Finite Group Databasebeta

← #15776203

Subgroups — #15776203

Order 3328.

310 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 67 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#13126181C211yesmaximal, characteristic
2#13117038C212yesmaximal
3#13112847C212yesmaximal
4#13112776C211yesmaximal, characteristic
5C13×#2087C211yesmaximal, characteristic
6#11719175—21no—
7C2×C13×#107C2211yescharacteristic
8C2×C13×C4⋊C8C2211yescharacteristic
9C13×#389—21no—
10#11718777—21no—
11#11718777C2212yes—
12#11718511—22no—
13#11718510—22no—
14C13×#340—21no—
15C13×#340C2211yescharacteristic
16C22⋊#6090C2212yes—
17#11718084—22no—
18#11718081—22no—
19C22×C8×C13D411yescharacteristic
20C22×C8×C13C2311yescharacteristic
21C2×C13×C4⋊C4—21no—
22C2×C13×C4⋊C4—21no—
23C2×C13×C4⋊C4—41no—
24C2×C42×C13D411yescharacteristic
25#88180—41no—
26#88178—22no—
27#88178—41no—
28C2×Dic52—21no—
29C2×Dic52D412yes—
30#88124—41no—
31#88123—21no—
32#88123—21no—
33C4×Dic26—22no—
34C4×Dic26—41no—
35C13×#107—22no—
36C13×C4⋊C8—22no—
37C13×#95—41no—
38#88058—21no—
39#88058D412yes—
40#88056—22no—
41#88056—22no—
42C2×#6090—22no—
43#12292—131nomaximal, Sylow
44C22×C4×C13—41no—
45C22×C4×C13—41no—
46C22×C4×C13D811yescharacteristic
47C22×C4×C13D811yescharacteristic
48C22×C4×C13C2×D411yescharacteristic
49C2×Dic26—22no—
50C2×Dic26—41no—
51C2×C8×C13—21no—
52C2×C8×C13—41no—
53C2×C8×C13—41no—
54C2×C8×C13C2×D412yes—
55C13×C4⋊C4—22no—
56C13×C4⋊C4—41no—
57C13×C4⋊C4—41no—
58C13×C4⋊C4—41no—
59C13×C4⋊C4—82no—
60C42×C13—21no—
61C42×C13—21no—
62C22⋊Dic13—42no—
63C4⋊Dic13—22no—
64C4⋊Dic13—41no—
65C4⋊Dic13—41no—
66C4⋊Dic13—41no—
67#6101—42no—
68#6101—42no—
69C4×Dic13—42no—
70Dic52—42no—
71Dic52—81no—
72#6090—42no—
73#3249—131no—
74#2236—132no—
75#2087D1311yescharacteristic
76#1348—132no—
77#1322—131no—
78C23×C13C2×D811yescharacteristic
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—41no—
85C2×C4×C13—42no—
86C2×C4×C13—81no—
87C2×C4×C13—81no—
88C2×C4×C13—81no—
89C2×C4×C13—81no—
90C2×C4×C13—81no—
91C2×C4×C13Q3212yes—
92C2×C4×C13#12011yescharacteristic
93C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
94C2×Dic13—42no—
95C2×Dic13—42no—
96Dic26—42no—
97Dic26—42no—
98Dic26—82no—
99C8×C13—22no—
100C8×C13—41no—
101#533—261no—
102#477—262no—
103#467—132no—
104#467—261no—
105#462—262no—
106C2×#107C2×D1311yescharacteristic
107C2×C4⋊C8C2×D1311yescharacteristic
108#389—21no—
109#366—262no—
110#358—262no—
111C22⋊C16—132no—
112#340—21no—
113#340C2×D1311yescharacteristic
114C22×C13—21no—
115C22×C13—21no—
116C22×C13#44711yescharacteristic
117C22×C13C2×Q3211yescharacteristic
118C22×C13#51011yescharacteristic
119C4×C13—21no—
120C4×C13—22no—
121C4×C13—41no—
122C4×C13—82no—
123C4×C13—161no—
124C4×C13#45611yescharacteristic
125C4×C13#45811yescharacteristic
126Dic13—82no—
127Dic13—82no—
128C2×Q16—132no—
129C2×Q16—261no—
130C22×C8C22⋊D1311yescharacteristic
131C22×C8C22×D1311yescharacteristic
132C4⋊Q8—261no—
133C4⋊Q8—261no—
134#125—521no—
135C22⋊Q8—262no—
136C22⋊Q8—521no—
137C4×Q8—262no—
138C4×Q8—521no—
139#117—521no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—41no—
143C2×C42C22⋊D1311yescharacteristic
144C2×C16—262no—
145#107—22no—
146#107—132no—
147#107—261no—
148C4⋊C8—22no—
149#103—262no—
150#103—262no—
151#95—41no—
152C2×C13—21no—
153C2×C13—21no—
154C2×C13#161011yescharacteristic
155C2×C13#218811yescharacteristic
156C2×C13#219011yescharacteristic
157C2×Q8—262no—
158C2×Q8—521no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4#610411yescharacteristic
162C22×C4#610411yescharacteristic
163C22×C4C2×C22⋊D1311yescharacteristic
164Q16—522no—
165Q16—1041no—
166C2×C8—21no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8D4×D1312yes—
170C4⋊C4—22no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—82no—
175C4⋊C4—262no—
176C4⋊C4—521no—
177C4⋊C4—521no—
178C4⋊C4—522no—
179C4⋊C4—521no—
180C4⋊C4—522no—
181C22⋊C4—522no—
182C42—21no—
183C42—21no—
184C42—522no—
185C16—522no—
186C13#1229211yescharacteristic, complemented, Sylow
187C23C2×#610411yescharacteristic
188Q8—522no—
189Q8—522no—
190Q8—1042no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—81no—
199C2×C4—81no—
200C2×C4—81no—
201C2×C4—81no—
202C2×C4—81no—
203C2×C4—522no—
204C2×C4—522no—
205C2×C4#8806912yes—
206C2×C4#8819111yescharacteristic
207C2×C4#8820311yescharacteristic
208C8—22no—
209C8—41no—
210C22—21no—
211C22—21no—
212C22#1171869711yescharacteristic
213C22C2×#8806911yescharacteristic
214C22#1171885611yescharacteristic
215C4—22no—
216C4—21no—
217C4—41no—
218C4—82no—
219C4—161no—
220C4—1042no—
221C4—1042no—
222C4#1171871411yescharacteristic
223C4#1171875611yescharacteristic
224C2—21no—
225C2—21no—
226C2#1311383811yescharacteristic
227C2#1311676911yescharacteristic
228C2#1311678111yescharacteristic
subgroupG/H
centerC22#11718697
commutator, cosocleC22×C8×C13C23
FrattiniC22×C8C22×D13
FittingC13×#2087C2
socleC22×C13#447
prime radicalC23×C13C2×D8
hypercenter#2087D13
hypocenterC13#12292
LCSG ▷ C22×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #2087

Complements

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

NH ≅ G/Ntype
186. C13#12292semidirect

Maximal subgroups

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

subgroupindex
#131261812
#131170382
#131128472
#131127762
C13×#20872
#1229213