Finite Group Databasebeta

← #15772237

Subgroups — #15772237

Order 3328.

418 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#11718386C211yesmaximal, characteristic
2#13116636C212yesmaximal, complemented
3#13112760C211yesmaximal, characteristic, complemented
4#13112759C212yesmaximal, complemented
5C13×#1314C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊D13C411yescharacteristic
7C23×#1055C411yescharacteristic
8C22×C8×D13C411yescharacteristic
9C2×C13×C22⋊C8C2211yescharacteristic
10C2×#88060C2211yescharacteristic
11C2×#88054C411yescharacteristic
12C2×C8×Dic13C2211yescharacteristic
13#11718386—22no—
14#11718386—22no—
15C13×C22⋊C16C2212yes—
16C22⋊#6090C2212yes—
17#11718094—22no—
18#11718093—22no—
19C23×C4×C13C2×C411yescharacteristic
20C22×C22⋊D13C811yescharacteristic
21C22×C4×D13C2×C411yescharacteristic
22C22×C8×C13C2×C411yescharacteristic
23C22×C8×C13C2311yescharacteristic
24C2×C22⋊Dic13C811yescharacteristic
25C4×C22⋊D13—22no—
26C4×C22⋊D13—22no—
27C2×#6103C811yescharacteristic
28C2×#6101C811yescharacteristic
29C2×C4×Dic13C2×C411yescharacteristic
30C22×#1055—21no—
31C22×#1055—21no—
32C22×#1055—42no—
33C22×#1055C2×C411yescharacteristic
34C22×#1055C2×C411yescharacteristic
35C2×C8×D13—21no—
36C2×C8×D13—21no—
37C2×C8×D13—42no—
38C2×C13×C16—22no—
39C13×C22⋊C8—22no—
40#88060—22no—
41#88054—22no—
42C8×Dic13D412yes—
43C8×Dic13D412yes—
44C2×#6090—22no—
45#11488—131nomaximal, Sylow
46C24×C13C2×C811yescharacteristic
47C23×D13C2×C811yescharacteristic
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13—41no—
51C22×C4×C13—41no—
52C22×C4×C13C2×C811yescharacteristic
53C22×C4×C13C22×C411yescharacteristic
54C2×C22⋊D13—22no—
55C2×C22⋊D13—22no—
56C2×C22⋊D13—22no—
57C22×Dic13C2×C811yescharacteristic
58C22×Dic13C2×C811yescharacteristic
59C22×Dic13C2×C811yescharacteristic
60C2×C4×D13—21no—
61C2×C4×D13—21no—
62C2×C4×D13—41no—
63C2×C4×D13—41no—
64C2×C8×C13—21no—
65C2×C8×C13—41no—
66C2×C8×C13—41no—
67C2×C8×C13C2×D412yes—
68C22⋊Dic13—22no—
69#6103—22no—
70#6101—22no—
71C4×Dic13C22⋊C412yes—
72C4×Dic13M1612yes—
73C2×#1055—22no—
74C2×#1055—21no—
75C2×#1055—42no—
76C2×#1055—42no—
77C2×#1055—41no—
78C2×#1055C22⋊C411yescharacteristic
79C2×#1055C22⋊C411yescharacteristic
80C8×D13—42no—
81C8×D13—42no—
82C13×C16—42no—
83#6090—42no—
84C2×C8×D4—131no—
85#2163—132no—
86#1314—131no—
87#1314—132no—
88#1314D1311yescharacteristic, complemented
89C23×C13—21no—
90C23×C13—21no—
91C23×C13—41no—
92C23×C13—41no—
93C23×C13M3212yes—
94C23×C13C22×C811yescharacteristic
95C22×D13—21no—
96C22×D13—21no—
97C22×D13—41no—
98C22×D13—41no—
99C22×D13M3212yes—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—42no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13C2×C22⋊C411yescharacteristic
108C2×C4×C13C2×M1611yescharacteristic
109C22⋊D13—28no—
110C2×Dic13—21no—
111C2×Dic13—21no—
112C2×Dic13—21no—
113C2×Dic13—41no—
114C2×Dic13—41no—
115C2×Dic13C22⋊C812yes—
116C2×Dic13C22⋊C812yes—
117C4×D13—42no—
118C4×D13—41no—
119C4×D13—41no—
120C8×C13—22no—
121C8×C13—41no—
122#1055—21no—
123#1055—41no—
124#1055#10012yes—
125C23×C8—131no—
126C23×C8—131no—
127C2×C4×D4—131no—
128C8×D4—262no—
129C8×D4—262no—
130C2×C4⋊C8—131no—
131C2×C22⋊C8—131no—
132C2×C22⋊C8C2×D1311yescharacteristic
133C2×C4×C8—131no—
134C4⋊C16—262no—
135C22⋊C16—132no—
136C22⋊C16C2×D1312yes—
137#346—262no—
138C22×C13—21no—
139C22×C13—21no—
140C22×C13—22no—
141C22×C13—42no—
142C22×C13—42no—
143C22×C13—41no—
144C22×C13—41no—
145C22×C13C2×C22⋊C811yescharacteristic
146C22×C13C2×M3211yescharacteristic
147C22×C13C2×M3211yescharacteristic
148C2×D13—22no—
149C2×D13—42no—
150C2×D13—41no—
151C2×D13—41no—
152C2×D13—42no—
153C4×C13—21no—
154C4×C13—41no—
155C4×C13#41011yescharacteristic
156C4×C13C2×#10011yescharacteristic
157Dic13—22no—
158Dic13—22no—
159Dic13—41no—
160C22×D4—131no—
161C23×C4—131no—
162C23×C4C4×D1311yescharacteristic
163C22×C8—131no—
164C22×C8—131no—
165C22×C8—261no—
166C22×C8—261no—
167C22×C8—261no—
168C22×C8—261no—
169C22×C8—522no—
170C22×C8—522no—
171C22×C8C4×D1311yescharacteristic
172C22×C8C22×D1311yescharacteristic
173C4×D4—262no—
174C4×D4—262no—
175C2×C4⋊C4—131no—
176C2×C22⋊C4—131no—
177C2×C22⋊C4—131no—
178C2×C42—131no—
179C2×C16—22no—
180C2×C16—262no—
181C4⋊C8—262no—
182C22⋊C8—22no—
183C22⋊C8—262no—
184C4×C8—132no—
185C4×C8—132no—
186C2×C13—21no—
187C2×C13—21no—
188C2×C13—42no—
189C2×C13#146011yescharacteristic
190C2×C13#211211yescharacteristic
191C2×C13#211511yescharacteristic
192D13—42no—
193C24—131no—
194C24C8×D1311yescharacteristic
195C2×D4—262no—
196C2×D4—262no—
197C2×D4—262no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—131no—
203C22×C4—131no—
204C22×C4—131no—
205C22×C4—261no—
206C22×C4—261no—
207C22×C4—521no—
208C22×C4—521no—
209C22×C4C8×D1311yescharacteristic
210C22×C4C2×C4×D1311yescharacteristic
211C2×C8—21no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—131no—
215C2×C8—131no—
216C2×C8—262no—
217C2×C8—261no—
218C2×C8—522no—
219C2×C8—522no—
220C2×C8—522no—
221C2×C8—522no—
222C2×C8—521no—
223C2×C8D4×D1312yes—
224C4⋊C4—262no—
225C22⋊C4—262no—
226C22⋊C4—262no—
227C42—132no—
228C42—132no—
229C16—42no—
230C16—522no—
231C13#1148811yescharacteristic, complemented, Sylow
232C23—21no—
233C23—21no—
234C23—41no—
235C23—41no—
236C23—132no—
237C23—261no—
238C23—261no—
239C23—521no—
240C23—521no—
241C23#8803812yes—
242C23C2×C8×D1311yescharacteristic
243D4—268no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—132no—
252C2×C4—132no—
253C2×C4—261no—
254C2×C4—261no—
255C2×C4—261no—
256C2×C4—522no—
257C2×C4—521no—
258C2×C4—521no—
259C2×C4—521no—
260C2×C4—521no—
261C2×C4C22⋊C4×D1311yescharacteristic
262C2×C4M16×D1311yescharacteristic
263C8—22no—
264C8—41no—
265C8—132no—
266C8—261no—
267C8—521no—
268C22—21no—
269C22—21no—
270C22—22no—
271C22—42no—
272C22—42no—
273C22—41no—
274C22—41no—
275C22—262no—
276C22—522no—
277C22—522no—
278C22—521no—
279C22—521no—
280C22D13×C22⋊C811yescharacteristic
281C22C2×#8803811yescharacteristic
282C22D13×M3211yescharacteristic
283C4—21no—
284C4—41no—
285C4—262no—
286C4—262no—
287C4—521no—
288C4#1171840111yescharacteristic
289C4D13×#10011yescharacteristic
290C2—21no—
291C2—21no—
292C2—42no—
293C2—522no—
294C2#1311315511yescharacteristic
295C2#1311644511yescharacteristic
296C2#1311645511yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC23×C13C22×C8
FrattiniC22×C8C22×D13
FittingC13×#1314C2
socleC22×C13C2×C22⋊C8
prime radicalC22×C22⋊D13C8
cosocleC22×C8×C13C23
hypercenter#1314D13
hypocenterC13#11488
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1314

Complements

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

NH ≅ G/Ntype
2. #13116636C2semidirect
3. #13112760C2semidirect
4. #13112759C2semidirect
5. C13×#1314C2semidirect
88. #1314D13semidirect
231. C13#11488semidirect

Maximal subgroups

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

subgroupindex
C2×#117183862
#131166362
#131127602
#131127592
C13×#13142
#1148813