Finite Group Databasebeta

← #11868109

Subgroups — #11868109

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
1C3×#5750C211yesmaximal, characteristic, complemented
2#10595470C211yesmaximal, characteristic, complemented
3D3×#949C211yesmaximal, characteristic, complemented
4C2×#63794C211yesmaximal, characteristic, complemented
5#10592841C211yesmaximal, characteristic, complemented
6C3×#5141C211yesmaximal, characteristic, complemented
7#10591680C211yesmaximal, characteristic, complemented
8#10591677C211yesmaximal, characteristic, complemented
9#10591007C211yesmaximal, characteristic, complemented
10D3×#823C211yesmaximal, characteristic, complemented
11#10590998C211yesmaximal, characteristic, complemented
12#10590997C211yesmaximal, characteristic, complemented
13#10590927C211yesmaximal, characteristic, complemented
14#10590925C211yesmaximal, characteristic, complemented
15#10590912C211yesmaximal, characteristic, complemented
16#83814—31nomaximal
17#80930—31nomaximal
18C3×D3×#41C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21C32×#131C2211yescharacteristic, complemented
22#64158C2211yescharacteristic
23#64158C2211yescharacteristic, complemented
24C2×#3745C2211yescharacteristic, complemented
25C3×#951C2211yescharacteristic, complemented
26C3×#949C2211yescharacteristic
27C3×#948C2211yescharacteristic, complemented
28C3×#907—21no—
29C3×#907C2211yescharacteristic, complemented
30C3×D3×M16—21no—
31C3×D3×M16C2211yescharacteristic
32C2×C3×#204C2211yescharacteristic, complemented
33C3×#901—21no—
34C3×#901C2211yescharacteristic, complemented
35C2×C3×ΓL(1,𝔽25)—21no—
36C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
37#63949—21no—
38#63948—21no—
39#63939—21no—
40D3×#215—21no—
41#63935—21no—
42#63934—21no—
43#63925—21no—
44D3×#213—21no—
45C2×#3717C2211yescharacteristic, complemented
46#63827C2211yescharacteristic, complemented
47#63825C2211yescharacteristic
48#63825C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50#63823C2211yescharacteristic
51D3×#208C2211yescharacteristic
52D3×#208C2211yescharacteristic
53#63794—21no—
54#63794—21no—
55#63794—21no—
56#63794—21no—
57#63650C2211yescharacteristic, complemented
58#63650C2211yescharacteristic, complemented
59#63646C2211yescharacteristic, complemented
60C3×#824C2211yescharacteristic, complemented
61C3×#823C2211yescharacteristic, complemented
62C3×#819C2211yescharacteristic, complemented
63#63577C2211yescharacteristic, complemented
64#63577C2211yescharacteristic, complemented
65#63560C2211yescharacteristic, complemented
66#63559C2211yescharacteristic, complemented
67#63559C2211yescharacteristic, complemented
68#63558C2211yescharacteristic, complemented
69C3×#568—31no—
70#5822—31no—
71C2×#949—31no—
72#5777—31no—
73D3×AGL(1,ℤ/8)—31no—
74C2×#914—31no—
75#5750D311yescharacteristic, complemented
76C2×#908—31no—
77C3×#471—31no—
78#5203—31no—
79#5199—31no—
80#5177—31no—
81#5142—31no—
82#5142—31no—
83#5142—31no—
84#5142—31no—
85#5142—31no—
86#5142—61no—
87#5141—31no—
88#5141—31no—
89#5141—31no—
90#5141D311yescharacteristic, complemented
91#5132—31no—
92C2×#823—31no—
93#5125—31no—
94#4897—31no—
95#4893—31no—
96#4754—31no—
97#4751—31no—
98#4749—31no—
99D3×#100—31no—
100C22×D32—21no—
101C32×#41C2311yescharacteristic
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C3×#239D411yescharacteristic
105C3×D3×Q8D411yescharacteristic
106C3×#237—21no—
107C3×#237D411yescharacteristic
108C3×D3×D4—21no—
109C3×D3×D4D411yescharacteristic
110C3×#235—21no—
111C3×#235C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×#626—21no—
117C2×#626—21no—
118C2×#624—21no—
119D3×D12—21no—
120D3×D12—21no—
121D3×D12—21no—
122D3×D12—21no—
123#3799—21no—
124#3799—21no—
125#3799—21no—
126#3799—21no—
127C32×M16—21no—
128C32×M16C2311yescharacteristic
129C2×C32×C8—21no—
130C2×C32×C8C2311yescharacteristic
131#3755—21no—
132#3755—21no—
133#3753—21no—
134#3753—21no—
135#3748C2311yescharacteristic
136#3748C2311yescharacteristic
137#3745—21no—
138#3745—21no—
139C3×#216—21no—
140C3×#215—21no—
141C3×#214—21no—
142C3×#213—21no—
143C3×#208—21no—
144C3×#208C2311yescharacteristic
145C3×#208C2311yescharacteristic
146C3×#208C2311yescharacteristic
147C2×C3×C3⋊C8—21no—
148C2×C3×C3⋊C8C2311yescharacteristic
149C3×#204—21no—
150C3×#204—21no—
151C3×ΓL(1,𝔽25)—21no—
152C3×ΓL(1,𝔽25)—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—
159C3×D3×C8—21no—
160C3×D3×C8—21no—
161#3718—21no—
162#3717—21no—
163#3717—21no—
164#3717—21no—
165#3717—21no—
166#3715—21no—
167#3715—21no—
168#3714—21no—
169#3714—21no—
170#3714—21no—
171#3714—21no—
172#3713—21no—
173#3711—21no—
174#3711—21no—
175D3×C3⋊C8—21no—
176D3×C3⋊C8—21no—
177#3068—91noSylow
178C2×C3×#41—31no—
179D3×#41C2×D311yescharacteristic
180C2×#239—31no—
181C2×D3×D4—31no—
182C2×#235—31no—
183C22×D12—31no—
184C3×#137—31no—
185C3×AGL(1,ℤ/8)—31no—
186C2×C3×SD16—31no—
187C3×#131—21no—
188C3×#131—31no—
189C3×#131—31no—
190C3×#131—31no—
191C3×#131—61no—
192C3×#131—61no—
193C3×#131C2×D311yescharacteristic, complemented
194C3×#131C2×D311yescharacteristic, complemented
195C2×C3×M16—31no—
196C2×C3×M16—31no—
197C2×C3×M16—61no—
198C2×C3×M16—61no—
199#951—31no—
200#951C2×D311yescharacteristic, complemented
201#950—61no—
202#950—61no—
203#949—31no—
204#949—31no—
205#949—31no—
206#949—31no—
207#949—31no—
208#949—31no—
209#949—31no—
210#949—61no—
211#949—61no—
212#949—61no—
213#949—61no—
214#949C2×D311yescharacteristic
215#948C2×D311yescharacteristic, complemented
216#942—31no—
217#942—61no—
218C2×#215—31no—
219C2×#215—61no—
220#932—31no—
221#932—61no—
222C2×#213—31no—
223C2×#213—61no—
224C2×#208—31no—
225C2×#208—31no—
226#919—61no—
227#918—61no—
228#916—61no—
229#914—61no—
230#914—61no—
231#914—61no—
232#914—61no—
233#914—61no—
234#914—61no—
235D3×SD16—61no—
236#911—61no—
237D3×D8—61no—
238#908—31no—
239#908—31no—
240#908—61no—
241#908—61no—
242#908—61no—
243#908—61no—
244#907—21no—
245#907C2×D311yescharacteristic, complemented
246D3×M16—21no—
247D3×M16—31no—
248D3×M16—31no—
249D3×M16C2×D311yescharacteristic
250C2×D24—31no—
251C2×D24—31no—
252C2×D24—31no—
253C2×D24—61no—
254C2×#204—31no—
255C2×#204C2×D311yescharacteristic, complemented
256#901—21no—
257#901C2×D311yescharacteristic, complemented
258C2×ΓL(1,𝔽25)—21no—
259C2×ΓL(1,𝔽25)C2×D311yescharacteristic
260C3×#108—31no—
261C3×#101—31no—
262C3×#100—31no—
263#836—31no—
264#833—31no—
265#824—31no—
266#824C2×D311yescharacteristic, complemented
267#823—31no—
268#823—31no—
269#823—31no—
270#823—31no—
271#823—31no—
272#823—31no—
273#823—31no—
274#823—31no—
275#823—31no—
276#823—61no—
277#823—61no—
278#823C2×D311yescharacteristic, complemented
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
287C22×C3⋊D3—21no—
288C22×C3⋊D3—21no—
289C22×C3×D3—21no—
290C22×C3×D3—21no—
291C22×C3×D3#4111yescharacteristic
292C2×D32—41no—
293C2×D32—41no—
294C2×D32—82no—
295C32×Q8C2×D411yescharacteristic
296C32×D4—21no—
297C32×D4C2×D411yescharacteristic
298C2×C32×C4—21no—
299C2×C32×C4C2411yescharacteristic
300C4⋊(C3⋊D3)—21no—
301C4⋊(C3⋊D3)—21no—
302C4⋊(C3⋊D3)—21no—
303C4⋊(C3⋊D3)—21no—
304C3×#67—21no—
305C3×#67—21no—
306C3×#67—21no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—21no—
309C2×C3×Dic3#4111yescharacteristic
310C3×D12—21no—
311C3×D12—21no—
312C3×D12—21no—
313C3×D12C2×D411yescharacteristic
314C3×C4×D3—21no—
315C3×C4×D3—21no—
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×Dic6—21no—
324C3×Dic6C2×D411yescharacteristic
325#626—41no—
326#626—41no—
327#626—41no—
328#626—41no—
329#624—41no—
330#624—41no—
331C32×C8—21no—
332C32×C8C2×D411yescharacteristic
333C32×C8C2×D411yescharacteristic
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)—91no—
343C2×AGL(1,ℤ/8)—91no—
344#568—31no—
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—
356C23×D3—61no—
357C23×D3—61no—
358C3×#41—21no—
359C3×#41—31no—
360C3×#41—31no—
361C3×#41—31no—
362C3×#41—61no—
363C3×#41—61no—
364C3×#41C22×D311yescharacteristic
365C3×#41C22×D311yescharacteristic
366C2×C3×Q8—31no—
367C2×C3×Q8—31no—
368C2×C3×D4—31no—
369C2×C3×D4—31no—
370C2×C3×D4—61no—
371C22×C3×C4—31no—
372C22×C3×C4—61no—
373C2×#67—61no—
374C2×#67—61no—
375#239—61no—
376#239—61no—
377#239—61no—
378#239—61no—
379#239D1211yescharacteristic
380D3×Q8D1211yescharacteristic
381#237—21no—
382#237D1211yescharacteristic
383D3×D4—21no—
384D3×D4—61no—
385D3×D4—61no—
386D3×D4—61no—
387D3×D4—61no—
388D3×D4D1211yescharacteristic
389#235—21no—
390#235—61no—
391#235—61no—
392#235—61no—
393#235—61no—
394#235C22×D311yescharacteristic
395C2×D12—31no—
396C2×D12—31no—
397C2×D12—31no—
398C2×D12—31no—
399C2×D12—61no—
400C2×D12—61no—
401C2×D12—61no—
402C2×D12—61no—
403C2×D12—61no—
404C2×D12—61no—
405C2×D12—61no—
406C2×D12—61no—
407C2×D12C22×D311yescharacteristic
408C2×C4×D3—21no—
409C2×C4×D3—61no—
410C2×C4×D3—61no—
411C2×C4×D3C22×D311yescharacteristic
412C2×Dic6C22×D311yescharacteristic
413C3×Q16—61no—
414C3×SD16—61no—
415C3×SD16—61no—
416C3×SD16—61no—
417C3×SD16—61no—
418C3×D8—61no—
419C3×M16—21no—
420C3×M16—21no—
421C3×M16—21no—
422C3×M16—31no—
423C3×M16—31no—
424C3×M16—31no—
425C3×M16—31no—
426C3×M16—31no—
427C3×M16—31no—
428C3×M16—31no—
429C3×M16—41no—
430C3×M16—61no—
431C3×M16—61no—
432C3×M16—61no—
433C3×M16—61no—
434C3×M16C22×D311yescharacteristic
435C3×M16C22×D311yescharacteristic
436C2×C3×C8—21no—
437C2×C3×C8—21no—
438C2×C3×C8—21no—
439C2×C3×C8—31no—
440C2×C3×C8—41no—
441C2×C3×C8—61no—
442C2×C3×C8—61no—
443C2×C3×C8—61no—
444C2×C3×C8—61no—
445C2×C3×C8C22×D311yescharacteristic
446C2×C3×C8C22×D311yescharacteristic
447#216—21no—
448#216—61no—
449#216—61no—
450#215—21no—
451#215—61no—
452#215—61no—
453#215—61no—
454#215—61no—
455#215—61no—
456#215—61no—
457#215—61no—
458#215—61no—
459#215—61no—
460#215—61no—
461#215—121no—
462#215—121no—
463#214—21no—
464#214—61no—
465#214—61no—
466#213—21no—
467#213—61no—
468#213—61no—
469#213—61no—
470#213—61no—
471#213—61no—
472#213—61no—
473#213—61no—
474#213—61no—
475#213—61no—
476#213—61no—
477#213—121no—
478#213—121no—
479#208—21no—
480#208—31no—
481#208—31no—
482#208—31no—
483#208—31no—
484#208—61no—
485#208—61no—
486#208—61no—
487#208—61no—
488#208C22×D311yescharacteristic
489#208C22×D311yescharacteristic
490#208C22×D311yescharacteristic
491C2×C3⋊C8—21no—
492C2×C3⋊C8—61no—
493C2×C3⋊C8—61no—
494C2×C3⋊C8C22×D311yescharacteristic
495D24—61no—
496D24—61no—
497D24—61no—
498D24—61no—
499D24—61no—
500D24—61no—
501D24—61no—
502D24—61no—
503D24—121no—
504D24—121no—
505#204—21no—
506#204—21no—
507#204—61no—
508#204—61no—
509#204—61no—
510#204—61no—
511ΓL(1,𝔽25)—21no—
512ΓL(1,𝔽25)—21no—
513ΓL(1,𝔽25)—21no—
514ΓL(1,𝔽25)—61no—
515ΓL(1,𝔽25)—61no—
516ΓL(1,𝔽25)#6711yescharacteristic
517ΓL(1,𝔽25)#6711yescharacteristic
518ΓL(1,𝔽25)#6711yescharacteristic
519ΓL(1,𝔽25)#6711yescharacteristic
520D3×C8—21no—
521D3×C8—21no—
522D3×C8—21no—
523D3×C8—61no—
524D3×C8—61no—
525C22×C32—21no—
526C22×C32C2×#4111yescharacteristic
527C2×C3⋊D3—41no—
528C2×C3⋊D3—41no—
529C2×C3⋊D3—81no—
530C2×C3⋊D3—81no—
531C2×C3×D3—21no—
532C2×C3×D3—41no—
533C2×C3×D3—41no—
534C2×C3×D3—81no—
535C2×C3×D3—81no—
536C2×C3×D3#12111yescharacteristic
537C2×C3×D3#12111yescharacteristic
538D32—82no—
539D32—82no—
540C32×C4—21no—
541C32×C4C22×D411yescharacteristic
542C32×C4C22×D411yescharacteristic
543C3×Dic3—21no—
544C3×Dic3—41no—
545C3×Dic3#12111yescharacteristic
546C3×Dic3#12111yescharacteristic
547C2×#41—31no—
548C2×#41—91no—
549C22×D4—91no—
550#137—31no—
551#137—91no—
552#137—181no—
553AGL(1,ℤ/8)—31no—
554AGL(1,ℤ/8)—91no—
555AGL(1,ℤ/8)—91no—
556AGL(1,ℤ/8)—91no—
557AGL(1,ℤ/8)—91no—
558AGL(1,ℤ/8)—91no—
559AGL(1,ℤ/8)—181no—
560AGL(1,ℤ/8)—181no—
561AGL(1,ℤ/8)—181no—
562AGL(1,ℤ/8)—181no—
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—91no—
570C2×SD16—181no—
571C2×D8—91no—
572C2×D8—91no—
573C2×D8—181no—
574#131—31no—
575#131—31no—
576#131—31no—
577#131—61no—
578#131—61no—
579#131D3211yescharacteristic, complemented
580C2×M16—31no—
581C2×M16—31no—
582C2×M16—61no—
583C2×M16—61no—
584C2×M16—91no—
585C2×M16—91no—
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—31no—
599C23×C3—61no—
600C23×C3—61no—
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—61no—
604C22×D3—61no—
605C22×D3—61no—
606C22×D3—61no—
607C22×D3—121no—
608C22×D3—121no—
609C22×D3—121no—
610C22×D3—121no—
611C22×D3—121no—
612C22×D3—121no—
613C22×D3—242no—
614C22×D3—242no—
615C22×D3#23511yescharacteristic
616C3×Q8—21no—
617C3×Q8—31no—
618C3×Q8—61no—
619C3×Q8—61no—
620C3×Q8—61no—
621C3×Q8C2×D1211yescharacteristic
622C3×Q8D3×D411yescharacteristic
623C3×D4—21no—
624C3×D4—21no—
625C3×D4—21no—
626C3×D4—31no—
627C3×D4—41no—
628C3×D4—61no—
629C3×D4—61no—
630C3×D4—61no—
631C3×D4—61no—
632C3×D4—61no—
633C3×D4—61no—
634C3×D4C2×D1211yescharacteristic
635C3×D4D3×D411yescharacteristic
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—31no—
640C2×C3×C4—31no—
641C2×C3×C4—31no—
642C2×C3×C4—31no—
643C2×C3×C4—31no—
644C2×C3×C4—41no—
645C2×C3×C4—61no—
646C2×C3×C4—61no—
647C2×C3×C4—61no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4C23×D311yescharacteristic
651C2×C3×C4C23×D311yescharacteristic
652#67—21no—
653#67—21no—
654#67—21no—
655#67—121no—
656#67—121no—
657#67—121no—
658#67—121no—
659C2×Dic3—21no—
660C2×Dic3—21no—
661C2×Dic3#23511yescharacteristic
662D12—21no—
663D12—21no—
664D12—21no—
665D12—61no—
666D12—61no—
667D12—61no—
668D12—61no—
669D12—61no—
670D12—61no—
671D12—61no—
672D12—61no—
673D12—121no—
674D12—121no—
675D12—121no—
676D12—121no—
677D12—121no—
678D12—121no—
679D12—121no—
680D12—121no—
681D12C2×D1211yescharacteristic
682C4×D3—21no—
683C4×D3—21no—
684C4×D3—21no—
685C4×D3—121no—
686C4×D3—121no—
687C4×D3—121no—
688C4×D3—121no—
689C4×D3C2×D1211yescharacteristic
690C4×D3C2×D1211yescharacteristic
691C4×D3C2×#6711yescharacteristic
692C4×D3C2×#6711yescharacteristic
693Dic6—21no—
694Dic6—21no—
695Dic6—21no—
696Dic6C2×D1211yescharacteristic
697C3×C8—21no—
698C3×C8—21no—
699C3×C8—21no—
700C3×C8—21no—
701C3×C8—31no—
702C3×C8—31no—
703C3×C8—41no—
704C3×C8—61no—
705C3×C8—61no—
706C3×C8—61no—
707C3×C8D3×D411yescharacteristic
708C3×C8D3×D411yescharacteristic
709C3×C8C2×#6711yescharacteristic
710C3×C8C2×#6711yescharacteristic
711C3⋊C8—21no—
712C3⋊C8—21no—
713C3⋊C8—21no—
714C3⋊C8—61no—
715C3⋊C8—61no—
716C3⋊C8—61no—
717C3⋊C8—61no—
718C3⋊C8—121no—
719C3⋊C8—121no—
720C3⋊C8C2×#6711yescharacteristic
721C3⋊C8C2×#6711yescharacteristic
722C2×C32—21no—
723C2×C32—41no—
724C2×C32C2×#12111yescharacteristic
725C3⋊D3—81no—
726C3⋊D3—81no—
727C3×D3—21no—
728C3×D3—21no—
729C3×D3—41no—
730C3×D3—81no—
731C24—181no—
732#41—31no—
733#41—31no—
734#41—31no—
735#41—61no—
736#41—61no—
737#41—181no—
738#41—181no—
739#41—181no—
740#41—181no—
741#41C2×D3211yescharacteristic
742C2×Q8—31no—
743C2×Q8—31no—
744C2×D4—31no—
745C2×D4—31no—
746C2×D4—61no—
747C2×D4—91no—
748C2×D4—91no—
749C2×D4—181no—
750C2×D4—181no—
751C2×D4—181no—
752C2×D4—181no—
753C2×D4—181no—
754C2×D4—181no—
755C22×C4—31no—
756C22×C4—61no—
757C22×C4—181no—
758Q16—61no—
759Q16—181no—
760SD16—61no—
761SD16—61no—
762SD16—61no—
763SD16—61no—
764SD16—181no—
765SD16—181no—
766SD16—181no—
767SD16—181no—
768SD16—181no—
769SD16—181no—
770SD16—181no—
771SD16—181no—
772D8—61no—
773D8—181no—
774D8—181no—
775D8—181no—
776D8—181no—
777D8—181no—
778D8—181no—
779D8—181no—
780D8—181no—
781D8—181no—
782M16—21no—
783M16—31no—
784M16—31no—
785M16—31no—
786M16—31no—
787M16—31no—
788M16—31no—
789M16—31no—
790M16—61no—
791M16—61no—
792M16—61no—
793M16—61no—
794M16—91no—
795M16—91no—
796M16—181no—
797M16—181no—
798M16C2×D3211yescharacteristic
799C2×C8—21no—
800C2×C8—31no—
801C2×C8—61no—
802C2×C8—61no—
803C2×C8—61no—
804C2×C8—61no—
805C2×C8—181no—
806C2×C8—181no—
807C2×C8C2×D3211yescharacteristic
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—31no—
812C22×C3—31no—
813C22×C3—41no—
814C22×C3—61no—
815C22×C3—121no—
816C22×C3—121no—
817C22×C3—241no—
818C22×C3—241no—
819C22×C3C2×#23511yescharacteristic
820C22×C3D3×#4111yescharacteristic
821C2×D3—21no—
822C2×D3—41no—
823C2×D3—41no—
824C2×D3—81no—
825C2×D3—81no—
826C2×D3—121no—
827C2×D3—121no—
828C2×D3—121no—
829C2×D3—121no—
830C2×D3—241no—
831C2×D3—241no—
832C2×D3—242no—
833C2×D3—242no—
834C2×D3—242no—
835C2×D3—242no—
836C2×D3—241no—
837C2×D3—241no—
838C2×D3—241no—
839C2×D3—241no—
840C2×D3—481no—
841C2×D3—481no—
842C2×D3#93011yescharacteristic
843C2×D3#93011yescharacteristic
844C3×C4—21no—
845C3×C4—21no—
846C3×C4—21no—
847C3×C4—21no—
848C3×C4—31no—
849C3×C4—31no—
850C3×C4—41no—
851C3×C4—61no—
852C3×C4—121no—
853C3×C4C22×D1211yescharacteristic
854C3×C4C2×D3×D411yescharacteristic
855C3×C4C2×D3×D411yescharacteristic
856C3×C4C22×#6711yescharacteristic
857Dic3—21no—
858Dic3—41no—
859Dic3#93011yescharacteristic
860Dic3#93011yescharacteristic
861C32#306811yescharacteristic, complemented, Sylow
862C23—31no—
863C23—61no—
864C23—61no—
865C23—181no—
866C23—181no—
867C23—361no—
868C23—361no—
869C23—722no—
870Q8—31no—
871Q8—61no—
872Q8—61no—
873Q8—61no—
874Q8D3×D1211yescharacteristic
875D4—21no—
876D4—31no—
877D4—61no—
878D4—61no—
879D4—61no—
880D4—61no—
881D4—61no—
882D4—61no—
883D4—181no—
884D4—181no—
885D4—181no—
886D4—181no—
887D4—361no—
888D4—361no—
889D4—361no—
890D4—361no—
891D4D3×D1211yescharacteristic
892C2×C4—21no—
893C2×C4—31no—
894C2×C4—31no—
895C2×C4—31no—
896C2×C4—31no—
897C2×C4—31no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—361no—
904C2×C4—361no—
905C2×C4C22×D3211yescharacteristic
906C8—21no—
907C8—31no—
908C8—31no—
909C8—61no—
910C8—61no—
911C8—61no—
912C8—181no—
913C8—181no—
914C8D3×#6711yescharacteristic
915C8D3×#6711yescharacteristic
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—41no—
920C2×C3—41no—
921C2×C3—41no—
922C2×C3—61no—
923C2×C3—61no—
924C2×C3—81no—
925C2×C3—121no—
926C2×C3—241no—
927C2×C3D3×#12111yescharacteristic
928C2×C3C2×#93011yescharacteristic
929D3—21no—
930D3—21no—
931D3—41no—
932D3—81no—
933D3—241no—
934D3—241no—
935D3—241no—
936D3—241no—
937D3—481no—
938D3—481no—
939C22—21no—
940C22—31no—
941C22—31no—
942C22—61no—
943C22—121no—
944C22—121no—
945C22—241no—
946C22—241no—
947C22—361no—
948C22—361no—
949C22—721no—
950C22—721no—
951C22—722no—
952C22—722no—
953C22D3×#23511yescharacteristic
954C4—21no—
955C4—31no—
956C4—31no—
957C4—61no—
958C4—121no—
959C4C2×D3×D1211yescharacteristic
960C4C2×D3×#6711yescharacteristic
961C3—21no—
962C3#8093011yescharacteristic, complemented
963C3#8381411yescharacteristic, complemented
964C2—21no—
965C2—41no—
966C2—61no—
967C2—61no—
968C2—121no—
969C2—241no—
970C2—721no—
971C2—721no—
972C2D3×#93011yescharacteristic
subgroupG/H
centerC2D3×#930
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#131C22
socleC2×C32C2×#121
hypercenter#131D32
hypocenterC32#3068
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131

Complements

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

NH ≅ G/Ntype
1. C3×#5750C2semidirect
2. #10595470C2semidirect
3. D3×#949C2semidirect
4. C2×#63794C2semidirect
5. #10592841C2semidirect
6. C3×#5141C2semidirect
7. #10591680C2semidirect
8. #10591677C2semidirect
9. #10591007C2semidirect
10. D3×#823C2semidirect
11. #10590998C2semidirect
12. #10590997C2semidirect
13. #10590927C2semidirect
14. #10590925C2semidirect
15. #10590912C2semidirect
21. C32×#131C22semidirect
23. #64158C22semidirect
24. C2×#3745C22semidirect
25. C3×#951C22semidirect
27. C3×#948C22semidirect
29. C3×#907C22semidirect
32. C2×C3×#204C22semidirect
34. C3×#901C22semidirect
45. C2×#3717C22semidirect
46. #63827C22semidirect
48. #63825C22semidirect
49. C2×#3714C22semidirect
57. #63650C22semidirect
58. #63650C22semidirect
59. #63646C22semidirect
60. C3×#824C22semidirect
61. C3×#823C22semidirect
62. C3×#819C22semidirect
63. #63577C22semidirect
64. #63577C22semidirect
65. #63560C22semidirect
66. #63559C22semidirect
67. #63559C22semidirect
68. #63558C22semidirect
75. #5750D3semidirect
90. #5141D3semidirect
193. C3×#131C2×D3semidirect
194. C3×#131C2×D3semidirect
200. #951C2×D3semidirect
215. #948C2×D3semidirect
245. #907C2×D3semidirect
255. C2×#204C2×D3semidirect
257. #901C2×D3semidirect
266. #824C2×D3semidirect
278. #823C2×D3semidirect
286. #819C2×D3semidirect
579. #131D32semidirect
861. C32#3068semidirect
962. C3#80930semidirect
963. C3#83814semidirect

Maximal subgroups

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

subgroupindex
C3×#57502
#105954702
D3×#9492
C2×#637942
#105928412
C3×#51412
#105916802
#105916772
#105910072
D3×#8232
#105909982
#105909972
#105909272
#105909252
#105909122
#838143
#809303