Finite Group Databasebeta

← #16781971

Subgroups — #16781971

Order 3328.

320 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 86 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#13130398C211yesmaximal, characteristic
2#13130396C211yesmaximal, characteristic
3#13130327C212yesmaximal
4#13129742C212yesmaximal
5#13123768C211yesmaximal, characteristic
6#11719222C2211yescharacteristic
7#11719130C2212yes—
8#11719130C2212yes—
9C13×#405C411yescharacteristic
10#11718780C411yescharacteristic
11#11718779C2211yescharacteristic
12#11718762C411yescharacteristic
13C2×C8×Dic13C2211yescharacteristic
14#11718660C411yescharacteristic
15#11718362—21no—
16#11718362—21no—
17C8×Dic26—21no—
18C8×Dic26—21no—
19#11718256—21no—
20#11718255—21no—
21#11718254—21no—
22#11718253—21no—
23#11718242—22no—
24#11718242—22no—
25C2×C13×M16C2×C411yescharacteristic
26C22×C8×C13C2×C411yescharacteristic
27C13×#117C2×C411yescharacteristic
28#88180C2×C411yescharacteristic
29C2×C4×Dic13C2311yescharacteristic
30C2×#6099C2×C411yescharacteristic
31C22×#1055C2×C411yescharacteristic
32#88144D411yescharacteristic
33#88144D411yescharacteristic
34#88142Q811yescharacteristic
35#88142Q811yescharacteristic
36#88132—21no—
37#88132—21no—
38C4×Dic26—21no—
39C4×Dic26—21no—
40C22⋊#1057—22no—
41C22⋊#1057—22no—
42#88110—22no—
43#88110—22no—
44C4⋊#1057—22no—
45C4⋊#1057—22no—
46C13×#97—21no—
47C4×C8×C13—21no—
48#88055—21no—
49#88054—21no—
50#88054—21no—
51#88054—21no—
52#88054—21no—
53C8×Dic13—21no—
54C8×Dic13D411yescharacteristic
55C8×Dic13D411yescharacteristic
56C8×Dic13D411yescharacteristic
57C8×Dic13D411yescharacteristic
58C4⋊#1055—21no—
59C4⋊#1055—21no—
60#8635—131nomaximal, Sylow
61C22×C4×C13C22×C411yescharacteristic
62C22×Dic13#4111yescharacteristic
63C22×Dic13#4111yescharacteristic
64C2×Dic26—21no—
65C2×Dic26—21no—
66C2×#1057—42no—
67C2×#1057—42no—
68C13×M16—41no—
69C2×C8×C13—22no—
70C2×C8×C13—21no—
71C2×C8×C13C22⋊C411yescharacteristic
72C2×C8×C13C22⋊C411yescharacteristic
73C13×C4⋊C4C4⋊C411yescharacteristic
74C13×C4⋊C4C4⋊C411yescharacteristic
75C13×C22⋊C4—21no—
76C42×C13—21no—
77C22⋊Dic13—21no—
78C4⋊Dic13—21no—
79C4⋊Dic13—21no—
80C4⋊Dic13C4⋊C411yescharacteristic
81C4⋊Dic13C4⋊C411yescharacteristic
82#6101—21no—
83#6101—21no—
84#6101—21no—
85#6101—21no—
86C4×Dic13—21no—
87C4×Dic13C2×D411yescharacteristic
88C4×Dic13C2×D411yescharacteristic
89C4×Dic13C2×D411yescharacteristic
90C4×Dic13C2×Q811yescharacteristic
91#6099—41no—
92C2×#1055—21no—
93C2×#1055—41no—
94C2×#1055C22⋊C411yescharacteristic
95C2×#1055C22⋊C411yescharacteristic
96#2960—131no—
97#1568—131no—
98#1568—131no—
99#1537—132no—
100#1307—132no—
101C23×C13#11711yescharacteristic
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13C2×C22⋊C411yescharacteristic
107C2×C4×C13C2×C4⋊C411yescharacteristic
108C2×Dic13—21no—
109C2×Dic13—21no—
110C2×Dic13—41no—
111C2×Dic13—41no—
112C2×Dic13#12111yescharacteristic
113C2×Dic13#12111yescharacteristic
114C2×Dic13C22⋊Q811yescharacteristic
115C2×Dic13C22⋊Q811yescharacteristic
116Dic26—42no—
117Dic26—42no—
118#1057—82no—
119#1057—82no—
120C8×C13—21no—
121C8×C13—41no—
122C8×C13#10112yes—
123#1055—21no—
124#1055—21no—
125#1055—41no—
126#533—131no—
127#446—261no—
128#446—261no—
129C8×Q8—261no—
130C8×Q8—261no—
131#432—132no—
132#432—132no—
133#424—131no—
134#424—131no—
135#423—131no—
136#405—131no—
137#405#26111yescharacteristic
138C2×C4×C8—131no—
139#335—261no—
140#335—261no—
141#334—261no—
142#334—261no—
143#330—262no—
144#330—262no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—21no—
148C22×C13#38011yescharacteristic
149C4×C13—21no—
150C4×C13—41no—
151C4×C13—41no—
152C4×C13C2×#10111yescharacteristic
153C4×C13#41311yescharacteristic
154Dic13—21no—
155Dic13—21no—
156Dic13—21no—
157Dic13—21no—
158Dic13—41no—
159Dic13—41no—
160C2×M16—131no—
161C2×M16C2×#26111yescharacteristic
162C22×C8—131no—
163C22×C8C2×#26111yescharacteristic
164C4⋊Q8—131no—
165C4⋊Q8—131no—
166#125—131no—
167#125—131no—
168C22⋊Q8—261no—
169C22⋊Q8—261no—
170C4×Q8—261no—
171C4×Q8—261no—
172#117—131no—
173#117C2×#26111yescharacteristic
174C2×C42—131no—
175C4⋊C8—261no—
176C4⋊C8—261no—
177C4⋊C8—261no—
178C4⋊C8—261no—
179C4⋊C8—262no—
180C4⋊C8—262no—
181C4⋊C8—261no—
182C4⋊C8—261no—
183C22⋊C8—262no—
184C22⋊C8—262no—
185#97—21no—
186#97—262no—
187#97—262no—
188#97—261no—
189C4×C8—21no—
190C4×C8—131no—
191C4×C8—131no—
192C4×C8—131no—
193C4×C8—131no—
194C4×C8—261no—
195C2×C13—41no—
196C2×C13#180111yescharacteristic
197C2×C13#181411yescharacteristic
198C2×C13#181411yescharacteristic
199C2×Q8—261no—
200C2×Q8—261no—
201C22×C4—131no—
202C22×C4—131no—
203C22×C4C22×#26111yescharacteristic
204M16—41no—
205M16—521no—
206C2×C8—22no—
207C2×C8—21no—
208C2×C8—131no—
209C2×C8—131no—
210C2×C8—261no—
211C2×C8—521no—
212C2×C8—522no—
213C2×C8—522no—
214C2×C8C22⋊#26111yescharacteristic
215C2×C8C22⋊#26111yescharacteristic
216C4⋊C4—131no—
217C4⋊C4—131no—
218C4⋊C4—261no—
219C4⋊C4—261no—
220C4⋊C4—261no—
221C4⋊C4—261no—
222C4⋊C4—261no—
223C4⋊C4—261no—
224C4⋊C4C4⋊#26111yescharacteristic
225C4⋊C4C4⋊#26111yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—261no—
228C42—21no—
229C42—131no—
230C42—131no—
231C42—131no—
232C42—131no—
233C42—261no—
234C13#863511yescharacteristic, complemented, Sylow
235C23#8823711yescharacteristic
236Q8—522no—
237Q8—522no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—131no—
243C2×C4—131no—
244C2×C4—131no—
245C2×C4—131no—
246C2×C4—261no—
247C2×C4—261no—
248C2×C4—521no—
249C2×C4—521no—
250C2×C4C2×C4⋊#26111yescharacteristic
251C2×C4C2×C22⋊#26111yescharacteristic
252C8—21no—
253C8—41no—
254C8—261no—
255C8—261no—
256C8—521no—
257C8—1042no—
258C8—1042no—
259C8#8811312yes—
260C22—21no—
261C22—21no—
262C22—21no—
263C22#1171913611yescharacteristic
264C4—21no—
265C4—41no—
266C4—41no—
267C4—261no—
268C4—261no—
269C4—261no—
270C4—261no—
271C4—521no—
272C4—521no—
273C4C2×#8811311yescharacteristic
274C4#1171913211yescharacteristic
275C2—41no—
276C2#1313070211yescharacteristic
277C2#1313072211yescharacteristic
278C2#1313072311yescharacteristic
subgroupG/H
centerC22#11719136
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#405C4
socleC22×C13#380
prime radicalC23×C13#117
cosocleC2×C4×Dic13C23
hypercenter#405#261
hypocenterC13#8635
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #405

Complements

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

NH ≅ G/Ntype
234. C13#8635semidirect

Maximal subgroups

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

subgroupindex
#131303982
#131303962
#131303272
#131297422
#131237682
#863513