Finite Group Databasebeta

← C2×#22550247 #30649135

Subgroups — C2×#22550247 #30649135

Order 16256.

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

normal subgroups only

This group has 656 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
2C22×#14523236C211yesmaximal, characteristic, complemented
3C22×#14523235C211yesmaximal, characteristic, complemented
4C2×#16861207C211yesmaximal, characteristic, complemented
5C2×#16861205C211yesmaximal, characteristic
6#22550247C218yesmaximal, direct product factor
7C2×C8×Dic127C211yesmaximal, characteristic, complemented
8C22×SD16×C127C211yesmaximal, characteristic, complemented
9C22×Dic254C2211yescharacteristic
10C22×D508C2211yescharacteristic
11C22×C22⋊D127—22no—
12C2×#14523237—24no—
13C2×#14523237C2214yescomplemented
14C2×#14523236—24no—
15C2×#14523236C2214yescomplemented
16C2×#14523235—24no—
17C2×#14523235C2214yescomplemented
18C22×C127⋊C8C2211yescharacteristic
19#16861207—22no—
20#16861207C2214yescomplemented
21#16861205—22no—
22#16861205C2214yes—
23C2×Dic127⋊C4—22no—
24C2×C4×Dic127C2211yescharacteristic
25C8×Dic127C2214yescomplemented
26C22×Q8×C127C2211yescharacteristic
27C22×D4×C127C2211yescharacteristic
28C2×SD16×C127—24no—
29C2×SD16×C127C2214yescomplemented
30C22×C8×C127C2211yescharacteristic
31C23×D127—21no—
32C2×Dic254—21no—
33C2×Dic254—22no—
34C2×Dic254—22no—
35C2×Dic254C2312yes—
36C2×D508—22no—
37C2×D508—22no—
38C2×D508—21no—
39C2×D508C2312yes—
40C2×C22⋊D127—28no—
41C2×C22⋊D127—48no—
42C22×Dic127—21no—
43C22×Dic127D412yes—
44#14523237—28no—
45#14523236—28no—
46#14523235—28no—
47C2×C127⋊C8D414yescomplemented
48C2×C127⋊C8C2312yes—
49Dic127⋊C4—28no—
50C4×Dic127D412yes—
51C4×Dic127C2312yes—
52C24×C127—21no—
53C2×Q8×C127—21no—
54C2×Q8×C127—22no—
55C2×Q8×C127—22no—
56C2×Q8×C127C2312yes—
57C2×D4×C127—22no—
58C2×D4×C127—22no—
59C2×D4×C127—21no—
60C2×D4×C127C2312yes—
61C22×C4×C127—21no—
62C22×C4×C127C2311yescharacteristic
63SD16×C127—28no—
64C2×C8×C127D414yescomplemented
65C2×C8×C127C2312yes—
66C22×D127—22no—
67C22×D127—42no—
68C22×D127—44no—
69Dic254—22no—
70Dic254—22no—
71Dic254—42no—
72D508—22no—
73D508—22no—
74D508—42no—
75C22⋊D127—416no—
76C2×Dic127—22no—
77C2×Dic127—42no—
78C2×Dic127SD1618yescomplemented
79C2×Dic127C2×D414yes—
80C127⋊C8C2×D414yescomplemented
81C23×C127—22no—
82C23×C127—42no—
83C23×C127—44no—
84C23×C127C2×D411yescharacteristic
85Q8×C127—22no—
86Q8×C127—22no—
87Q8×C127—42no—
88D4×C127—22no—
89D4×C127—22no—
90D4×C127—42no—
91C2×C4×C127—22no—
92C2×C4×C127—42no—
93C2×C4×C127C2×D411yescharacteristic
94C2×C4×C127C2×D412yes—
95C2×C4×C127C2×D412yes—
96C2×C4×C127C2411yescharacteristic
97C8×C127C2×D414yescomplemented
98C22×C127—42no—
99C22×C127—44no—
100C22×C127—84no—
101C22×C127#12712yes—
102C22×C127C2×SD1614yes—
103C22×C127C22×D411yescharacteristic
104C2×D127—42no—
105C2×D127—44no—
106C2×D127—84no—
107C4×C127—42no—
108C4×C127#12712yes—
109C4×C127C22×D411yescharacteristic
110C4×C127C22×D411yescharacteristic
111Dic127—42no—
112Dic127C2×SD1618yescomplemented
113C2×C127—82no—
114C2×C127#49214yescomplemented
115C2×C127C2×#12711yescharacteristic
116C2×C127C22×SD1612yes—
117D127—82no—
118C2×#492—1271nomaximal, Sylow
119C127C2×#49211yescharacteristic, complemented, Sylow
120C22×SD16—1271no—
121C22×SD16—1271no—
122C22×SD16—1271no—
123C22×SD16D12711yescharacteristic, complemented
124C2×C4⋊Q8—1271no—
125C2×#127—1271no—
126#492—1278no—
127C2×C4×C8—1271no—
128C22×Q8—1271no—
129C22×Q8C2×D12711yescharacteristic
130C22×D4—1271no—
131C22×D4—2542no—
132C22×D4C2×D12711yescharacteristic
133C2×SD16—24no—
134C2×SD16—1274no—
135C2×SD16—1274no—
136C2×SD16—1274no—
137C2×SD16—2544no—
138C2×SD16—2544no—
139C2×SD16—2544no—
140C2×SD16C2×D12714yescomplemented
141C22×C8—1271no—
142C22×C8C2×D12711yescharacteristic
143C4⋊Q8—1274no—
144C4⋊Q8—2542no—
145#127—1274no—
146#127—2542no—
147C2×C4⋊C4—2542no—
148C2×C42—1271no—
149C4×C8—1274no—
150C24—21no—
151C24—2541no—
152C2×Q8—21no—
153C2×Q8—22no—
154C2×Q8—22no—
155C2×Q8—1272no—
156C2×Q8—2542no—
157C2×Q8—2542no—
158C2×Q8—2541no—
159C2×Q8C22×D12712yes—
160C2×D4—22no—
161C2×D4—21no—
162C2×D4—22no—
163C2×D4—1272no—
164C2×D4—5088no—
165C2×D4—2548no—
166C2×D4—2541no—
167C2×D4—2542no—
168C2×D4—2542no—
169C2×D4C22×D12712yes—
170C22×C4—21no—
171C22×C4—1272no—
172C22×C4—2541no—
173C22×C4C22×D12711yescharacteristic
174SD16—28no—
175SD16—2548no—
176SD16—2548no—
177SD16—2548no—
178C2×C8—1274no—
179C2×C8—1272no—
180C2×C8C22⋊D12714yescomplemented
181C2×C8C22×D12712yes—
182C4⋊C4—2548no—
183C42—1272no—
184C42—1272no—
185C23—22no—
186C23—42no—
187C23—44no—
188C23—5082no—
189C23—5084no—
190C23—2542no—
191C23D4×D12711yescharacteristic
192Q8—22no—
193Q8—22no—
194Q8—42no—
195Q8—5082no—
196Q8—2542no—
197Q8—2542no—
198D4—22no—
199D4—22no—
200D4—42no—
201D4—50816no—
202D4—5082no—
203D4—2542no—
204D4—2542no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—1278no—
208C2×C4—1274no—
209C2×C4—5082no—
210C2×C4—2542no—
211C2×C4D4×D12711yescharacteristic
212C2×C4D4×D12712yes—
213C2×C4C2×C22⋊D12712yes—
214C2×C4C23×D12711yescharacteristic
215C8—1274no—
216C8C2×C22⋊D12714yescomplemented
217C22—44no—
218C22—42no—
219C22—84no—
220C22—10164no—
221C22—5084no—
222C22—5082no—
223C22#1686120512yes—
224C22SD16×D12714yes—
225C22C2×D4×D12711yescharacteristic
226C4—42no—
227C4—1278no—
228C4—5082no—
229C4#1686120512yes—
230C4C2×D4×D12711yescharacteristic
231C4C22×C22⋊D12711yescharacteristic
232C2—82no—
233C2—10162no—
234C2#2255024714yesdirect product factor
235C2C2×#1686120511yescharacteristic
236C2C2×SD16×D12712yes—
subgroupG/H
centerC23D4×D127
commutator, cosocleC2×C4×C127C24
FrattiniC2×C4C23×D127
FittingC22×SD16×C127C2
socleC23×C127C2×D4
prime radicalC2×#16861205C2
hypercenterC22×SD16D127
hypocenterC127C2×#492
LCSG ▷ C2×C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×#14523237C2semidirect
2. C22×#14523236C2semidirect
3. C22×#14523235C2semidirect
4. C2×#16861207C2semidirect
6. #22550247C2direct (N × H)
7. C2×C8×Dic127C2semidirect
8. C22×SD16×C127C2semidirect
13. C2×#14523237C22semidirect
15. C2×#14523236C22semidirect
17. C2×#14523235C22semidirect
20. #16861207C22semidirect
25. C8×Dic127C22semidirect
29. C2×SD16×C127C22semidirect
47. C2×C127⋊C8D4semidirect
64. C2×C8×C127D4semidirect
78. C2×Dic127SD16semidirect
80. C127⋊C8C2×D4semidirect
97. C8×C127C2×D4semidirect
112. Dic127C2×SD16semidirect
114. C2×C127#492semidirect
119. C127C2×#492semidirect
123. C22×SD16D127semidirect
140. C2×SD16C2×D127semidirect
180. C2×C8C22⋊D127semidirect
216. C8C2×C22⋊D127semidirect
234. C2#22550247direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145232372
C22×#145232362
C22×#145232352
C2×#168612072
C2×#168612052
#225502472
C2×C8×Dic1272
C22×SD16×C1272
C2×#492127