Finite Group Databasebeta

← #16778396

Subgroups — #16778396

Order 3328.

440 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 106 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#13130764C212yesmaximal
2#13129657C212yesmaximal
3#13129656C212yesmaximal
4C4×#88198C211yesmaximal, characteristic
5C2×C4×Q8×C13C411yescharacteristic
6C2×#88198C411yescharacteristic
7C2×C4×Dic26C411yescharacteristic
8#11718891C2211yescharacteristic
9#11718637C411yescharacteristic
10#11718635C2211yescharacteristic
11#11718633—22no—
12C4×#6101—22no—
13C42×Dic13C2211yescharacteristic
14#11718290—22no—
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#88198C814yescomplemented
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#88071—22no—
38#88071—22no—
39#7605—131nomaximal, Sylow
40C2×Q8×C13—21no—
41C2×Q8×C13—41no—
42C2×Q8×C13—41no—
43C2×Q8×C13C2×C812yes—
44C22×C4×C13—21no—
45C22×C4×C13—21no—
46C22×C4×C13C22⋊C411yescharacteristic
47C22×C4×C13C22⋊C411yescharacteristic
48C22×C4×C13C22×C411yescharacteristic
49C22×Dic13—21no—
50C22×Dic13—21no—
51C22×Dic13C22⋊C412yes—
52C22×Dic13C2×D412yes—
53C2×Dic26—21no—
54C2×Dic26—41no—
55C2×Dic26—41no—
56C2×Dic26C2×C812yes—
57C2×#1057—44no—
58C2×#1057—44no—
59C2×#1057—44no—
60C13×C4⋊C4—41no—
61C13×C4⋊C4—42no—
62C42×C13—22no—
63C42×C13—42no—
64C4⋊Dic13—41no—
65#6101—28no—
66#6101—44no—
67#6101—42no—
68C4×Dic13—24no—
69C4×Dic13—42no—
70C4×Dic13—41no—
71C4×Dic13—42no—
72C4×Dic13C2×C812yes—
73C4×Dic13M1612yes—
74C4×C4⋊Q8—131no—
75#1839—132no—
76#1272—132no—
77#1272—132no—
78C23×C13C2×C22⋊C411yescharacteristic
79Q8×C13—42no—
80Q8×C13—42no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—21no—
86C2×C4×C13—22no—
87C2×C4×C13—41no—
88C2×C4×C13—41no—
89C2×C4×C13—41no—
90C2×C4×C13—42no—
91C2×C4×C13#10012yes—
92C2×C4×C13C22×C811yescharacteristic
93C2×C4×C13C2×M1611yescharacteristic
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—41no—
100C2×Dic13—41no—
101C2×Dic13—41no—
102C2×Dic13—42no—
103C2×Dic13C22⋊C814yes—
104C2×Dic13#13714yes—
105Dic26—42no—
106Dic26—42no—
107#1057—84no—
108C2×C4⋊Q8—131no—
109C2×C4×Q8—131no—
110C2×C4×Q8#26111yescharacteristic
111#391—131no—
112#391—131no—
113#389—262no—
114#384—131no—
115C4×C4⋊C4—262no—
116C43—131no—
117#336—134no—
118#336—262no—
119#336—262no—
120C22×C13C2×C22⋊C811yescharacteristic
121C22×C13#41011yescharacteristic
122C22×C13C2×#10011yescharacteristic
123C22×C13#41912yes—
124C22×C13#42112yes—
125C4×C13—22no—
126C4×C13—21no—
127C4×C13—21no—
128C4×C13—41no—
129C4×C13—42no—
130C4×C13—81no—
131Dic13—24no—
132Dic13—24no—
133Dic13—42no—
134Dic13—81no—
135C22×Q8—131no—
136C22×Q8C2×#26111yescharacteristic
137C22×C8—264no—
138C4⋊Q8—134no—
139C4⋊Q8—262no—
140C4×Q8—42no—
141C4×Q8—522no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—131no—
144C2×C4⋊C4—262no—
145C2×C4⋊C4—262no—
146C2×C4⋊C4—261no—
147C2×C4⋊C4C2×#26111yescharacteristic
148C2×C42—21no—
149C2×C42—131no—
150C2×C42—132no—
151C2×C42—132no—
152C2×C42—131no—
153C2×C42—261no—
154C2×C42C2×#26111yescharacteristic
155#95—262no—
156#95—262no—
157C2×C13#146011yescharacteristic
158C2×C13#147912yes—
159C2×C13#151512yes—
160C2×C13#153611yescharacteristic
161C2×C13#155811yescharacteristic
162C2×Q8—21no—
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8—132no—
166C2×Q8—261no—
167C2×Q8—521no—
168C2×Q8—521no—
169C2×Q8D13⋊C812yes—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—132no—
173C22×C4—132no—
174C22×C4—261no—
175C22×C4—261no—
176C22×C4C22⋊#26111yescharacteristic
177C22×C4C22⋊#26111yescharacteristic
178C22×C4C22×#26111yescharacteristic
179C2×C8—524no—
180C2×C8—524no—
181C2×C8—524no—
182C4⋊C4—41no—
183C4⋊C4—42no—
184C4⋊C4—268no—
185C4⋊C4—521no—
186C4⋊C4—522no—
187C4⋊C4—524no—
188C42—22no—
189C42—42no—
190C42—132no—
191C42—132no—
192C42—264no—
193C42—521no—
194C42—522no—
195C42—522no—
196C13#760511yescharacteristic, complemented, Sylow
197C23C2×C22⋊#26111yescharacteristic
198Q8—42no—
199Q8—42no—
200Q8—522no—
201Q8—522no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—134no—
213C2×C4—134no—
214C2×C4—262no—
215C2×C4—262no—
216C2×C4—262no—
217C2×C4—262no—
218C2×C4—262no—
219C2×C4—521no—
220C2×C4—521no—
221C2×C4—521no—
222C2×C4—522no—
223C2×C4#8812112yes—
224C2×C4C2×D13⋊C811yescharacteristic
225C2×C4D13⋊M1611yescharacteristic
226C8—1044no—
227C22#1171911611yescharacteristic
228C22D13⋊(C22⋊C8)11yescharacteristic
229C22#1171915312yes—
230C22#1171916612yes—
231C22C2×#8812111yescharacteristic
232C4—21no—
233C4—21no—
234C4—22no—
235C4—41no—
236C4—42no—
237C4—81no—
238C4—264no—
239C4—264no—
240C4—522no—
241C4—1041no—
242C2#1313007511yescharacteristic
243C2#1313013912yes—
244C2#1313025812yes—
245C2#1313032411yescharacteristic
246C2#1313036911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C4×Q8×C13C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4×Q8#261
hypocenterC13#7605
LCSG ▷ C2×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
26. #88198C8semidirect
196. C13#7605semidirect

Maximal subgroups

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

subgroupindex
#131307642
#131296572
#131296562
C4×#881982
#760513