Finite Group Databasebeta

← #22549792

Subgroups — #22549792

Order 8128.

238 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C22×C22⋊D127C211yesmaximal, characteristic
2C2×C4⋊Dic127C211yesmaximal, characteristic, complemented
3C2×C22⋊Dic127C211yesmaximal, characteristic, complemented
4C2×(C2×D127)⋊C4C211yesmaximal, characteristic, complemented
5C2×(C2×D127)⋊C4C211yesmaximal, characteristic, complemented
6C127⋊#95C211yesmaximal, characteristic, complemented
7C2×C22⋊C4×C127C211yesmaximal, characteristic, complemented
8C23×D127C2211yescharacteristic
9C2×C22⋊D127—22no—
10C2×C22⋊D127—22no—
11C2×C22⋊D127—22no—
12C22×Dic127C2211yescharacteristic
13C22×Dic127C2211yescharacteristic
14C22×Dic127C2211yescharacteristic
15C4⋊Dic127—22no—
16C22⋊Dic127—22no—
17(C2×D127)⋊C4—22no—
18(C2×D127)⋊C4—22no—
19C24×C127C2211yescharacteristic
20C22×C4×C127C2211yescharacteristic
21C22×C4×C127C2211yescharacteristic
22C22⋊C4×C127—22no—
23C22×D127—21no—
24C22×D127—21no—
25C22×D127—21no—
26C22×D127—21no—
27C22×D127—21no—
28C22×D127—21no—
29C22×D127D412yes—
30C22⋊D127—28no—
31C2×Dic127—21no—
32C2×Dic127—21no—
33C2×Dic127—21no—
34C2×Dic127—21no—
35C2×Dic127—21no—
36C2×Dic127—21no—
37C2×Dic127—21no—
38C2×Dic127—21no—
39C2×Dic127D412yes—
40C23×C127—21no—
41C23×C127—21no—
42C23×C127—21no—
43C23×C127—21no—
44C23×C127—21no—
45C23×C127—21no—
46C23×C127D412yes—
47C23×C127C2311yescharacteristic
48C2×C4×C127—21no—
49C2×C4×C127—21no—
50C2×C4×C127—21no—
51C2×C4×C127—21no—
52C2×C4×C127—21no—
53C2×C4×C127D412yescomplemented
54C22×C127—22no—
55C22×C127—22no—
56C22×C127—22no—
57C22×C127—41no—
58C22×C127—41no—
59C22×C127—41no—
60C22×C127—41no—
61C22×C127C2×D411yescharacteristic
62C22×C127C2×D411yescharacteristic
63C22×C127C2×D411yescharacteristic
64C22×C127C2×D411yescharacteristic
65C22×C127#4111yescharacteristic
66C22×C127#4111yescharacteristic
67C22×C127#4111yescharacteristic
68C2×D127—22no—
69C2×D127—22no—
70C2×D127—22no—
71C2×D127—41no—
72C2×D127—41no—
73C2×D127—41no—
74C2×D127—41no—
75C4×C127—22no—
76C4×C127—41no—
77Dic127—22no—
78Dic127—41no—
79Dic127—41no—
80C2×C127—42no—
81C2×C127#12011yescharacteristic
82C2×C127#12111yescharacteristic
83C2×C127#12111yescharacteristic
84C2×C127#12111yescharacteristic
85C2×C127#12311yescharacteristic
86C2×C127#12311yescharacteristic
87C2×C127#12411yescharacteristic
88D127—42no—
89C127#39411yescharacteristic, complemented, Sylow
90#394—1271nomaximal, Sylow
91C22×D4—1271no—
92C2×C4⋊C4—1271no—
93C2×C22⋊C4—1271no—
94C2×C22⋊C4—1271no—
95C2×C22⋊C4—1271no—
96C2×C22⋊C4D12711yescharacteristic, complemented
97#95—1271no—
98C24—1271no—
99C24C2×D12711yescharacteristic
100C2×D4—2542no—
101C2×D4—2542no—
102C2×D4—2542no—
103C22×C4—1271no—
104C22×C4—1271no—
105C22×C4—1271no—
106C22×C4C2×D12711yescharacteristic
107C22×C4C2×D12711yescharacteristic
108C4⋊C4—2542no—
109C22⋊C4—22no—
110C22⋊C4—2542no—
111C22⋊C4—2542no—
112C22⋊C4—2542no—
113C23—21no—
114C23—21no—
115C23—21no—
116C23—21no—
117C23—21no—
118C23—21no—
119C23—1272no—
120C23—2541no—
121C23—2541no—
122C23—2541no—
123C23—2541no—
124C23—2541no—
125C23—2541no—
126C23D50812yes—
127C23C22×D12711yescharacteristic
128D4—2548no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—1272no—
135C2×C4—2541no—
136C2×C4—2541no—
137C2×C4—2541no—
138C2×C4—2541no—
139C2×C4—2541no—
140C2×C4—2541no—
141C2×C4—2541no—
142C2×C4—2541no—
143C2×C4C22⋊D12712yescomplemented
144C22—22no—
145C22—22no—
146C22—22no—
147C22—41no—
148C22—41no—
149C22—41no—
150C22—41no—
151C22—5081no—
152C22—5081no—
153C22—5081no—
154C22—5081no—
155C22—2542no—
156C22—2542no—
157C22—2542no—
158C22D4×D12711yescharacteristic
159C22D4×D12711yescharacteristic
160C22C2×C22⋊D12711yescharacteristic
161C22C2×D50811yescharacteristic
162C22#1452324711yescharacteristic
163C22#1452324711yescharacteristic
164C22#1452324811yescharacteristic
165C4—22no—
166C4—41no—
167C4—5081no—
168C4—5081no—
169C4—2542no—
170C2—42no—
171C2—5082no—
172C2#1686117911yescharacteristic
173C2#1686118011yescharacteristic
174C2#1686118111yescharacteristic
175C2#1686118311yescharacteristic
176C2#1686119111yescharacteristic
177C2#1686119311yescharacteristic
178C2#1686119511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D127
commutator, socleC23×C127C23
FittingC2×C22⋊C4×C127C2
hypercenterC2×C22⋊C4D127
hypocenterC127#394
LCSG ▷ C23×C127 ▷ C127
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊Dic127C2semidirect
3. C2×C22⋊Dic127C2semidirect
4. C2×(C2×D127)⋊C4C2semidirect
5. C2×(C2×D127)⋊C4C2semidirect
6. C127⋊#95C2semidirect
7. C2×C22⋊C4×C127C2semidirect
53. C2×C4×C127D4semidirect
89. C127#394semidirect
96. C2×C22⋊C4D127semidirect
143. C2×C4C22⋊D127semidirect