Finite Group Databasebeta

← #15752228

Subgroups — #15752228

Order 3328.

350 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 83 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#13122824C211yesmaximal, characteristic
2#13116398C212yesmaximal
3#13112662C211yesmaximal, characteristic
4#13112658C212yesmaximal
5C13×#2095C211yesmaximal, characteristic
6C2×C13×#107—21no—
7C2×C13×#103—21no—
8C13×#391C2211yescharacteristic
9C13×#384C2211yescharacteristic
10#11718891—21no—
11#11718647—21no—
12#11718589C2212yes—
13#11718322—22no—
14#11718316—22no—
15C13×#336C2211yescharacteristic
16#11718121—22no—
17#11718121—22no—
18#11718116C2212yes—
19C22×Q8×C13D411yescharacteristic
20C22×C8×C13—21no—
21C2×C13×C4⋊C4—21no—
22C2×C13×C4⋊C4—22no—
23C2×C13×C4⋊C4D411yescharacteristic
24C2×C42×C13C2311yescharacteristic
25C2×C4⋊Dic13—21no—
26C2×C4⋊Dic13—21no—
27C2×C4⋊Dic13D412yes—
28C2×C4⋊Dic13D412yes—
29C2×#6101—22no—
30C2×C4×Dic13—21no—
31C22×#1055—22no—
32C13×#107—42no—
33C13×#103—42no—
34C13×#95—22no—
35#88071—21no—
36#88071—22no—
37#88071—22no—
38#88071—22no—
39#7831—131nomaximal, Sylow
40C2×Q8×C13—21no—
41C2×Q8×C13—41no—
42C2×Q8×C13—41no—
43C2×Q8×C13Q1612yes—
44C22×C4×C13—21no—
45C22×C4×C13—21no—
46C22×C4×C13—41no—
47C22×C4×C13C2×D412yes—
48C22×C4×C13C2×D411yescharacteristic
49C22×Dic13—22no—
50C22×Dic13—22no—
51C2×C8×C13—22no—
52C2×C8×C13—41no—
53C2×C8×C13—41no—
54C13×C4⋊C4—41no—
55C13×C4⋊C4—41no—
56C13×C4⋊C4—41no—
57C13×C4⋊C4—44no—
58C42×C13—41no—
59C4⋊Dic13—22no—
60C4⋊Dic13—22no—
61C4⋊Dic13—42no—
62C4⋊Dic13—81no—
63C4⋊Dic13—81no—
64#6101—42no—
65#6101—42no—
66C4×Dic13—81no—
67C2×#1055—42no—
68C2×#1055—42no—
69C2×#1055—42no—
70#2809—131no—
71#2100—132no—
72#2095D1311yescharacteristic
73#1272—131no—
74#1271—132no—
75C23×C13#12011yescharacteristic
76Q8×C13—42no—
77Q8×C13—81no—
78C2×C4×C13—21no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—21no—
82C2×C4×C13—22no—
83C2×C4×C13—41no—
84C2×C4×C13—41no—
85C2×C4×C13—41no—
86C2×C4×C13—42no—
87C2×C4×C13—81no—
88C2×C4×C13—82no—
89C2×C4×C13C2×Q1611yescharacteristic
90C2×C4×C13#13512yes—
91C2×C4×C13#13711yescharacteristic
92C2×C4×C13#13712yes—
93C2×Dic13—42no—
94C2×Dic13—42no—
95C2×Dic13—42no—
96C2×Dic13—42no—
97C2×Dic13—42no—
98C2×Dic13—42no—
99C8×C13—42no—
100#1055—82no—
101C2×#107—21no—
102C2×#103—21no—
103#400—261no—
104#398—262no—
105#391—261no—
106#391C2×D1311yescharacteristic
107#389—132no—
108#387—262no—
109#384C2×D1311yescharacteristic
110#340—262no—
111#340—262no—
112#336—132no—
113#336C2×D1311yescharacteristic
114C22×C13#45111yescharacteristic
115C22×C13#45212yes—
116C22×C13#45311yescharacteristic
117C22×C13#45412yes—
118C22×C13#45811yescharacteristic
119C4×C13—21no—
120C4×C13—21no—
121C4×C13—22no—
122C4×C13—22no—
123C4×C13—42no—
124C4×C13—81no—
125C4×C13—161no—
126Dic13—82no—
127Dic13—82no—
128C22×Q8C22⋊D1311yescharacteristic
129C22×C8—21no—
130C22×C8—262no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—132no—
134C2×C4⋊C4—132no—
135C2×C4⋊C4—262no—
136C2×C4⋊C4—261no—
137C2×C4⋊C4—261no—
138C2×C4⋊C4C22⋊D1311yescharacteristic
139C2×C42—261no—
140C2×C42C22×D1311yescharacteristic
141#107—42no—
142#103—42no—
143#95—22no—
144#95—261no—
145#95—262no—
146#95—262no—
147#95—262no—
148C2×C13#161411yescharacteristic
149C2×C13#161512yes—
150C2×C13#163411yescharacteristic
151C2×C13#163612yes—
152C2×C13#165711yescharacteristic
153C2×Q8—21no—
154C2×Q8—41no—
155C2×Q8—41no—
156C2×Q8#610712yes—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—41no—
160C22×C4—262no—
161C22×C4—262no—
162C22×C4D4×D1312yes—
163C22×C4C2×C22⋊D1311yescharacteristic
164C2×C8—22no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—522no—
168C2×C8—522no—
169C2×C8—522no—
170C4⋊C4—41no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—44no—
174C4⋊C4—262no—
175C4⋊C4—262no—
176C4⋊C4—522no—
177C4⋊C4—522no—
178C4⋊C4—522no—
179C4⋊C4—1041no—
180C4⋊C4—1041no—
181C42—41no—
182C42—1041no—
183C13#783111yescharacteristic, complemented, Sylow
184C23#8819111yescharacteristic
185Q8—42no—
186Q8—81no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—42no—
196C2×C4—81no—
197C2×C4—82no—
198C2×C4—522no—
199C2×C4—522no—
200C2×C4—522no—
201C2×C4—522no—
202C2×C4—522no—
203C2×C4—522no—
204C2×C4#8817212yes—
205C2×C4#8817312yes—
206C2×C4C2×#610711yescharacteristic
207C2×C4#8820511yescharacteristic
208C8—42no—
209C8—1042no—
210C22#1171871111yescharacteristic
211C22#1171871411yescharacteristic
212C22#1171873811yescharacteristic
213C22#1171884812yes—
214C22#1171886212yes—
215C4—21no—
216C4—21no—
217C4—22no—
218C4—22no—
219C4—42no—
220C4—81no—
221C4—161no—
222C4—1042no—
223C4—1042no—
224C2#1311386011yescharacteristic
225C2#1311386612yes—
226C2#1311397911yescharacteristic
227C2#1311399312yes—
228C2#1311413211yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2095C2
socle, prime radicalC23×C13#120
hypercenter#2095D13
hypocenterC13#7831
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2095

Complements

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

NH ≅ G/Ntype
183. C13#7831semidirect

Maximal subgroups

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

subgroupindex
#131228242
#131163982
#131126622
#131126582
C13×#20952
#783113