Finite Group Databasebeta

← #18084833

Subgroups — #18084833

Order 4864.

466 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 105 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#14574781C212yesmaximal
2#14574159C211yesmaximal, characteristic
3#14564455C211yesmaximal, characteristic
4#14562200C212yesmaximal
5C19×#1281C211yesmaximal, characteristic
6#11927101C2212yes—
7C2×#10597315C2211yescharacteristic
8#11926953—22no—
9#11926953—22no—
10#11926942—22no—
11#11926895—22no—
12#11926875—24no—
13#11926830—24no—
14#11926582—22no—
15C2×#10597273—22no—
16#11926410C2211yescharacteristic
17#11926282—24no—
18C19×#431C2212yes—
19C2×C19×#97C2211yescharacteristic
20C22×Dic38—21no—
21C22×C8×C19D412yes—
22C2×C42×C19C2311yescharacteristic
23#10597372—22no—
24C2×C4⋊Dic19—22no—
25C2×C4⋊Dic19—21no—
26#10597370—22no—
27#10597370—22no—
28#10597316—22no—
29#10597315—22no—
30#10597315—21no—
31#10597315D412yes—
32#10597315D412yes—
33#10597315D412yes—
34C4×Dic38—22no—
35C4×Dic38—22no—
36C19×C4⋊C8—22no—
37C19×C22⋊C8D414yes—
38C19×#97—22no—
39C4×C8×C19—22no—
40C19⋊#95—22no—
41#10597275—24no—
42#10597274—28no—
43#10597274—22no—
44#10597274—22no—
45#10597273—28no—
46#10597273—44no—
47C22×C4×C19C2×D412yes—
48C22×C4×C19C2×D411yescharacteristic
49C22×Dic19—41no—
50C22×Dic19—41no—
51C2×Dic38—22no—
52C2×Dic38—22no—
53C2×Dic38—22no—
54C2×Dic38—42no—
55C2×Dic38—42no—
56C2×Dic38—41no—
57C2×C8×C19—22no—
58C2×C8×C19—22no—
59C2×C8×C19—24no—
60C2×C8×C19SD1614yes—
61C42×C19C2×D412yes—
62C42×C19C2×D411yescharacteristic
63C42×C19#4111yescharacteristic
64C22⋊Dic19—42no—
65C4⋊Dic19—24no—
66C4⋊Dic19—22no—
67C4⋊Dic19—22no—
68C4⋊Dic19—22no—
69C4⋊Dic19—22no—
70C4⋊Dic19—42no—
71C4⋊Dic19—42no—
72Dic19⋊C4—42no—
73Dic19⋊C4—42no—
74C4×Dic19—42no—
75#10227—191nomaximal, Sylow
76C23×C19#12711yescharacteristic
77C2×C4×C19—42no—
78C2×C4×C19#12012yes—
79C2×C4×C19#12011yescharacteristic
80C2×C4×C19#12112yes—
81C2×C4×C19#12111yescharacteristic
82C2×C4×C19C2×SD1612yes—
83C2×C4×C19#13712yes—
84C2×Dic19—42no—
85C2×Dic19—42no—
86C2×Dic19—42no—
87C2×Dic19—81no—
88C2×Dic19—81no—
89C2×Dic19—82no—
90C2×Dic19—81no—
91Dic38—44no—
92Dic38—44no—
93Dic38—82no—
94Dic38—82no—
95C8×C19—24no—
96C8×C19—44no—
97#3229—192no—
98#3162—191no—
99#1960—191no—
100#1518—192no—
101#1281D1911yescharacteristic
102C22×C19—22no—
103C22×C19#39211yescharacteristic
104C22×C19#49211yescharacteristic
105C22×C19#49711yescharacteristic
106C4×C19—22no—
107C4×C19—22no—
108C4×C19#44812yes—
109C4×C19#46112yes—
110Dic19—82no—
111Dic19—82no—
112Dic19—82no—
113Dic19—161no—
114#533—192no—
115C2×C4⋊Q8—191no—
116#501—382no—
117#501—382no—
118#498—382no—
119#487—382no—
120#483—384no—
121#475—384no—
122#431C2×D1912yes—
123#427—382no—
124C2×#103—382no—
125C2×#97C2×D1911yescharacteristic
126#382—191no—
127#328—384no—
128C2×C19—21no—
129C2×C19—21no—
130C2×C19#200912yes—
131C2×C19#201311yescharacteristic
132C22×Q8—381no—
133C22×C8D7612yes—
134C4⋊Q8—192no—
135C4⋊Q8—192no—
136C4⋊Q8—192no—
137C4⋊Q8—382no—
138C4⋊Q8—381no—
139#125—382no—
140C22⋊Q8—382no—
141C22⋊Q8—382no—
142C4×Q8—382no—
143C4×Q8—382no—
144#117—382no—
145C2×C4⋊C4—382no—
146C2×C4⋊C4—381no—
147C2×C42C22×D1911yescharacteristic
148#107—384no—
149#106—382no—
150#106—382no—
151#106—388no—
152C4⋊C8—22no—
153#103—388no—
154#103—764no—
155C22⋊C8D7614yes—
156#97—22no—
157C4×C8—22no—
158#95—382no—
159C19#1022711yescharacteristic, complemented, Sylow
160C2×Q8—382no—
161C2×Q8—382no—
162C2×Q8—382no—
163C2×Q8—761no—
164C2×Q8—762no—
165C2×Q8—762no—
166C22×C4—761no—
167C22×C4—761no—
168C22×C4C2×D7612yes—
169C22×C4C2×D7611yescharacteristic
170C2×C8—22no—
171C2×C8—22no—
172C2×C8—24no—
173C2×C8#6451614yes—
174C4⋊C4—384no—
175C4⋊C4—382no—
176C4⋊C4—382no—
177C4⋊C4—382no—
178C4⋊C4—382no—
179C4⋊C4—762no—
180C4⋊C4—762no—
181C4⋊C4—762no—
182C4⋊C4—762no—
183C22⋊C4—762no—
184C42—762no—
185C42D4×D1912yes—
186C42D4×D1911yescharacteristic
187C42#6454511yescharacteristic
188C23#1059732011yescharacteristic
189Q8—764no—
190Q8—764no—
191Q8—1522no—
192Q8—1522no—
193C2×C4—42no—
194C2×C4—762no—
195C2×C4—762no—
196C2×C4—762no—
197C2×C4—1522no—
198C2×C4—1521no—
199C2×C4—1521no—
200C2×C4—1521no—
201C2×C4#1059732812yes—
202C2×C4#1059732811yescharacteristic
203C2×C4#1059734112yes—
204C2×C4#1059734111yescharacteristic
205C2×C4C2×#6451612yes—
206C2×C4#1059735512yes—
207C8—24no—
208C8—44no—
209C22—22no—
210C22#1192645411yescharacteristic
211C22#1192691711yescharacteristic
212C22#1192693811yescharacteristic
213C4—22no—
214C4—22no—
215C4—3041no—
216C4—1522no—
217C4—1522no—
218C4—1522no—
219C4#1192668512yes—
220C4#1192675012yes—
221C2—21no—
222C2—21no—
223C2#1456469812yes—
224C2#1456472011yescharacteristic
subgroupG/H
centerC22#11926454
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1281C2
socleC22×C19#392
prime radicalC23×C19#127
hypercenter#1281D19
hypocenterC19#10227
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1281

Complements

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

NH ≅ G/Ntype
159. C19#10227semidirect

Maximal subgroups

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

subgroupindex
#145747812
#145741592
#145644552
#145622002
C19×#12812
#1022719