Finite Group Databasebeta

← #27205383

Subgroups — #27205383

Order 13184.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268394C211yesmaximal, characteristic, complemented
2#20268265C211yesmaximal, characteristic, complemented
3#20268115C211yesmaximal, characteristic, complemented
4#20268094C211yesmaximal, characteristic, complemented
5#20268090C211yesmaximal, characteristic, complemented
6#20267985C211yesmaximal, characteristic, complemented
7#20267985C211yesmaximal, characteristic, complemented
8#20267927C211yesmaximal, characteristic, complemented
9#20267924C211yesmaximal, characteristic, complemented
10#20267902C211yesmaximal, characteristic, complemented
11#20267900C211yesmaximal, characteristic, complemented
12#20267873C211yesmaximal, characteristic, complemented
13#20267871C211yesmaximal, characteristic, complemented
14#20267849C211yesmaximal, characteristic, complemented
15#482×C103C211yesmaximal, characteristic, complemented
16C22×D412C2211yescharacteristic
17C2×D824C2211yescharacteristic
18C2×D824C2211yescharacteristic
19C2×#13110090C2211yescharacteristic
20C2×#13110090C2211yescharacteristic
21#15693017C2211yescharacteristic, complemented
22#15693012C2211yescharacteristic, complemented
23#15693005—21no—
24#15693003—21no—
25#15692995C2211yescharacteristic
26#15692993—21no—
27#15692992—21no—
28C4×D412—21no—
29C4×D412—21no—
30D4×Dic103C2211yescharacteristic, complemented
31#15692983C2211yescharacteristic
32#15692983C2211yescharacteristic
33#15692983C2211yescharacteristic
34#15692983C2211yescharacteristic
35#15692983C2211yescharacteristic, complemented
36#15692980C2211yescharacteristic
37C22⋊C4×D103—21no—
38C22⋊C4×D103—21no—
39#15692954C2211yescharacteristic, complemented
40#15692952C2211yescharacteristic, complemented
41Dic103⋊C8C2211yescharacteristic, complemented
42Dic103⋊C8C2211yescharacteristic, complemented
43#15692943C2211yescharacteristic
44#15692943C2211yescharacteristic
45#15692941C2211yescharacteristic
46#15692941C2211yescharacteristic
47#15692941C2211yescharacteristic, complemented
48#15692941C2211yescharacteristic, complemented
49C22⋊(C103⋊C8)C2211yescharacteristic
50#15692931C2211yescharacteristic, complemented
51C8×Dic103C2211yescharacteristic, complemented
52#121×C103C2211yescharacteristic
53#117×C103C2211yescharacteristic
54#107×C103C2211yescharacteristic, complemented
55#106×C103C2211yescharacteristic, complemented
56#102×C103C2211yescharacteristic, complemented
57#102×C103C2211yescharacteristic, complemented
58C22⋊C8×C103C2211yescharacteristic
59C23×D103—21no—
60C2×D412—21no—
61C2×D412—22no—
62C2×D412—22no—
63C2×D412C2311yescharacteristic
64C2×D412C2311yescharacteristic
65C2×D412C2311yescharacteristic
66C2×C22⋊D103—21no—
67C2×C22⋊D103—21no—
68C2×C22⋊D103—21no—
69C22×Dic103—21no—
70C2×C4×D103—21no—
71C2×C4×D103—21no—
72C2×C4×D103—21no—
73C2×C4×D103—21no—
74C2×C4×D103—21no—
75D824—22no—
76D824—22no—
77#13110090—22no—
78#13110090—22no—
79C2×C103⋊C8C2311yescharacteristic
80C2×C103⋊C8C2311yescharacteristic
81C4⋊Dic103—21no—
82C4⋊Dic103D411yescharacteristic
83C4⋊Dic103D411yescharacteristic
84C4⋊Dic103C2311yescharacteristic
85Dic103⋊C4—21no—
86C22⋊Dic103—21no—
87C22⋊Dic103D411yescharacteristic
88C22⋊Dic103D411yescharacteristic
89(C2×D103)⋊C4—21no—
90(C2×D103)⋊C4—21no—
91(C2×D103)⋊C4—21no—
92(C2×D103)⋊C4—21no—
93(C2×D103)⋊C4—21no—
94(C2×D103)⋊C4—21no—
95C4×Dic103C2311yescharacteristic
96C4×Dic103C2311yescharacteristic
97C2×D4×C103—21no—
98C2×D4×C103C2311yescharacteristic
99C22×C4×C103C2311yescharacteristic
100C2×C8×C103C2311yescharacteristic
101C2×C8×C103C2311yescharacteristic
102C4⋊C4×C103C2311yescharacteristic
103C4⋊C4×C103C2311yescharacteristic
104C4⋊C4×C103C2311yescharacteristic
105C22⋊C4×C103—21no—
106C22⋊C4×C103—21no—
107C42×C103—21no—
108C23×C103—21no—
109C23×C103C2×D411yescharacteristic
110C22×D103—21no—
111C22×D103—21no—
112C22×D103—24no—
113C22×D103—21no—
114C22×D103—81no—
115C22×D103—81no—
116D4×C103—21no—
117D4×C103—21no—
118D4×C103—81no—
119C2×C4×C103—21no—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103—21no—
124C2×C4×C103C2×D411yescharacteristic
125C2×C4×C103C2411yescharacteristic
126C22⋊D103—81no—
127C22⋊D103—81no—
128C22⋊D103—81no—
129C2×Dic103—21no—
130C2×Dic103—81no—
131C2×Dic103C2×D411yescharacteristic
132C2×Dic103C2×D411yescharacteristic
133C2×Dic103C2×D411yescharacteristic
134C2×Dic103C2×D411yescharacteristic
135D412—24no—
136D412—21no—
137D412—21no—
138D412—21no—
139D412—21no—
140D412#4112yes—
141D412#4112yes—
142C4×D103—81no—
143C4×D103—81no—
144C4×D103—81no—
145C4×D103—81no—
146C4×D103—81no—
147C8×C103—21no—
148C8×C103—21no—
149C103⋊C8—21no—
150C103⋊C8—21no—
151C22×C103—21no—
152C22×C103—21no—
153C22×C103—21no—
154C22×C103—41no—
155C22×C103—41no—
156C22×C103—41no—
157C22×C103C22×D411yescharacteristic
158C2×D103—22no—
159C2×D103—22no—
160C2×D103—41no—
161C2×D103—41no—
162C2×D103—41no—
163C2×D103—41no—
164C2×D103—41no—
165C2×D103—41no—
166C2×D103—41no—
167C2×D103—84no—
168C4×C103—21no—
169C4×C103—41no—
170C4×C103—41no—
171C4×C103—41no—
172C4×C103C2×#4111yescharacteristic
173C4×C103C2×#4111yescharacteristic
174Dic103—21no—
175Dic103—21no—
176Dic103—21no—
177Dic103—21no—
178Dic103—41no—
179C2×C103—41no—
180C2×C103—81no—
181C2×C103#52511yescharacteristic
182C2×C103#57611yescharacteristic
183C2×C103#57611yescharacteristic
184D103—42no—
185D103—42no—
186D103—81no—
187#3122—1031nomaximal, Sylow
188C103#312211yescharacteristic, complemented, Sylow
189#540—1031no—
190#518—1031no—
191#482—1031no—
192#482D10311yescharacteristic, complemented
193#478—1031no—
194#478—1031no—
195#459—1031no—
196#459—1031no—
197#447—1031no—
198#447—1031no—
199#442—1031no—
200#442—1031no—
201C4×D8—1031no—
202C4×D8—1031no—
203#433—1031no—
204C22×D4—1031no—
205C2×D8—1031no—
206C2×D8—1031no—
207C2×D8—1031no—
208C2×D8—1031no—
209#127—1031no—
210#125—1031no—
211#123—2061no—
212#123—2061no—
213#121—1031no—
214#121—2061no—
215#121—2061no—
216#121C2×D10311yescharacteristic
217C4×D4—1031no—
218C4×D4—1031no—
219C4×D4—1031no—
220C4×D4—1031no—
221C4×D4—1031no—
222C4×D4—1031no—
223C4×D4—2061no—
224C4×D4—2061no—
225#117—1031no—
226#117C2×D10311yescharacteristic
227C2×C22⋊C4—2061no—
228C2×C22⋊C4—2061no—
229#107—1031no—
230#107C2×D10311yescharacteristic, complemented
231#106—1031no—
232#106C2×D10311yescharacteristic, complemented
233C4⋊C8—1031no—
234C4⋊C8—1031no—
235#102—1031no—
236#102—1031no—
237#102—1031no—
238#102—1031no—
239#102—1031no—
240#102—1031no—
241#102C2×D10311yescharacteristic, complemented
242#102C2×D10311yescharacteristic, complemented
243C22⋊C8—1031no—
244C22⋊C8C2×D10311yescharacteristic
245#97—1031no—
246C4×C8—1031no—
247C24—2061no—
248C2×D4—21no—
249C2×D4—1031no—
250C2×D4—1031no—
251C2×D4—1031no—
252C2×D4—2062no—
253C2×D4—2062no—
254C2×D4—2061no—
255C2×D4—2061no—
256C2×D4—2061no—
257C2×D4—2061no—
258C2×D4C22×D10311yescharacteristic
259C22×C4—2061no—
260C22×C4—2061no—
261C22×C4—2061no—
262C22×C4—2061no—
263C22×C4—2061no—
264C22×C4—2061no—
265C22×C4C22×D10311yescharacteristic
266D8—2062no—
267D8—2062no—
268D8—2062no—
269D8—2062no—
270C2×C8—1031no—
271C2×C8—1031no—
272C2×C8C22×D10311yescharacteristic
273C2×C8C22×D10311yescharacteristic
274C4⋊C4—1031no—
275C4⋊C4—1031no—
276C4⋊C4—1031no—
277C4⋊C4—2061no—
278C4⋊C4—2061no—
279C4⋊C4C22×D10311yescharacteristic
280C4⋊C4C22×D10311yescharacteristic
281C4⋊C4C22×D10311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
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—
293C42—21no—
294C42—1031no—
295C42—1031no—
296C23—21no—
297C23—8241no—
298C23—8241no—
299C23—2064no—
300C23—2061no—
301C23—2061no—
302C23—2061no—
303C23D4×D10311yescharacteristic
304D4—21no—
305D4—21no—
306D4—81no—
307D4—8241no—
308D4—8241no—
309D4—8241no—
310D4—1032no—
311D4—1032no—
312D4—2064no—
313D4—2061no—
314D4—2061no—
315D4—2061no—
316D4—2061no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—8241no—
323C2×C4—8241no—
324C2×C4—8241no—
325C2×C4—8241no—
326C2×C4—8241no—
327C2×C4—8241no—
328C2×C4—1031no—
329C2×C4—1031no—
330C2×C4—1031no—
331C2×C4—1031no—
332C2×C4—2061no—
333C2×C4D4×D10311yescharacteristic
334C2×C4C23×D10311yescharacteristic
335C8—21no—
336C8—21no—
337C8—2061no—
338C8—2061no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—8244no—
346C22—4121no—
347C22—4121no—
348C22—4121no—
349C22—4121no—
350C22—4121no—
351C22—4121no—
352C22—4121no—
353C22—2062no—
354C22—2062no—
355C22C2×D4×D10311yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—4121no—
361C4—2061no—
362C4—2061no—
363C4—2061no—
364C4—2061no—
365C4#41×D10311yescharacteristic
366C4#41×D10311yescharacteristic
367C2—41no—
368C2—81no—
369C2—8241no—
370C2—4122no—
371C2—4122no—
372C2#2026829911yescharacteristic
373C2#2026859311yescharacteristic
374C2#2026859511yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#482×C103C2
socleC22×C103C22×D4
hypercenter#482D103
hypocenterC103#3122
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #20268394C2semidirect
2. #20268265C2semidirect
3. #20268115C2semidirect
4. #20268094C2semidirect
5. #20268090C2semidirect
6. #20267985C2semidirect
7. #20267985C2semidirect
8. #20267927C2semidirect
9. #20267924C2semidirect
10. #20267902C2semidirect
11. #20267900C2semidirect
12. #20267873C2semidirect
13. #20267871C2semidirect
14. #20267849C2semidirect
15. #482×C103C2semidirect
21. #15693017C22semidirect
22. #15693012C22semidirect
30. D4×Dic103C22semidirect
35. #15692983C22semidirect
39. #15692954C22semidirect
40. #15692952C22semidirect
41. Dic103⋊C8C22semidirect
42. Dic103⋊C8C22semidirect
47. #15692941C22semidirect
48. #15692941C22semidirect
50. #15692931C22semidirect
51. C8×Dic103C22semidirect
54. #107×C103C22semidirect
55. #106×C103C22semidirect
56. #102×C103C22semidirect
57. #102×C103C22semidirect
188. C103#3122semidirect
192. #482D103semidirect
230. #107C2×D103semidirect
232. #106C2×D103semidirect
241. #102C2×D103semidirect
242. #102C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683942
#202682652
#202681152
#202680942
#202680902
#202679852
#202679272
#202679242
#202679022
#202679002
#202678732
#202678712
#202678492
#482×C1032
#3122103