Finite Group Databasebeta

← #16019250

Subgroups — #16019250

Order 3328.

502 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 131 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#13125407C212yesmaximal, complemented
2#13117002C212yesmaximal, complemented
3#13116996C212yesmaximal, complemented
4#13116934C212yesmaximal, complemented
5#13116922C211yesmaximal, characteristic
6#13116900C212yesmaximal, complemented
7#13116894C212yesmaximal, complemented
8C2×#11718093C211yesmaximal, characteristic, complemented
9C13×#2216C211yesmaximal, characteristic, complemented
10#11719329—22no—
11C2×C13×Q32C2211yescharacteristic
12C22×C13×C16C2211yescharacteristic
13C13×#467C2212yes—
14#11718852C2212yes—
15Q16×Dic13C2212yes—
16C2×#88068C2212yes—
17#11718776C2212yes—
18C2×C8×Dic13C2211yescharacteristic
19C22×#6090C2211yescharacteristic
20#11718709—22no—
21C2×D208C2211yescharacteristic
22#11718539C2212yes—
23#11718533C2212yes—
24#11718461—22no—
25#11718449—22no—
26C13×#366C2211yescharacteristic
27C13×#358C2212yes—
28#11718156C2212yes—
29#11718101C2212yes—
30#11718096C2211yescharacteristic
31#11718093C2212yes—
32#11718093C2212yes—
33#11718083C2212yes—
34#11718082C2212yes—
35C2×C13×Q16C2312yes—
36C22×C8×C13C2311yescharacteristic
37C13×C22⋊Q8—22no—
38#88201—22no—
39Q8×Dic13—22no—
40C2×#6106—22no—
41#88184—22no—
42C2×C4×Dic13D411yescharacteristic
43C22×#1055D411yescharacteristic
44C2×D104C2312yes—
45#88152—42no—
46#88147—22no—
47#88146—42no—
48#88144—22no—
49#88140—42no—
50#88135—42no—
51C13×Q32—41no—
52C2×C13×C16—41no—
53C2×C13×C16C2311yescharacteristic
54C2×C13×C16C2311yescharacteristic
55C13×#107C2312yes—
56C13×#103—22no—
57#88075—22no—
58#88068—42no—
59#88061—22no—
60#88058C2312yes—
61C8×Dic13D412yes—
62C8×Dic13C2312yes—
63C2×#6090—41no—
64C2×#6090C2312yes—
65#88049—22no—
66#88048—22no—
67D208—41no—
68#33816—131nomaximal, Sylow
69C2×Q8×C13—22no—
70C22×C4×C13C2×D411yescharacteristic
71C2×C22⋊D13—42no—
72C22×Dic13D811yescharacteristic
73C22×Dic13D811yescharacteristic
74C2×D52—22no—
75C2×C4×D13—42no—
76C13×Q16—22no—
77C13×Q16—22no—
78C2×C8×C13—21no—
79C2×C8×C13—21no—
80C2×C8×C13C2×D411yescharacteristic
81C2×C8×C13C2411yescharacteristic
82C13×C4⋊C4—22no—
83C13×C4⋊C4—42no—
84C13×C22⋊C4—42no—
85#6106—44no—
86#6103—42no—
87#6103—42no—
88#6103—42no—
89#6103—42no—
90C4⋊Dic13—22no—
91C4⋊Dic13—42no—
92C4⋊Dic13—42no—
93#6101—42no—
94C4×Dic13—42no—
95C4×Dic13D812yes—
96C4×Dic13C2×D412yes—
97C2×#1055—41no—
98C2×#1055C2×D412yes—
99D104—22no—
100D104—22no—
101C13×C16—21no—
102C13×C16—21no—
103#6090—22no—
104#3168—132no—
105#2229—132no—
106#2228—132no—
107#2217—132no—
108#2216D1311yescharacteristic, complemented
109#2215—131no—
110#2211—132no—
111#2210—132no—
112C2×C4⋊C16—131no—
113C23×C13C2×D811yescharacteristic
114C22×D13—42no—
115Q8×C13—42no—
116Q8×C13—42no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13C2×D811yescharacteristic
122C2×C4×C13C22×D411yescharacteristic
123C22⋊D13—84no—
124C2×Dic13—22no—
125C2×Dic13—41no—
126C2×Dic13—42no—
127C2×Dic13C2×D812yes—
128C2×Dic13C2×D812yes—
129D52—42no—
130D52—42no—
131C4×D13—84no—
132C8×C13—21no—
133C8×C13H(5,𝔽2)11yescharacteristic
134C8×C132−1+411yescharacteristic
135#1055—22no—
136#529—262no—
137C2×Q32C2×D1311yescharacteristic
138C2×SD32—132no—
139C2×D16—131no—
140C22×C16—131no—
141C22×C16C2×D1311yescharacteristic
142#499—132no—
143#495—132no—
144#488—262no—
145#467C2×D1312yes—
146#466—132no—
147#465—262no—
148C4×Q16—132no—
149C4×SD16—262no—
150C4×D8—132no—
151C2×C4×C8—131no—
152#367—132no—
153#366—131no—
154#366C2×D1311yescharacteristic
155C4⋊C16—132no—
156C4⋊C16—132no—
157#358—132no—
158#358C2×D1312yes—
159#357—132no—
160#357—132no—
161C22×C13—21no—
162C22×C13—21no—
163C22×C13#50812yes—
164C22×C13C22×D811yescharacteristic
165C2×D13—82no—
166C2×D13—82no—
167C2×D13—82no—
168C4×C13—21no—
169C4×C13—82no—
170C4×C13—82no—
171C4×C13#53711yescharacteristic
172C4×C13#57511yescharacteristic
173Dic13—22no—
174Dic13—22no—
175Dic13—82no—
176C2×Q16C22×D1312yes—
177C2×SD16—262no—
178C2×D8—132no—
179C22×C8—131no—
180C22×C8C22×D1311yescharacteristic
181#126—522no—
182#125—262no—
183#124—262no—
184#123—522no—
185C22⋊Q8—22no—
186#121—262no—
187C4×Q8—262no—
188C4×D4—262no—
189C4×D4—522no—
190#117—522no—
191C2×C42—131no—
192Q32—41no—
193SD32—522no—
194D16—521no—
195C2×C16—41no—
196C2×C16—132no—
197C2×C16—521no—
198C2×C16C22×D1311yescharacteristic
199C2×C16C22×D1311yescharacteristic
200#107—132no—
201#107C22×D1312yes—
202#106—262no—
203#103—22no—
204#103—262no—
205#102—262no—
206#102—262no—
207C4×C8—132no—
208C4×C8—132no—
209C2×C13—22no—
210C2×C13#324511yescharacteristic
211C2×C13C2×#50811yescharacteristic
212C2×C13#341411yescharacteristic
213D13—162no—
214C2×Q8—22no—
215C2×D4—262no—
216C2×D4—522no—
217C22×C4—131no—
218C22×C4—131no—
219C22×C4—522no—
220C22×C4D4×D1311yescharacteristic
221Q16—22no—
222Q16—22no—
223SD16—524no—
224D8—262no—
225D8—262no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—132no—
229C2×C8—521no—
230C2×C8D4×D1311yescharacteristic
231C2×C8C23×D1311yescharacteristic
232C4⋊C4—22no—
233C4⋊C4—42no—
234C4⋊C4—262no—
235C4⋊C4—522no—
236C4⋊C4—522no—
237C4⋊C4—522no—
238C22⋊C4—42no—
239C22⋊C4—522no—
240C22⋊C4—522no—
241C22⋊C4—522no—
242C22⋊C4—522no—
243C42—132no—
244C42—132no—
245C42—522no—
246C16—21no—
247C16—21no—
248C16—262no—
249C13#3381611yescharacteristic, complemented, Sylow
250C23—522no—
251C23D8×D1311yescharacteristic
252Q8—42no—
253Q8—42no—
254D4—522no—
255D4—522no—
256D4—1044no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—132no—
262C2×C4—132no—
263C2×C4—262no—
264C2×C4—521no—
265C2×C4—522no—
266C2×C4—1044no—
267C2×C4D8×D1311yescharacteristic
268C2×C4C2×D4×D1311yescharacteristic
269C8—21no—
270C8—262no—
271C8#8825111yescharacteristic
272C8#8825711yescharacteristic
273C22—21no—
274C22—21no—
275C22—1042no—
276C22—1042no—
277C22—1042no—
278C22#1171858012yes—
279C22C2×D8×D1311yescharacteristic
280C4—21no—
281C4—82no—
282C4—82no—
283C4—262no—
284C4—262no—
285C4—1042no—
286C4#1171930211yescharacteristic
287C4#1171947311yescharacteristic
288C2—22no—
289C2—2082no—
290C2#1312614211yescharacteristic
291C2C2×#1171858011yescharacteristic
292C2#1312796911yescharacteristic
subgroupG/H
centerC22C2×D8×D13
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#2216C2
socleC22×C13C22×D8
prime radical#13116922C2
hypercenter#2216D13
hypocenterC13#33816
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2216

Complements

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

NH ≅ G/Ntype
1. #13125407C2semidirect
2. #13117002C2semidirect
3. #13116996C2semidirect
4. #13116934C2semidirect
6. #13116900C2semidirect
7. #13116894C2semidirect
8. C2×#11718093C2semidirect
9. C13×#2216C2semidirect
108. #2216D13semidirect
249. C13#33816semidirect

Maximal subgroups

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

subgroupindex
#131254072
#131170022
#131169962
#131169342
#131169222
#131169002
#131168942
C2×#117180932
C13×#22162
#3381613