Finite Group Databasebeta

← #15751038

Subgroups — #15751038

Order 3328.

608 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 111 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#13117400C211yesmaximal, characteristic
2#13114978C212yesmaximal, complemented
3#13112657C211yesmaximal, characteristic, complemented
4#13112656C212yesmaximal, complemented
5C13×#1270C211yesmaximal, characteristic, complemented
6C2×#88194C411yescharacteristic
7C2×D4×Dic13C411yescharacteristic
8C2×#88147C411yescharacteristic
9C2×#88135—22no—
10C13×#390C2211yescharacteristic
11#11718637C411yescharacteristic
12#11718618—22no—
13#11718600C2211yescharacteristic
14C42×Dic13C2211yescharacteristic
15C13×#336C2212yes—
16#11718142—22no—
17#11718142—22no—
18#11718116C2212yes—
19C22×D4×C13C2×C411yescharacteristic
20C22×C22⋊D13—22no—
21C23×Dic13—21no—
22C22×D52C2×C411yescharacteristic
23C22×C4×D13—21no—
24C22×C8×C13—22no—
25C2×C13×C4⋊C4C2×C411yescharacteristic
26C2×C13×C22⋊C4—22no—
27C2×C42×C13C2311yescharacteristic
28C2×C22⋊Dic13—21no—
29#88194—22no—
30#88194C814yescomplemented
31D4×Dic13—42no—
32C2×#6103—22no—
33C2×#6103—21no—
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×#6101—22no—
36C2×C4×Dic13C2×C411yescharacteristic
37C2×C4×Dic13C2×C411yescharacteristic
38C2×C4×Dic13D412yes—
39C2×C4×Dic13D412yes—
40C22×#1055—22no—
41#88147—42no—
42#88135—44no—
43#88135—44no—
44#7603—131nomaximal, Sylow
45C24×C13—21no—
46C23×D13—21no—
47C2×D4×C13—21no—
48C2×D4×C13—41no—
49C2×D4×C13—41no—
50C2×D4×C13C2×C812yes—
51C22×C4×C13—21no—
52C22×C4×C13C22×C411yescharacteristic
53C22×C4×C13C2×D412yes—
54C2×C22⋊D13—28no—
55C2×C22⋊D13—44no—
56C2×C22⋊D13—44no—
57C22×Dic13—21no—
58C22×Dic13—44no—
59C22×Dic13—42no—
60C22×Dic13C22⋊C411yescharacteristic
61C22×Dic13C22⋊C412yes—
62C22×Dic13C22⋊C411yescharacteristic
63C2×D52—21no—
64C2×D52—41no—
65C2×D52—41no—
66C2×D52C2×C812yes—
67C2×C4×D13—44no—
68C2×C4×D13—42no—
69C2×C8×C13—42no—
70C2×C8×C13—42no—
71C2×C8×C13—42no—
72C13×C4⋊C4—41no—
73C13×C22⋊C4—42no—
74C13×C22⋊C4—42no—
75C42×C13—41no—
76C22⋊Dic13—42no—
77#6103—42no—
78#6103—42no—
79#6103—42no—
80C4⋊Dic13—41no—
81#6101—44no—
82C4×Dic13—22no—
83C4×Dic13—22no—
84C4×Dic13—22no—
85C4×Dic13—42no—
86C4×Dic13C2×C812yes—
87C4×Dic13M1612yes—
88C2×#1055—42no—
89C2×#1055—42no—
90C2×#1055—42no—
91C4×#127—131no—
92#1839—132no—
93#1270—131no—
94#1270—132no—
95#1270D1311yescharacteristic, complemented
96C23×C13—22no—
97C23×C13—41no—
98C23×C13—41no—
99C23×C13—42no—
100C23×C13—42no—
101C23×C13C2×C22⋊C411yescharacteristic
102C22×D13—22no—
103C22×D13—41no—
104C22×D13—41no—
105C22×D13—42no—
106C22×D13—42no—
107D4×C13—42no—
108D4×C13—42no—
109C2×C4×C13—22no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—22no—
113C2×C4×C13—41no—
114C2×C4×C13—42no—
115C2×C4×C13C22×C811yescharacteristic
116C2×C4×C13C2×M1611yescharacteristic
117C2×C4×C13AGL(1,ℤ/8)12yes—
118C2×C4×C13AGL(1,ℤ/8)12yes—
119C22⋊D13—416no—
120C2×Dic13—22no—
121C2×Dic13—22no—
122C2×Dic13—22no—
123C2×Dic13—21no—
124C2×Dic13—22no—
125C2×Dic13—41no—
126C2×Dic13—42no—
127C2×Dic13—84no—
128C2×Dic13C22⋊C814yes—
129C2×Dic13#10012yes—
130D52—42no—
131D52—42no—
132C4×D13—84no—
133C8×C13—82no—
134#1055—82no—
135C2×#127—131no—
136C2×C4×D4—131no—
137C2×C4×D4—131no—
138C2×C4×D4—262no—
139#390—131no—
140#390—262no—
141#390C2×D1311yescharacteristic
142#384—131no—
143C43—131no—
144#336—132no—
145#336—262no—
146#336—262no—
147#336C2×D1312yes—
148C22×C13—42no—
149C22×C13—44no—
150C22×C13—81no—
151C22×C13—81no—
152C22×C13—82no—
153C22×C13C2×C22⋊C811yescharacteristic
154C22×C13#41011yescharacteristic
155C22×C13C2×#10011yescharacteristic
156C22×C13#41812yes—
157C22×C13#42112yes—
158C2×D13—42no—
159C2×D13—44no—
160C2×D13—81no—
161C2×D13—81no—
162C2×D13—82no—
163C4×C13—21no—
164C4×C13—21no—
165C4×C13—22no—
166C4×C13—22no—
167C4×C13—81no—
168Dic13—22no—
169Dic13—24no—
170Dic13—41no—
171Dic13—81no—
172C22×D4—131no—
173C22×D4—262no—
174C22×D4C4×D1311yescharacteristic
175C23×C4—261no—
176C23×C4—261no—
177C22×C8—22no—
178C22×C8—262no—
179#127—134no—
180#127—262no—
181C4×D4—524no—
182C4×D4—524no—
183C4×D4—522no—
184C4×D4—522no—
185C2×C4⋊C4—131no—
186C2×C4⋊C4—262no—
187C2×C4⋊C4C4×D1311yescharacteristic
188C2×C22⋊C4—22no—
189C2×C22⋊C4—261no—
190C2×C22⋊C4—261no—
191C2×C22⋊C4—262no—
192C2×C42—131no—
193C2×C42—131no—
194C2×C42—132no—
195C2×C42—132no—
196C2×C42C22×D1311yescharacteristic
197C2×C13—82no—
198C2×C13#146011yescharacteristic
199C2×C13#147812yes—
200C2×C13#151412yes—
201C2×C13#153611yescharacteristic
202C2×C13#155511yescharacteristic
203D13—82no—
204C24—21no—
205C24—261no—
206C2×D4—21no—
207C2×D4—41no—
208C2×D4—41no—
209C2×D4—132no—
210C2×D4—268no—
211C2×D4—261no—
212C2×D4—521no—
213C2×D4—521no—
214C2×D4—524no—
215C2×D4—524no—
216C2×D4C8×D1312yes—
217C22×C4—21no—
218C22×C4—132no—
219C22×C4—131no—
220C22×C4—131no—
221C22×C4—261no—
222C22×C4—522no—
223C22×C4—524no—
224C22×C4—522no—
225C22×C4—524no—
226C22×C4C2×C4×D1311yescharacteristic
227C22×C4D4×D1312yes—
228C2×C8—42no—
229C2×C8—42no—
230C2×C8—42no—
231C2×C8—522no—
232C2×C8—522no—
233C2×C8—522no—
234C4⋊C4—41no—
235C4⋊C4—521no—
236C4⋊C4—524no—
237C22⋊C4—42no—
238C22⋊C4—42no—
239C22⋊C4—522no—
240C22⋊C4—522no—
241C22⋊C4—522no—
242C22⋊C4—522no—
243C42—41no—
244C42—132no—
245C42—132no—
246C42—262no—
247C42—262no—
248C42—262no—
249C42—522no—
250C13#760311yescharacteristic, complemented, Sylow
251C23—22no—
252C23—41no—
253C23—41no—
254C23—42no—
255C23—42no—
256C23—262no—
257C23—521no—
258C23—521no—
259C23—522no—
260C23—522no—
261C23C22⋊C4×D1311yescharacteristic
262D4—42no—
263D4—42no—
264D4—522no—
265D4—522no—
266D4—5216no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—132no—
274C2×C4—134no—
275C2×C4—262no—
276C2×C4—262no—
277C2×C4—262no—
278C2×C4—261no—
279C2×C4—262no—
280C2×C4—521no—
281C2×C4—522no—
282C2×C4—1044no—
283C2×C4—1044no—
284C2×C4C2×C8×D1311yescharacteristic
285C2×C4M16×D1311yescharacteristic
286C2×C4#8816512yes—
287C2×C4#8816812yes—
288C8—82no—
289C8—1042no—
290C22—42no—
291C22—44no—
292C22—82no—
293C22—81no—
294C22—81no—
295C22—522no—
296C22—524no—
297C22—1042no—
298C22—1041no—
299C22—1041no—
300C22D13×C22⋊C811yescharacteristic
301C22#1171840111yescharacteristic
302C22D13×#10011yescharacteristic
303C22#1171843112yes—
304C22#1171848212yes—
305C4—22no—
306C4—22no—
307C4—21no—
308C4—21no—
309C4—81no—
310C4—264no—
311C4—262no—
312C4—521no—
313C4—1041no—
314C2—82no—
315C2—1042no—
316C2#1311315511yescharacteristic
317C2#1311322512yes—
318C2#1311338112yes—
319C2#1311346911yescharacteristic
320C2#1311354811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1270C2
socleC23×C13C2×C22⋊C4
prime radicalC2×#88194C4
cosocleC2×C42×C13C23
hypercenter#1270D13
hypocenterC13#7603
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #13114978C2semidirect
3. #13112657C2semidirect
4. #13112656C2semidirect
5. C13×#1270C2semidirect
30. #88194C8semidirect
95. #1270D13semidirect
250. C13#7603semidirect

Maximal subgroups

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

subgroupindex
#131174002
#131149782
#131126572
#131126562
C13×#12702
#760313