Finite Group Databasebeta

← #18080234

Subgroups — #18080234

Order 4864.

448 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 111 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#14572720C211yesmaximal, characteristic
2#14562352C212yesmaximal
3#14561979C211yesmaximal, characteristic
4#14561491C212yesmaximal
5C19×#2567C211yesmaximal, characteristic
6#11926675—24no—
7#11926601—21no—
8#11926601C2212yes—
9#11926601C2212yes—
10#11926597—21no—
11#11926290—24no—
12#11926270—21no—
13#11926270—21no—
14C2×C19×C4⋊Q8C2211yescharacteristic
15C2×C4×Q8×C19C2211yescharacteristic
16C19×#395—21no—
17C19×#395—21no—
18C19×#391C412yes—
19C19×#389—21no—
20C19×#389—21no—
21C19×#384C412yes—
22C4×C4⋊C4×C19C2211yescharacteristic
23C22×Q8×C19—21no—
24C22×Q8×C19C2×C411yescharacteristic
25C19×C4⋊Q8—22no—
26C19×C4⋊Q8—22no—
27C4×Q8×C19—22no—
28C4×Q8×C19—22no—
29C2×C4⋊C4×C19—21no—
30C2×C4⋊C4×C19—21no—
31C2×C4⋊C4×C19—22no—
32C2×C4⋊C4×C19—22no—
33C2×C4⋊C4×C19C2×C412yes—
34C2×C4⋊C4×C19C2×C411yescharacteristic
35C2×C4⋊C4×C19D411yescharacteristic
36C2×C4⋊C4×C19D411yescharacteristic
37C2×C42×C19C2×C412yes—
38C2×C42×C19D411yescharacteristic
39C2×C42×C19D411yescharacteristic
40C2×C42×C19C2311yescharacteristic
41C19×#95—22no—
42C19×#95—22no—
43C19×#95—21no—
44C22⋊(C19⋊C8)—22no—
45C22⋊(C19⋊C8)—22no—
46C4⋊(C19⋊C8)—22no—
47C4⋊(C19⋊C8)—22no—
48C4⋊(C19⋊C8)—22no—
49C4⋊(C19⋊C8)D414yes—
50#10597260—22no—
51#10597260—22no—
52#10597260—22no—
53C4×C19⋊C8—22no—
54C2×Q8×C19—22no—
55C2×Q8×C19—22no—
56C2×Q8×C19—41no—
57C2×Q8×C19—42no—
58C2×Q8×C19—82no—
59C22×C4×C19—22no—
60C22×C4×C19—22no—
61C22×C4×C19C22⋊C411yescharacteristic
62C22×C4×C19C22⋊C411yescharacteristic
63C22×C4×C19C22⋊C411yescharacteristic
64C22×C4×C19C22⋊C411yescharacteristic
65C22×C4×C19C22×C411yescharacteristic
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19C2×D411yescharacteristic
68C4⋊C4×C19—24no—
69C4⋊C4×C19—22no—
70C4⋊C4×C19—22no—
71C4⋊C4×C19—22no—
72C4⋊C4×C19—24no—
73C4⋊C4×C19—41no—
74C4⋊C4×C19—41no—
75C4⋊C4×C19—82no—
76C4⋊C4×C19—82no—
77C42×C19—21no—
78C42×C19—21no—
79C42×C19—21no—
80C42×C19—21no—
81C42×C19—42no—
82C42×C19C2×D412yes—
83C42×C19#4112yes—
84C2×C19⋊C8—24no—
85C2×C19⋊C8—42no—
86#9454—191nomaximal, Sylow
87C23×C19C2×C22⋊C411yescharacteristic
88Q8×C19—44no—
89Q8×C19—84no—
90C2×C4×C19—21no—
91C2×C4×C19—21no—
92C2×C4×C19—21no—
93C2×C4×C19—21no—
94C2×C4×C19—22no—
95C2×C4×C19—24no—
96C2×C4×C19—21no—
97C2×C4×C19—21no—
98C2×C4×C19—21no—
99C2×C4×C19—21no—
100C2×C4×C19—21no—
101C2×C4×C19—41no—
102C2×C4×C19—42no—
103C2×C4×C19—42no—
104C2×C4×C19—41no—
105C2×C4×C19—41no—
106C2×C4×C19—42no—
107C2×C4×C19—42no—
108C2×C4×C19—42no—
109C2×C4×C19#10112yes—
110C2×C4×C19C4×D412yes—
111C2×C4×C19#12011yescharacteristic
112C2×C4×C19#12112yes—
113C2×C4×C19#12311yescharacteristic
114C19⋊C8—44no—
115C19⋊C8—82no—
116#2983—191no—
117#2567D1911yescharacteristic
118#1556—192no—
119#1467—191no—
120#1285—192no—
121C22×C19—21no—
122C22×C19—21no—
123C22×C19#38611yescharacteristic
124C22×C19C2×#10111yescharacteristic
125C22×C19#41311yescharacteristic
126C4×C19—21no—
127C4×C19—22no—
128C4×C19—22no—
129C4×C19—22no—
130C4×C19—44no—
131C4×C19—41no—
132C4×C19—41no—
133C4×C19—41no—
134C4×C19—82no—
135C4×C19#45612yes—
136C2×C4⋊Q8C2×D1911yescharacteristic
137C2×C4×Q8C2×D1911yescharacteristic
138#446—384no—
139#432—192no—
140#432—192no—
141#432—381no—
142#431—381no—
143#395—21no—
144#395—21no—
145#391Dic1912yes—
146#389—21no—
147#389—21no—
148#384Dic1912yes—
149C4×C4⋊C4C2×D1911yescharacteristic
150#332—384no—
151#324—381no—
152#324—381no—
153C2×C19—21no—
154C2×C19—21no—
155C2×C19#188611yescharacteristic
156C2×C19#190111yescharacteristic
157C2×C19#191011yescharacteristic
158C22×Q8—21no—
159C22×Q8C2×Dic1911yescharacteristic
160C4⋊Q8—22no—
161C4⋊Q8—22no—
162C4×Q8—22no—
163C4×Q8—22no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4C2×Dic1912yes—
169C2×C4⋊C4C2×Dic1911yescharacteristic
170C2×C4⋊C4C22⋊D1911yescharacteristic
171C2×C4⋊C4C22⋊D1911yescharacteristic
172C2×C42C2×Dic1912yes—
173C2×C42C22⋊D1911yescharacteristic
174C2×C42C22⋊D1911yescharacteristic
175C2×C42C22×D1911yescharacteristic
176C4⋊C8—194no—
177C4⋊C8—382no—
178C4⋊C8—382no—
179C4⋊C8—382no—
180C22⋊C8—382no—
181C22⋊C8—382no—
182#97—382no—
183#97—382no—
184#97—382no—
185C4×C8—382no—
186#95—22no—
187#95—22no—
188#95—21no—
189C19#945411yescharacteristic, complemented, Sylow
190C2×Q8—22no—
191C2×Q8—22no—
192C2×Q8—41no—
193C2×Q8—42no—
194C2×Q8—82no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4C22⋊Dic1911yescharacteristic
198C22×C4C22⋊Dic1911yescharacteristic
199C22×C4C22⋊Dic1911yescharacteristic
200C22×C4C22⋊Dic1911yescharacteristic
201C22×C4C22×Dic1911yescharacteristic
202C22×C4C2×C22⋊D1911yescharacteristic
203C22×C4C2×C22⋊D1911yescharacteristic
204C2×C8—384no—
205C2×C8—762no—
206C4⋊C4—24no—
207C4⋊C4—22no—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—24no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—82no—
214C4⋊C4—82no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—42no—
220C42D4×D1912yes—
221C42#6454312yes—
222C23C2×C22⋊Dic1911yescharacteristic
223Q8—44no—
224Q8—84no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—24no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4#1059729312yes—
245C2×C4D4×Dic1912yes—
246C2×C4#1059738111yescharacteristic
247C2×C4#1059738311yescharacteristic
248C2×C4#1059738512yes—
249C8—764no—
250C8—1522no—
251C22—21no—
252C22—21no—
253C22#1192642411yescharacteristic
254C22C2×#1059729311yescharacteristic
255C22#1192652811yescharacteristic
256C4—22no—
257C4—22no—
258C4—22no—
259C4—21no—
260C4—44no—
261C4—41no—
262C4—41no—
263C4—41no—
264C4—82no—
265C4#1192672612yes—
266C2—21no—
267C2—21no—
268C2#1456402911yescharacteristic
269C2#1456410411yescharacteristic
270C2#1456416311yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2567C2
socleC22×C19#386
prime radicalC23×C19C2×C22⋊C4
cosocleC2×C42×C19C23
hypercenter#2567D19
hypocenterC19#9454
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2567

Complements

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

NH ≅ G/Ntype
189. C19#9454semidirect

Maximal subgroups

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

subgroupindex
#145727202
#145623522
#145619792
#145614912
C19×#25672
#945419