Finite Group Databasebeta

← C127×#7043 #44570716

Subgroups — C127×#7043 #44570716

Order 32512.

284 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 98 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×#1839C211yesmaximal, characteristic
2C127×#1767C211yesmaximal, characteristic
3C127×#1745C211yesmaximal, characteristic
4C2×C4⋊C8×C127—21no—
5C2×#97×C127—21no—
6C2×#97×C127C412yes—
7C43×C127C2211yescharacteristic
8#336×C127—21no—
9#336×C127—21no—
10#336×C127—21no—
11#336×C127—21no—
12#336×C127C412yes—
13#336×C127C412yes—
14C22×C8×C127—22no—
15C22×C8×C127—22no—
16C22×C8×C127—22no—
17C2×C42×C127C2×C411yescharacteristic
18C2×C42×C127C2×C411yescharacteristic
19C2×C42×C127C2×C411yescharacteristic
20C2×C42×C127D411yescharacteristic
21C2×C42×C127D411yescharacteristic
22C2×C42×C127D411yescharacteristic
23C2×C42×C127Q811yescharacteristic
24C4⋊C8×C127—24no—
25#97×C127—24no—
26#97×C127—42no—
27C22×C4×C127C4211yescharacteristic
28C22×C4×C127C22⋊C411yescharacteristic
29C22×C4×C127C22⋊C411yescharacteristic
30C22×C4×C127C22⋊C411yescharacteristic
31C22×C4×C127C4⋊C411yescharacteristic
32C22×C4×C127C4⋊C411yescharacteristic
33C22×C4×C127C4⋊C411yescharacteristic
34C2×C8×C127—24no—
35C2×C8×C127—24no—
36C2×C8×C127—42no—
37C2×C8×C127—42no—
38C2×C8×C127—42no—
39C2×C8×C127—42no—
40C2×C8×C127—42no—
41C2×C8×C127—42no—
42C2×C8×C127—42no—
43C42×C127—21no—
44C42×C127—21no—
45C42×C127—22no—
46C42×C127—22no—
47C42×C127—22no—
48C42×C127—41no—
49C42×C127—41no—
50C42×C127—41no—
51C23×C127#9511yescharacteristic
52C2×C4×C127—21no—
53C2×C4×C127—21no—
54C2×C4×C127—21no—
55C2×C4×C127—21no—
56C2×C4×C127—21no—
57C2×C4×C127—21no—
58C2×C4×C127—21no—
59C2×C4×C127—21no—
60C2×C4×C127—21no—
61C2×C4×C127—21no—
62C2×C4×C127—21no—
63C2×C4×C127—21no—
64C2×C4×C127—21no—
65C2×C4×C127—21no—
66C2×C4×C127—21no—
67C2×C4×C127—21no—
68C2×C4×C127—21no—
69C2×C4×C127#10011yescharacteristic
70C2×C4×C127#10111yescharacteristic
71C2×C4×C127#10412yes—
72C2×C4×C127#10412yes—
73C2×C4×C127#10812yes—
74C8×C127—44no—
75C8×C127—44no—
76C8×C127—82no—
77C22×C127H(3,ℤ/4)11yescharacteristic
78C22×C127#33911yescharacteristic
79C22×C127#33911yescharacteristic
80C22×C127#34111yescharacteristic
81C22×C127#34311yescharacteristic
82C22×C127#34411yescharacteristic
83C22×C127#34411yescharacteristic
84C4×C127—21no—
85C4×C127—21no—
86C4×C127—22no—
87C4×C127—22no—
88C4×C127—22no—
89C4×C127—41no—
90C4×C127—41no—
91C4×C127—41no—
92#7043C12711yesmaximal, characteristic, direct product factor, Sylow
93C2×C127#128511yescharacteristic
94C2×C127#128711yescharacteristic
95C2×C127#128811yescharacteristic
96C2×C127#129911yescharacteristic
97C2×C127#130011yescharacteristic
98C2×C127#130211yescharacteristic
99C2×C127#130711yescharacteristic
100#1839C2×C12711yescharacteristic
101#1767C2×C12711yescharacteristic
102#1745C2×C12711yescharacteristic
103C127#704311yescharacteristic, direct product factor, Sylow
104C2×C4⋊C8—21no—
105C2×#97—21no—
106C2×#97C4×C12712yes—
107C43C22×C12711yescharacteristic
108#336—21no—
109#336—21no—
110#336—21no—
111#336—21no—
112#336C4×C12712yes—
113#336C4×C12712yes—
114C22×C8—22no—
115C22×C8—22no—
116C22×C8—22no—
117C2×C42C2×C4×C12711yescharacteristic
118C2×C42C2×C4×C12711yescharacteristic
119C2×C42C2×C4×C12711yescharacteristic
120C2×C42D4×C12711yescharacteristic
121C2×C42D4×C12711yescharacteristic
122C2×C42D4×C12711yescharacteristic
123C2×C42Q8×C12711yescharacteristic
124C4⋊C8—24no—
125#97—24no—
126#97—42no—
127C22×C4C42×C12711yescharacteristic
128C22×C4C22⋊C4×C12711yescharacteristic
129C22×C4C22⋊C4×C12711yescharacteristic
130C22×C4C22⋊C4×C12711yescharacteristic
131C22×C4C4⋊C4×C12711yescharacteristic
132C22×C4C4⋊C4×C12711yescharacteristic
133C22×C4C4⋊C4×C12711yescharacteristic
134C2×C8—24no—
135C2×C8—24no—
136C2×C8—42no—
137C2×C8—42no—
138C2×C8—42no—
139C2×C8—42no—
140C2×C8—42no—
141C2×C8—42no—
142C2×C8—42no—
143C42—21no—
144C42—21no—
145C42—22no—
146C42—22no—
147C42—22no—
148C42—41no—
149C42—41no—
150C42—41no—
151C23#95×C12711yescharacteristic
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4#100×C12711yescharacteristic
170C2×C4#101×C12711yescharacteristic
171C2×C4#104×C12712yes—
172C2×C4#104×C12712yes—
173C2×C4#108×C12712yes—
174C8—44no—
175C8—44no—
176C8—82no—
177C22H(3,ℤ/4)×C12711yescharacteristic
178C22#339×C12711yescharacteristic
179C22#339×C12711yescharacteristic
180C22#341×C12711yescharacteristic
181C22#343×C12711yescharacteristic
182C22#344×C12711yescharacteristic
183C22#344×C12711yescharacteristic
184C4—22no—
185C4—22no—
186C4—22no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—41no—
191C4—41no—
192C2C127×#128511yescharacteristic
193C2C127×#128711yescharacteristic
194C2C127×#128811yescharacteristic
195C2C127×#129911yescharacteristic
196C2C127×#130011yescharacteristic
197C2C127×#130211yescharacteristic
198C2C127×#130711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C127#95
commutatorC22×C4C42×C127
Frattini, cosocleC43C22×C127
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C43×C127 ◁ G

Complements

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

NH ≅ G/Ntype
92. #7043C127direct (N × H)
103. C127#7043direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#18392
C127×#17672
C127×#17452
#7043127