Finite Group Databasebeta

← #18069569

Subgroups — #18069569

Order 4864.

422 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 75 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#14561867C211yesmaximal, characteristic
3C19×#1821C211yesmaximal, characteristic
4C22×C4×Dic19C411yescharacteristic
5#11926508—21no—
6C2×C19⋊#95—21no—
7C2×C19⋊#95—21no—
8C2×C19⋊#95C411yescharacteristic
9#11926270—21no—
10#11926270C412yescomplemented
11C22×C4⋊C4×C19C2211yescharacteristic
12C19×#407—21no—
13C19×#343—21no—
14C19×#343C412yescomplemented
15C23×C4×C19C2×C411yescharacteristic
16C23×C4×C19D411yescharacteristic
17C23×C4×C19D411yescharacteristic
18C23×Dic19—21no—
19C23×Dic19—21no—
20C2×M16×C19—22no—
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×C4×Dic19—41no—
28C2×C4×Dic19—42no—
29C2×#64520—41no—
30C19×C22⋊C8—41no—
31C19×C22⋊C8—41no—
32C19⋊#95—24no—
33C19⋊#95—42no—
34C19⋊#95—41no—
35C22⋊(C19⋊C8)—22no—
36C22⋊(C19⋊C8)—41no—
37C24×C19C22⋊C411yescharacteristic
38C22×C4×C19—21no—
39C22×C4×C19—21no—
40C22×C4×C19—21no—
41C22×C4×C19—21no—
42C22×C4×C19—21no—
43C22×C4×C19—21no—
44C22×C4×C19—22no—
45C22×C4×C19—41no—
46C22×C4×C19—41no—
47C22×C4×C19—41no—
48C22×C4×C19—41no—
49C22×C4×C19—41no—
50C22×C4×C19C4211yescharacteristic
51C22×C4×C19C22⋊C411yescharacteristic
52C22×C4×C19C22⋊C411yescharacteristic
53C22×C4×C19C4⋊C411yescharacteristic
54C22×C4×C19C4⋊C411yescharacteristic
55C22×C4×C19C4⋊C411yescharacteristic
56C22×Dic19—22no—
57C22×Dic19—22no—
58C22×Dic19—22no—
59C22×Dic19—22no—
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—
69C22×Dic19—41no—
70M16×C19—42no—
71M16×C19—42no—
72C2×C8×C19—42no—
73C4⋊C4×C19—41no—
74C4⋊C4×C19—41no—
75C4⋊C4×C19—41no—
76C4⋊C4×C19—41no—
77C4×Dic19—42no—
78C4×Dic19—42no—
79#64520—81no—
80#64520—81no—
81C2×C19⋊C8—42no—
82#7215—191nomaximal, Sylow
83C23×C19—21no—
84C23×C19—21no—
85C23×C19—21no—
86C23×C19—21no—
87C23×C19—21no—
88C23×C19—21no—
89C23×C19#9511yescharacteristic
90C23×C19#9911yescharacteristic
91C23×C19#9911yescharacteristic
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—21no—
100C2×C4×C19—21no—
101C2×C4×C19—42no—
102C2×C4×C19—42no—
103C2×C4×C19—42no—
104C2×C4×C19—41no—
105C2×C4×C19—41no—
106C2×C4×C19—41no—
107C2×C4×C19—41no—
108C2×C4×C19—41no—
109C2×C4×C19—41no—
110C2×C4×C19—41no—
111C2×C4×C19—41no—
112C2×C4×C19—81no—
113C2×C4×C19#10412yes—
114C2×Dic19—24no—
115C2×Dic19—42no—
116C2×Dic19—42no—
117C2×Dic19—42no—
118C2×Dic19—42no—
119C2×Dic19—42no—
120C2×Dic19—42no—
121C2×Dic19—42no—
122C2×Dic19—42no—
123C2×Dic19—42no—
124C2×Dic19—81no—
125C2×Dic19—81no—
126C2×Dic19—81no—
127C2×Dic19—81no—
128C8×C19—82no—
129C19⋊C8—82no—
130#1821D1911yescharacteristic
131#1463—191no—
132#1436—191no—
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—21no—
145C22×C19—21no—
146C22×C19—21no—
147C22×C19H(3,ℤ/4)11yescharacteristic
148C22×C19#33911yescharacteristic
149C22×C19#34211yescharacteristic
150C22×C19AΣL(1,𝔽16)11yescharacteristic
151C22×C19#35211yescharacteristic
152C22×C19#35511yescharacteristic
153C22×C19#35611yescharacteristic
154C4×C19—22no—
155C4×C19—41no—
156C4×C19—41no—
157C4×C19—41no—
158C4×C19—41no—
159C4×C19—41no—
160Dic19—44no—
161Dic19—82no—
162C22×C4⋊C4C2×D1911yescharacteristic
163C22×C42—191no—
164#407—21no—
165#407—381no—
166C2×#95—191no—
167C2×#95—381no—
168C2×#95—381no—
169#343—21no—
170#343Dic1912yescomplemented
171#324—192no—
172#324—381no—
173C2×C19—21no—
174C2×C19—21no—
175C2×C19—21no—
176C2×C19—21no—
177C2×C19—21no—
178C2×C19—21no—
179C2×C19#128411yescharacteristic
180C2×C19#139011yescharacteristic
181C2×C19#139411yescharacteristic
182C23×C4—381no—
183C23×C4—381no—
184C23×C4C4×D1911yescharacteristic
185C23×C4D7611yescharacteristic
186C23×C4C22⋊D1911yescharacteristic
187C2×M16—22no—
188C2×M16—761no—
189C2×C4⋊C4—41no—
190C2×C4⋊C4—41no—
191C2×C4⋊C4Dic3811yescharacteristic
192C2×C4⋊C4C4×D1911yescharacteristic
193C2×C4⋊C4C2×Dic1911yescharacteristic
194C2×C4⋊C4C22⋊D1911yescharacteristic
195C2×C42—761no—
196C2×C42—762no—
197C22⋊C8—41no—
198C22⋊C8—41no—
199C22⋊C8—382no—
200C22⋊C8—761no—
201#95—384no—
202#95—761no—
203#95—762no—
204C19#721511yescharacteristic, complemented, Sylow
205C24(C2×D19)⋊C411yescharacteristic
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—382no—
219C22×C4—382no—
220C22×C4—382no—
221C22×C4—382no—
222C22×C4—761no—
223C22×C4—761no—
224C22×C4—761no—
225C22×C4—761no—
226C22×C4—761no—
227C22×C4—761no—
228C22×C4—761no—
229C22×C4—761no—
230C22×C4—761no—
231C22×C4—761no—
232C22×C4C4×Dic1911yescharacteristic
233C22×C4Dic19⋊C411yescharacteristic
234C22×C4Dic19⋊C411yescharacteristic
235C22×C4C4⋊Dic1911yescharacteristic
236C22×C4(C2×D19)⋊C411yescharacteristic
237C22×C4C22⋊Dic1911yescharacteristic
238M16—42no—
239M16—42no—
240M16—1521no—
241M16—1521no—
242C2×C8—42no—
243C2×C8—762no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C42—762no—
249C42—762no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23#1059726311yescharacteristic
257C23#1059726311yescharacteristic
258C23C19⋊#9511yescharacteristic
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—81no—
280C2×C4—384no—
281C2×C4—762no—
282C2×C4—762no—
283C2×C4—762no—
284C2×C4—762no—
285C2×C4—762no—
286C2×C4—762no—
287C2×C4—762no—
288C2×C4—762no—
289C2×C4—762no—
290C2×C4—1521no—
291C2×C4—1521no—
292C2×C4—1521no—
293C2×C4—1521no—
294C2×C4#1059729412yes—
295C8—82no—
296C8—1522no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22#1192630011yescharacteristic
312C22#1192630311yescharacteristic
313C22#1192631011yescharacteristic
314C22#1192633211yescharacteristic
315C22#1192633511yescharacteristic
316C22#1192634011yescharacteristic
317C22#1192634211yescharacteristic
318C4—22no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—764no—
325C4—1522no—
326C2—21no—
327C2—21no—
328C2—21no—
329C2—21no—
330C2—21no—
331C2—21no—
332C2#1456148711yescharacteristic
333C2#1456175411yescharacteristic
334C2#1456176111yescharacteristic
subgroupG/H
centerC22#11926310
commutatorC22×C4×C19C42
FrattiniC22×C4⋊C4C2×D19
FittingC19×#1821C2
socleC22×C19#342
prime radicalC24×C19C22⋊C4
cosocleC22×C4⋊C4×C19C22
hypercenter#1821D19
hypocenterC19#7215
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
10. #11926270C4semidirect
14. C19×#343C4semidirect
170. #343Dic19semidirect
204. C19#7215semidirect

Maximal subgroups

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

subgroupindex
#145619652
#145618672
C19×#18212
#721519