Finite Group Databasebeta

← #18083498

Subgroups — #18083498

Order 4864.

468 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 85 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#14573761C212yesmaximal
2#14564574C211yesmaximal, characteristic
3#14562250C212yesmaximal
4#14561505C211yesmaximal, characteristic
5C19×#3249C211yesmaximal, characteristic
6C2×C4×Dic38C2211yescharacteristic
7#11926872—22no—
8#11926826—22no—
9#11926751—22no—
10#11926699—22no—
11#11926649—24no—
12#11926601C2212yes—
13C2×#10597260C2211yescharacteristic
14#11926298—22no—
15#11926286—24no—
16C19×#533C2212yes—
17C19×#477—22no—
18C19×#467—22no—
19C19×#462—22no—
20C2×C19×C4⋊C8C2211yescharacteristic
21C22×Dic38D411yescharacteristic
22C2×Q16×C19—22no—
23C22×C8×C19D412yes—
24C19×C4⋊Q8D412yes—
25C19×C4⋊Q8D412yes—
26C19×#125—22no—
27C19×C22⋊Q8—22no—
28C19×C22⋊Q8—22no—
29C4×Q8×C19—22no—
30C4×Q8×C19—22no—
31C19×#117—22no—
32C2×C42×C19C2311yescharacteristic
33C2×#64528—24no—
34C2×C4⋊Dic19D411yescharacteristic
35C2×Dic19⋊C4—21no—
36C2×C4×Dic19—21no—
37C22×C19⋊C8—21no—
38C4×Dic38—22no—
39C4×Dic38—22no—
40C19×#107—22no—
41C19×C4⋊C8—22no—
42C19×#103—24no—
43#10597292—24no—
44C22⋊(C19⋊C8)—22no—
45#10597267—24no—
46#10597265—24no—
47C4⋊(C19⋊C8)—22no—
48#10597260—22no—
49#10597260D414yes—
50C2×Q8×C19—22no—
51C2×Q8×C19—22no—
52C22×C4×C19C2×D411yescharacteristic
53C22×C4×C19C2×D411yescharacteristic
54C22×C4×C19#4111yescharacteristic
55C22×Dic19—21no—
56C22×Dic19—21no—
57C2×Dic38—22no—
58C2×Dic38—42no—
59Q16×C19—82no—
60C2×C8×C19—22no—
61C2×C8×C19—42no—
62C4⋊C4×C19—22no—
63C4⋊C4×C19—22no—
64C4⋊C4×C19—22no—
65C4⋊C4×C19—22no—
66C4⋊C4×C19—42no—
67C4⋊C4×C19—42no—
68C22⋊C4×C19—42no—
69C42×C19—42no—
70C42×C19C2×D412yes—
71C42×C19C2×D412yes—
72#64528—48no—
73C4⋊Dic19—22no—
74Dic19⋊C4—42no—
75C4×Dic19—41no—
76C4×Dic19—41no—
77C2×C19⋊C8—22no—
78C2×C19⋊C8—24no—
79C2×C19⋊C8—41no—
80C2×C19⋊C8—41no—
81#10031—191nomaximal, Sylow
82C23×C19#12111yescharacteristic
83Q8×C19—44no—
84Q8×C19—42no—
85Q8×C19—42no—
86C2×C4×C19—22no—
87C2×C4×C19—21no—
88C2×C4×C19—21no—
89C2×C4×C19—41no—
90C2×C4×C19—42no—
91C2×C4×C19—42no—
92C2×C4×C19#12012yes—
93C2×C4×C19#12011yescharacteristic
94C2×C4×C19#12112yes—
95C2×C4×C19#12711yescharacteristic
96C2×Dic19—22no—
97C2×Dic19—41no—
98C2×Dic19—41no—
99C2×Dic19—41no—
100C2×Dic19—42no—
101Dic38—24no—
102Dic38—42no—
103C8×C19—42no—
104C19⋊C8—42no—
105C19⋊C8—44no—
106#3249D1911yescharacteristic
107#3113—192no—
108#1985—191no—
109#1531—192no—
110#1290—191no—
111C22×C19—21no—
112C22×C19—21no—
113C22×C19#39211yescharacteristic
114C22×C19#47312yes—
115C4×C19—21no—
116C4×C19—22no—
117C4×C19—22no—
118C4×C19—82no—
119C4×C19—82no—
120C4×C19#45511yescharacteristic
121C4×C19#45611yescharacteristic
122Dic19—42no—
123Dic19—81no—
124#533C2×D1912yes—
125C2×C4×Q8—191no—
126#483—382no—
127#477—22no—
128#475—382no—
129#467—22no—
130#462—22no—
131#462—382no—
132#451—382no—
133#441—384no—
134#432—192no—
135C2×C4⋊C8C2×D1911yescharacteristic
136C2×#97—191no—
137#336—382no—
138#330—384no—
139C2×C19—22no—
140C2×C19#200711yescharacteristic
141C2×C19#201011yescharacteristic
142C2×C19#202011yescharacteristic
143C22×Q8—191no—
144C2×Q16—22no—
145C2×Q16—384no—
146C22×C8—381no—
147C22×C8C22⋊D1912yes—
148C4⋊Q8C22⋊D1912yes—
149C4⋊Q8C22⋊D1912yes—
150#125—22no—
151C22⋊Q8—22no—
152C22⋊Q8—22no—
153C4×Q8—22no—
154C4×Q8—22no—
155C4×Q8—382no—
156C4×Q8—382no—
157#117—22no—
158C2×C4⋊C4—191no—
159C2×C4⋊C4—381no—
160C2×C42—381no—
161C2×C42C22×D1911yescharacteristic
162#107—22no—
163#106—384no—
164C4⋊C8—22no—
165C4⋊C8—382no—
166#103—24no—
167#103—384no—
168#103—384no—
169C22⋊C8—382no—
170#97—194no—
171#97—382no—
172C19#1003111yescharacteristic, complemented, Sylow
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—382no—
176C2×Q8—762no—
177C22×C4—381no—
178C22×C4—381no—
179C22×C4D4×D1911yescharacteristic
180C22×C4#6454311yescharacteristic
181C22×C4C2×C22⋊D1911yescharacteristic
182Q16—82no—
183Q16—768no—
184C2×C8—22no—
185C2×C8—42no—
186C2×C8—382no—
187C2×C8—384no—
188C2×C8—761no—
189C2×C8—761no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—382no—
197C4⋊C4—762no—
198C22⋊C4—42no—
199C42—42no—
200C42—761no—
201C42—761no—
202C42D4×D1912yes—
203C42C2×C22⋊D1912yes—
204C23#1059738411yescharacteristic
205Q8—44no—
206Q8—42no—
207Q8—42no—
208Q8—384no—
209Q8—762no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—382no—
217C2×C4—761no—
218C2×C4—761no—
219C2×C4—762no—
220C2×C4—761no—
221C2×C4#1059738312yes—
222C2×C4#1059738512yes—
223C2×C4#1059738611yescharacteristic
224C2×C4#1059739911yescharacteristic
225C8—42no—
226C8—762no—
227C8—764no—
228C22—21no—
229C22—21no—
230C22#1192645211yescharacteristic
231C22#1192681612yes—
232C4—21no—
233C4—22no—
234C4—22no—
235C4—82no—
236C4—82no—
237C4—762no—
238C4—1521no—
239C4#1192672211yescharacteristic
240C4#1192672711yescharacteristic
241C2—22no—
242C2#1456468211yescharacteristic
243C2#1456469911yescharacteristic
244C2#1456475411yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#3249C2
socleC22×C19#392
prime radicalC23×C19#121
hypercenter#3249D19
hypocenterC19#10031
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3249

Complements

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

NH ≅ G/Ntype
172. C19#10031semidirect

Maximal subgroups

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

subgroupindex
#145737612
#145645742
#145622502
#145615052
C19×#32492
#1003119