Finite Group Databasebeta

← #18084770

Subgroups — #18084770

Order 4864.

430 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 79 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#14575029C211yesmaximal, characteristic
2#14574845C212yesmaximal
3#14562146C212yesmaximal
4#14561546C211yesmaximal, characteristic
5C19×#1995C211yesmaximal, characteristic
6#11927101C2212yes—
7#11926950—22no—
8#11926912—22no—
9#11926882—24no—
10#11926839—22no—
11#11926830—22no—
12#11926829—22no—
13#11926802—22no—
14#11926755—22no—
15#11926601C2212yes—
16#11926280—24no—
17C19×#533C2211yescharacteristic
18C19×#423C2211yescharacteristic
19C19×#376C2211yescharacteristic
20C19×#339—22no—
21C2×M16×C19D412yes—
22C19×C4⋊Q8D412yes—
23C19×#125—21no—
24C19×C22⋊Q8—22no—
25C4×Q8×C19—22no—
26C19×#117—21no—
27C2×C42×C19—21no—
28C2×C42×C19C2311yescharacteristic
29#10597372—22no—
30#10597370—22no—
31#10597370—22no—
32C2×Dic76—22no—
33#10597316—22no—
34#10597315D412yes—
35#10597315D412yes—
36C4×Dic38—22no—
37C4×Dic38—22no—
38C19×C4⋊C8—22no—
39C19×#95—22no—
40#10597292—24no—
41#10597292—24no—
42C22⋊(C19⋊C8)D414yes—
43#10597274—22no—
44#10597273—24no—
45#10597265—24no—
46#10597264—24no—
47C4⋊(C19⋊C8)—22no—
48#10597260—22no—
49C2×Q8×C19—22no—
50C22×C4×C19—41no—
51C22×C4×C19C2×D412yes—
52C22×C4×C19C2×D411yescharacteristic
53C2×Dic38—22no—
54C2×Dic38—22no—
55M16×C19—42no—
56C2×C8×C19—22no—
57C4⋊C4×C19—22no—
58C4⋊C4×C19—22no—
59C4⋊C4×C19—42no—
60C22⋊C4×C19—41no—
61C42×C19—22no—
62C42×C19—41no—
63C42×C19—41no—
64C42×C19C2×D411yescharacteristic
65C42×C19C2×D412yes—
66C42×C19#4111yescharacteristic
67C22⋊Dic19—42no—
68C4⋊Dic19—22no—
69C4⋊Dic19—22no—
70C4⋊Dic19—22no—
71C4⋊Dic19—22no—
72Dic19⋊C4—42no—
73Dic19⋊C4—42no—
74C4×Dic19—42no—
75C2×C19⋊C8—24no—
76Dic76—82no—
77#10217—191nomaximal, Sylow
78C23×C19#12711yescharacteristic
79Q8×C19—44no—
80C2×C4×C19—21no—
81C2×C4×C19—21no—
82C2×C4×C19—42no—
83C2×C4×C19—42no—
84C2×C4×C19—42no—
85C2×C4×C19—82no—
86C2×C4×C19#12011yescharacteristic
87C2×C4×C19#12012yes—
88C2×C4×C19#12111yescharacteristic
89C2×C4×C19#12112yes—
90C2×Dic19—42no—
91C2×Dic19—42no—
92Dic38—42no—
93Dic38—42no—
94Dic38—82no—
95C8×C19—42no—
96C19⋊C8—44no—
97#3255—191no—
98#3237—192no—
99#1995D1911yescharacteristic
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—192no—
115#533C2×D1911yescharacteristic
116#501—382no—
117#491—382no—
118#485—384no—
119#477—382no—
120#475—382no—
121#475—382no—
122#470—382no—
123#462—382no—
124#432—192no—
125#423C2×D1911yescharacteristic
126#376C2×D1911yescharacteristic
127#339—22no—
128#328—384no—
129C2×C19—41no—
130C2×C19#200711yescharacteristic
131C2×C19#200912yes—
132C2×Q16—382no—
133C2×M16C22⋊D1912yes—
134C4⋊Q8—192no—
135C4⋊Q8—192no—
136C4⋊Q8D7612yes—
137#125—21no—
138#125—382no—
139C22⋊Q8—22no—
140C22⋊Q8—382no—
141C22⋊Q8—382no—
142C4×Q8—22no—
143C4×Q8—382no—
144C4×Q8—382no—
145#117—21no—
146#117—382no—
147C2×C42—21no—
148C2×C42C22×D1911yescharacteristic
149#107—384no—
150#106—384no—
151#106—382no—
152C4⋊C8—22no—
153C4⋊C8—382no—
154#103—384no—
155#103—384no—
156#103—384no—
157C22⋊C8—194no—
158#97—382no—
159#95—22no—
160C19#1021711yescharacteristic, complemented, Sylow
161C2×Q8—22no—
162C2×Q8—382no—
163C2×Q8—382no—
164C22×C4—41no—
165C22×C4D4×D1912yes—
166C22×C4C2×C22⋊D1911yescharacteristic
167Q16—1522no—
168M16—42no—
169C2×C8—22no—
170C2×C8—384no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—42no—
174C4⋊C4—382no—
175C4⋊C4—382no—
176C4⋊C4—382no—
177C4⋊C4—382no—
178C4⋊C4—762no—
179C4⋊C4—762no—
180C22⋊C4—41no—
181C22⋊C4—762no—
182C42—22no—
183C42—41no—
184C42—41no—
185C42—762no—
186C42C2×D7611yescharacteristic
187C42#6454111yescharacteristic
188C42D4×D1912yes—
189C23#1059738611yescharacteristic
190Q8—44no—
191Q8—762no—
192Q8—762no—
193Q8—1522no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—82no—
200C2×C4—762no—
201C2×C4—762no—
202C2×C4#1059732812yes—
203C2×C4#1059733012yes—
204C2×C4#1059737611yescharacteristic
205C2×C4#1059738311yescharacteristic
206C8—42no—
207C8—764no—
208C22—21no—
209C22—22no—
210C22#1192645311yescharacteristic
211C4—21no—
212C4—22no—
213C4—22no—
214C4—82no—
215C4—82no—
216C4—1522no—
217C4—1522no—
218C4#1192672111yescharacteristic
219C4#1192672611yescharacteristic
220C2—41no—
221C2#1456468111yescharacteristic
222C2#1456469612yes—
subgroupG/H
centerC22#11926453
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1995C2
socleC22×C19#392
prime radicalC23×C19#127
hypercenter#1995D19
hypocenterC19#10217
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1995

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
#145750292
#145748452
#145621462
#145615462
C19×#19952
#1021719