Finite Group Databasebeta

← #15767889

Subgroups — #15767889

Order 3328.

356 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 93 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#13115634C211yesmaximal, characteristic
2#13114977C211yesmaximal, characteristic, complemented
3#13113611C211yesmaximal, characteristic, complemented
4#13113607C211yesmaximal, characteristic, complemented
5#13113262C211yesmaximal, characteristic
6#13113262C211yesmaximal, characteristic
7C13×#1275C211yesmaximal, characteristic, complemented
8C2×C4×D52C2211yescharacteristic
9C13×#431C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C2×C13×#97C2211yescharacteristic
12C2×#88060—22no—
13#11718585C2211yescharacteristic
14#11718585C2211yescharacteristic
15C2×C4⋊#1055C2211yescharacteristic
16#11718144—22no—
17#11718051—22no—
18#11718051—22no—
19#11718050—22no—
20#11718049—22no—
21C22×D52Q811yescharacteristic
22C22×C4×D13—21no—
23C22×C8×C13D412yes—
24C2×C42×C13C2311yescharacteristic
25C2×#6103—21no—
26C2×C4⋊Dic13Q811yescharacteristic
27C2×#6099—21no—
28C2×#6099—21no—
29C22×#1055—21no—
30C4×D52—21no—
31C4×D52—21no—
32C4×D52—21no—
33C4×D52—21no—
34C13×C4⋊C8—21no—
35C13×C4⋊C8—21no—
36C13×C22⋊C8—21no—
37C13×C22⋊C8—21no—
38C13×#97—21no—
39C13×#97—21no—
40C4×C8×C13D412yes—
41C4×C8×C13D412yes—
42#88060—44no—
43C4⋊#1055—21no—
44C4⋊#1055—21no—
45C4⋊#1055—21no—
46C4⋊#1055—21no—
47C4⋊#1055—21no—
48C4⋊#1055—21no—
49#10659—131nomaximal, Sylow
50C23×D13—21no—
51C22×C4×C13C2×D411yescharacteristic
52C22×C4×C13C2×Q811yescharacteristic
53C22×C4×C13#4111yescharacteristic
54C22×Dic13—21no—
55C2×D52—21no—
56C2×D52—21no—
57C2×D52—42no—
58C2×C4×D13—41no—
59C2×C4×D13—41no—
60C2×C4×D13—42no—
61C2×C4×D13—42no—
62C2×C8×C13—22no—
63C2×C8×C13—22no—
64C2×C8×C13—22no—
65C2×C8×C13—22no—
66C2×C8×C13—22no—
67C42×C13C2×D411yescharacteristic
68C42×C13C2×D411yescharacteristic
69C42×C13#4111yescharacteristic
70C42×C13#4111yescharacteristic
71#6103—41no—
72#6103—41no—
73C4⋊Dic13—21no—
74C4⋊Dic13—21no—
75#6099—42no—
76#6099—42no—
77C2×#1055—41no—
78C2×#1055—41no—
79C2×#1055—41no—
80C2×#1055—42no—
81#1955—131no—
82#1838—131no—
83#1571—131no—
84#1570—131no—
85#1486—131no—
86#1486—131no—
87#1275D1311yescharacteristic, complemented
88C23×C13C22⋊Q811yescharacteristic
89C22×D13—22no—
90C22×D13—41no—
91C22×D13—42no—
92C22×D13—41no—
93C22×D13—42no—
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13C22⋊Q811yescharacteristic
97C2×C4×C13C22⋊Q811yescharacteristic
98C2×C4×C13#12311yescharacteristic
99C2×C4×C13#12311yescharacteristic
100C2×C4×C13#12311yescharacteristic
101C2×C4×C13#12711yescharacteristic
102C2×C4×C13#13512yes—
103C2×C4×C13AGL(1,ℤ/8)12yes—
104C2×Dic13—41no—
105C2×Dic13—42no—
106D52—22no—
107D52—22no—
108D52—41no—
109D52—41no—
110C4×D13—82no—
111C4×D13—81no—
112C4×D13—81no—
113C8×C13—42no—
114C8×C13—42no—
115C8×C13—42no—
116#1055—81no—
117#1055—81no—
118#1055—81no—
119C2×C4×D4—131no—
120#431C2×D1311yescharacteristic
121#431C2×D1311yescharacteristic
122#423—131no—
123#423—131no—
124C2×C4⋊C8—131no—
125C2×C22⋊C8—262no—
126C2×#97C2×D1311yescharacteristic
127#341—262no—
128#335—262no—
129#334—262no—
130D4⋊C8—262no—
131D4⋊C8—262no—
132C22×C13—21no—
133C22×C13—21no—
134C22×C13#39911yescharacteristic
135C22×C13#47812yes—
136C2×D13—44no—
137C2×D13—42no—
138C2×D13—82no—
139C2×D13—81no—
140C2×D13—81no—
141C4×C13—21no—
142C4×C13—21no—
143C4×C13—21no—
144C4×C13—21no—
145C4×C13#48212yes—
146C4×C13#49511yescharacteristic
147C4×C13#49611yescharacteristic
148Dic13—81no—
149C22×D4—131no—
150C23×C4—261no—
151C2×M16—261no—
152C2×M16—261no—
153C22×C8—261no—
154C22×C8D5212yes—
155C4×D4—261no—
156C4×D4—261no—
157C4×D4—261no—
158C4×D4—261no—
159C2×C4⋊C4—131no—
160C2×C22⋊C4—261no—
161C2×C42C22×D1311yescharacteristic
162C4⋊C8—21no—
163C4⋊C8—21no—
164C4⋊C8—261no—
165C4⋊C8—261no—
166C4⋊C8—261no—
167C4⋊C8—261no—
168C4⋊C8—261no—
169C4⋊C8—261no—
170C22⋊C8—21no—
171C22⋊C8—21no—
172C22⋊C8—524no—
173#97—21no—
174#97—21no—
175C4×C8D5212yes—
176C4×C8D5212yes—
177C2×C13—22no—
178C2×C13#209111yescharacteristic
179C2×C13#209211yescharacteristic
180C2×C13#209811yescharacteristic
181D13—82no—
182C24—261no—
183C2×D4—261no—
184C2×D4—261no—
185C2×D4—522no—
186C22×C4—261no—
187C22×C4—521no—
188C22×C4—521no—
189C22×C4—522no—
190C22×C4—522no—
191C22×C4C2×D5211yescharacteristic
192C22×C4#612911yescharacteristic
193C22×C4Q8×D1311yescharacteristic
194M16—522no—
195M16—522no—
196C2×C8—22no—
197C2×C8—22no—
198C2×C8—22no—
199C2×C8—22no—
200C2×C8—22no—
201C2×C8—521no—
202C2×C8—521no—
203C2×C8—521no—
204C2×C8—522no—
205C4⋊C4—261no—
206C4⋊C4—261no—
207C22⋊C4—521no—
208C22⋊C4—521no—
209C42C2×D5211yescharacteristic
210C42C2×D5211yescharacteristic
211C42#612911yescharacteristic
212C42#612911yescharacteristic
213C13#1065911yescharacteristic, complemented, Sylow
214C23—262no—
215C23—521no—
216C23—522no—
217C23—522no—
218C23—521no—
219C23#8815111yescharacteristic
220D4—262no—
221D4—262no—
222D4—521no—
223D4—521no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—522no—
227C2×C4—521no—
228C2×C4—1041no—
229C2×C4—1041no—
230C2×C4—1042no—
231C2×C4#8812811yescharacteristic
232C2×C4#8814011yescharacteristic
233C2×C4#8814011yescharacteristic
234C2×C4#8814011yescharacteristic
235C2×C4#8815111yescharacteristic
236C2×C4#8815111yescharacteristic
237C2×C4#8815812yes—
238C2×C4#8816212yes—
239C8—42no—
240C8—42no—
241C8—42no—
242C8—1041no—
243C8—1041no—
244C8—1041no—
245C22—21no—
246C22—21no—
247C22—524no—
248C22—522no—
249C22—1042no—
250C22—1041no—
251C22—1041no—
252C22#1171833811yescharacteristic
253C22#1171850812yes—
254C4—21no—
255C4—21no—
256C4—21no—
257C4—21no—
258C4—1041no—
259C4#1171835711yescharacteristic
260C4#1171837311yescharacteristic
261C4#1171839812yes—
262C2—22no—
263C2—1042no—
264C2#1311635311yescharacteristic
265C2#1311635611yescharacteristic
266C2#1311639011yescharacteristic
subgroupG/H
centerC2×C4#88128
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1275C2
socleC22×C13#399
prime radicalC22×D52Q8
hypercenter#1275D13
hypocenterC13#10659
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1275

Complements

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

NH ≅ G/Ntype
2. #13114977C2semidirect
3. #13113611C2semidirect
4. #13113607C2semidirect
7. C13×#1275C2semidirect
87. #1275D13semidirect
213. C13#10659semidirect

Maximal subgroups

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

subgroupindex
#131156342
#131149772
#131136112
#131136072
#131132622
C13×#12752
#1065913