Finite Group Databasebeta

← #15772230

Subgroups — #15772230

Order 3328.

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

normal subgroups only

This group has 364 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#13123551C211yesmaximal, characteristic
2#13116455C212yesmaximal, complemented
3#13112786C212yesmaximal, complemented
4#13112774C211yesmaximal, characteristic, complemented
5C13×#1321C211yesmaximal, characteristic, complemented
6#11719537C411yescharacteristic
7C2×#88202C411yescharacteristic
8C2×#88161C2211yescharacteristic
9C13×#408C2211yescharacteristic
10#11718779C2211yescharacteristic
11#11718771C411yescharacteristic
12C2×#88055C411yescharacteristic
13D13×M32—22no—
14#11718391—22no—
15#11718389—22no—
16C13×#349C2212yes—
17#11718145C2212yes—
18#11718106—22no—
19C2×C13×#41C2×C411yescharacteristic
20C2×#6127C2×C411yescharacteristic
21C2×C13×M16C2311yescharacteristic
22C22×C8×C13C2×C411yescharacteristic
23#88202—42no—
24#88201C811yescharacteristic
25#88198C811yescharacteristic
26#88194C811yescharacteristic
27#88193—22no—
28#88190C811yescharacteristic
29C4×C22⋊D13—22no—
30C2×C4×Dic13C2×C411yescharacteristic
31C2×#6099—21no—
32C2×#6099C2×C411yescharacteristic
33C22×#1055—21no—
34C22×#1055C2×C411yescharacteristic
35#88161—42no—
36C2×#6094D412yes—
37C2×C8×D13D412yes—
38C13×M32—22no—
39C13×C22⋊C8—22no—
40#88060—22no—
41#88055—21no—
42#88055—21no—
43#88054—22no—
44#88052—22no—
45#88038—42no—
46C16×D13—42no—
47#11486—131nomaximal, Sylow
48C13×#41—41no—
49C13×#41—41no—
50C2×Q8×C13C2×C811yescharacteristic
51C2×D4×C13—21no—
52C2×D4×C13C2×C811yescharacteristic
53C22×C4×C13—21no—
54C22×C4×C13C22×C411yescharacteristic
55C2×C22⋊D13—22no—
56C2×C22⋊D13M1612yes—
57C22×Dic13—21no—
58#6127—41no—
59#6127—41no—
60C2×D52C2×C811yescharacteristic
61C2×C4×D13C22⋊C412yes—
62C2×Dic26C2×C811yescharacteristic
63C13×M16—41no—
64C2×C8×C13—21no—
65C2×C8×C13—41no—
66C2×C8×C13C2×D412yes—
67C22⋊Dic13—22no—
68#6103—22no—
69#6101—22no—
70C4×Dic13—21no—
71C4×Dic13C2×C811yescharacteristic
72C4×Dic13C2×C811yescharacteristic
73#6099—42no—
74#6099—41no—
75C2×#1055—22no—
76C2×#1055—21no—
77C2×#1055—42no—
78C2×#1055C22⋊C411yescharacteristic
79C2×#1055C22⋊C411yescharacteristic
80#6094—42no—
81C8×D13—22no—
82C8×D13—22no—
83C13×C16—42no—
84#6090—42no—
85#2932—131no—
86#2115—132no—
87#1327—132no—
88#1321—131no—
89#1321D1311yescharacteristic, complemented
90C23×C13—21no—
91C23×C13C2×M1611yescharacteristic
92C22×D13C22⋊C812yes—
93Q8×C13—41no—
94D4×C13—41no—
95D4×C13—42no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—41no—
100C2×C4×C13—41no—
101C2×C4×C13C2×C22⋊C411yescharacteristic
102C2×C4×C13C22×C811yescharacteristic
103C22⋊D13—42no—
104C22⋊D13—82no—
105C2×Dic13—21no—
106C2×Dic13—21no—
107C2×Dic13—81no—
108C2×Dic13C22⋊C812yes—
109D52—41no—
110C4×D13—22no—
111C4×D13—22no—
112Dic26—41no—
113C8×C13—22no—
114C8×C13—41no—
115#1055—21no—
116#1055—41no—
117#1055#9912yes—
118C2×#131—131no—
119C2×#131—131no—
120#532—131no—
121C2×M32—262no—
122#435—262no—
123#435—262no—
124#423—131no—
125#408—131no—
126#408C2×D1311yescharacteristic
127C2×#97—131no—
128#349—132no—
129#349—262no—
130#349C2×D1312yes—
131C22×C13—21no—
132C22×C13—41no—
133C22×C13—42no—
134C22×C13—41no—
135C22×C13C2×C22⋊C811yescharacteristic
136C2×D13—22no—
137C2×D13—42no—
138C4×C13—21no—
139C4×C13—41no—
140C4×C13C2×#9911yescharacteristic
141C4×C13#41311yescharacteristic
142Dic13—22no—
143Dic13—41no—
144Dic13—41no—
145C2×#41—131no—
146C2×#41C4×D1311yescharacteristic
147#131—522no—
148#131—522no—
149C2×M16—132no—
150C2×M16—131no—
151C2×M16—261no—
152C2×M16C22×D1311yescharacteristic
153C22×C8—131no—
154C22×C8—132no—
155C22×C8—261no—
156C22×C8C4×D1311yescharacteristic
157C4⋊Q8—131no—
158#127—131no—
159#124—131no—
160#124—131no—
161#121—262no—
162C4×D4—262no—
163C2×C42—131no—
164M32—22no—
165M32—262no—
166M32—522no—
167C2×C16—522no—
168C4⋊C8—262no—
169C22⋊C8—22no—
170C22⋊C8—262no—
171#97—261no—
172#97—261no—
173C2×C13—21no—
174C2×C13—41no—
175C2×C13—81no—
176C2×C13#145911yescharacteristic
177D13—42no—
178#41—41no—
179#41—41no—
180#41—521no—
181#41—521no—
182C2×Q8—131no—
183C2×Q8C8×D1311yescharacteristic
184C2×D4—21no—
185C2×D4—132no—
186C2×D4—131no—
187C2×D4—262no—
188C2×D4C8×D1311yescharacteristic
189C22×C4—21no—
190C22×C4—132no—
191C22×C4—261no—
192C22×C4C2×C4×D1311yescharacteristic
193M16—41no—
194M16—522no—
195M16—522no—
196M16—521no—
197C2×C8—21no—
198C2×C8—41no—
199C2×C8—131no—
200C2×C8—131no—
201C2×C8—262no—
202C2×C8—262no—
203C2×C8—262no—
204C2×C8—261no—
205C2×C8—522no—
206C2×C8D4×D1312yes—
207C4⋊C4—262no—
208C22⋊C4—262no—
209C22⋊C4—262no—
210C42—131no—
211C42—131no—
212C42—261no—
213C16—42no—
214C16—522no—
215C13#1148611yescharacteristic, complemented, Sylow
216C23—21no—
217C23—132no—
218C23M16×D1311yescharacteristic
219Q8—41no—
220Q8—521no—
221D4—41no—
222D4—42no—
223D4—521no—
224D4—522no—
225D4—1042no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—132no—
232C2×C4—262no—
233C2×C4—262no—
234C2×C4—261no—
235C2×C4—261no—
236C2×C4—1041no—
237C2×C4C22⋊C4×D1311yescharacteristic
238C2×C4C2×C8×D1311yescharacteristic
239C8—22no—
240C8—41no—
241C8—132no—
242C8—261no—
243C8—521no—
244C22—21no—
245C22—41no—
246C22—42no—
247C22—41no—
248C22—262no—
249C22—522no—
250C22D13×C22⋊C811yescharacteristic
251C4—21no—
252C4—41no—
253C4—262no—
254C4—521no—
255C4—521no—
256C4D13×#9911yescharacteristic
257C4#1171840611yescharacteristic
258C2—21no—
259C2—41no—
260C2—81no—
261C2—522no—
262C2#1311315111yescharacteristic
subgroupG/H
centerC4D13×#99
commutatorC2×C4×C13C22×C8
FrattiniC2×M16C22×D13
FittingC13×#1321C2
socleC2×C13#1459
prime radical#11719537C4
cosocleC2×C13×M16C23
hypercenter#1321D13
hypocenterC13#11486
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1321

Complements

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

NH ≅ G/Ntype
2. #13116455C2semidirect
3. #13112786C2semidirect
4. #13112774C2semidirect
5. C13×#1321C2semidirect
89. #1321D13semidirect
215. C13#11486semidirect

Maximal subgroups

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

subgroupindex
#131235512
#131164552
#131127862
#131127742
C13×#13212
#1148613