Finite Group Databasebeta

← #13113466

Subgroups — #13113466

Order 1664.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#11719396C211yesmaximal, characteristic
2#11718366C211yesmaximal, characteristic, complemented
3#11718366C211yesmaximal, characteristic, complemented
4C13×#330C211yesmaximal, characteristic, complemented
5#11718135C211yesmaximal, characteristic, complemented
6#11718056C211yesmaximal, characteristic, complemented
7#11718056C211yesmaximal, characteristic, complemented
8C13×#125C2211yescharacteristic
9#88152—21no—
10#88151C411yescharacteristic
11#88149C411yescharacteristic
12#88148—21no—
13#88147—21no—
14#88147C411yescharacteristic
15#88146—21no—
16#88141C411yescharacteristic
17#88129C2211yescharacteristic
18C42×D13C2211yescharacteristic
19C13×#97C2211yescharacteristic
20C13×#97C2211yescharacteristic
21#88060—21no—
22#88060—21no—
23#88054—21no—
24#88054—21no—
25#88043C2211yescharacteristic
26#88043C2211yescharacteristic
27C2×D52—21no—
28C2×D52C2×C411yescharacteristic
29C2×C4×D13—21no—
30C2×C4×D13C2×C411yescharacteristic
31C2×C4×D13D411yescharacteristic
32C2×C4×D13D411yescharacteristic
33C2×Dic26C2×C411yescharacteristic
34C2×C8×C13—21no—
35C2×C8×C13—21no—
36C13×C4⋊C4—21no—
37C13×C4⋊C4—21no—
38C13×C4⋊C4C2×C411yescharacteristic
39C13×C4⋊C4C2×C411yescharacteristic
40C42×C13C2311yescharacteristic
41#6103—21no—
42#6103—21no—
43#6103—21no—
44#6103—21no—
45#6103—21no—
46C4⋊Dic13—21no—
47#6101—21no—
48C4×Dic13—21no—
49C4×Dic13C2×C411yescharacteristic
50C4×Dic13D411yescharacteristic
51C4×Dic13D411yescharacteristic
52C2×#1055—21no—
53C2×#1055—21no—
54#1535—131nomaximal, Sylow
55C22×D13—21no—
56C22×D13C22⋊C411yescharacteristic
57C2×C4×C13—21no—
58C2×C4×C13—21no—
59C2×C4×C13C22×C411yescharacteristic
60C2×C4×C13C2×D411yescharacteristic
61C2×C4×C13C2×D411yescharacteristic
62C2×Dic13—21no—
63C2×Dic13C22⋊C411yescharacteristic
64C2×Dic13C22⋊C411yescharacteristic
65C2×Dic13C22⋊C411yescharacteristic
66D52—41no—
67D52—42no—
68C4×D13—41no—
69C4×D13—41no—
70C4×D13—41no—
71C4×D13—42no—
72Dic26—41no—
73C8×C13—41no—
74C8×C13—41no—
75#1055—41no—
76#1055—41no—
77#529—131no—
78#432—131no—
79#432—131no—
80#330—131no—
81#330D1311yescharacteristic, complemented
82#329—131no—
83#329—131no—
84C22×C13C2×C22⋊C411yescharacteristic
85C2×D13—21no—
86C2×D13—21no—
87C2×D13—21no—
88C2×D13—41no—
89C2×D13—41no—
90C2×D13—41no—
91C4×C13—21no—
92C4×C13—21no—
93C4×C13—21no—
94C4×C13—41no—
95C4×C13—41no—
96Dic13—21no—
97Dic13—21no—
98Dic13—21no—
99Dic13—41no—
100#126—261no—
101#125C2×D1311yescharacteristic
102#124—131no—
103#123—261no—
104C22⋊Q8—131no—
105#121—131no—
106C4×Q8—131no—
107C4×D4—131no—
108C4×D4—261no—
109#117—261no—
110C2×C42—131no—
111C4⋊C8—261no—
112C4⋊C8—261no—
113C22⋊C8—261no—
114C22⋊C8—261no—
115#97—131no—
116#97—131no—
117#97C2×D1311yescharacteristic
118#97C2×D1311yescharacteristic
119C2×C13#41311yescharacteristic
120C2×C13#42111yescharacteristic
121C2×C13#42111yescharacteristic
122D13—41no—
123D13—81no—
124C2×Q8—131no—
125C2×D4—131no—
126C2×D4—261no—
127C22×C4—131no—
128C22×C4—131no—
129C22×C4—131no—
130C22×C4—261no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—261no—
134C2×C8—261no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—261no—
138C4⋊C4—261no—
139C4⋊C4C4×D1311yescharacteristic
140C4⋊C4C4×D1311yescharacteristic
141C22⋊C4—261no—
142C22⋊C4—261no—
143C22⋊C4—261no—
144C22⋊C4—261no—
145C22⋊C4—261no—
146C42—131no—
147C42—131no—
148C42—131no—
149C42—261no—
150C42C22×D1311yescharacteristic
151C13#153511yescharacteristic, complemented, Sylow
152C23—131no—
153C23—261no—
154Q8—521no—
155D4—521no—
156D4—522no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—131no—
160C2×C4—131no—
161C2×C4—131no—
162C2×C4—261no—
163C2×C4—521no—
164C2×C4—521no—
165C2×C4—521no—
166C2×C4—522no—
167C2×C4C2×C4×D1311yescharacteristic
168C2×C4D4×D1311yescharacteristic
169C2×C4D4×D1311yescharacteristic
170C8—41no—
171C8—41no—
172C8—521no—
173C8—521no—
174C22—261no—
175C22—261no—
176C22—261no—
177C22—521no—
178C22—521no—
179C22—521no—
180C22C22⋊C4×D1311yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—41no—
186C4—261no—
187C4—261no—
188C4—261no—
189C4—521no—
190C2—521no—
191C2—1041no—
192C2#1171841211yescharacteristic
193C2#1171848211yescharacteristic
194C2#1171848211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D13
commutatorC2×C4×C13C22×C4
FrattiniC42C22×D13
FittingC13×#330C2
socleC22×C13C2×C22⋊C4
prime radical#88149C4
cosocleC42×C13C23
hypercenter#330D13
hypocenterC13#1535
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #11718366C2semidirect
3. #11718366C2semidirect
4. C13×#330C2semidirect
5. #11718135C2semidirect
6. #11718056C2semidirect
7. #11718056C2semidirect
81. #330D13semidirect
151. C13#1535semidirect

Maximal subgroups

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

subgroupindex
#117193962
#117183662
C13×#3302
#117181352
#117180562
#153513