Finite Group Databasebeta

← #15776647

Subgroups — #15776647

Order 3328.

296 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 69 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#13127701C211yesmaximal, characteristic
2#13117064C211yesmaximal, characteristic, complemented
3#13116881C211yesmaximal, characteristic
4#13114207C211yesmaximal, characteristic, complemented
5#13112895C211yesmaximal, characteristic, complemented
6#13112816C211yesmaximal, characteristic, complemented
7C13×#1331C211yesmaximal, characteristic
8#11719248—21no—
9C4×C13×D8C2211yescharacteristic
10D8×Dic13—21no—
11C2×#88067—21no—
12#11718669—21no—
13#11718539—21no—
14#11718512—21no—
15#11718427—22no—
16#11718360C2211yescharacteristic
17#11718343C2211yescharacteristic
18C8×Dic26C2211yescharacteristic
19C4×C13×C16C2211yescharacteristic
20C13×#335C2211yescharacteristic
21#11718095—22no—
22#11718084—21no—
23#11718078—21no—
24C4⋊#6090C2211yescharacteristic
25C2×C13×D8D411yescharacteristic
26C4×D4×C13—21no—
27D4×Dic13—22no—
28C2×C4⋊Dic13—41no—
29#88178—41no—
30C2×Dic52—21no—
31C2×Dic52—21no—
32#88144—22no—
33#88132—42no—
34#88123—21no—
35#88123—21no—
36C4×Dic26D411yescharacteristic
37C2×C13×C16—21no—
38C13×#107D411yescharacteristic
39C13×C4⋊C8—21no—
40C13×#102—21no—
41C4×C8×C13C2311yescharacteristic
42#88072—22no—
43#88067—42no—
44#88058—21no—
45#88058D412yes—
46#88057—41no—
47#88056—41no—
48#88054—21no—
49C8×Dic13—21no—
50C2×#6090—21no—
51#88048—22no—
52C4⋊#1055D411yescharacteristic
53#12359—131nomaximal, Sylow
54C2×D4×C13—21no—
55C22×C4×C13—41no—
56C22×Dic13—42no—
57C2×Dic26—41no—
58C2×Dic26—41no—
59C2×Dic26D811yescharacteristic
60C13×D8—21no—
61C13×D8SD1612yes—
62C2×C8×C13—41no—
63C2×C8×C13C2×D411yescharacteristic
64C2×C8×C13C2×D411yescharacteristic
65C13×C4⋊C4—21no—
66C13×C22⋊C4—41no—
67C42×C13C2×D411yescharacteristic
68C22⋊Dic13—42no—
69C4⋊Dic13—22no—
70C4⋊Dic13—42no—
71C4⋊Dic13—41no—
72C4⋊Dic13—41no—
73C4⋊Dic13—41no—
74C4⋊Dic13D811yescharacteristic
75#6101—21no—
76#6101—42no—
77C4×Dic13—21no—
78C2×#1055—21no—
79Dic52—42no—
80Dic52—41no—
81Dic52—41no—
82C13×C16—41no—
83#6090—41no—
84#3380—131no—
85#2241—131no—
86#2208—131no—
87#1670—131no—
88#1365—131no—
89Q8⋊C16—131no—
90#1331D1311yescharacteristic
91C23×C13—41no—
92D4×C13—22no—
93D4×C13—41no—
94C2×C4×C13—41no—
95C2×C4×C13—81no—
96C2×C4×C13—81no—
97C2×C4×C13#12011yescharacteristic
98C2×C4×C13C2×D811yescharacteristic
99C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
100C2×Dic13—21no—
101C2×Dic13—21no—
102C2×Dic13—42no—
103C2×Dic13—81no—
104C2×Dic13—162no—
105Dic26—21no—
106Dic26—21no—
107Dic26—81no—
108Dic26—81no—
109Dic26—161no—
110C8×C13—21no—
111C8×C13—81no—
112C8×C13C2×SD1611yescharacteristic
113C8×C13#13711yescharacteristic
114#1055—41no—
115#554—261no—
116C2×SD32—261no—
117#500—131no—
118#499—261no—
119#494—131no—
120#478—262no—
121#476—261no—
122#475—261no—
123C8×Q8—131no—
124C4×D8—261no—
125C4×D8C2×D1311yescharacteristic
126C4⋊C16—131no—
127#358—262no—
128#358—261no—
129C4×C16C2×D1311yescharacteristic
130#335C2×D1311yescharacteristic
131#332—261no—
132C22×C13—42no—
133C22×C13—81no—
134C22×C13—81no—
135C22×C13#44711yescharacteristic
136C4×C13—21no—
137C4×C13—81no—
138C4×C13#44811yescharacteristic
139C4×C13#45411yescharacteristic
140C4×C13#50811yescharacteristic
141C4×C13#51011yescharacteristic
142Dic13—41no—
143Dic13—41no—
144Dic13—82no—
145Dic13—161no—
146C2×Q16—261no—
147C2×Q16—261no—
148C2×D8D5211yescharacteristic
149C4⋊Q8—261no—
150C4⋊Q8—261no—
151#125—262no—
152C22⋊Q8—522no—
153C22⋊Q8—521no—
154C4×Q8—131no—
155C4×D4—21no—
156C4×D4—262no—
157C2×C4⋊C4—521no—
158SD32—522no—
159C2×C16—21no—
160C2×C16—261no—
161#107—132no—
162#107—261no—
163#107D5211yescharacteristic
164#106—262no—
165#106—521no—
166C4⋊C8—21no—
167C4⋊C8—131no—
168C4⋊C8—261no—
169#103—521no—
170#102—21no—
171#102—262no—
172C4×C8—261no—
173C4×C8C22×D1311yescharacteristic
174C2×C13—82no—
175C2×C13#162711yescharacteristic
176C2×C13#218911yescharacteristic
177C2×C13#219411yescharacteristic
178C2×Q8—131no—
179C2×Q8—521no—
180C2×Q8—521no—
181C2×D4—21no—
182C22×C4—41no—
183C22×C4—522no—
184Q16—522no—
185Q16—521no—
186Q16—521no—
187D8—21no—
188D8#609512yes—
189C2×C8—41no—
190C2×C8—261no—
191C2×C8C2×D5211yescharacteristic
192C2×C8D4×D1311yescharacteristic
193C4⋊C4—21no—
194C4⋊C4—131no—
195C4⋊C4—261no—
196C4⋊C4—262no—
197C4⋊C4—522no—
198C4⋊C4—522no—
199C4⋊C4—521no—
200C4⋊C4—521no—
201C4⋊C4—521no—
202C22⋊C4—41no—
203C22⋊C4—522no—
204C42—261no—
205C42D4×D1311yescharacteristic
206C16—41no—
207C16—521no—
208C13#1235911yescharacteristic, complemented, Sylow
209C23—41no—
210Q8—261no—
211Q8—261no—
212Q8—1041no—
213Q8—1041no—
214Q8—2081no—
215D4—22no—
216D4—41no—
217C2×C4—41no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—261no—
221C2×C4—261no—
222C2×C4—522no—
223C2×C4—1041no—
224C2×C4—2082no—
225C2×C4#8813611yescharacteristic
226C2×C4D8×D1311yescharacteristic
227C2×C4#8816811yescharacteristic
228C8—21no—
229C8—81no—
230C8—521no—
231C8C2×#609511yescharacteristic
232C8#8816311yescharacteristic
233C22—42no—
234C22—81no—
235C22—81no—
236C22#1171843411yescharacteristic
237C4—21no—
238C4—81no—
239C4—521no—
240C4—521no—
241C4—1042no—
242C4—2081no—
243C4#1171839911yescharacteristic
244C4#1171848811yescharacteristic
245C4#1171857311yescharacteristic
246C4#1171857611yescharacteristic
247C2—82no—
248C2#1311394211yescharacteristic
249C2#1311677711yescharacteristic
250C2#1311680811yescharacteristic
subgroupG/H
centerC22#11718434
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1331C2
socleC22×C13#447
prime radicalC2×C13×D8D4
hypercenter#1331D13
hypocenterC13#12359
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1331

Complements

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

NH ≅ G/Ntype
2. #13117064C2semidirect
4. #13114207C2semidirect
5. #13112895C2semidirect
6. #13112816C2semidirect
208. C13#12359semidirect

Maximal subgroups

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

subgroupindex
#131277012
#131170642
#131168812
#131142072
#131128952
#131128162
C13×#13312
#1235913