Finite Group Databasebeta

← #16787015

Subgroups — #16787015

Order 3328.

510 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 80 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#13130087C212yesmaximal
2#13129766C214yesmaximal, complemented
3#13117422C211yesmaximal, characteristic
4C23×Q8×C13C411yescharacteristic
5C2×#88180C411yescharacteristic
6C2×#88180C2211yescharacteristic
7#11719128—22no—
8#11718891—22no—
9#11718891C412yes—
10#11718891C2212yes—
11#11718872—22no—
12#11718305—22no—
13#11718285C2214yes—
14C22×Q8×C13—24no—
15C22×Q8×C13—21no—
16C22×Q8×C13—42no—
17C22×Q8×C13—42no—
18C22×Q8×C13C2×C412yes—
19C23×C4×C13—21no—
20C23×C4×C13C2×C411yescharacteristic
21C2×C22⋊Dic13—21no—
22C2×C22⋊Dic13D412yes—
23#88180—42no—
24#88180—42no—
25C2×C4⋊Dic13—21no—
26C2×C4⋊Dic13C2×C411yescharacteristic
27C2×C4⋊Dic13C2311yescharacteristic
28C2×C4×Dic13C2×C412yes—
29C2×C4×Dic13D412yes—
30C22⋊#1057—24no—
31#88112—42no—
32#88110—42no—
33#88071—24no—
34#88071—24no—
35#11510—131nomaximal, Sylow
36C24×C13C22⋊C411yescharacteristic
37C2×Q8×C13—24no—
38C2×Q8×C13—22no—
39C2×Q8×C13—416no—
40C2×Q8×C13—42no—
41C2×Q8×C13—42no—
42C2×Q8×C13—42no—
43C2×Q8×C13—42no—
44C2×Q8×C13M1614yes—
45C22×C4×C13—22no—
46C22×C4×C13—22no—
47C22×C4×C13—22no—
48C22×C4×C13—24no—
49C22×C4×C13—22no—
50C22×C4×C13—42no—
51C22×C4×C13—42no—
52C22×C4×C13C22⋊C411yescharacteristic
53C22×C4×C13C22×C411yescharacteristic
54C22×Dic13—22no—
55C22×Dic13C22⋊C412yes—
56C22×Dic13C2×D412yes—
57C2×#1057—44no—
58C22⋊Dic13—42no—
59C22⋊Dic13—42no—
60C4⋊Dic13—41no—
61C4⋊Dic13—41no—
62C4⋊Dic13—42no—
63C4×Dic13—22no—
64C4×Dic13—22no—
65C4×Dic13—42no—
66#2310—131no—
67#1464—132no—
68#1319—134no—
69C23×C13—21no—
70C23×C13—21no—
71C23×C13—41no—
72C23×C13—41no—
73C23×C13#10012yes—
74C23×C13C2×C22⋊C411yescharacteristic
75Q8×C13—48no—
76Q8×C13—44no—
77Q8×C13—44no—
78C2×C4×C13—28no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—24no—
84C2×C4×C13—48no—
85C2×C4×C13—42no—
86C2×C4×C13—42no—
87C2×C4×C13#9912yes—
88C2×C4×C13C2×M1612yes—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—42no—
92C2×Dic13—42no—
93C2×Dic13—42no—
94C2×Dic13—42no—
95C2×Dic13—42no—
96#1057—84no—
97C23×Q8#26111yescharacteristic
98C2×#117—131no—
99C2×#117—131no—
100#432—262no—
101#391—132no—
102#391—132no—
103#391—262no—
104#381—262no—
105#324—134no—
106#323—262no—
107C22×C13—21no—
108C22×C13—21no—
109C22×C13—22no—
110C22×C13—42no—
111C22×C13—42no—
112C22×C13—41no—
113C22×C13—41no—
114C22×C13#40711yescharacteristic
115C22×C13C2×#9911yescharacteristic
116C22×C13C2×#10011yescharacteristic
117C4×C13—22no—
118C4×C13—22no—
119C4×C13—44no—
120Dic13—42no—
121Dic13—42no—
122Dic13—82no—
123C22×Q8—24no—
124C22×Q8—21no—
125C22×Q8—42no—
126C22×Q8—42no—
127C22×Q8C2×#26112yes—
128C23×C4—21no—
129C23×C4C2×#26111yescharacteristic
130#117—522no—
131#117—522no—
132C2×C4⋊C4—131no—
133C2×C4⋊C4—131no—
134C2×C4⋊C4—261no—
135C2×C22⋊C4—132no—
136C2×C22⋊C4—261no—
137C2×C42—132no—
138C2×C42—132no—
139C4⋊C8—522no—
140C22⋊C8—264no—
141#97—522no—
142#95—264no—
143#95—264no—
144C2×C13—21no—
145C2×C13—21no—
146C2×C13—42no—
147C2×C13#146211yescharacteristic
148C2×C13#212911yescharacteristic
149C2×C13#213511yescharacteristic
150C24C22⋊#26111yescharacteristic
151C2×Q8—24no—
152C2×Q8—22no—
153C2×Q8—416no—
154C2×Q8—42no—
155C2×Q8—42no—
156C2×Q8—42no—
157C2×Q8—42no—
158C2×Q8#612214yes—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—24no—
163C22×C4—22no—
164C22×C4—42no—
165C22×C4—42no—
166C22×C4—132no—
167C22×C4—132no—
168C22×C4—262no—
169C22×C4C22⋊#26111yescharacteristic
170C22×C4C22×#26111yescharacteristic
171C2×C8—524no—
172C4⋊C4—521no—
173C4⋊C4—521no—
174C4⋊C4—522no—
175C22⋊C4—522no—
176C22⋊C4—522no—
177C42—262no—
178C42—262no—
179C42—522no—
180C13#1151011yescharacteristic, complemented, Sylow
181C23—21no—
182C23—21no—
183C23—41no—
184C23—41no—
185C23#8812112yes—
186C23C2×C22⋊#26111yescharacteristic
187Q8—44no—
188Q8—48no—
189Q8—44no—
190C2×C4—28no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—24no—
196C2×C4—48no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—262no—
200C2×C4—262no—
201C2×C4—522no—
202C2×C4—522no—
203C2×C4—522no—
204C2×C4—522no—
205C2×C4—522no—
206C2×C4#8811912yes—
207C2×C4C2×#612212yes—
208C8—1044no—
209C22—21no—
210C22—21no—
211C22—22no—
212C22—42no—
213C22—42no—
214C22—41no—
215C22—41no—
216C22C2×#8811911yescharacteristic
217C22#1171916911yescharacteristic
218C22C2×#8812111yescharacteristic
219C4—22no—
220C4—22no—
221C4—44no—
222C4—522no—
223C4—522no—
224C4—1042no—
225C2—21no—
226C2—21no—
227C2—42no—
228C2#1313008111yescharacteristic
229C2#1313111811yescharacteristic
230C2#1313113811yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC23×Q8×C13C4
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C4⋊Dic13C23
hypercenterC23×Q8#261
hypocenterC13#11510
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C23×Q8

Complements

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

NH ≅ G/Ntype
2. #13129766C2semidirect
180. C13#11510semidirect

Maximal subgroups

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

subgroupindex
#131300872
#131297662
#131174222
#1151013