Finite Group Databasebeta

← #14574551

Subgroups — #14574551

Order 2432.

532 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927089C211yesmaximal, characteristic, complemented
2C2×#10597386C211yesmaximal, characteristic, complemented
3#11926919C212yesmaximal, complemented
4#11926889C212yesmaximal, complemented
5#11926738C212yesmaximal, complemented
6#11926737C212yesmaximal, complemented
7#11926680C211yesmaximal, characteristic, complemented
8#11926678C211yesmaximal, characteristic, complemented
9#11926677C211yesmaximal, characteristic, complemented
10#11926594C211yesmaximal, characteristic, complemented
11C19×#447C211yesmaximal, characteristic, complemented
12C22×D4×C19C2211yescharacteristic
13C22×C22⋊D19—21no—
14C22×C22⋊D19—21no—
15C2×#64543—21no—
16C22×D76C2211yescharacteristic
17C2×D8×C19C2212yescomplemented
18C19×#121C2211yescharacteristic
19#10597386—21no—
20#10597386—21no—
21#10597386C2212yes—
22#10597386C2212yes—
23#10597386C2211yescharacteristic, complemented
24#10597385—21no—
25D4×Dic19C2211yescharacteristic, complemented
26C2×#64525C2212yescomplemented
27C2×#64525C2212yescomplemented
28#10597376C2211yescharacteristic
29C2×C4×Dic19C2211yescharacteristic
30C2×D152C2212yescomplemented
31#10597339C2211yescharacteristic, complemented
32#10597334C2211yescharacteristic, complemented
33#10597331—21no—
34(C22⋊D19)⋊C4—21no—
35C19×#102C2212yescomplemented
36C19×C22⋊C8C2211yescharacteristic
37#10597289C2212yescomplemented
38C22⋊(C19⋊C8)C2211yescharacteristic
39#10597278C2212yescomplemented
40Dic19⋊C8C2212yescomplemented
41C8×Dic19C2212yescomplemented
42#10597266C2212yescomplemented
43C24×C19—21no—
44C23×D19—21no—
45C2×D4×C19—21no—
46C2×D4×C19—21no—
47C2×D4×C19—42no—
48C2×D4×C19C2311yescharacteristic
49C2×D4×C19C2312yes—
50C22×C4×C19C2311yescharacteristic
51C2×C22⋊D19—21no—
52C2×C22⋊D19—21no—
53C2×C22⋊D19—22no—
54C2×C22⋊D19—22no—
55C2×C22⋊D19—22no—
56C2×C22⋊D19—22no—
57C2×C22⋊D19—21no—
58C2×C22⋊D19—44no—
59C2×C22⋊D19—44no—
60C22×Dic19—21no—
61C22×Dic19D411yescharacteristic
62C22×Dic19D411yescharacteristic
63#64543—44no—
64C2×D76—21no—
65C2×D76—42no—
66C2×D76C2311yescharacteristic
67C2×D76C2312yes—
68C2×C4×D19—21no—
69C2×Dic38—21no—
70D8×C19—42no—
71C2×C8×C19C2312yes—
72C4⋊C4×C19C2311yescharacteristic
73C22⋊C4×C19—21no—
74C22⋊Dic19—21no—
75#64525—42no—
76#64525—42no—
77(C2×D19)⋊C4—21no—
78(C2×D19)⋊C4—21no—
79C4⋊Dic19C2311yescharacteristic
80Dic19⋊C4—21no—
81C4×Dic19D411yescharacteristic
82C4×Dic19D411yescharacteristic
83C4×Dic19C2311yescharacteristic
84C4×Dic19C2311yescharacteristic
85C2×C19⋊C8C2312yes—
86D152—42no—
87C23×C19—21no—
88C23×C19—22no—
89C23×C19—42no—
90C23×C19—42no—
91C23×C19—42no—
92C23×C19C2×D411yescharacteristic
93C22×D19—21no—
94C22×D19—22no—
95C22×D19—42no—
96C22×D19—42no—
97C22×D19—42no—
98D4×C19—22no—
99D4×C19—22no—
100D4×C19—22no—
101D4×C19—42no—
102D4×C19—42no—
103C2×C4×C19—22no—
104C2×C4×C19—21no—
105C2×C4×C19C2×D411yescharacteristic
106C2×C4×C19C2411yescharacteristic
107C22⋊D19—44no—
108C22⋊D19—42no—
109C22⋊D19—42no—
110C22⋊D19—44no—
111C22⋊D19—44no—
112C22⋊D19—42no—
113C22⋊D19—44no—
114C2×Dic19—22no—
115C2×Dic19—21no—
116C2×Dic19—42no—
117C2×Dic19D814yescomplemented
118C2×Dic19C2×D411yescharacteristic
119C2×Dic19C2×D411yescharacteristic
120C2×Dic19C2×D411yescharacteristic
121C2×Dic19C2×D411yescharacteristic
122D76—22no—
123D76—22no—
124D76—22no—
125D76—42no—
126C4×D19—42no—
127Dic38—42no—
128C8×C19—22no—
129C19⋊C8—22no—
130#3205—191nomaximal, Sylow
131C22×C19—21no—
132C22×C19—21no—
133C22×C19—42no—
134C22×C19—41no—
135C22×C19—41no—
136C22×C19—42no—
137C22×C19—42no—
138C22×C19—41no—
139C22×C19—84no—
140C22×C19C2×D812yes—
141C22×C19C22×D411yescharacteristic
142C2×D19—42no—
143C2×D19—41no—
144C2×D19—41no—
145C2×D19—42no—
146C2×D19—42no—
147C2×D19—41no—
148C2×D19—84no—
149C4×C19—21no—
150C4×C19—41no—
151C4×C19H(5,𝔽2)12yes—
152Dic19—21no—
153Dic19—41no—
154Dic19C2×D812yes—
155Dic19C2×D812yes—
156Dic19AGL(1,ℤ/8)12yes—
157#532—191no—
158C2×#127—191no—
159#493—192no—
160#486—192no—
161#459—192no—
162#459—192no—
163#447—191no—
164#447—191no—
165#447—191no—
166#447D1911yescharacteristic, complemented
167#431—191no—
168C2×C19—22no—
169C2×C19—81no—
170C2×C19—82no—
171C2×C19#53511yescharacteristic
172C2×C19C22×D811yescharacteristic
173C2×C19C2×AGL(1,ℤ/8)11yescharacteristic
174D19—81no—
175D19—82no—
176C2×#41—381no—
177C22×D4—191no—
178C22×D4—381no—
179C22×D4—381no—
180C22×D4C2×D1911yescharacteristic
181C2×D8—192no—
182C2×D8—192no—
183C2×D8—192no—
184C2×D8C2×D1912yescomplemented
185C4⋊Q8—191no—
186#127—192no—
187#127—192no—
188#127—191no—
189#127—381no—
190#127—381no—
191#124—381no—
192#121—191no—
193#121—381no—
194#121C2×D1911yescharacteristic
195C4×D4—191no—
196C4×D4—191no—
197C4×D4—381no—
198C2×C42—191no—
199C4⋊C8—192no—
200#102—192no—
201#102—192no—
202#102—192no—
203#102C2×D1912yescomplemented
204C22⋊C8—191no—
205C22⋊C8C2×D1911yescharacteristic
206C4×C8—192no—
207C19#320511yescharacteristic, complemented, Sylow
208C24—21no—
209C24—381no—
210#41—764no—
211C2×Q8—381no—
212C2×D4—21no—
213C2×D4—21no—
214C2×D4—42no—
215C2×D4—192no—
216C2×D4—191no—
217C2×D4—381no—
218C2×D4—381no—
219C2×D4—382no—
220C2×D4—382no—
221C2×D4—382no—
222C2×D4—382no—
223C2×D4—381no—
224C2×D4—381no—
225C2×D4—762no—
226C2×D4—764no—
227C2×D4—764no—
228C2×D4C22×D1912yes—
229C2×D4C22×D1911yescharacteristic
230C22×C4—191no—
231C22×C4—191no—
232C22×C4—381no—
233C22×C4—381no—
234C22×C4C22×D1911yescharacteristic
235D8—42no—
236D8—762no—
237D8—762no—
238D8—762no—
239C2×C8—192no—
240C2×C8C22×D1912yes—
241C4⋊C4—191no—
242C4⋊C4—381no—
243C4⋊C4C22×D1911yescharacteristic
244C22⋊C4—21no—
245C22⋊C4—381no—
246C22⋊C4—381no—
247C22⋊C4—381no—
248C42—191no—
249C42—191no—
250C42—191no—
251C42—191no—
252C23—21no—
253C23—22no—
254C23—42no—
255C23—42no—
256C23—42no—
257C23—381no—
258C23—382no—
259C23—762no—
260C23—762no—
261C23—762no—
262C23D4×D1911yescharacteristic
263Q8—762no—
264D4—22no—
265D4—22no—
266D4—22no—
267D4—42no—
268D4—42no—
269D4—382no—
270D4—382no—
271D4—382no—
272D4—762no—
273D4—764no—
274D4—764no—
275D4—764no—
276D4—762no—
277D4—762no—
278D4—764no—
279D4—762no—
280C2×C4—22no—
281C2×C4—21no—
282C2×C4—191no—
283C2×C4—191no—
284C2×C4—191no—
285C2×C4—194no—
286C2×C4—191no—
287C2×C4—382no—
288C2×C4—381no—
289C2×C4—762no—
290C2×C4—762no—
291C2×C4D4×D1911yescharacteristic
292C2×C4C23×D1911yescharacteristic
293C8—22no—
294C8—382no—
295C22—21no—
296C22—21no—
297C22—41no—
298C22—42no—
299C22—42no—
300C22—41no—
301C22—42no—
302C22—41no—
303C22—84no—
304C22—761no—
305C22—762no—
306C22—762no—
307C22—761no—
308C22—762no—
309C22—761no—
310C22—1524no—
311C22D8×D1912yes—
312C22C2×D4×D1911yescharacteristic
313C4—21no—
314C4—41no—
315C4—192no—
316C4—192no—
317C4—192no—
318C4—381no—
319C4—761no—
320C4#1059743012yes—
321C2—22no—
322C2—82no—
323C2—81no—
324C2—1522no—
325C2—1521no—
326C2#1192710911yescharacteristic
327C2C2×D8×D1911yescharacteristic
328C2AGL(1,ℤ/8)×D1911yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#447C2
socleC22×C19C22×D4
hypercenter#447D19
hypocenterC19#3205
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #11927089C2semidirect
2. C2×#10597386C2semidirect
3. #11926919C2semidirect
4. #11926889C2semidirect
5. #11926738C2semidirect
6. #11926737C2semidirect
7. #11926680C2semidirect
8. #11926678C2semidirect
9. #11926677C2semidirect
10. #11926594C2semidirect
11. C19×#447C2semidirect
17. C2×D8×C19C22semidirect
23. #10597386C22semidirect
25. D4×Dic19C22semidirect
26. C2×#64525C22semidirect
27. C2×#64525C22semidirect
30. C2×D152C22semidirect
31. #10597339C22semidirect
32. #10597334C22semidirect
35. C19×#102C22semidirect
37. #10597289C22semidirect
39. #10597278C22semidirect
40. Dic19⋊C8C22semidirect
41. C8×Dic19C22semidirect
42. #10597266C22semidirect
117. C2×Dic19D8semidirect
166. #447D19semidirect
184. C2×D8C2×D19semidirect
203. #102C2×D19semidirect
207. C19#3205semidirect

Maximal subgroups

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

subgroupindex
#119270892
C2×#105973862
#119269192
#119268892
#119267382
#119267372
#119266802
#119266782
#119266772
#119265942
C19×#4472
#320519