Finite Group Databasebeta

← #14575309

Subgroups — #14575309

Order 2432.

620 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C22×D152C211yesmaximal, characteristic, complemented
2C2×D8×D19C211yesmaximal, characteristic, complemented
3#11927178C212yesmaximal, complemented
4#11926919C211yesmaximal, characteristic, complemented
5#11926781C211yesmaximal, characteristic, complemented
6#11926738C212yesmaximal, complemented
7#11926679C212yesmaximal, complemented
8#11926677C212yesmaximal, complemented
9#11926626C211yesmaximal, characteristic, complemented
10C8×C22⋊D19C211yesmaximal, characteristic, complemented
11C19×#466C211yesmaximal, characteristic, complemented
12C2×D4×D19—22no—
13C2×D4×D19C2212yescomplemented
14C22×D76C2212yescomplemented
15C2×D8×C19C2211yescharacteristic, complemented
16C22×C8×C19C2211yescharacteristic, complemented
17C19×#121C2212yescomplemented
18#10597386C2212yescomplemented
19#10597383—22no—
20C2×#64525C2212yescomplemented
21C2×#64525C2212yescomplemented
22C4×C22⋊D19C2211yescharacteristic
23D8×D19—24no—
24C2×D152—24no—
25C2×D152C2211yescharacteristic
26C2×D152C2211yescharacteristic, complemented
27C2×D152C2212yescomplemented
28C2×C8×D19C2211yescharacteristic, complemented
29#10597341C2212yescomplemented
30#10597339C2212yescomplemented
31#10597330—22no—
32#10597328—22no—
33C19×#107C2211yescharacteristic, complemented
34C19×#102C2212yescomplemented
35C22⋊(C19⋊C8)C2211yescharacteristic, complemented
36(C2×D19)⋊C8C2211yescharacteristic, complemented
37Dic19⋊C8C2211yescharacteristic, complemented
38C8×Dic19C2211yescharacteristic, complemented
39#10597266C2212yescomplemented
40#10597266C2212yescomplemented
41C23×D19—22no—
42C23×D19—22no—
43C2×D4×C19—22no—
44C2×D4×C19C2312yes—
45C22×C4×C19C2311yescharacteristic
46C2×C22⋊D19—22no—
47C2×C22⋊D19—22no—
48C2×C22⋊D19—22no—
49C2×C22⋊D19D411yescharacteristic
50D4×D19—24no—
51D4×D19—42no—
52D4×D19—48no—
53C2×D76—24no—
54C2×D76—22no—
55C2×D76—22no—
56C2×D76—42no—
57C2×D76C2312yes—
58C2×D76C2312yes—
59C2×C4×D19—22no—
60C2×C4×D19C2311yescharacteristic
61D8×C19—22no—
62C2×C8×C19—22no—
63C2×C8×C19C2311yescharacteristic
64C2×C8×C19C2311yescharacteristic
65C4⋊C4×C19C2312yes—
66C22⋊C4×C19—22no—
67C22⋊Dic19D411yescharacteristic
68#64525—24no—
69#64525—42no—
70(C2×D19)⋊C4—22no—
71(C2×D19)⋊C4—22no—
72(C2×D19)⋊C4D411yescharacteristic
73Dic19⋊C4D411yescharacteristic
74C4×Dic19C2311yescharacteristic
75C2×C19⋊C8C2311yescharacteristic
76C2×C19⋊C8C2311yescharacteristic
77D152—24no—
78D152—22no—
79D152D414yescomplemented
80C8×D19—22no—
81C23×C19—22no—
82C23×C19C2×D411yescharacteristic
83C22×D19—22no—
84C22×D19—22no—
85C22×D19—44no—
86C22×D19—44no—
87C22×D19—44no—
88C22×D19—44no—
89C22×D19—82no—
90C22×D19—82no—
91C22×D19C2×D411yescharacteristic
92D4×C19—22no—
93D4×C19—22no—
94D4×C19—44no—
95C2×C4×C19—21no—
96C2×C4×C19—21no—
97C2×C4×C19—22no—
98C2×C4×C19C2×D411yescharacteristic
99C2×C4×C19C2411yescharacteristic
100C22⋊D19—44no—
101C22⋊D19—44no—
102C22⋊D19—82no—
103C22⋊D19D814yescomplemented
104C2×Dic19C2×D411yescharacteristic
105C2×Dic19C2×D411yescharacteristic
106C2×Dic19C2×D411yescharacteristic
107D76—22no—
108D76—22no—
109D76—22no—
110D76—44no—
111D76—44no—
112D76C2×D414yescomplemented
113C4×D19—21no—
114C4×D19—21no—
115C4×D19—44no—
116C8×C19—21no—
117C8×C19C2×D412yescomplemented
118C19⋊C8—21no—
119C19⋊C8—21no—
120D4×D8—191nomaximal, Sylow
121C22×C19—21no—
122C22×C19—21no—
123C22×C19—42no—
124C22×C19—42no—
125C22×C19—42no—
126C22×C19C2×D812yescomplemented
127C22×C19C22×D411yescharacteristic
128C2×D19—21no—
129C2×D19—21no—
130C2×D19—24no—
131C2×D19—42no—
132C2×D19—42no—
133C2×D19—42no—
134C2×D19—42no—
135C2×D19—42no—
136C2×D19—88no—
137C2×D19—88no—
138C2×D19C2×D812yescomplemented
139C4×C19—21no—
140C4×C19—42no—
141C4×C19C22×D411yescharacteristic
142C4×C19H(5,𝔽2)11yescharacteristic
143Dic19—21no—
144Dic19—21no—
145Dic19C2×D812yescomplemented
146C22×D8—191no—
147C22×D8—191no—
148D42—192no—
149#493—191no—
150#466—191no—
151#466D1911yescharacteristic, complemented
152#459—192no—
153#447—192no—
154#447—192no—
155C4×D8—191no—
156C8×D4—191no—
157C2×C19—22no—
158C2×C19—82no—
159C2×C19D4211yescharacteristic
160C2×C19C22×D811yescharacteristic
161C2×C19#57611yescharacteristic
162D19—22no—
163D19—44no—
164D19—82no—
165C22×D4—192no—
166C22×D4—192no—
167C22×D4—382no—
168C2×D8—192no—
169C2×D8—192no—
170C2×D8—191no—
171C2×D8—192no—
172C2×D8—191no—
173C2×D8—384no—
174C2×D8—384no—
175C2×D8C2×D1911yescharacteristic, complemented
176C22×C8—191no—
177C22×C8C2×D1911yescharacteristic, complemented
178#127—192no—
179#121—192no—
180#121—382no—
181#121C2×D1912yescomplemented
182#120—382no—
183#120—382no—
184C4×D4—191no—
185C4×D4—192no—
186#107C2×D1911yescharacteristic, complemented
187C4⋊C8—191no—
188#102—192no—
189#102—192no—
190#102C2×D1912yescomplemented
191C22⋊C8—191no—
192C22⋊C8—191no—
193C4×C8—191no—
194C19D4×D811yescharacteristic, complemented, Sylow
195C24—382no—
196C24—382no—
197C2×D4—22no—
198C2×D4—191no—
199C2×D4—192no—
200C2×D4—192no—
201C2×D4—384no—
202C2×D4—382no—
203C2×D4—382no—
204C2×D4—382no—
205C2×D4—382no—
206C2×D4—384no—
207C2×D4—382no—
208C2×D4—762no—
209C2×D4—762no—
210C2×D4—768no—
211C2×D4C22×D1912yes—
212C22×C4—191no—
213C22×C4—382no—
214C22×C4C22×D1911yescharacteristic
215D8—22no—
216D8—194no—
217D8—384no—
218D8—384no—
219D8—382no—
220D8—762no—
221C2×C8—22no—
222C2×C8—191no—
223C2×C8—191no—
224C2×C8—382no—
225C2×C8C22×D1911yescharacteristic
226C2×C8C22×D1911yescharacteristic
227C4⋊C4—191no—
228C4⋊C4C22×D1912yes—
229C22⋊C4—22no—
230C22⋊C4—191no—
231C22⋊C4—191no—
232C22⋊C4—382no—
233C22⋊C4—382no—
234C42—191no—
235C23—22no—
236C23—191no—
237C23—382no—
238C23—382no—
239C23—764no—
240C23—764no—
241C23—764no—
242C23—764no—
243C23—1522no—
244C23—1522no—
245C23D4×D1911yescharacteristic
246D4—22no—
247D4—22no—
248D4—44no—
249D4—194no—
250D4—194no—
251D4—382no—
252D4—382no—
253D4—382no—
254D4—764no—
255D4—764no—
256D4—764no—
257D4—764no—
258D4—1522no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—191no—
263C2×C4—191no—
264C2×C4—191no—
265C2×C4—381no—
266C2×C4—381no—
267C2×C4—764no—
268C2×C4D4×D1911yescharacteristic
269C2×C4C23×D1911yescharacteristic
270C8—21no—
271C8—381no—
272C8—381no—
273C8D4×D1912yescomplemented
274C22—21no—
275C22—21no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—192no—
280C22—381no—
281C22—381no—
282C22—384no—
283C22—762no—
284C22—762no—
285C22—762no—
286C22—762no—
287C22—762no—
288C22—1528no—
289C22—1528no—
290C22D8×D1912yescomplemented
291C22C2×D4×D1911yescharacteristic
292C4—21no—
293C4—42no—
294C4—192no—
295C4—381no—
296C4—381no—
297C4C2×D4×D1911yescharacteristic
298C4#1059743511yescharacteristic
299C2—22no—
300C2—82no—
301C2—382no—
302C2—764no—
303C2—1522no—
304C2#1192717811yescharacteristic
305C2C2×D8×D1911yescharacteristic
306C2#1192734611yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#466C2
socleC22×C19C22×D4
hypercenter#466D19
hypocenterC19D4×D8
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. C22×D152C2semidirect
2. C2×D8×D19C2semidirect
3. #11927178C2semidirect
4. #11926919C2semidirect
5. #11926781C2semidirect
6. #11926738C2semidirect
7. #11926679C2semidirect
8. #11926677C2semidirect
9. #11926626C2semidirect
10. C8×C22⋊D19C2semidirect
11. C19×#466C2semidirect
13. C2×D4×D19C22semidirect
14. C22×D76C22semidirect
15. C2×D8×C19C22semidirect
16. C22×C8×C19C22semidirect
17. C19×#121C22semidirect
18. #10597386C22semidirect
20. C2×#64525C22semidirect
21. C2×#64525C22semidirect
26. C2×D152C22semidirect
27. C2×D152C22semidirect
28. C2×C8×D19C22semidirect
29. #10597341C22semidirect
30. #10597339C22semidirect
33. C19×#107C22semidirect
34. C19×#102C22semidirect
35. C22⋊(C19⋊C8)C22semidirect
36. (C2×D19)⋊C8C22semidirect
37. Dic19⋊C8C22semidirect
38. C8×Dic19C22semidirect
39. #10597266C22semidirect
40. #10597266C22semidirect
79. D152D4semidirect
103. C22⋊D19D8semidirect
112. D76C2×D4semidirect
117. C8×C19C2×D4semidirect
126. C22×C19C2×D8semidirect
138. C2×D19C2×D8semidirect
145. Dic19C2×D8semidirect
151. #466D19semidirect
175. C2×D8C2×D19semidirect
177. C22×C8C2×D19semidirect
181. #121C2×D19semidirect
186. #107C2×D19semidirect
190. #102C2×D19semidirect
194. C19D4×D8semidirect
273. C8D4×D19semidirect
290. C22D8×D19semidirect

Maximal subgroups

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

subgroupindex
C22×D1522
C2×D8×D192
#119271782
#119269192
#119267812
#119267382
#119266792
#119266772
#119266262
C8×C22⋊D192
C19×#4662
D4×D819