Finite Group Databasebeta

← #13119787

Subgroups — #13119787

Order 1664.

676 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 185 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×D4×Dic13C211yesmaximal, characteristic
2C2×#88142C211yesmaximal, characteristic, complemented
3C2×#88132C214yesmaximal, complemented
4C13×#390C211yesmaximal, characteristic
5#11718882C211yesmaximal, characteristic
6#11718637C211yesmaximal, characteristic, complemented
7#11718610C214yesmaximal, complemented
8#11718596C211yesmaximal, characteristic, complemented
9C4×#6101C211yesmaximal, characteristic, complemented
10C22×D4×C13C2211yescharacteristic
11C23×Dic13C2212yes—
12C22×Dic26C2212yes—
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C22⋊C4C2214yes—
15C2×C42×C13C2211yescharacteristic
16C2×C22⋊Dic13C2214yes—
17C2×C22⋊Dic13C2212yes—
18D4×Dic13—24no—
19C2×C4⋊Dic13C2214yes—
20C2×C4⋊Dic13C2211yescharacteristic
21C2×C4⋊Dic13C2211yescharacteristic
22C2×#6101C2214yes—
23C2×#6101C2212yes—
24C2×#6101C2212yes—
25C2×C4×Dic13C2211yescharacteristic
26C2×C4×Dic13C2211yescharacteristic
27#88142—24no—
28#88132—216no—
29#88071C2212yes—
30C24×C13C2312yes—
31C2×D4×C13—22no—
32C2×D4×C13—22no—
33C2×D4×C13Q814yescomplemented
34C22×C4×C13C2312yes—
35C22×C4×C13C2312yes—
36C22×C4×C13C2311yescharacteristic
37C22×Dic13—28no—
38C22×Dic13—24no—
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C22×Dic13C2311yescharacteristic
42C22×Dic13C2312yes—
43C22×Dic13C2311yescharacteristic
44C2×Dic26—28no—
45C2×Dic26—24no—
46C13×C4⋊C4—22no—
47C13×C22⋊C4—28no—
48C42×C13—22no—
49C22⋊Dic13—28no—
50C22⋊Dic13—24no—
51C4⋊Dic13—28no—
52C4⋊Dic13—22no—
53C4⋊Dic13—22no—
54#6101—28no—
55#6101—24no—
56#6101D418yescomplemented
57C4×Dic13—22no—
58C4×Dic13D414yes—
59#2542—131nomaximal, Sylow
60C23×C13—24no—
61C23×C13—22no—
62C23×C13—22no—
63C23×C13—24no—
64C23×C13C2×Q814yes—
65C23×C13C2411yescharacteristic
66D4×C13—28no—
67C2×C4×C13—22no—
68C2×C4×C13—22no—
69C2×C4×C13—24no—
70C2×C4×C13—22no—
71C2×C4×C13C2×D414yes—
72C2×C4×C13C2×D412yes—
73C2×C4×C13C2×Q812yes—
74C2×C4×C13#4112yes—
75C2×Dic13—22no—
76C2×Dic13—22no—
77C2×Dic13—22no—
78C2×Dic13—22no—
79C2×Dic13—24no—
80C2×Dic13—24no—
81C2×Dic13—22no—
82C2×Dic13—48no—
83C2×Dic13C2×D412yes—
84C2×Dic13C2×D414yes—
85C2×Dic13C2×D412yes—
86C2×Dic13C2×D414yes—
87Dic26—48no—
88C2×C4⋊Q8—131no—
89C2×C22⋊Q8—134no—
90C2×C4×D4—131no—
91#399—134no—
92#390—131no—
93#390D1311yescharacteristic
94#384—131no—
95#384—131no—
96C4×C4⋊C4—131no—
97C22×C13—24no—
98C22×C13—28no—
99C22×C13—42no—
100C22×C13—42no—
101C22×C13—44no—
102C22×C13C22×D411yescharacteristic
103C22×C13C22×D412yes—
104C22×C13C22×Q811yescharacteristic
105C22×C13C2×#4111yescharacteristic
106C22×C132−1+412yes—
107C4×C13—24no—
108C4×C13—42no—
109C4×C13C22⋊Q814yescomplemented
110Dic13—22no—
111Dic13—24no—
112Dic13—42no—
113Dic13—42no—
114Dic13#12714yes—
115C22×Q8—132no—
116C22×D4C2×D1311yescharacteristic
117C23×C4—132no—
118C4⋊Q8—264no—
119C22⋊Q8—2616no—
120C4×D4—264no—
121C2×C4⋊C4—132no—
122C2×C4⋊C4—131no—
123C2×C4⋊C4—134no—
124C2×C4⋊C4—134no—
125C2×C4⋊C4—132no—
126C2×C4⋊C4—131no—
127C2×C4⋊C4C2×D1311yescharacteristic
128C2×C22⋊C4—132no—
129C2×C22⋊C4—134no—
130C2×C22⋊C4C2×D1314yes—
131C2×C42—131no—
132C2×C42—131no—
133C2×C42C2×D1311yescharacteristic
134#95—132no—
135C2×C13—44no—
136C2×C13C2×C22⋊Q811yescharacteristic
137C2×C13C2×#12711yescharacteristic
138C2×C13#53611yescharacteristic
139C2×C13#54712yes—
140C2×C13D4×Q812yes—
141C24C22×D1312yes—
142C2×Q8—268no—
143C2×Q8—264no—
144C2×D4—22no—
145C2×D4—22no—
146C2×D4Dic2614yescomplemented
147C22×C4—131no—
148C22×C4—131no—
149C22×C4—132no—
150C22×C4—132no—
151C22×C4—132no—
152C22×C4—264no—
153C22×C4—268no—
154C22×C4C22×D1312yes—
155C22×C4C22×D1312yes—
156C22×C4C22×D1311yescharacteristic
157C4⋊C4—22no—
158C4⋊C4—138no—
159C4⋊C4—268no—
160C4⋊C4—264no—
161C4⋊C4—262no—
162C4⋊C4—268no—
163C4⋊C4—262no—
164C22⋊C4—28no—
165C22⋊C4—264no—
166C22⋊C4—268no—
167C42—22no—
168C42—134no—
169C42—262no—
170C13#254211yescharacteristic, complemented, Sylow
171C23—24no—
172C23—22no—
173C23—22no—
174C23—24no—
175C23C2×Dic2614yes—
176C23C23×D1311yescharacteristic
177Q8—528no—
178D4—28no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—22no—
183C2×C4—132no—
184C2×C4—134no—
185C2×C4—132no—
186C2×C4—134no—
187C2×C4—262no—
188C2×C4—262no—
189C2×C4—262no—
190C2×C4—262no—
191C2×C4—264no—
192C2×C4—264no—
193C2×C4—262no—
194C2×C4—528no—
195C2×C4C2×Dic2612yes—
196C2×C4D4×D1314yes—
197C2×C4D4×D1312yes—
198C2×C4#612912yes—
199C22—24no—
200C22—28no—
201C22—44no—
202C22—42no—
203C22—42no—
204C22C22×Dic2611yescharacteristic
205C22C2×D4×D1311yescharacteristic
206C22C2×D4×D1312yes—
207C22C2×#612911yescharacteristic
208C22#8825712yes—
209C4—24no—
210C4—42no—
211C4—134no—
212C4—264no—
213C4—262no—
214C4—522no—
215C4—522no—
216C4#8813214yescomplemented
217C2—44no—
218C2C2×#8813211yescharacteristic
219C2D4×Dic2612yes—
220C2#1171931612yes—
221C2#1171938011yescharacteristic
222C2D13×#12711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#390C2
prime radicalC22×D4×C13C22
hypercenter#390D13
hypocenterC13#2542
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#88142C2semidirect
3. C2×#88132C2semidirect
6. #11718637C2semidirect
7. #11718610C2semidirect
8. #11718596C2semidirect
9. C4×#6101C2semidirect
33. C2×D4×C13Q8semidirect
56. #6101D4semidirect
109. C4×C13C22⋊Q8semidirect
146. C2×D4Dic26semidirect
170. C13#2542semidirect
216. C4#88132semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic132
C2×#881422
C2×#881322
C13×#3902
#117188822
#117186372
#117186102
#117185962
C4×#61012
#254213