Finite Group Databasebeta

← #11884008

Subgroups — #11884008

Order 1152.

1152 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63795C211yesmaximal, characteristic, complemented
2C2×D3×#204C211yesmaximal, characteristic, complemented
3#10594004C211yesmaximal, characteristic, complemented
4#10593905C211yesmaximal, characteristic, complemented
5#10592409C211yesmaximal, characteristic, complemented
6C3×#4712C211yesmaximal, characteristic, complemented
7C3×#4706C211yesmaximal, characteristic, complemented
8#10590962C211yesmaximal, characteristic, complemented
9#10590944C211yesmaximal, characteristic, complemented
10#10590942C211yesmaximal, characteristic, complemented
11#10590833C211yesmaximal, characteristic, complemented
12#10590831C211yesmaximal, characteristic, complemented
13#10590822C211yesmaximal, characteristic, complemented
14#10590377C211yesmaximal, characteristic, complemented
15#10590356C211yesmaximal, characteristic, complemented
16#81857—31nomaximal
17#79494—31nomaximal
18C2×#3802—21no—
19C2×D3×D12C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22C2×D3×Dic6C2211yescharacteristic, complemented
23C2×#3744C2211yescharacteristic
24C4×C4⋊(C3⋊D3)C2211yescharacteristic
25C4×#634C2211yescharacteristic, complemented
26C2×C3×D24C2211yescharacteristic, complemented
27C2×C3×D24C2211yescharacteristic, complemented
28C2×C3×#204C2211yescharacteristic, complemented
29C2×C3×#204C2211yescharacteristic, complemented
30C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
31C2×C3×D3×C8C2211yescharacteristic, complemented
32C3×#875C2211yescharacteristic, complemented
33C3×#874C2211yescharacteristic
34C3×C4×D12C2211yescharacteristic
35#63922—21no—
36#63922—21no—
37#63916—21no—
38#63915—21no—
39#63908C2211yescharacteristic
40#63908C2211yescharacteristic
41#63908C2211yescharacteristic, complemented
42#63902—21no—
43#63899—21no—
44#63885—21no—
45#63856C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic
47C2×#3716C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50#63795—24no—
51D3×#204—24no—
52C32×#97C2211yescharacteristic, complemented
53#63648C2211yescharacteristic
54#63645C2211yescharacteristic, complemented
55#63643C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63C2×D3×SD16—31no—
64C2×#911—31no—
65C2×#908—31no—
66C22×#204—31no—
67#5717—31no—
68#5677—31no—
69#5552—31no—
70D4×D12—31no—
71C3×#496—31no—
72C3×#435—31no—
73#5174—31no—
74#5170—31no—
75#5169—31no—
76#5158—31no—
77#5157—31no—
78#5156—31no—
79#5134—31no—
80#5115—31no—
81#5075—31no—
82#5057—31no—
83#4848—31no—
84#4844—31no—
85#4738—31no—
86#4734—31no—
87#4732—31no—
88#4731—31no—
89#4712D311yescharacteristic, complemented
90#4710—31no—
91#4710—31no—
92#4710—61no—
93#4706D311yescharacteristic, complemented
94C22×D32—21no—
95C22×D32—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×#634C2311yescharacteristic
99C2×C3×D12—21no—
100C2×C3×D12—21no—
101C2×C3×D12D411yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#627—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#625—21no—
112C2×#625—21no—
113C2×#625—21no—
114C2×#625—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117#3802—44no—
118D3×D12—22no—
119D3×D12—22no—
120D3×D12—41no—
121D3×D12—41no—
122#3795—22no—
123#3795—41no—
124D3×Dic6—22no—
125D3×Dic6—41no—
126C2×C32×C8C2311yescharacteristic
127C2×C32×C8C2311yescharacteristic
128C32×C42C2311yescharacteristic
129#3752—21no—
130C4⋊(C3⋊Dic3)C2311yescharacteristic
131C4⋊(C3⋊Dic3)C2311yescharacteristic
132#3750—21no—
133C4×C3⋊Dic3—21no—
134#3744D414yescomplemented
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4D411yescharacteristic
138C3×(C2×D3)⋊C4D411yescharacteristic
139C3×C4⋊Dic3D411yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×D24—22no—
143C3×D24—41no—
144C3×#204—22no—
145C3×#204—41no—
146C3×ΓL(1,𝔽25)—22no—
147C3×D3×C8—22no—
148#3724—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3—21no—
153#3717—22no—
154#3716—22no—
155#3716—22no—
156#3714—22no—
157#3265—91noSylow
158C2×D3×Q8—31no—
159C2×#237—31no—
160C2×D3×D4—31no—
161C2×D3×D4—31no—
162C2×D3×D4—61no—
163C2×D3×D4—61no—
164C2×#235—31no—
165C22×D12—31no—
166C22×D12—31no—
167C22×Dic6—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×D8—31no—
171C2×C3×D8—31no—
172C2×C3×M16—31no—
173C22×C3×C8—31no—
174C3×#127—31no—
175C3×#124—31no—
176C3×C4×D4—31no—
177#946—31no—
178C2×#215—31no—
179#939—61no—
180#938—31no—
181#938—31no—
182#938—31no—
183#938—61no—
184#937—61no—
185#937—61no—
186C2×#214—31no—
187C2×#214—31no—
188C2×#213—31no—
189#930—31no—
190#930—31no—
191#930—31no—
192#924—31no—
193D3×SD16—64no—
194#911—64no—
195#908—64no—
196C2×D24—31no—
197C2×D24C2×D311yescharacteristic, complemented
198C2×D24C2×D311yescharacteristic, complemented
199C2×#204—31no—
200C2×#204—31no—
201C2×#204—31no—
202C2×#204—31no—
203C2×#204—31no—
204C2×#204—61no—
205C2×#204—64no—
206C2×#204C2×D311yescharacteristic, complemented
207C2×#204C2×D311yescharacteristic, complemented
208C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
209C2×D3×C8C2×D311yescharacteristic, complemented
210#896—61no—
211#895—61no—
212#885—61no—
213#885—61no—
214#884—61no—
215#882—61no—
216#882—61no—
217#67⋊C4—61no—
218#67⋊C4—61no—
219#878—61no—
220#875C2×D311yescharacteristic, complemented
221#874C2×D311yescharacteristic
222C4×D12—31no—
223C4×D12—31no—
224C4×D12—61no—
225C4×D12C2×D311yescharacteristic
226C4×Dic6—31no—
227C4×Dic6—31no—
228C4×Dic6—61no—
229C3×C4⋊C8—31no—
230C3×C22⋊C8—31no—
231C3×C22⋊C8—31no—
232C3×#97—21no—
233C3×#97C2×D311yescharacteristic, complemented
234C3×#97C2×D311yescharacteristic, complemented
235#835—31no—
236#832—31no—
237#832—31no—
238#832—31no—
239#821—31no—
240#821—31no—
241#821—31no—
242#821—31no—
243#821—31no—
244#821—61no—
245(C2×D3)⋊C8C2×D311yescharacteristic, complemented
246(C2×D3)⋊C8C2×D311yescharacteristic, complemented
247#818—31no—
248#818—31no—
249#818—61no—
250#816—31no—
251#816—31no—
252#816—31no—
253#816—61no—
254C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
255C22×C3⋊D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3C2×D411yescharacteristic
260C22×C3×D3C2×D411yescharacteristic
261C2×D32—42no—
262C2×D32—42no—
263C2×D32—42no—
264C2×D32—42no—
265C2×D32—81no—
266C2×D32—81no—
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2411yescharacteristic
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)C2×D412yes—
275C4×C3⋊D3—42no—
276#634—21no—
277#634C2×D412yescomplemented
278C2×C3×Dic3—21no—
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C3×D12—22no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—42no—
289C3×D12—81no—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296#627—42no—
297#626—42no—
298#626—42no—
299#625—42no—
300#625—42no—
301#625—42no—
302#625—42no—
303D3×Dic3—42no—
304D3×Dic3—42no—
305C32×C8—21no—
306C32×C8C2×D412yescomplemented
307C3×C3⋊C8—21no—
308C3×C3⋊C8—21no—
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—91no—
311#548—91no—
312D42—91no—
313#496—31no—
314#468—91no—
315#466—91no—
316#463—91no—
317#460—91no—
318#450—91no—
319#449—91no—
320#448—91no—
321#447—91no—
322#440—91no—
323#435—31no—
324C23×D3—61no—
325C23×D3—61no—
326C23×D3—61no—
327C23×D3—61no—
328C2×C3×Q8—31no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C22×Dic3—61no—
348C22×Dic3—61no—
349D3×Q8—62no—
350D3×Q8—121no—
351#237—62no—
352#237—121no—
353D3×D4—62no—
354D3×D4—62no—
355D3×D4—121no—
356D3×D4—121no—
357D3×D4—124no—
358D3×D4—124no—
359#235—62no—
360#235—121no—
361C2×D12—21no—
362C2×D12—21no—
363C2×D12—31no—
364C2×D12—31no—
365C2×D12—61no—
366C2×D12—62no—
367C2×D12—62no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12—121no—
371C2×D12—121no—
372C2×D12D1211yescharacteristic
373C2×D12C22×D311yescharacteristic
374C2×D12C22×D311yescharacteristic
375C2×D12C22×D311yescharacteristic
376C2×C4×D3—61no—
377C2×C4×D3—61no—
378C2×C4×D3—61no—
379C2×C4×D3—61no—
380C2×C4×D3—121no—
381C2×C4×D3C22×D311yescharacteristic
382C2×C4×D3C22×D311yescharacteristic
383C2×Dic6—31no—
384C2×Dic6—31no—
385C2×Dic6—61no—
386C2×Dic6—62no—
387C2×Dic6—61no—
388C2×Dic6—61no—
389C2×Dic6—121no—
390C2×Dic6C22×D311yescharacteristic
391C3×SD16—62no—
392C3×SD16—121no—
393C3×D8—62no—
394C3×D8—121no—
395C3×M16—62no—
396C2×C3×C8—21no—
397C2×C3×C8—21no—
398C2×C3×C8—31no—
399C2×C3×C8—31no—
400C2×C3×C8—62no—
401C2×C3×C8C22×D311yescharacteristic
402C2×C3×C8C22×D311yescharacteristic
403C2×C3×C8C22×D311yescharacteristic
404C2×C3×C8C22×D311yescharacteristic
405C3×C4⋊C4—31no—
406C3×C22⋊C4—31no—
407C3×C22⋊C4—31no—
408C3×C22⋊C4—61no—
409C3×C22⋊C4—61no—
410C3×C42—21no—
411C3×C42C22×D311yescharacteristic
412C3×C42C22×D311yescharacteristic
413#217—61no—
414#217—61no—
415#217—61no—
416#217—61no—
417#215—62no—
418#214—62no—
419#214—62no—
420#213—62no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—121no—
430(C2×D3)⋊C4D1211yescharacteristic
431(C2×D3)⋊C4D1211yescharacteristic
432C4⋊Dic3—31no—
433C4⋊Dic3—31no—
434C4⋊Dic3—31no—
435C4⋊Dic3—31no—
436C4⋊Dic3—61no—
437C4⋊Dic3—61no—
438C4⋊Dic3D1211yescharacteristic
439Dic3⋊C4—61no—
440Dic3⋊C4—61no—
441Dic3⋊C4—61no—
442Dic3⋊C4—61no—
443Dic3⋊C4—121no—
444C4×Dic3—61no—
445C4×Dic3—61no—
446C4×Dic3—121no—
447C2×C3⋊C8C22×D311yescharacteristic
448C2×C3⋊C8C22×D311yescharacteristic
449D24—22no—
450D24—41no—
451D24—62no—
452#204—22no—
453#204—34no—
454#204—34no—
455#204—41no—
456#204—64no—
457#204—62no—
458#204—62no—
459#204—62no—
460ΓL(1,𝔽25)—22no—
461D3×C8—22no—
462C22×C32C22×D411yescharacteristic
463C2×C3⋊D3—22no—
464C2×C3⋊D3—41no—
465C2×C3⋊D3—41no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
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—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3AGL(1,ℤ/8)12yescomplemented
481D32—84no—
482D32—84no—
483C32×C4—21no—
484C32×C4—21no—
485C32×C4C22×D411yescharacteristic
486C32×C4H(5,𝔽2)11yescharacteristic
487C3⋊Dic3—22no—
488C3⋊Dic3—41no—
489C3⋊Dic3—41no—
490C3×Dic3—21no—
491C3×Dic3—21no—
492C3×Dic3—41no—
493C2×#41—91no—
494C22×Q8—91no—
495C22×D4—91no—
496C22×D4—91no—
497C22×D4—181no—
498AGL(1,ℤ/8)—184no—
499C2×SD16—31no—
500C2×SD16—31no—
501C2×SD16—91no—
502C2×SD16—91no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—184no—
506C2×D8—31no—
507C2×D8—31no—
508C2×D8—91no—
509C2×M16—31no—
510C22×C8—31no—
511#127—31no—
512#124—31no—
513#124—181no—
514C22⋊Q8—91no—
515C22⋊Q8—181no—
516#121—91no—
517#121—91no—
518#121—91no—
519#121—181no—
520#121—181no—
521#120—181no—
522#120—181no—
523C4×Q8—91no—
524C4×D4—31no—
525C4×D4—91no—
526C4×D4—181no—
527#107—91no—
528C4⋊C8—31no—
529#103—91no—
530#103—91no—
531#102—91no—
532#102—91no—
533#102—91no—
534#102—91no—
535C22⋊C8—31no—
536C22⋊C8—31no—
537#97D3211yescharacteristic, complemented
538C23×C3—31no—
539C23×C3—31no—
540C23×C3—61no—
541C23×C3—61no—
542C23×C3—61no—
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—121no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3—122no—
554C22×D3—122no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—241no—
558C22×D3—241no—
559C22×D3—241no—
560C22×D3—241no—
561C22×D3C2×D1211yescharacteristic
562C22×D3C2×D1211yescharacteristic
563C3×Q8—61no—
564C3×Q8—61no—
565C3×D4—62no—
566C3×D4—61no—
567C3×D4—61no—
568C3×D4—61no—
569C3×D4—61no—
570C3×D4—61no—
571C3×D4—61no—
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—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4C2×D1211yescharacteristic
585C2×C3×C4C2×D1211yescharacteristic
586C2×C3×C4D3×D411yescharacteristic
587C2×C3×C4D3×D411yescharacteristic
588C2×C3×C4C23×D311yescharacteristic
589C2×C3×C4C23×D311yescharacteristic
590#67—122no—
591#67—122no—
592#67—122no—
593#67—122no—
594#67—122no—
595#67—122no—
596#67—122no—
597#67—122no—
598#67—122no—
599#67—122no—
600C2×Dic3—21no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—121no—
608C2×Dic3—121no—
609C2×Dic3—121no—
610C2×Dic3—122no—
611C2×Dic3—122no—
612C2×Dic3C2×D1211yescharacteristic
613C2×Dic3C2×D1211yescharacteristic
614D12—22no—
615D12—21no—
616D12—21no—
617D12—21no—
618D12—21no—
619D12—21no—
620D12—21no—
621D12—32no—
622D12—32no—
623D12—42no—
624D12—62no—
625D12—61no—
626D12—61no—
627D12—81no—
628D12—121no—
629D12—122no—
630D12—122no—
631C4×D3—21no—
632C4×D3—21no—
633C4×D3—21no—
634C4×D3—21no—
635C4×D3—122no—
636C4×D3—122no—
637C4×D3—122no—
638C4×D3—122no—
639C4×D3—242no—
640Dic6—21no—
641Dic6—21no—
642Dic6—32no—
643Dic6—32no—
644Dic6—62no—
645Dic6—61no—
646Dic6—61no—
647Dic6—121no—
648Dic6—122no—
649Dic6—122no—
650C3×C8—21no—
651C3×C8—21no—
652C3×C8—22no—
653C3×C8—41no—
654C3×C8—61no—
655C3×C8—61no—
656C3×C8D3×D412yescomplemented
657C3×C8D3×D412yescomplemented
658C3⋊C8—21no—
659C3⋊C8—21no—
660C2×C32D4211yescharacteristic
661C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
662C2×C32#57711yescharacteristic
663C3⋊D3—42no—
664C3×D3—22no—
665C3×D3—41no—
666C3×D3—81no—
667C3×D3—81no—
668C3×D3—81no—
669C24—181no—
670C24—181no—
671#41—182no—
672#41—361no—
673C2×Q8—31no—
674C2×Q8—91no—
675C2×Q8—181no—
676C2×Q8—182no—
677C2×Q8—361no—
678C2×D4—31no—
679C2×D4—31no—
680C2×D4—31no—
681C2×D4—31no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—91no—
685C2×D4—181no—
686C2×D4—181no—
687C2×D4—182no—
688C2×D4—182no—
689C2×D4—181no—
690C2×D4—181no—
691C2×D4—181no—
692C2×D4—181no—
693C2×D4—361no—
694C2×D4—361no—
695C2×D4—364no—
696C22×C4—31no—
697C22×C4—31no—
698C22×C4—181no—
699C22×C4—181no—
700C22×C4—181no—
701SD16—62no—
702SD16—94no—
703SD16—121no—
704SD16—182no—
705SD16—182no—
706SD16—182no—
707D8—62no—
708D8—121no—
709D8—182no—
710M16—62no—
711C2×C8—31no—
712C2×C8—31no—
713C2×C8—62no—
714C2×C8C2×D3211yescharacteristic
715C2×C8C2×D3211yescharacteristic
716C4⋊C4—31no—
717C4⋊C4—91no—
718C4⋊C4—91no—
719C4⋊C4—181no—
720C4⋊C4—181no—
721C22⋊C4—31no—
722C22⋊C4—31no—
723C22⋊C4—61no—
724C22⋊C4—61no—
725C22⋊C4—181no—
726C22⋊C4—181no—
727C22⋊C4—181no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C42—181no—
731C42C2×D3211yescharacteristic
732C22×C3—21no—
733C22×C3—32no—
734C22×C3—61no—
735C22×C3—61no—
736C22×C3—61no—
737C22×C3—61no—
738C22×C3—61no—
739C22×C3—121no—
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×C3C22×D1211yescharacteristic
749C22×C3C2×D3×D411yescharacteristic
750C2×D3—21no—
751C2×D3—21no—
752C2×D3—21no—
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—62no—
765C2×D3—62no—
766C2×D3—122no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—241no—
772C2×D3—241no—
773C2×D3—244no—
774C2×D3—244no—
775C2×D3—244no—
776C2×D3—244no—
777C2×D3#90812yescomplemented
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—21no—
783C3×C4—21no—
784C3×C4—41no—
785C3×C4—41no—
786C3×C4—61no—
787C3×C4—61no—
788C3×C4—121no—
789C3×C4C2×D3×D411yescharacteristic
790C3×C4C2×D3×D411yescharacteristic
791C3×C4#100411yescharacteristic
792C3×C4#100911yescharacteristic
793Dic3—21no—
794Dic3—21no—
795Dic3—41no—
796Dic3—62no—
797Dic3—62no—
798Dic3—122no—
799Dic3—121no—
800Dic3—121no—
801Dic3—121no—
802Dic3—121no—
803Dic3—241no—
804Dic3—241no—
805C32#326511yescharacteristic, complemented, Sylow
806C23—31no—
807C23—31no—
808C23—61no—
809C23—61no—
810C23—61no—
811C23—181no—
812C23—362no—
813C23—362no—
814C23—362no—
815C23—362no—
816C23—721no—
817C23—721no—
818Q8—61no—
819Q8—61no—
820Q8—92no—
821Q8—181no—
822Q8—362no—
823D4—62no—
824D4—61no—
825D4—61no—
826D4—61no—
827D4—61no—
828D4—61no—
829D4—61no—
830D4—92no—
831D4—122no—
832D4—181no—
833D4—241no—
834D4—362no—
835D4—362no—
836D4—362no—
837D4—362no—
838D4—362no—
839D4—362no—
840C2×C4—31no—
841C2×C4—31no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—181no—
848C2×C4—181no—
849C2×C4—181no—
850C2×C4—362no—
851C2×C4—362no—
852C2×C4—362no—
853C2×C4D3×D1211yescharacteristic
854C2×C4D3×D1211yescharacteristic
855C2×C4C22×D3211yescharacteristic
856C8—21no—
857C8—61no—
858C8—61no—
859C8#380212yescomplemented
860C2×C3—21no—
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—62no—
864C2×C3—121no—
865C2×C3—241no—
866C2×C3—241no—
867C2×C3—241no—
868C2×C3D4×D1211yescharacteristic
869C2×C3#571711yescharacteristic
870C2×C3C2×#90811yescharacteristic
871C2×C3#575111yescharacteristic
872C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
873C2×C3#577511yescharacteristic
874D3—22no—
875D3—41no—
876D3—81no—
877D3—81no—
878D3—81no—
879D3—122no—
880D3—122no—
881D3—242no—
882C22—32no—
883C22—61no—
884C22—61no—
885C22—61no—
886C22—61no—
887C22—61no—
888C22—121no—
889C22—121no—
890C22—121no—
891C22—121no—
892C22—121no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—182no—
898C22—361no—
899C22—361no—
900C22—724no—
901C22—724no—
902C22C2×D3×D1211yescharacteristic
903C4—21no—
904C4—21no—
905C4—61no—
906C4—61no—
907C4—121no—
908C4—182no—
909C4—361no—
910C4—361no—
911C4C2×#380211yescharacteristic
912C4#6430711yescharacteristic
913C3—21no—
914C3#7949411yescharacteristic, complemented
915C3#8185711yescharacteristic, complemented
916C2—62no—
917C2—121no—
918C2—241no—
919C2—241no—
920C2—241no—
921C2—362no—
922C2#1059400411yescharacteristic
923C2D3×#90811yescharacteristic
924C2#1059471311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
hypercenter#97D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
1. C2×#63795C2semidirect
2. C2×D3×#204C2semidirect
3. #10594004C2semidirect
4. #10593905C2semidirect
5. #10592409C2semidirect
6. C3×#4712C2semidirect
7. C3×#4706C2semidirect
8. #10590962C2semidirect
9. #10590944C2semidirect
10. #10590942C2semidirect
11. #10590833C2semidirect
12. #10590831C2semidirect
13. #10590822C2semidirect
14. #10590377C2semidirect
15. #10590356C2semidirect
21. C2×#3795C22semidirect
22. C2×D3×Dic6C22semidirect
25. C4×#634C22semidirect
26. C2×C3×D24C22semidirect
27. C2×C3×D24C22semidirect
28. C2×C3×#204C22semidirect
29. C2×C3×#204C22semidirect
30. C2×C3×ΓL(1,𝔽25)C22semidirect
31. C2×C3×D3×C8C22semidirect
32. C3×#875C22semidirect
41. #63908C22semidirect
45. #63856C22semidirect
47. C2×#3716C22semidirect
48. C2×#3716C22semidirect
52. C32×#97C22semidirect
54. #63645C22semidirect
55. #63643C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×C4⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
60. #63563C22semidirect
61. #63563C22semidirect
62. #63563C22semidirect
89. #4712D3semidirect
93. #4706D3semidirect
134. #3744D4semidirect
197. C2×D24C2×D3semidirect
198. C2×D24C2×D3semidirect
206. C2×#204C2×D3semidirect
207. C2×#204C2×D3semidirect
208. C2×ΓL(1,𝔽25)C2×D3semidirect
209. C2×D3×C8C2×D3semidirect
220. #875C2×D3semidirect
233. C3×#97C2×D3semidirect
234. C3×#97C2×D3semidirect
245. (C2×D3)⋊C8C2×D3semidirect
246. (C2×D3)⋊C8C2×D3semidirect
254. C4⋊(C3⋊C8)C2×D3semidirect
277. #634C2×D4semidirect
306. C32×C8C2×D4semidirect
480. C2×C3×D3AGL(1,ℤ/8)semidirect
537. #97D32semidirect
656. C3×C8D3×D4semidirect
657. C3×C8D3×D4semidirect
777. C2×D3#908semidirect
805. C32#3265semidirect
859. C8#3802semidirect
914. C3#79494semidirect
915. C3#81857semidirect

Maximal subgroups

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

subgroupindex
C2×#637952
C2×D3×#2042
#105940042
#105939052
#105924092
C3×#47122
C3×#47062
#105909622
#105909442
#105909422
#105908332
#105908312
#105908222
#105903772
#105903562
#818573
#794943