Finite Group Databasebeta

← #15777118

Subgroups — #15777118

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#13116886C211yesmaximal, characteristic, complemented
2#13116876C211yesmaximal, characteristic
3#13114442C211yesmaximal, characteristic
4#13112906C211yesmaximal, characteristic, complemented
5#13112884C211yesmaximal, characteristic, complemented
6#13112881C211yesmaximal, characteristic
7C8×C13×Q16C211yesmaximal, characteristic, complemented
8C8×Q8×C13—21no—
9C4×C13×Q16C2211yescharacteristic
10C2×#88069—21no—
11C2×#88068—21no—
12#11718360C2211yescharacteristic
13#11718356C2211yescharacteristic
14#11718355—21no—
15#11718355—21no—
16C13×#335C2211yescharacteristic
17C13×Q8⋊C8—21no—
18C82×C13C2211yescharacteristic
19#11718084—21no—
20#11718083—21no—
21C4⋊#6090C2211yescharacteristic
22C4⋊#6090C2211yescharacteristic
23C2×C13×Q16D411yescharacteristic
24C4×Q8×C13—21no—
25C2×Dic52—21no—
26C2×Dic52—21no—
27C2×D104—21no—
28C2×D104—21no—
29#88128—21no—
30#88123—21no—
31C13×#107D411yescharacteristic
32C13×C4⋊C8—21no—
33C13×C4⋊C8—41no—
34C13×#103—21no—
35C4×C8×C13—41no—
36C4×C8×C13D411yescharacteristic
37C4×C8×C13D411yescharacteristic
38C4×C8×C13C2311yescharacteristic
39#88069—42no—
40#88068—42no—
41#88061—42no—
42#88061—41no—
43#88061—41no—
44C2×#6090—21no—
45C2×#6090—21no—
46#12429—131nomaximal, Sylow
47C2×Q8×C13—21no—
48C2×D52—41no—
49C2×D52—41no—
50C2×D52—41no—
51C2×Dic26—41no—
52C13×Q16—21no—
53C13×Q16D812yes—
54C2×C8×C13—21no—
55C2×C8×C13—41no—
56C2×C8×C13D811yescharacteristic
57C2×C8×C13D811yescharacteristic
58C2×C8×C13C2×D411yescharacteristic
59C2×C8×C13#4111yescharacteristic
60C13×C4⋊C4—21no—
61C13×C4⋊C4—41no—
62C42×C13—41no—
63C42×C13C2×D411yescharacteristic
64C4⋊Dic13—41no—
65C4⋊Dic13—41no—
66Dic52—41no—
67Dic52—41no—
68Dic52—81no—
69D104—41no—
70D104—41no—
71D104—81no—
72#6090—41no—
73#6090—41no—
74#2209—131no—
75#2207—131no—
76#1709—131no—
77C8×Q16D1311yescharacteristic, complemented
78#1370—131no—
79#1362—131no—
80#1361—131no—
81C22×D13—81no—
82Q8×C13—22no—
83Q8×C13—41no—
84C2×C4×C13—41no—
85C2×C4×C13—41no—
86C2×C4×C13#12111yescharacteristic
87C2×C4×C13C2×D811yescharacteristic
88C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
89C2×Dic13—81no—
90D52—82no—
91D52—81no—
92D52—81no—
93D52—81no—
94D52—81no—
95Dic26—81no—
96Dic26—81no—
97C8×C13—21no—
98C8×C13—21no—
99C8×C13—21no—
100C8×C13—41no—
101C8×C13—81no—
102C8×C13C2×D811yescharacteristic
103C8×C13#13511yescharacteristic
104C2×Q32—261no—
105C2×SD32—261no—
106#494—131no—
107#493—131no—
108#486—261no—
109#486—261no—
110C8×Q8—21no—
111C4×Q16C2×D1311yescharacteristic
112C4⋊C16—131no—
113C4⋊C16—131no—
114#358—261no—
115#357—261no—
116#335C2×D1311yescharacteristic
117Q8⋊C8—21no—
118C82C2×D1311yescharacteristic
119C22×C13#45911yescharacteristic
120C2×D13—161no—
121C2×D13—161no—
122C2×D13—161no—
123C4×C13—21no—
124C4×C13—42no—
125C4×C13—81no—
126C4×C13#46611yescharacteristic
127C4×C13#47211yescharacteristic
128C4×C13#50811yescharacteristic
129C4×C13#51011yescharacteristic
130Dic13—161no—
131C2×Q16—261no—
132C2×Q16—261no—
133C2×Q16D5211yescharacteristic
134C2×D8—261no—
135C2×D8—261no—
136C4⋊Q8—261no—
137#127—261no—
138C4×Q8—21no—
139Q32—522no—
140SD32—522no—
141C2×C16—261no—
142C2×C16—261no—
143#107D5211yescharacteristic
144C4⋊C8—21no—
145C4⋊C8—41no—
146#103—21no—
147#102—522no—
148#102—521no—
149#102—521no—
150C4×C8—41no—
151C4×C8C22⋊D1311yescharacteristic
152C4×C8C22⋊D1311yescharacteristic
153C4×C8C22×D1311yescharacteristic
154C2×C13#166711yescharacteristic
155C2×C13#221111yescharacteristic
156C2×C13#221211yescharacteristic
157D13—321no—
158C2×Q8—21no—
159C2×Q8—521no—
160C2×D4—521no—
161C2×D4—521no—
162C2×D4—521no—
163Q16—21no—
164Q16—521no—
165Q16—521no—
166Q16—1041no—
167Q16D10412yes—
168D8—521no—
169D8—521no—
170D8—1041no—
171C2×C8—21no—
172C2×C8—41no—
173C2×C8#610411yescharacteristic
174C2×C8#610411yescharacteristic
175C2×C8C2×D5211yescharacteristic
176C2×C8#612711yescharacteristic
177C4⋊C4—21no—
178C4⋊C4—41no—
179C4⋊C4—521no—
180C4⋊C4—521no—
181C42—41no—
182C42C2×C22⋊D1311yescharacteristic
183C16—521no—
184C16—521no—
185C13#1242911yescharacteristic, complemented, Sylow
186C23—1041no—
187Q8—22no—
188Q8—41no—
189Q8—1041no—
190Q8—1041no—
191D4—1042no—
192D4—1041no—
193D4—1041no—
194D4—1041no—
195D4—1041no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—1041no—
199C2×C4#8818411yescharacteristic
200C2×C4C2×#610411yescharacteristic
201C2×C4#8820311yescharacteristic
202C8—21no—
203C8—21no—
204C8—21no—
205C8—41no—
206C8—81no—
207C8C2×D10411yescharacteristic
208C8#8815811yescharacteristic
209C22—2081no—
210C22—2081no—
211C22—2081no—
212C22#1171867611yescharacteristic
213C4—21no—
214C4—42no—
215C4—81no—
216C4—2081no—
217C4#1171877611yescharacteristic
218C4#1171880311yescharacteristic
219C4#1171884011yescharacteristic
220C4#1171885511yescharacteristic
221C2—4161no—
222C2#1311419111yescharacteristic
223C2#1311689811yescharacteristic
224C2#1311690511yescharacteristic
subgroupG/H
centerC22#11718676
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC8×C13×Q16C2
socleC22×C13#459
prime radical#11718356C22
hypercenterC8×Q16D13
hypocenterC13#12429
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C82 ◁ C8×Q16

Complements

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

NH ≅ G/Ntype
1. #13116886C2semidirect
4. #13112906C2semidirect
5. #13112884C2semidirect
7. C8×C13×Q16C2semidirect
77. C8×Q16D13semidirect
185. C13#12429semidirect

Maximal subgroups

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

subgroupindex
#131168862
#131168762
#131144422
#131129062
#131128842
#131128812
C8×C13×Q162
#1242913