Finite Group Databasebeta

← #43248230

Subgroups — #43248230

Order 28352.

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×#20296788C211yesmaximal, characteristic, complemented
2C22×C4×D443C211yesmaximal, characteristic, complemented
3#28381871C212yesmaximal, complemented
4#28381862C211yesmaximal, characteristic, complemented
5#28381861C211yesmaximal, characteristic, complemented
6#28381860C211yesmaximal, characteristic, complemented
7#28381856C212yesmaximal, complemented
8#28381848C212yesmaximal, complemented
9(C22⋊D443)⋊C4C212yesmaximal, complemented
10#28381844C211yesmaximal, characteristic, complemented
11C22⋊Q8×C443C211yesmaximal, characteristic, complemented
12C23×D443C2211yescharacteristic
13#20296788—24no—
14C2×D1772C2212yes—
15C2×D1772C2212yes—
16C2×D1772C2211yescharacteristic, complemented
17C2×C22⋊D443C2212yes—
18C22×Dic443C2211yescharacteristic
19C2×C4×D443—24no—
20C2×C4×D443C2211yescharacteristic
21C2×C4×D443C2211yescharacteristic
22C2×C4×D443C2211yescharacteristic
23C2×C4×D443C2211yescharacteristic
24C2×C4×D443C2212yescomplemented
25C4⋊Dic443C2211yescharacteristic, complemented
26Dic443⋊C4C2212yescomplemented
27(C2×D443)⋊C4C2212yes—
28(C2×D443)⋊C4C2212yes—
29(C2×D443)⋊C4C2212yescomplemented
30(C2×D443)⋊C4C2212yescomplemented
31C4×Dic443C2212yescomplemented
32C2×Q8×C443C2211yescharacteristic, complemented
33C22×C4×C443C2211yescharacteristic
34C4⋊C4×C443C2211yescharacteristic, complemented
35C4⋊C4×C443C2212yescomplemented
36C22⋊C4×C443C2212yes—
37C22×D443—22no—
38C22×D443—22no—
39C22×D443—22no—
40C22×D443C2312yes—
41C22×D443C2311yescharacteristic
42C22×D443C2311yescharacteristic
43D1772—24no—
44D1772—24no—
45D1772—22no—
46C22⋊D443—24no—
47C2×Dic443—22no—
48C2×Dic443C2312yes—
49C2×Dic443C2311yescharacteristic
50C2×Dic443C2311yescharacteristic
51C4×D443—22no—
52C4×D443—22no—
53C4×D443—22no—
54C4×D443—24no—
55C4×D443D414yescomplemented
56C23×C443C2311yescharacteristic
57Q8×C443—22no—
58C2×C4×C443—22no—
59C2×C4×C443C2312yes—
60C2×C4×C443C2312yes—
61C2×C4×C443C2311yescharacteristic
62C2×C4×C443C2311yescharacteristic
63C22×C443—21no—
64C22×C443—21no—
65C22×C443#4112yescomplemented
66C22×C443C2411yescharacteristic
67C2×D443—28no—
68C2×D443—21no—
69C2×D443—21no—
70C2×D443—21no—
71C2×D443—21no—
72C2×D443—22no—
73C2×D443—22no—
74C2×D443—22no—
75C2×D443C2×D412yes—
76C2×D443#4112yescomplemented
77C4×C443—21no—
78C4×C443—22no—
79C4×C443—22no—
80C4×C443C2×D412yes—
81Dic443—21no—
82Dic443—22no—
83Dic443C2×D412yes—
84C2×C443—22no—
85C2×C443C22×D411yescharacteristic
86C2×C443C2×#4111yescharacteristic
87C2×C443C2×#4111yescharacteristic
88D443—22no—
89D443—22no—
90D443—42no—
91C443#52511yescharacteristic, complemented, Sylow
92#525—4431nomaximal, Sylow
93C2×#41—4431no—
94C23×C4—4431no—
95#123—4432no—
96C22⋊Q8—4431no—
97C22⋊Q8D44311yescharacteristic, complemented
98#121—4431no—
99#121—4431no—
100#120—4432no—
101C4×D4—4432no—
102C4×D4—4432no—
103#117—4431no—
104C24—4431no—
105#41—8864no—
106C2×Q8C2×D44311yescharacteristic, complemented
107C2×D4—4432no—
108C2×D4—4432no—
109C2×D4—4432no—
110C2×D4—4431no—
111C22×C4—8864no—
112C22×C4—4431no—
113C22×C4—4431no—
114C22×C4—4431no—
115C22×C4—4431no—
116C22×C4—4432no—
117C22×C4—4431no—
118C22×C4C2×D44311yescharacteristic
119C4⋊C4—4432no—
120C4⋊C4—4431no—
121C4⋊C4C2×D44311yescharacteristic, complemented
122C4⋊C4C2×D44312yescomplemented
123C22⋊C4—4432no—
124C22⋊C4—4432no—
125C22⋊C4—4432no—
126C22⋊C4—4432no—
127C22⋊C4C2×D44312yes—
128C42—4432no—
129C23—8862no—
130C23—8862no—
131C23—8862no—
132C23—4432no—
133C23—4431no—
134C23—4431no—
135C23C22×D44311yescharacteristic
136Q8—22no—
137D4—8864no—
138D4—8864no—
139D4—8864no—
140D4—8862no—
141C2×C4—22no—
142C2×C4—8862no—
143C2×C4—8862no—
144C2×C4—8864no—
145C2×C4—8862no—
146C2×C4—8862no—
147C2×C4—4432no—
148C2×C4—4431no—
149C2×C4—4431no—
150C2×C4—4434no—
151C2×C4C22×D44312yes—
152C2×C4C22×D44311yescharacteristic
153C2×C4C22×D44312yes—
154C2×C4C22×D44311yescharacteristic
155C22—21no—
156C22—21no—
157C22—8868no—
158C22—8861no—
159C22—8861no—
160C22—8861no—
161C22—8861no—
162C22—8862no—
163C22—8862no—
164C22—8862no—
165C22—4432no—
166C22—4432no—
167C22#2029678812yescomplemented
168C22C23×D44311yescharacteristic
169C4—21no—
170C4—22no—
171C4—22no—
172C4—8861no—
173C4—8862no—
174C4—4432no—
175C4D4×D44312yes—
176C2—22no—
177C2—8862no—
178C2—8862no—
179C2—17722no—
180C2C2×D4×D44311yescharacteristic
181C2#41×D44311yescharacteristic
182C2C2×#2029678811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D443
commutator, socle, cosocleC22×C443C24
FittingC22⋊Q8×C443C2
hypercenterC22⋊Q8D443
hypocenterC443#525
LCSG ▷ C22×C443 ▷ C443
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#20296788C2semidirect
2. C22×C4×D443C2semidirect
3. #28381871C2semidirect
4. #28381862C2semidirect
5. #28381861C2semidirect
6. #28381860C2semidirect
7. #28381856C2semidirect
8. #28381848C2semidirect
9. (C22⋊D443)⋊C4C2semidirect
10. #28381844C2semidirect
11. C22⋊Q8×C443C2semidirect
16. C2×D1772C22semidirect
24. C2×C4×D443C22semidirect
25. C4⋊Dic443C22semidirect
26. Dic443⋊C4C22semidirect
29. (C2×D443)⋊C4C22semidirect
30. (C2×D443)⋊C4C22semidirect
31. C4×Dic443C22semidirect
32. C2×Q8×C443C22semidirect
34. C4⋊C4×C443C22semidirect
35. C4⋊C4×C443C22semidirect
55. C4×D443D4semidirect
65. C22×C443#41semidirect
76. C2×D443#41semidirect
91. C443#525semidirect
97. C22⋊Q8D443semidirect
106. C2×Q8C2×D443semidirect
121. C4⋊C4C2×D443semidirect
122. C4⋊C4C2×D443semidirect
167. C22#20296788semidirect

Maximal subgroups

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

subgroupindex
C2×#202967882
C22×C4×D4432
#283818712
#283818622
#283818612
#283818602
#283818562
#283818482
(C22⋊D443)⋊C42
#283818442
C22⋊Q8×C4432
#525443