Finite Group Databasebeta

← #18076033

Subgroups — #18076033

Order 4864.

384 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 91 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#14566133C211yesmaximal, characteristic
2#14561969C211yesmaximal, characteristic
3#14561492C212yesmaximal, complemented
4#14561490C212yesmaximal, complemented
5C19×#1464C211yesmaximal, characteristic
6#11926601C2212yes—
7#11926437—21no—
8#11926437—21no—
9#11926430—21no—
10#11926430—21no—
11C4×C4⋊Dic19C2211yescharacteristic
12C4×C4⋊Dic19C2211yescharacteristic
13C4×C22⋊Dic19C411yescharacteristic
14C4×C22⋊Dic19C411yescharacteristic
15#11926390C411yescharacteristic
16C42×Dic19C411yescharacteristic
17#11926270—21no—
18#11926268—21no—
19C2×C19×#117C2211yescharacteristic
20C19×#432C2212yes—
21C19×#324—21no—
22C19×#323—21no—
23C23×C4×C19C2×C411yescharacteristic
24C19×#117—22no—
25C19×#117—22no—
26C2×C4⋊C4×C19D411yescharacteristic
27C2×C4⋊C4×C19D411yescharacteristic
28C2×C22⋊C4×C19D411yescharacteristic
29C2×C22⋊C4×C19D411yescharacteristic
30C2×C42×C19C2×C411yescharacteristic
31C2×C42×C19C2311yescharacteristic
32C2×C22⋊Dic19—21no—
33C2×C22⋊Dic19—21no—
34C2×C4⋊Dic19—21no—
35C2×C4⋊Dic19—21no—
36C2×C4×Dic19—21no—
37C2×C4×Dic19—21no—
38C2×C4×Dic19C2×C411yescharacteristic
39C2×C4×Dic19C2×C411yescharacteristic
40C2×C4×Dic19C2×C411yescharacteristic
41C2×C4×Dic19C2×C411yescharacteristic
42C19×C4⋊C8—22no—
43C19×C22⋊C8—22no—
44C19×#97—22no—
45C19⋊#95—21no—
46C19⋊#95—21no—
47C19⋊#95—21no—
48C19⋊#95—21no—
49C19⋊#95—21no—
50C19⋊#95—21no—
51C22⋊(C19⋊C8)—22no—
52C4⋊(C19⋊C8)—22no—
53#10597260—22no—
54C24×C19C22⋊C411yescharacteristic
55C22×C4×C19—21no—
56C22×C4×C19—21no—
57C22×C4×C19—41no—
58C22×C4×C19—41no—
59C22×C4×C19C22⋊C411yescharacteristic
60C22×C4×C19C22⋊C411yescharacteristic
61C22×C4×C19C22⋊C411yescharacteristic
62C22×C4×C19C22×C411yescharacteristic
63C22×C4×C19C2×D411yescharacteristic
64C22×C4×C19C2×D411yescharacteristic
65C22×Dic19—21no—
66C22×Dic19—21no—
67C22×Dic19—21no—
68C22×Dic19—21no—
69C2×C8×C19—42no—
70C4⋊C4×C19—22no—
71C4⋊C4×C19—22no—
72C22⋊C4×C19—22no—
73C22⋊C4×C19—22no—
74C42×C19—21no—
75C42×C19—21no—
76C42×C19#4112yes—
77C42×C19#4112yes—
78C22⋊Dic19—42no—
79C22⋊Dic19—42no—
80C4⋊Dic19—42no—
81C4⋊Dic19—42no—
82C4×Dic19—42no—
83C4×Dic19—42no—
84C4×Dic19—41no—
85C4×Dic19—41no—
86C4×Dic19—41no—
87C4×Dic19—41no—
88C2×C19⋊C8—42no—
89#8745—191nomaximal, Sylow
90C23×C19—21no—
91C23×C19—21no—
92C23×C19—21no—
93C23×C19—41no—
94C23×C19—41no—
95C23×C19C2×C22⋊C411yescharacteristic
96C2×C4×C19—21no—
97C2×C4×C19—21no—
98C2×C4×C19—21no—
99C2×C4×C19—21no—
100C2×C4×C19—21no—
101C2×C4×C19—21no—
102C2×C4×C19—21no—
103C2×C4×C19—41no—
104C2×C4×C19—41no—
105C2×C4×C19—42no—
106C2×C4×C19—42no—
107C2×C4×C19—41no—
108C2×C4×C19—41no—
109C2×C4×C19#11711yescharacteristic
110C2×C4×C19#11711yescharacteristic
111C2×C4×C19#12312yes—
112C2×C4×C19#12312yes—
113C2×Dic19—22no—
114C2×Dic19—22no—
115C2×Dic19—41no—
116C2×Dic19—41no—
117C2×Dic19—41no—
118C2×Dic19—41no—
119C2×Dic19—41no—
120C2×Dic19—41no—
121C2×Dic19—41no—
122C2×Dic19—41no—
123C2×Dic19—41no—
124C2×Dic19—41no—
125C8×C19—82no—
126C19⋊C8—82no—
127#2298—191no—
128#1464—191no—
129#1464D1911yescharacteristic
130#1285—192no—
131#1285—192no—
132C22×C19—21no—
133C22×C19—21no—
134C22×C19—41no—
135C22×C19—41no—
136C22×C19—41no—
137C22×C19—81no—
138C22×C19—81no—
139C22×C19#38111yescharacteristic
140C22×C19#41311yescharacteristic
141C22×C19#41311yescharacteristic
142C4×C19—21no—
143C4×C19—21no—
144C4×C19—22no—
145C4×C19—22no—
146C4×C19—41no—
147C4×C19—41no—
148C4×C19—41no—
149Dic19—42no—
150Dic19—42no—
151Dic19—81no—
152Dic19—81no—
153C2×#117C2×D1911yescharacteristic
154#432—192no—
155#432C2×D1912yes—
156#388—381no—
157#388—381no—
158#387—381no—
159#387—381no—
160C4×C4⋊C4—191no—
161C4×C4⋊C4—191no—
162C4×C22⋊C4—191no—
163C4×C22⋊C4—191no—
164#376—191no—
165C43—191no—
166#324—21no—
167#324—381no—
168#323—21no—
169#323—381no—
170C2×C19—21no—
171C2×C19—21no—
172C2×C19—81no—
173C2×C19#182211yescharacteristic
174C2×C19#182711yescharacteristic
175C2×C19#182711yescharacteristic
176C23×C4C4×D1911yescharacteristic
177#117—22no—
178#117—22no—
179C2×C4⋊C4—381no—
180C2×C4⋊C4—381no—
181C2×C4⋊C4D7611yescharacteristic
182C2×C4⋊C4C22⋊D1911yescharacteristic
183C2×C22⋊C4—381no—
184C2×C22⋊C4—381no—
185C2×C22⋊C4D7611yescharacteristic
186C2×C22⋊C4C22⋊D1911yescharacteristic
187C2×C42—191no—
188C2×C42—191no—
189C2×C42—191no—
190C2×C42—191no—
191C2×C42—381no—
192C2×C42—381no—
193C2×C42C4×D1911yescharacteristic
194C2×C42C22×D1911yescharacteristic
195C4⋊C8—22no—
196C4⋊C8—382no—
197C22⋊C8—22no—
198C22⋊C8—382no—
199#97—22no—
200#97—382no—
201#95—381no—
202#95—381no—
203#95—381no—
204#95—381no—
205#95—381no—
206#95—381no—
207C19#874511yescharacteristic, complemented, Sylow
208C24(C2×D19)⋊C411yescharacteristic
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—381no—
214C22×C4—381no—
215C22×C4—381no—
216C22×C4—381no—
217C22×C4(C2×D19)⋊C411yescharacteristic
218C22×C4(C2×D19)⋊C411yescharacteristic
219C22×C4(C2×D19)⋊C411yescharacteristic
220C22×C4C2×C4×D1911yescharacteristic
221C22×C4C2×D7611yescharacteristic
222C22×C4C2×C22⋊D1911yescharacteristic
223C2×C8—42no—
224C2×C8—762no—
225C4⋊C4—22no—
226C4⋊C4—22no—
227C4⋊C4—762no—
228C4⋊C4—762no—
229C22⋊C4—22no—
230C22⋊C4—22no—
231C22⋊C4—762no—
232C22⋊C4—762no—
233C42—21no—
234C42—21no—
235C42—761no—
236C42—761no—
237C42—761no—
238C42—761no—
239C42—762no—
240C42—762no—
241C42#6454312yes—
242C42#6454312yes—
243C23—21no—
244C23—21no—
245C23—21no—
246C23—41no—
247C23—41no—
248C23C2×(C2×D19)⋊C411yescharacteristic
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—382no—
263C2×C4—382no—
264C2×C4—761no—
265C2×C4—761no—
266C2×C4—761no—
267C2×C4—761no—
268C2×C4—761no—
269C2×C4—761no—
270C2×C4—761no—
271C2×C4—761no—
272C2×C4—761no—
273C2×C4—761no—
274C2×C4#1059732311yescharacteristic
275C2×C4#1059732311yescharacteristic
276C2×C4#1059733212yes—
277C2×C4#1059738112yes—
278C8—82no—
279C8—1522no—
280C22—21no—
281C22—21no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—81no—
286C22—81no—
287C22#1192640511yescharacteristic
288C22#1192652611yescharacteristic
289C22#1192652611yescharacteristic
290C4—21no—
291C4—21no—
292C4—22no—
293C4—22no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—762no—
298C4—762no—
299C4—1521no—
300C4—1521no—
301C2—21no—
302C2—21no—
303C2—81no—
304C2#1456371611yescharacteristic
305C2#1456373611yescharacteristic
306C2#1456374011yescharacteristic
subgroupG/H
centerC22#11926405
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1464C2
socleC22×C19#381
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#1464D19
hypocenterC19#8745
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
3. #14561492C2semidirect
4. #14561490C2semidirect
207. C19#8745semidirect

Maximal subgroups

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

subgroupindex
#145661332
#145619692
#145614922
#145614902
C19×#14642
#874519