Finite Group Databasebeta

← #27205322

Subgroups — #27205322

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#20268265C211yesmaximal, characteristic, complemented
2#20268129C211yesmaximal, characteristic, complemented
3#20268112C211yesmaximal, characteristic, complemented
4#20268078C211yesmaximal, characteristic, complemented
5#20268068C211yesmaximal, characteristic, complemented
6#20268003C211yesmaximal, characteristic, complemented
7#20268003C211yesmaximal, characteristic, complemented
8#20267941C211yesmaximal, characteristic, complemented
9#20267924C211yesmaximal, characteristic
10#20267901C211yesmaximal, characteristic, complemented
11#20267889C211yesmaximal, characteristic, complemented
12C4×#13110092C211yesmaximal, characteristic, complemented
13C4×#13110090C211yesmaximal, characteristic, complemented
14#20267852C211yesmaximal, characteristic, complemented
15#542×C103C211yesmaximal, characteristic, complemented
16C22×D412C2211yescharacteristic
17C2×#13110092C2211yescharacteristic
18C2×#13110092C2211yescharacteristic
19C2×#13110090C2211yescharacteristic
20C2×#13110090C2211yescharacteristic
21C4×D412C2211yescharacteristic
22C4×D412C2211yescharacteristic
23C4×D412C2211yescharacteristic
24C4×D412C2211yescharacteristic
25#15692983—21no—
26#15692983—21no—
27#15692980C2211yescharacteristic
28C22⋊C4×D103—21no—
29C22⋊C4×D103—21no—
30#15692954C2211yescharacteristic, complemented
31#15692954C2211yescharacteristic, complemented
32#15692952C2211yescharacteristic, complemented
33#15692952C2211yescharacteristic, complemented
34C4⋊(C103⋊C8)C2211yescharacteristic, complemented
35C4⋊(C103⋊C8)C2211yescharacteristic, complemented
36#15692945C2211yescharacteristic, complemented
37#15692945C2211yescharacteristic, complemented
38#15692942C2211yescharacteristic, complemented
39#15692942C2211yescharacteristic, complemented
40#15692941C2211yescharacteristic
41#15692941C2211yescharacteristic
42#15692941C2211yescharacteristic
43#15692941C2211yescharacteristic
44C22⋊(C103⋊C8)C2211yescharacteristic
45C22⋊(C103⋊C8)C2211yescharacteristic
46#15692932C2211yescharacteristic, complemented
47C4×C103⋊C8C2211yescharacteristic, complemented
48C4⋊Q8×C103C2211yescharacteristic, complemented
49#126×C103—21no—
50#124×C103—21no—
51#124×C103C2211yescharacteristic, complemented
52#123×C103—21no—
53C22⋊Q8×C103—21no—
54C22⋊Q8×C103C2211yescharacteristic
55#121×C103C2211yescharacteristic
56C4×Q8×C103C2211yescharacteristic, complemented
57C4×D4×C103C2211yescharacteristic, complemented
58#117×C103C2211yescharacteristic
59C23×D103—21no—
60C2×D412—21no—
61C2×D412—22no—
62C2×D412—22no—
63C2×D412C2311yescharacteristic
64C2×D412C2311yescharacteristic
65C2×C4×D103—21no—
66C2×C4×D103—21no—
67C2×C4×D103—21no—
68C2×C4×D103—21no—
69#13110092—22no—
70#13110092—22no—
71#13110090—22no—
72#13110090—22no—
73C2×C103⋊C8C2311yescharacteristic
74C2×C103⋊C8C2311yescharacteristic
75C2×C103⋊C8C2311yescharacteristic
76C2×C103⋊C8C2311yescharacteristic
77C4⋊Dic103C2311yescharacteristic
78C4⋊Dic103C2311yescharacteristic
79C22⋊Dic103—21no—
80(C2×D103)⋊C4—21no—
81(C2×D103)⋊C4—21no—
82(C2×D103)⋊C4—21no—
83(C2×D103)⋊C4—21no—
84C4×Dic103—21no—
85C2×Q8×C103—21no—
86C2×Q8×C103C2311yescharacteristic
87C2×D4×C103—21no—
88C2×D4×C103C2311yescharacteristic
89C22×C4×C103—21no—
90C22×C4×C103C2311yescharacteristic
91C4⋊C4×C103—21no—
92C4⋊C4×C103—21no—
93C4⋊C4×C103—21no—
94C4⋊C4×C103D411yescharacteristic
95C4⋊C4×C103D411yescharacteristic
96C4⋊C4×C103C2311yescharacteristic
97C4⋊C4×C103C2311yescharacteristic
98C22⋊C4×C103—21no—
99C22⋊C4×C103—21no—
100C22⋊C4×C103—21no—
101C22⋊C4×C103—21no—
102C22⋊C4×C103—21no—
103C22⋊C4×C103D411yescharacteristic
104C22⋊C4×C103D411yescharacteristic
105C42×C103—21no—
106C42×C103C2311yescharacteristic
107C42×C103C2311yescharacteristic
108C23×C103—21no—
109C23×C103C2×D411yescharacteristic
110C22×D103—21no—
111C22×D103—21no—
112C22×D103—24no—
113C22×D103—81no—
114C22×D103—81no—
115Q8×C103—21no—
116Q8×C103—21no—
117Q8×C103—81no—
118D4×C103—21no—
119D4×C103—21no—
120D4×C103—81no—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103—21no—
124C2×C4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103—81no—
127C2×C4×C103C2×D411yescharacteristic
128C2×C4×C103C2×D411yescharacteristic
129C2×C4×C103C2×D411yescharacteristic
130C2×C4×C103C2×D411yescharacteristic
131C2×C4×C103C2×D411yescharacteristic
132C2×C4×C103C2411yescharacteristic
133C2×Dic103—21no—
134C2×Dic103—21no—
135D412—24no—
136D412—21no—
137D412—21no—
138D412#4112yes—
139D412#4112yes—
140C4×D103—81no—
141C4×D103—81no—
142C4×D103—81no—
143C4×D103—81no—
144C103⋊C8—21no—
145C103⋊C8—21no—
146C103⋊C8—21no—
147C103⋊C8—21no—
148C22×C103—21no—
149C22×C103—21no—
150C22×C103—21no—
151C22×C103—41no—
152C22×C103—41no—
153C22×C103—41no—
154C22×C103C22×D411yescharacteristic
155C2×D103—22no—
156C2×D103—22no—
157C2×D103—41no—
158C2×D103—41no—
159C2×D103—41no—
160C2×D103—41no—
161C2×D103—84no—
162C4×C103—21no—
163C4×C103—21no—
164C4×C103—21no—
165C4×C103—21no—
166C4×C103—21no—
167C4×C103—41no—
168C4×C103—41no—
169C4×C103—41no—
170C4×C103C2×#4111yescharacteristic
171C4×C103C2×#4111yescharacteristic
172Dic103—41no—
173Dic103—41no—
174C2×C103—41no—
175C2×C103—81no—
176C2×C103#52511yescharacteristic
177C2×C103#57611yescharacteristic
178C2×C103#57711yescharacteristic
179D103—42no—
180D103—42no—
181#3118—1031nomaximal, Sylow
182C103#311811yescharacteristic, complemented, Sylow
183#542D10311yescharacteristic, complemented
184#518—1031no—
185#485—1031no—
186#482—1031no—
187#476—1031no—
188#474—1031no—
189#463—1031no—
190#463—1031no—
191#450—1031no—
192#447—1031no—
193#442—1031no—
194#440—1031no—
195C4×SD16—1031no—
196C4×D8—1031no—
197#433—1031no—
198C22×D4—1031no—
199C2×SD16—1031no—
200C2×SD16—1031no—
201C2×D8—1031no—
202C2×D8—1031no—
203C4⋊Q8C2×D10311yescharacteristic, complemented
204#126—21no—
205#124—21no—
206#124C2×D10311yescharacteristic, complemented
207#123—21no—
208C22⋊Q8—21no—
209C22⋊Q8C2×D10311yescharacteristic
210#121C2×D10311yescharacteristic
211C4×Q8C2×D10311yescharacteristic, complemented
212C4×D4—1031no—
213C4×D4—1031no—
214C4×D4—1031no—
215C4×D4—1031no—
216C4×D4—2061no—
217C4×D4—2061no—
218C4×D4C2×D10311yescharacteristic, complemented
219#117—1031no—
220#117C2×D10311yescharacteristic
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#102—1031no—
236#102—1031no—
237C22⋊C8—1031no—
238C22⋊C8—1031no—
239#97—1031no—
240C4×C8—1031no—
241C24—2061no—
242C2×Q8—21no—
243C2×Q8C22×D10311yescharacteristic
244C2×D4—21no—
245C2×D4—1031no—
246C2×D4—1031no—
247C2×D4—2062no—
248C2×D4—2062no—
249C2×D4—2061no—
250C2×D4C22×D10311yescharacteristic
251C22×C4—21no—
252C22×C4—2061no—
253C22×C4—2061no—
254C22×C4—2061no—
255C22×C4—2061no—
256C22×C4C22×D10311yescharacteristic
257SD16—2062no—
258SD16—2062no—
259D8—2062no—
260D8—2062no—
261C2×C8—1031no—
262C2×C8—1031no—
263C2×C8—1031no—
264C2×C8—1031no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—1031no—
269C4⋊C4—1031no—
270C4⋊C4C22⋊D10311yescharacteristic
271C4⋊C4C22⋊D10311yescharacteristic
272C4⋊C4C22×D10311yescharacteristic
273C4⋊C4C22×D10311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—2061no—
280C22⋊C4—2061no—
281C22⋊C4—2061no—
282C22⋊C4—2061no—
283C22⋊C4—2061no—
284C22⋊C4C22⋊D10311yescharacteristic
285C22⋊C4C22⋊D10311yescharacteristic
286C42—21no—
287C42—2061no—
288C42C22×D10311yescharacteristic
289C42C22×D10311yescharacteristic
290C23—21no—
291C23—8241no—
292C23—8241no—
293C23—2064no—
294C23—2061no—
295C23—2061no—
296C23C2×C22⋊D10311yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—81no—
300D4—21no—
301D4—21no—
302D4—81no—
303D4—1032no—
304D4—1032no—
305D4—2064no—
306D4—2061no—
307D4—2061no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—81no—
314C2×C4—8241no—
315C2×C4—8241no—
316C2×C4—8241no—
317C2×C4—8241no—
318C2×C4—2061no—
319C2×C4—2061no—
320C2×C4C2×C22⋊D10311yescharacteristic
321C2×C4C2×C22⋊D10311yescharacteristic
322C2×C4C2×C22⋊D10311yescharacteristic
323C2×C4C2×C22⋊D10311yescharacteristic
324C2×C4C2×C22⋊D10311yescharacteristic
325C2×C4C23×D10311yescharacteristic
326C8—2061no—
327C8—2061no—
328C8—2061no—
329C8—2061no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—8244no—
337C22—4121no—
338C22—4121no—
339C22—4121no—
340C22—4121no—
341C22—2062no—
342C22—2062no—
343C22C22×C22⋊D10311yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—4121no—
353C4—4121no—
354C4#41×D10311yescharacteristic
355C4#41×D10311yescharacteristic
356C2—41no—
357C2—81no—
358C2—4122no—
359C2—4122no—
360C2#2026829811yescharacteristic
361C2#2026859411yescharacteristic
362C2#2026859911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#542×C103C2
socleC22×C103C22×D4
prime radical#20267924C2
hypercenter#542D103
hypocenterC103#3118
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #20268265C2semidirect
2. #20268129C2semidirect
3. #20268112C2semidirect
4. #20268078C2semidirect
5. #20268068C2semidirect
6. #20268003C2semidirect
7. #20268003C2semidirect
8. #20267941C2semidirect
10. #20267901C2semidirect
11. #20267889C2semidirect
12. C4×#13110092C2semidirect
13. C4×#13110090C2semidirect
14. #20267852C2semidirect
15. #542×C103C2semidirect
30. #15692954C22semidirect
31. #15692954C22semidirect
32. #15692952C22semidirect
33. #15692952C22semidirect
34. C4⋊(C103⋊C8)C22semidirect
35. C4⋊(C103⋊C8)C22semidirect
36. #15692945C22semidirect
37. #15692945C22semidirect
38. #15692942C22semidirect
39. #15692942C22semidirect
46. #15692932C22semidirect
47. C4×C103⋊C8C22semidirect
48. C4⋊Q8×C103C22semidirect
51. #124×C103C22semidirect
56. C4×Q8×C103C22semidirect
57. C4×D4×C103C22semidirect
182. C103#3118semidirect
183. #542D103semidirect
203. C4⋊Q8C2×D103semidirect
206. #124C2×D103semidirect
211. C4×Q8C2×D103semidirect
218. C4×D4C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202682652
#202681292
#202681122
#202680782
#202680682
#202680032
#202679412
#202679242
#202679012
#202678892
C4×#131100922
C4×#131100902
#202678522
#542×C1032
#3118103