Finite Group Databasebeta

← #28393854

Subgroups — #28393854

Order 14464.

840 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 163 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×#16813584C213yesmaximal, complemented
2C2×#16813582C213yesmaximal, complemented
3#20298533C213yesmaximal, complemented
4#20298508C211yesmaximal, characteristic, complemented
5#20298507C213yesmaximal, complemented
6#20298443C211yesmaximal, characteristic, complemented
7#399×C113C211yesmaximal, characteristic, complemented
8C22×D452C2213yes—
9C22×C22⋊D113C2213yes—
10C23×Dic113C2211yescharacteristic
11C22×C4×D113C2213yes—
12#16813584—212no—
13#16813582—212no—
14C2×#14268626C2213yes—
15C2×#14268624C2216yes—
16C2×#14268624C2213yes—
17C2×C4×Dic113C2213yes—
18#16813529C2213yes—
19C2×C4⋊C4×C113C2213yes—
20C2×C22⋊C4×C113C2213yes—
21#95×C113C2211yescharacteristic
22C23×D113C2313yes—
23C2×D452—212no—
24C2×D452—26no—
25C2×C22⋊D113—26no—
26C2×C22⋊D113—26no—
27C2×C22⋊D113—26no—
28C22×Dic113—26no—
29C22×Dic113C2311yescharacteristic
30C22×Dic113C2313yes—
31C22×Dic113C2311yescharacteristic
32C2×C4×D113—26no—
33C2×C4×D113—212no—
34#14268626—26no—
35#14268624—26no—
36#14268624—212no—
37C4×Dic113D4112yescomplemented
38C24×C113C2311yescharacteristic
39C22×C4×C113C2313yes—
40C22×C4×C113C2313yes—
41C4⋊C4×C113—26no—
42C22⋊C4×C113—26no—
43C23×C113—23no—
44C23×C113—23no—
45C23×C113#4112yes—
46C23×C113C2411yescharacteristic
47C22×D113—23no—
48C22×D113—26no—
49C22×D113—23no—
50C22×D113—26no—
51C22×D113#4116yes—
52C2×C4×C113—26no—
53C2×C4×C113—23no—
54C2×C4×C113—26no—
55C2×C4×C113C2×D416yes—
56C22⋊D113—224no—
57C2×Dic113—23no—
58C2×Dic113—23no—
59C2×Dic113—23no—
60C2×Dic113—44no—
61C2×Dic113C2×D416yes—
62C2×Dic113C2×D416yes—
63D452—224no—
64C4×D113—412no—
65C22×C113—26no—
66C22×C113—43no—
67C22×C113—41no—
68C22×C113C22×D413yes—
69C22×C113C2×#4113yes—
70C22×C113C2×#4111yescharacteristic
71C2×D113—212no—
72C2×D113—26no—
73C2×D113—43no—
74C2×D113—46no—
75C2×D113—43no—
76C4×C113—26no—
77C4×C113—43no—
78Dic113—26no—
79Dic113—41no—
80Dic113#12714yes—
81C2×C113—42no—
82C2×C113#52513yes—
83C2×C113#52513yes—
84C2×C113C2×#12711yescharacteristic
85D113—46no—
86#2397—1131nomaximal, Sylow
87C113#239711yescharacteristic, complemented, Sylow
88C2×C4×D4—1133no—
89C2×C4×D4—1133no—
90#399—1133no—
91#399D11311yescharacteristic, complemented
92#392—1133no—
93#392—1131no—
94#376—1131no—
95C22×D4—1133no—
96C22×D4—1133no—
97C23×C4—1131no—
98C23×C4—1133no—
99C4×D4—22612no—
100C4×D4—22612no—
101C2×C4⋊C4—1133no—
102C2×C4⋊C4C2×D11313yes—
103C2×C22⋊C4—1136no—
104C2×C22⋊C4—1133no—
105C2×C22⋊C4C2×D11313yes—
106C2×C42—1133no—
107#95—1133no—
108#95C2×D11311yescharacteristic
109C24—1133no—
110C24C22×D11311yescharacteristic
111C2×D4—22612no—
112C2×D4—2266no—
113C2×D4—2266no—
114C2×D4—2266no—
115C2×D4—2266no—
116C22×C4—1131no—
117C22×C4—1133no—
118C22×C4—1131no—
119C22×C4—2266no—
120C22×C4—22612no—
121C22×C4—2266no—
122C22×C4C22×D11313yes—
123C22×C4C22×D11313yes—
124C4⋊C4—26no—
125C4⋊C4—2266no—
126C22⋊C4—26no—
127C22⋊C4—22612no—
128C22⋊C4—2266no—
129C42—11312no—
130C23—23no—
131C23—23no—
132C23—1136no—
133C23—2263no—
134C23—2266no—
135C23—2266no—
136C23—2263no—
137C23#1426864812yes—
138C23C23×D11311yescharacteristic
139D4—22624no—
140D4—22624no—
141C2×C4—26no—
142C2×C4—23no—
143C2×C4—26no—
144C2×C4—1136no—
145C2×C4—1136no—
146C2×C4—45212no—
147C2×C4—4524no—
148C2×C4—2263no—
149C2×C4—2263no—
150C2×C4—2263no—
151C2×C4D4×D11316yes—
152C22—26no—
153C22—43no—
154C22—41no—
155C22—4523no—
156C22—4526no—
157C22—4523no—
158C22—22612no—
159C22—2266no—
160C22C2×D4×D11313yes—
161C22#41×D11313yes—
162C22C2×#1426864811yescharacteristic
163C4—26no—
164C4—43no—
165C4—1134no—
166C4—4521no—
167C4—2266no—
168C2—42no—
169C2—4526no—
170C2#2029910613yes—
171C2#2029911113yes—
172C2#127×D11311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutator, socle, cosocleC23×C113C24
Fitting#399×C113C2
hypercenter#399D113
hypocenterC113#2397
LCSG ▷ C23×C113 ▷ C113
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#16813584C2semidirect
2. C2×#16813582C2semidirect
3. #20298533C2semidirect
4. #20298508C2semidirect
5. #20298507C2semidirect
6. #20298443C2semidirect
7. #399×C113C2semidirect
37. C4×Dic113D4semidirect
87. C113#2397semidirect
91. #399D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168135842
C2×#168135822
#202985332
#202985082
#202985072
#202984432
#399×C1132
#2397113