Finite Group Databasebeta

← C127×#19073 #44582746

Subgroups — C127×#19073 #44582746

Order 32512.

1252 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 230 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×#3549C211yesmaximal, characteristic, complemented
2C127×#3151C213yesmaximal, complemented
3C127×#1655C218yesmaximal, complemented
4C127×#1525C213yesmaximal, complemented
5C2×AGL(1,ℤ/8)×C127—26no—
6H(3,𝔽4)×C127C2214yescomplemented
7#555×C127—23no—
8D42×C127—23no—
9#535×C127—26no—
10#532×C127C2213yes—
11C2×#127×C127C2211yescharacteristic, complemented
12#496×C127C22112yescomplemented
13#493×C127—23no—
14#492×C127—23no—
15C4×M16×C127C2213yescomplemented
16#329×C127C22112yescomplemented
17C2×#41×C127D416yes—
18C22×D4×C127—26no—
19C22×D4×C127—23no—
20AGL(1,ℤ/8)×C127—424no—
21C2×SD16×C127—212no—
22C2×D8×C127—212no—
23C2×M16×C127—23no—
24C4⋊Q8×C127D413yes—
25#127×C127—24no—
26#127×C127—23no—
27#127×C127D413yes—
28#127×C127C2312yes—
29#124×C127—212no—
30#124×C127C2316yes—
31#121×C127—212no—
32#121×C127—26no—
33#120×C127—24no—
34#120×C127—212no—
35C4×D4×C127—26no—
36#117×C127—26no—
37C2×C42×C127C2311yescharacteristic
38#97×C127C2316yes—
39C4×C8×C127—23no—
40C24×C127—24no—
41C24×C127—41no—
42#41×C127—412no—
43C2×Q8×C127C2×D416yes—
44C2×D4×C127—212no—
45C2×D4×C127—26no—
46C2×D4×C127—26no—
47C2×D4×C127—26no—
48C2×D4×C127—412no—
49C2×D4×C127—43no—
50C2×D4×C127—812no—
51C2×D4×C127C2×D416yes—
52C22×C4×C127—26no—
53C22×C4×C127C2×D413yes—
54SD16×C127—424no—
55D8×C127—424no—
56M16×C127—212no—
57C2×C8×C127—26no—
58C4⋊C4×C127—26no—
59C22⋊C4×C127—212no—
60C22⋊C4×C127—212no—
61C42×C127—24no—
62C42×C127C2×D413yes—
63C42×C127C2411yescharacteristic
64C23×C127—26no—
65C23×C127—42no—
66C23×C127—86no—
67C23×C127—812no—
68C23×C127#12011yescharacteristic
69Q8×C127—46no—
70D4×C127—46no—
71D4×C127—412no—
72D4×C127—412no—
73D4×C127—86no—
74D4×C127—812no—
75D4×C127—86no—
76C2×C4×C127—26no—
77C2×C4×C127—26no—
78C2×C4×C127—412no—
79C2×C4×C127#12013yes—
80C2×C4×C127C22×D413yes—
81C8×C127—212no—
82C22×C127—23no—
83C22×C127—46no—
84C22×C127—412no—
85C22×C127—86no—
86C22×C127—164no—
87C22×C127—168no—
88C22×C127C2×#12011yescharacteristic
89C4×C127—23no—
90C4×C127—46no—
91C4×C127#45316yes—
92#19073C12711yesmaximal, characteristic, direct product factor, Sylow
93C2×C127—41no—
94C2×C127—86no—
95C2×C127—162no—
96C2×C127C2×#45313yes—
97#3549C2×C12711yescharacteristic, complemented
98#3151C2×C12713yescomplemented
99#1655C2×C12718yescomplemented
100#1525C2×C12713yescomplemented
101C127#1907311yescharacteristic, direct product factor, Sylow
102C2×AGL(1,ℤ/8)—26no—
103H(3,𝔽4)C22×C12714yescomplemented
104#555—23no—
105D42—23no—
106#535—26no—
107#532C22×C12713yes—
108C2×#127C22×C12711yescharacteristic, complemented
109#496C22×C127112yescomplemented
110#493—23no—
111#492—23no—
112C4×M16C22×C12713yescomplemented
113#329C22×C127112yescomplemented
114C2×#41D4×C12716yes—
115C22×D4—26no—
116C22×D4—23no—
117AGL(1,ℤ/8)—424no—
118C2×SD16—212no—
119C2×D8—212no—
120C2×M16—23no—
121C4⋊Q8D4×C12713yes—
122#127—24no—
123#127—23no—
124#127D4×C12713yes—
125#127C23×C12712yes—
126#124—212no—
127#124C23×C12716yes—
128#121—212no—
129#121—26no—
130#120—24no—
131#120—212no—
132C4×D4—26no—
133#117—26no—
134C2×C42C23×C12711yescharacteristic
135#97C23×C12716yes—
136C4×C8—23no—
137C24—24no—
138C24—41no—
139#41—412no—
140C2×Q8C2×D4×C12716yes—
141C2×D4—212no—
142C2×D4—26no—
143C2×D4—26no—
144C2×D4—26no—
145C2×D4—412no—
146C2×D4—43no—
147C2×D4—812no—
148C2×D4C2×D4×C12716yes—
149C22×C4—26no—
150C22×C4C2×D4×C12713yes—
151SD16—424no—
152D8—424no—
153M16—212no—
154C2×C8—26no—
155C4⋊C4—26no—
156C22⋊C4—212no—
157C22⋊C4—212no—
158C42—24no—
159C42C2×D4×C12713yes—
160C42C24×C12711yescharacteristic
161C23—26no—
162C23—42no—
163C23—86no—
164C23—812no—
165C23#120×C12711yescharacteristic
166Q8—46no—
167D4—46no—
168D4—412no—
169D4—412no—
170D4—86no—
171D4—812no—
172D4—86no—
173C2×C4—26no—
174C2×C4—26no—
175C2×C4—412no—
176C2×C4#120×C12713yes—
177C2×C4C22×D4×C12713yes—
178C8—212no—
179C22—23no—
180C22—46no—
181C22—412no—
182C22—86no—
183C22—164no—
184C22—168no—
185C22C2×#120×C12711yescharacteristic
186C4—23no—
187C4—46no—
188C4#453×C12716yes—
189C2—41no—
190C2—86no—
191C2—162no—
192C2C2×#453×C12713yes—
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC42C24×C127
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3549C2semidirect
2. C127×#3151C2semidirect
3. C127×#1655C2semidirect
4. C127×#1525C2semidirect
6. H(3,𝔽4)×C127C22semidirect
11. C2×#127×C127C22semidirect
12. #496×C127C22semidirect
15. C4×M16×C127C22semidirect
16. #329×C127C22semidirect
92. #19073C127direct (N × H)
97. #3549C2×C127semidirect
98. #3151C2×C127semidirect
99. #1655C2×C127semidirect
100. #1525C2×C127semidirect
101. C127#19073direct (N × H)
103. H(3,𝔽4)C22×C127semidirect
108. C2×#127C22×C127semidirect
109. #496C22×C127semidirect
112. C4×M16C22×C127semidirect
113. #329C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35492
C127×#31512
C127×#16552
C127×#15252
#19073127