Finite Group Databasebeta

← #14574416

Subgroups — #14574416

Order 2432.

420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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#11927055C211yesmaximal, characteristic
2#11926882C212yesmaximal, complemented
3#11926874C211yesmaximal, characteristic, complemented
4#11926857C211yesmaximal, characteristic, complemented
5#11926783C212yesmaximal, complemented
6#11926775C212yesmaximal, complemented
7#11926704C212yesmaximal, complemented
8#11926700C211yesmaximal, characteristic, complemented
9#11926683C211yesmaximal, characteristic, complemented
10C2×C22⋊(C19⋊C8)C211yesmaximal, characteristic, complemented
11C2×C19×C22⋊Q8C211yesmaximal, characteristic, complemented
12C22×Q8×C19C2211yescharacteristic
13C23×C4×C19C2211yescharacteristic
14C2×#64541C2211yescharacteristic
15C19×C22⋊Q8—21no—
16C19×C22⋊Q8—21no—
17C19×C22⋊Q8C2212yes—
18C19×C22⋊Q8C2212yes—
19C2×C4⋊C4×C19—21no—
20C2×C4⋊C4×C19C2211yescharacteristic
21C2×C22⋊C4×C19—21no—
22#10597399—21no—
23C2×#64528C2212yescomplemented
24C2×#64527C2212yescomplemented
25#10597376C2211yescharacteristic
26#10597376C2211yescharacteristic
27#10597375—21no—
28C4×C22⋊D19—21no—
29C4×C22⋊D19—21no—
30#10597372C2211yescharacteristic
31#10597370C2211yescharacteristic
32#10597370C2211yescharacteristic
33C22×C19⋊C8C2212yes—
34#10597292C2212yescomplemented
35#10597292C2212yescomplemented
36C22⋊(C19⋊C8)C2211yescharacteristic
37C22⋊(C19⋊C8)C2211yescharacteristic
38C22⋊(C19⋊C8)C2212yes—
39#10597267C2212yescomplemented
40#10597266C2212yescomplemented
41#10597265C2212yescomplemented
42#10597264C2212yescomplemented
43C24×C19D411yescharacteristic
44C2×Q8×C19—21no—
45C2×Q8×C19—42no—
46C2×Q8×C19C2312yes—
47C22×C4×C19—21no—
48C22×C4×C19—21no—
49C22×C4×C19—42no—
50C22×C4×C19D411yescharacteristic
51C22×C4×C19D411yescharacteristic
52C22×C4×C19D411yescharacteristic
53C22×C4×C19C2311yescharacteristic
54C22×C4×C19C2311yescharacteristic
55C22×C4×C19C2311yescharacteristic
56C2×C22⋊D19—21no—
57C2×C22⋊D19—21no—
58C2×C22⋊D19—21no—
59#64541—42no—
60C2×D76C2311yescharacteristic
61C2×C4×D19—21no—
62C2×Dic38C2311yescharacteristic
63C4⋊C4×C19—22no—
64C4⋊C4×C19—22no—
65C4⋊C4×C19—21no—
66C4⋊C4×C19C2312yes—
67C22⋊C4×C19—22no—
68C22⋊C4×C19—22no—
69C22⋊Dic19—21no—
70C22⋊Dic19—21no—
71C22⋊Dic19—21no—
72#64528—42no—
73#64527—42no—
74(C2×D19)⋊C4—21no—
75(C2×D19)⋊C4—21no—
76C4⋊Dic19C2311yescharacteristic
77C4⋊Dic19C2311yescharacteristic
78Dic19⋊C4—21no—
79Dic19⋊C4—21no—
80C4×Dic19—21no—
81C2×C19⋊C8—42no—
82C2×C19⋊C8C2312yes—
83C2×C19⋊C8C2312yes—
84C23×C19—22no—
85C23×C19—22no—
86C23×C19—41no—
87C23×C19C2×D411yescharacteristic
88C23×C19C2×D411yescharacteristic
89C23×C19C2×D411yescharacteristic
90C22×D19—21no—
91Q8×C19—22no—
92Q8×C19—22no—
93Q8×C19—42no—
94C2×C4×C19—22no—
95C2×C4×C19—22no—
96C2×C4×C19—22no—
97C2×C4×C19—22no—
98C2×C4×C19—22no—
99C2×C4×C19—41no—
100C2×C4×C19—41no—
101C2×C4×C19—41no—
102C2×C4×C19—42no—
103C2×C4×C19—42no—
104C2×C4×C19C2×D411yescharacteristic
105C2×C4×C19C2×D411yescharacteristic
106C2×C4×C19C2×D411yescharacteristic
107C2×C4×C19C2411yescharacteristic
108C22⋊D19—42no—
109C22⋊D19—42no—
110C22⋊D19—42no—
111C2×Dic19—21no—
112C2×Dic19—21no—
113C2×Dic19—21no—
114D76—22no—
115C4×D19—42no—
116Dic38—22no—
117C19⋊C8—22no—
118C19⋊C8—22no—
119#3190—191nomaximal, Sylow
120C22×C19—21no—
121C22×C19—21no—
122C22×C19—21no—
123C22×C19—21no—
124C22×C19—21no—
125C22×C19—21no—
126C22×C19—21no—
127C22×C19—44no—
128C22×C19#13512yes—
129C22×C19#13712yes—
130C22×C19C22×D411yescharacteristic
131C2×D19—41no—
132C2×D19—41no—
133C2×D19—41no—
134C4×C19—21no—
135C4×C19—21no—
136C4×C19—21no—
137C4×C19—42no—
138C4×C19—42no—
139C4×C19H(5,𝔽2)12yes—
140Dic19—41no—
141Dic19—41no—
142Dic19—41no—
143#525—191no—
144C2×C22⋊Q8D1911yescharacteristic, complemented
145#485—192no—
146#483—191no—
147#480—191no—
148#467—192no—
149#465—192no—
150#452—192no—
151#451—191no—
152#448—191no—
153C2×C22⋊C8—191no—
154C2×C19—22no—
155C2×C19—22no—
156C2×C19—41no—
157C2×C19#53411yescharacteristic
158C2×C19C2×#13511yescharacteristic
159C2×C19C2×#13711yescharacteristic
160D19—81no—
161C2×#41—191no—
162C22×Q8C2×D1911yescharacteristic
163C23×C4C2×D1911yescharacteristic
164C2×Q16—192no—
165C2×SD16—192no—
166C22×C8—192no—
167#123—381no—
168C22⋊Q8—21no—
169C22⋊Q8—21no—
170C22⋊Q8—191no—
171C22⋊Q8—191no—
172C22⋊Q8C2×D1912yes—
173C22⋊Q8C2×D1912yes—
174#121—191no—
175#121—191no—
176#120—381no—
177C4×D4—381no—
178C4×D4—381no—
179#117—191no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4C2×D1911yescharacteristic
182C2×C22⋊C4—21no—
183#107—192no—
184#106—192no—
185#103—192no—
186#103—192no—
187#103—192no—
188#102—192no—
189C22⋊C8—191no—
190C22⋊C8—191no—
191C22⋊C8—192no—
192C19#319011yescharacteristic, complemented, Sylow
193C24C22⋊D1911yescharacteristic
194#41—762no—
195C2×Q8—21no—
196C2×Q8—42no—
197C2×Q8—191no—
198C2×Q8C22×D1912yes—
199C2×D4—191no—
200C2×D4—381no—
201C2×D4—381no—
202C2×D4—381no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—42no—
206C22×C4—381no—
207C22×C4C22⋊D1911yescharacteristic
208C22×C4C22⋊D1911yescharacteristic
209C22×C4C22⋊D1911yescharacteristic
210C22×C4C22×D1911yescharacteristic
211C22×C4C22×D1911yescharacteristic
212C22×C4C22×D1911yescharacteristic
213Q16—762no—
214SD16—762no—
215C2×C8—192no—
216C2×C8—192no—
217C2×C8—762no—
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—21no—
221C4⋊C4—191no—
222C4⋊C4—191no—
223C4⋊C4—381no—
224C4⋊C4—381no—
225C4⋊C4C22×D1912yes—
226C22⋊C4—22no—
227C22⋊C4—22no—
228C22⋊C4—381no—
229C22⋊C4—381no—
230C22⋊C4—381no—
231C22⋊C4—381no—
232C22⋊C4—381no—
233C42—381no—
234C23—22no—
235C23—22no—
236C23—41no—
237C23—381no—
238C23C2×C22⋊D1911yescharacteristic
239C23C2×C22⋊D1911yescharacteristic
240C23C2×C22⋊D1911yescharacteristic
241Q8—22no—
242Q8—22no—
243Q8—42no—
244Q8—382no—
245D4—382no—
246D4—762no—
247D4—762no—
248D4—762no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—381no—
260C2×C4—381no—
261C2×C4—381no—
262C2×C4—762no—
263C2×C4C2×C22⋊D1911yescharacteristic
264C2×C4C2×C22⋊D1911yescharacteristic
265C2×C4C2×C22⋊D1911yescharacteristic
266C2×C4C23×D1911yescharacteristic
267C8—382no—
268C8—382no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—44no—
277C22—761no—
278C22—761no—
279C22—761no—
280C22#1059738812yes—
281C22#1059739612yes—
282C22C22×C22⋊D1911yescharacteristic
283C4—21no—
284C4—21no—
285C4—21no—
286C4—42no—
287C4—42no—
288C4—761no—
289C4—761no—
290C4—761no—
291C4#1059743012yes—
292C2—22no—
293C2—22no—
294C2—41no—
295C2—1521no—
296C2#1192710311yescharacteristic
297C2C2×#1059739611yescharacteristic
298C2C2×#1059738811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC2×C19×C22⋊Q8C2
socleC22×C19C22×D4
prime radical#11927055C2
hypercenterC2×C22⋊Q8D19
hypocenterC19#3190
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11926882C2semidirect
3. #11926874C2semidirect
4. #11926857C2semidirect
5. #11926783C2semidirect
6. #11926775C2semidirect
7. #11926704C2semidirect
8. #11926700C2semidirect
9. #11926683C2semidirect
10. C2×C22⋊(C19⋊C8)C2semidirect
11. C2×C19×C22⋊Q8C2semidirect
23. C2×#64528C22semidirect
24. C2×#64527C22semidirect
34. #10597292C22semidirect
35. #10597292C22semidirect
39. #10597267C22semidirect
40. #10597266C22semidirect
41. #10597265C22semidirect
42. #10597264C22semidirect
144. C2×C22⋊Q8D19semidirect
192. C19#3190semidirect

Maximal subgroups

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

subgroupindex
#119270552
#119268822
#119268742
#119268572
#119267832
#119267752
#119267042
#119267002
#119266832
C2×C22⋊(C19⋊C8)2
C2×C19×C22⋊Q82
#319019