Finite Group Databasebeta

← #27206981

Subgroups — #27206981

Order 13184.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268481C211yesmaximal, characteristic, complemented
2#20268437C211yesmaximal, characteristic
3#20268146C211yesmaximal, characteristic, complemented
4#20268122C211yesmaximal, characteristic, complemented
5#20268116C211yesmaximal, characteristic, complemented
6#20268092C211yesmaximal, characteristic, complemented
7#20268032C211yesmaximal, characteristic, complemented
8#20268020C211yesmaximal, characteristic, complemented
9#20268014C211yesmaximal, characteristic, complemented
10#20267955C211yesmaximal, characteristic, complemented
11#20267944C211yesmaximal, characteristic, complemented
12C4×#13110094C211yesmaximal, characteristic, complemented
13#20267788C211yesmaximal, characteristic, complemented
14C2×#15692943C211yesmaximal, characteristic, complemented
15C8×D4×C103C211yesmaximal, characteristic, complemented
16C2×#13110105C2211yescharacteristic
17C22×D412C2211yescharacteristic
18C2×Dic412C2211yescharacteristic, complemented
19C2×#13110094C2211yescharacteristic
20C2×#13110094C2211yescharacteristic
21#15693014—21no—
22#15693013C2211yescharacteristic, complemented
23#15693011—21no—
24#15693009C2211yescharacteristic
25#15693006—21no—
26#15693002—21no—
27#15693000C2211yescharacteristic
28#15693000C2211yescharacteristic
29#15693000C2211yescharacteristic, complemented
30#15692995C2211yescharacteristic
31#15692994—21no—
32#15692989—21no—
33C4×Dic206C2211yescharacteristic, complemented
34C4×D412C2211yescharacteristic
35#15692980C2211yescharacteristic, complemented
36#15692977—21no—
37C2×C4⋊Dic103C2211yescharacteristic
38C22⋊C4×D103—21no—
39#15692955C2211yescharacteristic, complemented
40#15692953C2211yescharacteristic, complemented
41#15692953C2211yescharacteristic, complemented
42#15692946C2211yescharacteristic, complemented
43#15692946C2211yescharacteristic, complemented
44#15692946C2211yescharacteristic, complemented
45#15692946C2211yescharacteristic, complemented
46#15692943C2211yescharacteristic
47#15692943C2211yescharacteristic
48#15692943C2211yescharacteristic
49#15692943C2211yescharacteristic
50#15692943C2211yescharacteristic
51#15692943C2211yescharacteristic
52C22×C8×C103C2211yescharacteristic
53C22×C8×C103C2211yescharacteristic, complemented
54C4×D4×C103C2211yescharacteristic
55C4⋊C8×C103C2211yescharacteristic, complemented
56C22⋊C8×C103C2211yescharacteristic
57C22⋊C8×C103C2211yescharacteristic, complemented
58C4×C8×C103C2211yescharacteristic, complemented
59C23×D103—21no—
60#13110105—22no—
61#13110105—41no—
62C2×Dic206C2311yescharacteristic
63C2×Dic206C2311yescharacteristic
64C2×D412—22no—
65C2×D412—21no—
66C2×D412—41no—
67C2×D412C2311yescharacteristic
68C2×D412C2311yescharacteristic
69C2×C22⋊D103—21no—
70C2×C22⋊D103—21no—
71C22×Dic103—21no—
72C2×C4×D103—21no—
73C2×C4×D103—21no—
74Dic412—41no—
75#13110094—22no—
76#13110094—41no—
77C4⋊Dic103—21no—
78C4⋊Dic103C2311yescharacteristic
79C4⋊Dic103C2311yescharacteristic
80C4⋊Dic103C2311yescharacteristic
81C4⋊Dic103C2311yescharacteristic
82Dic103⋊C4—21no—
83Dic103⋊C4—21no—
84Dic103⋊C4—21no—
85Dic103⋊C4—21no—
86Dic103⋊C4—21no—
87Dic103⋊C4—21no—
88C22⋊Dic103—21no—
89C22⋊Dic103—21no—
90C22⋊Dic103—21no—
91C22⋊Dic103—21no—
92(C2×D103)⋊C4—21no—
93(C2×D103)⋊C4—21no—
94(C2×D103)⋊C4—21no—
95(C2×D103)⋊C4—21no—
96C4×Dic103—21no—
97C4×Dic103—21no—
98C2×D4×C103D411yescharacteristic
99C22×C4×C103C2311yescharacteristic
100C22×C4×C103C2311yescharacteristic
101C2×C8×C103—41no—
102C2×C8×C103—41no—
103C2×C8×C103C2311yescharacteristic
104C2×C8×C103C2311yescharacteristic
105C2×C8×C103C2311yescharacteristic
106C2×C8×C103C2311yescharacteristic
107C4⋊C4×C103D411yescharacteristic
108C22⋊C4×C103D411yescharacteristic
109C22⋊C4×C103D411yescharacteristic
110C42×C103C2311yescharacteristic
111C23×C103C2×D411yescharacteristic
112C23×C103C2×D411yescharacteristic
113C22×D103—21no—
114C22×D103—21no—
115C22×D103—42no—
116C22×D103—42no—
117C22×D103—81no—
118D4×C103—22no—
119C2×C4×C103—21no—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103C2×D411yescharacteristic
124C2×C4×C103C2×D411yescharacteristic
125C2×C4×C103C2×D411yescharacteristic
126C2×C4×C103C2×D411yescharacteristic
127C2×C4×C103C2411yescharacteristic
128C22⋊D103—42no—
129C22⋊D103—81no—
130C2×Dic103—21no—
131C2×Dic103—21no—
132C2×Dic103—21no—
133C2×Dic103—21no—
134C2×Dic103—21no—
135C2×Dic103—21no—
136C2×Dic103—42no—
137D412—21no—
138D412—21no—
139D412—21no—
140D412—42no—
141D412#4112yes—
142C4×D103—42no—
143C4×D103—81no—
144Dic206—21no—
145Dic206—21no—
146Dic206—21no—
147Dic206—21no—
148C8×C103—21no—
149C8×C103—21no—
150C8×C103—21no—
151C8×C103—21no—
152C22×C103—21no—
153C22×C103—21no—
154C22×C103—21no—
155C22×C103—21no—
156C22×C103—21no—
157C22×C103#13512yes—
158C22×C103C22×D411yescharacteristic
159C2×D103—22no—
160C2×D103—41no—
161C2×D103—41no—
162C2×D103—41no—
163C2×D103—41no—
164C2×D103—41no—
165C2×D103—84no—
166C4×C103—21no—
167C4×C103—21no—
168C4×C103—21no—
169C4×C103—21no—
170C4×C103C2×#4111yescharacteristic
171C4×C103H(5,𝔽2)11yescharacteristic
172Dic103—41no—
173Dic103—41no—
174Dic103—41no—
175Dic103—41no—
176Dic103—41no—
177Dic103—41no—
178C2×C103—22no—
179C2×C103—41no—
180C2×C103#54611yescharacteristic
181C2×C103C2×#13511yescharacteristic
182C2×C103#57711yescharacteristic
183D103—42no—
184D103—81no—
185#3296—1031nomaximal, Sylow
186C103#329611yescharacteristic, complemented, Sylow
187#552—1031no—
188#546—1031no—
189#488—1031no—
190#483—1031no—
191#482—1031no—
192#478—1031no—
193#467—1031no—
194#465—1031no—
195#464—1031no—
196#452—1031no—
197#450—1031no—
198C4×SD16—1031no—
199C8×D4D10311yescharacteristic, complemented
200#416—1031no—
201C2×#102—1031no—
202C2×#41—1031no—
203C22×D4—1031no—
204C2×Q16—1031no—
205C2×SD16—1031no—
206C2×SD16—1031no—
207C22×C8C2×D10311yescharacteristic
208C22×C8C2×D10311yescharacteristic, complemented
209#126—2061no—
210#125—1031no—
211#125—2061no—
212#124—1031no—
213#123—2061no—
214#123—2061no—
215C22⋊Q8—1031no—
216C22⋊Q8—1031no—
217C22⋊Q8—1031no—
218#121—1031no—
219#121—2061no—
220#120—2061no—
221C4×Q8—1031no—
222C4×D4—1031no—
223C4×D4C2×D10311yescharacteristic
224#117—1031no—
225#117—2061no—
226C2×C4⋊C4—1031no—
227C2×C22⋊C4—2061no—
228#107—1031no—
229#106—1031no—
230#106—1031no—
231C4⋊C8C2×D10311yescharacteristic, complemented
232#103—1031no—
233#103—1031no—
234#103—1031no—
235#103—1031no—
236#102—1031no—
237#102—1031no—
238#102—1031no—
239#102—1031no—
240#102—1031no—
241#102—1031no—
242C22⋊C8C2×D10311yescharacteristic
243C22⋊C8C2×D10311yescharacteristic, complemented
244C4×C8C2×D10311yescharacteristic, complemented
245C24—2061no—
246#41—4121no—
247#41—2062no—
248C2×Q8—1031no—
249C2×Q8—1031no—
250C2×D4—1031no—
251C2×D4—1031no—
252C2×D4—4121no—
253C2×D4—2062no—
254C2×D4—2061no—
255C2×D4—2061no—
256C2×D4—2061no—
257C2×D4D41211yescharacteristic
258C22×C4—2061no—
259C22×C4—2061no—
260C22×C4—2061no—
261C22×C4C22×D10311yescharacteristic
262C22×C4C22×D10311yescharacteristic
263Q16—4121no—
264SD16—4121no—
265SD16—2062no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8C22×D10311yescharacteristic
269C2×C8C22×D10311yescharacteristic
270C2×C8C22×D10311yescharacteristic
271C2×C8C22×D10311yescharacteristic
272C4⋊C4—1031no—
273C4⋊C4—1031no—
274C4⋊C4—1031no—
275C4⋊C4—1031no—
276C4⋊C4—2061no—
277C4⋊C4—2061no—
278C4⋊C4—2061no—
279C4⋊C4—2061no—
280C4⋊C4—2061no—
281C4⋊C4—2061no—
282C4⋊C4—2061no—
283C4⋊C4D41211yescharacteristic
284C22⋊C4—2061no—
285C22⋊C4—2061no—
286C22⋊C4—2061no—
287C22⋊C4—2061no—
288C22⋊C4—2061no—
289C22⋊C4—2061no—
290C22⋊C4—2061no—
291C22⋊C4—2061no—
292C22⋊C4D41211yescharacteristic
293C22⋊C4D41211yescharacteristic
294C42—2061no—
295C42—2061no—
296C42C22×D10311yescharacteristic
297C23—8241no—
298C23—4122no—
299C23—4122no—
300C23—2061no—
301C23—2061no—
302C23C2×D41211yescharacteristic
303C23C2×D41211yescharacteristic
304Q8—2061no—
305Q8—2061no—
306Q8—2061no—
307Q8—2061no—
308D4—22no—
309D4—8241no—
310D4—1032no—
311D4—4122no—
312D4—4122no—
313D4—2061no—
314D4—2061no—
315D4—2061no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—8241no—
321C2×C4—4122no—
322C2×C4—4122no—
323C2×C4—2061no—
324C2×C4—2061no—
325C2×C4—2061no—
326C2×C4—2061no—
327C2×C4—2061no—
328C2×C4—2061no—
329C2×C4C2×D41211yescharacteristic
330C2×C4C2×D41211yescharacteristic
331C2×C4C2×D41211yescharacteristic
332C2×C4C2×D41211yescharacteristic
333C2×C4C23×D10311yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—8244no—
344C22—4121no—
345C22—4121no—
346C22—4121no—
347C22—4121no—
348C22—4121no—
349C22—2062no—
350C22#1569304312yes—
351C22C22×D41211yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—4121no—
357C4—4121no—
358C4—4121no—
359C4—4121no—
360C4—4121no—
361C4—4121no—
362C4#41×D10311yescharacteristic
363C4#1569306611yescharacteristic
364C2—22no—
365C2—41no—
366C2—8241no—
367C2—4122no—
368C2#2026843611yescharacteristic
369C2C2×#1569304311yescharacteristic
370C2#2026860311yescharacteristic
subgroupG/H
centerC22C22×D412
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC8×D4×C103C2
socleC22×C103C22×D4
prime radical#20268437C2
hypercenterC8×D4D103
hypocenterC103#3296
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #20268481C2semidirect
3. #20268146C2semidirect
4. #20268122C2semidirect
5. #20268116C2semidirect
6. #20268092C2semidirect
7. #20268032C2semidirect
8. #20268020C2semidirect
9. #20268014C2semidirect
10. #20267955C2semidirect
11. #20267944C2semidirect
12. C4×#13110094C2semidirect
13. #20267788C2semidirect
14. C2×#15692943C2semidirect
15. C8×D4×C103C2semidirect
18. C2×Dic412C22semidirect
22. #15693013C22semidirect
29. #15693000C22semidirect
33. C4×Dic206C22semidirect
35. #15692980C22semidirect
39. #15692955C22semidirect
40. #15692953C22semidirect
41. #15692953C22semidirect
42. #15692946C22semidirect
43. #15692946C22semidirect
44. #15692946C22semidirect
45. #15692946C22semidirect
53. C22×C8×C103C22semidirect
55. C4⋊C8×C103C22semidirect
57. C22⋊C8×C103C22semidirect
58. C4×C8×C103C22semidirect
186. C103#3296semidirect
199. C8×D4D103semidirect
208. C22×C8C2×D103semidirect
231. C4⋊C8C2×D103semidirect
243. C22⋊C8C2×D103semidirect
244. C4×C8C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202684812
#202684372
#202681462
#202681222
#202681162
#202680922
#202680322
#202680202
#202680142
#202679552
#202679442
C4×#131100942
#202677882
C2×#156929432
C8×D4×C1032
#3296103