Finite Group Databasebeta

← #15777070

Subgroups — #15777070

Order 3328.

218 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 75 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#13116988C211yesmaximal, characteristic
2#13116886C211yesmaximal, characteristic
3#13114433C211yesmaximal, characteristic
4#13112900C211yesmaximal, characteristic
5#13112895C211yesmaximal, characteristic
6#13112884C211yesmaximal, characteristic
7C8×C13×Q16C211yesmaximal, characteristic
8C8×Q8×C13—21no—
9C4×C13×Q16C2211yescharacteristic
10C2×#88069—21no—
11#11718360C2211yescharacteristic
12#11718343C2211yescharacteristic
13#11718342—21no—
14#11718341—21no—
15C13×#335C2211yescharacteristic
16C13×Q8⋊C8—21no—
17C82×C13C2211yescharacteristic
18#11718156—21no—
19#11718084—21no—
20#11718081—21no—
21C4⋊#6090C2211yescharacteristic
22C4⋊#6090C2211yescharacteristic
23C2×C13×Q16D411yescharacteristic
24C4×Q8×C13—21no—
25C2×Dic52—21no—
26C2×Dic52—21no—
27#88123—21no—
28#88123—21no—
29C13×#107D411yescharacteristic
30C13×C4⋊C8—21no—
31C13×C4⋊C8—41no—
32C13×#103—21no—
33C4×C8×C13—41no—
34C4×C8×C13D411yescharacteristic
35C4×C8×C13D411yescharacteristic
36C4×C8×C13C2311yescharacteristic
37#88069—42no—
38#88058—21no—
39#88058—21no—
40#88057—41no—
41#88057—41no—
42#88056—42no—
43C2×#6090—21no—
44C2×#6090—21no—
45#12421—131nomaximal, Sylow
46C2×Q8×C13—21no—
47C2×Dic26—41no—
48C2×Dic26—41no—
49C13×Q16—21no—
50C13×Q16SD1612yes—
51C2×C8×C13—21no—
52C2×C8×C13—41no—
53C2×C8×C13D811yescharacteristic
54C2×C8×C13D811yescharacteristic
55C2×C8×C13C2×D411yescharacteristic
56C2×C8×C13#4111yescharacteristic
57C13×C4⋊C4—21no—
58C13×C4⋊C4—41no—
59C42×C13—41no—
60C42×C13C2×D411yescharacteristic
61C4⋊Dic13—41no—
62C4⋊Dic13—41no—
63C4⋊Dic13—41no—
64C4⋊Dic13—41no—
65Dic52—41no—
66Dic52—41no—
67Dic52—81no—
68#6090—41no—
69#6090—41no—
70#2227—131no—
71#2209—131no—
72#1707—131no—
73C8×Q16D1311yescharacteristic
74#1367—131no—
75#1365—131no—
76#1362—131no—
77Q8×C13—22no—
78Q8×C13—41no—
79C2×C4×C13—41no—
80C2×C4×C13—41no—
81C2×C4×C13#12111yescharacteristic
82C2×C4×C13C2×D811yescharacteristic
83C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
84C2×Dic13—81no—
85C2×Dic13—81no—
86Dic26—82no—
87Dic26—81no—
88Dic26—81no—
89C8×C13—21no—
90C8×C13—21no—
91C8×C13—41no—
92C8×C13—81no—
93C8×C13Q3212yescomplemented
94C8×C13C2×SD1611yescharacteristic
95C8×C13#13511yescharacteristic
96C2×Q32—261no—
97#500—131no—
98#498—261no—
99#494—131no—
100#487—261no—
101C8×Q8—21no—
102C4×Q16C2×D1311yescharacteristic
103#366—261no—
104C4⋊C16—131no—
105C4⋊C16—131no—
106#358—261no—
107#358—261no—
108#335C2×D1311yescharacteristic
109Q8⋊C8—21no—
110C82C2×D1311yescharacteristic
111C22×C13#45911yescharacteristic
112C4×C13—21no—
113C4×C13—42no—
114C4×C13—81no—
115C4×C13#46511yescharacteristic
116C4×C13#47111yescharacteristic
117C4×C13C2×Q3211yescharacteristic
118C4×C13#51011yescharacteristic
119Dic13—161no—
120Dic13—161no—
121C2×Q16—261no—
122C2×Q16—261no—
123C2×Q16D5211yescharacteristic
124C4⋊Q8—261no—
125C4⋊Q8—261no—
126C4×Q8—21no—
127Q32—522no—
128C2×C16—261no—
129C2×C16—261no—
130#107—261no—
131#107—261no—
132#107D5211yescharacteristic
133#106—521no—
134#106—521no—
135C4⋊C8—21no—
136C4⋊C8—41no—
137#103—21no—
138#103—522no—
139C4×C8—41no—
140C4×C8C22⋊D1311yescharacteristic
141C4×C8C22⋊D1311yescharacteristic
142C4×C8C22×D1311yescharacteristic
143C2×C13#166511yescharacteristic
144C2×C13#220911yescharacteristic
145C2×C13#221211yescharacteristic
146C2×Q8—21no—
147C2×Q8—521no—
148C2×Q8—521no—
149Q16—21no—
150Q16—521no—
151Q16—521no—
152Q16—1041no—
153Q16#609512yes—
154C2×C8—21no—
155C2×C8—41no—
156C2×C8#610411yescharacteristic
157C2×C8#610411yescharacteristic
158C2×C8C2×D5211yescharacteristic
159C2×C8#612711yescharacteristic
160C4⋊C4—21no—
161C4⋊C4—41no—
162C4⋊C4—521no—
163C4⋊C4—521no—
164C4⋊C4—521no—
165C4⋊C4—521no—
166C42—41no—
167C42C2×C22⋊D1311yescharacteristic
168C16—521no—
169C16—521no—
170C13#1242111yescharacteristic, complemented, Sylow
171Q8—22no—
172Q8—41no—
173Q8—1042no—
174Q8—1041no—
175Q8—1041no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—1041no—
179C2×C4—1041no—
180C2×C4#8818411yescharacteristic
181C2×C4C2×#610411yescharacteristic
182C2×C4#8820311yescharacteristic
183C8—21no—
184C8—21no—
185C8—41no—
186C8—81no—
187C8#8806912yescomplemented
188C8C2×#609511yescharacteristic
189C8#8815811yescharacteristic
190C22#1171867611yescharacteristic
191C4—21no—
192C4—42no—
193C4—81no—
194C4—2081no—
195C4—2081no—
196C4#1171877511yescharacteristic
197C4#1171880211yescharacteristic
198C4C2×#8806911yescharacteristic
199C4#1171885611yescharacteristic
200C2#1311417711yescharacteristic
201C2#1311688611yescharacteristic
202C2#1311690511yescharacteristic
subgroupG/H
centerC22#11718676
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC8×C13×Q16C2
socle, prime radicalC22×C13#459
hypercenterC8×Q16D13
hypocenterC13#12421
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
93. C8×C13Q32semidirect
170. C13#12421semidirect
187. C8#88069semidirect

Maximal subgroups

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

subgroupindex
#131169882
#131168862
#131144332
#131129002
#131128952
#131128842
C8×C13×Q162
#1242113