Finite Group Databasebeta

← #15752017

Subgroups — #15752017

Order 3328.

478 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 95 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#13116307C212yesmaximal, complemented
3#13112659C212yesmaximal, complemented
4#13112657C211yesmaximal, characteristic
5C13×#2683C211yesmaximal, characteristic
6C2×C13×C22⋊Q8—22no—
7C13×#396—22no—
8C13×#395—21no—
9C13×#390C2211yescharacteristic
10C13×#389C2212yes—
11C13×#386—21no—
12C2×#88072—21no—
13C2×#88047—22no—
14C2×#88047—21no—
15#11718596C2211yescharacteristic
16#11718121—22no—
17#11718116C2212yes—
18#11718116C2211yescharacteristic
19C22×Q8×C13—21no—
20C22×D4×C13D411yescharacteristic
21C23×C4×C13—21no—
22C13×C22⋊Q8—44no—
23C13×C22⋊Q8—44no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4D412yes—
27C2×C13×C4⋊C4D412yes—
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C22⋊C4—22no—
30C2×C13×C22⋊C4—22no—
31C2×C13×C22⋊C4—21no—
32C2×C42×C13C2311yescharacteristic
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—22no—
35C22×#1055—21no—
36C22×#1055—22no—
37C13×#95—21no—
38C13×#95—22no—
39#88072—42no—
40#88047—42no—
41#88047—44no—
42#7797—131nomaximal, Sylow
43C24×C13—21no—
44C2×Q8×C13—44no—
45C2×Q8×C13—81no—
46C2×D4×C13—21no—
47C2×D4×C13—41no—
48C2×D4×C13—41no—
49C2×D4×C13Q1612yes—
50C22×C4×C13—22no—
51C22×C4×C13—22no—
52C22×C4×C13—21no—
53C22×C4×C13—44no—
54C22×C4×C13—81no—
55C22×C4×C13C2×D412yes—
56C22×C4×C13C2×D411yescharacteristic
57C22×Dic13—41no—
58C13×C4⋊C4—22no—
59C13×C4⋊C4—42no—
60C13×C4⋊C4—41no—
61C13×C4⋊C4—44no—
62C13×C4⋊C4—42no—
63C13×C4⋊C4—42no—
64C13×C4⋊C4D814yes—
65C13×C22⋊C4—44no—
66C13×C22⋊C4—42no—
67C13×C22⋊C4—42no—
68C13×C22⋊C4—81no—
69C42×C13—41no—
70C4⋊Dic13—41no—
71C4⋊Dic13—41no—
72C4⋊Dic13—42no—
73C4⋊Dic13—42no—
74C2×#1055—22no—
75C2×#1055—24no—
76C2×#1055—42no—
77C2×#1055—41no—
78C2×#1055—42no—
79C2×#1055—41no—
80#2683D1311yescharacteristic
81#2093—131no—
82#2083—132no—
83#1271—132no—
84#1270—131no—
85C23×C13—22no—
86C23×C13—42no—
87C23×C13—41no—
88C23×C13—42no—
89C23×C13—41no—
90C23×C13#12011yescharacteristic
91Q8×C13—84no—
92D4×C13—42no—
93D4×C13—81no—
94C2×C4×C13—21no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—21no—
98C2×C4×C13—24no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—41no—
104C2×C4×C13—42no—
105C2×C4×C13—42no—
106C2×C4×C13—84no—
107C2×C4×C13C2×D812yes—
108C2×C4×C13C2×Q1611yescharacteristic
109C2×C4×C13AGL(1,ℤ/8)12yes—
110C2×C4×C13#13711yescharacteristic
111C2×Dic13—82no—
112C2×Dic13—81no—
113#1055—44no—
114#1055—42no—
115C2×C22⋊Q8—22no—
116C2×#107—262no—
117C2×#107—261no—
118C2×#102—261no—
119#396—22no—
120#395—21no—
121#390C2×D1311yescharacteristic
122#389C2×D1312yes—
123#386—21no—
124#384—131no—
125#340—262no—
126#336—132no—
127#336—131no—
128C22×C13—42no—
129C22×C13—44no—
130C22×C13—82no—
131C22×C13—81no—
132C22×C13—81no—
133C22×C13#44712yes—
134C22×C13#45111yescharacteristic
135C22×C13#45311yescharacteristic
136C22×C13#45612yes—
137C22×C13#45811yescharacteristic
138C4×C13—22no—
139C4×C13—22no—
140C4×C13—21no—
141C4×C13—21no—
142C4×C13—44no—
143C4×C13—82no—
144C4×C13—81no—
145Dic13—161no—
146C22×Q8—21no—
147C22×D4C22⋊D1311yescharacteristic
148C23×C4—21no—
149C22×C8—262no—
150C22×C8—261no—
151C22⋊Q8—44no—
152C22⋊Q8—44no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—262no—
156C2×C4⋊C4—261no—
157C2×C4⋊C4C22⋊D1312yes—
158C2×C4⋊C4C22⋊D1312yes—
159C2×C4⋊C4C22⋊D1311yescharacteristic
160C2×C22⋊C4—22no—
161C2×C22⋊C4—22no—
162C2×C22⋊C4—21no—
163C2×C42C22×D1311yescharacteristic
164#107—522no—
165#107—524no—
166#102—522no—
167#95—21no—
168#95—22no—
169C2×C13—82no—
170C2×C13#161012yes—
171C2×C13#161411yescharacteristic
172C2×C13#161911yescharacteristic
173C2×C13#164912yes—
174C2×C13#166011yescharacteristic
175C24—21no—
176C2×Q8—44no—
177C2×Q8—81no—
178C2×D4—21no—
179C2×D4—41no—
180C2×D4—41no—
181C2×D4#610712yes—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—21no—
185C22×C4—44no—
186C22×C4—81no—
187C22×C4—521no—
188C22×C4C2×C22⋊D1312yes—
189C22×C4C2×C22⋊D1311yescharacteristic
190C2×C8—262no—
191C2×C8—264no—
192C2×C8—522no—
193C2×C8—521no—
194C2×C8—522no—
195C2×C8—521no—
196C4⋊C4—22no—
197C4⋊C4—41no—
198C4⋊C4—42no—
199C4⋊C4—44no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—521no—
203C4⋊C4—521no—
204C4⋊C4—522no—
205C4⋊C4—522no—
206C4⋊C4#610414yes—
207C22⋊C4—44no—
208C22⋊C4—42no—
209C22⋊C4—42no—
210C22⋊C4—81no—
211C42—41no—
212C13#779711yescharacteristic, complemented, Sylow
213C23—22no—
214C23—42no—
215C23—41no—
216C23—41no—
217C23—42no—
218C23#8820711yescharacteristic
219Q8—84no—
220D4—42no—
221D4—81no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—24no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—84no—
235C2×C4—1042no—
236C2×C4—1041no—
237C2×C4C2×#610412yes—
238C2×C4#8818612yes—
239C2×C4#8819611yescharacteristic
240C2×C4C2×#610711yescharacteristic
241C8—522no—
242C8—524no—
243C22—42no—
244C22—44no—
245C22—81no—
246C22—81no—
247C22—82no—
248C22#1171887812yes—
249C22#1171888911yescharacteristic
250C22#1171890211yescharacteristic
251C22#1171890411yescharacteristic
252C22#1171890712yes—
253C4—21no—
254C4—21no—
255C4—22no—
256C4—22no—
257C4—44no—
258C4—81no—
259C4—82no—
260C4—2081no—
261C2—82no—
262C2#1311383912yes—
263C2#1311386111yescharacteristic
264C2#1311389011yescharacteristic
265C2#1311408512yes—
266C2#1311414711yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2683C2
socleC23×C13#120
prime radicalC22×D4×C13D4
hypercenter#2683D13
hypocenterC13#7797
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2683

Complements

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

NH ≅ G/Ntype
2. #13116307C2semidirect
3. #13112659C2semidirect
212. C13#7797semidirect

Maximal subgroups

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

subgroupindex
#131163642
#131163072
#131126592
#131126572
C13×#26832
#779713