Finite Group Databasebeta

← C2×#22550040 #30647941

Subgroups — C2×#22550040 #30647941

Order 16256.

760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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×#14523248C211yesmaximal, characteristic
2C22×Dic508C211yesmaximal, characteristic, complemented
3C22×#14523237C211yesmaximal, characteristic, complemented
4C2×#16861188C211yesmaximal, characteristic, complemented
5#22550040C218yesmaximal, direct product factor
6C2×#16861134C211yesmaximal, characteristic, complemented
7C2×#16861131C211yesmaximal, characteristic, complemented
8C2×C22⋊C8×C127C211yesmaximal, characteristic, complemented
9C2×#14523248—24no—
10C2×#14523248—24no—
11C2×#14523248—22no—
12C2×#14523248C2214yes—
13C22×Dic254C2211yescharacteristic
14C22×Dic254C2211yescharacteristic
15C22×D508C2211yescharacteristic
16C22×C22⋊D127—21no—
17C22×C4×D127—21no—
18C2×Dic508—24no—
19C2×Dic508C2214yescomplemented
20C2×#14523237—24no—
21C2×#14523237C2214yescomplemented
22#16861188—22no—
23#16861188C2214yescomplemented
24C2×C4⋊Dic127C2211yescharacteristic
25C2×Dic127⋊C4—21no—
26C2×C22⋊Dic127—21no—
27#16861134C2214yescomplemented
28#16861131C2214yescomplemented
29C23×C4×C127C2211yescharacteristic
30C22×C8×C127C2211yescharacteristic
31C22×C8×C127C2211yescharacteristic
32C22⋊C8×C127C2214yescomplemented
33C23×D127—21no—
34#14523248—216no—
35#14523248—28no—
36#14523248—28no—
37C2×Dic254—22no—
38C2×Dic254—21no—
39C2×Dic254—21no—
40C2×Dic254—22no—
41C2×Dic254—22no—
42C2×Dic254D414yes—
43C2×Dic254C2312yes—
44C2×Dic254C2312yes—
45C2×D508—22no—
46C2×D508—21no—
47C2×D508D414yes—
48C2×D508C2312yes—
49C2×C22⋊D127—28no—
50C2×C22⋊D127—24no—
51C22×Dic127—21no—
52C22×Dic127—21no—
53C22×Dic127—21no—
54C2×C4×D127—28no—
55C2×C4×D127—24no—
56Dic508—28no—
57#14523237—28no—
58C4⋊Dic127—21no—
59C4⋊Dic127C2312yes—
60Dic127⋊C4—24no—
61C22⋊Dic127—24no—
62C24×C127D411yescharacteristic
63C22×C4×C127—22no—
64C22×C4×C127—22no—
65C22×C4×C127D412yes—
66C22×C4×C127D411yescharacteristic
67C22×C4×C127C2312yes—
68C22×C4×C127C2311yescharacteristic
69C2×C8×C127—22no—
70C2×C8×C127—22no—
71C2×C8×C127C2312yes—
72C2×C8×C127C2312yes—
73C22×D127—24no—
74C22×D127—22no—
75C22×D127—42no—
76C22×D127—42no—
77Dic254—24no—
78Dic254—22no—
79Dic254—22no—
80Dic254—22no—
81Dic254—42no—
82Dic254C2×D414yes—
83D508—24no—
84D508—22no—
85D508C2×D414yes—
86C22⋊D127—216no—
87C2×Dic127—24no—
88C2×Dic127—22no—
89C2×Dic127—22no—
90C2×Dic127—22no—
91C2×Dic127—42no—
92C2×Dic127—42no—
93C4×D127—216no—
94C23×C127—22no—
95C23×C127—22no—
96C23×C127—22no—
97C23×C127C2×D412yes—
98C23×C127C2×D411yescharacteristic
99C2×C4×C127—22no—
100C2×C4×C127—24no—
101C2×C4×C127—22no—
102C2×C4×C127—22no—
103C2×C4×C127C2×D412yes—
104C2×C4×C127C2×D412yes—
105C2×C4×C127C2×D412yes—
106C2×C4×C127C2×D411yescharacteristic
107C2×C4×C127C2411yescharacteristic
108C8×C127—22no—
109C8×C127—22no—
110C22×C127—22no—
111C22×C127—22no—
112C22×C127—22no—
113C22×C127—44no—
114C22×C127#12012yes—
115C22×C127#13512yes—
116C22×C127#13712yes—
117C22×C127C22×D411yescharacteristic
118C2×D127—24no—
119C2×D127—42no—
120C2×D127—42no—
121C2×D127—48no—
122C4×C127—22no—
123C4×C127#12012yes—
124C4×C127C22×D411yescharacteristic
125C4×C127C22×D411yescharacteristic
126Dic127—24no—
127Dic127—42no—
128Dic127—42no—
129C2×C127—42no—
130C2×C127#45214yescomplemented
131C2×C127C2×#12011yescharacteristic
132C2×C127C2×#13511yescharacteristic
133C2×C127C2×#13711yescharacteristic
134D127—44no—
135C2×#452—1271nomaximal, Sylow
136C127C2×#45211yescharacteristic, complemented, Sylow
137C22×#41—1271no—
138C22×Q16—1271no—
139C22×SD16—1271no—
140C2×C22⋊Q8—1271no—
141#452—1278no—
142C2×#103—1271no—
143C2×#102—1271no—
144C2×C22⋊C8D12711yescharacteristic, complemented
145C2×#41—1274no—
146C2×#41—2544no—
147C2×#41—2544no—
148C2×#41—2542no—
149C22×Q8—1271no—
150C22×Q8—1271no—
151C22×D4—1271no—
152C22×D4—2541no—
153C23×C4—2541no—
154C23×C4C2×D12711yescharacteristic
155C2×Q16—1274no—
156C2×Q16—2544no—
157C2×SD16—1274no—
158C2×SD16—2544no—
159C22×C8C2×D12711yescharacteristic
160C22×C8C2×D12711yescharacteristic
161C22⋊Q8—1274no—
162C22⋊Q8—2542no—
163C2×C4⋊C4—1271no—
164C2×C4⋊C4—2541no—
165C2×C22⋊C4—2541no—
166#103—1274no—
167#102—1274no—
168C22⋊C8C2×D12714yescomplemented
169C24—2541no—
170C24D50811yescharacteristic
171#41—2548no—
172#41—2548no—
173#41—25416no—
174C2×Q8—1274no—
175C2×Q8—1272no—
176C2×Q8—1272no—
177C2×Q8—2542no—
178C2×Q8—2542no—
179C2×Q8—2542no—
180C2×Q8—2541no—
181C2×Q8—2541no—
182C2×D4—1274no—
183C2×D4—1272no—
184C2×D4—2548no—
185C2×D4—2544no—
186C2×D4—2542no—
187C2×D4—2541no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—2548no—
191C22×C4—2541no—
192C22×C4—2541no—
193C22×C4—2541no—
194C22×C4—2544no—
195C22×C4D50812yes—
196C22×C4D50811yescharacteristic
197C22×C4C22×D12712yes—
198C22×C4C22×D12711yescharacteristic
199Q16—2548no—
200SD16—2548no—
201C2×C8—22no—
202C2×C8—22no—
203C2×C8C22×D12712yes—
204C2×C8C22×D12712yes—
205C4⋊C4—1272no—
206C4⋊C4—2544no—
207C4⋊C4—2541no—
208C22⋊C4—2544no—
209C23—22no—
210C23—22no—
211C23—22no—
212C23—5082no—
213C23—5082no—
214C23—2542no—
215C23—2544no—
216C23C2×D50812yes—
217C23C2×D50811yescharacteristic
218Q8—1274no—
219Q8—5082no—
220Q8—2542no—
221Q8—2542no—
222Q8—2542no—
223Q8—2544no—
224D4—1274no—
225D4—25416no—
226D4—2542no—
227D4—2544no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—24no—
232C2×C4—5082no—
233C2×C4—5082no—
234C2×C4—25416no—
235C2×C4—2542no—
236C2×C4—2542no—
237C2×C4—2542no—
238C2×C4—2544no—
239C2×C4D4×D12712yes—
240C2×C4D4×D12712yes—
241C2×C4C2×D50812yes—
242C2×C4C2×D50811yescharacteristic
243C2×C4C23×D12711yescharacteristic
244C8—22no—
245C8—22no—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—44no—
250C22—5088no—
251C22—5082no—
252C22—5082no—
253C22—2544no—
254C22#1686117912yes—
255C22#1686123112yes—
256C22#1686124212yes—
257C22C22×D50811yescharacteristic
258C4—22no—
259C4—5082no—
260C4—5082no—
261C4—2544no—
262C4#1686117912yes—
263C4C2×D4×D12711yescharacteristic
264C4C2×D4×D12711yescharacteristic
265C2—42no—
266C2—5084no—
267C2#2255004014yesdirect product factor
268C2C2×#1686117911yescharacteristic
269C2C2×#1686123111yescharacteristic
270C2C2×#1686124211yescharacteristic
subgroupG/H
centerC23C2×D508
commutator, cosocleC2×C4×C127C24
FrattiniC2×C4C23×D127
FittingC2×C22⋊C8×C127C2
socleC23×C127C2×D4
prime radicalC22×#14523248C2
hypercenterC2×C22⋊C8D127
hypocenterC127C2×#452
LCSG ▷ C2×C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C22×Dic508C2semidirect
3. C22×#14523237C2semidirect
4. C2×#16861188C2semidirect
5. #22550040C2direct (N × H)
6. C2×#16861134C2semidirect
7. C2×#16861131C2semidirect
8. C2×C22⋊C8×C127C2semidirect
19. C2×Dic508C22semidirect
21. C2×#14523237C22semidirect
23. #16861188C22semidirect
27. #16861134C22semidirect
28. #16861131C22semidirect
32. C22⋊C8×C127C22semidirect
130. C2×C127#452semidirect
136. C127C2×#452semidirect
144. C2×C22⋊C8D127semidirect
168. C22⋊C8C2×D127semidirect
267. C2#22550040direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145232482
C22×Dic5082
C22×#145232372
C2×#168611882
#225500402
C2×#168611342
C2×#168611312
C2×C22⋊C8×C1272
C2×#452127