Finite Group Databasebeta

← #15752224

Subgroups — #15752224

Order 3328.

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

normal subgroups only

This group has 494 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#13116374C211yesmaximal, characteristic, complemented
2#13116369C212yesmaximal, complemented
3#13112662C211yesmaximal, characteristic, complemented
4#13112657C212yesmaximal, complemented
5C13×#2733C211yesmaximal, characteristic
6C2×C13×#124—21no—
7C13×#394—21no—
8C13×#392—22no—
9C13×#391C2211yescharacteristic
10C13×#390C2212yes—
11C13×#388—22no—
12C2×#88075—21no—
13C2×#88072—22no—
14C2×#88048—22no—
15C2×#88047—21no—
16#11718596C2211yescharacteristic
17#11718116C2211yescharacteristic
18#11718116C2212yes—
19C22×Q8×C13D411yescharacteristic
20C22×D4×C13—21no—
21C22×D4×C13—21no—
22C22×D4×C13D412yes—
23C13×#124—42no—
24C13×#124—42no—
25C2×C13×C4⋊C4D412yes—
26C2×C13×C4⋊C4D411yescharacteristic
27C2×C13×C22⋊C4—22no—
28C2×C13×C22⋊C4—22no—
29C2×C13×C22⋊C4—22no—
30C2×C13×C22⋊C4—22no—
31C2×C42×C13—21no—
32C2×C42×C13C2311yescharacteristic
33C2×C4⋊Dic13—22no—
34C2×C4⋊Dic13—21no—
35C22×#1055—22no—
36C22×#1055—21no—
37C13×#95—21no—
38C13×#95—22no—
39#88075—42no—
40#88072—44no—
41#88048—44no—
42#88047—42no—
43#7830—131nomaximal, Sylow
44C24×C13—22no—
45C2×Q8×C13—21no—
46C2×Q8×C13—41no—
47C2×Q8×C13—41no—
48C2×Q8×C13SD1612yes—
49C2×D4×C13—22no—
50C2×D4×C13—22no—
51C2×D4×C13—42no—
52C2×D4×C13—42no—
53C2×D4×C13—42no—
54C2×D4×C13—81no—
55C2×D4×C13—81no—
56C2×D4×C13—82no—
57C2×D4×C13—81no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—22no—
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D412yes—
63C22×Dic13—41no—
64C13×C4⋊C4—41no—
65C13×C4⋊C4—42no—
66C13×C22⋊C4—44no—
67C13×C22⋊C4—42no—
68C13×C22⋊C4—42no—
69C13×C22⋊C4—42no—
70C13×C22⋊C4—42no—
71C13×C22⋊C4—82no—
72C42×C13—41no—
73C42×C13—42no—
74C4⋊Dic13—42no—
75C4⋊Dic13—41no—
76C4⋊Dic13—41no—
77C4⋊Dic13—42no—
78C2×#1055—24no—
79C2×#1055—22no—
80C2×#1055—42no—
81C2×#1055—41no—
82C2×#1055—42no—
83C2×#1055—41no—
84#2733D1311yescharacteristic
85#2095—131no—
86#2094—132no—
87#1272—131no—
88#1270—132no—
89C23×C13—42no—
90C23×C13—42no—
91C23×C13—42no—
92C23×C13—42no—
93C23×C13—42no—
94C23×C13—42no—
95C23×C13—42no—
96C23×C13#12011yescharacteristic
97Q8×C13—42no—
98Q8×C13—81no—
99D4×C13—44no—
100D4×C13—82no—
101D4×C13—84no—
102D4×C13—84no—
103C2×C4×C13—22no—
104C2×C4×C13—21no—
105C2×C4×C13—22no—
106C2×C4×C13—21no—
107C2×C4×C13—22no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—41no—
115C2×C4×C13C2×SD1611yescharacteristic
116C2×C4×C13#13512yes—
117C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C13#13712yes—
119C2×Dic13—81no—
120C2×Dic13—82no—
121#1055—42no—
122#1055—44no—
123C2×#124—21no—
124C2×#107—261no—
125C2×#106—262no—
126C2×#103—261no—
127C2×#102—262no—
128#394—21no—
129#392—22no—
130#391C2×D1311yescharacteristic
131#390C2×D1312yes—
132#388—22no—
133#384—131no—
134#336—132no—
135#336—131no—
136C22×C13—82no—
137C22×C13—82no—
138C22×C13—82no—
139C22×C13—82no—
140C22×C13—82no—
141C22×C13—82no—
142C22×C13—82no—
143C22×C13#45011yescharacteristic
144C22×C13#45212yes—
145C22×C13#45311yescharacteristic
146C22×C13#45312yes—
147C22×C13#45811yescharacteristic
148C4×C13—21no—
149C4×C13—21no—
150C4×C13—22no—
151C4×C13—22no—
152C4×C13—42no—
153C4×C13—82no—
154C4×C13—81no—
155Dic13—161no—
156C22×Q8C22⋊D1311yescharacteristic
157C22×D4—21no—
158C22×D4—21no—
159C22×D4C22⋊D1312yes—
160C22×C8—262no—
161C22×C8—261no—
162#124—42no—
163#124—42no—
164C2×C4⋊C4—262no—
165C2×C4⋊C4—261no—
166C2×C4⋊C4C22⋊D1312yes—
167C2×C4⋊C4C22⋊D1311yescharacteristic
168C2×C22⋊C4—22no—
169C2×C22⋊C4—22no—
170C2×C22⋊C4—22no—
171C2×C22⋊C4—22no—
172C2×C42—21no—
173C2×C42C22×D1311yescharacteristic
174#107—522no—
175#106—524no—
176#103—522no—
177#102—524no—
178#95—21no—
179#95—22no—
180C2×C13—162no—
181C2×C13#161311yescharacteristic
182C2×C13#161812yes—
183C2×C13#163112yes—
184C2×C13#163411yescharacteristic
185C2×C13#165511yescharacteristic
186C24—22no—
187C2×Q8—21no—
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8#610512yes—
191C2×D4—22no—
192C2×D4—22no—
193C2×D4—42no—
194C2×D4—42no—
195C2×D4—42no—
196C2×D4—81no—
197C2×D4—81no—
198C2×D4—82no—
199C2×D4—81no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—22no—
203C22×C4—521no—
204C22×C4C2×C22⋊D1311yescharacteristic
205C22×C4C2×C22⋊D1312yes—
206C2×C8—264no—
207C2×C8—262no—
208C2×C8—522no—
209C2×C8—521no—
210C2×C8—521no—
211C2×C8—522no—
212C4⋊C4—42no—
213C4⋊C4—41no—
214C4⋊C4—522no—
215C4⋊C4—521no—
216C4⋊C4—522no—
217C4⋊C4—521no—
218C22⋊C4—44no—
219C22⋊C4—42no—
220C22⋊C4—42no—
221C22⋊C4—42no—
222C22⋊C4—42no—
223C22⋊C4—82no—
224C42—41no—
225C42—42no—
226C13#783011yescharacteristic, complemented, Sylow
227C23—42no—
228C23—42no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23—42no—
233C23—42no—
234C23#8820711yescharacteristic
235Q8—42no—
236Q8—81no—
237D4—44no—
238D4—82no—
239D4—84no—
240D4—84no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—1041no—
254C2×C4—1042no—
255C2×C4#8818611yescharacteristic
256C2×C4C2×#610511yescharacteristic
257C2×C4#8820412yes—
258C2×C4#8820512yes—
259C8—522no—
260C8—524no—
261C22—82no—
262C22—82no—
263C22—82no—
264C22—82no—
265C22—82no—
266C22—82no—
267C22—82no—
268C22#1171887911yescharacteristic
269C22#1171890012yes—
270C22#1171890211yescharacteristic
271C22#1171890212yes—
272C22#1171890411yescharacteristic
273C4—21no—
274C4—21no—
275C4—22no—
276C4—22no—
277C4—42no—
278C4—81no—
279C4—82no—
280C4—2081no—
281C2—162no—
282C2#1311385611yescharacteristic
283C2#1311388412yes—
284C2#1311396312yes—
285C2#1311398111yescharacteristic
286C2#1311412511yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
Fitting, prime radicalC13×#2733C2
socleC23×C13#120
hypercenter#2733D13
hypocenterC13#7830
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2733

Complements

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

NH ≅ G/Ntype
1. #13116374C2semidirect
2. #13116369C2semidirect
3. #13112662C2semidirect
4. #13112657C2semidirect
226. C13#7830semidirect

Maximal subgroups

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

subgroupindex
#131163742
#131163692
#131126622
#131126572
C13×#27332
#783013