Finite Group Databasebeta

← #14574382

Subgroups — #14574382

Order 2432.

520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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#121×D19C212yesmaximal, complemented
2#11926859C212yesmaximal, complemented
3#11926856C212yesmaximal, complemented
4#11926780C211yesmaximal, characteristic, complemented
5#11926778C212yesmaximal, complemented
6#11926679C212yesmaximal, complemented
7#11926676C212yesmaximal, complemented
8C2×(C2×D19)⋊C8C211yesmaximal, characteristic, complemented
9C19×#466C211yesmaximal, characteristic, complemented
10C2×D4×D19—22no—
11C2×D4×D19C2212yescomplemented
12C22×C4×D19C2211yescharacteristic
13C2×D8×C19C2211yescharacteristic, complemented
14C22×C8×C19C2211yescharacteristic, complemented
15C19×#121C2212yescomplemented
16#10597385—22no—
17#10597384C2212yes—
18C2×#64525C2212yescomplemented
19#10597376C2212yescomplemented
20C22×C19⋊C8C2211yescharacteristic, complemented
21C2×D152C2211yescharacteristic, complemented
22#10597341C2212yes—
23C4⋊C4×D19C2212yescomplemented
24#10597330—22no—
25C22⋊C4×D19—22no—
26C19×#107C2211yescharacteristic, complemented
27C19×#102C2212yescomplemented
28#10597289C2212yescomplemented
29#10597278C2212yescomplemented
30(C2×D19)⋊C8C2212yescomplemented
31(C2×D19)⋊C8C2212yescomplemented
32#10597275C2211yescharacteristic, complemented
33#10597266C2212yescomplemented
34#10597264C2212yescomplemented
35C23×D19—22no—
36C23×D19D411yescharacteristic
37C2×D4×C19—22no—
38C2×D4×C19C2312yes—
39C22×C4×C19C2311yescharacteristic
40C2×C22⋊D19—22no—
41C2×C22⋊D19—22no—
42C2×C22⋊D19—22no—
43C22×Dic19D411yescharacteristic
44D4×D19—42no—
45D4×D19—42no—
46D4×D19—48no—
47C2×D76—22no—
48C2×D76C2312yes—
49C2×C4×D19—22no—
50C2×C4×D19—41no—
51C2×C4×D19—41no—
52C2×C4×D19D412yes—
53C2×C4×D19C2312yes—
54D8×C19—41no—
55C2×C8×C19—41no—
56C2×C8×C19C2311yescharacteristic
57C2×C8×C19C2311yescharacteristic
58C4⋊C4×C19C2312yes—
59C22⋊C4×C19—22no—
60C22⋊Dic19—22no—
61#64525—42no—
62(C2×D19)⋊C4—22no—
63(C2×D19)⋊C4—22no—
64C4⋊Dic19C2312yes—
65Dic19⋊C4—22no—
66C2×C19⋊C8—41no—
67C2×C19⋊C8C2312yes—
68D152—41no—
69C23×C19—22no—
70C23×C19C2×D411yescharacteristic
71C22×D19—22no—
72C22×D19—41no—
73C22×D19—41no—
74C22×D19—44no—
75C22×D19—44no—
76C22×D19—44no—
77C22×D19D814yescomplemented
78C22×D19C2×D412yes—
79D4×C19—22no—
80D4×C19—22no—
81D4×C19—44no—
82C2×C4×C19—21no—
83C2×C4×C19—21no—
84C2×C4×C19—22no—
85C2×C4×C19C2×D411yescharacteristic
86C2×C4×C19C2411yescharacteristic
87C22⋊D19—44no—
88C22⋊D19—44no—
89C22⋊D19—44no—
90C2×Dic19—22no—
91C2×Dic19—41no—
92C2×Dic19C2×D412yes—
93D76—22no—
94D76—22no—
95D76—44no—
96C4×D19—22no—
97C4×D19—22no—
98C4×D19—42no—
99C4×D19—44no—
100C8×C19—21no—
101C8×C19—21no—
102C19⋊C8—22no—
103#3186—191nomaximal, Sylow
104C22×C19—21no—
105C22×C19—21no—
106C22×C19—42no—
107C22×C19—42no—
108C22×C19—42no—
109C22×C19C2×D812yes—
110C22×C19C22×D411yescharacteristic
111C2×D19—22no—
112C2×D19—22no—
113C2×D19—44no—
114C2×D19—42no—
115C2×D19—42no—
116C2×D19—42no—
117C2×D19—88no—
118C2×D19C2×D814yes—
119C4×C19—21no—
120C4×C19—42no—
121C4×C19H(5,𝔽2)11yescharacteristic
122C4×C19H(5,𝔽2)11yescharacteristic
123Dic19—22no—
124Dic19—42no—
125C2×#121—192no—
126#480—192no—
127#480—192no—
128#466—191no—
129#466—192no—
130#466D1911yescharacteristic, complemented
131#447—192no—
132#447—192no—
133C2×C22⋊C8—191no—
134C2×C19—22no—
135C2×C19—82no—
136C2×C19#53411yescharacteristic
137C2×C19C22×D811yescharacteristic
138C2×C19#57511yescharacteristic
139D19—24no—
140D19—82no—
141C22×D4—192no—
142C22×D4—382no—
143C23×C4—191no—
144C2×D8—192no—
145C2×D8—191no—
146C2×D8C2×D1911yescharacteristic, complemented
147C22×C8—191no—
148C22×C8C2×D1911yescharacteristic, complemented
149#121—192no—
150#121—192no—
151#121—192no—
152#121—382no—
153#121—382no—
154#121C2×D1912yescomplemented
155C2×C4⋊C4—192no—
156C2×C22⋊C4—382no—
157#107—191no—
158#107—192no—
159#107C2×D1911yescharacteristic, complemented
160#102—192no—
161#102—192no—
162#102—192no—
163#102C2×D1912yescomplemented
164C22⋊C8—192no—
165C22⋊C8—192no—
166C19#318611yescharacteristic, complemented, Sylow
167C24—191no—
168C24—382no—
169C2×D4—22no—
170C2×D4—192no—
171C2×D4—382no—
172C2×D4—382no—
173C2×D4—382no—
174C2×D4—382no—
175C2×D4—762no—
176C2×D4—762no—
177C2×D4—768no—
178C2×D4C22×D1912yes—
179C22×C4—191no—
180C22×C4—192no—
181C22×C4—192no—
182C22×C4—382no—
183C22×C4—761no—
184C22×C4—761no—
185C22×C4C22×D1911yescharacteristic
186D8—41no—
187D8—761no—
188D8—762no—
189C2×C8—41no—
190C2×C8—192no—
191C2×C8—761no—
192C2×C8C22×D1911yescharacteristic
193C2×C8C22×D1911yescharacteristic
194C4⋊C4—192no—
195C4⋊C4—382no—
196C4⋊C4C22×D1912yes—
197C22⋊C4—22no—
198C22⋊C4—382no—
199C22⋊C4—382no—
200C22⋊C4—382no—
201C23—22no—
202C23—192no—
203C23—194no—
204C23—382no—
205C23—761no—
206C23—761no—
207C23—764no—
208C23—764no—
209C23—764no—
210C23D4×D1911yescharacteristic
211D4—22no—
212D4—22no—
213D4—44no—
214D4—382no—
215D4—382no—
216D4—764no—
217D4—764no—
218D4—764no—
219D4—764no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—192no—
224C2×C4—382no—
225C2×C4—382no—
226C2×C4—382no—
227C2×C4—762no—
228C2×C4—764no—
229C2×C4—761no—
230C2×C4D4×D1911yescharacteristic
231C2×C4C23×D1911yescharacteristic
232C8—21no—
233C8—21no—
234C8—382no—
235C22—21no—
236C22—21no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—194no—
241C22—382no—
242C22—382no—
243C22—764no—
244C22—762no—
245C22—762no—
246C22—762no—
247C22—1528no—
248C22D8×D1912yes—
249C22C2×D4×D1911yescharacteristic
250C4—21no—
251C4—42no—
252C4—382no—
253C4—762no—
254C4#1059743011yescharacteristic
255C4#1059743511yescharacteristic
256C2—22no—
257C2—82no—
258C2—384no—
259C2—1522no—
260C2#1192710211yescharacteristic
261C2C2×D8×D1911yescharacteristic
262C2#1192734111yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#466C2
socleC22×C19C22×D4
hypercenter#466D19
hypocenterC19#3186
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #121×D19C2semidirect
2. #11926859C2semidirect
3. #11926856C2semidirect
4. #11926780C2semidirect
5. #11926778C2semidirect
6. #11926679C2semidirect
7. #11926676C2semidirect
8. C2×(C2×D19)⋊C8C2semidirect
9. C19×#466C2semidirect
11. C2×D4×D19C22semidirect
13. C2×D8×C19C22semidirect
14. C22×C8×C19C22semidirect
15. C19×#121C22semidirect
18. C2×#64525C22semidirect
19. #10597376C22semidirect
20. C22×C19⋊C8C22semidirect
21. C2×D152C22semidirect
23. C4⋊C4×D19C22semidirect
26. C19×#107C22semidirect
27. C19×#102C22semidirect
28. #10597289C22semidirect
29. #10597278C22semidirect
30. (C2×D19)⋊C8C22semidirect
31. (C2×D19)⋊C8C22semidirect
32. #10597275C22semidirect
33. #10597266C22semidirect
34. #10597264C22semidirect
77. C22×D19D8semidirect
130. #466D19semidirect
146. C2×D8C2×D19semidirect
148. C22×C8C2×D19semidirect
154. #121C2×D19semidirect
159. #107C2×D19semidirect
163. #102C2×D19semidirect
166. C19#3186semidirect

Maximal subgroups

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

subgroupindex
#121×D192
#119268592
#119268562
#119267802
#119267782
#119266792
#119266762
C2×(C2×D19)⋊C82
C19×#4662
#318619