Finite Group Databasebeta

← #27206975

Subgroups — #27206975

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#20268476C211yesmaximal, characteristic, complemented
2#20268435C211yesmaximal, characteristic
3#20268144C211yesmaximal, characteristic, complemented
4#20268121C211yesmaximal, characteristic, complemented
5#20268113C211yesmaximal, characteristic, complemented
6#20268089C211yesmaximal, characteristic, complemented
7#20268032C211yesmaximal, characteristic, complemented
8#20268019C211yesmaximal, characteristic, complemented
9#20268012C211yesmaximal, characteristic, complemented
10#20267954C211yesmaximal, characteristic, complemented
11#20267942C211yesmaximal, characteristic, complemented
12#20267882C211yesmaximal, characteristic, complemented
13C8×C22⋊D103C211yesmaximal, characteristic, complemented
14#20267784C211yesmaximal, characteristic, complemented
15C2×#102×C103C211yesmaximal, characteristic, complemented
16C2×#13110104C2211yescharacteristic
17C2×Dic412C2211yescharacteristic, complemented
18C2×#13110093C2211yescharacteristic
19C2×#13110093C2211yescharacteristic
20C2×C8×D103C2211yescharacteristic, complemented
21#15693016—21no—
22#15693012C2211yescharacteristic, complemented
23#15693011—21no—
24#15693008C2211yescharacteristic
25#15693004—21no—
26#15693002—21no—
27#15693001C2211yescharacteristic, complemented
28#15693000C2211yescharacteristic
29#15693000C2211yescharacteristic
30#15692993—21no—
31#15692992C2211yescharacteristic
32#15692990—21no—
33#15692986C2211yescharacteristic, complemented
34D4×Dic103C2211yescharacteristic
35C4×C22⋊D103C2211yescharacteristic
36#15692980—21no—
37#15692979C2211yescharacteristic, complemented
38C2×C22⋊Dic103—21no—
39#15692955C2211yescharacteristic, complemented
40#15692952C2211yescharacteristic, complemented
41#15692952C2211yescharacteristic, complemented
42Dic103⋊C8C2211yescharacteristic, complemented
43#15692946C2211yescharacteristic, complemented
44#15692946C2211yescharacteristic, complemented
45#15692944C2211yescharacteristic, complemented
46#15692944C2211yescharacteristic, complemented
47#15692942C2211yescharacteristic
48#15692942C2211yescharacteristic
49C22⋊(C103⋊C8)C2211yescharacteristic
50(C2×D103)⋊C8C2211yescharacteristic, complemented
51C8×Dic103C2211yescharacteristic, complemented
52C22×D4×C103C2211yescharacteristic
53C22×C8×C103C2211yescharacteristic
54C2×C4⋊C4×C103C2211yescharacteristic
55#102×C103C2211yescharacteristic
56#102×C103C2211yescharacteristic
57#102×C103C2211yescharacteristic
58#102×C103C2211yescharacteristic
59#13110104—22no—
60#13110104—41no—
61C2×Dic206C2311yescharacteristic
62C2×Dic206C2311yescharacteristic
63C2×C22⋊D103—21no—
64C2×C22⋊D103—21no—
65C2×C22⋊D103D411yescharacteristic
66C22×Dic103—21no—
67C22×Dic103—21no—
68C2×C4×D103C2311yescharacteristic
69Dic412—41no—
70#13110093—22no—
71#13110093—41no—
72C2×C103⋊C8C2311yescharacteristic
73C2×C103⋊C8C2311yescharacteristic
74C8×D103—41no—
75C4⋊Dic103—21no—
76C4⋊Dic103—21no—
77C4⋊Dic103C2311yescharacteristic
78C4⋊Dic103C2311yescharacteristic
79Dic103⋊C4—21no—
80Dic103⋊C4—21no—
81Dic103⋊C4—21no—
82Dic103⋊C4—21no—
83Dic103⋊C4D411yescharacteristic
84C22⋊Dic103—21no—
85C22⋊Dic103—21no—
86C22⋊Dic103—21no—
87C22⋊Dic103—21no—
88C22⋊Dic103—21no—
89C22⋊Dic103—21no—
90C22⋊Dic103D411yescharacteristic
91(C2×D103)⋊C4—21no—
92(C2×D103)⋊C4—21no—
93(C2×D103)⋊C4D411yescharacteristic
94C4×Dic103—21no—
95C4×Dic103—21no—
96C4×Dic103C2311yescharacteristic
97C24×C103—21no—
98C2×D4×C103—22no—
99C2×D4×C103—21no—
100C2×D4×C103—41no—
101C2×D4×C103C2311yescharacteristic
102C2×D4×C103C2311yescharacteristic
103C22×C4×C103—21no—
104C22×C4×C103C2311yescharacteristic
105C2×C8×C103—41no—
106C2×C8×C103C2311yescharacteristic
107C2×C8×C103C2311yescharacteristic
108C4⋊C4×C103—21no—
109C4⋊C4×C103C2311yescharacteristic
110C4⋊C4×C103C2311yescharacteristic
111C23×C103—21no—
112C23×C103—21no—
113C23×C103—42no—
114C23×C103—42no—
115C23×C103—81no—
116C23×C103C2×D411yescharacteristic
117C22×D103C2×D411yescharacteristic
118D4×C103—21no—
119D4×C103—21no—
120D4×C103—21no—
121D4×C103—42no—
122D4×C103#4112yes—
123C2×C4×C103—21no—
124C2×C4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103—42no—
128C2×C4×C103C2×D411yescharacteristic
129C2×C4×C103C2411yescharacteristic
130C22⋊D103—22no—
131C22⋊D103—42no—
132C22⋊D103—81no—
133C2×Dic103—21no—
134C2×Dic103—21no—
135C2×Dic103—21no—
136C2×Dic103—21no—
137C2×Dic103—42no—
138C2×Dic103—81no—
139C2×Dic103C2×D411yescharacteristic
140C2×Dic103C2×D411yescharacteristic
141C2×Dic103C2×D411yescharacteristic
142C4×D103—21no—
143C4×D103—21no—
144Dic206—21no—
145Dic206—21no—
146Dic206—21no—
147Dic206—21no—
148C8×C103—21no—
149C8×C103—21no—
150C103⋊C8—21no—
151C103⋊C8—21no—
152C22×C103—21no—
153C22×C103—21no—
154C22×C103—22no—
155C22×C103—41no—
156C22×C103—41no—
157C22×C103—41no—
158C22×C103—41no—
159C22×C103—41no—
160C22×C103—84no—
161C22×C103#13512yes—
162C22×C103C22×D411yescharacteristic
163C2×D103—21no—
164C2×D103—21no—
165C2×D103—21no—
166C4×C103—21no—
167C4×C103—41no—
168C4×C103—41no—
169C4×C103C2×#4111yescharacteristic
170C4×C103H(5,𝔽2)11yescharacteristic
171Dic103—21no—
172Dic103—21no—
173Dic103—21no—
174Dic103—41no—
175Dic103—41no—
176Dic103—41no—
177Dic103—41no—
178C2×C103—22no—
179C2×C103—42no—
180C2×C103—81no—
181C2×C103#54611yescharacteristic
182C2×C103C2×#13511yescharacteristic
183C2×C103#57711yescharacteristic
184D103—41no—
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×D4—1031no—
200#416—1031no—
201C2×#102D10311yescharacteristic, complemented
202C2×#41—1031no—
203C22×D4C2×D10311yescharacteristic
204C2×Q16—1031no—
205C2×SD16—1031no—
206C2×SD16—1031no—
207C22×C8—1031no—
208C22×C8C2×D10311yescharacteristic
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×D4—1031no—
224#117—1031no—
225#117—2061no—
226C2×C4⋊C4C2×D10311yescharacteristic
227C2×C22⋊C4—2061no—
228#107—1031no—
229#106—1031no—
230#106—1031no—
231C4⋊C8—1031no—
232#103—1031no—
233#103—1031no—
234#103—1031no—
235#103—1031no—
236#102—1031no—
237#102—1031no—
238#102C2×D10311yescharacteristic
239#102C2×D10311yescharacteristic
240#102C2×D10311yescharacteristic
241#102C2×D10311yescharacteristic
242C22⋊C8—1031no—
243C22⋊C8—1031no—
244C4×C8—1031no—
245C24—21no—
246#41—4121no—
247#41—2062no—
248C2×Q8—1031no—
249C2×Q8—1031no—
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—1031no—
254C2×D4—2061no—
255C2×D4—2061no—
256C2×D4C22×D10311yescharacteristic
257C2×D4C22×D10311yescharacteristic
258C22×C4—21no—
259C22×C4—1031no—
260C22×C4—2061no—
261C22×C4—2061no—
262C22×C4C22×D10311yescharacteristic
263Q16—4121no—
264SD16—4121no—
265SD16—2062no—
266C2×C8—41no—
267C2×C8—1031no—
268C2×C8—1031no—
269C2×C8—4121no—
270C2×C8C22×D10311yescharacteristic
271C2×C8C22×D10311yescharacteristic
272C4⋊C4—21no—
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⋊C4C22×D10311yescharacteristic
283C4⋊C4C22×D10311yescharacteristic
284C22⋊C4—1031no—
285C22⋊C4—1031no—
286C22⋊C4—2061no—
287C22⋊C4—2061no—
288C22⋊C4—2061no—
289C22⋊C4—2061no—
290C22⋊C4—2061no—
291C22⋊C4—2061no—
292C22⋊C4—2061no—
293C22⋊C4—2061no—
294C42—1031no—
295C42—2061no—
296C42—2061no—
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—1031no—
303C23D4×D10311yescharacteristic
304Q8—2061no—
305Q8—2061no—
306Q8—2061no—
307Q8—2061no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—42no—
312D4—8241no—
313D4—4122no—
314D4—2062no—
315D4#1311010512yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—8241no—
322C2×C4—1031no—
323C2×C4—1031no—
324C2×C4—1031no—
325C2×C4—4122no—
326C2×C4—2061no—
327C2×C4—2061no—
328C2×C4—2061no—
329C2×C4—2061no—
330C2×C4—2061no—
331C2×C4—2061no—
332C2×C4D4×D10311yescharacteristic
333C2×C4C23×D10311yescharacteristic
334C8—21no—
335C8—21no—
336C8—2061no—
337C8—2061no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—84no—
347C22—2061no—
348C22—2061no—
349C22—2061no—
350C22#1569304012yes—
351C22C2×D4×D10311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—4121no—
356C4—4121no—
357C4—4121no—
358C4—4121no—
359C4—2061no—
360C4—2061no—
361C4—2061no—
362C4C2×#1311010511yescharacteristic
363C4#1569306611yescharacteristic
364C2—22no—
365C2—42no—
366C2—81no—
367C2—4121no—
368C2#2026843111yescharacteristic
369C2C2×#1569304011yescharacteristic
370C2#2026859711yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×#102×C103C2
socleC22×C103C22×D4
prime radical#20268435C2
hypercenterC2×#102D103
hypocenterC103#3296
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #20268476C2semidirect
3. #20268144C2semidirect
4. #20268121C2semidirect
5. #20268113C2semidirect
6. #20268089C2semidirect
7. #20268032C2semidirect
8. #20268019C2semidirect
9. #20268012C2semidirect
10. #20267954C2semidirect
11. #20267942C2semidirect
12. #20267882C2semidirect
13. C8×C22⋊D103C2semidirect
14. #20267784C2semidirect
15. C2×#102×C103C2semidirect
17. C2×Dic412C22semidirect
20. C2×C8×D103C22semidirect
22. #15693012C22semidirect
27. #15693001C22semidirect
33. #15692986C22semidirect
37. #15692979C22semidirect
39. #15692955C22semidirect
40. #15692952C22semidirect
41. #15692952C22semidirect
42. Dic103⋊C8C22semidirect
43. #15692946C22semidirect
44. #15692946C22semidirect
45. #15692944C22semidirect
46. #15692944C22semidirect
50. (C2×D103)⋊C8C22semidirect
51. C8×Dic103C22semidirect
186. C103#3296semidirect
201. C2×#102D103semidirect

Maximal subgroups

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

subgroupindex
#202684762
#202684352
#202681442
#202681212
#202681132
#202680892
#202680322
#202680192
#202680122
#202679542
#202679422
#202678822
C8×C22⋊D1032
#202677842
C2×#102×C1032
#3296103