Finite Group Databasebeta

← #15777121

Subgroups — #15777121

Order 3328.

240 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 63 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#13116883C211yesmaximal, characteristic, complemented
2#13116877C211yesmaximal, characteristic
3#13114443C211yesmaximal, characteristic
4#13113642C211yesmaximal, characteristic, complemented
5#13112905C211yesmaximal, characteristic, complemented
6#13112881C211yesmaximal, characteristic
7C13×#1362C211yesmaximal, characteristic, complemented
8C13×#494C2211yescharacteristic
9C2×#88069—21no—
10#11718749—21no—
11#11718749—21no—
12C2×#88040—21no—
13#11718491—21no—
14C4×Dic52C2211yescharacteristic
15#11718356C2211yescharacteristic
16C13×C4⋊C16C2211yescharacteristic
17C13×#335C2211yescharacteristic
18#11718156—21no—
19#11718101—21no—
20#11718076—21no—
21C4⋊#6090C2211yescharacteristic
22C8×#1055C2211yescharacteristic
23C2×C13×Q16—21no—
24C2×C13×Q16—21no—
25C13×C4⋊Q8—21no—
26C2×Dic52D411yescharacteristic
27C2×D104—21no—
28C2×D104—21no—
29#88128—21no—
30C4×Dic26—21no—
31C2×C13×C16—21no—
32C13×C4⋊C8—21no—
33C4×C8×C13C2311yescharacteristic
34#88069—42no—
35#88058D411yescharacteristic
36#88056—21no—
37#88054—41no—
38C8×Dic13—41no—
39C2×#6090—21no—
40#88049—42no—
41#88049—41no—
42#88049—41no—
43C4×#1055D411yescharacteristic
44C4×#1055D411yescharacteristic
45#88040—42no—
46#12429—131nomaximal, Sylow
47C2×Q8×C13—41no—
48C2×D52—41no—
49C2×D52—41no—
50C2×D52—41no—
51C2×Dic26—21no—
52C13×Q16—41no—
53C13×Q16—41no—
54C13×Q16—81no—
55C2×C8×C13—41no—
56C2×C8×C13C2×D411yescharacteristic
57C2×C8×C13#4111yescharacteristic
58C13×C4⋊C4—41no—
59C13×C4⋊C4—41no—
60C42×C13C2×D411yescharacteristic
61C4⋊Dic13—21no—
62#6101—41no—
63C4×Dic13—41no—
64C2×#1055—21no—
65C2×#1055D811yescharacteristic
66C2×#1055D811yescharacteristic
67Dic52—21no—
68Dic52D812yes—
69D104—41no—
70D104—41no—
71D104—81no—
72C13×C16—41no—
73#6090—41no—
74#2209—131no—
75#2207—131no—
76#1709—131no—
77C8×Q16—131no—
78#1370—131no—
79#1362D1311yescharacteristic, complemented
80#1361—131no—
81C22×D13—81no—
82Q8×C13—81no—
83Q8×C13—81no—
84C2×C4×C13—81no—
85C2×C4×C13#12111yescharacteristic
86C2×C4×C13C2×D811yescharacteristic
87C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
88C2×Dic13—41no—
89C2×Dic13—41no—
90D52—82no—
91D52—81no—
92D52—81no—
93D52—81no—
94D52—81no—
95Dic26—22no—
96Dic26—41no—
97C8×C13—21no—
98C8×C13—81no—
99C8×C13C2×D811yescharacteristic
100C8×C13#13511yescharacteristic
101#1055—21no—
102#1055—21no—
103#1055—41no—
104C2×Q32—261no—
105C2×SD32—261no—
106#494C2×D1311yescharacteristic
107#493—131no—
108#486—261no—
109#486—261no—
110C8×Q8—261no—
111C4×Q16—131no—
112C4⋊C16—131no—
113C4⋊C16C2×D1311yescharacteristic
114#358—261no—
115#357—261no—
116#335C2×D1311yescharacteristic
117Q8⋊C8—261no—
118C82—131no—
119C22×C13#45911yescharacteristic
120C2×D13—161no—
121C2×D13—161no—
122C2×D13—161no—
123C4×C13—21no—
124C4×C13—161no—
125C4×C13#46611yescharacteristic
126C4×C13#47211yescharacteristic
127C4×C13#50811yescharacteristic
128C4×C13#51011yescharacteristic
129Dic13—42no—
130Dic13—81no—
131C2×Q16—21no—
132C2×Q16—21no—
133C2×Q16—131no—
134C2×D8—261no—
135C2×D8—261no—
136C4⋊Q8—21no—
137#127—261no—
138C4×Q8—261no—
139Q32—522no—
140SD32—522no—
141C2×C16—21no—
142C2×C16—261no—
143#107—131no—
144C4⋊C8—21no—
145C4⋊C8—521no—
146#103—261no—
147#102—521no—
148#102—521no—
149#102—522no—
150C4×C8—131no—
151C4×C8—131no—
152C4×C8—521no—
153C4×C8C22×D1311yescharacteristic
154C2×C13#166711yescharacteristic
155C2×C13#221111yescharacteristic
156C2×C13#221211yescharacteristic
157D13—321no—
158C2×Q8—41no—
159C2×Q8—261no—
160C2×D4—521no—
161C2×D4—521no—
162C2×D4—521no—
163Q16—41no—
164Q16—41no—
165Q16—81no—
166Q16—132no—
167Q16—261no—
168D8—521no—
169D8—521no—
170D8—1041no—
171C2×C8—41no—
172C2×C8—131no—
173C2×C8—131no—
174C2×C8—261no—
175C2×C8#612711yescharacteristic
176C2×C8D4×D1311yescharacteristic
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—261no—
180C4⋊C4—521no—
181C42—521no—
182C42D4×D1311yescharacteristic
183C16—41no—
184C16—521no—
185C13#1242911yescharacteristic, complemented, Sylow
186C23—1041no—
187Q8—81no—
188Q8—81no—
189Q8—262no—
190Q8—521no—
191D4—1042no—
192D4—1041no—
193D4—1041no—
194D4—1041no—
195D4—1041no—
196C2×C4—81no—
197C2×C4—521no—
198C2×C4—521no—
199C2×C4#8813811yescharacteristic
200C2×C4D8×D1311yescharacteristic
201C2×C4#8816811yescharacteristic
202C8—21no—
203C8—81no—
204C8—261no—
205C8—261no—
206C8—521no—
207C8D8×D1311yescharacteristic
208C8#8817011yescharacteristic
209C22—2081no—
210C22—2081no—
211C22—2081no—
212C22#1171844711yescharacteristic
213C4—21no—
214C4—161no—
215C4—522no—
216C4—1041no—
217C4#1171841011yescharacteristic
218C4#1171843611yescharacteristic
219C4#1171857711yescharacteristic
220C4#1171857911yescharacteristic
221C2—4161no—
222C2#1311419011yescharacteristic
223C2#1311690111yescharacteristic
224C2#1311690811yescharacteristic
subgroupG/H
centerC22#11718447
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1362C2
socleC22×C13#459
prime radical#11718356C22
hypercenter#1362D13
hypocenterC13#12429
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
1. #13116883C2semidirect
4. #13113642C2semidirect
5. #13112905C2semidirect
7. C13×#1362C2semidirect
79. #1362D13semidirect
185. C13#12429semidirect

Maximal subgroups

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

subgroupindex
#131168832
#131168772
#131144432
#131136422
#131129052
#131128812
C13×#13622
#1242913