Finite Group Databasebeta

← C2×#13117093 #16018313

Subgroups — C2×#13117093 #16018313

Order 3328.

918 conjugacy classes of subgroups; only the 251 normal subgroups are shown.

normal subgroups only

This group has 918 conjugacy classes of subgroups — too many to draw. Only its 251 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×#88068C214yesmaximal, complemented
2C2×#11718356C211yesmaximal, characteristic
3#13117093C218yesmaximal, direct product factor
4C2×C4×#6090C211yesmaximal, characteristic, complemented
5C2×C13×#494C211yesmaximal, characteristic, complemented
6C22×C13×Q16—21no—
7C22×C13×Q16C2212yes—
8C2×C13×C4⋊Q8—21no—
9C22×D104—21no—
10C22×D104C2212yes—
11C2×#88128—21no—
12C13×#494—22no—
13C13×#494C2214yescomplemented
14C2×C4×C8×C13C2211yescharacteristic
15C2×#88068—216no—
16C2×#88068C22116yescomplemented
17C22×#6090C2212yes—
18#11718356—22no—
19#11718356C2214yes—
20C4×#6090C2214yescomplemented
21C22×Q8×C13—22no—
22C22×D52—22no—
23C22×D52—42no—
24C2×C13×Q16—28no—
25C2×C13×Q16—22no—
26C2×C13×Q16—24no—
27C2×C13×Q16—44no—
28C2×C13×Q16C2314yes—
29C22×C8×C13D411yescharacteristic
30C22×C8×C13C2311yescharacteristic
31C13×C4⋊Q8—24no—
32C13×C4⋊Q8—42no—
33C2×C13×C4⋊C4—42no—
34C2×C42×C13D411yescharacteristic
35C2×D104—28no—
36C2×D104—24no—
37C2×D104—22no—
38C2×D104—44no—
39C2×D104C2314yes—
40#88128—24no—
41#88128—42no—
42C4×C8×C13D412yes—
43C4×C8×C13C2312yes—
44#88068—232no—
45C2×#6090D418yescomplemented
46C2×#6090C2314yes—
47C2×#2248—131nomaximal, Sylow
48C23×D13—42no—
49C2×Q8×C13—24no—
50C2×Q8×C13—42no—
51C2×Q8×C13—44no—
52C2×Q8×C13—44no—
53C22×C4×C13—42no—
54C22×C4×C13D812yes—
55C22×C4×C13C2×D411yescharacteristic
56C2×D52—24no—
57C2×D52—44no—
58C2×D52—44no—
59C2×D52—48no—
60C2×D52—42no—
61C2×D52—88no—
62C13×Q16—28no—
63C13×Q16—44no—
64C13×Q16—48no—
65C2×C8×C13D814yes—
66C2×C8×C13C2×D411yescharacteristic
67C2×C8×C13C2×D414yes—
68C2×C8×C13C2×D412yes—
69C2×C8×C13C2411yescharacteristic
70C13×C4⋊C4—48no—
71C42×C13D812yes—
72C42×C13C2×D412yes—
73D104—28no—
74D104—44no—
75D104—48no—
76#6090C2×D418yescomplemented
77C22×SD32—134no—
78C2×#494D1311yescharacteristic, complemented
79C2×#493—131no—
80#2248—138no—
81C2×C4×C16—131no—
82C23×C13C2×D811yescharacteristic
83C22×D13—44no—
84C22×D13—84no—
85C22×D13—88no—
86Q8×C13—44no—
87Q8×C13—44no—
88Q8×C13—84no—
89C2×C4×C13—44no—
90C2×C4×C13—84no—
91C2×C4×C13SD3218yescomplemented
92C2×C4×C13#12712yes—
93C2×C4×C13C2×D812yes—
94C2×C4×C13C2×D811yescharacteristic
95C2×C4×C13C2×D814yes—
96C2×C4×C13C22×D411yescharacteristic
97D52—44no—
98D52—44no—
99D52—84no—
100D52—816no—
101C8×C13#12712yes—
102C8×C13C2×D814yes—
103C8×C13C22×D412yes—
104C22×Q16—21no—
105C22×Q16C2×D1312yes—
106C22×D8—132no—
107C22×D8—261no—
108C2×C4⋊Q8—21no—
109C2×#127—261no—
110C2×SD32—1316no—
111C2×SD32—2616no—
112C22×C16—132no—
113#494—22no—
114#494C2×D1314yescomplemented
115#493—134no—
116#493—262no—
117C2×C4×C8C2×D1311yescharacteristic
118C4×C16—134no—
119C22×C13#49312yes—
120C22×C13C2×SD3214yes—
121C22×C13C22×D811yescharacteristic
122C2×D13—84no—
123C2×D13—88no—
124C2×D13—168no—
125C4×C13—84no—
126C4×C13#49312yes—
127C4×C13C2×SD3218yescomplemented
128C4×C13C2×#12711yescharacteristic
129C4×C13C22×D811yescharacteristic
130C22×Q8—22no—
131C22×D4—262no—
132C22×D4—522no—
133C2×Q16—28no—
134C2×Q16—24no—
135C2×Q16—22no—
136C2×Q16—44no—
137C2×Q16C22×D1314yes—
138C2×D8—134no—
139C2×D8—268no—
140C2×D8—262no—
141C2×D8—264no—
142C2×D8—524no—
143C22×C8C22⋊D1311yescharacteristic
144C22×C8C22×D1311yescharacteristic
145C4⋊Q8—24no—
146C4⋊Q8—42no—
147#127—264no—
148#127—522no—
149C2×C4⋊C4—42no—
150C2×C42C22⋊D1311yescharacteristic
151SD32—2632no—
152C2×C16—138no—
153C2×C16—134no—
154C4×C8C22⋊D1312yes—
155C4×C8C22×D1312yes—
156C2×C13#224814yescomplemented
157C2×C13C2×#49311yescharacteristic
158C2×C13C22×SD3212yes—
159D13—164no—
160C24—522no—
161C2×Q8—24no—
162C2×Q8—42no—
163C2×Q8—44no—
164C2×Q8—44no—
165C2×D4—264no—
166C2×D4—524no—
167C2×D4—528no—
168C2×D4—522no—
169C2×D4—524no—
170C2×D4—1048no—
171C22×C4—42no—
172C22×C4#610412yes—
173C22×C4C2×C22⋊D1311yescharacteristic
174Q16—28no—
175Q16—48no—
176Q16—44no—
177D8—268no—
178D8—528no—
179D8—524no—
180C2×C8#610414yes—
181C2×C8D4×D1314yes—
182C2×C8C2×C22⋊D1312yes—
183C2×C8C2×C22⋊D1311yescharacteristic
184C2×C8C23×D1311yescharacteristic
185C4⋊C4—48no—
186C42#610412yes—
187C42C2×C22⋊D1312yes—
188C16—138no—
189C13C2×#224811yescharacteristic, complemented, Sylow
190C23—524no—
191C23—1044no—
192C23—1048no—
193C23C2×#610411yescharacteristic
194Q8—44no—
195Q8—44no—
196Q8—84no—
197D4—524no—
198D4—524no—
199D4—1044no—
200D4—10416no—
201C2×C4—44no—
202C2×C4—84no—
203C2×C4#8806818yescomplemented
204C2×C4C2×#610412yes—
205C2×C4C2×#610411yescharacteristic
206C2×C4C2×#610414yes—
207C2×C4#8819412yes—
208C2×C4C22×C22⋊D1311yescharacteristic
209C8C2×#610414yes—
210C8#8819412yes—
211C8C2×D4×D1312yes—
212C22—1048no—
213C22—1044no—
214C22—2088no—
215C22#1171873412yes—
216C22C2×#8806814yes—
217C22C22×#610411yescharacteristic
218C4—84no—
219C4#1171873412yes—
220C4C2×#8806818yescomplemented
221C4C22×#610411yescharacteristic
222C4C2×#8819411yescharacteristic
223C2—2084no—
224C2#1311709314yesdirect product factor
225C2C2×#1171873411yescharacteristic
226C2C22×#8806812yes—
subgroupG/H
centerC23C2×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC2×C13×#494C2
socleC23×C13C2×D8
prime radicalC2×#11718356C2
hypercenterC2×#494D13
hypocenterC13C2×#2248
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#494

Complements

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

NH ≅ G/Ntype
1. C22×#88068C2semidirect
3. #13117093C2direct (N × H)
4. C2×C4×#6090C2semidirect
5. C2×C13×#494C2semidirect
13. C13×#494C22semidirect
16. C2×#88068C22semidirect
20. C4×#6090C22semidirect
45. C2×#6090D4semidirect
76. #6090C2×D4semidirect
78. C2×#494D13semidirect
91. C2×C4×C13SD32semidirect
114. #494C2×D13semidirect
127. C4×C13C2×SD32semidirect
156. C2×C13#2248semidirect
189. C13C2×#2248semidirect
203. C2×C4#88068semidirect
220. C4C2×#88068semidirect
224. C2#13117093direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#880682
C2×#117183562
#131170932
C2×C4×#60902
C2×C13×#4942
C2×#224813