Finite Group Databasebeta

← #18083501

Subgroups — #18083501

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#14574980C211yesmaximal, characteristic
2#14573766C212yesmaximal
3#14564574C211yesmaximal, characteristic
4#14562251C212yesmaximal
5C19×#1290C211yesmaximal, characteristic
6#11927101C2212yes—
7C2×C4×Dic38C2211yescharacteristic
8#11926875—22no—
9#11926840—22no—
10#11926830—22no—
11#11926785—22no—
12#11926755—22no—
13#11926755—22no—
14#11926702—22no—
15#11926652—24no—
16C2×#10597260C2211yescharacteristic
17#11926298—22no—
18#11926285—24no—
19C19×#432C2212yes—
20C2×C19×C4⋊C8C2211yescharacteristic
21C22×Dic38D411yescharacteristic
22C22×C8×C19D412yes—
23C2×C42×C19C2311yescharacteristic
24#10597372—22no—
25C2×C4⋊Dic19D411yescharacteristic
26#10597370—22no—
27#10597370—22no—
28C2×Dic19⋊C4—21no—
29C2×C4×Dic19—21no—
30C22×C19⋊C8—21no—
31C2×Dic76—24no—
32C2×Dic76—22no—
33#10597316—22no—
34#10597315D412yes—
35#10597315D412yes—
36C4×Dic38—22no—
37C4×Dic38—22no—
38C4×Dic38—22no—
39C4×Dic38—22no—
40C19×C4⋊C8—22no—
41C19×C4⋊C8—22no—
42C19×C22⋊C8—22no—
43C19×#97D414yes—
44#10597275—22no—
45#10597274—24no—
46#10597273—24no—
47#10597273—24no—
48#10597273—24no—
49#10597260—22no—
50C22×C4×C19C2×D411yescharacteristic
51C22×C4×C19C2×D411yescharacteristic
52C22×C4×C19#4111yescharacteristic
53C22×Dic19—21no—
54C22×Dic19—21no—
55C2×Dic38—22no—
56C2×Dic38—22no—
57C2×Dic38—22no—
58C2×Dic38—42no—
59C2×C8×C19—22no—
60C2×C8×C19—24no—
61C2×C8×C19—42no—
62C42×C19C2×D412yes—
63C42×C19C2×D412yes—
64C22⋊Dic19—42no—
65C4⋊Dic19—22no—
66C4⋊Dic19—22no—
67C4⋊Dic19—22no—
68C4⋊Dic19—22no—
69C4⋊Dic19—22no—
70Dic19⋊C4—42no—
71Dic19⋊C4—42no—
72Dic19⋊C4—42no—
73C4×Dic19—41no—
74C4×Dic19—42no—
75C4×Dic19—41no—
76C2×C19⋊C8—22no—
77C2×C19⋊C8—41no—
78C2×C19⋊C8—41no—
79Dic76—48no—
80Dic76—82no—
81#10031—191nomaximal, Sylow
82C23×C19#12111yescharacteristic
83C2×C4×C19—22no—
84C2×C4×C19—21no—
85C2×C4×C19—21no—
86C2×C4×C19—41no—
87C2×C4×C19#12012yes—
88C2×C4×C19#12011yescharacteristic
89C2×C4×C19#12112yes—
90C2×C4×C19#12711yescharacteristic
91C2×Dic19—22no—
92C2×Dic19—41no—
93C2×Dic19—41no—
94C2×Dic19—41no—
95C2×Dic19—42no—
96C2×Dic19—42no—
97C2×Dic19—42no—
98Dic38—24no—
99Dic38—42no—
100Dic38—44no—
101Dic38—42no—
102Dic38—42no—
103C8×C19—44no—
104C8×C19—42no—
105C19⋊C8—42no—
106#3249—191no—
107#3113—192no—
108#1985—191no—
109#1531—192no—
110#1290D1911yescharacteristic
111C22×C19—21no—
112C22×C19—21no—
113C22×C19#39211yescharacteristic
114C22×C19#47312yes—
115C4×C19—21no—
116C4×C19—22no—
117C4×C19—22no—
118C4×C19#45511yescharacteristic
119C4×C19#45611yescharacteristic
120Dic19—42no—
121Dic19—82no—
122Dic19—82no—
123Dic19—81no—
124#533—192no—
125C2×C4×Q8—191no—
126#483—382no—
127#477—382no—
128#475—382no—
129#467—382no—
130#462—382no—
131#462—382no—
132#451—382no—
133#441—384no—
134#432C2×D1912yes—
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—384no—
145C2×Q16—382no—
146C22×C8—381no—
147C22×C8D7612yes—
148C4⋊Q8—192no—
149C4⋊Q8—192no—
150#125—382no—
151C22⋊Q8—382no—
152C22⋊Q8—382no—
153C4×Q8—382no—
154C4×Q8—382no—
155C4×Q8—382no—
156C4×Q8—382no—
157#117—382no—
158C2×C4⋊C4—191no—
159C2×C4⋊C4—381no—
160C2×C42—381no—
161C2×C42C22×D1911yescharacteristic
162#107—382no—
163#106—384no—
164C4⋊C8—22no—
165C4⋊C8—22no—
166#103—384no—
167#103—384no—
168#103—384no—
169C22⋊C8—22no—
170#97—382no—
171#97D7614yes—
172C19#1003111yescharacteristic, complemented, Sylow
173C2×Q8—382no—
174C2×Q8—382no—
175C2×Q8—382no—
176C2×Q8—762no—
177C22×C4—381no—
178C22×C4—381no—
179C22×C4C2×D7611yescharacteristic
180C22×C4D4×D1911yescharacteristic
181C22×C4#6454511yescharacteristic
182Q16—768no—
183Q16—1522no—
184C2×C8—24no—
185C2×C8—22no—
186C2×C8—42no—
187C2×C8—382no—
188C2×C8—761no—
189C2×C8—761no—
190C4⋊C4—382no—
191C4⋊C4—382no—
192C4⋊C4—382no—
193C4⋊C4—382no—
194C4⋊C4—382no—
195C4⋊C4—762no—
196C4⋊C4—762no—
197C4⋊C4—762no—
198C22⋊C4—762no—
199C42—761no—
200C42—761no—
201C42—762no—
202C42C2×D7612yes—
203C42D4×D1912yes—
204C23#1059734111yescharacteristic
205Q8—384no—
206Q8—762no—
207Q8—764no—
208Q8—762no—
209Q8—762no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—382no—
215C2×C4—761no—
216C2×C4—761no—
217C2×C4—762no—
218C2×C4—761no—
219C2×C4—762no—
220C2×C4—762no—
221C2×C4#1059732011yescharacteristic
222C2×C4#1059732812yes—
223C2×C4#1059732811yescharacteristic
224C2×C4#1059734112yes—
225C8—44no—
226C8—42no—
227C8—762no—
228C22—21no—
229C22—21no—
230C22#1192645411yescharacteristic
231C22#1192682012yes—
232C4—21no—
233C4—22no—
234C4—22no—
235C4—762no—
236C4—1522no—
237C4—1522no—
238C4—1521no—
239C4#1192672411yescharacteristic
240C4#1192672911yescharacteristic
241C2—22no—
242C2#1456468411yescharacteristic
243C2#1456470311yescharacteristic
244C2#1456475711yescharacteristic
subgroupG/H
centerC22#11926454
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1290C2
socleC22×C19#392
prime radicalC23×C19#121
hypercenter#1290D19
hypocenterC19#10031
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1290

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
#145749802
#145737662
#145645742
#145622512
C19×#12902
#1003119