Finite Group Databasebeta

← #15776141

Subgroups — #15776141

Order 3328.

344 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 67 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#13125611C211yesmaximal, characteristic
2#13117038C212yesmaximal, complemented
3#13112847C212yesmaximal, complemented
4#13112760C211yesmaximal, characteristic
5C13×#2076C211yesmaximal, characteristic
6C2×#88178—21no—
7C2×C13×#107C2211yescharacteristic
8C2×C13×C22⋊C8C2211yescharacteristic
9C13×#380—21no—
10#11718777—21no—
11#11718777C2212yes—
12#11718400—22no—
13#11718383—22no—
14C13×#340—21no—
15C13×#340C2211yescharacteristic
16C22⋊#6090C2212yes—
17#11718084—22no—
18#11718081—22no—
19C23×C4×C13D411yescharacteristic
20C22×Dic26—21no—
21C22×C8×C13D411yescharacteristic
22C22×C8×C13C2311yescharacteristic
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C22⋊C4—41no—
26C2×C22⋊Dic13—41no—
27C2×C4⋊Dic13—21no—
28#88178—22no—
29#88178—22no—
30#88178—41no—
31#88178—41no—
32C2×#6101—41no—
33C2×Dic52—21no—
34C2×Dic52D412yes—
35C13×#107—22no—
36C13×C22⋊C8—22no—
37C13×#95—41no—
38#88058—21no—
39#88058D412yes—
40#88056—22no—
41#88056—22no—
42C2×#6090—22no—
43#12282—131nomaximal, Sylow
44C24×C13D811yescharacteristic
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13—41no—
48C22×C4×C13—41no—
49C22×C4×C13—41no—
50C22×C4×C13—41no—
51C22×C4×C13D811yescharacteristic
52C22×C4×C13C2×D411yescharacteristic
53C22×Dic13—41no—
54C22×Dic13—41no—
55C2×Dic26—22no—
56C2×Dic26—41no—
57C2×Dic26—81no—
58C2×Dic26—81no—
59C2×C8×C13—21no—
60C2×C8×C13—41no—
61C2×C8×C13—41no—
62C2×C8×C13C2×D412yes—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—41no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—41no—
67C13×C22⋊C4—82no—
68C22⋊Dic13—42no—
69C22⋊Dic13—42no—
70C4⋊Dic13—22no—
71C4⋊Dic13—41no—
72#6101—42no—
73#6101—42no—
74Dic52—42no—
75Dic52—81no—
76#6090—42no—
77#3189—131no—
78#2236—132no—
79#2076D1311yescharacteristic
80#1348—132no—
81#1314—131no—
82C23×C13—21no—
83C23×C13—21no—
84C23×C13—41no—
85C23×C13—41no—
86C23×C13Q3212yes—
87C23×C13C2×D811yescharacteristic
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—41no—
92C2×C4×C13—41no—
93C2×C4×C13—41no—
94C2×C4×C13—81no—
95C2×C4×C13—81no—
96C2×C4×C13—81no—
97C2×C4×C13—81no—
98C2×C4×C13—81no—
99C2×C4×C13—81no—
100C2×C4×C13—81no—
101C2×C4×C13#12011yescharacteristic
102C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
103C2×Dic13—42no—
104C2×Dic13—42no—
105C2×Dic13—82no—
106C2×Dic13—82no—
107Dic26—42no—
108Dic26—42no—
109Dic26—82no—
110C8×C13—22no—
111C8×C13—41no—
112C2×C22⋊Q8—261no—
113#484—262no—
114#467—132no—
115#467—261no—
116#451—262no—
117C2×#107C2×D1311yescharacteristic
118C2×C22⋊C8C2×D1311yescharacteristic
119#380—21no—
120#366—262no—
121#358—262no—
122C22⋊C16—132no—
123#340—21no—
124#340C2×D1311yescharacteristic
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—161no—
138C4×C13—161no—
139C4×C13#45511yescharacteristic
140C4×C13#45811yescharacteristic
141Dic13—82no—
142Dic13—82no—
143C22×Q8—261no—
144C23×C4C22⋊D1311yescharacteristic
145C2×Q16—132no—
146C2×Q16—261no—
147C22×C8C22⋊D1311yescharacteristic
148C22×C8C22×D1311yescharacteristic
149C22⋊Q8—262no—
150C22⋊Q8—262no—
151C22⋊Q8—521no—
152C22⋊Q8—521no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—261no—
156C2×C4⋊C4—521no—
157C2×C22⋊C4—41no—
158C2×C22⋊C4—521no—
159C2×C16—262no—
160#107—22no—
161#107—132no—
162#107—261no—
163#103—262no—
164#103—262no—
165C22⋊C8—22no—
166#95—41no—
167C2×C13—21no—
168C2×C13—21no—
169C2×C13—42no—
170C2×C13#160711yescharacteristic
171C2×C13#218811yescharacteristic
172C2×C13#219011yescharacteristic
173C24#610411yescharacteristic
174C2×Q8—262no—
175C2×Q8—521no—
176C2×Q8—1041no—
177C2×Q8—1041no—
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—522no—
189Q16—1041no—
190C2×C8—21no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8D4×D1312yes—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—262no—
199C4⋊C4—521no—
200C4⋊C4—522no—
201C4⋊C4—522no—
202C22⋊C4—82no—
203C22⋊C4—522no—
204C22⋊C4—522no—
205C16—522no—
206C13#1228211yescharacteristic, complemented, Sylow
207C23—21no—
208C23—21no—
209C23—41no—
210C23—41no—
211C23#8806912yes—
212C23C2×#610411yescharacteristic
213Q8—522no—
214Q8—522no—
215Q8—1042no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—81no—
223C2×C4—81no—
224C2×C4—81no—
225C2×C4—81no—
226C2×C4—81no—
227C2×C4—81no—
228C2×C4—81no—
229C2×C4—522no—
230C2×C4—522no—
231C2×C4—1042no—
232C2×C4—1042no—
233C2×C4#8819111yescharacteristic
234C2×C4#8820311yescharacteristic
235C8—22no—
236C8—41no—
237C22—21no—
238C22—21no—
239C22—22no—
240C22—42no—
241C22—41no—
242C22—41no—
243C22—81no—
244C22#1171869711yescharacteristic
245C22C2×#8806911yescharacteristic
246C22#1171885611yescharacteristic
247C4—21no—
248C4—41no—
249C4—161no—
250C4—161no—
251C4—1042no—
252C4—1042no—
253C4#1171871411yescharacteristic
254C4#1171872211yescharacteristic
255C2—21no—
256C2—21no—
257C2—42no—
258C2#1311382111yescharacteristic
259C2#1311676911yescharacteristic
260C2#1311678111yescharacteristic
subgroupG/H
centerC22#11718697
commutator, cosocleC22×C8×C13C23
FrattiniC22×C8C22×D13
FittingC13×#2076C2
socleC22×C13#447
prime radicalC24×C13D8
hypercenter#2076D13
hypocenterC13#12282
LCSG ▷ C22×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #2076

Complements

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

NH ≅ G/Ntype
2. #13117038C2semidirect
3. #13112847C2semidirect
206. C13#12282semidirect

Maximal subgroups

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

subgroupindex
#131256112
#131170382
#131128472
#131127602
C13×#20762
#1228213