Finite Group Databasebeta

← #15776614

Subgroups — #15776614

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#13127704C211yesmaximal, characteristic, complemented
2#13117059C211yesmaximal, characteristic, complemented
3#13116868C211yesmaximal, characteristic
4#13112895C211yesmaximal, characteristic, complemented
5Q8⋊#6090C211yesmaximal, characteristic, complemented
6#13112796C211yesmaximal, characteristic, complemented
7C13×#1668C211yesmaximal, characteristic, complemented
8#11719284—21no—
9C13×#493C2211yescharacteristic
10C13×#460—21no—
11C8×Q8×C13C2211yescharacteristic
12C2×#88066—21no—
13#11718508—22no—
14#11718503—21no—
15C4×D104—21no—
16C4×D104C2211yescharacteristic
17#11718344—21no—
18#11718343C2211yescharacteristic
19C13×#335C2211yescharacteristic
20C13×#331—21no—
21#11718154—22no—
22#11718154—21no—
23C4⋊#6090C2211yescharacteristic
24C4×#6090C2211yescharacteristic
25C2×C13×SD16—41no—
26C2×C13×D8—21no—
27C2×C13×D8—21no—
28C13×#127—21no—
29C4×Q8×C13D411yescharacteristic
30#88200—41no—
31C2×D104D411yescharacteristic
32#88150—42no—
33C4⋊C4×D13—41no—
34C4×D52—22no—
35C4×D52—21no—
36#88124—22no—
37#88123—21no—
38C13×C4⋊C8—21no—
39C13×C4⋊C8—21no—
40C13×C4⋊C8D411yescharacteristic
41C13×#102—41no—
42C4×C8×C13—21no—
43C4×C8×C13C2311yescharacteristic
44#88066—42no—
45#88061—22no—
46#88061—21no—
47#88058—21no—
48#88058D412yes—
49#88058D411yescharacteristic
50#88057—22no—
51C2×#6090—21no—
52C2×#6090—21no—
53#12355—131nomaximal, Sylow
54C2×Q8×C13D811yescharacteristic
55C2×D4×C13—41no—
56C2×D4×C13—41no—
57C2×D4×C13—41no—
58C2×D52—21no—
59C2×C4×D13—41no—
60C2×C4×D13—42no—
61C2×Dic26—41no—
62C13×SD16—82no—
63C13×D8—42no—
64C13×D8—41no—
65C13×D8—41no—
66C2×C8×C13—21no—
67C2×C8×C13—41no—
68C2×C8×C13C2×D411yescharacteristic
69C2×C8×C13C2×D411yescharacteristic
70C13×C4⋊C4—21no—
71C13×C4⋊C4D811yescharacteristic
72C42×C13—21no—
73C42×C13C2×D411yescharacteristic
74#6103—42no—
75#6103—41no—
76C4⋊Dic13—22no—
77C4⋊Dic13—21no—
78C4⋊Dic13—41no—
79#6101—42no—
80#6101—42no—
81D104—21no—
82D104SD1612yescomplemented
83#6090—41no—
84#6090—41no—
85#3380—131no—
86#2240—131no—
87#2206—131no—
88#1668D1311yescharacteristic, complemented
89#1365—131no—
90Q8⋊C16—131no—
91#1331—131no—
92C23×C13—81no—
93C22×D13—41no—
94Q8×C13—21no—
95Q8×C13—21no—
96D4×C13—81no—
97D4×C13—81no—
98D4×C13—81no—
99D4×C13—81no—
100D4×C13—161no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13#12011yescharacteristic
104C2×C4×C13C2×D811yescharacteristic
105C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
106C2×Dic13—41no—
107C2×Dic13—42no—
108D52—22no—
109D52—41no—
110C4×D13—81no—
111C4×D13—81no—
112C4×D13—162no—
113Dic26—161no—
114C8×C13—21no—
115C8×C13—41no—
116C8×C13—81no—
117C8×C13C2×SD1611yescharacteristic
118C8×C13#13711yescharacteristic
119#554—261no—
120C2×D16—261no—
121#500—131no—
122#499—261no—
123#493C2×D1311yescharacteristic
124#478—262no—
125#476—261no—
126#460—21no—
127C8×Q8C2×D1311yescharacteristic
128C4×D8—131no—
129C4×D8—261no—
130C4⋊C16—131no—
131#357—261no—
132#357—262no—
133C4×C16—131no—
134#335C2×D1311yescharacteristic
135#331—21no—
136C22×C13—161no—
137C22×C13—161no—
138C22×C13—161no—
139C22×C13#44711yescharacteristic
140C2×D13—42no—
141C2×D13—81no—
142C2×D13—81no—
143C4×C13—21no—
144C4×C13—41no—
145C4×C13—41no—
146C4×C13#44811yescharacteristic
147C4×C13#45411yescharacteristic
148C4×C13#50811yescharacteristic
149C4×C13#50911yescharacteristic
150Dic13—81no—
151Dic13—82no—
152C2×SD16—41no—
153C2×D8—21no—
154C2×D8—21no—
155C2×D8—131no—
156C4⋊Q8—261no—
157#127—21no—
158#125—262no—
159C22⋊Q8—522no—
160C22⋊Q8—521no—
161C4×Q8C22⋊D1311yescharacteristic
162C4×D4—262no—
163C4×D4—261no—
164C2×C4⋊C4—521no—
165D16—522no—
166C2×C16—261no—
167C2×C16—261no—
168#107—131no—
169#107—132no—
170#107—261no—
171#106—262no—
172C4⋊C8—21no—
173C4⋊C8—21no—
174C4⋊C8C22⋊D1311yescharacteristic
175#102—41no—
176#102—262no—
177#102—261no—
178C4×C8—21no—
179C4×C8C22×D1311yescharacteristic
180C2×C13—321no—
181C2×C13#162711yescharacteristic
182C2×C13#218611yescharacteristic
183C2×C13#219211yescharacteristic
184D13—82no—
185C2×Q8—521no—
186C2×Q8#610411yescharacteristic
187C2×D4—41no—
188C2×D4—41no—
189C2×D4—41no—
190C2×D4—261no—
191C22×C4—522no—
192C22×C4—521no—
193SD16—82no—
194D8—42no—
195D8—41no—
196D8—41no—
197D8—132no—
198D8—261no—
199C2×C8—21no—
200C2×C8—41no—
201C2×C8D4×D1311yescharacteristic
202C2×C8D4×D1311yescharacteristic
203C4⋊C4—21no—
204C4⋊C4—261no—
205C4⋊C4—262no—
206C4⋊C4—522no—
207C4⋊C4—522no—
208C4⋊C4—521no—
209C4⋊C4#610411yescharacteristic
210C22⋊C4—522no—
211C22⋊C4—521no—
212C42—21no—
213C42C2×C22⋊D1311yescharacteristic
214C16—521no—
215C16—521no—
216C13#1235511yescharacteristic, complemented, Sylow
217C23—81no—
218C23—521no—
219Q8—21no—
220Q8—21no—
221Q8—2081no—
222D4—81no—
223D4—81no—
224D4—81no—
225D4—81no—
226D4—161no—
227D4—262no—
228D4—521no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—521no—
232C2×C4—522no—
233C2×C4—1041no—
234C2×C4—1041no—
235C2×C4—2082no—
236C2×C4C2×#610411yescharacteristic
237C2×C4#8819111yescharacteristic
238C2×C4#8820311yescharacteristic
239C8—21no—
240C8—41no—
241C8—81no—
242C8SD16×D1311yescharacteristic
243C8#8816911yescharacteristic
244C22—161no—
245C22—161no—
246C22—161no—
247C22—522no—
248C22—1041no—
249C22—1041no—
250C22#1171869711yescharacteristic
251C4—21no—
252C4—41no—
253C4—41no—
254C4—1041no—
255C4—1042no—
256C4#1171880811yescharacteristic
257C4#1171883111yescharacteristic
258C4#1171885511yescharacteristic
259C4#1171886211yescharacteristic
260C2—321no—
261C2—1042no—
262C2#1311393711yescharacteristic
263C2#1311675711yescharacteristic
264C2#1311679111yescharacteristic
subgroupG/H
centerC22#11718697
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1668C2
socleC22×C13#447
prime radical#13116868C2
hypercenter#1668D13
hypocenterC13#12355
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #1668

Complements

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

NH ≅ G/Ntype
1. #13127704C2semidirect
2. #13117059C2semidirect
4. #13112895C2semidirect
5. Q8⋊#6090C2semidirect
6. #13112796C2semidirect
7. C13×#1668C2semidirect
82. D104SD16semidirect
88. #1668D13semidirect
216. C13#12355semidirect

Maximal subgroups

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

subgroupindex
#131277042
#131170592
#131168682
#131128952
Q8⋊#60902
#131127962
C13×#16682
#1235513