Finite Group Databasebeta

← #15777152

Subgroups — #15777152

Order 3328.

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

normal subgroups only

This group has 246 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#13117092C211yesmaximal, characteristic, complemented
2#13114201C211yesmaximal, characteristic, complemented
3#13114191C211yesmaximal, characteristic
4#13112908C211yesmaximal, characteristic, complemented
5#13112886C211yesmaximal, characteristic, complemented
6#13112883C211yesmaximal, characteristic, complemented
7C13×#2169C211yesmaximal, characteristic, complemented
8C2×C13×M32—21no—
9C8×D4×C13C2211yescharacteristic
10#11718676—21no—
11#11718668—21no—
12C2×#88040—21no—
13C2×#88040—21no—
14#11718360C2211yescharacteristic
15#11718356C2211yescharacteristic
16C13×C4⋊C16C2211yescharacteristic
17C13×C22⋊C16—21no—
18C4×C13×C16C2211yescharacteristic
19#11718077—21no—
20#11718074—21no—
21#11718050C2211yescharacteristic
22#11718050C2211yescharacteristic
23C22×C8×C13—21no—
24C4×D4×C13D411yescharacteristic
25C2×#6104—41no—
26C2×Dic52—21no—
27C2×Dic52—21no—
28C2×D104—21no—
29C2×D104—21no—
30#88128—21no—
31#88123—21no—
32C13×M32—42no—
33C2×C13×C16—21no—
34C2×C13×C16D411yescharacteristic
35C2×C13×C16D411yescharacteristic
36C13×C4⋊C8D411yescharacteristic
37C13×C22⋊C8—21no—
38C4×C8×C13C2311yescharacteristic
39#88072—41no—
40#88049—41no—
41#88047—41no—
42C4⋊#1055—21no—
43C4⋊#1055—21no—
44#88040—42no—
45#88040—42no—
46#12435—131nomaximal, Sylow
47C2×D4×C13D811yescharacteristic
48C22×C4×C13—21no—
49C2×D52—41no—
50C2×D52—41no—
51C2×D52—41no—
52C2×Dic26—41no—
53C2×C8×C13—21no—
54C2×C8×C13—41no—
55C2×C8×C13—41no—
56C2×C8×C13C2×D411yescharacteristic
57C2×C8×C13#4111yescharacteristic
58C13×C4⋊C4D811yescharacteristic
59C13×C22⋊C4—21no—
60C42×C13C2×D411yescharacteristic
61#6104—82no—
62C4⋊Dic13—41no—
63C4⋊Dic13—41no—
64C2×#1055—41no—
65C2×#1055—41no—
66Dic52—41no—
67Dic52—41no—
68Dic52—81no—
69D104—41no—
70D104—41no—
71D104—81no—
72C13×C16—21no—
73C13×C16—41no—
74C13×C16D812yescomplemented
75#2248—131no—
76#2169D1311yescharacteristic, complemented
77#1669—131no—
78#1667—131no—
79#1371—131no—
80#1362—131no—
81#1361—131no—
82C23×C13—21no—
83C22×D13—81no—
84D4×C13—21no—
85D4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—41no—
88C2×C4×C13—41no—
89C2×C4×C13#12111yescharacteristic
90C2×C4×C13C2×D811yescharacteristic
91C2×C4×C13#13511yescharacteristic
92C2×Dic13—81no—
93D52—81no—
94D52—81no—
95D52—81no—
96D52—81no—
97D52—161no—
98Dic26—81no—
99Dic26—81no—
100C8×C13—21no—
101C8×C13—41no—
102C8×C13C2×D811yescharacteristic
103C8×C13AGL(1,ℤ/8)11yescharacteristic
104#1055—81no—
105#1055—81no—
106C2×SD32—261no—
107C2×SD32—261no—
108C2×M32—21no—
109#494—131no—
110#493—131no—
111#474—261no—
112#459—261no—
113C8×D4C2×D1311yescharacteristic
114C4⋊C16C2×D1311yescharacteristic
115C22⋊C16—21no—
116C4×C16C2×D1311yescharacteristic
117#335—131no—
118#335—131no—
119#332—261no—
120#331—261no—
121C22×C13—41no—
122C22×C13—41no—
123C22×C13—41no—
124C22×C13#46611yescharacteristic
125C2×D13—161no—
126C2×D13—161no—
127C2×D13—161no—
128C4×C13—21no—
129C4×C13—41no—
130C4×C13#45911yescharacteristic
131C4×C13#47211yescharacteristic
132C4×C13#50911yescharacteristic
133C4×C13#51011yescharacteristic
134Dic13—161no—
135C2×Q16—261no—
136C2×Q16—261no—
137C2×D8—261no—
138C2×D8—261no—
139C2×D8—521no—
140C22×C8—21no—
141C4⋊Q8—261no—
142#127—261no—
143C4×D4D5211yescharacteristic
144SD32—522no—
145SD32—522no—
146M32—42no—
147C2×C16—21no—
148C2×C16C22⋊D1311yescharacteristic
149C2×C16C22⋊D1311yescharacteristic
150#107—521no—
151C4⋊C8—261no—
152C4⋊C8—261no—
153C4⋊C8D5211yescharacteristic
154#102—521no—
155#102—521no—
156C22⋊C8—21no—
157C4×C8C22×D1311yescharacteristic
158C2×C13—81no—
159C2×C13#166711yescharacteristic
160C2×C13#222011yescharacteristic
161C2×C13#222311yescharacteristic
162D13—321no—
163C2×Q8—521no—
164C2×D4—521no—
165C2×D4—521no—
166C2×D4—521no—
167C2×D4D10411yescharacteristic
168C22×C4—21no—
169Q16—521no—
170Q16—521no—
171Q16—1041no—
172D8—521no—
173D8—521no—
174D8—1041no—
175D8—1042no—
176C2×C8—21no—
177C2×C8—41no—
178C2×C8—41no—
179C2×C8—521no—
180C2×C8—521no—
181C2×C8#612711yescharacteristic
182C2×C8C2×C22⋊D1311yescharacteristic
183C4⋊C4—521no—
184C4⋊C4—521no—
185C4⋊C4D10411yescharacteristic
186C22⋊C4—21no—
187C42C2×D5211yescharacteristic
188C16—21no—
189C16—41no—
190C16#610412yescomplemented
191C13#1243511yescharacteristic, complemented, Sylow
192C23—21no—
193C23—1041no—
194Q8—1041no—
195Q8—1041no—
196D4—21no—
197D4—21no—
198D4—1041no—
199D4—1041no—
200D4—1041no—
201D4—1041no—
202D4—2081no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—1041no—
207C2×C4C2×D10411yescharacteristic
208C2×C4#8815811yescharacteristic
209C2×C4#8818411yescharacteristic
210C8—21no—
211C8—41no—
212C8—1041no—
213C8—1041no—
214C8C2×#610411yescharacteristic
215C8#8820311yescharacteristic
216C22—41no—
217C22—41no—
218C22—41no—
219C22—2081no—
220C22—2081no—
221C22—2081no—
222C22#1171877611yescharacteristic
223C4—21no—
224C4—41no—
225C4—2081no—
226C4#1171856911yescharacteristic
227C4#1171857011yescharacteristic
228C4#1171867611yescharacteristic
229C4#1171880311yescharacteristic
230C2—81no—
231C2—4161no—
232C2#1311419111yescharacteristic
233C2#1311694911yescharacteristic
234C2#1311696611yescharacteristic
subgroupG/H
centerC22#11718776
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#2169C2
socleC22×C13#466
prime radical#13114191C2
hypercenter#2169D13
hypocenterC13#12435
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #2169

Complements

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

NH ≅ G/Ntype
1. #13117092C2semidirect
2. #13114201C2semidirect
4. #13112908C2semidirect
5. #13112886C2semidirect
6. #13112883C2semidirect
7. C13×#2169C2semidirect
74. C13×C16D8semidirect
76. #2169D13semidirect
190. C16#6104semidirect
191. C13#12435semidirect

Maximal subgroups

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

subgroupindex
#131170922
#131142012
#131141912
#131129082
#131128862
#131128832
C13×#21692
#1243513