Finite Group Databasebeta

← #15761323

Subgroups — #15761323

Order 3328.

386 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115797C211yesmaximal, characteristic
2#13115759C211yesmaximal, characteristic
3#13115594C211yesmaximal, characteristic
4C2×#11718078C211yesmaximal, characteristic
5#13112720C211yesmaximal, characteristic
6#13112671C211yesmaximal, characteristic
7C13×#1770C211yesmaximal, characteristic
8C2×#88123C2211yescharacteristic
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C13×#97—21no—
11C2×C4×C8×C13C2211yescharacteristic
12C4×C13×C4⋊C4C2211yescharacteristic
13C2×#88050—21no—
14C2×#88050—21no—
15C2×#88047—21no—
16#11718596C2211yescharacteristic
17C2×C4⋊#1055C2211yescharacteristic
18C2×C4⋊#1055C2211yescharacteristic
19C13×#336—21no—
20#11718143—21no—
21#11718143—21no—
22#11718121—21no—
23#11718078C414yescomplemented
24C22×Dic26—21no—
25C22×C8×C13—21no—
26C22×C8×C13D411yescharacteristic
27C22×C8×C13D411yescharacteristic
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C42×C13—21no—
31C2×C42×C13C2311yescharacteristic
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C22×#1055—21no—
38C22×#1055—21no—
39#88123—21no—
40#88123—21no—
41#88123—21no—
42#88123C2×C412yes—
43C13×C4⋊C8—21no—
44C13×C4⋊C8C2×C412yes—
45C13×#97—42no—
46C4×C8×C13—21no—
47C4×C8×C13—21no—
48C13×#95—21no—
49#88050—42no—
50#88050—42no—
51#88047—42no—
52C4⋊#1055—21no—
53C4⋊#1055—21no—
54C4⋊#1055—21no—
55C4⋊#1055C2×C412yes—
56#9574—131nomaximal, Sylow
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13C2×D411yescharacteristic
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13#4111yescharacteristic
62C22×Dic13—41no—
63C22×Dic13—41no—
64C2×Dic26—22no—
65C2×Dic26—41no—
66C2×Dic26—41no—
67C2×Dic26—41no—
68C2×Dic26—41no—
69C2×Dic26—41no—
70C2×C8×C13—21no—
71C2×C8×C13—21no—
72C2×C8×C13—22no—
73C2×C8×C13—21no—
74C2×C8×C13—21no—
75C2×C8×C13—21no—
76C2×C8×C13—41no—
77C2×C8×C13—41no—
78C2×C8×C13Q1612yes—
79C13×C4⋊C4—21no—
80C13×C4⋊C4—21no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4—21no—
83C42×C13—41no—
84C42×C13—41no—
85C42×C13C22×C411yescharacteristic
86C42×C13#4111yescharacteristic
87C42×C13#4111yescharacteristic
88C42×C13#4111yescharacteristic
89C4⋊Dic13—22no—
90C4⋊Dic13—22no—
91C4⋊Dic13—41no—
92C4⋊Dic13—41no—
93C4⋊Dic13—41no—
94C4⋊Dic13—41no—
95C4⋊Dic13—41no—
96C4⋊Dic13—41no—
97C4⋊Dic13—81no—
98C2×#1055—22no—
99C2×#1055—41no—
100C2×#1055—41no—
101C2×#1055—41no—
102C2×#1055—41no—
103C2×#1055—41no—
104#1990—131no—
105#1981—131no—
106#1947—131no—
107#1770D1311yescharacteristic
108C2×#332—131no—
109#1296—131no—
110#1277—131no—
111C23×C13#12111yescharacteristic
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13#11711yescharacteristic
121C2×C4×C13C4×D411yescharacteristic
122C2×C4×C13C4×D411yescharacteristic
123C2×C4×C13#12311yescharacteristic
124C2×C4×C13#12411yescharacteristic
125C2×C4×C13#12611yescharacteristic
126C2×C4×C13C2×Q1611yescharacteristic
127C2×C4×C13#13511yescharacteristic
128C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C13#13711yescharacteristic
133C2×C4×C13#13711yescharacteristic
134C2×Dic13—42no—
135C2×Dic13—81no—
136C2×Dic13—81no—
137C2×Dic13—81no—
138C2×Dic13—81no—
139C2×Dic13—81no—
140Dic26—42no—
141Dic26—42no—
142Dic26—81no—
143Dic26—81no—
144C8×C13—22no—
145C8×C13—42no—
146C8×C13—41no—
147#1055—42no—
148#1055—81no—
149C2×C4⋊Q8—131no—
150C2×#107—261no—
151C2×C4⋊C8—131no—
152C2×C4⋊C8—131no—
153C2×C4⋊C8C2×D1311yescharacteristic
154C2×#103—261no—
155C2×#103—261no—
156C2×#97—21no—
157C2×C4×C8C2×D1311yescharacteristic
158#384—131no—
159C4×C4⋊C4C2×D1311yescharacteristic
160#340—261no—
161#340—261no—
162#340—261no—
163#336—21no—
164#332—134no—
165C22×C13#38811yescharacteristic
166C22×C13#46211yescharacteristic
167C22×C13#46311yescharacteristic
168C22×C13#46811yescharacteristic
169C22×C13#46911yescharacteristic
170C22×C13#47111yescharacteristic
171C22×C13#47311yescharacteristic
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—81no—
175C4×C13—81no—
176C4×C13C4×Q1611yescharacteristic
177C4×C13#44011yescharacteristic
178C4×C13#44011yescharacteristic
179C4×C13#44211yescharacteristic
180C4×C13#48411yescharacteristic
181C4×C13#48511yescharacteristic
182C4×C13#48911yescharacteristic
183C4×C13#49011yescharacteristic
184Dic13—82no—
185Dic13—161no—
186C22×Q8—261no—
187C22×C8—21no—
188C22×C8—261no—
189C22×C8—261no—
190C22×C8C22⋊D1311yescharacteristic
191C22×C8C22⋊D1311yescharacteristic
192C4⋊Q8—132no—
193C4⋊Q8—261no—
194C4⋊Q8—261no—
195C4⋊Q8—261no—
196C2×C4⋊C4—261no—
197C2×C4⋊C4—261no—
198C2×C4⋊C4—261no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4D5211yescharacteristic
202C2×C4⋊C4D5211yescharacteristic
203C2×C42—21no—
204C2×C42C22×D1311yescharacteristic
205#107—522no—
206C4⋊C8—21no—
207C4⋊C8—132no—
208C4⋊C8—261no—
209C4⋊C8—261no—
210C4⋊C8—261no—
211C4⋊C8C4×D1312yes—
212#103—522no—
213#103—522no—
214#97—42no—
215C4×C8—21no—
216C4×C8—21no—
217#95—21no—
218C2×C13#169211yescharacteristic
219C2×C13#169411yescharacteristic
220C2×C13#169911yescharacteristic
221C2×C13#170111yescharacteristic
222C2×C13#192811yescharacteristic
223C2×C13#193011yescharacteristic
224C2×C13#193611yescharacteristic
225C2×Q8—262no—
226C2×Q8—521no—
227C2×Q8—521no—
228C2×Q8—521no—
229C2×Q8—521no—
230C2×Q8—521no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—521no—
234C22×C4—521no—
235C22×C4C2×D5211yescharacteristic
236C22×C4#612711yescharacteristic
237C22×C4C2×C22⋊D1311yescharacteristic
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—22no—
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—21no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—262no—
247C2×C8—521no—
248C2×C8—521no—
249C2×C8—521no—
250C2×C8—521no—
251C2×C8—521no—
252C2×C8#610712yes—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—262no—
258C4⋊C4—262no—
259C4⋊C4—521no—
260C4⋊C4—521no—
261C4⋊C4—521no—
262C4⋊C4—521no—
263C4⋊C4—521no—
264C4⋊C4—521no—
265C4⋊C4—1041no—
266C42—41no—
267C42—41no—
268C42C2×C4×D1311yescharacteristic
269C42#612711yescharacteristic
270C42#612711yescharacteristic
271C42#612711yescharacteristic
272C13#957411yescharacteristic, complemented, Sylow
273C23#8818411yescharacteristic
274Q8—522no—
275Q8—522no—
276Q8—1041no—
277Q8—1041no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—522no—
287C2×C4—1041no—
288C2×C4—1041no—
289C2×C4—1041no—
290C2×C4—1041no—
291C2×C4—1041no—
292C2×C4#8812611yescharacteristic
293C2×C4C4×D5211yescharacteristic
294C2×C4#8812911yescharacteristic
295C2×C4#8813011yescharacteristic
296C2×C4#8816211yescharacteristic
297C2×C4#8816211yescharacteristic
298C2×C4#8816211yescharacteristic
299C2×C4#8816311yescharacteristic
300C2×C4C4×C22⋊D1311yescharacteristic
301C2×C4#8818311yescharacteristic
302C2×C4#8818611yescharacteristic
303C2×C4C2×#610711yescharacteristic
304C2×C4#8820411yescharacteristic
305C2×C4#8820511yescharacteristic
306C8—22no—
307C8—41no—
308C8—42no—
309C8—522no—
310C8—1041no—
311C22#1171860111yescharacteristic
312C22#1171867711yescharacteristic
313C22#1171869211yescharacteristic
314C22#1171879511yescharacteristic
315C22#1171879611yescharacteristic
316C22#1171880211yescharacteristic
317C22#1171880411yescharacteristic
318C4—21no—
319C4—21no—
320C4—81no—
321C4—81no—
322C4—1042no—
323C4—2081no—
324C4#1171837111yescharacteristic
325C4#1171837211yescharacteristic
326C4#1171837411yescharacteristic
327C4#1171837511yescharacteristic
328C4#1171863111yescharacteristic
329C4#1171865711yescharacteristic
330C4#1171867911yescharacteristic
331C4C4×#610711yescharacteristic
332C2#1311434211yescharacteristic
333C2#1311435411yescharacteristic
334C2#1311438311yescharacteristic
335C2#1311439711yescharacteristic
336C2#1311547711yescharacteristic
337C2#1311549111yescharacteristic
338C2#1311553311yescharacteristic
subgroupG/H
centerC23#88184
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1770C2
socle, prime radicalC23×C13#121
cosocleC2×C42×C13C23
hypercenter#1770D13
hypocenterC13#9574
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1770

Complements

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

NH ≅ G/Ntype
23. #11718078C4semidirect
272. C13#9574semidirect

Maximal subgroups

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

subgroupindex
#131157972
#131157592
#131155942
C2×#117180782
#131127202
#131126712
C13×#17702
#957413