Finite Group Databasebeta

← #15782606

Subgroups — #15782606

Order 3328.

384 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 81 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#13115050C211yesmaximal, characteristic
2#13115050C212yesmaximal
3#13112963C211yesmaximal, characteristic
4#13112963C212yesmaximal
5C13×#2809C211yesmaximal, characteristic
6#11719517C2211yescharacteristic
7C13×#400—21no—
8C13×#398—22no—
9C13×#391C2211yescharacteristic
10C13×#391C2212yes—
11C13×#389—21no—
12C13×#387—22no—
13C2×#88076C2212yes—
14C2×#88076C2211yescharacteristic
15#11718625—22no—
16#11718625—21no—
17#11718115—22no—
18#11718115—21no—
19C22×Q8×C13C2311yescharacteristic
20C2×C13×C4⋊C4—22no—
21C2×C13×C4⋊C4—21no—
22C2×C13×C4⋊C4—21no—
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4D412yes—
25C2×C13×C4⋊C4D411yescharacteristic
26C2×C42×C13D412yes—
27C2×C42×C13D411yescharacteristic
28Q8×Dic13—41no—
29Q8×Dic13—41no—
30#88180—22no—
31#88180—21no—
32C2×#6099—22no—
33C2×#6099—21no—
34C13×#95—21no—
35C13×#95—22no—
36C13×#95—22no—
37C13×#95—22no—
38C13×#95—22no—
39#88076—22no—
40#88076—21no—
41#88076Q814yes—
42#88076Q812yes—
43#88048—42no—
44#88048—41no—
45#88047—42no—
46#88047—41no—
47#13465—131nomaximal, Sylow
48C2×Q8×C13—41no—
49C2×Q8×C13—41no—
50C2×Q8×C13C2×Q812yes—
51C2×Q8×C13C2×Q811yescharacteristic
52C2×Q8×C13#4111yescharacteristic
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13C2×D412yes—
58C22×C4×C13C2×D411yescharacteristic
59C13×C4⋊C4—42no—
60C13×C4⋊C4—41no—
61C13×C4⋊C4—44no—
62C13×C4⋊C4—42no—
63C13×C4⋊C4—81no—
64C13×C4⋊C4—81no—
65C42×C13—41no—
66C42×C13—42no—
67C22⋊Dic13—41no—
68C4⋊Dic13—21no—
69C4⋊Dic13—22no—
70C4⋊Dic13—22no—
71C4⋊Dic13—21no—
72C4×Dic13—42no—
73C4×Dic13—41no—
74#6099—24no—
75#6099—22no—
76#6099—41no—
77#6099—42no—
78C2×#1055—42no—
79C2×#1055—41no—
80#2809D1311yescharacteristic
81#1857—132no—
82#1857—131no—
83#1394—131no—
84#1394—132no—
85C23×C13#12011yescharacteristic
86Q8×C13—42no—
87Q8×C13—41no—
88Q8×C13—41no—
89C2×C4×C13—22no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—41no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13C22⋊Q812yes—
105C2×C4×C13C22⋊Q811yescharacteristic
106C2×C4×C13C4⋊Q812yes—
107C2×C4×C13C4⋊Q811yescharacteristic
108C2×Dic13—41no—
109C2×Dic13—41no—
110#1055—44no—
111#1055—42no—
112#519—131no—
113#428—262no—
114#428—261no—
115C2×#101—132no—
116C2×#101—131no—
117#400—21no—
118#398—22no—
119#391C2×D1311yescharacteristic
120#391C2×D1312yes—
121#389—21no—
122#387—22no—
123#339—262no—
124#339—261no—
125C22×C13—21no—
126C22×C13—21no—
127C22×C13#39511yescharacteristic
128C22×C13B(4,𝔽2)11yescharacteristic
129C22×C13#45811yescharacteristic
130C4×C13—22no—
131C4×C13—21no—
132C4×C13—22no—
133C4×C13—21no—
134C4×C13—42no—
135C4×C13—82no—
136C4×C13—81no—
137C4×C13—82no—
138Dic13—81no—
139Dic13—81no—
140C22×Q8C22×D1311yescharacteristic
141C2×M16—262no—
142C2×M16—261no—
143C4×Q8—521no—
144C4×Q8—521no—
145#117—262no—
146#117—261no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4C22⋊D1312yes—
152C2×C4⋊C4C22⋊D1311yescharacteristic
153C2×C42C22⋊D1312yes—
154C2×C42C22⋊D1311yescharacteristic
155#107—522no—
156#107—521no—
157#106—522no—
158#106—521no—
159#101—134no—
160#101—132no—
161#101—262no—
162#101—261no—
163#95—21no—
164#95—22no—
165#95—22no—
166#95—22no—
167#95—22no—
168C2×C13—21no—
169C2×C13—21no—
170C2×C13#206211yescharacteristic
171C2×C13#220311yescharacteristic
172C2×C13#220411yescharacteristic
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8Q8×D1311yescharacteristic
176C2×Q8Q8×D1312yes—
177C2×Q8#613111yescharacteristic
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4C2×C22⋊D1312yes—
183C22×C4C2×C22⋊D1311yescharacteristic
184M16—264no—
185M16—262no—
186M16—521no—
187M16—522no—
188C2×C8—522no—
189C2×C8—521no—
190C4⋊C4—42no—
191C4⋊C4—41no—
192C4⋊C4—44no—
193C4⋊C4—42no—
194C4⋊C4—81no—
195C4⋊C4—81no—
196C4⋊C4—262no—
197C4⋊C4—261no—
198C4⋊C4—261no—
199C4⋊C4—262no—
200C22⋊C4—521no—
201C42—41no—
202C42—42no—
203C42—522no—
204C42—521no—
205C13#1346511yescharacteristic, complemented, Sylow
206C23#8820711yescharacteristic
207Q8—41no—
208Q8—42no—
209Q8—41no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—42no—
225C2×C4—521no—
226C2×C4—521no—
227C2×C4#8819812yes—
228C2×C4#8819811yescharacteristic
229C2×C4#8820012yes—
230C2×C4#8820011yescharacteristic
231C8—522no—
232C8—524no—
233C22—21no—
234C22—21no—
235C22#1171889011yescharacteristic
236C22#1171890411yescharacteristic
237C22#1171890511yescharacteristic
238C4—21no—
239C4—22no—
240C4—21no—
241C4—22no—
242C4—42no—
243C4—82no—
244C4—81no—
245C4—82no—
246C4—1041no—
247C4—1041no—
248C2—21no—
249C2—21no—
250C2#1311618811yescharacteristic
251C2#1311685711yescharacteristic
252C2#1311686211yescharacteristic
subgroupG/H
centerC22#11718905
commutator, cosocleC22×Q8×C13C23
FrattiniC22×Q8C22×D13
FittingC13×#2809C2
socleC22×C13B(4,𝔽2)
prime radicalC23×C13#120
hypercenter#2809D13
hypocenterC13#13465
LCSG ▷ C22×Q8×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #2809

Complements

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

NH ≅ G/Ntype
205. C13#13465semidirect

Maximal subgroups

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

subgroupindex
#131150502
#131129632
C13×#28092
#1346513