Finite Group Databasebeta

← #11888002

Subgroups — #11888002

Order 1152.

1158 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596112C211yesmaximal, characteristic, complemented
2#10596102C211yesmaximal, characteristic
3C32×#467C211yesmaximal, characteristic, complemented
4#10592886C211yesmaximal, characteristic, complemented
5#10592881C211yesmaximal, characteristic, complemented
6#10592812C211yesmaximal, characteristic, complemented
7C8×#638C211yesmaximal, characteristic, complemented
8#10592746C211yesmaximal, characteristic, complemented
9#10592744C211yesmaximal, characteristic, complemented
10#10592589C211yesmaximal, characteristic, complemented
11#10592587C211yesmaximal, characteristic, complemented
12#10592512C211yesmaximal, characteristic, complemented
13#10592503C211yesmaximal, characteristic, complemented
14#10592491C211yesmaximal, characteristic, complemented
15#10592487C211yesmaximal, characteristic, complemented
16#80776—34nomaximal
17C2×#3832C2211yescharacteristic
18C2×#3828C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic
23#64155C2211yescharacteristic
24Q8×C3⋊Dic3C2211yescharacteristic
25#64153C2211yescharacteristic
26C2×#3756C2211yescharacteristic
27C2×#3755C2211yescharacteristic
28C4×#638C2211yescharacteristic
29#64135C2211yescharacteristic
30C2×C8×C3⋊D3C2211yescharacteristic
31#64107—21no—
32#64106C2211yescharacteristic
33#64103—21no—
34#64102C2211yescharacteristic
35#64101C2211yescharacteristic
36C4⋊C4×C3⋊D3—21no—
37#64097C2211yescharacteristic
38#64096—21no—
39#64094—21no—
40#64093—21no—
41#64092—21no—
42#64088—21no—
43C32×#107C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#103C2211yescharacteristic
46#63662C2211yescharacteristic
47#63662C2211yescharacteristic
48#63657C2211yescharacteristic
49#63648C2211yescharacteristic
50#63648C2211yescharacteristic
51#63647C2211yescharacteristic
52#63643C2211yescharacteristic
53#63643C2211yescharacteristic
54#63641C2211yescharacteristic
55C8×C3⋊Dic3C2211yescharacteristic
56#63637C2211yescharacteristic
57#63636C2211yescharacteristic
58#63635C2211yescharacteristic
59#63634C2211yescharacteristic
60#5641—34no—
61#5631—34no—
62C3×#467D314yescomplemented
63#5187—34no—
64#5182—34no—
65#5113—34no—
66C8×#67—34no—
67#5047—34no—
68#5045—34no—
69#4890—34no—
70#4888—34no—
71#4813—34no—
72#4804—34no—
73#4792—34no—
74#4788—34no—
75C2×C32×Q8C2311yescharacteristic
76C2×C32×Q8C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C2×#638—21no—
79C2×#638D411yescharacteristic
80#3832—22no—
81#3832—41no—
82#3828—22no—
83#3828—41no—
84C2×C4⋊(C3⋊D3)—21no—
85C2×C4⋊(C3⋊D3)C2311yescharacteristic
86C2×C4×C3⋊D3—21no—
87C2×C4×C3⋊D3—21no—
88C2×C4×C3⋊D3—21no—
89C2×C4×C3⋊D3C2311yescharacteristic
90C2×#634—21no—
91C2×#634C2311yescharacteristic
92C32×Q16—41no—
93C2×C32×C8—41no—
94C2×C32×C8C2311yescharacteristic
95C2×C32×C8C2311yescharacteristic
96C32×C4⋊C4—21no—
97C32×C4⋊C4—21no—
98C32×C4⋊C4C2311yescharacteristic
99C32×C4⋊C4C2311yescharacteristic
100C32×C22⋊C4—21no—
101C32×C22⋊C4—21no—
102#3757—21no—
103#3757D411yescharacteristic
104#3756—41no—
105#3755—22no—
106#3752—21no—
107#3752—21no—
108#3752—21no—
109#3752—21no—
110#3752D411yescharacteristic
111C4⋊(C3⋊Dic3)—21no—
112C4⋊(C3⋊Dic3)—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116#3750—21no—
117#3750—21no—
118#3750—21no—
119#3750D411yescharacteristic
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C8×C3⋊D3—41no—
127#3302—91noSylow
128C2×#239—34no—
129C2×#235—34no—
130C2×C3×Q16C2×D314yes—
131C22×C3×C8C2×D314yes—
132C3×C22⋊Q8C2×D314yes—
133C3×C22⋊Q8C2×D314yes—
134#946—34no—
135Q8×Dic3—34no—
136#944—34no—
137C2×#216—34no—
138C2×#215—34no—
139C4×#67—34no—
140#926—34no—
141C2×D3×C8—34no—
142#898—64no—
143#897—34no—
144#894—64no—
145#893—34no—
146#892—34no—
147D3×C4⋊C4—64no—
148#888—34no—
149#887—64no—
150#885—64no—
151#884—64no—
152#883—64no—
153#879—64no—
154C3×#107C2×D314yes—
155C3×#103C2×D314yes—
156C3×#103C2×D314yes—
157#835—34no—
158#835—34no—
159#830—34no—
160#821—34no—
161#821—34no—
162(C2×D3)⋊C8—34no—
163#816—34no—
164#816—34no—
165Dic3⋊C8—34no—
166C8×Dic3—34no—
167#810—34no—
168#809—34no—
169#808—34no—
170#807—34no—
171C23×C32C2×D411yescharacteristic
172C22×C3⋊D3—21no—
173C22×C3⋊D3C2×D411yescharacteristic
174C32×Q8—21no—
175C32×Q8—21no—
176C32×Q8—21no—
177C32×Q8—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2411yescharacteristic
186#638—22no—
187#638—42no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3C2×D411yescharacteristic
192C2×C3⋊Dic3C2×D411yescharacteristic
193C2×C3⋊Dic3C2×D411yescharacteristic
194C4⋊(C3⋊D3)—21no—
195C4⋊(C3⋊D3)—42no—
196C4⋊(C3⋊D3)#4112yes—
197C4×C3⋊D3—21no—
198C4×C3⋊D3—21no—
199C4×C3⋊D3—42no—
200C4×C3⋊D3—42no—
201C4×C3⋊D3—42no—
202#634—21no—
203#634—21no—
204#634—42no—
205C32×C8—21no—
206C32×C8—21no—
207C3⋊(C3⋊C8)—21no—
208C3⋊(C3⋊C8)—21no—
209#556—91no—
210#547—91no—
211#487—91no—
212#485—91no—
213#485—91no—
214#474—91no—
215#467—91no—
216#467C3⋊D311yescharacteristic, complemented
217#462—91no—
218#452—91no—
219#452—91no—
220C4×SD16—91no—
221C8×D4—91no—
222#416—91no—
223#416—91no—
224C2×C3×Q8C22×D314yes—
225C2×C3×Q8C22×D314yes—
226C22×C3×C4C22×D314yes—
227C2×#67—34no—
228C2×#67—64no—
229#239—68no—
230#239—124no—
231#235—68no—
232#235—124no—
233C2×D12—34no—
234C2×D12—64no—
235C2×C4×D3—34no—
236C2×C4×D3—64no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×Dic6—34no—
240C2×Dic6—64no—
241C3×Q16—44no—
242C2×C3×C8—44no—
243C2×C3×C8C22×D314yes—
244C2×C3×C8C22×D314yes—
245C3×C4⋊C4—24no—
246C3×C4⋊C4—24no—
247C3×C4⋊C4C22×D314yes—
248C3×C4⋊C4C22×D314yes—
249C3×C22⋊C4—24no—
250C3×C22⋊C4—24no—
251#217—34no—
252#217—64no—
253#216—124no—
254#215—68no—
255(C2×D3)⋊C4—34no—
256(C2×D3)⋊C4—64no—
257(C2×D3)⋊C4—64no—
258(C2×D3)⋊C4—64no—
259(C2×D3)⋊C4—64no—
260C4⋊Dic3—34no—
261C4⋊Dic3—34no—
262C4⋊Dic3—64no—
263C4⋊Dic3—64no—
264Dic3⋊C4—34no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267Dic3⋊C4—64no—
268Dic3⋊C4—64no—
269C4×Dic3—34no—
270C4×Dic3—64no—
271C4×Dic3—64no—
272C4×Dic3—64no—
273C2×C3⋊C8—34no—
274C2×C3⋊C8—34no—
275D3×C8—124no—
276C22×C32—21no—
277C22×C32—21no—
278C22×C32—21no—
279C22×C32C22×D411yescharacteristic
280C2×C3⋊D3—21no—
281C2×C3⋊D3—22no—
282C2×C3⋊D3—21no—
283C2×C3⋊D3—21no—
284C2×C3⋊D3—41no—
285C2×C3⋊D3—41no—
286C32×C4—21no—
287C32×C4—41no—
288C32×C4—41no—
289C32×C4—41no—
290C32×C4—41no—
291C32×C4C2×#4111yescharacteristic
292C32×C4H(5,𝔽2)11yescharacteristic
293C3⋊Dic3—21no—
294C3⋊Dic3—21no—
295C3⋊Dic3—41no—
296C3⋊Dic3—41no—
297C3⋊Dic3—41no—
298C3⋊Dic3#13512yes—
299C2×#41—91no—
300C2×#41—91no—
301C2×Q16—91no—
302C2×Q16C2×C3⋊D311yescharacteristic
303C2×SD16—91no—
304C22×C8—91no—
305C22×C8C2×C3⋊D311yescharacteristic
306C4⋊Q8—91no—
307C4⋊Q8—91no—
308#126—181no—
309#126—181no—
310#124—181no—
311#123—181no—
312#123—181no—
313C22⋊Q8—91no—
314C22⋊Q8—91no—
315C22⋊Q8C2×C3⋊D311yescharacteristic
316C22⋊Q8C2×C3⋊D311yescharacteristic
317#121—181no—
318C4×Q8—91no—
319C4×Q8—181no—
320C4×D4—91no—
321C4×D4—91no—
322#117—91no—
323#117—91no—
324C2×C4⋊C4—181no—
325#107—91no—
326#107C2×C3⋊D311yescharacteristic
327#106—91no—
328C4⋊C8—91no—
329#103—91no—
330#103—91no—
331#103—91no—
332#103—91no—
333#103—91no—
334#103C2×C3⋊D311yescharacteristic
335#103C2×C3⋊D311yescharacteristic
336#102—91no—
337#102—91no—
338#102—91no—
339C22⋊C8—91no—
340C22⋊C8—91no—
341C4×C8—91no—
342C23×C3D3×D414yes—
343C22×D3—34no—
344C22×D3—64no—
345C3×Q8—24no—
346C3×Q8—24no—
347C3×Q8—24no—
348C3×Q8—24no—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4—24no—
352C2×C3×C4—24no—
353C2×C3×C4—24no—
354C2×C3×C4—24no—
355C2×C3×C4D3×D414yes—
356C2×C3×C4C23×D314yes—
357#67—68no—
358#67—128no—
359C2×Dic3—34no—
360C2×Dic3—34no—
361C2×Dic3—34no—
362C2×Dic3—64no—
363C2×Dic3—64no—
364C2×Dic3—64no—
365D12—38no—
366D12—64no—
367D12—128no—
368C4×D3—64no—
369C4×D3—64no—
370C4×D3—128no—
371C4×D3—128no—
372C4×D3—128no—
373Dic6—64no—
374Dic6—64no—
375Dic6—128no—
376C3×C8—24no—
377C3×C8—24no—
378C3⋊C8—64no—
379C3⋊C8—64no—
380C2×C32—41no—
381C2×C32#54611yescharacteristic
382C2×C32C2×#13511yescharacteristic
383C2×C32#57811yescharacteristic
384C3⋊D3—41no—
385C3⋊D3—42no—
386#41—182no—
387#41—182no—
388#41—361no—
389#41—361no—
390C2×Q8—91no—
391C2×Q8—181no—
392C2×Q8C22×C3⋊D311yescharacteristic
393C2×Q8C22×C3⋊D311yescharacteristic
394C2×D4—91no—
395C2×D4—91no—
396C2×D4—181no—
397C2×D4—181no—
398C22×C4—91no—
399C22×C4—181no—
400C22×C4—181no—
401C22×C4—181no—
402C22×C4C22×C3⋊D311yescharacteristic
403Q16—41no—
404Q16—361no—
405SD16—182no—
406C2×C8—41no—
407C2×C8—91no—
408C2×C8—91no—
409C2×C8—361no—
410C2×C8C22×C3⋊D311yescharacteristic
411C2×C8C22×C3⋊D311yescharacteristic
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—91no—
415C4⋊C4—91no—
416C4⋊C4—91no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C4⋊C4—181no—
423C4⋊C4C22×C3⋊D311yescharacteristic
424C4⋊C4C22×C3⋊D311yescharacteristic
425C22⋊C4—21no—
426C22⋊C4—21no—
427C22⋊C4—91no—
428C22⋊C4—91no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C22⋊C4—181no—
434C42—91no—
435C42—181no—
436C42—181no—
437C42—181no—
438C22×C3—24no—
439C22×C3—24no—
440C22×C3—24no—
441C22×C3C2×D3×D414yes—
442C2×D3—64no—
443C2×D3—64no—
444C2×D3—64no—
445C2×D3—68no—
446C2×D3—124no—
447C2×D3—124no—
448C3×C4—24no—
449C3×C4—44no—
450C3×C4—44no—
451C3×C4—44no—
452C3×C4—44no—
453C3×C4#100414yes—
454C3×C4D3×#4114yes—
455Dic3—38no—
456Dic3—64no—
457Dic3—64no—
458Dic3—124no—
459Dic3—124no—
460Dic3—124no—
461C32#330211yescharacteristic, complemented, Sylow
462C23—91no—
463C23—181no—
464C23D4×C3⋊D311yescharacteristic
465Q8—21no—
466Q8—21no—
467Q8—21no—
468Q8—21no—
469Q8—181no—
470Q8—181no—
471Q8—362no—
472D4—92no—
473D4—182no—
474D4—181no—
475D4—362no—
476D4—362no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—91no—
484C2×C4—91no—
485C2×C4—91no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—181no—
491C2×C4—362no—
492C2×C4—362no—
493C2×C4—362no—
494C2×C4D4×C3⋊D311yescharacteristic
495C2×C4C23×C3⋊D311yescharacteristic
496C8—21no—
497C8—21no—
498C8—181no—
499C8—181no—
500C2×C3—44no—
501C2×C3#561014yes—
502C2×C3#576614yes—
503C2×C3D3×#13514yes—
504D3—124no—
505D3—128no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—181no—
510C22—181no—
511C22—181no—
512C22—182no—
513C22—361no—
514C22—361no—
515C22C2×D4×C3⋊D311yescharacteristic
516C4—21no—
517C4—41no—
518C4—41no—
519C4—41no—
520C4—41no—
521C4—92no—
522C4—181no—
523C4—181no—
524C4—361no—
525C4—361no—
526C4—361no—
527C4#6436111yescharacteristic
528C4#41×C3⋊D311yescharacteristic
529C3#8077614yescomplemented
530C2—41no—
531C2—361no—
532C2—362no—
533C2#1059608111yescharacteristic
534C2#1059623711yescharacteristic
535C2C3⋊D3×#13511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#467C2
socleC22×C32C22×D4
prime radical#10596102C2
hypercenter#467C3⋊D3
hypocenterC32#3302
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #10596112C2semidirect
3. C32×#467C2semidirect
4. #10592886C2semidirect
5. #10592881C2semidirect
6. #10592812C2semidirect
7. C8×#638C2semidirect
8. #10592746C2semidirect
9. #10592744C2semidirect
10. #10592589C2semidirect
11. #10592587C2semidirect
12. #10592512C2semidirect
13. #10592503C2semidirect
14. #10592491C2semidirect
15. #10592487C2semidirect
62. C3×#467D3semidirect
216. #467C3⋊D3semidirect
461. C32#3302semidirect
529. C3#80776semidirect

Maximal subgroups

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

subgroupindex
#105961122
#105961022
C32×#4672
#105928862
#105928812
#105928122
C8×#6382
#105927462
#105927442
#105925892
#105925872
#105925122
#105925032
#105924912
#105924872
#807763