Finite Group Databasebeta

← #15777134

Subgroups — #15777134

Order 3328.

252 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 65 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#13117091C211yesmaximal, characteristic, complemented
2#13116655C211yesmaximal, characteristic, complemented
3#13114202C211yesmaximal, characteristic, complemented
4#13114188C211yesmaximal, characteristic
5#13112909C211yesmaximal, characteristic, complemented
6#13112886C211yesmaximal, characteristic, complemented
7C13×#1361C211yesmaximal, characteristic, complemented
8C13×#493C2211yescharacteristic
9C2×#88067—21no—
10C2×#88067—21no—
11#11718733—21no—
12C2×C16×D13—21no—
13#11718507—21no—
14#11718360C2211yescharacteristic
15C8×D52C2211yescharacteristic
16C13×C4⋊C16C2211yescharacteristic
17C13×#335C2211yescharacteristic
18#11718136—21no—
19#11718099—21no—
20#11718078—21no—
21C4×#6090C2211yescharacteristic
22#11718050C2211yescharacteristic
23C2×C13×D8—21no—
24C2×C13×D8—21no—
25C13×#127—21no—
26C2×#6104—41no—
27C2×Dic52—21no—
28C2×Dic52—21no—
29C2×C8×D13—21no—
30C4×D52D411yescharacteristic
31#88123—21no—
32C2×C13×C16—21no—
33C13×C4⋊C8—21no—
34C4×C8×C13C2311yescharacteristic
35#88072—41no—
36#88067—42no—
37#88067—42no—
38#88061—41no—
39#88060—21no—
40#88058—41no—
41C2×#6090D411yescharacteristic
42C2×#6090D411yescharacteristic
43C4⋊#1055—21no—
44C4⋊#1055D411yescharacteristic
45C16×D13—42no—
46#12432—131nomaximal, Sylow
47C2×D4×C13—41no—
48C2×D4×C13—41no—
49C2×D4×C13—41no—
50C2×D52D811yescharacteristic
51C2×C4×D13—21no—
52C2×Dic26—41no—
53C13×D8—41no—
54C13×D8—41no—
55C13×D8—81no—
56C2×C8×C13—41no—
57C2×C8×C13C2×D411yescharacteristic
58C2×C8×C13#4111yescharacteristic
59C42×C13C2×D411yescharacteristic
60#6104—82no—
61#6103—21no—
62C4⋊Dic13—41no—
63C4⋊Dic13—41no—
64C4⋊Dic13D811yescharacteristic
65C2×#1055—21no—
66C2×#1055—41no—
67Dic52—41no—
68Dic52—41no—
69Dic52—81no—
70C8×D13—41no—
71C8×D13—41no—
72C13×C16—41no—
73#6090—21no—
74#6090D812yescomplemented
75#2248—131no—
76D4×C16—131no—
77#1669—131no—
78#1667—131no—
79#1372—131no—
80#1362—131no—
81#1361D1311yescharacteristic, complemented
82C23×C13—81no—
83C22×D13—21no—
84D4×C13—81no—
85D4×C13—81no—
86D4×C13—81no—
87D4×C13—81no—
88D4×C13—161no—
89C2×C4×C13#12111yescharacteristic
90C2×C4×C13C2×D811yescharacteristic
91C2×C4×C13#13511yescharacteristic
92C2×Dic13—21no—
93C2×Dic13—81no—
94D52—21no—
95D52SD3212yescomplemented
96C4×D13—41no—
97C4×D13—41no—
98Dic26—81no—
99Dic26—81no—
100C8×C13—21no—
101C8×C13—81no—
102C8×C13C2×D811yescharacteristic
103C8×C13AGL(1,ℤ/8)11yescharacteristic
104#1055—41no—
105#1055—81no—
106C2×SD32—261no—
107C2×SD32—261no—
108C22×C16—261no—
109#494—131no—
110#493C2×D1311yescharacteristic
111#474—261no—
112#459—261no—
113C8×D4—131no—
114C4⋊C16C2×D1311yescharacteristic
115C22⋊C16—261no—
116C4×C16—131no—
117#335—131no—
118#335C2×D1311yescharacteristic
119#332—261no—
120#331—261no—
121C22×C13—161no—
122C22×C13—161no—
123C22×C13—161no—
124C22×C13#46611yescharacteristic
125C2×D13—22no—
126C2×D13—41no—
127C2×D13—41no—
128C4×C13—21no—
129C4×C13#45911yescharacteristic
130C4×C13#47211yescharacteristic
131C4×C13C2×SD3211yescharacteristic
132C4×C13#50811yescharacteristic
133Dic13—41no—
134Dic13—161no—
135C2×Q16—261no—
136C2×Q16—261no—
137C2×D8—21no—
138C2×D8—21no—
139C2×D8—521no—
140C22×C8—261no—
141C4⋊Q8—261no—
142#127—21no—
143C4×D4—131no—
144SD32—522no—
145SD32—522no—
146C2×C16—21no—
147C2×C16—131no—
148C2×C16—131no—
149C2×C16—522no—
150#107—521no—
151C4⋊C8—21no—
152C4⋊C8—131no—
153C4⋊C8—261no—
154#102—521no—
155#102—521no—
156C22⋊C8—261no—
157C4×C8C22×D1311yescharacteristic
158C2×C13—321no—
159C2×C13#166711yescharacteristic
160C2×C13#221711yescharacteristic
161C2×C13#222311yescharacteristic
162D13—42no—
163C2×Q8—521no—
164C2×D4—41no—
165C2×D4—41no—
166C2×D4—41no—
167C2×D4—131no—
168C22×C4—261no—
169Q16—521no—
170Q16—521no—
171Q16—1041no—
172D8—41no—
173D8—41no—
174D8—81no—
175D8—1042no—
176C2×C8—41no—
177C2×C8—261no—
178C2×C8—521no—
179C2×C8—521no—
180C2×C8—521no—
181C2×C8#612711yescharacteristic
182C2×C8D4×D1311yescharacteristic
183C4⋊C4—131no—
184C4⋊C4—521no—
185C4⋊C4—521no—
186C22⋊C4—261no—
187C42D4×D1311yescharacteristic
188C16—41no—
189C16—132no—
190C16—261no—
191C13#1243211yescharacteristic, complemented, Sylow
192C23—81no—
193C23—261no—
194Q8—1041no—
195Q8—1041no—
196D4—81no—
197D4—81no—
198D4—81no—
199D4—81no—
200D4—132no—
201D4—161no—
202D4—261no—
203C2×C4—261no—
204C2×C4—521no—
205C2×C4—521no—
206C2×C4—1041no—
207C2×C4#8813811yescharacteristic
208C2×C4D8×D1311yescharacteristic
209C2×C4#8817011yescharacteristic
210C8—21no—
211C8—81no—
212C8—521no—
213C8—1041no—
214C8D8×D1311yescharacteristic
215C8#8816811yescharacteristic
216C22—161no—
217C22—161no—
218C22—161no—
219C22—262no—
220C22—521no—
221C22—521no—
222C22#1171843611yescharacteristic
223C4—21no—
224C4—521no—
225C4—2081no—
226C4#1171841011yescharacteristic
227C4#1171844711yescharacteristic
228C4#1171857311yescharacteristic
229C4D13×SD3211yescharacteristic
230C2—321no—
231C2—522no—
232C2#1311419011yescharacteristic
233C2#1311693111yescharacteristic
234C2#1311696511yescharacteristic
subgroupG/H
centerC22#11718436
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1361C2
socleC22×C13#466
prime radical#13114188C2
hypercenter#1361D13
hypocenterC13#12432
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
1. #13117091C2semidirect
2. #13116655C2semidirect
3. #13114202C2semidirect
5. #13112909C2semidirect
6. #13112886C2semidirect
7. C13×#1361C2semidirect
74. #6090D8semidirect
81. #1361D13semidirect
95. D52SD32semidirect
191. C13#12432semidirect

Maximal subgroups

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

subgroupindex
#131170912
#131166552
#131142022
#131141882
#131129092
#131128862
C13×#13612
#1243213