Finite Group Databasebeta

← #44470550

Subgroups — #44470550

Order 29888.

330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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×#21418744C211yesmaximal, characteristic, complemented
2C22×C4×D467C211yesmaximal, characteristic, complemented
3#28417938C212yesmaximal, complemented
4#28417929C211yesmaximal, characteristic, complemented
5#28417928C211yesmaximal, characteristic, complemented
6#28417927C211yesmaximal, characteristic, complemented
7#28417923C212yesmaximal, complemented
8#28417915C212yesmaximal, complemented
9(C22⋊D467)⋊C4C212yesmaximal, complemented
10#28417911C211yesmaximal, characteristic, complemented
11C22⋊Q8×C467C211yesmaximal, characteristic, complemented
12C23×D467C2211yescharacteristic
13#21418744—24no—
14C2×D1868C2212yes—
15C2×D1868C2212yes—
16C2×D1868C2211yescharacteristic, complemented
17C2×C22⋊D467C2212yes—
18C22×Dic467C2211yescharacteristic
19C2×C4×D467—24no—
20C2×C4×D467C2211yescharacteristic
21C2×C4×D467C2211yescharacteristic
22C2×C4×D467C2211yescharacteristic
23C2×C4×D467C2211yescharacteristic
24C2×C4×D467C2212yescomplemented
25C4⋊Dic467C2211yescharacteristic, complemented
26Dic467⋊C4C2212yescomplemented
27(C2×D467)⋊C4C2212yes—
28(C2×D467)⋊C4C2212yes—
29(C2×D467)⋊C4C2212yescomplemented
30(C2×D467)⋊C4C2212yescomplemented
31C4×Dic467C2212yescomplemented
32C2×Q8×C467C2211yescharacteristic, complemented
33C22×C4×C467C2211yescharacteristic
34C4⋊C4×C467C2211yescharacteristic, complemented
35C4⋊C4×C467C2212yescomplemented
36C22⋊C4×C467C2212yes—
37C22×D467—22no—
38C22×D467—22no—
39C22×D467—22no—
40C22×D467C2312yes—
41C22×D467C2311yescharacteristic
42C22×D467C2311yescharacteristic
43D1868—24no—
44D1868—24no—
45D1868—22no—
46C22⋊D467—24no—
47C2×Dic467—22no—
48C2×Dic467C2312yes—
49C2×Dic467C2311yescharacteristic
50C2×Dic467C2311yescharacteristic
51C4×D467—22no—
52C4×D467—22no—
53C4×D467—22no—
54C4×D467—24no—
55C4×D467D414yescomplemented
56C23×C467C2311yescharacteristic
57Q8×C467—22no—
58C2×C4×C467—22no—
59C2×C4×C467C2312yes—
60C2×C4×C467C2312yes—
61C2×C4×C467C2311yescharacteristic
62C2×C4×C467C2311yescharacteristic
63C22×C467—21no—
64C22×C467—21no—
65C22×C467#4112yescomplemented
66C22×C467C2411yescharacteristic
67C2×D467—28no—
68C2×D467—21no—
69C2×D467—21no—
70C2×D467—21no—
71C2×D467—21no—
72C2×D467—22no—
73C2×D467—22no—
74C2×D467—22no—
75C2×D467C2×D412yes—
76C2×D467#4112yescomplemented
77C4×C467—21no—
78C4×C467—22no—
79C4×C467—22no—
80C4×C467C2×D412yes—
81Dic467—21no—
82Dic467—22no—
83Dic467C2×D412yes—
84C2×C467—22no—
85C2×C467C22×D411yescharacteristic
86C2×C467C2×#4111yescharacteristic
87C2×C467C2×#4111yescharacteristic
88D467—22no—
89D467—22no—
90D467—42no—
91C467#52511yescharacteristic, complemented, Sylow
92#525—4671nomaximal, Sylow
93C2×#41—4671no—
94C23×C4—4671no—
95#123—4672no—
96C22⋊Q8—4671no—
97C22⋊Q8D46711yescharacteristic, complemented
98#121—4671no—
99#121—4671no—
100#120—4672no—
101C4×D4—4672no—
102C4×D4—4672no—
103#117—4671no—
104C24—4671no—
105#41—9344no—
106C2×Q8C2×D46711yescharacteristic, complemented
107C2×D4—4672no—
108C2×D4—4672no—
109C2×D4—4672no—
110C2×D4—4671no—
111C22×C4—9344no—
112C22×C4—4671no—
113C22×C4—4671no—
114C22×C4—4672no—
115C22×C4—4671no—
116C22×C4—4671no—
117C22×C4—4671no—
118C22×C4C2×D46711yescharacteristic
119C4⋊C4—4671no—
120C4⋊C4—4672no—
121C4⋊C4C2×D46711yescharacteristic, complemented
122C4⋊C4C2×D46712yescomplemented
123C22⋊C4—4672no—
124C22⋊C4—4672no—
125C22⋊C4—4672no—
126C22⋊C4—4672no—
127C22⋊C4C2×D46712yes—
128C42—4672no—
129C23—9342no—
130C23—9342no—
131C23—9342no—
132C23—4672no—
133C23—4671no—
134C23—4671no—
135C23C22×D46711yescharacteristic
136Q8—22no—
137D4—9344no—
138D4—9344no—
139D4—9344no—
140D4—9342no—
141C2×C4—22no—
142C2×C4—9342no—
143C2×C4—9342no—
144C2×C4—9344no—
145C2×C4—9342no—
146C2×C4—9342no—
147C2×C4—4672no—
148C2×C4—4671no—
149C2×C4—4671no—
150C2×C4—4674no—
151C2×C4C22×D46712yes—
152C2×C4C22×D46711yescharacteristic
153C2×C4C22×D46712yes—
154C2×C4C22×D46711yescharacteristic
155C22—21no—
156C22—21no—
157C22—9348no—
158C22—9342no—
159C22—9342no—
160C22—9342no—
161C22—9341no—
162C22—9341no—
163C22—9341no—
164C22—9341no—
165C22—4672no—
166C22—4672no—
167C22#2141874412yescomplemented
168C22C23×D46711yescharacteristic
169C4—21no—
170C4—22no—
171C4—22no—
172C4—9341no—
173C4—9342no—
174C4—4672no—
175C4D4×D46712yes—
176C2—22no—
177C2—18682no—
178C2—9342no—
179C2—9342no—
180C2C2×D4×D46711yescharacteristic
181C2#41×D46711yescharacteristic
182C2C2×#2141874411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D467
commutator, socle, cosocleC22×C467C24
FittingC22⋊Q8×C467C2
hypercenterC22⋊Q8D467
hypocenterC467#525
LCSG ▷ C22×C467 ▷ C467
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#21418744C2semidirect
2. C22×C4×D467C2semidirect
3. #28417938C2semidirect
4. #28417929C2semidirect
5. #28417928C2semidirect
6. #28417927C2semidirect
7. #28417923C2semidirect
8. #28417915C2semidirect
9. (C22⋊D467)⋊C4C2semidirect
10. #28417911C2semidirect
11. C22⋊Q8×C467C2semidirect
16. C2×D1868C22semidirect
24. C2×C4×D467C22semidirect
25. C4⋊Dic467C22semidirect
26. Dic467⋊C4C22semidirect
29. (C2×D467)⋊C4C22semidirect
30. (C2×D467)⋊C4C22semidirect
31. C4×Dic467C22semidirect
32. C2×Q8×C467C22semidirect
34. C4⋊C4×C467C22semidirect
35. C4⋊C4×C467C22semidirect
55. C4×D467D4semidirect
65. C22×C467#41semidirect
76. C2×D467#41semidirect
91. C467#525semidirect
97. C22⋊Q8D467semidirect
106. C2×Q8C2×D467semidirect
121. C4⋊C4C2×D467semidirect
122. C4⋊C4C2×D467semidirect
167. C22#21418744semidirect

Maximal subgroups

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

subgroupindex
C2×#214187442
C22×C4×D4672
#284179382
#284179292
#284179282
#284179272
#284179232
#284179152
(C22⋊D467)⋊C42
#284179112
C22⋊Q8×C4672
#525467