Finite Group Databasebeta

← #15773623

Subgroups — #15773623

Order 3328.

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

normal subgroups only

This group has 388 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#13114919C211yesmaximal, characteristic
2#13113170C211yesmaximal, characteristic
3#13112842C214yesmaximal, complemented
4C13×#2621C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×C13×C22⋊Q8—21no—
7C2×C13×#117C2211yescharacteristic
8C13×#398—21no—
9C13×#398C2212yes—
10C13×#397—21no—
11C13×#397C412yes—
12C13×#391—21no—
13C13×#382C411yescharacteristic
14#11718868—21no—
15#11718587—21no—
16#11718122—21no—
17#11718122C2212yes—
18#11718120C2212yes—
19#11718117—21no—
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⋊C4D411yescharacteristic
32C2×C13×C4⋊C4C2311yescharacteristic
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4C2×C411yescharacteristic
35C2×C13×C22⋊C4D411yescharacteristic
36C2×C42×C13C2×C411yescharacteristic
37C2×C42×C13D411yescharacteristic
38C2×#6099—22no—
39C13×#95—21no—
40C13×#95—22no—
41C13×#95—22no—
42C13×#95C2×C412yes—
43C22⋊#1055—22no—
44C22⋊#1055—41no—
45C22⋊#1055—41no—
46C4⋊#1055—41no—
47#88043—41no—
48#11807—131nomaximal, Sylow
49C24×C13C22⋊C411yescharacteristic
50C2×Q8×C13—42no—
51C2×Q8×C13—42no—
52C2×Q8×C13—41no—
53C2×Q8×C13—41no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—22no—
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×C13C2×D411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C13×C4⋊C4—41no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—42no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—44no—
72C13×C22⋊C4—41no—
73C13×C22⋊C4—41no—
74C13×C22⋊C4—44no—
75C42×C13—21no—
76C42×C13—21no—
77C42×C13—21no—
78C42×C13—21no—
79#6099—42no—
80#6099—42no—
81C2×#1055—42no—
82C2×#1055—42no—
83#2621D1311yescharacteristic
84#1822—131no—
85#1464—131no—
86#1346—134no—
87C23×C13—21no—
88C23×C13—21no—
89C23×C13—21no—
90C23×C13—41no—
91C23×C13—41no—
92C23×C13C2×C22⋊C411yescharacteristic
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—42no—
104C2×C4×C13—42no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13#9911yescharacteristic
116C2×C4×C13#9911yescharacteristic
117C2×C4×C13AGL(1,ℤ/8)12yes—
118#1055—82no—
119#1055—82no—
120C2×C4⋊Q8Dic1311yescharacteristic
121C2×C22⋊Q8—21no—
122C2×#117C2×D1311yescharacteristic
123#432—261no—
124#407—261no—
125#398—21no—
126#398C2×D1312yes—
127#397—21no—
128#397Dic1312yes—
129#391—21no—
130#382Dic1311yescharacteristic
131#343—132no—
132#343—261no—
133#324—132no—
134#323—261no—
135C22×C13—21no—
136C22×C13—21no—
137C22×C13—42no—
138C22×C13—41no—
139C22×C13—41no—
140C22×C13—41no—
141C22×C13—81no—
142C22×C13C2×#9911yescharacteristic
143C22×C13#41811yescharacteristic
144C22×C13#42111yescharacteristic
145C4×C13—22no—
146C4×C13—21no—
147C4×C13—21no—
148C4×C13—41no—
149C4×C13—41no—
150C4×C13—41no—
151C4×C13—41no—
152C4×C13—82no—
153C4×C13—82no—
154C22×Q8—21no—
155C23×C4C22⋊D1311yescharacteristic
156C2×M16—262no—
157C4⋊Q8—41no—
158C4⋊Q8—41no—
159C22⋊Q8—44no—
160#117—41no—
161#117—41no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4C2×Dic1312yes—
166C2×C4⋊C4C22⋊D1311yescharacteristic
167C2×C4⋊C4C22×D1311yescharacteristic
168C2×C22⋊C4—22no—
169C2×C22⋊C4C2×Dic1311yescharacteristic
170C2×C22⋊C4C22⋊D1311yescharacteristic
171C2×C42C2×Dic1311yescharacteristic
172C2×C42C22⋊D1311yescharacteristic
173C4⋊C8—521no—
174C22⋊C8—262no—
175C22⋊C8—521no—
176C22⋊C8—521no—
177#97—521no—
178#95—21no—
179#95—22no—
180#95—22no—
181#95C2×Dic1312yes—
182C2×C13—21no—
183C2×C13—21no—
184C2×C13—81no—
185C2×C13#151011yescharacteristic
186C2×C13#212311yescharacteristic
187C2×C13#213511yescharacteristic
188C24C22⋊Dic1311yescharacteristic
189C2×Q8—42no—
190C2×Q8—42no—
191C2×Q8—41no—
192C2×Q8—41no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—41no—
199C22×C4C22⋊Dic1311yescharacteristic
200C22×C4C22⋊Dic1311yescharacteristic
201C22×C4C22⋊Dic1311yescharacteristic
202C22×C4C22×Dic1311yescharacteristic
203C22×C4C2×C22⋊D1311yescharacteristic
204C22×C4C2×C22⋊D1311yescharacteristic
205M16—522no—
206M16—522no—
207C2×C8—522no—
208C2×C8—522no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—42no—
212C4⋊C4—42no—
213C4⋊C4—42no—
214C4⋊C4—44no—
215C22⋊C4—41no—
216C22⋊C4—41no—
217C22⋊C4—44no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—21no—
222C13#1180711yescharacteristic, complemented, Sylow
223C23—21no—
224C23—21no—
225C23—21no—
226C23—41no—
227C23—41no—
228C23C2×C22⋊Dic1311yescharacteristic
229Q8—82no—
230Q8—82no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4#8807411yescharacteristic
252C2×C4#8807411yescharacteristic
253C2×C4#8818612yes—
254C8—1042no—
255C8—1042no—
256C22—21no—
257C22—21no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—81no—
263C22#1171887611yescharacteristic
264C22C2×#8807411yescharacteristic
265C22#1171889711yescharacteristic
266C4—22no—
267C4—21no—
268C4—21no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—41no—
273C4—82no—
274C4—82no—
275C2—21no—
276C2—21no—
277C2—81no—
278C2#1311336511yescharacteristic
279C2#1311649011yescharacteristic
280C2#1311653111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2621C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2621D13
hypocenterC13#11807
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
3. #13112842C2semidirect
222. C13#11807semidirect

Maximal subgroups

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

subgroupindex
#131149192
#131131702
#131128422
C13×#26212
#1180713