Finite Group Databasebeta

← #15766023

Subgroups — #15766023

Order 3328.

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

normal subgroups only

This group has 400 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#13123199C211yesmaximal, characteristic
2#13115813C211yesmaximal, characteristic
3#13113401C212yesmaximal
4#13112695C212yesmaximal
5C13×#1276C211yesmaximal, characteristic
6#11719175C2211yescharacteristic
7C2×#88124—21no—
8C13×#431C2212yes—
9C43×C13C2211yescharacteristic
10#11718597C2212yes—
11#11718596—21no—
12#11718589—24no—
13#11718585C2211yescharacteristic
14#11718115—21no—
15#11718115—21no—
16#11718059—24no—
17C2×C42×C13—22no—
18C2×C42×C13D411yescharacteristic
19C2×C42×C13D411yescharacteristic
20C2×C42×C13C2311yescharacteristic
21#88180—21no—
22C2×C4⋊Dic13—24no—
23C2×C4⋊Dic13—22no—
24#88178—22no—
25C2×#6101—24no—
26C2×#6099—21no—
27#88124—21no—
28#88124—42no—
29#88124—42no—
30#88123Q812yes—
31C4×Dic26—22no—
32C13×C4⋊C8—22no—
33C13×C22⋊C8—22no—
34C4×C8×C13—22no—
35#88071—22no—
36#88071D414yes—
37C4⋊#1055—22no—
38#10365—131nomaximal, Sylow
39C22×C4×C13—21no—
40C22×C4×C13—21no—
41C22×C4×C13C2×D411yescharacteristic
42C22×C4×C13C2×D412yes—
43C22×Dic13—24no—
44C2×Dic26—22no—
45C2×C8×C13—42no—
46C42×C13—21no—
47C42×C13—21no—
48C42×C13—44no—
49C42×C13SD1612yes—
50C42×C13Q1612yes—
51C42×C13C2×Q811yescharacteristic
52C42×C13#4112yes—
53C42×C13#4111yescharacteristic
54C22⋊Dic13—41no—
55C4⋊Dic13—22no—
56C4⋊Dic13—22no—
57C4⋊Dic13—48no—
58C4⋊Dic13—42no—
59C4⋊Dic13—42no—
60#6101—48no—
61#6101—42no—
62C4×Dic13—41no—
63#6099—41no—
64#6099—41no—
65C2×#1055—41no—
66#2859—131no—
67#1994—131no—
68#1518—132no—
69#1286—132no—
70#1276D1311yescharacteristic
71C23×C13#12011yescharacteristic
72C2×C4×C13—24no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—42no—
76C2×C4×C13—42no—
77C2×C4×C13C22⋊Q812yes—
78C2×C4×C13C22⋊Q811yescharacteristic
79C2×C4×C13#12412yes—
80C2×C4×C13#12411yescharacteristic
81C2×C4×C13C2×SD1611yescharacteristic
82C2×C4×C13C2×Q1611yescharacteristic
83C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
84C2×C4×C13#13711yescharacteristic
85C2×Dic13—48no—
86C2×Dic13—42no—
87C2×Dic13—44no—
88Dic26—82no—
89C8×C13—82no—
90#1055—81no—
91#533—131no—
92C2×#125—261no—
93#431C2×D1312yes—
94#423—131no—
95#389—264no—
96#384—261no—
97#382—132no—
98C43C2×D1311yescharacteristic
99#339—261no—
100#339—261no—
101#328—264no—
102C22×C13—22no—
103C22×C13#39311yescharacteristic
104C22×C13#45011yescharacteristic
105C22×C13#45111yescharacteristic
106C4×C13—24no—
107C4×C13—22no—
108C4×C13—22no—
109C4×C13—42no—
110C4×C13#47511yescharacteristic
111C4×C13#47711yescharacteristic
112C4×C13#48711yescharacteristic
113C4×C13#48911yescharacteristic
114Dic13—84no—
115Dic13—82no—
116C2×M16—261no—
117C4⋊Q8—132no—
118#125—261no—
119#125—522no—
120#125—522no—
121C22⋊Q8—262no—
122C4×Q8—262no—
123#117—261no—
124C2×C4⋊C4—264no—
125C2×C4⋊C4—264no—
126C2×C4⋊C4—262no—
127C2×C42—22no—
128C2×C42D5211yescharacteristic
129C2×C42D5211yescharacteristic
130C2×C42C22×D1311yescharacteristic
131C4⋊C8—22no—
132C4⋊C8—262no—
133C22⋊C8—22no—
134C4×C8—22no—
135#95—134no—
136#95—262no—
137C2×C13—21no—
138C2×C13—21no—
139C2×C13#202411yescharacteristic
140C2×C13#203112yes—
141C2×Q8—262no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—264no—
145C22×C4C2×D5211yescharacteristic
146C22×C4D4×D1312yes—
147M16—521no—
148M16—521no—
149C2×C8—42no—
150C2×C8—521no—
151C4⋊C4—262no—
152C4⋊C4—262no—
153C4⋊C4—528no—
154C4⋊C4—528no—
155C4⋊C4—522no—
156C4⋊C4—522no—
157C4⋊C4—522no—
158C22⋊C4—521no—
159C42—21no—
160C42—21no—
161C42—44no—
162C42—521no—
163C42#609512yes—
164C42Dic5212yes—
165C42#612712yes—
166C42#612911yescharacteristic
167C42Q8×D1311yescharacteristic
168C13#1036511yescharacteristic, complemented, Sylow
169C23#8813611yescharacteristic
170Q8—1042no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—528no—
177C2×C4—522no—
178C2×C4—524no—
179C2×C4#8812911yescharacteristic
180C2×C4#8813912yes—
181C2×C4#8815012yes—
182C2×C4#8815111yescharacteristic
183C2×C4C2×#609511yescharacteristic
184C2×C4C2×Dic5211yescharacteristic
185C2×C4#8816211yescharacteristic
186C2×C4#8816311yescharacteristic
187C8—82no—
188C8—1041no—
189C22—22no—
190C22#1171833411yescharacteristic
191C22#1171839211yescharacteristic
192C22#1171840011yescharacteristic
193C4—24no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—1044no—
198C4—1042no—
199C4#1171834211yescharacteristic
200C4#1171837511yescharacteristic
201C4#1171851111yescharacteristic
202C4#1171851211yescharacteristic
203C2—21no—
204C2—21no—
205C2#1311597811yescharacteristic
206C2#1311600912yes—
subgroupG/H
centerC22#11718334
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1276C2
socleC22×C13#393
prime radicalC23×C13#120
hypercenter#1276D13
hypocenterC13#10365
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
168. C13#10365semidirect

Maximal subgroups

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

subgroupindex
#131231992
#131158132
#131134012
#131126952
C13×#12762
#1036513