Finite Group Databasebeta

← #15777043

Subgroups — #15777043

Order 3328.

240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 71 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#13116979C211yesmaximal, characteristic, complemented
2#13116877C211yesmaximal, characteristic
3#13114428C211yesmaximal, characteristic
4C8×Dic52C211yesmaximal, characteristic, complemented
5#13112890C211yesmaximal, characteristic, complemented
6#13112883C211yesmaximal, characteristic
7C13×#1367C211yesmaximal, characteristic, complemented
8C2×#88040—21no—
9C4×Dic52C2211yescharacteristic
10#11718356C2211yescharacteristic
11#11718355—21no—
12#11718354—21no—
13#11718343C2211yescharacteristic
14C8×Dic26—21no—
15C13×C4⋊C16C2211yescharacteristic
16C13×C4⋊C16C2211yescharacteristic
17C82×C13C2211yescharacteristic
18#11718101—21no—
19#11718097—21no—
20#11718095—21no—
21#11718050C2211yescharacteristic
22#11718048—21no—
23C2×Dic52D411yescharacteristic
24C2×D104—21no—
25C2×D104—21no—
26C2×#6095—41no—
27C2×#6095—41no—
28#88128—21no—
29#88123—21no—
30C4×Dic26—21no—
31C2×C13×C16—21no—
32C2×C13×C16—21no—
33C4×C8×C13D411yescharacteristic
34C4×C8×C13D411yescharacteristic
35C4×C8×C13C2311yescharacteristic
36#88061—42no—
37#88058—21no—
38#88058—21no—
39#88058D411yescharacteristic
40#88056—21no—
41#88054—41no—
42C8×Dic13—41no—
43C4⋊#1055—21no—
44#88040—42no—
45#12417—131nomaximal, Sylow
46C2×D52—41no—
47C2×D52—41no—
48C2×D52—41no—
49C2×Dic26—21no—
50C2×Dic26—41no—
51C2×C8×C13—21no—
52C2×C8×C13D811yescharacteristic
53C2×C8×C13D811yescharacteristic
54C2×C8×C13C2×D411yescharacteristic
55C2×C8×C13#4111yescharacteristic
56C42×C13C2×D411yescharacteristic
57C4⋊Dic13—21no—
58C4⋊Dic13—41no—
59C4⋊Dic13—41no—
60#6101—41no—
61C4×Dic13—41no—
62C2×#1055—41no—
63Dic52—21no—
64Dic52SD1612yescomplemented
65D104—41no—
66D104—41no—
67D104—81no—
68#6095—82no—
69#6095—82no—
70C13×C16—41no—
71C13×C16—41no—
72#2225—131no—
73#2207—131no—
74#1706—131no—
75C8×Q16—131no—
76#1367D1311yescharacteristic, complemented
77#1364—131no—
78#1361—131no—
79C22×D13—81no—
80C2×C4×C13#12111yescharacteristic
81C2×C4×C13C2×D811yescharacteristic
82C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
83C2×Dic13—41no—
84C2×Dic13—41no—
85C2×Dic13—81no—
86D52—82no—
87D52—81no—
88D52—81no—
89D52—81no—
90D52—81no—
91Dic26—22no—
92Dic26—41no—
93Dic26—81no—
94Dic26—81no—
95C8×C13—21no—
96C8×C13—21no—
97C8×C13—41no—
98C8×C13SD3212yescomplemented
99C8×C13C2×SD1611yescharacteristic
100C8×C13#13511yescharacteristic
101#1055—81no—
102C2×SD32—261no—
103#500—131no—
104#493—131no—
105#492—261no—
106#486—261no—
107C8×Q8—261no—
108C4×Q16—131no—
109#367—261no—
110C4⋊C16C2×D1311yescharacteristic
111C4⋊C16C2×D1311yescharacteristic
112#358—261no—
113#357—261no—
114#335—131no—
115Q8⋊C8—261no—
116C82C2×D1311yescharacteristic
117C22×C13#45911yescharacteristic
118C2×D13—161no—
119C2×D13—161no—
120C2×D13—161no—
121C4×C13—21no—
122C4×C13#46511yescharacteristic
123C4×C13#47111yescharacteristic
124C4×C13C2×SD3211yescharacteristic
125C4×C13#50911yescharacteristic
126Dic13—42no—
127Dic13—81no—
128Dic13—161no—
129C2×Q16—131no—
130C2×SD16—521no—
131C2×SD16—521no—
132C2×D8—261no—
133C2×D8—261no—
134C4⋊Q8—261no—
135#127—261no—
136C4×Q8—261no—
137SD32—522no—
138C2×C16—21no—
139C2×C16—21no—
140#107—131no—
141#107—261no—
142#107—261no—
143C4⋊C8—261no—
144C4⋊C8—521no—
145#103—261no—
146#102—522no—
147C4×C8—521no—
148C4×C8D5211yescharacteristic
149C4×C8D5211yescharacteristic
150C4×C8C22×D1311yescharacteristic
151C2×C13#166511yescharacteristic
152C2×C13#220711yescharacteristic
153C2×C13#221211yescharacteristic
154D13—321no—
155C2×Q8—261no—
156C2×Q8—521no—
157C2×D4—521no—
158C2×D4—521no—
159C2×D4—521no—
160Q16—132no—
161Q16—261no—
162SD16—1042no—
163SD16—1042no—
164D8—521no—
165D8—521no—
166D8—1041no—
167C2×C8—21no—
168C2×C8—521no—
169C2×C8D10411yescharacteristic
170C2×C8D10411yescharacteristic
171C2×C8D4×D1311yescharacteristic
172C2×C8#613111yescharacteristic
173C4⋊C4—261no—
174C4⋊C4—521no—
175C4⋊C4—521no—
176C4⋊C4—521no—
177C42—521no—
178C42C2×D5211yescharacteristic
179C16—41no—
180C16—41no—
181C13#1241711yescharacteristic, complemented, Sylow
182C23—1041no—
183Q8—262no—
184Q8—521no—
185Q8—1041no—
186Q8—1041no—
187D4—1042no—
188D4—1041no—
189D4—1041no—
190D4—1041no—
191D4—1041no—
192C2×C4—521no—
193C2×C4—521no—
194C2×C4—1041no—
195C2×C4#8814911yescharacteristic
196C2×C4C2×D10411yescharacteristic
197C2×C4#8816211yescharacteristic
198C8—21no—
199C8—21no—
200C8—41no—
201C8—1041no—
202C8#8804012yescomplemented
203C8SD16×D1311yescharacteristic
204C8#8817011yescharacteristic
205C22—2081no—
206C22—2081no—
207C22—2081no—
208C22#1171850411yescharacteristic
209C4—21no—
210C4—522no—
211C4—1041no—
212C4—2081no—
213C4#1171852511yescharacteristic
214C4#1171855911yescharacteristic
215C4C2×#8804011yescharacteristic
216C4#1171856911yescharacteristic
217C2—4161no—
218C2#1311417811yescharacteristic
219C2#1311687711yescharacteristic
220C2#1311690611yescharacteristic
subgroupG/H
centerC22#11718504
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1367C2
socleC22×C13#459
prime radical#11718356C22
hypercenter#1367D13
hypocenterC13#12417
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C82 ◁ #1367

Complements

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

NH ≅ G/Ntype
1. #13116979C2semidirect
4. C8×Dic52C2semidirect
5. #13112890C2semidirect
7. C13×#1367C2semidirect
64. Dic52SD16semidirect
76. #1367D13semidirect
98. C8×C13SD32semidirect
181. C13#12417semidirect
202. C8#88040semidirect

Maximal subgroups

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

subgroupindex
#131169792
#131168772
#131144282
C8×Dic522
#131128902
#131128832
C13×#13672
#1241713