Finite Group Databasebeta

← #16788070

Subgroups — #16788070

Order 3328.

434 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 74 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#13130735C211yesmaximal, characteristic
2#13130086C211yesmaximal, characteristic
3#13129834C214yesmaximal, complemented
4C2×#11718320C211yesmaximal, characteristic
5C22×C4⋊Dic13C411yescharacteristic
6C22×#6101C2211yescharacteristic
7#11719169—21no—
8#11719169—21no—
9C2×C13×#95C411yescharacteristic
10C2×#88071—21no—
11C2×#88071—21no—
12#11718320—21no—
13#11718320—21no—
14#11718320C412yes—
15#11718320C2212yes—
16#11718291—21no—
17#11718291C2212yes—
18#11718286—21no—
19#11718286C2212yes—
20C23×C4×C13—21no—
21C23×C4×C13C2×C411yescharacteristic
22C23×Dic13—21no—
23C23×Dic13D411yescharacteristic
24C23×Dic13D411yescharacteristic
25C2×#6122—22no—
26C2×#6122—41no—
27C2×C4⋊Dic13—21no—
28C2×C4⋊Dic13—41no—
29C2×C4⋊Dic13—41no—
30C2×C4⋊Dic13C2×C412yes—
31C2×#6101—41no—
32C2×#6101—41no—
33C2×#6101C2×C411yescharacteristic
34C2×#6101D411yescharacteristic
35C2×#6101D411yescharacteristic
36C2×#6101C2311yescharacteristic
37C22⋊#1057—22no—
38C22⋊#1057—41no—
39C22⋊#1057—41no—
40C22⋊#1057—41no—
41C13×#95—21no—
42C13×#95C2×C412yes—
43#88071—22no—
44#88071—22no—
45#88071—22no—
46#88071—22no—
47#11814—131nomaximal, Sylow
48C24×C13C22⋊C411yescharacteristic
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13—22no—
52C22×C4×C13—42no—
53C22×C4×C13—42no—
54C22×C4×C13—42no—
55C22×C4×C13—42no—
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22×C411yescharacteristic
58C22×Dic13—21no—
59C22×Dic13—21no—
60C22×Dic13—21no—
61C22×Dic13—21no—
62C22×Dic13—22no—
63C22×Dic13—22no—
64C22×Dic13—41no—
65C22×Dic13—42no—
66C22×Dic13—44no—
67C22×Dic13—41no—
68C22×Dic13—41no—
69C22×Dic13C22⋊C411yescharacteristic
70C22×Dic13C22⋊C411yescharacteristic
71C22×Dic13C2×D411yescharacteristic
72C22×Dic13C2×D411yescharacteristic
73#6122—42no—
74#6122—42no—
75#6122—82no—
76C2×#1057—42no—
77C2×#1057—42no—
78C4⋊Dic13—42no—
79C4⋊Dic13—42no—
80#6101—41no—
81#6101—41no—
82#6101—41no—
83#6101—41no—
84C2×#400—131no—
85#1821—131no—
86#1463—131no—
87#1353—134no—
88C23×C13—22no—
89C23×C13—22no—
90C23×C13—21no—
91C23×C13—21no—
92C23×C13#9911yescharacteristic
93C23×C13#9911yescharacteristic
94C23×C13C2×C22⋊C411yescharacteristic
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—41no—
100C2×C4×C13—41no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—84no—
105C2×Dic13—21no—
106C2×Dic13—21no—
107C2×Dic13—21no—
108C2×Dic13—21no—
109C2×Dic13—21no—
110C2×Dic13—21no—
111C2×Dic13—21no—
112C2×Dic13—42no—
113C2×Dic13—42no—
114C2×Dic13—42no—
115C2×Dic13—41no—
116C2×Dic13—41no—
117C2×Dic13—44no—
118C2×Dic13—42no—
119C2×Dic13—81no—
120C2×Dic13—82no—
121C2×Dic13—82no—
122C2×Dic13#13712yes—
123#1057—82no—
124#1057—82no—
125C22×C4⋊C4—131no—
126C22×C4⋊C4—131no—
127#407—261no—
128#407—261no—
129#400—132no—
130#400—132no—
131#400—261no—
132#400—261no—
133C2×#95—261no—
134C2×#95—261no—
135C2×#95#26111yescharacteristic
136#343—132no—
137#343—261no—
138#324—132no—
139#324—261no—
140C22×C13—24no—
141C22×C13—24no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—21no—
148C22×C13#35212yes—
149C22×C13#35512yes—
150C22×C13C2×#9911yescharacteristic
151C22×C13#41911yescharacteristic
152C22×C13#42111yescharacteristic
153C4×C13—41no—
154C4×C13—41no—
155C4×C13—82no—
156Dic13—22no—
157Dic13—41no—
158Dic13—41no—
159Dic13—41no—
160Dic13—82no—
161C23×C4—21no—
162C23×C4—131no—
163C23×C4—131no—
164C23×C4—261no—
165C23×C4C2×#26111yescharacteristic
166C2×M16—262no—
167C2×M16—521no—
168C2×C4⋊C4—131no—
169C2×C4⋊C4—131no—
170C2×C4⋊C4—131no—
171C2×C4⋊C4—131no—
172C2×C4⋊C4—132no—
173C2×C4⋊C4—261no—
174C2×C4⋊C4—521no—
175C2×C4⋊C4—521no—
176C2×C4⋊C4—521no—
177C2×C4⋊C4—521no—
178C22⋊C8—262no—
179C22⋊C8—521no—
180C22⋊C8—521no—
181C22⋊C8—521no—
182#95—21no—
183#95—262no—
184#95—262no—
185#95—262no—
186#95—262no—
187#95C2×#26112yes—
188C2×C13—21no—
189C2×C13—22no—
190C2×C13—22no—
191C2×C13—21no—
192C2×C13#151111yescharacteristic
193C2×C13C2×#35211yescharacteristic
194C2×C13C2×#35511yescharacteristic
195C24C22⋊#26111yescharacteristic
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—22no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—131no—
204C22×C4—131no—
205C22×C4—131no—
206C22×C4—131no—
207C22×C4—262no—
208C22×C4—261no—
209C22×C4—261no—
210C22×C4—261no—
211C22×C4—261no—
212C22×C4—262no—
213C22×C4—521no—
214C22×C4—522no—
215C22×C4—524no—
216C22×C4—521no—
217C22×C4—521no—
218C22×C4C22⋊#26111yescharacteristic
219C22×C4C22×#26111yescharacteristic
220M16—522no—
221M16—522no—
222M16—1042no—
223C2×C8—522no—
224C2×C8—522no—
225C4⋊C4—521no—
226C4⋊C4—521no—
227C4⋊C4—521no—
228C4⋊C4—521no—
229C4⋊C4—522no—
230C4⋊C4—522no—
231C13#1181411yescharacteristic, complemented, Sylow
232C23—22no—
233C23—22no—
234C23—21no—
235C23—21no—
236C23#8810711yescharacteristic
237C23#8810711yescharacteristic
238C23C2×C22⋊#26111yescharacteristic
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—84no—
249C2×C4—132no—
250C2×C4—261no—
251C2×C4—261no—
252C2×C4—261no—
253C2×C4—261no—
254C2×C4—261no—
255C2×C4—261no—
256C2×C4—261no—
257C2×C4—522no—
258C2×C4—522no—
259C2×C4—522no—
260C2×C4—521no—
261C2×C4—521no—
262C2×C4—524no—
263C2×C4—522no—
264C2×C4—1041no—
265C2×C4—1042no—
266C2×C4—1042no—
267C8—1042no—
268C8—1042no—
269C22—24no—
270C22—24no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22#1171822812yes—
278C22#1171823712yes—
279C22C2×#8810711yescharacteristic
280C22#1171914011yescharacteristic
281C22#1171915311yescharacteristic
282C4—41no—
283C4—41no—
284C4—82no—
285C4—262no—
286C4—521no—
287C4—521no—
288C4—521no—
289C4—1042no—
290C2—21no—
291C2—22no—
292C2—22no—
293C2—21no—
294C2#1313024411yescharacteristic
295C2C2×#1171823711yescharacteristic
296C2C2×#1171822811yescharacteristic
subgroupG/H
centerC22C2×#88107
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×#95C4
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×#6101C23
hypercenterC2×#95#261
hypocenterC13#11814
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
3. #13129834C2semidirect
231. C13#11814semidirect

Maximal subgroups

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

subgroupindex
#131307352
#131300862
#131298342
C2×#117183202
#1181413