Finite Group Databasebeta

← #15776516

Subgroups — #15776516

Order 3328.

306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 67 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#13127267C211yesmaximal, characteristic, complemented
2#13117059C211yesmaximal, characteristic, complemented
3#13116873C211yesmaximal, characteristic, complemented
4#13112892C211yesmaximal, characteristic, complemented
5#13112799C211yesmaximal, characteristic, complemented
6D4⋊#6090C211yesmaximal, characteristic, complemented
7C13×#1667C211yesmaximal, characteristic
8#11719247—21no—
9C13×#493C2211yescharacteristic
10C13×#459—21no—
11C8×D4×C13C2211yescharacteristic
12C2×#88067—21no—
13#11718777—21no—
14#11718767—21no—
15#11718512—21no—
16#11718384—22no—
17C4×Dic52C2211yescharacteristic
18#11718343C2211yescharacteristic
19C13×#335C2211yescharacteristic
20C13×#331—21no—
21#11718154—22no—
22#11718154—21no—
23C4⋊#6090C2211yescharacteristic
24C4×#6090C2211yescharacteristic
25C2×C13×D8—21no—
26C2×C13×D8—21no—
27C2×C13×D8—41no—
28C22×C8×C13—21no—
29C13×#127—21no—
30C4×D4×C13D411yescharacteristic
31#88190—41no—
32#88180—22no—
33#88178—22no—
34C2×Dic52D411yescharacteristic
35#88141—41no—
36#88133—42no—
37#88123—21no—
38C4×Dic26—21no—
39C13×C4⋊C8—21no—
40C13×C4⋊C8D411yescharacteristic
41C13×#102—41no—
42C13×C22⋊C8—21no—
43C4×C8×C13C2311yescharacteristic
44#88067—42no—
45#88058—21no—
46#88058D411yescharacteristic
47#88058D412yes—
48#88057—22no—
49#88056—22no—
50#88056—21no—
51C2×#6090—21no—
52C2×#6090—21no—
53#12341—131nomaximal, Sylow
54C2×D4×C13—41no—
55C2×D4×C13—41no—
56C2×D4×C13—41no—
57C2×D4×C13D811yescharacteristic
58C22×C4×C13—21no—
59C2×Dic26—21no—
60C2×Dic26—41no—
61C13×D8—42no—
62C13×D8—41no—
63C13×D8—41no—
64C13×D8—82no—
65C2×C8×C13—21no—
66C2×C8×C13—41no—
67C2×C8×C13—41no—
68C2×C8×C13—41no—
69C2×C8×C13C2×D411yescharacteristic
70C2×C8×C13C2×D411yescharacteristic
71C13×C4⋊C4D811yescharacteristic
72C13×C22⋊C4—21no—
73C42×C13C2×D411yescharacteristic
74C22⋊Dic13—42no—
75C22⋊Dic13—42no—
76C4⋊Dic13—21no—
77C4⋊Dic13—22no—
78C4⋊Dic13—41no—
79#6101—42no—
80#6101—41no—
81C4×Dic13—42no—
82C4×Dic13—41no—
83Dic52—21no—
84Dic52—21no—
85#6090—41no—
86#6090—41no—
87#3342—131no—
88#2240—131no—
89#2207—131no—
90#1667D1311yescharacteristic
91#1364—131no—
92#1332—131no—
93D4⋊C16—131no—
94C23×C13—21no—
95C23×C13—81no—
96D4×C13—21no—
97D4×C13—21no—
98D4×C13—81no—
99D4×C13—81no—
100D4×C13—81no—
101D4×C13—81no—
102D4×C13—161no—
103C2×C4×C13—21no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13#12011yescharacteristic
107C2×C4×C13C2×D811yescharacteristic
108C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
109C2×Dic13—41no—
110C2×Dic13—41no—
111C2×Dic13—42no—
112Dic26—41no—
113Dic26—41no—
114Dic26—81no—
115Dic26—81no—
116C8×C13—21no—
117C8×C13—41no—
118C8×C13—81no—
119C8×C13#13511yescharacteristic
120C8×C13AGL(1,ℤ/8)11yescharacteristic
121#556—261no—
122C2×SD32—261no—
123#500—131no—
124#493C2×D1311yescharacteristic
125#485—262no—
126#475—261no—
127#467—261no—
128#459—21no—
129C4×Q16—131no—
130C8×D4C2×D1311yescharacteristic
131#427—261no—
132C4⋊C16—131no—
133#357—261no—
134#357—262no—
135C4×C16—131no—
136#335C2×D1311yescharacteristic
137#331—21no—
138C22×C13—41no—
139C22×C13—41no—
140C22×C13—41no—
141C22×C13—161no—
142C22×C13—161no—
143C22×C13—161no—
144C22×C13#44711yescharacteristic
145C4×C13—21no—
146C4×C13—41no—
147C4×C13#44911yescharacteristic
148C4×C13#45411yescharacteristic
149C4×C13#50811yescharacteristic
150C4×C13#50911yescharacteristic
151Dic13—81no—
152Dic13—82no—
153Dic13—81no—
154C2×Q16—131no—
155C2×D8—21no—
156C2×D8—21no—
157C2×D8—41no—
158C22×C8—21no—
159C4⋊Q8—261no—
160#127—21no—
161#126—522no—
162#124—521no—
163C22⋊Q8—262no—
164C4×Q8—261no—
165C4×Q8—521no—
166C4×D4C22⋊D1311yescharacteristic
167#117—262no—
168SD32—522no—
169C2×C16—261no—
170C2×C16—261no—
171#107—131no—
172#107—132no—
173#107—261no—
174#106—262no—
175C4⋊C8—21no—
176C4⋊C8C22⋊D1311yescharacteristic
177#103—262no—
178#103—261no—
179#102—41no—
180C22⋊C8—21no—
181C4×C8C22×D1311yescharacteristic
182C2×C13—81no—
183C2×C13—321no—
184C2×C13#162511yescharacteristic
185C2×C13#218611yescharacteristic
186C2×C13#219311yescharacteristic
187C2×Q8—261no—
188C2×Q8—521no—
189C2×D4—41no—
190C2×D4—41no—
191C2×D4—41no—
192C2×D4#610411yescharacteristic
193C22×C4—21no—
194Q16—261no—
195Q16—261no—
196D8—42no—
197D8—41no—
198D8—41no—
199D8—82no—
200C2×C8—21no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8D4×D1311yescharacteristic
205C2×C8D4×D1311yescharacteristic
206C4⋊C4—261no—
207C4⋊C4—262no—
208C4⋊C4—522no—
209C4⋊C4—521no—
210C4⋊C4—521no—
211C4⋊C4#610411yescharacteristic
212C22⋊C4—21no—
213C22⋊C4—522no—
214C22⋊C4—522no—
215C42—522no—
216C42—521no—
217C42C2×C22⋊D1311yescharacteristic
218C16—521no—
219C16—521no—
220C13#1234111yescharacteristic, complemented, Sylow
221C23—21no—
222C23—81no—
223Q8—521no—
224Q8—521no—
225Q8—1041no—
226Q8—1041no—
227D4—21no—
228D4—21no—
229D4—81no—
230D4—81no—
231D4—81no—
232D4—81no—
233D4—161no—
234C2×C4—21no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—521no—
238C2×C4—522no—
239C2×C4—521no—
240C2×C4C2×#610411yescharacteristic
241C2×C4#8819111yescharacteristic
242C2×C4#8820311yescharacteristic
243C8—21no—
244C8—41no—
245C8—81no—
246C8#8816511yescharacteristic
247C8#8816611yescharacteristic
248C22—41no—
249C22—41no—
250C22—41no—
251C22—161no—
252C22—161no—
253C22—161no—
254C22#1171869711yescharacteristic
255C4—21no—
256C4—41no—
257C4—1041no—
258C4—1042no—
259C4—1041no—
260C4#1171880811yescharacteristic
261C4#1171881911yescharacteristic
262C4#1171885511yescharacteristic
263C4#1171886211yescharacteristic
264C2—81no—
265C2—321no—
266C2#1311392311yescharacteristic
267C2#1311675711yescharacteristic
268C2#1311679811yescharacteristic
subgroupG/H
centerC22#11718697
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
Fitting, prime radicalC13×#1667C2
socleC22×C13#447
hypercenter#1667D13
hypocenterC13#12341
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #1667

Complements

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

NH ≅ G/Ntype
1. #13127267C2semidirect
2. #13117059C2semidirect
3. #13116873C2semidirect
4. #13112892C2semidirect
5. #13112799C2semidirect
6. D4⋊#6090C2semidirect
220. C13#12341semidirect

Maximal subgroups

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

subgroupindex
#131272672
#131170592
#131168732
#131128922
#131127992
D4⋊#60902
C13×#16672
#1234113