Finite Group Databasebeta

← #15776796

Subgroups — #15776796

Order 3328.

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

normal subgroups only

This group has 288 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#13127841C211yesmaximal, characteristic
2#13117065C211yesmaximal, characteristic
3#13114227C211yesmaximal, characteristic
4#13112886C211yesmaximal, characteristic
5#13112814C211yesmaximal, characteristic
6#13112800C211yesmaximal, characteristic
7C13×#2225C211yesmaximal, characteristic
8#11719272—21no—
9C13×#500C2211yescharacteristic
10C4×C13×Q16C2211yescharacteristic
11#11718842—21no—
12#11718751—21no—
13#11718692—21no—
14#11718534—21no—
15#11718454—22no—
16#11718360C2211yescharacteristic
17C8×Dic26C2211yescharacteristic
18C13×#367—21no—
19C13×C4⋊C16C2211yescharacteristic
20C13×#358—21no—
21#11718139—21no—
22#11718084—22no—
23C4×#6090C2211yescharacteristic
24#11718050C2211yescharacteristic
25C2×C13×Q16D411yescharacteristic
26C13×C4⋊Q8—21no—
27C4×Q8×C13—21no—
28#88198—22no—
29C2×#6107—22no—
30C2×#6107—41no—
31C2×Dic52—21no—
32C2×Dic52D412yes—
33#88143—42no—
34#88141—22no—
35#88124—41no—
36#88123—21no—
37C4×Dic26—41no—
38C4×Dic26D411yescharacteristic
39C2×C13×C16—21no—
40C13×#107—21no—
41C13×#107—21no—
42C13×#107D411yescharacteristic
43C13×#103—21no—
44C4×C8×C13C2311yescharacteristic
45#88075—41no—
46#88054—21no—
47C8×Dic13—21no—
48C2×#6090—21no—
49#88050—22no—
50C4⋊#1055—21no—
51C4⋊#1055D411yescharacteristic
52#12382—131nomaximal, Sylow
53C2×Q8×C13—21no—
54C2×Q8×C13—41no—
55C2×Dic26—22no—
56C2×Dic26D811yescharacteristic
57C13×Q16—21no—
58C13×Q16—21no—
59C2×C8×C13C2×D411yescharacteristic
60C2×C8×C13C2×D411yescharacteristic
61C13×C4⋊C4—21no—
62C13×C4⋊C4—41no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—41no—
65C42×C13—41no—
66C42×C13C2×D411yescharacteristic
67#6107—82no—
68#6107—82no—
69C4⋊Dic13—41no—
70C4⋊Dic13—41no—
71C4⋊Dic13D811yescharacteristic
72#6101—21no—
73#6101—42no—
74#6101—42no—
75#6101—42no—
76C4×Dic13—21no—
77C4×Dic13—42no—
78C2×#1055—21no—
79C2×#1055—41no—
80Dic52—42no—
81Dic52—41no—
82Dic52—41no—
83C13×C16—41no—
84#6090—41no—
85#3395—131no—
86#2241—131no—
87#2225D1311yescharacteristic
88#1674—131no—
89#1362—131no—
90Q8⋊C16—131no—
91#1332—131no—
92Q8×C13—41no—
93Q8×C13—41no—
94Q8×C13—81no—
95Q8×C13—81no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13—81no—
99C2×C4×C13#12011yescharacteristic
100C2×C4×C13C2×D811yescharacteristic
101C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
102C2×Dic13—21no—
103C2×Dic13—21no—
104C2×Dic13—42no—
105Dic26—21no—
106Dic26—42no—
107Dic26—42no—
108Dic26SD3212yes—
109C8×C13—21no—
110C8×C13#13511yescharacteristic
111C8×C13#13711yescharacteristic
112#1055—41no—
113#1055—81no—
114#557—261no—
115#500C2×D1311yescharacteristic
116#494—131no—
117#494—261no—
118#462—262no—
119#462—261no—
120#462—261no—
121C8×Q8—131no—
122C4×Q16—261no—
123C4×Q16C2×D1311yescharacteristic
124#367—21no—
125C4⋊C16C2×D1311yescharacteristic
126#358—21no—
127#358—262no—
128C4×C16—131no—
129#335—131no—
130#332—261no—
131C22×C13#44711yescharacteristic
132C4×C13—21no—
133C4×C13—81no—
134C4×C13—81no—
135C4×C13—161no—
136C4×C13#45211yescharacteristic
137C4×C13#45511yescharacteristic
138C4×C13C2×SD3211yescharacteristic
139C4×C13#51011yescharacteristic
140Dic13—22no—
141Dic13—41no—
142Dic13—82no—
143C2×Q16—132no—
144C2×Q16—262no—
145C2×Q16—261no—
146C2×Q16—521no—
147C2×Q16C22⋊D1311yescharacteristic
148C4⋊Q8—21no—
149C4⋊Q8—262no—
150C4⋊Q8—261no—
151#125—521no—
152#125—522no—
153C4×Q8—21no—
154C4×Q8—131no—
155C4×Q8—262no—
156C4×Q8—521no—
157C2×C16—21no—
158C2×C16—261no—
159#107—21no—
160#107—21no—
161#107C22⋊D1311yescharacteristic
162C4⋊C8—131no—
163C4⋊C8—261no—
164C4⋊C8—261no—
165#103—21no—
166#103—262no—
167#103—521no—
168C4×C8—261no—
169C4×C8C22×D1311yescharacteristic
170C2×C13#164111yescharacteristic
171C2×C13#218511yescharacteristic
172C2×C13#219511yescharacteristic
173C2×Q8—21no—
174C2×Q8—41no—
175C2×Q8—131no—
176C2×Q8—262no—
177Q16—21no—
178Q16—21no—
179Q16—522no—
180Q16—521no—
181Q16—521no—
182Q16—1042no—
183Q16—1042no—
184C2×C8—261no—
185C2×C8—521no—
186C2×C8D4×D1311yescharacteristic
187C2×C8C2×C22⋊D1311yescharacteristic
188C4⋊C4—21no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—131no—
193C4⋊C4—261no—
194C4⋊C4—522no—
195C4⋊C4—522no—
196C4⋊C4—522no—
197C4⋊C4—521no—
198C4⋊C4—521no—
199C42—41no—
200C42—261no—
201C42—522no—
202C42D4×D1311yescharacteristic
203C16—41no—
204C16—521no—
205C13#1238211yescharacteristic, complemented, Sylow
206Q8—41no—
207Q8—41no—
208Q8—81no—
209Q8—81no—
210Q8—132no—
211Q8—261no—
212Q8—522no—
213Q8—522no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—81no—
217C2×C4—261no—
218C2×C4—261no—
219C2×C4—522no—
220C2×C4D8×D1311yescharacteristic
221C2×C4#8816511yescharacteristic
222C2×C4#8819111yescharacteristic
223C8—21no—
224C8—521no—
225C8—1041no—
226C8#8819611yescharacteristic
227C8#8820411yescharacteristic
228C22#1171881711yescharacteristic
229C4—21no—
230C4—81no—
231C4—81no—
232C4—161no—
233C4—262no—
234C4—521no—
235C4—1042no—
236C4D13×SD3211yescharacteristic
237C4#1171857611yescharacteristic
238C4#1171870811yescharacteristic
239C4#1171886311yescharacteristic
240C2#1311402811yescharacteristic
241C2#1311675111yescharacteristic
242C2#1311681111yescharacteristic
subgroupG/H
centerC22#11718817
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#2225C2
socle, prime radicalC22×C13#447
hypercenter#2225D13
hypocenterC13#12382
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2225

Complements

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

NH ≅ G/Ntype
205. C13#12382semidirect

Maximal subgroups

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

subgroupindex
#131278412
#131170652
#131142272
#131128862
#131128142
#131128002
C13×#22252
#1238213