Finite Group Databasebeta

← #18084768

Subgroups — #18084768

Order 4864.

430 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 81 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#14574849C212yesmaximal
2#14564615C211yesmaximal, characteristic
3#14562147C212yesmaximal
4#14561546C211yesmaximal, characteristic
5C19×#3255C211yesmaximal, characteristic
6#11927101C2211yescharacteristic
7#11926954—22no—
8#11926914—22no—
9#11926885—24no—
10#11926836—22no—
11#11926826—22no—
12#11926601C2212yes—
13#11926390C2211yescharacteristic
14#11926305—22no—
15#11926281—24no—
16C19×#533C2212yes—
17C19×#475—22no—
18C19×#470—22no—
19C19×#462—22no—
20C19×#423C2211yescharacteristic
21C2×Q16×C19—22no—
22C2×M16×C19D412yes—
23C19×C4⋊Q8D412yes—
24C19×C4⋊Q8D412yes—
25C19×#125—22no—
26C19×C22⋊Q8—22no—
27C19×C22⋊Q8—22no—
28C4×Q8×C19—22no—
29C4×Q8×C19—22no—
30C19×#117—22no—
31C2×C42×C19C2311yescharacteristic
32#10597372—21no—
33#10597370—22no—
34C2×C4×Dic19—21no—
35#10597316—21no—
36#10597315D412yes—
37C4×Dic38—22no—
38C19×#106—22no—
39C19×C4⋊C8—22no—
40C19×#103—24no—
41C19⋊#95—22no—
42C22⋊(C19⋊C8)D414yes—
43#10597267—24no—
44#10597267—24no—
45#10597265—24no—
46#10597264—24no—
47C4⋊(C19⋊C8)—22no—
48#10597260—22no—
49C2×Q8×C19—22no—
50C2×Q8×C19—22no—
51C22×C4×C19C2×D412yes—
52C22×C4×C19C2×D411yescharacteristic
53C22×Dic19—41no—
54C2×Dic38—22no—
55Q16×C19—82no—
56M16×C19—42no—
57C2×C8×C19—22no—
58C4⋊C4×C19—22no—
59C4⋊C4×C19—22no—
60C4⋊C4×C19—22no—
61C4⋊C4×C19—22no—
62C4⋊C4×C19—42no—
63C4⋊C4×C19—42no—
64C22⋊C4×C19—42no—
65C42×C19—42no—
66C42×C19C2×D411yescharacteristic
67C42×C19C2×D412yes—
68C42×C19#4111yescharacteristic
69C22⋊Dic19—41no—
70C4⋊Dic19—22no—
71C4⋊Dic19—22no—
72Dic19⋊C4—42no—
73C4×Dic19—22no—
74C4×Dic19—41no—
75C4×Dic19—41no—
76C2×C19⋊C8—24no—
77#10217—191nomaximal, Sylow
78C23×C19#12711yescharacteristic
79Q8×C19—42no—
80Q8×C19—42no—
81Q8×C19—82no—
82C2×C4×C19—21no—
83C2×C4×C19—21no—
84C2×C4×C19—42no—
85C2×C4×C19—42no—
86C2×C4×C19—42no—
87C2×C4×C19#12012yes—
88C2×C4×C19#12011yescharacteristic
89C2×C4×C19#12111yescharacteristic
90C2×C4×C19#12112yes—
91C2×Dic19—42no—
92C2×Dic19—42no—
93C2×Dic19—82no—
94Dic38—44no—
95C8×C19—42no—
96C19⋊C8—44no—
97#3255D1911yescharacteristic
98#3237—192no—
99#1995—191no—
100#1506—192no—
101#1307—191no—
102C22×C19—21no—
103C22×C19—22no—
104C22×C19#39211yescharacteristic
105C4×C19—21no—
106C4×C19—22no—
107C4×C19—22no—
108C4×C19—82no—
109C4×C19—82no—
110C4×C19#45511yescharacteristic
111C4×C19#45611yescharacteristic
112Dic19—82no—
113Dic19—82no—
114#533—191no—
115#533C2×D1912yes—
116#501—382no—
117#491—382no—
118#485—384no—
119#477—382no—
120#475—22no—
121#475—382no—
122#470—22no—
123#462—22no—
124#432—192no—
125#423C2×D1911yescharacteristic
126#376—191no—
127#339—382no—
128#328—384no—
129C2×C19—41no—
130C2×C19#200711yescharacteristic
131C2×C19#200912yes—
132C2×Q16—22no—
133C2×M16C22⋊D1912yes—
134C4⋊Q8—192no—
135C4⋊Q8C22⋊D1912yes—
136C4⋊Q8C22⋊D1912yes—
137#125—22no—
138#125—381no—
139C22⋊Q8—22no—
140C22⋊Q8—22no—
141C22⋊Q8—382no—
142C4×Q8—22no—
143C4×Q8—22no—
144C4×Q8—382no—
145#117—22no—
146#117—381no—
147C2×C42—381no—
148C2×C42C22×D1911yescharacteristic
149#107—384no—
150#106—22no—
151#106—384no—
152C4⋊C8—22no—
153C4⋊C8—382no—
154#103—24no—
155#103—384no—
156#103—384no—
157C22⋊C8—194no—
158#97—382no—
159#95—382no—
160C19#1021711yescharacteristic, complemented, Sylow
161C2×Q8—22no—
162C2×Q8—22no—
163C2×Q8—382no—
164C22×C4—761no—
165C22×C4D4×D1912yes—
166C22×C4C2×C22⋊D1911yescharacteristic
167Q16—82no—
168M16—42no—
169C2×C8—22no—
170C2×C8—384no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—22no—
175C4⋊C4—42no—
176C4⋊C4—42no—
177C4⋊C4—382no—
178C4⋊C4—382no—
179C4⋊C4—762no—
180C22⋊C4—42no—
181C22⋊C4—761no—
182C42—42no—
183C42—382no—
184C42—761no—
185C42—761no—
186C42D4×D1911yescharacteristic
187C42#6454311yescharacteristic
188C42C2×C22⋊D1912yes—
189C23#1059738611yescharacteristic
190Q8—42no—
191Q8—42no—
192Q8—82no—
193Q8—764no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—762no—
200C2×C4—762no—
201C2×C4—1522no—
202C2×C4#1059738312yes—
203C2×C4#1059738411yescharacteristic
204C2×C4#1059738512yes—
205C2×C4#1059739911yescharacteristic
206C8—42no—
207C8—764no—
208C22—21no—
209C22—22no—
210C22#1192645211yescharacteristic
211C4—21no—
212C4—22no—
213C4—22no—
214C4—82no—
215C4—82no—
216C4—1522no—
217C4—1522no—
218C4#1192672211yescharacteristic
219C4#1192672711yescharacteristic
220C2—41no—
221C2#1456468211yescharacteristic
222C2#1456469312yes—
subgroupG/H
centerC22#11926452
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#3255C2
socleC22×C19#392
prime radicalC23×C19#127
hypercenter#3255D19
hypocenterC19#10217
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3255

Complements

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

NH ≅ G/Ntype
160. C19#10217semidirect

Maximal subgroups

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

subgroupindex
#145748492
#145646152
#145621472
#145615462
C19×#32552
#1021719