Finite Group Databasebeta

← #11884402

Subgroups — #11884402

Order 1152.

1076 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#914C211yesmaximal, characteristic, complemented
2#10595412C211yesmaximal, characteristic, complemented
3C2×#63947C211yesmaximal, characteristic, complemented
4#10595228C211yesmaximal, characteristic, complemented
5#10592865C211yesmaximal, characteristic, complemented
6C3×#5172C211yesmaximal, characteristic, complemented
7#10591599C211yesmaximal, characteristic, complemented
8#10591572C211yesmaximal, characteristic, complemented
9#10591498C211yesmaximal, characteristic, complemented
10#10591485C211yesmaximal, characteristic, complemented
11#10591447C211yesmaximal, characteristic, complemented
12#10590962C211yesmaximal, characteristic, complemented
13#10590828C211yesmaximal, characteristic, complemented
14#10590749C211yesmaximal, characteristic, complemented
15#10590724C211yesmaximal, characteristic, complemented
16#83955—31nomaximal
17#80123—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic, complemented
20C2×C3×D3×D4C2211yescharacteristic
21C2×#3795C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic, complemented
24C2×#3756C2211yescharacteristic, complemented
25#64145C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic
27C3×#938C2211yescharacteristic
28C2×C3×#213C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic
30C3×#914—24no—
31C2×C3×D24C2211yescharacteristic
32C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
33#63976—21no—
34#63970—21no—
35#63969—21no—
36D3×#217—21no—
37#63947—24no—
38#63914—21no—
39#63914C2211yescharacteristic, complemented
40#63908—21no—
41#63908—21no—
42#63908C2211yescharacteristic
43#63908C2211yescharacteristic, complemented
44C4×#625—21no—
45C4×#625C2211yescharacteristic
46#63898C2211yescharacteristic
47#63857C2211yescharacteristic
48C2×#3716C2211yescharacteristic, complemented
49C2×#3716C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63659C2211yescharacteristic
53#63643C2211yescharacteristic, complemented
54#63641C2211yescharacteristic, complemented
55C3×#835C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58#63575C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63555C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64#5834—31no—
65#5834—31no—
66C2×#950—31no—
67#5806—31no—
68C2×#916—31no—
69C2×#914D311yescharacteristic, complemented
70#5612—31no—
71C3×#449—31no—
72#5239—31no—
73#5217—31no—
74#5172D311yescharacteristic, complemented
75#5166—31no—
76#5166—31no—
77#5166—61no—
78#5164—31no—
79#5158—31no—
80#5157—31no—
81#5156—31no—
82#5154—31no—
83#5154—31no—
84#5150—31no—
85#5134—31no—
86#5127—31no—
87#5038—31no—
88#4817—31no—
89#4808—31no—
90#4786—31no—
91#4780—31no—
92#4734—31no—
93#4730—31no—
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C3×#239—22no—
101C3×#239—22no—
102C3×#239—41no—
103C3×#239—41no—
104C3×D3×D4—22no—
105C3×D3×D4—41no—
106C2×C3×D12—21no—
107C2×C3×D12—21no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×#625—21no—
116C2×#625—21no—
117C2×#625—21no—
118C2×#625—21no—
119C2×#625—21no—
120C2×#625D411yescharacteristic
121C2×D3×Dic3—21no—
122C2×D3×Dic3—21no—
123#3795—22no—
124#3795—41no—
125C32×SD16—22no—
126C2×C32×C8C2311yescharacteristic
127#3757—21no—
128#3757—21no—
129#3756—22no—
130C4⋊(C3⋊Dic3)—21no—
131C4⋊(C3⋊Dic3)C2311yescharacteristic
132C4×C3⋊Dic3—21no—
133C4×C3⋊Dic3C2311yescharacteristic
134C2×C3⋊(C3⋊C8)C2311yescharacteristic
135C3×#217—21no—
136C3×#215D414yescomplemented
137C3×#213—22no—
138C3×#213—41no—
139C3×C4⋊Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×D24—22no—
143C3×ΓL(1,𝔽25)—22no—
144#3724D411yescharacteristic
145Dic3⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3D411yescharacteristic
151(C2×D3)⋊Dic3D411yescharacteristic
152#3716—22no—
153#3716—41no—
154#3713—22no—
155D3×C3⋊C8—22no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C22×C3×D4—31no—
160C2×#239C2×D311yescharacteristic
161C2×#239C2×D311yescharacteristic, complemented
162C2×#237—31no—
163C2×D3×D4C2×D311yescharacteristic
164C2×#235—31no—
165C3×AGL(1,ℤ/8)—64no—
166C2×C3×SD16—21no—
167C2×C3×SD16—31no—
168C2×C3×SD16C2×D311yescharacteristic
169C2×C3×SD16C2×D311yescharacteristic
170C2×C3×D8—31no—
171C2×C3×D8—31no—
172C2×C3×D8—31no—
173C2×C3×M16—31no—
174C3×#121—31no—
175#953—61no—
176C2×#217—61no—
177#950—64no—
178Q8×Dic3—31no—
179Q8×Dic3—31no—
180Q8×Dic3—61no—
181C2×#216—31no—
182C2×#216—31no—
183C2×#216—61no—
184C2×#215C2×D311yescharacteristic
185#940—31no—
186#940—31no—
187#940—61no—
188#940—61no—
189#939—61no—
190#938—31no—
191#938—31no—
192#938—61no—
193#938—61no—
194#938—61no—
195#938C2×D311yescharacteristic
196#937—61no—
197#936—31no—
198#936—31no—
199#936—61no—
200#935—61no—
201D4×Dic3—31no—
202C2×#214—31no—
203C2×#214—31no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213C2×D311yescharacteristic
207C2×#213C2×D311yescharacteristic
208#930—31no—
209#930—31no—
210#930—61no—
211#930—61no—
212C4×#67—31no—
213C4×#67—31no—
214C4×#67—61no—
215C4×#67—61no—
216#924—31no—
217C22×C3⋊C8—31no—
218#916—64no—
219#914—24no—
220C2×D24C2×D311yescharacteristic
221C2×#204—31no—
222C2×#204—31no—
223C2×ΓL(1,𝔽25)C2×D311yescharacteristic
224C2×D3×C8—31no—
225#897—31no—
226#893—31no—
227#883—61no—
228D3×C22⋊C4—61no—
229C3×#103—31no—
230C3×#102—31no—
231C3×C22⋊C8—31no—
232#835C2×D311yescharacteristic, complemented
233#832—31no—
234#832—31no—
235#832—31no—
236#832—31no—
237#832—61no—
238#830—31no—
239#821—31no—
240#821C2×D311yescharacteristic, complemented
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8C2×D311yescharacteristic, complemented
243#818—31no—
244#816—31no—
245#816—31no—
246#816—61no—
247#815—31no—
248#815—31no—
249Dic3⋊C8—31no—
250Dic3⋊C8—31no—
251Dic3⋊C8—61no—
252#809—31no—
253#807—31no—
254C23×C32—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3—81no—
261C22×C3×D3C2×D411yescharacteristic
262C22×C3×D3C2×D411yescharacteristic
263C32×Q8—21no—
264C32×Q8C2×D412yes—
265C32×D4—21no—
266C32×D4—21no—
267C2×C32×C4—21no—
268C2×C32×C4C2411yescharacteristic
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3C2×D411yescharacteristic
272C2×C3⋊Dic3C2×D411yescharacteristic
273#634—21no—
274#634—21no—
275C3×#67—42no—
276C3×#67—81no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—42no—
286C3×D12—42no—
287C3×D12C2×D412yes—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—42no—
293C3×C4×D3—42no—
294#625—41no—
295#625—42no—
296#625—42no—
297#625—81no—
298#625—81no—
299#625—81no—
300D3×Dic3—42no—
301D3×Dic3—81no—
302C32×C8—21no—
303C3⋊(C3⋊C8)—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×AGL(1,ℤ/8)—31no—
307C2×#135—91no—
308#550—91no—
309#546—91no—
310#496—91no—
311#468—91no—
312#466—91no—
313#464—91no—
314#459—91no—
315#452—91no—
316#449—31no—
317#449—91no—
318#447—91no—
319#440—91no—
320#435—91no—
321C24×C3—61no—
322C23×D3—21no—
323C3×#41—62no—
324C3×#41—62no—
325C3×#41—121no—
326C3×#41—121no—
327C2×C3×Q8—21no—
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×D4—21no—
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C2×C3×D4—62no—
338C2×C3×D4—61no—
339C2×C3×D4—121no—
340C2×C3×D4C22×D311yescharacteristic
341C2×C3×D4C22×D311yescharacteristic
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—61no—
345C22×C3×C4—61no—
346C2×#67—21no—
347C2×#67—21no—
348C2×#67—31no—
349C2×#67—31no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67—61no—
360C22×Dic3—61no—
361C22×Dic3—61no—
362#239—22no—
363#239—22no—
364#239—41no—
365#239—41no—
366#237—62no—
367#237—121no—
368D3×D4—22no—
369D3×D4—41no—
370#235—62no—
371#235—121no—
372C2×D12—21no—
373C2×D12—21no—
374C2×D12C22×D311yescharacteristic
375C2×D12C22×D311yescharacteristic
376C2×D12C22×D311yescharacteristic
377C2×C4×D3—21no—
378C2×C4×D3—21no—
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3C22×D311yescharacteristic
382C2×C4×D3C22×D311yescharacteristic
383C2×Dic6—31no—
384C2×Dic6—31no—
385C2×Dic6—61no—
386C3×SD16—22no—
387C3×SD16—22no—
388C3×SD16—34no—
389C3×SD16—42no—
390C3×D8—62no—
391C3×D8—62no—
392C3×D8—121no—
393C3×M16—62no—
394C2×C3×C8—21no—
395C2×C3×C8—31no—
396C2×C3×C8—31no—
397C2×C3×C8C22×D311yescharacteristic
398C2×C3×C8C22×D311yescharacteristic
399C3×C4⋊C4—31no—
400C3×C22⋊C4—61no—
401#217—21no—
402#217—31no—
403#217—31no—
404#217—61no—
405#217—61no—
406#217—61no—
407#217—61no—
408#217—61no—
409#217—61no—
410#217—61no—
411#217—61no—
412#217—121no—
413#217—121no—
414#216—62no—
415#216—62no—
416#216—122no—
417#215#6714yescomplemented
418#214—62no—
419#214—121no—
420#213—22no—
421#213—41no—
422#213—62no—
423#213—62no—
424(C2×D3)⋊C4—31no—
425(C2×D3)⋊C4—31no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430C4⋊Dic3—31no—
431C4⋊Dic3—31no—
432C4⋊Dic3—61no—
433C4⋊Dic3—61no—
434C4⋊Dic3—61no—
435C4⋊Dic3—61no—
436C4⋊Dic3—121no—
437C4⋊Dic3C22×D311yescharacteristic
438Dic3⋊C4—31no—
439Dic3⋊C4—31no—
440Dic3⋊C4—61no—
441C4×Dic3—31no—
442C4×Dic3—31no—
443C4×Dic3—61no—
444C4×Dic3—61no—
445C4×Dic3—61no—
446C4×Dic3—121no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—61no—
450C2×C3⋊C8—62no—
451C2×C3⋊C8C22×D311yescharacteristic
452C2×C3⋊C8C22×D311yescharacteristic
453D24—22no—
454#204—62no—
455#204—121no—
456ΓL(1,𝔽25)—22no—
457D3×C8—62no—
458C22×C32—41no—
459C22×C32—41no—
460C22×C32—41no—
461C22×C32C22×D411yescharacteristic
462C2×C3×D3—22no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—84no—
478C32×C4—22no—
479C32×C4C22×D411yescharacteristic
480C32×C4H(5,𝔽2)11yescharacteristic
481C3⋊Dic3—21no—
482C3⋊Dic3—21no—
483C3⋊Dic3—41no—
484C3⋊Dic3—41no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—41no—
488C2×#41—31no—
489C2×#41—31no—
490C2×#41—91no—
491C22×D4—31no—
492AGL(1,ℤ/8)—64no—
493#135—184no—
494C2×Q16—91no—
495C2×SD16—31no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×SD16D3211yescharacteristic
499C2×D8—31no—
500C2×D8—31no—
501C2×D8—31no—
502C2×D8—91no—
503C2×M16—31no—
504C22×C8—91no—
505#127—91no—
506#127—181no—
507#124—91no—
508#123—181no—
509C22⋊Q8—91no—
510#121—31no—
511#121—91no—
512#121—91no—
513#121—181no—
514#121—181no—
515#121—181no—
516#120—181no—
517C4×Q8—91no—
518C4×D4—91no—
519C4×D4—91no—
520C4×D4—181no—
521C2×C22⋊C4—181no—
522#107—91no—
523C4⋊C8—91no—
524#103—31no—
525#103—91no—
526#102—31no—
527#102—91no—
528#102—91no—
529#102—91no—
530C22⋊C8—31no—
531C22⋊C8—91no—
532#97—91no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—31no—
536C23×C3—31no—
537C23×C3—41no—
538C23×C3—61no—
539C23×C3—61no—
540C23×C3—61no—
541C23×C3—122no—
542C23×C3—122no—
543C23×C3—241no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—42no—
548C22×D3—42no—
549C22×D3—81no—
550C22×D3D3×D411yescharacteristic
551C22×D3D3×D411yescharacteristic
552C3×Q8—21no—
553C3×Q8—21no—
554C3×Q8—22no—
555C3×Q8—41no—
556C3×Q8D3×D412yes—
557C3×Q8C2×#6712yes—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—21no—
562C3×D4—32no—
563C3×D4—41no—
564C3×D4—41no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—61no—
568C3×D4—61no—
569C3×D4—61no—
570C3×D4—122no—
571C3×D4—122no—
572C3×D4—122no—
573C3×D4—241no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—31no—
578C2×C3×C4—31no—
579C2×C3×C4—41no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—122no—
586C2×C3×C4—122no—
587C2×C3×C4C23×D311yescharacteristic
588C2×C3×C4C23×D311yescharacteristic
589#67—42no—
590#67—81no—
591#67—121no—
592#67—121no—
593#67—122no—
594#67—122no—
595#67—122no—
596#67—122no—
597#67—241no—
598#67—241no—
599#67—241no—
600#67—241no—
601#67—241no—
602#67—241no—
603C2×Dic3—21no—
604C2×Dic3—31no—
605C2×Dic3—31no—
606C2×Dic3—31no—
607C2×Dic3—31no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—121no—
615C2×Dic3—121no—
616C2×Dic3—122no—
617C2×Dic3—241no—
618C2×Dic3D3×D411yescharacteristic
619C2×Dic3D3×D411yescharacteristic
620D12—21no—
621D12—21no—
622D12—21no—
623D12—21no—
624D12—21no—
625D12—42no—
626D12—42no—
627D12C2×#6712yes—
628C4×D3—21no—
629C4×D3—21no—
630C4×D3—21no—
631C4×D3—21no—
632C4×D3—42no—
633C4×D3—42no—
634C4×D3—122no—
635C4×D3—241no—
636Dic6—61no—
637Dic6—61no—
638Dic6—61no—
639Dic6—61no—
640Dic6—121no—
641Dic6—121no—
642C3×C8—21no—
643C3×C8—21no—
644C3×C8—32no—
645C3×C8—41no—
646C3×C8—61no—
647C3⋊C8—21no—
648C3⋊C8—61no—
649C3⋊C8—61no—
650C3⋊C8—121no—
651C3⋊C8C2×#6712yes—
652C2×C32—81no—
653C2×C32D4211yescharacteristic
654C2×C32#57511yescharacteristic
655C2×C32#57611yescharacteristic
656C3×D3—41no—
657C3×D3—41no—
658C3×D3—42no—
659C3×D3—81no—
660C3×D3—81no—
661C24—61no—
662#41—62no—
663#41—62no—
664#41—121no—
665#41—121no—
666#41—182no—
667#41—361no—
668C2×Q8—91no—
669C2×Q8C2×D3211yescharacteristic
670C2×D4—31no—
671C2×D4—31no—
672C2×D4—31no—
673C2×D4—61no—
674C2×D4—61no—
675C2×D4—61no—
676C2×D4—62no—
677C2×D4—61no—
678C2×D4—91no—
679C2×D4—121no—
680C2×D4—181no—
681C2×D4—181no—
682C2×D4—181no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4C2×D3211yescharacteristic
686C22×C4—31no—
687C22×C4—31no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—181no—
691C22×C4—181no—
692Q16—182no—
693SD16—22no—
694SD16—34no—
695SD16—182no—
696SD16—361no—
697D8—62no—
698D8—62no—
699D8—121no—
700D8—182no—
701M16—62no—
702C2×C8—31no—
703C2×C8—31no—
704C2×C8—91no—
705C2×C8—182no—
706C2×C8C2×D3211yescharacteristic
707C4⋊C4—31no—
708C4⋊C4—91no—
709C4⋊C4—91no—
710C4⋊C4—181no—
711C4⋊C4—181no—
712C22⋊C4—61no—
713C22⋊C4—91no—
714C22⋊C4—91no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C22⋊C4—181no—
718C22⋊C4—181no—
719C22⋊C4—181no—
720C22⋊C4—181no—
721C42—91no—
722C42—181no—
723C22×C3—21no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—61no—
731C22×C3—61no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3—61no—
735C22×C3—62no—
736C22×C3—61no—
737C22×C3—81no—
738C22×C3—81no—
739C22×C3—81no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—244no—
749C22×C3C2×D3×D411yescharacteristic
750C22×C3C2×D3×D411yescharacteristic
751C2×D3—21no—
752C2×D3—21no—
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—21no—
756C2×D3—22no—
757C2×D3—21no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—84no—
767C3×C4—22no—
768C3×C4—22no—
769C3×C4—21no—
770C3×C4—21no—
771C3×C4—42no—
772C3×C4—61no—
773C3×C4—61no—
774C3×C4—121no—
775C3×C4C2×D3×D411yescharacteristic
776C3×C4#100411yescharacteristic
777C3×C4#100411yescharacteristic
778C3×C4C22×#6711yescharacteristic
779Dic3—21no—
780Dic3—21no—
781Dic3—41no—
782Dic3—61no—
783Dic3—61no—
784Dic3—61no—
785Dic3—61no—
786Dic3—121no—
787Dic3—121no—
788Dic3—121no—
789Dic3—121no—
790Dic3—121no—
791Dic3—121no—
792Dic3—241no—
793Dic3—241no—
794C32#326811yescharacteristic, complemented, Sylow
795C23—21no—
796C23—31no—
797C23—31no—
798C23—61no—
799C23—61no—
800C23—61no—
801C23—122no—
802C23—122no—
803C23—241no—
804Q8—21no—
805Q8—181no—
806Q8—181no—
807Q8D3×#6712yes—
808D4—21no—
809D4—21no—
810D4—32no—
811D4—61no—
812D4—61no—
813D4—61no—
814D4—61no—
815D4—61no—
816D4—122no—
817D4—122no—
818D4—122no—
819D4—241no—
820D4—361no—
821D4—362no—
822D4—362no—
823D4—721no—
824D4—721no—
825D4—721no—
826C2×C4—21no—
827C2×C4—31no—
828C2×C4—31no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—91no—
835C2×C4—91no—
836C2×C4—122no—
837C2×C4—122no—
838C2×C4—181no—
839C2×C4—181no—
840C2×C4—362no—
841C2×C4—721no—
842C2×C4C22×D3211yescharacteristic
843C8—21no—
844C8—32no—
845C8—61no—
846C8—181no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—81no—
851C2×C3—81no—
852C2×C3—121no—
853C2×C3—121no—
854C2×C3—122no—
855C2×C3—161no—
856C2×C3—241no—
857C2×C3—241no—
858C2×C3#559011yescharacteristic
859C2×C3#576811yescharacteristic
860C2×C3#577311yescharacteristic
861C2×C3#577411yescharacteristic
862C2×C3#577411yescharacteristic
863C2×C3D4×#6711yescharacteristic
864D3—41no—
865D3—42no—
866D3—41no—
867D3—81no—
868D3—81no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—61no—
873C22—61no—
874C22—61no—
875C22—61no—
876C22—61no—
877C22—61no—
878C22—62no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—121no—
885C22—121no—
886C22—121no—
887C22—244no—
888C22D32×D411yescharacteristic
889C4—22no—
890C4—61no—
891C4—61no—
892C4—121no—
893C4—181no—
894C4—181no—
895C4—361no—
896C4—361no—
897C4#6431311yescharacteristic
898C4C2×D3×#6711yescharacteristic
899C3—21no—
900C3#8012311yescharacteristic, complemented
901C3#8395511yescharacteristic, complemented
902C2—81no—
903C2—121no—
904C2—121no—
905C2—122no—
906C2—241no—
907C2—241no—
908C2#1059474511yescharacteristic
909C2#1059475011yescharacteristic
910C2#1059528711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#914C2semidirect
2. #10595412C2semidirect
3. C2×#63947C2semidirect
4. #10595228C2semidirect
5. #10592865C2semidirect
6. C3×#5172C2semidirect
7. #10591599C2semidirect
8. #10591572C2semidirect
9. #10591498C2semidirect
10. #10591485C2semidirect
11. #10591447C2semidirect
12. #10590962C2semidirect
13. #10590828C2semidirect
14. #10590749C2semidirect
15. #10590724C2semidirect
19. C2×C3×#239C22semidirect
23. Q8×C3⋊Dic3C22semidirect
24. C2×#3756C22semidirect
39. #63914C22semidirect
43. #63908C22semidirect
48. C2×#3716C22semidirect
49. C2×#3716C22semidirect
51. C2×D3×C3⋊C8C22semidirect
53. #63643C22semidirect
54. #63641C22semidirect
55. C3×#835C22semidirect
56. C3×#821C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. #63575C22semidirect
60. #63562C22semidirect
62. #63555C22semidirect
69. C2×#914D3semidirect
74. #5172D3semidirect
136. C3×#215D4semidirect
161. C2×#239C2×D3semidirect
232. #835C2×D3semidirect
240. #821C2×D3semidirect
242. (C2×D3)⋊C8C2×D3semidirect
417. #215#67semidirect
794. C32#3268semidirect
900. C3#80123semidirect
901. C3#83955semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9142
#105954122
C2×#639472
#105952282
#105928652
C3×#51722
#105915992
#105915722
#105914982
#105914852
#105914472
#105909622
#105908282
#105907492
#105907242
#839553
#801233