Finite Group Databasebeta

← C127×#11482 #44575155

Subgroups — C127×#11482 #44575155

Order 32512.

392 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 130 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×#2327C211yesmaximal, characteristic
2C127×#1461C212yesmaximal
3C127×#1324C212yesmaximal
4C127×#1319C212yesmaximal
5C2×C4⋊Q8×C127C411yescharacteristic
6C2×C4×Q8×C127C411yescharacteristic
7C2×C4×Q8×C127C2211yescharacteristic
8#431×C127—22no—
9#391×C127C411yescharacteristic
10#391×C127C2211yescharacteristic
11#387×C127—22no—
12#387×C127—22no—
13#382×C127C2211yescharacteristic
14#376×C127C411yescharacteristic
15#324×C127—22no—
16#324×C127C2214yes—
17C22×Q8×C127C2×C411yescharacteristic
18C22×Q8×C127C2×C411yescharacteristic
19C4⋊Q8×C127—22no—
20C4⋊Q8×C127C814yescomplemented
21C4×Q8×C127—42no—
22C4×Q8×C127—42no—
23C2×C4⋊C4×C127—22no—
24C2×C4⋊C4×C127—21no—
25C2×C4⋊C4×C127C2×C411yescharacteristic
26C2×C4⋊C4×C127D412yes—
27C2×C4⋊C4×C127C2311yescharacteristic
28C2×C42×C127—21no—
29C2×C42×C127C2×C411yescharacteristic
30C2×C42×C127C2×C411yescharacteristic
31C2×C42×C127C2×C411yescharacteristic
32C2×C42×C127D412yes—
33C4⋊C8×C127—42no—
34C22⋊C8×C127—24no—
35C4×C8×C127—42no—
36#95×C127—21no—
37#95×C127—22no—
38#95×C127—21no—
39#95×C127—22no—
40#95×C127—22no—
41C2×Q8×C127—21no—
42C2×Q8×C127—41no—
43C2×Q8×C127—41no—
44C2×Q8×C127—41no—
45C2×Q8×C127—41no—
46C2×Q8×C127C2×C812yes—
47C2×Q8×C127C2×C812yes—
48C2×Q8×C127M1612yes—
49C22×C4×C127—21no—
50C22×C4×C127—21no—
51C22×C4×C127—21no—
52C22×C4×C127—21no—
53C22×C4×C127C22⋊C412yes—
54C22×C4×C127C22⋊C411yescharacteristic
55C22×C4×C127C22⋊C411yescharacteristic
56C22×C4×C127C22×C411yescharacteristic
57C22×C4×C127C2×D412yes—
58C2×C8×C127—44no—
59C4⋊C4×C127—28no—
60C4⋊C4×C127—42no—
61C4⋊C4×C127—41no—
62C4⋊C4×C127—41no—
63C4⋊C4×C127—42no—
64C42×C127—22no—
65C42×C127—22no—
66C42×C127—22no—
67C42×C127—21no—
68C42×C127—41no—
69C42×C127—42no—
70C42×C127C2×C812yes—
71C23×C127C2×C22⋊C411yescharacteristic
72Q8×C127—42no—
73Q8×C127—42no—
74Q8×C127—42no—
75Q8×C127—42no—
76C2×C4×C127—21no—
77C2×C4×C127—22no—
78C2×C4×C127—21no—
79C2×C4×C127—22no—
80C2×C4×C127—22no—
81C2×C4×C127—22no—
82C2×C4×C127—21no—
83C2×C4×C127—22no—
84C2×C4×C127—41no—
85C2×C4×C127—41no—
86C2×C4×C127—41no—
87C2×C4×C127—41no—
88C2×C4×C127—41no—
89C2×C4×C127—41no—
90C2×C4×C127—42no—
91C2×C4×C127—41no—
92C2×C4×C127—41no—
93C2×C4×C127—42no—
94C2×C4×C127—41no—
95C2×C4×C127—41no—
96C2×C4×C127C22⋊C814yes—
97C2×C4×C127#9912yes—
98C2×C4×C127C22×C811yescharacteristic
99C2×C4×C127C2×M1611yescharacteristic
100C8×C127—84no—
101C22×C127—21no—
102C22×C127—21no—
103C22×C127C2×C22⋊C811yescharacteristic
104C22×C127C2×#9911yescharacteristic
105C22×C127#41311yescharacteristic
106C4×C127—22no—
107C4×C127—24no—
108C4×C127—21no—
109C4×C127—21no—
110C4×C127—42no—
111C4×C127—42no—
112C4×C127—41no—
113C4×C127—42no—
114C4×C127—81no—
115C4×C127—81no—
116#11482C12711yesmaximal, characteristic, direct product factor, Sylow
117C2×C127—21no—
118C2×C127—21no—
119C2×C127#145911yescharacteristic
120C2×C127#212911yescharacteristic
121C2×C127#213311yescharacteristic
122#2327C2×C12711yescharacteristic
123#1461C2×C12712yes—
124#1324C2×C12712yes—
125#1319C2×C12712yes—
126C127#1148211yescharacteristic, direct product factor, Sylow
127C2×C4⋊Q8C4×C12711yescharacteristic
128C2×C4×Q8C4×C12711yescharacteristic
129C2×C4×Q8C22×C12711yescharacteristic
130#431—22no—
131#391C4×C12711yescharacteristic
132#391C22×C12711yescharacteristic
133#387—22no—
134#387—22no—
135#382C22×C12711yescharacteristic
136#376C4×C12711yescharacteristic
137#324—22no—
138#324C22×C12714yes—
139C22×Q8C2×C4×C12711yescharacteristic
140C22×Q8C2×C4×C12711yescharacteristic
141C4⋊Q8—22no—
142C4⋊Q8C8×C12714yescomplemented
143C4×Q8—42no—
144C4×Q8—42no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4C2×C4×C12711yescharacteristic
148C2×C4⋊C4D4×C12712yes—
149C2×C4⋊C4C23×C12711yescharacteristic
150C2×C42—21no—
151C2×C42C2×C4×C12711yescharacteristic
152C2×C42C2×C4×C12711yescharacteristic
153C2×C42C2×C4×C12711yescharacteristic
154C2×C42D4×C12712yes—
155C4⋊C8—42no—
156C22⋊C8—24no—
157C4×C8—42no—
158#95—21no—
159#95—21no—
160#95—22no—
161#95—22no—
162#95—22no—
163C2×Q8—21no—
164C2×Q8—41no—
165C2×Q8—41no—
166C2×Q8—41no—
167C2×Q8—41no—
168C2×Q8C2×C8×C12712yes—
169C2×Q8C2×C8×C12712yes—
170C2×Q8M16×C12712yes—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4C22⋊C4×C12712yes—
176C22×C4C22⋊C4×C12711yescharacteristic
177C22×C4C22⋊C4×C12711yescharacteristic
178C22×C4C22×C4×C12711yescharacteristic
179C22×C4C2×D4×C12712yes—
180C2×C8—44no—
181C4⋊C4—28no—
182C4⋊C4—42no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C4⋊C4—42no—
186C42—22no—
187C42—22no—
188C42—22no—
189C42—21no—
190C42—41no—
191C42—42no—
192C42C2×C8×C12712yes—
193C23C2×C22⋊C4×C12711yescharacteristic
194Q8—42no—
195Q8—42no—
196Q8—42no—
197Q8—42no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4C22⋊C8×C12714yes—
219C2×C4#99×C12712yes—
220C2×C4C22×C8×C12711yescharacteristic
221C2×C4C2×M16×C12711yescharacteristic
222C8—84no—
223C22—21no—
224C22—21no—
225C22C2×C22⋊C8×C12711yescharacteristic
226C22C2×#99×C12711yescharacteristic
227C22#413×C12711yescharacteristic
228C4—22no—
229C4—24no—
230C4—21no—
231C4—21no—
232C4—42no—
233C4—42no—
234C4—41no—
235C4—42no—
236C4—81no—
237C4—81no—
238C2—21no—
239C2—21no—
240C2C127×#145911yescharacteristic
241C2C127×#212911yescharacteristic
242C2C127×#213311yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC2×C4C22×C8×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC23×C127C2×C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
20. C4⋊Q8×C127C8semidirect
116. #11482C127direct (N × H)
126. C127#11482direct (N × H)
142. C4⋊Q8C8×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#23272
C127×#14612
C127×#13242
C127×#13192
#11482127