Finite Group Databasebeta

← C127×#11456 #44575129

Subgroups — C127×#11456 #44575129

Order 32512.

364 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 138 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×#2905C211yesmaximal, characteristic
2C2×#349×C127C212yesmaximal
3C127×#1327C214yesmaximal, complemented
4C22×M16×C127C411yescharacteristic
5C22×M16×C127C2211yescharacteristic
6C2×#117×C127C411yescharacteristic
7C2×M32×C127—22no—
8#424×C127—22no—
9#424×C127—22no—
10#423×C127C412yes—
11#423×C127C2212yes—
12#349×C127—22no—
13#349×C127C2214yes—
14C23×C4×C127C2×C411yescharacteristic
15C2×M16×C127—21no—
16C2×M16×C127—42no—
17C2×M16×C127—42no—
18C2×M16×C127C2×C412yes—
19C2×M16×C127C2×C411yescharacteristic
20C2×M16×C127D412yes—
21C2×M16×C127C2311yescharacteristic
22C22×C8×C127—21no—
23C22×C8×C127D412yes—
24#117×C127—21no—
25#117×C127—21no—
26#117×C127C812yes—
27#117×C127C812yes—
28C2×C4⋊C4×C127—21no—
29C2×C22⋊C4×C127—21no—
30C2×C42×C127C2×C412yes—
31M32×C127—24no—
32M32×C127—42no—
33C2×C16×C127—42no—
34C4⋊C8×C127—24no—
35C4⋊C8×C127—24no—
36C24×C127M1611yescharacteristic
37C22×C4×C127—22no—
38C22×C4×C127—22no—
39C22×C4×C127—22no—
40C22×C4×C127C22⋊C411yescharacteristic
41C22×C4×C127C22⋊C411yescharacteristic
42C22×C4×C127C2×C811yescharacteristic
43C22×C4×C127C2×C811yescharacteristic
44C22×C4×C127M1611yescharacteristic
45C22×C4×C127C22×C411yescharacteristic
46M16×C127—41no—
47M16×C127—42no—
48M16×C127—41no—
49M16×C127—42no—
50M16×C127—42no—
51C2×C8×C127—22no—
52C2×C8×C127—22no—
53C2×C8×C127—22no—
54C2×C8×C127—42no—
55C2×C8×C127C22⋊C412yes—
56C2×C8×C127C2×D412yes—
57C4⋊C4×C127—22no—
58C4⋊C4×C127—22no—
59C22⋊C4×C127—22no—
60C22⋊C4×C127—22no—
61C42×C127—22no—
62C42×C127C2×C814yes—
63C16×C127—44no—
64C23×C127—22no—
65C23×C127—81no—
66C23×C127C22⋊C811yescharacteristic
67C23×C127C22⋊C811yescharacteristic
68C23×C127C2×M1611yescharacteristic
69C2×C4×C127—22no—
70C2×C4×C127—22no—
71C2×C4×C127—22no—
72C2×C4×C127—21no—
73C2×C4×C127—21no—
74C2×C4×C127—21no—
75C2×C4×C127—21no—
76C2×C4×C127—24no—
77C2×C4×C127—82no—
78C2×C4×C127C22⋊C811yescharacteristic
79C2×C4×C127C22⋊C811yescharacteristic
80C2×C4×C127#9912yes—
81C2×C4×C127#10112yes—
82C2×C4×C127C2×C22⋊C411yescharacteristic
83C2×C4×C127C22×C811yescharacteristic
84C8×C127—22no—
85C8×C127—22no—
86C8×C127—42no—
87C22×C127—21no—
88C22×C127—21no—
89C22×C127—41no—
90C22×C127—41no—
91C22×C127—41no—
92C22×C127—82no—
93C22×C127#32412yes—
94C22×C127C2×C22⋊C811yescharacteristic
95C4×C127—21no—
96C4×C127—21no—
97C4×C127—44no—
98C4×C127#32412yes—
99C4×C127C2×#9911yescharacteristic
100C4×C127C2×#10111yescharacteristic
101#11456C12711yesmaximal, characteristic, direct product factor, Sylow
102C2×C127—21no—
103C2×C127—22no—
104C2×C127—41no—
105C2×C127—41no—
106C2×C127C2×#32411yescharacteristic
107#2905C2×C12711yescharacteristic
108C2×#349C2×C12712yes—
109#1327C2×C12714yescomplemented
110C127#1145611yescharacteristic, direct product factor, Sylow
111C22×M16C4×C12711yescharacteristic
112C22×M16C22×C12711yescharacteristic
113C2×#117C4×C12711yescharacteristic
114C2×M32—22no—
115#424—22no—
116#424—22no—
117#423C4×C12712yes—
118#423C22×C12712yes—
119#349—22no—
120#349C22×C12714yes—
121C23×C4C2×C4×C12711yescharacteristic
122C2×M16—21no—
123C2×M16—42no—
124C2×M16—42no—
125C2×M16C2×C4×C12712yes—
126C2×M16C2×C4×C12711yescharacteristic
127C2×M16D4×C12712yes—
128C2×M16C23×C12711yescharacteristic
129C22×C8—21no—
130C22×C8D4×C12712yes—
131#117—21no—
132#117—21no—
133#117C8×C12712yes—
134#117C8×C12712yes—
135C2×C4⋊C4—21no—
136C2×C22⋊C4—21no—
137C2×C42C2×C4×C12712yes—
138M32—24no—
139M32—42no—
140C2×C16—42no—
141C4⋊C8—24no—
142C4⋊C8—24no—
143C24M16×C12711yescharacteristic
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4C22⋊C4×C12711yescharacteristic
148C22×C4C22⋊C4×C12711yescharacteristic
149C22×C4C2×C8×C12711yescharacteristic
150C22×C4C2×C8×C12711yescharacteristic
151C22×C4M16×C12711yescharacteristic
152C22×C4C22×C4×C12711yescharacteristic
153M16—41no—
154M16—42no—
155M16—41no—
156M16—42no—
157M16—42no—
158C2×C8—22no—
159C2×C8—22no—
160C2×C8—22no—
161C2×C8—42no—
162C2×C8C22⋊C4×C12712yes—
163C2×C8C2×D4×C12712yes—
164C4⋊C4—22no—
165C4⋊C4—22no—
166C22⋊C4—22no—
167C22⋊C4—22no—
168C42—22no—
169C42C2×C8×C12714yes—
170C16—44no—
171C23—22no—
172C23—81no—
173C23C22⋊C8×C12711yescharacteristic
174C23C22⋊C8×C12711yescharacteristic
175C23C2×M16×C12711yescharacteristic
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—24no—
184C2×C4—82no—
185C2×C4C22⋊C8×C12711yescharacteristic
186C2×C4C22⋊C8×C12711yescharacteristic
187C2×C4#99×C12712yes—
188C2×C4#101×C12712yes—
189C2×C4C2×C22⋊C4×C12711yescharacteristic
190C2×C4C22×C8×C12711yescharacteristic
191C8—22no—
192C8—22no—
193C8—42no—
194C22—21no—
195C22—21no—
196C22—41no—
197C22—41no—
198C22—41no—
199C22—82no—
200C22#324×C12712yes—
201C22C2×C22⋊C8×C12711yescharacteristic
202C4—21no—
203C4—21no—
204C4—44no—
205C4#324×C12712yes—
206C4C2×#99×C12711yescharacteristic
207C4C2×#101×C12711yescharacteristic
208C2—21no—
209C2—22no—
210C2—41no—
211C2—41no—
212C2C2×#324×C12711yescharacteristic
subgroupG/H
centerC4×C127C2×#99
commutatorC2×C4C22×C8×C127
Frattini, cosocleC2×M16C23×C127
socleC2×C127C2×#324
prime radicalC24×C127M16
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C22×C4×C127 ◁ C22×M16×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1327C2semidirect
101. #11456C127direct (N × H)
109. #1327C2×C127semidirect
110. C127#11456direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#29052
C2×#349×C1272
C127×#13272
#11456127