Finite Group Databasebeta

← #15781124

Subgroups — #15781124

Order 3328.

438 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 115 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#13123532C211yesmaximal, characteristic
2#13116602C211yesmaximal, characteristic, complemented
3#13116463C212yesmaximal, complemented
4#13116446C212yesmaximal, complemented
5C13×#2110C211yesmaximal, characteristic, complemented
6C2×#88155C2211yescharacteristic
7C22×C8×D13C2211yescharacteristic
8#11719229C411yescharacteristic
9C2×C13×M32C2212yes—
10C13×#405C2211yescharacteristic
11#11718790C411yescharacteristic
12#11718787C411yescharacteristic
13C2×#88052C2212yes—
14#11718660C411yescharacteristic
15#11718367—22no—
16C8×D52—22no—
17C13×#347—22no—
18#11718100—24no—
19#11718099—24no—
20#11718055—22no—
21C2×#6127C2×C411yescharacteristic
22C22×C4×D13C2×C411yescharacteristic
23C2×C13×M16C2×C411yescharacteristic
24C22×C8×C13C2311yescharacteristic
25C13×#117C2×C411yescharacteristic
26C2×#6099C2×C411yescharacteristic
27C22×#1055C2×C411yescharacteristic
28#88155—22no—
29#88155—22no—
30C2×#6094—21no—
31C2×C8×D13—21no—
32C2×C8×D13—22no—
33C2×C8×D13—21no—
34C2×C8×D13—21no—
35C2×C8×D13—22no—
36#88151—21no—
37#88149—21no—
38#88140—21no—
39#88136—21no—
40C4×D52—22no—
41C13×M32—22no—
42C13×M32—22no—
43C2×C13×C16D414yescomplemented
44C13×#97D412yes—
45C4×C8×C13D412yes—
46#88060—22no—
47#88060—22no—
48#88052—22no—
49#88052—22no—
50C2×#6090—22no—
51C4⋊#1055—22no—
52#13200—131nomaximal, Sylow
53C23×D13M1611yescharacteristic
54C22×C4×C13C22×C411yescharacteristic
55C2×C22⋊D13—21no—
56C22×Dic13M1611yescharacteristic
57#6127—22no—
58#6127—22no—
59C2×D52—22no—
60C2×D52M1611yescharacteristic
61C2×C4×D13—21no—
62C2×C4×D13—21no—
63C2×C4×D13—22no—
64C2×C4×D13—21no—
65C2×C4×D13—22no—
66C2×Dic26M1611yescharacteristic
67C13×M16—22no—
68C2×C8×C13C22⋊C412yes—
69C2×C8×C13C2×D411yescharacteristic
70C2×C8×C13C2×D412yes—
71C2×C8×C13C2×D411yescharacteristic
72C2×C8×C13#4112yes—
73C13×C4⋊C4—21no—
74C13×C22⋊C4—21no—
75C42×C13C22⋊C412yes—
76#6103—22no—
77#6103—22no—
78C4⋊Dic13—22no—
79#6099—22no—
80C2×#1055—21no—
81C2×#1055—21no—
82C2×#1055—22no—
83#6094—42no—
84C8×D13—42no—
85C8×D13—41no—
86C8×D13—41no—
87C8×D13—41no—
88C8×D13—41no—
89C13×C16—24no—
90#6090—42no—
91#2929—131no—
92#2153—131no—
93#2117—132no—
94#2112—132no—
95#2110D1311yescharacteristic, complemented
96C23×C13C2×M1611yescharacteristic
97C22×D13—21no—
98C22×D13—22no—
99C22×D13—21no—
100C22×D13—42no—
101C2×C4×C13—22no—
102C2×C4×C13C2×C22⋊C411yescharacteristic
103C2×C4×C13C4×D412yes—
104C2×C4×C13C2×M1611yescharacteristic
105C2×C4×C13#13112yes—
106C22⋊D13—42no—
107C2×Dic13—21no—
108C2×Dic13—21no—
109C2×Dic13—22no—
110D52—22no—
111D52—44no—
112C4×D13—41no—
113C4×D13—41no—
114C4×D13—41no—
115C4×D13—41no—
116C4×D13—42no—
117Dic26—22no—
118C8×C13—22no—
119C8×C13#12112yes—
120C8×C13#12411yescharacteristic
121C8×C13#12711yescharacteristic
122#1055—41no—
123#1055—41no—
124C2×#131—131no—
125C23×C8—131no—
126#525—131no—
127C2×M32—132no—
128C2×M32C2×D1312yes—
129#435—262no—
130C8×D4—262no—
131#424—131no—
132#408—131no—
133#407—131no—
134#405C2×D1311yescharacteristic
135#364—262no—
136#350—264no—
137C22⋊C16—264no—
138#347—22no—
139C22×C13—41no—
140C22×C13#40711yescharacteristic
141C22×C13#43512yes—
142C2×D13—22no—
143C2×D13—24no—
144C2×D13—41no—
145C2×D13—42no—
146C2×D13—41no—
147C2×D13—42no—
148C2×D13—41no—
149C4×C13—42no—
150C4×C13#39011yescharacteristic
151C4×C13#40811yescharacteristic
152C4×C13#43512yes—
153Dic13—41no—
154Dic13—41no—
155C2×#41—131no—
156C23×C4—131no—
157#131—262no—
158#131—262no—
159C2×M16—131no—
160C2×M16—261no—
161C2×M16C4×D1311yescharacteristic
162C22×C8—131no—
163C22×C8—262no—
164C22×C8—261no—
165C22×C8—261no—
166C22×C8—262no—
167C22×C8—261no—
168C22×C8C22×D1311yescharacteristic
169#123—261no—
170C22⋊Q8—261no—
171#121—261no—
172#120—261no—
173C4×D4—262no—
174#117C4×D1311yescharacteristic
175M32—22no—
176M32—22no—
177M32—262no—
178M32—262no—
179C2×C16—262no—
180C2×C16D5214yescomplemented
181C4⋊C8—262no—
182C22⋊C8—262no—
183C22⋊C8—262no—
184#97C22⋊D1312yes—
185C4×C8D5212yes—
186C2×C13—21no—
187C2×C13—22no—
188C2×C13#195511yescharacteristic
189D13—42no—
190D13—81no—
191C24—131no—
192#41—262no—
193#41—262no—
194C2×Q8—131no—
195C2×D4—131no—
196C2×D4—262no—
197C2×D4—261no—
198C22×C4—131no—
199C22×C4—262no—
200C22×C4—261no—
201C22×C4—262no—
202C22×C4—261no—
203C22×C4—261no—
204C22×C4C2×C4×D1311yescharacteristic
205M16—22no—
206M16—262no—
207M16—522no—
208C2×C8—262no—
209C2×C8—261no—
210C2×C8—261no—
211C2×C8—521no—
212C2×C8—521no—
213C2×C8—521no—
214C2×C8—521no—
215C2×C8—522no—
216C2×C8#610312yes—
217C2×C8C2×D5211yescharacteristic
218C2×C8C2×D5212yes—
219C2×C8#612712yes—
220C2×C8C2×C22⋊D1311yescharacteristic
221C4⋊C4—21no—
222C4⋊C4—262no—
223C22⋊C4—21no—
224C22⋊C4—262no—
225C22⋊C4—262no—
226C42#610312yes—
227C16—24no—
228C16—522no—
229C13#1320011yescharacteristic, complemented, Sylow
230C23—261no—
231C23—262no—
232C23—261no—
233C23—522no—
234C23M16×D1311yescharacteristic
235Q8—262no—
236D4—262no—
237D4—524no—
238D4—522no—
239C2×C4—22no—
240C2×C4—261no—
241C2×C4—261no—
242C2×C4—262no—
243C2×C4—521no—
244C2×C4—521no—
245C2×C4—521no—
246C2×C4—521no—
247C2×C4—522no—
248C2×C4C4×D5212yes—
249C2×C4M16×D1311yescharacteristic
250C2×C4#8816112yes—
251C2×C4C2×#610311yescharacteristic
252C8—22no—
253C8—521no—
254C8—521no—
255C8#8812811yescharacteristic
256C8#8812911yescharacteristic
257C8#8818412yes—
258C22—41no—
259C22—262no—
260C22—264no—
261C22—521no—
262C22—522no—
263C22—522no—
264C22—521no—
265C22—521no—
266C22#1171836712yes—
267C22#1171878711yescharacteristic
268C4—42no—
269C4—521no—
270C4—521no—
271C4#1171836712yes—
272C4#1171860011yescharacteristic
273C4#1171879011yescharacteristic
274C2—21no—
275C2—22no—
276C2—522no—
277C2—1041no—
278C2#1311563411yescharacteristic
subgroupG/H
centerC8#88128
commutatorC22×C4×C13C22×C4
FrattiniC22×C8C22×D13
FittingC13×#2110C2
socleC2×C13#1955
prime radical#11719229C4
cosocleC22×C8×C13C23
hypercenter#2110D13
hypocenterC13#13200
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2110

Complements

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

NH ≅ G/Ntype
2. #13116602C2semidirect
3. #13116463C2semidirect
4. #13116446C2semidirect
5. C13×#2110C2semidirect
43. C2×C13×C16D4semidirect
95. #2110D13semidirect
180. C2×C16D52semidirect
229. C13#13200semidirect

Maximal subgroups

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

subgroupindex
#131235322
#131166022
#131164632
#131164462
C13×#21102
#1320013