Finite Group Databasebeta

← #15766009

Subgroups — #15766009

Order 3328.

416 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 101 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#13115813C211yesmaximal, characteristic
2#13113399C212yesmaximal
3#13112694C212yesmaximal
4#13112669C211yesmaximal, characteristic
5C13×#2862C211yesmaximal, characteristic
6C2×C13×C4⋊Q8—21no—
7#11719175C2211yescharacteristic
8C13×#391—24no—
9C13×#382—21no—
10C13×#382C2212yes—
11C43×C13C2211yescharacteristic
12#11718586C2212yes—
13#11718585C2211yescharacteristic
14#11718115—21no—
15#11718115—21no—
16#11718044—24no—
17C22×Q8×C13—22no—
18C13×C4⋊Q8—42no—
19C13×C4⋊Q8—42no—
20C2×C13×C4⋊C4—22no—
21C2×C13×C4⋊C4—22no—
22C2×C42×C13—22no—
23C2×C42×C13D411yescharacteristic
24C2×C42×C13D411yescharacteristic
25C2×C42×C13C2311yescharacteristic
26#88180—21no—
27#88178—22no—
28C2×#6099—21no—
29#88124—21no—
30#88123Q812yescomplemented
31C4×Dic26—22no—
32C13×#95—24no—
33C13×#95—22no—
34C13×#95D414yes—
35C22⋊#1055—22no—
36C4⋊#1055—22no—
37C4⋊#1055—22no—
38C4×#1055—22no—
39#10363—131nomaximal, Sylow
40C2×Q8×C13—44no—
41C2×Q8×C13—48no—
42C22×C4×C13—21no—
43C22×C4×C13—21no—
44C22×C4×C13—24no—
45C22×C4×C13C2×D412yes—
46C22×C4×C13C2×D411yescharacteristic
47C2×Dic26—22no—
48C13×C4⋊C4—44no—
49C13×C4⋊C4—42no—
50C13×C4⋊C4—42no—
51C42×C13—21no—
52C42×C13—21no—
53C42×C13—44no—
54C42×C13SD1612yes—
55C42×C13Q1612yes—
56C42×C13C2×Q811yescharacteristic
57C42×C13#4112yes—
58C42×C13#4111yescharacteristic
59C22⋊Dic13—41no—
60C4⋊Dic13—22no—
61C4⋊Dic13—22no—
62#6101—42no—
63C4×Dic13—41no—
64#6099—41no—
65#6099—41no—
66C2×#1055—42no—
67C2×#1055—41no—
68#2862D1311yescharacteristic
69#1994—131no—
70#1518—132no—
71#1286—132no—
72#1276—131no—
73C23×C13#12011yescharacteristic
74Q8×C13—88no—
75C2×C4×C13—24no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—42no—
79C2×C4×C13—42no—
80C2×C4×C13—48no—
81C2×C4×C13—44no—
82C2×C4×C13C22⋊Q812yes—
83C2×C4×C13C22⋊Q811yescharacteristic
84C2×C4×C13#12412yes—
85C2×C4×C13#12411yescharacteristic
86C2×C4×C13C2×SD1611yescharacteristic
87C2×C4×C13C2×Q1611yescharacteristic
88C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
89C2×C4×C13#13711yescharacteristic
90C2×Dic13—42no—
91Dic26—82no—
92#1055—82no—
93#1055—81no—
94#533—131no—
95C2×C4⋊Q8—21no—
96#431—132no—
97#423—131no—
98#391—24no—
99#382—21no—
100#382C2×D1312yes—
101C43C2×D1311yescharacteristic
102#339—261no—
103#339—261no—
104#328—264no—
105C22×C13—22no—
106C22×C13#39311yescharacteristic
107C22×C13#45011yescharacteristic
108C22×C13#45111yescharacteristic
109C4×C13—24no—
110C4×C13—22no—
111C4×C13—22no—
112C4×C13—42no—
113C4×C13—84no—
114C4×C13#47511yescharacteristic
115C4×C13#47711yescharacteristic
116C4×C13#48711yescharacteristic
117C4×C13#48911yescharacteristic
118Dic13—82no—
119C22×Q8—22no—
120C2×M16—261no—
121C4⋊Q8—42no—
122C4⋊Q8—42no—
123C4⋊Q8—132no—
124#125—261no—
125C22⋊Q8—262no—
126C4×Q8—262no—
127#117—261no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C42—22no—
131C2×C42C22⋊D1311yescharacteristic
132C2×C42C22⋊D1311yescharacteristic
133C2×C42C22×D1311yescharacteristic
134C4⋊C8—262no—
135C4⋊C8—262no—
136C22⋊C8—262no—
137C4×C8—262no—
138#95—24no—
139#95—22no—
140#95C22⋊D1314yes—
141C2×C13—21no—
142C2×C13—21no—
143C2×C13#202411yescharacteristic
144C2×C13#203112yes—
145C2×Q8—44no—
146C2×Q8—48no—
147C2×Q8—262no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—24no—
151C22×C4C2×C22⋊D1312yes—
152C22×C4C2×C22⋊D1311yescharacteristic
153M16—521no—
154M16—521no—
155C2×C8—522no—
156C2×C8—521no—
157C4⋊C4—44no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C4⋊C4—262no—
161C4⋊C4—262no—
162C4⋊C4—522no—
163C22⋊C4—521no—
164C42—21no—
165C42—21no—
166C42—44no—
167C42—521no—
168C42#610512yes—
169C42#610712yes—
170C42Q8×D1311yescharacteristic
171C42#613111yescharacteristic
172C42#613112yes—
173C13#1036311yescharacteristic, complemented, Sylow
174C23#8820711yescharacteristic
175Q8—88no—
176Q8—1042no—
177C2×C4—24no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—48no—
183C2×C4—44no—
184C2×C4—522no—
185C2×C4#8818611yescharacteristic
186C2×C4C2×#610511yescharacteristic
187C2×C4#8819611yescharacteristic
188C2×C4C2×#610711yescharacteristic
189C2×C4#8820012yes—
190C2×C4#8820011yescharacteristic
191C2×C4#8820112yes—
192C2×C4#8820111yescharacteristic
193C8—1042no—
194C8—1041no—
195C22—22no—
196C22#1171887911yescharacteristic
197C22#1171888911yescharacteristic
198C22#1171889211yescharacteristic
199C4—24no—
200C4—22no—
201C4—22no—
202C4—42no—
203C4—84no—
204C4—1042no—
205C4#1171875011yescharacteristic
206C4#1171875211yescharacteristic
207C4#1171875411yescharacteristic
208C4#1171875511yescharacteristic
209C2—21no—
210C2—21no—
211C2#1311597411yescharacteristic
212C2#1311600512yes—
subgroupG/H
centerC22#11718892
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2862C2
socleC22×C13#393
prime radicalC23×C13#120
hypercenter#2862D13
hypocenterC13#10363
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2862

Complements

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

NH ≅ G/Ntype
30. #88123Q8semidirect
173. C13#10363semidirect

Maximal subgroups

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

subgroupindex
#131158132
#131133992
#131126942
#131126692
C13×#28622
#1036313