Finite Group Databasebeta

← #11887087

Subgroups — #11887087

Order 1152.

1386 conjugacy classes of subgroups.

The subgroup lattice has 411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596201C211yesmaximal, characteristic, complemented
2D4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
3C32×#476C211yesmaximal, characteristic, complemented
4#10592787C211yesmaximal, characteristic, complemented
5C4×#3754C211yesmaximal, characteristic, complemented
6#10592563C212yesmaximal, complemented
7#10592562C212yesmaximal, complemented
8#10592547C211yesmaximal, characteristic, complemented
9#10592533C211yesmaximal, characteristic, complemented
10#10592475C212yesmaximal, complemented
11C3⋊D3×#102C212yesmaximal, complemented
12#81075—34nomaximal
13C2×D4×C3⋊D3C2212yes—
14C22×C4⋊(C3⋊D3)—21no—
15C32×C4⋊Q8C2211yescharacteristic, complemented
16C32×C4×D4C2211yescharacteristic
17#64155—22no—
18C2×#3754C2211yescharacteristic
19#64139—21no—
20C2×#3744C2212yescomplemented
21C2×C8×C3⋊D3C2212yescomplemented
22#64106C2212yescomplemented
23#64104C2212yes—
24#64102—21no—
25C4⋊C4×C3⋊D3C2212yescomplemented
26#64099—21no—
27#64091—22no—
28#64083C2211yescharacteristic
29C4×C4⋊(C3⋊D3)C2211yescharacteristic
30C4×#634C2211yescharacteristic, complemented
31C32×#106C2212yescomplemented
32C32×C4⋊C8C2211yescharacteristic, complemented
33C32×#102C2212yes—
34#63659C2211yescharacteristic
35#63648C2212yescomplemented
36#63647C2212yescomplemented
37#63637C2211yescharacteristic, complemented
38#63636C2212yescomplemented
39#63636C2212yescomplemented
40#63635C2211yescharacteristic, complemented
41C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
42#5730—34no—
43D4×D12—34no—
44C3×#476D314yescomplemented
45#5088—34no—
46C4×#214—34no—
47#4864—38no—
48#4863—38no—
49#4848—34no—
50#4834—34no—
51#4776—38no—
52D3×#102—38no—
53C23×C3⋊D3—22no—
54C2×C32×Q8—21no—
55C2×C32×D4C2311yescharacteristic
56C22×C32×C4—21no—
57C2×#638—22no—
58D4×C3⋊D3—24no—
59D4×C3⋊D3—42no—
60C2×C4⋊(C3⋊D3)—22no—
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)—21no—
63C2×C4⋊(C3⋊D3)—44no—
64C2×C4⋊(C3⋊D3)D411yescharacteristic
65C2×C4⋊(C3⋊D3)C2312yes—
66C2×C4×C3⋊D3—22no—
67C2×C4×C3⋊D3C2312yes—
68C2×#634C2311yescharacteristic
69C2×C32×C8C2312yes—
70C32×C4⋊C4—21no—
71C32×C4⋊C4C2312yes—
72C32×C4⋊C4C2311yescharacteristic
73C32×C22⋊C4—21no—
74C32×C42C2311yescharacteristic
75#3754—22no—
76#3752—22no—
77#3752—22no—
78#3752D412yes—
79C4⋊(C3⋊Dic3)—22no—
80C4⋊(C3⋊Dic3)D411yescharacteristic
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82#3750—21no—
83#3750—22no—
84C4×C3⋊Dic3—21no—
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87#3744—42no—
88C8×C3⋊D3—42no—
89#3295—91noSylow
90C2×D3×D4—38no—
91C22×D12—64no—
92C3×C4⋊Q8C2×D314yescomplemented
93C3×C4×D4C2×D314yes—
94#946—68no—
95C2×#214—34no—
96#930—64no—
97C2×#204—38no—
98C2×D3×C8—38no—
99#897—38no—
100#895—38no—
101#893—64no—
102D3×C4⋊C4—38no—
103#890—64no—
104#882—68no—
105#874—34no—
106C4×D12—34no—
107C4×Dic6—34no—
108C3×#106C2×D318yescomplemented
109C3×C4⋊C8C2×D314yescomplemented
110C3×#102C2×D318yes—
111#832—34no—
112#821—38no—
113(C2×D3)⋊C8—38no—
114#810—34no—
115#809—38no—
116#809—38no—
117#808—34no—
118C4×C3⋊C8—34no—
119C23×C32—21no—
120C22×C3⋊D3—22no—
121C22×C3⋊D3—44no—
122C22×C3⋊D3—44no—
123C22×C3⋊D3—82no—
124C22×C3⋊D3C2×D412yes—
125C32×Q8—81no—
126C32×D4—21no—
127C32×D4#4112yes—
128C2×C32×C4—22no—
129C2×C32×C4—21no—
130C2×C32×C4—42no—
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2411yescharacteristic
134#638—44no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3C2×D412yes—
138C4⋊(C3⋊D3)—22no—
139C4⋊(C3⋊D3)—22no—
140C4⋊(C3⋊D3)—44no—
141C4⋊(C3⋊D3)—42no—
142C4⋊(C3⋊D3)—81no—
143C4⋊(C3⋊D3)SD1614yescomplemented
144C4×C3⋊D3—22no—
145C4×C3⋊D3—22no—
146C4×C3⋊D3—82no—
147#634—21no—
148#634—21no—
149C32×C8—22no—
150C3⋊(C3⋊C8)—21no—
151C3⋊(C3⋊C8)—21no—
152#554—91no—
153D42—91no—
154#486—91no—
155#481—92no—
156#476C3⋊D311yescharacteristic, complemented
157#465—92no—
158#460—91no—
159#450—92no—
160C4×SD16—91no—
161C8×D4—91no—
162C2×#102—92no—
163C23×D3—68no—
164C2×C3×Q8—24no—
165C2×C3×D4C22×D314yes—
166C22×C3×C4—24no—
167C2×#67—68no—
168D3×D4—616no—
169D3×D4—128no—
170C2×D12—34no—
171C2×D12—38no—
172C2×D12—68no—
173C2×D12—64no—
174C2×D12—64no—
175C2×D12—1216no—
176C2×C4×D3—38no—
177C2×C4×D3—68no—
178C2×Dic6—34no—
179C2×C3×C8C22×D318yes—
180C3×C4⋊C4—24no—
181C3×C4⋊C4C22×D314yes—
182C3×C4⋊C4C22×D318yes—
183C3×C22⋊C4—24no—
184C3×C42C22×D314yes—
185#214—68no—
186(C2×D3)⋊C4—38no—
187(C2×D3)⋊C4—68no—
188(C2×D3)⋊C4—68no—
189C4⋊Dic3—34no—
190C4⋊Dic3—34no—
191C4⋊Dic3—68no—
192Dic3⋊C4—68no—
193Dic3⋊C4—64no—
194C4×Dic3—64no—
195C2×C3⋊C8—34no—
196C2×C3⋊C8—34no—
197#204—128no—
198D3×C8—128no—
199C22×C32—22no—
200C22×C32—41no—
201C22×C32—41no—
202C22×C32C22×D411yescharacteristic
203C2×C3⋊D3—22no—
204C2×C3⋊D3—22no—
205C2×C3⋊D3—42no—
206C2×C3⋊D3—42no—
207C2×C3⋊D3—42no—
208C2×C3⋊D3—88no—
209C2×C3⋊D3C2×SD1614yes—
210C32×C4—21no—
211C32×C4—41no—
212C32×C4—42no—
213C32×C4C2×SD1612yes—
214C32×C4C2×#4111yescharacteristic
215C32×C4H(5,𝔽2)11yescharacteristic
216C3⋊Dic3—22no—
217C3⋊Dic3—41no—
218C3⋊Dic3—41no—
219C22×D4—92no—
220C22×D4—181no—
221C2×SD16—91no—
222C2×SD16—92no—
223C22×C8—92no—
224C4⋊Q8C2×C3⋊D311yescharacteristic, complemented
225#127—91no—
226#125—181no—
227C22⋊Q8—92no—
228C22⋊Q8—182no—
229#121—92no—
230#121—181no—
231#120—182no—
232C4×Q8—91no—
233C4×D4—91no—
234C4×D4—181no—
235C4×D4C2×C3⋊D311yescharacteristic
236C2×C4⋊C4—92no—
237#106—91no—
238#106C2×C3⋊D312yescomplemented
239C4⋊C8C2×C3⋊D311yescharacteristic, complemented
240#103—91no—
241#102—91no—
242#102—92no—
243#102—92no—
244#102—92no—
245#102C2×C3⋊D312yes—
246C22⋊C8—92no—
247C4×C8—91no—
248C23×C3—24no—
249C22×D3—38no—
250C22×D3—68no—
251C22×D3—1216no—
252C22×D3—1216no—
253C22×D3—248no—
254C3×Q8—84no—
255C3×D4—24no—
256C3×D4#23918yes—
257C2×C3×C4—28no—
258C2×C3×C4—24no—
259C2×C3×C4—48no—
260C2×C3×C4D3×D414yes—
261C2×C3×C4D3×D414yes—
262C2×C3×C4C23×D314yes—
263#67—1216no—
264C2×Dic3—38no—
265C2×Dic3—64no—
266C2×Dic3—64no—
267D12—316no—
268D12—68no—
269D12—68no—
270D12—1216no—
271D12—128no—
272D12—244no—
273C4×D3—68no—
274C4×D3—68no—
275C4×D3—248no—
276Dic6—64no—
277Dic6—64no—
278C3×C8—28no—
279C3⋊C8—64no—
280C3⋊C8—64no—
281C2×C32—42no—
282C2×C32#54611yescharacteristic
283C2×C32C22×SD1611yescharacteristic
284C2×C32#57611yescharacteristic
285C3⋊D3—24no—
286C3⋊D3—82no—
287C24—182no—
288C2×Q8—21no—
289C2×Q8—91no—
290C2×D4—92no—
291C2×D4—91no—
292C2×D4—182no—
293C2×D4—182no—
294C2×D4—184no—
295C2×D4—181no—
296C2×D4—181no—
297C2×D4—364no—
298C2×D4—362no—
299C2×D4C22×C3⋊D311yescharacteristic
300C22×C4—21no—
301C22×C4—92no—
302C22×C4—182no—
303SD16—182no—
304SD16—362no—
305C2×C8—91no—
306C2×C8—91no—
307C2×C8—362no—
308C2×C8C22×C3⋊D312yes—
309C4⋊C4—21no—
310C4⋊C4—91no—
311C4⋊C4—91no—
312C4⋊C4—182no—
313C4⋊C4—182no—
314C4⋊C4—181no—
315C4⋊C4C22×C3⋊D312yes—
316C4⋊C4C22×C3⋊D311yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—92no—
319C22⋊C4—182no—
320C22⋊C4—182no—
321C42—181no—
322C42C22×C3⋊D311yescharacteristic
323C22×C3—28no—
324C22×C3—44no—
325C22×C3—44no—
326C22×C3C2×D3×D414yes—
327C2×D3—316no—
328C2×D3—68no—
329C2×D3—68no—
330C2×D3—128no—
331C2×D3—128no—
332C2×D3—128no—
333C2×D3—2432no—
334C3×C4—24no—
335C3×C4—44no—
336C3×C4—48no—
337C3×C4D3×SD1618yes—
338C3×C4C2×#23914yes—
339C3×C4#100914yes—
340Dic3—68no—
341Dic3—124no—
342Dic3—124no—
343C32#329511yescharacteristic, complemented, Sylow
344C23—21no—
345C23—92no—
346C23—182no—
347C23—364no—
348C23—364no—
349C23—722no—
350Q8—81no—
351Q8—181no—
352Q8—181no—
353D4—21no—
354D4—94no—
355D4—182no—
356D4—182no—
357D4—364no—
358D4—364no—
359D4—362no—
360D4—721no—
361D4#383212yes—
362C2×C4—21no—
363C2×C4—22no—
364C2×C4—42no—
365C2×C4—92no—
366C2×C4—182no—
367C2×C4—182no—
368C2×C4—181no—
369C2×C4—181no—
370C2×C4—722no—
371C2×C4D4×C3⋊D311yescharacteristic
372C2×C4D4×C3⋊D311yescharacteristic
373C2×C4C23×C3⋊D311yescharacteristic
374C8—22no—
375C8—181no—
376C8—181no—
377C2×C3—48no—
378C2×C3#563014yes—
379C2×C3C2×D3×SD1614yes—
380C2×C3#577414yes—
381D3—616no—
382D3—248no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—94no—
387C22—182no—
388C22—182no—
389C22—362no—
390C22—362no—
391C22—362no—
392C22—728no—
393C22C2×D4×C3⋊D311yescharacteristic
394C4—21no—
395C4—41no—
396C4—42no—
397C4—182no—
398C4—361no—
399C4—361no—
400C4SD16×C3⋊D312yes—
401C4C2×#383211yescharacteristic
402C4#6436611yescharacteristic
403C3#8107514yescomplemented
404C2—42no—
405C2—184no—
406C2—722no—
407C2#1059610111yescharacteristic
408C2C2×SD16×C3⋊D311yescharacteristic
409C2#1059624511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#476C2
socleC22×C32C22×D4
prime radicalD4×C4⋊(C3⋊D3)C2
hypercenter#476C3⋊D3
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #10596201C2semidirect
3. C32×#476C2semidirect
4. #10592787C2semidirect
5. C4×#3754C2semidirect
6. #10592563C2semidirect
7. #10592562C2semidirect
8. #10592547C2semidirect
9. #10592533C2semidirect
10. #10592475C2semidirect
11. C3⋊D3×#102C2semidirect
15. C32×C4⋊Q8C22semidirect
20. C2×#3744C22semidirect
21. C2×C8×C3⋊D3C22semidirect
22. #64106C22semidirect
25. C4⋊C4×C3⋊D3C22semidirect
30. C4×#634C22semidirect
31. C32×#106C22semidirect
32. C32×C4⋊C8C22semidirect
35. #63648C22semidirect
36. #63647C22semidirect
37. #63637C22semidirect
38. #63636C22semidirect
39. #63636C22semidirect
40. #63635C22semidirect
41. C4×C3⋊(C3⋊C8)C22semidirect
44. C3×#476D3semidirect
92. C3×C4⋊Q8C2×D3semidirect
108. C3×#106C2×D3semidirect
109. C3×C4⋊C8C2×D3semidirect
143. C4⋊(C3⋊D3)SD16semidirect
156. #476C3⋊D3semidirect
224. C4⋊Q8C2×C3⋊D3semidirect
238. #106C2×C3⋊D3semidirect
239. C4⋊C8C2×C3⋊D3semidirect
343. C32#3295semidirect
403. C3#81075semidirect

Maximal subgroups

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

subgroupindex
#105962012
D4×C4⋊(C3⋊D3)2
C32×#4762
#105927872
C4×#37542
#105925632
#105925622
#105925472
#105925332
#105924752
C3⋊D3×#1022
#810753