Finite Group Databasebeta

← C127×#1889 #30634841

Subgroups — C127×#1889 #30634841

Order 16256.

578 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 112 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×#120×C127C211yesmaximal, characteristic
2#518×C127C211yesmaximal, characteristic, complemented
3C2×#99×C127C211yesmaximal, characteristic, complemented
4#379×C127C212yesmaximal, complemented
5#342×C127C212yesmaximal, complemented
6C25×C127C2211yescharacteristic
7C22×D4×C127—21no—
8C22×D4×C127C2211yescharacteristic
9#120×C127—22no—
10#120×C127C414yescomplemented
11C4×D4×C127—24no—
12#117×C127—21no—
13C2×C22⋊C4×C127—21no—
14C2×C22⋊C4×C127—21no—
15C2×C22⋊C4×C127—24no—
16C2×C22⋊C4×C127C2212yes—
17C2×C22⋊C4×C127C2212yes—
18C2×C22⋊C4×C127C2211yescharacteristic
19#99×C127—22no—
20C24×C127—22no—
21C24×C127—21no—
22C24×C127—21no—
23C24×C127—22no—
24C24×C127—44no—
25C24×C127C2×C412yescomplemented
26C24×C127D411yescharacteristic
27C24×C127C2311yescharacteristic
28C2×D4×C127—22no—
29C2×D4×C127—22no—
30C2×D4×C127—24no—
31C2×D4×C127—44no—
32C2×D4×C127C2×C412yes—
33C2×D4×C127D412yes—
34C22×C4×C127—21no—
35C22×C4×C127—22no—
36C22×C4×C127—22no—
37C22×C4×C127D411yescharacteristic
38C22×C4×C127D414yescomplemented
39C4⋊C4×C127—22no—
40C22⋊C4×C127—22no—
41C22⋊C4×C127—22no—
42C22⋊C4×C127—22no—
43C22⋊C4×C127—21no—
44C22⋊C4×C127—24no—
45C22⋊C4×C127—22no—
46C22⋊C4×C127—22no—
47C22⋊C4×C127—48no—
48C22⋊C4×C127C2×C412yescomplemented
49C42×C127—22no—
50C23×C127—28no—
51C23×C127—24no—
52C23×C127—22no—
53C23×C127—24no—
54C23×C127—21no—
55C23×C127—21no—
56C23×C127—44no—
57C23×C127—42no—
58C23×C127—44no—
59C23×C127—42no—
60C23×C127—44no—
61C23×C127—48no—
62C23×C127—42no—
63C23×C127—41no—
64C23×C127—42no—
65C23×C127—41no—
66C23×C127C22⋊C412yescomplemented
67C23×C127C22×C411yescharacteristic
68C23×C127C2×D411yescharacteristic
69C23×C127C2×D412yes—
70C23×C127C2×D411yescharacteristic
71C23×C127#4112yes—
72D4×C127—24no—
73D4×C127—24no—
74D4×C127—48no—
75C2×C4×C127—21no—
76C2×C4×C127—21no—
77C2×C4×C127—22no—
78C2×C4×C127—24no—
79C2×C4×C127—42no—
80C2×C4×C127—44no—
81C2×C4×C127—44no—
82C2×C4×C127—42no—
83C2×C4×C127—82no—
84C2×C4×C127C22⋊C412yescomplemented
85C22×C127—24no—
86C22×C127—22no—
87C22×C127—24no—
88C22×C127—28no—
89C22×C127—22no—
90C22×C127—41no—
91C22×C127—41no—
92C22×C127—42no—
93C22×C127—42no—
94C22×C127—42no—
95C22×C127—48no—
96C22×C127—44no—
97C22×C127—44no—
98C22×C127—42no—
99C22×C127—42no—
100C22×C127—44no—
101C22×C127—81no—
102C22×C127C2×C22⋊C411yescharacteristic
103C22×C127C4×D412yes—
104C22×C127#12011yescharacteristic
105C22×C127#12112yes—
106C22×C127#12311yescharacteristic
107C4×C127—22no—
108C4×C127—42no—
109C4×C127—44no—
110C4×C127—82no—
111C2×C127—21no—
112C2×C127—22no—
113C2×C127—22no—
114C2×C127—21no—
115C2×C127—44no—
116C2×C127—42no—
117C2×C127#38611yescharacteristic
118C2×C127B(4,𝔽2)12yes—
119#1889C12711yesmaximal, characteristic, direct product factor, Sylow
120C127#188911yescharacteristic, direct product factor, Sylow
121C2×#120C2×C12711yescharacteristic
122#518C2×C12711yescharacteristic, complemented
123C2×#99C2×C12711yescharacteristic, complemented
124#379C2×C12712yescomplemented
125#342C2×C12712yescomplemented
126C25C22×C12711yescharacteristic
127C22×D4—21no—
128C22×D4C22×C12711yescharacteristic
129#120—22no—
130#120C4×C12714yescomplemented
131C4×D4—24no—
132#117—21no—
133C2×C22⋊C4—21no—
134C2×C22⋊C4—21no—
135C2×C22⋊C4—24no—
136C2×C22⋊C4C22×C12712yes—
137C2×C22⋊C4C22×C12712yes—
138C2×C22⋊C4C22×C12711yescharacteristic
139#99—22no—
140C24—22no—
141C24—21no—
142C24—21no—
143C24—22no—
144C24—44no—
145C24C2×C4×C12712yescomplemented
146C24D4×C12711yescharacteristic
147C24C23×C12711yescharacteristic
148C2×D4—22no—
149C2×D4—22no—
150C2×D4—24no—
151C2×D4—44no—
152C2×D4C2×C4×C12712yes—
153C2×D4D4×C12712yes—
154C22×C4—21no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4D4×C12711yescharacteristic
158C22×C4D4×C12714yescomplemented
159C4⋊C4—22no—
160C22⋊C4—22no—
161C22⋊C4—22no—
162C22⋊C4—22no—
163C22⋊C4—21no—
164C22⋊C4—24no—
165C22⋊C4—22no—
166C22⋊C4—22no—
167C22⋊C4—48no—
168C22⋊C4C2×C4×C12712yescomplemented
169C42—22no—
170C23—28no—
171C23—24no—
172C23—22no—
173C23—24no—
174C23—21no—
175C23—21no—
176C23—44no—
177C23—42no—
178C23—44no—
179C23—42no—
180C23—44no—
181C23—48no—
182C23—42no—
183C23—41no—
184C23—42no—
185C23—41no—
186C23C22⋊C4×C12712yescomplemented
187C23C22×C4×C12711yescharacteristic
188C23C2×D4×C12711yescharacteristic
189C23C2×D4×C12712yes—
190C23C2×D4×C12711yescharacteristic
191C23#41×C12712yes—
192D4—24no—
193D4—24no—
194D4—48no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—24no—
199C2×C4—42no—
200C2×C4—44no—
201C2×C4—44no—
202C2×C4—42no—
203C2×C4—82no—
204C2×C4C22⋊C4×C12712yescomplemented
205C22—24no—
206C22—22no—
207C22—24no—
208C22—28no—
209C22—22no—
210C22—41no—
211C22—41no—
212C22—42no—
213C22—42no—
214C22—42no—
215C22—48no—
216C22—44no—
217C22—44no—
218C22—42no—
219C22—42no—
220C22—44no—
221C22—81no—
222C22C2×C22⋊C4×C12711yescharacteristic
223C22C4×D4×C12712yes—
224C22#120×C12711yescharacteristic
225C22#121×C12712yes—
226C22#123×C12711yescharacteristic
227C4—22no—
228C4—42no—
229C4—44no—
230C4—82no—
231C2—21no—
232C2—22no—
233C2—22no—
234C2—21no—
235C2—44no—
236C2—42no—
237C2#386×C12711yescharacteristic
238C2B(4,𝔽2)×C12712yes—
subgroupG/H
center, socleC22×C127#120
commutatorC23C22×C4×C127
Frattini, cosocleC24C23×C127
prime radicalC2×#120×C127C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. #518×C127C2semidirect
3. C2×#99×C127C2semidirect
4. #379×C127C2semidirect
5. #342×C127C2semidirect
10. #120×C127C4semidirect
25. C24×C127C2×C4semidirect
38. C22×C4×C127D4semidirect
48. C22⋊C4×C127C2×C4semidirect
66. C23×C127C22⋊C4semidirect
84. C2×C4×C127C22⋊C4semidirect
119. #1889C127direct (N × H)
120. C127#1889direct (N × H)
122. #518C2×C127semidirect
123. C2×#99C2×C127semidirect
124. #379C2×C127semidirect
125. #342C2×C127semidirect
130. #120C4×C127semidirect
145. C24C2×C4×C127semidirect
158. C22×C4D4×C127semidirect
168. C22⋊C4C2×C4×C127semidirect
186. C23C22⋊C4×C127semidirect
204. C2×C4C22⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#120×C1272
#518×C1272
C2×#99×C1272
#379×C1272
#342×C1272
#1889127