Finite Group Databasebeta

← #15750010

Subgroups — #15750010

Order 3328.

376 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 87 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#13114824C212yesmaximal
2C13×#1954C211yesmaximal, characteristic
3C2×C4×D4×C13C2211yescharacteristic
4C2×C13×C4⋊C8C411yescharacteristic, complemented
5C2×C13×C22⋊C8—22no—
6C2×C4×C8×C13C411yescharacteristic, complemented
7C2×#88074—22no—
8#11718873—22no—
9#11718118C414yescomplemented
10C22×D4×C13D411yescharacteristic
11C23×C4×C13D412yes—
12C22×C8×C13—21no—
13C22×C8×C13—21no—
14C4×D4×C13—41no—
15C4×D4×C13—41no—
16C2×C13×C4⋊C4Q811yescharacteristic
17C2×C13×C22⋊C4C2×C412yes—
18C2×C42×C13C2×C411yescharacteristic
19C2×C22⋊Dic13—24no—
20C2×C4⋊Dic13—42no—
21C13×C4⋊C8—41no—
22C13×C22⋊C8—44no—
23C4×C8×C13—41no—
24#88074—42no—
25#88074—42no—
26#88071—42no—
27#7237—131nomaximal, Sylow
28C24×C13C22⋊C412yes—
29C2×D4×C13—41no—
30C2×D4×C13—41no—
31C2×D4×C13D811yescharacteristic
32C2×D4×C13SD1612yes—
33C2×D4×C13Q1611yescharacteristic
34C22×C4×C13—22no—
35C22×C4×C13—22no—
36C22×C4×C13—42no—
37C22×C4×C13—42no—
38C22×C4×C13C4211yescharacteristic
39C22×C4×C13C22⋊C411yescharacteristic
40C22×C4×C13C4⋊C412yes—
41C22×C4×C13C4⋊C411yescharacteristic
42C22×Dic13—44no—
43C2×C8×C13—22no—
44C2×C8×C13—41no—
45C2×C8×C13—41no—
46C2×C8×C13—42no—
47C2×C8×C13—41no—
48C13×C4⋊C4—41no—
49C13×C22⋊C4—42no—
50C42×C13—21no—
51C42×C13—21no—
52C22⋊Dic13—44no—
53C22⋊Dic13—44no—
54C4⋊Dic13—82no—
55C4⋊Dic13—82no—
56#1954D1311yescharacteristic
57#1799—132no—
58C23×C13—22no—
59C23×C13—22no—
60C23×C13—42no—
61C23×C13—42no—
62C23×C13#9511yescharacteristic
63C23×C13#10212yes—
64C23×C13#10312yes—
65D4×C13—41no—
66D4×C13—42no—
67D4×C13—41no—
68C2×C4×C13—21no—
69C2×C4×C13—21no—
70C2×C4×C13—21no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—22no—
74C2×C4×C13—42no—
75C2×C4×C13—42no—
76C2×C4×C13—42no—
77C2×C4×C13—41no—
78C2×C4×C13—82no—
79C2×C4×C13#9911yescharacteristic
80C2×C4×C13#9911yescharacteristic
81C2×C4×C13#10611yescharacteristic
82C2×C4×C13#10711yescharacteristic
83C2×Dic13—84no—
84C2×Dic13—84no—
85C2×Dic13—84no—
86C8×C13—42no—
87C8×C13—81no—
88C2×C4×D4C2×D1311yescharacteristic
89C2×C4⋊C8Dic1311yescharacteristic, complemented
90C2×#99—262no—
91C2×C22⋊C8—22no—
92C2×C4×C8Dic1311yescharacteristic, complemented
93#380—262no—
94#342—134no—
95C22×C13—21no—
96C22×C13—21no—
97C22×C13—22no—
98C22×C13—22no—
99C22×C13—42no—
100C22×C13—42no—
101C22×C13—42no—
102C22×C13—42no—
103C22×C13—82no—
104C22×C13H(3,ℤ/4)11yescharacteristic
105C22×C13#34011yescharacteristic
106C22×C13#34211yescharacteristic
107C4×C13—21no—
108C4×C13—21no—
109C4×C13—21no—
110C4×C13—41no—
111C4×C13—42no—
112C4×C13#35311yescharacteristic
113C4×C13#35411yescharacteristic
114Dic13—164no—
115C22×D4D5211yescharacteristic
116C23×C4C22⋊D1312yes—
117C22×C8—21no—
118C22×C8—21no—
119C4×D4—41no—
120C4×D4—41no—
121C2×C4⋊C4—522no—
122C2×C4⋊C4Dic2611yescharacteristic
123C2×C22⋊C4—264no—
124C2×C22⋊C4C4×D1312yes—
125C2×C42C2×Dic1311yescharacteristic
126C4⋊C8—41no—
127#99—522no—
128#99—522no—
129C22⋊C8—44no—
130C4×C8—41no—
131#95—522no—
132C2×C13—21no—
133C2×C13—21no—
134C2×C13—42no—
135C2×C13—42no—
136C2×C13#128911yescharacteristic
137C2×C13#139111yescharacteristic
138C2×C13#139311yescharacteristic
139C24#610312yes—
140C2×D4—41no—
141C2×D4—41no—
142C2×D4#609512yes—
143C2×D4D10411yescharacteristic
144C2×D4Dic5211yescharacteristic
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—42no—
148C22×C4—42no—
149C22×C4—524no—
150C22×C4C4×Dic1311yescharacteristic
151C22×C4#610112yes—
152C22×C4C4⋊Dic1311yescharacteristic
153C22×C4C22⋊Dic1311yescharacteristic
154C2×C8—22no—
155C2×C8—41no—
156C2×C8—41no—
157C2×C8—42no—
158C2×C8—41no—
159C4⋊C4—41no—
160C4⋊C4—1042no—
161C4⋊C4—1042no—
162C22⋊C4—42no—
163C22⋊C4—524no—
164C22⋊C4—524no—
165C42—21no—
166C42—21no—
167C13#723711yescharacteristic, complemented, Sylow
168C23—22no—
169C23—22no—
170C23—42no—
171C23—42no—
172C23#8805612yes—
173C23#8806112yes—
174C23#8807111yescharacteristic
175D4—42no—
176D4—41no—
177D4—41no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—41no—
188C2×C4—82no—
189C2×C4—1044no—
190C2×C4—1044no—
191C2×C4—1044no—
192C2×C4#8805711yescharacteristic
193C2×C4#8805811yescharacteristic
194C2×C4#8807411yescharacteristic
195C2×C4#8807411yescharacteristic
196C8—42no—
197C8—81no—
198C22—21no—
199C22—21no—
200C22—22no—
201C22—22no—
202C22—42no—
203C22—42no—
204C22—42no—
205C22—42no—
206C22—82no—
207C22#1171811811yescharacteristic
208C22#1171814311yescharacteristic
209C22#1171814911yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—41no—
214C4—42no—
215C4—2084no—
216C4#1171813311yescharacteristic
217C4#1171813711yescharacteristic
218C2—21no—
219C2—21no—
220C2—42no—
221C2—42no—
222C2#1311270411yescharacteristic
223C2#1311295711yescharacteristic
224C2#1311296111yescharacteristic
subgroupG/H
centerC22#11718118
commutatorC22×C4×C13C42
FrattiniC2×C4×D4C2×D13
FittingC13×#1954C2
socleC22×C13#342
prime radicalC22×D4×C13D4
cosocleC2×C4×D4×C13C22
hypercenter#1954D13
hypocenterC13#7237
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1954

Complements

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

NH ≅ G/Ntype
4. C2×C13×C4⋊C8C4semidirect
6. C2×C4×C8×C13C4semidirect
9. #11718118C4semidirect
89. C2×C4⋊C8Dic13semidirect
92. C2×C4×C8Dic13semidirect
167. C13#7237semidirect

Maximal subgroups

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

subgroupindex
#131148242
C13×#19542
#723713