Finite Group Databasebeta

← #15773316

Subgroups — #15773316

Order 3328.

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

normal subgroups only

This group has 358 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#13120712C211yesmaximal, characteristic
2#13113160C211yesmaximal, characteristic
3#13112862C212yesmaximal
4#13112841C212yesmaximal
5C4×C13×#101C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88124C411yescharacteristic
8C2×C13×#101—21no—
9C4×C13×M16—21no—
10#11718890—21no—
11#11718647C411yescharacteristic
12#11718647C2211yescharacteristic
13#11718644C411yescharacteristic
14#11718644C2211yescharacteristic
15#11718643—21no—
16#11718598C411yescharacteristic
17#11718594—21no—
18#11718594—21no—
19#11718586—21no—
20C13×#343C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C22×Q8×C13D411yescharacteristic
24C2×C13×M16—22no—
25C4×Q8×C13—41no—
26C4×Q8×C13—41no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C4⋊C4C2311yescharacteristic
30C2×C42×C13C2×C411yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×#6101—21no—
36C2×#6101—21no—
37C2×#6101—21no—
38C2×#6101—21no—
39#88124—41no—
40#88124—41no—
41C13×#101—24no—
42C13×#97—41no—
43C4×C8×C13—41no—
44#88071—21no—
45#88071—21no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071C2×C411yescharacteristic
53#88071C2×C411yescharacteristic
54C22⋊#1055—22no—
55C4⋊#1055—41no—
56C4×#1055—41no—
57#11740—131nomaximal, Sylow
58C2×Q8×C13—22no—
59C2×Q8×C13—22no—
60C2×Q8×C13—41no—
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22×C411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13—21no—
71C22×Dic13—21no—
72C13×M16—24no—
73C13×M16—42no—
74C2×C8×C13—42no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C42×C13—21no—
79C42×C13—21no—
80C42×C13—21no—
81C42×C13—21no—
82C42×C13—21no—
83C42×C13—21no—
84C4⋊Dic13—41no—
85C4⋊Dic13—41no—
86#6101—42no—
87#6101—41no—
88#6101—41no—
89#6101—42no—
90#6101—42no—
91C2×#1055—42no—
92#2634—131no—
93C4×#101D1311yescharacteristic
94#1461—131no—
95#1353—132no—
96#1346—132no—
97C23×C13C2×C22⋊C411yescharacteristic
98Q8×C13—44no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13#9911yescharacteristic
114C2×C4×C13#9911yescharacteristic
115C2×C4×C13#10412yes—
116C2×C4×C13#13512yes—
117C2×Dic13—41no—
118C2×Dic13—41no—
119C2×Dic13—41no—
120C2×Dic13—41no—
121C2×Dic13—42no—
122C2×Dic13—41no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C8×C13—44no—
129#1055—82no—
130C2×#125—131no—
131C2×C4×Q8C2×D1311yescharacteristic
132#431—261no—
133C2×#101—21no—
134C4×M16—21no—
135#400—131no—
136#400—131no—
137#400—261no—
138#398—131no—
139#398—131no—
140#395—261no—
141#387—261no—
142#387—261no—
143#383—131no—
144#343C2×D1312yes—
145#324—132no—
146#324—261no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13C2×#9911yescharacteristic
150C22×C13#41611yescharacteristic
151C22×C13C2×#10411yescharacteristic
152C4×C13—21no—
153C4×C13—21no—
154C4×C13—22no—
155C4×C13—22no—
156C4×C13—41no—
157C4×C13—41no—
158C4×C13—41no—
159C4×C13—41no—
160Dic13—81no—
161Dic13—81no—
162Dic13—81no—
163Dic13—81no—
164C22×Q8C22⋊D1311yescharacteristic
165C2×M16—22no—
166#125—521no—
167#125—521no—
168C4×Q8—41no—
169C4×Q8—41no—
170C2×C4⋊C4—131no—
171C2×C4⋊C4—131no—
172C2×C4⋊C4—261no—
173C2×C4⋊C4—261no—
174C2×C4⋊C4—261no—
175C2×C4⋊C4—261no—
176C2×C4⋊C4C4×D1311yescharacteristic
177C2×C4⋊C4D5211yescharacteristic
178C2×C4⋊C4C22×D1311yescharacteristic
179C2×C42C4×D1311yescharacteristic
180C2×C42D5211yescharacteristic
181C2×C42C22⋊D1311yescharacteristic
182C4⋊C8—521no—
183#101—24no—
184C22⋊C8—262no—
185#97—41no—
186C4×C8—41no—
187C4×C8—521no—
188#95—131no—
189#95—131no—
190#95—261no—
191#95—261no—
192#95—261no—
193#95—261no—
194#95—261no—
195#95—261no—
196#95—261no—
197#95—261no—
198C2×C13—21no—
199C2×C13—21no—
200C2×C13#150111yescharacteristic
201C2×C13#212311yescharacteristic
202C2×C13#213311yescharacteristic
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8—41no—
206C22×C4—261no—
207C22×C4—261no—
208C22×C4—261no—
209C22×C4—261no—
210C22×C4#610311yescharacteristic
211C22×C4#610311yescharacteristic
212C22×C4#610311yescharacteristic
213C22×C4#610311yescharacteristic
214C22×C4C2×C4×D1311yescharacteristic
215C22×C4C2×D5211yescharacteristic
216C22×C4C2×C22⋊D1311yescharacteristic
217M16—24no—
218M16—42no—
219C2×C8—42no—
220C2×C8—522no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—521no—
225C4⋊C4—521no—
226C4⋊C4—522no—
227C4⋊C4—522no—
228C4⋊C4—522no—
229C4⋊C4—521no—
230C4⋊C4—521no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—21no—
237C13#1174011yescharacteristic, complemented, Sylow
238C23C2×#610311yescharacteristic
239Q8—44no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—521no—
255C2×C4—521no—
256C2×C4—521no—
257C2×C4—521no—
258C2×C4—522no—
259C2×C4—521no—
260C2×C4—521no—
261C2×C4—521no—
262C2×C4—521no—
263C2×C4—521no—
264C2×C4—521no—
265C2×C4#8804512yes—
266C2×C4#8804611yescharacteristic
267C2×C4#8804611yescharacteristic
268C2×C4#8820412yes—
269C8—44no—
270C8—1042no—
271C22—21no—
272C22—21no—
273C22C2×#8804511yescharacteristic
274C22C2×#8804611yescharacteristic
275C22#1171866311yescharacteristic
276C4—21no—
277C4—21no—
278C4—22no—
279C4—22no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—1041no—
285C4—1041no—
286C4—1041no—
287C4—1041no—
288C2—21no—
289C2—21no—
290C2#1311332511yescharacteristic
291C2#1311649111yescharacteristic
292C2#1311652311yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC4×C13×#101C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenterC4×#101D13
hypocenterC13#11740
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
237. C13#11740semidirect

Maximal subgroups

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

subgroupindex
#131207122
#131131602
#131128622
#131128412
C4×C13×#1012
#1174013