Finite Group Databasebeta

← #18086934

Subgroups — #18086934

Order 4864.

490 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 99 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#14564621C212yesmaximal
2#14564059C212yesmaximal
3#14563812C211yesmaximal, characteristic
4#14561503C211yesmaximal, characteristic
5C19×#3189C211yesmaximal, characteristic
6C23×C19⋊C8C2211yescharacteristic
7C2×Dic19⋊C8—21no—
8C2×#10597292—22no—
9#11926404C2212yes—
10C4×C22⋊Dic19C2211yescharacteristic
11#11926311—22no—
12#11926311—22no—
13#11926306—22no—
14#11926298—21no—
15C2×C19×C22⋊Q8C2212yes—
16C19×#484—22no—
17C19×#467—21no—
18C19×#467—21no—
19C19×#451—22no—
20C2×C19×C22⋊C8C2211yescharacteristic
21C22×Q8×C19D412yes—
22C23×C4×C19C2311yescharacteristic
23C2×Q16×C19—21no—
24C2×Q16×C19—21no—
25C22×C8×C19D411yescharacteristic
26C22×C8×C19D411yescharacteristic
27C19×C22⋊Q8—22no—
28C19×C22⋊Q8—22no—
29C19×C22⋊Q8—22no—
30C19×C22⋊Q8—22no—
31C2×C4⋊C4×C19—22no—
32C2×C4⋊C4×C19D412yes—
33C2×C22⋊C4×C19—22no—
34C2×C22⋊Dic19—22no—
35C2×C22⋊Dic19D411yescharacteristic
36C2×C22⋊Dic19D411yescharacteristic
37C2×C4⋊Dic19—22no—
38C2×C4×Dic19—21no—
39C22×C19⋊C8—22no—
40C22×C19⋊C8—21no—
41C22×C19⋊C8—42no—
42C19×#107—21no—
43C19×#107—21no—
44C19×#103—22no—
45C19×#103—22no—
46C19×C22⋊C8—22no—
47#10597292—44no—
48C19⋊#95—21no—
49C19⋊#95—22no—
50Dic19⋊C8—42no—
51C24×C19C2×D411yescharacteristic
52C2×Q8×C19—22no—
53C2×Q8×C19—22no—
54C2×Q8×C19—42no—
55C2×Q8×C19—42no—
56C22×C4×C19—22no—
57C22×C4×C19—22no—
58C22×C4×C19—41no—
59C22×C4×C19—41no—
60C22×C4×C19C2×D412yes—
61C22×C4×C19C2×D411yescharacteristic
62C22×C4×C19#4111yescharacteristic
63C22×C4×C19#4112yes—
64C22×Dic19—21no—
65C22×Dic19—21no—
66C22×Dic19—42no—
67Q16×C19—81no—
68Q16×C19—81no—
69C2×C8×C19—21no—
70C2×C8×C19—21no—
71C2×C8×C19—41no—
72C2×C8×C19—41no—
73C4⋊C4×C19—22no—
74C4⋊C4×C19—22no—
75C4⋊C4×C19—42no—
76C4⋊C4×C19—42no—
77C22⋊C4×C19—42no—
78C22⋊C4×C19—42no—
79C22⋊Dic19—21no—
80C22⋊Dic19—22no—
81C22⋊Dic19—42no—
82C22⋊Dic19—42no—
83C22⋊Dic19Q1612yescomplemented
84C4⋊Dic19—42no—
85C4⋊Dic19—42no—
86C4×Dic19—41no—
87C4×Dic19—41no—
88C2×C19⋊C8—22no—
89C2×C19⋊C8—24no—
90C2×C19⋊C8—41no—
91C2×C19⋊C8—42no—
92C2×C19⋊C8—41no—
93#10566—191nomaximal, Sylow
94C23×C19—41no—
95C23×C19—41no—
96C23×C19#12111yescharacteristic
97C23×C19#12112yes—
98C23×C19C2×Q1611yescharacteristic
99C23×C19#13511yescharacteristic
100C23×C19#13712yes—
101Q8×C19—44no—
102Q8×C19—42no—
103Q8×C19—42no—
104C2×C4×C19—21no—
105C2×C4×C19—22no—
106C2×C4×C19—21no—
107C2×C4×C19—22no—
108C2×C4×C19—41no—
109C2×C4×C19—42no—
110C2×C4×C19—42no—
111C2×C4×C19—42no—
112C2×C4×C19—82no—
113C2×C4×C19—82no—
114C2×C4×C19#12011yescharacteristic
115C2×C4×C19#12312yes—
116C2×C4×C19#12411yescharacteristic
117C2×Dic19—22no—
118C2×Dic19—41no—
119C2×Dic19—41no—
120C2×Dic19—41no—
121C2×Dic19—41no—
122C2×Dic19—41no—
123C2×Dic19—82no—
124C2×Dic19—82no—
125C2×Dic19—82no—
126C8×C19—41no—
127C8×C19—41no—
128C19⋊C8—42no—
129#3189D1911yescharacteristic
130#1996—192no—
131#1892—192no—
132#1850—191no—
133#1289—191no—
134C22×C19—21no—
135C22×C19—22no—
136C22×C19—21no—
137C22×C19—22no—
138C22×C19—41no—
139C22×C19—41no—
140C22×C19—42no—
141C22×C19#39411yescharacteristic
142C22×C19#46212yes—
143C22×C19#46412yes—
144C22×C19#46711yescharacteristic
145C22×C19#47011yescharacteristic
146C4×C19—22no—
147C4×C19—21no—
148C4×C19—82no—
149C4×C19—82no—
150C4×C19B(4,𝔽2)11yescharacteristic
151C4×C19#45811yescharacteristic
152Dic19—42no—
153Dic19—81no—
154Dic19—162no—
155C23×C8—191no—
156C2×C22⋊Q8C2×D1912yes—
157#484—22no—
158#467—21no—
159#467—21no—
160#451—22no—
161C2×C4⋊C8—381no—
162C2×#103—382no—
163C2×C22⋊C8C2×D1911yescharacteristic
164#380—192no—
165C4×C22⋊C4—191no—
166#342—382no—
167#342—382no—
168#340—382no—
169#336—381no—
170C2×C19—21no—
171C2×C19—21no—
172C2×C19—22no—
173C2×C19—22no—
174C2×C19#204411yescharacteristic
175C2×C19#205311yescharacteristic
176C2×C19#205611yescharacteristic
177C22×Q8C22⋊D1912yes—
178C23×C4C22×D1911yescharacteristic
179C2×Q16—21no—
180C2×Q16—21no—
181C22×C8—381no—
182C22×C8—382no—
183C22×C8—762no—
184C22×C8C22⋊D1911yescharacteristic
185C22×C8C22⋊D1911yescharacteristic
186C22⋊Q8—22no—
187C22⋊Q8—22no—
188C22⋊Q8—22no—
189C22⋊Q8—22no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—382no—
192C2×C4⋊C4C22⋊D1912yes—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—191no—
195C2×C22⋊C4—191no—
196C2×C22⋊C4—382no—
197C2×C42—381no—
198#107—21no—
199#107—21no—
200C4⋊C8—762no—
201#103—22no—
202#103—22no—
203#103—764no—
204C22⋊C8—22no—
205#95—381no—
206#95—382no—
207C19#1056611yescharacteristic, complemented, Sylow
208C24D4×D1911yescharacteristic
209C2×Q8—22no—
210C2×Q8—22no—
211C2×Q8—42no—
212C2×Q8—42no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—381no—
218C22×C4—381no—
219C22×C4—762no—
220C22×C4#6454311yescharacteristic
221C22×C4#6454312yes—
222C22×C4C2×C22⋊D1912yes—
223C22×C4C2×C22⋊D1911yescharacteristic
224Q16—81no—
225Q16—81no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—384no—
231C2×C8—382no—
232C2×C8—761no—
233C2×C8—762no—
234C2×C8—761no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—762no—
240C4⋊C4—762no—
241C22⋊C4—42no—
242C22⋊C4—42no—
243C22⋊C4—192no—
244C22⋊C4—381no—
245C22⋊C4—382no—
246C22⋊C4—762no—
247C22⋊C4—762no—
248C42—761no—
249C42—761no—
250C23—41no—
251C23—41no—
252C23Q16×D1911yescharacteristic
253C23#1059736412yes—
254C23#1059736511yescharacteristic
255C23#1059738411yescharacteristic
256C23#1059738512yes—
257Q8—44no—
258Q8—42no—
259Q8—42no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—41no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4—382no—
271C2×C4—761no—
272C2×C4—761no—
273C2×C4—761no—
274C2×C4—761no—
275C2×C4—761no—
276C2×C4—1522no—
277C2×C4—1522no—
278C2×C4—1522no—
279C2×C4#1059738112yes—
280C2×C4#1059738211yescharacteristic
281C2×C4#1059739911yescharacteristic
282C8—41no—
283C8—41no—
284C8—762no—
285C22—22no—
286C22—21no—
287C22—22no—
288C22—21no—
289C22—41no—
290C22—42no—
291C22—41no—
292C22#1192645811yescharacteristic
293C22#1192675212yes—
294C22#1192676812yes—
295C22#1192678211yescharacteristic
296C22#1192679911yescharacteristic
297C4—22no—
298C4—21no—
299C4—82no—
300C4—82no—
301C4—3042no—
302C4—762no—
303C4—1521no—
304C4#1192673111yescharacteristic
305C4#1192673411yescharacteristic
306C2—22no—
307C2—21no—
308C2—21no—
309C2—22no—
310C2#1456488311yescharacteristic
311C2#1456493811yescharacteristic
312C2#1456495511yescharacteristic
subgroupG/H
centerC22#11926458
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#3189C2
socleC22×C19#394
prime radicalC24×C19C2×D4
hypercenter#3189D19
hypocenterC19#10566
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3189

Complements

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

NH ≅ G/Ntype
83. C22⋊Dic19Q16semidirect
207. C19#10566semidirect

Maximal subgroups

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

subgroupindex
#145646212
#145640592
#145638122
#145615032
C19×#31892
#1056619