Finite Group Databasebeta

← #15773511

Subgroups — #15773511

Order 3328.

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

normal subgroups only

This group has 482 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#13119835C211yesmaximal, characteristic
2C4×#88076C211yesmaximal, characteristic, complemented
3#13112840C214yesmaximal, complemented
4C13×#1467C211yesmaximal, characteristic, complemented
5C2×C4×Q8×C13C2211yescharacteristic
6C2×#88201—21no—
7C2×#88128C411yescharacteristic
8C13×#432—21no—
9C2×#88076—21no—
10#11718652C412yes—
11#11718652C2212yes—
12#11718649—21no—
13#11718600—21no—
14#11718600—21no—
15C4×C4⋊Dic13C411yescharacteristic
16C4×#6099—21no—
17C13×#324—21no—
18C13×#324C2212yes—
19#11718122C2212yes—
20C22×Q8×C13D411yescharacteristic
21C22×D52—21no—
22C22×D52—21no—
23C22×D52C2×C412yes—
24C4×Q8×C13—41no—
25C4×Q8×C13—41no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C4⋊C4C2311yescharacteristic
29C2×C42×C13C2×C411yescharacteristic
30C2×C42×C13D411yescharacteristic
31C2×C42×C13D411yescharacteristic
32#88201—44no—
33C2×#6103—22no—
34C2×#6103—22no—
35C2×#6103—22no—
36C2×#6103—22no—
37C2×C4⋊Dic13—21no—
38C2×C4×Dic13—21no—
39C2×#6099—22no—
40#88128—41no—
41#88128—41no—
42C13×C4⋊C8—41no—
43C13×C22⋊C8—22no—
44C13×#97—41no—
45#88076—24no—
46#88071C2×C412yes—
47#88043—41no—
48C4×#1055—41no—
49#11781—131nomaximal, Sylow
50C23×D13—22no—
51C2×Q8×C13—22no—
52C2×Q8×C13—22no—
53C2×Q8×C13—41no—
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22×C411yescharacteristic
59C22×C4×C13C2×D411yescharacteristic
60C22×C4×C13C2×D411yescharacteristic
61C22×Dic13—22no—
62C2×D52—42no—
63C2×D52—42no—
64C2×D52—42no—
65C2×D52—42no—
66C2×D52—42no—
67C2×D52—41no—
68C2×D52—41no—
69C2×D52—42no—
70C2×D52—82no—
71C2×C8×C13—42no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C42×C13—21no—
76C42×C13—21no—
77C42×C13—21no—
78C42×C13—21no—
79C42×C13—21no—
80C42×C13—21no—
81#6103—44no—
82#6103—44no—
83#6103—82no—
84#6103—82no—
85C4⋊Dic13—42no—
86C4×Dic13—42no—
87#6099—24no—
88#6099—42no—
89C2×#1055—42no—
90#2548—131no—
91C4×#101—131no—
92#1467D1311yescharacteristic, complemented
93#1345—134no—
94C23×C13C2×C22⋊C411yescharacteristic
95C22×D13—42no—
96C22×D13—42no—
97C22×D13—42no—
98C22×D13—42no—
99C22×D13—42no—
100C22×D13—42no—
101C22×D13—42no—
102Q8×C13—44no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—22no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13#9911yescharacteristic
118C2×C4×C13#9911yescharacteristic
119C2×C4×C13#10412yes—
120C2×C4×C13AGL(1,ℤ/8)12yes—
121C2×Dic13—42no—
122C2×Dic13—42no—
123C2×Dic13—42no—
124D52—82no—
125D52—84no—
126D52—84no—
127D52—82no—
128C8×C13—82no—
129#1055—44no—
130C2×#127—131no—
131C2×#124—261no—
132C2×C4×Q8C2×D1311yescharacteristic
133#432—21no—
134C2×#101—261no—
135C4×M16—261no—
136#394—132no—
137#394—132no—
138#390—261no—
139#390—261no—
140#390—261no—
141C4×C4⋊C4—131no—
142#343—132no—
143#324—21no—
144#324C2×D1312yes—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13C2×#9911yescharacteristic
148C22×C13#41811yescharacteristic
149C22×C13C2×#10411yescharacteristic
150C2×D13—82no—
151C2×D13—82no—
152C2×D13—82no—
153C2×D13—82no—
154C2×D13—82no—
155C2×D13—82no—
156C2×D13—82no—
157C4×C13—21no—
158C4×C13—22no—
159C4×C13—22no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13—41no—
164C4×C13#35512yes—
165Dic13—82no—
166C22×Q8D5211yescharacteristic
167C22×D4—132no—
168C22×D4—261no—
169C22×D4—261no—
170C2×M16—262no—
171#127—521no—
172#127—521no—
173#124—524no—
174C4×Q8—41no—
175C4×Q8—41no—
176C2×C4⋊C4—261no—
177C2×C4⋊C4C4×D1311yescharacteristic
178C2×C4⋊C4C22⋊D1311yescharacteristic
179C2×C4⋊C4C22×D1311yescharacteristic
180C2×C22⋊C4—262no—
181C2×C22⋊C4—262no—
182C2×C22⋊C4—262no—
183C2×C22⋊C4—262no—
184C2×C42—261no—
185C2×C42C4×D1311yescharacteristic
186C2×C42D5211yescharacteristic
187C2×C42C22⋊D1311yescharacteristic
188C4⋊C8—41no—
189#101—264no—
190C22⋊C8—22no—
191#97—41no—
192#97—521no—
193C4×C8—521no—
194#95—132no—
195C2×C13—21no—
196C2×C13—21no—
197C2×C13#150711yescharacteristic
198C2×C13#212211yescharacteristic
199C2×C13C2×#35511yescharacteristic
200D13—162no—
201C24—262no—
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—41no—
205C2×D4—522no—
206C2×D4—522no—
207C2×D4—522no—
208C2×D4—522no—
209C2×D4—522no—
210C2×D4—522no—
211C2×D4—521no—
212C2×D4—521no—
213C2×D4—1042no—
214C22×C4—262no—
215C22×C4#610311yescharacteristic
216C22×C4#610311yescharacteristic
217C22×C4#610311yescharacteristic
218C22×C4#610311yescharacteristic
219C22×C4C2×C4×D1311yescharacteristic
220C22×C4C2×D5211yescharacteristic
221C22×C4C2×C22⋊D1311yescharacteristic
222M16—264no—
223M16—522no—
224C2×C8—42no—
225C2×C8—522no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—522no—
230C22⋊C4—524no—
231C22⋊C4—524no—
232C22⋊C4—1042no—
233C22⋊C4—1042no—
234C42—21no—
235C42—21no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—522no—
241C13#1178111yescharacteristic, complemented, Sylow
242C23—522no—
243C23—522no—
244C23—522no—
245C23—522no—
246C23—522no—
247C23—522no—
248C23—522no—
249C23C2×#610311yescharacteristic
250Q8—44no—
251D4—1044no—
252D4—1042no—
253D4—1044no—
254D4—1042no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—522no—
270C2×C4—522no—
271C2×C4—522no—
272C2×C4#8804611yescharacteristic
273C2×C4#8804611yescharacteristic
274C2×C4#8806512yes—
275C2×C4#8816212yes—
276C8—82no—
277C8—524no—
278C22—21no—
279C22—21no—
280C22—1042no—
281C22—1042no—
282C22—1042no—
283C22—1042no—
284C22—1042no—
285C22—1042no—
286C22—1042no—
287C22C2×#8804611yescharacteristic
288C22#1171879211yescharacteristic
289C22C2×#8806511yescharacteristic
290C4—22no—
291C4—22no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—1042no—
298C4#1171806912yes—
299C2—21no—
300C2—21no—
301C2—2082no—
302C2#1311335311yescharacteristic
303C2#1311648511yescharacteristic
304C2C2×#1171806911yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1467C2
socleC22×C13C2×#99
prime radicalC2×#88128C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1467D13
hypocenterC13#11781
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
2. C4×#88076C2semidirect
3. #13112840C2semidirect
4. C13×#1467C2semidirect
92. #1467D13semidirect
241. C13#11781semidirect

Maximal subgroups

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

subgroupindex
#131198352
C4×#880762
#131128402
C13×#14672
#1178113