Finite Group Databasebeta

← #11868100

Subgroups — #11868100

Order 1152.

983 conjugacy classes of subgroups.

The subgroup lattice has 971 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594718C211yesmaximal, characteristic, complemented
2#10594716C211yesmaximal, characteristic, complemented
3C2×#63798C211yesmaximal, characteristic, complemented
4#10594670C211yesmaximal, characteristic, complemented
5#10592592C211yesmaximal, characteristic, complemented
6C3×#4898C211yesmaximal, characteristic, complemented
7C3×#4897C211yesmaximal, characteristic, complemented
8#10591010C211yesmaximal, characteristic, complemented
9#10591001C211yesmaximal, characteristic, complemented
10#10590982C211yesmaximal, characteristic, complemented
11#10590982C211yesmaximal, characteristic, complemented
12#10590980C211yesmaximal, characteristic, complemented
13#10590979C211yesmaximal, characteristic, complemented
14#10590926C211yesmaximal, characteristic, complemented
15#10590925C211yesmaximal, characteristic, complemented
16#80938—31nomaximal
17#80930—31nomaximal
18#64306C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20C2×#3796C2211yescharacteristic
21M16×C3⋊D3C2211yescharacteristic
22M16×C3⋊D3C2211yescharacteristic
23C2×#3743C2211yescharacteristic
24C3×#909C2211yescharacteristic, complemented
25C3×#908C2211yescharacteristic
26C3×#908C2211yescharacteristic
27C3×#908C2211yescharacteristic, complemented
28C2×C3×D24C2211yescharacteristic, complemented
29C2×C3×#204C2211yescharacteristic, complemented
30C3×#901C2211yescharacteristic, complemented
31C3×#901C2211yescharacteristic, complemented
32#63827C2211yescharacteristic, complemented
33C2×#3715C2211yescharacteristic, complemented
34#63823C2211yescharacteristic
35#63823C2211yescharacteristic
36#63823C2211yescharacteristic, complemented
37C2×#3713C2211yescharacteristic, complemented
38#63818C2211yescharacteristic
39#63815C2211yescharacteristic, complemented
40#63815C2211yescharacteristic, complemented
41#63811—21no—
42#63810—21no—
43#63809—21no—
44#63804—21no—
45#63804—21no—
46#63798—21no—
47#63798—21no—
48#63798—21no—
49#63798—21no—
50#63798—21no—
51#63798—21no—
52#63798—21no—
53#63797—21no—
54#63796—21no—
55D3×ΓL(1,𝔽25)—21no—
56D3×ΓL(1,𝔽25)—21no—
57C32×#108C2211yescharacteristic, complemented
58#63649C2211yescharacteristic, complemented
59#63649C2211yescharacteristic, complemented
60#63646C2211yescharacteristic, complemented
61C3×#824C2211yescharacteristic, complemented
62C3×#823C2211yescharacteristic, complemented
63C3×#823C2211yescharacteristic, complemented
64C3×#823C2211yescharacteristic, complemented
65#63560C2211yescharacteristic, complemented
66#63558C2211yescharacteristic, complemented
67#63558C2211yescharacteristic, complemented
68#63558C2211yescharacteristic, complemented
69#5777—31no—
70#5773—31no—
71D3×AGL(1,ℤ/8)—31no—
72D3×AGL(1,ℤ/8)—31no—
73C2×#914—31no—
74C2×#911—31no—
75#5750—31no—
76#5750—31no—
77C3×#472—31no—
78C3×#471—31no—
79#5203—31no—
80#5200—31no—
81#5199—31no—
82#5199—31no—
83#5177—31no—
84#5160—31no—
85#5142—31no—
86#5141—31no—
87#4898D311yescharacteristic, complemented
88#4897D311yescharacteristic, complemented
89#4893—31no—
90#4893—31no—
91#4893—61no—
92#4754—31no—
93#4751—31no—
94#4749—31no—
95#4749—31no—
96#4748—31no—
97#4745—31no—
98D3×#100—31no—
99D3×#100—31no—
100C22×D32—21no—
101C2×C4×C3⋊D3C2311yescharacteristic
102C3×#235C2311yescharacteristic
103C3×#235C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108#3811—21no—
109C2×#626—21no—
110C2×#625—21no—
111#3805—21no—
112C2×D3×Dic3—21no—
113#3802—21no—
114#3802—21no—
115#3802—21no—
116#3802—21no—
117#3802D411yescharacteristic
118C4×D32—21no—
119#3798—21no—
120#3797D411yescharacteristic
121#3796—21no—
122#3796—21no—
123#3796—21no—
124#3796—21no—
125#3796D411yescharacteristic
126#3796D411yescharacteristic
127C32×M16C2311yescharacteristic
128C32×M16C2311yescharacteristic
129C2×C32×C8C2311yescharacteristic
130#3748C2311yescharacteristic
131#3748C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133#3743—21no—
134#3743—21no—
135#3743D411yescharacteristic
136#3743D411yescharacteristic
137#3743D411yescharacteristic
138#3743D411yescharacteristic
139C8×C3⋊D3—21no—
140C8×C3⋊D3—21no—
141C3×#208C2311yescharacteristic
142C3×#208C2311yescharacteristic
143C3×Dic12—21no—
144C3×D24—21no—
145C3×D24—21no—
146C3×D24—21no—
147C3×D24—21no—
148C3×D24—21no—
149C3×#204—21no—
150C3×#204—21no—
151C3×#204—21no—
152C3×#204—21no—
153C3×#204—21no—
154C3×#204—21no—
155C3×ΓL(1,𝔽25)—21no—
156C3×ΓL(1,𝔽25)—21no—
157C3×D3×C8—21no—
158C3×D3×C8—21no—
159#3718—21no—
160#3715—21no—
161#3715—21no—
162#3715—21no—
163#3715—21no—
164#3715—21no—
165#3715—21no—
166#3713—21no—
167#3713—21no—
168#3713—21no—
169#3713—21no—
170#3713—21no—
171#3712—21no—
172#3711—21no—
173#3711—21no—
174#3710—21no—
175D3×C3⋊C8—21no—
176D3×C3⋊C8—21no—
177#3068—91noSylow
178D3×#41—31no—
179D3×#41—31no—
180C2×#239—31no—
181C2×#237—31no—
182C2×D3×D4—31no—
183C2×D3×D4—31no—
184C3×#137—31no—
185C3×AGL(1,ℤ/8)—31no—
186C3×AGL(1,ℤ/8)—31no—
187C3×AGL(1,ℤ/8)—31no—
188C2×C3×SD16—31no—
189C2×C3×D8—31no—
190C3×#131—31no—
191C3×#131—31no—
192#951—31no—
193#949—31no—
194#949—31no—
195#949—31no—
196#948—31no—
197#948—31no—
198#942—31no—
199C2×#215—31no—
200C2×#214—31no—
201#932—31no—
202#932—31no—
203#932—31no—
204C2×#213—31no—
205C2×#213—31no—
206#919—61no—
207#918—61no—
208#916—61no—
209#916—61no—
210#915—61no—
211#914—61no—
212#914—61no—
213#914—61no—
214#914—61no—
215#914—61no—
216#914—61no—
217#914—61no—
218D3×SD16—61no—
219D3×SD16—61no—
220#912—61no—
221#911—61no—
222#911—61no—
223#911—61no—
224#911—61no—
225#911—61no—
226#911—61no—
227#911—61no—
228D3×D8—61no—
229D3×D8—61no—
230#909C2×D311yescharacteristic, complemented
231#908C2×D311yescharacteristic
232#908C2×D311yescharacteristic
233#908C2×D311yescharacteristic, complemented
234#907—31no—
235#907—31no—
236#907—61no—
237#907—61no—
238D3×M16—31no—
239D3×M16—31no—
240D3×M16—31no—
241D3×M16—31no—
242D3×M16—31no—
243D3×M16—31no—
244D3×M16—61no—
245D3×M16—61no—
246D3×M16—61no—
247D3×M16—61no—
248C2×D24C2×D311yescharacteristic, complemented
249C2×#204C2×D311yescharacteristic, complemented
250#901—61no—
251#901—61no—
252#901C2×D311yescharacteristic, complemented
253#901C2×D311yescharacteristic, complemented
254C2×ΓL(1,𝔽25)—31no—
255C2×ΓL(1,𝔽25)—31no—
256C2×ΓL(1,𝔽25)—61no—
257C2×ΓL(1,𝔽25)—61no—
258C2×ΓL(1,𝔽25)—61no—
259C3×#108—21no—
260C3×#108C2×D311yescharacteristic, complemented
261C3×#108C2×D311yescharacteristic, complemented
262C3×#101—31no—
263C3×#100—31no—
264C3×#100—31no—
265C3×#100—31no—
266#836—31no—
267#833—31no—
268#833—31no—
269#833—31no—
270#824—31no—
271#824C2×D311yescharacteristic, complemented
272#823—31no—
273#823—31no—
274#823—31no—
275#823C2×D311yescharacteristic, complemented
276#823C2×D311yescharacteristic, complemented
277#823C2×D311yescharacteristic, complemented
278#822—31no—
279#822—31no—
280#822—31no—
281#822—31no—
282#822—61no—
283#822—61no—
284#819—31no—
285#819—31no—
286#819—61no—
287C22×C3⋊D3#4111yescharacteristic
288C22×C3×D3—21no—
289C22×C3×D3—21no—
290C22×C3×D3—21no—
291C2×D32—21no—
292C2×D32—41no—
293C2×D32—41no—
294C2×D32—82no—
295C2×C32×C4C2411yescharacteristic
296C2×C3⋊Dic3#4111yescharacteristic
297C4×C3⋊D3C2×D411yescharacteristic
298C4×C3⋊D3C2×D411yescharacteristic
299C4×C3⋊D3C2×D411yescharacteristic
300C4×C3⋊D3C2×D411yescharacteristic
301C3×#67—21no—
302C3×#67—21no—
303C2×C3×Dic3—21no—
304C3×D12—21no—
305C3×D12—21no—
306C3×D12—21no—
307C3×D12—21no—
308C3×D12—21no—
309C3×D12—21no—
310C3×D12C2×D411yescharacteristic
311C3×D12C2×D411yescharacteristic
312C3×C4×D3—21no—
313C3×C4×D3—21no—
314C3×Dic6—21no—
315C3×Dic6—21no—
316C3×Dic6C2×D411yescharacteristic
317C3×Dic6C2×D411yescharacteristic
318#627—21no—
319#626—21no—
320#626—21no—
321#626—41no—
322#626—41no—
323#625—21no—
324#625—41no—
325#625—41no—
326#624—21no—
327D3×Dic3—21no—
328D3×Dic3—21no—
329D3×Dic3—41no—
330D3×Dic3—41no—
331C32×C8—21no—
332C32×C8—21no—
333C32×C8C2×D411yescharacteristic
334C32×C8C2×D411yescharacteristic
335C3⋊(C3⋊C8)—21no—
336C3⋊(C3⋊C8)—21no—
337C3⋊(C3⋊C8)C2×D411yescharacteristic
338C3⋊(C3⋊C8)C2×D411yescharacteristic
339C3×C3⋊C8—21no—
340C3×C3⋊C8—21no—
341#575—91no—
342C2×AGL(1,ℤ/8)—91no—
343C2×AGL(1,ℤ/8)—91no—
344#568—91no—
345#472—31no—
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—31no—
359C3×#41—31no—
360C2×C3×Q8—31no—
361C2×C3×D4—31no—
362C2×C3×D4—31no—
363C2×C3×D4—31no—
364C2×#67—61no—
365C2×#67—61no—
366C2×#67—61no—
367C22×Dic3—61no—
368#239—31no—
369#239—31no—
370#239—61no—
371#239—61no—
372#239—61no—
373#239—61no—
374D3×Q8—31no—
375D3×Q8—31no—
376#237—31no—
377#237—31no—
378#237—61no—
379#237—61no—
380#237—61no—
381#237—61no—
382#237—61no—
383#237—61no—
384D3×D4—31no—
385D3×D4—31no—
386D3×D4—61no—
387D3×D4—61no—
388D3×D4—61no—
389D3×D4—61no—
390D3×D4—61no—
391D3×D4—61no—
392D3×D4—61no—
393D3×D4—61no—
394D3×D4—61no—
395D3×D4—61no—
396#235—61no—
397#235—61no—
398#235C22×D311yescharacteristic
399#235C22×D311yescharacteristic
400C2×D12—61no—
401C2×D12C22×D311yescharacteristic
402C2×D12C22×D311yescharacteristic
403C2×D12C22×D311yescharacteristic
404C2×C4×D3—31no—
405C2×C4×D3—31no—
406C2×C4×D3—61no—
407C2×C4×D3—61no—
408C2×C4×D3—61no—
409C2×C4×D3—61no—
410C2×Dic6C22×D311yescharacteristic
411C3×Q16—61no—
412C3×SD16—61no—
413C3×SD16—61no—
414C3×SD16—61no—
415C3×SD16—61no—
416C3×SD16—61no—
417C3×SD16—61no—
418C3×D8—61no—
419C3×D8—61no—
420C3×D8—61no—
421C3×D8—61no—
422C3×D8—61no—
423C3×M16—21no—
424C3×M16—21no—
425C3×M16—31no—
426C3×M16—31no—
427C3×M16—61no—
428C3×M16—61no—
429C3×M16C22×D311yescharacteristic
430C3×M16C22×D311yescharacteristic
431C3×M16C22×D311yescharacteristic
432C3×M16C22×D311yescharacteristic
433C2×C3×C8—21no—
434C2×C3×C8—61no—
435C2×C3×C8—61no—
436C2×C3×C8C22×D311yescharacteristic
437C2×C3×C8C22×D311yescharacteristic
438#216—61no—
439#216—61no—
440#215—61no—
441#215—61no—
442#215—61no—
443#215—61no—
444#215—61no—
445#215—61no—
446#214—61no—
447#214—61no—
448#214—61no—
449#214—61no—
450#214—61no—
451#214—61no—
452#213—61no—
453#213—61no—
454#213—61no—
455#213—61no—
456#213—61no—
457#213—61no—
458#213—61no—
459#213—61no—
460#213—61no—
461#213—61no—
462#208—31no—
463#208—31no—
464#208—31no—
465#208—31no—
466#208—61no—
467#208—61no—
468#208—61no—
469#208—61no—
470#208C22×D311yescharacteristic
471#208C22×D311yescharacteristic
472C2×C3⋊C8—31no—
473C2×C3⋊C8—31no—
474C2×C3⋊C8—61no—
475C2×C3⋊C8—61no—
476C2×C3⋊C8—61no—
477Dic12—21no—
478D24—21no—
479D24—21no—
480D24—21no—
481D24—21no—
482D24—21no—
483#204—21no—
484#204—21no—
485#204—21no—
486#204—21no—
487#204—21no—
488#204—21no—
489ΓL(1,𝔽25)—21no—
490ΓL(1,𝔽25)—21no—
491ΓL(1,𝔽25)—31no—
492ΓL(1,𝔽25)—31no—
493ΓL(1,𝔽25)—31no—
494ΓL(1,𝔽25)—31no—
495ΓL(1,𝔽25)—31no—
496ΓL(1,𝔽25)—31no—
497ΓL(1,𝔽25)—31no—
498ΓL(1,𝔽25)—31no—
499ΓL(1,𝔽25)—61no—
500ΓL(1,𝔽25)—61no—
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)—61no—
510ΓL(1,𝔽25)—61no—
511ΓL(1,𝔽25)—121no—
512ΓL(1,𝔽25)—121no—
513D3×C8—21no—
514D3×C8—21no—
515D3×C8—61no—
516D3×C8—61no—
517D3×C8—61no—
518D3×C8—61no—
519D3×C8—61no—
520D3×C8—61no—
521D3×C8—61no—
522D3×C8—61no—
523D3×C8—121no—
524D3×C8—121no—
525C22×C32C2×#4111yescharacteristic
526C2×C3⋊D3—41no—
527C2×C3⋊D3#12111yescharacteristic
528C2×C3⋊D3#12111yescharacteristic
529C2×C3×D3—21no—
530C2×C3×D3—21no—
531C2×C3×D3—41no—
532C2×C3×D3—41no—
533C2×C3×D3—41no—
534C2×C3×D3—81no—
535C2×C3×D3—81no—
536C2×C3×D3—81no—
537D32—81no—
538D32—82no—
539D32—82no—
540C32×C4C22×D411yescharacteristic
541C32×C4C22×D411yescharacteristic
542C3⋊Dic3#12111yescharacteristic
543C3⋊Dic3#12111yescharacteristic
544C3×Dic3—21no—
545C3×Dic3—21no—
546C3×Dic3—41no—
547C2×#41—91no—
548C2×#41—91no—
549C22×D4—91no—
550#137—31no—
551#137—91no—
552#137—181no—
553AGL(1,ℤ/8)—31no—
554AGL(1,ℤ/8)—31no—
555AGL(1,ℤ/8)—31no—
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—31no—
572C2×D8—91no—
573C2×D8—181no—
574#131—31no—
575#131—31no—
576#131—91no—
577#131—91no—
578#131—181no—
579#131—181no—
580C2×M16—91no—
581C2×M16—91no—
582C2×M16—91no—
583C2×M16—91no—
584C2×M16—181no—
585C2×M16—181no—
586#108—91no—
587#108—91no—
588#108—91no—
589#108D3211yescharacteristic, complemented
590#101—31no—
591#101—91no—
592#100—31no—
593#100—31no—
594#100—31no—
595#100—91no—
596#100—91no—
597#100—91no—
598C23×C3—61no—
599C23×C3—61no—
600C23×C3—61no—
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—31no—
605C22×D3—31no—
606C22×D3—61no—
607C22×D3—61no—
608C22×D3—61no—
609C22×D3—121no—
610C22×D3—121no—
611C22×D3—121no—
612C22×D3—121no—
613C22×D3—242no—
614C22×D3—242no—
615C3×Q8—31no—
616C3×Q8—31no—
617C3×Q8—61no—
618C3×Q8—61no—
619C3×D4—31no—
620C3×D4—31no—
621C3×D4—61no—
622C3×D4—61no—
623C3×D4—61no—
624C3×D4—61no—
625C3×D4—61no—
626C3×D4—61no—
627C3×D4—61no—
628C3×D4—61no—
629C2×C3×C4—21no—
630C2×C3×C4—61no—
631C2×C3×C4—61no—
632C2×C3×C4—61no—
633C2×C3×C4C23×D311yescharacteristic
634C2×C3×C4C23×D311yescharacteristic
635#67—21no—
636#67—21no—
637#67—61no—
638#67—61no—
639#67—61no—
640#67—61no—
641#67—121no—
642#67—121no—
643#67—121no—
644#67—121no—
645#67—121no—
646#67—121no—
647C2×Dic3—21no—
648C2×Dic3—31no—
649C2×Dic3—31no—
650C2×Dic3—61no—
651C2×Dic3—61no—
652C2×Dic3—61no—
653C2×Dic3—121no—
654C2×Dic3—121no—
655D12—21no—
656D12—21no—
657D12—21no—
658D12—21no—
659D12—21no—
660D12—21no—
661D12—61no—
662D12—61no—
663D12—121no—
664D12—121no—
665D12D3×D411yescharacteristic
666D12D3×D411yescharacteristic
667C4×D3—21no—
668C4×D3—21no—
669C4×D3—31no—
670C4×D3—31no—
671C4×D3—31no—
672C4×D3—31no—
673C4×D3—31no—
674C4×D3—31no—
675C4×D3—31no—
676C4×D3—31no—
677C4×D3—61no—
678C4×D3—61no—
679C4×D3—61no—
680C4×D3—61no—
681C4×D3—61no—
682C4×D3—61no—
683C4×D3—61no—
684C4×D3—61no—
685C4×D3—121no—
686C4×D3—121no—
687Dic6—21no—
688Dic6—21no—
689Dic6—61no—
690Dic6—61no—
691Dic6D3×D411yescharacteristic
692Dic6D3×D411yescharacteristic
693C3×C8—21no—
694C3×C8—21no—
695C3×C8—21no—
696C3×C8—21no—
697C3×C8—21no—
698C3×C8—21no—
699C3×C8—41no—
700C3×C8—41no—
701C3×C8—61no—
702C3×C8—61no—
703C3×C8D3×D411yescharacteristic
704C3×C8D3×D411yescharacteristic
705C3×C8D3×D411yescharacteristic
706C3×C8D3×D411yescharacteristic
707C3⋊C8—21no—
708C3⋊C8—21no—
709C3⋊C8—31no—
710C3⋊C8—31no—
711C3⋊C8—31no—
712C3⋊C8—31no—
713C3⋊C8—61no—
714C3⋊C8—61no—
715C3⋊C8—61no—
716C3⋊C8—61no—
717C3⋊C8—61no—
718C3⋊C8—61no—
719C3⋊C8—121no—
720C3⋊C8—121no—
721C2×C32—21no—
722C2×C32C2×#12111yescharacteristic
723C3⋊D3—21no—
724C3⋊D3—21no—
725C3×D3—41no—
726C3×D3—41no—
727C3×D3—81no—
728C3×D3—81no—
729C3×D3—81no—
730C24—181no—
731#41—31no—
732#41—31no—
733#41—91no—
734#41—91no—
735#41—181no—
736#41—181no—
737#41—181no—
738#41—181no—
739#41—181no—
740#41—181no—
741C2×Q8—31no—
742C2×Q8—91no—
743C2×D4—31no—
744C2×D4—31no—
745C2×D4—31no—
746C2×D4—91no—
747C2×D4—181no—
748C2×D4—181no—
749C2×D4—181no—
750C2×D4—181no—
751C2×D4—181no—
752C2×D4—181no—
753C2×D4—181no—
754C22×C4—91no—
755C22×C4—181no—
756C22×C4—181no—
757Q16—61no—
758Q16—181no—
759SD16—61no—
760SD16—61no—
761SD16—61no—
762SD16—61no—
763SD16—61no—
764SD16—61no—
765SD16—181no—
766SD16—181no—
767SD16—181no—
768SD16—181no—
769SD16—181no—
770SD16—181no—
771D8—61no—
772D8—61no—
773D8—61no—
774D8—61no—
775D8—61no—
776D8—181no—
777D8—181no—
778D8—181no—
779D8—181no—
780D8—181no—
781M16—31no—
782M16—31no—
783M16—61no—
784M16—61no—
785M16—91no—
786M16—91no—
787M16—91no—
788M16—91no—
789M16—91no—
790M16—91no—
791M16—181no—
792M16—181no—
793M16—181no—
794M16—181no—
795M16—181no—
796M16C2×D3211yescharacteristic
797M16C2×D3211yescharacteristic
798C2×C8—61no—
799C2×C8—61no—
800C2×C8—91no—
801C2×C8—181no—
802C2×C8—181no—
803C2×C8—181no—
804C2×C8—181no—
805C2×C8—181no—
806C2×C8C2×D3211yescharacteristic
807C22×C3—21no—
808C22×C3—61no—
809C22×C3—61no—
810C22×C3—121no—
811C22×C3—121no—
812C22×C3—121no—
813C22×C3—241no—
814C22×C3—241no—
815C22×C3—241no—
816C22×C3D3×#4111yescharacteristic
817C22×C3D3×#4111yescharacteristic
818C2×D3—21no—
819C2×D3—21no—
820C2×D3—31no—
821C2×D3—31no—
822C2×D3—31no—
823C2×D3—31no—
824C2×D3—41no—
825C2×D3—41no—
826C2×D3—41no—
827C2×D3—61no—
828C2×D3—61no—
829C2×D3—81no—
830C2×D3—81no—
831C2×D3—81no—
832C2×D3—121no—
833C2×D3—121no—
834C2×D3—241no—
835C2×D3—241no—
836C2×D3—241no—
837C2×D3—242no—
838C2×D3—242no—
839C2×D3—242no—
840C2×D3—242no—
841C3×C4—21no—
842C3×C4—21no—
843C3×C4—61no—
844C3×C4—61no—
845C3×C4—121no—
846C3×C4C2×D3×D411yescharacteristic
847C3×C4C2×D3×D411yescharacteristic
848C3×C4C2×D3×D411yescharacteristic
849C3×C4C2×D3×D411yescharacteristic
850Dic3—21no—
851Dic3—21no—
852Dic3—31no—
853Dic3—31no—
854Dic3—31no—
855Dic3—31no—
856Dic3—41no—
857Dic3—61no—
858Dic3—61no—
859C32#306811yescharacteristic, complemented, Sylow
860C23—61no—
861C23—61no—
862C23—61no—
863C23—91no—
864C23—181no—
865C23—361no—
866C23—361no—
867C23—722no—
868Q8—31no—
869Q8—31no—
870Q8—61no—
871Q8—61no—
872Q8—181no—
873D4—31no—
874D4—31no—
875D4—61no—
876D4—61no—
877D4—61no—
878D4—61no—
879D4—61no—
880D4—61no—
881D4—61no—
882D4—61no—
883D4—181no—
884D4—181no—
885D4—181no—
886D4—361no—
887D4—361no—
888D4—361no—
889D4—361no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—91no—
894C2×C4—91no—
895C2×C4—91no—
896C2×C4—91no—
897C2×C4—91no—
898C2×C4—181no—
899C2×C4—181no—
900C2×C4—181no—
901C2×C4—361no—
902C2×C4—361no—
903C2×C4C22×D3211yescharacteristic
904C8—21no—
905C8—21no—
906C8—61no—
907C8—61no—
908C8—91no—
909C8—91no—
910C8—181no—
911C8—181no—
912C8#380211yescharacteristic
913C8#380211yescharacteristic
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—41no—
918C2×C3—121no—
919C2×C3—121no—
920C2×C3—241no—
921C2×C3—241no—
922C2×C3—241no—
923C2×C3D3×#12111yescharacteristic
924C2×C3D3×#12111yescharacteristic
925D3—41no—
926D3—41no—
927D3—61no—
928D3—61no—
929D3—61no—
930D3—61no—
931D3—81no—
932D3—81no—
933D3—81no—
934D3—121no—
935D3—121no—
936C22—61no—
937C22—61no—
938C22—91no—
939C22—91no—
940C22—121no—
941C22—121no—
942C22—121no—
943C22—241no—
944C22—241no—
945C22—241no—
946C22—361no—
947C22—721no—
948C22—722no—
949C22—722no—
950C22#6431911yescharacteristic
951C4—61no—
952C4—61no—
953C4—91no—
954C4—91no—
955C4—121no—
956C4C2×#380211yescharacteristic
957C4D32×D411yescharacteristic
958C3—21no—
959C3#8093011yescharacteristic, complemented
960C3#8093811yescharacteristic, complemented
961C2—21no—
962C2—121no—
963C2—121no—
964C2—181no—
965C2—181no—
966C2—241no—
967C2—241no—
968C2—241no—
969C2#1059461211yescharacteristic
subgroupG/H
centerC2#10594612
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#108C22
socleC2×C32C2×#121
hypercenter#108D32
hypocenterC32#3068
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #108

Complements

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

NH ≅ G/Ntype
1. #10594718C2semidirect
2. #10594716C2semidirect
3. C2×#63798C2semidirect
4. #10594670C2semidirect
5. #10592592C2semidirect
6. C3×#4898C2semidirect
7. C3×#4897C2semidirect
8. #10591010C2semidirect
9. #10591001C2semidirect
10. #10590982C2semidirect
11. #10590982C2semidirect
12. #10590980C2semidirect
13. #10590979C2semidirect
14. #10590926C2semidirect
15. #10590925C2semidirect
24. C3×#909C22semidirect
27. C3×#908C22semidirect
28. C2×C3×D24C22semidirect
29. C2×C3×#204C22semidirect
30. C3×#901C22semidirect
31. C3×#901C22semidirect
32. #63827C22semidirect
33. C2×#3715C22semidirect
36. #63823C22semidirect
37. C2×#3713C22semidirect
39. #63815C22semidirect
40. #63815C22semidirect
57. C32×#108C22semidirect
58. #63649C22semidirect
59. #63649C22semidirect
60. #63646C22semidirect
61. C3×#824C22semidirect
62. C3×#823C22semidirect
63. C3×#823C22semidirect
64. C3×#823C22semidirect
65. #63560C22semidirect
66. #63558C22semidirect
67. #63558C22semidirect
68. #63558C22semidirect
87. #4898D3semidirect
88. #4897D3semidirect
230. #909C2×D3semidirect
233. #908C2×D3semidirect
248. C2×D24C2×D3semidirect
249. C2×#204C2×D3semidirect
252. #901C2×D3semidirect
253. #901C2×D3semidirect
260. C3×#108C2×D3semidirect
261. C3×#108C2×D3semidirect
271. #824C2×D3semidirect
275. #823C2×D3semidirect
276. #823C2×D3semidirect
277. #823C2×D3semidirect
589. #108D32semidirect
859. C32#3068semidirect
959. C3#80930semidirect
960. C3#80938semidirect

Maximal subgroups

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

subgroupindex
#105947182
#105947162
C2×#637982
#105946702
#105925922
C3×#48982
C3×#48972
#105910102
#105910012
#105909822
#105909802
#105909792
#105909262
#105909252
#809383
#809303