Finite Group Databasebeta

← #27206963

Subgroups — #27206963

Order 13184.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268499C211yesmaximal, characteristic, complemented
2#20268425C211yesmaximal, characteristic
3#20268136C211yesmaximal, characteristic, complemented
4#20268111C211yesmaximal, characteristic, complemented
5#20268107C211yesmaximal, characteristic, complemented
6#20268080C211yesmaximal, characteristic, complemented
7#20268023C211yesmaximal, characteristic, complemented
8#20267989C211yesmaximal, characteristic, complemented
9#20267941C211yesmaximal, characteristic, complemented
10#20267940C211yesmaximal, characteristic, complemented
11#20267876C211yesmaximal, characteristic, complemented
12C8×C22⋊D103C211yesmaximal, characteristic, complemented
13C2×#15692943C211yesmaximal, characteristic, complemented
14#102×D103C211yesmaximal, characteristic, complemented
15#465×C103C211yesmaximal, characteristic, complemented
16C22×D412C2211yescharacteristic
17C2×D4×D103—21no—
18C2×D4×D103C2211yescharacteristic
19C2×#13110092C2211yescharacteristic
20C2×#13110092C2211yescharacteristic, complemented
21C2×C8×D103C2211yescharacteristic, complemented
22#15693020C2211yescharacteristic, complemented
23#15693017C2211yescharacteristic
24#15693011—21no—
25#15693001—21no—
26#15692998—21no—
27#15692997C2211yescharacteristic, complemented
28#15692996C2211yescharacteristic
29#15692994—21no—
30#15692991—21no—
31#15692989—21no—
32Q8×Dic103C2211yescharacteristic, complemented
33#15692983C2211yescharacteristic
34C4×C22⋊D103C2211yescharacteristic
35(C22⋊D103)⋊C4—21no—
36C2×C4⋊Dic103C2211yescharacteristic, complemented
37C4⋊C4×D103C2211yescharacteristic, complemented
38#15692952C2211yescharacteristic, complemented
39#15692952C2211yescharacteristic, complemented
40Dic103⋊C8C2211yescharacteristic, complemented
41#15692943C2211yescharacteristic
42#15692943C2211yescharacteristic
43#15692943C2211yescharacteristic, complemented
44#15692943C2211yescharacteristic, complemented
45#15692942C2211yescharacteristic, complemented
46#15692942C2211yescharacteristic, complemented
47#15692941C2211yescharacteristic
48#15692941C2211yescharacteristic, complemented
49C22⋊(C103⋊C8)C2211yescharacteristic, complemented
50(C2×D103)⋊C8C2211yescharacteristic, complemented
51C8×Dic103C2211yescharacteristic, complemented
52C2×SD16×C103C2211yescharacteristic, complemented
53C22×C8×C103C2211yescharacteristic, complemented
54C22⋊Q8×C103C2211yescharacteristic, complemented
55#121×C103C2211yescharacteristic
56#106×C103C2211yescharacteristic, complemented
57#103×C103C2211yescharacteristic, complemented
58#102×C103C2211yescharacteristic, complemented
59C23×D103—21no—
60C23×D103—21no—
61C2×Dic206—21no—
62C2×D412—22no—
63C2×D412—21no—
64C2×D412—21no—
65C2×D412—41no—
66C2×D412C2311yescharacteristic
67C2×D412C2311yescharacteristic
68C2×C22⋊D103—21no—
69C2×C22⋊D103—21no—
70C2×C22⋊D103—21no—
71C2×C22⋊D103D411yescharacteristic
72D4×D103—22no—
73D4×D103—41no—
74D4×D103—44no—
75C22×Dic103—21no—
76C2×C4×D103—21no—
77C2×C4×D103—21no—
78C2×C4×D103C2311yescharacteristic
79#13110092—22no—
80#13110092—41no—
81C2×C103⋊C8C2311yescharacteristic
82C2×C103⋊C8C2311yescharacteristic
83C8×D103—41no—
84C4⋊Dic103—21no—
85C4⋊Dic103—21no—
86C4⋊Dic103C2311yescharacteristic
87C4⋊Dic103C2311yescharacteristic
88Dic103⋊C4—21no—
89Dic103⋊C4—21no—
90Dic103⋊C4—21no—
91Dic103⋊C4D411yescharacteristic
92C22⋊Dic103D411yescharacteristic
93(C2×D103)⋊C4—21no—
94(C2×D103)⋊C4—21no—
95(C2×D103)⋊C4—21no—
96(C2×D103)⋊C4D411yescharacteristic
97C4×Dic103—21no—
98C4×Dic103C2311yescharacteristic
99C2×Q8×C103C2311yescharacteristic
100C2×D4×C103—21no—
101C2×D4×C103C2311yescharacteristic
102C22×C4×C103C2311yescharacteristic
103SD16×C103—41no—
104C2×C8×C103—41no—
105C2×C8×C103C2311yescharacteristic
106C2×C8×C103C2311yescharacteristic
107C4⋊C4×C103—21no—
108C4⋊C4×C103C2311yescharacteristic
109C4⋊C4×C103C2311yescharacteristic
110C22⋊C4×C103—21no—
111C22⋊C4×C103—21no—
112C23×C103—21no—
113C23×C103C2×D411yescharacteristic
114C22×D103—21no—
115C22×D103—21no—
116C22×D103—42no—
117C22×D103—42no—
118C22×D103—42no—
119C22×D103—42no—
120C22×D103—81no—
121C22×D103—81no—
122C22×D103C2×D411yescharacteristic
123Q8×C103—21no—
124Q8×C103—21no—
125D4×C103—21no—
126D4×C103—21no—
127D4×C103—42no—
128C2×C4×C103—21no—
129C2×C4×C103—21no—
130C2×C4×C103—21no—
131C2×C4×C103—21no—
132C2×C4×C103—21no—
133C2×C4×C103C2×D411yescharacteristic
134C2×C4×C103C2411yescharacteristic
135C22⋊D103—42no—
136C22⋊D103—42no—
137C22⋊D103—81no—
138C22⋊D103SD1614yescomplemented
139C2×Dic103—21no—
140C2×Dic103—21no—
141C2×Dic103—81no—
142C2×Dic103C2×D411yescharacteristic
143C2×Dic103C2×D411yescharacteristic
144C2×Dic103C2×D411yescharacteristic
145D412—21no—
146D412—21no—
147D412—21no—
148D412—42no—
149D412—42no—
150D412#4112yes—
151C4×D103—21no—
152C4×D103—21no—
153C4×D103—42no—
154C4×D103—81no—
155Dic206—81no—
156C8×C103—21no—
157C8×C103—21no—
158C103⋊C8—21no—
159C103⋊C8—21no—
160C22×C103—21no—
161C22×C103—21no—
162C22×C103—41no—
163C22×C103—41no—
164C22×C103—41no—
165C22×C103C2×SD1612yes—
166C22×C103C22×D411yescharacteristic
167C2×D103—21no—
168C2×D103—21no—
169C2×D103—22no—
170C2×D103—41no—
171C2×D103—41no—
172C2×D103—41no—
173C2×D103—41no—
174C2×D103—41no—
175C2×D103—84no—
176C2×D103—84no—
177C2×D103C2×SD1612yes—
178C4×C103—21no—
179C4×C103—41no—
180C4×C103—41no—
181C4×C103—41no—
182C4×C103C2×#4111yescharacteristic
183C4×C103H(5,𝔽2)11yescharacteristic
184Dic103—21no—
185Dic103—21no—
186Dic103—41no—
187Dic103—41no—
188Dic103C2×SD1612yes—
189C2×C103—22no—
190C2×C103—81no—
191C2×C103#54611yescharacteristic
192C2×C103C22×SD1611yescharacteristic
193C2×C103#57611yescharacteristic
194D103—22no—
195D103—42no—
196D103—81no—
197#3295—1031nomaximal, Sylow
198C103#329511yescharacteristic, complemented, Sylow
199#554—1031no—
200D42—1031no—
201#486—1031no—
202#481—1031no—
203#481—1031no—
204#476—1031no—
205#465—1031no—
206#465D10311yescharacteristic, complemented
207#460—1031no—
208#450—1031no—
209#450—1031no—
210C4×SD16—1031no—
211C8×D4—1031no—
212C2×#102—1031no—
213C2×#102—1031no—
214C22×D4—1031no—
215C22×D4—1031no—
216C22×D4—2061no—
217C2×SD16—1031no—
218C2×SD16—1031no—
219C2×SD16C2×D10311yescharacteristic, complemented
220C22×C8—1031no—
221C22×C8C2×D10311yescharacteristic, complemented
222C4⋊Q8—1031no—
223#127—1031no—
224#125—2061no—
225C22⋊Q8—1031no—
226C22⋊Q8—2061no—
227C22⋊Q8—2061no—
228C22⋊Q8C2×D10311yescharacteristic, complemented
229#121—1031no—
230#121—2061no—
231#121C2×D10311yescharacteristic
232#120—2061no—
233#120—2061no—
234C4×Q8—1031no—
235C4×D4—1031no—
236C4×D4—1031no—
237C4×D4—2061no—
238C2×C4⋊C4—1031no—
239C2×C4⋊C4—1031no—
240#106—1031no—
241#106—1031no—
242#106C2×D10311yescharacteristic, complemented
243C4⋊C8—1031no—
244#103C2×D10311yescharacteristic, complemented
245#102—1031no—
246#102—1031no—
247#102—1031no—
248#102—1031no—
249#102—1031no—
250#102—1031no—
251#102—1031no—
252#102—1031no—
253#102C2×D10311yescharacteristic, complemented
254C22⋊C8—1031no—
255C22⋊C8—1031no—
256C4×C8—1031no—
257C24—2061no—
258C24—2061no—
259C2×Q8—2061no—
260C2×Q8C22×D10311yescharacteristic
261C2×D4—21no—
262C2×D4—1031no—
263C2×D4—1031no—
264C2×D4—1031no—
265C2×D4—4121no—
266C2×D4—4124no—
267C2×D4—4121no—
268C2×D4—2062no—
269C2×D4—2061no—
270C2×D4—2061no—
271C2×D4—2061no—
272C2×D4—2061no—
273C2×D4—2062no—
274C2×D4—2061no—
275C2×D4C22×D10311yescharacteristic
276C22×C4—1031no—
277C22×C4—2061no—
278C22×C4—2061no—
279C22×C4—2061no—
280C22×C4C22×D10311yescharacteristic
281SD16—41no—
282SD16—4121no—
283SD16—2062no—
284C2×C8—41no—
285C2×C8—1031no—
286C2×C8—1031no—
287C2×C8—4121no—
288C2×C8C22×D10311yescharacteristic
289C2×C8C22×D10311yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—1031no—
292C4⋊C4—1031no—
293C4⋊C4—1031no—
294C4⋊C4—2061no—
295C4⋊C4—2061no—
296C4⋊C4—2061no—
297C4⋊C4—2061no—
298C4⋊C4—2061no—
299C4⋊C4C22×D10311yescharacteristic
300C4⋊C4C22×D10311yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—1031no—
304C22⋊C4—1031no—
305C22⋊C4—2061no—
306C22⋊C4—2061no—
307C22⋊C4—2061no—
308C42—1031no—
309C42—2061no—
310C23—21no—
311C23—8241no—
312C23—8241no—
313C23—1031no—
314C23—4122no—
315C23—4122no—
316C23—4122no—
317C23—4122no—
318C23—2061no—
319C23—2061no—
320C23D4×D10311yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—8241no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—8241no—
328D4—1034no—
329D4—1032no—
330D4—4122no—
331D4—4122no—
332D4—4122no—
333D4—4122no—
334D4—2061no—
335D4—2061no—
336D4—2061no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—8241no—
343C2×C4—8241no—
344C2×C4—1031no—
345C2×C4—1031no—
346C2×C4—1031no—
347C2×C4—4122no—
348C2×C4—2061no—
349C2×C4—2061no—
350C2×C4—2061no—
351C2×C4—2061no—
352C2×C4D4×D10311yescharacteristic
353C2×C4C23×D10311yescharacteristic
354C8—21no—
355C8—21no—
356C8—2061no—
357C8—2061no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—8244no—
364C22—8244no—
365C22—1032no—
366C22—4121no—
367C22—4121no—
368C22—4121no—
369C22—4121no—
370C22—4121no—
371C22—2062no—
372C22—2061no—
373C22—2061no—
374C22SD16×D10312yes—
375C22C2×D4×D10311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—1032no—
381C4—4121no—
382C4—4121no—
383C4—2061no—
384C4—2061no—
385C4#41×D10311yescharacteristic
386C4#1569306611yescharacteristic
387C2—22no—
388C2—81no—
389C2—8241no—
390C2—4122no—
391C2—2062no—
392C2#2026843011yescharacteristic
393C2C2×SD16×D10311yescharacteristic
394C2#2026859311yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#465×C103C2
socleC22×C103C22×D4
prime radical#20268425C2
hypercenter#465D103
hypocenterC103#3295
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #20268499C2semidirect
3. #20268136C2semidirect
4. #20268111C2semidirect
5. #20268107C2semidirect
6. #20268080C2semidirect
7. #20268023C2semidirect
8. #20267989C2semidirect
9. #20267941C2semidirect
10. #20267940C2semidirect
11. #20267876C2semidirect
12. C8×C22⋊D103C2semidirect
13. C2×#15692943C2semidirect
14. #102×D103C2semidirect
15. #465×C103C2semidirect
20. C2×#13110092C22semidirect
21. C2×C8×D103C22semidirect
22. #15693020C22semidirect
27. #15692997C22semidirect
32. Q8×Dic103C22semidirect
36. C2×C4⋊Dic103C22semidirect
37. C4⋊C4×D103C22semidirect
38. #15692952C22semidirect
39. #15692952C22semidirect
40. Dic103⋊C8C22semidirect
43. #15692943C22semidirect
44. #15692943C22semidirect
45. #15692942C22semidirect
46. #15692942C22semidirect
48. #15692941C22semidirect
49. C22⋊(C103⋊C8)C22semidirect
50. (C2×D103)⋊C8C22semidirect
51. C8×Dic103C22semidirect
52. C2×SD16×C103C22semidirect
53. C22×C8×C103C22semidirect
54. C22⋊Q8×C103C22semidirect
56. #106×C103C22semidirect
57. #103×C103C22semidirect
58. #102×C103C22semidirect
138. C22⋊D103SD16semidirect
198. C103#3295semidirect
206. #465D103semidirect
219. C2×SD16C2×D103semidirect
221. C22×C8C2×D103semidirect
228. C22⋊Q8C2×D103semidirect
242. #106C2×D103semidirect
244. #103C2×D103semidirect
253. #102C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202684992
#202684252
#202681362
#202681112
#202681072
#202680802
#202680232
#202679892
#202679412
#202679402
#202678762
C8×C22⋊D1032
C2×#156929432
#102×D1032
#465×C1032
#3295103