Finite Group Databasebeta

← #18085797

Subgroups — #18085797

Order 4864.

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

normal subgroups only

This group has 746 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#14571899C211yesmaximal, characteristic, complemented
2#14563550C212yesmaximal
3C19⋊#1304C212yesmaximal, complemented
4C19⋊#1304C211yesmaximal, characteristic, complemented
5C19×#1781C211yesmaximal, characteristic
6C2×#10597291—24no—
7#11926480—22no—
8#11926467—24no—
9#11926400C2212yes—
10#11926400C2212yes—
11C23×D4×C19C2211yescharacteristic
12C2×C19×#99—22no—
13C19×#379C2211yescharacteristic
14C19×#379C2211yescharacteristic
15C25×C19Q811yescharacteristic
16C25×C19C2311yescharacteristic
17C22×D4×C19—21no—
18C22×D4×C19—22no—
19C22×D4×C19—21no—
20C22×D4×C19—22no—
21C22×D4×C19—44no—
22C23×C4×C19Q811yescharacteristic
23C2×C22⋊C4×C19—21no—
24C2×C22⋊C4×C19—22no—
25C2×C22⋊C4×C19—22no—
26C2×C22⋊C4×C19D412yes—
27C2×C22⋊Dic19—22no—
28C2×C22⋊Dic19—22no—
29C2×C22⋊Dic19—22no—
30C2×C22⋊Dic19—22no—
31C2×C22⋊Dic19—22no—
32C2×C22⋊Dic19D414yes—
33C2×C4⋊Dic19—22no—
34C2×Dic19⋊C4—24no—
35C19×#99—44no—
36#10597291—48no—
37C19⋊#95—22no—
38C24×C19—22no—
39C24×C19—21no—
40C24×C19—42no—
41C24×C19—42no—
42C24×C19—82no—
43C24×C19—82no—
44C24×C19C2×D412yes—
45C24×C19C2×D411yescharacteristic
46C24×C19C2×Q811yescharacteristic
47C24×C19#4111yescharacteristic
48C24×C19#4112yes—
49C2×D4×C19—28no—
50C2×D4×C19—24no—
51C2×D4×C19—42no—
52C2×D4×C19—44no—
53C2×D4×C19—42no—
54C2×D4×C19—44no—
55C2×D4×C19—44no—
56C2×D4×C19—42no—
57C2×D4×C19—41no—
58C2×D4×C19—41no—
59C2×D4×C19—42no—
60C22×C4×C19—22no—
61C22×C4×C19—21no—
62C22×C4×C19—22no—
63C22×C4×C19—42no—
64C22×C4×C19—41no—
65C22×Dic19—24no—
66C22×Dic19—42no—
67C22⋊C4×C19—42no—
68C22⋊C4×C19—42no—
69C22⋊C4×C19—82no—
70C22⋊C4×C19—82no—
71C22⋊Dic19—44no—
72C22⋊Dic19—44no—
73C22⋊Dic19—82no—
74C22⋊Dic19—82no—
75C22⋊Dic19—82no—
76C22⋊Dic19—82no—
77C4⋊Dic19—82no—
78Dic19⋊C4—84no—
79#10392—191nomaximal, Sylow
80C23×C19—24no—
81C23×C19—22no—
82C23×C19—24no—
83C23×C19—22no—
84C23×C19—41no—
85C23×C19—42no—
86C23×C19—42no—
87C23×C19—42no—
88C23×C19—42no—
89C23×C19—42no—
90C23×C19—42no—
91C23×C19—42no—
92C23×C19—41no—
93C23×C19—42no—
94C23×C19—42no—
95C23×C19—41no—
96C23×C19—41no—
97C23×C19—82no—
98C23×C19—82no—
99C23×C19—82no—
100C23×C19—88no—
101C23×C19—88no—
102C23×C19#12011yescharacteristic
103C23×C19C22⋊Q812yes—
104C23×C19C22⋊Q811yescharacteristic
105C23×C19#12411yescharacteristic
106C23×C19#12412yes—
107D4×C19—48no—
108D4×C19—44no—
109D4×C19—44no—
110C2×C4×C19—24no—
111C2×C4×C19—22no—
112C2×C4×C19—42no—
113C2×C4×C19—41no—
114C2×C4×C19—41no—
115C2×C4×C19—44no—
116C2×C4×C19—42no—
117C2×C4×C19—81no—
118C2×C4×C19—82no—
119C2×Dic19—44no—
120C2×Dic19—44no—
121C2×Dic19—44no—
122C2×Dic19—82no—
123C2×Dic19—82no—
124C2×Dic19—82no—
125#2842—191no—
126#1781—192no—
127#1781D1911yescharacteristic
128#1304—192no—
129#1304—191no—
130C22×C19—22no—
131C22×C19—22no—
132C22×C19—22no—
133C22×C19—21no—
134C22×C19—21no—
135C22×C19—22no—
136C22×C19—22no—
137C22×C19—22no—
138C22×C19—22no—
139C22×C19—22no—
140C22×C19—22no—
141C22×C19—44no—
142C22×C19—42no—
143C22×C19—84no—
144C22×C19—82no—
145C22×C19—82no—
146C22×C19—84no—
147C22×C19—84no—
148C22×C19—82no—
149C22×C19—84no—
150C22×C19—82no—
151C22×C19—82no—
152C22×C19#39311yescharacteristic
153C22×C19B(4,𝔽2)12yes—
154C4×C19—42no—
155C4×C19—82no—
156C4×C19—161no—
157Dic19—84no—
158Dic19—162no—
159C23×D4C2×D1911yescharacteristic
160C2×#99—22no—
161C2×#99—384no—
162#399—382no—
163#396—384no—
164#379—192no—
165#379—192no—
166#379C2×D1911yescharacteristic
167#379C2×D1911yescharacteristic
168C2×C19—22no—
169C2×C19—42no—
170C2×C19—41no—
171C2×C19—42no—
172C2×C19—41no—
173C2×C19—82no—
174C2×C19#202911yescharacteristic
175C2×C19#203212yes—
176C25Dic3811yescharacteristic
177C25C22×D1911yescharacteristic
178C22×D4—22no—
179C22×D4—21no—
180C22×D4—21no—
181C22×D4—22no—
182C22×D4—44no—
183C23×C4Dic3811yescharacteristic
184C2×C4⋊C4—384no—
185C2×C4⋊C4—382no—
186C2×C22⋊C4—21no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—194no—
190C2×C22⋊C4—382no—
191C2×C22⋊C4—382no—
192C2×C22⋊C4—382no—
193C2×C22⋊C4—382no—
194C2×C22⋊C4—382no—
195C2×C22⋊C4C22⋊D1912yes—
196#99—44no—
197#99—768no—
198#95—382no—
199C19#1039211yescharacteristic, complemented, Sylow
200C24—22no—
201C24—21no—
202C24—42no—
203C24—42no—
204C24—82no—
205C24—82no—
206C24C2×Dic3811yescharacteristic
207C24#6454111yescharacteristic
208C24D4×D1912yes—
209C24#6454312yes—
210C24C2×C22⋊D1911yescharacteristic
211C2×D4—24no—
212C2×D4—28no—
213C2×D4—42no—
214C2×D4—44no—
215C2×D4—42no—
216C2×D4—44no—
217C2×D4—42no—
218C2×D4—44no—
219C2×D4—41no—
220C2×D4—41no—
221C2×D4—42no—
222C22×C4—22no—
223C22×C4—21no—
224C22×C4—22no—
225C22×C4—42no—
226C22×C4—41no—
227C22×C4—384no—
228C22×C4—762no—
229C4⋊C4—1524no—
230C4⋊C4—1522no—
231C22⋊C4—42no—
232C22⋊C4—42no—
233C22⋊C4—82no—
234C22⋊C4—82no—
235C22⋊C4—764no—
236C22⋊C4—764no—
237C22⋊C4—1522no—
238C22⋊C4—1522no—
239C22⋊C4—1522no—
240C22⋊C4—1522no—
241C23—22no—
242C23—24no—
243C23—24no—
244C23—22no—
245C23—41no—
246C23—42no—
247C23—42no—
248C23—42no—
249C23—42no—
250C23—42no—
251C23—42no—
252C23—42no—
253C23—41no—
254C23—42no—
255C23—42no—
256C23—41no—
257C23—41no—
258C23—82no—
259C23—82no—
260C23—82no—
261C23—88no—
262C23—88no—
263C23#1059732412yes—
264C23#1059733112yes—
265C23#1059737011yescharacteristic
266C23#1059738211yescharacteristic
267C23#1059738311yescharacteristic
268D4—44no—
269D4—48no—
270D4—44no—
271C2×C4—24no—
272C2×C4—22no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—44no—
277C2×C4—42no—
278C2×C4—81no—
279C2×C4—82no—
280C2×C4—764no—
281C2×C4—764no—
282C2×C4—764no—
283C2×C4—1522no—
284C2×C4—1522no—
285C2×C4—1522no—
286C22—22no—
287C22—22no—
288C22—21no—
289C22—21no—
290C22—22no—
291C22—22no—
292C22—22no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—44no—
298C22—42no—
299C22—82no—
300C22—84no—
301C22—84no—
302C22—82no—
303C22—84no—
304C22—82no—
305C22—84no—
306C22—82no—
307C22—82no—
308C22#1192645611yescharacteristic
309C22#1192673012yes—
310C4—42no—
311C4—82no—
312C4—161no—
313C4—3042no—
314C4—1524no—
315C2—22no—
316C2—41no—
317C2—42no—
318C2—42no—
319C2—41no—
320C2—82no—
321C2#1456479911yescharacteristic
322C2#1456481212yes—
subgroupG/H
centerC22#11926456
commutator, cosocleC25×C19C23
FrattiniC25C22×D19
FittingC19×#1781C2
socleC22×C19#393
prime radicalC23×D4×C19C22
hypercenter#1781D19
hypocenterC19#10392
LCSG ▷ C25×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C25 ◁ #1781

Complements

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

NH ≅ G/Ntype
1. #14571899C2semidirect
3. C19⋊#1304C2semidirect
4. C19⋊#1304C2semidirect
199. C19#10392semidirect

Maximal subgroups

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

subgroupindex
#145718992
#145635502
C19⋊#13042
C19×#17812
#1039219