Finite Group Databasebeta

← #15772570

Subgroups — #15772570

Order 3328.

480 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 95 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#13113174C211yesmaximal, characteristic
2#13113154C211yesmaximal, characteristic
3#13112782C214yesmaximal, complemented
4C13×#2542C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×C13×C22⋊Q8—21no—
7C2×C13×C22⋊Q8—21no—
8C2×C4×D4×C13C2211yescharacteristic
9C13×#399—21no—
10C13×#399—21no—
11C13×#390C412yes—
12C13×#384C2212yes—
13C4×C13×C4⋊C4C411yescharacteristic
14#11718868—21no—
15C2×C22⋊#1055—21no—
16#11718120C2212yes—
17#11718120C2212yes—
18#11718117—21no—
19#11718117—21no—
20C22×Q8×C13—21no—
21C22×D4×C13C2×C411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C13×C4⋊Q8—41no—
25C13×C4⋊Q8—41no—
26C13×C22⋊Q8—44no—
27C13×C22⋊Q8—44no—
28C4×D4×C13—41no—
29C4×D4×C13—41no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C4⋊C4C2×C412yes—
35C2×C13×C4⋊C4C2311yescharacteristic
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4D411yescharacteristic
39C2×C13×C22⋊C4D411yescharacteristic
40C2×C42×C13C2×C412yes—
41C2×C42×C13C2×C411yescharacteristic
42C2×#6099—41no—
43C22×#1055—41no—
44C13×#95—21no—
45C22⋊#1055—22no—
46C22⋊#1055—22no—
47C22⋊#1055—41no—
48C22⋊#1055—41no—
49#11570—131nomaximal, Sylow
50C24×C13C22⋊C411yescharacteristic
51C24×C13C22⋊C411yescharacteristic
52C2×Q8×C13—42no—
53C2×Q8×C13—42no—
54C2×Q8×C13—41no—
55C2×Q8×C13—41no—
56C2×D4×C13—22no—
57C2×D4×C13—22no—
58C2×D4×C13—41no—
59C22×C4×C13—22no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—22no—
65C22×C4×C13—42no—
66C22×C4×C13—42no—
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C13×C4⋊C4—24no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—42no—
75C13×C4⋊C4—44no—
76C13×C4⋊C4—44no—
77C13×C4⋊C4—42no—
78C13×C22⋊C4—41no—
79C13×C22⋊C4—41no—
80C13×C22⋊C4—44no—
81C13×C22⋊C4—44no—
82C42×C13—21no—
83C42×C13—21no—
84C42×C13—24no—
85#6099—82no—
86C2×#1055—42no—
87C2×#1055—42no—
88C2×#1055—82no—
89#2542D1311yescharacteristic
90#1465—131no—
91#1459—131no—
92#1325—134no—
93C23×C13—21no—
94C23×C13—21no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—41no—
99C23×C13—41no—
100C23×C13—41no—
101C23×C13—41no—
102C23×C13#10112yes—
103C23×C13C2×C22⋊C411yescharacteristic
104Q8×C13—82no—
105Q8×C13—82no—
106D4×C13—44no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—22no—
110C2×C4×C13—24no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—81no—
125C2×C4×C13—81no—
126C2×C4×C13#9911yescharacteristic
127C2×C4×C13#9911yescharacteristic
128C2×C4×C13#13112yes—
129#1055—82no—
130#1055—82no—
131C2×C4⋊Q8Dic1311yescharacteristic
132C2×C22⋊Q8—21no—
133C2×C22⋊Q8—21no—
134C2×C4×D4C2×D1311yescharacteristic
135#407—261no—
136C2×C22⋊C8—261no—
137#399—21no—
138#399—21no—
139#390Dic1312yes—
140#384C2×D1312yes—
141C4×C4⋊C4Dic1311yescharacteristic
142#324—132no—
143#324—132no—
144#323—261no—
145#323—261no—
146C22×C13—21no—
147C22×C13—21no—
148C22×C13—22no—
149C22×C13—42no—
150C22×C13—42no—
151C22×C13—41no—
152C22×C13—41no—
153C22×C13—41no—
154C22×C13—41no—
155C22×C13—41no—
156C22×C13—81no—
157C22×C13—81no—
158C22×C13#40811yescharacteristic
159C22×C13C2×#9911yescharacteristic
160C22×C13C2×#10111yescharacteristic
161C4×C13—21no—
162C4×C13—22no—
163C4×C13—44no—
164C4×C13—41no—
165C4×C13—41no—
166C4×C13—41no—
167C4×C13—82no—
168C4×C13#35312yes—
169C22×Q8—21no—
170C22×D4C2×Dic1311yescharacteristic
171C23×C4C22⋊D1311yescharacteristic
172C23×C4C22⋊D1311yescharacteristic
173C2×M16—521no—
174C22×C8—521no—
175C4⋊Q8—41no—
176C4⋊Q8—41no—
177C22⋊Q8—44no—
178C22⋊Q8—44no—
179C4×D4—41no—
180C4×D4—41no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4C2×Dic1312yes—
186C2×C4⋊C4C22×D1311yescharacteristic
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4C22⋊D1311yescharacteristic
190C2×C22⋊C4C22⋊D1311yescharacteristic
191C2×C42C2×Dic1312yes—
192C2×C42C2×Dic1311yescharacteristic
193C22⋊C8—262no—
194C22⋊C8—262no—
195C22⋊C8—521no—
196C22⋊C8—521no—
197#95—21no—
198C2×C13—21no—
199C2×C13—21no—
200C2×C13—42no—
201C2×C13—81no—
202C2×C13#147211yescharacteristic
203C2×C13C2×#35311yescharacteristic
204C2×C13#213511yescharacteristic
205C24C22⋊Dic1311yescharacteristic
206C24C22⋊Dic1311yescharacteristic
207C2×Q8—42no—
208C2×Q8—42no—
209C2×Q8—41no—
210C2×Q8—41no—
211C2×D4—22no—
212C2×D4—22no—
213C2×D4—41no—
214C22×C4—22no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—22no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4C22⋊Dic1311yescharacteristic
223C22×C4C22⋊Dic1311yescharacteristic
224C22×C4C22×Dic1311yescharacteristic
225C22×C4C2×C22⋊D1311yescharacteristic
226C22×C4C2×C22⋊D1311yescharacteristic
227M16—1042no—
228C2×C8—522no—
229C2×C8—522no—
230C2×C8—1042no—
231C4⋊C4—24no—
232C4⋊C4—41no—
233C4⋊C4—42no—
234C4⋊C4—44no—
235C4⋊C4—44no—
236C4⋊C4—42no—
237C22⋊C4—41no—
238C22⋊C4—41no—
239C22⋊C4—44no—
240C22⋊C4—44no—
241C42—21no—
242C42—21no—
243C42—24no—
244C13#1157011yescharacteristic, complemented, Sylow
245C23—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23—41no—
251C23—41no—
252C23—41no—
253C23—41no—
254C23#8807612yes—
255C23C2×C22⋊Dic1311yescharacteristic
256Q8—82no—
257Q8—82no—
258D4—44no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—24no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4#8807411yescharacteristic
279C2×C4#8807411yescharacteristic
280C2×C4#8820212yes—
281C8—1042no—
282C8—1042no—
283C22—21no—
284C22—21no—
285C22—22no—
286C22—42no—
287C22—42no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—81no—
294C22—81no—
295C22C2×#8807411yescharacteristic
296C22C2×#8807611yescharacteristic
297C22#1171889511yescharacteristic
298C4—21no—
299C4—22no—
300C4—44no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—82no—
305C4#1171813712yes—
306C2—21no—
307C2—21no—
308C2—42no—
309C2—81no—
310C2#1311320011yescharacteristic
311C2C2×#1171813711yescharacteristic
312C2#1311653111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2542C2
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2542D13
hypocenterC13#11570
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2542

Complements

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

NH ≅ G/Ntype
3. #13112782C2semidirect
244. C13#11570semidirect

Maximal subgroups

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

subgroupindex
#131131742
#131131542
#131127822
C13×#25422
#1157013