Finite Group Databasebeta

← #13126228

Subgroups — #13126228

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×#462C211yesmaximal, characteristic, complemented
4#11718850C212yesmaximal
5#11718843C212yesmaximal, complemented
6#11718751C211yesmaximal, characteristic, complemented
7#11718681C211yesmaximal, characteristic, complemented
8#11718512C211yesmaximal, characteristic, complemented
9#11718498C211yesmaximal, characteristic
10#11718477C212yesmaximal
11#11718452C212yesmaximal, complemented
12C2×C13×Q16C2212yes—
13C13×C4⋊Q8C2211yescharacteristic
14C4×Q8×C13C2211yescharacteristic
15#88200C2212yes—
16#88200C2211yescharacteristic
17Q8×Dic13C2212yes—
18#88198C2211yescharacteristic
19C2×#6107C2212yes—
20C2×#6094C2212yes—
21#88151—21no—
22#88151C2211yescharacteristic
23#88150—21no—
24#88146—21no—
25#88144—21no—
26#88143—21no—
27#88142C2211yescharacteristic
28#88141—21no—
29#88126—21no—
30C42×D13C2211yescharacteristic
31#88123C2211yescharacteristic
32C4×Dic26—21no—
33C4×Dic26C2211yescharacteristic
34C13×C4⋊C8C2211yescharacteristic
35C13×#103C2212yes—
36#88075C2212yes—
37#88075C2212yes—
38#88057C2212yes—
39#88056C2212yes—
40#88054C2212yes—
41#88048C2212yes—
42C4⋊#1055C2211yescharacteristic
43C2×Q8×C13C2311yescharacteristic
44C2×Q8×C13C2312yes—
45C2×C4×D13D411yescharacteristic
46C2×C4×D13D411yescharacteristic
47C2×C4×D13C2311yescharacteristic
48C2×Dic26—21no—
49C2×Dic26—21no—
50C2×Dic26C2311yescharacteristic
51C13×Q16—42no—
52C2×C8×C13C2312yes—
53C13×C4⋊C4—21no—
54C13×C4⋊C4—21no—
55C13×C4⋊C4—21no—
56C13×C4⋊C4C2311yescharacteristic
57C42×C13—21no—
58C42×C13C2311yescharacteristic
59#6107—42no—
60#6103—21no—
61#6103—21no—
62#6103—22no—
63C4⋊Dic13—21no—
64C4⋊Dic13—21no—
65C4⋊Dic13—22no—
66C4⋊Dic13C2311yescharacteristic
67C4⋊Dic13C2312yes—
68#6101—21no—
69#6101—21no—
70#6101—21no—
71#6101—21no—
72#6101—21no—
73#6101—22no—
74C4×Dic13—21no—
75C4×Dic13—22no—
76C4×Dic13D411yescharacteristic
77C4×Dic13D411yescharacteristic
78C4×Dic13C2311yescharacteristic
79C2×#1055C2312yes—
80#6094—42no—
81#3255—131nomaximal, Sylow
82C22×D13C2×D411yescharacteristic
83Q8×C13—22no—
84Q8×C13—21no—
85Q8×C13—21no—
86Q8×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13C2×D411yescharacteristic
91C2×C4×C13C2×D411yescharacteristic
92C2×C4×C13C2411yescharacteristic
93C2×Dic13—21no—
94C2×Dic13—21no—
95C2×Dic13—22no—
96C2×Dic13C2×D411yescharacteristic
97C2×Dic13C2×D411yescharacteristic
98C2×Dic13C2×D411yescharacteristic
99C4×D13—22no—
100C4×D13—21no—
101C4×D13—21no—
102C4×D13—22no—
103Dic26—21no—
104Dic26—21no—
105Dic26—42no—
106Dic26—42no—
107C8×C13—22no—
108#1055—22no—
109#533—131no—
110#533—131no—
111#475—131no—
112#475—131no—
113#475—132no—
114#470—132no—
115#470—132no—
116#462—132no—
117#462—131no—
118#462D1311yescharacteristic, complemented
119#423—131no—
120C22×C13C22×D411yescharacteristic
121C2×D13—21no—
122C2×D13—21no—
123C2×D13—21no—
124C4×C13—21no—
125C4×C13—42no—
126C4×C13—41no—
127C4×C13—41no—
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×Q16C2×D1312yes—
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—132no—
148C22⋊Q8—131no—
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#106—132no—
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—131no—
173C2×Q8—261no—
174C2×Q8—261no—
175C2×Q8C22×D1311yescharacteristic
176C2×Q8C22×D1312yes—
177C22×C4—131no—
178C22×C4—131no—
179C22×C4—131no—
180Q16—42no—
181Q16—522no—
182M16—522no—
183C2×C8—132no—
184C2×C8C22×D1312yes—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—131no—
189C4⋊C4—132no—
190C4⋊C4—261no—
191C4⋊C4—261no—
192C4⋊C4—262no—
193C4⋊C4—261no—
194C4⋊C4—262no—
195C4⋊C4—261no—
196C4⋊C4—261no—
197C4⋊C4—261no—
198C4⋊C4—261no—
199C4⋊C4C22×D1311yescharacteristic
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—22no—
214Q8—21no—
215Q8—22no—
216Q8—261no—
217Q8—261no—
218Q8—522no—
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—262no—
231C2×C4—261no—
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—41no—
244C4—41no—
245C4—42no—
246C4—132no—
247C4—261no—
248C4—261no—
249C4—522no—
250C4—521no—
251C4—521no—
252C4#8817212yes—
253C4#8825111yescharacteristic
254C4#8825711yescharacteristic
255C2—521no—
256C2#1171931311yescharacteristic
257C2C2×#8817211yescharacteristic
258C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#462C2
socleC22×C13C22×D4
prime radicalC22×D13C2×D4
hypercenter#462D13
hypocenterC13#3255
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
3. C13×#462C2semidirect
5. #11718843C2semidirect
6. #11718751C2semidirect
7. #11718681C2semidirect
8. #11718512C2semidirect
11. #11718452C2semidirect
118. #462D13semidirect
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×#4622
#117188502
#117188432
#117187512
#117186812
#117185122
#117184982
#117184772
#117184522
#325513