Finite Group Databasebeta

← #15868237

Subgroups — #15868237

Order 3328.

1214 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128132C211yesmaximal, characteristic
2#13123469C211yesmaximal, characteristic, complemented
3#13115817C212yesmaximal, complemented
4#13115668C212yesmaximal, complemented
5#13115279C214yesmaximal, complemented
6#13114647C214yesmaximal, complemented
7C2×C13×#376C211yesmaximal, characteristic, complemented
8C22×C42×C13C2212yes—
9C22×C42×C13C2211yescharacteristic
10#11719496—22no—
11#11719496C2212yes—
12#11719184—22no—
13#11719184—22no—
14#11719184C414yescomplemented
15#11719182C412yescomplemented
16#11719182C2211yescharacteristic
17C4×#6127—22no—
18C4×#6127C2212yes—
19#11719175C412yescomplemented
20#11719175C2211yescharacteristic
21C13×#376—22no—
22C13×#376C2212yes—
23C13×#376C2212yes—
24C2×C13×#95—22no—
25#11718868C2212yes—
26C2×#88045C2218yes—
27#11718587—22no—
28#11718586—22no—
29#11718585C2212yes—
30C4×#6099C2212yes—
31#11718115C2218yes—
32C23×C4×C13—22no—
33C23×C4×C13D412yes—
34C23×C4×C13C2311yescharacteristic
35C2×#6127—22no—
36C2×#6127C2312yes—
37C2×C42×C13—22no—
38C2×C42×C13—28no—
39C2×C42×C13C2×C412yes—
40C2×C42×C13C2×C412yes—
41C2×C42×C13D412yes—
42C2×C42×C13D412yes—
43C2×C42×C13D412yes—
44C2×C42×C13C2314yes—
45C2×C42×C13C2311yescharacteristic
46C2×C42×C13C2311yescharacteristic
47#88207—22no—
48#88184—22no—
49#88184—22no—
50#88184C2×C414yes—
51#88183—24no—
52#88183—22no—
53C4×C22⋊D13—24no—
54C4×C22⋊D13—24no—
55C4×C22⋊D13—24no—
56#88180—22no—
57#88180C2312yes—
58#88178—22no—
59#88178—22no—
60#88178C2×C414yes—
61C2×#6099C2314yes—
62#88130—24no—
63#88129—22no—
64#88129C2×C412yescomplemented
65#88128C2×C411yescharacteristic, complemented
66C4×D52—22no—
67C4×D52—22no—
68C4×D52C2×C414yescomplemented
69#88126—24no—
70#88126—22no—
71C42×D13—22no—
72#88124—22no—
73#88124C2×C412yescomplemented
74#88123C2×C411yescharacteristic, complemented
75#88123C2×C412yescomplemented
76C4×Dic26—22no—
77C4×Dic26—22no—
78C4×Dic26C2×C414yescomplemented
79C13×#95—24no—
80C13×#95—24no—
81C22⋊#1055—24no—
82#88045—216no—
83C4⋊#1055—24no—
84#88043—22no—
85C4×#1055—22no—
86#21417—131nomaximal, Sylow
87C24×C13C2×D411yescharacteristic
88C22×C4×C13—24no—
89C22×C4×C13—28no—
90C22×C4×C13—24no—
91C22×C4×C13—44no—
92C22×C4×C13—48no—
93C22×C4×C13C22⋊C412yes—
94C22×C4×C13C22⋊C412yes—
95C22×C4×C13C22⋊C412yes—
96C22×C4×C13C22⋊C412yes—
97C22×C4×C13C22×C412yes—
98C22×C4×C13C2×D412yes—
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D412yes—
101C22×C4×C13C2×D412yes—
102C22×C4×C13C2411yescharacteristic
103C2×C22⋊D13—24no—
104C2×C22⋊D13—22no—
105#6127—28no—
106#6127—48no—
107C2×D52—22no—
108C2×D52C22×C412yes—
109C2×C4×D13—24no—
110C2×C4×D13—22no—
111C2×Dic26—22no—
112C2×Dic26C22×C412yes—
113C42×C13—28no—
114C42×C13—24no—
115C42×C13C22⋊C412yes—
116C42×C13C22⋊C412yes—
117C42×C13C22⋊C412yes—
118C42×C13C22⋊C412yes—
119C42×C13C22×C412yes—
120C42×C13C22×C411yescharacteristic
121C42×C13C22×C411yescharacteristic
122C42×C13C2×D412yes—
123C42×C13C2×D411yescharacteristic
124C42×C13C2×D411yescharacteristic
125C42×C13#4118yescomplemented
126C22⋊Dic13—24no—
127C22⋊Dic13—22no—
128#6103—24no—
129#6103—24no—
130#6103—24no—
131C4⋊Dic13—22no—
132C4⋊Dic13—22no—
133C4⋊Dic13C22×C414yes—
134#6101—24no—
135#6101—24no—
136#6101—24no—
137C4×Dic13—24no—
138C4×Dic13—22no—
139#6099—28no—
140C2×#1055—24no—
141#3444—131no—
142#2920—131no—
143C2×#376D1311yescharacteristic, complemented
144#1995—132no—
145#1963—132no—
146#1896—134no—
147#1759—134no—
148C23×C13—22no—
149C23×C13—24no—
150C23×C13C2×C22⋊C412yes—
151C23×C13C22×D411yescharacteristic
152C22×D13—22no—
153C2×C4×C13—22no—
154C2×C4×C13—24no—
155C2×C4×C13—24no—
156C2×C4×C13—24no—
157C2×C4×C13—24no—
158C2×C4×C13—28no—
159C2×C4×C13—42no—
160C2×C4×C13—42no—
161C2×C4×C13—42no—
162C2×C4×C13—42no—
163C2×C4×C13—416no—
164C2×C4×C13—48no—
165C2×C4×C13C2×C22⋊C412yes—
166C2×C4×C13C2×C22⋊C412yes—
167C2×C4×C13C2×C22⋊C412yes—
168C2×C4×C13C2×C22⋊C412yes—
169C2×C4×C13C2×C22⋊C412yes—
170C2×C4×C13C23×C411yescharacteristic
171C2×C4×C13C22×D411yescharacteristic
172C2×C4×C13C2×#4114yes—
173C22⋊D13—44no—
174C22⋊D13—48no—
175C2×Dic13—22no—
176C2×Dic13—24no—
177D52—24no—
178D52—44no—
179C4×D13—48no—
180C4×D13—44no—
181Dic26—24no—
182Dic26—44no—
183#1055—44no—
184#533—132no—
185#533—131no—
186#532—132no—
187#532—131no—
188#529—134no—
189#529—262no—
190#529—262no—
191#525—132no—
192#525—262no—
193C4×#41—132no—
194C4×#41—262no—
195C22×C42C2×D1312yes—
196C22×C42C2×D1311yescharacteristic
197#432—262no—
198#431—262no—
199#423—132no—
200C2×#104—138no—
201#407—132no—
202C4×M16—132no—
203#376—22no—
204#376C2×D1312yes—
205#376C2×D1312yes—
206C2×#95—22no—
207#339—138no—
208C22×C13—28no—
209C22×C13—22no—
210C22×C13—22no—
211C22×C13—22no—
212C22×C13#42114yes—
213C22×C13C22×C22⋊C411yescharacteristic
214C22×C13#52512yes—
215C2×D13—44no—
216C2×D13—42no—
217C4×C13—22no—
218C4×C13—22no—
219C4×C13—22no—
220C4×C13—22no—
221C4×C13—22no—
222C4×C13—48no—
223C4×C13C4×#4112yes—
224C4×C13#53212yes—
225Dic13—44no—
226Dic13—42no—
227C2×#41—132no—
228C2×#41—262no—
229C23×C4—22no—
230C23×C4C22⋊D1312yes—
231C23×C4C22×D1311yescharacteristic
232C2×M16—134no—
233C4⋊Q8—132no—
234C4⋊Q8—131no—
235#127—131no—
236#126—264no—
237#125—132no—
238#125—262no—
239#124—132no—
240#124—262no—
241#123—264no—
242#123—262no—
243C22⋊Q8—134no—
244C22⋊Q8—262no—
245C22⋊Q8—262no—
246#121—134no—
247#121—262no—
248#121—262no—
249#120—262no—
250C4×Q8—134no—
251C4×Q8—262no—
252C4×Q8—262no—
253C4×D4—134no—
254C4×D4—264no—
255C4×D4—264no—
256C4×D4—264no—
257C4×D4—262no—
258C4×D4—262no—
259#117—132no—
260#117—262no—
261#117—264no—
262#117—262no—
263C2×C42—22no—
264C2×C42—28no—
265C2×C42—262no—
266C2×C42C4×D1312yes—
267C2×C42C4×D1312yes—
268C2×C42D5212yes—
269C2×C42D5212yes—
270C2×C42C22⋊D1312yes—
271C2×C42C22×D1314yes—
272C2×C42C22×D1311yescharacteristic
273C2×C42C22×D1311yescharacteristic
274C4⋊C8—264no—
275#104—2616no—
276C22⋊C8—264no—
277#97—262no—
278C4×C8—262no—
279#95—24no—
280#95—24no—
281C2×C13—22no—
282C2×C13—24no—
283C2×C13#229711yescharacteristic
284C2×C13C2×#42112yes—
285D13—82no—
286C24C2×C22⋊D1311yescharacteristic
287#41—268no—
288#41—528no—
289C2×Q8—132no—
290C2×Q8—262no—
291C2×D4—132no—
292C2×D4—264no—
293C2×D4—262no—
294C2×D4—262no—
295C22×C4—24no—
296C22×C4—28no—
297C22×C4—24no—
298C22×C4—44no—
299C22×C4—48no—
300C22×C4—264no—
301C22×C4—262no—
302C22×C4#610312yes—
303C22×C4#610312yes—
304C22×C4#610312yes—
305C22×C4#610312yes—
306C22×C4C2×C4×D1312yes—
307C22×C4C2×D5212yes—
308C22×C4C2×C22⋊D1311yescharacteristic
309C22×C4C2×C22⋊D1312yes—
310C22×C4C2×C22⋊D1312yes—
311C22×C4C23×D1311yescharacteristic
312M16—268no—
313C2×C8—264no—
314C4⋊C4—134no—
315C4⋊C4—264no—
316C4⋊C4—262no—
317C4⋊C4—262no—
318C4⋊C4—264no—
319C4⋊C4—264no—
320C22⋊C4—264no—
321C22⋊C4—262no—
322C22⋊C4—264no—
323C22⋊C4—264no—
324C22⋊C4—264no—
325C42—28no—
326C42—24no—
327C42—264no—
328C42—262no—
329C42#610312yes—
330C42#610312yes—
331C42#610312yes—
332C42#610312yes—
333C42C2×C4×D1312yes—
334C42C2×C4×D1311yescharacteristic
335C42C2×C4×D1311yescharacteristic
336C42C2×D5211yescharacteristic
337C42C2×D5211yescharacteristic
338C42C2×D5212yes—
339C42#612718yescomplemented
340C13#2141711yescharacteristic, complemented, Sylow
341C23—24no—
342C23—22no—
343C23—262no—
344C23C2×#610312yes—
345C23C22×C22⋊D1311yescharacteristic
346Q8—264no—
347Q8—524no—
348D4—264no—
349D4—524no—
350D4—528no—
351D4—524no—
352C2×C4—24no—
353C2×C4—24no—
354C2×C4—22no—
355C2×C4—24no—
356C2×C4—24no—
357C2×C4—28no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—416no—
363C2×C4—48no—
364C2×C4—264no—
365C2×C4—262no—
366C2×C4—528no—
367C2×C4—524no—
368C2×C4C2×#610312yes—
369C2×C4C2×#610312yes—
370C2×C4C2×#610312yes—
371C2×C4C2×#610312yes—
372C2×C4C2×#610312yes—
373C2×C4C22×C4×D1311yescharacteristic
374C2×C4C22×D5211yescharacteristic
375C2×C4C2×#612714yes—
376C8—524no—
377C22—28no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—524no—
382C22—522no—
383C22#1171866614yes—
384C22C22×#610311yescharacteristic
385C22#1171949612yes—
386C4—22no—
387C4—22no—
388C4—22no—
389C4—22no—
390C4—22no—
391C4—48no—
392C4—524no—
393C4—522no—
394C4C4×#612712yes—
395C4#1171918212yes—
396C2—22no—
397C2—24no—
398C2—1042no—
399C2#1311732611yescharacteristic
400C2C2×#1171866612yes—
subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#376C2
socleC22×C13C22×C22⋊C4
prime radical#13128132C2
cosocleC22×C4×C13C24
hypercenterC2×#376D13
hypocenterC13#21417
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×#376

Complements

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

NH ≅ G/Ntype
2. #13123469C2semidirect
3. #13115817C2semidirect
4. #13115668C2semidirect
5. #13115279C2semidirect
6. #13114647C2semidirect
7. C2×C13×#376C2semidirect
14. #11719184C4semidirect
15. #11719182C4semidirect
19. #11719175C4semidirect
64. #88129C2×C4semidirect
65. #88128C2×C4semidirect
68. C4×D52C2×C4semidirect
73. #88124C2×C4semidirect
74. #88123C2×C4semidirect
75. #88123C2×C4semidirect
78. C4×Dic26C2×C4semidirect
125. C42×C13#41semidirect
143. C2×#376D13semidirect
339. C42#6127semidirect
340. C13#21417semidirect

Maximal subgroups

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

subgroupindex
#131281322
#131234692
#131158172
#131156682
#131152792
#131146472
C2×C13×#3762
#2141713