Finite Group Databasebeta

← C2×C127×#1412 #44577266

Subgroups — C2×C127×#1412 #44577266

Order 32512.

390 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 94 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×#490×C127C211yesmaximal, characteristic
2C2×#353×C127C212yesmaximal
3C127×#1412C214yesmaximal, direct product factor
4C2×#127×C127C2211yescharacteristic
5C2×#125×C127C411yescharacteristic, complemented
6#490×C127—22no—
7#490×C127C412yescomplemented
8#490×C127C2212yes—
9C2×#102×C127—22no—
10C2×#99×C127—22no—
11C2×#97×C127C411yescharacteristic, complemented
12#353×C127—22no—
13#353×C127C2214yes—
14C22×D4×C127—41no—
15C22×D4×C127D412yes—
16C22×C8×C127—21no—
17#127×C127—41no—
18#127×C127C2×C411yescharacteristic
19#127×C127D412yes—
20#127×C127C2311yescharacteristic
21#125×C127—21no—
22#125×C127—41no—
23#125×C127C2×C412yescomplemented
24C2×C4⋊C4×C127—21no—
25C2×C4⋊C4×C127—41no—
26C2×C22⋊C4×C127—42no—
27C2×C42×C127C2×C411yescharacteristic
28#102×C127—24no—
29#102×C127—24no—
30#99×C127—24no—
31#99×C127—42no—
32#97×C127—21no—
33#97×C127C2×C412yescomplemented
34C24×C127—22no—
35C2×D4×C127—22no—
36C2×D4×C127—42no—
37C2×D4×C127—42no—
38C2×D4×C127—41no—
39C2×D4×C127—42no—
40C2×D4×C127—41no—
41C2×D4×C127—84no—
42C2×D4×C127C22⋊C412yes—
43C2×D4×C127C2×D412yes—
44C22×C4×C127—21no—
45C22×C4×C127—41no—
46C22×C4×C127—82no—
47C22×C4×C127C22⋊C411yescharacteristic
48C2×C8×C127—22no—
49C2×C8×C127—41no—
50C2×C8×C127—41no—
51C4⋊C4×C127—22no—
52C4⋊C4×C127—42no—
53C4⋊C4×C127—42no—
54C4⋊C4×C127—41no—
55C22⋊C4×C127—44no—
56C22⋊C4×C127—82no—
57C42×C127—21no—
58C42×C127C22⋊C411yescharacteristic
59C42×C127C22×C411yescharacteristic
60C23×C127—22no—
61C23×C127—22no—
62C23×C127—42no—
63C23×C127—42no—
64C23×C127—84no—
65C23×C127#9911yescharacteristic
66D4×C127—42no—
67D4×C127—42no—
68D4×C127—82no—
69D4×C127—82no—
70D4×C127—84no—
71D4×C127—82no—
72C2×C4×C127—21no—
73C2×C4×C127—21no—
74C2×C4×C127—21no—
75C2×C4×C127—21no—
76C2×C4×C127—42no—
77C2×C4×C127—42no—
78C2×C4×C127—82no—
79C2×C4×C127—84no—
80C2×C4×C127—164no—
81C2×C4×C127#9911yescharacteristic
82C2×C4×C127C2×C22⋊C411yescharacteristic
83C8×C127—42no—
84C22×C127—22no—
85C22×C127—42no—
86C22×C127—42no—
87C22×C127—82no—
88C22×C127—82no—
89C22×C127—84no—
90C22×C127—162no—
91C22×C127#35411yescharacteristic
92C22×C127#35411yescharacteristic
93C22×C127C2×#9911yescharacteristic
94C4×C127—21no—
95C4×C127—21no—
96C4×C127—41no—
97C4×C127—41no—
98C4×C127—82no—
99C4×C127—164no—
100C2×#1412C12711yesmaximal, characteristic, direct product factor, Sylow
101C2×C127—21no—
102C2×C127—21no—
103C2×C127—82no—
104C2×C127—82no—
105C2×C127#141212yesdirect product factor
106C2×C127C2×#35411yescharacteristic
107C2×#490C2×C12711yescharacteristic
108C2×#353C2×C12712yes—
109#1412C2×C12714yesdirect product factor
110C127C2×#141211yescharacteristic, direct product factor, Sylow
111C2×#127C22×C12711yescharacteristic
112C2×#125C4×C12711yescharacteristic, complemented
113#490—22no—
114#490C4×C12712yescomplemented
115#490C22×C12712yes—
116C2×#102—22no—
117C2×#99—22no—
118C2×#97C4×C12711yescharacteristic, complemented
119#353—22no—
120#353C22×C12714yes—
121C22×D4—41no—
122C22×D4D4×C12712yes—
123C22×C8—21no—
124#127—41no—
125#127C2×C4×C12711yescharacteristic
126#127D4×C12712yes—
127#127C23×C12711yescharacteristic
128#125—21no—
129#125—41no—
130#125C2×C4×C12712yescomplemented
131C2×C4⋊C4—21no—
132C2×C4⋊C4—41no—
133C2×C22⋊C4—42no—
134C2×C42C2×C4×C12711yescharacteristic
135#102—24no—
136#102—24no—
137#99—24no—
138#99—42no—
139#97—21no—
140#97C2×C4×C12712yescomplemented
141C24—22no—
142C2×D4—22no—
143C2×D4—42no—
144C2×D4—42no—
145C2×D4—41no—
146C2×D4—42no—
147C2×D4—41no—
148C2×D4—84no—
149C2×D4C22⋊C4×C12712yes—
150C2×D4C2×D4×C12712yes—
151C22×C4—21no—
152C22×C4—41no—
153C22×C4—82no—
154C22×C4C22⋊C4×C12711yescharacteristic
155C2×C8—22no—
156C2×C8—41no—
157C2×C8—41no—
158C4⋊C4—22no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C4⋊C4—41no—
162C22⋊C4—44no—
163C22⋊C4—82no—
164C42—21no—
165C42C22⋊C4×C12711yescharacteristic
166C42C22×C4×C12711yescharacteristic
167C23—22no—
168C23—22no—
169C23—42no—
170C23—42no—
171C23—84no—
172C23#99×C12711yescharacteristic
173D4—42no—
174D4—42no—
175D4—82no—
176D4—82no—
177D4—84no—
178D4—82no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—82no—
186C2×C4—84no—
187C2×C4—164no—
188C2×C4#99×C12711yescharacteristic
189C2×C4C2×C22⋊C4×C12711yescharacteristic
190C8—42no—
191C22—22no—
192C22—42no—
193C22—42no—
194C22—82no—
195C22—82no—
196C22—84no—
197C22—162no—
198C22#354×C12711yescharacteristic
199C22#354×C12711yescharacteristic
200C22C2×#99×C12711yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—41no—
205C4—82no—
206C4—164no—
207C2—21no—
208C2—21no—
209C2—82no—
210C2—82no—
211C2C127×#141212yesdirect product factor
212C2C2×#354×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#354
commutatorC42C22×C4×C127
Frattini, cosocle#127C23×C127
prime radicalC2×#127×C127C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C127 ◁ C22×C4×C127 ◁ C2×#127×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1412C2direct (N × H)
5. C2×#125×C127C4semidirect
7. #490×C127C4semidirect
11. C2×#97×C127C4semidirect
23. #125×C127C2×C4semidirect
33. #97×C127C2×C4semidirect
100. C2×#1412C127direct (N × H)
105. C2×C127#1412direct (N × H)
109. #1412C2×C127direct (N × H)
110. C127C2×#1412direct (N × H)
112. C2×#125C4×C127semidirect
114. #490C4×C127semidirect
118. C2×#97C4×C127semidirect
130. #125C2×C4×C127semidirect
140. #97C2×C4×C127semidirect
211. C2C127×#1412direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#490×C1272
C2×#353×C1272
C127×#14122
C2×#1412127