Finite Group Databasebeta

← #15763019

Subgroups — #15763019

Order 3328.

432 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123223C211yesmaximal, characteristic
2#13114689C211yesmaximal, characteristic
3#13112718C212yesmaximal
4#13112718C212yesmaximal
5C4×C13×#97C211yesmaximal, characteristic
6C2×C13×#97—21no—
7C2×C13×#97C2212yes—
8C2×C4×C8×C13—21no—
9C43×C13C2211yescharacteristic
10#11718597C2211yescharacteristic
11#11718597C2211yescharacteristic
12#11718594—21no—
13#11718594—21no—
14#11718594—21no—
15#11718594—21no—
16#11718589C411yescharacteristic
17#11718589C411yescharacteristic
18#11718589C411yescharacteristic
19#11718589C411yescharacteristic
20C2×C4⋊#1055—21no—
21C2×#88043C2212yes—
22#11718116—21no—
23C22×C8×C13—22no—
24C2×C42×C13C2×C411yescharacteristic
25C2×C42×C13C2×C411yescharacteristic
26C2×C42×C13D411yescharacteristic
27C2×C42×C13D411yescharacteristic
28C2×C42×C13D411yescharacteristic
29C2×C42×C13D411yescharacteristic
30C2×C42×C13C2311yescharacteristic
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×#6101—21no—
36C2×#6101—21no—
37C2×#6101—21no—
38C2×#6101—21no—
39C22×#1055—22no—
40C13×#97—24no—
41C13×#97—22no—
42C13×#97Q814yes—
43C4×C8×C13—24no—
44#88071—21no—
45#88071—21no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52C4⋊#1055—24no—
53#88043—24no—
54#9892—131nomaximal, Sylow
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22×C411yescharacteristic
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×Dic13—21no—
63C22×Dic13—21no—
64C22×Dic13—21no—
65C22×Dic13—21no—
66C2×C8×C13—24no—
67C2×C8×C13—24no—
68C2×C8×C13—24no—
69C42×C13—22no—
70C42×C13—22no—
71C42×C13—22no—
72C42×C13—41no—
73C42×C13—41no—
74C42×C13—41no—
75C42×C13C2×Q812yes—
76C42×C13#4112yes—
77C4⋊Dic13—41no—
78C4⋊Dic13—41no—
79C4⋊Dic13—41no—
80C4⋊Dic13—41no—
81#6101—42no—
82#6101—42no—
83#6101—42no—
84#6101—42no—
85C2×#1055—24no—
86C2×#1055—42no—
87C2×#1055—42no—
88#2864—131no—
89#1767—131no—
90C4×#97D1311yescharacteristic
91#1295—132no—
92#1295—132no—
93C23×C13C2×C22⋊C411yescharacteristic
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
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#10412yes—
110C2×C4×C13#10412yes—
111C2×C4×C13#10412yes—
112C2×C4×C13C4×Q812yes—
113C2×C4×C13C22⋊Q812yes—
114C2×C4×C13#12411yescharacteristic
115C2×C4×C13C4⋊Q811yescharacteristic
116C2×Dic13—41no—
117C2×Dic13—41no—
118C2×Dic13—41no—
119C2×Dic13—41no—
120C2×Dic13—41no—
121C2×Dic13—41no—
122C2×Dic13—41no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C8×C13—28no—
129#1055—44no—
130C2×C4⋊C8—261no—
131C2×#97—21no—
132C2×#97—132no—
133C2×#97C2×D1312yes—
134C2×C4×C8—21no—
135#389—131no—
136#389—131no—
137#389—131no—
138#389—131no—
139#387—261no—
140#387—261no—
141#387—261no—
142#387—261no—
143#382—131no—
144#382—131no—
145C43C2×D1311yescharacteristic
146#336—261no—
147C22×C13#39111yescharacteristic
148C22×C13#41311yescharacteristic
149C22×C13#41311yescharacteristic
150C22×C13C2×#10411yescharacteristic
151C22×C13C2×#10411yescharacteristic
152C22×C13C2×#10411yescharacteristic
153C22×C13#42111yescharacteristic
154C4×C13—21no—
155C4×C13—21no—
156C4×C13—22no—
157C4×C13—22no—
158C4×C13—22no—
159C4×C13—22no—
160C4×C13—22no—
161C4×C13—41no—
162Dic13—81no—
163Dic13—81no—
164Dic13—81no—
165Dic13—81no—
166C22×C8—22no—
167C22×C8—262no—
168C2×C4⋊C4—131no—
169C2×C4⋊C4—131no—
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×C42C4×D1311yescharacteristic
177C2×C42C4×D1311yescharacteristic
178C2×C42D5211yescharacteristic
179C2×C42D5211yescharacteristic
180C2×C42C22⋊D1311yescharacteristic
181C2×C42C22⋊D1311yescharacteristic
182C2×C42C22×D1311yescharacteristic
183C4⋊C8—264no—
184#97—24no—
185#97—22no—
186#97—264no—
187#97Dic2614yes—
188C4×C8—24no—
189#95—261no—
190#95—261no—
191#95—261no—
192#95—261no—
193#95—261no—
194#95—261no—
195#95—261no—
196#95—261no—
197C2×C13#152411yescharacteristic
198C2×C13#152411yescharacteristic
199C2×C13#152911yescharacteristic
200C2×C13#153211yescharacteristic
201C2×C13#198611yescharacteristic
202C2×C13#199411yescharacteristic
203C2×C13#199811yescharacteristic
204C22×C4—261no—
205C22×C4—261no—
206C22×C4—261no—
207C22×C4—261no—
208C22×C4#610311yescharacteristic
209C22×C4#610311yescharacteristic
210C22×C4#610311yescharacteristic
211C22×C4#610311yescharacteristic
212C22×C4C2×C4×D1311yescharacteristic
213C22×C4C2×D5211yescharacteristic
214C22×C4C2×C22⋊D1311yescharacteristic
215C2×C8—24no—
216C2×C8—24no—
217C2×C8—24no—
218C2×C8—264no—
219C2×C8—522no—
220C2×C8—522no—
221C4⋊C4—521no—
222C4⋊C4—521no—
223C4⋊C4—521no—
224C4⋊C4—521no—
225C4⋊C4—522no—
226C4⋊C4—522no—
227C4⋊C4—522no—
228C4⋊C4—522no—
229C42—22no—
230C42—22no—
231C42—22no—
232C42—41no—
233C42—41no—
234C42—41no—
235C42C2×Dic2612yes—
236C42#612712yes—
237C13#989211yescharacteristic, complemented, Sylow
238C23C2×#610311yescharacteristic
239C2×C4—21no—
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—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—521no—
255C2×C4—521no—
256C2×C4—521no—
257C2×C4—521no—
258C2×C4—521no—
259C2×C4—521no—
260C2×C4—521no—
261C2×C4—521no—
262C2×C4—521no—
263C2×C4—521no—
264C2×C4—521no—
265C2×C4—521no—
266C2×C4#8804512yes—
267C2×C4#8804512yes—
268C2×C4#8806512yes—
269C2×C4C4×Dic2612yes—
270C2×C4#8812311yescharacteristic
271C2×C4#8812911yescharacteristic
272C2×C4#8817812yes—
273C8—28no—
274C8—524no—
275C22C2×#8804511yescharacteristic
276C22C2×#8804511yescharacteristic
277C22#1171859011yescharacteristic
278C22#1171879311yescharacteristic
279C22#1171879311yescharacteristic
280C22C2×#8806511yescharacteristic
281C22#1171880011yescharacteristic
282C4—22no—
283C4—22no—
284C4—22no—
285C4—21no—
286C4—21no—
287C4—22no—
288C4—22no—
289C4—41no—
290C4—1041no—
291C4—1041no—
292C4—1041no—
293C4—1041no—
294C2#1311342211yescharacteristic
295C2#1311342511yescharacteristic
296C2#1311344111yescharacteristic
297C2#1311345411yescharacteristic
298C2#1311578011yescharacteristic
299C2#1311581311yescharacteristic
300C2#1311582911yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC4×C13×#97C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenterC4×#97D13
hypocenterC13#9892
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ C4×#97

Complements

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

NH ≅ G/Ntype
237. C13#9892semidirect

Maximal subgroups

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

subgroupindex
#131232232
#131146892
#131127182
C4×C13×#972
#989213