Finite Group Databasebeta

← #15772244

Subgroups — #15772244

Order 3328.

364 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 91 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#13123544C211yesmaximal, characteristic
2#13116632C212yesmaximal, complemented
3#13112762C211yesmaximal, characteristic, complemented
4#13112761C212yesmaximal, complemented
5C13×#1315C211yesmaximal, characteristic, complemented
6#11719537C411yescharacteristic
7C2×#88202C411yescharacteristic
8C2×#88161C411yescharacteristic
9C13×#408C2211yescharacteristic
10#11718779C411yescharacteristic
11#11718771C2211yescharacteristic
12C2×C8×Dic13C2211yescharacteristic
13#11718390—22no—
14#11718386—22no—
15C13×C22⋊C16C2212yes—
16C22⋊#6090C2212yes—
17#11718093—22no—
18C16×Dic13—22no—
19C2×C13×#41C2×C411yescharacteristic
20C2×#6127C2×C411yescharacteristic
21C2×C13×M16C2×C411yescharacteristic
22C22×C8×C13C2311yescharacteristic
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×#6094—21no—
37C2×C8×D13—21no—
38C2×C13×C16—22no—
39C13×C22⋊C8—22no—
40#88060—22no—
41#88054—22no—
42C8×Dic13D412yes—
43C8×Dic13D412yes—
44C2×#6090—22no—
45#11490—131nomaximal, Sylow
46C13×#41—41no—
47C13×#41—41no—
48C2×Q8×C13C2×C811yescharacteristic
49C2×D4×C13—21no—
50C2×D4×C13C2×C811yescharacteristic
51C22×C4×C13—21no—
52C22×C4×C13C22×C411yescharacteristic
53C2×C22⋊D13—21no—
54C2×C22⋊D13—22no—
55C22×Dic13M1612yes—
56#6127—41no—
57#6127—41no—
58C2×D52C2×C811yescharacteristic
59C2×C4×D13—21no—
60C2×Dic26C2×C811yescharacteristic
61C13×M16—41no—
62C2×C8×C13—21no—
63C2×C8×C13—41no—
64C2×C8×C13C2×D412yes—
65C22⋊Dic13—22no—
66#6103—22no—
67#6101—22no—
68C4×Dic13C22⋊C412yes—
69C4×Dic13C2×C811yescharacteristic
70C4×Dic13C2×C811yescharacteristic
71#6099—42no—
72#6099—41no—
73C2×#1055—22no—
74C2×#1055—21no—
75C2×#1055—42no—
76C2×#1055C22⋊C411yescharacteristic
77C2×#1055C22⋊C411yescharacteristic
78#6094—42no—
79C8×D13—42no—
80C13×C16—42no—
81#6090—42no—
82#2931—131no—
83#2162—132no—
84#1315—131no—
85#1315—132no—
86#1315D1311yescharacteristic, complemented
87C23×C13—21no—
88C23×C13C2×M1611yescharacteristic
89C22×D13—21no—
90Q8×C13—41no—
91D4×C13—41no—
92D4×C13—42no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13C2×C22⋊C411yescharacteristic
99C2×C4×C13C22×C811yescharacteristic
100C22⋊D13—42no—
101C22⋊D13—44no—
102C2×Dic13—24no—
103C2×Dic13—21no—
104C2×Dic13C22⋊C812yes—
105C2×Dic13C22⋊C812yes—
106D52—41no—
107C4×D13—41no—
108C4×D13—41no—
109Dic26—41no—
110C8×C13—22no—
111C8×C13—41no—
112#1055—21no—
113#1055—41no—
114#1055#10012yes—
115C2×#131—131no—
116C2×#131—131no—
117#532—131no—
118#436—262no—
119C8×D4—262no—
120#423—131no—
121#408—131no—
122#408C2×D1311yescharacteristic
123C2×C4×C8—131no—
124C4⋊C16—262no—
125C22⋊C16—132no—
126C22⋊C16C2×D1312yes—
127C4×C16—262no—
128C22×C13—22no—
129C22×C13—21no—
130C22×C13—42no—
131C22×C13—41no—
132C22×C13C2×C22⋊C811yescharacteristic
133C2×D13—42no—
134C2×D13—41no—
135C4×C13—21no—
136C4×C13—41no—
137C4×C13#41011yescharacteristic
138C4×C13C2×#10011yescharacteristic
139Dic13—22no—
140Dic13—41no—
141Dic13#35014yes—
142C2×#41—131no—
143C2×#41C4×D1311yescharacteristic
144#131—522no—
145#131—522no—
146C2×M16—131no—
147C2×M16—261no—
148C2×M16—261no—
149C2×M16C4×D1311yescharacteristic
150C22×C8—131no—
151C22×C8—261no—
152C22×C8—261no—
153C22×C8C22×D1311yescharacteristic
154C4⋊Q8—131no—
155#127—131no—
156#124—131no—
157#124—131no—
158#121—262no—
159C4×D4—262no—
160C2×C42—131no—
161C2×C16—22no—
162C2×C16—262no—
163C4⋊C8—262no—
164C22⋊C8—22no—
165C22⋊C8—262no—
166C4×C8—132no—
167C4×C8—132no—
168C2×C13—41no—
169C2×C13—81no—
170C2×C13#146011yescharacteristic
171C2×C13C2×#35012yes—
172D13—81no—
173#41—41no—
174#41—41no—
175#41—521no—
176#41—521no—
177C2×Q8—131no—
178C2×Q8C8×D1311yescharacteristic
179C2×D4—21no—
180C2×D4—131no—
181C2×D4—262no—
182C2×D4—261no—
183C2×D4C8×D1311yescharacteristic
184C22×C4—21no—
185C22×C4—132no—
186C22×C4—261no—
187C22×C4C2×C4×D1311yescharacteristic
188M16—41no—
189M16—522no—
190M16—522no—
191M16—521no—
192C2×C8—21no—
193C2×C8—41no—
194C2×C8—131no—
195C2×C8—131no—
196C2×C8—262no—
197C2×C8—261no—
198C2×C8—522no—
199C2×C8—522no—
200C2×C8D4×D1312yes—
201C4⋊C4—262no—
202C22⋊C4—262no—
203C22⋊C4—262no—
204C42—132no—
205C42—131no—
206C42—131no—
207C16—42no—
208C16—522no—
209C13#1149011yescharacteristic, complemented, Sylow
210C23—21no—
211C23—261no—
212C23M16×D1311yescharacteristic
213Q8—41no—
214Q8—521no—
215D4—41no—
216D4—42no—
217D4—521no—
218D4—524no—
219D4—522no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—132no—
226C2×C4—132no—
227C2×C4—264no—
228C2×C4—261no—
229C2×C4—521no—
230C2×C4—521no—
231C2×C4C22⋊C4×D1311yescharacteristic
232C2×C4C2×C8×D1311yescharacteristic
233C8—22no—
234C8—41no—
235C8—132no—
236C8—261no—
237C8—521no—
238C22—22no—
239C22—21no—
240C22—42no—
241C22—41no—
242C22—522no—
243C22—521no—
244C22D13×C22⋊C811yescharacteristic
245C4—21no—
246C4—41no—
247C4—134no—
248C4—262no—
249C4—521no—
250C4#1171840111yescharacteristic
251C4D13×#10011yescharacteristic
252C2—41no—
253C2—81no—
254C2—1041no—
255C2#1311315511yescharacteristic
256C2D13×#35012yes—
subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC2×C4×C13C22×C8
FrattiniC22×C8C22×D13
FittingC13×#1315C2
socleC22×C13C2×C22⋊C8
prime radical#11719537C4
cosocleC22×C8×C13C23
hypercenter#1315D13
hypocenterC13#11490
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1315

Complements

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

NH ≅ G/Ntype
2. #13116632C2semidirect
3. #13112762C2semidirect
4. #13112761C2semidirect
5. C13×#1315C2semidirect
86. #1315D13semidirect
209. C13#11490semidirect

Maximal subgroups

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

subgroupindex
#131235442
#131166322
#131127622
#131127612
C13×#13152
#1149013