Finite Group Databasebeta

← C127×#2629 #30635581

Subgroups — C127×#2629 #30635581

Order 16256.

472 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 216 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×#125×C127C211yesmaximal, characteristic, complemented
2C2×#117×C127C211yesmaximal, characteristic
3#398×C127C214yesmaximal, complemented
4#396×C127C214yesmaximal
5#389×C127C212yesmaximal, complemented
6#384×C127C211yesmaximal, characteristic, complemented
7#380×C127C212yesmaximal
8C23×C4×C127C2211yescharacteristic
9#125×C127—24no—
10#117×C127—24no—
11C2×C4⋊C4×C127C2212yes—
12C2×C4⋊C4×C127C2212yes—
13C2×C4⋊C4×C127C2214yes—
14C2×C4⋊C4×C127C2212yes—
15C2×C4⋊C4×C127C2214yes—
16C2×C4⋊C4×C127C2214yes—
17C2×C22⋊C4×C127C2212yes—
18C2×C22⋊C4×C127C2214yes—
19C2×C42×C127C2211yescharacteristic
20C2×C42×C127C2211yescharacteristic
21#95×C127C2214yes—
22#95×C127C2214yes—
23C24×C127C2311yescharacteristic
24C22×C4×C127—22no—
25C22×C4×C127—22no—
26C22×C4×C127Q814yes—
27C22×C4×C127C2312yes—
28C22×C4×C127C2314yes—
29C22×C4×C127C2314yes—
30C22×C4×C127C2312yes—
31C22×C4×C127C2311yescharacteristic
32C22×C4×C127C2311yescharacteristic
33C4⋊C4×C127—24no—
34C4⋊C4×C127—28no—
35C4⋊C4×C127—24no—
36C4⋊C4×C127—24no—
37C4⋊C4×C127—44no—
38C4⋊C4×C127—44no—
39C22⋊C4×C127—24no—
40C22⋊C4×C127—44no—
41C42×C127—22no—
42C42×C127D414yes—
43C23×C127—21no—
44C23×C127—21no—
45C23×C127—22no—
46C23×C127—22no—
47C23×C127C2×Q812yes—
48C23×C127C2411yescharacteristic
49C2×C4×C127—21no—
50C2×C4×C127—21no—
51C2×C4×C127—22no—
52C2×C4×C127—22no—
53C2×C4×C127—28no—
54C2×C4×C127—22no—
55C2×C4×C127—24no—
56C2×C4×C127—24no—
57C2×C4×C127—24no—
58C2×C4×C127—24no—
59C2×C4×C127—22no—
60C2×C4×C127—24no—
61C2×C4×C127—22no—
62C2×C4×C127—24no—
63C2×C4×C127C2×D414yes—
64C2×C4×C127C2×D412yes—
65C2×C4×C127C2×Q812yes—
66C2×C4×C127C2×Q812yes—
67C2×C4×C127#4112yes—
68C22×C127—22no—
69C22×C127—24no—
70C22×C127—42no—
71C22×C127—41no—
72C22×C127—41no—
73C22×C127C22×D411yescharacteristic
74C22×C127C22×Q811yescharacteristic
75C22×C127C2×#4111yescharacteristic
76C22×C127H(5,𝔽2)12yes—
77C22×C1272−1+412yes—
78C4×C127—22no—
79C4×C127—24no—
80C4×C127—42no—
81C4×C127—44no—
82C4×C127—44no—
83C4×C127C22⋊Q814yes—
84C2×C127—42no—
85C2×C127C2×C22⋊Q811yescharacteristic
86C2×C127#53712yes—
87C2×C127#54011yescharacteristic
88C2×C127#54111yescharacteristic
89C2×C127#54412yes—
90#2629C12711yesmaximal, characteristic, direct product factor, Sylow
91C127#262911yescharacteristic, direct product factor, Sylow
92C2×#125C2×C12711yescharacteristic, complemented
93C2×#117C2×C12711yescharacteristic
94#398C2×C12714yescomplemented
95#396C2×C12714yes—
96#389C2×C12712yescomplemented
97#384C2×C12711yescharacteristic, complemented
98#380C2×C12712yes—
99C23×C4C22×C12711yescharacteristic
100#125—24no—
101#117—24no—
102C2×C4⋊C4C22×C12712yes—
103C2×C4⋊C4C22×C12712yes—
104C2×C4⋊C4C22×C12714yes—
105C2×C4⋊C4C22×C12712yes—
106C2×C4⋊C4C22×C12714yes—
107C2×C4⋊C4C22×C12714yes—
108C2×C22⋊C4C22×C12712yes—
109C2×C22⋊C4C22×C12714yes—
110C2×C42C22×C12711yescharacteristic
111C2×C42C22×C12711yescharacteristic
112#95C22×C12714yes—
113#95C22×C12714yes—
114C24C23×C12711yescharacteristic
115C22×C4—22no—
116C22×C4—22no—
117C22×C4Q8×C12714yes—
118C22×C4C23×C12712yes—
119C22×C4C23×C12714yes—
120C22×C4C23×C12714yes—
121C22×C4C23×C12712yes—
122C22×C4C23×C12711yescharacteristic
123C22×C4C23×C12711yescharacteristic
124C4⋊C4—24no—
125C4⋊C4—28no—
126C4⋊C4—24no—
127C4⋊C4—24no—
128C4⋊C4—44no—
129C4⋊C4—44no—
130C22⋊C4—24no—
131C22⋊C4—44no—
132C42—22no—
133C42D4×C12714yes—
134C23—21no—
135C23—21no—
136C23—22no—
137C23—22no—
138C23C2×Q8×C12712yes—
139C23C24×C12711yescharacteristic
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—28no—
145C2×C4—22no—
146C2×C4—24no—
147C2×C4—24no—
148C2×C4—24no—
149C2×C4—24no—
150C2×C4—22no—
151C2×C4—24no—
152C2×C4—22no—
153C2×C4—24no—
154C2×C4C2×D4×C12714yes—
155C2×C4C2×D4×C12712yes—
156C2×C4C2×Q8×C12712yes—
157C2×C4C2×Q8×C12712yes—
158C2×C4#41×C12712yes—
159C22—22no—
160C22—24no—
161C22—42no—
162C22—41no—
163C22—41no—
164C22C22×D4×C12711yescharacteristic
165C22C22×Q8×C12711yescharacteristic
166C22C2×#41×C12711yescharacteristic
167C22H(5,𝔽2)×C12712yes—
168C222−1+4×C12712yes—
169C4—22no—
170C4—24no—
171C4—42no—
172C4—44no—
173C4—44no—
174C4C22⋊Q8×C12714yes—
175C2—42no—
176C2C2×C22⋊Q8×C12711yescharacteristic
177C2#537×C12712yes—
178C2#540×C12711yescharacteristic
179C2#541×C12711yescharacteristic
180C2#544×C12712yes—
subgroupG/H
center, socleC23×C127C24
commutator, Frattini, cosocleC23C24×C127
prime radicalC24×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#125×C127C2semidirect
3. #398×C127C2semidirect
5. #389×C127C2semidirect
6. #384×C127C2semidirect
90. #2629C127direct (N × H)
91. C127#2629direct (N × H)
92. C2×#125C2×C127semidirect
94. #398C2×C127semidirect
96. #389C2×C127semidirect
97. #384C2×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#125×C1272
C2×#117×C1272
#398×C1272
#396×C1272
#389×C1272
#384×C1272
#380×C1272
#2629127