Finite Group Databasebeta

← #15766161

Subgroups — #15766161

Order 3328.

594 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 75 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#13120506C211yesmaximal, characteristic, complemented
2#13114780C212yesmaximal
3#13112744C211yesmaximal, characteristic, complemented
4#13112688C212yesmaximal, complemented
5C13×#1782C211yesmaximal, characteristic
6C22×C13×#41C2211yescharacteristic
7C2×C13×#99—22no—
8C13×#381C2211yescharacteristic
9C13×#381C2211yescharacteristic
10C2×#88077—22no—
11C2×#88077—22no—
12C4×C22⋊Dic13C2212yes—
13#11718868C2212yes—
14#11718609—22no—
15#11718315—22no—
16#11718308—22no—
17C2×C13×#41—22no—
18C2×C13×#41—22no—
19C2×C13×#41—44no—
20C22×Q8×C13Q811yescharacteristic
21C22×D4×C13—21no—
22C22×D4×C13Q811yescharacteristic
23C23×C4×C13—21no—
24C23×C4×C13C2311yescharacteristic
25C2×C13×C22⋊C4—21no—
26C2×C13×C22⋊C4D412yes—
27C2×C22⋊Dic13—22no—
28C2×C4⋊Dic13—22no—
29C2×#6101—22no—
30C2×#6101—22no—
31C2×C4×Dic13D412yes—
32C2×C4×Dic13D412yes—
33C2×#6099—22no—
34C13×#99—44no—
35C13×#95—22no—
36C13×#95—22no—
37#88077—44no—
38#88077—44no—
39#88071—22no—
40#88071—22no—
41C22⋊#1055—22no—
42C22⋊#1055—22no—
43#10388—131nomaximal, Sylow
44C24×C13—21no—
45C24×C13C2×D411yescharacteristic
46C13×#41—24no—
47C13×#41—24no—
48C13×#41—42no—
49C13×#41—42no—
50C13×#41—44no—
51C13×#41—44no—
52C2×Q8×C13—22no—
53C2×Q8×C13—42no—
54C2×D4×C13—24no—
55C2×D4×C13—22no—
56C2×D4×C13—42no—
57C2×D4×C13—42no—
58C2×D4×C13—41no—
59C2×D4×C13—41no—
60C22×C4×C13—21no—
61C22×C4×C13—22no—
62C22×C4×C13—42no—
63C22×C4×C13—42no—
64C22×C4×C13—42no—
65C22×C4×C13—42no—
66C22×C4×C13—41no—
67C22×C4×C13C2×D412yes—
68C22×C4×C13C2×Q811yescharacteristic
69C22×C4×C13#4111yescharacteristic
70C22×C4×C13#4112yes—
71C22×Dic13—22no—
72C22×Dic13—22no—
73C13×C22⋊C4—42no—
74C13×C22⋊C4—42no—
75C22⋊Dic13—44no—
76C4⋊Dic13—44no—
77#6101—44no—
78#6101—82no—
79C4×Dic13—42no—
80C4×Dic13—42no—
81#6099—42no—
82#6099—42no—
83C2×#1055—42no—
84#2608—131no—
85#1789—132no—
86#1782D1311yescharacteristic
87#1306—131no—
88#1284—132no—
89C23×C13—22no—
90C23×C13—22no—
91C23×C13—42no—
92C23×C13—41no—
93C23×C13—41no—
94C23×C13—82no—
95C23×C13#12011yescharacteristic
96C23×C13C22⋊Q811yescharacteristic
97C23×C13#12411yescharacteristic
98Q8×C13—24no—
99Q8×C13—42no—
100D4×C13—24no—
101D4×C13—42no—
102D4×C13—44no—
103D4×C13—44no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13—22no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—42no—
110C2×C4×C13—44no—
111C2×C4×C13—44no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—81no—
118C2×C4×C13—82no—
119C2×C4×C13C22⋊Q812yes—
120C2×C4×C13#12412yes—
121C2×Dic13—24no—
122C2×Dic13—42no—
123C2×Dic13—42no—
124C2×Dic13—42no—
125C2×Dic13—42no—
126C2×Dic13—42no—
127#1055—82no—
128C22×#41C2×D1311yescharacteristic
129C2×#104—262no—
130C2×#104—262no—
131C2×#99—22no—
132#407—132no—
133#396—262no—
134#389—262no—
135#387—262no—
136#381C2×D1311yescharacteristic
137#381C2×D1311yescharacteristic
138C4×C22⋊C4—132no—
139C22×C13—22no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13—22no—
143C22×C13—22no—
144C22×C13—42no—
145C22×C13—82no—
146C22×C13—82no—
147C22×C13—82no—
148C22×C13—82no—
149C22×C13#39311yescharacteristic
150C22×C13B(4,𝔽2)12yes—
151C4×C13—22no—
152C4×C13—22no—
153C4×C13—42no—
154C4×C13—82no—
155C4×C13—161no—
156Dic13—44no—
157Dic13—82no—
158C2×#41—22no—
159C2×#41—22no—
160C2×#41—44no—
161C22×Q8Dic2611yescharacteristic
162C22×D4—21no—
163C22×D4Dic2611yescharacteristic
164C23×C4—21no—
165C23×C4C22×D1311yescharacteristic
166C2×M16—262no—
167C2×C4⋊C4—262no—
168C2×C4⋊C4—262no—
169C2×C4⋊C4—262no—
170C2×C22⋊C4—21no—
171C2×C22⋊C4—262no—
172C2×C22⋊C4C22⋊D1312yes—
173C2×C42—132no—
174C2×C42—132no—
175#104—524no—
176#104—524no—
177#99—44no—
178C22⋊C8—262no—
179C22⋊C8—262no—
180#95—22no—
181#95—22no—
182#95—262no—
183#95—262no—
184C2×C13—22no—
185C2×C13—41no—
186C2×C13—41no—
187C2×C13—82no—
188C2×C13#202911yescharacteristic
189C2×C13#203112yes—
190C24—21no—
191C24C2×C22⋊D1311yescharacteristic
192#41—24no—
193#41—24no—
194#41—42no—
195#41—42no—
196#41—44no—
197#41—44no—
198C2×Q8—22no—
199C2×Q8—42no—
200C2×D4—24no—
201C2×D4—22no—
202C2×D4—42no—
203C2×D4—42no—
204C2×D4—41no—
205C2×D4—41no—
206C22×C4—21no—
207C22×C4—22no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—41no—
213C22×C4—262no—
214C22×C4—262no—
215C22×C4C2×Dic2611yescharacteristic
216C22×C4#612711yescharacteristic
217C22×C4D4×D1312yes—
218C22×C4#612912yes—
219M16—522no—
220M16—522no—
221C2×C8—522no—
222C4⋊C4—524no—
223C4⋊C4—524no—
224C4⋊C4—1042no—
225C22⋊C4—42no—
226C22⋊C4—42no—
227C22⋊C4—524no—
228C42—522no—
229C42—522no—
230C13#1038811yescharacteristic, complemented, Sylow
231C23—22no—
232C23—22no—
233C23—42no—
234C23—41no—
235C23—41no—
236C23—82no—
237C23#8817811yescharacteristic
238C23#8819011yescharacteristic
239C23#8819111yescharacteristic
240Q8—24no—
241Q8—42no—
242D4—24no—
243D4—42no—
244D4—44no—
245D4—44no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—44no—
253C2×C4—44no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—81no—
260C2×C4—82no—
261C2×C4—264no—
262C2×C4—522no—
263C2×C4—522no—
264C2×C4—522no—
265C2×C4—522no—
266C2×C4—522no—
267C2×C4#8813212yes—
268C2×C4#8813912yes—
269C8—1042no—
270C22—22no—
271C22—21no—
272C22—21no—
273C22—22no—
274C22—22no—
275C22—42no—
276C22—82no—
277C22—82no—
278C22—82no—
279C22—82no—
280C22#1171860811yescharacteristic
281C22#1171869312yes—
282C4—22no—
283C4—22no—
284C4—42no—
285C4—82no—
286C4—161no—
287C4—524no—
288C4—1042no—
289C2—22no—
290C2—41no—
291C2—41no—
292C2—82no—
293C2#1311600011yescharacteristic
294C2#1311601012yes—
subgroupG/H
centerC22#11718608
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#1782C2
socleC22×C13#393
prime radicalC22×C13×#41C22
hypercenter#1782D13
hypocenterC13#10388
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1782

Complements

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

NH ≅ G/Ntype
1. #13120506C2semidirect
3. #13112744C2semidirect
4. #13112688C2semidirect
230. C13#10388semidirect

Maximal subgroups

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

subgroupindex
#131205062
#131147802
#131127442
#131126882
C13×#17822
#1038813