Finite Group Databasebeta

← #13115995

Subgroups — #13115995

Order 1664.

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

normal subgroups only

This group has 246 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#11719224C211yesmaximal, characteristic
2C13×#419C211yesmaximal, characteristic
3#11718891C211yesmaximal, characteristic
4#11718886C211yesmaximal, characteristic
5#11718147C211yesmaximal, characteristic
6#11718146C211yesmaximal, characteristic
7#11718124C211yesmaximal, characteristic
8C22×Q8×C13C2211yescharacteristic
9C2×C13×M16C2211yescharacteristic
10C13×#117C2211yescharacteristic
11#88180C2211yescharacteristic
12C2×C4⋊Dic13C2211yescharacteristic
13C2×C4×Dic13C2211yescharacteristic
14C2×#6099C2211yescharacteristic
15#88144—21no—
16#88142—21no—
17#88132—22no—
18#88124—21no—
19#88123—21no—
20C13×#103—21no—
21C13×#103—21no—
22#88075—21no—
23#88075—21no—
24#88071—22no—
25C2×Q8×C13—21no—
26C2×Q8×C13—21no—
27C2×Q8×C13—21no—
28C2×Q8×C13—21no—
29C2×Q8×C13—21no—
30C2×Q8×C13Q812yescomplemented
31C22×C4×C13—21no—
32C22×C4×C13C2311yescharacteristic
33C22×Dic13—21no—
34C22×Dic13D412yes—
35C2×Dic26—22no—
36C13×M16—21no—
37C13×M16—21no—
38C2×C8×C13—21no—
39C13×C4⋊C4D411yescharacteristic
40C13×C4⋊C4D411yescharacteristic
41C13×C22⋊C4—21no—
42C42×C13—21no—
43C22⋊Dic13—21no—
44C4⋊Dic13—22no—
45C4⋊Dic13—21no—
46C4⋊Dic13—21no—
47C4⋊Dic13D411yescharacteristic
48C4⋊Dic13D411yescharacteristic
49#6101—22no—
50#6101—22no—
51C4×Dic13—21no—
52C4×Dic13—21no—
53C4×Dic13—21no—
54#6099—21no—
55#6099—21no—
56C2×#1055—21no—
57#2028—131nomaximal, Sylow
58C23×C13C2×D411yescharacteristic
59Q8×C13—22no—
60Q8×C13—22no—
61Q8×C13—41no—
62Q8×C13—41no—
63C2×C4×C13—21no—
64C2×C4×C13—21no—
65C2×C4×C13—22no—
66C2×C4×C13—41no—
67C2×C4×C13—41no—
68C2×C4×C13C2×D411yescharacteristic
69C2×C4×C13C2×D411yescharacteristic
70C2×C4×C13C2×Q811yescharacteristic
71C2×C4×C13#4111yescharacteristic
72C2×C4×C13#4111yescharacteristic
73C2×C4×C13#4111yescharacteristic
74C2×Dic13—22no—
75C2×Dic13—21no—
76C2×Dic13—21no—
77C2×Dic13—22no—
78C2×Dic13—41no—
79C2×Dic13—41no—
80C2×Dic13—42no—
81Dic26—82no—
82C8×C13—41no—
83#1055—41no—
84#544—131no—
85#419—131no—
86#419D1311yescharacteristic
87#391—131no—
88#343—131no—
89#339—131no—
90#339—131no—
91C22×C13—21no—
92C22×C13—21no—
93C22×C13#12011yescharacteristic
94C22×C13C22⋊Q811yescharacteristic
95C22×C13#12411yescharacteristic
96C4×C13—42no—
97C4×C13—41no—
98C4×C13—41no—
99C4×C13C22⋊Q811yescharacteristic
100C4×C13C22⋊Q811yescharacteristic
101C4×C13#12411yescharacteristic
102C4×C13#12411yescharacteristic
103Dic13—42no—
104Dic13—41no—
105Dic13—42no—
106Dic13—41no—
107C22×Q8C2×D1311yescharacteristic
108C2×M16—131no—
109C2×M16C2×D1311yescharacteristic
110C4⋊Q8—261no—
111C4⋊Q8—261no—
112#125—261no—
113#125—261no—
114C22⋊Q8—262no—
115#117—131no—
116#117C2×D1311yescharacteristic
117C2×C4⋊C4—131no—
118C2×C42—131no—
119#103—21no—
120#103—21no—
121#103—261no—
122#103—261no—
123#95—262no—
124C2×C13—21no—
125C2×C13—21no—
126C2×C13#39311yescharacteristic
127C2×C13#45511yescharacteristic
128C2×C13#45611yescharacteristic
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—262no—
135C2×Q8Dic2612yescomplemented
136C22×C4—21no—
137C22×C4—132no—
138C22×C4—261no—
139C22×C4C22×D1311yescharacteristic
140M16—21no—
141M16—21no—
142M16—261no—
143M16—261no—
144C2×C8—21no—
145C2×C8—261no—
146C4⋊C4—131no—
147C4⋊C4—131no—
148C4⋊C4—262no—
149C4⋊C4—262no—
150C4⋊C4—262no—
151C4⋊C4—261no—
152C4⋊C4—261no—
153C4⋊C4C22⋊D1311yescharacteristic
154C4⋊C4C22⋊D1311yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—261no—
157C42—21no—
158C42—261no—
159C42—261no—
160C42—261no—
161C13#202811yescharacteristic, complemented, Sylow
162C23D4×D1311yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—41no—
166Q8—41no—
167Q8—1042no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—262no—
174C2×C4—261no—
175C2×C4—261no—
176C2×C4—262no—
177C2×C4—521no—
178C2×C4—521no—
179C2×C4—522no—
180C2×C4C2×Dic2611yescharacteristic
181C2×C4#612711yescharacteristic
182C2×C4D4×D1311yescharacteristic
183C2×C4#612911yescharacteristic
184C2×C4#612911yescharacteristic
185C2×C4C2×C22⋊D1311yescharacteristic
186C8—41no—
187C8—521no—
188C22—21no—
189C22—21no—
190C22#8813211yescharacteristic
191C22#8813911yescharacteristic
192C22#8819111yescharacteristic
193C4—41no—
194C4—42no—
195C4—41no—
196C4—522no—
197C4—522no—
198C4—521no—
199C4—521no—
200C4#8813211yescharacteristic
201C4#8813911yescharacteristic
202C4#8817811yescharacteristic
203C4#8819011yescharacteristic
204C2—21no—
205C2—21no—
206C2#1171860811yescharacteristic
207C2#1171886311yescharacteristic
208C2#1171886611yescharacteristic
subgroupG/H
centerC22#88191
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
FittingC13×#419C2
socleC22×C13#120
prime radicalC23×C13C2×D4
hypercenter#419D13
hypocenterC13#2028
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
30. C2×Q8×C13Q8semidirect
135. C2×Q8Dic26semidirect
161. C13#2028semidirect

Maximal subgroups

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

subgroupindex
#117192242
C13×#4192
#117188912
#117188862
#117181472
#117181462
#117181242
#202813