Finite Group Databasebeta

← #13121795

Subgroups — #13121795

Order 1664.

476 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 133 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×#88133C212yesmaximal, complemented
2C13×#390C211yesmaximal, characteristic
3#11718883C212yesmaximal
4#11718633C212yesmaximal, complemented
5#11718612C212yesmaximal, complemented
6#11718610C212yesmaximal, complemented
7#11718609C212yesmaximal, complemented
8#11718589C211yesmaximal, characteristic, complemented
9#11718589C211yesmaximal, characteristic, complemented
10C22×D4×C13C2211yescharacteristic
11C2×C13×C4⋊C4C2211yescharacteristic
12C2×C13×C22⋊C4C2212yes—
13C2×C13×C22⋊C4C2212yes—
14C2×C42×C13C2211yescharacteristic
15C2×C22⋊Dic13C2212yes—
16C2×C22⋊Dic13C2212yes—
17C2×C22⋊Dic13C2212yes—
18C2×C22⋊Dic13C2212yes—
19C2×C4⋊Dic13C2211yescharacteristic
20C2×C4⋊Dic13C2211yescharacteristic
21C2×C4⋊Dic13C2211yescharacteristic
22C2×C4⋊Dic13C2211yescharacteristic
23C2×#6101C2212yes—
24C2×#6101C2212yes—
25C2×#6101C2212yes—
26C2×#6101C2212yes—
27C2×C4×Dic13C2212yes—
28#88133—28no—
29#88071C2212yes—
30#88071C2212yes—
31#88071C2212yes—
32C24×C13C2312yes—
33C2×D4×C13—22no—
34C2×D4×C13—41no—
35C2×D4×C13—41no—
36C22×C4×C13C2312yes—
37C22×C4×C13C2311yescharacteristic
38C22×C4×C13C2311yescharacteristic
39C22×C4×C13C2311yescharacteristic
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C22×Dic13C2312yes—
43C22×Dic13C2312yes—
44C13×C4⋊C4—41no—
45C13×C22⋊C4—24no—
46C13×C22⋊C4—24no—
47C42×C13—41no—
48C22⋊Dic13—24no—
49C22⋊Dic13—24no—
50C22⋊Dic13—42no—
51C22⋊Dic13—42no—
52C4⋊Dic13—22no—
53C4⋊Dic13—41no—
54C4⋊Dic13—41no—
55C4⋊Dic13D414yescomplemented
56#6101—24no—
57#6101—24no—
58#6101—24no—
59#6101—42no—
60C4×Dic13—24no—
61#2727—131nomaximal, Sylow
62C23×C13—22no—
63C23×C13—22no—
64C23×C13—22no—
65C23×C13—22no—
66C23×C13—22no—
67C23×C13—22no—
68C23×C13—22no—
69C23×C13C2411yescharacteristic
70D4×C13—44no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13C2×D412yes—
81C2×C4×C13#4112yes—
82C2×C4×C13#4112yes—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13—22no—
88C2×Dic13—22no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13C2×D414yes—
95C2×#126—132no—
96#399—132no—
97#396—132no—
98#394—132no—
99#390D1311yescharacteristic
100#389—132no—
101#389—131no—
102#389—131no—
103#388—132no—
104C22×C13—42no—
105C22×C13—42no—
106C22×C13—42no—
107C22×C13—42no—
108C22×C13—42no—
109C22×C13—42no—
110C22×C13—42no—
111C22×C13C22×D411yescharacteristic
112C22×C13C2×#4111yescharacteristic
113C22×C13C2×#4111yescharacteristic
114C22×C13H(5,𝔽2)11yescharacteristic
115C22×C13H(5,𝔽2)11yescharacteristic
116C22×C132−1+411yescharacteristic
117C22×C132−1+411yescharacteristic
118C4×C13—22no—
119C4×C13—22no—
120C4×C13—22no—
121C4×C13—42no—
122Dic13—24no—
123Dic13—42no—
124Dic13—42no—
125Dic13—42no—
126C22×D4C2×D1311yescharacteristic
127#126—268no—
128C2×C4⋊C4—131no—
129C2×C4⋊C4—132no—
130C2×C4⋊C4—132no—
131C2×C4⋊C4—132no—
132C2×C4⋊C4—131no—
133C2×C4⋊C4—132no—
134C2×C4⋊C4—131no—
135C2×C4⋊C4—131no—
136C2×C4⋊C4C2×D1311yescharacteristic
137C2×C22⋊C4—132no—
138C2×C22⋊C4—132no—
139C2×C22⋊C4—132no—
140C2×C22⋊C4—132no—
141C2×C22⋊C4C2×D1312yes—
142C2×C22⋊C4C2×D1312yes—
143C2×C42—132no—
144C2×C42C2×D1311yescharacteristic
145#95—132no—
146#95—132no—
147#95—132no—
148C2×C13—82no—
149C2×C13#53711yescharacteristic
150C2×C13#53811yescharacteristic
151C2×C13#53911yescharacteristic
152C2×C13#54711yescharacteristic
153C2×C13#55011yescharacteristic
154C2×C13#55611yescharacteristic
155C2×C13#56311yescharacteristic
156C24C22×D1312yes—
157C2×D4—22no—
158C2×D4—41no—
159C2×D4—41no—
160C22×C4—132no—
161C22×C4—132no—
162C22×C4—132no—
163C22×C4—132no—
164C22×C4C22×D1312yes—
165C22×C4C22×D1311yescharacteristic
166C22×C4C22×D1311yescharacteristic
167C22×C4C22×D1311yescharacteristic
168C4⋊C4—41no—
169C4⋊C4—134no—
170C4⋊C4—264no—
171C4⋊C4—264no—
172C4⋊C4—264no—
173C4⋊C4—262no—
174C4⋊C4—522no—
175C4⋊C4—521no—
176C4⋊C4—521no—
177C22⋊C4—24no—
178C22⋊C4—24no—
179C22⋊C4—264no—
180C22⋊C4—264no—
181C22⋊C4—522no—
182C22⋊C4—522no—
183C42—41no—
184C42—264no—
185C13#272711yescharacteristic, complemented, Sylow
186C23—22no—
187C23—22no—
188C23—22no—
189C23—22no—
190C23—22no—
191C23—22no—
192C23—22no—
193C23C23×D1311yescharacteristic
194D4—44no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—134no—
205C2×C4—262no—
206C2×C4—262no—
207C2×C4—262no—
208C2×C4—262no—
209C2×C4—262no—
210C2×C4—262no—
211C2×C4—262no—
212C2×C4—262no—
213C2×C4—262no—
214C2×C4—262no—
215C2×C4—262no—
216C2×C4#612712yes—
217C2×C4D4×D1312yes—
218C2×C4#612912yes—
219C22—42no—
220C22—42no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22—42no—
225C22—42no—
226C22C2×#612711yescharacteristic
227C22C2×D4×D1311yescharacteristic
228C22C2×#612911yescharacteristic
229C22#8825111yescharacteristic
230C22#8825111yescharacteristic
231C22#8825711yescharacteristic
232C22#8825711yescharacteristic
233C4—22no—
234C4—22no—
235C4—22no—
236C4—42no—
237C4—264no—
238C4—522no—
239C4—522no—
240C4—522no—
241C2—82no—
242C2#1171919911yescharacteristic
243C2#1171924711yescharacteristic
244C2#1171925611yescharacteristic
245C2#1171930211yescharacteristic
246C2#1171930711yescharacteristic
247C2#1171937711yescharacteristic
248C2#1171942311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#390C2
prime radicalC22×D4×C13C22
hypercenter#390D13
hypocenterC13#2727
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#88133C2semidirect
4. #11718633C2semidirect
5. #11718612C2semidirect
6. #11718610C2semidirect
7. #11718609C2semidirect
8. #11718589C2semidirect
9. #11718589C2semidirect
55. C4⋊Dic13D4semidirect
185. C13#2727semidirect

Maximal subgroups

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

subgroupindex
C2×#881332
C13×#3902
#117188832
#117186332
#117186122
#117186102
#117186092
#117185892
#272713