Finite Group Databasebeta

← #11868022

Subgroups — #11868022

Order 1152.

956 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#916C211yesmaximal, characteristic, complemented
2#10595317C211yesmaximal, characteristic, complemented
3#10595095C211yesmaximal, characteristic, complemented
4D3×#901C211yesmaximal, characteristic, complemented
5#10592876C211yesmaximal, characteristic, complemented
6C3×#5177C211yesmaximal, characteristic, complemented
7#10591641C211yesmaximal, characteristic, complemented
8#10591637C211yesmaximal, characteristic, complemented
9#10591543C211yesmaximal, characteristic, complemented
10#10591505C211yesmaximal, characteristic, complemented
11#10591501C211yesmaximal, characteristic, complemented
12#10591406C211yesmaximal, characteristic, complemented
13#10590928C211yesmaximal, characteristic, complemented
14#10590925C211yesmaximal, characteristic, complemented
15D3×#819C211yesmaximal, characteristic, complemented
16#83928—31nomaximal
17#80929—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20D3×#235C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic, complemented
22#64151C2211yescharacteristic
23#64141C2211yescharacteristic
24#64110C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic, complemented
26C3×#942C2211yescharacteristic
27C3×#932C2211yescharacteristic
28C2×C3×#213C2211yescharacteristic, complemented
29C3×#916—21no—
30C3×#916—21no—
31C3×#916—21no—
32C3×#916—21no—
33C2×C3×#204C2211yescharacteristic, complemented
34C3×#901C2211yescharacteristic
35C2×C3×D3×C8C2211yescharacteristic
36#63949—21no—
37#63947—21no—
38#63943—21no—
39#63939—21no—
40#63935—21no—
41#63933—21no—
42#63929—21no—
43#63925—21no—
44#63833C2211yescharacteristic
45#63830C2211yescharacteristic
46#63827C2211yescharacteristic
47#63823C2211yescharacteristic
48#63817C2211yescharacteristic
49#63814C2211yescharacteristic
50D3×#208C2211yescharacteristic
51D3×#208C2211yescharacteristic
52D3×#208C2211yescharacteristic
53#63804—21no—
54#63803—21no—
55D3×ΓL(1,𝔽25)—21no—
56D32×C8—21no—
57#63663C2211yescharacteristic, complemented
58#63660C2211yescharacteristic, complemented
59#63646C2211yescharacteristic, complemented
60C3×#836C2211yescharacteristic, complemented
61C3×#833C2211yescharacteristic, complemented
62C3×#819C2211yescharacteristic, complemented
63#63577C2211yescharacteristic, complemented
64#63577C2211yescharacteristic, complemented
65#63560C2211yescharacteristic, complemented
66#63560C2211yescharacteristic, complemented
67#63558C2211yescharacteristic, complemented
68#63558C2211yescharacteristic, complemented
69C2×C3×#135—31no—
70#5822—31no—
71#5822—31no—
72#5777—31no—
73#5773—31no—
74C2×#916D311yescharacteristic, complemented
75D3×#131—31no—
76C2×#901—31no—
77C3×#471—31no—
78#5237—31no—
79#5237—31no—
80#5204—31no—
81#5199—31no—
82#5192—31no—
83#5192—31no—
84#5177—31no—
85#5177—31no—
86#5177—31no—
87#5177—31no—
88#5177—61no—
89#5177D311yescharacteristic, complemented
90#5160—31no—
91#5160—31no—
92#5141—31no—
93C2×#819—31no—
94#4898—31no—
95D3×#108—31no—
96#4755—31no—
97#4751—31no—
98#4749—31no—
99#4745—31no—
100C2×C32×Q8C2311yescharacteristic
101C2×C32×D4C2311yescharacteristic
102#3828C2311yescharacteristic
103C2×C3×#67—21no—
104C22×C3×Dic3—21no—
105C3×#239—21no—
106C3×#239—21no—
107C3×#239—21no—
108C3×#239—21no—
109C3×#237—21no—
110C3×#237—21no—
111C3×#237—21no—
112C3×#237—21no—
113C3×#235C2311yescharacteristic
114C2×C3×D12—21no—
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119D3×#67—21no—
120#3804—21no—
121D3×D12D411yescharacteristic
122C4×D32—21no—
123#3799D411yescharacteristic
124#3798—21no—
125#3795D411yescharacteristic
126D3×Dic6D411yescharacteristic
127C32×SD16—21no—
128C32×SD16—21no—
129C2×C32×C8C2311yescharacteristic
130#3756—21no—
131#3755—21no—
132#3754—21no—
133#3753—21no—
134#3748C2311yescharacteristic
135#3748C2311yescharacteristic
136#3748C2311yescharacteristic
137#3743—21no—
138C8×C3⋊D3—21no—
139C3×#216—21no—
140C3×#216—21no—
141C3×#216—21no—
142C3×#215—21no—
143C3×#214—21no—
144C3×#213—21no—
145C3×#213—21no—
146C3×#213—21no—
147C3×#208C2311yescharacteristic
148C3×#208C2311yescharacteristic
149C3×#208C2311yescharacteristic
150C2×C3×C3⋊C8C2311yescharacteristic
151C3×#204—21no—
152C3×#204—21no—
153C3×ΓL(1,𝔽25)—21no—
154C3×D3×C8—21no—
155C3×D3×C8D411yescharacteristic
156C3×D3×C8D411yescharacteristic
157C3×D3×C8D411yescharacteristic
158C3×D3×C8D411yescharacteristic
159#3719—21no—
160#3718—21no—
161#3717—21no—
162#3716—21no—
163#3715—21no—
164#3715—21no—
165#3714—21no—
166#3713—21no—
167#3712—21no—
168#3711—21no—
169#3711—21no—
170#3711—21no—
171#3711—21no—
172#3710—21no—
173D3×C3⋊C8—21no—
174D3×C3⋊C8—21no—
175D3×C3⋊C8—21no—
176D3×C3⋊C8—21no—
177#3067—91noSylow
178C2×C3×#41—31no—
179C2×C3×#41—31no—
180D3×#41—31no—
181C2×#239C2×D311yescharacteristic
182C2×#237C2×D311yescharacteristic
183C2×#235—31no—
184C3×#137—31no—
185C3×AGL(1,ℤ/8)—31no—
186C3×#135—61no—
187C3×#135—61no—
188C3×#135—61no—
189C3×#135—61no—
190C2×C3×Q16—31no—
191C2×C3×SD16—21no—
192C2×C3×SD16—31no—
193C2×C3×SD16C2×D311yescharacteristic, complemented
194C2×C3×SD16C2×D311yescharacteristic, complemented
195C2×C3×D8—31no—
196C3×#131—31no—
197C22×C3×C8—31no—
198#951—31no—
199#951—61no—
200#951—61no—
201#950—61no—
202#950—61no—
203#950—61no—
204#950—61no—
205#949—31no—
206#949—61no—
207#949—61no—
208#948—31no—
209C2×#216C2×D311yescharacteristic, complemented
210#942—31no—
211#942—31no—
212#942—31no—
213#942—31no—
214#942—61no—
215#942C2×D311yescharacteristic
216#932—31no—
217#932—31no—
218#932—31no—
219#932—31no—
220#932—61no—
221#932C2×D311yescharacteristic
222C2×#213C2×D311yescharacteristic, complemented
223C2×#208—31no—
224C2×#208—31no—
225C2×#208—31no—
226#919—61no—
227#918—61no—
228#916—21no—
229#916—21no—
230#916—21no—
231#916—21no—
232#916—61no—
233#916—61no—
234#915—61no—
235#914—61no—
236#912—61no—
237#911—61no—
238#909—31no—
239#908—31no—
240#907—31no—
241#907—61no—
242D3×M16—31no—
243D3×M16—31no—
244D3×M16—31no—
245D3×M16—61no—
246C2×#204C2×D311yescharacteristic, complemented
247#901—31no—
248#901—31no—
249#901—31no—
250#901—31no—
251#901—61no—
252#901—61no—
253#901—61no—
254#901—61no—
255#901C2×D311yescharacteristic
256C2×ΓL(1,𝔽25)—61no—
257C2×D3×C8—61no—
258C2×D3×C8—61no—
259C2×D3×C8C2×D311yescharacteristic
260C3×#108—31no—
261C3×#101—31no—
262C3×#100—31no—
263#836—31no—
264#836—31no—
265#836—31no—
266#836—31no—
267#836—61no—
268#836C2×D311yescharacteristic, complemented
269#833—31no—
270#833—31no—
271#833—31no—
272#833—31no—
273#833—61no—
274#833C2×D311yescharacteristic, complemented
275#824—31no—
276#824—31no—
277#823—31no—
278#823—31no—
279#822—31no—
280#822—31no—
281#819—31no—
282#819—31no—
283#819—31no—
284#819—31no—
285#819—61no—
286#819C2×D311yescharacteristic, complemented
287C23×C32—21no—
288C22×C3×D3—21no—
289C22×C3×D3#4111yescharacteristic
290C2×D32—21no—
291C32×Q8—21no—
292C32×Q8—21no—
293C32×D4—21no—
294C32×D4—21no—
295C2×C32×C4—21no—
296C2×C32×C4C2411yescharacteristic
297#638—21no—
298C4⋊(C3⋊D3)C2×D411yescharacteristic
299C4×C3⋊D3—21no—
300#634C2×D411yescharacteristic
301C3×#67—21no—
302C3×#67—41no—
303C3×#67—41no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—41no—
306C2×C3×Dic3—41no—
307C2×C3×Dic3#4111yescharacteristic
308C3×D12—21no—
309C3×D12—21no—
310C3×D12—41no—
311C3×D12—41no—
312C3×D12C2×D411yescharacteristic
313C3×C4×D3—21no—
314C3×C4×D3—41no—
315C3×C4×D3—41no—
316C3×C4×D3C2×D411yescharacteristic
317C3×C4×D3C2×D411yescharacteristic
318C3×C4×D3C2×D411yescharacteristic
319C3×C4×D3C2×D411yescharacteristic
320C3×Dic6—21no—
321C3×Dic6—21no—
322C3×Dic6C2×D411yescharacteristic
323#627—21no—
324#626—21no—
325#626—21no—
326#625—21no—
327#624—21no—
328D3×Dic3—21no—
329D3×Dic3—21no—
330C32×C8C2×D411yescharacteristic
331C32×C8C2×D411yescharacteristic
332C3⋊(C3⋊C8)—21no—
333C3⋊(C3⋊C8)—21no—
334C3⋊(C3⋊C8)—21no—
335C3×C3⋊C8—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C3×C3⋊C8C2×D411yescharacteristic
339C3×C3⋊C8C2×D411yescharacteristic
340#575—91no—
341#575—91no—
342C2×#135—31no—
343C2×#131—91no—
344#473—91no—
345#473—91no—
346#472—91no—
347#472—91no—
348#471—31no—
349#471—91no—
350#471—91no—
351#471—91no—
352C2×#108—91no—
353#413—91no—
354#413—91no—
355C3×#41—31no—
356C3×#41—61no—
357C3×#41—61no—
358C3×#41—61no—
359C3×#41—61no—
360C3×#41—61no—
361C3×#41—61no—
362C3×#41—61no—
363C3×#41—61no—
364C2×C3×Q8—21no—
365C2×C3×Q8—31no—
366C2×C3×Q8C22×D311yescharacteristic
367C2×C3×Q8C22×D311yescharacteristic
368C2×C3×D4—21no—
369C2×C3×D4—31no—
370C2×C3×D4—61no—
371C2×C3×D4—61no—
372C2×C3×D4C22×D311yescharacteristic
373C2×C3×D4C22×D311yescharacteristic
374C22×C3×C4—31no—
375C22×C3×C4—61no—
376C22×C3×C4—61no—
377C2×#67—21no—
378C2×#67—61no—
379C22×Dic3—21no—
380#239—21no—
381#239—21no—
382#239—21no—
383#239—21no—
384#239—31no—
385D3×Q8—31no—
386#237—21no—
387#237—21no—
388#237—21no—
389#237—21no—
390#237—31no—
391#237—61no—
392D3×D4—31no—
393D3×D4—61no—
394#235—31no—
395#235—31no—
396#235—31no—
397#235—31no—
398#235—61no—
399#235—61no—
400#235—61no—
401#235—61no—
402#235C22×D311yescharacteristic
403C2×D12—21no—
404C2×D12—31no—
405C2×D12C22×D311yescharacteristic
406C2×C4×D3—21no—
407C2×C4×D3—61no—
408C2×C4×D3—61no—
409C2×C4×D3C22×D311yescharacteristic
410C2×Dic6—31no—
411C2×Dic6C22×D311yescharacteristic
412C3×Q16—61no—
413C3×Q16—61no—
414C3×Q16—61no—
415C3×SD16—21no—
416C3×SD16—21no—
417C3×SD16—21no—
418C3×SD16—21no—
419C3×SD16—41no—
420C3×SD16—41no—
421C3×SD16—61no—
422C3×SD16—61no—
423C3×SD16—61no—
424C3×SD16—61no—
425C3×D8—61no—
426C3×D8—61no—
427C3×D8—61no—
428C3×M16—31no—
429C3×M16—31no—
430C3×M16—31no—
431C3×M16—61no—
432C2×C3×C8—21no—
433C2×C3×C8—31no—
434C2×C3×C8—31no—
435C2×C3×C8—31no—
436C2×C3×C8—31no—
437C2×C3×C8—31no—
438C2×C3×C8—61no—
439C2×C3×C8C22×D311yescharacteristic
440C2×C3×C8C22×D311yescharacteristic
441#216—21no—
442#216—21no—
443#216—21no—
444#216—61no—
445#216—61no—
446#216—61no—
447#216—61no—
448#216—61no—
449#216—121no—
450#215—21no—
451#215—61no—
452#215—61no—
453#215—61no—
454#215—61no—
455#215—61no—
456#215—121no—
457#214—21no—
458#214—61no—
459#214—61no—
460#214—61no—
461#214—61no—
462#214—61no—
463#214—121no—
464#213—21no—
465#213—21no—
466#213—21no—
467#213—61no—
468#213—61no—
469#213—61no—
470#213—61no—
471#213—61no—
472#213—121no—
473#208—31no—
474#208—31no—
475#208—31no—
476#208—31no—
477#208—31no—
478#208—31no—
479#208—61no—
480#208—61no—
481#208—61no—
482#208—61no—
483#208—61no—
484#208—61no—
485#208—61no—
486#208C22×D311yescharacteristic
487#208C22×D311yescharacteristic
488#208C22×D311yescharacteristic
489C2×C3⋊C8—61no—
490C2×C3⋊C8—61no—
491C2×C3⋊C8—61no—
492C2×C3⋊C8—61no—
493C2×C3⋊C8C22×D311yescharacteristic
494Dic12—61no—
495D24—61no—
496#204—21no—
497#204—21no—
498#204—61no—
499#204—61no—
500ΓL(1,𝔽25)—21no—
501ΓL(1,𝔽25)—61no—
502ΓL(1,𝔽25)—61no—
503ΓL(1,𝔽25)—61no—
504ΓL(1,𝔽25)—61no—
505ΓL(1,𝔽25)—61no—
506ΓL(1,𝔽25)—61no—
507ΓL(1,𝔽25)—61no—
508ΓL(1,𝔽25)—61no—
509ΓL(1,𝔽25)—121no—
510D3×C8—21no—
511D3×C8—61no—
512D3×C8—61no—
513D3×C8—61no—
514D3×C8—61no—
515D3×C8—61no—
516D3×C8—61no—
517D3×C8—61no—
518D3×C8—61no—
519D3×C8—121no—
520D3×C8#6711yescharacteristic
521D3×C8#6711yescharacteristic
522D3×C8#6711yescharacteristic
523D3×C8#6711yescharacteristic
524C22×C32—41no—
525C22×C32—81no—
526C22×C32C2×#4111yescharacteristic
527C2×C3⋊D3—21no—
528C2×C3×D3—21no—
529C2×C3×D3—41no—
530C2×C3×D3—41no—
531C2×C3×D3—81no—
532C2×C3×D3#12111yescharacteristic
533C2×C3×D3#12111yescharacteristic
534D32—42no—
535C32×C4—41no—
536C32×C4C22×D411yescharacteristic
537C32×C4C22×D411yescharacteristic
538C3⋊Dic3—21no—
539C3×Dic3—21no—
540C3×Dic3—41no—
541C3×Dic3#12111yescharacteristic
542C3×Dic3#12111yescharacteristic
543C2×#41—31no—
544C2×#41—31no—
545C2×#41—91no—
546#137—31no—
547#137—91no—
548#137—91no—
549#137—91no—
550#137—181no—
551#137—181no—
552AGL(1,ℤ/8)—31no—
553AGL(1,ℤ/8)—91no—
554AGL(1,ℤ/8)—91no—
555AGL(1,ℤ/8)—91no—
556AGL(1,ℤ/8)—181no—
557AGL(1,ℤ/8)—181no—
558#135—61no—
559#135—61no—
560#135—61no—
561#135—61no—
562#135—181no—
563#135—181no—
564#135—181no—
565#135—181no—
566C2×Q16—31no—
567C2×SD16—31no—
568C2×SD16D3211yescharacteristic, complemented
569C2×D8—31no—
570#131—31no—
571#131—91no—
572#131—91no—
573#131—91no—
574#131—181no—
575#131—181no—
576C2×M16—91no—
577C2×M16—91no—
578C2×M16—91no—
579C2×M16—181no—
580C22×C8—31no—
581C22×C8—181no—
582#108—31no—
583#108—91no—
584#108—91no—
585#108—91no—
586#101—31no—
587#101—91no—
588#101—91no—
589#101—91no—
590#100—31no—
591#100—91no—
592#100—91no—
593#100—91no—
594C23×C3—21no—
595C23×C3—21no—
596C23×C3—31no—
597C23×C3—41no—
598C23×C3—61no—
599C22×D3—21no—
600C22×D3—61no—
601C22×D3—61no—
602C22×D3#23711yescharacteristic
603C3×Q8—21no—
604C3×Q8—21no—
605C3×Q8—21no—
606C3×Q8—21no—
607C3×Q8—31no—
608C3×Q8—41no—
609C3×Q8—41no—
610C3×Q8—61no—
611C3×Q8—61no—
612C3×D4—21no—
613C3×D4—21no—
614C3×D4—21no—
615C3×D4—21no—
616C3×D4—31no—
617C3×D4—41no—
618C3×D4—41no—
619C3×D4—61no—
620C3×D4—61no—
621C3×D4—61no—
622C3×D4—121no—
623C3×D4—121no—
624C3×D4—121no—
625C3×D4—121no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—31no—
630C2×C3×C4—31no—
631C2×C3×C4—31no—
632C2×C3×C4—31no—
633C2×C3×C4—31no—
634C2×C3×C4—41no—
635C2×C3×C4—61no—
636C2×C3×C4—61no—
637C2×C3×C4—121no—
638C2×C3×C4—121no—
639C2×C3×C4—121no—
640C2×C3×C4—121no—
641C2×C3×C4C23×D311yescharacteristic
642C2×C3×C4C23×D311yescharacteristic
643#67—21no—
644#67—41no—
645#67—41no—
646#67—61no—
647#67—61no—
648#67—61no—
649#67—61no—
650#67—61no—
651#67—61no—
652#67—121no—
653C2×Dic3—21no—
654C2×Dic3—41no—
655C2×Dic3—41no—
656C2×Dic3—61no—
657C2×Dic3—61no—
658C2×Dic3#23711yescharacteristic
659D12—21no—
660D12—21no—
661D12—31no—
662D12—31no—
663D12—41no—
664D12—41no—
665D12—61no—
666D12—61no—
667D12—61no—
668D12D3×D411yescharacteristic
669C4×D3—21no—
670C4×D3—41no—
671C4×D3—41no—
672C4×D3—61no—
673C4×D3—61no—
674C4×D3—61no—
675C4×D3—61no—
676C4×D3—61no—
677C4×D3—61no—
678C4×D3—121no—
679C4×D3D3×D411yescharacteristic
680C4×D3D3×D411yescharacteristic
681C4×D3C2×#6711yescharacteristic
682C4×D3C2×#6711yescharacteristic
683Dic6—21no—
684Dic6—21no—
685Dic6—31no—
686Dic6—31no—
687Dic6—61no—
688Dic6—61no—
689Dic6—61no—
690Dic6D3×D411yescharacteristic
691C3×C8—21no—
692C3×C8—21no—
693C3×C8—31no—
694C3×C8—31no—
695C3×C8—61no—
696C3×C8—61no—
697C3×C8—61no—
698C3×C8D3×D411yescharacteristic
699C3×C8D3×D411yescharacteristic
700C3×C8C2×#6711yescharacteristic
701C3×C8C2×#6711yescharacteristic
702C3⋊C8—21no—
703C3⋊C8—21no—
704C3⋊C8—21no—
705C3⋊C8—61no—
706C3⋊C8—61no—
707C3⋊C8—61no—
708C3⋊C8—61no—
709C3⋊C8—61no—
710C3⋊C8—61no—
711C3⋊C8—121no—
712C3⋊C8—121no—
713C3⋊C8—121no—
714C3⋊C8C2×#6711yescharacteristic
715C3⋊C8C2×#6711yescharacteristic
716C2×C32—21no—
717C2×C32—81no—
718C2×C32C2×#12111yescharacteristic
719C3⋊D3—41no—
720C3×D3—21no—
721C3×D3—21no—
722C3×D3—41no—
723C3×D3—81no—
724#41—31no—
725#41—61no—
726#41—61no—
727#41—61no—
728#41—61no—
729#41—61no—
730#41—61no—
731#41—61no—
732#41—61no—
733#41—91no—
734#41—91no—
735#41—91no—
736#41—181no—
737#41—181no—
738C2×Q8—31no—
739C2×Q8—91no—
740C2×Q8C2×D3211yescharacteristic
741C2×D4—31no—
742C2×D4—61no—
743C2×D4—61no—
744C2×D4—91no—
745C2×D4—181no—
746C2×D4C2×D3211yescharacteristic
747C22×C4—31no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—181no—
751Q16—61no—
752Q16—61no—
753Q16—61no—
754Q16—181no—
755Q16—181no—
756Q16—181no—
757SD16—21no—
758SD16—21no—
759SD16—61no—
760SD16—61no—
761SD16—61no—
762SD16—61no—
763SD16—181no—
764SD16—181no—
765SD16—181no—
766SD16—181no—
767SD16—181no—
768SD16—181no—
769D8—61no—
770D8—61no—
771D8—61no—
772D8—181no—
773D8—181no—
774D8—181no—
775M16—31no—
776M16—31no—
777M16—31no—
778M16—61no—
779M16—91no—
780M16—91no—
781M16—91no—
782M16—181no—
783M16—181no—
784M16—181no—
785M16—181no—
786M16—181no—
787M16—181no—
788C2×C8—31no—
789C2×C8—31no—
790C2×C8—31no—
791C2×C8—31no—
792C2×C8—31no—
793C2×C8—61no—
794C2×C8—181no—
795C2×C8—181no—
796C2×C8—181no—
797C2×C8—181no—
798C2×C8—181no—
799C2×C8—181no—
800C2×C8C2×D3211yescharacteristic
801C22×C3—21no—
802C22×C3—31no—
803C22×C3—31no—
804C22×C3—41no—
805C22×C3—41no—
806C22×C3—61no—
807C22×C3—81no—
808C22×C3—81no—
809C22×C3—81no—
810C22×C3—121no—
811C22×C3—121no—
812C22×C3—161no—
813C22×C3—241no—
814C22×C3C2×#23711yescharacteristic
815C22×C3D3×#4111yescharacteristic
816C2×D3—21no—
817C2×D3—41no—
818C2×D3—41no—
819C2×D3—61no—
820C2×D3—61no—
821C2×D3—81no—
822C2×D3—121no—
823C2×D3—122no—
824C2×D3—122no—
825C2×D3#93811yescharacteristic
826C2×D3#93811yescharacteristic
827C3×C4—21no—
828C3×C4—21no—
829C3×C4—31no—
830C3×C4—31no—
831C3×C4—41no—
832C3×C4—41no—
833C3×C4—61no—
834C3×C4—81no—
835C3×C4—121no—
836C3×C4C2×D3×D411yescharacteristic
837C3×C4C2×D3×D411yescharacteristic
838C3×C4C2×D3×D411yescharacteristic
839C3×C4C22×#6711yescharacteristic
840Dic3—21no—
841Dic3—41no—
842Dic3—61no—
843Dic3—61no—
844Dic3—121no—
845Dic3#93811yescharacteristic
846Dic3#93811yescharacteristic
847C32#306711yescharacteristic, complemented, Sylow
848C23—21no—
849C23—31no—
850C23—61no—
851C23—181no—
852Q8—21no—
853Q8—21no—
854Q8—31no—
855Q8—61no—
856Q8—61no—
857Q8—91no—
858Q8—181no—
859D4—21no—
860D4—21no—
861D4—31no—
862D4—61no—
863D4—61no—
864D4—61no—
865D4—91no—
866D4—121no—
867D4—121no—
868D4—121no—
869D4—121no—
870D4—181no—
871D4—181no—
872D4—181no—
873D4—181no—
874C2×C4—21no—
875C2×C4—31no—
876C2×C4—31no—
877C2×C4—31no—
878C2×C4—31no—
879C2×C4—31no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—121no—
883C2×C4—121no—
884C2×C4—121no—
885C2×C4—121no—
886C2×C4—181no—
887C2×C4—181no—
888C2×C4—181no—
889C2×C4—181no—
890C2×C4C22×D3211yescharacteristic
891C8—31no—
892C8—31no—
893C8—61no—
894C8—61no—
895C8—61no—
896C8—181no—
897C8—181no—
898C8—181no—
899C8D3×#6711yescharacteristic
900C8D3×#6711yescharacteristic
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—21no—
904C2×C3—41no—
905C2×C3—61no—
906C2×C3—61no—
907C2×C3—81no—
908C2×C3—81no—
909C2×C3—121no—
910C2×C3—161no—
911C2×C3—241no—
912C2×C3D3×#12111yescharacteristic
913C2×C3C2×#93811yescharacteristic
914D3—21no—
915D3—21no—
916D3—41no—
917D3—81no—
918D3—121no—
919D3—121no—
920D3—241no—
921C22—31no—
922C22—31no—
923C22—41no—
924C22—61no—
925C22—81no—
926C22—121no—
927C22—121no—
928C22—181no—
929C22—241no—
930C22—362no—
931C22D3×#23711yescharacteristic
932C4—31no—
933C4—31no—
934C4—41no—
935C4—61no—
936C4—121no—
937C4—181no—
938C4D32×D411yescharacteristic
939C4C2×D3×#6711yescharacteristic
940C3—21no—
941C3#8092911yescharacteristic, complemented
942C3#8392811yescharacteristic, complemented
943C2—21no—
944C2—61no—
945C2—61no—
946C2—81no—
947C2—121no—
948C2—241no—
949C2—361no—
950C2D3×#93811yescharacteristic
subgroupG/H
centerC2D3×#938
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC2×C32C2×#121
hypercenterC2×SD16D32
hypocenterC32#3067
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. C2×C3×#916C2semidirect
2. #10595317C2semidirect
3. #10595095C2semidirect
4. D3×#901C2semidirect
5. #10592876C2semidirect
6. C3×#5177C2semidirect
7. #10591641C2semidirect
8. #10591637C2semidirect
9. #10591543C2semidirect
10. #10591505C2semidirect
11. #10591501C2semidirect
12. #10591406C2semidirect
13. #10590928C2semidirect
14. #10590925C2semidirect
15. D3×#819C2semidirect
21. C2×C32×SD16C22semidirect
25. C2×C3×#216C22semidirect
28. C2×C3×#213C22semidirect
33. C2×C3×#204C22semidirect
57. #63663C22semidirect
58. #63660C22semidirect
59. #63646C22semidirect
60. C3×#836C22semidirect
61. C3×#833C22semidirect
62. C3×#819C22semidirect
63. #63577C22semidirect
64. #63577C22semidirect
65. #63560C22semidirect
66. #63560C22semidirect
67. #63558C22semidirect
68. #63558C22semidirect
74. C2×#916D3semidirect
89. #5177D3semidirect
193. C2×C3×SD16C2×D3semidirect
194. C2×C3×SD16C2×D3semidirect
209. C2×#216C2×D3semidirect
222. C2×#213C2×D3semidirect
246. C2×#204C2×D3semidirect
268. #836C2×D3semidirect
274. #833C2×D3semidirect
286. #819C2×D3semidirect
568. C2×SD16D32semidirect
847. C32#3067semidirect
941. C3#80929semidirect
942. C3#83928semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9162
#105953172
#105950952
D3×#9012
#105928762
C3×#51772
#105916412
#105916372
#105915432
#105915052
#105915012
#105914062
#105909282
#105909252
D3×#8192
#839283
#809293