Finite Group Databasebeta

← #18085481

Subgroups — #18085481

Order 4864.

754 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 754 conjugacy classes of subgroups — too many to draw. Only its 87 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#14574459C211yesmaximal, characteristic
2#14567275C212yesmaximal
3#14562156C212yesmaximal
4#14561520C211yesmaximal, characteristic
5C19×#1784C211yesmaximal, characteristic
6C2×#10597390—22no—
7C2×#10597370C2212yes—
8#11926875—22no—
9#11926802—22no—
10#11926702—22no—
11#11926463—24no—
12#11926451—22no—
13#11926417—24no—
14C4×C22⋊Dic19C2212yes—
15#11926282—24no—
16C23×Q8×C19C2211yescharacteristic
17C2×C19×#101—22no—
18C19×#407C2211yescharacteristic
19C19×#407C2211yescharacteristic
20C22×Q8×C19—22no—
21C22×Q8×C19—21no—
22C22×Q8×C19—22no—
23C22×Q8×C19—21no—
24C22×Q8×C19—44no—
25C23×C4×C19D412yes—
26C23×C4×C19C2311yescharacteristic
27C22×Dic38D412yes—
28C2×M16×C19—21no—
29C2×M16×C19D412yes—
30C2×C22⋊Dic19—22no—
31C2×C22⋊Dic19—22no—
32#10597390—48no—
33C2×C4⋊Dic19D412yes—
34#10597370—22no—
35#10597370—22no—
36#10597370—22no—
37#10597370—22no—
38C2×Dic19⋊C4—28no—
39C2×Dic19⋊C4—22no—
40C2×C4×Dic19—22no—
41C2×Dic76—22no—
42C19×#101—44no—
43C19×C22⋊C8—22no—
44C19×C22⋊C8—22no—
45C19⋊#95—28no—
46C19⋊#95D414yes—
47#10597274—22no—
48#10597273—24no—
49C24×C19C2×D411yescharacteristic
50C2×Q8×C19—28no—
51C2×Q8×C19—24no—
52C2×Q8×C19—44no—
53C2×Q8×C19—42no—
54C2×Q8×C19—48no—
55C2×Q8×C19—44no—
56C2×Q8×C19—41no—
57C2×Q8×C19—42no—
58C2×Q8×C19—41no—
59C22×C4×C19—24no—
60C22×C4×C19—22no—
61C22×C4×C19—44no—
62C22×C4×C19—42no—
63C22×C4×C19C2×D412yes—
64C22×C4×C19C2×D412yes—
65C22×C4×C19C2×D411yescharacteristic
66C22×C4×C19#4111yescharacteristic
67C22×Dic19—24no—
68C22×Dic19—22no—
69C22×Dic19—22no—
70C2×Dic38—22no—
71C2×Dic38—22no—
72C2×Dic38—44no—
73M16×C19—42no—
74M16×C19—42no—
75C2×C8×C19—22no—
76C2×C8×C19—41no—
77C22⋊Dic19—28no—
78C22⋊Dic19—42no—
79C22⋊Dic19—42no—
80C4⋊Dic19—22no—
81C4⋊Dic19—22no—
82Dic19⋊C4—416no—
83Dic19⋊C4—42no—
84Dic19⋊C4—42no—
85C4×Dic19—44no—
86Dic76—82no—
87#10334—191nomaximal, Sylow
88C23×C19—24no—
89C23×C19—41no—
90C23×C19#12012yes—
91C23×C19#12111yescharacteristic
92Q8×C19—44no—
93Q8×C19—48no—
94Q8×C19—44no—
95C2×C4×C19—24no—
96C2×C4×C19—22no—
97C2×C4×C19—28no—
98C2×C4×C19—24no—
99C2×C4×C19—42no—
100C2×C4×C19—41no—
101C2×C4×C19—44no—
102C2×C4×C19—42no—
103C2×C4×C19—42no—
104C2×C4×C19#12011yescharacteristic
105C2×C4×C19#12112yes—
106C2×C4×C19#12711yescharacteristic
107C2×Dic19—28no—
108C2×Dic19—44no—
109C2×Dic19—44no—
110C2×Dic19—44no—
111C2×Dic19—42no—
112C2×Dic19—42no—
113C2×Dic19—44no—
114Dic38—44no—
115Dic38—82no—
116C8×C19—42no—
117C8×C19—81no—
118#3195—191no—
119#2434—192no—
120#1784D1911yescharacteristic
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—44no—
133C4×C19B(4,𝔽2)12yes—
134Dic19—48no—
135Dic19—82no—
136Dic19—82no—
137C23×Q8C2×D1911yescharacteristic
138C2×C4⋊Q8—382no—
139C2×C22⋊Q8—192no—
140#483—382no—
141#470—382no—
142#451—382no—
143C2×#101—22no—
144#407C2×D1911yescharacteristic
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—21no—
156C22×Q8—22no—
157C22×Q8—22no—
158C22×Q8—21no—
159C22×Q8—44no—
160C22×Q8—192no—
161C23×C4D7612yes—
162C23×C4C22×D1911yescharacteristic
163C2×Q16—382no—
164C2×M16—21no—
165C2×M16C22⋊D1912yes—
166C4⋊Q8—768no—
167C22⋊Q8—382no—
168C22⋊Q8—382no—
169C22⋊Q8—382no—
170C22⋊Q8—382no—
171C2×C4⋊C4—192no—
172C2×C4⋊C4—388no—
173C2×C4⋊C4—382no—
174C2×C22⋊C4—382no—
175C2×C22⋊C4—382no—
176C2×C42—382no—
177#106—382no—
178#103—384no—
179#101—44no—
180C22⋊C8—22no—
181C22⋊C8—22no—
182#95—194no—
183#95—388no—
184C19#1033411yescharacteristic, complemented, Sylow
185C24C2×D7611yescharacteristic
186C2×Q8—24no—
187C2×Q8—28no—
188C2×Q8—44no—
189C2×Q8—42no—
190C2×Q8—48no—
191C2×Q8—44no—
192C2×Q8—41no—
193C2×Q8—41no—
194C2×Q8—42no—
195C2×Q8—382no—
196C2×Q8—382no—
197C2×Q8—764no—
198C22×C4—22no—
199C22×C4—24no—
200C22×C4—44no—
201C22×C4—42no—
202C22×C4—384no—
203C22×C4—382no—
204C22×C4—382no—
205C22×C4#6454111yescharacteristic
206C22×C4D4×D1912yes—
207C22×C4D4×D1912yes—
208C22×C4C2×C22⋊D1911yescharacteristic
209Q16—1522no—
210M16—42no—
211M16—42no—
212C2×C8—22no—
213C2×C8—41no—
214C4⋊C4—382no—
215C4⋊C4—382no—
216C4⋊C4—7616no—
217C4⋊C4—762no—
218C4⋊C4—762no—
219C22⋊C4—388no—
220C22⋊C4—762no—
221C22⋊C4—762no—
222C42—764no—
223C23—24no—
224C23—41no—
225C23#1059732812yes—
226C23#1059737611yescharacteristic
227Q8—44no—
228Q8—48no—
229Q8—44no—
230Q8—764no—
231Q8—1522no—
232C2×C4—24no—
233C2×C4—22no—
234C2×C4—28no—
235C2×C4—24no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—44no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—388no—
242C2×C4—764no—
243C2×C4—764no—
244C2×C4—764no—
245C2×C4—762no—
246C2×C4—762no—
247C2×C4—764no—
248C2×C4#1059733012yes—
249C2×C4#1059738311yescharacteristic
250C2×C4#1059738611yescharacteristic
251C8—42no—
252C8—81no—
253C22—22no—
254C22—22no—
255C22—22no—
256C22—21no—
257C22—44no—
258C22#1192645311yescharacteristic
259C22#1192672914yes—
260C4—21no—
261C4—22no—
262C4—44no—
263C4—768no—
264C4—1522no—
265C4—1522no—
266C4#1192673012yes—
267C2—24no—
268C2—41no—
269C2#1456467312yes—
270C2#1456476111yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1784C2
socleC22×C19#392
prime radicalC24×C19C2×D4
hypercenter#1784D19
hypocenterC19#10334
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1784

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
#145744592
#145672752
#145621562
#145615202
C19×#17842
#1033419