Finite Group Databasebeta

← #11868102

Subgroups — #11868102

Order 1152.

986 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#911C211yesmaximal, characteristic, complemented
2#10595095C211yesmaximal, characteristic, complemented
3D3×#932C211yesmaximal, characteristic, complemented
4#10594668C211yesmaximal, characteristic, complemented
5#10592859C211yesmaximal, characteristic, complemented
6C3×#5160C211yesmaximal, characteristic, complemented
7#10591506C211yesmaximal, characteristic, complemented
8#10591505C211yesmaximal, characteristic, complemented
9#10591501C211yesmaximal, characteristic, complemented
10D3×#833C211yesmaximal, characteristic, complemented
11#10591407C211yesmaximal, characteristic, complemented
12#10591406C211yesmaximal, characteristic, complemented
13#10590928C211yesmaximal, characteristic, complemented
14#10590925C211yesmaximal, characteristic, complemented
15#10590912C211yesmaximal, characteristic, complemented
16#83963—31nomaximal
17#80938—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20D3×#235C2211yescharacteristic
21C2×C32×D8C2211yescharacteristic, complemented
22#64141C2211yescharacteristic
23#64141C2211yescharacteristic, complemented
24#64110C2211yescharacteristic, complemented
25C2×C3×#214C2211yescharacteristic, complemented
26C3×#932C2211yescharacteristic
27C3×#932C2211yescharacteristic, complemented
28C2×C3×#213C2211yescharacteristic, complemented
29C3×#911—21no—
30C3×#911—21no—
31C3×#911—21no—
32C3×#911—21no—
33C2×C3×#204C2211yescharacteristic, complemented
34C3×#901C2211yescharacteristic, complemented
35C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
36#63935—21no—
37#63934—21no—
38#63933—21no—
39#63932—21no—
40#63929—21no—
41D3×#214—21no—
42#63925—21no—
43D3×#213—21no—
44#63833C2211yescharacteristic, complemented
45#63830C2211yescharacteristic
46#63827C2211yescharacteristic, complemented
47#63823C2211yescharacteristic
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#63660C2211yescharacteristic, complemented
58#63660C2211yescharacteristic, complemented
59#63646C2211yescharacteristic, complemented
60C3×#833C2211yescharacteristic, 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×AGL(1,ℤ/8)—31no—
70#5822—31no—
71C2×#932—31no—
72#5773—31no—
73D3×AGL(1,ℤ/8)—31no—
74C2×#911D311yescharacteristic, complemented
75#5750—31no—
76#5745—31no—
77C3×#472—31no—
78#5237—31no—
79C2×#833—31no—
80#5200—31no—
81#5199—31no—
82#5177—31no—
83#5177—31no—
84#5177—31no—
85#5177—31no—
86#5160—31no—
87#5160—31no—
88#5160—31no—
89#5160—31no—
90#5160—61no—
91#5160D311yescharacteristic, complemented
92#5141—31no—
93#5125—31no—
94#4898—31no—
95#4893—31no—
96#4749—31no—
97#4748—31no—
98#4745—31no—
99D3×#100—31no—
100C23×C3×D3—21no—
101C2×C32×D4C2311yescharacteristic
102C2×C32×D4C2311yescharacteristic
103#3828C2311yescharacteristic
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C22×C3×Dic3—21no—
107C3×#237—21no—
108C3×#237—21no—
109C3×#237—21no—
110C3×#237—21no—
111C3×D3×D4—21no—
112C3×D3×D4—21no—
113C3×D3×D4—21no—
114C3×D3×D4—21no—
115C3×#235C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
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×D8—21no—
128C32×D8—21no—
129C2×C32×C8C2311yescharacteristic
130#3754—21no—
131#3754—21no—
132#3753—21no—
133#3753—21no—
134#3748C2311yescharacteristic
135#3748C2311yescharacteristic
136#3748C2311yescharacteristic
137#3743—21no—
138C8×C3⋊D3—21no—
139C3×#214—21no—
140C3×#214—21no—
141C3×#214—21no—
142C3×#214—21no—
143C3×#213—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×ΓL(1,𝔽25)D411yescharacteristic
155C3×ΓL(1,𝔽25)D411yescharacteristic
156C3×ΓL(1,𝔽25)D411yescharacteristic
157C3×ΓL(1,𝔽25)D411yescharacteristic
158C3×D3×C8—21no—
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#3068—91noSylow
178C2×C3×#41—31no—
179C22×C3×D4—31no—
180D3×#41—31no—
181C2×#237C2×D311yescharacteristic
182C2×D3×D4C2×D311yescharacteristic
183C2×#235—31no—
184C3×AGL(1,ℤ/8)—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—31no—
191C2×C3×SD16—31no—
192C2×C3×D8—21no—
193C2×C3×D8—31no—
194C2×C3×D8C2×D311yescharacteristic, complemented
195C2×C3×D8C2×D311yescharacteristic, complemented
196C3×#131—31no—
197C2×C3×M16—31no—
198#951—31no—
199#951—61no—
200#950—61no—
201#950—61no—
202#949—31no—
203#949—61no—
204#948—31no—
205#942—31no—
206#942—31no—
207C2×#214—61no—
208C2×#214C2×D311yescharacteristic, complemented
209#932—31no—
210#932—31no—
211#932—31no—
212#932—31no—
213#932—31no—
214#932—31no—
215#932—61no—
216#932—61no—
217#932—61no—
218#932—61no—
219#932C2×D311yescharacteristic
220#932C2×D311yescharacteristic, complemented
221C2×#213—61no—
222C2×#213C2×D311yescharacteristic, complemented
223C2×#208—31no—
224C2×#208—31no—
225C2×#208—31no—
226#916—61no—
227#915—61no—
228#914—61no—
229D3×SD16—61no—
230#912—61no—
231#911—21no—
232#911—21no—
233#911—21no—
234#911—21no—
235#911—61no—
236#911—61no—
237D3×D8—61no—
238#909—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×#204C2×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×#100—31no—
262C3×#100—31no—
263#836—31no—
264#836—31no—
265#833—31no—
266#833—31no—
267#833—31no—
268#833—31no—
269#833—31no—
270#833—31no—
271#833—61no—
272#833—61no—
273#833C2×D311yescharacteristic, complemented
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—
288C23×C32—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×D4—21no—
296C32×D4—21no—
297C32×D4—21no—
298C32×D4—21no—
299C2×C32×C4C2411yescharacteristic
300#638—21no—
301C4⋊(C3⋊D3)C2×D411yescharacteristic
302C4×C3⋊D3—21no—
303#634C2×D411yescharacteristic
304C3×#67—21no—
305C3×#67—41no—
306C3×#67—41no—
307C3×#67—41no—
308C3×#67—41no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3—41no—
311C2×C3×Dic3—41no—
312C2×C3×Dic3#4111yescharacteristic
313C3×D12—21no—
314C3×D12—21no—
315C3×D12C2×D411yescharacteristic
316C3×C4×D3—21no—
317C3×C4×D3C2×D411yescharacteristic
318C3×C4×D3C2×D411yescharacteristic
319C3×C4×D3C2×D411yescharacteristic
320C3×C4×D3C2×D411yescharacteristic
321C3×Dic6—21no—
322C3×Dic6—21no—
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—31no—
346#472—91no—
347#472—91no—
348#472—91no—
349#471—91no—
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—31no—
364C2×C3×D4—21no—
365C2×C3×D4—21no—
366C2×C3×D4—31no—
367C2×C3×D4—61no—
368C2×C3×D4—61no—
369C2×C3×D4—61no—
370C2×C3×D4—61no—
371C2×C3×D4—61no—
372C2×C3×D4—61no—
373C2×C3×D4C22×D311yescharacteristic
374C2×C3×D4C22×D311yescharacteristic
375C2×C3×D4C22×D311yescharacteristic
376C2×C3×D4C22×D311yescharacteristic
377C22×C3×C4—31no—
378C22×C3×C4—61no—
379C2×#67—21no—
380C2×#67—21no—
381C2×#67—61no—
382C22×Dic3—21no—
383#239—31no—
384D3×Q8—31no—
385#237—21no—
386#237—21no—
387#237—21no—
388#237—21no—
389#237—31no—
390#237—61no—
391D3×D4—21no—
392D3×D4—21no—
393D3×D4—21no—
394D3×D4—21no—
395D3×D4—31no—
396D3×D4—61no—
397#235—31no—
398#235—31no—
399#235—31no—
400#235—31no—
401#235—61no—
402#235—61no—
403#235—61no—
404#235—61no—
405#235C22×D311yescharacteristic
406C2×D12—31no—
407C2×D12C22×D311yescharacteristic
408C2×C4×D3—61no—
409C2×C4×D3—61no—
410C2×C4×D3C22×D311yescharacteristic
411C2×Dic6—31no—
412C2×Dic6C22×D311yescharacteristic
413C3×SD16—61no—
414C3×SD16—61no—
415C3×SD16—61no—
416C3×SD16—61no—
417C3×SD16—61no—
418C3×SD16—61no—
419C3×D8—21no—
420C3×D8—21no—
421C3×D8—21no—
422C3×D8—21no—
423C3×D8—41no—
424C3×D8—41no—
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—61no—
443#216—61no—
444#216—61no—
445#215—61no—
446#215—61no—
447#215—61no—
448#214—21no—
449#214—21no—
450#214—21no—
451#214—21no—
452#214—61no—
453#214—61no—
454#214—61no—
455#214—61no—
456#214—61no—
457#214—61no—
458#214—61no—
459#214—121no—
460#214—121no—
461#213—21no—
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—121no—
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
495Dic12—61no—
496D24—61no—
497#204—21no—
498#204—21no—
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—41no—
527C22×C32—81no—
528C22×C32—81no—
529C22×C32C2×#4111yescharacteristic
530C2×C3⋊D3—21no—
531C2×C3×D3—21no—
532C2×C3×D3—41no—
533C2×C3×D3—41no—
534C2×C3×D3—82no—
535C2×C3×D3—82no—
536C2×C3×D3—81no—
537C2×C3×D3#12111yescharacteristic
538C2×C3×D3#12111yescharacteristic
539D32—81no—
540C32×C4C22×D411yescharacteristic
541C32×C4C22×D411yescharacteristic
542C3⋊Dic3—21no—
543C3×Dic3—21no—
544C3×Dic3—41no—
545C3×Dic3#12111yescharacteristic
546C3×Dic3#12111yescharacteristic
547C2×#41—31no—
548C2×#41—91no—
549C22×D4—31no—
550#137—91no—
551#137—91no—
552#137—181no—
553AGL(1,ℤ/8)—31no—
554AGL(1,ℤ/8)—31no—
555AGL(1,ℤ/8)—61no—
556AGL(1,ℤ/8)—61no—
557AGL(1,ℤ/8)—61no—
558AGL(1,ℤ/8)—61no—
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—31no—
570C2×SD16—181no—
571C2×D8—31no—
572C2×D8—181no—
573C2×D8D3211yescharacteristic, complemented
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—91no—
591#101—91no—
592#100—31no—
593#100—31no—
594#100—91no—
595#100—91no—
596#100—91no—
597#100—91no—
598C23×C3—21no—
599C23×C3—21no—
600C23×C3—21no—
601C23×C3—21no—
602C23×C3—31no—
603C23×C3—41no—
604C23×C3—41no—
605C23×C3—61no—
606C23×C3—121no—
607C23×C3—121no—
608C23×C3—242no—
609C22×D3—21no—
610C22×D3—41no—
611C22×D3—41no—
612C22×D3—61no—
613C22×D3—61no—
614C22×D3—82no—
615C22×D3#23711yescharacteristic
616C3×Q8—31no—
617C3×Q8—61no—
618C3×Q8—61no—
619C3×D4—21no—
620C3×D4—21no—
621C3×D4—21no—
622C3×D4—21no—
623C3×D4—21no—
624C3×D4—21no—
625C3×D4—21no—
626C3×D4—21no—
627C3×D4—31no—
628C3×D4—41no—
629C3×D4—41no—
630C3×D4—41no—
631C3×D4—41no—
632C3×D4—61no—
633C3×D4—61no—
634C3×D4—61no—
635C3×D4—121no—
636C3×D4—121no—
637C3×D4—121no—
638C3×D4—121no—
639C2×C3×C4—21no—
640C2×C3×C4—31no—
641C2×C3×C4—31no—
642C2×C3×C4—31no—
643C2×C3×C4—31no—
644C2×C3×C4—31no—
645C2×C3×C4—61no—
646C2×C3×C4—61no—
647C2×C3×C4—121no—
648C2×C3×C4—121no—
649C2×C3×C4C23×D311yescharacteristic
650C2×C3×C4C23×D311yescharacteristic
651#67—21no—
652#67—41no—
653#67—41no—
654#67—41no—
655#67—41no—
656#67—61no—
657#67—61no—
658#67—61no—
659#67—61no—
660#67—61no—
661#67—61no—
662#67—121no—
663C2×Dic3—21no—
664C2×Dic3—41no—
665C2×Dic3—41no—
666C2×Dic3—61no—
667C2×Dic3—61no—
668C2×Dic3#23711yescharacteristic
669D12—21no—
670D12—21no—
671D12—31no—
672D12—31no—
673D12—61no—
674D12—61no—
675D12—61no—
676D12D3×D411yescharacteristic
677C4×D3—21no—
678C4×D3—61no—
679C4×D3—61no—
680C4×D3—61no—
681C4×D3—61no—
682C4×D3—61no—
683C4×D3—61no—
684C4×D3—121no—
685C4×D3D3×D411yescharacteristic
686C4×D3D3×D411yescharacteristic
687C4×D3C2×#6711yescharacteristic
688C4×D3C2×#6711yescharacteristic
689Dic6—21no—
690Dic6—21no—
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×C32—81no—
725C2×C32C2×#12111yescharacteristic
726C3⋊D3—41no—
727C3×D3—21no—
728C3×D3—21no—
729C3×D3—41no—
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—31no—
743C2×Q8—91no—
744C2×D4—31no—
745C2×D4—61no—
746C2×D4—61no—
747C2×D4—61no—
748C2×D4—61no—
749C2×D4—61no—
750C2×D4—61no—
751C2×D4—91no—
752C2×D4—181no—
753C2×D4C2×D3211yescharacteristic
754C2×D4C2×D3211yescharacteristic
755C22×C4—31no—
756C22×C4—61no—
757C22×C4—181no—
758Q16—181no—
759Q16—181no—
760SD16—61no—
761SD16—61no—
762SD16—61no—
763SD16—61no—
764SD16—61no—
765SD16—61no—
766SD16—181no—
767SD16—181no—
768SD16—181no—
769SD16—181no—
770SD16—181no—
771SD16—181no—
772D8—21no—
773D8—21no—
774D8—61no—
775D8—61no—
776D8—61no—
777D8—61no—
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—41no—
814C22×C3—41no—
815C22×C3—61no—
816C22×C3—81no—
817C22×C3—81no—
818C22×C3—81no—
819C22×C3—81no—
820C22×C3—81no—
821C22×C3—81no—
822C22×C3—121no—
823C22×C3—121no—
824C22×C3—161no—
825C22×C3—161no—
826C22×C3—241no—
827C22×C3—242no—
828C22×C3—242no—
829C22×C3C2×#23711yescharacteristic
830C22×C3D3×#4111yescharacteristic
831C2×D3—21no—
832C2×D3—41no—
833C2×D3—41no—
834C2×D3—61no—
835C2×D3—61no—
836C2×D3—82no—
837C2×D3—82no—
838C2×D3—81no—
839C2×D3—121no—
840C2×D3—241no—
841C2×D3—241no—
842C2×D3#93811yescharacteristic
843C2×D3#93811yescharacteristic
844C3×C4—21no—
845C3×C4—21no—
846C3×C4—31no—
847C3×C4—31no—
848C3×C4—61no—
849C3×C4—121no—
850C3×C4C2×D3×D411yescharacteristic
851C3×C4C2×D3×D411yescharacteristic
852C3×C4C2×D3×D411yescharacteristic
853C3×C4C22×#6711yescharacteristic
854Dic3—21no—
855Dic3—41no—
856Dic3—61no—
857Dic3—61no—
858Dic3—121no—
859Dic3#93811yescharacteristic
860Dic3#93811yescharacteristic
861C32#306811yescharacteristic, complemented, Sylow
862C23—21no—
863C23—21no—
864C23—31no—
865C23—61no—
866C23—121no—
867C23—121no—
868C23—181no—
869C23—242no—
870Q8—31no—
871Q8—61no—
872Q8—61no—
873Q8—91no—
874Q8—181no—
875D4—21no—
876D4—21no—
877D4—21no—
878D4—21no—
879D4—31no—
880D4—61no—
881D4—61no—
882D4—61no—
883D4—91no—
884D4—121no—
885D4—121no—
886D4—121no—
887D4—121no—
888D4—181no—
889D4—181no—
890D4—181no—
891D4—181no—
892C2×C4—31no—
893C2×C4—31no—
894C2×C4—31no—
895C2×C4—31no—
896C2×C4—31no—
897C2×C4—61no—
898C2×C4—61no—
899C2×C4—121no—
900C2×C4—121no—
901C2×C4—181no—
902C2×C4—181no—
903C2×C4—181no—
904C2×C4—181no—
905C2×C4C22×D3211yescharacteristic
906C8—31no—
907C8—31no—
908C8—61no—
909C8—61no—
910C8—61no—
911C8—181no—
912C8—181no—
913C8—181no—
914C8D3×#6711yescharacteristic
915C8D3×#6711yescharacteristic
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—41no—
920C2×C3—61no—
921C2×C3—61no—
922C2×C3—81no—
923C2×C3—81no—
924C2×C3—81no—
925C2×C3—81no—
926C2×C3—121no—
927C2×C3—161no—
928C2×C3—161no—
929C2×C3—241no—
930C2×C3D3×#12111yescharacteristic
931C2×C3C2×#93811yescharacteristic
932D3—21no—
933D3—21no—
934D3—41no—
935D3—81no—
936D3—121no—
937D3—121no—
938D3—241no—
939C22—31no—
940C22—31no—
941C22—41no—
942C22—41no—
943C22—61no—
944C22—81no—
945C22—81no—
946C22—121no—
947C22—121no—
948C22—181no—
949C22—241no—
950C22—242no—
951C22—242no—
952C22—721no—
953C22D3×#23711yescharacteristic
954C4—31no—
955C4—31no—
956C4—61no—
957C4—121no—
958C4—181no—
959C4D32×D411yescharacteristic
960C4C2×D3×#6711yescharacteristic
961C3—21no—
962C3#8093811yescharacteristic, complemented
963C3#8396311yescharacteristic, complemented
964C2—21no—
965C2—61no—
966C2—61no—
967C2—81no—
968C2—81no—
969C2—121no—
970C2—241no—
971C2—361no—
972C2D3×#93811yescharacteristic
subgroupG/H
centerC2D3×#938
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC2×C32C2×#121
hypercenterC2×D8D32
hypocenterC32#3068
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. C2×C3×#911C2semidirect
2. #10595095C2semidirect
3. D3×#932C2semidirect
4. #10594668C2semidirect
5. #10592859C2semidirect
6. C3×#5160C2semidirect
7. #10591506C2semidirect
8. #10591505C2semidirect
9. #10591501C2semidirect
10. D3×#833C2semidirect
11. #10591407C2semidirect
12. #10591406C2semidirect
13. #10590928C2semidirect
14. #10590925C2semidirect
15. #10590912C2semidirect
21. C2×C32×D8C22semidirect
23. #64141C22semidirect
24. #64110C22semidirect
25. C2×C3×#214C22semidirect
27. C3×#932C22semidirect
28. C2×C3×#213C22semidirect
33. C2×C3×#204C22semidirect
34. C3×#901C22semidirect
44. #63833C22semidirect
46. #63827C22semidirect
48. #63817C22semidirect
49. #63814C22semidirect
57. #63660C22semidirect
58. #63660C22semidirect
59. #63646C22semidirect
60. C3×#833C22semidirect
61. C3×#833C22semidirect
62. C3×#819C22semidirect
63. #63577C22semidirect
64. #63577C22semidirect
65. #63560C22semidirect
66. #63560C22semidirect
67. #63558C22semidirect
68. #63558C22semidirect
74. C2×#911D3semidirect
91. #5160D3semidirect
194. C2×C3×D8C2×D3semidirect
195. C2×C3×D8C2×D3semidirect
208. C2×#214C2×D3semidirect
220. #932C2×D3semidirect
222. C2×#213C2×D3semidirect
250. C2×#204C2×D3semidirect
257. #901C2×D3semidirect
273. #833C2×D3semidirect
274. #833C2×D3semidirect
286. #819C2×D3semidirect
573. C2×D8D32semidirect
861. C32#3068semidirect
962. C3#80938semidirect
963. C3#83963semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9112
#105950952
D3×#9322
#105946682
#105928592
C3×#51602
#105915062
#105915052
#105915012
D3×#8332
#105914072
#105914062
#105909282
#105909252
#105909122
#839633
#809383