Finite Group Databasebeta

← #18085436

Subgroups — #18085436

Order 4864.

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

normal subgroups only

This group has 806 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#14574435C211yesmaximal, characteristic
2#14567289C212yesmaximal, complemented
3#14562152C212yesmaximal, complemented
4#14561520C211yesmaximal, characteristic, complemented
5C19×#1784C211yesmaximal, characteristic, complemented
6C2×#10597393—22no—
7C2×#10597376C2212yes—
8#11926863—22no—
9#11926797—22no—
10#11926680—22no—
11#11926455—24no—
12#11926451—22no—
13#11926423—24no—
14C4×C22⋊Dic19C2212yes—
15#11926279—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×C22⋊D19—22no—
28C22×D76D412yes—
29C2×M16×C19—21no—
30C2×M16×C19D412yes—
31C2×C22⋊Dic19—22no—
32#10597393—48no—
33#10597376—22no—
34#10597376—22no—
35#10597376—22no—
36#10597376—22no—
37C2×(C2×D19)⋊C4—28no—
38C2×(C2×D19)⋊C4—22no—
39C2×C4⋊Dic19D412yes—
40C2×C4×Dic19—22no—
41C2×D152—22no—
42C19×#101—44no—
43C19×C22⋊C8—22no—
44C19×C22⋊C8—22no—
45C19⋊#95—28no—
46C19⋊#95D414yes—
47#10597278—24no—
48#10597274—22no—
49C24×C19C2×D411yescharacteristic
50C23×D19—22no—
51C2×Q8×C19—28no—
52C2×Q8×C19—24no—
53C2×Q8×C19—44no—
54C2×Q8×C19—42no—
55C2×Q8×C19—48no—
56C2×Q8×C19—44no—
57C2×Q8×C19—41no—
58C2×Q8×C19—42no—
59C2×Q8×C19—41no—
60C22×C4×C19—24no—
61C22×C4×C19—22no—
62C22×C4×C19—44no—
63C22×C4×C19—42no—
64C22×C4×C19C2×D412yes—
65C22×C4×C19C2×D412yes—
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19#4111yescharacteristic
68C2×C22⋊D19—48no—
69C2×C22⋊D19—42no—
70C2×C22⋊D19—42no—
71C22×Dic19—24no—
72C22×Dic19—22no—
73C2×D76—22no—
74C2×D76—22no—
75C2×D76—44no—
76M16×C19—42no—
77M16×C19—42no—
78C2×C8×C19—22no—
79C2×C8×C19—41no—
80C22⋊Dic19—44no—
81(C2×D19)⋊C4—416no—
82(C2×D19)⋊C4—42no—
83(C2×D19)⋊C4—42no—
84C4⋊Dic19—22no—
85C4⋊Dic19—22no—
86C4×Dic19—44no—
87D152—82no—
88#10327—191nomaximal, Sylow
89C23×C19—24no—
90C23×C19—41no—
91C23×C19#12012yes—
92C23×C19#12111yescharacteristic
93C22×D19—44no—
94C22×D19—44no—
95C22×D19—42no—
96C22×D19—44no—
97Q8×C19—44no—
98Q8×C19—48no—
99Q8×C19—44no—
100C2×C4×C19—24no—
101C2×C4×C19—22no—
102C2×C4×C19—28no—
103C2×C4×C19—24no—
104C2×C4×C19—42no—
105C2×C4×C19—41no—
106C2×C4×C19—44no—
107C2×C4×C19—42no—
108C2×C4×C19—42no—
109C2×C4×C19#12011yescharacteristic
110C2×C4×C19#12112yes—
111C2×C4×C19#12711yescharacteristic
112C22⋊D19—84no—
113C22⋊D19—84no—
114C2×Dic19—44no—
115C2×Dic19—44no—
116C2×Dic19—44no—
117C2×Dic19—42no—
118C2×Dic19—44no—
119D76—44no—
120D76—82no—
121C8×C19—42no—
122C8×C19—81no—
123#3192—191no—
124#2436—192no—
125#1784D1911yescharacteristic, complemented
126#1507—192no—
127#1297—191no—
128C22×C19—22no—
129C22×C19—22no—
130C22×C19—22no—
131C22×C19—21no—
132C22×C19—44no—
133C22×C19#39211yescharacteristic
134C22×C19#45414yes—
135C2×D19—88no—
136C2×D19—82no—
137C2×D19—82no—
138C2×D19—82no—
139C4×C19—21no—
140C4×C19—22no—
141C4×C19—44no—
142C4×C19B(4,𝔽2)12yes—
143Dic19—84no—
144Dic19—82no—
145C23×Q8C2×D1911yescharacteristic
146C2×#124—382no—
147C2×#121—192no—
148#481—382no—
149#469—382no—
150#447—382no—
151C2×#101—22no—
152#407C2×D1911yescharacteristic
153#407C2×D1911yescharacteristic
154#393—384no—
155#391—382no—
156#386—384no—
157C4×C22⋊C4—192no—
158#327—384no—
159C2×C19—24no—
160C2×C19—41no—
161C2×C19#200312yes—
162C2×C19#202111yescharacteristic
163D19—162no—
164C22×Q8—21no—
165C22×Q8—22no—
166C22×Q8—22no—
167C22×Q8—21no—
168C22×Q8—44no—
169C22×D4—192no—
170C22×D4—382no—
171C23×C4D7612yes—
172C23×C4C22×D1911yescharacteristic
173C2×D8—382no—
174C2×M16—21no—
175C2×M16C22⋊D1912yes—
176#124—768no—
177#121—382no—
178#121—382no—
179#121—382no—
180#121—382no—
181C2×C4⋊C4—192no—
182C2×C22⋊C4—388no—
183C2×C22⋊C4—382no—
184C2×C22⋊C4—382no—
185C2×C42—382no—
186#106—382no—
187#102—384no—
188#101—44no—
189C22⋊C8—22no—
190C22⋊C8—22no—
191#95—194no—
192#95—388no—
193C19#1032711yescharacteristic, complemented, Sylow
194C24—382no—
195C24C2×D7611yescharacteristic
196C2×Q8—24no—
197C2×Q8—28no—
198C2×Q8—44no—
199C2×Q8—42no—
200C2×Q8—48no—
201C2×Q8—44no—
202C2×Q8—41no—
203C2×Q8—41no—
204C2×Q8—42no—
205C2×D4—382no—
206C2×D4—382no—
207C2×D4—764no—
208C2×D4—768no—
209C2×D4—762no—
210C2×D4—762no—
211C22×C4—22no—
212C22×C4—24no—
213C22×C4—44no—
214C22×C4—42no—
215C22×C4—384no—
216C22×C4—382no—
217C22×C4#6454111yescharacteristic
218C22×C4D4×D1912yes—
219C22×C4D4×D1912yes—
220C22×C4C2×C22⋊D1911yescharacteristic
221D8—1522no—
222M16—42no—
223M16—42no—
224C2×C8—22no—
225C2×C8—41no—
226C4⋊C4—382no—
227C4⋊C4—382no—
228C22⋊C4—7616no—
229C22⋊C4—764no—
230C22⋊C4—762no—
231C22⋊C4—762no—
232C42—764no—
233C23—24no—
234C23—41no—
235C23—764no—
236C23—764no—
237C23—762no—
238C23—764no—
239C23#1059732812yes—
240C23#1059737611yescharacteristic
241Q8—44no—
242Q8—48no—
243Q8—44no—
244D4—764no—
245D4—1522no—
246D4—1524no—
247D4—1524no—
248C2×C4—24no—
249C2×C4—22no—
250C2×C4—28no—
251C2×C4—24no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—44no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—764no—
258C2×C4—764no—
259C2×C4—764no—
260C2×C4—762no—
261C2×C4—764no—
262C2×C4#1059733012yes—
263C2×C4#1059738311yescharacteristic
264C2×C4#1059738611yescharacteristic
265C8—42no—
266C8—81no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22—21no—
271C22—44no—
272C22—1528no—
273C22—1522no—
274C22—1522no—
275C22—1522no—
276C22#1192645311yescharacteristic
277C22#1192671914yes—
278C4—21no—
279C4—22no—
280C4—44no—
281C4—1524no—
282C4—1522no—
283C4#1192673012yes—
284C2—24no—
285C2—41no—
286C2—3042no—
287C2#1456465912yes—
288C2#1456476111yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1784C2
socleC22×C19#392
prime radical#14574435C2
hypercenter#1784D19
hypocenterC19#10327
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
2. #14567289C2semidirect
3. #14562152C2semidirect
4. #14561520C2semidirect
5. C19×#1784C2semidirect
125. #1784D19semidirect
193. C19#10327semidirect

Maximal subgroups

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

subgroupindex
#145744352
#145672892
#145621522
#145615202
C19×#17842
#1032719