Finite Group Databasebeta

← C2×#22550108 #30648293

Subgroups — C2×#22550108 #30648293

Order 16256.

564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14523235C211yesmaximal, characteristic, complemented
2C22×C8×D127C211yesmaximal, characteristic, complemented
3C2×#16861185C211yesmaximal, characteristic, complemented
4C2×#16861184C211yesmaximal, characteristic
5#22550108C218yesmaximal, direct product factor
6C2×#16861140C211yesmaximal, characteristic, complemented
7C2×#16861131C211yesmaximal, characteristic, complemented
8C2×#103×C127C211yesmaximal, characteristic, complemented
9C22×D508—21no—
10C22×D508C2211yescharacteristic
11C22×C4×D127C2211yescharacteristic
12C2×#14523235—24no—
13C2×#14523235C2214yescomplemented
14C22×C127⋊C8C2211yescharacteristic
15C2×C8×D127—24no—
16C2×C8×D127C2214yescomplemented
17#16861185—22no—
18#16861185C2214yescomplemented
19#16861184—22no—
20#16861184C2214yes—
21C2×C4⋊Dic127C2211yescharacteristic
22C2×Dic127⋊C4—21no—
23C2×(C2×D127)⋊C4—21no—
24C2×(C2×D127)⋊C4—21no—
25#16861140C2214yescomplemented
26#16861131C2214yescomplemented
27C22×Q8×C127C2211yescharacteristic
28C22×C8×C127C2211yescharacteristic
29C2×C4⋊C4×C127C2211yescharacteristic
30#103×C127C2214yescomplemented
31C23×D127—21no—
32C23×D127D411yescharacteristic
33C2×D508—24no—
34C2×D508—22no—
35C2×D508—21no—
36C2×D508—22no—
37C2×D508—44no—
38C2×D508C2312yes—
39C22×Dic127—21no—
40C22×Dic127D411yescharacteristic
41C2×C4×D127—22no—
42C2×C4×D127—22no—
43C2×C4×D127D412yes—
44C2×C4×D127C2312yes—
45#14523235—28no—
46C2×C127⋊C8D414yescomplemented
47C2×C127⋊C8C2312yes—
48C8×D127—28no—
49C4⋊Dic127—21no—
50C4⋊Dic127C2312yes—
51Dic127⋊C4—24no—
52(C2×D127)⋊C4—24no—
53(C2×D127)⋊C4—24no—
54C2×Q8×C127—21no—
55C2×Q8×C127—22no—
56C2×Q8×C127—22no—
57C2×Q8×C127C2312yes—
58C22×C4×C127—21no—
59C22×C4×C127—21no—
60C22×C4×C127C2311yescharacteristic
61C2×C8×C127—22no—
62C2×C8×C127C2312yes—
63C4⋊C4×C127—21no—
64C4⋊C4×C127C2312yes—
65C22×D127—22no—
66C22×D127—22no—
67C22×D127—22no—
68C22×D127—42no—
69C22×D127—42no—
70C22×D127—42no—
71C22×D127SD1614yescomplemented
72C22×D127C2×D412yes—
73D508—22no—
74D508—22no—
75D508—48no—
76D508—42no—
77C2×Dic127—22no—
78C2×Dic127—22no—
79C2×Dic127—42no—
80C2×Dic127C2×D412yes—
81C4×D127—24no—
82C4×D127—22no—
83C4×D127—22no—
84C127⋊C8C2×D414yescomplemented
85C23×C127C2×D411yescharacteristic
86Q8×C127—22no—
87Q8×C127—22no—
88Q8×C127—42no—
89C2×C4×C127—22no—
90C2×C4×C127—22no—
91C2×C4×C127—42no—
92C2×C4×C127—42no—
93C2×C4×C127C2×D411yescharacteristic
94C2×C4×C127C2×D412yes—
95C2×C4×C127#4112yes—
96C2×C4×C127C2411yescharacteristic
97C8×C127—22no—
98C22×C127#12112yes—
99C22×C127C2×SD1612yes—
100C22×C127#13512yes—
101C22×C127C22×D411yescharacteristic
102C2×D127—22no—
103C2×D127—22no—
104C2×D127—28no—
105C2×D127—42no—
106C2×D127—42no—
107C2×D127—42no—
108C2×D127—84no—
109C2×D127C2×SD1614yescomplemented
110C4×C127—42no—
111C4×C127—42no—
112C4×C127#12112yes—
113C4×C127C22×D411yescharacteristic
114C4×C127C2×#4111yescharacteristic
115Dic127—22no—
116Dic127—42no—
117C2×C127#46514yescomplemented
118C2×C127C2×#12111yescharacteristic
119C2×C127C22×SD1611yescharacteristic
120C2×C127C2×#13511yescharacteristic
121D127—24no—
122D127—82no—
123C2×#465—1271nomaximal, Sylow
124C127C2×#46511yescharacteristic, complemented, Sylow
125C22×SD16—1271no—
126C23×C8—1271no—
127C2×C22⋊Q8—1271no—
128C2×#121—1271no—
129#465—1278no—
130C2×#106—1271no—
131C2×#103D12711yescharacteristic, complemented
132C2×#102—1271no—
133C22×Q8C2×D12711yescharacteristic
134C22×D4—1271no—
135C22×D4—2541no—
136C23×C4—1271no—
137C2×SD16—1274no—
138C2×SD16—2544no—
139C22×C8—1271no—
140C22×C8—1274no—
141C22×C8—2544no—
142C22×C8C2×D12711yescharacteristic
143C22⋊Q8—1274no—
144C22⋊Q8—2542no—
145#121—1274no—
146#121—2542no—
147C2×C4⋊C4—1271no—
148C2×C4⋊C4—2541no—
149C2×C4⋊C4C2×D12711yescharacteristic
150C2×C22⋊C4—2541no—
151C2×C22⋊C4—2541no—
152#106—1274no—
153#103C2×D12714yescomplemented
154#102—1274no—
155C24—1271no—
156C24—2541no—
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D12712yes—
161C2×D4—1272no—
162C2×D4—5084no—
163C2×D4—2544no—
164C2×D4—2541no—
165C2×D4—2542no—
166C2×D4—2542no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—1271no—
170C22×C4—1272no—
171C22×C4—1272no—
172C22×C4—2541no—
173C22×C4—2542no—
174C22×C4—2542no—
175C22×C4C22×D12711yescharacteristic
176SD16—2548no—
177C2×C8—22no—
178C2×C8—1274no—
179C2×C8—1272no—
180C2×C8—2548no—
181C2×C8C22×D12712yes—
182C4⋊C4—21no—
183C4⋊C4—1272no—
184C4⋊C4—2544no—
185C4⋊C4—2541no—
186C4⋊C4C22×D12712yes—
187C22⋊C4—2544no—
188C22⋊C4—2544no—
189C23—1274no—
190C23—1272no—
191C23—5082no—
192C23—5082no—
193C23—5082no—
194C23—2542no—
195C23—2542no—
196C23—2542no—
197C23D4×D12711yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—42no—
201D4—5088no—
202D4—5082no—
203D4—2542no—
204D4—2542no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—1272no—
210C2×C4—5082no—
211C2×C4—2542no—
212C2×C4—2542no—
213C2×C4—2542no—
214C2×C4—2542no—
215C2×C4—2544no—
216C2×C4D4×D12712yes—
217C2×C4D4×D12711yescharacteristic
218C2×C4#1452324812yes—
219C2×C4C23×D12711yescharacteristic
220C8—22no—
221C8—1274no—
222C22—1274no—
223C22—10164no—
224C22—5082no—
225C22—5082no—
226C22—5082no—
227C22—2548no—
228C22—2542no—
229C22—2542no—
230C22#1686118212yes—
231C22SD16×D12712yes—
232C22#1686123212yes—
233C22C2×D4×D12711yescharacteristic
234C4—42no—
235C4—42no—
236C4—5082no—
237C4—2542no—
238C4#1686118212yes—
239C4C2×D4×D12711yescharacteristic
240C4C2×#1452324811yescharacteristic
241C2—10162no—
242C2—2544no—
243C2#2255010814yesdirect product factor
244C2C2×#1686118211yescharacteristic
245C2C2×SD16×D12711yescharacteristic
246C2C2×#1686123211yescharacteristic
subgroupG/H
centerC23D4×D127
commutator, cosocleC2×C4×C127C24
FrattiniC2×C4C23×D127
FittingC2×#103×C127C2
socleC23×C127C2×D4
prime radicalC2×#16861184C2
hypercenterC2×#103D127
hypocenterC127C2×#465
LCSG ▷ C2×C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C22×#14523235C2semidirect
2. C22×C8×D127C2semidirect
3. C2×#16861185C2semidirect
5. #22550108C2direct (N × H)
6. C2×#16861140C2semidirect
7. C2×#16861131C2semidirect
8. C2×#103×C127C2semidirect
13. C2×#14523235C22semidirect
16. C2×C8×D127C22semidirect
18. #16861185C22semidirect
25. #16861140C22semidirect
26. #16861131C22semidirect
30. #103×C127C22semidirect
46. C2×C127⋊C8D4semidirect
71. C22×D127SD16semidirect
84. C127⋊C8C2×D4semidirect
109. C2×D127C2×SD16semidirect
117. C2×C127#465semidirect
124. C127C2×#465semidirect
131. C2×#103D127semidirect
153. #103C2×D127semidirect
243. C2#22550108direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145232352
C22×C8×D1272
C2×#168611852
C2×#168611842
#225501082
C2×#168611402
C2×#168611312
C2×#103×C1272
C2×#465127