Finite Group Databasebeta

← #18071380

Subgroups — #18071380

Order 4864.

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

normal subgroups only

This group has 424 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#14571623C211yesmaximal, characteristic
2#14564965C212yesmaximal
3#14561461C211yesmaximal, characteristic
4#14561457C212yesmaximal
5C19×#2016C211yesmaximal, characteristic
6C2×#10597265—22no—
7#11926483—21no—
8#11926476—22no—
9#11926451—21no—
10#11926442C2212yes—
11#11926431—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
21C2×Q16×C19—42no—
22C2×Q16×C19—42no—
23C2×Q16×C19—42no—
24C22×C8×C19—21no—
25C19×C4⋊Q8—42no—
26C2×C4⋊C4×C19—22no—
27C2×C4⋊C4×C19D411yescharacteristic
28C2×C42×C19C2311yescharacteristic
29C2×C4⋊Dic19—21no—
30C2×C4⋊Dic19—21no—
31C2×C4⋊Dic19D412yes—
32C2×C4⋊Dic19D412yes—
33C2×Dic19⋊C4—22no—
34C2×C4×Dic19—21no—
35C22×C19⋊C8—22no—
36C19×#103—42no—
37C19×#95—22no—
38C19⋊#95—21no—
39C19⋊#95—22no—
40C19⋊#95—22no—
41C19⋊#95—22no—
42#10597265—44no—
43C2×Q8×C19—21no—
44C2×Q8×C19—22no—
45C2×Q8×C19—41no—
46C2×Q8×C19—41no—
47C2×Q8×C19—41no—
48C2×Q8×C19—41no—
49C2×Q8×C19—41no—
50C2×Q8×C19—41no—
51C2×Q8×C19—41no—
52C2×Q8×C19SD1612yes—
53C22×C4×C19—21no—
54C22×C4×C19—21no—
55C22×C4×C19—41no—
56C22×C4×C19C2×D412yes—
57C22×C4×C19C2×D411yescharacteristic
58C22×Dic19—22no—
59C22×Dic19—22no—
60Q16×C19—48no—
61C2×C8×C19—22no—
62C2×C8×C19—41no—
63C2×C8×C19—41no—
64C4⋊C4×C19—24no—
65C4⋊C4×C19—41no—
66C4⋊C4×C19—42no—
67C42×C19—41no—
68C4⋊Dic19—22no—
69C4⋊Dic19—22no—
70C4⋊Dic19—42no—
71C4⋊Dic19—81no—
72C4⋊Dic19—81no—
73Dic19⋊C4—42no—
74Dic19⋊C4—42no—
75C4×Dic19—81no—
76C2×C19⋊C8—24no—
77C2×C19⋊C8—42no—
78C2×C19⋊C8—42no—
79#7760—191nomaximal, Sylow
80C23×C19#12011yescharacteristic
81Q8×C19—42no—
82Q8×C19—42no—
83Q8×C19—42no—
84Q8×C19—81no—
85Q8×C19—81no—
86Q8×C19—81no—
87C2×C4×C19—21no—
88C2×C4×C19—22no—
89C2×C4×C19—22no—
90C2×C4×C19—21no—
91C2×C4×C19—22no—
92C2×C4×C19—41no—
93C2×C4×C19—41no—
94C2×C4×C19—41no—
95C2×C4×C19—42no—
96C2×C4×C19—42no—
97C2×C4×C19—81no—
98C2×C4×C19—81no—
99C2×C4×C19C2×SD1611yescharacteristic
100C2×C4×C19#13512yes—
101C2×C4×C19#13711yescharacteristic
102C2×C4×C19#13712yes—
103C2×Dic19—42no—
104C2×Dic19—42no—
105C2×Dic19—42no—
106C2×Dic19—42no—
107C2×Dic19—42no—
108C2×Dic19—42no—
109C8×C19—42no—
110C19⋊C8—44no—
111#2809—191no—
112#2058—192no—
113#2016D1911yescharacteristic
114#1272—191no—
115#1271—192no—
116C22×C19#44811yescharacteristic
117C22×C19#45212yes—
118C22×C19#45311yescharacteristic
119C22×C19#45612yes—
120C22×C19B(4,𝔽2)11yescharacteristic
121C4×C19—21no—
122C4×C19—21no—
123C4×C19—22no—
124C4×C19—22no—
125C4×C19—42no—
126C4×C19—82no—
127C4×C19—81no—
128Dic19—82no—
129Dic19—82no—
130C22×Q16—21no—
131C2×C4⋊Q8C2×D1911yescharacteristic
132C2×#106—382no—
133C2×#103—21no—
134#400—381no—
135#398—382no—
136#391—381no—
137#391C2×D1911yescharacteristic
138#389—192no—
139#387—382no—
140#340—382no—
141#336—192no—
142#336C2×D1911yescharacteristic
143C2×C19#159611yescharacteristic
144C2×C19#160312yes—
145C2×C19#163411yescharacteristic
146C2×C19#165312yes—
147C2×C19#166011yescharacteristic
148C22×Q8—21no—
149C22×Q8C22⋊D1911yescharacteristic
150C2×Q16—42no—
151C2×Q16—42no—
152C2×Q16—42no—
153C22×C8—21no—
154C22×C8—382no—
155C4⋊Q8—42no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—192no—
158C2×C4⋊C4—192no—
159C2×C4⋊C4—382no—
160C2×C4⋊C4—381no—
161C2×C4⋊C4—381no—
162C2×C4⋊C4C22⋊D1911yescharacteristic
163C2×C42—381no—
164C2×C42C22×D1911yescharacteristic
165#106—764no—
166#103—42no—
167#95—22no—
168#95—381no—
169#95—382no—
170#95—382no—
171#95—382no—
172C19#776011yescharacteristic, complemented, Sylow
173C2×Q8—21no—
174C2×Q8—22no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8—41no—
180C2×Q8—41no—
181C2×Q8—41no—
182C2×Q8#6452612yes—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—41no—
186C22×C4—382no—
187C22×C4—382no—
188C22×C4D4×D1912yes—
189C22×C4C2×C22⋊D1911yescharacteristic
190Q16—48no—
191C2×C8—22no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—384no—
195C2×C8—762no—
196C2×C8—762no—
197C4⋊C4—24no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—382no—
201C4⋊C4—382no—
202C4⋊C4—762no—
203C4⋊C4—762no—
204C4⋊C4—762no—
205C4⋊C4—1521no—
206C4⋊C4—1521no—
207C42—41no—
208C42—1521no—
209C23#1059738311yescharacteristic
210Q8—42no—
211Q8—42no—
212Q8—42no—
213Q8—81no—
214Q8—81no—
215Q8—81no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—81no—
227C2×C4—81no—
228C2×C4—762no—
229C2×C4—762no—
230C2×C4—762no—
231C2×C4—762no—
232C2×C4—762no—
233C2×C4—762no—
234C2×C4#1059736412yes—
235C2×C4#1059736512yes—
236C2×C4C2×#6452611yescharacteristic
237C2×C4#1059739711yescharacteristic
238C8—42no—
239C8—764no—
240C22#1192668211yescharacteristic
241C22#1192670512yes—
242C22#1192671111yescharacteristic
243C22#1192672512yes—
244C22#1192673011yescharacteristic
245C4—22no—
246C4—22no—
247C4—21no—
248C4—21no—
249C4—42no—
250C4—81no—
251C4—82no—
252C4—1522no—
253C4—1522no—
254C2#1456255711yescharacteristic
255C2#1456259712yes—
256C2#1456277811yescharacteristic
257C2#1456291012yes—
258C2#1456294411yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2016C2
socle, prime radicalC23×C19#120
hypercenter#2016D19
hypocenterC19#7760
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
172. C19#7760semidirect

Maximal subgroups

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

subgroupindex
#145716232
#145649652
#145614612
#145614572
C19×#20162
#776019