Finite Group Databasebeta

← #16781983

Subgroups — #16781983

Order 3328.

336 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 90 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#13130393C211yesmaximal, characteristic
2#13130390C211yesmaximal, characteristic
3#13130375C212yesmaximal
4#13129744C212yesmaximal
5#13123768C211yesmaximal, characteristic
6#11719222C2211yescharacteristic
7#11719129C2212yes—
8#11719129C2212yes—
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#11718245—22no—
24#11718245—22no—
25C2×#6122—22no—
26C2×#6122—22no—
27C2×C13×M16C2×C411yescharacteristic
28C22×C8×C13C2×C411yescharacteristic
29C13×#117C2×C411yescharacteristic
30#88180C2×C411yescharacteristic
31C2×C4×Dic13C2311yescharacteristic
32C2×#6099C2×C411yescharacteristic
33C22×#1055C2×C411yescharacteristic
34#88144Q811yescharacteristic
35#88144Q811yescharacteristic
36#88142D411yescharacteristic
37#88142D411yescharacteristic
38#88132—21no—
39#88132—21no—
40C4×Dic26—21no—
41C4×Dic26—21no—
42#88112—22no—
43#88112—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#8641—131nomaximal, Sylow
61C22×C4×C13C22×C411yescharacteristic
62C22×Dic13#4111yescharacteristic
63C22×Dic13#4111yescharacteristic
64C2×Dic26—21no—
65C2×Dic26—21no—
66#6122—82no—
67#6122—82no—
68C2×#1057—42no—
69C2×#1057—42no—
70C13×M16—41no—
71C2×C8×C13—22no—
72C2×C8×C13—21no—
73C2×C8×C13C22⋊C411yescharacteristic
74C2×C8×C13C22⋊C411yescharacteristic
75C13×C4⋊C4C4⋊C411yescharacteristic
76C13×C4⋊C4C4⋊C411yescharacteristic
77C13×C22⋊C4—21no—
78C42×C13—21no—
79C22⋊Dic13—21no—
80C4⋊Dic13—21no—
81C4⋊Dic13—21no—
82C4⋊Dic13C4⋊C411yescharacteristic
83C4⋊Dic13C4⋊C411yescharacteristic
84#6101—21no—
85#6101—21no—
86#6101—21no—
87#6101—21no—
88C4×Dic13—21no—
89C4×Dic13C2×D411yescharacteristic
90C4×Dic13C2×D411yescharacteristic
91C4×Dic13C2×D411yescharacteristic
92C4×Dic13C2×Q811yescharacteristic
93#6099—41no—
94C2×#1055—21no—
95C2×#1055—41no—
96C2×#1055C22⋊C411yescharacteristic
97C2×#1055C22⋊C411yescharacteristic
98#2960—131no—
99#1567—131no—
100#1566—131no—
101#1561—132no—
102#1309—132no—
103C23×C13#11711yescharacteristic
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13C2×C22⋊C411yescharacteristic
109C2×C4×C13C2×C4⋊C411yescharacteristic
110C2×Dic13—22no—
111C2×Dic13—21no—
112C2×Dic13—21no—
113C2×Dic13—21no—
114C2×Dic13—21no—
115C2×Dic13#12111yescharacteristic
116C2×Dic13#12111yescharacteristic
117C2×Dic13C22⋊Q811yescharacteristic
118C2×Dic13C22⋊Q811yescharacteristic
119Dic26—42no—
120Dic26—41no—
121Dic26—41no—
122#1057—82no—
123#1057—82no—
124C8×C13—21no—
125C8×C13—41no—
126C8×C13#10112yes—
127#1055—21no—
128#1055—21no—
129#1055—41no—
130#533—131no—
131#446—261no—
132#446—261no—
133C8×Q8—261no—
134C8×Q8—261no—
135#424—131no—
136#424—131no—
137#423—131no—
138#423—132no—
139#423—132no—
140#405—131no—
141#405#26111yescharacteristic
142C2×C4×C8—131no—
143#335—261no—
144#335—261no—
145#334—261no—
146#334—261no—
147#332—262no—
148#332—262no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13—21no—
152C22×C13#38011yescharacteristic
153C4×C13—21no—
154C4×C13—41no—
155C4×C13—41no—
156C4×C13C2×#10111yescharacteristic
157C4×C13#41311yescharacteristic
158Dic13—21no—
159Dic13—21no—
160Dic13—41no—
161Dic13—41no—
162Dic13#47112yes—
163Dic13#47211yescharacteristic
164Dic13#47311yescharacteristic
165C2×M16—131no—
166C2×M16—262no—
167C2×M16—262no—
168C2×M16C2×#26111yescharacteristic
169C22×C8—131no—
170C22×C8C2×#26111yescharacteristic
171C4⋊Q8—131no—
172C4⋊Q8—131no—
173#125—131no—
174#125—131no—
175C22⋊Q8—261no—
176C22⋊Q8—261no—
177C4×Q8—261no—
178C4×Q8—261no—
179#117—131no—
180#117C2×#26111yescharacteristic
181C2×C42—131no—
182C4⋊C8—261no—
183C4⋊C8—261no—
184C4⋊C8—261no—
185C4⋊C8—261no—
186C4⋊C8—262no—
187C4⋊C8—262no—
188C4⋊C8—262no—
189C4⋊C8—262no—
190C4⋊C8—261no—
191C4⋊C8—261no—
192#97—21no—
193#97—261no—
194C4×C8—21no—
195C4×C8—131no—
196C4×C8—131no—
197C4×C8—131no—
198C4×C8—131no—
199C4×C8—261no—
200C2×C13—41no—
201C2×C13#180111yescharacteristic
202C2×C13#181511yescharacteristic
203C2×C13#181611yescharacteristic
204C2×Q8—261no—
205C2×Q8—261no—
206C22×C4—131no—
207C22×C4—131no—
208C22×C4C22×#26111yescharacteristic
209M16—41no—
210M16—521no—
211M16—1042no—
212M16—1042no—
213C2×C8—22no—
214C2×C8—21no—
215C2×C8—131no—
216C2×C8—131no—
217C2×C8—261no—
218C2×C8—521no—
219C2×C8—522no—
220C2×C8—522no—
221C2×C8C22⋊#26111yescharacteristic
222C2×C8C22⋊#26111yescharacteristic
223C4⋊C4—131no—
224C4⋊C4—131no—
225C4⋊C4—261no—
226C4⋊C4—261no—
227C4⋊C4—261no—
228C4⋊C4—261no—
229C4⋊C4—261no—
230C4⋊C4—261no—
231C4⋊C4C4⋊#26111yescharacteristic
232C4⋊C4C4⋊#26111yescharacteristic
233C22⋊C4—21no—
234C22⋊C4—261no—
235C42—21no—
236C42—131no—
237C42—131no—
238C42—131no—
239C42—131no—
240C42—261no—
241C13#864111yescharacteristic, complemented, Sylow
242C23#8823711yescharacteristic
243Q8—522no—
244Q8—521no—
245Q8—521no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—131no—
251C2×C4—131no—
252C2×C4—131no—
253C2×C4—131no—
254C2×C4—261no—
255C2×C4—262no—
256C2×C4—261no—
257C2×C4—261no—
258C2×C4—261no—
259C2×C4C2×C4⋊#26111yescharacteristic
260C2×C4C2×C22⋊#26111yescharacteristic
261C8—21no—
262C8—41no—
263C8—261no—
264C8—261no—
265C8—521no—
266C8—1042no—
267C8—1042no—
268C8#8811312yes—
269C22—21no—
270C22—21no—
271C22—21no—
272C22#1171913611yescharacteristic
273C4—21no—
274C4—41no—
275C4—41no—
276C4—132no—
277C4—131no—
278C4—131no—
279C4—261no—
280C4—261no—
281C4—521no—
282C4—521no—
283C4C2×#8811311yescharacteristic
284C4#1171913211yescharacteristic
285C2—41no—
286C2#1313070211yescharacteristic
287C2#1313072411yescharacteristic
288C2#1313072511yescharacteristic
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#8641
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
241. C13#8641semidirect

Maximal subgroups

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

subgroupindex
#131303932
#131303902
#131303752
#131297442
#131237682
#864113