Finite Group Databasebeta

← #27206961

Subgroups — #27206961

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
2D4×C22⋊D103C211yesmaximal, characteristic
3#20268136C211yesmaximal, characteristic, complemented
4#20268110C211yesmaximal, characteristic, complemented
5#20268108C211yesmaximal, characteristic, complemented
6#20268079C211yesmaximal, characteristic, complemented
7#20268022C211yesmaximal, characteristic, complemented
8#20268017C211yesmaximal, characteristic, complemented
9#20267989C211yesmaximal, characteristic, complemented
10#20267940C211yesmaximal, characteristic, complemented
11SD16×Dic103C211yesmaximal, characteristic, complemented
12(C22⋊D103)⋊C8C211yesmaximal, characteristic, complemented
13C2×#15692942C211yesmaximal, characteristic, complemented
14#102×D103C211yesmaximal, characteristic, complemented
15#450×C103C211yesmaximal, characteristic, complemented
16C22×C22⋊D103—21no—
17C2×D4×D103C2211yescharacteristic
18C2×#13110092C2211yescharacteristic, complemented
19C22×C103⋊C8C2211yescharacteristic, complemented
20C2×C8×D103C2211yescharacteristic, complemented
21#15693020C2211yescharacteristic, complemented
22#15693017C2211yescharacteristic
23#15693011—21no—
24#15693001—21no—
25#15692998—21no—
26#15692997C2211yescharacteristic, complemented
27#15692995C2211yescharacteristic
28#15692993—21no—
29#15692992C2211yescharacteristic
30#15692990—21no—
31#15692989—21no—
32Q8×Dic103C2211yescharacteristic, complemented
33D4×Dic103C2211yescharacteristic
34C4×C22⋊D103C2211yescharacteristic
35(C22⋊D103)⋊C4—21no—
36C2×C4⋊Dic103C2211yescharacteristic, complemented
37C4⋊C4×D103C2211yescharacteristic, complemented
38#15692953C2211yescharacteristic, complemented
39#15692953C2211yescharacteristic, complemented
40#15692952C2211yescharacteristic, complemented
41Dic103⋊C8C2211yescharacteristic, complemented
42#15692945C2211yescharacteristic, complemented
43#15692943C2211yescharacteristic, complemented
44#15692943C2211yescharacteristic, complemented
45#15692942C2211yescharacteristic
46#15692942C2211yescharacteristic
47#15692942C2211yescharacteristic, complemented
48#15692942C2211yescharacteristic, complemented
49#15692941C2211yescharacteristic, complemented
50(C2×D103)⋊C8C2211yescharacteristic, complemented
51C8×Dic103C2211yescharacteristic, complemented
52C22×D4×C103C2211yescharacteristic
53C2×SD16×C103C2211yescharacteristic
54C2×SD16×C103C2211yescharacteristic, complemented
55C22⋊Q8×C103C2211yescharacteristic, complemented
56#102×C103C2211yescharacteristic
57#102×C103C2211yescharacteristic, complemented
58C22⋊C8×C103C2211yescharacteristic, complemented
59C23×D103—21no—
60C2×Dic206—21no—
61C2×D412C2311yescharacteristic
62C2×C22⋊D103—21no—
63C2×C22⋊D103—21no—
64C2×C22⋊D103—21no—
65C2×C22⋊D103—21no—
66C2×C22⋊D103—21no—
67C2×C22⋊D103—44no—
68C2×C22⋊D103D411yescharacteristic
69D4×D103—22no—
70D4×D103—41no—
71C22×Dic103—21no—
72C22×Dic103—21no—
73C2×C4×D103—21no—
74C2×C4×D103C2311yescharacteristic
75#13110092—41no—
76C2×C103⋊C8—41no—
77C2×C103⋊C8C2311yescharacteristic
78C2×C103⋊C8C2311yescharacteristic
79C8×D103—41no—
80C4⋊Dic103—21no—
81C4⋊Dic103—21no—
82C4⋊Dic103C2311yescharacteristic
83C4⋊Dic103C2311yescharacteristic
84C4⋊Dic103C2311yescharacteristic
85Dic103⋊C4—21no—
86Dic103⋊C4—21no—
87Dic103⋊C4—21no—
88Dic103⋊C4D411yescharacteristic
89C22⋊Dic103—21no—
90C22⋊Dic103—21no—
91C22⋊Dic103D411yescharacteristic
92(C2×D103)⋊C4—21no—
93(C2×D103)⋊C4—21no—
94(C2×D103)⋊C4D411yescharacteristic
95C4×Dic103—21no—
96C4×Dic103C2311yescharacteristic
97C24×C103—21no—
98C2×Q8×C103C2311yescharacteristic
99C2×D4×C103—22no—
100C2×D4×C103—21no—
101C2×D4×C103—41no—
102C2×D4×C103C2311yescharacteristic
103C2×D4×C103C2311yescharacteristic
104C22×C4×C103C2311yescharacteristic
105SD16×C103—22no—
106SD16×C103—41no—
107C2×C8×C103C2311yescharacteristic
108C2×C8×C103C2311yescharacteristic
109C4⋊C4×C103—21no—
110C4⋊C4×C103C2311yescharacteristic
111C22⋊C4×C103—21no—
112C23×C103—21no—
113C23×C103—21no—
114C23×C103—42no—
115C23×C103—42no—
116C23×C103—81no—
117C23×C103C2×D411yescharacteristic
118C22×D103—21no—
119C22×D103—42no—
120C22×D103—42no—
121C22×D103—81no—
122C22×D103C2×D411yescharacteristic
123Q8×C103—21no—
124Q8×C103—21no—
125D4×C103—21no—
126D4×C103—21no—
127D4×C103—21no—
128D4×C103—42no—
129D4×C103#4112yes—
130C2×C4×C103—21no—
131C2×C4×C103—21no—
132C2×C4×C103—21no—
133C2×C4×C103—21no—
134C2×C4×C103C2×D411yescharacteristic
135C2×C4×C103C2411yescharacteristic
136C22⋊D103—42no—
137C22⋊D103—42no—
138C22⋊D103—42no—
139C22⋊D103—42no—
140C22⋊D103—81no—
141C22⋊D103SD1614yescomplemented
142C2×Dic103—21no—
143C2×Dic103—21no—
144C2×Dic103—21no—
145C2×Dic103—42no—
146C2×Dic103—81no—
147C2×Dic103C2×D411yescharacteristic
148C2×Dic103C2×D411yescharacteristic
149C2×Dic103C2×D411yescharacteristic
150D412—21no—
151D412—21no—
152C4×D103—21no—
153C4×D103—21no—
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—22no—
163C22×C103—41no—
164C22×C103—41no—
165C22×C103—41no—
166C22×C103—41no—
167C22×C103—41no—
168C22×C103—84no—
169C22×C103C2×SD1612yes—
170C22×C103C22×D411yescharacteristic
171C2×D103—21no—
172C2×D103—21no—
173C2×D103—41no—
174C2×D103—41no—
175C2×D103—41no—
176C2×D103—84no—
177C2×D103C2×SD1612yes—
178C4×C103—21no—
179C4×C103—41no—
180C4×C103—41no—
181C4×C103C2×#4111yescharacteristic
182C4×C103H(5,𝔽2)11yescharacteristic
183Dic103—21no—
184Dic103—21no—
185Dic103—41no—
186Dic103—41no—
187Dic103—41no—
188Dic103C2×SD1612yes—
189C2×C103—22no—
190C2×C103—42no—
191C2×C103—81no—
192C2×C103#54611yescharacteristic
193C2×C103C22×SD1611yescharacteristic
194C2×C103#57611yescharacteristic
195D103—22no—
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#465—1031no—
207#460—1031no—
208#450—1031no—
209#450D10311yescharacteristic, complemented
210C4×SD16—1031no—
211C8×D4—1031no—
212C2×#102—1031no—
213C2×#102—1031no—
214C22×D4—1031no—
215C22×D4—2061no—
216C22×D4C2×D10311yescharacteristic
217C2×SD16—1031no—
218C2×SD16C2×D10311yescharacteristic
219C2×SD16C2×D10311yescharacteristic, complemented
220C22×C8—1031no—
221C22×C8—1031no—
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—1031no—
231#121—2061no—
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#106—1031no—
243C4⋊C8—1031no—
244#103—1031no—
245#102—1031no—
246#102—1031no—
247#102—1031no—
248#102—1031no—
249#102—1031no—
250#102—1031no—
251#102—1031no—
252#102C2×D10311yescharacteristic
253#102C2×D10311yescharacteristic, complemented
254C22⋊C8—1031no—
255C22⋊C8C2×D10311yescharacteristic, complemented
256C4×C8—1031no—
257C24—21no—
258C24—2061no—
259C2×Q8—2061no—
260C2×Q8C22×D10311yescharacteristic
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—1031no—
265C2×D4—1031no—
266C2×D4—4124no—
267C2×D4—4121no—
268C2×D4—2061no—
269C2×D4—2061no—
270C2×D4—2061no—
271C2×D4—2061no—
272C2×D4—2061no—
273C2×D4—2062no—
274C2×D4C22×D10311yescharacteristic
275C2×D4C22×D10311yescharacteristic
276C22×C4—1031no—
277C22×C4—2061no—
278C22×C4—2061no—
279C22×C4—2061no—
280C22×C4C22×D10311yescharacteristic
281SD16—22no—
282SD16—41no—
283SD16—4121no—
284C2×C8—1031no—
285C2×C8—1031no—
286C2×C8—4121no—
287C2×C8—4121no—
288C2×C8C22×D10311yescharacteristic
289C2×C8C22×D10311yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—1031no—
292C4⋊C4—1031no—
293C4⋊C4—1031no—
294C4⋊C4—1031no—
295C4⋊C4—2061no—
296C4⋊C4—2061no—
297C4⋊C4—2061no—
298C4⋊C4—2061no—
299C4⋊C4—2061no—
300C4⋊C4C22×D10311yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—1031no—
303C22⋊C4—1031no—
304C22⋊C4—2061no—
305C22⋊C4—2061no—
306C22⋊C4—2061no—
307C22⋊C4—2061no—
308C42—1031no—
309C42—2061no—
310C23—21no—
311C23—21no—
312C23—42no—
313C23—42no—
314C23—81no—
315C23—8241no—
316C23—1031no—
317C23—4122no—
318C23—4122no—
319C23—2061no—
320C23D4×D10311yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—8241no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—8241no—
329D4—1034no—
330D4—4122no—
331D4—4122no—
332D4—4122no—
333D4—4122no—
334D4—2061no—
335D4—2061no—
336D4#1311010412yes—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—8241no—
342C2×C4—8241no—
343C2×C4—1031no—
344C2×C4—1031no—
345C2×C4—1031no—
346C2×C4—4122no—
347C2×C4—2061no—
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—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—84no—
367C22—8244no—
368C22—1032no—
369C22—4121no—
370C22—4121no—
371C22—4121no—
372C22—2061no—
373C22—2061no—
374C22SD16×D10312yes—
375C22C2×D4×D10311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—1032no—
380C4—4121no—
381C4—4121no—
382C4—4121no—
383C4—2061no—
384C4—2061no—
385C4C2×#1311010411yescharacteristic
386C4#1569306611yescharacteristic
387C2—22no—
388C2—42no—
389C2—81no—
390C2—8241no—
391C2—2062no—
392C2#2026842811yescharacteristic
393C2C2×SD16×D10311yescharacteristic
394C2#2026859511yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#450×C103C2
socleC22×C103C22×D4
prime radicalD4×C22⋊D103C2
hypercenter#450D103
hypocenterC103#3295
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #20268499C2semidirect
3. #20268136C2semidirect
4. #20268110C2semidirect
5. #20268108C2semidirect
6. #20268079C2semidirect
7. #20268022C2semidirect
8. #20268017C2semidirect
9. #20267989C2semidirect
10. #20267940C2semidirect
11. SD16×Dic103C2semidirect
12. (C22⋊D103)⋊C8C2semidirect
13. C2×#15692942C2semidirect
14. #102×D103C2semidirect
15. #450×C103C2semidirect
18. C2×#13110092C22semidirect
19. C22×C103⋊C8C22semidirect
20. C2×C8×D103C22semidirect
21. #15693020C22semidirect
26. #15692997C22semidirect
32. Q8×Dic103C22semidirect
36. C2×C4⋊Dic103C22semidirect
37. C4⋊C4×D103C22semidirect
38. #15692953C22semidirect
39. #15692953C22semidirect
40. #15692952C22semidirect
41. Dic103⋊C8C22semidirect
42. #15692945C22semidirect
43. #15692943C22semidirect
44. #15692943C22semidirect
47. #15692942C22semidirect
48. #15692942C22semidirect
49. #15692941C22semidirect
50. (C2×D103)⋊C8C22semidirect
51. C8×Dic103C22semidirect
54. C2×SD16×C103C22semidirect
55. C22⋊Q8×C103C22semidirect
57. #102×C103C22semidirect
58. C22⋊C8×C103C22semidirect
141. C22⋊D103SD16semidirect
198. C103#3295semidirect
209. #450D103semidirect
219. C2×SD16C2×D103semidirect
228. C22⋊Q8C2×D103semidirect
253. #102C2×D103semidirect
255. C22⋊C8C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202684992
D4×C22⋊D1032
#202681362
#202681102
#202681082
#202680792
#202680222
#202680172
#202679892
#202679402
SD16×Dic1032
(C22⋊D103)⋊C82
C2×#156929422
#102×D1032
#450×C1032
#3295103