Finite Group Databasebeta

← C127×#11913 #44575586

Subgroups — C127×#11913 #44575586

Order 32512.

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

normal subgroups only

This group has 296 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×#3176C211yesmaximal, characteristic
2C127×#2166C211yesmaximal, characteristic, complemented
3C127×#2110C211yesmaximal, characteristic, complemented
4C127×#1355C214yesmaximal, complemented
5#540×C127C412yes—
6C2×M32×C127—21no—
7#499×C127C411yescharacteristic
8#493×C127C411yescharacteristic
9#490×C127C2212yes—
10#469×C127—21no—
11#466×C127—21no—
12#442×C127—21no—
13C4×D8×C127—21no—
14#405×C127C2211yescharacteristic
15#364×C127—21no—
16#349×C127—21no—
17#347×C127—21no—
18#347×C127C2212yes—
19#347×C127C2212yes—
20C2×D8×C127—21no—
21C2×D8×C127—21no—
22C2×M16×C127D411yescharacteristic
23C22×C8×C127D411yescharacteristic
24#127×C127C2×C412yes—
25#125×C127C2×C412yes—
26#123×C127—42no—
27#121×C127—22no—
28#121×C127—42no—
29C4×D4×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#102×C127—22no—
38#102×C127—22no—
39#97×C127D411yescharacteristic
40#97×C127C2311yescharacteristic
41C4×C8×C127C2×C411yescharacteristic
42C4×C8×C127D411yescharacteristic
43C2×D4×C127—22no—
44C2×D4×C127—42no—
45C2×D4×C127—42no—
46C22×C4×C127—42no—
47C22×C4×C127C22⋊C411yescharacteristic
48D8×C127—42no—
49D8×C127—41no—
50D8×C127—41no—
51M16×C127—41no—
52C2×C8×C127—21no—
53C2×C8×C127—21no—
54C2×C8×C127C22⋊C411yescharacteristic
55C2×C8×C127C22⋊C411yescharacteristic
56C2×C8×C127C2×D411yescharacteristic
57C2×C8×C127C2×D411yescharacteristic
58C4⋊C4×C127—21no—
59C4⋊C4×C127—22no—
60C4⋊C4×C127—42no—
61C22⋊C4×C127—21no—
62C22⋊C4×C127—42no—
63C22⋊C4×C127—42no—
64C42×C127C22⋊C411yescharacteristic
65C42×C127C22×C411yescharacteristic
66C16×C127—24no—
67C16×C127—42no—
68C23×C127—42no—
69C23×C127#10011yescharacteristic
70D4×C127—42no—
71D4×C127—42no—
72D4×C127—162no—
73D4×C127—162no—
74C2×C4×C127—21no—
75C2×C4×C127—21no—
76C2×C4×C127—21no—
77C2×C4×C127—21no—
78C2×C4×C127—42no—
79C2×C4×C127—162no—
80C2×C4×C127#10011yescharacteristic
81C2×C4×C127C2×C22⋊C411yescharacteristic
82C8×C127—21no—
83C8×C127—21no—
84C8×C127—21no—
85C8×C127#10411yescharacteristic
86C8×C127#10411yescharacteristic
87C22×C127—21no—
88C22×C127—41no—
89C22×C127—82no—
90C22×C127—82no—
91C22×C127—82no—
92C22×C127C2×#10011yescharacteristic
93C4×C127—21no—
94C4×C127—41no—
95C4×C127—41no—
96C4×C127—82no—
97C4×C127C2×#10411yescharacteristic
98C4×C127#42111yescharacteristic
99#11913C12711yesmaximal, characteristic, direct product factor, Sylow
100C2×C127—21no—
101C2×C127—41no—
102C2×C127—162no—
103C2×C127#153011yescharacteristic
104#3176C2×C12711yescharacteristic
105#2166C2×C12711yescharacteristic, complemented
106#2110C2×C12711yescharacteristic, complemented
107#1355C2×C12714yescomplemented
108C127#1191311yescharacteristic, direct product factor, Sylow
109#540C4×C12712yes—
110C2×M32—21no—
111#499C4×C12711yescharacteristic
112#493C4×C12711yescharacteristic
113#490C22×C12712yes—
114#469—21no—
115#466—21no—
116#442—21no—
117C4×D8—21no—
118#405C22×C12711yescharacteristic
119#364—21no—
120#349—21no—
121#347—21no—
122#347C22×C12712yes—
123#347C22×C12712yes—
124C2×D8—21no—
125C2×D8—21no—
126C2×M16D4×C12711yescharacteristic
127C22×C8D4×C12711yescharacteristic
128#127C2×C4×C12712yes—
129#125C2×C4×C12712yes—
130#123—42no—
131#121—22no—
132#121—42no—
133C4×D4—22no—
134#117C2×C4×C12711yescharacteristic
135M32—22no—
136M32—22no—
137M32—22no—
138C2×C16—22no—
139#107—21no—
140#106—21no—
141#102—22no—
142#102—22no—
143#97D4×C12711yescharacteristic
144#97C23×C12711yescharacteristic
145C4×C8C2×C4×C12711yescharacteristic
146C4×C8D4×C12711yescharacteristic
147C2×D4—22no—
148C2×D4—42no—
149C2×D4—42no—
150C22×C4—42no—
151C22×C4C22⋊C4×C12711yescharacteristic
152D8—42no—
153D8—41no—
154D8—41no—
155M16—41no—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8C22⋊C4×C12711yescharacteristic
159C2×C8C22⋊C4×C12711yescharacteristic
160C2×C8C2×D4×C12711yescharacteristic
161C2×C8C2×D4×C12711yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—22no—
164C4⋊C4—42no—
165C22⋊C4—21no—
166C22⋊C4—42no—
167C22⋊C4—42no—
168C42C22⋊C4×C12711yescharacteristic
169C42C22×C4×C12711yescharacteristic
170C16—24no—
171C16—42no—
172C23—42no—
173C23#100×C12711yescharacteristic
174D4—42no—
175D4—42no—
176D4—162no—
177D4—162no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—42no—
183C2×C4—162no—
184C2×C4#100×C12711yescharacteristic
185C2×C4C2×C22⋊C4×C12711yescharacteristic
186C8—21no—
187C8—21no—
188C8—21no—
189C8#104×C12711yescharacteristic
190C8#104×C12711yescharacteristic
191C22—21no—
192C22—41no—
193C22—82no—
194C22—82no—
195C22—82no—
196C22C2×#100×C12711yescharacteristic
197C4—21no—
198C4—41no—
199C4—41no—
200C4—82no—
201C4C2×#104×C12711yescharacteristic
202C4#421×C12711yescharacteristic
203C2—21no—
204C2—41no—
205C2—162no—
206C2C127×#153011yescharacteristic
subgroupG/H
center, socleC2×C127#1530
commutatorC42C22×C4×C127
Frattini, cosocle#97C23×C127
prime radicalC127×#3176C2
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
2. C127×#2166C2semidirect
3. C127×#2110C2semidirect
4. C127×#1355C2semidirect
99. #11913C127direct (N × H)
105. #2166C2×C127semidirect
106. #2110C2×C127semidirect
107. #1355C2×C127semidirect
108. C127#11913direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31762
C127×#21662
C127×#21102
C127×#13552
#11913127