Finite Group Databasebeta

← #18071382

Subgroups — #18071382

Order 4864.

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

normal subgroups only

This group has 424 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#14564968C212yesmaximal
2#14564734C211yesmaximal, characteristic
3#14561461C211yesmaximal, characteristic
4#14561458C212yesmaximal
5C19×#2809C211yesmaximal, characteristic
6C22×#64528—21no—
7C2×#10597315C2211yescharacteristic
8C2×#10597265—22no—
9C2×#10597267—21no—
10#11926306—22no—
11#11926299C2212yes—
12#11926299C2211yescharacteristic
13C19×#400—21no—
14C19×#398—22no—
15C19×#391—21no—
16C19×#391C2211yescharacteristic
17C19×#389C2212yes—
18C19×#387—22no—
19C22×Q8×C19D411yescharacteristic
20C22×Dic38—21no—
21C2×C4⋊C4×C19—22no—
22C2×C4⋊C4×C19—21no—
23C2×C4⋊C4×C19—21no—
24C2×C4⋊C4×C19D412yes—
25C2×C4⋊C4×C19D411yescharacteristic
26C2×C4⋊C4×C19D412yes—
27C2×C42×C19—21no—
28C2×C42×C19C2311yescharacteristic
29C2×#64528—42no—
30C2×#64528—42no—
31C2×#64528—42no—
32C2×C4⋊Dic19—22no—
33C22×C19⋊C8—21no—
34C22×C19⋊C8—22no—
35#10597315—42no—
36C19×#95—21no—
37C19×#95—22no—
38C19×#95—22no—
39C19×#95—22no—
40C19×#95—22no—
41#10597267—42no—
42#10597265—44no—
43C2×Q8×C19—21no—
44C2×Q8×C19—41no—
45C2×Q8×C19—41no—
46C2×Q8×C19SD1612yes—
47C22×C4×C19—21no—
48C22×C4×C19—22no—
49C22×C4×C19—22no—
50C22×C4×C19—21no—
51C22×C4×C19C2×D411yescharacteristic
52C22×C4×C19C2×D412yes—
53C22×Dic19—41no—
54C2×Dic38—22no—
55C2×Dic38—41no—
56C2×Dic38—41no—
57C2×Dic38—41no—
58C2×Dic38—41no—
59C2×Dic38—41no—
60C4⋊C4×C19—22no—
61C4⋊C4×C19—22no—
62C4⋊C4×C19—42no—
63C4⋊C4×C19—41no—
64C4⋊C4×C19—42no—
65C4⋊C4×C19—42no—
66C4⋊C4×C19—81no—
67C4⋊C4×C19—81no—
68C42×C19—41no—
69C42×C19—81no—
70#64528—48no—
71C4⋊Dic19—24no—
72C4⋊Dic19—42no—
73C2×C19⋊C8—22no—
74C2×C19⋊C8—24no—
75C2×C19⋊C8—41no—
76C2×C19⋊C8—42no—
77C2×C19⋊C8—41no—
78C2×C19⋊C8—42no—
79#7760—191nomaximal, Sylow
80C23×C19#12011yescharacteristic
81Q8×C19—42no—
82Q8×C19—81no—
83C2×C4×C19—21no—
84C2×C4×C19—22no—
85C2×C4×C19—22no—
86C2×C4×C19—21no—
87C2×C4×C19—22no—
88C2×C4×C19—41no—
89C2×C4×C19—41no—
90C2×C4×C19—42no—
91C2×C4×C19—42no—
92C2×C4×C19—42no—
93C2×C4×C19—41no—
94C2×C4×C19—42no—
95C2×C4×C19—42no—
96C2×C4×C19—42no—
97C2×C4×C19—42no—
98C2×C4×C19C2×SD1611yescharacteristic
99C2×C4×C19#13512yes—
100C2×C4×C19#13711yescharacteristic
101C2×C4×C19#13712yes—
102C2×Dic19—42no—
103C2×Dic19—81no—
104C2×Dic19—81no—
105Dic38—42no—
106Dic38—42no—
107Dic38—81no—
108Dic38—81no—
109C19⋊C8—44no—
110C19⋊C8—42no—
111#2809D1911yescharacteristic
112#2058—192no—
113#2016—191no—
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—82no—
128C4×C19—81no—
129Dic19—82no—
130C22×Q16—381no—
131C2×C4⋊Q8—191no—
132C2×#106—382no—
133C2×#103—381no—
134#400—21no—
135#398—22no—
136#391—21no—
137#391C2×D1911yescharacteristic
138#389C2×D1912yes—
139#387—22no—
140#340—382no—
141#336—192no—
142#336—191no—
143C2×C19#159611yescharacteristic
144C2×C19#160312yes—
145C2×C19#163411yescharacteristic
146C2×C19#165312yes—
147C2×C19#166011yescharacteristic
148C22×Q8—381no—
149C22×Q8C22⋊D1911yescharacteristic
150C2×Q16—762no—
151C2×Q16—762no—
152C2×Q16—762no—
153C22×C8—381no—
154C22×C8—382no—
155C4⋊Q8—762no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—382no—
160C2×C4⋊C4C22⋊D1912yes—
161C2×C4⋊C4C22⋊D1912yes—
162C2×C4⋊C4C22⋊D1911yescharacteristic
163C2×C42—21no—
164C2×C42C22×D1911yescharacteristic
165#106—764no—
166#103—762no—
167#95—21no—
168#95—22no—
169#95—22no—
170#95—22no—
171#95—22no—
172C19#776011yescharacteristic, complemented, Sylow
173C2×Q8—21no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—382no—
177C2×Q8—761no—
178C2×Q8—761no—
179C2×Q8—761no—
180C2×Q8—761no—
181C2×Q8—761no—
182C2×Q8#6452712yes—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—761no—
188C22×C4C2×C22⋊D1911yescharacteristic
189C22×C4C2×C22⋊D1912yes—
190Q16—768no—
191C2×C8—382no—
192C2×C8—384no—
193C2×C8—762no—
194C2×C8—761no—
195C2×C8—761no—
196C2×C8—762no—
197C4⋊C4—22no—
198C4⋊C4—22no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4—81no—
204C4⋊C4—81no—
205C4⋊C4—384no—
206C4⋊C4—762no—
207C42—41no—
208C42—81no—
209C23#1059739911yescharacteristic
210Q8—42no—
211Q8—81no—
212Q8—762no—
213Q8—762no—
214Q8—1521no—
215Q8—1521no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—762no—
232C2×C4—1521no—
233C2×C4—1521no—
234C2×C4C2×#6452711yescharacteristic
235C2×C4#1059738811yescharacteristic
236C2×C4#1059739612yes—
237C2×C4#1059739712yes—
238C8—762no—
239C8—764no—
240C22#1192668311yescharacteristic
241C22#1192670612yes—
242C22#1192671211yescharacteristic
243C22#1192672712yes—
244C22#1192673111yescharacteristic
245C4—22no—
246C4—22no—
247C4—21no—
248C4—21no—
249C4—42no—
250C4—82no—
251C4—81no—
252C4—82no—
253C4—1522no—
254C2#1456255811yescharacteristic
255C2#1456259812yes—
256C2#1456278011yescharacteristic
257C2#1456291212yes—
258C2#1456294611yescharacteristic
subgroupG/H
centerC23#10597399
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2809C2
socle, prime radicalC23×C19#120
hypercenter#2809D19
hypocenterC19#7760
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
172. C19#7760semidirect

Maximal subgroups

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

subgroupindex
#145649682
#145647342
#145614612
#145614582
C19×#28092
#776019