Finite Group Databasebeta

← #15760451

Subgroups — #15760451

Order 3328.

436 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 99 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#13125212C211yesmaximal, characteristic
2#13113549C212yesmaximal
3#13113474C211yesmaximal, characteristic, complemented
4#13112707C212yesmaximal, complemented
5C13×#2987C211yesmaximal, characteristic, complemented
6C13×#533C2211yescharacteristic
7C2×#88128C2211yescharacteristic
8C13×#446—24no—
9C13×#433—22no—
10C13×#432C2212yes—
11#11718749C414yes—
12#11718728—22no—
13#11718662—22no—
14#11718587C2212yes—
15C4×#6099C2211yescharacteristic
16#11718135—22no—
17#11718077—24no—
18C22×D52—21no—
19C22×D52—22no—
20C13×C4⋊Q8C2×C412yes—
21C13×#125D412yes—
22C13×C22⋊Q8—22no—
23C4×Q8×C13—22no—
24C13×#117D412yes—
25C2×C42×C13C2311yescharacteristic
26C2×#6099—21no—
27#88128—21no—
28#88128—22no—
29#88128C2×C412yes—
30C13×C4⋊C8—24no—
31C13×C4⋊C8D414yes—
32C13×C22⋊C8—22no—
33C13×#97—22no—
34C13×#97—22no—
35C4×C8×C13—22no—
36C22⋊#1055—22no—
37#88049—28no—
38C4⋊#1055—22no—
39#88043—21no—
40#88043—22no—
41C4×#1055C2×C412yes—
42#9424—131nomaximal, Sylow
43C23×D13—41no—
44C2×Q8×C13—22no—
45C22×C4×C13C2×D411yescharacteristic
46C22×C4×C13#4112yes—
47C2×D52—22no—
48C2×D52—24no—
49C2×D52—44no—
50C2×D52—41no—
51C2×D52—42no—
52C2×D52—84no—
53C2×C8×C13—24no—
54C13×C4⋊C4—22no—
55C13×C4⋊C4—24no—
56C13×C4⋊C4C22⋊C414yes—
57C13×C22⋊C4—22no—
58C42×C13—22no—
59C42×C13C22×C411yescharacteristic
60C42×C13C2×D411yescharacteristic
61C42×C13C2×D412yes—
62#6099—42no—
63C2×#1055—22no—
64C2×#1055—42no—
65#3138—131no—
66#2987D1311yescharacteristic, complemented
67#1555—132no—
68#1537—131no—
69#1291—132no—
70C23×C13#12311yescharacteristic
71C22×D13—42no—
72C22×D13—82no—
73C22×D13—84no—
74Q8×C13—82no—
75C2×C4×C13—22no—
76C2×C4×C13—24no—
77C2×C4×C13—42no—
78C2×C4×C13C2×C22⋊C411yescharacteristic
79C2×C4×C13C4×D412yes—
80C2×C4×C13#12011yescharacteristic
81C2×C4×C13#12112yes—
82D52—44no—
83D52—84no—
84D52—84no—
85D52—82no—
86C8×C13—44no—
87#1055—42no—
88#1055—82no—
89#533C2×D1311yescharacteristic
90C2×#127—131no—
91#490—262no—
92#486—134no—
93#446—24no—
94#433—22no—
95#432—132no—
96#432C2×D1312yes—
97#418—262no—
98C4×M16—131no—
99#331—264no—
100#330—262no—
101C22×C13—21no—
102C22×C13—22no—
103C22×C13#38611yescharacteristic
104C2×D13—82no—
105C2×D13—84no—
106C2×D13—164no—
107C4×C13—21no—
108C4×C13—22no—
109C4×C13—22no—
110C4×C13—44no—
111C4×C13#45412yes—
112C22×D4—262no—
113C22×D4—261no—
114C2×M16—261no—
115C4⋊Q8C4×D1312yes—
116#127—132no—
117#127—261no—
118#127—262no—
119#125D5212yes—
120C22⋊Q8—22no—
121C4×Q8—22no—
122#117C22⋊D1312yes—
123C2×C42C22×D1311yescharacteristic
124C4⋊C8—24no—
125C4⋊C8—262no—
126C4⋊C8C22⋊D1314yes—
127#102—268no—
128C22⋊C8—22no—
129C22⋊C8—262no—
130#97—22no—
131#97—22no—
132#97—261no—
133#97—262no—
134C4×C8—22no—
135C4×C8—132no—
136C2×C13—41no—
137C2×C13#188811yescharacteristic
138C2×C13#190312yes—
139D13—162no—
140C24—521no—
141C2×Q8—22no—
142C2×D4—262no—
143C2×D4—264no—
144C2×D4—524no—
145C2×D4—522no—
146C2×D4—521no—
147C2×D4—1044no—
148C22×C4#612712yes—
149C22×C4C2×C22⋊D1311yescharacteristic
150M16—522no—
151C2×C8—24no—
152C2×C8—262no—
153C2×C8—522no—
154C4⋊C4—22no—
155C4⋊C4—24no—
156C4⋊C4#610314yes—
157C22⋊C4—22no—
158C42—22no—
159C42C2×C4×D1311yescharacteristic
160C42C2×D5211yescharacteristic
161C42C2×C22⋊D1312yes—
162C13#942411yescharacteristic, complemented, Sylow
163C23—522no—
164C23—1042no—
165C23—1044no—
166C23#8818311yescharacteristic
167Q8—82no—
168D4—524no—
169D4—1044no—
170D4—1044no—
171D4—1042no—
172C2×C4—22no—
173C2×C4—24no—
174C2×C4—42no—
175C2×C4C2×#610311yescharacteristic
176C2×C4C4×C22⋊D1312yes—
177C2×C4#8818412yes—
178C2×C4#8820711yescharacteristic
179C8—44no—
180C8—522no—
181C8—1042no—
182C22—21no—
183C22—22no—
184C22—1042no—
185C22—1044no—
186C22—2084no—
187C22#1171887411yescharacteristic
188C4—21no—
189C4—22no—
190C4—22no—
191C4—44no—
192C4#1171890612yes—
193C2—41no—
194C2—2082no—
195C2#1311523911yescharacteristic
196C2#1311531612yes—
subgroupG/H
centerC22#11718874
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2987C2
socleC22×C13#386
prime radicalC2×#88128C22
cosocleC2×C42×C13C23
hypercenter#2987D13
hypocenterC13#9424
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2987

Complements

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

NH ≅ G/Ntype
3. #13113474C2semidirect
4. #13112707C2semidirect
5. C13×#2987C2semidirect
66. #2987D13semidirect
162. C13#9424semidirect

Maximal subgroups

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

subgroupindex
#131252122
#131135492
#131134742
#131127072
C13×#29872
#942413