Finite Group Databasebeta

← C127×#1931 #30634883

Subgroups — C127×#1931 #30634883

Order 16256.

232 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 96 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
1#428×C127C211yesmaximal, characteristic, complemented
2#418×C127C211yesmaximal, characteristic
3C2×#102×C127C211yesmaximal, characteristic
4C2×#100×C127C211yesmaximal, characteristic
5#405×C127C211yesmaximal, characteristic, complemented
6#343×C127C211yesmaximal, characteristic, complemented
7#341×C127C211yesmaximal, characteristic, complemented
8C22×D4×C127C2211yescharacteristic
9C2×M16×C127C2211yescharacteristic
10C2×M16×C127C2211yescharacteristic
11C2×M16×C127C2211yescharacteristic
12C22×C8×C127C2211yescharacteristic
13#117×C127C2211yescharacteristic
14C2×C4⋊C4×C127C2211yescharacteristic
15#107×C127—21no—
16#106×C127—21no—
17#102×C127—21no—
18#102×C127—21no—
19#102×C127—21no—
20#102×C127—21no—
21#100×C127C414yescomplemented
22#97×C127—21no—
23C4×C8×C127—21no—
24C24×C127—21no—
25C2×D4×C127—21no—
26C2×D4×C127—21no—
27C2×D4×C127—21no—
28C2×D4×C127—21no—
29C2×D4×C127—21no—
30C2×D4×C127C2×C412yes—
31C22×C4×C127—21no—
32C22×C4×C127C2311yescharacteristic
33M16×C127—21no—
34M16×C127—21no—
35M16×C127—21no—
36M16×C127—21no—
37M16×C127C2×C412yes—
38M16×C127C2×C412yes—
39C2×C8×C127—21no—
40C2×C8×C127—21no—
41C2×C8×C127—21no—
42C2×C8×C127—21no—
43C2×C8×C127—21no—
44C2×C8×C127D411yescharacteristic
45C2×C8×C127D411yescharacteristic
46C4⋊C4×C127—21no—
47C4⋊C4×C127—21no—
48C4⋊C4×C127D411yescharacteristic
49C4⋊C4×C127D411yescharacteristic
50C22⋊C4×C127—21no—
51C42×C127—21no—
52C23×C127—22no—
53C23×C127—41no—
54C23×C127—41no—
55C23×C127—81no—
56C23×C127—81no—
57C23×C127#4111yescharacteristic
58D4×C127—22no—
59D4×C127—22no—
60D4×C127—41no—
61D4×C127—41no—
62C2×C4×C127—21no—
63C2×C4×C127—21no—
64C2×C4×C127—41no—
65C2×C4×C127—81no—
66C2×C4×C127C22×C411yescharacteristic
67C2×C4×C127C2×D411yescharacteristic
68C2×C4×C127C2×D411yescharacteristic
69C2×C4×C127#4111yescharacteristic
70C2×C4×C127#4111yescharacteristic
71C2×C4×C127#4111yescharacteristic
72C8×C127—22no—
73C8×C127—22no—
74C8×C127—21no—
75C8×C127—21no—
76C8×C127—41no—
77C22×C127—21no—
78C22×C127—21no—
79C22×C127—42no—
80C22×C127—82no—
81C22×C127—82no—
82C22×C127—81no—
83C22×C127—81no—
84C22×C127#11711yescharacteristic
85C22×C127#12111yescharacteristic
86C22×C127#12611yescharacteristic
87C4×C127—41no—
88C4×C127—41no—
89C4×C127—81no—
90C4×C127C4×D411yescharacteristic
91C4×C127C4×D411yescharacteristic
92C4×C127#12311yescharacteristic
93C4×C127#12411yescharacteristic
94C2×C127—21no—
95C2×C127—21no—
96C2×C127—82no—
97C2×C127#38811yescharacteristic
98C2×C127#47111yescharacteristic
99C2×C127#47211yescharacteristic
100#1931C12711yesmaximal, characteristic, direct product factor, Sylow
101C127#193111yescharacteristic, direct product factor, Sylow
102#428C2×C12711yescharacteristic, complemented
103#418C2×C12711yescharacteristic
104C2×#102C2×C12711yescharacteristic
105C2×#100C2×C12711yescharacteristic
106#405C2×C12711yescharacteristic, complemented
107#343C2×C12711yescharacteristic, complemented
108#341C2×C12711yescharacteristic, complemented
109C22×D4C22×C12711yescharacteristic
110C2×M16C22×C12711yescharacteristic
111C2×M16C22×C12711yescharacteristic
112C2×M16C22×C12711yescharacteristic
113C22×C8C22×C12711yescharacteristic
114#117C22×C12711yescharacteristic
115C2×C4⋊C4C22×C12711yescharacteristic
116#107—21no—
117#106—21no—
118#102—21no—
119#102—21no—
120#102—21no—
121#102—21no—
122#100C4×C12714yescomplemented
123#97—21no—
124C4×C8—21no—
125C24—21no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4C2×C4×C12712yes—
132C22×C4—21no—
133C22×C4C23×C12711yescharacteristic
134M16—21no—
135M16—21no—
136M16—21no—
137M16—21no—
138M16C2×C4×C12712yes—
139M16C2×C4×C12712yes—
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—21no—
144C2×C8—21no—
145C2×C8D4×C12711yescharacteristic
146C2×C8D4×C12711yescharacteristic
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4D4×C12711yescharacteristic
150C4⋊C4D4×C12711yescharacteristic
151C22⋊C4—21no—
152C42—21no—
153C23—22no—
154C23—41no—
155C23—41no—
156C23—81no—
157C23—81no—
158C23#41×C12711yescharacteristic
159D4—22no—
160D4—22no—
161D4—41no—
162D4—41no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—81no—
167C2×C4C22×C4×C12711yescharacteristic
168C2×C4C2×D4×C12711yescharacteristic
169C2×C4C2×D4×C12711yescharacteristic
170C2×C4#41×C12711yescharacteristic
171C2×C4#41×C12711yescharacteristic
172C2×C4#41×C12711yescharacteristic
173C8—22no—
174C8—22no—
175C8—21no—
176C8—21no—
177C8—41no—
178C22—21no—
179C22—21no—
180C22—42no—
181C22—82no—
182C22—82no—
183C22—81no—
184C22—81no—
185C22#117×C12711yescharacteristic
186C22#121×C12711yescharacteristic
187C22#126×C12711yescharacteristic
188C4—41no—
189C4—41no—
190C4—81no—
191C4C4×D4×C12711yescharacteristic
192C4C4×D4×C12711yescharacteristic
193C4#123×C12711yescharacteristic
194C4#124×C12711yescharacteristic
195C2—21no—
196C2—21no—
197C2—82no—
198C2#388×C12711yescharacteristic
199C2#471×C12711yescharacteristic
200C2#472×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#121
commutatorC2×C4C22×C4×C127
Frattini, cosocleC22×C4C23×C127
prime radicalC22×D4×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. #428×C127C2semidirect
5. #405×C127C2semidirect
6. #343×C127C2semidirect
7. #341×C127C2semidirect
21. #100×C127C4semidirect
100. #1931C127direct (N × H)
101. C127#1931direct (N × H)
102. #428C2×C127semidirect
106. #405C2×C127semidirect
107. #343C2×C127semidirect
108. #341C2×C127semidirect
122. #100C4×C127semidirect

Maximal subgroups

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

subgroupindex
#428×C1272
#418×C1272
C2×#102×C1272
C2×#100×C1272
#405×C1272
#343×C1272
#341×C1272
#1931127