Finite Group Databasebeta

← #11885730

Subgroups — #11885730

Order 1152.

1860 conjugacy classes of subgroups; only the 249 normal subgroups are shown.

normal subgroups only

This group has 1860 conjugacy classes of subgroups — too many to draw. Only its 249 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×C3⋊D3C212yesmaximal, complemented
2#10596188C212yesmaximal, complemented
3C32×#493C211yesmaximal, characteristic, complemented
4#10592856C212yesmaximal, complemented
5#10592855C214yesmaximal, complemented
6#10592771C212yesmaximal, complemented
7C4×#3745C211yesmaximal, characteristic, complemented
8C8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
9#81789—34nomaximal
10C2×D4×C3⋊D3—22no—
11C2×D4×C3⋊D3C2214yescomplemented
12C2×C32×D8C2212yescomplemented
13C2×C32×D8C2212yescomplemented
14C32×#127C2212yescomplemented
15#64147—22no—
16#64147C2214yescomplemented
17#64146—24no—
18C2×#3753C2214yescomplemented
19D8×C3⋊D3—28no—
20C2×#3745C2211yescharacteristic
21C2×C8×C3⋊D3C2212yescomplemented
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C4×C4⋊(C3⋊D3)C2212yescomplemented
24C32×C4×C8C2211yescharacteristic, complemented
25#63659C2214yescomplemented
26#63648C2212yescomplemented
27#63647C2212yescomplemented
28#63645C2211yescharacteristic, complemented
29C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
30C2×D3×D8—38no—
31#5717—38no—
32C3×#493D314yescomplemented
33#5157—38no—
34#5156—316no—
35#5072—38no—
36C4×D24—34no—
37C8×D12—34no—
38C23×C3⋊D3—24no—
39C2×C32×D4—22no—
40C2×C32×D4—22no—
41C2×C32×D4C2314yes—
42C2×#638—24no—
43C2×#638—24no—
44D4×C3⋊D3—28no—
45D4×C3⋊D3—44no—
46D4×C3⋊D3—48no—
47C2×C4⋊(C3⋊D3)D411yescharacteristic
48C2×C4⋊(C3⋊D3)C2312yes—
49C2×C4×C3⋊D3—22no—
50C2×C4×C3⋊D3C2312yes—
51C32×D8—24no—
52C32×D8—42no—
53C2×C32×C8C2311yescharacteristic
54C2×C32×C8C2311yescharacteristic
55C32×C42C2311yescharacteristic
56#3757—24no—
57#3753—28no—
58#3752—22no—
59#3752D412yes—
60C4⋊(C3⋊Dic3)D411yescharacteristic
61C4⋊(C3⋊Dic3)C2312yes—
62C2×C3⋊(C3⋊C8)C2312yes—
63#3745D414yescomplemented
64C8×C3⋊D3—24no—
65D4×D8—91noSylow
66C2×D3×D4—316no—
67C2×D3×D4—68no—
68C2×C3×D8C2×D318yescomplemented
69C2×C3×D8C2×D318yescomplemented
70C3×#127C2×D318yescomplemented
71#938—316no—
72#938—68no—
73#937—616no—
74C2×#213—316no—
75D3×D8—632no—
76C2×D24—34no—
77C2×D3×C8—38no—
78C4×D12—34no—
79C4×D12—38no—
80C3×C4×C8C2×D314yescomplemented
81#832—316no—
82#821—38no—
83(C2×D3)⋊C8—38no—
84#818—34no—
85C4⋊(C3⋊C8)—34no—
86C23×C32—24no—
87C22×C3⋊D3—22no—
88C22×C3⋊D3—48no—
89C22×C3⋊D3—48no—
90C22×C3⋊D3—84no—
91C22×C3⋊D3C2×D412yes—
92C32×D4—24no—
93C32×D4—24no—
94C32×D4—44no—
95C32×D4—82no—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2411yescharacteristic
99#638—48no—
100#638—48no—
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3C2×D412yes—
103C4⋊(C3⋊D3)—22no—
104C4⋊(C3⋊D3)D814yescomplemented
105C4⋊(C3⋊D3)C2×D414yescomplemented
106C4×C3⋊D3—22no—
107C4×C3⋊D3—22no—
108C4×C3⋊D3—44no—
109C32×C8—21no—
110C32×C8C2×D412yescomplemented
111C3⋊(C3⋊C8)—22no—
112C22×D8—92no—
113D42—92no—
114#493C3⋊D311yescharacteristic, complemented
115#466—92no—
116#459—92no—
117#447—94no—
118C4×D8—91no—
119C8×D4—91no—
120C23×D3—616no—
121C2×C3×D4—28no—
122C2×C3×D4—28no—
123C2×C3×D4C22×D3116yes—
124C2×#67—616no—
125C2×#67—616no—
126D3×D4—632no—
127D3×D4—1216no—
128D3×D4—1232no—
129C2×D12—34no—
130C2×D12—38no—
131C2×C4×D3—38no—
132C2×C4×D3—68no—
133C3×D8—216no—
134C3×D8—48no—
135C2×C3×C8C22×D314yes—
136C2×C3×C8C22×D314yes—
137C3×C42C22×D314yes—
138#217—616no—
139#213—632no—
140(C2×D3)⋊C4—38no—
141(C2×D3)⋊C4—68no—
142C4⋊Dic3—34no—
143C4⋊Dic3—38no—
144C2×C3⋊C8—38no—
145D24—316no—
146D3×C8—616no—
147C22×C32—44no—
148C22×C32—44no—
149C22×C32—44no—
150C22×C32C22×D411yescharacteristic
151C2×C3⋊D3—22no—
152C2×C3⋊D3—22no—
153C2×C3⋊D3—24no—
154C2×C3⋊D3—42no—
155C2×C3⋊D3—42no—
156C2×C3⋊D3—816no—
157C2×C3⋊D3C2×D814yescomplemented
158C32×C4—21no—
159C32×C4C2×D812yescomplemented
160C32×C4C22×D411yescharacteristic
161C32×C4H(5,𝔽2)11yescharacteristic
162C3⋊Dic3—22no—
163C3⋊Dic3—42no—
164C22×D4—94no—
165C22×D4—182no—
166C2×D8—94no—
167C2×D8—91no—
168C2×D8—188no—
169C2×D8C2×C3⋊D312yescomplemented
170C2×D8C2×C3⋊D312yescomplemented
171C22×C8—92no—
172#127C2×C3⋊D312yescomplemented
173#121—94no—
174#121—182no—
175#120—184no—
176C4×D4—91no—
177C4×D4—92no—
178#107—91no—
179C4⋊C8—91no—
180#102—94no—
181#102—92no—
182C22⋊C8—92no—
183C4×C8C2×C3⋊D311yescharacteristic, complemented
184C23×C3—216no—
185C22×D3—38no—
186C22×D3—68no—
187C22×D3—1232no—
188C22×D3—1232no—
189C22×D3—2416no—
190C3×D4—216no—
191C3×D4—216no—
192C3×D4—416no—
193C3×D4—88no—
194C2×C3×C4D3×D414yes—
195C2×C3×C4D3×D414yes—
196C2×C3×C4C23×D314yes—
197#67—1232no—
198#67—1232no—
199C2×Dic3—38no—
200C2×Dic3—68no—
201D12—316no—
202D12—316no—
203D12—68no—
204C4×D3—68no—
205C4×D3—68no—
206C4×D3—1216no—
207C3×C8—24no—
208C3×C8D3×D418yescomplemented
209C3⋊C8—68no—
210C2×C32—84no—
211C2×C32D4211yescharacteristic
212C2×C32C22×D811yescharacteristic
213C2×C32#57611yescharacteristic
214C3⋊D3—24no—
215C3⋊D3—44no—
216C24—184no—
217C2×D4—22no—
218C2×D4—22no—
219C2×D4—92no—
220C2×D4—91no—
221C2×D4—184no—
222C2×D4—188no—
223C2×D4—184no—
224C2×D4—364no—
225C2×D4—368no—
226C2×D4C22×C3⋊D314yes—
227C22×C4—92no—
228C22×C4—182no—
229D8—24no—
230D8—42no—
231D8—94no—
232D8—188no—
233C2×C8—92no—
234C2×C8—184no—
235C2×C8C22×C3⋊D311yescharacteristic
236C2×C8C22×C3⋊D311yescharacteristic
237C4⋊C4—91no—
238C4⋊C4—92no—
239C22⋊C4—92no—
240C22⋊C4—184no—
241C22⋊C4—182no—
242C42C22×C3⋊D311yescharacteristic
243C22×C3—416no—
244C22×C3—416no—
245C22×C3—416no—
246C22×C3C2×D3×D414yes—
247C2×D3—316no—
248C2×D3—68no—
249C2×D3—68no—
250C2×D3—616no—
251C2×D3—128no—
252C2×D3—128no—
253C2×D3—2464no—
254C3×C4—24no—
255C3×C4D3×D818yescomplemented
256C3×C4C2×D3×D414yes—
257C3×C4#100414yes—
258Dic3—68no—
259Dic3—128no—
260C32D4×D811yescharacteristic, complemented, Sylow
261C23—24no—
262C23—92no—
263C23—182no—
264C23—368no—
265C23—368no—
266C23—724no—
267D4—24no—
268D4—24no—
269D4—44no—
270D4—82no—
271D4—94no—
272D4—94no—
273D4—182no—
274D4—368no—
275D4—368no—
276C2×C4—92no—
277C2×C4—182no—
278C2×C4—182no—
279C2×C4—182no—
280C2×C4—364no—
281C2×C4D4×C3⋊D311yescharacteristic
282C2×C4D4×C3⋊D311yescharacteristic
283C2×C4C23×C3⋊D311yescharacteristic
284C8—21no—
285C8—182no—
286C8D4×C3⋊D312yescomplemented
287C2×C3—816no—
288C2×C3#571714yes—
289C2×C3C2×D3×D814yes—
290C2×C3#575714yes—
291D3—616no—
292D3—1216no—
293C22—44no—
294C22—44no—
295C22—44no—
296C22—94no—
297C22—182no—
298C22—182no—
299C22—184no—
300C22—362no—
301C22—362no—
302C22—7216no—
303C22C2×D4×C3⋊D311yescharacteristic
304C4—21no—
305C4—182no—
306C4—362no—
307C4D8×C3⋊D312yescomplemented
308C4C2×D4×C3⋊D311yescharacteristic
309C4#6436111yescharacteristic
310C3#8178914yescomplemented
311C2—84no—
312C2—184no—
313C2—364no—
314C2#1059618811yescharacteristic
315C2C2×D8×C3⋊D311yescharacteristic
316C2#1059622811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#493C2
socleC22×C32C22×D4
hypercenter#493C3⋊D3
hypocenterC32D4×D8
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. C2×D8×C3⋊D3C2semidirect
2. #10596188C2semidirect
3. C32×#493C2semidirect
4. #10592856C2semidirect
5. #10592855C2semidirect
6. #10592771C2semidirect
7. C4×#3745C2semidirect
8. C8×C4⋊(C3⋊D3)C2semidirect
11. C2×D4×C3⋊D3C22semidirect
12. C2×C32×D8C22semidirect
13. C2×C32×D8C22semidirect
14. C32×#127C22semidirect
16. #64147C22semidirect
18. C2×#3753C22semidirect
21. C2×C8×C3⋊D3C22semidirect
23. C4×C4⋊(C3⋊D3)C22semidirect
24. C32×C4×C8C22semidirect
25. #63659C22semidirect
26. #63648C22semidirect
27. #63647C22semidirect
28. #63645C22semidirect
29. C4⋊(C3⋊(C3⋊C8))C22semidirect
32. C3×#493D3semidirect
63. #3745D4semidirect
68. C2×C3×D8C2×D3semidirect
69. C2×C3×D8C2×D3semidirect
70. C3×#127C2×D3semidirect
80. C3×C4×C8C2×D3semidirect
104. C4⋊(C3⋊D3)D8semidirect
105. C4⋊(C3⋊D3)C2×D4semidirect
110. C32×C8C2×D4semidirect
114. #493C3⋊D3semidirect
157. C2×C3⋊D3C2×D8semidirect
159. C32×C4C2×D8semidirect
169. C2×D8C2×C3⋊D3semidirect
170. C2×D8C2×C3⋊D3semidirect
172. #127C2×C3⋊D3semidirect
183. C4×C8C2×C3⋊D3semidirect
208. C3×C8D3×D4semidirect
255. C3×C4D3×D8semidirect
260. C32D4×D8semidirect
286. C8D4×C3⋊D3semidirect
307. C4D8×C3⋊D3semidirect
310. C3#81789semidirect

Maximal subgroups

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

subgroupindex
C2×D8×C3⋊D32
#105961882
C32×#4932
#105928562
#105928552
#105927712
C4×#37452
C8×C4⋊(C3⋊D3)2
#817893