Finite Group Databasebeta

← #18071289

Subgroups — #18071289

Order 4864.

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

normal subgroups only

This group has 492 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#14564869C212yesmaximal
2#14564722C211yesmaximal, characteristic
3#14561461C211yesmaximal, characteristic, complemented
4#14561458C212yesmaximal, complemented
5C19×#2809C211yesmaximal, characteristic, complemented
6C22×#64527—21no—
7C2×#10597320C2211yescharacteristic
8C2×#10597266—22no—
9C2×#10597266—22no—
10C2×#10597266—21no—
11#11926299C2212yes—
12#11926299C2211yescharacteristic
13C19×#400—21no—
14C19×#398—22no—
15C19×#391—21no—
16C19×#391C2211yescharacteristic
17C19×#389C2212yes—
18C19×#387—22no—
19C22×Q8×C19D411yescharacteristic
20C22×D76—22no—
21C22×D76—21no—
22C2×C4⋊C4×C19—22no—
23C2×C4⋊C4×C19—21no—
24C2×C4⋊C4×C19—21no—
25C2×C4⋊C4×C19D412yes—
26C2×C4⋊C4×C19D412yes—
27C2×C4⋊C4×C19D411yescharacteristic
28C2×C42×C19—21no—
29C2×C42×C19C2311yescharacteristic
30C2×#64527—42no—
31C2×#64527—42no—
32C2×#64527—42no—
33C22×C19⋊C8—21no—
34C22×C19⋊C8—22no—
35#10597320—42no—
36C19×#95—21no—
37C19×#95—22no—
38C19×#95—22no—
39C19×#95—22no—
40C19×#95—22no—
41#10597266—42no—
42#10597266—44no—
43#10597266—44no—
44C23×D19—41no—
45C2×Q8×C19—21no—
46C2×Q8×C19—41no—
47C2×Q8×C19—41no—
48C2×Q8×C19SD1612yes—
49C22×C4×C19—21no—
50C22×C4×C19—22no—
51C22×C4×C19—22no—
52C22×C4×C19—21no—
53C22×C4×C19C2×D411yescharacteristic
54C22×C4×C19C2×D412yes—
55C2×D76—22no—
56C2×D76—24no—
57C2×D76—41no—
58C2×D76—42no—
59C2×D76—42no—
60C2×D76—41no—
61C2×D76—41no—
62C2×D76—42no—
63C2×D76—42no—
64C2×D76—41no—
65C2×D76—42no—
66C2×D76—41no—
67C4⋊C4×C19—22no—
68C4⋊C4×C19—22no—
69C4⋊C4×C19—41no—
70C4⋊C4×C19—42no—
71C4⋊C4×C19—42no—
72C4⋊C4×C19—42no—
73C4⋊C4×C19—81no—
74C4⋊C4×C19—81no—
75C42×C19—41no—
76C42×C19—81no—
77#64527—48no—
78C2×C19⋊C8—22no—
79C2×C19⋊C8—41no—
80C2×C19⋊C8—41no—
81C2×C19⋊C8—42no—
82C2×C19⋊C8—42no—
83C2×C19⋊C8—42no—
84#7743—191nomaximal, Sylow
85C23×C19#12011yescharacteristic
86C22×D19—42no—
87C22×D19—81no—
88C22×D19—82no—
89C22×D19—81no—
90C22×D19—82no—
91Q8×C19—42no—
92Q8×C19—81no—
93C2×C4×C19—21no—
94C2×C4×C19—22no—
95C2×C4×C19—22no—
96C2×C4×C19—21no—
97C2×C4×C19—22no—
98C2×C4×C19—41no—
99C2×C4×C19—41no—
100C2×C4×C19—42no—
101C2×C4×C19—42no—
102C2×C4×C19—42no—
103C2×C4×C19—41no—
104C2×C4×C19—42no—
105C2×C4×C19—42no—
106C2×C4×C19—42no—
107C2×C4×C19—42no—
108C2×C4×C19C2×SD1611yescharacteristic
109C2×C4×C19#13512yes—
110C2×C4×C19AGL(1,ℤ/8)12yes—
111C2×C4×C19#13711yescharacteristic
112D76—42no—
113D76—42no—
114D76—44no—
115D76—44no—
116D76—81no—
117D76—81no—
118D76—82no—
119D76—82no—
120C19⋊C8—42no—
121C19⋊C8—82no—
122#2809D1911yescharacteristic, complemented
123#2041—192no—
124#2014—191no—
125#1272—191no—
126#1271—192no—
127C22×C19#44811yescharacteristic
128C22×C19#44912yes—
129C22×C19#45311yescharacteristic
130C22×C19#45412yes—
131C22×C19B(4,𝔽2)11yescharacteristic
132C2×D19—82no—
133C2×D19—84no—
134C2×D19—161no—
135C2×D19—162no—
136C2×D19—161no—
137C4×C19—21no—
138C4×C19—21no—
139C4×C19—22no—
140C4×C19—22no—
141C4×C19—42no—
142C4×C19—82no—
143C4×C19—82no—
144C4×C19—81no—
145C22×SD16—381no—
146C2×#127—191no—
147C2×#102—381no—
148C2×#102—382no—
149C2×#102—382no—
150#400—21no—
151#398—22no—
152#391—21no—
153#391C2×D1911yescharacteristic
154#389C2×D1912yes—
155#387—22no—
156#336—191no—
157#336—192no—
158C2×C19#159611yescharacteristic
159C2×C19#159712yes—
160C2×C19#162411yescharacteristic
161C2×C19#162612yes—
162C2×C19#165711yescharacteristic
163D19—162no—
164C22×Q8C22⋊D1911yescharacteristic
165C22×D4—381no—
166C22×D4—382no—
167C2×SD16—762no—
168C2×SD16—762no—
169C2×SD16—762no—
170C22×C8—381no—
171C22×C8—382no—
172#127—762no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4C22⋊D1912yes—
177C2×C4⋊C4C22⋊D1912yes—
178C2×C4⋊C4C22⋊D1911yescharacteristic
179C2×C42—21no—
180C2×C42C22×D1911yescharacteristic
181#102—764no—
182#102—762no—
183#102—764no—
184#95—21no—
185#95—22no—
186#95—22no—
187#95—22no—
188#95—22no—
189C19#774311yescharacteristic, complemented, Sylow
190C24—761no—
191C2×Q8—21no—
192C2×Q8—41no—
193C2×Q8—41no—
194C2×Q8#6452712yes—
195C2×D4—384no—
196C2×D4—382no—
197C2×D4—761no—
198C2×D4—761no—
199C2×D4—762no—
200C2×D4—762no—
201C2×D4—762no—
202C2×D4—761no—
203C2×D4—761no—
204C2×D4—761no—
205C2×D4—762no—
206C2×D4—762no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4C2×C22⋊D1911yescharacteristic
212C22×C4C2×C22⋊D1912yes—
213SD16—768no—
214C2×C8—382no—
215C2×C8—761no—
216C2×C8—761no—
217C2×C8—762no—
218C2×C8—762no—
219C2×C8—762no—
220C4⋊C4—22no—
221C4⋊C4—22no—
222C4⋊C4—41no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—81no—
227C4⋊C4—81no—
228C42—41no—
229C42—81no—
230C23—762no—
231C23—1521no—
232C23—1522no—
233C23—1521no—
234C23—1522no—
235C23#1059739911yescharacteristic
236Q8—42no—
237Q8—81no—
238D4—762no—
239D4—764no—
240D4—764no—
241D4—762no—
242D4—1522no—
243D4—1522no—
244D4—1521no—
245D4—1521no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4C2×#6452711yescharacteristic
262C2×C4#1059738811yescharacteristic
263C2×C4#1059739512yes—
264C2×C4#1059739612yes—
265C8—762no—
266C8—1522no—
267C22—3041no—
268C22—3041no—
269C22—3042no—
270C22—1524no—
271C22—1522no—
272C22#1192668311yescharacteristic
273C22#1192668912yes—
274C22#1192671211yescharacteristic
275C22#1192671712yes—
276C22#1192673111yescharacteristic
277C4—22no—
278C4—22no—
279C4—21no—
280C4—21no—
281C4—42no—
282C4—82no—
283C4—81no—
284C4—82no—
285C2—3042no—
286C2#1456255811yescharacteristic
287C2#1456256412yes—
288C2#1456271811yescharacteristic
289C2#1456273112yes—
290C2#1456293311yescharacteristic
subgroupG/H
centerC23#10597399
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2809C2
socleC23×C19#120
prime radicalC2×#10597320C22
hypercenter#2809D19
hypocenterC19#7743
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2809

Complements

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

NH ≅ G/Ntype
3. #14561461C2semidirect
4. #14561458C2semidirect
5. C19×#2809C2semidirect
122. #2809D19semidirect
189. C19#7743semidirect

Maximal subgroups

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

subgroupindex
#145648692
#145647222
#145614612
#145614582
C19×#28092
#774319