Finite Group Databasebeta

← #18085478

Subgroups — #18085478

Order 4864.

754 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 754 conjugacy classes of subgroups — too many to draw. Only its 89 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#14567280C212yesmaximal
2#14563558C211yesmaximal, characteristic
3#14562155C212yesmaximal
4#14561520C211yesmaximal, characteristic
5C19×#3195C211yesmaximal, characteristic
6C23×Dic38C2211yescharacteristic
7C2×#10597390—22no—
8C2×#10597281—22no—
9#11926508C2211yescharacteristic
10#11926464—24no—
11#11926449—22no—
12#11926416—24no—
13C4×C22⋊Dic19C2212yes—
14#11926281—24no—
15C2×C19×C22⋊Q8C2212yes—
16C19×#483—22no—
17C19×#470—22no—
18C19×#451—22no—
19C19×#407C2211yescharacteristic
20C22×Q8×C19D412yes—
21C23×C4×C19C2311yescharacteristic
22C23×Dic19D412yes—
23C22×Dic38—22no—
24C22×Dic38—21no—
25C22×Dic38—22no—
26C22×Dic38—21no—
27C22×Dic38—44no—
28C2×Q16×C19—22no—
29C2×M16×C19D412yes—
30C19×C22⋊Q8—22no—
31C19×C22⋊Q8—22no—
32C19×C22⋊Q8—22no—
33C19×C22⋊Q8—22no—
34C2×C4⋊C4×C19—22no—
35C2×C4⋊C4×C19D412yes—
36C2×C22⋊C4×C19—22no—
37C2×C22⋊Dic19—22no—
38#10597390—48no—
39C2×Dic19⋊C4—28no—
40C2×C4×Dic19—22no—
41C2×#64520—21no—
42C19×#106—22no—
43C19×#103—24no—
44C19×C22⋊C8—22no—
45C19⋊#95—28no—
46C19⋊#95D414yes—
47C22⋊(C19⋊C8)—22no—
48#10597281—44no—
49C24×C19C2×D411yescharacteristic
50C2×Q8×C19—22no—
51C2×Q8×C19—22no—
52C2×Q8×C19—44no—
53C22×C4×C19—22no—
54C22×C4×C19—22no—
55C22×C4×C19—42no—
56C22×C4×C19C2×D412yes—
57C22×C4×C19C2×D412yes—
58C22×C4×C19C2×D411yescharacteristic
59C22×C4×C19#4111yescharacteristic
60C22×Dic19—24no—
61C22×Dic19—24no—
62C22×Dic19—22no—
63C22×Dic19—44no—
64C2×Dic38—28no—
65C2×Dic38—24no—
66C2×Dic38—48no—
67C2×Dic38—44no—
68C2×Dic38—42no—
69C2×Dic38—44no—
70C2×Dic38—41no—
71C2×Dic38—42no—
72C2×Dic38—41no—
73Q16×C19—82no—
74M16×C19—42no—
75C2×C8×C19—22no—
76C4⋊C4×C19—22no—
77C4⋊C4×C19—22no—
78C4⋊C4×C19—42no—
79C4⋊C4×C19—42no—
80C22⋊C4×C19—42no—
81C22⋊C4×C19—42no—
82C22⋊Dic19—28no—
83Dic19⋊C4—416no—
84C4×Dic19—44no—
85#64520—42no—
86C2×C19⋊C8—41no—
87#10334—191nomaximal, Sylow
88C23×C19—24no—
89C23×C19—41no—
90C23×C19#12012yes—
91C23×C19#12111yescharacteristic
92Q8×C19—44no—
93Q8×C19—82no—
94C2×C4×C19—22no—
95C2×C4×C19—24no—
96C2×C4×C19—42no—
97C2×C4×C19—41no—
98C2×C4×C19—44no—
99C2×C4×C19—42no—
100C2×C4×C19—42no—
101C2×C4×C19—44no—
102C2×C4×C19#12011yescharacteristic
103C2×C4×C19#12112yes—
104C2×C4×C19#12711yescharacteristic
105C2×Dic19—28no—
106C2×Dic19—28no—
107C2×Dic19—24no—
108C2×Dic19—44no—
109C2×Dic19—44no—
110C2×Dic19—42no—
111C2×Dic19—42no—
112C2×Dic19—44no—
113Dic38—44no—
114Dic38—48no—
115Dic38—44no—
116C8×C19—42no—
117C19⋊C8—81no—
118#3195D1911yescharacteristic
119#2434—192no—
120#1784—191no—
121#1508—192no—
122#1297—191no—
123C22×C19—22no—
124C22×C19—22no—
125C22×C19—22no—
126C22×C19—21no—
127C22×C19—44no—
128C22×C19#39211yescharacteristic
129C22×C19#45614yes—
130C4×C19—21no—
131C4×C19—22no—
132C4×C19—82no—
133C4×C19—82no—
134C4×C19B(4,𝔽2)12yes—
135Dic19—48no—
136Dic19—44no—
137C23×Q8—191no—
138C2×C4⋊Q8—382no—
139C2×C22⋊Q8C2×D1912yes—
140#483—22no—
141#470—22no—
142#451—22no—
143C2×#101—382no—
144#407—191no—
145#407C2×D1911yescharacteristic
146#395—384no—
147#391—382no—
148#385—384no—
149C4×C22⋊C4—192no—
150#328—384no—
151C2×C19—24no—
152C2×C19—41no—
153C2×C19#200512yes—
154C2×C19#202111yescharacteristic
155C22×Q8—382no—
156C22×Q8—381no—
157C22×Q8—382no—
158C22×Q8—381no—
159C22×Q8—764no—
160C22×Q8C22⋊D1912yes—
161C23×C4—192no—
162C23×C4C22×D1911yescharacteristic
163C2×Q16—22no—
164C2×M16—381no—
165C2×M16C22⋊D1912yes—
166C4⋊Q8—768no—
167C22⋊Q8—22no—
168C22⋊Q8—22no—
169C22⋊Q8—22no—
170C22⋊Q8—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—388no—
173C2×C4⋊C4C22⋊D1912yes—
174C2×C22⋊C4—22no—
175C2×C22⋊C4—382no—
176C2×C42—382no—
177#106—22no—
178#103—24no—
179#101—764no—
180C22⋊C8—22no—
181C22⋊C8—382no—
182#95—194no—
183#95—388no—
184C19#1033411yescharacteristic, complemented, Sylow
185C24D4×D1911yescharacteristic
186C2×Q8—22no—
187C2×Q8—22no—
188C2×Q8—44no—
189C2×Q8—384no—
190C2×Q8—388no—
191C2×Q8—764no—
192C2×Q8—762no—
193C2×Q8—768no—
194C2×Q8—764no—
195C2×Q8—762no—
196C2×Q8—761no—
197C2×Q8—761no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—42no—
201C22×C4—384no—
202C22×C4—384no—
203C22×C4—382no—
204C22×C4—764no—
205C22×C4D4×D1912yes—
206C22×C4#6454311yescharacteristic
207C22×C4C2×C22⋊D1912yes—
208C22×C4C2×C22⋊D1911yescharacteristic
209Q16—82no—
210M16—42no—
211M16—762no—
212C2×C8—22no—
213C2×C8—761no—
214C4⋊C4—22no—
215C4⋊C4—22no—
216C4⋊C4—42no—
217C4⋊C4—42no—
218C4⋊C4—7616no—
219C22⋊C4—42no—
220C22⋊C4—42no—
221C22⋊C4—388no—
222C42—764no—
223C23—24no—
224C23—41no—
225C23#1059738312yes—
226C23#1059738411yescharacteristic
227Q8—44no—
228Q8—82no—
229Q8—764no—
230Q8—768no—
231Q8—764no—
232C2×C4—24no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—44no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—44no—
240C2×C4—388no—
241C2×C4—388no—
242C2×C4—384no—
243C2×C4—764no—
244C2×C4—764no—
245C2×C4—762no—
246C2×C4—762no—
247C2×C4—764no—
248C2×C4#1059738512yes—
249C2×C4#1059738611yescharacteristic
250C2×C4#1059739911yescharacteristic
251C8—42no—
252C8—1521no—
253C22—22no—
254C22—22no—
255C22—22no—
256C22—21no—
257C22—44no—
258C22#1192645211yescharacteristic
259C22#1192672514yes—
260C4—21no—
261C4—22no—
262C4—82no—
263C4—82no—
264C4—768no—
265C4—764no—
266C4#1192673112yes—
267C2—24no—
268C2—41no—
269C2#1456466812yes—
270C2#1456475911yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#3195C2
socleC22×C19#392
prime radicalC24×C19C2×D4
hypercenter#3195D19
hypocenterC19#10334
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3195

Complements

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

NH ≅ G/Ntype
184. C19#10334semidirect

Maximal subgroups

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

subgroupindex
#145672802
#145635582
#145621552
#145615202
C19×#31952
#1033419