Finite Group Databasebeta

← C127×#2832 #30635784

Subgroups — C127×#2832 #30635784

Order 16256.

416 conjugacy classes of subgroups.

The subgroup lattice has 234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#400×C127C212yesmaximal, complemented
2#397×C127C212yesmaximal, complemented
3#395×C127C211yesmaximal, characteristic, complemented
4#394×C127C212yesmaximal
5#394×C127C211yesmaximal, characteristic
6#393×C127C212yesmaximal, complemented
7#393×C127C212yesmaximal, complemented
8#391×C127C211yesmaximal, characteristic, complemented
9#388×C127C212yesmaximal, complemented
10C22×Q8×C127C2211yescharacteristic
11C22×Q8×C127C2211yescharacteristic
12C22×D4×C127C2211yescharacteristic
13C2×C4⋊C4×C127C2212yes—
14C2×C4⋊C4×C127C2211yescharacteristic
15C2×C4⋊C4×C127C2212yes—
16C2×C22⋊C4×C127C2212yes—
17C2×C22⋊C4×C127C2212yes—
18C2×C22⋊C4×C127C2212yes—
19C2×C22⋊C4×C127C2212yes—
20C2×C22⋊C4×C127C2212yes—
21C2×C22⋊C4×C127C2212yes—
22C2×C42×C127C2211yescharacteristic
23#95×C127C2212yes—
24#95×C127C2212yes—
25#95×C127C2212yes—
26#95×C127C2212yes—
27#95×C127C2212yes—
28#95×C127C2212yes—
29#95×C127C2211yescharacteristic
30#95×C127C2211yescharacteristic
31C24×C127C2312yes—
32C2×Q8×C127—22no—
33C2×Q8×C127—41no—
34C2×Q8×C127—41no—
35C2×Q8×C127—41no—
36C2×Q8×C127—42no—
37C2×D4×C127—41no—
38C2×D4×C127—42no—
39C22×C4×C127C2312yes—
40C22×C4×C127C2312yes—
41C22×C4×C127C2312yes—
42C22×C4×C127C2312yes—
43C22×C4×C127C2312yes—
44C22×C4×C127C2311yescharacteristic
45C22×C4×C127C2311yescharacteristic
46C22×C4×C127C2311yescharacteristic
47C4⋊C4×C127—41no—
48C4⋊C4×C127—42no—
49C4⋊C4×C127—42no—
50C22⋊C4×C127—24no—
51C22⋊C4×C127—42no—
52C22⋊C4×C127—42no—
53C22⋊C4×C127—42no—
54C22⋊C4×C127—42no—
55C22⋊C4×C127—42no—
56C42×C127—41no—
57C23×C127—22no—
58C23×C127—22no—
59C23×C127—22no—
60C23×C127—22no—
61C23×C127—22no—
62C23×C127—22no—
63C23×C127—22no—
64C23×C127C2411yescharacteristic
65Q8×C127—44no—
66Q8×C127—44no—
67D4×C127—44no—
68C2×C4×C127—21no—
69C2×C4×C127—21no—
70C2×C4×C127—22no—
71C2×C4×C127—22no—
72C2×C4×C127—22no—
73C2×C4×C127—22no—
74C2×C4×C127—22no—
75C2×C4×C127—22no—
76C2×C4×C127—22no—
77C2×C4×C127—22no—
78C2×C4×C127—22no—
79C2×C4×C127—22no—
80C2×C4×C127—22no—
81C2×C4×C127—22no—
82C2×C4×C127—21no—
83C2×C4×C127—22no—
84C2×C4×C127—21no—
85C2×C4×C127—22no—
86C2×C4×C127—22no—
87C2×C4×C127—22no—
88C2×C4×C127—22no—
89C2×C4×C127#4112yes—
90C22×C127—42no—
91C22×C127—42no—
92C22×C127—42no—
93C22×C127—42no—
94C22×C127—42no—
95C22×C127—42no—
96C22×C127—42no—
97C22×C127C2×#4111yescharacteristic
98C22×C127H(5,𝔽2)11yescharacteristic
99C22×C127H(5,𝔽2)11yescharacteristic
100C22×C127H(5,𝔽2)12yes—
101C22×C1272−1+412yes—
102C4×C127—22no—
103C4×C127—42no—
104C4×C127—42no—
105C4×C127—41no—
106C4×C127—42no—
107C4×C127—41no—
108C4×C127—42no—
109C4×C127—42no—
110C2×C127—82no—
111C2×C127#53811yescharacteristic
112C2×C127#54212yes—
113C2×C127H(3,𝔽4)11yescharacteristic
114C2×C127#56212yes—
115C2×C127#56311yescharacteristic
116#2832C12711yesmaximal, characteristic, direct product factor, Sylow
117C127#283211yescharacteristic, direct product factor, Sylow
118#400C2×C12712yescomplemented
119#397C2×C12712yescomplemented
120#395C2×C12711yescharacteristic, complemented
121#394C2×C12712yes—
122#394C2×C12711yescharacteristic
123#393C2×C12712yescomplemented
124#393C2×C12712yescomplemented
125#391C2×C12711yescharacteristic, complemented
126#388C2×C12712yescomplemented
127C22×Q8C22×C12711yescharacteristic
128C22×Q8C22×C12711yescharacteristic
129C22×D4C22×C12711yescharacteristic
130C2×C4⋊C4C22×C12712yes—
131C2×C4⋊C4C22×C12711yescharacteristic
132C2×C4⋊C4C22×C12712yes—
133C2×C22⋊C4C22×C12712yes—
134C2×C22⋊C4C22×C12712yes—
135C2×C22⋊C4C22×C12712yes—
136C2×C22⋊C4C22×C12712yes—
137C2×C22⋊C4C22×C12712yes—
138C2×C22⋊C4C22×C12712yes—
139C2×C42C22×C12711yescharacteristic
140#95C22×C12712yes—
141#95C22×C12712yes—
142#95C22×C12712yes—
143#95C22×C12712yes—
144#95C22×C12712yes—
145#95C22×C12712yes—
146#95C22×C12711yescharacteristic
147#95C22×C12711yescharacteristic
148C24C23×C12712yes—
149C2×Q8—22no—
150C2×Q8—41no—
151C2×Q8—41no—
152C2×Q8—41no—
153C2×Q8—42no—
154C2×D4—41no—
155C2×D4—42no—
156C22×C4C23×C12712yes—
157C22×C4C23×C12712yes—
158C22×C4C23×C12712yes—
159C22×C4C23×C12712yes—
160C22×C4C23×C12712yes—
161C22×C4C23×C12711yescharacteristic
162C22×C4C23×C12711yescharacteristic
163C22×C4C23×C12711yescharacteristic
164C4⋊C4—41no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C22⋊C4—24no—
168C22⋊C4—42no—
169C22⋊C4—42no—
170C22⋊C4—42no—
171C22⋊C4—42no—
172C22⋊C4—42no—
173C42—41no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23—22no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23C24×C12711yescharacteristic
182Q8—44no—
183Q8—44no—
184D4—44no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4#41×C12712yes—
207C22—42no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—42no—
214C22C2×#41×C12711yescharacteristic
215C22H(5,𝔽2)×C12711yescharacteristic
216C22H(5,𝔽2)×C12711yescharacteristic
217C22H(5,𝔽2)×C12712yes—
218C222−1+4×C12712yes—
219C4—22no—
220C4—42no—
221C4—42no—
222C4—41no—
223C4—42no—
224C4—41no—
225C4—42no—
226C4—42no—
227C2—82no—
228C2#538×C12711yescharacteristic
229C2#542×C12712yes—
230C2H(3,𝔽4)×C12711yescharacteristic
231C2#562×C12712yes—
232C2#563×C12711yescharacteristic
subgroupG/H
center, socleC23×C127C24
commutator, Frattini, cosocleC23C24×C127
prime radicalC22×D4×C127C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. #400×C127C2semidirect
2. #397×C127C2semidirect
3. #395×C127C2semidirect
6. #393×C127C2semidirect
7. #393×C127C2semidirect
8. #391×C127C2semidirect
9. #388×C127C2semidirect
116. #2832C127direct (N × H)
117. C127#2832direct (N × H)
118. #400C2×C127semidirect
119. #397C2×C127semidirect
120. #395C2×C127semidirect
123. #393C2×C127semidirect
124. #393C2×C127semidirect
125. #391C2×C127semidirect
126. #388C2×C127semidirect

Maximal subgroups

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

subgroupindex
#400×C1272
#397×C1272
#395×C1272
#394×C1272
#393×C1272
#391×C1272
#388×C1272
#2832127