Finite Group Databasebeta

← #43248225

Subgroups — #43248225

Order 28352.

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

normal subgroups only

This group has 330 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×#20296786C211yesmaximal, characteristic, complemented
2C22×C4×D443C211yesmaximal, characteristic, complemented
3#28381869C211yesmaximal, characteristic, complemented
4#28381864C212yesmaximal, complemented
5#28381859C212yesmaximal, complemented
6#28381856C211yesmaximal, characteristic, complemented
7#28381854C211yesmaximal, characteristic, complemented
8#28381848C212yesmaximal, complemented
9(C22⋊D443)⋊C4C212yesmaximal, complemented
10#28381842C211yesmaximal, characteristic, complemented
11#123×C443C211yesmaximal, characteristic, complemented
12C23×D443C2211yescharacteristic
13#20296786—24no—
14C2×Dic886C2211yescharacteristic, complemented
15C2×D1772C2212yes—
16C2×C22⋊D443C2212yes—
17C2×C22⋊D443C2211yescharacteristic
18C2×C22⋊D443C2211yescharacteristic, complemented
19C22×Dic443C2211yescharacteristic
20C22×Dic443C2211yescharacteristic, complemented
21C2×C4×D443—24no—
22C2×C4×D443C2212yes—
23C2×C4×D443C2212yes—
24C2×C4×D443C2211yescharacteristic, complemented
25Dic443⋊C4C2212yescomplemented
26Dic443⋊C4C2212yescomplemented
27C22⋊Dic443C2211yescharacteristic
28(C2×D443)⋊C4C2212yes—
29(C2×D443)⋊C4C2212yes—
30(C2×D443)⋊C4C2212yescomplemented
31C4×Dic443C2212yescomplemented
32C2×D4×C443C2211yescharacteristic
33C22×C4×C443C2211yescharacteristic
34C4⋊C4×C443C2212yescomplemented
35C22⋊C4×C443C2211yescharacteristic
36C22⋊C4×C443C2212yescomplemented
37C22×D443—22no—
38C22×D443—24no—
39C22×D443C2311yescharacteristic
40C22×D443C2312yes—
41Dic886—22no—
42D1772—24no—
43C22⋊D443—22no—
44C22⋊D443—24no—
45C22⋊D443—22no—
46C2×Dic443—22no—
47C2×Dic443D414yescomplemented
48C2×Dic443C2312yes—
49C2×Dic443C2311yescharacteristic
50C2×Dic443C2311yescharacteristic
51C2×Dic443C2311yescharacteristic
52C4×D443—24no—
53C4×D443—24no—
54C4×D443—22no—
55C23×C443C2311yescharacteristic
56C23×C443C2311yescharacteristic
57D4×C443—22no—
58C2×C4×C443—22no—
59C2×C4×C443C2312yes—
60C2×C4×C443C2312yes—
61C2×C4×C443C2311yescharacteristic
62C22×C443—22no—
63C22×C443—21no—
64C22×C443—22no—
65C22×C443C2×D412yes—
66C22×C443C2411yescharacteristic
67C2×D443—28no—
68C2×D443—22no—
69C2×D443—22no—
70C2×D443—21no—
71C2×D443—22no—
72C2×D443#4114yescomplemented
73C4×C443—22no—
74C4×C443—21no—
75C4×C443—22no—
76Dic443—21no—
77Dic443—22no—
78Dic443C2×D412yes—
79Dic443C2×D412yes—
80C2×C443—22no—
81C2×C443—41no—
82C2×C443C22×D411yescharacteristic
83C2×C443C2×#4112yes—
84D443—24no—
85D443—41no—
86C443#52511yescharacteristic, complemented, Sylow
87#525—4431nomaximal, Sylow
88C2×#41—4431no—
89C23×C4—4431no—
90#123—4431no—
91#123D44311yescharacteristic, complemented
92C22⋊Q8—4432no—
93#121—4432no—
94#120—4431no—
95#120—4431no—
96C4×D4—4432no—
97C4×D4—4432no—
98#117—4431no—
99C24—4431no—
100#41—8864no—
101C2×Q8—4431no—
102C2×D4—4432no—
103C2×D4—4431no—
104C2×D4—4431no—
105C2×D4—4432no—
106C2×D4C2×D44311yescharacteristic
107C22×C4—8864no—
108C22×C4—4431no—
109C22×C4—4432no—
110C22×C4—4432no—
111C22×C4—4431no—
112C22×C4—4431no—
113C22×C4C2×D44311yescharacteristic
114C4⋊C4—4432no—
115C4⋊C4—4432no—
116C4⋊C4C2×D44312yescomplemented
117C22⋊C4—4431no—
118C22⋊C4—4432no—
119C22⋊C4—4432no—
120C22⋊C4—4432no—
121C22⋊C4C2×D44311yescharacteristic
122C22⋊C4C2×D44312yescomplemented
123C42—4432no—
124C23—8864no—
125C23—8862no—
126C23—4431no—
127C23—4432no—
128C23C22×D44311yescharacteristic
129C23C22×D44311yescharacteristic
130Q8—8862no—
131D4—22no—
132D4—8864no—
133D4—8864no—
134D4—8862no—
135D4—8862no—
136C2×C4—22no—
137C2×C4—8864no—
138C2×C4—8864no—
139C2×C4—8862no—
140C2×C4—8862no—
141C2×C4—4432no—
142C2×C4—4431no—
143C2×C4—4434no—
144C2×C4—4431no—
145C2×C4—4431no—
146C2×C4C22×D44312yes—
147C2×C4C22×D44311yescharacteristic
148C2×C4C22×D44312yes—
149C22—22no—
150C22—21no—
151C22—22no—
152C22—8868no—
153C22—8862no—
154C22—8862no—
155C22—8861no—
156C22—8862no—
157C22—4434no—
158C22D4×D44312yes—
159C22C23×D44311yescharacteristic
160C4—22no—
161C4—21no—
162C4—22no—
163C4—8861no—
164C4—8862no—
165C4—4432no—
166C4—4432no—
167C2—22no—
168C2—41no—
169C2—8864no—
170C2—17721no—
171C2C2×D4×D44311yescharacteristic
172C2#41×D44312yes—
subgroupG/H
center, FrattiniC22C23×D443
commutator, socle, cosocleC22×C443C24
Fitting#123×C443C2
hypercenter#123D443
hypocenterC443#525
LCSG ▷ C22×C443 ▷ C443
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#20296786C2semidirect
2. C22×C4×D443C2semidirect
3. #28381869C2semidirect
4. #28381864C2semidirect
5. #28381859C2semidirect
6. #28381856C2semidirect
7. #28381854C2semidirect
8. #28381848C2semidirect
9. (C22⋊D443)⋊C4C2semidirect
10. #28381842C2semidirect
11. #123×C443C2semidirect
14. C2×Dic886C22semidirect
18. C2×C22⋊D443C22semidirect
20. C22×Dic443C22semidirect
24. C2×C4×D443C22semidirect
25. Dic443⋊C4C22semidirect
26. Dic443⋊C4C22semidirect
30. (C2×D443)⋊C4C22semidirect
31. C4×Dic443C22semidirect
34. C4⋊C4×C443C22semidirect
36. C22⋊C4×C443C22semidirect
47. C2×Dic443D4semidirect
72. C2×D443#41semidirect
86. C443#525semidirect
91. #123D443semidirect
116. C4⋊C4C2×D443semidirect
122. C22⋊C4C2×D443semidirect

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
#283818692
#283818642
#283818592
#283818562
#283818542
#283818482
(C22⋊D443)⋊C42
#283818422
#123×C4432
#525443