Finite Group Databasebeta

← #28334776

Subgroups — #28334776

Order 13696.

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

normal subgroups only

This group has 332 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
1C2×(C22⋊D107)⋊C4C211yesmaximal, characteristic
2C22⋊C8×D107C212yesmaximal, complemented
3#20292352C212yesmaximal, complemented
4#20292351C211yesmaximal, characteristic, complemented
5#323×C107C211yesmaximal, characteristic, complemented
6C22×C22⋊D107C411yescharacteristic
7C23×Dic107C411yescharacteristic
8C22×C4×D107C2211yescharacteristic
9C2×C8×D107—22no—
10(C22⋊D107)⋊C4—22no—
11(C22⋊D107)⋊C4—22no—
12C2×Dic107⋊C4C2211yescharacteristic
13C2×(C2×D107)⋊C4C411yescharacteristic
14C2×C4×Dic107C411yescharacteristic
15C22⋊(C107⋊C8)C2212yes—
16(C2×D107)⋊C8—22no—
17C2×C22⋊C4×C107C2211yescharacteristic
18C22⋊C8×C107C2212yes—
19C23×D107C2×C411yescharacteristic
20C2×C22⋊D107—22no—
21C2×C22⋊D107—22no—
22C2×C22⋊D107C814yescomplemented
23C22×Dic107—21no—
24C22×Dic107—21no—
25C22×Dic107—42no—
26C22×Dic107C2×C411yescharacteristic
27C22×Dic107C2×C411yescharacteristic
28C22×Dic107C2×C411yescharacteristic
29C2×C4×D107—42no—
30C2×C4×D107D412yes—
31C2×C4×D107D412yes—
32C2×C107⋊C8—22no—
33C8×D107—44no—
34Dic107⋊C4—22no—
35(C2×D107)⋊C4—22no—
36C4×Dic107—21no—
37C4×Dic107—21no—
38C24×C107C2×C411yescharacteristic
39C22×C4×C107C2×C411yescharacteristic
40C22×C4×C107C2311yescharacteristic
41C2×C8×C107—22no—
42C22⋊C4×C107—22no—
43C23×C107—21no—
44C23×C107—21no—
45C23×C107—41no—
46C23×C107—41no—
47C23×C107C2×C812yescomplemented
48C23×C107C22×C411yescharacteristic
49C22×D107—41no—
50C22×D107—41no—
51C22×D107C22⋊C412yes—
52C22×D107C2×C812yes—
53C22×D107M1612yes—
54C2×C4×C107—21no—
55C2×C4×C107—41no—
56C2×C4×C107—41no—
57C2×C4×C107C2×D412yes—
58C22⋊D107—28no—
59C2×Dic107—21no—
60C2×Dic107—21no—
61C2×Dic107—22no—
62C2×Dic107—21no—
63C2×Dic107—42no—
64C2×Dic107—42no—
65C2×Dic107—41no—
66C2×Dic107C22⋊C411yescharacteristic
67C2×Dic107C22⋊C411yescharacteristic
68C2×Dic107C2×C812yescomplemented
69C4×D107—24no—
70C4×D107—42no—
71C8×C107—42no—
72C107⋊C8—42no—
73C22×C107—21no—
74C22×C107—21no—
75C22×C107—22no—
76C22×C107—42no—
77C22×C107—42no—
78C22×C107—41no—
79C22×C107—41no—
80C22×C107C2×C22⋊C411yescharacteristic
81C22×C107C22×C811yescharacteristic
82C22×C107C2×M1611yescharacteristic
83C2×D107—22no—
84C2×D107—22no—
85C2×D107—42no—
86C2×D107—42no—
87C2×D107C22⋊C814yes—
88C4×C107—22no—
89C4×C107—41no—
90Dic107—22no—
91Dic107—21no—
92Dic107—41no—
93Dic107#9912yes—
94C2×C107—21no—
95C2×C107—21no—
96C2×C107—42no—
97C2×C107C2×C22⋊C811yescharacteristic
98C2×C107C2×#9911yescharacteristic
99C2×C107#41311yescharacteristic
100D107—24no—
101#1459—1071nomaximal, Sylow
102C107#145911yescharacteristic, complemented, Sylow
103C2×C4×D4—1071no—
104C2×C22⋊C8—1072no—
105#324—1072no—
106#323—1071no—
107#323D10711yescharacteristic, complemented
108C22×D4—1071no—
109C23×C4—1071no—
110C23×C4—1071no—
111C22×C8—2142no—
112C4×D4—2142no—
113C4×D4—2142no—
114C2×C4⋊C4—1071no—
115C2×C22⋊C4—1071no—
116C2×C22⋊C4C2×D10711yescharacteristic
117C2×C42—1071no—
118C22⋊C8—1072no—
119C22⋊C8—2142no—
120C22⋊C8C2×D10712yes—
121C24—1071no—
122C24C4×D10711yescharacteristic
123C2×D4—1074no—
124C2×D4—2142no—
125C2×D4—2142no—
126C22×C4—1071no—
127C22×C4—1071no—
128C22×C4—1072no—
129C22×C4—1072no—
130C22×C4—1071no—
131C22×C4—4282no—
132C22×C4—4282no—
133C22×C4—2141no—
134C22×C4—2141no—
135C22×C4C4×D10711yescharacteristic
136C22×C4C22×D10711yescharacteristic
137C2×C8—22no—
138C2×C8—4284no—
139C2×C8—2142no—
140C4⋊C4—2142no—
141C22⋊C4—22no—
142C22⋊C4—2142no—
143C42—2141no—
144C42—2141no—
145C23—21no—
146C23—21no—
147C23—41no—
148C23—41no—
149C23—1072no—
150C23—1072no—
151C23—1072no—
152C23—4281no—
153C23—4281no—
154C23C8×D10712yescomplemented
155C23C2×C4×D10711yescharacteristic
156D4—2148no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—1071no—
161C2×C4—1071no—
162C2×C4—1072no—
163C2×C4—4282no—
164C2×C4—4282no—
165C2×C4—4282no—
166C2×C4—4281no—
167C2×C4—2144no—
168C2×C4—2142no—
169C2×C4—2141no—
170C2×C4—2141no—
171C2×C4—2141no—
172C2×C4D4×D10712yes—
173C8—42no—
174C8—4282no—
175C22—21no—
176C22—21no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—1074no—
183C22—4282no—
184C22—4282no—
185C22—2142no—
186C22—2142no—
187C22C22⋊C4×D10711yescharacteristic
188C22C2×C8×D10711yescharacteristic
189C22M16×D10711yescharacteristic
190C4—22no—
191C4—41no—
192C4—1072no—
193C4—4281no—
194C4—2142no—
195C4—2141no—
196C2—21no—
197C2—21no—
198C2—42no—
199C2—2144no—
200C2C22⋊C8×D10711yescharacteristic
201C2#99×D10711yescharacteristic
202C2#2029260811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D107
commutatorC22×C107C22×C8
FrattiniC22×C4C22×D107
Fitting#323×C107C2
socleC22×C107C2×C22⋊C4
prime radicalC22×C22⋊D107C4
cosocleC22×C4×C107C23
hypercenter#323D107
hypocenterC107#1459
LCSG ▷ C22×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D107C2semidirect
3. #20292352C2semidirect
4. #20292351C2semidirect
5. #323×C107C2semidirect
22. C2×C22⋊D107C8semidirect
47. C23×C107C2×C8semidirect
68. C2×Dic107C2×C8semidirect
102. C107#1459semidirect
107. #323D107semidirect
154. C23C8×D107semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D107)⋊C42
C22⋊C8×D1072
#202923522
#202923512
#323×C1072
#1459107