Finite Group Databasebeta

← #15772584

Subgroups — #15772584

Order 3328.

358 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 95 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#13113180C211yesmaximal, characteristic
2#13113160C211yesmaximal, characteristic
3#13112780C214yesmaximal
4C13×#2568C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C13×#400—21no—
8C13×#400—21no—
9C13×#391—21no—
10C13×#391—21no—
11C13×#391C412yes—
12C13×#382C2212yes—
13C4×C13×C4⋊C4C411yescharacteristic
14#11718587—21no—
15#11718586—21no—
16#11718120—21no—
17#11718120—21no—
18#11718120C2212yes—
19#11718120C2212yes—
20C22×Q8×C13—21no—
21C22×Q8×C13C2×C411yescharacteristic
22C13×C4⋊Q8—41no—
23C13×C4⋊Q8—41no—
24C4×Q8×C13—41no—
25C4×Q8×C13—41no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4C2×C412yes—
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C4⋊C4C2311yescharacteristic
32C2×C42×C13C2×C412yes—
33C2×C42×C13C2×C411yescharacteristic
34C2×C42×C13D411yescharacteristic
35C2×C42×C13D411yescharacteristic
36C13×#95—21no—
37C13×#95—22no—
38C13×#95—22no—
39C13×#95—22no—
40C13×#95—22no—
41C22⋊#1055—22no—
42C22⋊#1055—22no—
43C4⋊#1055—41no—
44C4⋊#1055—41no—
45#88043—41no—
46C4×#1055—41no—
47#11573—131nomaximal, Sylow
48C2×Q8×C13—22no—
49C2×Q8×C13—22no—
50C2×Q8×C13—41no—
51C2×Q8×C13—44no—
52C2×Q8×C13—41no—
53C2×Q8×C13—41no—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22×C411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C13×C4⋊C4—41no—
64C13×C4⋊C4—41no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—42no—
67C13×C4⋊C4—42no—
68C13×C4⋊C4—42no—
69C42×C13—21no—
70C42×C13—21no—
71C42×C13—21no—
72C42×C13—21no—
73C42×C13—21no—
74C42×C13—21no—
75C42×C13—24no—
76C2×#1055—42no—
77C2×#1055—42no—
78#2568D1311yescharacteristic
79#1467—131no—
80#1461—131no—
81#1324—134no—
82C23×C13C2×C22⋊C411yescharacteristic
83Q8×C13—44no—
84Q8×C13—82no—
85Q8×C13—82no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—22no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13—41no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—44no—
103C2×C4×C13—42no—
104C2×C4×C13—42no—
105C2×C4×C13#9911yescharacteristic
106C2×C4×C13#9911yescharacteristic
107C2×C4×C13#10112yes—
108C2×C4×C13#13112yes—
109#1055—82no—
110#1055—82no—
111C2×C4⋊Q8Dic1311yescharacteristic
112C2×C4×Q8C2×D1311yescharacteristic
113#432—261no—
114#431—261no—
115#400—21no—
116#400—21no—
117#391—21no—
118#391—21no—
119#391Dic1312yes—
120#382C2×D1312yes—
121C4×C4⋊C4Dic1311yescharacteristic
122#324—132no—
123#324—132no—
124#324—261no—
125#324—261no—
126C22×C13—21no—
127C22×C13—21no—
128C22×C13#40811yescharacteristic
129C22×C13C2×#9911yescharacteristic
130C22×C13C2×#10111yescharacteristic
131C4×C13—21no—
132C4×C13—22no—
133C4×C13—22no—
134C4×C13—41no—
135C4×C13—41no—
136C4×C13—41no—
137C4×C13—41no—
138C4×C13—82no—
139C4×C13—82no—
140C4×C13#35512yes—
141C22×Q8—21no—
142C22×Q8C2×Dic1311yescharacteristic
143C4⋊Q8—41no—
144C4⋊Q8—41no—
145C4×Q8—41no—
146C4×Q8—41no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4C2×Dic1312yes—
150C2×C4⋊C4C22⋊D1311yescharacteristic
151C2×C4⋊C4C22⋊D1311yescharacteristic
152C2×C4⋊C4C22×D1311yescharacteristic
153C2×C42C2×Dic1312yes—
154C2×C42C2×Dic1311yescharacteristic
155C2×C42C22⋊D1311yescharacteristic
156C2×C42C22⋊D1311yescharacteristic
157C4⋊C8—521no—
158C4⋊C8—521no—
159C22⋊C8—262no—
160C22⋊C8—262no—
161#97—521no—
162C4×C8—521no—
163#95—21no—
164#95—22no—
165#95—22no—
166#95—22no—
167#95—22no—
168C2×C13—21no—
169C2×C13—21no—
170C2×C13#147211yescharacteristic
171C2×C13#212911yescharacteristic
172C2×C13C2×#35511yescharacteristic
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—41no—
176C2×Q8—44no—
177C2×Q8—41no—
178C2×Q8—41no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4C22⋊Dic1311yescharacteristic
182C22×C4C22⋊Dic1311yescharacteristic
183C22×C4C22⋊Dic1311yescharacteristic
184C22×C4C22⋊Dic1311yescharacteristic
185C22×C4C22×Dic1311yescharacteristic
186C22×C4C2×C22⋊D1311yescharacteristic
187C22×C4C2×C22⋊D1311yescharacteristic
188C2×C8—522no—
189C2×C8—522no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C42—21no—
197C42—21no—
198C42—21no—
199C42—21no—
200C42—21no—
201C42—21no—
202C42—24no—
203C13#1157311yescharacteristic, complemented, Sylow
204C23C2×C22⋊Dic1311yescharacteristic
205Q8—44no—
206Q8—82no—
207Q8—82no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—44no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4#8807411yescharacteristic
228C2×C4#8807411yescharacteristic
229C2×C4#8807612yes—
230C2×C4#8820212yes—
231C8—1042no—
232C8—1042no—
233C22—21no—
234C22—21no—
235C22C2×#8807411yescharacteristic
236C22C2×#8807611yescharacteristic
237C22#1171889511yescharacteristic
238C4—21no—
239C4—22no—
240C4—22no—
241C4—41no—
242C4—41no—
243C4—41no—
244C4—41no—
245C4—82no—
246C4—82no—
247C4#1171813412yes—
248C2—21no—
249C2—21no—
250C2#1311320011yescharacteristic
251C2#1311651111yescharacteristic
252C2C2×#1171813411yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2568C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2568D13
hypocenterC13#11573
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2568

Complements

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

NH ≅ G/Ntype
203. C13#11573semidirect

Maximal subgroups

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

subgroupindex
#131131802
#131131602
#131127802
C13×#25682
#1157313