Finite Group Databasebeta

← #15752173

Subgroups — #15752173

Order 3328.

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

normal subgroups only

This group has 422 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#13116364C211yesmaximal, characteristic
2#13116244C212yesmaximal, complemented
3#13112662C212yesmaximal, complemented
4#13112657C211yesmaximal, characteristic
5C13×#2804C211yesmaximal, characteristic
6C13×#400—21no—
7C13×#393—22no—
8C13×#391C2212yes—
9C13×#390C2211yescharacteristic
10C13×#386—21no—
11C13×#385—22no—
12C2×#88075—22no—
13C2×#88072—21no—
14C2×#88047—21no—
15#11718596C2211yescharacteristic
16#11718121—22no—
17#11718116C2212yes—
18#11718116C2211yescharacteristic
19C22×Q8×C13D412yes—
20C22×D4×C13D411yescharacteristic
21C23×C4×C13—21no—
22C2×C13×C4⋊C4—21no—
23C2×C13×C4⋊C4D412yes—
24C2×C13×C4⋊C4D411yescharacteristic
25C2×C13×C22⋊C4—22no—
26C2×C13×C22⋊C4—22no—
27C2×C13×C22⋊C4—21no—
28C2×C42×C13C2311yescharacteristic
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13—22no—
31C22×#1055—21no—
32C22×#1055—22no—
33C13×#95—22no—
34C13×#95—21no—
35C13×#95—22no—
36C13×#95—22no—
37#88075—44no—
38#88072—42no—
39#88047—42no—
40#7821—131nomaximal, Sylow
41C24×C13—21no—
42C2×Q8×C13—22no—
43C2×Q8×C13—22no—
44C2×Q8×C13—42no—
45C2×Q8×C13—42no—
46C2×D4×C13—21no—
47C2×D4×C13—41no—
48C2×D4×C13—41no—
49C2×D4×C13Q1612yes—
50C22×C4×C13—22no—
51C22×C4×C13—21no—
52C22×C4×C13—22no—
53C22×C4×C13—81no—
54C22×C4×C13—82no—
55C22×C4×C13C2×D411yescharacteristic
56C22×C4×C13C2×D412yes—
57C22×Dic13—41no—
58C13×C4⋊C4—42no—
59C13×C4⋊C4—41no—
60C13×C4⋊C4—81no—
61C13×C22⋊C4—42no—
62C13×C22⋊C4—42no—
63C13×C22⋊C4—82no—
64C13×C22⋊C4—81no—
65C42×C13—41no—
66C4⋊Dic13—41no—
67C4⋊Dic13—41no—
68C4⋊Dic13—42no—
69C4⋊Dic13—42no—
70C2×#1055—22no—
71C2×#1055—41no—
72C2×#1055—41no—
73C2×#1055—42no—
74C2×#1055—42no—
75C2×#1055—42no—
76#2804D1311yescharacteristic
77#2093—131no—
78#2072—132no—
79#1272—132no—
80#1270—131no—
81C23×C13—22no—
82C23×C13—42no—
83C23×C13—41no—
84C23×C13—42no—
85C23×C13—41no—
86C23×C13#12011yescharacteristic
87Q8×C13—44no—
88Q8×C13—82no—
89D4×C13—42no—
90D4×C13—81no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—21no—
94C2×C4×C13—22no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—41no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—84no—
104C2×C4×C13C2×Q1611yescharacteristic
105C2×C4×C13#13512yes—
106C2×C4×C13AGL(1,ℤ/8)12yes—
107C2×C4×C13#13711yescharacteristic
108C2×Dic13—82no—
109C2×Dic13—81no—
110#1055—42no—
111#1055—82no—
112C2×#107—261no—
113C2×#103—262no—
114C2×#102—261no—
115#400—21no—
116#393—22no—
117#391C2×D1312yes—
118#390C2×D1311yescharacteristic
119#386—21no—
120#385—22no—
121#384—131no—
122#340—262no—
123#336—132no—
124#336—131no—
125C22×C13—42no—
126C22×C13—44no—
127C22×C13—82no—
128C22×C13—81no—
129C22×C13—81no—
130C22×C13#44912yes—
131C22×C13#45111yescharacteristic
132C22×C13#45311yescharacteristic
133C22×C13#45512yes—
134C22×C13#45811yescharacteristic
135C4×C13—22no—
136C4×C13—22no—
137C4×C13—21no—
138C4×C13—21no—
139C4×C13—82no—
140C4×C13—81no—
141C4×C13—82no—
142Dic13—161no—
143C22×Q8C22⋊D1312yes—
144C22×D4C22⋊D1311yescharacteristic
145C23×C4—21no—
146C22×C8—261no—
147C22×C8—262no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—262no—
150C2×C4⋊C4—261no—
151C2×C4⋊C4C22⋊D1312yes—
152C2×C4⋊C4C22⋊D1311yescharacteristic
153C2×C22⋊C4—22no—
154C2×C22⋊C4—22no—
155C2×C22⋊C4—21no—
156C2×C42C22×D1311yescharacteristic
157#107—522no—
158#103—524no—
159#102—522no—
160#95—22no—
161#95—21no—
162#95—22no—
163#95—22no—
164C2×C13—82no—
165C2×C13#161212yes—
166C2×C13#161411yescharacteristic
167C2×C13#162011yescharacteristic
168C2×C13#164412yes—
169C2×C13#165911yescharacteristic
170C24—21no—
171C2×Q8—22no—
172C2×Q8—22no—
173C2×Q8—42no—
174C2×Q8—42no—
175C2×D4—21no—
176C2×D4—41no—
177C2×D4—41no—
178C2×D4#610712yes—
179C22×C4—22no—
180C22×C4—21no—
181C22×C4—22no—
182C22×C4—81no—
183C22×C4—82no—
184C22×C4—521no—
185C22×C4C2×C22⋊D1311yescharacteristic
186C22×C4C2×C22⋊D1312yes—
187C2×C8—262no—
188C2×C8—521no—
189C2×C8—521no—
190C2×C8—522no—
191C2×C8—522no—
192C2×C8—522no—
193C4⋊C4—41no—
194C4⋊C4—42no—
195C4⋊C4—81no—
196C4⋊C4—521no—
197C4⋊C4—521no—
198C4⋊C4—522no—
199C4⋊C4—522no—
200C22⋊C4—42no—
201C22⋊C4—42no—
202C22⋊C4—82no—
203C22⋊C4—81no—
204C42—41no—
205C13#782111yescharacteristic, complemented, Sylow
206C23—22no—
207C23—42no—
208C23—41no—
209C23—42no—
210C23—41no—
211C23#8820711yescharacteristic
212Q8—44no—
213Q8—82no—
214D4—42no—
215D4—81no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—84no—
229C2×C4—1042no—
230C2×C4—1041no—
231C2×C4#8819611yescharacteristic
232C2×C4C2×#610711yescharacteristic
233C2×C4#8820312yes—
234C2×C4#8820412yes—
235C8—522no—
236C8—1042no—
237C22—42no—
238C22—44no—
239C22—81no—
240C22—81no—
241C22—82no—
242C22#1171888911yescharacteristic
243C22#1171889912yes—
244C22#1171890211yescharacteristic
245C22#1171890312yes—
246C22#1171890411yescharacteristic
247C4—21no—
248C4—21no—
249C4—22no—
250C4—22no—
251C4—82no—
252C4—81no—
253C4—82no—
254C4—2081no—
255C2—82no—
256C2#1311385012yes—
257C2#1311386111yescharacteristic
258C2#1311389511yescharacteristic
259C2#1311405012yes—
260C2#1311414211yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2804C2
socleC23×C13#120
prime radicalC22×D4×C13D4
hypercenter#2804D13
hypocenterC13#7821
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2804

Complements

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

NH ≅ G/Ntype
2. #13116244C2semidirect
3. #13112662C2semidirect
205. C13#7821semidirect

Maximal subgroups

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

subgroupindex
#131163642
#131162442
#131126622
#131126572
C13×#28042
#782113