Finite Group Databasebeta

← #11868097

Subgroups — #11868097

Order 1152.

984 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#914C211yesmaximal, characteristic, complemented
2#10595317C211yesmaximal, characteristic, complemented
3D3×#932C211yesmaximal, characteristic, complemented
4#10594668C211yesmaximal, characteristic, complemented
5#10592876C211yesmaximal, characteristic, complemented
6C3×#5177C211yesmaximal, characteristic, complemented
7#10591642C211yesmaximal, characteristic, complemented
8#10591637C211yesmaximal, characteristic, complemented
9#10591542C211yesmaximal, characteristic, complemented
10#10591505C211yesmaximal, characteristic, complemented
11D3×#833C211yesmaximal, characteristic, complemented
12#10591406C211yesmaximal, characteristic, complemented
13#10590929C211yesmaximal, characteristic, complemented
14#10590926C211yesmaximal, characteristic, complemented
15#10590912C211yesmaximal, characteristic, complemented
16#83963—31nomaximal
17#80930—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20D3×#235C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic, complemented
22#64151C2211yescharacteristic, complemented
23#64141C2211yescharacteristic
24#64110C2211yescharacteristic, complemented
25C3×#942C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic, complemented
27C3×#932C2211yescharacteristic
28C2×C3×#213C2211yescharacteristic, complemented
29C3×#914—21no—
30C3×#914—21no—
31C3×#914—21no—
32C3×#914—21no—
33C2×C3×D24C2211yescharacteristic, complemented
34C3×#901C2211yescharacteristic, complemented
35C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
36#63949—21no—
37#63947—21no—
38#63943—21no—
39#63939—21no—
40#63934—21no—
41#63932—21no—
42D3×#214—21no—
43D3×#213—21no—
44#63830C2211yescharacteristic
45#63830C2211yescharacteristic, complemented
46#63823C2211yescharacteristic
47#63823C2211yescharacteristic, complemented
48#63817C2211yescharacteristic, complemented
49#63814C2211yescharacteristic, complemented
50D3×#208C2211yescharacteristic
51D3×#208C2211yescharacteristic
52D3×#208C2211yescharacteristic
53#63805—21no—
54#63804—21no—
55#63791—21no—
56D3×ΓL(1,𝔽25)—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#63558C2211yescharacteristic, complemented
66#63558C2211yescharacteristic, complemented
67#63558C2211yescharacteristic, complemented
68#63558C2211yescharacteristic, complemented
69C2×C3×AGL(1,ℤ/8)—31no—
70#5822—31no—
71C2×#932—31no—
72#5777—31no—
73D3×AGL(1,ℤ/8)—31no—
74C2×#914D311yescharacteristic, complemented
75#5750—31no—
76#5745—31no—
77C3×#471—31no—
78#5237—31no—
79C2×#833—31no—
80#5203—31no—
81#5199—31no—
82#5177—31no—
83#5177—31no—
84#5177—31no—
85#5177—31no—
86#5177—61no—
87#5177D311yescharacteristic, complemented
88#5160—31no—
89#5160—31no—
90#5160—31no—
91#5160—31no—
92#5142—31no—
93#5125—31no—
94#4897—31no—
95#4893—31no—
96#4754—31no—
97#4751—31no—
98#4749—31no—
99D3×#100—31no—
100C23×C3×D3—21no—
101C2×C32×Q8C2311yescharacteristic
102C2×C32×D4C2311yescharacteristic
103#3828C2311yescharacteristic
104C2×C3×#67—21no—
105C3×#239—21no—
106C3×#239—21no—
107C3×#239—21no—
108C3×#239—21no—
109C3×D3×D4—21no—
110C3×D3×D4—21no—
111C3×D3×D4—21no—
112C3×D3×D4—21no—
113C3×#235C2311yescharacteristic
114C2×C3×D12—21no—
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3C2311yescharacteristic
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×#215—21no—
141C3×#215—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×D24—21no—
152C3×D24—21no—
153C3×ΓL(1,𝔽25)—21no—
154C3×ΓL(1,𝔽25)D411yescharacteristic
155C3×ΓL(1,𝔽25)D411yescharacteristic
156C3×ΓL(1,𝔽25)D411yescharacteristic
157C3×ΓL(1,𝔽25)D411yescharacteristic
158C3×D3×C8—21no—
159#3716—21no—
160#3716—21no—
161#3715—21no—
162#3715—21no—
163#3714—21no—
164#3714—21no—
165#3713—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#3068—91noSylow
178C2×C3×#41—31no—
179C22×C3×D4—31no—
180D3×#41—31no—
181C2×#239C2×D311yescharacteristic
182C2×D3×D4C2×D311yescharacteristic
183C2×#235—31no—
184C3×#137—31no—
185C3×AGL(1,ℤ/8)—31no—
186C3×AGL(1,ℤ/8)—61no—
187C3×AGL(1,ℤ/8)—61no—
188C3×AGL(1,ℤ/8)—61no—
189C3×AGL(1,ℤ/8)—61no—
190C2×C3×SD16—21no—
191C2×C3×SD16—31no—
192C2×C3×SD16C2×D311yescharacteristic, complemented
193C2×C3×SD16C2×D311yescharacteristic, complemented
194C2×C3×D8—31no—
195C2×C3×D8—31no—
196C3×#131—31no—
197C2×C3×M16—31no—
198#951—61no—
199#950—61no—
200#950—61no—
201#949—31no—
202#949—31no—
203#949—61no—
204#948—31no—
205#942—31no—
206#942—31no—
207#942—61no—
208#942C2×D311yescharacteristic, complemented
209C2×#215C2×D311yescharacteristic, complemented
210C2×#214—61no—
211#932—31no—
212#932—31no—
213#932—31no—
214#932—31no—
215#932—31no—
216#932—31no—
217#932—61no—
218#932—61no—
219#932—61no—
220#932C2×D311yescharacteristic
221C2×#213—61no—
222C2×#213C2×D311yescharacteristic, complemented
223C2×#208—31no—
224C2×#208—31no—
225C2×#208—31no—
226#919—61no—
227#918—61no—
228#916—61no—
229#914—21no—
230#914—21no—
231#914—21no—
232#914—21no—
233#914—61no—
234#914—61no—
235D3×SD16—61no—
236#911—61no—
237D3×D8—61no—
238#908—31no—
239#908—31no—
240#907—31no—
241#907—61no—
242#907—61no—
243#907—61no—
244D3×M16—31no—
245D3×M16—31no—
246D3×M16—31no—
247D3×M16—61no—
248D3×M16—61no—
249D3×M16—61no—
250C2×D24C2×D311yescharacteristic, complemented
251#901—31no—
252#901—31no—
253#901—31no—
254#901—31no—
255#901—61no—
256#901—61no—
257#901C2×D311yescharacteristic, complemented
258C2×ΓL(1,𝔽25)—61no—
259C2×ΓL(1,𝔽25)C2×D311yescharacteristic
260C3×#108—31no—
261C3×#101—31no—
262C3×#100—31no—
263#836—31no—
264#836—31no—
265#836—61no—
266#836C2×D311yescharacteristic, complemented
267#833—31no—
268#833—31no—
269#833—31no—
270#833—31no—
271#833—31no—
272#833—31no—
273#833—61no—
274#833C2×D311yescharacteristic, complemented
275#823—31no—
276#823—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—21no—
290C22×C3×D3—41no—
291C22×C3×D3—41no—
292C22×C3×D3—82no—
293C22×C3×D3#4111yescharacteristic
294C2×D32—21no—
295C32×Q8—21no—
296C32×Q8—21no—
297C32×D4—21no—
298C32×D4—21no—
299C2×C32×C4—21no—
300C2×C32×C4C2411yescharacteristic
301#638—21no—
302C4⋊(C3⋊D3)C2×D411yescharacteristic
303C4×C3⋊D3—21no—
304#634C2×D411yescharacteristic
305C3×#67—21no—
306C3×#67—41no—
307C3×#67—41no—
308C2×C3×Dic3#4111yescharacteristic
309C3×D12—21no—
310C3×D12—21no—
311C3×D12—21no—
312C3×D12—21no—
313C3×D12—41no—
314C3×D12—41no—
315C3×D12C2×D411yescharacteristic
316C3×C4×D3—21no—
317C3×C4×D3—41no—
318C3×C4×D3—41no—
319C3×C4×D3C2×D411yescharacteristic
320C3×C4×D3C2×D411yescharacteristic
321C3×C4×D3C2×D411yescharacteristic
322C3×C4×D3C2×D411yescharacteristic
323C3×Dic6C2×D411yescharacteristic
324#627—21no—
325#626—21no—
326#626—21no—
327#625—21no—
328#624—21no—
329D3×Dic3—21no—
330D3×Dic3—21no—
331C32×C8C2×D411yescharacteristic
332C32×C8C2×D411yescharacteristic
333C3⋊(C3⋊C8)—21no—
334C3⋊(C3⋊C8)—21no—
335C3⋊(C3⋊C8)—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C3×C3⋊C8—21no—
339C3×C3⋊C8C2×D411yescharacteristic
340C3×C3⋊C8C2×D411yescharacteristic
341#575—91no—
342C2×AGL(1,ℤ/8)—31no—
343C2×AGL(1,ℤ/8)—91no—
344#568—91no—
345#472—91no—
346#472—91no—
347#472—91no—
348#472—91no—
349#471—31no—
350#471—91no—
351#471—91no—
352#471—91no—
353#430—91no—
354#413—91no—
355C2×#100—91no—
356C24×C3—61no—
357C23×D3—21no—
358C3×#41—31no—
359C3×#41—61no—
360C3×#41—61no—
361C3×#41—61no—
362C3×#41—61no—
363C2×C3×Q8—21no—
364C2×C3×Q8C22×D311yescharacteristic
365C2×C3×Q8C22×D311yescharacteristic
366C2×C3×D4—21no—
367C2×C3×D4—31no—
368C2×C3×D4—31no—
369C2×C3×D4—61no—
370C2×C3×D4—61no—
371C2×C3×D4—61no—
372C2×C3×D4—61no—
373C2×C3×D4—61no—
374C2×C3×D4—61no—
375C2×C3×D4C22×D311yescharacteristic
376C2×C3×D4C22×D311yescharacteristic
377C22×C3×C4—31no—
378C22×C3×C4—61no—
379C2×#67—21no—
380C2×#67—61no—
381#239—21no—
382#239—21no—
383#239—21no—
384#239—21no—
385#239—31no—
386D3×Q8—31no—
387#237—31no—
388#237—61no—
389D3×D4—21no—
390D3×D4—21no—
391D3×D4—21no—
392D3×D4—21no—
393D3×D4—31no—
394D3×D4—61no—
395#235—31no—
396#235—31no—
397#235—31no—
398#235—31no—
399#235—61no—
400#235—61no—
401#235—61no—
402#235—61no—
403#235C22×D311yescharacteristic
404C2×D12—21no—
405C2×D12—31no—
406C2×D12C22×D311yescharacteristic
407C2×D12C22×D311yescharacteristic
408C2×C4×D3—21no—
409C2×C4×D3—61no—
410C2×C4×D3—61no—
411C2×C4×D3C22×D311yescharacteristic
412C2×Dic6—31no—
413C3×Q16—61no—
414C3×SD16—21no—
415C3×SD16—21no—
416C3×SD16—21no—
417C3×SD16—21no—
418C3×SD16—41no—
419C3×SD16—41no—
420C3×SD16—61no—
421C3×SD16—61no—
422C3×SD16—61no—
423C3×SD16—61no—
424C3×D8—61no—
425C3×D8—61no—
426C3×D8—61no—
427C3×D8—61no—
428C3×D8—61no—
429C3×M16—31no—
430C3×M16—31no—
431C3×M16—31no—
432C3×M16—31no—
433C3×M16—31no—
434C3×M16—31no—
435C3×M16—31no—
436C3×M16—61no—
437C2×C3×C8—21no—
438C2×C3×C8—31no—
439C2×C3×C8—61no—
440C2×C3×C8C22×D311yescharacteristic
441C2×C3×C8C22×D311yescharacteristic
442#216—21no—
443#216—61no—
444#216—61no—
445#216—121no—
446#215—21no—
447#215—21no—
448#215—21no—
449#215—61no—
450#215—61no—
451#215—61no—
452#215—61no—
453#215—121no—
454#214—21no—
455#214—61no—
456#214—61no—
457#214—61no—
458#214—61no—
459#214—61no—
460#214—61no—
461#214—121no—
462#213—21no—
463#213—21no—
464#213—21no—
465#213—61no—
466#213—61no—
467#213—61no—
468#213—61no—
469#213—61no—
470#213—61no—
471#213—61no—
472#213—61no—
473#213—121no—
474#208—31no—
475#208—31no—
476#208—31no—
477#208—31no—
478#208—31no—
479#208—31no—
480#208—61no—
481#208—61no—
482#208—61no—
483#208—61no—
484#208—61no—
485#208—61no—
486#208—61no—
487#208C22×D311yescharacteristic
488#208C22×D311yescharacteristic
489#208C22×D311yescharacteristic
490C2×C3⋊C8—61no—
491C2×C3⋊C8—61no—
492C2×C3⋊C8—61no—
493C2×C3⋊C8—61no—
494C2×C3⋊C8C22×D311yescharacteristic
495D24—21no—
496D24—21no—
497D24—61no—
498D24—61no—
499#204—61no—
500#204—61no—
501ΓL(1,𝔽25)—21no—
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)—61no—
510ΓL(1,𝔽25)—121no—
511ΓL(1,𝔽25)#6711yescharacteristic
512ΓL(1,𝔽25)#6711yescharacteristic
513ΓL(1,𝔽25)#6711yescharacteristic
514ΓL(1,𝔽25)#6711yescharacteristic
515D3×C8—21no—
516D3×C8—61no—
517D3×C8—61no—
518D3×C8—61no—
519D3×C8—61no—
520D3×C8—61no—
521D3×C8—61no—
522D3×C8—61no—
523D3×C8—61no—
524D3×C8—121no—
525C22×C32—41no—
526C22×C32—81no—
527C22×C32C2×#4111yescharacteristic
528C2×C3⋊D3—21no—
529C2×C3×D3—21no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532C2×C3×D3—41no—
533C2×C3×D3—82no—
534C2×C3×D3—82no—
535C2×C3×D3—81no—
536C2×C3×D3—81no—
537C2×C3×D3#12111yescharacteristic
538C2×C3×D3#12111yescharacteristic
539D32—81no—
540C32×C4—41no—
541C32×C4C22×D411yescharacteristic
542C32×C4C22×D411yescharacteristic
543C3⋊Dic3—21no—
544C3×Dic3—21no—
545C3×Dic3#12111yescharacteristic
546C3×Dic3#12111yescharacteristic
547C2×#41—31no—
548C2×#41—91no—
549C22×D4—31no—
550#137—31no—
551#137—91no—
552#137—181no—
553AGL(1,ℤ/8)—31no—
554AGL(1,ℤ/8)—61no—
555AGL(1,ℤ/8)—61no—
556AGL(1,ℤ/8)—61no—
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—
566#135—181no—
567#135—181no—
568C2×SD16—31no—
569C2×SD16—181no—
570C2×SD16D3211yescharacteristic, complemented
571C2×D8—31no—
572C2×D8—31no—
573C2×D8—181no—
574#131—31no—
575#131—91no—
576#131—91no—
577#131—91no—
578#131—181no—
579#131—181no—
580C2×M16—31no—
581C2×M16—91no—
582C2×M16—91no—
583C2×M16—91no—
584C2×M16—181no—
585C2×M16—181no—
586#108—31no—
587#108—91no—
588#108—91no—
589#108—91no—
590#101—31no—
591#101—91no—
592#100—31no—
593#100—91no—
594#100—91no—
595#100—91no—
596#100—91no—
597#100—91no—
598C23×C3—21no—
599C23×C3—21no—
600C23×C3—31no—
601C23×C3—41no—
602C23×C3—61no—
603C23×C3—61no—
604C23×C3—121no—
605C23×C3—121no—
606C23×C3—242no—
607C22×D3—21no—
608C22×D3—21no—
609C22×D3—41no—
610C22×D3—41no—
611C22×D3—61no—
612C22×D3—61no—
613C22×D3—82no—
614C22×D3#23711yescharacteristic
615C3×Q8—21no—
616C3×Q8—21no—
617C3×Q8—21no—
618C3×Q8—21no—
619C3×Q8—31no—
620C3×Q8—41no—
621C3×Q8—41no—
622C3×D4—21no—
623C3×D4—21no—
624C3×D4—21no—
625C3×D4—21no—
626C3×D4—31no—
627C3×D4—41no—
628C3×D4—41no—
629C3×D4—61no—
630C3×D4—61no—
631C3×D4—61no—
632C3×D4—61no—
633C3×D4—61no—
634C3×D4—121no—
635C3×D4—121no—
636C3×D4—121no—
637C3×D4—121no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—31no—
642C2×C3×C4—31no—
643C2×C3×C4—31no—
644C2×C3×C4—31no—
645C2×C3×C4—31no—
646C2×C3×C4—41no—
647C2×C3×C4—61no—
648C2×C3×C4—121no—
649C2×C3×C4—121no—
650C2×C3×C4C23×D311yescharacteristic
651C2×C3×C4C23×D311yescharacteristic
652#67—21no—
653#67—41no—
654#67—41no—
655#67—61no—
656#67—61no—
657#67—61no—
658#67—61no—
659#67—61no—
660#67—61no—
661#67—121no—
662C2×Dic3—61no—
663C2×Dic3—61no—
664C2×Dic3#23711yescharacteristic
665D12—21no—
666D12—21no—
667D12—21no—
668D12—21no—
669D12—31no—
670D12—31no—
671D12—41no—
672D12—41no—
673D12—61no—
674D12—61no—
675D12—61no—
676D12D3×D411yescharacteristic
677C4×D3—21no—
678C4×D3—41no—
679C4×D3—41no—
680C4×D3—61no—
681C4×D3—61no—
682C4×D3—61no—
683C4×D3—61no—
684C4×D3—61no—
685C4×D3—61no—
686C4×D3—121no—
687C4×D3D3×D411yescharacteristic
688C4×D3D3×D411yescharacteristic
689C4×D3C2×#6711yescharacteristic
690C4×D3C2×#6711yescharacteristic
691Dic6—31no—
692Dic6—31no—
693Dic6—61no—
694Dic6—61no—
695Dic6—61no—
696Dic6D3×D411yescharacteristic
697C3×C8—21no—
698C3×C8—21no—
699C3×C8—31no—
700C3×C8—31no—
701C3×C8—61no—
702C3×C8—61no—
703C3×C8—61no—
704C3×C8D3×D411yescharacteristic
705C3×C8D3×D411yescharacteristic
706C3×C8C2×#6711yescharacteristic
707C3×C8C2×#6711yescharacteristic
708C3⋊C8—21no—
709C3⋊C8—21no—
710C3⋊C8—21no—
711C3⋊C8—61no—
712C3⋊C8—61no—
713C3⋊C8—61no—
714C3⋊C8—61no—
715C3⋊C8—61no—
716C3⋊C8—61no—
717C3⋊C8—121no—
718C3⋊C8—121no—
719C3⋊C8—121no—
720C3⋊C8C2×#6711yescharacteristic
721C3⋊C8C2×#6711yescharacteristic
722C2×C32—21no—
723C2×C32—81no—
724C2×C32C2×#12111yescharacteristic
725C3⋊D3—41no—
726C3×D3—21no—
727C3×D3—21no—
728C3×D3—41no—
729C3×D3—81no—
730C3×D3—81no—
731C24—61no—
732#41—31no—
733#41—61no—
734#41—61no—
735#41—61no—
736#41—61no—
737#41—91no—
738#41—91no—
739#41—91no—
740#41—181no—
741#41—181no—
742C2×Q8—91no—
743C2×Q8C2×D3211yescharacteristic
744C2×D4—31no—
745C2×D4—31no—
746C2×D4—61no—
747C2×D4—61no—
748C2×D4—61no—
749C2×D4—61no—
750C2×D4—61no—
751C2×D4—61no—
752C2×D4—91no—
753C2×D4—181no—
754C2×D4C2×D3211yescharacteristic
755C22×C4—31no—
756C22×C4—61no—
757C22×C4—181no—
758Q16—61no—
759Q16—181no—
760SD16—21no—
761SD16—21no—
762SD16—61no—
763SD16—61no—
764SD16—61no—
765SD16—61no—
766SD16—181no—
767SD16—181no—
768SD16—181no—
769SD16—181no—
770SD16—181no—
771SD16—181no—
772D8—61no—
773D8—61no—
774D8—61no—
775D8—61no—
776D8—61no—
777D8—181no—
778D8—181no—
779D8—181no—
780D8—181no—
781D8—181no—
782M16—31no—
783M16—31no—
784M16—31no—
785M16—31no—
786M16—31no—
787M16—31no—
788M16—31no—
789M16—61no—
790M16—91no—
791M16—91no—
792M16—91no—
793M16—181no—
794M16—181no—
795M16—181no—
796M16—181no—
797M16—181no—
798M16—181no—
799C2×C8—31no—
800C2×C8—61no—
801C2×C8—181no—
802C2×C8—181no—
803C2×C8—181no—
804C2×C8—181no—
805C2×C8—181no—
806C2×C8—181no—
807C2×C8C2×D3211yescharacteristic
808C22×C3—21no—
809C22×C3—31no—
810C22×C3—31no—
811C22×C3—41no—
812C22×C3—41no—
813C22×C3—61no—
814C22×C3—81no—
815C22×C3—81no—
816C22×C3—81no—
817C22×C3—121no—
818C22×C3—121no—
819C22×C3—121no—
820C22×C3—161no—
821C22×C3—241no—
822C22×C3—241no—
823C22×C3—242no—
824C22×C3—242no—
825C22×C3C2×#23711yescharacteristic
826C22×C3D3×#4111yescharacteristic
827C2×D3—21no—
828C2×D3—41no—
829C2×D3—41no—
830C2×D3—41no—
831C2×D3—61no—
832C2×D3—61no—
833C2×D3—82no—
834C2×D3—82no—
835C2×D3—81no—
836C2×D3—81no—
837C2×D3—121no—
838C2×D3—241no—
839C2×D3—241no—
840C2×D3#93811yescharacteristic
841C2×D3#93811yescharacteristic
842C3×C4—21no—
843C3×C4—21no—
844C3×C4—31no—
845C3×C4—31no—
846C3×C4—41no—
847C3×C4—41no—
848C3×C4—61no—
849C3×C4—81no—
850C3×C4C2×D3×D411yescharacteristic
851C3×C4C2×D3×D411yescharacteristic
852C3×C4C2×D3×D411yescharacteristic
853C3×C4C22×#6711yescharacteristic
854Dic3—21no—
855Dic3—61no—
856Dic3—61no—
857Dic3—121no—
858Dic3#93811yescharacteristic
859Dic3#93811yescharacteristic
860C32#306811yescharacteristic, complemented, Sylow
861C23—21no—
862C23—31no—
863C23—61no—
864C23—61no—
865C23—121no—
866C23—121no—
867C23—181no—
868C23—242no—
869Q8—21no—
870Q8—21no—
871Q8—31no—
872Q8—91no—
873Q8—181no—
874D4—21no—
875D4—21no—
876D4—31no—
877D4—61no—
878D4—61no—
879D4—61no—
880D4—61no—
881D4—61no—
882D4—91no—
883D4—121no—
884D4—121no—
885D4—121no—
886D4—121no—
887D4—181no—
888D4—181no—
889D4—181no—
890D4—181no—
891C2×C4—21no—
892C2×C4—31no—
893C2×C4—31no—
894C2×C4—31no—
895C2×C4—31no—
896C2×C4—31no—
897C2×C4—61no—
898C2×C4—121no—
899C2×C4—121no—
900C2×C4—181no—
901C2×C4—181no—
902C2×C4—181no—
903C2×C4—181no—
904C2×C4C22×D3211yescharacteristic
905C8—31no—
906C8—31no—
907C8—61no—
908C8—61no—
909C8—61no—
910C8—181no—
911C8—181no—
912C8—181no—
913C8D3×#6711yescharacteristic
914C8D3×#6711yescharacteristic
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—41no—
919C2×C3—61no—
920C2×C3—61no—
921C2×C3—81no—
922C2×C3—81no—
923C2×C3—121no—
924C2×C3—161no—
925C2×C3—241no—
926C2×C3—241no—
927C2×C3D3×#12111yescharacteristic
928C2×C3C2×#93811yescharacteristic
929D3—21no—
930D3—21no—
931D3—41no—
932D3—81no—
933D3—81no—
934D3—121no—
935D3—121no—
936D3—241no—
937C22—31no—
938C22—31no—
939C22—41no—
940C22—61no—
941C22—81no—
942C22—121no—
943C22—121no—
944C22—121no—
945C22—181no—
946C22—241no—
947C22—241no—
948C22—242no—
949C22—242no—
950C22—721no—
951C22D3×#23711yescharacteristic
952C4—31no—
953C4—31no—
954C4—41no—
955C4—61no—
956C4—181no—
957C4D32×D411yescharacteristic
958C4C2×D3×#6711yescharacteristic
959C3—21no—
960C3#8093011yescharacteristic, complemented
961C3#8396311yescharacteristic, complemented
962C2—21no—
963C2—61no—
964C2—61no—
965C2—81no—
966C2—121no—
967C2—241no—
968C2—241no—
969C2—361no—
970C2D3×#93811yescharacteristic
subgroupG/H
centerC2D3×#938
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC2×C32C2×#121
hypercenterC2×SD16D32
hypocenterC32#3068
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×#914C2semidirect
2. #10595317C2semidirect
3. D3×#932C2semidirect
4. #10594668C2semidirect
5. #10592876C2semidirect
6. C3×#5177C2semidirect
7. #10591642C2semidirect
8. #10591637C2semidirect
9. #10591542C2semidirect
10. #10591505C2semidirect
11. D3×#833C2semidirect
12. #10591406C2semidirect
13. #10590929C2semidirect
14. #10590926C2semidirect
15. #10590912C2semidirect
21. C2×C32×SD16C22semidirect
22. #64151C22semidirect
24. #64110C22semidirect
25. C3×#942C22semidirect
26. C2×C3×#215C22semidirect
28. C2×C3×#213C22semidirect
33. C2×C3×D24C22semidirect
34. C3×#901C22semidirect
45. #63830C22semidirect
47. #63823C22semidirect
48. #63817C22semidirect
49. #63814C22semidirect
57. #63663C22semidirect
58. #63660C22semidirect
59. #63646C22semidirect
60. C3×#836C22semidirect
61. C3×#833C22semidirect
62. C3×#819C22semidirect
63. #63577C22semidirect
64. #63577C22semidirect
65. #63558C22semidirect
66. #63558C22semidirect
67. #63558C22semidirect
68. #63558C22semidirect
74. C2×#914D3semidirect
87. #5177D3semidirect
192. C2×C3×SD16C2×D3semidirect
193. C2×C3×SD16C2×D3semidirect
208. #942C2×D3semidirect
209. C2×#215C2×D3semidirect
222. C2×#213C2×D3semidirect
250. C2×D24C2×D3semidirect
257. #901C2×D3semidirect
266. #836C2×D3semidirect
274. #833C2×D3semidirect
286. #819C2×D3semidirect
570. C2×SD16D32semidirect
860. C32#3068semidirect
960. C3#80930semidirect
961. C3#83963semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9142
#105953172
D3×#9322
#105946682
#105928762
C3×#51772
#105916422
#105916372
#105915422
#105915052
D3×#8332
#105914062
#105909292
#105909262
#105909122
#839633
#809303