Finite Group Databasebeta

← C127×#11491 #44575164

Subgroups — C127×#11491 #44575164

Order 32512.

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

normal subgroups only

This group has 356 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×#2931C211yesmaximal, characteristic
2C127×#2163C212yesmaximal, complemented
3C127×#1315C214yesmaximal, complemented
4C2×#131×C127C412yes—
5#532×C127C411yescharacteristic
6#436×C127—22no—
7C8×D4×C127—22no—
8#423×C127C411yescharacteristic
9#408×C127C2212yes—
10C2×C4×C8×C127C2211yescharacteristic
11C4⋊C16×C127—22no—
12C22⋊C16×C127C2214yes—
13#346×C127—22no—
14C2×#41×C127C2×C412yes—
15#131×C127—44no—
16C2×M16×C127—22no—
17C2×M16×C127C2×C412yes—
18C22×C8×C127—22no—
19C22×C8×C127C2×C411yescharacteristic
20C22×C8×C127C2311yescharacteristic
21C4⋊Q8×C127C811yescharacteristic
22#127×C127C811yescharacteristic
23#124×C127C812yes—
24#121×C127—22no—
25C4×D4×C127—22no—
26C2×C42×C127C2×C411yescharacteristic
27C2×C16×C127—24no—
28C4⋊C8×C127—22no—
29C22⋊C8×C127—24no—
30C4×C8×C127D412yes—
31C4×C8×C127D412yes—
32#41×C127—42no—
33#41×C127—42no—
34C2×Q8×C127C2×C812yes—
35C2×D4×C127—22no—
36C2×D4×C127—22no—
37C2×D4×C127C2×C812yes—
38C22×C4×C127—22no—
39C22×C4×C127M1612yes—
40C22×C4×C127C22×C411yescharacteristic
41M16×C127—44no—
42M16×C127—42no—
43C2×C8×C127—22no—
44C2×C8×C127—22no—
45C2×C8×C127—41no—
46C2×C8×C127—44no—
47C2×C8×C127C22⋊C411yescharacteristic
48C2×C8×C127C22⋊C411yescharacteristic
49C2×C8×C127C2×D412yes—
50C4⋊C4×C127—22no—
51C22⋊C4×C127—24no—
52C42×C127C22⋊C412yes—
53C42×C127C2×C811yescharacteristic
54C42×C127C2×C811yescharacteristic
55C16×C127—44no—
56C23×C127—22no—
57C23×C127C2×M1611yescharacteristic
58Q8×C127—42no—
59D4×C127—42no—
60D4×C127—44no—
61D4×C127—44no—
62C2×C4×C127—21no—
63C2×C4×C127—21no—
64C2×C4×C127—22no—
65C2×C4×C127—42no—
66C2×C4×C127—42no—
67C2×C4×C127—42no—
68C2×C4×C127C22⋊C812yes—
69C2×C4×C127C22⋊C812yes—
70C2×C4×C127C2×C22⋊C411yescharacteristic
71C2×C4×C127C22×C811yescharacteristic
72C8×C127—22no—
73C8×C127—21no—
74C8×C127—42no—
75C8×C127#10012yes—
76C22×C127—22no—
77C22×C127—21no—
78C22×C127—44no—
79C22×C127—42no—
80C22×C127C2×C22⋊C811yescharacteristic
81C4×C127—22no—
82C4×C127—22no—
83C4×C127—21no—
84C4×C127—42no—
85C4×C127#41011yescharacteristic
86C4×C127C2×#10011yescharacteristic
87#11491C12711yesmaximal, characteristic, direct product factor, Sylow
88C2×C127—41no—
89C2×C127—82no—
90C2×C127#146011yescharacteristic
91C2×C127#211712yes—
92#2931C2×C12711yescharacteristic
93#2163C2×C12712yescomplemented
94#1315C2×C12714yescomplemented
95C127#1149111yescharacteristic, direct product factor, Sylow
96C2×#131C4×C12712yes—
97#532C4×C12711yescharacteristic
98#436—22no—
99C8×D4—22no—
100#423C4×C12711yescharacteristic
101#408C22×C12712yes—
102C2×C4×C8C22×C12711yescharacteristic
103C4⋊C16—22no—
104C22⋊C16C22×C12714yes—
105#346—22no—
106C2×#41C2×C4×C12712yes—
107#131—44no—
108C2×M16—22no—
109C2×M16C2×C4×C12712yes—
110C22×C8—22no—
111C22×C8C2×C4×C12711yescharacteristic
112C22×C8C23×C12711yescharacteristic
113C4⋊Q8C8×C12711yescharacteristic
114#127C8×C12711yescharacteristic
115#124C8×C12712yes—
116#121—22no—
117C4×D4—22no—
118C2×C42C2×C4×C12711yescharacteristic
119C2×C16—24no—
120C4⋊C8—22no—
121C22⋊C8—24no—
122C4×C8D4×C12712yes—
123C4×C8D4×C12712yes—
124#41—42no—
125#41—42no—
126C2×Q8C2×C8×C12712yes—
127C2×D4—22no—
128C2×D4—22no—
129C2×D4C2×C8×C12712yes—
130C22×C4—22no—
131C22×C4M16×C12712yes—
132C22×C4C22×C4×C12711yescharacteristic
133M16—44no—
134M16—42no—
135C2×C8—22no—
136C2×C8—22no—
137C2×C8—41no—
138C2×C8—44no—
139C2×C8C22⋊C4×C12711yescharacteristic
140C2×C8C22⋊C4×C12711yescharacteristic
141C2×C8C2×D4×C12712yes—
142C4⋊C4—22no—
143C22⋊C4—24no—
144C42C22⋊C4×C12712yes—
145C42C2×C8×C12711yescharacteristic
146C42C2×C8×C12711yescharacteristic
147C16—44no—
148C23—22no—
149C23C2×M16×C12711yescharacteristic
150Q8—42no—
151D4—42no—
152D4—44no—
153D4—44no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—42no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4C22⋊C8×C12712yes—
161C2×C4C22⋊C8×C12712yes—
162C2×C4C2×C22⋊C4×C12711yescharacteristic
163C2×C4C22×C8×C12711yescharacteristic
164C8—22no—
165C8—21no—
166C8—42no—
167C8#100×C12712yes—
168C22—22no—
169C22—21no—
170C22—44no—
171C22—42no—
172C22C2×C22⋊C8×C12711yescharacteristic
173C4—22no—
174C4—22no—
175C4—21no—
176C4—42no—
177C4#410×C12711yescharacteristic
178C4C2×#100×C12711yescharacteristic
179C2—41no—
180C2—82no—
181C2C127×#146011yescharacteristic
182C2C127×#211712yes—
subgroupG/H
centerC2×C4×C127C2×C22⋊C4
commutatorC2×C4C22×C8×C127
Frattini, cosocleC22×C8C23×C127
socleC22×C127C2×C22⋊C8
prime radical#532×C127C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2163C2semidirect
3. C127×#1315C2semidirect
87. #11491C127direct (N × H)
93. #2163C2×C127semidirect
94. #1315C2×C127semidirect
95. C127#11491direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#29312
C127×#21632
C127×#13152
#11491127