Finite Group Databasebeta

← #18069861

Subgroups — #18069861

Order 4864.

374 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 71 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#14561965C211yesmaximal, characteristic
2#14561903C211yesmaximal, characteristic
3C19×#1463C211yesmaximal, characteristic
4#11926508—21no—
5C2×C19⋊#95—21no—
6C2×C19⋊#95—21no—
7C2×C19⋊#95C411yescharacteristic
8C2×C19⋊#95C411yescharacteristic
9#11926270—21no—
10#11926270C412yescomplemented
11C22×C4⋊C4×C19C2211yescharacteristic
12C19×#407—21no—
13C19×#324—21no—
14C19×#324C412yescomplemented
15C23×C4×C19C2×C411yescharacteristic
16C23×C4×C19D411yescharacteristic
17C23×C4×C19D411yescharacteristic
18C23×Dic19—21no—
19C23×Dic19—21no—
20C2×M16×C19—41no—
21C2×C4⋊C4×C19—41no—
22C2×C4⋊C4×C19—41no—
23C2×C4⋊C4×C19C2×C411yescharacteristic
24C2×C4⋊C4×C19C2×C411yescharacteristic
25C2×C4⋊C4×C19D411yescharacteristic
26C2×C4⋊C4×C19Q811yescharacteristic
27C2×#64520—41no—
28C19×C22⋊C8—22no—
29C19×C22⋊C8—41no—
30C19⋊#95—42no—
31C19⋊#95—42no—
32C19⋊#95—41no—
33C19⋊#95—41no—
34C22⋊(C19⋊C8)—22no—
35C22⋊(C19⋊C8)—41no—
36C24×C19C22⋊C411yescharacteristic
37C22×C4×C19—21no—
38C22×C4×C19—21no—
39C22×C4×C19—21no—
40C22×C4×C19—21no—
41C22×C4×C19—21no—
42C22×C4×C19—21no—
43C22×C4×C19—41no—
44C22×C4×C19—41no—
45C22×C4×C19—41no—
46C22×C4×C19—41no—
47C22×C4×C19—41no—
48C22×C4×C19—41no—
49C22×C4×C19C4211yescharacteristic
50C22×C4×C19C22⋊C411yescharacteristic
51C22×C4×C19C22⋊C411yescharacteristic
52C22×C4×C19C4⋊C411yescharacteristic
53C22×C4×C19C4⋊C411yescharacteristic
54C22×C4×C19C4⋊C411yescharacteristic
55C22×Dic19—22no—
56C22×Dic19—22no—
57C22×Dic19—41no—
58C22×Dic19—41no—
59C22×Dic19—41no—
60C22×Dic19—41no—
61C22×Dic19—41no—
62C22×Dic19—41no—
63C22×Dic19—41no—
64C22×Dic19—41no—
65C22×Dic19—41no—
66C22×Dic19—41no—
67C22×Dic19—41no—
68C22×Dic19—41no—
69M16×C19—81no—
70M16×C19—81no—
71C2×C8×C19—42no—
72C4⋊C4×C19—41no—
73C4⋊C4×C19—41no—
74C4⋊C4×C19—41no—
75C4⋊C4×C19—41no—
76#64520—81no—
77#64520—81no—
78C2×C19⋊C8—42no—
79#7326—191nomaximal, Sylow
80C23×C19—21no—
81C23×C19—21no—
82C23×C19—21no—
83C23×C19—21no—
84C23×C19—21no—
85C23×C19—21no—
86C23×C19#9511yescharacteristic
87C23×C19#9911yescharacteristic
88C23×C19#9911yescharacteristic
89C2×C4×C19—21no—
90C2×C4×C19—21no—
91C2×C4×C19—21no—
92C2×C4×C19—21no—
93C2×C4×C19—21no—
94C2×C4×C19—21no—
95C2×C4×C19—21no—
96C2×C4×C19—21no—
97C2×C4×C19—21no—
98C2×C4×C19—21no—
99C2×C4×C19—42no—
100C2×C4×C19—42no—
101C2×C4×C19—41no—
102C2×C4×C19—41no—
103C2×C4×C19—41no—
104C2×C4×C19—41no—
105C2×C4×C19—41no—
106C2×C4×C19—41no—
107C2×C4×C19—41no—
108C2×C4×C19—41no—
109C2×C4×C19—81no—
110C2×C4×C19—81no—
111C2×Dic19—42no—
112C2×Dic19—42no—
113C2×Dic19—42no—
114C2×Dic19—42no—
115C2×Dic19—42no—
116C2×Dic19—42no—
117C2×Dic19—81no—
118C2×Dic19—81no—
119C2×Dic19—81no—
120C2×Dic19—81no—
121C2×Dic19—81no—
122C2×Dic19—81no—
123C2×Dic19—81no—
124C2×Dic19—81no—
125C8×C19—82no—
126C19⋊C8—82no—
127#1463—191no—
128#1463D1911yescharacteristic
129#1445—191no—
130C22×C19—21no—
131C22×C19—21no—
132C22×C19—21no—
133C22×C19—21no—
134C22×C19—21no—
135C22×C19—21no—
136C22×C19—21no—
137C22×C19—21no—
138C22×C19—21no—
139C22×C19—21no—
140C22×C19—21no—
141C22×C19—21no—
142C22×C19—21no—
143C22×C19—21no—
144C22×C19#34211yescharacteristic
145C22×C19#34411yescharacteristic
146C22×C19#34411yescharacteristic
147C22×C19#35311yescharacteristic
148C22×C19#35411yescharacteristic
149C22×C19#35511yescharacteristic
150C22×C19#35611yescharacteristic
151C4×C19—41no—
152C4×C19—41no—
153C4×C19—41no—
154C4×C19—41no—
155C4×C19—41no—
156C4×C19—41no—
157Dic19—82no—
158Dic19—82no—
159C22×C4⋊C4C2×D1911yescharacteristic
160#407—21no—
161#407—381no—
162C2×#95—191no—
163C2×#95—191no—
164C2×#95—381no—
165C2×#95—381no—
166#324—21no—
167#324—192no—
168#324—381no—
169#324Dic1912yescomplemented
170C2×C19—21no—
171C2×C19—21no—
172C2×C19—21no—
173C2×C19—21no—
174C2×C19—21no—
175C2×C19—21no—
176C2×C19#130611yescharacteristic
177C2×C19#139311yescharacteristic
178C2×C19#139411yescharacteristic
179C23×C4—381no—
180C23×C4—381no—
181C23×C4C4×D1911yescharacteristic
182C23×C4D7611yescharacteristic
183C23×C4C22⋊D1911yescharacteristic
184C2×M16—41no—
185C2×M16—761no—
186C2×C4⋊C4—41no—
187C2×C4⋊C4—41no—
188C2×C4⋊C4Dic3811yescharacteristic
189C2×C4⋊C4C4×D1911yescharacteristic
190C2×C4⋊C4C2×Dic1911yescharacteristic
191C2×C4⋊C4C22⋊D1911yescharacteristic
192C22⋊C8—22no—
193C22⋊C8—41no—
194C22⋊C8—382no—
195C22⋊C8—761no—
196#95—761no—
197#95—761no—
198#95—762no—
199#95—762no—
200C19#732611yescharacteristic, complemented, Sylow
201C24(C2×D19)⋊C411yescharacteristic
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—382no—
215C22×C4—382no—
216C22×C4—761no—
217C22×C4—761no—
218C22×C4—761no—
219C22×C4—761no—
220C22×C4—761no—
221C22×C4—761no—
222C22×C4—761no—
223C22×C4—761no—
224C22×C4—761no—
225C22×C4—761no—
226C22×C4—761no—
227C22×C4—761no—
228C22×C4C4×Dic1911yescharacteristic
229C22×C4Dic19⋊C411yescharacteristic
230C22×C4Dic19⋊C411yescharacteristic
231C22×C4C4⋊Dic1911yescharacteristic
232C22×C4(C2×D19)⋊C411yescharacteristic
233C22×C4C22⋊Dic1911yescharacteristic
234M16—81no—
235M16—81no—
236M16—1521no—
237M16—1521no—
238C2×C8—42no—
239C2×C8—762no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23#1059726311yescharacteristic
251C23#1059726311yescharacteristic
252C23C19⋊#9511yescharacteristic
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—762no—
276C2×C4—762no—
277C2×C4—762no—
278C2×C4—762no—
279C2×C4—762no—
280C2×C4—762no—
281C2×C4—1521no—
282C2×C4—1521no—
283C2×C4—1521no—
284C2×C4—1521no—
285C2×C4—1521no—
286C2×C4—1521no—
287C2×C4—1521no—
288C2×C4—1521no—
289C8—82no—
290C8—1522no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22#1192631011yescharacteristic
306C22#1192631511yescharacteristic
307C22#1192631611yescharacteristic
308C22#1192633611yescharacteristic
309C22#1192633811yescharacteristic
310C22#1192634011yescharacteristic
311C22#1192634211yescharacteristic
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—1522no—
319C4—1522no—
320C2—21no—
321C2—21no—
322C2—21no—
323C2—21no—
324C2—21no—
325C2—21no—
326C2#1456154411yescharacteristic
327C2#1456175911yescharacteristic
328C2#1456176111yescharacteristic
subgroupG/H
centerC22#11926310
commutatorC22×C4×C19C42
FrattiniC22×C4⋊C4C2×D19
FittingC19×#1463C2
socleC22×C19#342
prime radicalC24×C19C22⋊C4
cosocleC22×C4⋊C4×C19C22
hypercenter#1463D19
hypocenterC19#7326
LCSG ▷ C22×C4×C19 ▷ C23×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
10. #11926270C4semidirect
14. C19×#324C4semidirect
169. #324Dic19semidirect
200. C19#7326semidirect

Maximal subgroups

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

subgroupindex
#145619652
#145619032
C19×#14632
#732619