Finite Group Databasebeta

← #18085303

Subgroups — #18085303

Order 4864.

478 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 89 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#14575026C212yesmaximal
2#14564613C212yesmaximal
3#14564611C211yesmaximal, characteristic
4C19⋊#1309C211yesmaximal, characteristic
5C19×#3255C211yesmaximal, characteristic
6#11927101C2211yescharacteristic
7#11926829—22no—
8#11926826—22no—
9#11926800—24no—
10#11926754—22no—
11#11926751—22no—
12#11926568C2212yes—
13C42×Dic19C2211yescharacteristic
14#11926305—22no—
15#11926303—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
32C2×#64528—24no—
33#10597372—21no—
34#10597370—22no—
35C2×C4×Dic19—22no—
36C2×C4×Dic19—21no—
37C2×#64520D414yes—
38#10597316—21no—
39#10597315D412yes—
40C4×Dic38—22no—
41C19×#106—22no—
42C19×C4⋊C8—22no—
43C19×#103—24no—
44#10597292—24no—
45#10597267—24no—
46#10597265—24no—
47C4⋊(C19⋊C8)—22no—
48C4⋊(C19⋊C8)—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—
70#64528—84no—
71C4⋊Dic19—22no—
72C4⋊Dic19—22no—
73Dic19⋊C4—42no—
74C4×Dic19—24no—
75C4×Dic19—22no—
76C4×Dic19—42no—
77C4×Dic19—41no—
78C4×Dic19—41no—
79#64520—44no—
80C2×C19⋊C8—24no—
81#10303—191nomaximal, Sylow
82C23×C19#12711yescharacteristic
83Q8×C19—42no—
84Q8×C19—42no—
85Q8×C19—42no—
86Q8×C19—42no—
87C2×C4×C19—22no—
88C2×C4×C19—21no—
89C2×C4×C19—22no—
90C2×C4×C19—21no—
91C2×C4×C19—42no—
92C2×C4×C19—42no—
93C2×C4×C19#12012yes—
94C2×C4×C19#12011yescharacteristic
95C2×C4×C19#12111yescharacteristic
96C2×C4×C19#12112yes—
97C2×Dic19—44no—
98C2×Dic19—42no—
99C2×Dic19—42no—
100Dic38—42no—
101Dic38—42no—
102C8×C19—42no—
103C19⋊C8—44no—
104#3255—192no—
105#3255D1911yescharacteristic
106#1994—191no—
107#1994—192no—
108#1309—191no—
109C22×C19—22no—
110C22×C19—21no—
111C22×C19#39211yescharacteristic
112C4×C19—22no—
113C4×C19—21no—
114C4×C19—82no—
115C4×C19—82no—
116C4×C19#45512yes—
117C4×C19#45511yescharacteristic
118C4×C19#45612yes—
119C4×C19#45611yescharacteristic
120Dic19—44no—
121Dic19—82no—
122#533—191no—
123#533C2×D1912yes—
124#475—22no—
125#475—382no—
126#475—382no—
127#470—22no—
128#470—384no—
129#462—22no—
130#462—382no—
131#462—382no—
132#423—192no—
133#423C2×D1911yescharacteristic
134C43—191no—
135#339—384no—
136#339—382no—
137C2×C19—41no—
138C2×C19#200712yes—
139C2×C19#200711yescharacteristic
140C2×Q16—22no—
141C2×Q16—384no—
142C2×M16—194no—
143C2×M16C22⋊D1912yes—
144C4⋊Q8—192no—
145C4⋊Q8C22⋊D1912yes—
146C4⋊Q8C22⋊D1912yes—
147#125—22no—
148#125—381no—
149C22⋊Q8—22no—
150C22⋊Q8—22no—
151C22⋊Q8—382no—
152C4×Q8—22no—
153C4×Q8—22no—
154C4×Q8—382no—
155#117—22no—
156#117—381no—
157C2×C42—382no—
158C2×C42—381no—
159C2×C42C22×D1911yescharacteristic
160#106—22no—
161#106—384no—
162C4⋊C8—22no—
163C4⋊C8—382no—
164C4⋊C8—382no—
165#103—24no—
166#103—384no—
167#103—384no—
168C19#1030311yescharacteristic, complemented, Sylow
169C2×Q8—22no—
170C2×Q8—22no—
171C2×Q8—382no—
172C22×C4—761no—
173C22×C4D4×D1912yes—
174C22×C4C2×C22⋊D1911yescharacteristic
175Q16—82no—
176Q16—1524no—
177M16—42no—
178M16—764no—
179C2×C8—22no—
180C2×C8—384no—
181C4⋊C4—22no—
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—382no—
188C4⋊C4—382no—
189C4⋊C4—762no—
190C22⋊C4—42no—
191C22⋊C4—761no—
192C42—42no—
193C42—384no—
194C42—382no—
195C42—762no—
196C42—761no—
197C42—761no—
198C42D4×D1911yescharacteristic
199C42#6454311yescharacteristic
200C42C2×C22⋊D1912yes—
201C23#1059738611yescharacteristic
202Q8—42no—
203Q8—42no—
204Q8—42no—
205Q8—42no—
206Q8—762no—
207Q8—762no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—764no—
215C2×C4—762no—
216C2×C4—762no—
217C2×C4#1059738312yes—
218C2×C4#1059738411yescharacteristic
219C2×C4#1059738512yes—
220C2×C4#1059739911yescharacteristic
221C8—42no—
222C8—764no—
223C22—22no—
224C22—21no—
225C22#1192645211yescharacteristic
226C4—22no—
227C4—21no—
228C4—82no—
229C4—82no—
230C4—764no—
231C4—1522no—
232C4#1192672012yes—
233C4#1192672211yescharacteristic
234C4#1192672512yes—
235C4#1192672711yescharacteristic
236C2—41no—
237C2#1456468012yes—
238C2#1456468211yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#3255C2
socleC22×C19#392
prime radicalC23×C19#127
hypercenter#3255D19
hypocenterC19#10303
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
168. C19#10303semidirect

Maximal subgroups

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

subgroupindex
#145750262
#145646132
#145646112
C19⋊#13092
C19×#32552
#1030319