Finite Group Databasebeta

← #28391727

Subgroups — #28391727

Order 14464.

282 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 71 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
1#20298602C212yesmaximal
2#20298499C211yesmaximal, characteristic
3#20298367C211yesmaximal, characteristic, complemented
4#20298357C212yesmaximal, complemented
5#544×C113C211yesmaximal, characteristic, complemented
6C22×D452C2211yescharacteristic
7C2×#14268631C2212yes—
8C2×#14268624—22no—
9C2×C4×Dic113C2211yescharacteristic
10#16813542—22no—
11#16813542—22no—
12C4⋊Q8×C113—22no—
13#125×C113—22no—
14C22⋊Q8×C113—22no—
15#117×C113C2212yes—
16C2×C4⋊C4×C113C2211yescharacteristic
17C23×D113—21no—
18C2×D452—22no—
19C2×D452—22no—
20C2×D452—21no—
21C2×D452Q812yescomplemented
22C22×Dic113—21no—
23#14268631—22no—
24#14268631—22no—
25C2×#11744751—22no—
26#14268624—44no—
27C4×Dic113—22no—
28C2×Q8×C113—22no—
29C22×C4×C113D412yes—
30C22×C4×C113C2311yescharacteristic
31C4⋊C4×C113—22no—
32C4⋊C4×C113—24no—
33C4⋊C4×C113—22no—
34C4⋊C4×C113D412yes—
35C4⋊C4×C113D412yes—
36C22⋊C4×C113—22no—
37C42×C113—22no—
38C23×C113C2×D411yescharacteristic
39C22×D113—22no—
40C22×D113—42no—
41C22×D113—42no—
42C22×D113—41no—
43C22×D113—41no—
44Q8×C113—82no—
45C2×C4×C113—22no—
46C2×C4×C113—22no—
47C2×C4×C113—22no—
48C2×C4×C113—42no—
49C2×C4×C113C2×D412yes—
50C2×C4×C113C2×Q811yescharacteristic
51C2×C4×C113#4112yes—
52C2×C4×C113#4111yescharacteristic
53C2×Dic113—22no—
54C2×Dic113—41no—
55C2×Dic113—41no—
56D452—24no—
57D452—42no—
58#11744751—42no—
59C22×C113—21no—
60C22×C113—21no—
61C22×C113#12011yescharacteristic
62C22×C113C22⋊Q811yescharacteristic
63C22×C113#12411yescharacteristic
64C2×D113—44no—
65C2×D113—42no—
66C2×D113—82no—
67C2×D113—81no—
68C2×D113—81no—
69C4×C113—42no—
70C4×C113—42no—
71C4×C113—42no—
72C4×C113C22⋊Q812yes—
73C4×C113#12412yes—
74Dic113—42no—
75C2×C113—21no—
76C2×C113—21no—
77C2×C113#39311yescharacteristic
78C2×C113#45311yescharacteristic
79C2×C113#45411yescharacteristic
80D113—82no—
81#2027—1131nomaximal, Sylow
82C113#202711yescharacteristic, complemented, Sylow
83#544D11311yescharacteristic, complemented
84#418—1132no—
85#390—1131no—
86#343—1131no—
87#339—1132no—
88C22×D4—1131no—
89C2×M16—1132no—
90C4⋊Q8—22no—
91#125—22no—
92C22⋊Q8—22no—
93#117C2×D11312yes—
94C2×C4⋊C4C2×D11311yescharacteristic
95C2×C22⋊C4—2262no—
96C2×C42—1131no—
97#102—2262no—
98#102—2262no—
99C24—2261no—
100C2×Q8—22no—
101C2×D4—1132no—
102C2×D4—2262no—
103C2×D4—2261no—
104C2×D4—2262no—
105C22×C4—2261no—
106C22×C4C22⋊D11312yes—
107C22×C4C22×D11311yescharacteristic
108M16—2262no—
109M16—2262no—
110C2×C8—2262no—
111C4⋊C4—22no—
112C4⋊C4—24no—
113C4⋊C4—22no—
114C4⋊C4C22⋊D11312yes—
115C4⋊C4C22⋊D11312yes—
116C22⋊C4—22no—
117C22⋊C4—4524no—
118C42—22no—
119C42—2262no—
120C23—4522no—
121C23—4522no—
122C23—4521no—
123C23—4521no—
124C23—2262no—
125C23C2×C22⋊D11311yescharacteristic
126Q8—82no—
127D4—4522no—
128D4—2264no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—42no—
133C2×C4—4521no—
134C2×C4—4521no—
135C2×C4—2262no—
136C2×C4C2×C22⋊D11312yes—
137C2×C4Q8×D11311yescharacteristic
138C2×C4#1426864812yes—
139C2×C4#1426864811yescharacteristic
140C8—4522no—
141C22—21no—
142C22—21no—
143C22—9042no—
144C22—9041no—
145C22—9041no—
146C22—4524no—
147C22—4522no—
148C22#1681359111yescharacteristic
149C22#1681359811yescharacteristic
150C22#1681361111yescharacteristic
151C4—42no—
152C4—42no—
153C4—42no—
154C4—4522no—
155C4#1681359812yes—
156C4#1681361112yes—
157C2—21no—
158C2—21no—
159C2—9042no—
160C2#2029850911yescharacteristic
161C2#2029876611yescharacteristic
162C2#2029877111yescharacteristic
subgroupG/H
centerC22#16813591
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#544×C113C2
socleC22×C113#120
prime radicalC22×D452C22
hypercenter#544D113
hypocenterC113#2027
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
3. #20298367C2semidirect
4. #20298357C2semidirect
5. #544×C113C2semidirect
21. C2×D452Q8semidirect
82. C113#2027semidirect
83. #544D113semidirect

Maximal subgroups

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

subgroupindex
#202986022
#202984992
#202983672
#202983572
#544×C1132
#2027113