Finite Group Databasebeta

← #15750141

Subgroups — #15750141

Order 3328.

322 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 75 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#13115635C211yesmaximal, characteristic
2#13113154C211yesmaximal, characteristic
3C13×#1459C211yesmaximal, characteristic
4C2×C4×D4×C13C2211yescharacteristic
5C2×C13×C22⋊C8—21no—
6C2×C22⋊#1055—21no—
7C2×C22⋊#1055—21no—
8C2×C22⋊#1055—21no—
9C2×C4⋊#1055C411yescharacteristic
10C2×#88043C411yescharacteristic
11C13×#324—21no—
12C13×#323C412yes—
13#11718120—21no—
14#11718117C412yes—
15C22×D4×C13Q811yescharacteristic
16C23×C4×C13D411yescharacteristic
17C23×C4×C13D411yescharacteristic
18C22×C8×C13—41no—
19C4×D4×C13—41no—
20C4×D4×C13—41no—
21C2×C13×C4⋊C4D411yescharacteristic
22C2×C13×C22⋊C4C2×C411yescharacteristic
23C2×C13×C22⋊C4C2×C411yescharacteristic
24C2×C42×C13C2×C411yescharacteristic
25C22×#1055—21no—
26C22×#1055—21no—
27C22×#1055—41no—
28C13×C22⋊C8—22no—
29C13×C22⋊C8—41no—
30C22⋊#1055—22no—
31C22⋊#1055—42no—
32C22⋊#1055—42no—
33C22⋊#1055—41no—
34C4⋊#1055—41no—
35#88043—41no—
36#7287—131nomaximal, Sylow
37C24×C13C4⋊C411yescharacteristic
38C24×C13C4⋊C411yescharacteristic
39C2×D4×C13—22no—
40C2×D4×C13—22no—
41C2×D4×C13—41no—
42C22×C4×C13—21no—
43C22×C4×C13—21no—
44C22×C4×C13—21no—
45C22×C4×C13—21no—
46C22×C4×C13—41no—
47C22×C4×C13—41no—
48C22×C4×C13—41no—
49C22×C4×C13—41no—
50C22×C4×C13C4211yescharacteristic
51C22×C4×C13C22⋊C411yescharacteristic
52C22×C4×C13C22⋊C411yescharacteristic
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C4⋊C411yescharacteristic
55C2×C8×C13—42no—
56C2×C8×C13—81no—
57C2×C8×C13—81no—
58C13×C4⋊C4—41no—
59C13×C22⋊C4—41no—
60C13×C22⋊C4—41no—
61C42×C13—21no—
62C42×C13—21no—
63C2×#1055—22no—
64C2×#1055—41no—
65C2×#1055—41no—
66C2×#1055—42no—
67C2×#1055—41no—
68C2×#1055—41no—
69C2×#1055—41no—
70C2×#1055—81no—
71C2×#1055—81no—
72#1955—131no—
73#1459—131no—
74#1459D1311yescharacteristic
75C23×C13—21no—
76C23×C13—21no—
77C23×C13—21no—
78C23×C13—21no—
79C23×C13—41no—
80C23×C13—41no—
81C23×C13—41no—
82C23×C13—41no—
83C23×C13#9511yescharacteristic
84C23×C13#10812yes—
85C23×C13#10812yes—
86D4×C13—44no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—41no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13—41no—
100C2×C4×C13—41no—
101C2×C4×C13—41no—
102C2×C4×C13—81no—
103C2×C4×C13—81no—
104C2×C4×C13#9911yescharacteristic
105C2×C4×C13#9911yescharacteristic
106C8×C13—82no—
107#1055—42no—
108#1055—82no—
109#1055—81no—
110C2×C4×D4C2×D1311yescharacteristic
111C2×C4⋊C8—131no—
112C2×C22⋊C8—21no—
113C2×C22⋊C8—261no—
114C2×C22⋊C8—261no—
115C2×C22⋊C8—261no—
116C2×#97—131no—
117#324—21no—
118#324—261no—
119#323—132no—
120#323Dic1312yes—
121C22×C13—21no—
122C22×C13—21no—
123C22×C13—22no—
124C22×C13—22no—
125C22×C13—42no—
126C22×C13—42no—
127C22×C13—41no—
128C22×C13—41no—
129C22×C13—41no—
130C22×C13—41no—
131C22×C13—81no—
132C22×C13—81no—
133C22×C13#34111yescharacteristic
134C22×C13#34111yescharacteristic
135C22×C13#34211yescharacteristic
136C4×C13—21no—
137C4×C13—41no—
138C4×C13—41no—
139C4×C13—41no—
140C4×C13—41no—
141C4×C13#35311yescharacteristic
142C4×C13#35411yescharacteristic
143C22×D4Dic2611yescharacteristic
144C23×C4D5211yescharacteristic
145C23×C4C22⋊D1311yescharacteristic
146C22×C8—41no—
147C22×C8—261no—
148C22×C8—261no—
149C22×C8—521no—
150C4×D4—41no—
151C4×D4—41no—
152C2×C4⋊C4C22⋊D1311yescharacteristic
153C2×C22⋊C4C4×D1311yescharacteristic
154C2×C22⋊C4C2×Dic1311yescharacteristic
155C2×C42C4×D1311yescharacteristic
156C4⋊C8—521no—
157C22⋊C8—22no—
158C22⋊C8—41no—
159C22⋊C8—262no—
160C22⋊C8—522no—
161C22⋊C8—522no—
162C22⋊C8—521no—
163#97—521no—
164C2×C13—21no—
165C2×C13—21no—
166C2×C13—42no—
167C2×C13—42no—
168C2×C13#129811yescharacteristic
169C2×C13#139211yescharacteristic
170C2×C13#139311yescharacteristic
171C24#610111yescharacteristic
172C24C4⋊Dic1311yescharacteristic
173C2×D4—22no—
174C2×D4—22no—
175C2×D4—41no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4C4×Dic1311yescharacteristic
185C22×C4#610111yescharacteristic
186C22×C4#610311yescharacteristic
187C22×C4#610311yescharacteristic
188C22×C4C22⋊Dic1311yescharacteristic
189C2×C8—42no—
190C2×C8—81no—
191C2×C8—81no—
192C2×C8—262no—
193C2×C8—521no—
194C2×C8—521no—
195C2×C8—522no—
196C2×C8—521no—
197C2×C8—521no—
198C2×C8—521no—
199C2×C8—1041no—
200C2×C8—1041no—
201C4⋊C4—41no—
202C22⋊C4—41no—
203C22⋊C4—41no—
204C42—21no—
205C42—21no—
206C13#728711yescharacteristic, complemented, Sylow
207C23—21no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—41no—
212C23—41no—
213C23—41no—
214C23—41no—
215C23#8805912yes—
216C23#8806212yes—
217C23#8807111yescharacteristic
218D4—44no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—81no—
235C2×C4—81no—
236C2×C4#8804611yescharacteristic
237C2×C4#8804611yescharacteristic
238C8—82no—
239C8—522no—
240C8—1042no—
241C8—1041no—
242C22—21no—
243C22—21no—
244C22—22no—
245C22—22no—
246C22—42no—
247C22—42no—
248C22—41no—
249C22—41no—
250C22—41no—
251C22—41no—
252C22—81no—
253C22—81no—
254C22#1171811911yescharacteristic
255C22#1171814411yescharacteristic
256C22#1171815011yescharacteristic
257C4—21no—
258C4—41no—
259C4—41no—
260C4—41no—
261C4—41no—
262C4#1171806511yescharacteristic
263C4#1171806611yescharacteristic
264C2—21no—
265C2—21no—
266C2—42no—
267C2—42no—
268C2#1311272411yescharacteristic
269C2#1311295811yescharacteristic
270C2#1311296011yescharacteristic
subgroupG/H
centerC2×C4#88046
commutatorC22×C4×C13C42
FrattiniC2×C4×D4C2×D13
FittingC13×#1459C2
socleC22×C13#342
prime radicalC22×D4×C13Q8
cosocleC2×C4×D4×C13C22
hypercenter#1459D13
hypocenterC13#7287
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
206. C13#7287semidirect

Maximal subgroups

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

subgroupindex
#131156352
#131131542
C13×#14592
#728713