Finite Group Databasebeta

← #18071365

Subgroups — #18071365

Order 4864.

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

normal subgroups only

This group has 468 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#14570667C211yesmaximal, characteristic
2#14564960C212yesmaximal
3#14561461C211yesmaximal, characteristic
4#14561459C212yesmaximal
5C19×#2016C211yesmaximal, characteristic
6C2×#10597390—21no—
7C2×#10597264—22no—
8#11926474—21no—
9#11926465—22no—
10#11926442C2212yes—
11#11926429—22no—
12#11926306—22no—
13#11926299C2212yes—
14C22×Q16×C19—21no—
15C2×C19×C4⋊Q8C2211yescharacteristic
16C2×C19×#103—21no—
17C19×#391C2211yescharacteristic
18C19×#336C2211yescharacteristic
19C22×Q8×C19—21no—
20C22×Q8×C19D411yescharacteristic
21C22×Dic38—21no—
22C2×Q16×C19—42no—
23C2×Q16×C19—42no—
24C2×Q16×C19—42no—
25C22×C8×C19—21no—
26C19×C4⋊Q8—42no—
27C2×C4⋊C4×C19—22no—
28C2×C4⋊C4×C19D411yescharacteristic
29C2×C42×C19C2311yescharacteristic
30#10597390—42no—
31#10597390—42no—
32C2×C4⋊Dic19—21no—
33C2×C4⋊Dic19D412yes—
34C2×C4⋊Dic19D412yes—
35C2×Dic19⋊C4—22no—
36C2×Dic19⋊C4—22no—
37C2×C4×Dic19—21no—
38C22×C19⋊C8—22no—
39C19×#103—42no—
40C19×#95—22no—
41C19⋊#95—21no—
42C19⋊#95—22no—
43C19⋊#95—22no—
44#10597264—44no—
45C2×Q8×C19—21no—
46C2×Q8×C19—22no—
47C2×Q8×C19—41no—
48C2×Q8×C19—41no—
49C2×Q8×C19—41no—
50C2×Q8×C19—41no—
51C2×Q8×C19—41no—
52C2×Q8×C19—41no—
53C2×Q8×C19—41no—
54C2×Q8×C19D812yes—
55C22×C4×C19—21no—
56C22×C4×C19—21no—
57C22×C4×C19—41no—
58C22×C4×C19C2×D412yes—
59C22×C4×C19C2×D411yescharacteristic
60C22×Dic19—22no—
61C22×Dic19—22no—
62C2×Dic38—42no—
63C2×Dic38—81no—
64C2×Dic38—81no—
65Q16×C19—48no—
66C2×C8×C19—22no—
67C2×C8×C19—41no—
68C2×C8×C19—41no—
69C4⋊C4×C19—24no—
70C4⋊C4×C19—41no—
71C4⋊C4×C19—42no—
72C42×C19—41no—
73C4⋊Dic19—22no—
74C4⋊Dic19—42no—
75C4⋊Dic19—81no—
76C4⋊Dic19Q1614yescomplemented
77Dic19⋊C4—44no—
78Dic19⋊C4—42no—
79Dic19⋊C4—42no—
80C4×Dic19—42no—
81C2×C19⋊C8—24no—
82C2×C19⋊C8—42no—
83C2×C19⋊C8—42no—
84#7757—191nomaximal, Sylow
85C23×C19#12011yescharacteristic
86Q8×C19—42no—
87Q8×C19—42no—
88Q8×C19—42no—
89Q8×C19—81no—
90Q8×C19—81no—
91Q8×C19—81no—
92C2×C4×C19—21no—
93C2×C4×C19—22no—
94C2×C4×C19—22no—
95C2×C4×C19—21no—
96C2×C4×C19—22no—
97C2×C4×C19—41no—
98C2×C4×C19—41no—
99C2×C4×C19—41no—
100C2×C4×C19—42no—
101C2×C4×C19—42no—
102C2×C4×C19—81no—
103C2×C4×C19—81no—
104C2×C4×C19C2×D811yescharacteristic
105C2×C4×C19C2×Q1612yes—
106C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
107C2×C4×C19#13712yes—
108C2×Dic19—24no—
109C2×Dic19—42no—
110C2×Dic19—42no—
111C2×Dic19—42no—
112C2×Dic19—42no—
113C2×Dic19—42no—
114Dic38—84no—
115C8×C19—42no—
116C19⋊C8—44no—
117#2734—191no—
118#2057—192no—
119#2016D1911yescharacteristic
120#1272—191no—
121#1271—192no—
122C22×C19#44711yescharacteristic
123C22×C19#45112yes—
124C22×C19#45311yescharacteristic
125C22×C19#45612yes—
126C22×C19B(4,𝔽2)11yescharacteristic
127C4×C19—21no—
128C4×C19—21no—
129C4×C19—22no—
130C4×C19—22no—
131C4×C19—42no—
132C4×C19—82no—
133C4×C19—81no—
134Dic19—44no—
135Dic19—82no—
136C22×Q16—21no—
137C2×C4⋊Q8—381no—
138C2×C4⋊Q8C2×D1911yescharacteristic
139C2×#107—382no—
140C2×#103—21no—
141#398—381no—
142#395—382no—
143#391C2×D1911yescharacteristic
144#389—192no—
145#387—382no—
146#340—382no—
147#336—192no—
148#336C2×D1911yescharacteristic
149C2×C19#159511yescharacteristic
150C2×C19#160512yes—
151C2×C19#163311yescharacteristic
152C2×C19#164912yes—
153C2×C19#166011yescharacteristic
154C22×Q8—21no—
155C22×Q8—381no—
156C22×Q8C22⋊D1911yescharacteristic
157C2×Q16—42no—
158C2×Q16—42no—
159C2×Q16—42no—
160C22×C8—21no—
161C22×C8—382no—
162C4⋊Q8—42no—
163C4⋊Q8—762no—
164C4⋊Q8—762no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—192no—
167C2×C4⋊C4—192no—
168C2×C4⋊C4—382no—
169C2×C4⋊C4—382no—
170C2×C4⋊C4—381no—
171C2×C4⋊C4C22⋊D1911yescharacteristic
172C2×C42—381no—
173C2×C42C22×D1911yescharacteristic
174#107—764no—
175#103—42no—
176#95—22no—
177#95—381no—
178#95—382no—
179#95—382no—
180C19#775711yescharacteristic, complemented, Sylow
181C2×Q8—21no—
182C2×Q8—22no—
183C2×Q8—41no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8—41no—
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8—762no—
191C2×Q8—1521no—
192C2×Q8—1521no—
193C2×Q8#6452512yes—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—41no—
197C22×C4—382no—
198C22×C4—382no—
199C22×C4D4×D1912yes—
200C22×C4C2×C22⋊D1911yescharacteristic
201Q16—48no—
202C2×C8—22no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—384no—
206C2×C8—762no—
207C2×C8—762no—
208C4⋊C4—24no—
209C4⋊C4—41no—
210C4⋊C4—42no—
211C4⋊C4—194no—
212C4⋊C4—382no—
213C4⋊C4—762no—
214C4⋊C4—764no—
215C4⋊C4—762no—
216C4⋊C4—762no—
217C4⋊C4—1521no—
218C42—41no—
219C42—762no—
220C23#1059738311yescharacteristic
221Q8—42no—
222Q8—42no—
223Q8—42no—
224Q8—81no—
225Q8—81no—
226Q8—81no—
227Q8—1524no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—81no—
239C2×C4—81no—
240C2×C4—384no—
241C2×C4—762no—
242C2×C4—762no—
243C2×C4—762no—
244C2×C4—762no—
245C2×C4—762no—
246C2×C4Q16×D1912yes—
247C2×C4#1059736412yes—
248C2×C4C2×#6452511yescharacteristic
249C2×C4#1059739511yescharacteristic
250C8—42no—
251C8—764no—
252C22#1192667711yescharacteristic
253C22#1192669812yes—
254C22#1192671111yescharacteristic
255C22#1192672512yes—
256C22#1192673011yescharacteristic
257C4—22no—
258C4—22no—
259C4—21no—
260C4—21no—
261C4—42no—
262C4—81no—
263C4—82no—
264C4—764no—
265C4—1522no—
266C2#1456255211yescharacteristic
267C2#1456260712yes—
268C2#1456277311yescharacteristic
269C2#1456288212yes—
270C2#1456294411yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2016C2
socle, prime radicalC23×C19#120
hypercenter#2016D19
hypocenterC19#7757
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2016

Complements

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

NH ≅ G/Ntype
76. C4⋊Dic19Q16semidirect
180. C19#7757semidirect

Maximal subgroups

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

subgroupindex
#145706672
#145649602
#145614612
#145614592
C19×#20162
#775719