Finite Group Databasebeta

← #11884038

Subgroups — #11884038

Order 1152.

1154 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63794C211yesmaximal, characteristic, complemented
2C2×D3×#204C211yesmaximal, characteristic, complemented
3#10594004C211yesmaximal, characteristic, complemented
4#10593899C211yesmaximal, characteristic, complemented
5#10592543C211yesmaximal, characteristic, complemented
6C3×#4848C211yesmaximal, characteristic, complemented
7C3×#4836C211yesmaximal, characteristic, complemented
8#10590947C211yesmaximal, characteristic, complemented
9#10590946C211yesmaximal, characteristic, complemented
10#10590828C211yesmaximal, characteristic, complemented
11#10590826C211yesmaximal, characteristic, complemented
12#10590823C211yesmaximal, characteristic, complemented
13#10590822C211yesmaximal, characteristic, complemented
14#10590371C211yesmaximal, characteristic, complemented
15#10590362C211yesmaximal, characteristic, complemented
16#80404—31nomaximal
17#79494—31nomaximal
18C2×#3802—21no—
19C2×D3×D12C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×#3799C2211yescharacteristic, complemented
22C2×D3×Dic6C2211yescharacteristic, complemented
23C2×#3745C2211yescharacteristic
24C2×#3744C2211yescharacteristic
25#64084C2211yescharacteristic, complemented
26C4×C4⋊(C3⋊D3)C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic, complemented
28C2×C3×#204C2211yescharacteristic, complemented
29C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
30C2×C3×D3×C8C2211yescharacteristic, complemented
31C3×#874C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic, complemented
34#63922—21no—
35#63922—21no—
36#63916—21no—
37#63909C2211yescharacteristic, complemented
38#63908C2211yescharacteristic
39#63908C2211yescharacteristic
40#63895—21no—
41#63886—21no—
42#63880—21no—
43#63857C2211yescharacteristic, complemented
44#63852—21no—
45C2×#3717C2211yescharacteristic
46C2×#3716C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50#63794—24no—
51D3×#204—24no—
52C32×C4⋊C8C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63643C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#803C2211yescharacteristic, complemented
60#63575C2211yescharacteristic, complemented
61#63566C2211yescharacteristic, complemented
62#63564C2211yescharacteristic
63C2×#914—31no—
64C2×D3×SD16—31no—
65C2×#908—31no—
66C22×#204—31no—
67#5717—31no—
68#5576—31no—
69#5552—31no—
70D4×D12—31no—
71C3×#460—31no—
72C3×#435—31no—
73#5172—31no—
74#5170—31no—
75#5134—31no—
76#5115—31no—
77#5074—31no—
78#5026—31no—
79#4848D311yescharacteristic, complemented
80#4844—31no—
81#4844—31no—
82#4844—61no—
83#4836D311yescharacteristic, complemented
84#4780—31no—
85#4776—31no—
86#4775—31no—
87#4773—31no—
88#4738—31no—
89#4734—31no—
90#4732—31no—
91#4731—31no—
92#4712—31no—
93#4710—31no—
94C22×D32—21no—
95C22×D32—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×#634C2311yescharacteristic
100C2×C3×D12—21no—
101C2×C3×D12—21no—
102C2×C3×D12D411yescharacteristic
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×#626—21no—
112C2×#626—21no—
113C2×#625—21no—
114C2×#625—21no—
115C2×#624—21no—
116C2×D3×Dic3—21no—
117#3802—44no—
118D3×D12—22no—
119D3×D12—22no—
120D3×D12—41no—
121D3×D12—41no—
122#3799—22no—
123#3799—41no—
124D3×Dic6—22no—
125D3×Dic6—41no—
126C2×C32×C8C2311yescharacteristic
127C2×C32×C8C2311yescharacteristic
128C32×C42C2311yescharacteristic
129#3752—21no—
130#3752—21no—
131#3752—21no—
132C4⋊(C3⋊Dic3)C2311yescharacteristic
133#3745—22no—
134#3744—22no—
135C3×(C2×D3)⋊C4D411yescharacteristic
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×C4⋊Dic3D411yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic3⋊C4—21no—
140C3×C4×Dic3—21no—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×#204—22no—
144C3×#204—22no—
145C3×ΓL(1,𝔽25)—22no—
146C3×D3×C8—22no—
147Dic3⋊Dic3—21no—
148#3722—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152#3717D414yescomplemented
153#3716—22no—
154#3716—41no—
155#3714—22no—
156#3714—41no—
157#3265—91noSylow
158C2×#239—31no—
159C2×D3×Q8—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×M16—31no—
171C22×C3×C8—31no—
172C3×#127—31no—
173C3×C4×Q8—31no—
174C3×C4×D4—31no—
175C2×#215—31no—
176#939—61no—
177#938—31no—
178#938—31no—
179#938—61no—
180#937—61no—
181#937—61no—
182C2×#214—31no—
183C2×#214—31no—
184C2×#213—31no—
185C2×#213—31no—
186#930—31no—
187#930—31no—
188#930—31no—
189#924—31no—
190#914—64no—
191D3×SD16—64no—
192#908—64no—
193C2×D24—31no—
194C2×D24—31no—
195C2×D24—31no—
196C2×D24—31no—
197C2×D24—61no—
198C2×#204—31no—
199C2×#204—31no—
200C2×#204—31no—
201C2×#204—31no—
202C2×#204—31no—
203C2×#204—61no—
204C2×#204—64no—
205C2×#204C2×D311yescharacteristic, complemented
206C2×#204C2×D311yescharacteristic, complemented
207C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
208C2×D3×C8C2×D311yescharacteristic, complemented
209#897—31no—
210#897—61no—
211#896—61no—
212#895—31no—
213#895—61no—
214#895—61no—
215#885—61no—
216#882—61no—
217#882—61no—
218#67⋊C4—61no—
219#875—31no—
220#875—31no—
221#875—61no—
222#875—61no—
223#874C2×D311yescharacteristic
224C4×D12—31no—
225C4×D12—31no—
226C4×D12—61no—
227C4×D12—61no—
228C4×D12C2×D311yescharacteristic
229C4×Dic6C2×D311yescharacteristic, complemented
230C3×C4⋊C8—21no—
231C3×C4⋊C8C2×D311yescharacteristic, complemented
232C3×C4⋊C8C2×D311yescharacteristic, complemented
233C3×#102—31no—
234C3×#102—31no—
235C3×C22⋊C8—31no—
236C3×C22⋊C8—31no—
237C3×#97—31no—
238#835—31no—
239#821—31no—
240#821—31no—
241#821—31no—
242#821—61no—
243#821C2×D311yescharacteristic, complemented
244#821C2×D311yescharacteristic, complemented
245(C2×D3)⋊C8C2×D311yescharacteristic, complemented
246(C2×D3)⋊C8C2×D311yescharacteristic, complemented
247#818—31no—
248#816—31no—
249#816—31no—
250#816—31no—
251#816—61no—
252#809—31no—
253#807—31no—
254#803C2×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—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)C2×D412yes—
276C4×C3⋊D3—42no—
277#634—21no—
278#634—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×D12—22no—
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×Dic6C2×D412yescomplemented
296#627—42no—
297#626—42no—
298#626—42no—
299#626—42no—
300#626—42no—
301#625—42no—
302#625—42no—
303#624—42no—
304D3×Dic3—42no—
305C32×C8—21no—
306C32×C8—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8C2×D412yescomplemented
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—91no—
311#548—91no—
312D42—91no—
313#496—91no—
314#468—91no—
315#466—91no—
316#463—91no—
317#460—31no—
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—61no—
333C2×C3×D4—61no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C22×Dic3—61no—
345#239—62no—
346#239—121no—
347D3×Q8—62no—
348D3×Q8—121no—
349D3×D4—62no—
350D3×D4—62no—
351D3×D4—121no—
352D3×D4—121no—
353D3×D4—124no—
354D3×D4—124no—
355#235—62no—
356#235—121no—
357C2×D12—21no—
358C2×D12—21no—
359C2×D12—31no—
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—31no—
363C2×D12—61no—
364C2×D12—61no—
365C2×D12—62no—
366C2×D12—62no—
367C2×D12—61no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12—121no—
372C2×D12—121no—
373C2×D12D1211yescharacteristic
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—61no—
381C2×C4×D3—121no—
382C2×C4×D3C22×D311yescharacteristic
383C2×C4×D3C22×D311yescharacteristic
384C2×Dic6—31no—
385C2×Dic6—31no—
386C2×Dic6—61no—
387C2×Dic6—62no—
388C2×Dic6—61no—
389C2×Dic6—61no—
390C2×Dic6—121no—
391C2×Dic6C22×D311yescharacteristic
392C3×SD16—62no—
393C3×SD16—62no—
394C3×M16—62no—
395C2×C3×C8—21no—
396C2×C3×C8—21no—
397C2×C3×C8—31no—
398C2×C3×C8—31no—
399C2×C3×C8—62no—
400C2×C3×C8C22×D311yescharacteristic
401C2×C3×C8C22×D311yescharacteristic
402C2×C3×C8C22×D311yescharacteristic
403C2×C3×C8C22×D311yescharacteristic
404C3×C4⋊C4—31no—
405C3×C4⋊C4—31no—
406C3×C4⋊C4—61no—
407C3×C22⋊C4—31no—
408C3×C22⋊C4—31no—
409C3×C42—21no—
410C3×C42—61no—
411C3×C42C22×D311yescharacteristic
412C3×C42C22×D311yescharacteristic
413#217—61no—
414#217—61no—
415#217—61no—
416#215—34no—
417#214—62no—
418#214—121no—
419#213—62no—
420#213—121no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
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—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—121no—
433(C2×D3)⋊C4—121no—
434(C2×D3)⋊C4—121no—
435(C2×D3)⋊C4D1211yescharacteristic
436(C2×D3)⋊C4D1211yescharacteristic
437C4⋊Dic3—31no—
438C4⋊Dic3—31no—
439C4⋊Dic3—61no—
440C4⋊Dic3—61no—
441C4⋊Dic3D1211yescharacteristic
442C4⋊Dic3C22×D311yescharacteristic
443Dic3⋊C4—21no—
444Dic3⋊C4—61no—
445C4×Dic3—21no—
446C2×C3⋊C8C22×D311yescharacteristic
447C2×C3⋊C8C22×D311yescharacteristic
448D24—62no—
449D24—62no—
450D24—62no—
451D24—122no—
452D24—121no—
453#204—22no—
454#204—22no—
455#204—34no—
456#204—62no—
457#204—62no—
458#204—62no—
459#204—122no—
460#204—121no—
461ΓL(1,𝔽25)—22no—
462D3×C8—22no—
463C22×C32C22×D411yescharacteristic
464C2×C3⋊D3—22no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—21no—
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3AGL(1,ℤ/8)12yescomplemented
482D32—84no—
483D32—84no—
484C32×C4—21no—
485C32×C4—21no—
486C32×C4C22×D411yescharacteristic
487C32×C4H(5,𝔽2)11yescharacteristic
488C3⋊Dic3—41no—
489C3⋊Dic3—41no—
490C3×Dic3—22no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—41no—
494C2×#41—91no—
495C22×Q8—91no—
496C22×D4—91no—
497C22×D4—91no—
498C22×D4—181no—
499AGL(1,ℤ/8)—184no—
500C2×SD16—31no—
501C2×SD16—31no—
502C2×SD16—91no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—184no—
507C2×D8—91no—
508C2×D8—91no—
509C2×D8—91no—
510C2×M16—31no—
511C22×C8—31no—
512#127—31no—
513#124—91no—
514#124—181no—
515C22⋊Q8—91no—
516C22⋊Q8—181no—
517#121—91no—
518#121—91no—
519#121—91no—
520#121—181no—
521#121—181no—
522#120—181no—
523#120—181no—
524C4×Q8—31no—
525C4×D4—31no—
526C4×D4—91no—
527C4×D4—181no—
528#107—91no—
529C4⋊C8D3211yescharacteristic, complemented
530#103—91no—
531#103—91no—
532#102—31no—
533#102—31no—
534#102—91no—
535#102—91no—
536C22⋊C8—31no—
537C22⋊C8—31no—
538#97—31no—
539C23×C3—31no—
540C23×C3—31no—
541C23×C3—61no—
542C23×C3—61no—
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—121no—
550C22×D3—121no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3—122no—
554C22×D3—122no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—241no—
560C22×D3—241no—
561C22×D3—241no—
562C22×D3—241no—
563C22×D3C2×D1211yescharacteristic
564C22×D3C2×D1211yescharacteristic
565C3×Q8—32no—
566C3×Q8—61no—
567C3×D4—62no—
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×C4—61no—
585C2×C3×C4C2×D1211yescharacteristic
586C2×C3×C4C2×D1211yescharacteristic
587C2×C3×C4D3×D411yescharacteristic
588C2×C3×C4D3×D411yescharacteristic
589C2×C3×C4C23×D311yescharacteristic
590C2×C3×C4C23×D311yescharacteristic
591#67—122no—
592#67—122no—
593#67—122no—
594#67—122no—
595#67—122no—
596#67—122no—
597#67—122no—
598#67—122no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—121no—
606C2×Dic3—121no—
607C2×Dic3—122no—
608C2×Dic3C2×D1211yescharacteristic
609C2×Dic3C2×D1211yescharacteristic
610D12—22no—
611D12—21no—
612D12—21no—
613D12—21no—
614D12—21no—
615D12—32no—
616D12—32no—
617D12—42no—
618D12—62no—
619D12—61no—
620D12—61no—
621D12—61no—
622D12—61no—
623D12—61no—
624D12—61no—
625D12—81no—
626D12—121no—
627D12—121no—
628D12—121no—
629D12—122no—
630D12—122no—
631D12—122no—
632D12—122no—
633C4×D3—21no—
634C4×D3—21no—
635C4×D3—21no—
636C4×D3—21no—
637C4×D3—122no—
638C4×D3—122no—
639C4×D3—122no—
640C4×D3—122no—
641C4×D3—122no—
642C4×D3—242no—
643Dic6—21no—
644Dic6—61no—
645Dic6—61no—
646Dic6—61no—
647Dic6—61no—
648Dic6—121no—
649Dic6—121no—
650Dic6—122no—
651Dic6—122no—
652Dic6D3×D412yescomplemented
653C3×C8—21no—
654C3×C8—21no—
655C3×C8—21no—
656C3×C8—21no—
657C3×C8—32no—
658C3×C8—41no—
659C3×C8—41no—
660C3×C8—61no—
661C3⋊C8—21no—
662C3⋊C8D3×D412yescomplemented
663C2×C32D4211yescharacteristic
664C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
665C2×C32#57711yescharacteristic
666C3⋊D3—42no—
667C3⋊D3—81no—
668C3×D3—22no—
669C3×D3—41no—
670C3×D3—81no—
671C3×D3—81no—
672C24—181no—
673C24—181no—
674#41—182no—
675#41—361no—
676C2×Q8—31no—
677C2×Q8—91no—
678C2×Q8—181no—
679C2×Q8—182no—
680C2×Q8—361no—
681C2×D4—31no—
682C2×D4—31no—
683C2×D4—31no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—91no—
687C2×D4—91no—
688C2×D4—181no—
689C2×D4—181no—
690C2×D4—182no—
691C2×D4—182no—
692C2×D4—181no—
693C2×D4—181no—
694C2×D4—181no—
695C2×D4—181no—
696C2×D4—361no—
697C2×D4—361no—
698C2×D4—364no—
699C22×C4—31no—
700C22×C4—31no—
701C22×C4—181no—
702C22×C4—181no—
703C22×C4—181no—
704SD16—62no—
705SD16—62no—
706SD16—94no—
707SD16—182no—
708SD16—182no—
709SD16—361no—
710D8—182no—
711D8—182no—
712D8—361no—
713M16—62no—
714C2×C8—31no—
715C2×C8—31no—
716C2×C8—62no—
717C2×C8C2×D3211yescharacteristic
718C2×C8C2×D3211yescharacteristic
719C4⋊C4—31no—
720C4⋊C4—31no—
721C4⋊C4—61no—
722C4⋊C4—91no—
723C4⋊C4—181no—
724C22⋊C4—31no—
725C22⋊C4—31no—
726C22⋊C4—181no—
727C22⋊C4—181no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C22⋊C4—181no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C42—61no—
734C42C2×D3211yescharacteristic
735C22×C3—21no—
736C22×C3—32no—
737C22×C3—61no—
738C22×C3—61no—
739C22×C3—61no—
740C22×C3—61no—
741C22×C3—61no—
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—62no—
762C2×D3—62no—
763C2×D3—122no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—241no—
775C2×D3—241no—
776C2×D3—241no—
777C2×D3—241no—
778C2×D3—241no—
779C2×D3—244no—
780C2×D3—244no—
781C2×D3—244no—
782C2×D3—244no—
783C2×D3#90812yescomplemented
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—21no—
787C3×C4—21no—
788C3×C4—21no—
789C3×C4—21no—
790C3×C4—41no—
791C3×C4—41no—
792C3×C4—62no—
793C3×C4—61no—
794C3×C4—61no—
795C3×C4—121no—
796C3×C4C2×D3×D411yescharacteristic
797C3×C4C2×D3×D411yescharacteristic
798C3×C4#100911yescharacteristic
799C3×C4#100911yescharacteristic
800Dic3—21no—
801Dic3—21no—
802Dic3—22no—
803Dic3—41no—
804Dic3—121no—
805Dic3—121no—
806Dic3—121no—
807Dic3—121no—
808Dic3—241no—
809Dic3—241no—
810C32#326511yescharacteristic, complemented, Sylow
811C23—31no—
812C23—31no—
813C23—61no—
814C23—61no—
815C23—181no—
816C23—181no—
817C23—362no—
818C23—362no—
819C23—362no—
820C23—362no—
821C23—721no—
822C23—721no—
823Q8—32no—
824Q8—61no—
825Q8—181no—
826Q8—181no—
827Q8—362no—
828D4—62no—
829D4—61no—
830D4—61no—
831D4—61no—
832D4—61no—
833D4—92no—
834D4—122no—
835D4—181no—
836D4—181no—
837D4—181no—
838D4—241no—
839D4—362no—
840D4—362no—
841D4—362no—
842D4—362no—
843D4—362no—
844D4—362no—
845C2×C4—31no—
846C2×C4—31no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—181no—
854C2×C4—181no—
855C2×C4—362no—
856C2×C4—362no—
857C2×C4—362no—
858C2×C4D3×D1211yescharacteristic
859C2×C4D3×D1211yescharacteristic
860C2×C4C22×D3211yescharacteristic
861C8—21no—
862C8—21no—
863C8—32no—
864C8—61no—
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—62no—
869C2×C3—121no—
870C2×C3—241no—
871C2×C3—241no—
872C2×C3D4×D1211yescharacteristic
873C2×C3#560911yescharacteristic
874C2×C3C2×#90811yescharacteristic
875C2×C3#575111yescharacteristic
876C2×C3#576211yescharacteristic
877C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
878D3—22no—
879D3—41no—
880D3—81no—
881D3—81no—
882D3—122no—
883D3—122no—
884D3—242no—
885D3—241no—
886D3—241no—
887D3—481no—
888C22—32no—
889C22—61no—
890C22—61no—
891C22—61no—
892C22—61no—
893C22—61no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—182no—
901C22—361no—
902C22—361no—
903C22—361no—
904C22—361no—
905C22—361no—
906C22—724no—
907C22—724no—
908C22C2×D3×D1211yescharacteristic
909C4—21no—
910C4—21no—
911C4—61no—
912C4—61no—
913C4—62no—
914C4—121no—
915C4—361no—
916C4—361no—
917C4D32×D411yescharacteristic
918C4#6432011yescharacteristic
919C3—21no—
920C3#7949411yescharacteristic, complemented
921C3#8040411yescharacteristic, complemented
922C2—62no—
923C2—121no—
924C2—241no—
925C2—241no—
926C2—362no—
927C2—721no—
928C2#1059462111yescharacteristic
929C2#1059467711yescharacteristic
930C2D3×#90811yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#63794C2semidirect
2. C2×D3×#204C2semidirect
3. #10594004C2semidirect
4. #10593899C2semidirect
5. #10592543C2semidirect
6. C3×#4848C2semidirect
7. C3×#4836C2semidirect
8. #10590947C2semidirect
9. #10590946C2semidirect
10. #10590828C2semidirect
11. #10590826C2semidirect
12. #10590823C2semidirect
13. #10590822C2semidirect
14. #10590371C2semidirect
15. #10590362C2semidirect
21. C2×#3799C22semidirect
22. C2×D3×Dic6C22semidirect
25. #64084C22semidirect
27. C2×C3×#204C22semidirect
28. C2×C3×#204C22semidirect
29. C2×C3×ΓL(1,𝔽25)C22semidirect
30. C2×C3×D3×C8C22semidirect
33. C3×C4×Dic6C22semidirect
37. #63909C22semidirect
43. #63857C22semidirect
46. C2×#3716C22semidirect
47. C2×#3716C22semidirect
48. C2×#3714C22semidirect
49. C2×#3714C22semidirect
52. C32×C4⋊C8C22semidirect
53. #63648C22semidirect
54. #63643C22semidirect
55. C3×#821C22semidirect
56. C3×#821C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#803C22semidirect
60. #63575C22semidirect
61. #63566C22semidirect
79. #4848D3semidirect
83. #4836D3semidirect
152. #3717D4semidirect
205. C2×#204C2×D3semidirect
206. C2×#204C2×D3semidirect
207. C2×ΓL(1,𝔽25)C2×D3semidirect
208. C2×D3×C8C2×D3semidirect
229. C4×Dic6C2×D3semidirect
231. C3×C4⋊C8C2×D3semidirect
232. C3×C4⋊C8C2×D3semidirect
243. #821C2×D3semidirect
244. #821C2×D3semidirect
245. (C2×D3)⋊C8C2×D3semidirect
246. (C2×D3)⋊C8C2×D3semidirect
254. #803C2×D3semidirect
295. C3×Dic6C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
481. C2×C3×D3AGL(1,ℤ/8)semidirect
529. C4⋊C8D32semidirect
652. Dic6D3×D4semidirect
662. C3⋊C8D3×D4semidirect
783. C2×D3#908semidirect
810. C32#3265semidirect
920. C3#79494semidirect
921. C3#80404semidirect

Maximal subgroups

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

subgroupindex
C2×#637942
C2×D3×#2042
#105940042
#105938992
#105925432
C3×#48482
C3×#48362
#105909472
#105909462
#105908282
#105908262
#105908232
#105908222
#105903712
#105903622
#804043
#794943