Finite Group Databasebeta

← #15773597

Subgroups — #15773597

Order 3328.

402 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 87 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#13114913C211yesmaximal, characteristic
2#13113170C211yesmaximal, characteristic
3#13112836C214yesmaximal
4C13×#2621C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic, complemented
6C2×C13×C22⋊Q8—21no—
7C2×C13×#117C2211yescharacteristic
8C13×#398—21no—
9C13×#398C412yescomplemented
10C13×#397—21no—
11C13×#397C2212yes—
12C13×#391—21no—
13C13×#382C411yescharacteristic, complemented
14#11718872—21no—
15#11718587—21no—
16#11718120—21no—
17#11718118—21no—
18#11718118C2212yes—
19#11718117C2212yes—
20C22×Q8×C13—21no—
21C23×C4×C13D411yescharacteristic
22C13×C4⋊Q8—41no—
23C13×C4⋊Q8—41no—
24C13×C22⋊Q8—44no—
25C13×#117—41no—
26C13×#117—41no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4C2×C412yes—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4D411yescharacteristic
35C2×C13×C22⋊C4C2311yescharacteristic
36C2×C42×C13C2×C411yescharacteristic
37C2×C42×C13D411yescharacteristic
38C2×C22⋊Dic13—22no—
39C13×#95—21no—
40C13×#95—22no—
41C13×#95—22no—
42C13×#95C2×C412yes—
43#88071—41no—
44#88071—41no—
45C22⋊#1055—22no—
46C4⋊#1055—41no—
47#88043—41no—
48#11801—131nomaximal, Sylow
49C24×C13C2×D411yescharacteristic
50C2×Q8×C13—42no—
51C2×Q8×C13—42no—
52C2×Q8×C13—41no—
53C2×Q8×C13—41no—
54C22×C4×C13—22no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—22no—
58C22×C4×C13—22no—
59C22×C4×C13—41no—
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×Dic13—42no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—44no—
72C13×C4⋊C4—42no—
73C13×C22⋊C4—41no—
74C13×C22⋊C4—41no—
75C13×C22⋊C4—44no—
76C42×C13—21no—
77C42×C13—21no—
78C42×C13—21no—
79C42×C13—21no—
80C22⋊Dic13—42no—
81C22⋊Dic13—42no—
82C2×#1055—42no—
83#2621D1311yescharacteristic
84#1820—131no—
85#1464—131no—
86#1344—134no—
87C23×C13—21no—
88C23×C13—21no—
89C23×C13—41no—
90C23×C13—41no—
91C23×C13C2×C22⋊C411yescharacteristic
92C23×C13AGL(1,ℤ/8)12yes—
93Q8×C13—82no—
94Q8×C13—82no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
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—42no—
105C2×C4×C13—42no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13#9911yescharacteristic
117C2×C4×C13#9911yescharacteristic
118C2×Dic13—82no—
119C2×Dic13—82no—
120C2×Dic13—82no—
121#1055—82no—
122C2×C4⋊Q8Dic1311yescharacteristic, complemented
123C2×C22⋊Q8—21no—
124C2×#117C2×D1311yescharacteristic
125#432—261no—
126#398—21no—
127#398Dic1312yescomplemented
128#397—21no—
129#397C2×D1312yes—
130#391—21no—
131#382Dic1311yescharacteristic, complemented
132#381—261no—
133#342—132no—
134#342—261no—
135#324—261no—
136#323—132no—
137C22×C13—21no—
138C22×C13—21no—
139C22×C13—22no—
140C22×C13—42no—
141C22×C13—41no—
142C22×C13—41no—
143C22×C13—81no—
144C22×C13C2×#9911yescharacteristic
145C22×C13#41811yescharacteristic
146C22×C13#42111yescharacteristic
147C4×C13—21no—
148C4×C13—21no—
149C4×C13—41no—
150C4×C13—41no—
151C4×C13—41no—
152C4×C13—41no—
153C4×C13—41no—
154C4×C13—82no—
155C4×C13—82no—
156Dic13—162no—
157C22×Q8—21no—
158C23×C4C22⋊D1311yescharacteristic
159C4⋊Q8—41no—
160C4⋊Q8—41no—
161C22⋊Q8—44no—
162#117—41no—
163#117—41no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4C2×Dic1312yes—
168C2×C4⋊C4C2×Dic1311yescharacteristic
169C2×C4⋊C4C22⋊D1311yescharacteristic
170C2×C22⋊C4—22no—
171C2×C22⋊C4—262no—
172C2×C22⋊C4C22⋊D1311yescharacteristic
173C2×C22⋊C4C22×D1311yescharacteristic
174C2×C42C2×Dic1311yescharacteristic
175C2×C42C22⋊D1311yescharacteristic
176C4⋊C8—521no—
177C22⋊C8—262no—
178#97—521no—
179#95—21no—
180#95—22no—
181#95—22no—
182#95—521no—
183#95—521no—
184#95C2×Dic1312yes—
185C2×C13—21no—
186C2×C13—21no—
187C2×C13—42no—
188C2×C13#151011yescharacteristic
189C2×C13#212311yescharacteristic
190C2×C13#212911yescharacteristic
191C24C2×C22⋊D1311yescharacteristic
192C2×Q8—42no—
193C2×Q8—42no—
194C2×Q8—41no—
195C2×Q8—41no—
196C22×C4—22no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—41no—
202C22×C4—522no—
203C22×C4C22⋊Dic1311yescharacteristic
204C22×C4C22⋊Dic1311yescharacteristic
205C22×C4C22⋊Dic1311yescharacteristic
206C22×C4C22⋊Dic1311yescharacteristic
207C22×C4C22×Dic1311yescharacteristic
208C22×C4C2×C22⋊D1311yescharacteristic
209C2×C8—522no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—42no—
213C4⋊C4—42no—
214C4⋊C4—44no—
215C4⋊C4—42no—
216C22⋊C4—41no—
217C22⋊C4—41no—
218C22⋊C4—44no—
219C22⋊C4—522no—
220C22⋊C4—522no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—21no—
225C13#1180111yescharacteristic, complemented, Sylow
226C23—21no—
227C23—21no—
228C23—41no—
229C23—41no—
230C23#8818612yes—
231C23C2×C22⋊Dic1311yescharacteristic
232Q8—82no—
233Q8—82no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—1042no—
256C2×C4—1042no—
257C2×C4—1042no—
258C2×C4#8807411yescharacteristic
259C2×C4#8807411yescharacteristic
260C8—1042no—
261C22—21no—
262C22—21no—
263C22—22no—
264C22—42no—
265C22—41no—
266C22—41no—
267C22—81no—
268C22#1171887611yescharacteristic
269C22C2×#8807411yescharacteristic
270C22#1171889711yescharacteristic
271C4—21no—
272C4—21no—
273C4—41no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—41no—
278C4—82no—
279C4—82no—
280C4—2082no—
281C2—21no—
282C2—21no—
283C2—42no—
284C2#1311336511yescharacteristic
285C2#1311649011yescharacteristic
286C2#1311651111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2621C2
socleC22×C13C2×#99
prime radicalC24×C13C2×D4
cosocleC2×C13×C22⋊C4C23
hypercenter#2621D13
hypocenterC13#11801
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2621

Complements

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

NH ≅ G/Ntype
5. C2×C13×C4⋊Q8C4semidirect
9. C13×#398C4semidirect
13. C13×#382C4semidirect
122. C2×C4⋊Q8Dic13semidirect
127. #398Dic13semidirect
131. #382Dic13semidirect
225. C13#11801semidirect

Maximal subgroups

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

subgroupindex
#131149132
#131131702
#131128362
C13×#26212
#1180113