Finite Group Databasebeta

← #18085778

Subgroups — #18085778

Order 4864.

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

normal subgroups only

This group has 594 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#14563580C212yesmaximal
2#14563552C211yesmaximal, characteristic
3#14561543C211yesmaximal, characteristic, complemented
4#14561488C212yesmaximal, complemented
5C19×#2608C211yesmaximal, characteristic, complemented
6C22×#64541C2211yescharacteristic
7C2×#10597262—22no—
8C2×#10597262—22no—
9C2×#10597263—22no—
10#11926508C2212yes—
11#11926407C2211yescharacteristic
12C19×#396—22no—
13C19×#389—22no—
14C19×#387—22no—
15C19×#381C2211yescharacteristic
16C4×C22⋊C4×C19C2212yes—
17C23×C4×C19C2311yescharacteristic
18C22×C22⋊D19—21no—
19C2×#64541—22no—
20C2×#64541—22no—
21C2×#64541—44no—
22C22×D76Q811yescharacteristic
23C22×C4×D19—21no—
24C22×Dic38Q811yescharacteristic
25C2×C4⋊C4×C19—22no—
26C2×C4⋊C4×C19—22no—
27C2×C4⋊C4×C19—22no—
28C2×C22⋊C4×C19—22no—
29C2×C22⋊C4×C19D412yes—
30C2×C42×C19D412yes—
31C2×C42×C19D412yes—
32C2×C22⋊Dic19—21no—
33C2×#64520—22no—
34C19×#95—22no—
35C19×#95—22no—
36C19×#95—22no—
37C19⋊#95—22no—
38C22⋊(C19⋊C8)—22no—
39C22⋊(C19⋊C8)—22no—
40#10597263—44no—
41#10597262—44no—
42#10597262—44no—
43C24×C19C2×D411yescharacteristic
44C23×D19—21no—
45C22×C4×C19—22no—
46C22×C4×C19—22no—
47C22×C4×C19—22no—
48C22×C4×C19—42no—
49C22×C4×C19C2×D412yes—
50C22×C4×C19C2×Q811yescharacteristic
51C22×C4×C19#4112yes—
52C22×C4×C19#4111yescharacteristic
53C2×C22⋊D19—24no—
54C2×C22⋊D19—42no—
55C2×C22⋊D19—41no—
56C2×C22⋊D19—41no—
57C22×Dic19—21no—
58C22×Dic19—41no—
59#64541—24no—
60#64541—24no—
61#64541—44no—
62#64541—44no—
63#64541—42no—
64#64541—42no—
65C2×D76—22no—
66C2×D76—42no—
67C2×C4×D19—42no—
68C2×C4×D19—42no—
69C2×C4×D19—42no—
70C2×Dic38—22no—
71C2×Dic38—42no—
72C4⋊C4×C19—44no—
73C4⋊C4×C19—44no—
74C4⋊C4×C19—82no—
75C22⋊C4×C19—44no—
76C22⋊C4×C19—42no—
77C42×C19—42no—
78C42×C19—42no—
79C22⋊Dic19—42no—
80#64520—42no—
81#64520—42no—
82C2×C19⋊C8—42no—
83#10388—191nomaximal, Sylow
84C23×C19—22no—
85C23×C19—42no—
86C23×C19#12011yescharacteristic
87C23×C19C22⋊Q811yescharacteristic
88C23×C19#12411yescharacteristic
89C22×D19—22no—
90C22×D19—41no—
91C22×D19—41no—
92C22×D19—82no—
93C2×C4×C19—22no—
94C2×C4×C19—22no—
95C2×C4×C19—24no—
96C2×C4×C19—41no—
97C2×C4×C19—41no—
98C2×C4×C19—42no—
99C2×C4×C19—42no—
100C2×C4×C19—42no—
101C2×C4×C19—42no—
102C2×C4×C19—42no—
103C2×C4×C19—42no—
104C2×C4×C19—42no—
105C2×C4×C19—42no—
106C2×C4×C19—42no—
107C2×C4×C19C22⋊Q812yes—
108C2×C4×C19#12412yes—
109C22⋊D19—44no—
110C22⋊D19—44no—
111C2×Dic19—22no—
112C2×Dic19—41no—
113C2×Dic19—41no—
114C2×Dic19—81no—
115C2×Dic19—82no—
116D76—24no—
117D76—42no—
118C4×D19—44no—
119C4×D19—44no—
120Dic38—24no—
121Dic38—42no—
122C19⋊C8—82no—
123#2608D1911yescharacteristic, complemented
124#1789—192no—
125#1782—191no—
126#1306—191no—
127#1284—192no—
128C22×C19—22no—
129C22×C19—21no—
130C22×C19—21no—
131C22×C19—22no—
132C22×C19—22no—
133C22×C19—82no—
134C22×C19#39311yescharacteristic
135C22×C19B(4,𝔽2)12yes—
136C2×D19—42no—
137C2×D19—82no—
138C2×D19—82no—
139C2×D19—82no—
140C4×C19—22no—
141C4×C19—22no—
142C4×C19—44no—
143C4×C19—82no—
144C4×C19—82no—
145Dic19—42no—
146Dic19—161no—
147C22×#41—191no—
148C2×#104—382no—
149C2×#104—382no—
150C2×#99—382no—
151#407—192no—
152#396—22no—
153#389—22no—
154#387—22no—
155#381—191no—
156#381C2×D1911yescharacteristic
157C4×C22⋊C4C2×D1912yes—
158C2×C19—22no—
159C2×C19—41no—
160C2×C19—41no—
161C2×C19#202911yescharacteristic
162C2×C19#203112yes—
163D19—82no—
164C2×#41—382no—
165C2×#41—382no—
166C2×#41—764no—
167C22×Q8—191no—
168C22×D4—191no—
169C22×D4—381no—
170C23×C4—381no—
171C23×C4C22×D1911yescharacteristic
172C2×M16—382no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—381no—
178C2×C22⋊C4C22⋊D1912yes—
179C2×C42C22⋊D1912yes—
180C2×C42C22⋊D1912yes—
181#104—764no—
182#104—764no—
183#99—764no—
184C22⋊C8—382no—
185C22⋊C8—382no—
186#95—22no—
187#95—22no—
188#95—22no—
189#95—382no—
190C19#1038811yescharacteristic, complemented, Sylow
191C24—381no—
192C24C2×C22⋊D1911yescharacteristic
193#41—384no—
194#41—384no—
195#41—762no—
196#41—762no—
197#41—764no—
198#41—764no—
199C2×Q8—382no—
200C2×Q8—762no—
201C2×D4—384no—
202C2×D4—382no—
203C2×D4—762no—
204C2×D4—762no—
205C2×D4—761no—
206C2×D4—761no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—42no—
211C22×C4—381no—
212C22×C4—762no—
213C22×C4—762no—
214C22×C4—762no—
215C22×C4—761no—
216C22×C4Q8×D1911yescharacteristic
217C22×C4#6454512yes—
218C22×C4#6454511yescharacteristic
219C22×C4C2×C22⋊D1912yes—
220M16—762no—
221M16—762no—
222C2×C8—762no—
223C4⋊C4—44no—
224C4⋊C4—44no—
225C4⋊C4—82no—
226C22⋊C4—44no—
227C22⋊C4—42no—
228C22⋊C4—762no—
229C42—42no—
230C42—42no—
231C23—22no—
232C23—42no—
233C23—382no—
234C23—761no—
235C23—761no—
236C23—1522no—
237C23#1059739211yescharacteristic
238C23#1059739311yescharacteristic
239C23#1059739911yescharacteristic
240Q8—384no—
241Q8—762no—
242D4—384no—
243D4—762no—
244D4—764no—
245D4—764no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—24no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—382no—
261C2×C4—764no—
262C2×C4—764no—
263C2×C4—761no—
264C2×C4—761no—
265C2×C4—1521no—
266C2×C4—1522no—
267C2×C4#1059739212yes—
268C2×C4#1059739312yes—
269C8—1522no—
270C22—22no—
271C22—21no—
272C22—21no—
273C22—22no—
274C22—22no—
275C22—82no—
276C22—762no—
277C22—1522no—
278C22—1522no—
279C22—1522no—
280C22#1192645511yescharacteristic
281C22#1192673112yes—
282C4—22no—
283C4—22no—
284C4—44no—
285C4—82no—
286C4—82no—
287C4—3041no—
288C4—762no—
289C2—22no—
290C2—41no—
291C2—41no—
292C2—1522no—
293C2#1456479811yescharacteristic
294C2#1456480412yes—
subgroupG/H
centerC22#11926455
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#2608C2
socleC22×C19#393
prime radicalC22×#64541C22
hypercenter#2608D19
hypocenterC19#10388
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2608

Complements

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

NH ≅ G/Ntype
3. #14561543C2semidirect
4. #14561488C2semidirect
5. C19×#2608C2semidirect
123. #2608D19semidirect
190. C19#10388semidirect

Maximal subgroups

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

subgroupindex
#145635802
#145635522
#145615432
#145614882
C19×#26082
#1038819