Finite Group Databasebeta

← #15751472

Subgroups — #15751472

Order 3328.

410 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 115 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#13114979C211yesmaximal, characteristic
2#13114585C211yesmaximal, characteristic
3#13112662C214yesmaximal
4C13×#2862C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×C13×C4⋊Q8C411yescharacteristic
7C13×#391—21no—
8C13×#391—21no—
9C13×#391C412yes—
10C13×#391C2212yes—
11C13×#382—21no—
12C13×#382—21no—
13C43×C13C2211yescharacteristic
14C2×#88043—21no—
15#11718116—21no—
16#11718116—21no—
17#11718116—21no—
18#11718116C2212yes—
19#11718116C2212yes—
20C22×Q8×C13—21no—
21C22×Q8×C13C2×C412yes—
22C13×C4⋊Q8—42no—
23C13×C4⋊Q8—42no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4C2×C412yes—
28C2×C42×C13C2×C411yescharacteristic
29C2×C42×C13C2×C411yescharacteristic
30C2×C42×C13D411yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C42×C13D411yescharacteristic
34C2×C42×C13C2311yescharacteristic
35C22×#1055—22no—
36C22×#1055—22no—
37C13×#95—22no—
38C13×#95—22no—
39C13×#95—22no—
40C13×#95—22no—
41#88043—24no—
42#7702—131nomaximal, Sylow
43C2×Q8×C13—24no—
44C2×Q8×C13—42no—
45C2×Q8×C13—42no—
46C2×Q8×C13—42no—
47C2×Q8×C13—42no—
48C2×Q8×C13—42no—
49C22×C4×C13—22no—
50C22×C4×C13—22no—
51C22×C4×C13C22⋊C411yescharacteristic
52C22×C4×C13C22⋊C411yescharacteristic
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22×C411yescharacteristic
56C22×C4×C13C2×D411yescharacteristic
57C22×C4×C13C2×D411yescharacteristic
58C13×C4⋊C4—42no—
59C13×C4⋊C4—42no—
60C13×C4⋊C4—42no—
61C13×C4⋊C4—42no—
62C42×C13—22no—
63C42×C13—22no—
64C42×C13—22no—
65C42×C13—22no—
66C42×C13—22no—
67C42×C13—41no—
68C42×C13—41no—
69C2×#1055—24no—
70C2×#1055—42no—
71C2×#1055—42no—
72C2×#1055—42no—
73C2×#1055—42no—
74C2×#1055—42no—
75#2862D1311yescharacteristic
76#1839—131no—
77#1745—131no—
78#1272—134no—
79C23×C13C2×C22⋊C411yescharacteristic
80Q8×C13—84no—
81Q8×C13—84no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13#10012yes—
105C2×C4×C13#10412yes—
106C2×C4×C13#13112yes—
107C2×C4×C13#13712yes—
108C2×C4×C13#13712yes—
109#1055—44no—
110#1055—82no—
111C2×C4⋊Q8Dic1311yescharacteristic
112C2×C4⋊Q8Dic1311yescharacteristic
113C2×#97—261no—
114#391—21no—
115#391—21no—
116#391Dic1312yes—
117#391C2×D1312yes—
118#382—21no—
119#382—21no—
120C43C2×D1311yescharacteristic
121#336—132no—
122#336—132no—
123#336—261no—
124#336—261no—
125#336—261no—
126C22×C13#40811yescharacteristic
127C22×C13#41011yescharacteristic
128C22×C13C2×#10011yescharacteristic
129C22×C13#41911yescharacteristic
130C22×C13#41911yescharacteristic
131C22×C13C2×#10411yescharacteristic
132C22×C13#42111yescharacteristic
133C4×C13—22no—
134C4×C13—22no—
135C4×C13—22no—
136C4×C13—22no—
137C4×C13—22no—
138C4×C13—41no—
139C4×C13—41no—
140C4×C13—82no—
141C4×C13—82no—
142C22×Q8—21no—
143C22×Q8C2×Dic1312yes—
144C22×C8—262no—
145C22×C8—262no—
146C4⋊Q8—42no—
147C4⋊Q8—42no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4C2×Dic1312yes—
152C2×C42C2×Dic1311yescharacteristic
153C2×C42C2×Dic1311yescharacteristic
154C2×C42C22⋊D1311yescharacteristic
155C2×C42C22⋊D1311yescharacteristic
156C2×C42C22⋊D1311yescharacteristic
157C2×C42C22⋊D1311yescharacteristic
158C2×C42C22×D1311yescharacteristic
159#97—264no—
160#95—22no—
161#95—22no—
162#95—22no—
163#95—22no—
164C2×C13#146911yescharacteristic
165C2×C13#148511yescharacteristic
166C2×C13#149711yescharacteristic
167C2×C13#150611yescharacteristic
168C2×C13#151511yescharacteristic
169C2×C13#152711yescharacteristic
170C2×C13#155811yescharacteristic
171C2×Q8—24no—
172C2×Q8—42no—
173C2×Q8—42no—
174C2×Q8—42no—
175C2×Q8—42no—
176C2×Q8—42no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4C22⋊Dic1311yescharacteristic
180C22×C4C22⋊Dic1311yescharacteristic
181C22×C4C22⋊Dic1311yescharacteristic
182C22×C4C22⋊Dic1311yescharacteristic
183C22×C4C22×Dic1311yescharacteristic
184C22×C4C2×C22⋊D1311yescharacteristic
185C22×C4C2×C22⋊D1311yescharacteristic
186C2×C8—264no—
187C2×C8—522no—
188C2×C8—522no—
189C2×C8—522no—
190C2×C8—522no—
191C2×C8—522no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C42—22no—
197C42—22no—
198C42—22no—
199C42—22no—
200C42—22no—
201C42—41no—
202C42—41no—
203C13#770211yescharacteristic, complemented, Sylow
204C23C2×C22⋊Dic1311yescharacteristic
205Q8—84no—
206Q8—84no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4#8807312yes—
230C2×C4#8807712yes—
231C2×C4#8819612yes—
232C2×C4#8819612yes—
233C2×C4#8820212yes—
234C8—524no—
235C8—1042no—
236C22C2×#8807311yescharacteristic
237C22#1171888611yescharacteristic
238C22#1171888611yescharacteristic
239C22#1171889511yescharacteristic
240C22C2×#8807711yescharacteristic
241C22#1171889711yescharacteristic
242C22#1171890111yescharacteristic
243C4—22no—
244C4—22no—
245C4—22no—
246C4—22no—
247C4—22no—
248C4—41no—
249C4—41no—
250C4—82no—
251C4—82no—
252C2#1311318811yescharacteristic
253C2#1311325711yescharacteristic
254C2#1311330911yescharacteristic
255C2#1311334811yescharacteristic
256C2#1311338711yescharacteristic
257C2#1311343411yescharacteristic
258C2#1311356211yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2862C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2862D13
hypocenterC13#7702
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ #2862

Complements

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

NH ≅ G/Ntype
203. C13#7702semidirect

Maximal subgroups

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

subgroupindex
#131149792
#131145852
#131126622
C13×#28622
#770213