Finite Group Databasebeta

← #15778906

Subgroups — #15778906

Order 3328.

544 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 123 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×#11718133C212yesmaximal
2#13114824C212yesmaximal
3#13112961C212yesmaximal
4C4×C13×#124C211yesmaximal, characteristic
5C2×C13×#124C2211yescharacteristic
6C2×C4×Q8×C13C411yescharacteristic, complemented
7C2×C4×D4×C13C2211yescharacteristic
8C13×#391C411yescharacteristic, complemented
9C13×#390C2211yescharacteristic
10C13×#388—22no—
11C13×#382C411yescharacteristic, complemented
12C4×C13×C22⋊C4—22no—
13C43×C13C411yescharacteristic, complemented
14C2×#88074C2214yes—
15#11718873—22no—
16#11718133—24no—
17#11718118—22no—
18C22×Q8×C13C2×C411yescharacteristic
19C22×D4×C13C2311yescharacteristic
20C23×C4×C13D412yes—
21C13×#124—22no—
22C13×#124D412yes—
23C13×#124Q812yes—
24C4×Q8×C13—41no—
25C4×Q8×C13—41no—
26C4×D4×C13—41no—
27C4×D4×C13—41no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C22⋊C4—22no—
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4D412yes—
34C2×C42×C13—21no—
35C2×C42×C13—21no—
36C2×C42×C13—21no—
37C2×C42×C13C2×C411yescharacteristic
38C2×C42×C13C2×C411yescharacteristic
39C2×C42×C13C2×C411yescharacteristic
40C2×C22⋊Dic13—24no—
41C2×C4⋊Dic13—42no—
42C13×#95—22no—
43C13×#95—22no—
44#88074—24no—
45#88074—24no—
46#88071—42no—
47#12798—131nomaximal, Sylow
48C24×C13C2×D412yes—
49C2×Q8×C13—21no—
50C2×Q8×C13—41no—
51C2×Q8×C13—41no—
52C2×Q8×C13C4⋊C412yescomplemented
53C2×D4×C13—41no—
54C2×D4×C13—41no—
55C2×D4×C13C2×D411yescharacteristic
56C2×D4×C13C2×Q811yescharacteristic
57C2×D4×C13#4112yes—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—22no—
62C22×C4×C13—22no—
63C22×C4×C13—21no—
64C22×C4×C13—44no—
65C22×C4×C13C22⋊C412yes—
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22×C411yescharacteristic
69C22×Dic13—44no—
70C13×C4⋊C4—41no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—42no—
73C13×C22⋊C4—24no—
74C13×C22⋊C4—24no—
75C13×C22⋊C4—42no—
76C13×C22⋊C4—44no—
77C42×C13—21no—
78C42×C13—21no—
79C42×C13—21no—
80C42×C13—41no—
81C42×C13—42no—
82C42×C13—42no—
83C42×C13—41no—
84C42×C13—41no—
85C42×C13C4⋊C412yescomplemented
86C22⋊Dic13—44no—
87C22⋊Dic13—44no—
88C4⋊Dic13—84no—
89C4×#124D1311yescharacteristic
90C2×#354—132no—
91#1799—132no—
92#1393—132no—
93C23×C13—22no—
94C23×C13—22no—
95C23×C13—42no—
96C23×C13—42no—
97C23×C13C2×C22⋊C411yescharacteristic
98C23×C13#12112yes—
99C23×C13C22⋊Q812yes—
100Q8×C13—42no—
101Q8×C13—42no—
102D4×C13—41no—
103D4×C13—41no—
104D4×C13—42no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—22no—
108C2×C4×C13—22no—
109C2×C4×C13—22no—
110C2×C4×C13—22no—
111C2×C4×C13—21no—
112C2×C4×C13—22no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—44no—
120C2×C4×C13—41no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—41no—
124C2×C4×C13—82no—
125C2×C4×C13#9911yescharacteristic
126C2×C4×C13#9911yescharacteristic
127C2×C4×C13C2×C4⋊C411yescharacteristic
128C2×C4×C13#11711yescharacteristic
129C2×Dic13—84no—
130C2×Dic13—84no—
131C2×Dic13—84no—
132C2×#124C2×D1311yescharacteristic
133C2×C4×Q8Dic1311yescharacteristic, complemented
134C2×C4×D4C2×D1311yescharacteristic
135C2×#99—134no—
136#391Dic1311yescharacteristic, complemented
137#390C2×D1311yescharacteristic
138#388—22no—
139#382Dic1311yescharacteristic, complemented
140#380—262no—
141C4×C22⋊C4—22no—
142C43Dic1311yescharacteristic, complemented
143#354—264no—
144#342—262no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—22no—
148C22×C13—22no—
149C22×C13—42no—
150C22×C13—42no—
151C22×C13—42no—
152C22×C13—42no—
153C22×C13—82no—
154C22×C13#38011yescharacteristic
155C22×C13C2×#9911yescharacteristic
156C22×C13#41011yescharacteristic
157C4×C13—21no—
158C4×C13—21no—
159C4×C13—21no—
160C4×C13—42no—
161C4×C13—42no—
162C4×C13—42no—
163C4×C13—42no—
164C4×C13—41no—
165C4×C13—81no—
166C4×C13#35412yescomplemented
167Dic13—164no—
168C22×Q8C2×Dic1311yescharacteristic
169C22×D4C22×D1311yescharacteristic
170C23×C4C22⋊D1312yes—
171#124—22no—
172#124Dic2612yes—
173#124D5212yes—
174C4×Q8—41no—
175C4×Q8—41no—
176C4×D4—41no—
177C4×D4—41no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—522no—
180C2×C4⋊C4C2×Dic1311yescharacteristic
181C2×C4⋊C4C2×Dic1311yescharacteristic
182C2×C22⋊C4—22no—
183C2×C22⋊C4—22no—
184C2×C22⋊C4—264no—
185C2×C22⋊C4C22⋊D1312yes—
186C2×C42—21no—
187C2×C42—21no—
188C2×C42—21no—
189C2×C42C2×Dic1311yescharacteristic
190C2×C42C2×Dic1311yescharacteristic
191C2×C42C2×Dic1311yescharacteristic
192#99—264no—
193#99—264no—
194#95—22no—
195#95—22no—
196#95—522no—
197C2×C13—21no—
198C2×C13—21no—
199C2×C13—42no—
200C2×C13—42no—
201C2×C13#179911yescharacteristic
202C2×C13C2×#35411yescharacteristic
203C2×C13#212611yescharacteristic
204C24C2×C22⋊D1312yes—
205C2×Q8—21no—
206C2×Q8—41no—
207C2×Q8—41no—
208C2×Q8C4⋊Dic1312yescomplemented
209C2×D4—41no—
210C2×D4—41no—
211C2×D4C2×Dic2611yescharacteristic
212C2×D4C2×D5211yescharacteristic
213C2×D4#612712yes—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—21no—
220C22×C4—44no—
221C22×C4—524no—
222C22×C4C22⋊Dic1312yes—
223C22×C4C22⋊Dic1311yescharacteristic
224C22×C4C22⋊Dic1311yescharacteristic
225C22×C4C22×Dic1311yescharacteristic
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—42no—
229C4⋊C4—1044no—
230C22⋊C4—24no—
231C22⋊C4—24no—
232C22⋊C4—42no—
233C22⋊C4—44no—
234C22⋊C4—524no—
235C22⋊C4—524no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—41no—
240C42—42no—
241C42—42no—
242C42—41no—
243C42—41no—
244C42C4⋊Dic1312yescomplemented
245C13#1279811yescharacteristic, complemented, Sylow
246C23—22no—
247C23—22no—
248C23—42no—
249C23—42no—
250C23#8817812yes—
251C23#8818412yes—
252C23C2×C22⋊Dic1311yescharacteristic
253Q8—42no—
254Q8—42no—
255D4—41no—
256D4—41no—
257D4—42no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—44no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—82no—
278C2×C4—1044no—
279C2×C4—1044no—
280C2×C4—1044no—
281C2×C4#8807411yescharacteristic
282C2×C4#8807411yescharacteristic
283C2×C4C2×C4⋊Dic1311yescharacteristic
284C2×C4#8818011yescharacteristic
285C22—21no—
286C22—21no—
287C22—22no—
288C22—22no—
289C22—42no—
290C22—42no—
291C22—42no—
292C22—42no—
293C22—82no—
294C22#1171887311yescharacteristic
295C22C2×#8807411yescharacteristic
296C22#1171890111yescharacteristic
297C4—21no—
298C4—21no—
299C4—21no—
300C4—42no—
301C4—42no—
302C4—42no—
303C4—41no—
304C4—42no—
305C4—81no—
306C4—2084no—
307C4#1171813312yescomplemented
308C2—21no—
309C2—21no—
310C2—42no—
311C2—42no—
312C2#1311482411yescharacteristic
313C2C2×#1171813311yescharacteristic
314C2#1311650111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC22×D4C22×D13
FittingC4×C13×#124C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenterC4×#124D13
hypocenterC13#12798
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
6. C2×C4×Q8×C13C4semidirect
8. C13×#391C4semidirect
11. C13×#382C4semidirect
13. C43×C13C4semidirect
52. C2×Q8×C13C4⋊C4semidirect
85. C42×C13C4⋊C4semidirect
133. C2×C4×Q8Dic13semidirect
136. #391Dic13semidirect
139. #382Dic13semidirect
142. C43Dic13semidirect
166. C4×C13#354semidirect
208. C2×Q8C4⋊Dic13semidirect
244. C42C4⋊Dic13semidirect
245. C13#12798semidirect
307. C4#11718133semidirect

Maximal subgroups

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

subgroupindex
C2×#117181332
#131148242
#131129612
C4×C13×#1242
#1279813