Finite Group Databasebeta

← #27205493

Subgroups — #27205493

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#20268354C211yesmaximal, characteristic
3#20268155C211yesmaximal, characteristic, complemented
4#20268154C211yesmaximal, characteristic, complemented
5#20268153C211yesmaximal, characteristic, complemented
6#20268149C211yesmaximal, characteristic, complemented
7#20268146C211yesmaximal, characteristic, complemented
8#20268144C211yesmaximal, characteristic, complemented
9#20268136C211yesmaximal, characteristic, complemented
10#20267794C211yesmaximal, characteristic, complemented
11#20267789C211yesmaximal, characteristic, complemented
12#20267784C211yesmaximal, characteristic, complemented
13#102×D103C211yesmaximal, characteristic, complemented
14#20267745C211yesmaximal, characteristic, complemented
15#486×C103C211yesmaximal, characteristic, complemented
16C2×#13110104C2211yescharacteristic
17C2×D4×D103C2211yescharacteristic
18C2×#13110088C2211yescharacteristic
19C2×C8×D103C2211yescharacteristic
20#15693020C2211yescharacteristic, complemented
21#15693019—21no—
22#15693017C2211yescharacteristic
23#15693013C2211yescharacteristic, complemented
24#15693012C2211yescharacteristic, complemented
25#15693011—21no—
26#15693009C2211yescharacteristic
27#15693008C2211yescharacteristic
28#15692999—21no—
29#15692997—21no—
30#15692993—21no—
31#15692993—21no—
32#15692989—21no—
33#15692989—21no—
34#15692979C2211yescharacteristic
35#15692978C2211yescharacteristic
36C4⋊C4×D103C2211yescharacteristic
37#15692946C2211yescharacteristic, complemented
38#15692946C2211yescharacteristic, complemented
39#15692944C2211yescharacteristic, complemented
40#15692944C2211yescharacteristic, complemented
41#15692943C2211yescharacteristic
42#15692943C2211yescharacteristic
43#15692942C2211yescharacteristic
44#15692942C2211yescharacteristic
45#15692942C2211yescharacteristic, complemented
46#15692942C2211yescharacteristic, complemented
47#15692941C2211yescharacteristic
48#15692941C2211yescharacteristic
49#15692932C2211yescharacteristic, complemented
50#15692931C2211yescharacteristic, complemented
51C8×Dic103C2211yescharacteristic, complemented
52C4⋊Q8×C103C2211yescharacteristic, complemented
53#127×C103C2211yescharacteristic
54#102×C103C2211yescharacteristic
55#102×C103C2211yescharacteristic
56#102×C103C2211yescharacteristic, complemented
57#102×C103C2211yescharacteristic, complemented
58C4×C8×C103C2211yescharacteristic, complemented
59C23×D103—21no—
60#13110104—22no—
61#13110104—22no—
62C2×Dic206—21no—
63C2×Dic206C2311yescharacteristic
64C2×D412C2311yescharacteristic
65C2×C22⋊D103—21no—
66C2×C22⋊D103—21no—
67C2×C22⋊D103—21no—
68C2×C22⋊D103—21no—
69D4×D103—22no—
70D4×D103—22no—
71C22×Dic103—21no—
72C2×C4×D103—21no—
73C2×C4×D103C2311yescharacteristic
74#13110088—22no—
75C2×C103⋊C8C2311yescharacteristic
76C2×C103⋊C8C2311yescharacteristic
77C8×D103—22no—
78C4⋊Dic103—21no—
79C4⋊Dic103C2311yescharacteristic
80C4⋊Dic103C2311yescharacteristic
81Dic103⋊C4—21no—
82Dic103⋊C4—21no—
83Dic103⋊C4—21no—
84Dic103⋊C4—21no—
85Dic103⋊C4—21no—
86Dic103⋊C4D411yescharacteristic
87Dic103⋊C4D411yescharacteristic
88C22⋊Dic103—21no—
89C22⋊Dic103—21no—
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×D4×C103—21no—
99C2×D4×C103—21no—
100C2×D4×C103C2311yescharacteristic
101C2×D4×C103C2311yescharacteristic
102C2×C8×C103C2311yescharacteristic
103C2×C8×C103C2311yescharacteristic
104C4⋊C4×C103—21no—
105C4⋊C4×C103C2311yescharacteristic
106C4⋊C4×C103C2311yescharacteristic
107C42×C103C2311yescharacteristic
108C23×C103—21no—
109C23×C103—21no—
110C22×D103—21no—
111C22×D103—42no—
112C22×D103—81no—
113C22×D103—81no—
114C22×D103C2×D411yescharacteristic
115Q8×C103—81no—
116D4×C103—21no—
117D4×C103—21no—
118D4×C103—21no—
119D4×C103—21no—
120D4×C103—81no—
121D4×C103—81no—
122C2×C4×C103—21no—
123C2×C4×C103—21no—
124C2×C4×C103C2×D411yescharacteristic
125C2×C4×C103C2×D411yescharacteristic
126C2×C4×C103C2411yescharacteristic
127C22⋊D103—42no—
128C22⋊D103—42no—
129C22⋊D103—81no—
130C22⋊D103—81no—
131C2×Dic103—21no—
132C2×Dic103—21no—
133C2×Dic103—21no—
134C2×Dic103—42no—
135C2×Dic103C2×D411yescharacteristic
136C2×Dic103C2×D411yescharacteristic
137C2×Dic103C2×D411yescharacteristic
138D412—21no—
139D412—21no—
140C4×D103—81no—
141C4×D103#4112yes—
142C4×D103#4112yes—
143Dic206—21no—
144Dic206—21no—
145Dic206—81no—
146C8×C103—21no—
147C8×C103—21no—
148C103⋊C8—21no—
149C103⋊C8—21no—
150C22×C103—41no—
151C22×C103—41no—
152C22×C103—41no—
153C22×C103—41no—
154C22×C103—41no—
155C22×C103—41no—
156C22×C103C22×D411yescharacteristic
157C2×D103—21no—
158C2×D103—21no—
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×C103C2×#4111yescharacteristic
169C4×C103C2×#4111yescharacteristic
170Dic103—21no—
171Dic103—21no—
172Dic103—41no—
173Dic103—41no—
174Dic103—41no—
175Dic103#12412yes—
176C2×C103—81no—
177C2×C103—81no—
178C2×C103C2×#12411yescharacteristic
179C2×C103#57611yescharacteristic
180C2×C103#57711yescharacteristic
181D103—22no—
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#489—1031no—
191#488—1031no—
192#488—1031no—
193#486—1031no—
194#486D10311yescharacteristic, complemented
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#127C2×D10311yescharacteristic
209#125—1031no—
210#125—1031no—
211#125—2061no—
212#124—1031no—
213#124—1031no—
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#103—1031no—
226#103—1031no—
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#102C2×D10311yescharacteristic
236#102C2×D10311yescharacteristic
237#102C2×D10311yescharacteristic, complemented
238#102C2×D10311yescharacteristic, complemented
239#97—1031no—
240#97—1031no—
241C4×C8—1031no—
242C4×C8C2×D10311yescharacteristic, complemented
243C24—2061no—
244#41—2062no—
245#41—2062no—
246C2×Q8—21no—
247C2×Q8—1031no—
248C2×Q8—2061no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—1031no—
252C2×D4—2062no—
253C2×D4—2062no—
254C2×D4—2061no—
255C2×D4—2061no—
256C2×D4—2061no—
257C2×D4—2061no—
258C2×D4C22×D10311yescharacteristic
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—1031no—
283C22⋊C4—1031no—
284C22⋊C4—2061no—
285C22⋊C4—2061no—
286C22⋊C4—2061no—
287C22⋊C4—2061no—
288C22⋊C4—2061no—
289C42—1031no—
290C42—2061no—
291C42C22×D10311yescharacteristic
292C23—21no—
293C23—21no—
294C23—8241no—
295C23—8241no—
296C23—1031no—
297C23—4122no—
298C23—2061no—
299Q8—81no—
300Q8—8241no—
301Q8—2061no—
302Q8—2061no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—81no—
308D4—81no—
309D4—8241no—
310D4—8241no—
311D4—4122no—
312D4—4122no—
313D4—2061no—
314D4—2061no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—8241no—
318C2×C4—1031no—
319C2×C4—1032no—
320C2×C4—1032no—
321C2×C4—1031no—
322C2×C4—1031no—
323C2×C4—4122no—
324C2×C4—2061no—
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—41no—
338C22—41no—
339C22—41no—
340C22—8244no—
341C22—1032no—
342C22—4121no—
343C22—4121no—
344C22—4121no—
345C22—2061no—
346C22—2061no—
347C22C2×D4×D10311yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—1032no—
353C4—4121no—
354C4—4121no—
355C4—4121no—
356C4—2061no—
357C4—2061no—
358C4#41×D10311yescharacteristic
359C4#41×D10311yescharacteristic
360C2—81no—
361C2—81no—
362C2—8241no—
363C2—2062no—
364C2#124×D10311yescharacteristic
365C2#2026859211yescharacteristic
366C2#2026859711yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#486×C103C2
socleC22×C103C22×D4
prime radical#20268354C2
hypercenter#486D103
hypocenterC103#3136
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #20268418C2semidirect
3. #20268155C2semidirect
4. #20268154C2semidirect
5. #20268153C2semidirect
6. #20268149C2semidirect
7. #20268146C2semidirect
8. #20268144C2semidirect
9. #20268136C2semidirect
10. #20267794C2semidirect
11. #20267789C2semidirect
12. #20267784C2semidirect
13. #102×D103C2semidirect
14. #20267745C2semidirect
15. #486×C103C2semidirect
20. #15693020C22semidirect
23. #15693013C22semidirect
24. #15693012C22semidirect
37. #15692946C22semidirect
38. #15692946C22semidirect
39. #15692944C22semidirect
40. #15692944C22semidirect
45. #15692942C22semidirect
46. #15692942C22semidirect
49. #15692932C22semidirect
50. #15692931C22semidirect
51. C8×Dic103C22semidirect
52. C4⋊Q8×C103C22semidirect
56. #102×C103C22semidirect
57. #102×C103C22semidirect
58. C4×C8×C103C22semidirect
184. C103#3136semidirect
194. #486D103semidirect
206. C4⋊Q8C2×D103semidirect
237. #102C2×D103semidirect
238. #102C2×D103semidirect
242. C4×C8C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202684182
#202683542
#202681552
#202681542
#202681532
#202681492
#202681462
#202681442
#202681362
#202677942
#202677892
#202677842
#102×D1032
#202677452
#486×C1032
#3136103