Finite Group Databasebeta

← #14573986

Subgroups — #14573986

Order 2432.

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#11927171C211yesmaximal, characteristic, complemented
2#11927112C211yesmaximal, characteristic
3#11926909C211yesmaximal, characteristic, complemented
4#11926907C211yesmaximal, characteristic, complemented
5#11926905C211yesmaximal, characteristic, complemented
6#11926900C211yesmaximal, characteristic, complemented
7#11926898C211yesmaximal, characteristic, complemented
8#11926892C211yesmaximal, characteristic, complemented
9#11926889C211yesmaximal, characteristic, complemented
10#11926547C211yesmaximal, characteristic, complemented
11#11926544C211yesmaximal, characteristic, complemented
12#11926539C211yesmaximal, characteristic, complemented
13#102×D19C211yesmaximal, characteristic, complemented
14#11926501C211yesmaximal, characteristic, complemented
15C19×#489C211yesmaximal, characteristic, complemented
16C2×#64545C2211yescharacteristic
17C2×D4×D19C2211yescharacteristic
18C19×C4⋊Q8C2211yescharacteristic, complemented
19C19×#124C2211yescharacteristic
20#10597393C2211yescharacteristic
21#10597392—21no—
22#10597390—21no—
23#10597386C2211yescharacteristic
24C2×#64515C2211yescharacteristic
25C2×C8×D19C2211yescharacteristic
26#10597342—21no—
27#10597338C2211yescharacteristic
28C4⋊C4×D19C2211yescharacteristic
29#10597336C2211yescharacteristic, complemented
30#10597335—21no—
31#10597334C2211yescharacteristic, complemented
32#10597330—21no—
33#10597330—21no—
34#10597328—21no—
35#10597328—21no—
36#10597320C2211yescharacteristic
37#10597318C2211yescharacteristic
38#10597316C2211yescharacteristic, complemented
39C19×#103C2211yescharacteristic, complemented
40C19×#103C2211yescharacteristic, complemented
41C19×#102C2211yescharacteristic
42C19×#102C2211yescharacteristic
43C19×#97C2211yescharacteristic, complemented
44#10597292C2211yescharacteristic, complemented
45#10597292C2211yescharacteristic, complemented
46#10597289C2211yescharacteristic
47#10597289C2211yescharacteristic
48#10597278C2211yescharacteristic
49#10597278C2211yescharacteristic
50#10597278C2211yescharacteristic, complemented
51#10597278C2211yescharacteristic, complemented
52#10597272C2211yescharacteristic, complemented
53C8×Dic19C2211yescharacteristic, complemented
54#10597266C2211yescharacteristic
55#10597266C2211yescharacteristic
56#10597266C2211yescharacteristic, complemented
57#10597266C2211yescharacteristic, complemented
58C4×C19⋊C8C2211yescharacteristic, complemented
59C23×D19—21no—
60C2×Q8×C19—21no—
61C2×Q8×C19C2311yescharacteristic
62C2×D4×C19C2311yescharacteristic
63C2×C22⋊D19—21no—
64C2×C22⋊D19—21no—
65C2×C22⋊D19—21no—
66#64545—22no—
67#64545—22no—
68D4×D19—22no—
69D4×D19—22no—
70C2×D76—21no—
71C2×D76—21no—
72C2×D76—21no—
73C2×D76C2311yescharacteristic
74C2×D76C2311yescharacteristic
75C2×C4×D19—21no—
76C2×C4×D19—21no—
77C2×C4×D19C2311yescharacteristic
78C2×Dic38—21no—
79C2×C8×C19C2311yescharacteristic
80C2×C8×C19C2311yescharacteristic
81C4⋊C4×C19—21no—
82C4⋊C4×C19C2311yescharacteristic
83C4⋊C4×C19C2311yescharacteristic
84C22⋊C4×C19—21no—
85C22⋊C4×C19—21no—
86C42×C19C2311yescharacteristic
87(C2×D19)⋊C4—21no—
88(C2×D19)⋊C4—21no—
89(C2×D19)⋊C4—21no—
90(C2×D19)⋊C4D411yescharacteristic
91(C2×D19)⋊C4D411yescharacteristic
92C4⋊Dic19—21no—
93C4⋊Dic19C2311yescharacteristic
94C4⋊Dic19C2311yescharacteristic
95Dic19⋊C4—21no—
96Dic19⋊C4—21no—
97Dic19⋊C4—21no—
98Dic19⋊C4—21no—
99Dic19⋊C4—21no—
100Dic19⋊C4D411yescharacteristic
101Dic19⋊C4D411yescharacteristic
102C4×Dic19—21no—
103C4×Dic19C2311yescharacteristic
104C2×C19⋊C8C2311yescharacteristic
105C2×C19⋊C8C2311yescharacteristic
106#64515—22no—
107C8×D19—22no—
108C23×C19—21no—
109C22×D19—21no—
110C22×D19—21no—
111C22×D19—42no—
112C22×D19—81no—
113C22×D19—81no—
114C22×D19C2×D411yescharacteristic
115Q8×C19—21no—
116Q8×C19—21no—
117Q8×C19—81no—
118D4×C19—21no—
119D4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19C2×D411yescharacteristic
124C2×C4×C19C2×D411yescharacteristic
125C2×C4×C19C2411yescharacteristic
126C22⋊D19—42no—
127C22⋊D19—81no—
128C22⋊D19—81no—
129C2×Dic19—21no—
130C2×Dic19—21no—
131C2×Dic19C2×D411yescharacteristic
132C2×Dic19C2×D411yescharacteristic
133C2×Dic19C2×D411yescharacteristic
134D76—21no—
135D76—21no—
136D76—21no—
137D76—21no—
138D76—42no—
139D76—81no—
140D76—81no—
141C4×D19—42no—
142C4×D19—81no—
143C4×D19#4112yes—
144C4×D19#4112yes—
145Dic38—81no—
146C8×C19—21no—
147C8×C19—21no—
148C19⋊C8—21no—
149C19⋊C8—21no—
150#3136—191nomaximal, Sylow
151C22×C19—41no—
152C22×C19—41no—
153C22×C19—41no—
154C22×C19C22×D411yescharacteristic
155C2×D19—21no—
156C2×D19—21no—
157C2×D19—41no—
158C2×D19—41no—
159C2×D19—41no—
160C2×D19—41no—
161C2×D19—41no—
162C2×D19—41no—
163C2×D19—84no—
164C2×D19#12412yes—
165C4×C19—21no—
166C4×C19—21no—
167C4×C19—41no—
168C4×C19—41no—
169C4×C19—41no—
170C4×C19C2×#4111yescharacteristic
171C4×C19C2×#4111yescharacteristic
172Dic19—21no—
173Dic19—21no—
174Dic19—41no—
175Dic19—41no—
176Dic19#12412yes—
177#544—191no—
178#535—191no—
179#490—191no—
180#490—191no—
181#489—191no—
182#489D1911yescharacteristic, complemented
183#488—191no—
184#488—191no—
185#486—191no—
186#486—191no—
187#418—191no—
188#417—191no—
189#416—191no—
190C2×#102—191no—
191#405—191no—
192C2×C19—81no—
193C2×C19C2×#12411yescharacteristic
194C2×C19#57611yescharacteristic
195C2×C19#57711yescharacteristic
196D19—22no—
197D19—81no—
198D19—81no—
199C2×#41—191no—
200C22×D4—191no—
201C2×M16—191no—
202C22×C8—191no—
203C4⋊Q8—191no—
204C4⋊Q8—381no—
205C4⋊Q8C2×D1911yescharacteristic, complemented
206#127—191no—
207#127—191no—
208#125—191no—
209#125—191no—
210#125—381no—
211#124—191no—
212#124C2×D1911yescharacteristic
213C22⋊Q8—381no—
214C22⋊Q8—381no—
215#121—381no—
216#121—381no—
217#120—381no—
218#120—381no—
219#117—191no—
220#117—191no—
221C2×C4⋊C4—191no—
222#103—191no—
223#103—191no—
224#103C2×D1911yescharacteristic, complemented
225#103C2×D1911yescharacteristic, complemented
226#102—191no—
227#102—191no—
228#102—191no—
229#102—191no—
230#102—191no—
231#102—191no—
232#102—191no—
233#102—191no—
234#102—191no—
235#102—191no—
236#102C2×D1911yescharacteristic
237#102C2×D1911yescharacteristic
238#97—191no—
239#97C2×D1911yescharacteristic, complemented
240C4×C8—191no—
241C4×C8—191no—
242C19#313611yescharacteristic, complemented, Sylow
243C24—381no—
244#41—382no—
245#41—382no—
246C2×Q8—21no—
247C2×Q8—381no—
248C2×Q8C22×D1911yescharacteristic
249C2×D4—191no—
250C2×D4—191no—
251C2×D4—381no—
252C2×D4—382no—
253C2×D4—382no—
254C2×D4—381no—
255C2×D4—381no—
256C2×D4—381no—
257C2×D4—381no—
258C2×D4—381no—
259C2×D4C22×D1911yescharacteristic
260C22×C4—191no—
261C22×C4—381no—
262C22×C4—381no—
263M16—382no—
264C2×C8—191no—
265C2×C8—191no—
266C2×C8—382no—
267C2×C8C22×D1911yescharacteristic
268C2×C8C22×D1911yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—191no—
271C4⋊C4—191no—
272C4⋊C4—191no—
273C4⋊C4—191no—
274C4⋊C4—381no—
275C4⋊C4—381no—
276C4⋊C4—381no—
277C4⋊C4—381no—
278C4⋊C4—381no—
279C4⋊C4—381no—
280C4⋊C4C22×D1911yescharacteristic
281C4⋊C4C22×D1911yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—191no—
285C22⋊C4—191no—
286C22⋊C4—381no—
287C22⋊C4—381no—
288C22⋊C4—381no—
289C42—191no—
290C42—381no—
291C42C22×D1911yescharacteristic
292C23—21no—
293C23—191no—
294C23—381no—
295C23—381no—
296C23—762no—
297C23—1521no—
298C23—1521no—
299Q8—21no—
300Q8—21no—
301Q8—81no—
302Q8—1521no—
303D4—21no—
304D4—21no—
305D4—381no—
306D4—381no—
307D4—381no—
308D4—381no—
309D4—762no—
310D4—762no—
311D4—1521no—
312D4—1521no—
313D4—1521no—
314D4—1521no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—191no—
319C2×C4—192no—
320C2×C4—192no—
321C2×C4—191no—
322C2×C4—191no—
323C2×C4—381no—
324C2×C4—381no—
325C2×C4—762no—
326C2×C4—1521no—
327C2×C4D4×D1911yescharacteristic
328C2×C4D4×D1911yescharacteristic
329C2×C4C23×D1911yescharacteristic
330C8—21no—
331C8—21no—
332C8—381no—
333C8—381no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—192no—
338C22—381no—
339C22—381no—
340C22—761no—
341C22—761no—
342C22—761no—
343C22—761no—
344C22—761no—
345C22—761no—
346C22—1524no—
347C22C2×D4×D1911yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—192no—
354C4—381no—
355C4—381no—
356C4—761no—
357C4—761no—
358C4#41×D1911yescharacteristic
359C4#41×D1911yescharacteristic
360C2—81no—
361C2—382no—
362C2—1521no—
363C2—1521no—
364C2#124×D1911yescharacteristic
365C2#1192734811yescharacteristic
366C2#1192735311yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#489C2
socleC22×C19C22×D4
prime radical#11927112C2
hypercenter#489D19
hypocenterC19#3136
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #11927171C2semidirect
3. #11926909C2semidirect
4. #11926907C2semidirect
5. #11926905C2semidirect
6. #11926900C2semidirect
7. #11926898C2semidirect
8. #11926892C2semidirect
9. #11926889C2semidirect
10. #11926547C2semidirect
11. #11926544C2semidirect
12. #11926539C2semidirect
13. #102×D19C2semidirect
14. #11926501C2semidirect
15. C19×#489C2semidirect
18. C19×C4⋊Q8C22semidirect
29. #10597336C22semidirect
31. #10597334C22semidirect
38. #10597316C22semidirect
39. C19×#103C22semidirect
40. C19×#103C22semidirect
43. C19×#97C22semidirect
44. #10597292C22semidirect
45. #10597292C22semidirect
50. #10597278C22semidirect
51. #10597278C22semidirect
52. #10597272C22semidirect
53. C8×Dic19C22semidirect
56. #10597266C22semidirect
57. #10597266C22semidirect
58. C4×C19⋊C8C22semidirect
182. #489D19semidirect
205. C4⋊Q8C2×D19semidirect
224. #103C2×D19semidirect
225. #103C2×D19semidirect
239. #97C2×D19semidirect
242. C19#3136semidirect

Maximal subgroups

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

subgroupindex
#119271712
#119271122
#119269092
#119269072
#119269052
#119269002
#119268982
#119268922
#119268892
#119265472
#119265442
#119265392
#102×D192
#119265012
C19×#4892
#313619