Finite Group Databasebeta

← #18085476

Subgroups — #18085476

Order 4864.

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

normal subgroups only

This group has 914 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, complemented
2#14567282C212yesmaximal
3#14562156C212yesmaximal, complemented
4#14561520C211yesmaximal, characteristic, complemented
5C19×#1783C211yesmaximal, characteristic
6C2×#10597382—22no—
7C2×#10597370C2212yes—
8#11926875—22no—
9#11926802—22no—
10#11926702—22no—
11#11926458—24no—
12#11926447—22no—
13#11926400—24no—
14C4×C22⋊Dic19C2212yes—
15#11926282—24no—
16C23×D4×C19C2211yescharacteristic
17C2×C19×#100—22no—
18C19×#407C2211yescharacteristic
19C19×#407C2211yescharacteristic
20C25×C19D412yes—
21C22×D4×C19—22no—
22C22×D4×C19—21no—
23C22×D4×C19—22no—
24C22×D4×C19—21no—
25C22×D4×C19—44no—
26C23×C4×C19C2311yescharacteristic
27C22×Dic38D412yes—
28C2×M16×C19—21no—
29C2×M16×C19D412yes—
30C2×C22⋊Dic19—28no—
31C2×C22⋊Dic19—22no—
32C2×C22⋊Dic19—22no—
33C2×C22⋊Dic19—28no—
34#10597382—48no—
35C2×C4⋊Dic19D412yes—
36#10597370—22no—
37#10597370—22no—
38#10597370—22no—
39#10597370—22no—
40C2×Dic19⋊C4—22no—
41C2×C4×Dic19—22no—
42C2×Dic76—22no—
43C19×#100—44no—
44C19×C22⋊C8—22no—
45C19×C22⋊C8—22no—
46C19⋊#95D414yes—
47#10597274—22no—
48#10597273—24no—
49C24×C19—24no—
50C24×C19—22no—
51C24×C19—44no—
52C24×C19—48no—
53C24×C19C2×D411yescharacteristic
54C2×D4×C19—28no—
55C2×D4×C19—24no—
56C2×D4×C19—44no—
57C2×D4×C19—42no—
58C2×D4×C19—48no—
59C2×D4×C19—44no—
60C2×D4×C19—41no—
61C2×D4×C19—42no—
62C2×D4×C19—41no—
63C22×C4×C19—42no—
64C22×C4×C19C2×D412yes—
65C22×C4×C19C2×D412yes—
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19#4111yescharacteristic
68C22×Dic19—22no—
69C22×Dic19—24no—
70C22×Dic19—22no—
71C2×Dic38—22no—
72C2×Dic38—22no—
73C2×Dic38—44no—
74M16×C19—42no—
75M16×C19—42no—
76C2×C8×C19—22no—
77C2×C8×C19—41no—
78C22⋊Dic19—416no—
79C22⋊Dic19—44no—
80C22⋊Dic19—42no—
81C22⋊Dic19—42no—
82C22⋊Dic19—88no—
83C4⋊Dic19—22no—
84C4⋊Dic19—22no—
85Dic19⋊C4—42no—
86Dic19⋊C4—42no—
87C4×Dic19—44no—
88Dic76—82no—
89#10333—191nomaximal, Sylow
90C23×C19—24no—
91C23×C19—28no—
92C23×C19—24no—
93C23×C19—41no—
94C23×C19—44no—
95C23×C19—42no—
96C23×C19—48no—
97C23×C19—42no—
98C23×C19—48no—
99C23×C19—84no—
100C23×C19—816no—
101C23×C19#12012yes—
102C23×C19#12111yescharacteristic
103D4×C19—44no—
104D4×C19—48no—
105D4×C19—44no—
106C2×C4×C19—24no—
107C2×C4×C19—22no—
108C2×C4×C19—42no—
109C2×C4×C19—41no—
110C2×C4×C19#12011yescharacteristic
111C2×C4×C19#12112yes—
112C2×C4×C19#12711yescharacteristic
113C2×Dic19—44no—
114C2×Dic19—44no—
115C2×Dic19—44no—
116C2×Dic19—42no—
117C2×Dic19—42no—
118C2×Dic19—44no—
119C2×Dic19—44no—
120Dic38—44no—
121Dic38—82no—
122C8×C19—42no—
123C8×C19—81no—
124#3195—191no—
125#2435—192no—
126#1783D1911yescharacteristic
127#1508—192no—
128#1297—191no—
129C22×C19—22no—
130C22×C19—22no—
131C22×C19—22no—
132C22×C19—21no—
133C22×C19—44no—
134C22×C19—416no—
135C22×C19—44no—
136C22×C19—88no—
137C22×C19—84no—
138C22×C19—84no—
139C22×C19—84no—
140C22×C19#39211yescharacteristic
141C22×C19#45514yes—
142C4×C19—21no—
143C4×C19—22no—
144C4×C19B(4,𝔽2)12yes—
145Dic19—84no—
146Dic19—82no—
147Dic19—82no—
148C23×D4C2×D1911yescharacteristic
149C2×#124—382no—
150C2×C22⋊Q8—192no—
151#483—382no—
152#470—382no—
153#451—382no—
154C2×#100—22no—
155#407C2×D1911yescharacteristic
156#407C2×D1911yescharacteristic
157#394—384no—
158#390—382no—
159#379—384no—
160C4×C22⋊C4—192no—
161#328—384no—
162C2×C19—24no—
163C2×C19—41no—
164C2×C19—84no—
165C2×C19#200412yes—
166C2×C19#202111yescharacteristic
167C25D7612yes—
168C22×Q8—192no—
169C22×D4—21no—
170C22×D4—22no—
171C22×D4—22no—
172C22×D4—21no—
173C22×D4—44no—
174C23×C4C22×D1911yescharacteristic
175C2×Q16—382no—
176C2×M16—21no—
177C2×M16C22⋊D1912yes—
178#124—768no—
179C22⋊Q8—382no—
180C22⋊Q8—382no—
181C22⋊Q8—382no—
182C22⋊Q8—382no—
183C2×C4⋊C4—192no—
184C2×C4⋊C4—382no—
185C2×C22⋊C4—388no—
186C2×C22⋊C4—382no—
187C2×C22⋊C4—382no—
188C2×C22⋊C4—388no—
189C2×C42—382no—
190#106—382no—
191#103—384no—
192#100—44no—
193C22⋊C8—22no—
194C22⋊C8—22no—
195#95—194no—
196C19#1033311yescharacteristic, complemented, Sylow
197C24—24no—
198C24—22no—
199C24—44no—
200C24—48no—
201C24C2×D7611yescharacteristic
202C2×Q8—382no—
203C2×Q8—382no—
204C2×Q8—764no—
205C2×D4—24no—
206C2×D4—28no—
207C2×D4—44no—
208C2×D4—42no—
209C2×D4—44no—
210C2×D4—48no—
211C2×D4—41no—
212C2×D4—41no—
213C2×D4—42no—
214C22×C4—42no—
215C22×C4—384no—
216C22×C4—382no—
217C22×C4—382no—
218C22×C4#6454111yescharacteristic
219C22×C4D4×D1912yes—
220C22×C4D4×D1912yes—
221C22×C4C2×C22⋊D1911yescharacteristic
222Q16—1522no—
223M16—42no—
224M16—42no—
225C2×C8—22no—
226C2×C8—41no—
227C4⋊C4—382no—
228C4⋊C4—382no—
229C4⋊C4—762no—
230C4⋊C4—762no—
231C22⋊C4—764no—
232C22⋊C4—7616no—
233C22⋊C4—762no—
234C22⋊C4—762no—
235C22⋊C4—1528no—
236C42—764no—
237C23—24no—
238C23—28no—
239C23—24no—
240C23—41no—
241C23—44no—
242C23—42no—
243C23—48no—
244C23—42no—
245C23—48no—
246C23—84no—
247C23—816no—
248C23#1059732812yes—
249C23#1059737611yescharacteristic
250Q8—764no—
251Q8—1522no—
252D4—44no—
253D4—48no—
254D4—44no—
255C2×C4—24no—
256C2×C4—22no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—764no—
260C2×C4—764no—
261C2×C4—764no—
262C2×C4—762no—
263C2×C4—762no—
264C2×C4—764no—
265C2×C4—764no—
266C2×C4#1059733012yes—
267C2×C4#1059738311yescharacteristic
268C2×C4#1059738611yescharacteristic
269C8—42no—
270C8—81no—
271C22—22no—
272C22—22no—
273C22—22no—
274C22—21no—
275C22—44no—
276C22—416no—
277C22—44no—
278C22—88no—
279C22—84no—
280C22—84no—
281C22—84no—
282C22#1192645311yescharacteristic
283C22#1192672414yes—
284C4—21no—
285C4—22no—
286C4—1524no—
287C4—1522no—
288C4—1522no—
289C4#1192673012yes—
290C2—24no—
291C2—41no—
292C2—84no—
293C2#1456466612yes—
294C2#1456476111yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1783C2
socleC22×C19#392
prime radicalC23×D4×C19C22
hypercenter#1783D19
hypocenterC19#10333
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1783

Complements

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

NH ≅ G/Ntype
1. #14574459C2semidirect
3. #14562156C2semidirect
4. #14561520C2semidirect
196. C19#10333semidirect

Maximal subgroups

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

subgroupindex
#145744592
#145672822
#145621562
#145615202
C19×#17832
#1033319