Finite Group Databasebeta

← #15772399

Subgroups — #15772399

Order 3328.

412 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 99 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#13113180C212yesmaximal
2#13112782C212yesmaximal
3#13112770C212yesmaximal
4C4×C13×C4⋊Q8C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×C4×Q8×C13C411yescharacteristic
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#391C411yescharacteristic
9C13×#391C2211yescharacteristic
10C13×#389—22no—
11C13×#384C2211yescharacteristic
12C4×C13×C4⋊C4—22no—
13C43×C13C411yescharacteristic
14#11718587—22no—
15#11718120—22no—
16#11718120C2214yes—
17C22×Q8×C13C2×C411yescharacteristic
18C22×Q8×C13C2×C411yescharacteristic
19C13×C4⋊Q8—22no—
20C13×C4⋊Q8—22no—
21C4×Q8×C13—41no—
22C4×Q8×C13—41no—
23C4×Q8×C13—41no—
24C4×Q8×C13—41no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4D412yes—
30C2×C13×C4⋊C4C2311yescharacteristic
31C2×C42×C13—21no—
32C2×C42×C13—21no—
33C2×C42×C13—21no—
34C2×C42×C13C2×C411yescharacteristic
35C2×C42×C13C2×C411yescharacteristic
36C2×C42×C13C2×C411yescharacteristic
37C2×C42×C13D412yes—
38C13×#95—22no—
39C13×#95—22no—
40C22⋊#1055—24no—
41C4⋊#1055—42no—
42#88043—42no—
43#11532—131nomaximal, Sylow
44C2×Q8×C13—21no—
45C2×Q8×C13—21no—
46C2×Q8×C13—21no—
47C2×Q8×C13—41no—
48C2×Q8×C13—41no—
49C2×Q8×C13—41no—
50C2×Q8×C13—41no—
51C2×Q8×C13M1612yes—
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13C22⋊C412yes—
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22×C411yescharacteristic
60C22×C4×C13C2×D412yes—
61C13×C4⋊C4—28no—
62C13×C4⋊C4—42no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—41no—
65C13×C4⋊C4—44no—
66C13×C4⋊C4—42no—
67C42×C13—24no—
68C42×C13—21no—
69C42×C13—21no—
70C42×C13—22no—
71C42×C13—22no—
72C42×C13—21no—
73C42×C13—41no—
74C42×C13—42no—
75C42×C13—41no—
76C42×C13—41no—
77C42×C13M1612yes—
78C2×#1055—44no—
79C4×C4⋊Q8D1311yescharacteristic
80#1467—132no—
81#1325—132no—
82#1319—132no—
83C23×C13C2×C22⋊C411yescharacteristic
84Q8×C13—42no—
85Q8×C13—42no—
86Q8×C13—42no—
87Q8×C13—42no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13—21no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—41no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13—41no—
109C2×C4×C13#9911yescharacteristic
110C2×C4×C13#9911yescharacteristic
111C2×C4×C13C2×M1611yescharacteristic
112C2×C4×C13C2×M1611yescharacteristic
113#1055—84no—
114C2×C4⋊Q8Dic1311yescharacteristic
115C2×C4×Q8Dic1311yescharacteristic
116C2×C4×Q8C2×D1311yescharacteristic
117#432—262no—
118#391Dic1311yescharacteristic
119#391C2×D1311yescharacteristic
120#389—22no—
121#384C2×D1311yescharacteristic
122C4×C4⋊C4—22no—
123C43Dic1311yescharacteristic
124#324—134no—
125#324—262no—
126C22×C13—21no—
127C22×C13—21no—
128C22×C13#40711yescharacteristic
129C22×C13C2×#9911yescharacteristic
130C22×C13#41311yescharacteristic
131C4×C13—24no—
132C4×C13—21no—
133C4×C13—21no—
134C4×C13—21no—
135C4×C13—42no—
136C4×C13—42no—
137C4×C13—41no—
138C4×C13—42no—
139C4×C13—42no—
140C4×C13—81no—
141C4×C13#35612yes—
142C22×Q8C2×Dic1311yescharacteristic
143C22×Q8C2×Dic1311yescharacteristic
144C4⋊Q8—22no—
145C4⋊Q8—22no—
146C4×Q8—41no—
147C4×Q8—41no—
148C4×Q8—41no—
149C4×Q8—41no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4C2×Dic1311yescharacteristic
154C2×C4⋊C4C22⋊D1312yes—
155C2×C4⋊C4C22×D1311yescharacteristic
156C2×C42—21no—
157C2×C42—21no—
158C2×C42—21no—
159C2×C42C2×Dic1311yescharacteristic
160C2×C42C2×Dic1311yescharacteristic
161C2×C42C2×Dic1311yescharacteristic
162C2×C42C22⋊D1312yes—
163C4⋊C8—522no—
164C22⋊C8—264no—
165#97—522no—
166#95—22no—
167#95—22no—
168C2×C13—21no—
169C2×C13—21no—
170C2×C13#146511yescharacteristic
171C2×C13#212611yescharacteristic
172C2×C13C2×#35611yescharacteristic
173C2×Q8—21no—
174C2×Q8—21no—
175C2×Q8—21no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8—41no—
180C2×Q8#609912yes—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4C22⋊Dic1312yes—
186C22×C4C22⋊Dic1311yescharacteristic
187C22×C4C22⋊Dic1311yescharacteristic
188C22×C4C22×Dic1311yescharacteristic
189C22×C4C2×C22⋊D1312yes—
190C2×C8—524no—
191C4⋊C4—28no—
192C4⋊C4—42no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—42no—
196C4⋊C4—44no—
197C42—24no—
198C42—22no—
199C42—22no—
200C42—21no—
201C42—21no—
202C42—21no—
203C42—41no—
204C42—42no—
205C42—41no—
206C42—41no—
207C42#609912yes—
208C13#1153211yescharacteristic, complemented, Sylow
209C23C2×C22⋊Dic1311yescharacteristic
210Q8—42no—
211Q8—42no—
212Q8—42no—
213Q8—42no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—41no—
235C2×C4#8807411yescharacteristic
236C2×C4#8807411yescharacteristic
237C2×C4C2×#609911yescharacteristic
238C2×C4C2×#609911yescharacteristic
239C8—1044no—
240C22—21no—
241C22—21no—
242C22#1171886811yescharacteristic
243C22C2×#8807411yescharacteristic
244C22#1171889811yescharacteristic
245C4—24no—
246C4—21no—
247C4—21no—
248C4—21no—
249C4—42no—
250C4—42no—
251C4—41no—
252C4—42no—
253C4—42no—
254C4—81no—
255C4#1171814012yes—
256C2—21no—
257C2—21no—
258C2#1311317411yescharacteristic
259C2#1311650111yescharacteristic
260C2C2×#1171814011yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC4×C13×C4⋊Q8C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenterC4×C4⋊Q8D13
hypocenterC13#11532
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
208. C13#11532semidirect

Maximal subgroups

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

subgroupindex
#131131802
#131127822
#131127702
C4×C13×C4⋊Q82
#1153213