Finite Group Databasebeta

← #18084830

Subgroups — #18084830

Order 4864.

466 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 103 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#14574779C212yesmaximal
2#14574159C211yesmaximal, characteristic
3#14562198C212yesmaximal
4#14561480C211yesmaximal, characteristic
5C19×#1960C211yesmaximal, characteristic
6#11927101C2212yes—
7#11926953—22no—
8#11926953—22no—
9#11926940—22no—
10#11926896—22no—
11#11926874—24no—
12#11926826—24no—
13#11926597C2212yes—
14#11926582—22no—
15#11926280—24no—
16C2×C19×C4⋊Q8C2211yescharacteristic
17C2×C19×#103—22no—
18C2×C19×#97C2211yescharacteristic
19C19×#382C2211yescharacteristic
20C22×Q8×C19—21no—
21C22×C8×C19D412yes—
22C19×C4⋊Q8—22no—
23C19×C4⋊Q8—21no—
24C19×C4⋊Q8D412yes—
25C2×C4⋊C4×C19—22no—
26C2×C4⋊C4×C19—21no—
27C2×C42×C19C2311yescharacteristic
28#10597372—22no—
29#10597370—22no—
30#10597370—22no—
31#10597316—22no—
32#10597315D412yes—
33#10597315D412yes—
34C4×Dic38—22no—
35C4×Dic38—22no—
36C19×#103—44no—
37C19×#97—22no—
38C19×#95—22no—
39C22⋊(C19⋊C8)D414yes—
40#10597275—24no—
41#10597274—22no—
42#10597274—22no—
43#10597267—28no—
44#10597265—28no—
45C4⋊(C19⋊C8)—22no—
46C4×C19⋊C8—22no—
47C2×Q8×C19—22no—
48C2×Q8×C19—41no—
49C2×Q8×C19—42no—
50C2×Q8×C19—42no—
51C22×C4×C19—41no—
52C22×C4×C19—41no—
53C22×C4×C19C2×D412yes—
54C22×C4×C19C2×D411yescharacteristic
55C2×Dic38—22no—
56C2×Dic38—22no—
57C2×C8×C19—22no—
58C2×C8×C19—22no—
59C2×C8×C19SD1614yes—
60C4⋊C4×C19—24no—
61C4⋊C4×C19—42no—
62C4⋊C4×C19—42no—
63C42×C19C2×D411yescharacteristic
64C42×C19C2×D412yes—
65C42×C19#4111yescharacteristic
66C22⋊Dic19—42no—
67C4⋊Dic19—22no—
68C4⋊Dic19—22no—
69C4⋊Dic19—22no—
70C4⋊Dic19—22no—
71Dic19⋊C4—42no—
72Dic19⋊C4—42no—
73C4×Dic19—42no—
74C2×C19⋊C8—24no—
75#10227—191nomaximal, Sylow
76C23×C19#12711yescharacteristic
77Q8×C19—44no—
78Q8×C19—82no—
79C2×C4×C19—42no—
80C2×C4×C19—42no—
81C2×C4×C19—81no—
82C2×C4×C19—81no—
83C2×C4×C19—82no—
84C2×C4×C19—81no—
85C2×C4×C19#12011yescharacteristic
86C2×C4×C19#12012yes—
87C2×C4×C19#12111yescharacteristic
88C2×C4×C19#12112yes—
89C2×C4×C19C2×SD1612yes—
90C2×C4×C19#13712yes—
91C2×Dic19—42no—
92C2×Dic19—42no—
93Dic38—44no—
94Dic38—82no—
95C8×C19—24no—
96C19⋊C8—44no—
97#3229—192no—
98#3162—191no—
99#1960D1911yescharacteristic
100#1518—192no—
101#1281—191no—
102C22×C19—22no—
103C22×C19#39211yescharacteristic
104C22×C19#49211yescharacteristic
105C22×C19#49711yescharacteristic
106C4×C19—22no—
107C4×C19—22no—
108C4×C19—82no—
109C4×C19—161no—
110C4×C19#44812yes—
111C4×C19#46112yes—
112Dic19—82no—
113Dic19—82no—
114#533—192no—
115C2×C4⋊Q8C2×D1911yescharacteristic
116#501—382no—
117#501—382no—
118#498—382no—
119#487—382no—
120#483—384no—
121#475—384no—
122#431—192no—
123#427—382no—
124C2×#103—22no—
125C2×#97C2×D1911yescharacteristic
126#382C2×D1911yescharacteristic
127#328—384no—
128C2×C19—21no—
129C2×C19—21no—
130C2×C19#200912yes—
131C2×C19#201311yescharacteristic
132C22×Q8—21no—
133C22×C8C22⋊D1912yes—
134C4⋊Q8—21no—
135C4⋊Q8—22no—
136C4⋊Q8—192no—
137C4⋊Q8—192no—
138C4⋊Q8D7612yes—
139#125—382no—
140C22⋊Q8—382no—
141C22⋊Q8—382no—
142C4×Q8—382no—
143C4×Q8—382no—
144#117—382no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—21no—
147C2×C42C22×D1911yescharacteristic
148#107—384no—
149#106—388no—
150#106—382no—
151#106—382no—
152C4⋊C8—382no—
153#103—44no—
154#103—388no—
155C22⋊C8—194no—
156#97—22no—
157C4×C8—382no—
158#95—22no—
159C19#1022711yescharacteristic, complemented, Sylow
160C2×Q8—22no—
161C2×Q8—41no—
162C2×Q8—42no—
163C2×Q8—42no—
164C2×Q8—382no—
165C2×Q8—382no—
166C22×C4—41no—
167C22×C4—41no—
168C22×C4D4×D1912yes—
169C22×C4C2×C22⋊D1911yescharacteristic
170C2×C8—22no—
171C2×C8—22no—
172C2×C8—384no—
173C2×C8#6452614yes—
174C4⋊C4—24no—
175C4⋊C4—42no—
176C4⋊C4—42no—
177C4⋊C4—382no—
178C4⋊C4—382no—
179C4⋊C4—382no—
180C4⋊C4—382no—
181C4⋊C4—762no—
182C4⋊C4—762no—
183C22⋊C4—762no—
184C42—762no—
185C42C2×D7611yescharacteristic
186C42#6454111yescharacteristic
187C42D4×D1912yes—
188C23#1059738611yescharacteristic
189Q8—44no—
190Q8—82no—
191Q8—764no—
192Q8—1522no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—81no—
196C2×C4—81no—
197C2×C4—82no—
198C2×C4—81no—
199C2×C4—762no—
200C2×C4—762no—
201C2×C4#1059732812yes—
202C2×C4#1059733012yes—
203C2×C4#1059737611yescharacteristic
204C2×C4C2×#6452612yes—
205C2×C4#1059738311yescharacteristic
206C2×C4#1059739712yes—
207C8—24no—
208C8—764no—
209C22—22no—
210C22#1192645311yescharacteristic
211C22#1192691611yescharacteristic
212C22#1192693911yescharacteristic
213C4—22no—
214C4—22no—
215C4—82no—
216C4—161no—
217C4—1522no—
218C4—1522no—
219C4#1192668212yes—
220C4#1192674912yes—
221C2—21no—
222C2—21no—
223C2#1456469712yes—
224C2#1456471711yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1960C2
socleC22×C19#392
prime radicalC23×C19#127
hypercenter#1960D19
hypocenterC19#10227
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1960

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
#145747792
#145741592
#145621982
#145614802
C19×#19602
#1022719