Finite Group Databasebeta

← #15752237

Subgroups — #15752237

Order 3328.

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

normal subgroups only

This group has 438 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#13116374C212yesmaximal, complemented
2#13116369C211yesmaximal, characteristic
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×#88048—21no—
15C2×#88047—22no—
16#11718596C2211yescharacteristic
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#88048—42no—
40#88047—44no—
41#7833—131nomaximal, Sylow
42C24×C13—21no—
43C2×Q8×C13—22no—
44C2×Q8×C13—22no—
45C2×Q8×C13—42no—
46C2×Q8×C13—42no—
47C2×D4×C13—21no—
48C2×D4×C13—41no—
49C2×D4×C13—41no—
50C2×D4×C13Q1612yes—
51C22×C4×C13—22no—
52C22×C4×C13—21no—
53C22×C4×C13—22no—
54C22×C4×C13—82no—
55C22×C4×C13—81no—
56C22×C4×C13C2×D411yescharacteristic
57C22×C4×C13C2×D412yes—
58C22×Dic13—41no—
59C13×C4⋊C4—42no—
60C13×C4⋊C4—41no—
61C13×C4⋊C4—81no—
62C13×C22⋊C4—42no—
63C13×C22⋊C4—42no—
64C13×C22⋊C4—82no—
65C13×C22⋊C4—81no—
66C42×C13—41no—
67C4⋊Dic13—41no—
68C4⋊Dic13—42no—
69C4⋊Dic13—42no—
70C4⋊Dic13—41no—
71C2×#1055—22no—
72C2×#1055—24no—
73C2×#1055—41no—
74C2×#1055—42no—
75C2×#1055—42no—
76C2×#1055—41no—
77#2804D1311yescharacteristic
78#2095—132no—
79#2094—131no—
80#1272—132no—
81#1270—131no—
82C23×C13—22no—
83C23×C13—42no—
84C23×C13—42no—
85C23×C13—41no—
86C23×C13—41no—
87C23×C13#12011yescharacteristic
88Q8×C13—44no—
89Q8×C13—82no—
90D4×C13—42no—
91D4×C13—81no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—21no—
95C2×C4×C13—22no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—41no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—84no—
105C2×C4×C13C2×Q1611yescharacteristic
106C2×C4×C13#13512yes—
107C2×C4×C13#13711yescharacteristic
108C2×C4×C13#13712yes—
109C2×Dic13—81no—
110C2×Dic13—82no—
111#1055—42no—
112#1055—44no—
113C2×#107—262no—
114C2×#106—261no—
115C2×#103—262no—
116C2×#102—261no—
117#400—21no—
118#393—22no—
119#391C2×D1312yes—
120#390C2×D1311yescharacteristic
121#386—21no—
122#385—22no—
123#384—131no—
124#336—131no—
125#336—132no—
126C22×C13—42no—
127C22×C13—44no—
128C22×C13—82no—
129C22×C13—81no—
130C22×C13—81no—
131C22×C13#45111yescharacteristic
132C22×C13#45212yes—
133C22×C13#45311yescharacteristic
134C22×C13#45312yes—
135C22×C13#45811yescharacteristic
136C4×C13—21no—
137C4×C13—21no—
138C4×C13—22no—
139C4×C13—22no—
140C4×C13—82no—
141C4×C13—81no—
142C4×C13—82no—
143Dic13—161no—
144C22×Q8C22⋊D1312yes—
145C22×D4C22⋊D1311yescharacteristic
146C23×C4—21no—
147C22×C8—261no—
148C22×C8—262no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—261no—
151C2×C4⋊C4—262no—
152C2×C4⋊C4C22⋊D1312yes—
153C2×C4⋊C4C22⋊D1311yescharacteristic
154C2×C22⋊C4—22no—
155C2×C22⋊C4—22no—
156C2×C22⋊C4—21no—
157C2×C42C22×D1311yescharacteristic
158#107—524no—
159#106—522no—
160#103—524no—
161#102—522no—
162#95—22no—
163#95—21no—
164#95—22no—
165#95—22no—
166C2×C13—82no—
167C2×C13#161411yescharacteristic
168C2×C13#161812yes—
169C2×C13#163011yescharacteristic
170C2×C13#163212yes—
171C2×C13#165511yescharacteristic
172C24—21no—
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—42no—
176C2×Q8—42no—
177C2×D4—21no—
178C2×D4—41no—
179C2×D4—41no—
180C2×D4#610712yes—
181C22×C4—22no—
182C22×C4—21no—
183C22×C4—22no—
184C22×C4—82no—
185C22×C4—81no—
186C22×C4—521no—
187C22×C4C2×C22⋊D1311yescharacteristic
188C22×C4C2×C22⋊D1312yes—
189C2×C8—262no—
190C2×C8—264no—
191C2×C8—521no—
192C2×C8—522no—
193C2×C8—521no—
194C2×C8—522no—
195C4⋊C4—41no—
196C4⋊C4—42no—
197C4⋊C4—81no—
198C4⋊C4—521no—
199C4⋊C4—522no—
200C4⋊C4—521no—
201C4⋊C4—522no—
202C22⋊C4—42no—
203C22⋊C4—42no—
204C22⋊C4—82no—
205C22⋊C4—81no—
206C42—41no—
207C13#783311yescharacteristic, complemented, Sylow
208C23—22no—
209C23—42no—
210C23—42no—
211C23—41no—
212C23—41no—
213C23#8820711yescharacteristic
214Q8—44no—
215Q8—82no—
216D4—42no—
217D4—81no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—84no—
231C2×C4—1041no—
232C2×C4—1042no—
233C2×C4#8819611yescharacteristic
234C2×C4C2×#610711yescharacteristic
235C2×C4#8820412yes—
236C2×C4#8820512yes—
237C8—522no—
238C8—524no—
239C22—42no—
240C22—44no—
241C22—81no—
242C22—82no—
243C22—81no—
244C22#1171888911yescharacteristic
245C22#1171890012yes—
246C22#1171890211yescharacteristic
247C22#1171890212yes—
248C22#1171890411yescharacteristic
249C4—21no—
250C4—21no—
251C4—22no—
252C4—22no—
253C4—82no—
254C4—82no—
255C4—81no—
256C4—2081no—
257C2—82no—
258C2#1311386111yescharacteristic
259C2#1311388412yes—
260C2#1311395711yescharacteristic
261C2#1311397012yes—
262C2#1311412511yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2804C2
socleC23×C13#120
prime radicalC22×D4×C13D4
hypercenter#2804D13
hypocenterC13#7833
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
1. #13116374C2semidirect
3. #13112662C2semidirect
207. C13#7833semidirect

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×#28042
#783313