Finite Group Databasebeta

← #16786803

Subgroups — #16786803

Order 3328.

434 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 112 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#13130067C212yesmaximal
2#13129778C214yesmaximal, complemented
3#13117459C211yesmaximal, characteristic
4C2×C13×#117C411yescharacteristic
5C2×#88180C2211yescharacteristic
6C22×C4⋊Dic13C411yescharacteristic
7#11719119—22no—
8#11718646—22no—
9#11718611—22no—
10#11718597C412yes—
11#11718596C2212yes—
12#11718305—22no—
13#11718285C2214yes—
14C23×C4×C13C2×C411yescharacteristic
15C23×Dic13—21no—
16C13×#117—22no—
17C13×#117C814yescomplemented
18C2×C13×C4⋊C4—21no—
19C2×C13×C22⋊C4—21no—
20C2×C42×C13C2×C412yes—
21C2×C22⋊Dic13D412yes—
22#88180—42no—
23C2×C4⋊Dic13—21no—
24C2×C4⋊Dic13—24no—
25C2×C4⋊Dic13—42no—
26C2×C4⋊Dic13C2×C412yes—
27C2×C4⋊Dic13C2×C411yescharacteristic
28C2×C4⋊Dic13C2311yescharacteristic
29C2×C4×Dic13D412yes—
30C22⋊#1057—24no—
31C4⋊#1057—42no—
32C4×#1057—42no—
33#88071—24no—
34#11450—131nomaximal, Sylow
35C24×C13C22⋊C411yescharacteristic
36C22×C4×C13—22no—
37C22×C4×C13—22no—
38C22×C4×C13—22no—
39C22×C4×C13C22⋊C411yescharacteristic
40C22×C4×C13C2×C812yes—
41C22×C4×C13M1612yes—
42C22×C4×C13C22×C411yescharacteristic
43C22×Dic13—22no—
44C22×Dic13—42no—
45C22×Dic13—82no—
46C22×Dic13C22⋊C412yes—
47C22×Dic13C2×D412yes—
48C2×#1057—44no—
49C13×C4⋊C4—24no—
50C13×C22⋊C4—24no—
51C42×C13—22no—
52C42×C13C2×C814yes—
53C22⋊Dic13—42no—
54C4⋊Dic13—41no—
55C4⋊Dic13—41no—
56C4⋊Dic13—42no—
57C4⋊Dic13—42no—
58C4⋊Dic13—84no—
59C4×Dic13—22no—
60C4×Dic13—22no—
61#2317—131no—
62#1458—132no—
63#1325—134no—
64C23×C13—21no—
65C23×C13—21no—
66C23×C13—41no—
67C23×C13—41no—
68C23×C13C22⋊C812yes—
69C23×C13C2×C22⋊C411yescharacteristic
70C2×C4×C13—21no—
71C2×C4×C13—21no—
72C2×C4×C13—24no—
73C2×C4×C13—24no—
74C2×C4×C13—24no—
75C2×C4×C13—42no—
76C2×C4×C13—42no—
77C2×C4×C13C22⋊C812yes—
78C2×C4×C13#9912yes—
79C2×C4×C13#10112yes—
80C2×C4×C13C22×C811yescharacteristic
81C2×C4×C13C2×M1611yescharacteristic
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—42no—
85C2×Dic13—42no—
86C2×Dic13—44no—
87C2×Dic13—42no—
88C2×Dic13—84no—
89#1057—84no—
90C2×#117—131no—
91C2×#117#26111yescharacteristic
92C22×C4⋊C4—131no—
93#431—262no—
94#389—262no—
95#385—262no—
96#384—132no—
97#382—132no—
98#324—134no—
99#323—262no—
100C22×C13—21no—
101C22×C13—21no—
102C22×C13—22no—
103C22×C13—42no—
104C22×C13—42no—
105C22×C13—41no—
106C22×C13—41no—
107C22×C13C2×C22⋊C811yescharacteristic
108C22×C13C2×#9911yescharacteristic
109C22×C13C2×#10111yescharacteristic
110C4×C13—21no—
111C4×C13—21no—
112C4×C13—44no—
113C4×C13#32414yes—
114Dic13—42no—
115Dic13—42no—
116Dic13—82no—
117C23×C4—261no—
118C23×C4C2×#26111yescharacteristic
119#117—22no—
120#117—522no—
121#117#105714yescomplemented
122C2×C4⋊C4—21no—
123C2×C4⋊C4—131no—
124C2×C4⋊C4—131no—
125C2×C4⋊C4—132no—
126C2×C4⋊C4—261no—
127C2×C4⋊C4—264no—
128C2×C4⋊C4—522no—
129C2×C22⋊C4—21no—
130C2×C22⋊C4—132no—
131C2×C42—132no—
132C2×C42C2×#26112yes—
133C4⋊C8—522no—
134C22⋊C8—264no—
135C4×C8—522no—
136#95—264no—
137C2×C13—21no—
138C2×C13—21no—
139C2×C13—42no—
140C2×C13C2×#32411yescharacteristic
141C2×C13#212811yescharacteristic
142C2×C13#213511yescharacteristic
143C24C22⋊#26111yescharacteristic
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—132no—
148C22×C4—132no—
149C22×C4—262no—
150C22×C4—522no—
151C22×C4—1042no—
152C22×C4C2×#105712yes—
153C22×C4#612212yes—
154C22×C4C22⋊#26111yescharacteristic
155C22×C4C22×#26111yescharacteristic
156C2×C8—524no—
157C4⋊C4—24no—
158C4⋊C4—521no—
159C4⋊C4—521no—
160C4⋊C4—522no—
161C4⋊C4—522no—
162C4⋊C4—1044no—
163C22⋊C4—24no—
164C22⋊C4—522no—
165C42—22no—
166C42—262no—
167C42—262no—
168C42C2×#105714yes—
169C13#1145011yescharacteristic, complemented, Sylow
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23C22⋊#105712yes—
175C23C2×C22⋊#26111yescharacteristic
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—24no—
179C2×C4—24no—
180C2×C4—24no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—262no—
184C2×C4—262no—
185C2×C4—522no—
186C2×C4—522no—
187C2×C4—524no—
188C2×C4—522no—
189C2×C4—1044no—
190C2×C4#8810712yes—
191C2×C4#8811312yes—
192C2×C4C22⋊#105712yes—
193C2×C4C22×#105711yescharacteristic
194C2×C4C2×#612211yescharacteristic
195C8—1044no—
196C22—21no—
197C22—21no—
198C22—22no—
199C22—42no—
200C22—42no—
201C22—41no—
202C22—41no—
203C22C2×#8810711yescharacteristic
204C22C2×#8811311yescharacteristic
205C22C2×C22⋊#105711yescharacteristic
206C4—21no—
207C4—21no—
208C4—44no—
209C4—522no—
210C4—522no—
211C4—1042no—
212C4#1171828514yes—
213C2—21no—
214C2—21no—
215C2—42no—
216C2C2×#1171828511yescharacteristic
217C2#1313111711yescharacteristic
218C2#1313114011yescharacteristic
subgroupG/H
centerC22C2×#88107
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C13×#117C4
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C4⋊Dic13C23
hypercenterC2×#117#261
hypocenterC13#11450
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #13129778C2semidirect
17. C13×#117C8semidirect
121. #117#1057semidirect
169. C13#11450semidirect

Maximal subgroups

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

subgroupindex
#131300672
#131297782
#131174592
#1145013