Finite Group Databasebeta

← #49133075

Subgroups — #49133075

Order 36224.

494 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 139 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
1#31827119C211yesmaximal, characteristic, complemented
2D4×D1132C211yesmaximal, characteristic, complemented
3#31826812C211yesmaximal, characteristic, complemented
4#31826779C212yesmaximal, complemented
5#31826746C211yesmaximal, characteristic, complemented
6#31826701C212yesmaximal, complemented
7#31826661C211yesmaximal, characteristic, complemented
8#31826601C212yesmaximal, complemented
9C4×D2264C211yesmaximal, characteristic, complemented
10C2×#22583532C212yesmaximal, complemented
11C8×D4×C283C211yesmaximal, characteristic, complemented
12C2×#17985391—21no—
13C22×D1132C2212yes—
14C2×D4×D283—21no—
15C2×D2264C2211yescharacteristic
16C2×D2264C2212yescomplemented
17#22583610C2211yescharacteristic, complemented
18#22583607C2211yescharacteristic
19#22583594—22no—
20#22583590—21no—
21#22583585—21no—
22#22583584C2212yes—
23#22583584C2212yescomplemented
24#22583580—22no—
25C4×D1132C2211yescharacteristic
26C4×D1132C2211yescharacteristic, complemented
27C2×C4⋊Dic283C2212yescomplemented
28#22583544C2212yescomplemented
29#22583544C2211yescharacteristic, complemented
30#22583532C2211yescharacteristic
31#22583532C2212yes—
32#22583532C2211yescharacteristic, complemented
33#22583532C2212yescomplemented
34#22583532C2212yescomplemented
35#22583532C2212yescomplemented
36C22×C8×C283C2212yescomplemented
37C4×D4×C283C2211yescharacteristic
38C4⋊C8×C283C2211yescharacteristic, complemented
39C22⋊C8×C283C2212yescomplemented
40C4×C8×C283C2211yescharacteristic, complemented
41C23×D283—22no—
42#17985391—44no—
43C2×Dic566—21no—
44C2×D1132—24no—
45C2×D1132—22no—
46C2×D1132—21no—
47C2×D1132—21no—
48C2×D1132—42no—
49C2×D1132C2311yescharacteristic
50C2×D1132C2312yes—
51C2×D1132C2311yescharacteristic
52C2×C22⋊D283—22no—
53C2×C22⋊D283—22no—
54D4×D283—44no—
55C22×Dic283—22no—
56C2×C4×D283—21no—
57C2×C4×D283—21no—
58D2264—22no—
59D2264—42no—
60C4⋊Dic283—22no—
61C4⋊Dic283—21no—
62C4⋊Dic283C2311yescharacteristic
63C4⋊Dic283C2312yes—
64C4⋊Dic283C2311yescharacteristic
65(C2×D283)⋊C4—21no—
66(C2×D283)⋊C4—21no—
67(C2×D283)⋊C4—22no—
68(C2×D283)⋊C4—22no—
69C2×D4×C283D411yescharacteristic
70C22×C4×C283C2312yes—
71C2×C8×C283—42no—
72C2×C8×C283C2311yescharacteristic
73C2×C8×C283C2312yes—
74C2×C8×C283C2311yescharacteristic
75C4⋊C4×C283D411yescharacteristic
76C22⋊C4×C283D412yes—
77C42×C283C2311yescharacteristic
78C22×D283—21no—
79C22×D283—21no—
80C22×D283—22no—
81C22×D283—44no—
82C22×D283—44no—
83C22×D283—82no—
84Dic566—42no—
85D1132—21no—
86D1132—22no—
87D1132—21no—
88D1132—21no—
89D1132—22no—
90D1132—44no—
91D1132—42no—
92D1132—81no—
93D1132#4112yescomplemented
94C22⋊D283—44no—
95C22⋊D283—44no—
96C2×Dic283—21no—
97C2×Dic283—21no—
98C2×Dic283—22no—
99C2×Dic283—44no—
100C4×D283—42no—
101C4×D283—42no—
102C23×C283C2×D412yes—
103D4×C283D814yescomplemented
104C2×C4×C283—22no—
105C2×C4×C283—22no—
106C2×C4×C283C2×D411yescharacteristic
107C2×C4×C283C2×D412yes—
108C2×C4×C283C2×D411yescharacteristic
109C2×C4×C283C2411yescharacteristic
110C8×C283—21no—
111C8×C283—21no—
112C8×C283—22no—
113C22×C283—22no—
114C22×C283—22no—
115C22×C283C2×D814yes—
116C22×C283C22×D411yescharacteristic
117C2×D283—22no—
118C2×D283—41no—
119C2×D283—41no—
120C2×D283—42no—
121C2×D283—41no—
122C2×D283—41no—
123C2×D283—42no—
124C2×D283—42no—
125C2×D283—41no—
126C2×D283—88no—
127C4×C283—22no—
128C4×C283—21no—
129C4×C283C2×D812yes—
130C4×C283C2×#4111yescharacteristic
131C4×C283H(5,𝔽2)11yescharacteristic
132Dic283—41no—
133Dic283—41no—
134Dic283—42no—
135C2×C283—24no—
136C2×C283#54611yescharacteristic
137C2×C283C22×D811yescharacteristic
138C2×C283#57711yescharacteristic
139D283—42no—
140D283—81no—
141D283—82no—
142C283#329411yescharacteristic, complemented, Sylow
143#3294—2831nomaximal, Sylow
144#547—2831no—
145D42—2831no—
146#486—2831no—
147#480—2832no—
148#474—2831no—
149#466—2832no—
150#459—2831no—
151#447—2832no—
152C4×D8—2831no—
153C8×D4D28311yescharacteristic, complemented
154C2×#102—2832no—
155C2×#41—5661no—
156C22×D4—2832no—
157C22×D4—5661no—
158C2×D8—2831no—
159C2×D8—2832no—
160C22×C8C2×D28312yescomplemented
161C4⋊Q8—2831no—
162#127—2831no—
163#123—5662no—
164C22⋊Q8—5661no—
165#121—2832no—
166#121—2832no—
167#121—5661no—
168#120—5662no—
169C4×D4—2831no—
170C4×D4—2831no—
171C4×D4C2×D28311yescharacteristic
172C2×C4⋊C4—2832no—
173#107—2831no—
174#107—2832no—
175C4⋊C8C2×D28311yescharacteristic, complemented
176#102—2831no—
177#102—2832no—
178#102—2832no—
179#102—2832no—
180#102—2831no—
181#102—2832no—
182C22⋊C8C2×D28312yescomplemented
183C4×C8C2×D28311yescharacteristic, complemented
184C24—5662no—
185#41—11324no—
186C2×Q8—5661no—
187C2×D4—2831no—
188C2×D4—2832no—
189C2×D4—2831no—
190C2×D4—5664no—
191C2×D4—5662no—
192C2×D4—5662no—
193C2×D4—5662no—
194C2×D4—5661no—
195C2×D4—5661no—
196C2×D4—11322no—
197C2×D4—11324no—
198C2×D4D113211yescharacteristic
199C22×C4—5662no—
200C22×C4—5661no—
201C22×C4—5661no—
202C22×C4C22×D28312yes—
203D8—5662no—
204D8—11322no—
205C2×C8—42no—
206C2×C8C22×D28311yescharacteristic
207C2×C8C22×D28311yescharacteristic
208C2×C8C22×D28312yes—
209C4⋊C4—2831no—
210C4⋊C4—2832no—
211C4⋊C4—2831no—
212C4⋊C4—5662no—
213C4⋊C4—5661no—
214C4⋊C4D113211yescharacteristic
215C22⋊C4—5661no—
216C22⋊C4—5661no—
217C22⋊C4—5662no—
218C22⋊C4—5662no—
219C22⋊C4D113212yes—
220C42C22×D28311yescharacteristic
221C23—5661no—
222C23—5661no—
223C23—5662no—
224C23—11324no—
225C23—11324no—
226C23—22642no—
227C23C2×D113212yes—
228Q8—11322no—
229D4—2832no—
230D4—5661no—
231D4—5662no—
232D4—5661no—
233D4—5661no—
234D4—5662no—
235D4—11324no—
236D4—11324no—
237D4—11324no—
238D4—11322no—
239D4—22641no—
240D4D226414yescomplemented
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—5661no—
244C2×C4—5661no—
245C2×C4—5662no—
246C2×C4—11324no—
247C2×C4—11322no—
248C2×C4—11322no—
249C2×C4C2×D113211yescharacteristic
250C2×C4C2×D113212yes—
251C2×C4C2×D113211yescharacteristic
252C2×C4C23×D28311yescharacteristic
253C8—21no—
254C8—21no—
255C8—22no—
256C22—22no—
257C22—22no—
258C22—5662no—
259C22—11321no—
260C22—11321no—
261C22—11321no—
262C22—11322no—
263C22—11322no—
264C22—11321no—
265C22—11322no—
266C22—11321no—
267C22—22648no—
268C22C2×D226414yes—
269C22C22×D113211yescharacteristic
270C4—21no—
271C4—22no—
272C4—11321no—
273C4—11321no—
274C4—11322no—
275C4C2×D226412yes—
276C4#41×D28311yescharacteristic
277C4#2258365511yescharacteristic
278C2—24no—
279C2—11322no—
280C2—22642no—
281C2—22641no—
282C2#3182711011yescharacteristic
283C2C22×D226411yescharacteristic
284C2#3182727711yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC8×D4×C283C2
socleC22×C283C22×D4
hypercenterC8×D4D283
hypocenterC283#3294
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #31827119C2semidirect
2. D4×D1132C2semidirect
3. #31826812C2semidirect
4. #31826779C2semidirect
5. #31826746C2semidirect
6. #31826701C2semidirect
7. #31826661C2semidirect
8. #31826601C2semidirect
9. C4×D2264C2semidirect
10. C2×#22583532C2semidirect
11. C8×D4×C283C2semidirect
16. C2×D2264C22semidirect
17. #22583610C22semidirect
23. #22583584C22semidirect
26. C4×D1132C22semidirect
27. C2×C4⋊Dic283C22semidirect
28. #22583544C22semidirect
29. #22583544C22semidirect
32. #22583532C22semidirect
33. #22583532C22semidirect
34. #22583532C22semidirect
35. #22583532C22semidirect
36. C22×C8×C283C22semidirect
38. C4⋊C8×C283C22semidirect
39. C22⋊C8×C283C22semidirect
40. C4×C8×C283C22semidirect
93. D1132#41semidirect
103. D4×C283D8semidirect
142. C283#3294semidirect
153. C8×D4D283semidirect
160. C22×C8C2×D283semidirect
175. C4⋊C8C2×D283semidirect
182. C22⋊C8C2×D283semidirect
183. C4×C8C2×D283semidirect
240. D4D2264semidirect

Maximal subgroups

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

subgroupindex
#318271192
D4×D11322
#318268122
#318267792
#318267462
#318267012
#318266612
#318266012
C4×D22642
C2×#225835322
C8×D4×C2832
#3294283