Finite Group Databasebeta

← #18080231

Subgroups — #18080231

Order 4864.

448 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 103 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#14568840C211yesmaximal, characteristic
3#14562353C212yesmaximal
4#14561490C212yesmaximal
5C19×#1467C211yesmaximal, characteristic
6C2×#10597315C2211yescharacteristic
7#11926675—24no—
8#11926601—21no—
9#11926601C2212yes—
10#11926597—21no—
11#11926464—21no—
12#11926464—21no—
13#11926451C412yes—
14#11926442—21no—
15#11926442—21no—
16#11926413C412yes—
17C4×C4⋊Dic19C2211yescharacteristic
18#11926291—24no—
19C2×C4×Q8×C19C2211yescharacteristic
20C19×#432C2212yes—
21C19×#324—21no—
22C19×#324—21no—
23C22×Q8×C19C2×C411yescharacteristic
24C22×Dic38—21no—
25C4×Q8×C19—22no—
26C4×Q8×C19—22no—
27C2×C4⋊C4×C19C2×C411yescharacteristic
28C2×C4⋊C4×C19D411yescharacteristic
29C2×C4⋊C4×C19D411yescharacteristic
30C2×C42×C19D411yescharacteristic
31C2×C42×C19D411yescharacteristic
32C2×C42×C19C2311yescharacteristic
33C2×C4⋊Dic19—21no—
34C2×C4⋊Dic19—21no—
35C2×C4⋊Dic19C2×C412yes—
36C2×Dic19⋊C4—22no—
37C2×Dic19⋊C4—22no—
38C2×C4×Dic19C2×C412yes—
39#10597315—22no—
40#10597315—22no—
41C19×C4⋊C8—22no—
42C19×C22⋊C8—22no—
43C19×#97—22no—
44C19⋊#95—22no—
45C19⋊#95—22no—
46C19⋊#95—21no—
47C22⋊(C19⋊C8)—22no—
48C4⋊(C19⋊C8)—22no—
49C4⋊(C19⋊C8)—22no—
50C4⋊(C19⋊C8)D414yes—
51#10597260—22no—
52#10597260—22no—
53C4×C19⋊C8—22no—
54C2×Q8×C19—22no—
55C2×Q8×C19—22no—
56C2×Q8×C19—41no—
57C22×C4×C19C22⋊C411yescharacteristic
58C22×C4×C19C22⋊C411yescharacteristic
59C22×C4×C19C22⋊C411yescharacteristic
60C22×C4×C19C22⋊C411yescharacteristic
61C22×C4×C19C22×C411yescharacteristic
62C22×C4×C19C2×D411yescharacteristic
63C22×C4×C19C2×D411yescharacteristic
64C22×Dic19—22no—
65C22×Dic19—22no—
66C2×Dic38—42no—
67C2×Dic38—82no—
68C2×C8×C19—42no—
69C4⋊C4×C19—22no—
70C4⋊C4×C19—22no—
71C4⋊C4×C19—22no—
72C42×C19—21no—
73C42×C19—21no—
74C42×C19—21no—
75C42×C19—21no—
76C42×C19C2×D412yes—
77C42×C19#4112yes—
78C4⋊Dic19—24no—
79C4⋊Dic19—24no—
80C4⋊Dic19—41no—
81C4⋊Dic19—41no—
82Dic19⋊C4—82no—
83Dic19⋊C4—82no—
84C4×Dic19—42no—
85C2×C19⋊C8—24no—
86#9454—191nomaximal, Sylow
87C23×C19C2×C22⋊C411yescharacteristic
88Q8×C19—44no—
89C2×C4×C19—21no—
90C2×C4×C19—21no—
91C2×C4×C19—21no—
92C2×C4×C19—21no—
93C2×C4×C19—22no—
94C2×C4×C19—21no—
95C2×C4×C19—21no—
96C2×C4×C19—21no—
97C2×C4×C19—21no—
98C2×C4×C19—21no—
99C2×C4×C19—41no—
100C2×C4×C19—41no—
101C2×C4×C19—41no—
102C2×C4×C19#10112yes—
103C2×C4×C19C4×D412yes—
104C2×C4×C19#12011yescharacteristic
105C2×C4×C19#12112yes—
106C2×C4×C19#12311yescharacteristic
107C2×Dic19—24no—
108C2×Dic19—42no—
109C2×Dic19—42no—
110C2×Dic19—42no—
111C2×Dic19—42no—
112C2×Dic19—42no—
113Dic38—84no—
114C8×C19—82no—
115C19⋊C8—44no—
116#2983—191no—
117#2567—191no—
118#1556—192no—
119#1467D1911yescharacteristic
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—41no—
131C4×C19—41no—
132C4×C19—41no—
133C4×C19#45612yes—
134Dic19—44no—
135Dic19—82no—
136C2×C4⋊Q8—191no—
137C2×C4×Q8C2×D1911yescharacteristic
138#446—384no—
139#432—192no—
140#432—381no—
141#432C2×D1912yes—
142#431—381no—
143#395—381no—
144#395—381no—
145#391—192no—
146#389—381no—
147#389—381no—
148#384—192no—
149C4×C4⋊C4—191no—
150#332—384no—
151#324—21no—
152#324—21no—
153C2×C19—21no—
154C2×C19—21no—
155C2×C19#188611yescharacteristic
156C2×C19#190111yescharacteristic
157C2×C19#191011yescharacteristic
158C22×Q8—381no—
159C22×Q8C4×D1911yescharacteristic
160C4⋊Q8—382no—
161C4⋊Q8—382no—
162C4×Q8—22no—
163C4×Q8—22no—
164C2×C4⋊C4—192no—
165C2×C4⋊C4—381no—
166C2×C4⋊C4—381no—
167C2×C4⋊C4—382no—
168C2×C4⋊C4—382no—
169C2×C4⋊C4C4×D1911yescharacteristic
170C2×C4⋊C4C22⋊D1911yescharacteristic
171C2×C4⋊C4C22⋊D1911yescharacteristic
172C2×C42—192no—
173C2×C42D7611yescharacteristic
174C2×C42D7611yescharacteristic
175C2×C42C22×D1911yescharacteristic
176C4⋊C8—22no—
177C4⋊C8—194no—
178C4⋊C8—382no—
179C4⋊C8—382no—
180C22⋊C8—22no—
181C22⋊C8—382no—
182#97—22no—
183#97—382no—
184#97—382no—
185C4×C8—382no—
186#95—382no—
187#95—382no—
188#95—381no—
189C19#945411yescharacteristic, complemented, Sylow
190C2×Q8—22no—
191C2×Q8—22no—
192C2×Q8—41no—
193C2×Q8—762no—
194C2×Q8—1522no—
195C22×C4—382no—
196C22×C4—382no—
197C22×C4(C2×D19)⋊C411yescharacteristic
198C22×C4(C2×D19)⋊C411yescharacteristic
199C22×C4(C2×D19)⋊C411yescharacteristic
200C22×C4(C2×D19)⋊C411yescharacteristic
201C22×C4C2×C4×D1911yescharacteristic
202C22×C4C2×D7611yescharacteristic
203C22×C4C2×C22⋊D1911yescharacteristic
204C2×C8—42no—
205C2×C8—384no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—22no—
209C4⋊C4—384no—
210C4⋊C4—384no—
211C4⋊C4—761no—
212C4⋊C4—761no—
213C4⋊C4—1522no—
214C4⋊C4—1522no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—762no—
220C42D4×D1912yes—
221C42#6454312yes—
222C23C2×(C2×D19)⋊C411yescharacteristic
223Q8—44no—
224Q8—1524no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—384no—
239C2×C4—762no—
240C2×C4—762no—
241C2×C4—762no—
242C2×C4—762no—
243C2×C4—762no—
244C2×C4#1059728112yes—
245C2×C4(C22⋊D19)⋊C412yes—
246C2×C4#1059732811yescharacteristic
247C2×C4#1059733211yescharacteristic
248C2×C4#1059738512yes—
249C8—82no—
250C8—764no—
251C22—21no—
252C22—21no—
253C22#1192642111yescharacteristic
254C22C2×#1059728111yescharacteristic
255C22#1192652611yescharacteristic
256C4—22no—
257C4—22no—
258C4—22no—
259C4—21no—
260C4—41no—
261C4—41no—
262C4—41no—
263C4—764no—
264C4—1522no—
265C4#1192672912yes—
266C2—21no—
267C2—21no—
268C2#1456402611yescharacteristic
269C2#1456410111yescharacteristic
270C2#1456416011yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1467C2
socleC22×C19#386
prime radicalC23×C19C2×C22⋊C4
cosocleC2×C42×C19C23
hypercenter#1467D19
hypocenterC19#9454
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

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
#145688402
#145623532
#145614902
C19×#14672
#945419