Finite Group Databasebeta

← #18077574

Subgroups — #18077574

Order 4864.

572 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 135 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#14566238C211yesmaximal, characteristic
2#14563725C212yesmaximal
3C2×#11926270C211yesmaximal, characteristic
4#14561514C212yesmaximal
5C2×C19×#400C211yesmaximal, characteristic
6C2×C22⋊(C19⋊C8)C2212yes—
7#11926430—24no—
8#11926407—21no—
9#11926404C2212yes—
10C4×C22⋊Dic19—21no—
11#11926306—24no—
12#11926270—22no—
13C22×C4⋊C4×C19C2211yescharacteristic
14C22×C4⋊C4×C19C2211yescharacteristic
15C19×#400—22no—
16C19×#400C414yescomplemented
17C2×C19×#95—21no—
18C2×C19×#95—21no—
19C2×C19×#95C2211yescharacteristic
20C23×C4×C19—21no—
21C23×C4×C19—21no—
22C23×C4×C19D411yescharacteristic
23C23×C4×C19D411yescharacteristic
24C23×C4×C19C2311yescharacteristic
25C2×C4⋊C4×C19—22no—
26C2×C4⋊C4×C19—22no—
27C2×C4⋊C4×C19—22no—
28C2×C4⋊C4×C19—22no—
29C2×C4⋊C4×C19—21no—
30C2×C4⋊C4×C19C2×C412yes—
31C2×C4⋊C4×C19C2×C412yes—
32C2×C4⋊C4×C19D412yes—
33C2×C22⋊Dic19—22no—
34C2×C4⋊Dic19D414yes—
35C2×C4×Dic19—22no—
36C22×C19⋊C8—22no—
37C19×#95—24no—
38C19×#95—24no—
39C19×#95—21no—
40C19×#95C2×C412yes—
41C19⋊#95—22no—
42C19⋊#95—24no—
43C19⋊#95—22no—
44C22⋊(C19⋊C8)—22no—
45C22⋊(C19⋊C8)—22no—
46C24×C19C2×D411yescharacteristic
47C22×C4×C19—21no—
48C22×C4×C19—21no—
49C22×C4×C19—21no—
50C22×C4×C19—22no—
51C22×C4×C19—22no—
52C22×C4×C19—21no—
53C22×C4×C19—22no—
54C22×C4×C19—22no—
55C22×C4×C19—42no—
56C22×C4×C19—42no—
57C22×C4×C19—42no—
58C22×C4×C19—42no—
59C22×C4×C19—44no—
60C22×C4×C19—41no—
61C22×C4×C19—41no—
62C22×C4×C19—42no—
63C22×C4×C19C22⋊C412yes—
64C22×C4×C19C22⋊C412yes—
65C22×C4×C19C22×C411yescharacteristic
66C22×C4×C19C2×D412yes—
67C22×C4×C19C2×D411yescharacteristic
68C22×C4×C19#4112yes—
69C22×Dic19—24no—
70C4⋊C4×C19—24no—
71C4⋊C4×C19—24no—
72C4⋊C4×C19—24no—
73C4⋊C4×C19—42no—
74C22⋊Dic19—42no—
75C22⋊Dic19—42no—
76C4⋊Dic19—44no—
77C4×Dic19—82no—
78C2×C19⋊C8—44no—
79C2×C19⋊C8—42no—
80#9022—191nomaximal, Sylow
81C23×C19—22no—
82C23×C19—22no—
83C23×C19C2×C22⋊C411yescharacteristic
84C23×C19#12011yescharacteristic
85C23×C19#12311yescharacteristic
86C23×C19#13512yes—
87C23×C19#13712yes—
88C2×C4×C19—24no—
89C2×C4×C19—22no—
90C2×C4×C19—22no—
91C2×C4×C19—22no—
92C2×C4×C19—22no—
93C2×C4×C19—41no—
94C2×C4×C19—41no—
95C2×C4×C19—42no—
96C2×C4×C19—42no—
97C2×C4×C19—42no—
98C2×C4×C19—42no—
99C2×C4×C19—42no—
100C2×C4×C19—42no—
101C2×C4×C19—42no—
102C2×C4×C19—44no—
103C2×C4×C19—42no—
104C2×C4×C19—42no—
105C2×C4×C19—81no—
106C2×C4×C19—84no—
107C2×C4×C19—82no—
108C2×C4×C19—82no—
109C2×C4×C19C4×D412yes—
110C2×C4×C19#12112yes—
111C2×Dic19—44no—
112C2×Dic19—44no—
113C2×Dic19—44no—
114C19⋊C8—82no—
115C2×#400D1911yescharacteristic
116#2313—191no—
117#1824—192no—
118C2×#324—191no—
119#1294—192no—
120C22×C19—24no—
121C22×C19—24no—
122C22×C19—21no—
123C22×C19—21no—
124C22×C19—21no—
125C22×C19—21no—
126C22×C19#38611yescharacteristic
127C22×C19#41611yescharacteristic
128C22×C19#41911yescharacteristic
129C22×C19#45212yes—
130C22×C19#45412yes—
131C22×C19#45812yes—
132C22×C19#48512yes—
133C4×C19—22no—
134C4×C19—22no—
135C4×C19—42no—
136C4×C19—42no—
137C4×C19—82no—
138C4×C19—82no—
139Dic19—84no—
140C22×C4⋊C4C2×D1911yescharacteristic
141C22×C4⋊C4C2×D1911yescharacteristic
142C2×C22⋊C8—192no—
143#400—22no—
144#400Dic1914yescomplemented
145#387—384no—
146#381—381no—
147#380—192no—
148C4×C22⋊C4—381no—
149C2×#95—21no—
150C2×#95—21no—
151C2×#95C2×D1911yescharacteristic
152#340—384no—
153#324—382no—
154C2×C19—21no—
155C2×C19—21no—
156C2×C19—22no—
157C2×C19#161514yes—
158C2×C19#187311yescharacteristic
159C2×C19#188811yescharacteristic
160C2×C19#189011yescharacteristic
161C23×C4—21no—
162C23×C4—21no—
163C23×C4C22⋊D1911yescharacteristic
164C23×C4C22⋊D1911yescharacteristic
165C23×C4C22×D1911yescharacteristic
166C22×C8—382no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—194no—
173C2×C4⋊C4C2×Dic1912yes—
174C2×C4⋊C4C2×Dic1912yes—
175C2×C4⋊C4C22⋊D1912yes—
176C2×C22⋊C4—382no—
177C2×C42—382no—
178C22⋊C8—382no—
179C22⋊C8—382no—
180#95—24no—
181#95—24no—
182#95—21no—
183#95—382no—
184#95—384no—
185#95—382no—
186#95C2×Dic1912yes—
187C19#902211yescharacteristic, complemented, Sylow
188C24C2×C22⋊D1911yescharacteristic
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—42no—
198C22×C4—42no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—44no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—42no—
205C22×C4—384no—
206C22×C4C22⋊Dic1912yes—
207C22×C4C22⋊Dic1912yes—
208C22×C4D4×D1912yes—
209C22×C4#6454312yes—
210C22×C4C22×Dic1911yescharacteristic
211C22×C4C2×C22⋊D1911yescharacteristic
212C2×C8—764no—
213C2×C8—762no—
214C4⋊C4—24no—
215C4⋊C4—24no—
216C4⋊C4—24no—
217C4⋊C4—42no—
218C4⋊C4—764no—
219C22⋊C4—762no—
220C22⋊C4—762no—
221C42—1522no—
222C23—22no—
223C23—22no—
224C23#1059738111yescharacteristic
225C23#1059738311yescharacteristic
226C23#1059738812yes—
227C23#1059739612yes—
228C23C2×C22⋊Dic1911yescharacteristic
229C2×C4—24no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—44no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—81no—
247C2×C4—84no—
248C2×C4—82no—
249C2×C4—82no—
250C2×C4—764no—
251C2×C4—764no—
252C2×C4—764no—
253C2×C4D4×Dic1912yes—
254C2×C4#1059738512yes—
255C8—1522no—
256C22—24no—
257C22—24no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22#1192642411yescharacteristic
263C22#1192654011yescharacteristic
264C22#1192655311yescharacteristic
265C22#1192670412yes—
266C22#1192671612yes—
267C22#1192673312yes—
268C22#1192688212yes—
269C4—22no—
270C4—22no—
271C4—42no—
272C4—42no—
273C4—82no—
274C4—82no—
275C4—1524no—
276C2—21no—
277C2—21no—
278C2—22no—
279C2#1456266414yes—
280C2#1456394811yescharacteristic
281C2#1456403911yescharacteristic
282C2#1456404911yescharacteristic
subgroupG/H
centerC23#10597383
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#400C2
socleC23×C19#120
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenterC2×#400D19
hypocenterC19#9022
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
16. C19×#400C4semidirect
144. #400Dic19semidirect
187. C19#9022semidirect

Maximal subgroups

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

subgroupindex
#145662382
#145637252
C2×#119262702
#145615142
C2×C19×#4002
#902219