Finite Group Databasebeta

← #16786975

Subgroups — #16786975

Order 3328.

292 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 88 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#13131198C211yesmaximal, characteristic
2#13131194C211yesmaximal, characteristic
3#13129775C212yesmaximal
4#13129774C212yesmaximal
5#13123768C211yesmaximal, characteristic
6#11719222C411yescharacteristic
7C13×#405C411yescharacteristic
8#11718780C2211yescharacteristic
9#11718779C411yescharacteristic
10#11718762C411yescharacteristic
11C2×C8×Dic13C2211yescharacteristic
12#11718660C2211yescharacteristic
13#11718362—21no—
14#11718362—21no—
15C8×Dic26—21no—
16C8×Dic26—21no—
17C22⋊#6092C2212yes—
18C22⋊#6092C2212yes—
19#11718260—21no—
20#11718260—21no—
21#11718258—21no—
22#11718257—21no—
23C2×C13×M16C2×C411yescharacteristic
24C22×C8×C13C2×C411yescharacteristic
25C13×#117C2×C411yescharacteristic
26#88180C2×C411yescharacteristic
27C2×C4×Dic13C2×C411yescharacteristic
28C2×#6099C2×C411yescharacteristic
29C22×#1055C2311yescharacteristic
30#88144C811yescharacteristic
31#88144C811yescharacteristic
32#88142C811yescharacteristic
33#88142C811yescharacteristic
34#88132—21no—
35#88132—21no—
36C4×Dic26—21no—
37C4×Dic26—21no—
38C2×#6092—22no—
39C2×#6092—22no—
40C13×#97—21no—
41C4×C8×C13—21no—
42#88055—21no—
43#88054—21no—
44#88054—21no—
45#88054—21no—
46#88054—21no—
47C8×Dic13—21no—
48C8×Dic13D411yescharacteristic
49C8×Dic13D411yescharacteristic
50C8×Dic13D411yescharacteristic
51C8×Dic13D411yescharacteristic
52C4⋊#1055—21no—
53C4⋊#1055—21no—
54#11498—131nomaximal, Sylow
55C22×C4×C13C22×C411yescharacteristic
56C22×Dic13M1611yescharacteristic
57C22×Dic13M1611yescharacteristic
58C2×Dic26—21no—
59C2×Dic26—21no—
60C13×M16—41no—
61C2×C8×C13—22no—
62C2×C8×C13—21no—
63C2×C8×C13C22⋊C411yescharacteristic
64C2×C8×C13C22⋊C411yescharacteristic
65C13×C4⋊C4C2×C811yescharacteristic
66C13×C4⋊C4C2×C811yescharacteristic
67C13×C22⋊C4—21no—
68C42×C13—21no—
69C22⋊Dic13—21no—
70C4⋊Dic13—21no—
71C4⋊Dic13—21no—
72C4⋊Dic13C2×C811yescharacteristic
73C4⋊Dic13C2×C811yescharacteristic
74#6101—21no—
75#6101—21no—
76#6101—21no—
77#6101—21no—
78C4×Dic13—21no—
79C4×Dic13C22⋊C411yescharacteristic
80C4×Dic13C22⋊C411yescharacteristic
81C4×Dic13C2×C811yescharacteristic
82C4×Dic13C2×C811yescharacteristic
83#6099—41no—
84C2×#1055—21no—
85C2×#1055—41no—
86C2×#1055C2×D411yescharacteristic
87C2×#1055C2×D411yescharacteristic
88#6092—42no—
89#6092—42no—
90#2960—131no—
91#2163—131no—
92#2162—131no—
93#1323—132no—
94#1323—132no—
95C23×C13C2×M1611yescharacteristic
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13C2×C22⋊C411yescharacteristic
101C2×C4×C13C22×C811yescharacteristic
102C2×Dic13—22no—
103C2×Dic13—21no—
104C2×Dic13—21no—
105C2×Dic13—41no—
106C2×Dic13C22⋊C811yescharacteristic
107C2×Dic13C22⋊C811yescharacteristic
108C2×Dic13C22⋊C811yescharacteristic
109C2×Dic13C22⋊C811yescharacteristic
110Dic26—42no—
111Dic26—42no—
112C8×C13—21no—
113C8×C13—41no—
114C8×C13#10112yes—
115#1055—21no—
116#1055—21no—
117#1055—41no—
118#533—131no—
119#446—261no—
120#446—261no—
121C8×Q8—261no—
122C8×Q8—261no—
123#424—131no—
124#424—131no—
125#423—131no—
126#405—131no—
127#405#26111yescharacteristic
128C2×C4×C8—131no—
129C4⋊C16—261no—
130C4⋊C16—261no—
131C22⋊C16—132no—
132C22⋊C16—132no—
133#346—261no—
134C4×C16—261no—
135C22×C13—21no—
136C22×C13—21no—
137C22×C13—21no—
138C22×C13C2×C22⋊C811yescharacteristic
139C4×C13—21no—
140C4×C13—41no—
141C4×C13—41no—
142C4×C13#41011yescharacteristic
143C4×C13C2×#10111yescharacteristic
144Dic13—21no—
145Dic13—21no—
146Dic13—21no—
147Dic13—41no—
148Dic13—41no—
149Dic13#35012yes—
150C2×M16—131no—
151C2×M16C2×#26111yescharacteristic
152C22×C8—131no—
153C22×C8C2×#26111yescharacteristic
154C4⋊Q8—131no—
155C4⋊Q8—131no—
156#125—131no—
157#125—131no—
158C22⋊Q8—261no—
159C22⋊Q8—261no—
160C4×Q8—261no—
161C4×Q8—261no—
162#117—131no—
163#117C2×#26111yescharacteristic
164C2×C42—131no—
165C2×C16—262no—
166C2×C16—262no—
167C4⋊C8—261no—
168C4⋊C8—261no—
169C4⋊C8—261no—
170C4⋊C8—261no—
171C4⋊C8—261no—
172C4⋊C8—261no—
173#97—21no—
174#97—261no—
175C4×C8—21no—
176C4×C8—131no—
177C4×C8—131no—
178C4×C8—131no—
179C4×C8—131no—
180C4×C8—261no—
181C2×C13—41no—
182C2×C13#146111yescharacteristic
183C2×C13C2×#35011yescharacteristic
184C2×C13#211711yescharacteristic
185C2×Q8—261no—
186C2×Q8—261no—
187C22×C4—131no—
188C22×C4—131no—
189C22×C4C22×#26111yescharacteristic
190M16—41no—
191M16—521no—
192C2×C8—22no—
193C2×C8—21no—
194C2×C8—131no—
195C2×C8—131no—
196C2×C8—261no—
197C2×C8—521no—
198C2×C8C22⋊#26111yescharacteristic
199C2×C8C22⋊#26111yescharacteristic
200C4⋊C4—131no—
201C4⋊C4—131no—
202C4⋊C4—261no—
203C4⋊C4—261no—
204C4⋊C4—261no—
205C4⋊C4—261no—
206C4⋊C4—261no—
207C4⋊C4—261no—
208C4⋊C4D13⋊C811yescharacteristic
209C4⋊C4D13⋊C811yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—261no—
212C42—21no—
213C42—131no—
214C42—131no—
215C42—131no—
216C42—131no—
217C42—261no—
218C16—522no—
219C16—522no—
220C13#1149811yescharacteristic, complemented, Sylow
221C23D13⋊M1611yescharacteristic
222Q8—522no—
223Q8—522no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—131no—
229C2×C4—131no—
230C2×C4—131no—
231C2×C4—131no—
232C2×C4—262no—
233C2×C4—261no—
234C2×C4—261no—
235C2×C4—521no—
236C2×C4C2×D13⋊C811yescharacteristic
237C2×C4C2×C22⋊#26111yescharacteristic
238C8—21no—
239C8—41no—
240C8—261no—
241C8—261no—
242C8—521no—
243C8#8811312yes—
244C22—21no—
245C22—21no—
246C22—21no—
247C22D13⋊(C22⋊C8)11yescharacteristic
248C4—21no—
249C4—41no—
250C4—41no—
251C4—132no—
252C4—261no—
253C4—261no—
254C4—261no—
255C4—521no—
256C4—521no—
257C4#1171911611yescharacteristic
258C4C2×#8811311yescharacteristic
259C2—41no—
260C2#1313007811yescharacteristic
261C2D13⋊#35011yescharacteristic
262C2#1313107911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#405C4
socleC22×C13C2×C22⋊C8
prime radicalC23×C13C2×M16
cosocleC22×#1055C23
hypercenter#405#261
hypocenterC13#11498
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #405

Complements

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

NH ≅ G/Ntype
220. C13#11498semidirect

Maximal subgroups

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

subgroupindex
#131311982
#131311942
#131297752
#131297742
#131237682
#1149813