Finite Group Databasebeta

← #30637119

Subgroups — #30637119

Order 16256.

312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C4×D4×D127C211yesmaximal, characteristic
2#22549928C211yesmaximal, characteristic, complemented
3#22549927C211yesmaximal, characteristic, complemented
4#22549605C211yesmaximal, characteristic, complemented
5D4⋊(C127⋊C8)C211yesmaximal, characteristic, complemented
6#22549603C211yesmaximal, characteristic, complemented
7D4⋊C8×C127C211yesmaximal, characteristic, complemented
8C2×D4×D127C411yescharacteristic
9C22×C4×D127—21no—
10C4×D508C2211yescharacteristic
11D4×Dic127C411yescharacteristic
12#16861171C411yescharacteristic
13C4×C22⋊D127—21no—
14(C22⋊D127)⋊C4—21no—
15C4⋊C4×D127C411yescharacteristic
16C22⋊C4×D127—21no—
17C42×D127C2211yescharacteristic
18C4⋊(C127⋊C8)C2211yescharacteristic, complemented
19Dic127⋊C8—21no—
20(C2×D127)⋊C8—21no—
21(C2×D127)⋊C8—21no—
22C4×C127⋊C8C2211yescharacteristic, complemented
23C8×Dic127—21no—
24C4×D4×C127C2211yescharacteristic
25C4⋊C8×C127C2211yescharacteristic, complemented
26C4×C8×C127C2211yescharacteristic, complemented
27C23×D127—21no—
28C2×D508C2×C411yescharacteristic
29C2×C22⋊D127—21no—
30D4×D127—22no—
31D4×D127C814yescomplemented
32C22×Dic127—21no—
33C2×C4×D127—21no—
34C2×C4×D127—21no—
35C2×C4×D127—21no—
36C2×C4×D127—42no—
37C2×C4×D127—42no—
38C2×C4×D127C2×C411yescharacteristic
39C2×C4×D127D411yescharacteristic
40C2×C4×D127D411yescharacteristic
41C2×C127⋊C8—21no—
42C2×C127⋊C8—21no—
43C4⋊Dic127C2×C411yescharacteristic
44Dic127⋊C4—21no—
45C22⋊Dic127—21no—
46(C2×D127)⋊C4—21no—
47(C2×D127)⋊C4—21no—
48C4×Dic127C2×C411yescharacteristic
49C4×Dic127D411yescharacteristic
50C4×Dic127D411yescharacteristic
51C2×D4×C127C2×C411yescharacteristic
52C22×C4×C127—21no—
53C2×C8×C127—21no—
54C2×C8×C127—21no—
55C4⋊C4×C127C2×C411yescharacteristic
56C22⋊C4×C127—21no—
57C42×C127C2311yescharacteristic
58C22×D127—21no—
59C22×D127—24no—
60C22×D127—42no—
61C22×D127—42no—
62C22×D127C22⋊C411yescharacteristic
63D508—21no—
64D508C2×C812yes—
65C22⋊D127—24no—
66C2×Dic127—21no—
67C2×Dic127—42no—
68C2×Dic127C22⋊C411yescharacteristic
69C2×Dic127C22⋊C411yescharacteristic
70C2×Dic127C22⋊C411yescharacteristic
71C4×D127—21no—
72C4×D127—21no—
73C4×D127—41no—
74C4×D127—42no—
75C4×D127—42no—
76C4×D127—41no—
77C4×D127—41no—
78C4×D127C2×C812yes—
79C4×D127M1612yes—
80C127⋊C8—41no—
81C127⋊C8—41no—
82C23×C127—21no—
83D4×C127—21no—
84D4×C127C2×C812yes—
85C2×C4×C127—21no—
86C2×C4×C127—41no—
87C2×C4×C127—41no—
88C2×C4×C127C22×C411yescharacteristic
89C2×C4×C127C2×D411yescharacteristic
90C2×C4×C127C2×D411yescharacteristic
91C8×C127—41no—
92C8×C127—41no—
93C22×C127—22no—
94C22×C127—41no—
95C22×C127—41no—
96C22×C127C2×C22⋊C411yescharacteristic
97C2×D127—21no—
98C2×D127—21no—
99C2×D127—22no—
100C2×D127—48no—
101C2×D127—41no—
102C2×D127—41no—
103C2×D127C22⋊C812yes—
104C4×C127—21no—
105C4×C127—41no—
106C4×C127C22×C811yescharacteristic
107C4×C127C2×M1611yescharacteristic
108C4×C127AGL(1,ℤ/8)11yescharacteristic
109C4×C127AGL(1,ℤ/8)11yescharacteristic
110Dic127—21no—
111Dic127—21no—
112Dic127—41no—
113Dic127C22⋊C812yes—
114C2×C127—42no—
115C2×C127C2×C22⋊C811yescharacteristic
116C2×C127#41811yescharacteristic
117C2×C127#42111yescharacteristic
118D127—22no—
119D127—42no—
120#1478—1271nomaximal, Sylow
121C127#147811yescharacteristic, complemented, Sylow
122C2×C4×D4—1271no—
123#431—1271no—
124#431—1271no—
125D4⋊C8—1271no—
126D4⋊C8—1271no—
127D4⋊C8—1271no—
128D4⋊C8D12711yescharacteristic, complemented
129C22×D4—1271no—
130C23×C4—2541no—
131C4×D4—1271no—
132C4×D4—1271no—
133C4×D4—1271no—
134C4×D4—2541no—
135C4×D4—2541no—
136C4×D4C2×D12711yescharacteristic
137C2×C4⋊C4—1271no—
138C2×C22⋊C4—2541no—
139C2×C42—1271no—
140C4⋊C8—1271no—
141C4⋊C8—2541no—
142C4⋊C8C2×D12711yescharacteristic, complemented
143C22⋊C8—2541no—
144C22⋊C8—2541no—
145C4×C8—1271no—
146C4×C8—2541no—
147C4×C8C2×D12711yescharacteristic, complemented
148C24—2541no—
149C2×D4—1274no—
150C2×D4—1271no—
151C2×D4—2542no—
152C2×D4—2541no—
153C2×D4C4×D12711yescharacteristic
154C22×C4—21no—
155C22×C4—1271no—
156C22×C4—1271no—
157C22×C4—1271no—
158C22×C4—5082no—
159C22×C4—5082no—
160C22×C4—2541no—
161C22×C4—2541no—
162C22×C4—2541no—
163C22×C4—2541no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—2541no—
167C2×C8—2541no—
168C4⋊C4—1271no—
169C4⋊C4—2541no—
170C4⋊C4C4×D12711yescharacteristic
171C22⋊C4—21no—
172C22⋊C4—2541no—
173C22⋊C4—2541no—
174C22⋊C4—2541no—
175C42—1271no—
176C42—1271no—
177C42—1271no—
178C42C22×D12711yescharacteristic
179C23—21no—
180C23—1271no—
181C23—5082no—
182C23—5082no—
183C23—2544no—
184C23—2541no—
185D4—21no—
186D4—1272no—
187D4—2544no—
188D4—2541no—
189D4C8×D12712yes—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—1271no—
194C2×C4—1272no—
195C2×C4—1272no—
196C2×C4—1271no—
197C2×C4—1271no—
198C2×C4—5081no—
199C2×C4—5082no—
200C2×C4—5082no—
201C2×C4—5082no—
202C2×C4—5081no—
203C2×C4—5081no—
204C2×C4—2541no—
205C2×C4—2541no—
206C2×C4—2541no—
207C2×C4C2×C4×D12711yescharacteristic
208C2×C4D4×D12711yescharacteristic
209C2×C4D4×D12711yescharacteristic
210C8—41no—
211C8—41no—
212C8—5081no—
213C8—5081no—
214C22—22no—
215C22—41no—
216C22—41no—
217C22—1272no—
218C22—5088no—
219C22—5081no—
220C22—5081no—
221C22—2542no—
222C22—2541no—
223C22—2541no—
224C22C22⋊C4×D12711yescharacteristic
225C4—21no—
226C4—41no—
227C4—1272no—
228C4—5081no—
229C4—2541no—
230C4—2541no—
231C4C2×C8×D12711yescharacteristic
232C4M16×D12711yescharacteristic
233C4#1686123311yescharacteristic
234C4#1686123611yescharacteristic
235C2—42no—
236C2—5082no—
237C2—2542no—
238C2C22⋊C8×D12711yescharacteristic
239C2#2254987911yescharacteristic
240C2#2254989111yescharacteristic
subgroupG/H
centerC2×C4D4×D127
commutatorC4×C127C22×C8
FrattiniC42C22×D127
FittingD4⋊C8×C127C2
socleC22×C127C2×C22⋊C4
prime radicalC2×D4×D127C4
cosocleC42×C127C23
hypercenterD4⋊C8D127
hypocenterC127#1478
LCSG ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #22549928C2semidirect
3. #22549927C2semidirect
4. #22549605C2semidirect
5. D4⋊(C127⋊C8)C2semidirect
6. #22549603C2semidirect
7. D4⋊C8×C127C2semidirect
18. C4⋊(C127⋊C8)C22semidirect
22. C4×C127⋊C8C22semidirect
25. C4⋊C8×C127C22semidirect
26. C4×C8×C127C22semidirect
31. D4×D127C8semidirect
121. C127#1478semidirect
128. D4⋊C8D127semidirect
142. C4⋊C8C2×D127semidirect
147. C4×C8C2×D127semidirect

Maximal subgroups

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

subgroupindex
C4×D4×D1272
#225499282
#225499272
#225496052
D4⋊(C127⋊C8)2
#225496032
D4⋊C8×C1272
#1478127