Finite Group Databasebeta

← #22549799

Subgroups — #22549799

Order 8128.

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

normal subgroups only

This group has 186 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
1C2×C4⋊Dic127C211yesmaximal, characteristic, complemented
2C2×Dic127⋊C4C211yesmaximal, characteristic, complemented
3C2×Dic127⋊C4C211yesmaximal, characteristic, complemented
4C2×C22⋊Dic127C211yesmaximal, characteristic
5C2×C22⋊Dic127C211yesmaximal, characteristic
6C127⋊#95C211yesmaximal, characteristic, complemented
7C2×C22⋊C4×C127C211yesmaximal, characteristic
8C22×Dic127C2211yescharacteristic
9C22×Dic127C2211yescharacteristic
10C22×Dic127C2211yescharacteristic
11C22×Dic127C2211yescharacteristic
12C4⋊Dic127—22no—
13Dic127⋊C4—22no—
14Dic127⋊C4—22no—
15C22⋊Dic127—22no—
16C22⋊Dic127—22no—
17C24×C127C2211yescharacteristic
18C22×C4×C127C2211yescharacteristic
19C22×C4×C127C2211yescharacteristic
20C22⋊C4×C127—22no—
21C2×Dic127—21no—
22C2×Dic127—21no—
23C2×Dic127—21no—
24C2×Dic127—21no—
25C2×Dic127—21no—
26C2×Dic127—21no—
27C2×Dic127—21no—
28C2×Dic127—21no—
29C2×Dic127—21no—
30C2×Dic127—21no—
31C2×Dic127D412yes—
32C2×Dic127D412yes—
33C23×C127—21no—
34C23×C127—21no—
35C23×C127—21no—
36C23×C127—21no—
37C23×C127—21no—
38C23×C127—21no—
39C23×C127Q812yes—
40C23×C127C2311yescharacteristic
41C2×C4×C127—21no—
42C2×C4×C127—21no—
43C2×C4×C127—21no—
44C2×C4×C127—21no—
45C2×C4×C127—21no—
46C2×C4×C127D412yes—
47C22×C127—22no—
48C22×C127—22no—
49C22×C127—22no—
50C22×C127—41no—
51C22×C127—41no—
52C22×C127—41no—
53C22×C127—41no—
54C22×C127C2×D411yescharacteristic
55C22×C127C2×D411yescharacteristic
56C22×C127C2×D411yescharacteristic
57C22×C127C2×Q811yescharacteristic
58C22×C127#4111yescharacteristic
59C22×C127#4111yescharacteristic
60C22×C127#4111yescharacteristic
61C4×C127—22no—
62C4×C127—41no—
63Dic127—22no—
64Dic127—22no—
65Dic127—41no—
66Dic127—41no—
67C2×C127—42no—
68C2×C127#12111yescharacteristic
69C2×C127#12111yescharacteristic
70C2×C127#12111yescharacteristic
71C2×C127C22⋊Q811yescharacteristic
72C2×C127C22⋊Q811yescharacteristic
73C2×C127C22⋊Q811yescharacteristic
74C2×C127#12611yescharacteristic
75C127#39611yescharacteristic, complemented, Sylow
76#396—1271nomaximal, Sylow
77C2×C4⋊C4—1271no—
78C2×C4⋊C4—1271no—
79C2×C4⋊C4—1271no—
80C2×C22⋊C4—1271no—
81C2×C22⋊C4—1271no—
82C2×C22⋊C4D12711yescharacteristic
83#95—1271no—
84C24C2×D12711yescharacteristic
85C22×C4—1271no—
86C22×C4—1271no—
87C22×C4—1271no—
88C22×C4—1271no—
89C22×C4C2×D12711yescharacteristic
90C22×C4C2×D12711yescharacteristic
91C4⋊C4—2542no—
92C4⋊C4—2542no—
93C4⋊C4—2542no—
94C22⋊C4—22no—
95C22⋊C4—2542no—
96C22⋊C4—2542no—
97C23—21no—
98C23—21no—
99C23—21no—
100C23—21no—
101C23—21no—
102C23—21no—
103C23Dic25412yes—
104C23C22×D12711yescharacteristic
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—21no—
108C2×C4—21no—
109C2×C4—21no—
110C2×C4—1272no—
111C2×C4—1272no—
112C2×C4—2541no—
113C2×C4—2541no—
114C2×C4—2541no—
115C2×C4—2541no—
116C2×C4—2541no—
117C2×C4—2541no—
118C2×C4—2541no—
119C2×C4—2541no—
120C2×C4—2541no—
121C2×C4—2541no—
122C2×C4C22⋊D12712yes—
123C22—22no—
124C22—22no—
125C22—22no—
126C22—41no—
127C22—41no—
128C22—41no—
129C22—41no—
130C22D4×D12711yescharacteristic
131C22D4×D12711yescharacteristic
132C22C2×C22⋊D12711yescharacteristic
133C22C2×Dic25411yescharacteristic
134C22#1452324711yescharacteristic
135C22#1452324711yescharacteristic
136C22#1452324811yescharacteristic
137C4—22no—
138C4—41no—
139C4—5081no—
140C4—5081no—
141C4—2542no—
142C4—2542no—
143C2—42no—
144C2#1686118011yescharacteristic
145C2#1686118111yescharacteristic
146C2#1686118211yescharacteristic
147C2#1686118611yescharacteristic
148C2#1686118611yescharacteristic
149C2#1686118811yescharacteristic
150C2#1686120211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D127
commutator, socleC23×C127C23
FittingC2×C22⋊C4×C127C2
hypercenterC2×C22⋊C4D127
hypocenterC127#396
LCSG ▷ C23×C127 ▷ C127
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊Dic127C2semidirect
2. C2×Dic127⋊C4C2semidirect
3. C2×Dic127⋊C4C2semidirect
6. C127⋊#95C2semidirect
75. C127#396semidirect