Finite Group Databasebeta

← #14568528

Subgroups — #14568528

Order 2432.

800 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C2×#10597332C211yesmaximal, characteristic, complemented
2C2×#10597399C211yesmaximal, characteristic
3C2×(C22⋊D19)⋊C4C211yesmaximal, characteristic, complemented
4C22×C22⋊Dic19C211yesmaximal, characteristic, complemented
5#11926467C212yesmaximal, complemented
6#11926459C212yesmaximal, complemented
7#11926437C212yesmaximal, complemented
8#11926420C212yesmaximal, complemented
9#11926405C211yesmaximal, characteristic, complemented
10#11926402C211yesmaximal, characteristic, complemented
11C19×#379C211yesmaximal, characteristic, complemented
12C25×C19C2211yescharacteristic
13C22×C22⋊D19C2212yes—
14C22×C22⋊D19C2211yescharacteristic
15C23×Dic19C2211yescharacteristic
16C23×Dic19C2211yescharacteristic
17C22×C4×D19C2211yescharacteristic, complemented
18C2×C22⋊C4×C19C2211yescharacteristic
19C2×C22⋊C4×C19C2211yescharacteristic
20C2×C22⋊C4×C19C2212yes—
21C2×C22⋊C4×C19C2212yes—
22#10597399—24no—
23C2×C22⋊Dic19—24no—
24C2×C22⋊Dic19C2211yescharacteristic
25C2×C22⋊Dic19C2212yes—
26C2×C22⋊Dic19C2212yes—
27C2×C22⋊Dic19C2212yes—
28C2×(C2×D19)⋊C4C2212yescomplemented
29C2×(C2×D19)⋊C4C2211yescharacteristic, complemented
30C2×C4⋊Dic19C2212yescomplemented
31C2×Dic19⋊C4C2211yescharacteristic, complemented
32C2×Dic19⋊C4C2212yescomplemented
33C2×C4×Dic19C2211yescharacteristic, complemented
34#10597332—24no—
35(C22⋊D19)⋊C4—24no—
36C19⋊#95C2212yescomplemented
37C19⋊#95C2212yescomplemented
38C19⋊#95C2212yescomplemented
39C24×C19—22no—
40C24×C19—24no—
41C24×C19—22no—
42C24×C19—22no—
43C24×C19—42no—
44C24×C19C2312yes—
45C24×C19C2311yescharacteristic
46C23×D19C2311yescharacteristic
47C22×C4×C19C2311yescharacteristic
48C22×C4×C19C2311yescharacteristic
49C22×C4×C19C2312yes—
50C2×C22⋊D19—22no—
51C2×C22⋊D19—22no—
52C2×C22⋊D19—24no—
53C2×C22⋊D19—24no—
54C2×C22⋊D19—42no—
55C2×C22⋊D19D414yes—
56C22×Dic19—22no—
57C22×Dic19—22no—
58C22×Dic19—22no—
59C22×Dic19—42no—
60C22×Dic19D414yescomplemented
61C22×Dic19C2312yes—
62C22×Dic19C2312yes—
63C22×Dic19C2311yescharacteristic
64C22×Dic19C2311yescharacteristic
65C22×Dic19C2311yescharacteristic
66C2×C4×D19—22no—
67C2×C4×D19—42no—
68C22⋊C4×C19—22no—
69C22⋊C4×C19—22no—
70C22⋊C4×C19—24no—
71C22⋊C4×C19—42no—
72C22⋊Dic19—22no—
73C22⋊Dic19—24no—
74C22⋊Dic19—24no—
75C22⋊Dic19—24no—
76(C2×D19)⋊C4—24no—
77(C2×D19)⋊C4—22no—
78C4⋊Dic19—24no—
79Dic19⋊C4—22no—
80Dic19⋊C4—42no—
81C4×Dic19—22no—
82C23×C19—22no—
83C23×C19—22no—
84C23×C19—28no—
85C23×C19—22no—
86C23×C19—22no—
87C23×C19—22no—
88C23×C19—22no—
89C23×C19—22no—
90C23×C19—22no—
91C23×C19—48no—
92C23×C19—48no—
93C23×C19—44no—
94C23×C19—44no—
95C23×C19C2×D412yes—
96C23×C19C2×D412yes—
97C23×C19#4112yes—
98C23×C19#4114yes—
99C23×C19C2411yescharacteristic
100C22×D19—21no—
101C22×D19—21no—
102C22×D19—22no—
103C22×D19—22no—
104C22×D19C2×D412yes—
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—22no—
108C2×C4×C19—22no—
109C2×C4×C19—22no—
110C2×C4×C19—22no—
111C2×C4×C19—22no—
112C22⋊D19—28no—
113C22⋊D19—48no—
114C2×Dic19—21no—
115C2×Dic19—21no—
116C2×Dic19—22no—
117C2×Dic19—22no—
118C2×Dic19—22no—
119C2×Dic19—22no—
120C2×Dic19—22no—
121C2×Dic19—22no—
122C2×Dic19—22no—
123C2×Dic19—22no—
124C2×Dic19—44no—
125C2×Dic19—44no—
126C2×Dic19C2×D412yes—
127C2×Dic19C2×D412yes—
128C2×Dic19C2×D412yes—
129C4×D19—44no—
130#2534—191nomaximal, Sylow
131C22×C19—22no—
132C22×C19—22no—
133C22×C19—24no—
134C22×C19—24no—
135C22×C19—24no—
136C22×C19—24no—
137C22×C19—24no—
138C22×C19—416no—
139C22×C19—42no—
140C22×C19—42no—
141C22×C19—42no—
142C22×C19—42no—
143C22×C19#12114yes—
144C22×C19C22×D411yescharacteristic
145C22×C19C22×D411yescharacteristic
146C22×C19C2×#4111yescharacteristic
147C22×C19C2×#4112yes—
148C22×C19H(5,𝔽2)12yes—
149C2×D19—22no—
150C2×D19—24no—
151C2×D19—41no—
152C2×D19—41no—
153C2×D19—42no—
154C4×C19—41no—
155C4×C19—41no—
156C4×C19—42no—
157Dic19—22no—
158Dic19—22no—
159Dic19—22no—
160Dic19—42no—
161Dic19—42no—
162C2×#123—191no—
163C2×#120—191no—
164C2×C4×D4—191no—
165C22×C22⋊C4—191no—
166#396—192no—
167#394—192no—
168#388—192no—
169#386—192no—
170#381—191no—
171#380—191no—
172#379D1911yescharacteristic, complemented
173C2×C19—24no—
174C2×C19—44no—
175C2×C19C2×#12111yescharacteristic
176C2×C19#52511yescharacteristic
177C2×C19#53411yescharacteristic
178C2×C19#54612yes—
179C2×C19#55112yes—
180D19—42no—
181C25C2×D1911yescharacteristic
182C22×D4—191no—
183C22×D4—192no—
184C23×C4—191no—
185C23×C4—191no—
186C23×C4—191no—
187#123—384no—
188#120—384no—
189C4×D4—384no—
190C2×C4⋊C4—191no—
191C2×C4⋊C4—192no—
192C2×C4⋊C4—192no—
193C2×C22⋊C4—192no—
194C2×C22⋊C4—192no—
195C2×C22⋊C4—191no—
196C2×C22⋊C4—192no—
197C2×C22⋊C4—191no—
198C2×C22⋊C4—192no—
199C2×C22⋊C4—384no—
200C2×C22⋊C4C2×D1911yescharacteristic
201C2×C22⋊C4C2×D1911yescharacteristic
202C2×C22⋊C4C2×D1912yes—
203C2×C22⋊C4C2×D1912yes—
204C2×C42—191no—
205#95—192no—
206#95—192no—
207#95—192no—
208C19#253411yescharacteristic, complemented, Sylow
209C24—22no—
210C24—24no—
211C24—22no—
212C24—22no—
213C24—42no—
214C24—191no—
215C24C22×D1912yes—
216C24C22×D1911yescharacteristic
217C2×D4—194no—
218C2×D4—382no—
219C2×D4—382no—
220C2×D4—384no—
221C2×D4—384no—
222C2×D4—762no—
223C22×C4—191no—
224C22×C4—191no—
225C22×C4—191no—
226C22×C4—194no—
227C22×C4—192no—
228C22×C4—192no—
229C22×C4—382no—
230C22×C4—382no—
231C22×C4—382no—
232C22×C4—382no—
233C22×C4—762no—
234C22×C4—762no—
235C22×C4C22×D1911yescharacteristic
236C22×C4C22×D1911yescharacteristic
237C22×C4C22×D1912yes—
238C4⋊C4—382no—
239C4⋊C4—384no—
240C4⋊C4—762no—
241C22⋊C4—22no—
242C22⋊C4—22no—
243C22⋊C4—24no—
244C22⋊C4—42no—
245C22⋊C4—382no—
246C22⋊C4—384no—
247C22⋊C4—384no—
248C22⋊C4—384no—
249C22⋊C4—384no—
250C22⋊C4—382no—
251C42—382no—
252C23—22no—
253C23—22no—
254C23—28no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—22no—
259C23—22no—
260C23—22no—
261C23—48no—
262C23—48no—
263C23—44no—
264C23—44no—
265C23—192no—
266C23—381no—
267C23—381no—
268C23—382no—
269C23—382no—
270C23#6454112yes—
271C23D4×D1912yes—
272C23D4×D1912yes—
273C23#6454314yes—
274C23C23×D1911yescharacteristic
275D4—388no—
276D4—768no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—192no—
285C2×C4—192no—
286C2×C4—192no—
287C2×C4—381no—
288C2×C4—381no—
289C2×C4—382no—
290C2×C4—382no—
291C2×C4—382no—
292C2×C4—382no—
293C2×C4—382no—
294C2×C4—382no—
295C2×C4—382no—
296C2×C4—382no—
297C2×C4—764no—
298C2×C4—764no—
299C2×C4—764no—
300C22—22no—
301C22—22no—
302C22—24no—
303C22—24no—
304C22—24no—
305C22—24no—
306C22—24no—
307C22—416no—
308C22—42no—
309C22—42no—
310C22—42no—
311C22—42no—
312C22—384no—
313C22—382no—
314C22—761no—
315C22—761no—
316C22—762no—
317C22#1059733014yes—
318C22C2×#6454111yescharacteristic
319C22C2×D4×D1911yescharacteristic
320C22C2×D4×D1911yescharacteristic
321C22C2×#6454312yes—
322C22#1059743012yes—
323C4—41no—
324C4—41no—
325C4—42no—
326C4—382no—
327C4—382no—
328C4—382no—
329C4—762no—
330C4—762no—
331C2—24no—
332C2—44no—
333C2—762no—
334C2C2×#1059733011yescharacteristic
335C2#1192705011yescharacteristic
336C2#1192710411yescharacteristic
337C2#1192718112yes—
338C2#1192722012yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#379C2
prime radicalC2×#10597399C2
hypercenter#379D19
hypocenterC19#2534
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#10597332C2semidirect
3. C2×(C22⋊D19)⋊C4C2semidirect
4. C22×C22⋊Dic19C2semidirect
5. #11926467C2semidirect
6. #11926459C2semidirect
7. #11926437C2semidirect
8. #11926420C2semidirect
9. #11926405C2semidirect
10. #11926402C2semidirect
11. C19×#379C2semidirect
17. C22×C4×D19C22semidirect
28. C2×(C2×D19)⋊C4C22semidirect
29. C2×(C2×D19)⋊C4C22semidirect
30. C2×C4⋊Dic19C22semidirect
31. C2×Dic19⋊C4C22semidirect
32. C2×Dic19⋊C4C22semidirect
33. C2×C4×Dic19C22semidirect
36. C19⋊#95C22semidirect
37. C19⋊#95C22semidirect
38. C19⋊#95C22semidirect
60. C22×Dic19D4semidirect
172. #379D19semidirect
208. C19#2534semidirect

Maximal subgroups

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

subgroupindex
C2×#105973322
C2×#105973992
C2×(C22⋊D19)⋊C42
C22×C22⋊Dic192
#119264672
#119264592
#119264372
#119264202
#119264052
#119264022
C19×#3792
#253419