Finite Group Databasebeta

← #15766163

Subgroups — #15766163

Order 3328.

406 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 77 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#13114936C212yesmaximal
2#13114911C211yesmaximal, characteristic
3#13112744C211yesmaximal, characteristic
4#13112689C212yesmaximal
5C13×#2608C211yesmaximal, characteristic
6C2×#88180C2211yescharacteristic
7C13×#396—22no—
8C13×#389—22no—
9C13×#387—22no—
10C13×#381C2211yescharacteristic
11C4×C13×C22⋊C4C2212yes—
12#11718872C2211yescharacteristic
13#11718868C2212yes—
14#11718119—22no—
15#11718115—22no—
16#11718115—22no—
17C23×C4×C13C2311yescharacteristic
18C2×C13×C4⋊C4—22no—
19C2×C13×C4⋊C4—22no—
20C2×C13×C4⋊C4—22no—
21C2×C13×C22⋊C4—22no—
22C2×C13×C22⋊C4D412yes—
23C2×C42×C13D412yes—
24C2×C42×C13D412yes—
25C2×C22⋊Dic13—21no—
26C2×C22⋊Dic13—21no—
27#88180—22no—
28#88180—22no—
29C2×C4⋊Dic13Q812yes—
30C2×C4×Dic13—21no—
31C2×#6099—22no—
32C13×#95—22no—
33C13×#95—22no—
34C13×#95—22no—
35#88071—22no—
36C22⋊#1055—22no—
37C22⋊#1055—22no—
38#10389—131nomaximal, Sylow
39C24×C13C2×D411yescharacteristic
40C22×C4×C13—22no—
41C22×C4×C13—22no—
42C22×C4×C13—22no—
43C22×C4×C13—42no—
44C22×C4×C13C2×D412yes—
45C22×C4×C13C2×Q811yescharacteristic
46C22×C4×C13#4112yes—
47C22×C4×C13#4111yescharacteristic
48C22×Dic13—22no—
49C22×Dic13—41no—
50C13×C4⋊C4—44no—
51C13×C4⋊C4—44no—
52C13×C4⋊C4—82no—
53C13×C22⋊C4—44no—
54C13×C22⋊C4—42no—
55C42×C13—42no—
56C42×C13—42no—
57C22⋊Dic13—41no—
58C22⋊Dic13—41no—
59C22⋊Dic13—42no—
60C4⋊Dic13—24no—
61C4×Dic13—42no—
62#6099—42no—
63#6099—42no—
64C2×#1055—42no—
65#2608D1311yescharacteristic
66#1826—132no—
67#1820—131no—
68#1306—131no—
69#1284—132no—
70C23×C13—22no—
71C23×C13—42no—
72C23×C13#12011yescharacteristic
73C23×C13C22⋊Q811yescharacteristic
74C23×C13#12411yescharacteristic
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13—24no—
78C2×C4×C13—41no—
79C2×C4×C13—41no—
80C2×C4×C13—42no—
81C2×C4×C13—42no—
82C2×C4×C13—42no—
83C2×C4×C13—42no—
84C2×C4×C13—42no—
85C2×C4×C13—42no—
86C2×C4×C13—42no—
87C2×C4×C13—42no—
88C2×C4×C13—42no—
89C2×C4×C13C22⋊Q812yes—
90C2×C4×C13#12412yes—
91C2×Dic13—42no—
92C2×Dic13—82no—
93C2×Dic13—81no—
94C2×Dic13—82no—
95#1055—82no—
96C2×#117—131no—
97#407—132no—
98#396—22no—
99#389—22no—
100#387—22no—
101#381—131no—
102#381C2×D1311yescharacteristic
103C4×C22⋊C4C2×D1312yes—
104#342—262no—
105#339—262no—
106#339—262no—
107C22×C13—22no—
108C22×C13—21no—
109C22×C13—21no—
110C22×C13—22no—
111C22×C13—22no—
112C22×C13—82no—
113C22×C13#39311yescharacteristic
114C22×C13#45812yes—
115C4×C13—22no—
116C4×C13—22no—
117C4×C13—44no—
118C4×C13—82no—
119C4×C13—82no—
120Dic13—82no—
121Dic13—161no—
122C23×C4C22×D1311yescharacteristic
123C2×M16—262no—
124#117—262no—
125#117—262no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—132no—
130C2×C22⋊C4—22no—
131C2×C22⋊C4—261no—
132C2×C22⋊C4—261no—
133C2×C22⋊C4C22⋊D1312yes—
134C2×C42—261no—
135C2×C42C22⋊D1312yes—
136C2×C42C22⋊D1312yes—
137C22⋊C8—262no—
138C22⋊C8—262no—
139#95—22no—
140#95—22no—
141#95—22no—
142#95—262no—
143C2×C13—22no—
144C2×C13—41no—
145C2×C13—41no—
146C2×C13#203011yescharacteristic
147C2×C13#203112yes—
148C24C2×C22⋊D1311yescharacteristic
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—42no—
153C22×C4—262no—
154C22×C4—521no—
155C22×C4Q8×D1311yescharacteristic
156C22×C4#613112yes—
157C22×C4#613111yescharacteristic
158C22×C4C2×C22⋊D1312yes—
159M16—522no—
160M16—522no—
161C2×C8—522no—
162C4⋊C4—44no—
163C4⋊C4—44no—
164C4⋊C4—82no—
165C4⋊C4—264no—
166C22⋊C4—44no—
167C22⋊C4—42no—
168C22⋊C4—521no—
169C22⋊C4—521no—
170C22⋊C4—522no—
171C42—42no—
172C42—42no—
173C42—522no—
174C13#1038911yescharacteristic, complemented, Sylow
175C23—22no—
176C23—42no—
177C23#8820011yescharacteristic
178C23#8820111yescharacteristic
179C23#8820711yescharacteristic
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—24no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—522no—
195C2×C4—1042no—
196C2×C4—1041no—
197C2×C4—1042no—
198C2×C4#8820012yes—
199C2×C4#8820112yes—
200C8—1042no—
201C22—22no—
202C22—21no—
203C22—21no—
204C22—22no—
205C22—22no—
206C22—82no—
207C22#1171889211yescharacteristic
208C22#1171890412yes—
209C4—22no—
210C4—22no—
211C4—44no—
212C4—82no—
213C4—82no—
214C4—1042no—
215C4—2081no—
216C2—22no—
217C2—41no—
218C2—41no—
219C2#1311600211yescharacteristic
220C2#1311600512yes—
subgroupG/H
centerC22#11718892
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#2608C2
socleC22×C13#393
prime radicalC24×C13C2×D4
hypercenter#2608D13
hypocenterC13#10389
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2608

Complements

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

NH ≅ G/Ntype
174. C13#10389semidirect

Maximal subgroups

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

subgroupindex
#131149362
#131149112
#131127442
#131126892
C13×#26082
#1038913