Finite Group Databasebeta

← #15777045

Subgroups — #15777045

Order 3328.

240 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 65 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#13116975C211yesmaximal, characteristic, complemented
2#13116877C211yesmaximal, characteristic
3#13114429C211yesmaximal, characteristic
4#13113642C211yesmaximal, characteristic, complemented
5#13112899C211yesmaximal, characteristic, complemented
6#13112881C211yesmaximal, characteristic
7C13×#1364C211yesmaximal, characteristic, complemented
8C13×#500C2211yescharacteristic
9#11718749—21no—
10#11718746—21no—
11C2×#88040—21no—
12#11718491—21no—
13C4×Dic52C2211yescharacteristic
14#11718356C2211yescharacteristic
15C13×C4⋊C16C2211yescharacteristic
16C13×#335C2211yescharacteristic
17#11718101—21no—
18#11718084—21no—
19#11718082—21no—
20#11718076—21no—
21C4⋊#6090C2211yescharacteristic
22C8×#1055C2211yescharacteristic
23C13×C4⋊Q8—21no—
24C2×#6106—41no—
25C2×#6106—41no—
26C2×Dic52D411yescharacteristic
27C2×D104—21no—
28C2×D104—21no—
29#88128—21no—
30C4×Dic26—21no—
31C2×C13×C16—21no—
32C13×#107—21no—
33C13×#107—21no—
34C13×C4⋊C8—21no—
35C4×C8×C13C2311yescharacteristic
36#88058D411yescharacteristic
37#88056—21no—
38#88054—41no—
39C8×Dic13—41no—
40C2×#6090—21no—
41#88049—42no—
42C4×#1055D411yescharacteristic
43C4×#1055D411yescharacteristic
44#88040—42no—
45#12417—131nomaximal, Sylow
46C2×Q8×C13—41no—
47C2×D52—41no—
48C2×D52—41no—
49C2×D52—41no—
50C2×Dic26—21no—
51C2×C8×C13—41no—
52C2×C8×C13C2×D411yescharacteristic
53C2×C8×C13#4111yescharacteristic
54C13×C4⋊C4—41no—
55C13×C4⋊C4—41no—
56C42×C13C2×D411yescharacteristic
57#6106—82no—
58#6106—82no—
59C4⋊Dic13—21no—
60#6101—41no—
61C4×Dic13—41no—
62C2×#1055—21no—
63C2×#1055D811yescharacteristic
64C2×#1055D811yescharacteristic
65Dic52—21no—
66Dic52SD1612yescomplemented
67D104—41no—
68D104—41no—
69D104—81no—
70C13×C16—41no—
71#6090—41no—
72#2225—131no—
73#2207—131no—
74#1706—131no—
75C8×Q16—131no—
76#1367—131no—
77#1364D1311yescharacteristic, complemented
78#1361—131no—
79C22×D13—81no—
80Q8×C13—81no—
81Q8×C13—81no—
82C2×C4×C13—81no—
83C2×C4×C13#12111yescharacteristic
84C2×C4×C13C2×D811yescharacteristic
85C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
86C2×Dic13—41no—
87C2×Dic13—41no—
88D52—82no—
89D52—81no—
90D52—81no—
91D52—81no—
92D52—81no—
93Dic26—22no—
94Dic26—41no—
95C8×C13—21no—
96C8×C13—81no—
97C8×C13C2×SD1611yescharacteristic
98C8×C13#13511yescharacteristic
99#1055—21no—
100#1055—41no—
101#1055SD3212yescomplemented
102C2×SD32—261no—
103#500C2×D1311yescharacteristic
104#493—131no—
105#492—261no—
106#486—261no—
107C8×Q8—261no—
108C4×Q16—131no—
109#367—261no—
110C4⋊C16—131no—
111C4⋊C16C2×D1311yescharacteristic
112#358—261no—
113#357—261no—
114#335C2×D1311yescharacteristic
115Q8⋊C8—261no—
116C82—131no—
117C22×C13#45911yescharacteristic
118C2×D13—161no—
119C2×D13—161no—
120C2×D13—161no—
121C4×C13—21no—
122C4×C13—161no—
123C4×C13#46511yescharacteristic
124C4×C13#47111yescharacteristic
125C4×C13C2×SD3211yescharacteristic
126C4×C13#50911yescharacteristic
127Dic13—42no—
128Dic13—81no—
129C2×Q16—131no—
130C2×SD16—521no—
131C2×SD16—521no—
132C2×D8—261no—
133C2×D8—261no—
134C4⋊Q8—21no—
135#127—261no—
136C4×Q8—261no—
137SD32—522no—
138C2×C16—21no—
139C2×C16—261no—
140#107—21no—
141#107—21no—
142#107—131no—
143C4⋊C8—21no—
144C4⋊C8—521no—
145#103—261no—
146#102—522no—
147C4×C8—131no—
148C4×C8—131no—
149C4×C8—521no—
150C4×C8C22×D1311yescharacteristic
151C2×C13#166511yescharacteristic
152C2×C13#220711yescharacteristic
153C2×C13#221211yescharacteristic
154D13—321no—
155C2×Q8—41no—
156C2×Q8—261no—
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—41no—
168C2×C8—131no—
169C2×C8—131no—
170C2×C8—261no—
171C2×C8#612711yescharacteristic
172C2×C8D4×D1311yescharacteristic
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—261no—
176C4⋊C4—521no—
177C42—521no—
178C42D4×D1311yescharacteristic
179C16—41no—
180C16—521no—
181C13#1241711yescharacteristic, complemented, Sylow
182C23—1041no—
183Q8—81no—
184Q8—81no—
185Q8—262no—
186Q8—521no—
187D4—1042no—
188D4—1041no—
189D4—1041no—
190D4—1041no—
191D4—1041no—
192C2×C4—81no—
193C2×C4—521no—
194C2×C4—521no—
195C2×C4#8813811yescharacteristic
196C2×C4D8×D1311yescharacteristic
197C2×C4#8816811yescharacteristic
198C8—21no—
199C8—81no—
200C8—132no—
201C8—261no—
202C8—521no—
203C8SD16×D1311yescharacteristic
204C8#8817311yescharacteristic
205C22—2081no—
206C22—2081no—
207C22—2081no—
208C22#1171844711yescharacteristic
209C4—21no—
210C4—161no—
211C4—522no—
212C4—1041no—
213C4#1171841511yescharacteristic
214C4#1171846811yescharacteristic
215C4#1171857211yescharacteristic
216C4D13×SD3211yescharacteristic
217C2—4161no—
218C2#1311418011yescharacteristic
219C2#1311687511yescharacteristic
220C2#1311690811yescharacteristic
subgroupG/H
centerC22#11718447
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1364C2
socleC22×C13#459
prime radical#11718356C22
hypercenter#1364D13
hypocenterC13#12417
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

Complements

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

NH ≅ G/Ntype
1. #13116975C2semidirect
4. #13113642C2semidirect
5. #13112899C2semidirect
7. C13×#1364C2semidirect
66. Dic52SD16semidirect
77. #1364D13semidirect
101. #1055SD32semidirect
181. C13#12417semidirect

Maximal subgroups

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

subgroupindex
#131169752
#131168772
#131144292
#131136422
#131128992
#131128812
C13×#13642
#1241713