Finite Group Databasebeta

← #13113398

Subgroups — #13113398

Order 1664.

220 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 69 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#11719327C211yesmaximal, characteristic
2#11718379C211yesmaximal, characteristic
3#11718311C211yesmaximal, characteristic
4C13×#328C211yesmaximal, characteristic
5#11718130C211yesmaximal, characteristic
6#11718059C211yesmaximal, characteristic
7#11718044C211yesmaximal, characteristic
8C13×C22⋊Q8C2211yescharacteristic
9Q8×Dic13C411yescharacteristic, complemented
10#88198C411yescharacteristic, complemented
11#88178C2211yescharacteristic
12C2×#6101—21no—
13C2×C4×Dic13C2211yescharacteristic
14#88143—21no—
15#88142C411yescharacteristic, complemented
16#88141—21no—
17#88141C411yescharacteristic, complemented
18#88132—21no—
19#88131—21no—
20C13×C22⋊C8C2211yescharacteristic
21C13×#95C2211yescharacteristic
22#88071—21no—
23#88071C2211yescharacteristic
24C22⋊#1055C2211yescharacteristic
25#88054—21no—
26C8×Dic13—21no—
27C2×Q8×C13C2×C411yescharacteristic
28C22×C4×C13—21no—
29C22×C4×C13C2311yescharacteristic
30C22×Dic13—21no—
31C22×Dic13D411yescharacteristic
32C22×Dic13D411yescharacteristic
33C2×Dic26—21no—
34C2×Dic26C2×C411yescharacteristic
35C2×C8×C13—21no—
36C13×C4⋊C4—21no—
37C13×C4⋊C4C2×C411yescharacteristic
38C13×C22⋊C4—21no—
39C22⋊Dic13—21no—
40C4⋊Dic13—21no—
41C4⋊Dic13C2×C411yescharacteristic
42#6101—21no—
43#6101—21no—
44#6101—21no—
45#6101—21no—
46#6101—21no—
47#6101—42no—
48C4×Dic13—21no—
49C4×Dic13—21no—
50C4×Dic13C2×C411yescharacteristic
51C4×Dic13C2×C411yescharacteristic
52C4×Dic13D411yescharacteristic
53C4×Dic13D411yescharacteristic
54C2×#1055—21no—
55#1518—131nomaximal, Sylow
56C23×C13C2×D411yescharacteristic
57Q8×C13—41no—
58C2×C4×C13—21no—
59C2×C4×C13—21no—
60C2×C4×C13—41no—
61C2×C4×C13—41no—
62C2×C4×C13—41no—
63C2×C4×C13—41no—
64C2×C4×C13C22×C411yescharacteristic
65C2×C4×C13C2×D411yescharacteristic
66C2×Dic13—21no—
67C2×Dic13—21no—
68C2×Dic13—41no—
69C2×Dic13—41no—
70C2×Dic13—41no—
71C2×Dic13—41no—
72C2×Dic13C22⋊C411yescharacteristic
73C2×Dic13C22⋊C411yescharacteristic
74C2×Dic13C22⋊C411yescharacteristic
75C2×Dic13C22⋊C411yescharacteristic
76C2×Dic13SD1612yes—
77C2×Dic13Q1612yes—
78Dic26—42no—
79Dic26—41no—
80C8×C13—41no—
81#1055—41no—
82#533—131no—
83#431—131no—
84#382—131no—
85#328—131no—
86#328—131no—
87#328—131no—
88#328D1311yescharacteristic
89C22×C13—21no—
90C22×C13—21no—
91C22×C13C2×C22⋊C411yescharacteristic
92C22×C13C2×SD1611yescharacteristic
93C22×C13C2×Q1611yescharacteristic
94C4×C13—21no—
95C4×C13—21no—
96C4×C13—41no—
97C4×C13—41no—
98C4×C13—81no—
99Dic13—21no—
100Dic13—21no—
101Dic13—41no—
102Dic13—41no—
103Dic13—81no—
104Dic13#10312yes—
105Dic13#10312yes—
106C4⋊Q8—131no—
107C4⋊Q8—131no—
108#125—261no—
109C22⋊Q8—131no—
110C22⋊Q8—261no—
111C22⋊Q8C2×D1311yescharacteristic
112C4×Q8—131no—
113C4×Q8—131no—
114C4×Q8—261no—
115#117—261no—
116C2×C4⋊C4—261no—
117C2×C42—131no—
118C4⋊C8—261no—
119C22⋊C8—131no—
120C22⋊C8C2×D1311yescharacteristic
121C4×C8—261no—
122#95—131no—
123#95—261no—
124#95C2×D1311yescharacteristic
125C2×C13—21no—
126C2×C13—21no—
127C2×C13#41011yescharacteristic
128C2×C13C2×#10311yescharacteristic
129C2×C13#42111yescharacteristic
130C2×Q8—131no—
131C2×Q8—261no—
132C2×Q8C4×D1311yescharacteristic
133C22×C4—21no—
134C22×C4—131no—
135C22×C4—131no—
136C22×C4—261no—
137C22×C4C22×D1311yescharacteristic
138C2×C8—21no—
139C2×C8—261no—
140C4⋊C4—21no—
141C4⋊C4—131no—
142C4⋊C4—261no—
143C4⋊C4—261no—
144C4⋊C4—261no—
145C4⋊C4—261no—
146C4⋊C4—261no—
147C4⋊C4—261no—
148C4⋊C4—522no—
149C4⋊C4C4×D1311yescharacteristic
150C22⋊C4—21no—
151C22⋊C4—261no—
152C42—131no—
153C42—131no—
154C42—131no—
155C42—131no—
156C42—261no—
157C42—261no—
158C13#151811yescharacteristic, complemented, Sylow
159C23D4×D1311yescharacteristic
160Q8—41no—
161Q8—521no—
162Q8—522no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—131no—
170C2×C4—131no—
171C2×C4—132no—
172C2×C4—132no—
173C2×C4—131no—
174C2×C4—131no—
175C2×C4—261no—
176C2×C4—261no—
177C2×C4—521no—
178C2×C4—521no—
179C2×C4—521no—
180C2×C4—521no—
181C2×C4C2×C4×D1311yescharacteristic
182C2×C4D4×D1311yescharacteristic
183C8—41no—
184C8—521no—
185C22—21no—
186C22—21no—
187C22C22⋊C4×D1311yescharacteristic
188C22SD16×D1311yescharacteristic
189C22Q16×D1311yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—132no—
196C4—132no—
197C4—261no—
198C4—261no—
199C4—521no—
200C4—521no—
201C4—1041no—
202C2—21no—
203C2—21no—
204C2#1171840111yescharacteristic
205C2D13×#10311yescharacteristic
206C2#1171848211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D13
commutatorC2×C4×C13C22×C4
FrattiniC22×C4C22×D13
FittingC13×#328C2
socleC22×C13C2×C22⋊C4
prime radicalC23×C13C2×D4
cosocleC22×C4×C13C23
hypercenter#328D13
hypocenterC13#1518
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
9. Q8×Dic13C4semidirect
10. #88198C4semidirect
15. #88142C4semidirect
17. #88141C4semidirect
158. C13#1518semidirect

Maximal subgroups

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

subgroupindex
#117193272
#117183792
#117183112
C13×#3282
#117181302
#117180592
#117180442
#151813