Finite Group Databasebeta

← C127×#11452 #44575125

Subgroups — C127×#11452 #44575125

Order 32512.

462 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 142 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
1C127×#2296C211yesmaximal, characteristic
2C127×#1458C212yesmaximal
3C127×#1326C214yesmaximal
4C2×#117×C127C411yescharacteristic
5C2×#117×C127C2211yescharacteristic
6C22×C42×C127C411yescharacteristic
7#431×C127—22no—
8#389×C127—22no—
9#385×C127C412yes—
10#385×C127C2212yes—
11C4×C4⋊C4×C127—22no—
12#324×C127—22no—
13#323×C127C2214yes—
14C23×C4×C127C2×C411yescharacteristic
15C23×C4×C127C2×C412yes—
16#117×C127—22no—
17#117×C127—41no—
18#117×C127—41no—
19#117×C127C814yescomplemented
20C2×C4⋊C4×C127—21no—
21C2×C4⋊C4×C127—22no—
22C2×C4⋊C4×C127—22no—
23C2×C4⋊C4×C127D412yes—
24C2×C22⋊C4×C127C2×C412yes—
25C2×C22⋊C4×C127C2×C411yescharacteristic
26C2×C22⋊C4×C127C2311yescharacteristic
27C2×C42×C127—21no—
28C2×C42×C127—21no—
29C2×C42×C127—21no—
30C2×C42×C127—41no—
31C2×C42×C127—41no—
32C2×C42×C127D412yes—
33C4⋊C8×C127—42no—
34C22⋊C8×C127—24no—
35C4×C8×C127—42no—
36#95×C127—22no—
37#95×C127—22no—
38C24×C127C22×C411yescharacteristic
39C22×C4×C127—21no—
40C22×C4×C127—21no—
41C22×C4×C127—22no—
42C22×C4×C127—22no—
43C22×C4×C127—22no—
44C22×C4×C127—44no—
45C22×C4×C127—42no—
46C22×C4×C127C22⋊C411yescharacteristic
47C22×C4×C127C22⋊C412yes—
48C22×C4×C127C22⋊C411yescharacteristic
49C22×C4×C127C2×C812yes—
50C22×C4×C127M1612yes—
51C22×C4×C127C2×D412yes—
52C2×C8×C127—44no—
53C4⋊C4×C127—24no—
54C4⋊C4×C127—42no—
55C4⋊C4×C127—44no—
56C4⋊C4×C127—44no—
57C22⋊C4×C127—22no—
58C22⋊C4×C127—41no—
59C22⋊C4×C127—41no—
60C22⋊C4×C127C2×C814yes—
61C42×C127—24no—
62C42×C127—22no—
63C42×C127—22no—
64C42×C127—42no—
65C42×C127—41no—
66C42×C127—41no—
67C23×C127—21no—
68C23×C127—21no—
69C23×C127—42no—
70C23×C127C2×C22⋊C411yescharacteristic
71C23×C127C22×C811yescharacteristic
72C23×C127C2×M1611yescharacteristic
73C2×C4×C127—21no—
74C2×C4×C127—21no—
75C2×C4×C127—22no—
76C2×C4×C127—22no—
77C2×C4×C127—22no—
78C2×C4×C127—22no—
79C2×C4×C127—24no—
80C2×C4×C127—24no—
81C2×C4×C127—22no—
82C2×C4×C127—22no—
83C2×C4×C127—42no—
84C2×C4×C127—42no—
85C2×C4×C127—42no—
86C2×C4×C127—44no—
87C2×C4×C127—42no—
88C2×C4×C127—42no—
89C2×C4×C127—42no—
90C2×C4×C127—44no—
91C2×C4×C127C22⋊C812yes—
92C2×C4×C127C22⋊C812yes—
93C2×C4×C127#9911yescharacteristic
94C2×C4×C127#9911yescharacteristic
95C2×C4×C127#10112yes—
96C8×C127—84no—
97C22×C127—22no—
98C22×C127—21no—
99C22×C127—21no—
100C22×C127—41no—
101C22×C127—41no—
102C22×C127—42no—
103C22×C127—42no—
104C22×C127C2×C22⋊C811yescharacteristic
105C22×C127C2×#9911yescharacteristic
106C22×C127C2×#10111yescharacteristic
107C4×C127—22no—
108C4×C127—44no—
109C4×C127—42no—
110C4×C127—42no—
111C4×C127—44no—
112C4×C127#32412yes—
113C4×C127#32412yes—
114#11452C12711yesmaximal, characteristic, direct product factor, Sylow
115C2×C127—21no—
116C2×C127—21no—
117C2×C127—41no—
118C2×C127—41no—
119C2×C127C2×#32411yescharacteristic
120C2×C127#212012yes—
121#2296C2×C12711yescharacteristic
122#1458C2×C12712yes—
123#1326C2×C12714yes—
124C127#1145211yescharacteristic, direct product factor, Sylow
125C2×#117C4×C12711yescharacteristic
126C2×#117C22×C12711yescharacteristic
127C22×C42C4×C12711yescharacteristic
128#431—22no—
129#389—22no—
130#385C4×C12712yes—
131#385C22×C12712yes—
132C4×C4⋊C4—22no—
133#324—22no—
134#323C22×C12714yes—
135C23×C4C2×C4×C12711yescharacteristic
136C23×C4C2×C4×C12712yes—
137#117—22no—
138#117—41no—
139#117—41no—
140#117C8×C12714yescomplemented
141C2×C4⋊C4—21no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4D4×C12712yes—
145C2×C22⋊C4C2×C4×C12712yes—
146C2×C22⋊C4C2×C4×C12711yescharacteristic
147C2×C22⋊C4C23×C12711yescharacteristic
148C2×C42—21no—
149C2×C42—21no—
150C2×C42—21no—
151C2×C42—41no—
152C2×C42—41no—
153C2×C42D4×C12712yes—
154C4⋊C8—42no—
155C22⋊C8—24no—
156C4×C8—42no—
157#95—22no—
158#95—22no—
159C24C22×C4×C12711yescharacteristic
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—22no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4—44no—
166C22×C4—42no—
167C22×C4C22⋊C4×C12711yescharacteristic
168C22×C4C22⋊C4×C12712yes—
169C22×C4C22⋊C4×C12711yescharacteristic
170C22×C4C2×C8×C12712yes—
171C22×C4M16×C12712yes—
172C22×C4C2×D4×C12712yes—
173C2×C8—44no—
174C4⋊C4—24no—
175C4⋊C4—42no—
176C4⋊C4—44no—
177C4⋊C4—44no—
178C22⋊C4—22no—
179C22⋊C4—41no—
180C22⋊C4—41no—
181C22⋊C4C2×C8×C12714yes—
182C42—24no—
183C42—22no—
184C42—22no—
185C42—42no—
186C42—41no—
187C42—41no—
188C23—21no—
189C23—21no—
190C23—42no—
191C23C2×C22⋊C4×C12711yescharacteristic
192C23C22×C8×C12711yescharacteristic
193C23C2×M16×C12711yescharacteristic
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—24no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—44no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—44no—
212C2×C4C22⋊C8×C12712yes—
213C2×C4C22⋊C8×C12712yes—
214C2×C4#99×C12711yescharacteristic
215C2×C4#99×C12711yescharacteristic
216C2×C4#101×C12712yes—
217C8—84no—
218C22—22no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—42no—
224C22—42no—
225C22C2×C22⋊C8×C12711yescharacteristic
226C22C2×#99×C12711yescharacteristic
227C22C2×#101×C12711yescharacteristic
228C4—22no—
229C4—44no—
230C4—42no—
231C4—44no—
232C4—42no—
233C4#324×C12712yes—
234C4#324×C12712yes—
235C2—21no—
236C2—21no—
237C2—41no—
238C2—41no—
239C2C2×#324×C12711yescharacteristic
240C2C127×#212012yes—
subgroupG/H
centerC2×C4×C127#99
commutatorC23C22×C8×C127
Frattini, cosocleC2×C22⋊C4C23×C127
socleC22×C127C2×#99
prime radicalC24×C127C22×C4
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C22×C4×C127 ◁ C2×#117×C127 ◁ G

Complements

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

NH ≅ G/Ntype
19. #117×C127C8semidirect
114. #11452C127direct (N × H)
124. C127#11452direct (N × H)
140. #117C8×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#22962
C127×#14582
C127×#13262
#11452127