Finite Group Databasebeta

← #15781127

Subgroups — #15781127

Order 3328.

420 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 111 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#13123541C211yesmaximal, characteristic
2#13116463C212yesmaximal, complemented
3C2×#11718106C212yesmaximal, complemented
4#13116441C211yesmaximal, characteristic, complemented
5C13×#2153C211yesmaximal, characteristic, complemented
6C2×#88155C2211yescharacteristic
7C22×#6094C2211yescharacteristic
8#11719229C411yescharacteristic
9C2×C13×M32C2212yes—
10C13×#405C2211yescharacteristic
11#11718790C411yescharacteristic
12#11718787C411yescharacteristic
13C2×#88052C2212yes—
14#11718660C411yescharacteristic
15#11718367—22no—
16#11718349—22no—
17C13×#364—22no—
18#11718106—24no—
19#11718100—24no—
20#11718058—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×#6094—22no—
32C2×#6094—21no—
33C2×#6094—21no—
34C2×#6094—22no—
35C2×C8×D13—21no—
36#88151—21no—
37#88149—21no—
38#88140—21no—
39#88136—21no—
40C4×D52—22no—
41C13×M32—22no—
42C13×M32—22no—
43C2×C13×C16—22no—
44C13×#97D412yes—
45C4×C8×C13D412yes—
46#88060—22no—
47#88060—22no—
48#88052—22no—
49#88052D414yescomplemented
50C2×#6090—22no—
51C4⋊#1055—22no—
52#13201—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—
84#6094—41no—
85#6094—41no—
86#6094—41no—
87#6094—41no—
88C8×D13—42no—
89C13×C16—42no—
90#6090—24no—
91#2930—131no—
92#2153D1311yescharacteristic, complemented
93#2117—132no—
94C2×#349—132no—
95#2110—131no—
96C23×C13C2×M1611yescharacteristic
97C22×D13—21no—
98C22×D13—21no—
99C22×D13—22no—
100C22×D13—81no—
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—82no—
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—
125C22×M16—131no—
126#525—131no—
127C2×M32—132no—
128C2×M32C2×D1312yes—
129#436—262no—
130#435—262no—
131#424—131no—
132#408—131no—
133#407—131no—
134#405C2×D1311yescharacteristic
135#364—22no—
136#350—264no—
137#349—264no—
138#347—262no—
139C22×C13—41no—
140C22×C13#40711yescharacteristic
141C22×C13#43512yes—
142C2×D13—41no—
143C2×D13—42no—
144C2×D13—41no—
145C2×D13—41no—
146C2×D13—41no—
147C2×D13—82no—
148C4×C13—42no—
149C4×C13#39011yescharacteristic
150C4×C13#40811yescharacteristic
151C4×C13#43512yes—
152Dic13—41no—
153Dic13—41no—
154C2×#41—131no—
155C23×C4—131no—
156#131—262no—
157#131—262no—
158C2×M16—131no—
159C2×M16—261no—
160C2×M16—262no—
161C2×M16—262no—
162C2×M16—261no—
163C2×M16—261no—
164C2×M16C4×D1311yescharacteristic
165C22×C8—131no—
166C22×C8—261no—
167C22×C8C22×D1311yescharacteristic
168#123—261no—
169C22⋊Q8—261no—
170#121—261no—
171#120—261no—
172C4×D4—262no—
173#117C4×D1311yescharacteristic
174M32—22no—
175M32—22no—
176M32—134no—
177M32—262no—
178C2×C16—22no—
179C2×C16—262no—
180C4⋊C8—262no—
181C22⋊C8—262no—
182C22⋊C8—262no—
183#97D5212yes—
184C4×C8C22⋊D1312yes—
185C2×C13—21no—
186C2×C13—22no—
187C2×C13#195511yescharacteristic
188D13—81no—
189D13—81no—
190C24—131no—
191#41—262no—
192#41—262no—
193C2×Q8—131no—
194C2×D4—131no—
195C2×D4—262no—
196C2×D4—261no—
197C22×C4—131no—
198C22×C4—262no—
199C22×C4—262no—
200C22×C4—261no—
201C22×C4—261no—
202C22×C4—261no—
203C22×C4C2×C4×D1311yescharacteristic
204M16—22no—
205M16—262no—
206M16—522no—
207M16—521no—
208M16—521no—
209M16—521no—
210M16—521no—
211C2×C8—262no—
212C2×C8—261no—
213C2×C8—261no—
214C2×C8—522no—
215C2×C8#610312yes—
216C2×C8C2×D5211yescharacteristic
217C2×C8D4×D1312yes—
218C2×C8#613112yes—
219C2×C8C2×C22⋊D1311yescharacteristic
220C4⋊C4—21no—
221C4⋊C4—262no—
222C22⋊C4—21no—
223C22⋊C4—262no—
224C22⋊C4—262no—
225C42#610312yes—
226C16—42no—
227C16—264no—
228C13#1320111yescharacteristic, complemented, Sylow
229C23—261no—
230C23—261no—
231C23—262no—
232C23—1041no—
233C23M16×D1311yescharacteristic
234Q8—262no—
235D4—262no—
236D4—522no—
237D4—1042no—
238C2×C4—22no—
239C2×C4—262no—
240C2×C4—261no—
241C2×C4—261no—
242C2×C4—522no—
243C2×C4—521no—
244C2×C4—521no—
245C2×C4—521no—
246C2×C4—521no—
247C2×C4#8814712yes—
248C2×C4#8815512yes—
249C2×C4M16×D1311yescharacteristic
250C2×C4C2×#610311yescharacteristic
251C8—22no—
252C8—521no—
253C8—521no—
254C8#8814912yes—
255C8#8819411yescharacteristic
256C8#8820111yescharacteristic
257C22—41no—
258C22—521no—
259C22—522no—
260C22—521no—
261C22—521no—
262C22—521no—
263C22—1042no—
264C22#1171849712yes—
265C22#1171878711yescharacteristic
266C4—42no—
267C4—521no—
268C4—521no—
269C4#1171849712yes—
270C4#1171864911yescharacteristic
271C4#1171877111yescharacteristic
272C2—21no—
273C2—22no—
274C2—1041no—
275C2—1041no—
276C2#1311563311yescharacteristic
subgroupG/H
centerC4#11718649
commutatorC22×C4×C13C22×C4
FrattiniC22×C8C22×D13
FittingC13×#2153C2
socleC2×C13#1955
prime radical#11719229C4
cosocleC22×C8×C13C23
hypercenter#2153D13
hypocenterC13#13201
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C8 ◁ #2153

Complements

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

NH ≅ G/Ntype
2. #13116463C2semidirect
3. C2×#11718106C2semidirect
4. #13116441C2semidirect
5. C13×#2153C2semidirect
49. #88052D4semidirect
92. #2153D13semidirect
228. C13#13201semidirect

Maximal subgroups

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

subgroupindex
#131235412
#131164632
C2×#117181062
#131164412
C13×#21532
#1320113