Finite Group Databasebeta

← C2×SD16×#10624382 #37550469

Subgroups — C2×SD16×#10624382 #37550469

Order 23168.

552 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 178 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
1C2×Q8×#10624382C211yesmaximal, characteristic, complemented
2C2×D4×#10624382C211yesmaximal, characteristic
3SD16×#10624382C218yesmaximal, direct product factor
4C2×#19153884C211yesmaximal, characteristic, complemented
5C2×#19153879C211yesmaximal, characteristic, complemented
6C2×#19153878C211yesmaximal, characteristic
7C2×C8×#10624382C211yesmaximal, characteristic, complemented
8C2×SD16×D181C211yesmaximal, characteristic
9C23×#10624382—21no—
10C2×D181⋊C8C2211yescharacteristic
11Q8×#10624382—22no—
12Q8×#10624382C2214yescomplemented
13D4×#10624382—22no—
14D4×#10624382C2214yes—
15C2×C4⋊#10624382—21no—
16C2×C4⋊#10624382C2211yescharacteristic
17C2×C4⋊#10624382C2211yescharacteristic
18C2×C22⋊#10624382—21no—
19C2×C4×#10624382—21no—
20C2×C4×#10624382C2211yescharacteristic
21#19153884C2214yescomplemented
22#19153879C2214yescomplemented
23#19153878C2214yes—
24C8×#10624382C2214yescomplemented
25C2×Q8×D181C2211yescharacteristic
26C2×D4×D181C2211yescharacteristic
27C2×#15668438C411yescharacteristic, complemented
28C2×#15668437C411yescharacteristic, complemented
29C2×#15668436C411yescharacteristic, complemented
30SD16×D181C414yescomplemented
31SD16×D181C2214yes—
32C2×C8×D181C2211yescharacteristic
33C2×SD16×C181C411yescharacteristic, complemented
34C22×#10624382—24no—
35C22×#10624382—21no—
36C22×#10624382—21no—
37C22×#10624382—44no—
38C22×#10624382D411yescharacteristic
39C22×#10624382D411yescharacteristic
40D181⋊C8—21no—
41D181⋊C8C2312yes—
42C2×#13089685—21no—
43C4⋊#10624382—24no—
44C4⋊#10624382—21no—
45C4⋊#10624382—21no—
46C4⋊#10624382C2312yes—
47C4⋊#10624382C2312yes—
48C22⋊#10624382—24no—
49C4×#10624382—24no—
50C4×#10624382D412yes—
51C4×#10624382C2312yes—
52C23×D181—21no—
53C2×Dic362—21no—
54C2×Dic362C2×C411yescharacteristic, complemented
55Q8×D181—21no—
56Q8×D181—21no—
57Q8×D181C2×C412yescomplemented
58Q8×D181C2312yes—
59C2×D724C2×C411yescharacteristic
60C2×C22⋊D181—21no—
61D4×D181—21no—
62D4×D181—21no—
63D4×D181C2×C412yes—
64D4×D181C2312yes—
65C2×C4×D181—21no—
66C2×C4×D181C2311yescharacteristic
67#15668438C2×C414yescomplemented
68#15668437C2×C414yescomplemented
69#15668436C2×C414yescomplemented
70C2×#13089678C2×C411yescharacteristic, complemented
71C8×D181C2×C412yescomplemented
72C8×D181C2312yes—
73C2×Q8×C181C2×C411yescharacteristic, complemented
74C2×D4×C181C2×C411yescharacteristic
75SD16×C181C2×C414yescomplemented
76C2×C8×C181C2×C411yescharacteristic, complemented
77C2×#10624382—22no—
78C2×#10624382—22no—
79C2×#10624382—22no—
80C2×#10624382—42no—
81C2×#10624382—42no—
82C2×#10624382—48no—
83C2×#10624382SD1614yesdirect product factor
84C2×#10624382C2×D412yes—
85C2×#10624382C2×D412yes—
86#13089685—22no—
87C22×D181—21no—
88C22×D181—22no—
89C22×D181—22no—
90C22×D181—42no—
91C22×D181—42no—
92C22×D181C2×D411yescharacteristic
93Dic362—21no—
94Dic362—22no—
95Dic362—22no—
96Dic362C22×C412yescomplemented
97D724—21no—
98D724C22×C412yes—
99C22⋊D181—22no—
100C22⋊D181—22no—
101C2×Dic181—21no—
102C2×Dic181#4111yescharacteristic
103C4×D181—22no—
104C4×D181—22no—
105C4×D181C22×C411yescharacteristic
106C4×D181C2×D411yescharacteristic
107C4×D181#4111yescharacteristic
108C4×D181C2411yescharacteristic
109#13089678C22×C412yescomplemented
110C23×C181—21no—
111Q8×C181—21no—
112Q8×C181C22×C412yescomplemented
113D4×C181—21no—
114D4×C181C22×C412yes—
115C2×C4×C181—21no—
116C2×C4×C181C22×C411yescharacteristic
117C8×C181C22×C412yescomplemented
118C22×C181—22no—
119C22×C181—42no—
120C22×C181C4×D411yescharacteristic
121C2×D181—22no—
122C2×D181—42no—
123C2×D181—42no—
124C2×D181—42no—
125C2×D181—44no—
126C2×D181C4×D411yescharacteristic
127C2×D181C2×SD1612yes—
128C2×D181#13512yes—
129C2×D181C22×D411yescharacteristic
130#10624382—22no—
131#10624382—42no—
132#10624382—42no—
133#10624382C2×SD1614yesdirect product factor
134C4×C181—22no—
135C4×C181C4×D411yescharacteristic
136C4×C181C23×C411yescharacteristic
137Dic181—22no—
138Dic181C4×D411yescharacteristic
139Dic181C2×#4111yescharacteristic
140C2×C181—42no—
141C2×C181C4×SD1612yescomplemented
142C2×C181C2×C4×D411yescharacteristic
143D181—42no—
144D181C4×SD1612yescomplemented
145D181C22×SD1611yescharacteristic
146D181C2×#13511yescharacteristic
147C181C2×C4×SD1611yescharacteristic, complemented, Sylow
148C2×C4×SD16—1811nomaximal, Sylow
149C22×SD16—1811no—
150C2×C4×Q8—1811no—
151C2×C4×D4—1811no—
152C4×SD16—1818no—
153C2×#106—1811no—
154C2×#103—1811no—
155C2×#102—1811no—
156C2×C4×C8—1811no—
157C22×Q8—1811no—
158C22×D4—1811no—
159C23×C4—3621no—
160C2×SD16—1811no—
161C2×SD16—1811no—
162C2×SD16—1814no—
163C2×SD16—1814no—
164C2×SD16—1811no—
165C2×SD16#1062438211yescharacteristic, direct product factor
166C22×C8—1811no—
167C22×C8—1811no—
168C4×Q8—3622no—
169C4×Q8—1814no—
170C4×D4—3622no—
171C4×D4—1814no—
172C2×C4⋊C4—3621no—
173C2×C4⋊C4—1811no—
174C2×C4⋊C4—1811no—
175C2×C22⋊C4—3621no—
176C2×C42—3621no—
177C2×C42—1811no—
178#106—1814no—
179#103—1814no—
180#102—1814no—
181C4×C8—1814no—
182C24—3621no—
183C2×Q8—3621no—
184C2×Q8—3621no—
185C2×Q8—3621no—
186C2×Q8—1812no—
187C2×Q8—1812no—
188C2×Q8—1811no—
189C2×Q8C2×#1062438211yescharacteristic, complemented
190C2×D4—3621no—
191C2×D4—3621no—
192C2×D4—3621no—
193C2×D4—1812no—
194C2×D4—1812no—
195C2×D4—1811no—
196C2×D4C2×#1062438211yescharacteristic
197C22×C4—3621no—
198C22×C4—3621no—
199C22×C4—3621no—
200C22×C4—3624no—
201C22×C4—1811no—
202C22×C4—1811no—
203C22×C4—1811no—
204C22×C4—7244no—
205SD16—1814no—
206SD16—1814no—
207SD16—1814no—
208SD16C2×#1062438214yesdirect product factor
209C2×C8—3621no—
210C2×C8—3621no—
211C2×C8—1812no—
212C2×C8—1811no—
213C2×C8—1812no—
214C2×C8—1812no—
215C2×C8C2×#1062438211yescharacteristic, complemented
216C4⋊C4—3624no—
217C4⋊C4—3621no—
218C4⋊C4—3621no—
219C4⋊C4—1812no—
220C4⋊C4—1812no—
221C22⋊C4—3624no—
222C42—3624no—
223C42—1812no—
224C42—1812no—
225C23—21no—
226C23—3622no—
227C23—3622no—
228C23—3621no—
229C23—1811no—
230C23—7242no—
231C23—7242no—
232Q8—21no—
233Q8—3622no—
234Q8—3622no—
235Q8—3621no—
236Q8—1812no—
237Q8C22×#1062438212yescomplemented
238D4—21no—
239D4—3622no—
240D4—3622no—
241D4—3621no—
242D4—1812no—
243D4C22×#1062438212yes—
244C2×C4—21no—
245C2×C4—3622no—
246C2×C4—3622no—
247C2×C4—3622no—
248C2×C4—3621no—
249C2×C4—3622no—
250C2×C4—3622no—
251C2×C4—1812no—
252C2×C4—1812no—
253C2×C4—1814no—
254C2×C4—1811no—
255C2×C4—1811no—
256C2×C4—1811no—
257C2×C4—1811no—
258C2×C4—1811no—
259C2×C4—7248no—
260C2×C4—7242no—
261C2×C4—7242no—
262C2×C4C22×#1062438211yescharacteristic
263C8—3622no—
264C8—1812no—
265C8C22×#1062438212yescomplemented
266C22—22no—
267C22—42no—
268C22—3622no—
269C22—1812no—
270C22—1812no—
271C22—1811no—
272C22—1811no—
273C22—7242no—
274C22—7242no—
275C22—7244no—
276C22—7242no—
277C22D4×#1062438211yescharacteristic
278C4—22no—
279C4—3622no—
280C4—3622no—
281C4—1814no—
282C4—1811no—
283C4—1811no—
284C4—7242no—
285C4—7242no—
286C4D4×#1062438211yescharacteristic
287C4C23×#1062438211yescharacteristic
288C2—42no—
289C2—1811no—
290C2—1811no—
291C2—1812no—
292C2—7242no—
293C2SD16×#1062438212yesdirect product factor
294C2C2×D4×#1062438211yescharacteristic
subgroupG/H
centerC22D4×#10624382
commutatorC4×C181C23×C4
FrattiniC4C23×#10624382
FittingC2×SD16×C181C4
socleC22×C181C4×D4
prime radicalC2×D4×D181C22
cosocleC4×D181C24
hypercenterC2×SD16#10624382
hypocenterC181C2×C4×SD16
LCSG ▷ C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×Q8×#10624382C2semidirect
3. SD16×#10624382C2direct (N × H)
4. C2×#19153884C2semidirect
5. C2×#19153879C2semidirect
7. C2×C8×#10624382C2semidirect
12. Q8×#10624382C22semidirect
21. #19153884C22semidirect
22. #19153879C22semidirect
24. C8×#10624382C22semidirect
27. C2×#15668438C4semidirect
28. C2×#15668437C4semidirect
29. C2×#15668436C4semidirect
30. SD16×D181C4semidirect
33. C2×SD16×C181C4semidirect
54. C2×Dic362C2×C4semidirect
57. Q8×D181C2×C4semidirect
67. #15668438C2×C4semidirect
68. #15668437C2×C4semidirect
69. #15668436C2×C4semidirect
70. C2×#13089678C2×C4semidirect
71. C8×D181C2×C4semidirect
73. C2×Q8×C181C2×C4semidirect
75. SD16×C181C2×C4semidirect
76. C2×C8×C181C2×C4semidirect
83. C2×#10624382SD16direct (N × H)
96. Dic362C22×C4semidirect
109. #13089678C22×C4semidirect
112. Q8×C181C22×C4semidirect
117. C8×C181C22×C4semidirect
133. #10624382C2×SD16direct (N × H)
141. C2×C181C4×SD16semidirect
144. D181C4×SD16semidirect
147. C181C2×C4×SD16semidirect
165. C2×SD16#10624382direct (N × H)
189. C2×Q8C2×#10624382semidirect
208. SD16C2×#10624382direct (N × H)
215. C2×C8C2×#10624382semidirect
237. Q8C22×#10624382semidirect
265. C8C22×#10624382semidirect
293. C2SD16×#10624382direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×#106243822
C2×D4×#106243822
SD16×#106243822
C2×#191538842
C2×#191538792
C2×#191538782
C2×C8×#106243822
C2×SD16×D1812
C2×C4×SD16181