×C3×SD16—31no—
194C2×C3×SD16—61no—
195C2×C3×SD16C2×D311yescharacteristic, complemented
196C2×C3×SD16C2×D311yescharacteristic, complemented
197C2×C3×D8—31no—
198C2×C3×D8—31no—
199C3×#131—31no—
200C3×#127—31no—
201C3×#124—31no—
202#950—31no—
203#950—61no—
204#950—61no—
205#949—31no—
206#949—31no—
207#949—31no—
208#949—31no—
209#949—61no—
210#949—61no—
211#948—31no—
212#948—31no—
213#947C2×D311yescharacteristic, complemented
214#942—31no—
215#942—31no—
216#942—61no—
217#942—61no—
218#942C2×D311yescharacteristic, complemented
219C2×#215—61no—
220C2×#215C2×D311yescharacteristic, complemented
221#940C2×D311yescharacteristic, complemented
222#932—31no—
223#932—31no—
224#932—31no—
225#932—31no—
226#932—31no—
227#932—31no—
228#932—61no—
229#932—61no—
230#932C2×D311yescharacteristic, complemented
231C2×#213—61no—
232C2×#213C2×D311yescharacteristic, complemented
233#919—61no—
234#916—21no—
235#916—61no—
236#915—21no—
237#915—61no—
238#914—21no—
239#914—61no—
240#914—61no—
241#914—61no—
242D3×SD16—21no—
243D3×SD16—61no—
244#912—61no—
245#912—61no—
246#911—61no—
247#911—61no—
248#911—61no—
249#911—61no—
250D3×D8—61no—
251D3×D8—61no—
252D3×D8—61no—
253#904—31no—
254#904C2×D311yescharacteristic
255C2×D24C2×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#836—31no—
268#836—61no—
269#833—31no—
270#833—31no—
271#833—31no—
272#833—31no—
273#833—61no—
274#825—31no—
275#823—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—
288C22×C3×D3—21no—
289C22×C3×D3—21no—
290C22×C3×D3—41no—
291C2×D32—41no—
292C2×D32—41no—
293C32×Q8—21no—
294C32×Q8—21no—
295C32×D4—21no—
296C32×D4—21no—
297C2×C32×C4—21no—
298C2×C32×C4C2411yescharacteristic
299#638—21no—
300C4⋊(C3⋊D3)C2×D411yescharacteristic
301C4×C3⋊D3—21no—
302#634C2×D411yescharacteristic
303C3×#67—21no—
304C3×#67—21no—
305C3×#67—21no—
306C3×#67—41no—
307C3×#67—41no—
308C3×#67—82no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3—41no—
311C3×D12—21no—
312C3×D12—21no—
313C3×D12—21no—
314C3×D12—21no—
315C3×D12—41no—
316C3×D12C2×D411yescharacteristic
317C3×D12C2×D411yescharacteristic
318C3×D12C2×D411yescharacteristic
319C3×C4×D3—21no—
320C3×C4×D3—21no—
321C3×C4×D3—21no—
322C3×C4×D3—41no—
323C3×C4×D3—41no—
324C3×Dic6—41no—
325C3×Dic6C2×D411yescharacteristic
326C3×Dic6C2×D411yescharacteristic
327C3×Dic6C2×D411yescharacteristic
328#626—41no—
329#626—41no—
330#625—41no—
331#625—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—31no—
343#577—91no—
344#576—91no—
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—
364C3×#41—121no—
365C2×C3×Q8—21no—
366C2×C3×Q8—61no—
367C2×C3×Q8—61no—
368C2×C3×Q8C22×D311yescharacteristic
369C2×C3×Q8C22×D311yescharacteristic
370C2×C3×D4—21no—
371C2×C3×D4—31no—
372C2×C3×D4—31no—
373C2×C3×D4—61no—
374C2×C3×D4—61no—
375C2×C3×D4—121no—
376C2×C3×D4—121no—
377C2×C3×D4C22×D311yescharacteristic
378C2×C3×D4C22×D311yescharacteristic
379C2×#67—41no—
380C2×#67—41no—
381C2×#67—121no—
382C2×#67—121no—
383#239—21no—
384#239—21no—
385#239—61no—
386#239—61no—
387D3×Q8—21no—
388D3×Q8—21no—
389#237—21no—
390#237—21no—
391#237—61no—
392#237—61no—
393#237—61no—
394#237—61no—
395D3×D4—21no—
396D3×D4—21no—
397D3×D4—61no—
398D3×D4—61no—
399D3×D4—61no—
400D3×D4—61no—
401D3×D4—61no—
402D3×D4—61no—
403D3×D4—121no—
404D3×D4—121no—
405#235—31no—
406#235—31no—
407#235—41no—
408#235—61no—
409#235—61no—
410#235—61no—
411#235C22×D311yescharacteristic
412#235C22×D311yescharacteristic
413#235C22×D311yescharacteristic
414C2×D12—61no—
415C2×D12—61no—
416C2×D12C22×D311yescharacteristic
417C2×D12C22×D311yescharacteristic
418C3×Q16—31no—
419C3×Q16—61no—
420C3×SD16—21no—
421C3×SD16—21no—
422C3×SD16—21no—
423C3×SD16—21no—
424C3×SD16—31no—
425C3×SD16—31no—
426C3×SD16—41no—
427C3×SD16—41no—
428C3×SD16—61no—
429C3×SD16—61no—
430C3×SD16—61no—
431C3×SD16—61no—
432C3×D8—31no—
433C3×D8—61no—
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#216—21no—
448#216—31no—
449#216—61no—
450#216—61no—
451#216—121no—
452#215—21no—
453#215—21no—
454#215—21no—
455#215—31no—
456#215—61no—
457#215—61no—
458#215—61no—
459#215—61no—
460#215—61no—
461#215—61no—
462#215—121no—
463#214—21no—
464#214—31no—
465#214—61no—
466#214—61no—
467#214—61no—
468#214—61no—
469#214—61no—
470#214—61no—
471#214—121no—
472#213—21no—
473#213—21no—
474#213—21no—
475#213—31no—
476#213—61no—
477#213—61no—
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(C2×D3)⋊C4—41no—
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—21no—
507D24—21no—
508D24—31no—
509D24#6711yescharacteristic, complemented
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—81no—
528C22×C32H(5,𝔽2)11yescharacteristic
529C2×C3⋊D3—21no—
530C2×C3×D3—21no—
531C2×C3×D3—21no—
532C2×C3×D3—21no—
533C2×C3×D3—41no—
534C2×C3×D3—41no—
535C2×C3×D3—81no—
536C2×C3×D3—81no—
537C2×C3×D3—161no—
538D32—161no—
539D32—161no—
540C32×C4—41no—
541C32×C4C22×D411yescharacteristic
542C32×C4C22×D411yescharacteristic
543C3⋊Dic3—21no—
544C3×Dic3—21no—
545C3×Dic3—21no—
546C3×Dic3—21no—
547C3×Dic3—41no—
5482−1+4—31no—
549H(5,𝔽2)—31no—
550H(5,𝔽2)—91no—
551H(5,𝔽2)—91no—
552#137—31no—
553#137—61no—
554#137—91no—
555#137—181no—
556AGL(1,ℤ/8)—31no—
557AGL(1,ℤ/8)—61no—
558AGL(1,ℤ/8)—91no—
559AGL(1,ℤ/8)—91no—
560AGL(1,ℤ/8)—91no—
561AGL(1,ℤ/8)—91no—
562AGL(1,ℤ/8)—91no—
563AGL(1,ℤ/8)—181no—
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—61no—
576C2×SD16—181no—
577C2×SD16D3211yescharacteristic, complemented
578C2×D8—31no—
579C2×D8—31no—
580C2×D8—181no—
581C2×D8—181no—
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—41no—
602C23×C3—61no—
603C23×C3—61no—
604C23×C3—121no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—41no—
608C22×D3—121no—
609C22×D3—121no—
610C22×D3—121no—
611C22×D3—121no—
612C3×Q8—21no—
613C3×Q8—21no—
614C3×Q8—21no—
615C3×Q8—21no—
616C3×Q8—31no—
617C3×Q8—31no—
618C3×Q8—31no—
619C3×Q8—41no—
620C3×Q8—41no—
621C3×Q8—121no—
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—61no—
632C3×D4—61no—
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—242no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—41no—
646C2×C3×C4—61no—
647C2×C3×C4—61no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4—121no—
651C2×C3×C4—121no—
652C2×C3×C4—121no—
653C2×C3×C4C23×D311yescharacteristic
654C2×C3×C4C23×D311yescharacteristic
655#67—21no—
656#67—21no—
657#67—21no—
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—
668#67—121no—
669#67—121no—
670C2×Dic3—21no—
671C2×Dic3—41no—
672C2×Dic3—121no—
673C2×Dic3—121no—
674D12—21no—
675D12—21no—
676D12—21no—
677D12—21no—
678D12—31no—
679D12—31no—
680D12—41no—
681D12—61no—
682D12—121no—
683D12—121no—
684D12D3×D411yescharacteristic
685D12C2×#6711yescharacteristic
686D12C2×#6711yescharacteristic
687C4×D3—21no—
688C4×D3—21no—
689C4×D3—21no—
690C4×D3—41no—
691C4×D3—41no—
692C4×D3—61no—
693C4×D3—61no—
694C4×D3—121no—
695C4×D3—121no—
696C4×D3—121no—
697Dic6—31no—
698Dic6—31no—
699Dic6—41no—
700Dic6—61no—
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×C32D4211yescharacteristic
728C3⋊D3—41no—
729C3×D3—41no—
730C3×D3—41no—
731C3×D3—41no—
732C3×D3—81no—
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—121no—
743#41—181no—
744#41—181no—
745#41—181no—
746#41—181no—
747C2×Q8—61no—
748C2×Q8—61no—
749C2×Q8C2×D3211yescharacteristic
750C2×D4—31no—
751C2×D4—31no—
752C2×D4—61no—
753C2×D4—61no—
754C2×D4—121no—
755C2×D4—121no—
756C2×D4—181no—
757C2×D4—181no—
758C2×D4—181no—
759C2×D4—181no—
760C2×D4—361no—
761C2×D4—361no—
762C2×D4C2×D3211yescharacteristic
763Q16—31no—
764Q16—61no—
765Q16—91no—
766Q16—181no—
767SD16—21no—
768SD16—21no—
769SD16—31no—
770SD16—31no—
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—31no—
784D8—61no—
785D8—61no—
786D8—61no—
787D8—61no—
788D8—61no—
789D8—91no—
790D8—181no—
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—61no—
815C22×C3—61no—
816C22×C3—61no—
817C22×C3—81no—
818C22×C3—81no—
819C22×C3—81no—
820C22×C3—121no—
821C22×C3—121no—
822C22×C3—161no—
823C22×C3—241no—
824C22×C3—241no—
825C22×C3—481no—
826C22×C3#100411yescharacteristic
827C22×C3#100411yescharacteristic
828C2×D3—21no—
829C2×D3—21no—
830C2×D3—21no—
831C2×D3—41no—
832C2×D3—41no—
833C2×D3—61no—
834C2×D3—61no—
835C2×D3—81no—
836C2×D3—81no—
837C2×D3—121no—
838C2×D3—161no—
839C2×D3—481no—
840C2×D3—481no—
841C2×D3—481no—
842C2×D3—481no—
843C3×C4—21no—
844C3×C4—21no—
845C3×C4—41no—
846C3×C4—41no—
847C3×C4—61no—
848C3×C4—61no—
849C3×C4—61no—
850C3×C4—81no—
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—61no—
861Dic3—61no—
862Dic3—121no—
863C32#328811yescharacteristic, complemented, Sylow
864C23—21no—
865C23—61no—
866C23—61no—
867C23—121no—
868C23—361no—
869C23—361no—
870Q8—21no—
871Q8—21no—
872Q8—31no—
873Q8—31no—
874Q8—31no—
875Q8—91no—
876Q8—121no—
877D4—21no—
878D4—21no—
879D4—31no—
880D4—31no—
881D4—31no—
882D4—61no—
883D4—61no—
884D4—61no—
885D4—61no—
886D4—61no—
887D4—61no—
888D4—61no—
889D4—91no—
890D4—121no—
891D4—121no—
892D4—121no—
893D4—181no—
894D4—242no—
895D4—361no—
896D4—361no—
897D4—361no—
898D4—361no—
899C2×C4—21no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—61no—
904C2×C4—121no—
905C2×C4—121no—
906C2×C4—121no—
907C2×C4—181no—
908C2×C4—361no—
909C2×C4—361no—
910C2×C4C22×D3211yescharacteristic
911C8—31no—
912C8—31no—
913C8—61no—
914C8—181no—
915C8—181no—
916C8—181no—
917C8D3×#6711yescharacteristic
918C8D3×#6711yescharacteristic
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—41no—
923C2×C3—81no—
924C2×C3—81no—
925C2×C3—121no—
926C2×C3—121no—
927C2×C3—121no—
928C2×C3—161no—
929C2×C3—241no—
930C2×C3—241no—
931C2×C3#571711yescharacteristic
932C2×C3D4×#6711yescharacteristic
933D3—41no—
934D3—41no—
935D3—41no—
936D3—81no—
937D3—81no—
938D3—121no—
939D3—121no—
940D3—241no—
941C22—41no—
942C22—61no—
943C22—61no—
944C22—61no—
945C22—81no—
946C22—121no—
947C22—121no—
948C22—181no—
949C22—241no—
950C22—241no—
951C22—481no—
952C22—1441no—
953C22—1441no—
954C22#6431311yescharacteristic
955C4—41no—
956C4—61no—
957C4—61no—
958C4—61no—
959C4—121no—
960C4—181no—
961C4D32×D411yescharacteristic
962C4C2×D3×#6711yescharacteristic
963C3—21no—
964C3#8186011yescharacteristic, complemented
965C3#8401511yescharacteristic, complemented
966C2—21no—
967C2—81no—
968C2—121no—
969C2—121no—
970C2—121no—
971C2—241no—
972C2—241no—
973C2—361no—
974C2#1059529311yescharacteristic
subgroupG/H
centerC2#10595293
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC2×C32D42
hypercenterC2×SD16D32
hypocenterC32#3288
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C3×#5762C2semidirect
2. #10595318C2semidirect
3. #10595096C2semidirect
4. #10594687C2semidirect
5. #10592876C2semidirect
6. C3×#5176C2semidirect
7. #10591659C2semidirect
8. #10591645C2semidirect
9. #10591642C2semidirect
10. #10591523C2semidirect
11. #10591509C2semidirect
12. #10591505C2semidirect
13. #10590926C2semidirect
14. #10590924C2semidirect
15. #10590916C2semidirect
18. C3×#1007C22semidirect
19. C3×#1004C22semidirect
21. #64307C22semidirect
22. C2×C32×SD16C22semidirect
23. #64151C22semidirect
25. #64110C22semidirect
26. C3×#947C22semidirect
27. C3×#942C22semidirect
28. C2×C3×#215C22semidirect
29. C3×#940C22semidirect
30. C3×#932C22semidirect
31. C2×C3×#213C22semidirect
37. C2×C3×D24C22semidirect
38. C3×#901C22semidirect
49. #63823C22semidirect
50. #63823C22semidirect
51. #63823C22semidirect
52. #63814C22semidirect
53. #63814C22semidirect
58. #63663C22semidirect
59. #63660C22semidirect
60. #63646C22semidirect
61. C3×#815C22semidirect
62. #63577C22semidirect
63. #63570C22semidirect
64. #63569C22semidirect
65. #63569C22semidirect
66. #63569C22semidirect
67. #63558C22semidirect
68. #63558C22semidirect
74. #5762D3semidirect
89. #5176D3semidirect
153. C3×Dic12D4semidirect
156. C3×D24D4semidirect
157. C3×#204D4semidirect
158. C3×#204D4semidirect
161. #3719D4semidirect
162. #3717D4semidirect
163. #3716D4semidirect
168. #3714D4semidirect
182. #1007C2×D3semidirect
185. #1004C2×D3semidirect
195. C2×C3×SD16C2×D3semidirect
196. C2×C3×SD16C2×D3semidirect
213. #947C2×D3semidirect
218. #942C2×D3semidirect
220. C2×#215C2×D3semidirect
221. #940C2×D3semidirect
230. #932C2×D3semidirect
232. C2×#213C2×D3semidirect
255. C2×D24C2×D3semidirect
261. #901C2×D3semidirect
282. #815C2×D3semidirect
505. Dic12#67semidirect
509. D24#67semidirect
512. #204#67semidirect
513. #204#67semidirect
577. C2×SD16D32semidirect
863. C32#3288semidirect
964. C3#81860semidirect
965. C3#84015semidirect

Maximal subgroups

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

subgroupindex
C3×#57622
#105953182
#105950962
#105946872
#105928762
C3×#51762
#105916592
#105916452
#105916422
#105915232
#105915092
#105915052
#105909262
#105909242
#105909162
#840153
#818603