Finite Group Databasebeta

← C2×#22550105 #30648290

Subgroups — C2×#22550105 #30648290

Order 16256.

564 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C22×#14523237C211yesmaximal, characteristic, complemented
2C2×#16861188C211yesmaximal, characteristic, complemented
3C2×#16861183C211yesmaximal, characteristic
4#22550105C218yesmaximal, direct product factor
5C2×#16861141C211yesmaximal, characteristic, complemented
6C2×#16861134C211yesmaximal, characteristic, complemented
7C2×#16861131C211yesmaximal, characteristic, complemented
8C23×C8×C127C211yesmaximal, characteristic, complemented
9C22×Dic254C2211yescharacteristic
10C22×D508C2211yescharacteristic
11C22×C22⋊D127—21no—
12C2×#14523237—24no—
13C2×#14523237C2214yescomplemented
14#16861188—22no—
15#16861188C2214yescomplemented
16#16861183—22no—
17#16861183C2214yes—
18C2×C4⋊Dic127C2211yescharacteristic
19C2×C4⋊Dic127C2211yescharacteristic
20C2×Dic127⋊C4—21no—
21C2×C22⋊Dic127—21no—
22C2×(C2×D127)⋊C4—21no—
23#16861141C2214yescomplemented
24#16861134C2214yescomplemented
25#16861131C2214yescomplemented
26C23×C4×C127C2211yescharacteristic
27C22×C8×C127—24no—
28C22×C8×C127C2211yescharacteristic
29C22×C8×C127C2211yescharacteristic
30C22×C8×C127C2214yescomplemented
31C23×D127—21no—
32C2×Dic254—21no—
33C2×Dic254—22no—
34C2×Dic254—22no—
35C2×Dic254C2312yes—
36C2×D508—22no—
37C2×D508—21no—
38C2×D508—22no—
39C2×D508C2312yes—
40C2×C22⋊D127—24no—
41C2×C22⋊D127—44no—
42C22×Dic127—21no—
43C22×Dic127—21no—
44C22×Dic127—21no—
45#14523237—28no—
46C4⋊Dic127—21no—
47C4⋊Dic127—21no—
48C4⋊Dic127C2312yes—
49C4⋊Dic127C2312yes—
50Dic127⋊C4—24no—
51C22⋊Dic127—24no—
52(C2×D127)⋊C4—24no—
53C24×C127D411yescharacteristic
54C22×C4×C127—22no—
55C22×C4×C127—22no—
56C22×C4×C127D412yes—
57C22×C4×C127D411yescharacteristic
58C22×C4×C127C2312yes—
59C22×C4×C127C2311yescharacteristic
60C2×C8×C127—22no—
61C2×C8×C127—28no—
62C2×C8×C127D414yescomplemented
63C2×C8×C127C2312yes—
64C2×C8×C127C2312yes—
65C22×D127—22no—
66C22×D127—42no—
67C22×D127—42no—
68C22×D127—42no—
69Dic254—22no—
70Dic254—22no—
71Dic254—42no—
72D508—22no—
73D508—22no—
74D508—42no—
75C22⋊D127—48no—
76C2×Dic127—22no—
77C2×Dic127—22no—
78C2×Dic127—22no—
79C2×Dic127—42no—
80C2×Dic127—42no—
81C2×Dic127—42no—
82C23×C127—22no—
83C23×C127—22no—
84C23×C127SD1614yescomplemented
85C23×C127C2×D412yes—
86C23×C127C2×D411yescharacteristic
87C2×C4×C127—22no—
88C2×C4×C127—24no—
89C2×C4×C127—22no—
90C2×C4×C127—22no—
91C2×C4×C127C2×D412yes—
92C2×C4×C127C2×D412yes—
93C2×C4×C127C2×D411yescharacteristic
94C2×C4×C127#4112yes—
95C2×C4×C127C2411yescharacteristic
96C8×C127—22no—
97C8×C127C2×D414yescomplemented
98C22×C127—22no—
99C22×C127—22no—
100C22×C127—28no—
101C22×C127#12112yes—
102C22×C127C2×SD1612yes—
103C22×C127C2×SD1614yescomplemented
104C22×C127#13512yes—
105C22×C127C22×D411yescharacteristic
106C2×D127—42no—
107C2×D127—42no—
108C2×D127—42no—
109C2×D127—84no—
110C4×C127—22no—
111C4×C127#12112yes—
112C4×C127C22×D411yescharacteristic
113C4×C127C2×#4111yescharacteristic
114Dic127—42no—
115Dic127—42no—
116Dic127—42no—
117C2×C127—24no—
118C2×C127#46514yescomplemented
119C2×C127C2×#12111yescharacteristic
120C2×C127C22×SD1611yescharacteristic
121C2×C127C2×#13511yescharacteristic
122D127—82no—
123C2×#465—1271nomaximal, Sylow
124C127C2×#46511yescharacteristic, complemented, Sylow
125C22×SD16—1271no—
126C23×C8D12711yescharacteristic, complemented
127C2×C22⋊Q8—1271no—
128C2×#121—1271no—
129#465—1278no—
130C2×#106—1271no—
131C2×#103—1271no—
132C2×#102—1271no—
133C22×Q8—1271no—
134C22×D4—1271no—
135C22×D4—2541no—
136C23×C4C2×D12711yescharacteristic
137C2×SD16—1274no—
138C2×SD16—2544no—
139C22×C8—24no—
140C22×C8C2×D12711yescharacteristic
141C22×C8C2×D12711yescharacteristic
142C22×C8C2×D12714yescomplemented
143C22⋊Q8—1274no—
144C22⋊Q8—2542no—
145#121—1274no—
146#121—2542no—
147C2×C4⋊C4—1271no—
148C2×C4⋊C4—1271no—
149C2×C4⋊C4—2541no—
150C2×C22⋊C4—2541no—
151C2×C22⋊C4—2541no—
152#106—1274no—
153#103—1274no—
154#102—1274no—
155C24—2541no—
156C24D50811yescharacteristic
157C2×Q8—1272no—
158C2×Q8—2542no—
159C2×Q8—2542no—
160C2×Q8—2541no—
161C2×D4—1272no—
162C2×D4—5084no—
163C2×D4—2544no—
164C2×D4—2542no—
165C2×D4—2541no—
166C2×D4—2542no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—2541no—
170C22×C4—2541no—
171C22×C4—2541no—
172C22×C4D50812yes—
173C22×C4D50811yescharacteristic
174C22×C4C22×D12712yes—
175C22×C4C22×D12711yescharacteristic
176SD16—2548no—
177C2×C8—22no—
178C2×C8—28no—
179C2×C8C22⋊D12714yescomplemented
180C2×C8C22×D12712yes—
181C2×C8C22×D12712yes—
182C4⋊C4—1272no—
183C4⋊C4—1272no—
184C4⋊C4—2544no—
185C4⋊C4—2541no—
186C4⋊C4—2541no—
187C22⋊C4—2544no—
188C22⋊C4—2544no—
189C23—22no—
190C23—22no—
191C23—5082no—
192C23—5082no—
193C23—5082no—
194C23—2542no—
195C23#1452323714yescomplemented
196C23C2×D50812yes—
197C23C2×D50811yescharacteristic
198Q8—5082no—
199Q8—2542no—
200Q8—2542no—
201D4—5088no—
202D4—5082no—
203D4—2542no—
204D4—2542no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—24no—
209C2×C4—5082no—
210C2×C4—5082no—
211C2×C4—5082no—
212C2×C4—2542no—
213C2×C4—2542no—
214C2×C4—2542no—
215C2×C4C2×C22⋊D12712yes—
216C2×C4C2×D50812yes—
217C2×C4C2×D50811yescharacteristic
218C2×C4#1452324812yes—
219C2×C4C23×D12711yescharacteristic
220C8—22no—
221C8C2×C22⋊D12714yescomplemented
222C22—28no—
223C22—22no—
224C22—22no—
225C22—10164no—
226C22—5082no—
227C22—5082no—
228C22—5082no—
229C22#1686118312yes—
230C22C2×#1452323712yes—
231C22C2×#1452323714yescomplemented
232C22#1686123112yes—
233C22C22×D50811yescharacteristic
234C4—22no—
235C4—5082no—
236C4—5082no—
237C4—5082no—
238C4#1686118312yes—
239C4C22×C22⋊D12711yescharacteristic
240C4C2×#1452324811yescharacteristic
241C2—24no—
242C2—10162no—
243C2#2255010514yesdirect product factor
244C2C2×#1686118311yescharacteristic
245C2C22×#1452323711yescharacteristic
246C2C2×#1686123111yescharacteristic
subgroupG/H
centerC23C2×D508
commutator, cosocleC2×C4×C127C24
FrattiniC2×C4C23×D127
FittingC23×C8×C127C2
socleC23×C127C2×D4
prime radicalC2×#16861183C2
hypercenterC23×C8D127
hypocenterC127C2×#465
LCSG ▷ C2×C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
1. C22×#14523237C2semidirect
2. C2×#16861188C2semidirect
4. #22550105C2direct (N × H)
5. C2×#16861141C2semidirect
6. C2×#16861134C2semidirect
7. C2×#16861131C2semidirect
8. C23×C8×C127C2semidirect
13. C2×#14523237C22semidirect
15. #16861188C22semidirect
23. #16861141C22semidirect
24. #16861134C22semidirect
25. #16861131C22semidirect
30. C22×C8×C127C22semidirect
62. C2×C8×C127D4semidirect
84. C23×C127SD16semidirect
97. C8×C127C2×D4semidirect
103. C22×C127C2×SD16semidirect
118. C2×C127#465semidirect
124. C127C2×#465semidirect
126. C23×C8D127semidirect
142. C22×C8C2×D127semidirect
179. C2×C8C22⋊D127semidirect
195. C23#14523237semidirect
221. C8C2×C22⋊D127semidirect
231. C22C2×#14523237semidirect
243. C2#22550105direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145232372
C2×#168611882
C2×#168611832
#225501052
C2×#168611412
C2×#168611342
C2×#168611312
C23×C8×C1272
C2×#465127