Finite Group Databasebeta

← #44470678

Subgroups — #44470678

Order 29888.

334 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 107 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×D1868C211yesmaximal, characteristic, complemented
3#28417942C211yesmaximal, characteristic, complemented
4#28417938C212yesmaximal, complemented
5#28417928C211yesmaximal, characteristic, complemented
6#28417928C212yesmaximal, complemented
7#28417923C212yesmaximal, complemented
8#28417915C211yesmaximal, characteristic, complemented
9C4×C22⋊D467C211yesmaximal, characteristic, complemented
10C22⋊C4×D467C212yesmaximal, complemented
11C22⋊Q8×C467C211yesmaximal, characteristic, complemented
12C23×D467C2212yes—
13#21418744—24no—
14C2×D1868—24no—
15C2×D1868C2212yes—
16C2×D1868C2211yescharacteristic
17C2×D1868C2211yescharacteristic
18C2×D1868C2212yescomplemented
19C2×D1868C2212yescomplemented
20C2×C22⋊D467C2211yescharacteristic
21C2×C4×D467C2212yescomplemented
22C2×C4×D467C2211yescharacteristic, complemented
23C2×C4×D467C2212yescomplemented
24Dic467⋊C4C2211yescharacteristic, complemented
25C22⋊Dic467C2211yescharacteristic
26(C2×D467)⋊C4C2212yescomplemented
27(C2×D467)⋊C4C2212yescomplemented
28(C2×D467)⋊C4C2211yescharacteristic, complemented
29(C2×D467)⋊C4C2212yescomplemented
30(C2×D467)⋊C4C2212yescomplemented
31C4×Dic467C2211yescharacteristic, complemented
32C2×Q8×C467C2211yescharacteristic, complemented
33C22×C4×C467C2211yescharacteristic
34C4⋊C4×C467C2211yescharacteristic, complemented
35C4⋊C4×C467C2212yescomplemented
36C22⋊C4×C467C2212yes—
37C22×D467—24no—
38C22×D467—24no—
39C22×D467—42no—
40C22×D467C2312yes—
41C22×D467C2311yescharacteristic
42C22×D467C2312yes—
43D1868—24no—
44D1868—24no—
45D1868—22no—
46D1868—42no—
47D1868D414yescomplemented
48C22⋊D467—22no—
49C2×Dic467C2311yescharacteristic
50C2×Dic467C2311yescharacteristic
51C2×Dic467C2311yescharacteristic
52C4×D467—24no—
53C4×D467—22no—
54C4×D467—42no—
55C23×C467C2311yescharacteristic
56Q8×C467—22no—
57C2×C4×C467—22no—
58C2×C4×C467C2312yes—
59C2×C4×C467C2312yes—
60C2×C4×C467C2311yescharacteristic
61C2×C4×C467C2311yescharacteristic
62C22×C467—21no—
63C22×C467—21no—
64C22×C467#4112yescomplemented
65C22×C467C2411yescharacteristic
66C2×D467—22no—
67C2×D467—22no—
68C2×D467—21no—
69C2×D467—22no—
70C2×D467—21no—
71C2×D467—22no—
72C2×D467—21no—
73C2×D467—22no—
74C2×D467—48no—
75C2×D467C2×D414yes—
76C4×C467—21no—
77C4×C467—22no—
78C4×C467—22no—
79C4×C467C2×D412yes—
80Dic467—21no—
81Dic467—21no—
82Dic467—21no—
83C2×C467—22no—
84C2×C467C22×D411yescharacteristic
85C2×C467C2×#4111yescharacteristic
86C2×C467H(5,𝔽2)11yescharacteristic
87D467—24no—
88D467—41no—
89D467—42no—
90C467#54611yescharacteristic, complemented, Sylow
91#546—4671nomaximal, Sylow
92C2×#41—4671no—
93C22×D4—4671no—
94#124—4671no—
95#123—4672no—
96C22⋊Q8D46711yescharacteristic, complemented
97#121—4671no—
98#121—4672no—
99#120—4672no—
100C4×D4—4671no—
101C4×D4—4671no—
102C2×C22⋊C4—4672no—
103C24—4672no—
104#41—9344no—
105C2×Q8C2×D46711yescharacteristic, complemented
106C2×D4—9344no—
107C2×D4—4671no—
108C2×D4—4672no—
109C2×D4—4672no—
110C2×D4—4672no—
111C2×D4—4671no—
112C2×D4—4671no—
113C22×C4—4672no—
114C22×C4—4672no—
115C22×C4—4671no—
116C22×C4C2×D46711yescharacteristic
117C4⋊C4—4671no—
118C4⋊C4C2×D46711yescharacteristic, complemented
119C4⋊C4C2×D46712yescomplemented
120C22⋊C4—4671no—
121C22⋊C4—4672no—
122C22⋊C4—4672no—
123C22⋊C4—4672no—
124C22⋊C4—4671no—
125C22⋊C4—4672no—
126C22⋊C4C2×D46712yes—
127C42—4671no—
128C23—18682no—
129C23—9344no—
130C23—9344no—
131C23—4672no—
132C23—4671no—
133C23—4672no—
134C23C22×D46711yescharacteristic
135Q8—22no—
136D4—18682no—
137D4—9344no—
138D4—9344no—
139D4—9342no—
140D4—9342no—
141D4—4674no—
142C2×C4—22no—
143C2×C4—18682no—
144C2×C4—9344no—
145C2×C4—9342no—
146C2×C4—4671no—
147C2×C4—4671no—
148C2×C4—4671no—
149C2×C4C22×D46712yes—
150C2×C4C22×D46712yes—
151C2×C4C22×D46711yescharacteristic
152C2×C4C22×D46711yescharacteristic
153C22—21no—
154C22—21no—
155C22—18688no—
156C22—9341no—
157C22—9342no—
158C22—9341no—
159C22—9342no—
160C22—9341no—
161C22—9342no—
162C22—9342no—
163C22—9342no—
164C22—4674no—
165C22#2141874412yescomplemented
166C22C23×D46711yescharacteristic
167C4—21no—
168C4—22no—
169C4—22no—
170C4—9341no—
171C4—9341no—
172C4—9341no—
173C4D4×D46712yes—
174C2—22no—
175C2—18682no—
176C2—18681no—
177C2—9344no—
178C2C2×D4×D46711yescharacteristic
179C2C2×#2141874411yescharacteristic
180C2#2841799911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D467
commutator, socle, cosocleC22×C467C24
FittingC22⋊Q8×C467C2
hypercenterC22⋊Q8D467
hypocenterC467#546
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×D1868C2semidirect
3. #28417942C2semidirect
4. #28417938C2semidirect
5. #28417928C2semidirect
6. #28417928C2semidirect
7. #28417923C2semidirect
8. #28417915C2semidirect
9. C4×C22⋊D467C2semidirect
10. C22⋊C4×D467C2semidirect
11. C22⋊Q8×C467C2semidirect
18. C2×D1868C22semidirect
19. C2×D1868C22semidirect
21. C2×C4×D467C22semidirect
22. C2×C4×D467C22semidirect
23. C2×C4×D467C22semidirect
24. Dic467⋊C4C22semidirect
26. (C2×D467)⋊C4C22semidirect
27. (C2×D467)⋊C4C22semidirect
28. (C2×D467)⋊C4C22semidirect
29. (C2×D467)⋊C4C22semidirect
30. (C2×D467)⋊C4C22semidirect
31. C4×Dic467C22semidirect
32. C2×Q8×C467C22semidirect
34. C4⋊C4×C467C22semidirect
35. C4⋊C4×C467C22semidirect
47. D1868D4semidirect
64. C22×C467#41semidirect
90. C467#546semidirect
96. C22⋊Q8D467semidirect
105. C2×Q8C2×D467semidirect
118. C4⋊C4C2×D467semidirect
119. C4⋊C4C2×D467semidirect
165. 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×D18682
#284179422
#284179382
#284179282
#284179232
#284179152
C4×C22⋊D4672
C22⋊C4×D4672
C22⋊Q8×C4672
#546467