Finite Group Databasebeta

← #15776615

Subgroups — #15776615

Order 3328.

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

normal subgroups only

This group has 312 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, complemented
2#13117059C211yesmaximal, characteristic, complemented
3#13114193C211yesmaximal, characteristic, complemented
4#13112893C211yesmaximal, characteristic, complemented
5#13112814C211yesmaximal, characteristic, complemented
6#13112797C211yesmaximal, characteristic, complemented
7C13×#2206C211yesmaximal, characteristic
8#11719248—21no—
9C2×C13×D16—21no—
10C13×#493C2211yescharacteristic
11C4×C13×D8C2211yescharacteristic
12D8×Dic13—21no—
13#11718736—21no—
14#11718669—21no—
15#11718539—21no—
16#11718427—22no—
17#11718343C2211yescharacteristic
18C8×Dic26C2211yescharacteristic
19C13×C4⋊C16C2211yescharacteristic
20C13×#357—21no—
21#11718154—22no—
22#11718136—21no—
23C4×#6090C2211yescharacteristic
24#11718050C2211yescharacteristic
25C2×C13×D8—21no—
26C2×C13×D8—21no—
27C2×C13×D8D411yescharacteristic
28C13×#127—21no—
29C4×D4×C13—21no—
30D4×Dic13—22no—
31C2×#6105—41no—
32C2×C4⋊Dic13—41no—
33#88178—41no—
34#88144—22no—
35#88132—42no—
36#88123—21no—
37C4×Dic26D411yescharacteristic
38C13×D16—42no—
39C2×C13×C16—21no—
40C13×#107D411yescharacteristic
41C13×#102—21no—
42C4×C8×C13C2311yescharacteristic
43#88072—22no—
44#88072—41no—
45#88058—21no—
46#88058D412yes—
47#88054—21no—
48C8×Dic13—21no—
49C2×#6090—21no—
50#88048—22no—
51C4⋊#1055—21no—
52C4⋊#1055D411yescharacteristic
53#12355—131nomaximal, Sylow
54C2×D4×C13—21no—
55C2×D4×C13—41no—
56C2×D4×C13—41no—
57C2×D4×C13—41no—
58C22×C4×C13—41no—
59C22×Dic13—42no—
60C2×Dic26—41no—
61C2×Dic26D811yescharacteristic
62C13×D8—21no—
63C13×D8—42no—
64C13×D8—41no—
65C13×D8—41no—
66C13×D8SD1612yescomplemented
67C2×C8×C13C2×D411yescharacteristic
68C2×C8×C13C2×D411yescharacteristic
69C13×C4⋊C4—21no—
70C13×C22⋊C4—41no—
71C42×C13C2×D411yescharacteristic
72C22⋊Dic13—42no—
73#6105—82no—
74C4⋊Dic13—22no—
75C4⋊Dic13—42no—
76C4⋊Dic13—41no—
77C4⋊Dic13D811yescharacteristic
78#6101—21no—
79#6101—42no—
80C4×Dic13—21no—
81C2×#1055—21no—
82C2×#1055—41no—
83C13×C16—41no—
84#6090—41no—
85#3380—131no—
86#2240—131no—
87#2206D1311yescharacteristic
88#1668—131no—
89#1365—131no—
90Q8⋊C16—131no—
91#1331—131no—
92C23×C13—41no—
93C23×C13—81no—
94D4×C13—22no—
95D4×C13—41no—
96D4×C13—81no—
97D4×C13—81no—
98D4×C13—81no—
99D4×C13—81no—
100D4×C13—161no—
101C2×C4×C13—41no—
102C2×C4×C13—81no—
103C2×C4×C13—81no—
104C2×C4×C13#12011yescharacteristic
105C2×C4×C13C2×D811yescharacteristic
106C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
107C2×Dic13—21no—
108C2×Dic13—21no—
109C2×Dic13—42no—
110C2×Dic13—162no—
111Dic26—21no—
112Dic26—21no—
113Dic26—161no—
114C8×C13—21no—
115C8×C13C2×SD1611yescharacteristic
116C8×C13#13711yescharacteristic
117#1055—41no—
118#1055—81no—
119#554—261no—
120C2×D16—21no—
121#500—131no—
122#499—261no—
123#493C2×D1311yescharacteristic
124#478—262no—
125#476—261no—
126#460—261no—
127C8×Q8—131no—
128C4×D8—261no—
129C4×D8C2×D1311yescharacteristic
130C4⋊C16C2×D1311yescharacteristic
131#357—21no—
132#357—262no—
133C4×C16—131no—
134#335—131no—
135#331—261no—
136C22×C13—42no—
137C22×C13—81no—
138C22×C13—81no—
139C22×C13—161no—
140C22×C13—161no—
141C22×C13—161no—
142C22×C13#44711yescharacteristic
143C4×C13—21no—
144C4×C13—81no—
145C4×C13#44811yescharacteristic
146C4×C13#45411yescharacteristic
147C4×C13#50811yescharacteristic
148C4×C13#50911yescharacteristic
149Dic13—41no—
150Dic13—41no—
151Dic13—82no—
152C2×SD16—521no—
153C2×D8—21no—
154C2×D8—21no—
155C2×D8C22⋊D1311yescharacteristic
156C4⋊Q8—261no—
157#127—21no—
158#125—262no—
159C22⋊Q8—522no—
160C22⋊Q8—521no—
161C4×Q8—131no—
162C4×D4—21no—
163C4×D4—262no—
164C2×C4⋊C4—521no—
165D16—42no—
166C2×C16—21no—
167C2×C16—261no—
168#107—132no—
169#107—261no—
170#107C22⋊D1311yescharacteristic
171#106—262no—
172C4⋊C8—131no—
173C4⋊C8—261no—
174C4⋊C8—261no—
175#102—21no—
176#102—262no—
177#102—521no—
178C4×C8—261no—
179C4×C8C22×D1311yescharacteristic
180C2×C13—82no—
181C2×C13—321no—
182C2×C13#162711yescharacteristic
183C2×C13#218611yescharacteristic
184C2×C13#219211yescharacteristic
185C2×Q8—131no—
186C2×Q8—521no—
187C2×D4—21no—
188C2×D4—41no—
189C2×D4—41no—
190C2×D4—41no—
191C22×C4—41no—
192C22×C4—522no—
193SD16—1042no—
194D8—21no—
195D8—42no—
196D8—41no—
197D8—41no—
198D8#610512yescomplemented
199C2×C8—261no—
200C2×C8—521no—
201C2×C8D4×D1311yescharacteristic
202C2×C8C2×C22⋊D1311yescharacteristic
203C4⋊C4—21no—
204C4⋊C4—131no—
205C4⋊C4—261no—
206C4⋊C4—262no—
207C4⋊C4—522no—
208C4⋊C4—522no—
209C4⋊C4—521no—
210C22⋊C4—41no—
211C22⋊C4—522no—
212C42—261no—
213C42D4×D1311yescharacteristic
214C16—41no—
215C16—521no—
216C13#1235511yescharacteristic, complemented, Sylow
217C23—41no—
218C23—81no—
219Q8—261no—
220Q8—261no—
221Q8—2081no—
222D4—22no—
223D4—41no—
224D4—81no—
225D4—81no—
226D4—81no—
227D4—81no—
228D4—161no—
229C2×C4—41no—
230C2×C4—81no—
231C2×C4—81no—
232C2×C4—261no—
233C2×C4—261no—
234C2×C4—522no—
235C2×C4—2082no—
236C2×C4D8×D1311yescharacteristic
237C2×C4#8816511yescharacteristic
238C2×C4#8819111yescharacteristic
239C8—21no—
240C8—521no—
241C8—1041no—
242C8C2×#610511yescharacteristic
243C8#8820511yescharacteristic
244C22—42no—
245C22—81no—
246C22—81no—
247C22—161no—
248C22—161no—
249C22—161no—
250C22#1171881711yescharacteristic
251C4—21no—
252C4—81no—
253C4—521no—
254C4—521no—
255C4—1042no—
256C4#1171857211yescharacteristic
257C4#1171857311yescharacteristic
258C4#1171870111yescharacteristic
259C4#1171886211yescharacteristic
260C2—82no—
261C2—321no—
262C2#1311393811yescharacteristic
263C2#1311675611yescharacteristic
264C2#1311679011yescharacteristic
subgroupG/H
centerC22#11718817
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
Fitting, prime radicalC13×#2206C2
socleC22×C13#447
hypercenter#2206D13
hypocenterC13#12355
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2206

Complements

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

NH ≅ G/Ntype
1. #13127701C2semidirect
2. #13117059C2semidirect
3. #13114193C2semidirect
4. #13112893C2semidirect
5. #13112814C2semidirect
6. #13112797C2semidirect
66. C13×D8SD16semidirect
198. D8#6105semidirect
216. C13#12355semidirect

Maximal subgroups

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

subgroupindex
#131277012
#131170592
#131141932
#131128932
#131128142
#131127972
C13×#22062
#1235513