Finite Group Databasebeta

← #15776142

Subgroups — #15776142

Order 3328.

344 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 71 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#13117036C212yesmaximal, complemented
2#13116264C211yesmaximal, characteristic
3#13112848C212yesmaximal, complemented
4#13112760C211yesmaximal, characteristic
5C13×#3189C211yesmaximal, characteristic
6C2×C13×C22⋊Q8—21no—
7C13×#484—22no—
8C13×#467—21no—
9C13×#467C2212yes—
10C13×#451—22no—
11C2×C13×C22⋊C8C2211yescharacteristic
12#11718873—21no—
13C2×#88058C2211yescharacteristic
14#11718156—22no—
15#11718143—21no—
16#11718143C2211yescharacteristic
17C22⋊#6090C2212yes—
18#11718081—22no—
19C22×Q8×C13—21no—
20C23×C4×C13D411yescharacteristic
21C2×C13×Q16—21no—
22C2×C13×Q16D412yes—
23C22×C8×C13D411yescharacteristic
24C22×C8×C13C2311yescharacteristic
25C13×C22⋊Q8—22no—
26C13×C22⋊Q8—22no—
27C13×C22⋊Q8—41no—
28C13×C22⋊Q8—41no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—41no—
31C2×C13×C22⋊C4—41no—
32C2×C22⋊Dic13—41no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C13×#107—21no—
36C13×#107D412yes—
37C13×#103—22no—
38C13×#103—22no—
39C13×C22⋊C8—22no—
40#88071—41no—
41#88058—22no—
42C2×#6090—22no—
43#12282—131nomaximal, Sylow
44C24×C13D811yescharacteristic
45C2×Q8×C13—22no—
46C2×Q8×C13—41no—
47C2×Q8×C13—81no—
48C2×Q8×C13—81no—
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13—41no—
52C22×C4×C13—41no—
53C22×C4×C13—41no—
54C22×C4×C13—41no—
55C22×C4×C13D811yescharacteristic
56C22×C4×C13C2×D411yescharacteristic
57C22×Dic13—41no—
58C22×Dic13—41no—
59C13×Q16—42no—
60C13×Q16—81no—
61C2×C8×C13—21no—
62C2×C8×C13—41no—
63C2×C8×C13—41no—
64C2×C8×C13C2×D412yes—
65C13×C4⋊C4—22no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—42no—
68C13×C4⋊C4—42no—
69C13×C22⋊C4—42no—
70C13×C22⋊C4—42no—
71C22⋊Dic13—82no—
72C4⋊Dic13—41no—
73C4⋊Dic13—41no—
74C4⋊Dic13—41no—
75C4⋊Dic13—41no—
76#6090—42no—
77#3189D1311yescharacteristic
78#2236—132no—
79#2076—131no—
80#1348—132no—
81#1314—131no—
82C23×C13—21no—
83C23×C13—21no—
84C23×C13—41no—
85C23×C13—41no—
86C23×C13Q3212yes—
87C23×C13C2×D811yescharacteristic
88Q8×C13—42no—
89Q8×C13—42no—
90Q8×C13—82no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13—41no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—81no—
100C2×C4×C13—82no—
101C2×C4×C13—82no—
102C2×C4×C13#12011yescharacteristic
103C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
104C2×Dic13—81no—
105C2×Dic13—81no—
106C2×Dic13—81no—
107C2×Dic13—81no—
108C2×Dic13—81no—
109C2×Dic13—81no—
110C8×C13—22no—
111C8×C13—41no—
112C2×C22⋊Q8—21no—
113#484—22no—
114#467—21no—
115#467C2×D1312yes—
116#451—22no—
117C2×#107—131no—
118C2×C22⋊C8C2×D1311yescharacteristic
119#380—261no—
120#366—262no—
121#358—262no—
122C22⋊C16—132no—
123#340—131no—
124#340—261no—
125C22×C13—21no—
126C22×C13—21no—
127C22×C13—22no—
128C22×C13—42no—
129C22×C13—41no—
130C22×C13—41no—
131C22×C13—81no—
132C22×C13#44711yescharacteristic
133C22×C13C2×Q3211yescharacteristic
134C22×C13#51011yescharacteristic
135C4×C13—21no—
136C4×C13—41no—
137C4×C13—82no—
138C4×C13—82no—
139C4×C13#45511yescharacteristic
140C4×C13#45811yescharacteristic
141Dic13—161no—
142Dic13—161no—
143C22×Q8—21no—
144C23×C4C22⋊D1311yescharacteristic
145C2×Q16—21no—
146C2×Q16C22⋊D1312yes—
147C22×C8C22⋊D1311yescharacteristic
148C22×C8C22×D1311yescharacteristic
149C22⋊Q8—22no—
150C22⋊Q8—22no—
151C22⋊Q8—41no—
152C22⋊Q8—41no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4—261no—
156C2×C4⋊C4—261no—
157C2×C22⋊C4—41no—
158C2×C22⋊C4—521no—
159C2×C16—262no—
160#107—21no—
161#107—262no—
162#107C22⋊D1312yes—
163#103—22no—
164#103—22no—
165C22⋊C8—22no—
166#95—521no—
167C2×C13—21no—
168C2×C13—21no—
169C2×C13—42no—
170C2×C13#160711yescharacteristic
171C2×C13#218811yescharacteristic
172C2×C13#219011yescharacteristic
173C24#610411yescharacteristic
174C2×Q8—22no—
175C2×Q8—41no—
176C2×Q8—81no—
177C2×Q8—81no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—521no—
185C22×C4—521no—
186C22×C4#610411yescharacteristic
187C22×C4C2×C22⋊D1311yescharacteristic
188Q16—42no—
189Q16—81no—
190C2×C8—21no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8C2×C22⋊D1312yes—
194C4⋊C4—22no—
195C4⋊C4—41no—
196C4⋊C4—42no—
197C4⋊C4—42no—
198C4⋊C4—521no—
199C4⋊C4—521no—
200C4⋊C4—521no—
201C4⋊C4—521no—
202C22⋊C4—42no—
203C22⋊C4—42no—
204C22⋊C4—1042no—
205C16—522no—
206C13#1228211yescharacteristic, complemented, Sylow
207C23—21no—
208C23—21no—
209C23—41no—
210C23—41no—
211C23#8806912yes—
212C23C2×#610411yescharacteristic
213Q8—42no—
214Q8—42no—
215Q8—82no—
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—81no—
225C2×C4—82no—
226C2×C4—82no—
227C2×C4—1041no—
228C2×C4—1041no—
229C2×C4—1041no—
230C2×C4—1041no—
231C2×C4—1041no—
232C2×C4—1041no—
233C2×C4#8818611yescharacteristic
234C2×C4#8820711yescharacteristic
235C8—22no—
236C8—41no—
237C22—21no—
238C22—21no—
239C22—22no—
240C22—42no—
241C22—41no—
242C22—41no—
243C22—81no—
244C22#1171884011yescharacteristic
245C22C2×#8806911yescharacteristic
246C22#1171887811yescharacteristic
247C4—21no—
248C4—41no—
249C4—82no—
250C4—82no—
251C4—2081no—
252C4—2081no—
253C4#1171890311yescharacteristic
254C4#1171890411yescharacteristic
255C2—21no—
256C2—21no—
257C2—42no—
258C2#1311382211yescharacteristic
259C2#1311677011yescharacteristic
260C2#1311678211yescharacteristic
subgroupG/H
centerC22#11718878
commutator, cosocleC22×C8×C13C23
FrattiniC22×C8C22×D13
FittingC13×#3189C2
socleC22×C13#447
prime radicalC24×C13D8
hypercenter#3189D13
hypocenterC13#12282
LCSG ▷ C22×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #3189

Complements

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

NH ≅ G/Ntype
1. #13117036C2semidirect
3. #13112848C2semidirect
206. C13#12282semidirect

Maximal subgroups

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

subgroupindex
#131170362
#131162642
#131128482
#131127602
C13×#31892
#1228213