Finite Group Databasebeta

← #15772216

Subgroups — #15772216

Order 3328.

392 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 87 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#13117553C211yesmaximal, characteristic
2#13113158C212yesmaximal
3#13112780C211yesmaximal, characteristic
4#13112769C212yesmaximal
5C13×#1324C211yesmaximal, characteristic
6C2×#88141C411yescharacteristic
7C2×#88141C2211yescharacteristic
8C2×#88123C411yescharacteristic
9C13×#382C2211yescharacteristic
10#11718635C411yescharacteristic
11#11718635C2211yescharacteristic
12#11718593C411yescharacteristic
13#11718379—22no—
14#11718315—22no—
15#11718315—22no—
16C13×#324C2212yes—
17#11718120C2212yes—
18#11718061—22no—
19C22×Dic26C2×C411yescharacteristic
20C22×Dic26C2×C411yescharacteristic
21C2×C13×C4⋊C4C2×C411yescharacteristic
22C2×C13×C4⋊C4C2311yescharacteristic
23C2×C42×C13C2×C411yescharacteristic
24C2×C4⋊Dic13—22no—
25C2×#6101—21no—
26C2×#6101D412yes—
27C2×C4×Dic13—21no—
28C2×C4×Dic13C2×C411yescharacteristic
29C2×C4×Dic13C2×C411yescharacteristic
30C2×C4×Dic13D412yes—
31#88141—42no—
32#88141—42no—
33#88123—22no—
34#88123C814yescomplemented
35C13×C22⋊C8—22no—
36C13×#95—22no—
37#88071—22no—
38#88071—21no—
39#88071—21no—
40#88071—22no—
41C22⋊#1055—22no—
42#88054—42no—
43C8×Dic13—42no—
44#11482—131nomaximal, Sylow
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13C22×C411yescharacteristic
48C22×C4×C13C2×D412yes—
49C22×Dic13—21no—
50C22×Dic13—21no—
51C22×Dic13C22⋊C412yes—
52C22×Dic13C22⋊C411yescharacteristic
53C22×Dic13C22⋊C411yescharacteristic
54C2×Dic26—21no—
55C2×Dic26—41no—
56C2×Dic26—41no—
57C2×Dic26—41no—
58C2×Dic26—41no—
59C2×Dic26C2×C812yes—
60C2×Dic26C2×C812yes—
61C2×Dic26M1612yes—
62C2×C8×C13—42no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—41no—
65C42×C13—21no—
66C42×C13C2×C812yes—
67C4⋊Dic13—28no—
68#6101—42no—
69#6101—42no—
70C4×Dic13—22no—
71C4×Dic13—22no—
72C4×Dic13—22no—
73C4×Dic13—42no—
74C4×Dic13—41no—
75C2×#1055—42no—
76#2327—131no—
77#1461—132no—
78#1324—131no—
79#1324D1311yescharacteristic
80#1319—132no—
81C23×C13C2×C22⋊C411yescharacteristic
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—41no—
87C2×C4×C13—41no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13—41no—
91C2×C4×C13C22×C811yescharacteristic
92C2×C4×C13C2×M1611yescharacteristic
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—21no—
97C2×Dic13—41no—
98C2×Dic13—41no—
99C2×Dic13—41no—
100C2×Dic13—41no—
101C2×Dic13—41no—
102C2×Dic13—41no—
103C2×Dic13—41no—
104C2×Dic13C22⋊C814yes—
105C2×Dic13#9912yes—
106Dic26—42no—
107Dic26—42no—
108Dic26—42no—
109Dic26—42no—
110C8×C13—82no—
111#1055—82no—
112C2×C4⋊Q8—131no—
113C2×C4×Q8—131no—
114C2×C4×Q8—131no—
115#431—262no—
116#391—131no—
117#391—131no—
118#387—262no—
119#387—262no—
120#382C2×D1311yescharacteristic
121#376—131no—
122#324—132no—
123#324—262no—
124#324C2×D1312yes—
125C22×C13—21no—
126C22×C13—21no—
127C22×C13C2×C22⋊C811yescharacteristic
128C22×C13C2×#9911yescharacteristic
129C22×C13#41311yescharacteristic
130C4×C13—21no—
131C4×C13—21no—
132C4×C13—42no—
133C4×C13—42no—
134C4×C13—81no—
135Dic13—22no—
136Dic13—24no—
137Dic13—41no—
138Dic13—42no—
139Dic13—81no—
140C22×Q8—131no—
141C22×Q8—131no—
142C4⋊Q8—134no—
143C4⋊Q8—262no—
144C4×Q8—522no—
145C4×Q8—522no—
146C2×C4⋊C4—132no—
147C2×C4⋊C4—262no—
148C2×C4⋊C4—261no—
149C2×C4⋊C4C4×D1311yescharacteristic
150C2×C4⋊C4C22×D1311yescharacteristic
151C2×C42—131no—
152C2×C42—132no—
153C2×C42—131no—
154C2×C42—261no—
155C2×C42C4×D1311yescharacteristic
156C4⋊C8—522no—
157C22⋊C8—22no—
158C22⋊C8—262no—
159C4×C8—522no—
160#95—22no—
161#95—261no—
162#95—261no—
163#95—262no—
164#95—262no—
165C2×C13—21no—
166C2×C13—21no—
167C2×C13#145911yescharacteristic
168C2×C13#212911yescharacteristic
169C2×C13#213311yescharacteristic
170C2×Q8—132no—
171C2×Q8—132no—
172C2×Q8—132no—
173C2×Q8—261no—
174C2×Q8—521no—
175C2×Q8—521no—
176C2×Q8—521no—
177C2×Q8—521no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—132no—
181C22×C4—131no—
182C22×C4—131no—
183C22×C4—261no—
184C22×C4—261no—
185C22×C4C2×C4×D1311yescharacteristic
186C22×C4D4×D1312yes—
187C2×C8—42no—
188C2×C8—522no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—268no—
192C4⋊C4—522no—
193C4⋊C4—522no—
194C42—21no—
195C42—262no—
196C42—262no—
197C42—262no—
198C42—521no—
199C42—522no—
200C42C8×D1312yes—
201C13#1148211yescharacteristic, complemented, Sylow
202C23C22⋊C4×D1311yescharacteristic
203Q8—522no—
204Q8—522no—
205Q8—522no—
206Q8—522no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—41no—
216C2×C4—132no—
217C2×C4—134no—
218C2×C4—262no—
219C2×C4—262no—
220C2×C4—261no—
221C2×C4—262no—
222C2×C4—521no—
223C2×C4—521no—
224C2×C4—521no—
225C2×C4—521no—
226C2×C4—521no—
227C2×C4—521no—
228C2×C4—521no—
229C2×C4C2×C8×D1311yescharacteristic
230C2×C4M16×D1311yescharacteristic
231C8—82no—
232C8—1042no—
233C22—21no—
234C22—21no—
235C22D13×C22⋊C811yescharacteristic
236C22D13×#9911yescharacteristic
237C22#1171841211yescharacteristic
238C4—21no—
239C4—21no—
240C4—42no—
241C4—42no—
242C4—81no—
243C4—264no—
244C4—262no—
245C4—522no—
246C4—521no—
247C4—1041no—
248C2—21no—
249C2—21no—
250C2#1311315311yescharacteristic
251C2#1311650911yescharacteristic
252C2#1311652211yescharacteristic
subgroupG/H
centerC22D13×#99
commutatorC2×C4×C13C22×C8
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1324C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1324D13
hypocenterC13#11482
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
34. #88123C8semidirect
201. C13#11482semidirect

Maximal subgroups

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

subgroupindex
#131175532
#131131582
#131127802
#131127692
C13×#13242
#1148213