Finite Group Databasebeta

← #15772222

Subgroups — #15772222

Order 3328.

368 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 83 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#13123535C211yesmaximal, characteristic
2#13116455C212yesmaximal, complemented
3#13112788C212yesmaximal, complemented
4#13112772C211yesmaximal, characteristic, complemented
5C13×#1320C211yesmaximal, characteristic, complemented
6#11719496C411yescharacteristic
7C22×#6099C411yescharacteristic
8C2×#88161C2211yescharacteristic
9C13×#407C2211yescharacteristic
10#11718790C411yescharacteristic
11#11718783C411yescharacteristic
12#11718780C2211yescharacteristic
13D13×M32—22no—
14#11718390—22no—
15#11718389—22no—
16C13×#349C2212yes—
17#11718145C2212yes—
18#11718106—22no—
19C23×C4×C13C2×C411yescharacteristic
20C2×#6127C2×C411yescharacteristic
21C2×C13×M16C2×C411yescharacteristic
22C2×C13×M16C2311yescharacteristic
23#88207C812yes—
24#88184—21no—
25#88183C812yes—
26C4×C22⋊D13—22no—
27#88180C2×C411yescharacteristic
28#88178—21no—
29C2×#6099—21no—
30C2×#6099—21no—
31C2×#6099—42no—
32C22×#1055C2×C411yescharacteristic
33C22×#1055C2×C411yescharacteristic
34#88161—42no—
35C2×#6094D412yes—
36C2×C8×D13D412yes—
37C13×M32—22no—
38C13×C22⋊C8—22no—
39#88060—22no—
40#88055—21no—
41#88054—22no—
42C8×Dic13—21no—
43#88052—22no—
44#88038—42no—
45C16×D13—42no—
46#11484—131nomaximal, Sylow
47C24×C13C2×C811yescharacteristic
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13—41no—
51C22×C4×C13—41no—
52C22×C4×C13C2×C811yescharacteristic
53C22×C4×C13C22×C411yescharacteristic
54C2×C22⋊D13—22no—
55C2×C22⋊D13C2×C812yes—
56#6127—41no—
57#6127—41no—
58C2×D52M1611yescharacteristic
59C2×C4×D13C22⋊C412yes—
60C2×Dic26M1611yescharacteristic
61C13×M16—41no—
62C13×M16—41no—
63C2×C8×C13—21no—
64C2×C8×C13C2×D412yes—
65C22⋊Dic13—22no—
66C22⋊Dic13C2×C812yes—
67#6103—22no—
68C4⋊Dic13—21no—
69#6101—22no—
70C4×Dic13—21no—
71#6099—42no—
72#6099—42no—
73C2×#1055—22no—
74C2×#1055—21no—
75C2×#1055—41no—
76C2×#1055C22⋊C411yescharacteristic
77C2×#1055C22⋊C411yescharacteristic
78#6094—42no—
79C8×D13—22no—
80C8×D13—22no—
81C13×C16—42no—
82#6090—42no—
83#2930—131no—
84#2115—132no—
85#1328—132no—
86#1320—131no—
87#1320D1311yescharacteristic, complemented
88C23×C13—21no—
89C23×C13—41no—
90C23×C13—81no—
91C23×C13C22×C811yescharacteristic
92C22×D13C22⋊C812yes—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—42no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13—41no—
100C2×C4×C13C2×C22⋊C411yescharacteristic
101C2×C4×C13C2×M1611yescharacteristic
102C22⋊D13—42no—
103C22⋊D13—82no—
104C2×Dic13—22no—
105C2×Dic13C22⋊C812yes—
106D52—41no—
107C4×D13—22no—
108C4×D13—22no—
109Dic26—41no—
110C8×C13—22no—
111C8×C13—41no—
112#1055—21no—
113#1055—41no—
114#1055#9912yes—
115C2×#131—131no—
116C22×M16—131no—
117#525—131no—
118C2×M32—262no—
119#436—262no—
120#435—262no—
121#424—131no—
122#408—131no—
123#407C2×D1311yescharacteristic
124#405—131no—
125#349—132no—
126#349—262no—
127#349C2×D1312yes—
128C22×C13—21no—
129C22×C13—41no—
130C22×C13—41no—
131C22×C13—41no—
132C22×C13—41no—
133C22×C13—82no—
134C22×C13C2×C22⋊C811yescharacteristic
135C2×D13—22no—
136C2×D13—42no—
137C4×C13—21no—
138C4×C13—41no—
139C4×C13C2×#9911yescharacteristic
140C4×C13#41311yescharacteristic
141Dic13—22no—
142Dic13—42no—
143C2×#41—131no—
144C23×C4C4×D1311yescharacteristic
145#131—522no—
146C2×M16—132no—
147C2×M16—261no—
148C2×M16—261no—
149C2×M16—522no—
150C2×M16C4×D1311yescharacteristic
151C2×M16C22×D1311yescharacteristic
152C22×C8—131no—
153C22×C8—132no—
154C22×C8—131no—
155#123—132no—
156C22⋊Q8—261no—
157#121—261no—
158#120—132no—
159C4×D4—262no—
160#117—131no—
161M32—22no—
162M32—262no—
163M32—522no—
164C2×C16—522no—
165C4⋊C8—262no—
166C22⋊C8—22no—
167C22⋊C8—262no—
168#97—261no—
169C4×C8—261no—
170C2×C13—21no—
171C2×C13—41no—
172C2×C13—81no—
173C2×C13#145911yescharacteristic
174D13—42no—
175C24C8×D1311yescharacteristic
176#41—521no—
177#41—521no—
178C2×Q8—131no—
179C2×D4—132no—
180C2×D4—131no—
181C2×D4—262no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4—132no—
187C22×C4C8×D1311yescharacteristic
188C22×C4C2×C4×D1311yescharacteristic
189M16—41no—
190M16—41no—
191M16—522no—
192M16—522no—
193M16—522no—
194C2×C8—21no—
195C2×C8—131no—
196C2×C8—131no—
197C2×C8—262no—
198C2×C8—262no—
199C2×C8—262no—
200C2×C8—261no—
201C2×C8—521no—
202C2×C8D4×D1312yes—
203C4⋊C4—262no—
204C4⋊C4—261no—
205C22⋊C4—132no—
206C22⋊C4—262no—
207C22⋊C4—262no—
208C42—261no—
209C16—42no—
210C16—522no—
211C13#1148411yescharacteristic, complemented, Sylow
212C23—21no—
213C23—41no—
214C23—81no—
215C23—132no—
216C23C2×C8×D1311yescharacteristic
217Q8—521no—
218D4—521no—
219D4—522no—
220D4—1042no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—132no—
229C2×C4—262no—
230C2×C4—262no—
231C2×C4—262no—
232C2×C4C22⋊C4×D1311yescharacteristic
233C2×C4M16×D1311yescharacteristic
234C8—22no—
235C8—41no—
236C8—132no—
237C8—261no—
238C8—521no—
239C22—21no—
240C22—41no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22—82no—
245C22—262no—
246C22—522no—
247C22D13×C22⋊C811yescharacteristic
248C4—21no—
249C4—41no—
250C4—262no—
251C4—522no—
252C4D13×#9911yescharacteristic
253C4#1171840611yescharacteristic
254C2—21no—
255C2—41no—
256C2—81no—
257C2—522no—
258C2#1311315111yescharacteristic
subgroupG/H
centerC4D13×#99
commutatorC23×C13C22×C8
FrattiniC2×M16C22×D13
FittingC13×#1320C2
socleC2×C13#1459
prime radical#11719496C4
cosocleC2×C13×M16C23
hypercenter#1320D13
hypocenterC13#11484
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1320

Complements

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

NH ≅ G/Ntype
2. #13116455C2semidirect
3. #13112788C2semidirect
4. #13112772C2semidirect
5. C13×#1320C2semidirect
87. #1320D13semidirect
211. C13#11484semidirect

Maximal subgroups

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

subgroupindex
#131235352
#131164552
#131127882
#131127722
C13×#13202
#1148413