Finite Group Databasebeta

← #16778534

Subgroups — #16778534

Order 3328.

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

normal subgroups only

This group has 402 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#13130764C211yesmaximal, characteristic
2#13130752C211yesmaximal, characteristic
3#13129657C212yesmaximal
4#13129655C212yesmaximal
5#13117310C211yesmaximal, characteristic
6C2×C4×Dic26C411yescharacteristic
7C2×#88112—21no—
8C4×C13×C4⋊C4C411yescharacteristic
9#11718635C411yescharacteristic
10#11718635C2211yescharacteristic
11#11718634C411yescharacteristic
12#11718634C2211yescharacteristic
13#11718593—21no—
14C4×#6101—21no—
15C42×Dic13C2211yescharacteristic
16#11718313—21no—
17#11718313—21no—
18#11718290—21no—
19#11718290—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×Dic26C2×C411yescharacteristic
24C22×#1057—22no—
25C22×#1057—22no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C42×C13—21no—
29C2×C42×C13C2×C411yescharacteristic
30C2×C4⋊Dic13C2×C411yescharacteristic
31C2×#6101—21no—
32C2×#6101—21no—
33C2×#6101—21no—
34C2×C4×Dic13—21no—
35C2×C4×Dic13C2×C411yescharacteristic
36C2×C4×Dic13D411yescharacteristic
37C2×C4×Dic13D411yescharacteristic
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13C2311yescharacteristic
41C4×Dic26—22no—
42C4×Dic26—22no—
43#88112—42no—
44C13×#95—21no—
45#88071—21no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#7644—131nomaximal, Sylow
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22×C411yescharacteristic
57C22×Dic13—21no—
58C22×Dic13—21no—
59C22×Dic13C22⋊C411yescharacteristic
60C22×Dic13C22⋊C411yescharacteristic
61C22×Dic13C2×D411yescharacteristic
62C22×Dic13C2×D411yescharacteristic
63C2×Dic26—21no—
64C2×Dic26—41no—
65C2×Dic26—41no—
66C2×Dic26M1612yes—
67C2×#1057—42no—
68C2×#1057—42no—
69C2×#1057—42no—
70C2×#1057—42no—
71C2×#1057—42no—
72C2×#1057—42no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C42×C13—21no—
76C42×C13—21no—
77C42×C13—42no—
78C4⋊Dic13—21no—
79C4⋊Dic13M1612yes—
80#6101—24no—
81#6101—42no—
82#6101—42no—
83C4×Dic13—24no—
84C4×Dic13—22no—
85C4×Dic13—41no—
86C4×Dic13—41no—
87C4×Dic13—41no—
88C4×Dic13—41no—
89C4×Dic13SD1612yes—
90C4×Dic13Q1612yes—
91#2295—131no—
92#1839—131no—
93#1831—131no—
94#1272—132no—
95#1271—132no—
96C23×C13C2×C22⋊C411yescharacteristic
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13#10312yes—
111C2×C4×C13C2×M1611yescharacteristic
112C2×C4×C13C2×M1611yescharacteristic
113C2×Dic13—21no—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—22no—
120C2×Dic13—22no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13#10312yes—
129C2×Dic13C2×SD1611yescharacteristic
130C2×Dic13C2×Q1611yescharacteristic
131C2×Dic13#13512yes—
132Dic26—42no—
133Dic26—42no—
134#1057—82no—
135#1057—82no—
136C2×C4×Q8—131no—
137C2×C4⋊C8—261no—
138#391—131no—
139#391—131no—
140#389—131no—
141#389—131no—
142#387—261no—
143#387—261no—
144C4×C4⋊C4—261no—
145C4×C4⋊C4#26111yescharacteristic
146#376—261no—
147C43—131no—
148#336—132no—
149#336—132no—
150#336—261no—
151#336—261no—
152#336—261no—
153C22×C13#40711yescharacteristic
154C22×C13#41011yescharacteristic
155C22×C13#41311yescharacteristic
156C22×C13C2×#10311yescharacteristic
157C22×C13#41611yescharacteristic
158C22×C13#42111yescharacteristic
159C22×C13#42111yescharacteristic
160C4×C13—21no—
161C4×C13—21no—
162C4×C13—22no—
163C4×C13—41no—
164C4×C13—81no—
165C4×C13—81no—
166Dic13—22no—
167Dic13—21no—
168Dic13—21no—
169Dic13—22no—
170Dic13—42no—
171Dic13—42no—
172Dic13—41no—
173C22×Q8—131no—
174C22×C8—262no—
175C22×C8—262no—
176C4×Q8—262no—
177C4×Q8—262no—
178C2×C4⋊C4—131no—
179C2×C4⋊C4—261no—
180C2×C4⋊C4—261no—
181C2×C4⋊C4—261no—
182C2×C4⋊C4C2×#26111yescharacteristic
183C2×C4⋊C4C2×#26111yescharacteristic
184C2×C42—21no—
185C2×C42—131no—
186C2×C42—131no—
187C2×C42—131no—
188C2×C42—131no—
189C2×C42—131no—
190C2×C42—131no—
191C2×C42—261no—
192C2×C42C2×#26111yescharacteristic
193C4⋊C8—522no—
194#95—21no—
195#95—261no—
196#95—261no—
197#95—261no—
198#95—261no—
199#95—261no—
200#95—261no—
201C2×C13#146411yescharacteristic
202C2×C13#148711yescharacteristic
203C2×C13#148811yescharacteristic
204C2×C13#151811yescharacteristic
205C2×C13#152111yescharacteristic
206C2×C13#153511yescharacteristic
207C2×C13#154211yescharacteristic
208C2×Q8—132no—
209C2×Q8—261no—
210C2×Q8—521no—
211C2×Q8—521no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—131no—
215C22×C4—131no—
216C22×C4—131no—
217C22×C4—131no—
218C22×C4—261no—
219C22×C4—261no—
220C22×C4C22⋊#26111yescharacteristic
221C22×C4C22⋊#26111yescharacteristic
222C22×C4C22×#26111yescharacteristic
223C2×C8—522no—
224C2×C8—522no—
225C2×C8—522no—
226C2×C8—522no—
227C2×C8—522no—
228C2×C8—522no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—132no—
232C4⋊C4—264no—
233C4⋊C4—261no—
234C4⋊C4—522no—
235C4⋊C4—522no—
236C42—21no—
237C42—21no—
238C42—42no—
239C42—132no—
240C42—132no—
241C42—262no—
242C42—264no—
243C42—521no—
244C42—521no—
245C42—521no—
246C42—521no—
247C13#764411yescharacteristic, complemented, Sylow
248C23C2×C22⋊#26111yescharacteristic
249Q8—522no—
250Q8—522no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—131no—
265C2×C4—132no—
266C2×C4—131no—
267C2×C4—132no—
268C2×C4—261no—
269C2×C4—261no—
270C2×C4—261no—
271C2×C4—261no—
272C2×C4—261no—
273C2×C4—261no—
274C2×C4—262no—
275C2×C4—262no—
276C2×C4—261no—
277C2×C4—261no—
278C2×C4—261no—
279C2×C4—521no—
280C2×C4—521no—
281C2×C4—521no—
282C2×C4—521no—
283C2×C4#8811712yes—
284C2×C4D13⋊M1611yescharacteristic
285C2×C4D13⋊M1611yescharacteristic
286C8—1042no—
287C8—1042no—
288C22#1171911611yescharacteristic
289C22#1171912611yescharacteristic
290C22#1171913211yescharacteristic
291C22#1171914011yescharacteristic
292C22C2×#8811711yescharacteristic
293C22#1171916511yescharacteristic
294C22#1171916611yescharacteristic
295C4—21no—
296C4—21no—
297C4—22no—
298C4—41no—
299C4—81no—
300C4—81no—
301C4—261no—
302C4—261no—
303C4—262no—
304C4—262no—
305C4—521no—
306C4—522no—
307C4—522no—
308C2#1313008911yescharacteristic
309C2#1313016611yescharacteristic
310C2#1313016911yescharacteristic
311C2#1313026911yescharacteristic
312C2#1313027811yescharacteristic
313C2#1313032011yescharacteristic
314C2#1313033711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC4×C13×C4⋊C4C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC4×C4⋊C4#261
hypocenterC13#7644
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
247. C13#7644semidirect

Maximal subgroups

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

subgroupindex
#131307642
#131307522
#131296572
#131296552
#131173102
#764413