Finite Group Databasebeta

← #11868136

Subgroups — #11868136

Order 1152.

1025 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63937C211yesmaximal, characteristic, complemented
2#10595100C211yesmaximal, characteristic, complemented
3#10594718C211yesmaximal, characteristic, complemented
4#10594708C211yesmaximal, characteristic, complemented
5C3⋊D3×#100C211yesmaximal, characteristic, complemented
6C3×#4749C211yesmaximal, characteristic, complemented
7C3×#4748C211yesmaximal, characteristic, complemented
8#10591506C211yesmaximal, characteristic, complemented
9#10591505C211yesmaximal, characteristic, complemented
10#10591010C211yesmaximal, characteristic, complemented
11#10590998C211yesmaximal, characteristic, complemented
12#10590997C211yesmaximal, characteristic, complemented
13#10590985C211yesmaximal, characteristic, complemented
14#10590984C211yesmaximal, characteristic, complemented
15#10590974C211yesmaximal, characteristic, complemented
16#80938—31nomaximal
17#80930—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19#64306C2211yescharacteristic
20C2×#3796C2211yescharacteristic
21M16×C3⋊D3C2211yescharacteristic
22M16×C3⋊D3C2211yescharacteristic
23C2×C3×#214C2211yescharacteristic, complemented
24C3×#932C2211yescharacteristic
25C3×#932C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic, complemented
27C3×#909C2211yescharacteristic, complemented
28C3×#908C2211yescharacteristic, complemented
29C3×#907C2211yescharacteristic, complemented
30C3×#907C2211yescharacteristic, complemented
31#63937—21no—
32#63937—21no—
33#63937—21no—
34#63937—21no—
35#63937—21no—
36#63937—21no—
37#63930—21no—
38#63926—21no—
39C2×#3717C2211yescharacteristic, complemented
40#63827C2211yescharacteristic, complemented
41#63825C2211yescharacteristic
42#63825C2211yescharacteristic
43C2×#3714C2211yescharacteristic, complemented
44#63823C2211yescharacteristic, complemented
45C2×#3712C2211yescharacteristic
46#63818C2211yescharacteristic
47#63814C2211yescharacteristic, complemented
48#63814C2211yescharacteristic, complemented
49#63811—21no—
50#63810—21no—
51#63809—21no—
52#63805—21no—
53#63803—21no—
54#63798—21no—
55D3×ΓL(1,𝔽25)—21no—
56D3×ΓL(1,𝔽25)—21no—
57C32×#100C2211yescharacteristic, complemented
58#63660C2211yescharacteristic, complemented
59#63650C2211yescharacteristic, complemented
60#63650C2211yescharacteristic, complemented
61C3×#824C2211yescharacteristic, complemented
62C3×#823C2211yescharacteristic, complemented
63C3×#822C2211yescharacteristic, complemented
64C3×#822C2211yescharacteristic, complemented
65#63577C2211yescharacteristic, complemented
66#63577C2211yescharacteristic, complemented
67#63560C2211yescharacteristic, 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#4898—31no—
88#4897—31no—
89#4893—31no—
90#4893—31no—
91#4754—31no—
92#4751—31no—
93#4749—31no—
94#4749D311yescharacteristic, complemented
95#4748D311yescharacteristic, complemented
96#4745—31no—
97D3×#100—31no—
98D3×#100—31no—
99D3×#100—61no—
100C23×C3⋊D3—21no—
101C2×C32×D4C2311yescharacteristic
102C2×#638—21no—
103D4×C3⋊D3—21no—
104D4×C3⋊D3—21no—
105D4×C3⋊D3—21no—
106D4×C3⋊D3—21no—
107C2×C4⋊(C3⋊D3)C2311yescharacteristic
108C2×C4×C3⋊D3C2311yescharacteristic
109C3×#235C2311yescharacteristic
110C3×#235C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113#3811—21no—
114C2×#626—21no—
115#3805—21no—
116C2×D3×Dic3—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
129#3748C2311yescharacteristic
130#3748C2311yescharacteristic
131#3743—21no—
132#3743—21no—
133C8×C3⋊D3—21no—
134C8×C3⋊D3—21no—
135C3×#214—21no—
136C3×#214—21no—
137C3×#214—21no—
138C3×#214—21no—
139C3×#213—21no—
140C3×#213—21no—
141C3×#213—21no—
142C3×#213—21no—
143C3×#208C2311yescharacteristic
144C3×#208C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147C3×Dic12—21no—
148C3×D24—21no—
149C3×#204—21no—
150C3×#204—21no—
151C3×ΓL(1,𝔽25)—21no—
152C3×ΓL(1,𝔽25)—21no—
153C3×D3×C8—21no—
154C3×D3×C8—21no—
155#3718—21no—
156#3717—21no—
157#3717—21no—
158#3717—21no—
159#3717—21no—
160#3715—21no—
161#3715—21no—
162#3714—21no—
163#3714—21no—
164#3714—21no—
165#3714—21no—
166#3713—21no—
167#3712—21no—
168#3712D411yescharacteristic
169#3712D411yescharacteristic
170#3712D411yescharacteristic
171#3712D411yescharacteristic
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—
184C2×D3×D4—61no—
185C3×#137—31no—
186C3×AGL(1,ℤ/8)—31no—
187C3×AGL(1,ℤ/8)—31no—
188C3×AGL(1,ℤ/8)—31no—
189C2×C3×SD16—31no—
190C2×C3×D8—31no—
191C3×#131—31no—
192C3×#131—31no—
193#951—31no—
194#949—31no—
195#949—31no—
196#949—31no—
197#948—31no—
198#948—31no—
199#942—31no—
200C2×#215—31no—
201C2×#214C2×D311yescharacteristic, complemented
202#932—31no—
203#932C2×D311yescharacteristic
204#932C2×D311yescharacteristic
205C2×#213—31no—
206C2×#213C2×D311yescharacteristic, complemented
207#919—61no—
208#918—61no—
209#916—61no—
210#916—61no—
211#915—61no—
212#914—61no—
213#914—61no—
214#914—61no—
215#914—61no—
216#914—61no—
217#914—61no—
218#914—61no—
219D3×SD16—61no—
220D3×SD16—61no—
221#912—61no—
222#911—61no—
223#911—61no—
224#911—61no—
225#911—61no—
226#911—61no—
227#911—61no—
228#911—61no—
229D3×D8—61no—
230D3×D8—61no—
231#909C2×D311yescharacteristic, complemented
232#908—31no—
233#908—31no—
234#908C2×D311yescharacteristic, complemented
235#907—61no—
236#907—61no—
237#907C2×D311yescharacteristic, complemented
238#907C2×D311yescharacteristic, complemented
239D3×M16—31no—
240D3×M16—31no—
241D3×M16—31no—
242D3×M16—31no—
243D3×M16—31no—
244D3×M16—31no—
245D3×M16—61no—
246D3×M16—61no—
247D3×M16—61no—
248D3×M16—61no—
249C2×D24—31no—
250C2×#204—31no—
251#901—31no—
252#901—31no—
253#901—61no—
254#901—61no—
255C2×ΓL(1,𝔽25)—31no—
256C2×ΓL(1,𝔽25)—31no—
257C2×ΓL(1,𝔽25)—61no—
258C2×ΓL(1,𝔽25)—61no—
259C3×#108—31no—
260C3×#108—31no—
261C3×#101—31no—
262C3×#100—21no—
263C3×#100—31no—
264C3×#100C2×D311yescharacteristic, complemented
265C3×#100C2×D311yescharacteristic, complemented
266#836—31no—
267#833—31no—
268#833—31no—
269#833—31no—
270#833—61no—
271#824—31no—
272#824C2×D311yescharacteristic, complemented
273#823—31no—
274#823—31no—
275#823—31no—
276#823—31no—
277#823—31no—
278#823—61no—
279#823—61no—
280#823C2×D311yescharacteristic, complemented
281#822—31no—
282#822—31no—
283#822C2×D311yescharacteristic, complemented
284#822C2×D311yescharacteristic, complemented
285#819—31no—
286#819—31no—
287C23×C32—21no—
288C22×C3⋊D3—21no—
289C22×C3⋊D3—41no—
290C22×C3⋊D3—41no—
291C22×C3⋊D3—82no—
292C22×C3⋊D3#4111yescharacteristic
293C22×C3×D3—21no—
294C2×D32—21no—
295C32×D4—21no—
296C32×D4—21no—
297C2×C32×C4C2411yescharacteristic
298#638—41no—
299#638—41no—
300C2×C3⋊Dic3#4111yescharacteristic
301C4⋊(C3⋊D3)—21no—
302C4⋊(C3⋊D3)—21no—
303C4×C3⋊D3C2×D411yescharacteristic
304C4×C3⋊D3C2×D411yescharacteristic
305C4×C3⋊D3C2×D411yescharacteristic
306C4×C3⋊D3C2×D411yescharacteristic
307C3×#67—21no—
308C3×#67—21no—
309C2×C3×Dic3—21no—
310C3×D12—21no—
311C3×D12—21no—
312C3×D12C2×D411yescharacteristic
313C3×D12C2×D411yescharacteristic
314C3×C4×D3—21no—
315C3×C4×D3—21no—
316C3×Dic6—21no—
317C3×Dic6—21no—
318C3×Dic6C2×D411yescharacteristic
319C3×Dic6C2×D411yescharacteristic
320#627—21no—
321#626—21no—
322#626—21no—
323#626—41no—
324#626—41no—
325#625—21no—
326#624—21no—
327D3×Dic3—21no—
328D3×Dic3—21no—
329D3×Dic3—41no—
330D3×Dic3—41no—
331C32×C8—21no—
332C32×C8—21no—
333C3⋊(C3⋊C8)—21no—
334C3⋊(C3⋊C8)—21no—
335C3×C3⋊C8—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8C2×D411yescharacteristic
338C3×C3⋊C8C2×D411yescharacteristic
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—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—
358C23×D3—62no—
359C3×#41—31no—
360C3×#41—31no—
361C2×C3×Q8—31no—
362C2×C3×D4—21no—
363C2×C3×D4—31no—
364C2×C3×D4C22×D311yescharacteristic
365C2×C3×D4C22×D311yescharacteristic
366C2×#67—61no—
367C2×#67—61no—
368C2×#67—61no—
369C2×#67—62no—
370C22×Dic3—61no—
371#239—31no—
372#239—31no—
373#239—61no—
374#239—61no—
375#239—61no—
376#239—61no—
377D3×Q8—31no—
378D3×Q8—31no—
379#237—31no—
380#237—31no—
381#237—61no—
382#237—61no—
383#237—61no—
384#237—61no—
385#237—61no—
386#237—61no—
387D3×D4—31no—
388D3×D4—31no—
389D3×D4—61no—
390D3×D4—61no—
391D3×D4—61no—
392D3×D4—61no—
393D3×D4—61no—
394D3×D4—61no—
395D3×D4—61no—
396D3×D4—61no—
397D3×D4—61no—
398D3×D4—61no—
399D3×D4—121no—
400D3×D4—121no—
401D3×D4—121no—
402D3×D4—121no—
403#235—61no—
404#235—61no—
405#235C22×D311yescharacteristic
406#235C22×D311yescharacteristic
407C2×D12—31no—
408C2×D12—31no—
409C2×D12—61no—
410C2×D12—61no—
411C2×D12C22×D311yescharacteristic
412C2×C4×D3—31no—
413C2×C4×D3—31no—
414C2×C4×D3—61no—
415C2×C4×D3—61no—
416C2×C4×D3—61no—
417C2×C4×D3—61no—
418C2×Dic6C22×D311yescharacteristic
419C3×Q16—61no—
420C3×SD16—61no—
421C3×SD16—61no—
422C3×SD16—61no—
423C3×SD16—61no—
424C3×SD16—61no—
425C3×SD16—61no—
426C3×D8—61no—
427C3×D8—61no—
428C3×D8—61no—
429C3×D8—61no—
430C3×D8—61no—
431C3×M16—21no—
432C3×M16—21no—
433C3×M16—31no—
434C3×M16—31no—
435C3×M16—61no—
436C3×M16—61no—
437C3×M16C22×D311yescharacteristic
438C3×M16C22×D311yescharacteristic
439C3×M16C22×D311yescharacteristic
440C3×M16C22×D311yescharacteristic
441C2×C3×C8—31no—
442C2×C3×C8—31no—
443C2×C3×C8—61no—
444C2×C3×C8—61no—
445#216—61no—
446#216—61no—
447#215—61no—
448#215—61no—
449#215—61no—
450#215—61no—
451#215—61no—
452#215—61no—
453#214—21no—
454#214—21no—
455#214—21no—
456#214—21no—
457#214—61no—
458#214—61no—
459#213—21no—
460#213—21no—
461#213—21no—
462#213—21no—
463#213—61no—
464#213—61no—
465#213—61no—
466#213—61no—
467#213—61no—
468#213—61no—
469#208—31no—
470#208—31no—
471#208—31no—
472#208—31no—
473#208—61no—
474#208—61no—
475#208—61no—
476#208—61no—
477#208C22×D311yescharacteristic
478#208C22×D311yescharacteristic
479C2×C3⋊C8—61no—
480C2×C3⋊C8—61no—
481C2×C3⋊C8C22×D311yescharacteristic
482C2×C3⋊C8C22×D311yescharacteristic
483Dic12—21no—
484D24—21no—
485D24—61no—
486D24—61no—
487D24—61no—
488D24—61no—
489#204—21no—
490#204—21no—
491#204—61no—
492#204—61no—
493#204—61no—
494#204—61no—
495ΓL(1,𝔽25)—21no—
496ΓL(1,𝔽25)—21no—
497ΓL(1,𝔽25)—31no—
498ΓL(1,𝔽25)—31no—
499ΓL(1,𝔽25)—31no—
500ΓL(1,𝔽25)—31no—
501ΓL(1,𝔽25)—31no—
502ΓL(1,𝔽25)—31no—
503ΓL(1,𝔽25)—31no—
504ΓL(1,𝔽25)—31no—
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)—61no—
512ΓL(1,𝔽25)—61no—
513ΓL(1,𝔽25)—121no—
514ΓL(1,𝔽25)—121no—
515D3×C8—21no—
516D3×C8—21no—
517D3×C8—61no—
518D3×C8—61no—
519D3×C8—61no—
520D3×C8—61no—
521D3×C8—61no—
522D3×C8—61no—
523D3×C8—61no—
524D3×C8—61no—
525D3×C8—121no—
526D3×C8—121no—
527C22×C32—41no—
528C22×C32—81no—
529C22×C32C2×#4111yescharacteristic
530C2×C3⋊D3—41no—
531C2×C3⋊D3—41no—
532C2×C3⋊D3—82no—
533C2×C3⋊D3—82no—
534C2×C3⋊D3—81no—
535C2×C3⋊D3#12111yescharacteristic
536C2×C3⋊D3#12111yescharacteristic
537C2×C3×D3—21no—
538C2×C3×D3—21no—
539C2×C3×D3—41no—
540C2×C3×D3—81no—
541D32—81no—
542C32×C4C22×D411yescharacteristic
543C32×C4C22×D411yescharacteristic
544C3⋊Dic3#12111yescharacteristic
545C3⋊Dic3#12111yescharacteristic
546C3×Dic3—21no—
547C3×Dic3—21no—
548C3×Dic3—41no—
549C2×#41—91no—
550C2×#41—91no—
551C22×D4—91no—
552#137—31no—
553#137—91no—
554#137—181no—
555AGL(1,ℤ/8)—31no—
556AGL(1,ℤ/8)—31no—
557AGL(1,ℤ/8)—31no—
558AGL(1,ℤ/8)—91no—
559AGL(1,ℤ/8)—91no—
560AGL(1,ℤ/8)—91no—
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—
566AGL(1,ℤ/8)—181no—
567AGL(1,ℤ/8)—181no—
568#135—181no—
569#135—181no—
570C2×SD16—31no—
571C2×SD16—91no—
572C2×SD16—181no—
573C2×D8—31no—
574C2×D8—91no—
575C2×D8—181no—
576#131—31no—
577#131—31no—
578#131—91no—
579#131—91no—
580#131—181no—
581#131—181no—
582C2×M16—91no—
583C2×M16—91no—
584C2×M16—91no—
585C2×M16—91no—
586C2×M16—181no—
587C2×M16—181no—
588#108—31no—
589#108—31no—
590#108—91no—
591#108—91no—
592#101—31no—
593#101—91no—
594#100—31no—
595#100—91no—
596#100—91no—
597#100—91no—
598#100—91no—
599#100D3211yescharacteristic, complemented
600C23×C3—22no—
601C23×C3—21no—
602C23×C3—21no—
603C23×C3—61no—
604C22×D3—21no—
605C22×D3—31no—
606C22×D3—31no—
607C22×D3—61no—
608C22×D3—61no—
609C22×D3—61no—
610C22×D3—62no—
611C22×D3—61no—
612C22×D3—61no—
613C22×D3—121no—
614C22×D3—121no—
615C22×D3—121no—
616C22×D3—121no—
617C22×D3—122no—
618C22×D3—122no—
619C22×D3—242no—
620C22×D3—242no—
621C22×D3—244no—
622C3×Q8—31no—
623C3×Q8—31no—
624C3×Q8—61no—
625C3×Q8—61no—
626C3×D4—21no—
627C3×D4—21no—
628C3×D4—21no—
629C3×D4—21no—
630C3×D4—31no—
631C3×D4—31no—
632C3×D4—41no—
633C3×D4—41no—
634C3×D4—61no—
635C3×D4—61no—
636C3×D4—61no—
637C3×D4—61no—
638C2×C3×C4—21no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4C23×D311yescharacteristic
643C2×C3×C4C23×D311yescharacteristic
644#67—21no—
645#67—21no—
646#67—61no—
647#67—61no—
648#67—61no—
649#67—61no—
650#67—121no—
651#67—121no—
652#67—121no—
653#67—121no—
654#67—121no—
655#67—121no—
656#67—122no—
657#67—122no—
658C2×Dic3—21no—
659C2×Dic3—31no—
660C2×Dic3—31no—
661C2×Dic3—61no—
662C2×Dic3—61no—
663C2×Dic3—61no—
664C2×Dic3—121no—
665C2×Dic3—121no—
666D12—21no—
667D12—21no—
668D12—61no—
669D12—61no—
670D12—61no—
671D12—61no—
672D12—61no—
673D12—61no—
674D12—121no—
675D12—121no—
676D12—121no—
677D12—121no—
678D12D3×D411yescharacteristic
679D12D3×D411yescharacteristic
680C4×D3—21no—
681C4×D3—21no—
682C4×D3—31no—
683C4×D3—31no—
684C4×D3—31no—
685C4×D3—31no—
686C4×D3—31no—
687C4×D3—31no—
688C4×D3—31no—
689C4×D3—31no—
690C4×D3—61no—
691C4×D3—61no—
692C4×D3—61no—
693C4×D3—61no—
694C4×D3—61no—
695C4×D3—61no—
696C4×D3—61no—
697C4×D3—61no—
698C4×D3—121no—
699C4×D3—121no—
700Dic6—21no—
701Dic6—21no—
702Dic6—61no—
703Dic6—61no—
704Dic6D3×D411yescharacteristic
705Dic6D3×D411yescharacteristic
706C3×C8—21no—
707C3×C8—21no—
708C3×C8—21no—
709C3×C8—21no—
710C3×C8—31no—
711C3×C8—31no—
712C3×C8—31no—
713C3×C8—31no—
714C3×C8—41no—
715C3×C8—41no—
716C3×C8—61no—
717C3×C8—61no—
718C3⋊C8—21no—
719C3⋊C8—21no—
720C3⋊C8—61no—
721C3⋊C8—61no—
722C3⋊C8—61no—
723C3⋊C8—61no—
724C3⋊C8—121no—
725C3⋊C8—121no—
726C3⋊C8D3×D411yescharacteristic
727C3⋊C8D3×D411yescharacteristic
728C3⋊C8D3×D411yescharacteristic
729C3⋊C8D3×D411yescharacteristic
730C2×C32—21no—
731C2×C32—81no—
732C2×C32C2×#12111yescharacteristic
733C3⋊D3—21no—
734C3⋊D3—21no—
735C3⋊D3—81no—
736C3×D3—41no—
737C3×D3—41no—
738C3×D3—81no—
739C24—181no—
740#41—31no—
741#41—31no—
742#41—91no—
743#41—91no—
744#41—181no—
745#41—181no—
746#41—181no—
747#41—181no—
748#41—181no—
749#41—181no—
750C2×Q8—31no—
751C2×Q8—91no—
752C2×D4—31no—
753C2×D4—91no—
754C2×D4—91no—
755C2×D4—181no—
756C2×D4—181no—
757C2×D4—181no—
758C2×D4—181no—
759C2×D4—181no—
760C2×D4—181no—
761C2×D4—181no—
762C2×D4C2×D3211yescharacteristic
763C22×C4—91no—
764C22×C4—181no—
765C22×C4—181no—
766Q16—61no—
767Q16—181no—
768SD16—61no—
769SD16—61no—
770SD16—61no—
771SD16—61no—
772SD16—61no—
773SD16—61no—
774SD16—181no—
775SD16—181no—
776SD16—181no—
777SD16—181no—
778SD16—181no—
779SD16—181no—
780D8—61no—
781D8—61no—
782D8—61no—
783D8—61no—
784D8—61no—
785D8—181no—
786D8—181no—
787D8—181no—
788D8—181no—
789D8—181no—
790M16—31no—
791M16—31no—
792M16—61no—
793M16—61no—
794M16—91no—
795M16—91no—
796M16—91no—
797M16—91no—
798M16—91no—
799M16—91no—
800M16—181no—
801M16—181no—
802M16—181no—
803M16—181no—
804M16—181no—
805M16C2×D3211yescharacteristic
806M16C2×D3211yescharacteristic
807C2×C8—31no—
808C2×C8—31no—
809C2×C8—61no—
810C2×C8—61no—
811C2×C8—181no—
812C2×C8—181no—
813C2×C8—181no—
814C2×C8—181no—
815C2×C8—181no—
816C22×C3—21no—
817C22×C3—42no—
818C22×C3—41no—
819C22×C3—41no—
820C22×C3—61no—
821C22×C3—61no—
822C22×C3—81no—
823C22×C3—81no—
824C22×C3—82no—
825C22×C3—121no—
826C22×C3—241no—
827C22×C3D3×#4111yescharacteristic
828C22×C3D3×#4111yescharacteristic
829C2×D3—21no—
830C2×D3—21no—
831C2×D3—31no—
832C2×D3—31no—
833C2×D3—31no—
834C2×D3—31no—
835C2×D3—41no—
836C2×D3—61no—
837C2×D3—61no—
838C2×D3—81no—
839C2×D3—121no—
840C2×D3—121no—
841C2×D3—122no—
842C2×D3—122no—
843C2×D3—121no—
844C2×D3—121no—
845C2×D3—241no—
846C2×D3—241no—
847C2×D3—242no—
848C2×D3—242no—
849C2×D3—244no—
850C2×D3—242no—
851C2×D3—242no—
852C2×D3—244no—
853C2×D3—241no—
854C2×D3—241no—
855C2×D3—242no—
856C3×C4—21no—
857C3×C4—21no—
858C3×C4—61no—
859C3×C4—61no—
860C3×C4—121no—
861C3×C4C2×D3×D411yescharacteristic
862C3×C4C2×D3×D411yescharacteristic
863C3×C4C2×D3×D411yescharacteristic
864C3×C4C2×D3×D411yescharacteristic
865Dic3—21no—
866Dic3—21no—
867Dic3—31no—
868Dic3—31no—
869Dic3—31no—
870Dic3—31no—
871Dic3—41no—
872Dic3—61no—
873Dic3—61no—
874C32#306811yescharacteristic, complemented, Sylow
875C23—21no—
876C23—61no—
877C23—91no—
878C23—181no—
879C23—181no—
880C23—361no—
881C23—361no—
882C23—722no—
883Q8—31no—
884Q8—31no—
885Q8—61no—
886Q8—61no—
887Q8—181no—
888D4—21no—
889D4—21no—
890D4—31no—
891D4—31no—
892D4—61no—
893D4—61no—
894D4—61no—
895D4—61no—
896D4—181no—
897D4—181no—
898D4—181no—
899D4—181no—
900D4—181no—
901D4—361no—
902D4—361no—
903D4—361no—
904D4—361no—
905C2×C4—61no—
906C2×C4—61no—
907C2×C4—61no—
908C2×C4—91no—
909C2×C4—91no—
910C2×C4—91no—
911C2×C4—91no—
912C2×C4—91no—
913C2×C4—181no—
914C2×C4—181no—
915C2×C4—181no—
916C2×C4—361no—
917C2×C4—361no—
918C2×C4C22×D3211yescharacteristic
919C8—21no—
920C8—21no—
921C8—31no—
922C8—31no—
923C8—31no—
924C8—31no—
925C8—61no—
926C8—61no—
927C8—181no—
928C8—181no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—41no—
933C2×C3—82no—
934C2×C3—81no—
935C2×C3—81no—
936C2×C3—121no—
937C2×C3—121no—
938C2×C3—241no—
939C2×C3D3×#12111yescharacteristic
940C2×C3D3×#12111yescharacteristic
941D3—41no—
942D3—41no—
943D3—62no—
944D3—61no—
945D3—61no—
946D3—61no—
947D3—61no—
948D3—81no—
949D3—121no—
950D3—242no—
951D3—241no—
952D3—241no—
953C22—41no—
954C22—61no—
955C22—61no—
956C22—81no—
957C22—91no—
958C22—91no—
959C22—121no—
960C22—241no—
961C22—361no—
962C22—361no—
963C22—721no—
964C22—722no—
965C22—722no—
966C22—721no—
967C22#6430611yescharacteristic
968C4—61no—
969C4—61no—
970C4—91no—
971C4—91no—
972C4—121no—
973C4D32×D411yescharacteristic
974C4D32×D411yescharacteristic
975C3—21no—
976C3#8093011yescharacteristic, complemented
977C3#8093811yescharacteristic, complemented
978C2—21no—
979C2—81no—
980C2—121no—
981C2—121no—
982C2—181no—
983C2—181no—
984C2—241no—
985C2—721no—
986C2#1059426511yescharacteristic
subgroupG/H
centerC2#10594265
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#100C22
socleC2×C32C2×#121
hypercenter#100D32
hypocenterC32#3068
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #100

Complements

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

NH ≅ G/Ntype
1. C2×#63937C2semidirect
2. #10595100C2semidirect
3. #10594718C2semidirect
4. #10594708C2semidirect
5. C3⋊D3×#100C2semidirect
6. C3×#4749C2semidirect
7. C3×#4748C2semidirect
8. #10591506C2semidirect
9. #10591505C2semidirect
10. #10591010C2semidirect
11. #10590998C2semidirect
12. #10590997C2semidirect
13. #10590985C2semidirect
14. #10590984C2semidirect
15. #10590974C2semidirect
23. C2×C3×#214C22semidirect
26. C2×C3×#213C22semidirect
27. C3×#909C22semidirect
28. C3×#908C22semidirect
29. C3×#907C22semidirect
30. C3×#907C22semidirect
39. C2×#3717C22semidirect
40. #63827C22semidirect
43. C2×#3714C22semidirect
44. #63823C22semidirect
47. #63814C22semidirect
48. #63814C22semidirect
57. C32×#100C22semidirect
58. #63660C22semidirect
59. #63650C22semidirect
60. #63650C22semidirect
61. C3×#824C22semidirect
62. C3×#823C22semidirect
63. C3×#822C22semidirect
64. C3×#822C22semidirect
65. #63577C22semidirect
66. #63577C22semidirect
67. #63560C22semidirect
68. #63558C22semidirect
94. #4749D3semidirect
95. #4748D3semidirect
201. C2×#214C2×D3semidirect
206. C2×#213C2×D3semidirect
231. #909C2×D3semidirect
234. #908C2×D3semidirect
237. #907C2×D3semidirect
238. #907C2×D3semidirect
264. C3×#100C2×D3semidirect
265. C3×#100C2×D3semidirect
272. #824C2×D3semidirect
280. #823C2×D3semidirect
283. #822C2×D3semidirect
284. #822C2×D3semidirect
599. #100D32semidirect
874. C32#3068semidirect
976. C3#80930semidirect
977. C3#80938semidirect

Maximal subgroups

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

subgroupindex
C2×#639372
#105951002
#105947182
#105947082
C3⋊D3×#1002
C3×#47492
C3×#47482
#105915062
#105915052
#105910102
#105909982
#105909972
#105909852
#105909842
#105909742
#809383
#809303