Finite Group Databasebeta

← #27205329

Subgroups — #27205329

Order 13184.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268414C211yesmaximal, characteristic, complemented
2#20268266C211yesmaximal, characteristic, complemented
3#20268129C211yesmaximal, characteristic, complemented
4#20268116C211yesmaximal, characteristic, complemented
5#20268079C211yesmaximal, characteristic, complemented
6#20268069C211yesmaximal, characteristic, complemented
7#20268008C211yesmaximal, characteristic, complemented
8#20268008C211yesmaximal, characteristic, complemented
9#20267925C211yesmaximal, characteristic
10#20267900C211yesmaximal, characteristic, complemented
11#20267892C211yesmaximal, characteristic, complemented
12SD16×Dic103C211yesmaximal, characteristic, complemented
13#20267871C211yesmaximal, characteristic, complemented
14#20267849C211yesmaximal, characteristic, complemented
15#450×C103C211yesmaximal, characteristic, complemented
16C2×#13110090C2211yescharacteristic
17C2×#13110090C2211yescharacteristic
18#15693020C2211yescharacteristic, complemented
19#15693016—21no—
20#15693010C2211yescharacteristic, complemented
21#15693007—21no—
22#15693003—21no—
23#15693001—21no—
24#15692995C2211yescharacteristic
25Q8×Dic103C2211yescharacteristic, complemented
26D4×Dic103—21no—
27D4×Dic103—21no—
28D4×Dic103C2211yescharacteristic
29D4×Dic103C2211yescharacteristic
30D4×Dic103C2211yescharacteristic
31D4×Dic103C2211yescharacteristic
32#15692983C2211yescharacteristic, complemented
33#15692980C2211yescharacteristic
34#15692980C2211yescharacteristic
35C2×C22⋊Dic103—21no—
36C2×C22⋊Dic103—21no—
37#15692955C2211yescharacteristic, complemented
38#15692954C2211yescharacteristic, complemented
39#15692953C2211yescharacteristic, complemented
40#15692952C2211yescharacteristic, complemented
41Dic103⋊C8C2211yescharacteristic, complemented
42Dic103⋊C8C2211yescharacteristic, complemented
43#15692945C2211yescharacteristic, complemented
44#15692945C2211yescharacteristic, complemented
45#15692943C2211yescharacteristic, complemented
46#15692943C2211yescharacteristic, complemented
47#15692942C2211yescharacteristic
48#15692942C2211yescharacteristic
49C22⋊(C103⋊C8)C2211yescharacteristic
50#15692931C2211yescharacteristic, complemented
51C8×Dic103C2211yescharacteristic, complemented
52C22×D4×C103C2211yescharacteristic
53C2×SD16×C103C2211yescharacteristic
54C2×SD16×C103C2211yescharacteristic
55C22⋊Q8×C103C2211yescharacteristic
56#102×C103C2211yescharacteristic
57#102×C103C2211yescharacteristic
58C22⋊C8×C103C2211yescharacteristic
59C2×Dic206—21no—
60C2×D412C2311yescharacteristic
61C2×C22⋊D103—21no—
62C22×Dic103—21no—
63C22×Dic103—21no—
64C22×Dic103—21no—
65C22×Dic103—21no—
66C2×C4×D103—21no—
67#13110090—22no—
68#13110090—22no—
69C2×C103⋊C8C2311yescharacteristic
70C2×C103⋊C8C2311yescharacteristic
71C4⋊Dic103—21no—
72C4⋊Dic103D411yescharacteristic
73C4⋊Dic103D411yescharacteristic
74C4⋊Dic103C2311yescharacteristic
75C4⋊Dic103C2311yescharacteristic
76C4⋊Dic103C2311yescharacteristic
77Dic103⋊C4—21no—
78C22⋊Dic103—21no—
79C22⋊Dic103—21no—
80C22⋊Dic103—21no—
81C22⋊Dic103—21no—
82C22⋊Dic103—21no—
83C22⋊Dic103D411yescharacteristic
84C22⋊Dic103D411yescharacteristic
85(C2×D103)⋊C4—21no—
86(C2×D103)⋊C4—21no—
87(C2×D103)⋊C4—21no—
88(C2×D103)⋊C4—21no—
89C4×Dic103—21no—
90C4×Dic103—21no—
91C4×Dic103C2311yescharacteristic
92C4×Dic103C2311yescharacteristic
93C24×C103—21no—
94C2×Q8×C103C2311yescharacteristic
95C2×D4×C103—22no—
96C2×D4×C103—22no—
97C2×D4×C103—21no—
98C2×D4×C103C2311yescharacteristic
99C2×D4×C103C2311yescharacteristic
100C22×C4×C103C2311yescharacteristic
101SD16×C103—22no—
102SD16×C103—22no—
103C2×C8×C103C2311yescharacteristic
104C2×C8×C103C2311yescharacteristic
105C4⋊C4×C103—21no—
106C4⋊C4×C103C2311yescharacteristic
107C22⋊C4×C103—21no—
108C23×C103—24no—
109C23×C103—21no—
110C23×C103—21no—
111C23×C103—81no—
112C23×C103—81no—
113C23×C103C2×D411yescharacteristic
114C22×D103—21no—
115Q8×C103—21no—
116Q8×C103—21no—
117D4×C103—24no—
118D4×C103—21no—
119D4×C103—21no—
120D4×C103#4112yes—
121D4×C103#4112yes—
122C2×C4×C103—21no—
123C2×C4×C103—21no—
124C2×C4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103C2×D411yescharacteristic
127C2×C4×C103C2411yescharacteristic
128C22⋊D103—81no—
129C2×Dic103—21no—
130C2×Dic103—21no—
131C2×Dic103—21no—
132C2×Dic103—81no—
133C2×Dic103—81no—
134C2×Dic103—81no—
135C2×Dic103—81no—
136C2×Dic103C2×D411yescharacteristic
137C2×Dic103C2×D411yescharacteristic
138C2×Dic103C2×D411yescharacteristic
139C2×Dic103C2×D411yescharacteristic
140D412—21no—
141D412—21no—
142C4×D103—81no—
143Dic206—81no—
144C8×C103—21no—
145C8×C103—21no—
146C103⋊C8—21no—
147C103⋊C8—21no—
148C22×C103—21no—
149C22×C103—22no—
150C22×C103—22no—
151C22×C103—21no—
152C22×C103—21no—
153C22×C103—41no—
154C22×C103—41no—
155C22×C103—41no—
156C22×C103—41no—
157C22×C103—84no—
158C22×C103C22×D411yescharacteristic
159C2×D103—41no—
160C2×D103—41no—
161C2×D103—41no—
162C4×C103—21no—
163C4×C103—41no—
164C4×C103—41no—
165C4×C103C2×#4111yescharacteristic
166C4×C103C2×#4111yescharacteristic
167Dic103—21no—
168Dic103—21no—
169Dic103—21no—
170Dic103—21no—
171Dic103—41no—
172Dic103—41no—
173Dic103—41no—
174C2×C103—41no—
175C2×C103—42no—
176C2×C103—42no—
177C2×C103#52511yescharacteristic
178C2×C103#57611yescharacteristic
179C2×C103#57711yescharacteristic
180D103—81no—
181#3118—1031nomaximal, Sylow
182C103#311811yescharacteristic, complemented, Sylow
183#542—1031no—
184#518—1031no—
185#485—1031no—
186#482—1031no—
187#476—1031no—
188#474—1031no—
189#463—1031no—
190#463—1031no—
191#450D10311yescharacteristic, complemented
192#447—1031no—
193#442—1031no—
194#440—1031no—
195C4×SD16—1031no—
196C4×D8—1031no—
197#433—1031no—
198C22×D4C2×D10311yescharacteristic
199C2×SD16C2×D10311yescharacteristic
200C2×SD16C2×D10311yescharacteristic
201C2×D8—1031no—
202C2×D8—1031no—
203C4⋊Q8—1031no—
204#126—2061no—
205#124—1031no—
206#124—2061no—
207#123—2061no—
208C22⋊Q8—2061no—
209C22⋊Q8C2×D10311yescharacteristic
210#121—1031no—
211C4×Q8—1031no—
212C4×D4—1031no—
213C4×D4—1031no—
214C4×D4—1031no—
215C4×D4—1031no—
216C4×D4—1031no—
217C4×D4—2061no—
218C4×D4—2061no—
219#117—1031no—
220#117—1031no—
221C2×C22⋊C4—2061no—
222C2×C22⋊C4—2061no—
223#107—1031no—
224#107—1031no—
225#106—1031no—
226#106—1031no—
227C4⋊C8—1031no—
228C4⋊C8—1031no—
229#103—1031no—
230#103—1031no—
231#102—1031no—
232#102—1031no—
233#102—1031no—
234#102—1031no—
235#102C2×D10311yescharacteristic
236#102C2×D10311yescharacteristic
237C22⋊C8—1031no—
238C22⋊C8C2×D10311yescharacteristic
239#97—1031no—
240C4×C8—1031no—
241C24—21no—
242C2×Q8—2061no—
243C2×Q8C22×D10311yescharacteristic
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—1031no—
248C2×D4—2061no—
249C2×D4C22×D10311yescharacteristic
250C2×D4C22×D10311yescharacteristic
251C22×C4—2061no—
252C22×C4—2061no—
253C22×C4—2061no—
254C22×C4—2061no—
255C22×C4—2061no—
256C22×C4C22×D10311yescharacteristic
257SD16—22no—
258SD16—22no—
259D8—2062no—
260D8—2062no—
261C2×C8—1031no—
262C2×C8—1031no—
263C2×C8C22×D10311yescharacteristic
264C2×C8C22×D10311yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—1031no—
267C4⋊C4—1031no—
268C4⋊C4—1031no—
269C4⋊C4—1031no—
270C4⋊C4—1031no—
271C4⋊C4—2061no—
272C4⋊C4—2061no—
273C4⋊C4C22×D10311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—1031no—
276C22⋊C4—1031no—
277C22⋊C4—2061no—
278C22⋊C4—2061no—
279C22⋊C4—2061no—
280C22⋊C4—2061no—
281C22⋊C4—2061no—
282C22⋊C4—2061no—
283C22⋊C4—2061no—
284C22⋊C4—2061no—
285C22⋊C4—2061no—
286C42—1031no—
287C42—1031no—
288C42—2061no—
289C42—2061no—
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—2061no—
296C23D4×D10311yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—8241no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—8241no—
304D4—2061no—
305D4—2061no—
306D4#1311010412yes—
307D4#1311010412yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—8241no—
313C2×C4—8241no—
314C2×C4—8241no—
315C2×C4—8241no—
316C2×C4—8241no—
317C2×C4—1031no—
318C2×C4—1031no—
319C2×C4—1031no—
320C2×C4—1031no—
321C2×C4—2061no—
322C2×C4—2061no—
323C2×C4—2061no—
324C2×C4D4×D10311yescharacteristic
325C2×C4C23×D10311yescharacteristic
326C8—21no—
327C8—21no—
328C8—2061no—
329C8—2061no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—84no—
340C22—4121no—
341C22—4121no—
342C22—4121no—
343C22C2×D4×D10311yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—4121no—
348C4—4121no—
349C4—4121no—
350C4—2061no—
351C4—2061no—
352C4—2061no—
353C4—2061no—
354C4C2×#1311010411yescharacteristic
355C4C2×#1311010411yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—8241no—
360C2#2026829711yescharacteristic
361C2#2026859511yescharacteristic
362C2#2026859711yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#450×C103C2
socleC22×C103C22×D4
prime radical#20267925C2
hypercenter#450D103
hypocenterC103#3118
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #20268414C2semidirect
2. #20268266C2semidirect
3. #20268129C2semidirect
4. #20268116C2semidirect
5. #20268079C2semidirect
6. #20268069C2semidirect
7. #20268008C2semidirect
8. #20268008C2semidirect
10. #20267900C2semidirect
11. #20267892C2semidirect
12. SD16×Dic103C2semidirect
13. #20267871C2semidirect
14. #20267849C2semidirect
15. #450×C103C2semidirect
18. #15693020C22semidirect
20. #15693010C22semidirect
25. Q8×Dic103C22semidirect
32. #15692983C22semidirect
37. #15692955C22semidirect
38. #15692954C22semidirect
39. #15692953C22semidirect
40. #15692952C22semidirect
41. Dic103⋊C8C22semidirect
42. Dic103⋊C8C22semidirect
43. #15692945C22semidirect
44. #15692945C22semidirect
45. #15692943C22semidirect
46. #15692943C22semidirect
50. #15692931C22semidirect
51. C8×Dic103C22semidirect
182. C103#3118semidirect
191. #450D103semidirect

Maximal subgroups

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

subgroupindex
#202684142
#202682662
#202681292
#202681162
#202680792
#202680692
#202680082
#202679252
#202679002
#202678922
SD16×Dic1032
#202678712
#202678492
#450×C1032
#3118103