Finite Group Databasebeta

← #13122918

Subgroups — #13122918

Order 1664.

472 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C13×#392C211yesmaximal, characteristic
2#11718883C212yesmaximal, complemented
3#11718883C212yesmaximal, complemented
4#11718881C212yesmaximal, complemented
5#11718613C212yesmaximal, complemented
6#11718608C212yesmaximal, complemented
7#11718608C211yesmaximal, characteristic, complemented
8#11718607C211yesmaximal, characteristic, complemented
9#11718319C212yesmaximal, complemented
10C22×D4×C13C2212yes—
11C22×D4×C13C2211yescharacteristic
12C23×Dic13C2211yescharacteristic
13C22×Dic26C2211yescharacteristic
14C2×C13×C22⋊C4C2211yescharacteristic
15C2×C13×C22⋊C4C2212yes—
16C2×C22⋊Dic13C2211yescharacteristic
17C2×C22⋊Dic13C2212yes—
18C2×C22⋊Dic13C2212yes—
19C2×C22⋊Dic13C2212yes—
20C2×C22⋊Dic13C2212yes—
21C2×C22⋊Dic13C2212yes—
22C2×#6101C2212yes—
23C2×#6101C2212yes—
24C13×#95C2211yescharacteristic
25#88071C2212yes—
26#88071C2212yes—
27#88071C2212yes—
28#88071C2212yes—
29#88071C2212yes—
30#88071C2211yescharacteristic
31C24×C13C2312yes—
32C24×C13C2311yescharacteristic
33C2×D4×C13—24no—
34C2×D4×C13—42no—
35C2×D4×C13—42no—
36C2×D4×C13—42no—
37C2×D4×C13—41no—
38C22×C4×C13C2312yes—
39C22×C4×C13C2311yescharacteristic
40C22×C4×C13C2311yescharacteristic
41C22×Dic13—42no—
42C22×Dic13—41no—
43C22×Dic13C2312yes—
44C22×Dic13C2312yes—
45C22×Dic13C2312yes—
46C22×Dic13C2312yes—
47C2×Dic26—42no—
48C2×Dic26—41no—
49C13×C22⋊C4—41no—
50C13×C22⋊C4—42no—
51C22⋊Dic13—22no—
52C22⋊Dic13—42no—
53C22⋊Dic13—42no—
54C22⋊Dic13—42no—
55C22⋊Dic13—42no—
56C22⋊Dic13—42no—
57#6101—42no—
58#6101—42no—
59#2824—131nomaximal, Sylow
60C23×C13—22no—
61C23×C13—21no—
62C23×C13—22no—
63C23×C13—21no—
64C23×C13—22no—
65C23×C13—22no—
66C23×C13—22no—
67C23×C13—22no—
68C23×C13—22no—
69C23×C13—22no—
70C23×C13—22no—
71C23×C13#4112yes—
72C23×C13C2411yescharacteristic
73D4×C13—48no—
74D4×C13—44no—
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—21no—
80C2×C4×C13—22no—
81C2×C4×C13—21no—
82C2×Dic13—22no—
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×Dic13—44no—
95Dic26—44no—
96#400—132no—
97#397—132no—
98#394—132no—
99#394—132no—
100#393—132no—
101#393—131no—
102#392D1311yescharacteristic
103#386—132no—
104#385—131no—
105C22×C13—24no—
106C22×C13—22no—
107C22×C13—41no—
108C22×C13—41no—
109C22×C13—42no—
110C22×C13—42no—
111C22×C13—42no—
112C22×C13—42no—
113C22×C13—42no—
114C22×C13—42no—
115C22×C13—42no—
116C22×C13—42no—
117C22×C13C2×#4111yescharacteristic
118C22×C13H(5,𝔽2)12yes—
119C22×C13H(5,𝔽2)12yes—
120C22×C13H(5,𝔽2)11yescharacteristic
121C22×C132−1+411yescharacteristic
122C4×C13—42no—
123C4×C13—41no—
124C4×C13—41no—
125Dic13—42no—
126Dic13—42no—
127Dic13—42no—
128Dic13—42no—
129C22×Q8—131no—
130C22×D4C2×D1312yes—
131C22×D4C2×D1311yescharacteristic
132C23×C4—131no—
133C2×C4⋊C4—132no—
134C2×C4⋊C4—132no—
135C2×C22⋊C4—131no—
136C2×C22⋊C4—132no—
137C2×C22⋊C4—132no—
138C2×C22⋊C4—132no—
139C2×C22⋊C4—132no—
140C2×C22⋊C4—132no—
141C2×C22⋊C4C2×D1311yescharacteristic
142C2×C22⋊C4C2×D1312yes—
143#95—132no—
144#95—132no—
145#95—132no—
146#95—132no—
147#95—132no—
148#95—131no—
149#95C2×D1311yescharacteristic
150C2×C13—42no—
151C2×C13—82no—
152C2×C13#53812yes—
153C2×C13#53911yescharacteristic
154C2×C13#56011yescharacteristic
155C2×C13H(3,𝔽4)11yescharacteristic
156C2×C13#56212yes—
157C24C22×D1312yes—
158C24C22×D1311yescharacteristic
159C2×Q8—522no—
160C2×Q8—521no—
161C2×D4—24no—
162C2×D4—42no—
163C2×D4—41no—
164C2×D4—42no—
165C2×D4—42no—
166C22×C4—132no—
167C22×C4—132no—
168C22×C4—132no—
169C22×C4—132no—
170C22×C4—521no—
171C22×C4—522no—
172C22×C4C22×D1312yes—
173C22×C4C22×D1311yescharacteristic
174C22×C4C22×D1311yescharacteristic
175C4⋊C4—522no—
176C4⋊C4—522no—
177C22⋊C4—41no—
178C22⋊C4—42no—
179C22⋊C4—262no—
180C22⋊C4—522no—
181C22⋊C4—522no—
182C22⋊C4—522no—
183C22⋊C4—522no—
184C22⋊C4—522no—
185C13#282411yescharacteristic, complemented, Sylow
186C23—21no—
187C23—22no—
188C23—22no—
189C23—21no—
190C23—22no—
191C23—22no—
192C23—22no—
193C23—22no—
194C23—22no—
195C23—22no—
196C23—22no—
197C23#612912yes—
198C23C23×D1311yescharacteristic
199Q8—524no—
200D4—48no—
201D4—44no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—262no—
210C2×C4—262no—
211C2×C4—262no—
212C2×C4—262no—
213C2×C4—262no—
214C2×C4—262no—
215C2×C4—262no—
216C2×C4—262no—
217C2×C4—262no—
218C2×C4—262no—
219C2×C4—262no—
220C2×C4—262no—
221C2×C4—524no—
222C22—24no—
223C22—22no—
224C22—41no—
225C22—41no—
226C22—42no—
227C22—42no—
228C22—42no—
229C22—42no—
230C22—42no—
231C22—42no—
232C22—42no—
233C22—42no—
234C22C2×#612911yescharacteristic
235C22#8825112yes—
236C22#8825111yescharacteristic
237C22#8825112yes—
238C22#8825711yescharacteristic
239C4—41no—
240C4—42no—
241C4—41no—
242C4—522no—
243C4—522no—
244C4—522no—
245C4—522no—
246C2—42no—
247C2—82no—
248C2#1171929812yes—
249C2#1171929911yescharacteristic
250C2#1171930711yescharacteristic
251C2#1171932612yes—
252C2#1171942511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
Fitting, prime radicalC13×#392C2
hypercenter#392D13
hypocenterC13#2824
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
2. #11718883C2semidirect
3. #11718883C2semidirect
4. #11718881C2semidirect
5. #11718613C2semidirect
6. #11718608C2semidirect
7. #11718608C2semidirect
8. #11718607C2semidirect
9. #11718319C2semidirect
185. C13#2824semidirect

Maximal subgroups

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

subgroupindex
C13×#3922
#117188832
#117188812
#117186132
#117186082
#117186072
#117183192
#282413