Finite Group Databasebeta

← #13125920

Subgroups — #13125920

Order 1664.

364 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 109 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#11719429C211yesmaximal, characteristic
2#11719402C211yesmaximal, characteristic, complemented
3C13×#491C211yesmaximal, characteristic, complemented
4#11718753C211yesmaximal, characteristic, complemented
5#11718729C211yesmaximal, characteristic, complemented
6#11718471C212yesmaximal
7#11718469C212yesmaximal, complemented
8#11718459C212yesmaximal, complemented
9#11718454C212yesmaximal, complemented
10#11718376C211yesmaximal, characteristic, complemented
11#11718370C211yesmaximal, characteristic, complemented
12C2×#6131C2211yescharacteristic
13C2×Q8×D13C2211yescharacteristic
14C13×C4⋊Q8C2211yescharacteristic
15C13×#125C2211yescharacteristic
16#88201C2211yescharacteristic
17#88198C2211yescharacteristic
18C2×#6107C2212yes—
19C2×#6107C2212yes—
20C2×Dic52C2212yes—
21C2×#6095C2212yes—
22#88152—22no—
23#88151C2212yes—
24#88150—22no—
25#88148—22no—
26#88144—22no—
27#88141C2212yes—
28#88129C2211yescharacteristic
29#88126C2211yescharacteristic
30#88123C2211yescharacteristic
31C13×#103C2212yes—
32C13×#103C2212yes—
33C13×#97C2211yescharacteristic
34#88060C2212yes—
35#88054C2212yes—
36#88050C2212yes—
37#88049C2212yes—
38C4×#1055C2211yescharacteristic
39C2×Q8×C13C2311yescharacteristic
40C2×Q8×C13C2311yescharacteristic
41#6131—42no—
42Q8×D13—42no—
43C2×D52—21no—
44C2×D52C2311yescharacteristic
45C2×C4×D13—21no—
46C2×C4×D13—21no—
47C2×C4×D13C2311yescharacteristic
48C2×Dic26—21no—
49C2×Dic26C2312yes—
50C2×Dic26C2311yescharacteristic
51C2×C8×C13C2312yes—
52C13×C4⋊C4—22no—
53C13×C4⋊C4—22no—
54C13×C4⋊C4C2312yes—
55C42×C13C2311yescharacteristic
56#6107—42no—
57#6107—42no—
58#6103—22no—
59#6103—22no—
60#6103—22no—
61#6103D412yes—
62C4⋊Dic13—22no—
63C4⋊Dic13—22no—
64#6101—22no—
65#6101—22no—
66#6101D412yes—
67C4×Dic13—22no—
68C4×Dic13C2311yescharacteristic
69C2×#1055C2312yes—
70Dic52—42no—
71#6095—42no—
72#3223—131nomaximal, Sylow
73C22×D13—21no—
74C22×D13C2×D411yescharacteristic
75Q8×C13—22no—
76Q8×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—21no—
79C2×C4×C13—21no—
80C2×C4×C13C2×D412yes—
81C2×C4×C13C2411yescharacteristic
82C2×Dic13—22no—
83C2×Dic13—21no—
84C2×Dic13C2×D412yes—
85C2×Dic13C2×D411yescharacteristic
86D52—22no—
87D52—42no—
88C4×D13—22no—
89C4×D13—42no—
90C4×D13—42no—
91Dic26—22no—
92Dic26—22no—
93Dic26—22no—
94Dic26—42no—
95C8×C13—22no—
96#1055—22no—
97#541—131no—
98#536—131no—
99#497—131no—
100#494—131no—
101#491D1311yescharacteristic, complemented
102#488—131no—
103#464—132no—
104#462—132no—
105#452—132no—
106#451—132no—
107#433—131no—
108C22×C13C22×D411yescharacteristic
109C2×D13—21no—
110C2×D13—22no—
111C2×D13—41no—
112C2×D13—42no—
113C4×C13—22no—
114C4×C13—41no—
115C4×C13—41no—
116C4×C13—42no—
117C4×C13H(5,𝔽2)12yes—
118Dic13—21no—
119Dic13—22no—
120Dic13—41no—
121Dic13—42no—
122C2×#41—131no—
123C22×Q8—131no—
124C2×Q16—132no—
125C2×Q16—132no—
126C2×Q16—132no—
127C2×SD16—132no—
128C4⋊Q8—131no—
129C4⋊Q8—131no—
130C4⋊Q8C2×D1311yescharacteristic
131#126—262no—
132#125—262no—
133#125C2×D1311yescharacteristic
134#124—131no—
135#124—131no—
136#123—262no—
137C22⋊Q8—132no—
138C22⋊Q8—262no—
139C4×Q8—132no—
140#117—131no—
141C4⋊C8—132no—
142#103—132no—
143#103C2×D1312yes—
144#103C2×D1312yes—
145#102—132no—
146C22⋊C8—132no—
147#97C2×D1311yescharacteristic
148C4×C8—131no—
149C2×C13#53511yescharacteristic
150C2×C13#57812yes—
151D13—41no—
152D13—81no—
153#41—522no—
154C2×Q8—131no—
155C2×Q8—132no—
156C2×Q8—261no—
157C2×Q8—522no—
158C2×Q8C22×D1311yescharacteristic
159C2×Q8C22×D1311yescharacteristic
160C2×D4—131no—
161C2×D4—261no—
162C22×C4—131no—
163C22×C4—261no—
164C22×C4—261no—
165Q16—522no—
166Q16—522no—
167Q16—522no—
168SD16—522no—
169C2×C8—132no—
170C2×C8C22×D1312yes—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—132no—
174C4⋊C4—262no—
175C4⋊C4—262no—
176C4⋊C4—262no—
177C4⋊C4—262no—
178C4⋊C4C22×D1312yes—
179C22⋊C4—132no—
180C22⋊C4—262no—
181C22⋊C4—262no—
182C22⋊C4—262no—
183C42—131no—
184C42—262no—
185C42C22×D1311yescharacteristic
186C13#322311yescharacteristic, complemented, Sylow
187C23—131no—
188C23—261no—
189Q8—22no—
190Q8—22no—
191Q8—262no—
192Q8—262no—
193Q8—262no—
194Q8—522no—
195D4—262no—
196D4—522no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—132no—
201C2×C4—131no—
202C2×C4—262no—
203C2×C4—262no—
204C2×C4—261no—
205C2×C4—522no—
206C2×C4—522no—
207C2×C4D4×D1312yes—
208C2×C4C23×D1311yescharacteristic
209C8—22no—
210C8—262no—
211C22—262no—
212C22—261no—
213C22—522no—
214C22—521no—
215C22C2×D4×D1311yescharacteristic
216C4—22no—
217C4—42no—
218C4—41no—
219C4—41no—
220C4—262no—
221C4—261no—
222C4—521no—
223C4—522no—
224C4#8825612yes—
225C2—521no—
226C2—1041no—
227C2#1171937911yescharacteristic
228C2#1171948412yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#491C2
socleC22×C13C22×D4
prime radicalC2×#6131C22
hypercenter#491D13
hypocenterC13#3223
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #11719402C2semidirect
3. C13×#491C2semidirect
4. #11718753C2semidirect
5. #11718729C2semidirect
7. #11718469C2semidirect
8. #11718459C2semidirect
9. #11718454C2semidirect
10. #11718376C2semidirect
11. #11718370C2semidirect
101. #491D13semidirect
186. C13#3223semidirect

Maximal subgroups

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

subgroupindex
#117194292
#117194022
C13×#4912
#117187532
#117187292
#117184712
#117184692
#117184592
#117184542
#117183762
#117183702
#322313