Finite Group Databasebeta

← #28401221

Subgroups — #28401221

Order 14464.

386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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#20299202C212yesmaximal, complemented
2#20299000C211yesmaximal, characteristic, complemented
3#20298962C212yesmaximal, complemented
4#20298848C212yesmaximal, complemented
5#20298831C212yesmaximal, complemented
6#20298710C212yesmaximal, complemented
7D8×Dic113C212yesmaximal, complemented
8#20298552C211yesmaximal, characteristic, complemented
9#493×C113C211yesmaximal, characteristic, complemented
10C2×#14268630C2211yescharacteristic
11C2×C8×D113C2211yescharacteristic
12#16813614C2212yes—
13#16813603—24no—
14#16813594—24no—
15#16813593C2214yes—
16D4×Dic113C2214yes—
17#16813579C2211yescharacteristic
18#16813556C2212yes—
19#16813554C2212yes—
20#16813543C2214yes—
21#16813543C2214yes—
22#16813533C2211yescharacteristic
23#16813532C2211yescharacteristic
24C8×Dic113C2211yescharacteristic
25C2×D8×C113C2212yes—
26C2×D8×C113C2212yes—
27#127×C113C2212yes—
28C4×C8×C113C2211yescharacteristic
29C2×C22⋊D113—24no—
30C22×Dic113—24no—
31C2×C4×D113C2311yescharacteristic
32#14268630—22no—
33C2×#11744751C2311yescharacteristic
34C2×#11744751C2311yescharacteristic
35C8×D113—22no—
36C4⋊Dic113C2314yes—
37#14268626—24no—
38#14268626D412yes—
39C22⋊Dic113—24no—
40C22⋊Dic113—24no—
41#14268624D412yes—
42C4×Dic113C2311yescharacteristic
43C2×D4×C113—24no—
44C2×D4×C113C2314yes—
45D8×C113—24no—
46D8×C113—24no—
47C2×C8×C113C2311yescharacteristic
48C2×C8×C113C2311yescharacteristic
49C42×C113C2311yescharacteristic
50C23×C113—24no—
51C22×D113C2×D411yescharacteristic
52D4×C113—24no—
53D4×C113—24no—
54D4×C113—84no—
55C2×C4×C113C2×D412yes—
56C2×C4×C113C2411yescharacteristic
57C22⋊D113—84no—
58C2×Dic113—24no—
59C2×Dic113—84no—
60C2×Dic113C2×D412yes—
61C2×Dic113C2×D411yescharacteristic
62C4×D113—21no—
63C4×D113—21no—
64C8×C113#4112yes—
65C8×C113#4112yes—
66#11744751—21no—
67#11744751—21no—
68C22×C113—44no—
69C22×C113—44no—
70C22×C113—44no—
71C22×C113C22×D411yescharacteristic
72C2×D113—21no—
73C2×D113—22no—
74C4×C113—22no—
75C4×C113C2×#4111yescharacteristic
76C4×C113C2×#4111yescharacteristic
77Dic113—21no—
78Dic113—22no—
79Dic113—44no—
80C2×C113—84no—
81C2×C113#53211yescharacteristic
82C2×C113#57612yes—
83D113—41no—
84#3176—1131nomaximal, Sylow
85C113#317611yescharacteristic, complemented, Sylow
86#540—1132no—
87#499—1131no—
88#493D11311yescharacteristic, complemented
89#490—1132no—
90#469—1132no—
91#466—1132no—
92#442—1132no—
93C4×D8—1132no—
94#405—1131no—
95C2×D8C2×D11312yes—
96C2×D8C2×D11312yes—
97C2×M16—1131no—
98C22×C8—1131no—
99#127C2×D11312yes—
100#125—1132no—
101#123—2264no—
102#121—1134no—
103#121—2264no—
104C4×D4—1134no—
105#117—1131no—
106#107—1132no—
107#106—1132no—
108#102—1134no—
109#102—1134no—
110#97—1131no—
111#97—1131no—
112C4×C8—1131no—
113C4×C8C2×D11311yescharacteristic
114C2×D4—24no—
115C2×D4—2264no—
116C2×D4C22×D11314yes—
117C22×C4—1131no—
118C22×C4—2264no—
119D8—24no—
120D8—24no—
121M16—2262no—
122C2×C8—1131no—
123C2×C8—1131no—
124C2×C8—2262no—
125C2×C8C22×D11311yescharacteristic
126C2×C8C22×D11311yescharacteristic
127C4⋊C4—1132no—
128C4⋊C4—1134no—
129C4⋊C4—2264no—
130C22⋊C4—1132no—
131C22⋊C4—2264no—
132C22⋊C4—2264no—
133C42—1131no—
134C42C22×D11311yescharacteristic
135C23—24no—
136C23—1131no—
137D4—24no—
138D4—24no—
139D4—84no—
140D4—9044no—
141C2×C4—1132no—
142C2×C4—1131no—
143C2×C4—9044no—
144C2×C4—2264no—
145C2×C4—2261no—
146C2×C4—2261no—
147C2×C4D4×D11312yes—
148C2×C4C23×D11311yescharacteristic
149C8—2261no—
150C8—2261no—
151C8#1426864612yes—
152C8#1426864612yes—
153C22—44no—
154C22—44no—
155C22—44no—
156C22—2262no—
157C22—2261no—
158C22C2×D4×D11311yescharacteristic
159C4—22no—
160C4—4524no—
161C4—2262no—
162C4—2261no—
163C4C2×#1426864611yescharacteristic
164C4C2×#1426864611yescharacteristic
165C2—84no—
166C2—4521no—
167C2#2029914611yescharacteristic
168C2#2029939912yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#493×C113C2
socleC22×C113C22×D4
hypercenter#493D113
hypocenterC113#3176
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #20299202C2semidirect
2. #20299000C2semidirect
3. #20298962C2semidirect
4. #20298848C2semidirect
5. #20298831C2semidirect
6. #20298710C2semidirect
7. D8×Dic113C2semidirect
8. #20298552C2semidirect
9. #493×C113C2semidirect
85. C113#3176semidirect
88. #493D113semidirect

Maximal subgroups

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

subgroupindex
#202992022
#202990002
#202989622
#202988482
#202988312
#202987102
D8×Dic1132
#202985522
#493×C1132
#3176113