Finite Group Databasebeta

← #16778516

Subgroups — #16778516

Order 3328.

468 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 98 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#13130553C212yesmaximal
2#13129657C212yesmaximal
3#13129656C212yesmaximal
4C4×#88198C211yesmaximal, characteristic
5C2×C4×Q8×C13C411yescharacteristic
6C2×#88198C411yescharacteristic
7C2×C4×Dic26C411yescharacteristic
8C2×#88110—22no—
9#11718891C2211yescharacteristic
10#11718637C411yescharacteristic
11#11718635C2211yescharacteristic
12#11718633—22no—
13C4×#6101—22no—
14C42×Dic13C2211yescharacteristic
15#11718290—22no—
16#11718290C2214yes—
17C22×Q8×C13C2×C411yescharacteristic
18C22×Dic26C2×C411yescharacteristic
19C22×#1057—24no—
20C4×Q8×C13—42no—
21C2×C13×C4⋊C4—21no—
22C2×C13×C4⋊C4C2×C411yescharacteristic
23C2×C42×C13—21no—
24C2×C42×C13C2×C411yescharacteristic
25#88198—22no—
26#88198—22no—
27C2×C4⋊Dic13C2×C411yescharacteristic
28C2×#6101—22no—
29C2×#6101—21no—
30C2×#6101—22no—
31C2×C4×Dic13—21no—
32C2×C4×Dic13C2×C411yescharacteristic
33C2×C4×Dic13D412yes—
34C2×C4×Dic13D412yes—
35C2×C4×Dic13C2311yescharacteristic
36C4×Dic26—42no—
37#88110—28no—
38#88071—22no—
39#88071—22no—
40#7639—131nomaximal, Sylow
41C2×Q8×C13—21no—
42C2×Q8×C13—41no—
43C2×Q8×C13—41no—
44C2×Q8×C13M1612yes—
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13C22⋊C411yescharacteristic
48C22×C4×C13C22⋊C411yescharacteristic
49C22×C4×C13C22×C411yescharacteristic
50C22×Dic13—21no—
51C22×Dic13—21no—
52C22×Dic13C22⋊C412yes—
53C22×Dic13C2×D412yes—
54C2×Dic26—21no—
55C2×Dic26—41no—
56C2×Dic26—41no—
57C2×Dic26M1612yes—
58C2×#1057—28no—
59C2×#1057—44no—
60C2×#1057—44no—
61C13×C4⋊C4—41no—
62C13×C4⋊C4—42no—
63C42×C13—22no—
64C42×C13—42no—
65C4⋊Dic13—41no—
66#6101—28no—
67#6101—42no—
68#6101—44no—
69C4×Dic13—21no—
70C4×Dic13—21no—
71C4×Dic13—24no—
72C4×Dic13—24no—
73C4×Dic13—41no—
74C4×Dic13—42no—
75C4×C4⋊Q8—131no—
76#1745—132no—
77#1272—132no—
78#1272—132no—
79C23×C13C2×C22⋊C411yescharacteristic
80Q8×C13—42no—
81Q8×C13—42no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—21no—
87C2×C4×C13—22no—
88C2×C4×C13—41no—
89C2×C4×C13—41no—
90C2×C4×C13—41no—
91C2×C4×C13—42no—
92C2×C4×C13#10012yes—
93C2×C4×C13C2×M1611yescharacteristic
94C2×C4×C13C2×M1611yescharacteristic
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—41no—
101C2×Dic13—41no—
102C2×Dic13—41no—
103C2×Dic13—42no—
104C2×Dic13#10414yes—
105C2×Dic13#13714yes—
106Dic26—42no—
107Dic26—42no—
108#1057—48no—
109C2×C4⋊Q8—131no—
110C2×C4×Q8—131no—
111C2×C4×Q8#26111yescharacteristic
112C2×#97—262no—
113#391—131no—
114#391—131no—
115#389—262no—
116#384—131no—
117C4×C4⋊C4—262no—
118C43—131no—
119#336—134no—
120#336—262no—
121C22×C13#40711yescharacteristic
122C22×C13#41011yescharacteristic
123C22×C13C2×#10011yescharacteristic
124C22×C13#41912yes—
125C22×C13C2×#10412yes—
126C4×C13—22no—
127C4×C13—21no—
128C4×C13—21no—
129C4×C13—42no—
130C4×C13—41no—
131C4×C13—81no—
132Dic13—24no—
133Dic13—24no—
134Dic13—42no—
135Dic13—81no—
136C22×Q8—131no—
137C22×Q8C2×#26111yescharacteristic
138C22×C8—264no—
139C4⋊Q8—262no—
140C4⋊Q8—262no—
141C4×Q8—42no—
142C4×Q8—522no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—131no—
145C2×C4⋊C4—262no—
146C2×C4⋊C4—262no—
147C2×C4⋊C4—261no—
148C2×C4⋊C4C2×#26111yescharacteristic
149C2×C42—21no—
150C2×C42—132no—
151C2×C42—132no—
152C2×C42—131no—
153C2×C42—131no—
154C2×C42—261no—
155C2×C42C2×#26111yescharacteristic
156#97—268no—
157#95—262no—
158#95—262no—
159C2×C13#146611yescharacteristic
160C2×C13#149112yes—
161C2×C13#150612yes—
162C2×C13#152511yescharacteristic
163C2×C13#155811yescharacteristic
164C2×Q8—21no—
165C2×Q8—41no—
166C2×Q8—41no—
167C2×Q8—132no—
168C2×Q8—261no—
169C2×Q8—521no—
170C2×Q8—521no—
171C2×Q8#611812yes—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—132no—
175C22×C4—132no—
176C22×C4—261no—
177C22×C4—261no—
178C22×C4C22⋊#26111yescharacteristic
179C22×C4C22⋊#26111yescharacteristic
180C22×C4C22×#26111yescharacteristic
181C2×C8—268no—
182C2×C8—524no—
183C2×C8—524no—
184C4⋊C4—41no—
185C4⋊C4—42no—
186C4⋊C4—268no—
187C4⋊C4—521no—
188C4⋊C4—522no—
189C4⋊C4—524no—
190C42—22no—
191C42—42no—
192C42—264no—
193C42—264no—
194C42—261no—
195C42—261no—
196C42—521no—
197C42—522no—
198C13#763911yescharacteristic, complemented, Sylow
199C23C2×C22⋊#26111yescharacteristic
200Q8—42no—
201Q8—42no—
202Q8—522no—
203Q8—522no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—134no—
215C2×C4—134no—
216C2×C4—262no—
217C2×C4—262no—
218C2×C4—262no—
219C2×C4—262no—
220C2×C4—262no—
221C2×C4—521no—
222C2×C4—521no—
223C2×C4—521no—
224C2×C4—522no—
225C2×C4#8812112yes—
226C2×C4C2×#611811yescharacteristic
227C2×C4D13⋊M1611yescharacteristic
228C8—528no—
229C22#1171911611yescharacteristic
230C22#1171912711yescharacteristic
231C22#1171915312yes—
232C22D13⋊#10412yes—
233C22C2×#8812111yescharacteristic
234C4—21no—
235C4—21no—
236C4—22no—
237C4—41no—
238C4—42no—
239C4—81no—
240C4—264no—
241C4—264no—
242C4—522no—
243C4—1041no—
244C2#1313009511yescharacteristic
245C2#1313017912yes—
246C2#1313022912yes—
247C2#1313029011yescharacteristic
248C2#1313036911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C4×Q8×C13C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4×Q8#261
hypocenterC13#7639
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
198. C13#7639semidirect

Maximal subgroups

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

subgroupindex
#131305532
#131296572
#131296562
C4×#881982
#763913