Finite Group Databasebeta

← #43248227

Subgroups — #43248227

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×#20296786C211yesmaximal, characteristic, complemented
2C22×C4×D443C211yesmaximal, characteristic, complemented
3#28381868C212yesmaximal, complemented
4#28381866C211yesmaximal, characteristic, complemented
5#28381865C211yesmaximal, characteristic, complemented
6#28381857C211yesmaximal, characteristic, complemented
7#28381854C212yesmaximal, complemented
8D4×Dic443C212yesmaximal, complemented
9(C22⋊D443)⋊C4C212yesmaximal, complemented
10#28381844C211yesmaximal, characteristic, complemented
11#121×C443C211yesmaximal, characteristic, complemented
12C23×D443C2211yescharacteristic
13#20296786—24no—
14C2×Dic886C2211yescharacteristic, complemented
15C2×C22⋊D443C2212yes—
16C2×C22⋊D443C2212yes—
17C22×Dic443C2211yescharacteristic
18C22×Dic443C2212yescomplemented
19C2×C4×D443—24no—
20C2×C4×D443C2211yescharacteristic
21C2×C4×D443C2211yescharacteristic
22C2×C4×D443C2211yescharacteristic
23C2×C4×D443C2211yescharacteristic
24C4⋊Dic443C2211yescharacteristic, complemented
25C4⋊Dic443C2212yescomplemented
26Dic443⋊C4C2212yescomplemented
27C22⋊Dic443C2212yes—
28C22⋊Dic443C2212yescomplemented
29(C2×D443)⋊C4C2212yes—
30(C2×D443)⋊C4C2212yes—
31C4×Dic443C2212yescomplemented
32C2×D4×C443C2212yes—
33C2×D4×C443C2211yescharacteristic, complemented
34C22×C4×C443C2211yescharacteristic
35C4⋊C4×C443C2211yescharacteristic, complemented
36C22⋊C4×C443C2212yescomplemented
37C22×D443—22no—
38C22×D443—22no—
39C22×D443—22no—
40C22×D443C2311yescharacteristic
41C22×D443C2311yescharacteristic
42Dic886—22no—
43C22⋊D443—24no—
44C22⋊D443—24no—
45C2×Dic443—22no—
46C2×Dic443—24no—
47C2×Dic443C2312yes—
48C2×Dic443C2312yes—
49C2×Dic443C2311yescharacteristic
50C2×Dic443C2311yescharacteristic
51C4×D443—22no—
52C4×D443—22no—
53C4×D443—22no—
54C4×D443D414yescomplemented
55C23×C443C2312yes—
56C23×C443C2311yescharacteristic
57D4×C443—24no—
58D4×C443—22no—
59C2×C4×C443—22no—
60C2×C4×C443C2311yescharacteristic
61C2×C4×C443C2312yes—
62C2×C4×C443C2311yescharacteristic
63C22×C443—21no—
64C22×C443—21no—
65C22×C443—22no—
66C22×C443—22no—
67C22×C443—22no—
68C22×C443#4112yescomplemented
69C22×C443C2411yescharacteristic
70C2×D443—28no—
71C2×D443—21no—
72C2×D443—21no—
73C2×D443—21no—
74C2×D443—21no—
75C2×D443C2×D412yes—
76C2×D443#4112yescomplemented
77C4×C443—21no—
78C4×C443—22no—
79C4×C443C2×D412yes—
80Dic443—21no—
81Dic443—22no—
82Dic443—22no—
83Dic443C2×D412yes—
84C2×C443—22no—
85C2×C443—42no—
86C2×C443C22×D411yescharacteristic
87C2×C443C2×#4111yescharacteristic
88C2×C443C2×#4111yescharacteristic
89D443—22no—
90D443—22no—
91C443#52511yescharacteristic, complemented, Sylow
92#525—4431nomaximal, Sylow
93C2×#41—4431no—
94C23×C4—4431no—
95#123—4432no—
96C22⋊Q8—4431no—
97C22⋊Q8—4431no—
98#121—4431no—
99#121D44311yescharacteristic, complemented
100#120—4432no—
101C4×D4—4432no—
102C4×D4—4432no—
103#117—4431no—
104C24—4431no—
105#41—8864no—
106C2×Q8—4431no—
107C2×D4—4432no—
108C2×D4—4432no—
109C2×D4C2×D44312yes—
110C2×D4C2×D44311yescharacteristic, complemented
111C22×C4—8864no—
112C22×C4—4431no—
113C22×C4—4432no—
114C22×C4—4431no—
115C22×C4—4431no—
116C22×C4—4431no—
117C22×C4—4431no—
118C22×C4C2×D44311yescharacteristic
119C4⋊C4—4432no—
120C4⋊C4—4431no—
121C4⋊C4—4432no—
122C4⋊C4C2×D44311yescharacteristic, complemented
123C22⋊C4—4432no—
124C22⋊C4—4432no—
125C22⋊C4—4432no—
126C22⋊C4—4432no—
127C22⋊C4C2×D44312yescomplemented
128C42—4432no—
129C23—8862no—
130C23—8862no—
131C23—8862no—
132C23—4431no—
133C23—4431no—
134C23C22×D44312yes—
135C23C22×D44311yescharacteristic
136Q8—8862no—
137D4—24no—
138D4—22no—
139D4—8864no—
140D4—8864no—
141C2×C4—22no—
142C2×C4—8862no—
143C2×C4—8862no—
144C2×C4—8862no—
145C2×C4—8864no—
146C2×C4—8862no—
147C2×C4—4432no—
148C2×C4—4431no—
149C2×C4—4432no—
150C2×C4—4431no—
151C2×C4—4434no—
152C2×C4C22×D44312yes—
153C2×C4C22×D44311yescharacteristic
154C2×C4C22×D44311yescharacteristic
155C22—21no—
156C22—21no—
157C22—22no—
158C22—22no—
159C22—22no—
160C22—8868no—
161C22—8861no—
162C22—8861no—
163C22—8861no—
164C22—8861no—
165C22—4432no—
166C22—4432no—
167C22#2029678612yescomplemented
168C22C23×D44311yescharacteristic
169C4—21no—
170C4—22no—
171C4—8861no—
172C4—8862no—
173C4—8862no—
174C4—4432no—
175C4D4×D44312yes—
176C2—22no—
177C2—42no—
178C2—8862no—
179C2—8862no—
180C2C2×D4×D44311yescharacteristic
181C2#41×D44311yescharacteristic
182C2C2×#2029678611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D443
commutator, socle, cosocleC22×C443C24
Fitting#121×C443C2
hypercenter#121D443
hypocenterC443#525
LCSG ▷ C22×C443 ▷ C443
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#20296786C2semidirect
2. C22×C4×D443C2semidirect
3. #28381868C2semidirect
4. #28381866C2semidirect
5. #28381865C2semidirect
6. #28381857C2semidirect
7. #28381854C2semidirect
8. D4×Dic443C2semidirect
9. (C22⋊D443)⋊C4C2semidirect
10. #28381844C2semidirect
11. #121×C443C2semidirect
14. C2×Dic886C22semidirect
18. C22×Dic443C22semidirect
24. C4⋊Dic443C22semidirect
25. C4⋊Dic443C22semidirect
26. Dic443⋊C4C22semidirect
28. C22⋊Dic443C22semidirect
31. C4×Dic443C22semidirect
33. C2×D4×C443C22semidirect
35. C4⋊C4×C443C22semidirect
36. C22⋊C4×C443C22semidirect
54. C4×D443D4semidirect
68. C22×C443#41semidirect
76. C2×D443#41semidirect
91. C443#525semidirect
99. #121D443semidirect
110. C2×D4C2×D443semidirect
122. C4⋊C4C2×D443semidirect
127. C22⋊C4C2×D443semidirect
167. C22#20296786semidirect

Maximal subgroups

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

subgroupindex
C2×#202967862
C22×C4×D4432
#283818682
#283818662
#283818652
#283818572
#283818542
D4×Dic4432
(C22⋊D443)⋊C42
#283818442
#121×C4432
#525443