Finite Group Databasebeta

← #18083185

Subgroups — #18083185

Order 4864.

722 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 722 conjugacy classes of subgroups — too many to draw. Only its 79 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#14572895C212yesmaximal
2#14571672C211yesmaximal, characteristic, complemented
3#14562167C212yesmaximal, complemented
4#14561543C211yesmaximal, characteristic, complemented
5C19×#1782C211yesmaximal, characteristic
6C2×#10597397—22no—
7C2×#10597370C2212yes—
8#11926706—24no—
9#11926700—22no—
10#11926695—22no—
11#11926545—22no—
12#11926508C2212yes—
13#11926484—22no—
14#11926469—22no—
15#11926465—22no—
16#11926280—24no—
17C22×#41×C19C2211yescharacteristic
18C2×C19×#99—22no—
19C19×#381C2211yescharacteristic
20C19×#381C2211yescharacteristic
21C2×#41×C19—22no—
22C2×#41×C19—22no—
23C2×#41×C19—44no—
24C22×Q8×C19D411yescharacteristic
25C22×D4×C19—21no—
26C22×D4×C19D411yescharacteristic
27C23×C4×C19—21no—
28C23×C4×C19C2311yescharacteristic
29C22×Dic38D412yes—
30C2×C22⋊C4×C19—21no—
31C2×C22⋊C4×C19D412yes—
32C2×C22⋊Dic19—22no—
33#10597397—48no—
34C2×#64528—24no—
35C2×#64526—24no—
36C2×C4⋊Dic19—22no—
37C2×C4⋊Dic19D412yes—
38#10597370—22no—
39#10597370—22no—
40#10597370—22no—
41#10597370—22no—
42C2×Dic19⋊C4—22no—
43C2×#64520—22no—
44C19×#99—44no—
45C19×#95—22no—
46C19×#95—22no—
47#10597292—24no—
48#10597289—24no—
49C19⋊#95—24no—
50C19⋊#95—22no—
51C22⋊(C19⋊C8)—22no—
52C22⋊(C19⋊C8)D414yes—
53C24×C19—21no—
54C24×C19C2×D411yescharacteristic
55#41×C19—28no—
56#41×C19—44no—
57#41×C19—44no—
58#41×C19—44no—
59C2×Q8×C19—22no—
60C2×Q8×C19—42no—
61C2×D4×C19—24no—
62C2×D4×C19—22no—
63C2×D4×C19—42no—
64C2×D4×C19—42no—
65C2×D4×C19—41no—
66C2×D4×C19—41no—
67C22×C4×C19—21no—
68C22×C4×C19—22no—
69C22×C4×C19—42no—
70C22×C4×C19—42no—
71C22×C4×C19—42no—
72C22×C4×C19—42no—
73C22×C4×C19—41no—
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19C2×D412yes—
76C22×C4×C19C2×D412yes—
77C22×C4×C19#4111yescharacteristic
78C22×Dic19—22no—
79C22×Dic19—22no—
80C2×Dic38—22no—
81C2×Dic38—22no—
82C2×Dic38—44no—
83C22⋊C4×C19—42no—
84C22⋊C4×C19—42no—
85C22⋊Dic19—42no—
86C22⋊Dic19—42no—
87#64528—48no—
88#64526—48no—
89C4⋊Dic19—22no—
90C4⋊Dic19—22no—
91C4⋊Dic19—82no—
92Dic19⋊C4—42no—
93Dic19⋊C4—42no—
94#64520—44no—
95C2×C19⋊C8—24no—
96#9982—191nomaximal, Sylow
97C23×C19—22no—
98C23×C19—22no—
99C23×C19—42no—
100C23×C19—41no—
101C23×C19—41no—
102C23×C19—82no—
103C23×C19#12011yescharacteristic
104C23×C19#12111yescharacteristic
105C23×C19#12711yescharacteristic
106Q8×C19—24no—
107Q8×C19—42no—
108D4×C19—24no—
109D4×C19—42no—
110D4×C19—44no—
111D4×C19—44no—
112C2×C4×C19—24no—
113C2×C4×C19—22no—
114C2×C4×C19—41no—
115C2×C4×C19—41no—
116C2×C4×C19—42no—
117C2×C4×C19—48no—
118C2×C4×C19—41no—
119C2×C4×C19—41no—
120C2×C4×C19—44no—
121C2×C4×C19—42no—
122C2×C4×C19—81no—
123C2×C4×C19—82no—
124C2×C4×C19#12012yes—
125C2×C4×C19#12112yes—
126C2×Dic19—44no—
127C2×Dic19—42no—
128C2×Dic19—42no—
129C2×Dic19—44no—
130Dic38—44no—
131Dic38—82no—
132C19⋊C8—44no—
133#3007—192no—
134#2817—191no—
135#1782D1911yescharacteristic
136#1511—192no—
137#1306—191no—
138C22×C19—22no—
139C22×C19—22no—
140C22×C19—22no—
141C22×C19—21no—
142C22×C19—21no—
143C22×C19—42no—
144C22×C19—82no—
145C22×C19—82no—
146C22×C19—82no—
147C22×C19—82no—
148C22×C19#39211yescharacteristic
149C22×C19B(4,𝔽2)12yes—
150C4×C19—22no—
151C4×C19—22no—
152C4×C19—42no—
153C4×C19—82no—
154C4×C19—161no—
155Dic19—82no—
156Dic19—82no—
157C22×#41C2×D1911yescharacteristic
158C2×#137—382no—
159C2×C22⋊Q8—192no—
160#452—384no—
161#451—382no—
162#450—382no—
163#417—382no—
164C2×#99—22no—
165#407—192no—
166#400—382no—
167#397—382no—
168#395—382no—
169#381C2×D1911yescharacteristic
170#381C2×D1911yescharacteristic
171#328—384no—
172C2×C19—22no—
173C2×C19—41no—
174C2×C19—41no—
175C2×C19—82no—
176C2×C19#200912yes—
177C2×C19#202111yescharacteristic
178C2×#41—22no—
179C2×#41—22no—
180C2×#41—44no—
181C22×Q8—192no—
182C22×Q8D7611yescharacteristic
183C22×D4—21no—
184C22×D4D7611yescharacteristic
185C23×C4—21no—
186C23×C4C22×D1911yescharacteristic
187#137—768no—
188C2×Q16—384no—
189C2×SD16—384no—
190C2×M16—382no—
191C22⋊Q8—382no—
192C22⋊Q8—382no—
193C22⋊Q8—382no—
194C22⋊Q8—382no—
195C2×C4⋊C4—192no—
196C2×C4⋊C4—382no—
197C2×C4⋊C4—382no—
198C2×C22⋊C4—21no—
199C2×C22⋊C4—382no—
200C2×C22⋊C4C22⋊D1912yes—
201#103—384no—
202#102—384no—
203#99—44no—
204C22⋊C8—194no—
205C22⋊C8—382no—
206#95—22no—
207#95—22no—
208#95—384no—
209#95—382no—
210C19#998211yescharacteristic, complemented, Sylow
211C24—21no—
212C24C2×C22⋊D1911yescharacteristic
213#41—28no—
214#41—44no—
215#41—44no—
216#41—44no—
217C2×Q8—22no—
218C2×Q8—42no—
219C2×Q8—382no—
220C2×Q8—382no—
221C2×Q8—764no—
222C2×D4—24no—
223C2×D4—22no—
224C2×D4—42no—
225C2×D4—42no—
226C2×D4—41no—
227C2×D4—41no—
228C22×C4—21no—
229C22×C4—22no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—41no—
235C22×C4—382no—
236C22×C4—382no—
237C22×C4C2×D7611yescharacteristic
238C22×C4#6454111yescharacteristic
239C22×C4D4×D1912yes—
240C22×C4D4×D1912yes—
241Q16—768no—
242SD16—768no—
243M16—764no—
244C2×C8—384no—
245C4⋊C4—382no—
246C4⋊C4—382no—
247C4⋊C4—762no—
248C4⋊C4—762no—
249C4⋊C4—1522no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—762no—
253C22⋊C4—762no—
254C23—22no—
255C23—22no—
256C23—42no—
257C23—41no—
258C23—41no—
259C23—82no—
260C23#1059737611yescharacteristic
261C23#1059738311yescharacteristic
262C23#1059738611yescharacteristic
263Q8—24no—
264Q8—42no—
265Q8—764no—
266Q8—1522no—
267D4—24no—
268D4—42no—
269D4—44no—
270D4—44no—
271C2×C4—24no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—48no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—44no—
280C2×C4—42no—
281C2×C4—81no—
282C2×C4—82no—
283C2×C4—764no—
284C2×C4—762no—
285C2×C4—762no—
286C2×C4—764no—
287C2×C4#1059732812yes—
288C2×C4#1059733012yes—
289C8—764no—
290C22—22no—
291C22—22no—
292C22—22no—
293C22—21no—
294C22—21no—
295C22—42no—
296C22—82no—
297C22—82no—
298C22—82no—
299C22—82no—
300C22#1192645311yescharacteristic
301C22#1192673012yes—
302C4—22no—
303C4—22no—
304C4—42no—
305C4—82no—
306C4—161no—
307C4—1522no—
308C4—1522no—
309C2—22no—
310C2—41no—
311C2—41no—
312C2—82no—
313C2#1456469412yes—
314C2#1456476111yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1782C2
socleC22×C19#392
prime radicalC22×#41×C19C22
hypercenter#1782D19
hypocenterC19#9982
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1782

Complements

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

NH ≅ G/Ntype
2. #14571672C2semidirect
3. #14562167C2semidirect
4. #14561543C2semidirect
210. C19#9982semidirect

Maximal subgroups

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

subgroupindex
#145728952
#145716722
#145621672
#145615432
C19×#17822
#998219