Finite Group Databasebeta

← #18085794

Subgroups — #18085794

Order 4864.

746 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 746 conjugacy classes of subgroups — too many to draw. Only its 77 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#14563549C211yesmaximal, characteristic
2#14563549C212yesmaximal
3C19⋊#1304C211yesmaximal, characteristic, complemented
4C19⋊#1304C212yesmaximal, complemented
5C19×#2842C211yesmaximal, characteristic, complemented
6C23×C22⋊D19C2211yescharacteristic
7C2×#10597263—24no—
8C2×#10597263—22no—
9#11926400C2212yes—
10#11926400C2211yescharacteristic
11C19×#399—22no—
12C19×#396—24no—
13C19×#379C2211yescharacteristic
14C19×#379C2212yes—
15C25×C19C2311yescharacteristic
16C24×D19Q811yescharacteristic
17C22×C22⋊D19—22no—
18C22×C22⋊D19—21no—
19C22×C22⋊D19—22no—
20C22×C22⋊D19—21no—
21C22×C22⋊D19—44no—
22C23×Dic19Q811yescharacteristic
23C2×C4⋊C4×C19—24no—
24C2×C4⋊C4×C19—22no—
25C2×C22⋊C4×C19—22no—
26C2×C22⋊C4×C19—22no—
27C2×C22⋊C4×C19—22no—
28C2×C22⋊C4×C19D414yes—
29C2×C22⋊C4×C19D412yes—
30C2×C22⋊Dic19—22no—
31C2×C22⋊Dic19—21no—
32C2×C22⋊Dic19—22no—
33C2×C22⋊Dic19—22no—
34C2×C22⋊Dic19—22no—
35C19×#95—22no—
36#10597263—48no—
37#10597263—44no—
38C24×C19—42no—
39C24×C19—82no—
40C24×C19C2×D412yes—
41C24×C19C2×D411yescharacteristic
42C24×C19C2×Q811yescharacteristic
43C24×C19#4112yes—
44C24×C19#4111yescharacteristic
45C23×D19—22no—
46C23×D19—21no—
47C23×D19—42no—
48C23×D19—82no—
49C22×C4×C19—22no—
50C22×C4×C19—24no—
51C2×C22⋊D19—28no—
52C2×C22⋊D19—24no—
53C2×C22⋊D19—44no—
54C2×C22⋊D19—42no—
55C2×C22⋊D19—44no—
56C2×C22⋊D19—42no—
57C2×C22⋊D19—44no—
58C2×C22⋊D19—42no—
59C2×C22⋊D19—41no—
60C2×C22⋊D19—42no—
61C2×C22⋊D19—41no—
62C22×Dic19—22no—
63C22×Dic19—21no—
64C22×Dic19—42no—
65C22×Dic19—42no—
66C22×Dic19—41no—
67C4⋊C4×C19—84no—
68C4⋊C4×C19—82no—
69C22⋊C4×C19—44no—
70C22⋊C4×C19—42no—
71C22⋊C4×C19—82no—
72C22⋊C4×C19—82no—
73C22⋊C4×C19—82no—
74C22⋊Dic19—44no—
75C22⋊Dic19—42no—
76C22⋊Dic19—82no—
77C22⋊Dic19—82no—
78C22⋊Dic19—82no—
79#10392—191nomaximal, Sylow
80C23×C19—24no—
81C23×C19—22no—
82C23×C19—41no—
83C23×C19—42no—
84C23×C19—42no—
85C23×C19—42no—
86C23×C19—42no—
87C23×C19—42no—
88C23×C19—42no—
89C23×C19—42no—
90C23×C19—42no—
91C23×C19—41no—
92C23×C19—88no—
93C23×C19#12011yescharacteristic
94C23×C19C22⋊Q812yes—
95C23×C19C22⋊Q811yescharacteristic
96C23×C19#12412yes—
97C23×C19#12411yescharacteristic
98C22×D19—24no—
99C22×D19—22no—
100C22×D19—42no—
101C22×D19—41no—
102C22×D19—41no—
103C22×D19—88no—
104C22×D19—82no—
105C22×D19—82no—
106C22×D19—82no—
107C2×C4×C19—44no—
108C2×C4×C19—44no—
109C2×C4×C19—44no—
110C2×C4×C19—44no—
111C2×C4×C19—42no—
112C22⋊D19—48no—
113C22⋊D19—44no—
114C22⋊D19—44no—
115C2×Dic19—24no—
116C2×Dic19—22no—
117C2×Dic19—42no—
118C2×Dic19—41no—
119C2×Dic19—41no—
120C2×Dic19—82no—
121C2×Dic19—81no—
122C2×Dic19—82no—
123C2×Dic19—82no—
124C2×Dic19—82no—
125#2842D1911yescharacteristic, complemented
126#1781—191no—
127#1781—192no—
128#1304—191no—
129#1304—192no—
130C22×C19—22no—
131C22×C19—22no—
132C22×C19—21no—
133C22×C19—22no—
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—84no—
143C22×C19—82no—
144C22×C19—82no—
145C22×C19—84no—
146C22×C19#39311yescharacteristic
147C22×C19B(4,𝔽2)12yes—
148C2×D19—42no—
149C2×D19—84no—
150C2×D19—82no—
151C2×D19—82no—
152C2×D19—84no—
153C2×D19—82no—
154C4×C19—82no—
155C4×C19—84no—
156Dic19—42no—
157Dic19—162no—
158Dic19—161no—
159C23×D4—191no—
160C2×#99—384no—
161C2×#99—382no—
162#399—22no—
163#396—24no—
164#379—192no—
165#379—191no—
166#379C2×D1911yescharacteristic
167#379C2×D1912yes—
168C2×C19—22no—
169C2×C19—42no—
170C2×C19—41no—
171C2×C19—42no—
172C2×C19—41no—
173C2×C19#202911yescharacteristic
174C2×C19#203212yes—
175D19—82no—
176C25—191no—
177C25C22×D1911yescharacteristic
178C22×D4—382no—
179C22×D4—381no—
180C22×D4—382no—
181C22×D4—381no—
182C22×D4—764no—
183C23×C4—191no—
184C2×C4⋊C4—24no—
185C2×C4⋊C4—22no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—382no—
190C2×C22⋊C4—381no—
191C2×C22⋊C4—382no—
192C2×C22⋊C4—382no—
193C2×C22⋊C4—382no—
194C2×C22⋊C4C22⋊D1914yes—
195C2×C22⋊C4C22⋊D1912yes—
196#99—768no—
197#99—764no—
198#95—22no—
199C19#1039211yescharacteristic, complemented, Sylow
200C24—42no—
201C24—82no—
202C24—382no—
203C24—381no—
204C24—762no—
205C24—1522no—
206C24Q8×D1911yescharacteristic
207C24#6454512yes—
208C24#6454511yescharacteristic
209C24C2×C22⋊D1912yes—
210C24C2×C22⋊D1911yescharacteristic
211C2×D4—388no—
212C2×D4—384no—
213C2×D4—764no—
214C2×D4—762no—
215C2×D4—764no—
216C2×D4—762no—
217C2×D4—764no—
218C2×D4—762no—
219C2×D4—762no—
220C2×D4—761no—
221C2×D4—761no—
222C22×C4—22no—
223C22×C4—24no—
224C22×C4—382no—
225C22×C4—381no—
226C22×C4—762no—
227C22×C4—762no—
228C22×C4—761no—
229C4⋊C4—84no—
230C4⋊C4—82no—
231C22⋊C4—44no—
232C22⋊C4—42no—
233C22⋊C4—82no—
234C22⋊C4—82no—
235C22⋊C4—82no—
236C22⋊C4—764no—
237C22⋊C4—762no—
238C22⋊C4—1522no—
239C22⋊C4—1522no—
240C22⋊C4—1522no—
241C23—24no—
242C23—22no—
243C23—41no—
244C23—42no—
245C23—42no—
246C23—42no—
247C23—42no—
248C23—42no—
249C23—42no—
250C23—42no—
251C23—42no—
252C23—41no—
253C23—88no—
254C23—384no—
255C23—382no—
256C23—762no—
257C23—761no—
258C23—761no—
259C23—1522no—
260C23—1522no—
261C23—1522no—
262C23—1528no—
263C23#1059739212yes—
264C23#1059739211yescharacteristic
265C23#1059739312yes—
266C23#1059739311yescharacteristic
267C23#1059739911yescharacteristic
268D4—768no—
269D4—764no—
270D4—764no—
271C2×C4—44no—
272C2×C4—44no—
273C2×C4—44no—
274C2×C4—44no—
275C2×C4—42no—
276C2×C4—384no—
277C2×C4—382no—
278C2×C4—762no—
279C2×C4—761no—
280C2×C4—761no—
281C2×C4—1522no—
282C2×C4—1521no—
283C2×C4—1522no—
284C2×C4—1522no—
285C2×C4—1522no—
286C22—22no—
287C22—22no—
288C22—21no—
289C22—22no—
290C22—21no—
291C22—22no—
292C22—22no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—44no—
298C22—84no—
299C22—82no—
300C22—82no—
301C22—84no—
302C22—762no—
303C22—1524no—
304C22—1522no—
305C22—1524no—
306C22—1522no—
307C22—1522no—
308C22#1192645511yescharacteristic
309C22#1192673112yes—
310C4—82no—
311C4—84no—
312C4—3042no—
313C4—3041no—
314C4—762no—
315C2—22no—
316C2—42no—
317C2—41no—
318C2—42no—
319C2—41no—
320C2—1522no—
321C2#1456479811yescharacteristic
322C2#1456481112yes—
subgroupG/H
centerC22#11926455
commutator, cosocleC25×C19C23
FrattiniC25C22×D19
FittingC19×#2842C2
socleC22×C19#393
prime radicalC23×C22⋊D19C22
hypercenter#2842D19
hypocenterC19#10392
LCSG ▷ C25×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C25 ◁ #2842

Complements

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

NH ≅ G/Ntype
3. C19⋊#1304C2semidirect
4. C19⋊#1304C2semidirect
5. C19×#2842C2semidirect
125. #2842D19semidirect
199. C19#10392semidirect

Maximal subgroups

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

subgroupindex
#145635492
C19⋊#13042
C19×#28422
#1039219