Finite Group Databasebeta

← #13119788

Subgroups — #13119788

Order 1664.

676 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 177 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×#88150C214yesmaximal, complemented
2C2×#88147C211yesmaximal, characteristic
3C2×#88142C211yesmaximal, characteristic, complemented
4C13×#384C211yesmaximal, characteristic, complemented
5#11718653C214yesmaximal, complemented
6#11718649C211yesmaximal, characteristic
7#11718637C211yesmaximal, characteristic, complemented
8#11718600C211yesmaximal, characteristic
9C4×#6101C211yesmaximal, characteristic, complemented
10C22×D52C2211yescharacteristic
11C22×C4×D13C2212yes—
12C22×Dic26C2212yes—
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2214yes—
16C2×C42×C13C2211yescharacteristic
17C2×#6103C2212yes—
18C2×#6103C2214yes—
19C2×#6103C2214yes—
20C2×C4⋊Dic13C2211yescharacteristic
21C2×#6101C2212yes—
22C2×#6101C2214yes—
23C2×#6101C2212yes—
24C2×C4×Dic13C2211yescharacteristic
25C2×C4×Dic13C2211yescharacteristic
26#88150—216no—
27#88147—24no—
28#88142—24no—
29#88071C2212yes—
30C23×D13C2312yes—
31C22×C4×C13C2312yes—
32C22×C4×C13C2312yes—
33C22×C4×C13C2312yes—
34C22×C4×C13C2311yescharacteristic
35C22×Dic13C2312yes—
36C22×Dic13C2311yescharacteristic
37C22×Dic13C2312yes—
38C22×Dic13C2311yescharacteristic
39C2×D52—22no—
40C2×D52—22no—
41C2×D52Q814yescomplemented
42C2×C4×D13—24no—
43C2×C4×D13—28no—
44C2×Dic26—24no—
45C2×Dic26—28no—
46C13×C4⋊C4—22no—
47C13×C4⋊C4—22no—
48C13×C4⋊C4—28no—
49C42×C13—22no—
50#6103—28no—
51#6103—24no—
52#6103—28no—
53C4⋊Dic13—22no—
54#6101—24no—
55#6101—28no—
56#6101D418yescomplemented
57C4×Dic13—22no—
58C4×Dic13D414yes—
59#2542—131nomaximal, Sylow
60C23×C13C2411yescharacteristic
61C22×D13—24no—
62C22×D13—22no—
63C22×D13—22no—
64C22×D13—24no—
65C22×D13C2×Q814yes—
66C2×C4×C13—22no—
67C2×C4×C13—22no—
68C2×C4×C13—22no—
69C2×C4×C13—24no—
70C2×C4×C13—24no—
71C2×C4×C13—22no—
72C2×C4×C13C2×D414yes—
73C2×C4×C13C2×D412yes—
74C2×C4×C13C2×Q812yes—
75C2×C4×C13#4112yes—
76C2×Dic13—22no—
77C2×Dic13—22no—
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13—24no—
81C2×Dic13C2×D412yes—
82C2×Dic13C2×D414yes—
83C2×Dic13C2×D412yes—
84C2×Dic13C2×D414yes—
85D52—28no—
86C4×D13—48no—
87Dic26—48no—
88C2×C4⋊Q8—131no—
89C2×C22⋊Q8—134no—
90C2×C4×D4—131no—
91#399—134no—
92#390—131no—
93#390—131no—
94#384—131no—
95#384D1311yescharacteristic, complemented
96C4×C4⋊C4—131no—
97C22×C13C22×D411yescharacteristic
98C22×C13C22×D412yes—
99C22×C13C22×Q811yescharacteristic
100C22×C13C2×#4111yescharacteristic
101C22×C132−1+412yes—
102C2×D13—24no—
103C2×D13—28no—
104C2×D13—42no—
105C2×D13—42no—
106C2×D13—44no—
107C4×C13—24no—
108C4×C13—42no—
109C4×C13—42no—
110C4×C13C22⋊Q814yescomplemented
111Dic13—22no—
112Dic13—24no—
113Dic13—42no—
114Dic13#12714yes—
115C22×Q8—132no—
116C22×D4—131no—
117C23×C4—132no—
118C4⋊Q8—264no—
119C22⋊Q8—2616no—
120C4×D4—264no—
121C2×C4⋊C4—132no—
122C2×C4⋊C4—134no—
123C2×C4⋊C4—132no—
124C2×C4⋊C4—131no—
125C2×C4⋊C4C2×D1311yescharacteristic
126C2×C4⋊C4C2×D1314yes—
127C2×C4⋊C4C2×D1311yescharacteristic
128C2×C22⋊C4—132no—
129C2×C22⋊C4—134no—
130C2×C22⋊C4—134no—
131C2×C42—131no—
132C2×C42—131no—
133C2×C42C2×D1311yescharacteristic
134#95—132no—
135C2×C13C2×C22⋊Q811yescharacteristic
136C2×C13C2×#12711yescharacteristic
137C2×C13#53611yescharacteristic
138C2×C13#54712yes—
139C2×C13D4×Q812yes—
140D13—44no—
141C24—132no—
142C2×Q8—268no—
143C2×Q8—264no—
144C2×D4—134no—
145C2×D4—262no—
146C2×D4—262no—
147C22×C4—131no—
148C22×C4—131no—
149C22×C4—132no—
150C22×C4—132no—
151C22×C4—264no—
152C22×C4—268no—
153C22×C4C22×D1312yes—
154C22×C4C22×D1312yes—
155C22×C4C22×D1312yes—
156C22×C4C22×D1311yescharacteristic
157C4⋊C4—22no—
158C4⋊C4—28no—
159C4⋊C4—22no—
160C4⋊C4—138no—
161C4⋊C4—268no—
162C4⋊C4—264no—
163C4⋊C4—262no—
164C22⋊C4—264no—
165C22⋊C4—268no—
166C22⋊C4—268no—
167C42—22no—
168C42—134no—
169C42—262no—
170C13#254211yescharacteristic, complemented, Sylow
171C23—134no—
172C23—262no—
173C23—264no—
174C23—262no—
175C23—264no—
176C23C23×D1311yescharacteristic
177Q8—528no—
178D4—268no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—24no—
183C2×C4—24no—
184C2×C4—22no—
185C2×C4—132no—
186C2×C4—134no—
187C2×C4—132no—
188C2×C4—134no—
189C2×C4—262no—
190C2×C4—262no—
191C2×C4—262no—
192C2×C4—264no—
193C2×C4—262no—
194C2×C4—528no—
195C2×C4#612712yes—
196C2×C4D4×D1314yes—
197C2×C4D4×D1312yes—
198C2×C4Q8×D1312yes—
199C22—268no—
200C22—264no—
201C22—522no—
202C22—524no—
203C22—522no—
204C22C2×#612711yescharacteristic
205C22C2×D4×D1311yescharacteristic
206C22C2×D4×D1312yes—
207C22C2×Q8×D1311yescharacteristic
208C22#8825412yes—
209C4—24no—
210C4—42no—
211C4—42no—
212C4—134no—
213C4—262no—
214C4—264no—
215C4—522no—
216C4#8815014yescomplemented
217C2—524no—
218C2#1171921212yes—
219C2C2×#8815011yescharacteristic
220C2D13×#12711yescharacteristic
221C2#1171942911yescharacteristic
222C2#1171943212yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#384C2
prime radicalC22×D52C22
hypercenter#384D13
hypocenterC13#2542
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
1. C2×#88150C2semidirect
3. C2×#88142C2semidirect
4. C13×#384C2semidirect
5. #11718653C2semidirect
7. #11718637C2semidirect
9. C4×#6101C2semidirect
41. C2×D52Q8semidirect
56. #6101D4semidirect
95. #384D13semidirect
110. C4×C13C22⋊Q8semidirect
170. C13#2542semidirect
216. C4#88150semidirect

Maximal subgroups

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

subgroupindex
C2×#881502
C2×#881472
C2×#881422
C13×#3842
#117186532
#117186492
#117186372
#117186002
C4×#61012
#254213