Finite Group Databasebeta

← #15759902

Subgroups — #15759902

Order 3328.

360 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 85 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#13126042C211yesmaximal, characteristic
2#13123941C211yesmaximal, characteristic
3#13113547C211yesmaximal, characteristic
4#13113192C211yesmaximal, characteristic
5#13112748C211yesmaximal, characteristic
6#13112697C211yesmaximal, characteristic
7C13×#1534C211yesmaximal, characteristic
8C2×C13×#125C2211yescharacteristic
9#11719175C2211yescharacteristic
10C13×#432C2211yescharacteristic
11C13×#432C2211yescharacteristic
12#11718730—21no—
13#11718726—21no—
14#11718724—22no—
15#11718632C412yes—
16#11718631C412yes—
17#11718587C2211yescharacteristic
18#11718587C2211yescharacteristic
19#11718586C2211yescharacteristic
20#11718489—22no—
21#11718381—22no—
22#11718362—22no—
23C13×#330—22no—
24#11718120—22no—
25#11718074—21no—
26#11718073—21no—
27C13×#125—21no—
28C13×#125—21no—
29C13×#125—21no—
30C13×#125—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C42×C13C2311yescharacteristic
36#88180—21no—
37#88178—21no—
38#88178C2×C412yes—
39#88124—21no—
40#88123D411yescharacteristic
41#88123D411yescharacteristic
42C4×Dic26—21no—
43C4×Dic26D412yes—
44C13×C4⋊C8—21no—
45C13×C4⋊C8—21no—
46C13×C22⋊C8—21no—
47C13×C22⋊C8—21no—
48C13×#97—21no—
49C13×#97D412yes—
50C22⋊#1055—21no—
51C22⋊#1055C2×C412yes—
52C22⋊#1055D412yes—
53#88055—22no—
54#88054—24no—
55C8×Dic13—22no—
56#88050—22no—
57#88050—22no—
58#88048—22no—
59#88047—22no—
60C4⋊#1055—21no—
61C4⋊#1055—21no—
62C4⋊#1055—21no—
63#88043—21no—
64#88043—21no—
65C4×#1055—21no—
66#9336—131nomaximal, Sylow
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13#4111yescharacteristic
72C2×Dic26—21no—
73C2×Dic26C22⋊C412yes—
74C2×C8×C13—22no—
75C2×C8×C13—41no—
76C13×C4⋊C4—21no—
77C13×C4⋊C4—21no—
78C13×C4⋊C4—21no—
79C13×C4⋊C4—21no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C42×C13C2×D411yescharacteristic
85C42×C13C2×D411yescharacteristic
86C42×C13C2×D411yescharacteristic
87C42×C13#4111yescharacteristic
88C22⋊Dic13—22no—
89C4⋊Dic13—21no—
90C4⋊Dic13—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13C22⋊C412yes—
93#6101—22no—
94#6101—22no—
95C4×Dic13—22no—
96C2×#1055—22no—
97C2×#1055—22no—
98C2×#1055—41no—
99#3236—131no—
100#2987—131no—
101#1554—131no—
102#1534D1311yescharacteristic
103#1470—131no—
104#1308—131no—
105#1287—131no—
106C23×C13C4×D411yescharacteristic
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—42no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—81no—
114C2×C4×C13C2×C22⋊C411yescharacteristic
115C2×C4×C13C4×D411yescharacteristic
116C2×C4×C13#12011yescharacteristic
117C2×C4×C13#12111yescharacteristic
118C2×C4×C13#12111yescharacteristic
119C2×C4×C13#12311yescharacteristic
120C2×Dic13—22no—
121C2×Dic13—22no—
122Dic26—42no—
123Dic26—81no—
124C8×C13—42no—
125C8×C13—81no—
126#1055—42no—
127#1055—42no—
128#1055—81no—
129#533—131no—
130C2×#125C2×D1311yescharacteristic
131#501—261no—
132#491—261no—
133#484—132no—
134#483—132no—
135#479—262no—
136#446—262no—
137#446—262no—
138#433—262no—
139#432—131no—
140#432—131no—
141#432C2×D1311yescharacteristic
142#432C2×D1311yescharacteristic
143#431—131no—
144#333—261no—
145#332—261no—
146#330—22no—
147#324—262no—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13#38611yescharacteristic
152C4×C13—21no—
153C4×C13—21no—
154C4×C13—21no—
155C4×C13—21no—
156C4×C13—21no—
157C4×C13—21no—
158C4×C13—81no—
159C4×C13—81no—
160Dic13—42no—
161Dic13—42no—
162C4⋊Q8—131no—
163C4⋊Q8—131no—
164#125—21no—
165#125—21no—
166#125—21no—
167#125—21no—
168#125—261no—
169C22⋊Q8—132no—
170C22⋊Q8—261no—
171C4×Q8—132no—
172C4×Q8—261no—
173#117—261no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4C4×D1311yescharacteristic
177C2×C4⋊C4C4×D1311yescharacteristic
178C2×C42C22×D1311yescharacteristic
179#107—262no—
180#106—262no—
181C4⋊C8—21no—
182C4⋊C8—21no—
183C4⋊C8—264no—
184C4⋊C8—261no—
185C4⋊C8—261no—
186C4⋊C8—261no—
187#103—262no—
188#103—262no—
189C22⋊C8—21no—
190C22⋊C8—21no—
191C22⋊C8—132no—
192C22⋊C8—132no—
193C22⋊C8—261no—
194#97—21no—
195#97—262no—
196#97—261no—
197#97—261no—
198#97C22⋊D1312yes—
199C4×C8—262no—
200C4×C8—261no—
201C2×C13—41no—
202C2×C13#188111yescharacteristic
203C2×C13#190511yescharacteristic
204C2×C13#191511yescharacteristic
205C2×Q8—132no—
206C2×Q8—261no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4C2×C4×D1311yescharacteristic
210C22×C4D4×D1311yescharacteristic
211C22×C4#612911yescharacteristic
212C2×C8—22no—
213C2×C8—41no—
214C2×C8—262no—
215C2×C8—262no—
216C2×C8—521no—
217C4⋊C4—21no—
218C4⋊C4—21no—
219C4⋊C4—21no—
220C4⋊C4—21no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—132no—
226C4⋊C4—262no—
227C4⋊C4—261no—
228C4⋊C4—261no—
229C4⋊C4—262no—
230C4⋊C4—261no—
231C22⋊C4—262no—
232C42—262no—
233C42#612711yescharacteristic
234C42D4×D1311yescharacteristic
235C42D4×D1311yescharacteristic
236C42C2×C22⋊D1311yescharacteristic
237C13#933611yescharacteristic, complemented, Sylow
238C23#8813511yescharacteristic
239Q8—522no—
240Q8—1041no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—81no—
248C2×C4—262no—
249C2×C4—262no—
250C2×C4C22⋊C4×D1311yescharacteristic
251C2×C4#8813711yescharacteristic
252C2×C4#8813811yescharacteristic
253C2×C4C4×C22⋊D1311yescharacteristic
254C2×C4#8819111yescharacteristic
255C2×C4#8819211yescharacteristic
256C8—42no—
257C8—81no—
258C8—522no—
259C8—522no—
260C8—1041no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22#1171861711yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—21no—
271C4—81no—
272C4—81no—
273C4—522no—
274C4—522no—
275C2—41no—
276C2#1311519511yescharacteristic
277C2#1311532711yescharacteristic
278C2#1311538511yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1534C2
socleC22×C13#386
prime radicalC23×C13C4×D4
cosocleC2×C42×C13C23
hypercenter#1534D13
hypocenterC13#9336
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1534

Complements

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

NH ≅ G/Ntype
237. C13#9336semidirect

Maximal subgroups

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

subgroupindex
#131260422
#131239412
#131135472
#131131922
#131127482
#131126972
C13×#15342
#933613