Finite Group Databasebeta

← #15766013

Subgroups — #15766013

Order 3328.

416 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 97 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#13123214C211yesmaximal, characteristic
2#13115813C211yesmaximal, characteristic
3#13113401C212yesmaximal
4#13112695C212yesmaximal
5C13×#1276C211yesmaximal, characteristic
6#11719175C2211yescharacteristic
7C2×#88123—21no—
8C13×#431C2212yes—
9C43×C13C2211yescharacteristic
10#11718597—21no—
11#11718597C2212yes—
12#11718590—24no—
13#11718585C2211yescharacteristic
14#11718115—21no—
15#11718115—21no—
16#11718059—24no—
17C22×Dic26—22no—
18C2×C42×C13—22no—
19C2×C42×C13D411yescharacteristic
20C2×C42×C13D411yescharacteristic
21C2×C42×C13C2311yescharacteristic
22#88180—21no—
23C2×C4⋊Dic13—22no—
24C2×C4⋊Dic13—22no—
25#88178—22no—
26C2×#6099—21no—
27#88124—21no—
28#88123—42no—
29#88123—42no—
30#88123Q812yescomplemented
31C4×Dic26—22no—
32C13×C4⋊C8—22no—
33C13×C22⋊C8—22no—
34C4×C8×C13—22no—
35#88071—24no—
36#88071—22no—
37#88071D414yes—
38C4⋊#1055—22no—
39#10363—131nomaximal, Sylow
40C22×C4×C13—21no—
41C22×C4×C13—21no—
42C22×C4×C13C2×D411yescharacteristic
43C22×C4×C13C2×D412yes—
44C22×Dic13—24no—
45C2×Dic26—22no—
46C2×Dic26—44no—
47C2×Dic26—48no—
48C2×C8×C13—42no—
49C42×C13—21no—
50C42×C13—21no—
51C42×C13—44no—
52C42×C13SD1612yes—
53C42×C13Q1612yes—
54C42×C13C2×Q811yescharacteristic
55C42×C13#4112yes—
56C42×C13#4111yescharacteristic
57C22⋊Dic13—41no—
58C4⋊Dic13—22no—
59C4⋊Dic13—22no—
60C4⋊Dic13—44no—
61C4⋊Dic13—42no—
62C4⋊Dic13—42no—
63#6101—42no—
64C4×Dic13—41no—
65#6099—41no—
66#6099—41no—
67C2×#1055—41no—
68#2862—131no—
69#1994—131no—
70#1518—132no—
71#1286—132no—
72#1276D1311yescharacteristic
73C23×C13#12011yescharacteristic
74C2×C4×C13—24no—
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13—42no—
78C2×C4×C13—42no—
79C2×C4×C13C22⋊Q812yes—
80C2×C4×C13C22⋊Q811yescharacteristic
81C2×C4×C13#12412yes—
82C2×C4×C13#12411yescharacteristic
83C2×C4×C13C2×SD1611yescharacteristic
84C2×C4×C13C2×Q1611yescharacteristic
85C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
86C2×C4×C13#13711yescharacteristic
87C2×Dic13—48no—
88C2×Dic13—42no—
89C2×Dic13—44no—
90Dic26—88no—
91Dic26—82no—
92C8×C13—82no—
93#1055—81no—
94#533—131no—
95C2×C4⋊Q8—261no—
96#431C2×D1312yes—
97#423—131no—
98#391—264no—
99#382—132no—
100#382—261no—
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#47511yescharacteristic
114C4×C13#47711yescharacteristic
115C4×C13#48711yescharacteristic
116C4×C13#48911yescharacteristic
117Dic13—84no—
118Dic13—82no—
119C22×Q8—262no—
120C2×M16—261no—
121C4⋊Q8—132no—
122C4⋊Q8—522no—
123C4⋊Q8—522no—
124#125—261no—
125C22⋊Q8—262no—
126C4×Q8—262no—
127#117—261no—
128C2×C4⋊C4—262no—
129C2×C4⋊C4—262no—
130C2×C42—22no—
131C2×C42D5211yescharacteristic
132C2×C42D5211yescharacteristic
133C2×C42C22×D1311yescharacteristic
134C4⋊C8—22no—
135C4⋊C8—262no—
136C22⋊C8—22no—
137C4×C8—22no—
138#95—134no—
139#95—264no—
140#95—262no—
141C2×C13—21no—
142C2×C13—21no—
143C2×C13#202411yescharacteristic
144C2×C13#203112yes—
145C2×Q8—262no—
146C2×Q8—524no—
147C2×Q8—528no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—264no—
151C22×C4C2×D5211yescharacteristic
152C22×C4D4×D1312yes—
153M16—521no—
154M16—521no—
155C2×C8—42no—
156C2×C8—521no—
157C4⋊C4—262no—
158C4⋊C4—262no—
159C4⋊C4—524no—
160C4⋊C4—522no—
161C4⋊C4—522no—
162C4⋊C4—522no—
163C22⋊C4—521no—
164C42—21no—
165C42—21no—
166C42—44no—
167C42—521no—
168C42#609512yes—
169C42Dic5212yes—
170C42#612712yes—
171C42#612911yescharacteristic
172C42Q8×D1311yescharacteristic
173C13#1036311yescharacteristic, complemented, Sylow
174C23#8813611yescharacteristic
175Q8—1042no—
176Q8—1048no—
177C2×C4—24no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—528no—
183C2×C4—522no—
184C2×C4—524no—
185C2×C4#8812911yescharacteristic
186C2×C4#8813912yes—
187C2×C4#8815012yes—
188C2×C4#8815111yescharacteristic
189C2×C4C2×#609511yescharacteristic
190C2×C4C2×Dic5211yescharacteristic
191C2×C4#8816211yescharacteristic
192C2×C4#8816311yescharacteristic
193C8—82no—
194C8—1041no—
195C22—22no—
196C22#1171833411yescharacteristic
197C22#1171839211yescharacteristic
198C22#1171840011yescharacteristic
199C4—24no—
200C4—22no—
201C4—22no—
202C4—42no—
203C4—1044no—
204C4—1042no—
205C4#1171834211yescharacteristic
206C4#1171837511yescharacteristic
207C4#1171851111yescharacteristic
208C4#1171851211yescharacteristic
209C2—21no—
210C2—21no—
211C2#1311597811yescharacteristic
212C2#1311600912yes—
subgroupG/H
centerC22#11718334
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1276C2
socleC22×C13#393
prime radicalC23×C13#120
hypercenter#1276D13
hypocenterC13#10363
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

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
#131232142
#131158132
#131134012
#131126952
C13×#12762
#1036313