Finite Group Databasebeta

← C127×#11914 #44575587

Subgroups — C127×#11914 #44575587

Order 32512.

272 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 94 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×#3177C211yesmaximal, characteristic
2C127×#2166C211yesmaximal, characteristic
3C127×#2110C211yesmaximal, characteristic
4C127×#1356C214yesmaximal, complemented
5#541×C127C412yes—
6C2×M32×C127—21no—
7#499×C127C411yescharacteristic
8#494×C127C411yescharacteristic
9#491×C127C2212yes—
10#470×C127—21no—
11#467×C127—21no—
12#441×C127—21no—
13C4×Q16×C127—21no—
14#405×C127C2211yescharacteristic
15#364×C127—21no—
16#349×C127—21no—
17#347×C127—21no—
18#347×C127C2212yes—
19#347×C127C2212yes—
20C2×Q16×C127—21no—
21C2×Q16×C127—21no—
22C2×M16×C127D411yescharacteristic
23C22×C8×C127D411yescharacteristic
24C4⋊Q8×C127C2×C412yes—
25#126×C127—42no—
26#125×C127—42no—
27#125×C127C2×C412yes—
28C22⋊Q8×C127—22no—
29C4×Q8×C127—22no—
30#117×C127C2×C411yescharacteristic
31M32×C127—22no—
32M32×C127—22no—
33M32×C127—22no—
34C2×C16×C127—22no—
35#107×C127—21no—
36#106×C127—21no—
37#103×C127—22no—
38#103×C127—22no—
39#97×C127D411yescharacteristic
40#97×C127C2311yescharacteristic
41C4×C8×C127C2×C411yescharacteristic
42C4×C8×C127D411yescharacteristic
43C2×Q8×C127—22no—
44C22×C4×C127C22⋊C411yescharacteristic
45Q16×C127—42no—
46Q16×C127—41no—
47Q16×C127—41no—
48M16×C127—41no—
49C2×C8×C127—21no—
50C2×C8×C127—21no—
51C2×C8×C127C22⋊C411yescharacteristic
52C2×C8×C127C22⋊C411yescharacteristic
53C2×C8×C127C2×D411yescharacteristic
54C2×C8×C127C2×D411yescharacteristic
55C4⋊C4×C127—21no—
56C4⋊C4×C127—22no—
57C4⋊C4×C127—42no—
58C4⋊C4×C127—42no—
59C4⋊C4×C127—42no—
60C4⋊C4×C127—42no—
61C22⋊C4×C127—21no—
62C22⋊C4×C127—42no—
63C42×C127—42no—
64C42×C127C22⋊C411yescharacteristic
65C42×C127C22×C411yescharacteristic
66C16×C127—24no—
67C16×C127—42no—
68C23×C127#10011yescharacteristic
69Q8×C127—42no—
70Q8×C127—42no—
71C2×C4×C127—21no—
72C2×C4×C127—21no—
73C2×C4×C127—21no—
74C2×C4×C127—21no—
75C2×C4×C127—42no—
76C2×C4×C127—42no—
77C2×C4×C127#10011yescharacteristic
78C2×C4×C127C2×C22⋊C411yescharacteristic
79C8×C127—21no—
80C8×C127—21no—
81C8×C127—21no—
82C8×C127#10411yescharacteristic
83C8×C127#10411yescharacteristic
84C22×C127—21no—
85C22×C127—41no—
86C22×C127C2×#10011yescharacteristic
87C4×C127—21no—
88C4×C127—41no—
89C4×C127—41no—
90C4×C127—82no—
91C4×C127—82no—
92C4×C127C2×#10411yescharacteristic
93C4×C127#42111yescharacteristic
94#11914C12711yesmaximal, characteristic, direct product factor, Sylow
95C2×C127—21no—
96C2×C127—41no—
97C2×C127#153011yescharacteristic
98#3177C2×C12711yescharacteristic
99#2166C2×C12711yescharacteristic
100#2110C2×C12711yescharacteristic
101#1356C2×C12714yescomplemented
102C127#1191411yescharacteristic, direct product factor, Sylow
103#541C4×C12712yes—
104C2×M32—21no—
105#499C4×C12711yescharacteristic
106#494C4×C12711yescharacteristic
107#491C22×C12712yes—
108#470—21no—
109#467—21no—
110#441—21no—
111C4×Q16—21no—
112#405C22×C12711yescharacteristic
113#364—21no—
114#349—21no—
115#347—21no—
116#347C22×C12712yes—
117#347C22×C12712yes—
118C2×Q16—21no—
119C2×Q16—21no—
120C2×M16D4×C12711yescharacteristic
121C22×C8D4×C12711yescharacteristic
122C4⋊Q8C2×C4×C12712yes—
123#126—42no—
124#125—42no—
125#125C2×C4×C12712yes—
126C22⋊Q8—22no—
127C4×Q8—22no—
128#117C2×C4×C12711yescharacteristic
129M32—22no—
130M32—22no—
131M32—22no—
132C2×C16—22no—
133#107—21no—
134#106—21no—
135#103—22no—
136#103—22no—
137#97D4×C12711yescharacteristic
138#97C23×C12711yescharacteristic
139C4×C8C2×C4×C12711yescharacteristic
140C4×C8D4×C12711yescharacteristic
141C2×Q8—22no—
142C22×C4C22⋊C4×C12711yescharacteristic
143Q16—42no—
144Q16—41no—
145Q16—41no—
146M16—41no—
147C2×C8—21no—
148C2×C8—21no—
149C2×C8C22⋊C4×C12711yescharacteristic
150C2×C8C22⋊C4×C12711yescharacteristic
151C2×C8C2×D4×C12711yescharacteristic
152C2×C8C2×D4×C12711yescharacteristic
153C4⋊C4—21no—
154C4⋊C4—22no—
155C4⋊C4—42no—
156C4⋊C4—42no—
157C4⋊C4—42no—
158C4⋊C4—42no—
159C22⋊C4—21no—
160C22⋊C4—42no—
161C42—42no—
162C42C22⋊C4×C12711yescharacteristic
163C42C22×C4×C12711yescharacteristic
164C16—24no—
165C16—42no—
166C23#100×C12711yescharacteristic
167Q8—42no—
168Q8—42no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4#100×C12711yescharacteristic
176C2×C4C2×C22⋊C4×C12711yescharacteristic
177C8—21no—
178C8—21no—
179C8—21no—
180C8#104×C12711yescharacteristic
181C8#104×C12711yescharacteristic
182C22—21no—
183C22—41no—
184C22C2×#100×C12711yescharacteristic
185C4—21no—
186C4—41no—
187C4—41no—
188C4—82no—
189C4—82no—
190C4C2×#104×C12711yescharacteristic
191C4#421×C12711yescharacteristic
192C2—21no—
193C2—41no—
194C2C127×#153011yescharacteristic
subgroupG/H
center, socleC2×C127#1530
commutatorC42C22×C4×C127
Frattini, cosocle#97C23×C127
prime radicalC23×C127#100
LCSG ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ #405×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1356C2semidirect
94. #11914C127direct (N × H)
101. #1356C2×C127semidirect
102. C127#11914direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31772
C127×#21662
C127×#21102
C127×#13562
#11914127