Finite Group Databasebeta

← #28390675

Subgroups — #28390675

Order 14464.

262 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 81 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#41×Dic113C211yesmaximal, characteristic
2#20298582C211yesmaximal, characteristic
3#20298357C212yesmaximal, complemented
4#20298354C212yesmaximal, complemented
5#410×C113C211yesmaximal, characteristic
6C2×#14268631C2212yes—
7Q8×Dic113—21no—
8D4×Dic113—21no—
9D4×Dic113—22no—
10#16813581C412yescomplemented
11#16813581C2211yescharacteristic
12C2×C4×Dic113C412yescomplemented
13C2×C4×Dic113C2211yescharacteristic
14#16813541—21no—
15#16813539—21no—
16C2×#41×C113C2211yescharacteristic
17#117×C113C2212yes—
18#99×C113—22no—
19C22×Dic113—22no—
20C22×Dic113—21no—
21#14268631—22no—
22#14268631—22no—
23C2×#11744751—22no—
24C4⋊Dic113—22no—
25C4⋊Dic113—21no—
26C22⋊Dic113—22no—
27C22⋊Dic113—21no—
28C4×Dic113—22no—
29C4×Dic113—21no—
30C4×Dic113C2×C411yescharacteristic
31C4×Dic113C2×C412yes—
32C4×Dic113C2×C411yescharacteristic
33#41×C113—22no—
34#41×C113—22no—
35C2×Q8×C113D411yescharacteristic
36C2×D4×C113D411yescharacteristic
37C2×D4×C113D412yes—
38C22×C4×C113C2×C412yes—
39C22×C4×C113C2311yescharacteristic
40C4⋊C4×C113—22no—
41C22⋊C4×C113—22no—
42C42×C113—22no—
43C23×C113C22⋊C412yes—
44C23×C113C2×D411yescharacteristic
45Q8×C113—22no—
46D4×C113—24no—
47D4×C113—22no—
48C2×C4×C113—22no—
49C2×C4×C113—22no—
50C2×C4×C113—42no—
51C2×C4×C113C22⋊C412yes—
52C2×C4×C113C22×C411yescharacteristic
53C2×C4×C113C2×D411yescharacteristic
54C2×C4×C113#4112yes—
55C2×C4×C113#4112yes—
56C2×Dic113—21no—
57C2×Dic113—22no—
58C2×Dic113—21no—
59C2×Dic113—42no—
60C2×Dic113—44no—
61#11744751—42no—
62C22×C113—22no—
63C22×C113—41no—
64C22×C113—42no—
65C22×C113C2×C22⋊C411yescharacteristic
66C22×C113#12312yes—
67C4×C113—22no—
68C4×C113—82no—
69C4×C113#11711yescharacteristic
70C4×C113#11711yescharacteristic
71C4×C113#12312yes—
72Dic113—22no—
73Dic113—42no—
74Dic113—41no—
75C2×C113—21no—
76C2×C113—22no—
77C2×C113—42no—
78C2×C113#38111yescharacteristic
79#1827—1131nomaximal, Sylow
80C113#182711yescharacteristic, complemented, Sylow
81C4×#41—1131no—
82#413—1131no—
83#410D11311yescharacteristic
84#339—1132no—
85H(3,ℤ/4)—1132no—
86C2×#41C2×D11311yescharacteristic
87C2×M16—1132no—
88C4×Q8—2261no—
89C4×D4—2261no—
90C4×D4—2262no—
91#117—1132no—
92#117—1131no—
93#117C2×D11312yes—
94C2×C42—1132no—
95C2×C42—1131no—
96#101—2261no—
97#100—2261no—
98#99—22no—
99#41—22no—
100#41—22no—
101C2×Q8D45211yescharacteristic
102C2×D4D45211yescharacteristic
103C2×D4C22⋊D11312yes—
104C22×C4—2262no—
105C22×C4—2261no—
106C22×C4C4×D11312yes—
107C22×C4C22×D11311yescharacteristic
108M16—2262no—
109M16—2262no—
110C2×C8—2262no—
111C4⋊C4—22no—
112C4⋊C4—2262no—
113C4⋊C4—2261no—
114C22⋊C4—22no—
115C22⋊C4—2262no—
116C22⋊C4—2261no—
117C42—22no—
118C42—1131no—
119C42—1132no—
120C42—1131no—
121C42—2262no—
122C42—2261no—
123C23#1426862412yes—
124C23C2×C22⋊D11311yescharacteristic
125Q8—22no—
126D4—24no—
127D4—22no—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—42no—
131C2×C4—4522no—
132C2×C4—4524no—
133C2×C4—2262no—
134C2×C4—2261no—
135C2×C4—2261no—
136C2×C4#1426862412yes—
137C2×C4C2×C4×D11311yescharacteristic
138C2×C4C2×D45211yescharacteristic
139C2×C4#1426864612yes—
140C2×C4#1426864612yes—
141C8—4522no—
142C22—22no—
143C22—41no—
144C22—42no—
145C22C2×#1426862411yescharacteristic
146C22#1681360312yes—
147C4—22no—
148C4—82no—
149C4—4521no—
150C4—4522no—
151C4—2262no—
152C4#1681357811yescharacteristic
153C4#1681357811yescharacteristic
154C4#1681360612yes—
155C2—22no—
156C2—21no—
157C2—42no—
158C2#2029845911yescharacteristic
subgroupG/H
centerC4#16813578
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#410×C113C2
socleC2×C113#381
prime radicalC2×#41×C113C22
cosocleC22×C4×C113C23
hypercenter#410D113
hypocenterC113#1827
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #20298357C2semidirect
4. #20298354C2semidirect
10. #16813581C4semidirect
12. C2×C4×Dic113C4semidirect
80. C113#1827semidirect

Maximal subgroups

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

subgroupindex
#41×Dic1132
#202985822
#202983572
#202983542
#410×C1132
#1827113