Finite Group Databasebeta

← #18071723

Subgroups — #18071723

Order 4864.

478 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 83 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#14570661C211yesmaximal, characteristic
2#14565039C212yesmaximal, complemented
3#14561461C211yesmaximal, characteristic, complemented
4#14561455C212yesmaximal, complemented
5C19×#2096C211yesmaximal, characteristic, complemented
6C2×#10597393—21no—
7C2×#10597266—22no—
8#11926461—21no—
9#11926454—22no—
10#11926446C2212yes—
11#11926436—22no—
12#11926306—22no—
13#11926299C2212yes—
14C2×C19×#106—21no—
15C2×C19×#103—21no—
16C19×#391C2211yescharacteristic
17C19×#384C2211yescharacteristic
18C19×#336C2211yescharacteristic
19C22×Q8×C19D411yescharacteristic
20C22×D76—21no—
21C22×D76—21no—
22C22×D76D412yes—
23C22×C8×C19—21no—
24C2×C4⋊C4×C19—22no—
25C2×C4⋊C4×C19—21no—
26C2×C4⋊C4×C19D411yescharacteristic
27C2×C42×C19C2311yescharacteristic
28#10597393—42no—
29#10597393—42no—
30C2×(C2×D19)⋊C4—22no—
31C2×(C2×D19)⋊C4—22no—
32C2×(C2×D19)⋊C4—22no—
33C2×(C2×D19)⋊C4—22no—
34C2×C4⋊Dic19D412yes—
35C2×C4×Dic19—21no—
36C22×C19⋊C8—22no—
37C19×#106—42no—
38C19×#103—42no—
39C19×#95—22no—
40C19⋊#95—21no—
41#10597266—44no—
42C23×D19—22no—
43C2×Q8×C19—21no—
44C2×Q8×C19—41no—
45C2×Q8×C19—41no—
46C2×Q8×C19SD1612yes—
47C22×C4×C19—21no—
48C22×C4×C19—21no—
49C22×C4×C19—41no—
50C22×C4×C19C2×D412yes—
51C22×C4×C19C2×D411yescharacteristic
52C22×Dic19—22no—
53C2×D76—22no—
54C2×D76—22no—
55C2×D76—42no—
56C2×D76—42no—
57C2×D76—42no—
58C2×D76—81no—
59C2×D76—81no—
60C2×D76—81no—
61C2×D76—82no—
62C2×C8×C19—22no—
63C2×C8×C19—41no—
64C2×C8×C19—41no—
65C4⋊C4×C19—41no—
66C4⋊C4×C19—41no—
67C4⋊C4×C19—41no—
68C4⋊C4×C19—42no—
69C4⋊C4×C19—42no—
70C42×C19—41no—
71(C2×D19)⋊C4—44no—
72(C2×D19)⋊C4—42no—
73(C2×D19)⋊C4—42no—
74(C2×D19)⋊C4—42no—
75(C2×D19)⋊C4—42no—
76(C2×D19)⋊C4—82no—
77C4⋊Dic19—42no—
78C4×Dic19—42no—
79C2×C19⋊C8—42no—
80C2×C19⋊C8—42no—
81C2×C19⋊C8—42no—
82#7810—191nomaximal, Sylow
83C23×C19#12011yescharacteristic
84C22×D19—42no—
85C22×D19—42no—
86C22×D19—42no—
87C22×D19—42no—
88C22×D19—42no—
89C22×D19—42no—
90C22×D19—42no—
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—41no—
101C2×C4×C19—42no—
102C2×C4×C19—82no—
103C2×C4×C19—81no—
104C2×C4×C19C2×SD1611yescharacteristic
105C2×C4×C19#13512yes—
106C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
107C2×C4×C19AGL(1,ℤ/8)12yes—
108C2×Dic19—42no—
109C2×Dic19—42no—
110C2×Dic19—42no—
111D76—44no—
112D76—82no—
113D76—84no—
114D76—84no—
115C8×C19—42no—
116C19⋊C8—82no—
117#2733—191no—
118#2096D1911yescharacteristic, complemented
119#2071—192no—
120#1272—191no—
121#1270—192no—
122C22×C19#44912yes—
123C22×C19#45011yescharacteristic
124C22×C19#45311yescharacteristic
125C22×C19#45512yes—
126C22×C19#45811yescharacteristic
127C2×D19—82no—
128C2×D19—82no—
129C2×D19—82no—
130C2×D19—82no—
131C2×D19—82no—
132C2×D19—82no—
133C2×D19—82no—
134C4×C19—22no—
135C4×C19—22no—
136C4×C19—21no—
137C4×C19—21no—
138C4×C19—42no—
139C4×C19—81no—
140C4×C19—161no—
141Dic19—82no—
142C2×#124—381no—
143C2×#106—21no—
144C2×#103—21no—
145C2×#102—382no—
146#394—381no—
147#392—382no—
148#391C2×D1911yescharacteristic
149#390—192no—
150#388—382no—
151#384C2×D1911yescharacteristic
152#340—382no—
153#336—192no—
154#336C2×D1911yescharacteristic
155C2×C19#161212yes—
156C2×C19#161311yescharacteristic
157C2×C19#162411yescharacteristic
158C2×C19#164212yes—
159C2×C19#165911yescharacteristic
160D19—162no—
161C22×Q8C22⋊D1911yescharacteristic
162C22×D4—192no—
163C22×D4—381no—
164C22×D4—381no—
165C22×C8—21no—
166C22×C8—382no—
167#124—762no—
168#124—762no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—192no—
172C2×C4⋊C4C22⋊D1911yescharacteristic
173C2×C22⋊C4—382no—
174C2×C22⋊C4—382no—
175C2×C22⋊C4—382no—
176C2×C22⋊C4—382no—
177C2×C42—381no—
178C2×C42C22×D1911yescharacteristic
179#106—42no—
180#103—42no—
181#102—764no—
182#95—22no—
183#95—381no—
184C19#781011yescharacteristic, complemented, Sylow
185C24—382no—
186C2×Q8—21no—
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8#6452712yes—
190C2×D4—382no—
191C2×D4—382no—
192C2×D4—762no—
193C2×D4—762no—
194C2×D4—762no—
195C2×D4—1521no—
196C2×D4—1521no—
197C2×D4—1521no—
198C2×D4—1522no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—41no—
202C22×C4—382no—
203C22×C4D4×D1912yes—
204C22×C4C2×C22⋊D1911yescharacteristic
205C2×C8—22no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—762no—
209C2×C8—762no—
210C2×C8—762no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—42no—
215C4⋊C4—42no—
216C4⋊C4—762no—
217C22⋊C4—764no—
218C22⋊C4—762no—
219C22⋊C4—762no—
220C22⋊C4—762no—
221C22⋊C4—762no—
222C22⋊C4—1522no—
223C42—41no—
224C42—762no—
225C23—762no—
226C23—762no—
227C23—762no—
228C23—762no—
229C23—762no—
230C23—762no—
231C23—762no—
232C23#1059738311yescharacteristic
233Q8—42no—
234Q8—81no—
235D4—764no—
236D4—1522no—
237D4—1524no—
238D4—1524no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—82no—
249C2×C4—81no—
250C2×C4—762no—
251C2×C4—762no—
252C2×C4—762no—
253C2×C4#1059736012yes—
254C2×C4#1059736212yes—
255C2×C4C2×#6452711yescharacteristic
256C2×C4#1059739511yescharacteristic
257C8—42no—
258C8—1522no—
259C22—1522no—
260C22—1522no—
261C22—1522no—
262C22—1522no—
263C22—1522no—
264C22—1522no—
265C22—1522no—
266C22#1192668812yes—
267C22#1192669411yescharacteristic
268C22#1192671111yescharacteristic
269C22#1192672012yes—
270C22#1192673311yescharacteristic
271C4—22no—
272C4—22no—
273C4—21no—
274C4—21no—
275C4—42no—
276C4—81no—
277C4—161no—
278C4—1522no—
279C2—3042no—
280C2#1456264812yes—
281C2#1456265411yescharacteristic
282C2#1456271611yescharacteristic
283C2#1456283412yes—
284C2#1456293911yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2096C2
socleC23×C19#120
prime radical#14570661C2
hypercenter#2096D19
hypocenterC19#7810
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2096

Complements

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

NH ≅ G/Ntype
2. #14565039C2semidirect
3. #14561461C2semidirect
4. #14561455C2semidirect
5. C19×#2096C2semidirect
118. #2096D19semidirect
184. C19#7810semidirect

Maximal subgroups

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

subgroupindex
#145706612
#145650392
#145614612
#145614552
C19×#20962
#781019