Finite Group Databasebeta

← #27205495

Subgroups — #27205495

Order 13184.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268418C211yesmaximal, characteristic, complemented
2#20268359C211yesmaximal, characteristic
3#20268156C211yesmaximal, characteristic, complemented
4#20268154C211yesmaximal, characteristic, complemented
5#20268152C211yesmaximal, characteristic, complemented
6#20268147C211yesmaximal, characteristic, complemented
7#20268145C211yesmaximal, characteristic, complemented
8#20268139C211yesmaximal, characteristic, complemented
9#20268136C211yesmaximal, characteristic, complemented
10#20267794C211yesmaximal, characteristic, complemented
11#20267791C211yesmaximal, characteristic, complemented
12#20267786C211yesmaximal, characteristic, complemented
13#102×D103C211yesmaximal, characteristic, complemented
14#20267748C211yesmaximal, characteristic, complemented
15#489×C103C211yesmaximal, characteristic, complemented
16C2×#13110106C2211yescharacteristic
17C2×D4×D103C2211yescharacteristic
18C2×#13110088C2211yescharacteristic
19C2×C8×D103C2211yescharacteristic
20#15693020C2211yescharacteristic, complemented
21#15693019—21no—
22#15693018C2211yescharacteristic
23#15693017C2211yescharacteristic
24#15693013C2211yescharacteristic, complemented
25#15693012C2211yescharacteristic, complemented
26#15693011—21no—
27#15693010C2211yescharacteristic
28#15692999—21no—
29#15692997—21no—
30#15692994—21no—
31#15692994—21no—
32#15692991—21no—
33#15692991—21no—
34#15692979C2211yescharacteristic
35#15692978C2211yescharacteristic
36C4⋊C4×D103C2211yescharacteristic
37#15692945C2211yescharacteristic, complemented
38#15692945C2211yescharacteristic, complemented
39#15692943C2211yescharacteristic
40#15692943C2211yescharacteristic
41#15692943C2211yescharacteristic, complemented
42#15692943C2211yescharacteristic, complemented
43#15692942C2211yescharacteristic
44#15692942C2211yescharacteristic
45#15692941C2211yescharacteristic
46#15692941C2211yescharacteristic
47#15692941C2211yescharacteristic, complemented
48#15692941C2211yescharacteristic, complemented
49#15692931C2211yescharacteristic, complemented
50C4×C103⋊C8C2211yescharacteristic, complemented
51C8×Dic103C2211yescharacteristic, complemented
52C4⋊Q8×C103C2211yescharacteristic, complemented
53#124×C103C2211yescharacteristic
54#103×C103C2211yescharacteristic, complemented
55#103×C103C2211yescharacteristic, complemented
56#102×C103C2211yescharacteristic
57#102×C103C2211yescharacteristic
58#97×C103C2211yescharacteristic, complemented
59C23×D103—21no—
60#13110106—22no—
61#13110106—22no—
62C2×Dic206—21no—
63C2×D412—21no—
64C2×D412—21no—
65C2×D412—21no—
66C2×D412C2311yescharacteristic
67C2×D412C2311yescharacteristic
68C2×C22⋊D103—21no—
69C2×C22⋊D103—21no—
70C2×C22⋊D103—21no—
71D4×D103—22no—
72D4×D103—22no—
73C2×C4×D103—21no—
74C2×C4×D103—21no—
75C2×C4×D103C2311yescharacteristic
76#13110088—22no—
77C2×C103⋊C8C2311yescharacteristic
78C2×C103⋊C8C2311yescharacteristic
79C8×D103—22no—
80C4⋊Dic103—21no—
81C4⋊Dic103C2311yescharacteristic
82C4⋊Dic103C2311yescharacteristic
83Dic103⋊C4—21no—
84Dic103⋊C4—21no—
85Dic103⋊C4—21no—
86Dic103⋊C4—21no—
87Dic103⋊C4—21no—
88Dic103⋊C4D411yescharacteristic
89Dic103⋊C4D411yescharacteristic
90(C2×D103)⋊C4—21no—
91(C2×D103)⋊C4—21no—
92(C2×D103)⋊C4—21no—
93(C2×D103)⋊C4D411yescharacteristic
94(C2×D103)⋊C4D411yescharacteristic
95C4×Dic103—21no—
96C4×Dic103C2311yescharacteristic
97C2×Q8×C103—21no—
98C2×Q8×C103C2311yescharacteristic
99C2×D4×C103C2311yescharacteristic
100C2×C8×C103C2311yescharacteristic
101C2×C8×C103C2311yescharacteristic
102C4⋊C4×C103—21no—
103C4⋊C4×C103C2311yescharacteristic
104C4⋊C4×C103C2311yescharacteristic
105C22⋊C4×C103—21no—
106C22⋊C4×C103—21no—
107C42×C103C2311yescharacteristic
108C23×C103—21no—
109C22×D103—21no—
110C22×D103—21no—
111C22×D103—42no—
112C22×D103—81no—
113C22×D103—81no—
114C22×D103C2×D411yescharacteristic
115Q8×C103—21no—
116Q8×C103—21no—
117Q8×C103—81no—
118D4×C103—21no—
119D4×C103—21no—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103C2×D411yescharacteristic
124C2×C4×C103C2×D411yescharacteristic
125C2×C4×C103C2411yescharacteristic
126C22⋊D103—42no—
127C22⋊D103—81no—
128C22⋊D103—81no—
129C2×Dic103—21no—
130C2×Dic103—21no—
131C2×Dic103C2×D411yescharacteristic
132C2×Dic103C2×D411yescharacteristic
133C2×Dic103C2×D411yescharacteristic
134D412—21no—
135D412—21no—
136D412—21no—
137D412—21no—
138D412—42no—
139D412—81no—
140D412—81no—
141C4×D103—42no—
142C4×D103—81no—
143C4×D103#4112yes—
144C4×D103#4112yes—
145Dic206—81no—
146C8×C103—21no—
147C8×C103—21no—
148C103⋊C8—21no—
149C103⋊C8—21no—
150C22×C103—41no—
151C22×C103—41no—
152C22×C103—41no—
153C22×C103C22×D411yescharacteristic
154C2×D103—21no—
155C2×D103—21no—
156C2×D103—41no—
157C2×D103—41no—
158C2×D103—41no—
159C2×D103—41no—
160C2×D103—41no—
161C2×D103—41no—
162C2×D103—84no—
163C2×D103#12412yes—
164C4×C103—21no—
165C4×C103—21no—
166C4×C103—41no—
167C4×C103—41no—
168C4×C103—41no—
169C4×C103C2×#4111yescharacteristic
170C4×C103C2×#4111yescharacteristic
171Dic103—21no—
172Dic103—21no—
173Dic103—41no—
174Dic103—41no—
175Dic103#12412yes—
176C2×C103—81no—
177C2×C103C2×#12411yescharacteristic
178C2×C103#57611yescharacteristic
179C2×C103#57711yescharacteristic
180D103—22no—
181D103—81no—
182D103—81no—
183#3136—1031nomaximal, Sylow
184C103#313611yescharacteristic, complemented, Sylow
185#544—1031no—
186#535—1031no—
187#490—1031no—
188#490—1031no—
189#489—1031no—
190#489D10311yescharacteristic, complemented
191#488—1031no—
192#488—1031no—
193#486—1031no—
194#486—1031no—
195#418—1031no—
196#417—1031no—
197#416—1031no—
198C2×#102—1031no—
199#405—1031no—
200C2×#41—1031no—
201C22×D4—1031no—
202C2×M16—1031no—
203C22×C8—1031no—
204C4⋊Q8—1031no—
205C4⋊Q8—2061no—
206C4⋊Q8C2×D10311yescharacteristic, complemented
207#127—1031no—
208#127—1031no—
209#125—1031no—
210#125—1031no—
211#125—2061no—
212#124—1031no—
213#124C2×D10311yescharacteristic
214C22⋊Q8—2061no—
215C22⋊Q8—2061no—
216#121—2061no—
217#121—2061no—
218#120—2061no—
219#120—2061no—
220#117—1031no—
221#117—1031no—
222C2×C4⋊C4—1031no—
223#103—1031no—
224#103—1031no—
225#103C2×D10311yescharacteristic, complemented
226#103C2×D10311yescharacteristic, complemented
227#102—1031no—
228#102—1031no—
229#102—1031no—
230#102—1031no—
231#102—1031no—
232#102—1031no—
233#102—1031no—
234#102—1031no—
235#102—1031no—
236#102—1031no—
237#102C2×D10311yescharacteristic
238#102C2×D10311yescharacteristic
239#97—1031no—
240#97C2×D10311yescharacteristic, complemented
241C4×C8—1031no—
242C4×C8—1031no—
243C24—2061no—
244#41—2062no—
245#41—2062no—
246C2×Q8—21no—
247C2×Q8—2061no—
248C2×Q8C22×D10311yescharacteristic
249C2×D4—1031no—
250C2×D4—1031no—
251C2×D4—2061no—
252C2×D4—2062no—
253C2×D4—2062no—
254C2×D4—2061no—
255C2×D4—2061no—
256C2×D4—2061no—
257C2×D4—2061no—
258C2×D4—2061no—
259C2×D4C22×D10311yescharacteristic
260C22×C4—1031no—
261C22×C4—2061no—
262C22×C4—2061no—
263M16—2062no—
264C2×C8—1031no—
265C2×C8—1031no—
266C2×C8—2062no—
267C2×C8C22×D10311yescharacteristic
268C2×C8C22×D10311yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—1031no—
271C4⋊C4—1031no—
272C4⋊C4—1031no—
273C4⋊C4—1031no—
274C4⋊C4—2061no—
275C4⋊C4—2061no—
276C4⋊C4—2061no—
277C4⋊C4—2061no—
278C4⋊C4—2061no—
279C4⋊C4—2061no—
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—
289C42—1031no—
290C42—2061no—
291C42C22×D10311yescharacteristic
292C23—21no—
293C23—8241no—
294C23—8241no—
295C23—1031no—
296C23—4122no—
297C23—2061no—
298C23—2061no—
299Q8—21no—
300Q8—21no—
301Q8—81no—
302Q8—8241no—
303D4—21no—
304D4—21no—
305D4—8241no—
306D4—8241no—
307D4—8241no—
308D4—8241no—
309D4—4122no—
310D4—4122no—
311D4—2061no—
312D4—2061no—
313D4—2061no—
314D4—2061no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—8241no—
319C2×C4—1031no—
320C2×C4—1032no—
321C2×C4—1032no—
322C2×C4—1031no—
323C2×C4—1031no—
324C2×C4—4122no—
325C2×C4—2061no—
326C2×C4—2061no—
327C2×C4D4×D10311yescharacteristic
328C2×C4D4×D10311yescharacteristic
329C2×C4C23×D10311yescharacteristic
330C8—21no—
331C8—21no—
332C8—2061no—
333C8—2061no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—8244no—
338C22—1032no—
339C22—4121no—
340C22—4121no—
341C22—4121no—
342C22—4121no—
343C22—4121no—
344C22—4121no—
345C22—2061no—
346C22—2061no—
347C22C2×D4×D10311yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—1032no—
354C4—4121no—
355C4—4121no—
356C4—2061no—
357C4—2061no—
358C4#41×D10311yescharacteristic
359C4#41×D10311yescharacteristic
360C2—81no—
361C2—8241no—
362C2—8241no—
363C2—2062no—
364C2#124×D10311yescharacteristic
365C2#2026859511yescharacteristic
366C2#2026860011yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#489×C103C2
socleC22×C103C22×D4
prime radical#20268359C2
hypercenter#489D103
hypocenterC103#3136
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #20268418C2semidirect
3. #20268156C2semidirect
4. #20268154C2semidirect
5. #20268152C2semidirect
6. #20268147C2semidirect
7. #20268145C2semidirect
8. #20268139C2semidirect
9. #20268136C2semidirect
10. #20267794C2semidirect
11. #20267791C2semidirect
12. #20267786C2semidirect
13. #102×D103C2semidirect
14. #20267748C2semidirect
15. #489×C103C2semidirect
20. #15693020C22semidirect
24. #15693013C22semidirect
25. #15693012C22semidirect
37. #15692945C22semidirect
38. #15692945C22semidirect
41. #15692943C22semidirect
42. #15692943C22semidirect
47. #15692941C22semidirect
48. #15692941C22semidirect
49. #15692931C22semidirect
50. C4×C103⋊C8C22semidirect
51. C8×Dic103C22semidirect
52. C4⋊Q8×C103C22semidirect
54. #103×C103C22semidirect
55. #103×C103C22semidirect
58. #97×C103C22semidirect
184. C103#3136semidirect
190. #489D103semidirect
206. C4⋊Q8C2×D103semidirect
225. #103C2×D103semidirect
226. #103C2×D103semidirect
240. #97C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202684182
#202683592
#202681562
#202681542
#202681522
#202681472
#202681452
#202681392
#202681362
#202677942
#202677912
#202677862
#102×D1032
#202677482
#489×C1032
#3136103