Finite Group Databasebeta

← #15782609

Subgroups — #15782609

Order 3328.

384 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 79 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#13122824C211yesmaximal, characteristic
2#13115051C212yesmaximal
3#13112963C211yesmaximal, characteristic
4#13112962C212yesmaximal
5C13×#1857C211yesmaximal, characteristic
6C13×#519C2211yescharacteristic
7C13×#428—21no—
8C2×C13×#101C2211yescharacteristic
9C13×#391C2211yescharacteristic
10#11718891C2212yes—
11C2×#88076C2212yes—
12#11718656—22no—
13#11718647—21no—
14#11718589—21no—
15#11718322—22no—
16#11718316—22no—
17C13×#339—21no—
18#11718124—22no—
19C22×Q8×C13C2311yescharacteristic
20C2×C13×M16—21no—
21C4×Q8×C13—41no—
22C4×Q8×C13—41no—
23C13×#117—22no—
24C13×#117—21no—
25C2×C13×C4⋊C4D411yescharacteristic
26C2×C42×C13D411yescharacteristic
27C2×C4⋊Dic13—21no—
28C2×C4⋊Dic13—21no—
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13D412yes—
31C2×#6101—22no—
32C2×C4×Dic13D412yes—
33C2×#6099—22no—
34C13×#107—41no—
35C13×#106—41no—
36C13×#101—21no—
37C13×#101Q812yes—
38C13×#95—22no—
39#88076—22no—
40#88076Q814yes—
41#88071—21no—
42#88071—22no—
43#88071—22no—
44#88071—22no—
45#88048—42no—
46#88047—42no—
47#13465—131nomaximal, Sylow
48C2×Q8×C13—41no—
49C2×Q8×C13—41no—
50C2×Q8×C13C2×Q811yescharacteristic
51C2×Q8×C13C2×Q812yes—
52C2×Q8×C13#4111yescharacteristic
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13C2×D412yes—
56C22×C4×C13C2×D411yescharacteristic
57C22×Dic13—22no—
58C22×Dic13—22no—
59C13×M16—22no—
60C13×M16—41no—
61C2×C8×C13—41no—
62C13×C4⋊C4—21no—
63C13×C4⋊C4—21no—
64C13×C4⋊C4—22no—
65C13×C4⋊C4—22no—
66C13×C4⋊C4—41no—
67C13×C22⋊C4—41no—
68C42×C13—41no—
69C42×C13—42no—
70C42×C13—41no—
71C4⋊Dic13—42no—
72C4⋊Dic13—42no—
73C4⋊Dic13—81no—
74C4⋊Dic13—81no—
75#6101—44no—
76C4×Dic13—42no—
77#6099—24no—
78#6099—42no—
79C2×#1055—42no—
80#2809—131no—
81#1857—132no—
82#1857D1311yescharacteristic
83#1394—132no—
84#1394—131no—
85C23×C13#12011yescharacteristic
86Q8×C13—42no—
87Q8×C13—41no—
88Q8×C13—41no—
89C2×C4×C13—22no—
90C2×C4×C13—21no—
91C2×C4×C13—22no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13—42no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13—41no—
100C2×C4×C13C22⋊Q812yes—
101C2×C4×C13C22⋊Q811yescharacteristic
102C2×C4×C13C4⋊Q812yes—
103C2×C4×C13C4⋊Q811yescharacteristic
104C2×Dic13—42no—
105C2×Dic13—42no—
106C2×Dic13—42no—
107C2×Dic13—42no—
108C2×Dic13—42no—
109C2×Dic13—42no—
110C8×C13—42no—
111#1055—44no—
112#519C2×D1311yescharacteristic
113#428—21no—
114#428—262no—
115C2×#101—132no—
116C2×#101C2×D1311yescharacteristic
117#400—261no—
118#398—262no—
119#391—132no—
120#391C2×D1311yescharacteristic
121#389—261no—
122#387—262no—
123#339—21no—
124#339—262no—
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—81no—
136C4×C13—81no—
137C4×C13—81no—
138Dic13—82no—
139Dic13—82no—
140C22×Q8C22×D1311yescharacteristic
141C2×M16—21no—
142C2×M16—262no—
143C4×Q8—41no—
144C4×Q8—41no—
145#117—22no—
146#117—21no—
147C2×C4⋊C4—132no—
148C2×C4⋊C4—262no—
149C2×C4⋊C4—261no—
150C2×C4⋊C4—261no—
151C2×C4⋊C4—261no—
152C2×C4⋊C4C22⋊D1311yescharacteristic
153C2×C42—132no—
154C2×C42C22⋊D1311yescharacteristic
155#107—41no—
156#107—522no—
157#106—41no—
158#106—522no—
159#101—21no—
160#101—134no—
161#101—262no—
162#101Dic2612yes—
163#95—22no—
164#95—261no—
165#95—262no—
166#95—262no—
167#95—262no—
168C2×C13—21no—
169C2×C13—21no—
170C2×C13#206211yescharacteristic
171C2×C13#220311yescharacteristic
172C2×C13#220411yescharacteristic
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8C2×Dic2611yescharacteristic
176C2×Q8#612711yescharacteristic
177C2×Q8Q8×D1312yes—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—262no—
181C22×C4—262no—
182C22×C4D4×D1312yes—
183C22×C4C2×C22⋊D1311yescharacteristic
184M16—22no—
185M16—41no—
186M16—264no—
187M16—522no—
188C2×C8—41no—
189C2×C8—522no—
190C4⋊C4—21no—
191C4⋊C4—22no—
192C4⋊C4—21no—
193C4⋊C4—22no—
194C4⋊C4—41no—
195C4⋊C4—522no—
196C4⋊C4—524no—
197C4⋊C4—522no—
198C4⋊C4—1041no—
199C4⋊C4—1041no—
200C22⋊C4—41no—
201C42—41no—
202C42—41no—
203C42—42no—
204C42—522no—
205C13#1346511yescharacteristic, complemented, Sylow
206C23#8819111yescharacteristic
207Q8—41no—
208Q8—41no—
209Q8—42no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—522no—
222C2×C4—522no—
223C2×C4—522no—
224C2×C4—522no—
225C2×C4—522no—
226C2×C4—522no—
227C2×C4#8814212yes—
228C2×C4#8815012yes—
229C2×C4#8817811yescharacteristic
230C2×C4#8819811yescharacteristic
231C8—42no—
232C8—524no—
233C22—21no—
234C22—21no—
235C22#1171864011yescharacteristic
236C22#1171869311yescharacteristic
237C22#1171871411yescharacteristic
238C4—21no—
239C4—22no—
240C4—22no—
241C4—21no—
242C4—42no—
243C4—81no—
244C4—81no—
245C4—81no—
246C4—1042no—
247C4—1042no—
248C2—21no—
249C2—21no—
250C2#1311618911yescharacteristic
251C2#1311685611yescharacteristic
252C2#1311686111yescharacteristic
subgroupG/H
centerC22#11718693
commutator, cosocleC22×Q8×C13C23
FrattiniC22×Q8C22×D13
FittingC13×#1857C2
socleC22×C13B(4,𝔽2)
prime radicalC23×C13#120
hypercenter#1857D13
hypocenterC13#13465
LCSG ▷ C22×Q8×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1857

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
#131228242
#131150512
#131129632
#131129622
C13×#18572
#1346513