Finite Group Databasebeta

← #15772085

Subgroups — #15772085

Order 3328.

434 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 93 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#13117457C211yesmaximal, characteristic
2#13113149C212yesmaximal
3#13112782C211yesmaximal, characteristic, complemented
4#13112781C212yesmaximal, complemented
5C13×#1325C211yesmaximal, characteristic, complemented
6C2×#88146C2211yescharacteristic
7C2×C4⋊C4×D13C411yescharacteristic
8C2×#88126C411yescharacteristic
9C13×#384C2211yescharacteristic
10#11718650—22no—
11#11718638C411yescharacteristic
12#11718637C2211yescharacteristic
13#11718633—22no—
14#11718597C411yescharacteristic
15#11718379—22no—
16C13×#324C2212yes—
17#11718120C2212yes—
18#11718060—22no—
19C22×C4×D13—21no—
20C22×C4×D13C2×C411yescharacteristic
21C2×C13×C4⋊C4—22no—
22C2×C13×C4⋊C4C2×C411yescharacteristic
23C2×C13×C4⋊C4C2311yescharacteristic
24C2×C42×C13C2×C411yescharacteristic
25C2×#6103—21no—
26C2×#6103D412yes—
27C2×C4⋊Dic13C2×C411yescharacteristic
28C2×C4⋊Dic13C2×C411yescharacteristic
29C2×#6101—21no—
30C2×#6101—21no—
31C2×#6101—22no—
32C2×C4×Dic13C2×C411yescharacteristic
33C2×C4×Dic13D412yes—
34#88146—42no—
35C4⋊C4×D13—42no—
36#88126—22no—
37#88126C814yescomplemented
38C13×C22⋊C8—22no—
39#88071—22no—
40#88071—22no—
41C22⋊#1055—22no—
42#88054—42no—
43C8×Dic13—42no—
44#11450—131nomaximal, Sylow
45C23×D13C22⋊C411yescharacteristic
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13C22×C411yescharacteristic
49C22×C4×C13C2×D412yes—
50C22×Dic13—21no—
51C22×Dic13—21no—
52C22×Dic13C22⋊C412yes—
53C22×Dic13C22⋊C411yescharacteristic
54C2×C4×D13—22no—
55C2×C4×D13—22no—
56C2×C4×D13—42no—
57C2×C4×D13—82no—
58C2×C4×D13C2×C812yes—
59C2×C4×D13M1612yes—
60C2×C8×C13—42no—
61C13×C4⋊C4—41no—
62C13×C4⋊C4—41no—
63C13×C4⋊C4—82no—
64C42×C13—21no—
65C42×C13C2×C812yes—
66#6103—24no—
67#6103—42no—
68C4⋊Dic13—41no—
69C4⋊Dic13—41no—
70#6101—24no—
71#6101—42no—
72#6101—82no—
73C4×Dic13—21no—
74C4×Dic13—22no—
75C4×Dic13—22no—
76C4×Dic13C2×C812yes—
77C2×#1055—42no—
78#2317—131no—
79#1458—132no—
80#1325—131no—
81#1325—132no—
82#1325D1311yescharacteristic, complemented
83C23×C13C2×C22⋊C411yescharacteristic
84C22×D13—21no—
85C22×D13—21no—
86C22×D13—41no—
87C22×D13—41no—
88C22×D13C22⋊C812yes—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—41no—
94C2×C4×C13—41no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—41no—
98C2×C4×C13C22×C811yescharacteristic
99C2×C4×C13C2×M1611yescharacteristic
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—41no—
103C2×Dic13—41no—
104C2×Dic13—42no—
105C2×Dic13—42no—
106C2×Dic13—41no—
107C2×Dic13C22⋊C812yes—
108C2×Dic13#9912yes—
109C2×Dic13#10112yes—
110C4×D13—24no—
111C4×D13—24no—
112C4×D13—84no—
113C8×C13—82no—
114#1055—82no—
115C2×#117—131no—
116C2×#117—131no—
117C22×C4⋊C4—131no—
118#431—262no—
119#389—262no—
120#385—262no—
121#384—131no—
122#384C2×D1311yescharacteristic
123#382—131no—
124#382—131no—
125#324—132no—
126#324C2×D1312yes—
127#323—262no—
128C22×C13—21no—
129C22×C13—21no—
130C22×C13C2×C22⋊C811yescharacteristic
131C22×C13C2×#9911yescharacteristic
132C22×C13C2×#10111yescharacteristic
133C2×D13—22no—
134C2×D13—42no—
135C2×D13—41no—
136C2×D13—41no—
137C2×D13—42no—
138C4×C13—21no—
139C4×C13—21no—
140C4×C13—42no—
141C4×C13—42no—
142C4×C13—81no—
143Dic13—42no—
144Dic13—42no—
145Dic13—81no—
146Dic13#32414yes—
147C23×C4—131no—
148C23×C4—261no—
149#117—134no—
150#117—262no—
151#117—522no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—131no—
154C2×C4⋊C4—131no—
155C2×C4⋊C4—261no—
156C2×C4⋊C4—261no—
157C2×C4⋊C4—262no—
158C2×C4⋊C4—522no—
159C2×C4⋊C4C4×D1311yescharacteristic
160C2×C4⋊C4C22×D1311yescharacteristic
161C2×C22⋊C4—132no—
162C2×C22⋊C4—261no—
163C2×C42—131no—
164C2×C42—132no—
165C2×C42C4×D1311yescharacteristic
166C4⋊C8—522no—
167C22⋊C8—22no—
168C22⋊C8—262no—
169C4×C8—522no—
170#95—262no—
171#95—262no—
172C2×C13—21no—
173C2×C13—21no—
174C2×C13C2×#32411yescharacteristic
175C2×C13#212811yescharacteristic
176C2×C13#213511yescharacteristic
177D13—42no—
178C24—131no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—131no—
182C22×C4—132no—
183C22×C4—132no—
184C22×C4—132no—
185C22×C4—262no—
186C22×C4—262no—
187C22×C4—261no—
188C22×C4—261no—
189C22×C4—522no—
190C22×C4—1042no—
191C22×C4C2×C4×D1311yescharacteristic
192C22×C4D4×D1312yes—
193C2×C8—42no—
194C2×C8—522no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—82no—
198C4⋊C4—264no—
199C4⋊C4—521no—
200C4⋊C4—521no—
201C4⋊C4—522no—
202C4⋊C4—1042no—
203C22⋊C4—264no—
204C22⋊C4—522no—
205C42—21no—
206C42—132no—
207C42—262no—
208C42—262no—
209C42—261no—
210C42C8×D1312yes—
211C13#1145011yescharacteristic, complemented, Sylow
212C23—132no—
213C23—261no—
214C23—261no—
215C23—521no—
216C23—521no—
217C23C22⋊C4×D1311yescharacteristic
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—132no—
228C2×C4—132no—
229C2×C4—132no—
230C2×C4—264no—
231C2×C4—264no—
232C2×C4—262no—
233C2×C4—262no—
234C2×C4—521no—
235C2×C4—521no—
236C2×C4—522no—
237C2×C4—522no—
238C2×C4—521no—
239C2×C4—1044no—
240C2×C4C2×C8×D1311yescharacteristic
241C2×C4M16×D1311yescharacteristic
242C8—82no—
243C8—1042no—
244C22—21no—
245C22—21no—
246C22—262no—
247C22—522no—
248C22—522no—
249C22—521no—
250C22—521no—
251C22D13×C22⋊C811yescharacteristic
252C22D13×#9911yescharacteristic
253C22D13×#10111yescharacteristic
254C4—21no—
255C4—21no—
256C4—42no—
257C4—42no—
258C4—81no—
259C4—134no—
260C4—522no—
261C4—522no—
262C4—1041no—
263C2—21no—
264C2—21no—
265C2—522no—
266C2D13×#32411yescharacteristic
267C2#1311650611yescharacteristic
268C2#1311652911yescharacteristic
subgroupG/H
centerC22D13×#99
commutatorC2×C4×C13C22×C8
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1325C2
socleC22×C13C2×#99
prime radicalC23×D13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1325D13
hypocenterC13#11450
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
3. #13112782C2semidirect
4. #13112781C2semidirect
5. C13×#1325C2semidirect
37. #88126C8semidirect
82. #1325D13semidirect
211. C13#11450semidirect

Maximal subgroups

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

subgroupindex
#131174572
#131131492
#131127822
#131127812
C13×#13252
#1145013