Finite Group Databasebeta

← #13126229

Subgroups — #13126229

Order 1664.

342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 115 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
1#11719433C211yesmaximal, characteristic
2#11719283C211yesmaximal, characteristic
3C13×#475C211yesmaximal, characteristic, complemented
4#11718755C211yesmaximal, characteristic, complemented
5#11718692C211yesmaximal, characteristic, complemented
6#11718529C212yesmaximal
7#11718515C212yesmaximal, complemented
8#11718510C211yesmaximal, characteristic, complemented
9#11718498C211yesmaximal, characteristic
10#11718477C212yesmaximal
11#11718454C212yesmaximal, complemented
12C13×C4⋊Q8C2211yescharacteristic
13C4×Q8×C13C2211yescharacteristic
14#88200—21no—
15#88200C2211yescharacteristic
16Q8×Dic13—21no—
17#88198C2211yescharacteristic
18C2×#6107C2212yes—
19C2×Dic52C2212yes—
20C2×#6094C2212yes—
21#88151C2212yes—
22#88151C2211yescharacteristic
23#88150—21no—
24#88146—21no—
25#88144—21no—
26#88143—21no—
27#88142C2211yescharacteristic
28#88141C2212yes—
29#88126—21no—
30C42×D13C2211yescharacteristic
31#88123C2211yescharacteristic
32C4×Dic26—21no—
33C4×Dic26C2211yescharacteristic
34C13×#106C2212yes—
35C13×C4⋊C8C2211yescharacteristic
36C13×#103C2212yes—
37#88056C2212yes—
38#88054C2212yes—
39#88050C2212yes—
40#88050C2212yes—
41#88048C2212yes—
42C4⋊#1055C2211yescharacteristic
43C2×Q8×C13—21no—
44C2×Q8×C13C2311yescharacteristic
45C2×C4×D13D411yescharacteristic
46C2×C4×D13D411yescharacteristic
47C2×C4×D13C2311yescharacteristic
48C2×Dic26—21no—
49C2×Dic26C2311yescharacteristic
50C2×Dic26C2312yes—
51C2×C8×C13C2312yes—
52C13×C4⋊C4—21no—
53C13×C4⋊C4—21no—
54C13×C4⋊C4C2312yes—
55C13×C4⋊C4C2311yescharacteristic
56C42×C13—21no—
57C42×C13C2311yescharacteristic
58#6107—42no—
59#6103—21no—
60#6103—21no—
61#6103—22no—
62C4⋊Dic13—21no—
63C4⋊Dic13—21no—
64C4⋊Dic13—21no—
65C4⋊Dic13—22no—
66C4⋊Dic13C2311yescharacteristic
67#6101—21no—
68#6101—21no—
69#6101—21no—
70#6101—21no—
71#6101—21no—
72#6101—22no—
73C4×Dic13—21no—
74C4×Dic13—22no—
75C4×Dic13D411yescharacteristic
76C4×Dic13D411yescharacteristic
77C4×Dic13C2311yescharacteristic
78C2×#1055C2312yes—
79Dic52—42no—
80#6094—42no—
81#3255—131nomaximal, Sylow
82C22×D13C2×D411yescharacteristic
83Q8×C13—21no—
84Q8×C13—21no—
85Q8×C13—42no—
86C2×C4×C13—22no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13C2×D411yescharacteristic
90C2×C4×C13C2×D411yescharacteristic
91C2×C4×C13C2411yescharacteristic
92C2×Dic13—21no—
93C2×Dic13—21no—
94C2×Dic13—22no—
95C2×Dic13C2×D411yescharacteristic
96C2×Dic13C2×D411yescharacteristic
97C2×Dic13C2×D411yescharacteristic
98C4×D13—22no—
99C4×D13—21no—
100C4×D13—21no—
101C4×D13—22no—
102Dic26—21no—
103Dic26—22no—
104Dic26—21no—
105Dic26—22no—
106Dic26—42no—
107C8×C13—22no—
108#1055—22no—
109#533—131no—
110#533—131no—
111#475—131no—
112#475—132no—
113#475D1311yescharacteristic, complemented
114#470—132no—
115#470—132no—
116#462—131no—
117#462—131no—
118#462—132no—
119#423—131no—
120C22×C13C22×D411yescharacteristic
121C2×D13—21no—
122C2×D13—21no—
123C2×D13—21no—
124C4×C13—21no—
125C4×C13—41no—
126C4×C13—41no—
127C4×C13—42no—
128C4×C13#13712yes—
129C4×C13H(5,𝔽2)11yescharacteristic
130C4×C132−1+411yescharacteristic
131Dic13—21no—
132Dic13—21no—
133Dic13—41no—
134Dic13—42no—
135Dic13—41no—
136Dic13#13712yes—
137C2×Q16—132no—
138C2×Q16—132no—
139C2×M16—132no—
140C4⋊Q8—131no—
141C4⋊Q8—131no—
142C4⋊Q8—131no—
143C4⋊Q8C2×D1311yescharacteristic
144#125—261no—
145#125—261no—
146C22⋊Q8—131no—
147C22⋊Q8—131no—
148C22⋊Q8—132no—
149C22⋊Q8—261no—
150C22⋊Q8—261no—
151C4×Q8—132no—
152C4×Q8—131no—
153C4×Q8—261no—
154C4×Q8—261no—
155C4×Q8C2×D1311yescharacteristic
156#117—261no—
157#117—261no—
158C2×C42—131no—
159#106—132no—
160#106C2×D1312yes—
161C4⋊C8—132no—
162C4⋊C8—131no—
163C4⋊C8C2×D1311yescharacteristic
164#103—132no—
165#103—132no—
166#103—132no—
167#103C2×D1312yes—
168C2×C13#53711yescharacteristic
169C2×C13C2×#13711yescharacteristic
170C2×C13C2×#13711yescharacteristic
171D13—41no—
172C2×Q8—21no—
173C2×Q8—132no—
174C2×Q8—131no—
175C2×Q8—261no—
176C2×Q8C22×D1311yescharacteristic
177C22×C4—131no—
178C22×C4—131no—
179C22×C4—131no—
180Q16—522no—
181Q16—522no—
182M16—522no—
183C2×C8—132no—
184C2×C8C22×D1312yes—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—131no—
188C4⋊C4—261no—
189C4⋊C4—261no—
190C4⋊C4—262no—
191C4⋊C4—261no—
192C4⋊C4—261no—
193C4⋊C4—262no—
194C4⋊C4—261no—
195C4⋊C4—261no—
196C4⋊C4—261no—
197C4⋊C4—261no—
198C4⋊C4C22×D1311yescharacteristic
199C4⋊C4C22×D1312yes—
200C22⋊C4—261no—
201C22⋊C4—261no—
202C22⋊C4—262no—
203C42—21no—
204C42—131no—
205C42—131no—
206C42—131no—
207C42—262no—
208C42—261no—
209C42C22×D1311yescharacteristic
210C13#325511yescharacteristic, complemented, Sylow
211C23—131no—
212Q8—21no—
213Q8—21no—
214Q8—42no—
215Q8—261no—
216Q8—262no—
217Q8—261no—
218Q8—262no—
219Q8—522no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—131no—
224C2×C4—131no—
225C2×C4—131no—
226C2×C4—262no—
227C2×C4—262no—
228C2×C4—261no—
229C2×C4—261no—
230C2×C4—261no—
231C2×C4—262no—
232C2×C4—261no—
233C2×C4D4×D1311yescharacteristic
234C2×C4D4×D1311yescharacteristic
235C2×C4C23×D1311yescharacteristic
236C8—22no—
237C8—262no—
238C22—261no—
239C22—261no—
240C22—261no—
241C22C2×D4×D1311yescharacteristic
242C4—21no—
243C4—42no—
244C4—41no—
245C4—41no—
246C4—132no—
247C4—261no—
248C4—261no—
249C4—521no—
250C4—521no—
251C4—522no—
252C4#8816912yes—
253C4#8825411yescharacteristic
254C4#8825611yescharacteristic
255C2—521no—
256C2#1171933411yescharacteristic
257C2C2×#8816911yescharacteristic
258C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#475C2
socleC22×C13C22×D4
prime radicalC22×D13C2×D4
hypercenter#475D13
hypocenterC13#3255
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. C13×#475C2semidirect
4. #11718755C2semidirect
5. #11718692C2semidirect
7. #11718515C2semidirect
8. #11718510C2semidirect
11. #11718454C2semidirect
113. #475D13semidirect
210. C13#3255semidirect

Maximal subgroups

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

subgroupindex
#117194332
#117192832
C13×#4752
#117187552
#117186922
#117185292
#117185152
#117185102
#117184982
#117184772
#117184542
#325513