Finite Group Databasebeta

← C127×#17054 #44580727

Subgroups — C127×#17054 #44580727

Order 32512.

1002 conjugacy classes of subgroups; only the 310 normal subgroups are shown.

normal subgroups only

This group has 1002 conjugacy classes of subgroups — too many to draw. Only its 310 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×#1445C216yesmaximal
2C127×#1441C216yesmaximal
3C127×#1434C213yesmaximal
4C22×C4⋊C4×C127C2216yes—
5C22×C42×C127C2211yescharacteristic
6C2×#95×C127C2216yes—
7C2×#95×C127C2213yes—
8C2×#95×C127C2216yes—
9C2×#95×C127C2213yes—
10C2×#95×C127C2212yes—
11C2×#95×C127C2216yes—
12C2×#95×C127C2212yes—
13C23×C4×C127C2316yes—
14C23×C4×C127C2313yes—
15C23×C4×C127C2316yes—
16C2×C4⋊C4×C127—212no—
17C2×C4⋊C4×C127—212no—
18C2×C4⋊C4×C127—46no—
19C2×C42×C127—42no—
20C2×C42×C127Q814yes—
21#95×C127—212no—
22#95×C127—42no—
23#95×C127—46no—
24#95×C127—43no—
25#95×C127—43no—
26#95×C127—46no—
27#95×C127—42no—
28C24×C127C2411yescharacteristic
29C22×C4×C127—26no—
30C22×C4×C127—26no—
31C22×C4×C127—26no—
32C22×C4×C127—26no—
33C22×C4×C127—23no—
34C22×C4×C127—26no—
35C22×C4×C127—26no—
36C22×C4×C127—26no—
37C22×C4×C127—26no—
38C22×C4×C127—23no—
39C22×C4×C127—26no—
40C22×C4×C127—26no—
41C22×C4×C127—26no—
42C22×C4×C127—26no—
43C22×C4×C127—26no—
44C22×C4×C127—26no—
45C22×C4×C127—26no—
46C22×C4×C127C2×Q816yes—
47C22×C4×C127#41112yes—
48C4⋊C4×C127—424no—
49C42×C127—44no—
50C23×C127C22×Q811yescharacteristic
51C23×C127C2×#4116yes—
52C23×C127H(5,𝔽2)12yes—
53C23×C127H(5,𝔽2)13yes—
54C23×C1272−1+413yes—
55C2×C4×C127—26no—
56C2×C4×C127—212no—
57C2×C4×C127—26no—
58C2×C4×C127—26no—
59C2×C4×C127—212no—
60C2×C4×C127—212no—
61C2×C4×C127—46no—
62C2×C4×C127—46no—
63C2×C4×C127—46no—
64C2×C4×C127—46no—
65C2×C4×C127—46no—
66C2×C4×C127—46no—
67C2×C4×C127—46no—
68C2×C4×C127—46no—
69C2×C4×C127—46no—
70C2×C4×C127—46no—
71C2×C4×C127—46no—
72C2×C4×C127—46no—
73C2×C4×C127—46no—
74C22×C127#53313yes—
75C22×C127#53916yes—
76C22×C127#54016yes—
77C22×C127#54311yescharacteristic
78C22×C127#54413yes—
79C22×C127#55116yes—
80C22×C127#55616yes—
81C22×C127#56213yes—
82C22×C127#56411yescharacteristic
83C4×C127—46no—
84C4×C127—412no—
85C4×C127—86no—
86#17054C12711yesmaximal, characteristic, direct product factor, Sylow
87C2×C127#260513yes—
88C2×C127#266713yes—
89C2×C127#274016yes—
90C2×C127#281012yes—
91C2×C127#284511yescharacteristic
92#1445C2×C12716yes—
93#1441C2×C12716yes—
94#1434C2×C12713yes—
95C127#1705411yescharacteristic, direct product factor, Sylow
96C22×C4⋊C4C22×C12716yes—
97C22×C42C22×C12711yescharacteristic
98C2×#95C22×C12716yes—
99C2×#95C22×C12713yes—
100C2×#95C22×C12716yes—
101C2×#95C22×C12713yes—
102C2×#95C22×C12712yes—
103C2×#95C22×C12716yes—
104C2×#95C22×C12712yes—
105C23×C4C23×C12716yes—
106C23×C4C23×C12713yes—
107C23×C4C23×C12716yes—
108C2×C4⋊C4—212no—
109C2×C4⋊C4—212no—
110C2×C4⋊C4—46no—
111C2×C42—42no—
112C2×C42Q8×C12714yes—
113#95—212no—
114#95—42no—
115#95—46no—
116#95—43no—
117#95—43no—
118#95—46no—
119#95—42no—
120C24C24×C12711yescharacteristic
121C22×C4—26no—
122C22×C4—26no—
123C22×C4—26no—
124C22×C4—26no—
125C22×C4—23no—
126C22×C4—26no—
127C22×C4—26no—
128C22×C4—26no—
129C22×C4—26no—
130C22×C4—23no—
131C22×C4—26no—
132C22×C4—26no—
133C22×C4—26no—
134C22×C4—26no—
135C22×C4—26no—
136C22×C4—26no—
137C22×C4—26no—
138C22×C4C2×Q8×C12716yes—
139C22×C4#41×C127112yes—
140C4⋊C4—424no—
141C42—44no—
142C23C22×Q8×C12711yescharacteristic
143C23C2×#41×C12716yes—
144C23H(5,𝔽2)×C12712yes—
145C23H(5,𝔽2)×C12713yes—
146C232−1+4×C12713yes—
147C2×C4—26no—
148C2×C4—212no—
149C2×C4—26no—
150C2×C4—26no—
151C2×C4—212no—
152C2×C4—212no—
153C2×C4—46no—
154C2×C4—46no—
155C2×C4—46no—
156C2×C4—46no—
157C2×C4—46no—
158C2×C4—46no—
159C2×C4—46no—
160C2×C4—46no—
161C2×C4—46no—
162C2×C4—46no—
163C2×C4—46no—
164C2×C4—46no—
165C2×C4—46no—
166C22#533×C12713yes—
167C22#539×C12716yes—
168C22#540×C12716yes—
169C22#543×C12711yescharacteristic
170C22#544×C12713yes—
171C22#551×C12716yes—
172C22#556×C12716yes—
173C22#562×C12713yes—
174C22#564×C12711yescharacteristic
175C4—46no—
176C4—412no—
177C4—86no—
178C2C127×#260513yes—
179C2C127×#266713yes—
180C2C127×#274016yes—
181C2C127×#281012yes—
182C2C127×#284511yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C24
commutator, Frattini, cosocleC24C24×C127
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
86. #17054C127direct (N × H)
95. C127#17054direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#14452
C127×#14412
C127×#14342
#17054127