Finite Group Databasebeta

← #15767909

Subgroups — #15767909

Order 3328.

320 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 93 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#13115775C211yesmaximal, characteristic
2#13115010C211yesmaximal, characteristic
3#13113606C211yesmaximal, characteristic
4#13113266C211yesmaximal, characteristic
5#13113264C211yesmaximal, characteristic
6#13112666C211yesmaximal, characteristic
7C13×#1570C211yesmaximal, characteristic
8C2×C4×Dic26C2211yescharacteristic
9C13×#431C2211yescharacteristic
10C13×#423C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×#88062—22no—
13#11718586C2211yescharacteristic
14#11718585C2211yescharacteristic
15C2×#88043C2211yescharacteristic
16C13×#334—22no—
17#11718142—22no—
18#11718076—22no—
19#11718072—22no—
20#11718048—22no—
21C22×Dic26Q811yescharacteristic
22C2×C13×M16—21no—
23C22×C8×C13—21no—
24C2×C42×C13C2311yescharacteristic
25C2×C4⋊Dic13Q811yescharacteristic
26C2×#6101—21no—
27C2×C4×Dic13—21no—
28C2×#6099—21no—
29C22×#1055D412yes—
30C4×Dic26—21no—
31C4×Dic26—21no—
32C4×Dic26—21no—
33C4×Dic26—21no—
34C13×C4⋊C8—21no—
35C13×C4⋊C8—21no—
36C13×C4⋊C8—21no—
37C13×C4⋊C8—21no—
38C13×C4⋊C8—21no—
39C13×C22⋊C8—21no—
40C4×C8×C13D412yes—
41C22⋊#1055—21no—
42#88062—44no—
43C4⋊#1055—21no—
44C4⋊#1055—21no—
45C4⋊#1055—21no—
46#88043—21no—
47#88043—21no—
48C4×#1055D412yes—
49#10663—131nomaximal, Sylow
50C22×C4×C13C2×D411yescharacteristic
51C22×C4×C13C2×Q811yescharacteristic
52C22×C4×C13#4111yescharacteristic
53C22×Dic13—21no—
54C22×Dic13—21no—
55C2×Dic26—21no—
56C2×Dic26—21no—
57C2×Dic26—42no—
58C13×M16—42no—
59C2×C8×C13—22no—
60C2×C8×C13—41no—
61C2×C8×C13—41no—
62C2×C8×C13—42no—
63C42×C13C2×D411yescharacteristic
64C42×C13C2×D411yescharacteristic
65C42×C13#4111yescharacteristic
66C42×C13#4111yescharacteristic
67C4⋊Dic13—21no—
68C4⋊Dic13—21no—
69#6101—41no—
70#6101—41no—
71C4×Dic13—41no—
72C4×Dic13—41no—
73#6099—42no—
74C2×#1055—22no—
75C2×#1055—22no—
76C2×#1055—22no—
77C2×#1055—41no—
78C2×#1055SD1614yes—
79#1985—131no—
80#1849—131no—
81#1570—131no—
82#1570D1311yescharacteristic
83#1487—131no—
84#1487—131no—
85#1275—131no—
86C23×C13C22⋊Q811yescharacteristic
87C2×C4×C13—41no—
88C2×C4×C13—41no—
89C2×C4×C13C22⋊Q811yescharacteristic
90C2×C4×C13C22⋊Q811yescharacteristic
91C2×C4×C13#12311yescharacteristic
92C2×C4×C13#12311yescharacteristic
93C2×C4×C13#12311yescharacteristic
94C2×C4×C13#12711yescharacteristic
95C2×C4×C13C2×SD1612yes—
96C2×C4×C13#13712yes—
97C2×Dic13—22no—
98C2×Dic13—41no—
99C2×Dic13—41no—
100C2×Dic13—42no—
101C2×Dic13—41no—
102Dic26—22no—
103Dic26—22no—
104Dic26—41no—
105Dic26—41no—
106C8×C13—42no—
107C8×C13—81no—
108C8×C13—81no—
109#1055—24no—
110#1055—42no—
111#1055—81no—
112C2×C4×Q8—131no—
113#431—131no—
114#431C2×D1311yescharacteristic
115C2×#108—262no—
116#423—131no—
117#423C2×D1311yescharacteristic
118C2×C4⋊C8C2×D1311yescharacteristic
119C2×#97—131no—
120#336—262no—
121#334—22no—
122#334—262no—
123Q8⋊C8—262no—
124Q8⋊C8—262no—
125C22×C13—21no—
126C22×C13—21no—
127C22×C13#39911yescharacteristic
128C22×C13#47512yes—
129C4×C13—21no—
130C4×C13—21no—
131C4×C13—21no—
132C4×C13—21no—
133C4×C13#48312yes—
134C4×C13#49211yescharacteristic
135C4×C13#49711yescharacteristic
136Dic13—42no—
137Dic13—81no—
138C22×Q8—131no—
139C2×M16—21no—
140C2×M16—261no—
141C22×C8—21no—
142C22×C8—132no—
143C4×Q8—261no—
144C4×Q8—261no—
145C4×Q8—261no—
146C4×Q8—261no—
147C2×C4⋊C4—131no—
148C2×C4⋊C4—261no—
149C2×C42—261no—
150C2×C42C22×D1311yescharacteristic
151#108—524no—
152C4⋊C8—21no—
153C4⋊C8—21no—
154C4⋊C8—21no—
155C4⋊C8—21no—
156C4⋊C8—21no—
157C4⋊C8—261no—
158C4⋊C8—261no—
159C4⋊C8—261no—
160C22⋊C8—21no—
161C22⋊C8—261no—
162#97—261no—
163#97—261no—
164C4×C8—132no—
165C4×C8C22⋊D1312yes—
166C2×C13—22no—
167C2×C13#209111yescharacteristic
168C2×C13#209611yescharacteristic
169C2×C13#209811yescharacteristic
170C2×Q8—261no—
171C2×Q8—261no—
172C2×Q8—522no—
173C22×C4—261no—
174C22×C4—261no—
175C22×C4#612711yescharacteristic
176C22×C4D4×D1311yescharacteristic
177C22×C4Q8×D1311yescharacteristic
178M16—42no—
179M16—522no—
180C2×C8—22no—
181C2×C8—42no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8—134no—
185C2×C8—262no—
186C2×C8—262no—
187C2×C8—262no—
188C2×C8—521no—
189C4⋊C4—261no—
190C4⋊C4—261no—
191C4⋊C4—521no—
192C4⋊C4—521no—
193C42—521no—
194C42—521no—
195C42#612711yescharacteristic
196C42D4×D1311yescharacteristic
197C42#613111yescharacteristic
198C42C2×C22⋊D1311yescharacteristic
199C13#1066311yescharacteristic, complemented, Sylow
200C23#8815011yescharacteristic
201Q8—262no—
202Q8—262no—
203Q8—521no—
204Q8—521no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—262no—
208C2×C4—521no—
209C2×C4—521no—
210C2×C4—522no—
211C2×C4—521no—
212C2×C4#8814811yescharacteristic
213C2×C4#8814811yescharacteristic
214C2×C4#8815011yescharacteristic
215C2×C4SD16×D1312yes—
216C2×C4#8816912yes—
217C2×C4#8818311yescharacteristic
218C2×C4#8819411yescharacteristic
219C2×C4#8820011yescharacteristic
220C8—42no—
221C8—81no—
222C8—81no—
223C8—264no—
224C8—522no—
225C8—1041no—
226C22—21no—
227C22—21no—
228C22#1171851512yes—
229C22#1171865311yescharacteristic
230C4—21no—
231C4—21no—
232C4—21no—
233C4—21no—
234C4—522no—
235C4—1041no—
236C4#1171852312yes—
237C4#1171882811yescharacteristic
238C4#1171883611yescharacteristic
239C2—22no—
240C2#1311635111yescharacteristic
241C2#1311637611yescharacteristic
242C2#1311639211yescharacteristic
subgroupG/H
centerC2×C4#88194
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1570C2
socleC22×C13#399
prime radicalC23×C13C22⋊Q8
hypercenter#1570D13
hypocenterC13#10663
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
199. C13#10663semidirect

Maximal subgroups

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

subgroupindex
#131157752
#131150102
#131136062
#131132662
#131132642
#131126662
C13×#15702
#1066313