Finite Group Databasebeta

← C2×C127×#1413 #44577270

Subgroups — C2×C127×#1413 #44577270

Order 32512.

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

normal subgroups only

This group has 314 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
1C2×#491×C127C211yesmaximal, characteristic
2C2×#356×C127C212yesmaximal
3C127×#1413C214yesmaximal, direct product factor
4C2×C4⋊Q8×C127C2211yescharacteristic
5C2×#125×C127C411yescharacteristic
6#491×C127—22no—
7#491×C127C412yes—
8#491×C127C2212yes—
9C2×#103×C127—22no—
10C2×#101×C127—22no—
11C2×#97×C127C411yescharacteristic
12#356×C127—22no—
13#356×C127C2214yes—
14C22×Q8×C127D412yes—
15C2×M16×C127—42no—
16C22×C8×C127—21no—
17C4⋊Q8×C127—41no—
18C4⋊Q8×C127C2×C411yescharacteristic
19C4⋊Q8×C127D412yes—
20C4⋊Q8×C127C2311yescharacteristic
21#125×C127—21no—
22#125×C127—41no—
23#125×C127C2×C412yes—
24C2×C4⋊C4×C127—21no—
25C2×C4⋊C4×C127—41no—
26C2×C4⋊C4×C127—41no—
27C2×C42×C127C2×C411yescharacteristic
28#103×C127—24no—
29#103×C127—24no—
30#101×C127—24no—
31#101×C127—42no—
32#97×C127—21no—
33#97×C127C2×C412yes—
34C2×Q8×C127—22no—
35C2×Q8×C127—42no—
36C2×Q8×C127—42no—
37C2×Q8×C127C22⋊C412yes—
38C2×Q8×C127C2×D412yes—
39C22×C4×C127—21no—
40C22×C4×C127—22no—
41C22×C4×C127—41no—
42C22×C4×C127C22⋊C411yescharacteristic
43M16×C127—44no—
44M16×C127—82no—
45C2×C8×C127—22no—
46C2×C8×C127—41no—
47C2×C8×C127—41no—
48C2×C8×C127—82no—
49C4⋊C4×C127—22no—
50C4⋊C4×C127—41no—
51C4⋊C4×C127—42no—
52C4⋊C4×C127—41no—
53C4⋊C4×C127—42no—
54C4⋊C4×C127—42no—
55C4⋊C4×C127—41no—
56C42×C127—21no—
57C42×C127C22⋊C411yescharacteristic
58C42×C127C22×C411yescharacteristic
59C23×C127#9911yescharacteristic
60Q8×C127—42no—
61Q8×C127—42no—
62Q8×C127—82no—
63C2×C4×C127—21no—
64C2×C4×C127—21no—
65C2×C4×C127—21no—
66C2×C4×C127—21no—
67C2×C4×C127—22no—
68C2×C4×C127—22no—
69C2×C4×C127—42no—
70C2×C4×C127—42no—
71C2×C4×C127—42no—
72C2×C4×C127—42no—
73C2×C4×C127—82no—
74C2×C4×C127#9911yescharacteristic
75C2×C4×C127C2×C22⋊C411yescharacteristic
76C8×C127—42no—
77C8×C127—84no—
78C22×C127—22no—
79C22×C127#35411yescharacteristic
80C22×C127#35411yescharacteristic
81C22×C127C2×#9911yescharacteristic
82C4×C127—21no—
83C4×C127—21no—
84C4×C127—41no—
85C4×C127—41no—
86C4×C127—42no—
87C4×C127—42no—
88C4×C127—82no—
89C2×#1413C12711yesmaximal, characteristic, direct product factor, Sylow
90C2×C127—21no—
91C2×C127—21no—
92C2×C127#141312yesdirect product factor
93C2×C127C2×#35411yescharacteristic
94C2×#491C2×C12711yescharacteristic
95C2×#356C2×C12712yes—
96#1413C2×C12714yesdirect product factor
97C127C2×#141311yescharacteristic, direct product factor, Sylow
98C2×C4⋊Q8C22×C12711yescharacteristic
99C2×#125C4×C12711yescharacteristic
100#491—22no—
101#491C4×C12712yes—
102#491C22×C12712yes—
103C2×#103—22no—
104C2×#101—22no—
105C2×#97C4×C12711yescharacteristic
106#356—22no—
107#356C22×C12714yes—
108C22×Q8D4×C12712yes—
109C2×M16—42no—
110C22×C8—21no—
111C4⋊Q8—41no—
112C4⋊Q8C2×C4×C12711yescharacteristic
113C4⋊Q8D4×C12712yes—
114C4⋊Q8C23×C12711yescharacteristic
115#125—21no—
116#125—41no—
117#125C2×C4×C12712yes—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4—41no—
121C2×C42C2×C4×C12711yescharacteristic
122#103—24no—
123#103—24no—
124#101—24no—
125#101—42no—
126#97—21no—
127#97C2×C4×C12712yes—
128C2×Q8—22no—
129C2×Q8—42no—
130C2×Q8—42no—
131C2×Q8C22⋊C4×C12712yes—
132C2×Q8C2×D4×C12712yes—
133C22×C4—21no—
134C22×C4—22no—
135C22×C4—41no—
136C22×C4C22⋊C4×C12711yescharacteristic
137M16—44no—
138M16—82no—
139C2×C8—22no—
140C2×C8—41no—
141C2×C8—41no—
142C2×C8—82no—
143C4⋊C4—22no—
144C4⋊C4—41no—
145C4⋊C4—42no—
146C4⋊C4—41no—
147C4⋊C4—42no—
148C4⋊C4—42no—
149C4⋊C4—41no—
150C42—21no—
151C42C22⋊C4×C12711yescharacteristic
152C42C22×C4×C12711yescharacteristic
153C23#99×C12711yescharacteristic
154Q8—42no—
155Q8—42no—
156Q8—82no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—82no—
168C2×C4#99×C12711yescharacteristic
169C2×C4C2×C22⋊C4×C12711yescharacteristic
170C8—42no—
171C8—84no—
172C22—22no—
173C22#354×C12711yescharacteristic
174C22#354×C12711yescharacteristic
175C22C2×#99×C12711yescharacteristic
176C4—21no—
177C4—21no—
178C4—41no—
179C4—41no—
180C4—42no—
181C4—42no—
182C4—82no—
183C2—21no—
184C2—21no—
185C2C127×#141312yesdirect product factor
186C2C2×#354×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#354
commutatorC42C22×C4×C127
Frattini, cosocleC4⋊Q8C23×C127
prime radicalC23×C127#99
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C127 ◁ C22×C4×C127 ◁ C2×C4⋊Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1413C2direct (N × H)
89. C2×#1413C127direct (N × H)
92. C2×C127#1413direct (N × H)
96. #1413C2×C127direct (N × H)
97. C127C2×#1413direct (N × H)
185. C2C127×#1413direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#491×C1272
C2×#356×C1272
C127×#14132
C2×#1413127