Finite Group Databasebeta

← #22550558

Subgroups — #22550558

Order 8128.

214 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 95 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#16861204C211yesmaximal, characteristic, complemented
2#16861204C211yesmaximal, characteristic, complemented
3#16861199C211yesmaximal, characteristic, complemented
4#16861199C211yesmaximal, characteristic, complemented
5#16861194C211yesmaximal, characteristic
6#16861194C211yesmaximal, characteristic
7#16861187C211yesmaximal, characteristic, complemented
8#16861187C211yesmaximal, characteristic, complemented
9#16861174C211yesmaximal, characteristic, complemented
10#16861171C211yesmaximal, characteristic
11#16861167C211yesmaximal, characteristic, complemented
12#16861166C211yesmaximal, characteristic, complemented
13#16861166C211yesmaximal, characteristic, complemented
14C4⋊C4×D127C211yesmaximal, characteristic, complemented
15#125×C127C211yesmaximal, characteristic, complemented
16C2×Dic254C2211yescharacteristic
17C2×D508C2211yescharacteristic
18C2×C4×D127C2211yescharacteristic
19C2×C4×D127C2211yescharacteristic
20C2×C4×D127C2211yescharacteristic
21C2×C4×D127C2211yescharacteristic
22C4⋊Dic127C2211yescharacteristic
23C4⋊Dic127C2211yescharacteristic
24Dic127⋊C4C2211yescharacteristic
25Dic127⋊C4C2211yescharacteristic
26Dic127⋊C4C2211yescharacteristic
27Dic127⋊C4C2211yescharacteristic
28Dic127⋊C4C2211yescharacteristic
29Dic127⋊C4C2211yescharacteristic
30Dic127⋊C4C2211yescharacteristic
31Dic127⋊C4C2211yescharacteristic
32(C2×D127)⋊C4C2211yescharacteristic
33(C2×D127)⋊C4C2211yescharacteristic
34(C2×D127)⋊C4C2211yescharacteristic
35(C2×D127)⋊C4C2211yescharacteristic
36(C2×D127)⋊C4C2211yescharacteristic
37(C2×D127)⋊C4C2211yescharacteristic
38(C2×D127)⋊C4C2211yescharacteristic
39(C2×D127)⋊C4C2211yescharacteristic
40C4×Dic127C2211yescharacteristic
41C4×Dic127C2211yescharacteristic
42C4×Dic127C2211yescharacteristic
43C4×Dic127C2211yescharacteristic
44C4⋊C4×C127C2211yescharacteristic
45C4⋊C4×C127C2211yescharacteristic
46C4⋊C4×C127C2211yescharacteristic
47C4⋊C4×C127C2211yescharacteristic
48C4⋊C4×C127C2211yescharacteristic
49C4⋊C4×C127C2211yescharacteristic
50C42×C127C2211yescharacteristic
51C22×D127C2311yescharacteristic
52C22×D127C2311yescharacteristic
53Dic254—22no—
54D508—22no—
55C2×Dic127C2311yescharacteristic
56C2×Dic127C2311yescharacteristic
57C2×Dic127C2311yescharacteristic
58C2×Dic127C2311yescharacteristic
59C2×Dic127C2311yescharacteristic
60C2×Dic127C2311yescharacteristic
61C4×D127—22no—
62C4×D127—22no—
63C4×D127—22no—
64C4×D127—22no—
65C2×C4×C127C2311yescharacteristic
66C2×C4×C127C2311yescharacteristic
67C2×C4×C127C2311yescharacteristic
68C2×C4×C127C2311yescharacteristic
69C2×C4×C127C2311yescharacteristic
70C2×C4×C127C2311yescharacteristic
71C2×C4×C127C2311yescharacteristic
72C22×C127C2411yescharacteristic
73C2×D127—21no—
74C2×D127—21no—
75C2×D127—21no—
76C2×D127—21no—
77C2×D127—21no—
78C2×D127#4112yes—
79C4×C127—21no—
80C4×C127—21no—
81C4×C127—21no—
82C4×C127—21no—
83C4×C127—21no—
84C4×C127—21no—
85C4×C127—21no—
86Dic127—21no—
87Dic127—21no—
88Dic127—21no—
89Dic127—21no—
90Dic127—21no—
91Dic127#4112yes—
92C2×C127C2×#4111yescharacteristic
93C2×C127C2×#4111yescharacteristic
94C2×C1272−1+411yescharacteristic
95D127—22no—
96D127—41no—
97C127#55211yescharacteristic, complemented, Sylow
98#552—1271nomaximal, Sylow
99#126—1271no—
100#126—1271no—
101#125—1271no—
102#125—1271no—
103#125D12711yescharacteristic, complemented
104#123—1271no—
105#123—1271no—
106C22⋊Q8—1271no—
107C22⋊Q8—1271no—
108C4×Q8—1271no—
109C4×D4—1271no—
110#117—1271no—
111#117—1271no—
112#117—1271no—
113C2×C4⋊C4—1271no—
114C2×Q8—1271no—
115C2×D4—1271no—
116C22×C4—1271no—
117C22×C4—1271no—
118C22×C4—1271no—
119C22×C4—1271no—
120C4⋊C4—1271no—
121C4⋊C4—1271no—
122C4⋊C4—1271no—
123C4⋊C4—1271no—
124C4⋊C4—1271no—
125C4⋊C4—1271no—
126C4⋊C4—1271no—
127C4⋊C4—1271no—
128C4⋊C4—1271no—
129C4⋊C4—1271no—
130C4⋊C4C2×D12711yescharacteristic
131C4⋊C4C2×D12711yescharacteristic
132C4⋊C4C2×D12711yescharacteristic
133C4⋊C4C2×D12711yescharacteristic
134C4⋊C4C2×D12711yescharacteristic
135C4⋊C4C2×D12711yescharacteristic
136C22⋊C4—1271no—
137C22⋊C4—1271no—
138C22⋊C4—1271no—
139C22⋊C4—1271no—
140C22⋊C4—1271no—
141C22⋊C4—1271no—
142C22⋊C4—1271no—
143C22⋊C4—1271no—
144C42—1271no—
145C42—1271no—
146C42—1271no—
147C42—1271no—
148C42C2×D12711yescharacteristic
149C23—1271no—
150C23—1271no—
151Q8—2542no—
152D4—2542no—
153C2×C4—1271no—
154C2×C4—1271no—
155C2×C4—1271no—
156C2×C4—1271no—
157C2×C4—1271no—
158C2×C4—1271no—
159C2×C4—2542no—
160C2×C4—2542no—
161C2×C4—2542no—
162C2×C4—2542no—
163C2×C4C22×D12711yescharacteristic
164C2×C4C22×D12711yescharacteristic
165C2×C4C22×D12711yescharacteristic
166C2×C4C22×D12711yescharacteristic
167C2×C4C22×D12711yescharacteristic
168C2×C4C22×D12711yescharacteristic
169C2×C4C22×D12711yescharacteristic
170C22—1272no—
171C22—2541no—
172C22—2541no—
173C22—2541no—
174C22—2541no—
175C22—2541no—
176C22C23×D12711yescharacteristic
177C4—21no—
178C4—21no—
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—1272no—
185C4—2541no—
186C4—2541no—
187C4—2541no—
188C4—2541no—
189C4—2541no—
190C2—5081no—
191C2—2542no—
192C2#41×D12711yescharacteristic
193C2#41×D12711yescharacteristic
194C2#1686125711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D127
commutator, socleC22×C127C24
Fitting#125×C127C2
hypercenter#125D127
hypocenterC127#552
LCSG ▷ C22×C127 ▷ C127
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #16861204C2semidirect
2. #16861204C2semidirect
3. #16861199C2semidirect
4. #16861199C2semidirect
7. #16861187C2semidirect
8. #16861187C2semidirect
9. #16861174C2semidirect
11. #16861167C2semidirect
12. #16861166C2semidirect
13. #16861166C2semidirect
14. C4⋊C4×D127C2semidirect
15. #125×C127C2semidirect
97. C127#552semidirect
103. #125D127semidirect