Finite Group Databasebeta

← #18071738

Subgroups — #18071738

Order 4864.

398 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 87 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#14571628C211yesmaximal, characteristic
2#14565178C211yesmaximal, characteristic
3#14565045C212yesmaximal
4#14561460C212yesmaximal
5C19×#1272C211yesmaximal, characteristic
6C2×#10597265—21no—
7C2×#10597273—22no—
8C2×#10597292—21no—
9#11926465—22no—
10#11926464—21no—
11#11926451—21no—
12#11926450C2212yes—
13#11926448—22no—
14#11926414C2211yescharacteristic
15#11926307—22no—
16#11926299C2211yescharacteristic
17C19×#391C2211yescharacteristic
18C19×#336C2212yes—
19C22×Q8×C19D411yescharacteristic
20C22×Dic38—21no—
21C22×Dic38D412yes—
22C22×C8×C19—22no—
23C2×C4⋊C4×C19D411yescharacteristic
24C2×C42×C19C2311yescharacteristic
25C2×C4⋊Dic19—21no—
26C2×C4⋊Dic19—22no—
27C2×C4⋊Dic19—21no—
28C2×C4⋊Dic19D412yes—
29C2×Dic19⋊C4—22no—
30C2×C4×Dic19—21no—
31C22×C19⋊C8—21no—
32C19×#95—22no—
33#10597292—42no—
34C19⋊#95—21no—
35C19⋊#95—22no—
36C19⋊#95—22no—
37C19⋊#95—22no—
38#10597273—44no—
39#10597265—42no—
40C2×Q8×C19—21no—
41C2×Q8×C19—41no—
42C2×Q8×C19—41no—
43C2×Q8×C19Q1612yes—
44C22×C4×C19—21no—
45C22×C4×C19—21no—
46C22×C4×C19C2×D411yescharacteristic
47C22×C4×C19C2×D412yes—
48C22×Dic19—22no—
49C22×Dic19—22no—
50C22×Dic19—41no—
51C2×Dic38—22no—
52C2×Dic38—42no—
53C2×Dic38—42no—
54C2×Dic38—81no—
55C2×Dic38—82no—
56C2×Dic38SD1614yes—
57C2×C8×C19—42no—
58C2×C8×C19—42no—
59C2×C8×C19—42no—
60C4⋊C4×C19—41no—
61C42×C19—41no—
62C4⋊Dic19—42no—
63C4⋊Dic19—41no—
64C4⋊Dic19—41no—
65C4⋊Dic19—42no—
66C4⋊Dic19—42no—
67C4⋊Dic19—81no—
68Dic19⋊C4—82no—
69C4×Dic19—81no—
70C2×C19⋊C8—22no—
71C2×C19⋊C8—41no—
72C2×C19⋊C8—41no—
73#7812—191nomaximal, Sylow
74C23×C19#12011yescharacteristic
75Q8×C19—42no—
76Q8×C19—81no—
77C2×C4×C19—21no—
78C2×C4×C19—22no—
79C2×C4×C19—21no—
80C2×C4×C19—22no—
81C2×C4×C19—22no—
82C2×C4×C19—41no—
83C2×C4×C19—41no—
84C2×C4×C19—41no—
85C2×C4×C19—42no—
86C2×C4×C19C2×SD1612yes—
87C2×C4×C19C2×Q1611yescharacteristic
88C2×C4×C19#13711yescharacteristic
89C2×C4×C19#13712yes—
90C2×Dic19—24no—
91C2×Dic19—42no—
92C2×Dic19—42no—
93C2×Dic19—42no—
94C2×Dic19—42no—
95C2×Dic19—42no—
96C2×Dic19—82no—
97C2×Dic19—81no—
98Dic38—44no—
99Dic38—82no—
100Dic38—84no—
101C8×C19—82no—
102C19⋊C8—42no—
103#2811—191no—
104#2096—191no—
105#2072—192no—
106#1272—192no—
107#1272D1911yescharacteristic
108C22×C19#44812yes—
109C22×C19#45111yescharacteristic
110C22×C19#45311yescharacteristic
111C22×C19#45512yes—
112C22×C19#45811yescharacteristic
113C4×C19—22no—
114C4×C19—22no—
115C4×C19—21no—
116C4×C19—21no—
117C4×C19—42no—
118C4×C19—81no—
119Dic19—44no—
120Dic19—82no—
121Dic19—161no—
122C2×#106—381no—
123C2×#103—382no—
124C2×#103—381no—
125#395—382no—
126#395—381no—
127#391—192no—
128#391—382no—
129#391—381no—
130#391C2×D1911yescharacteristic
131#384—191no—
132#340—382no—
133#336—191no—
134#336C2×D1912yes—
135C2×C19#160812yes—
136C2×C19#161411yescharacteristic
137C2×C19#162311yescharacteristic
138C2×C19#164512yes—
139C2×C19#165911yescharacteristic
140C22×Q8—192no—
141C22×Q8—381no—
142C22×Q8D7611yescharacteristic
143C22×C8—22no—
144C22×C8—381no—
145C2×C4⋊C4—192no—
146C2×C4⋊C4—381no—
147C2×C4⋊C4—382no—
148C2×C4⋊C4—382no—
149C2×C4⋊C4—381no—
150C2×C4⋊C4D7611yescharacteristic
151C2×C42—381no—
152C2×C42C22×D1911yescharacteristic
153#106—762no—
154#103—764no—
155#103—762no—
156#95—22no—
157#95—382no—
158#95—381no—
159#95—382no—
160#95—382no—
161C19#781211yescharacteristic, complemented, Sylow
162C2×Q8—21no—
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8—194no—
166C2×Q8—382no—
167C2×Q8—762no—
168C2×Q8—762no—
169C2×Q8—1521no—
170C2×Q8—1522no—
171C2×Q8Dic7612yes—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—382no—
175C22×C4—382no—
176C22×C4—761no—
177C22×C4C2×D7611yescharacteristic
178C22×C4D4×D1912yes—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—42no—
182C2×C8—382no—
183C2×C8—761no—
184C2×C8—761no—
185C4⋊C4—41no—
186C4⋊C4—762no—
187C4⋊C4—761no—
188C4⋊C4—761no—
189C4⋊C4—762no—
190C4⋊C4—762no—
191C4⋊C4—1522no—
192C4⋊C4—1521no—
193C42—41no—
194C42—1521no—
195C23#1059732811yescharacteristic
196Q8—42no—
197Q8—81no—
198Q8—764no—
199Q8—1522no—
200Q8—1524no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—384no—
211C2×C4—762no—
212C2×C4—762no—
213C2×C4—762no—
214C2×C4—762no—
215C2×C4—762no—
216C2×C4—1522no—
217C2×C4—1521no—
218C2×C4C2×Dic7611yescharacteristic
219C2×C4#1059735511yescharacteristic
220C2×C4SD16×D1912yes—
221C2×C4#1059736412yes—
222C8—82no—
223C8—762no—
224C22#1192668412yes—
225C22#1192670211yescharacteristic
226C22#1192671411yescharacteristic
227C22#1192672312yes—
228C22#1192673511yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—42no—
234C4—81no—
235C4—3041no—
236C4—764no—
237C4—1522no—
238C2#1456262712yes—
239C2#1456266211yescharacteristic
240C2#1456271411yescharacteristic
241C2#1456285912yes—
242C2#1456294211yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1272C2
socle, prime radicalC23×C19#120
hypercenter#1272D19
hypocenterC19#7812
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
161. C19#7812semidirect

Maximal subgroups

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

subgroupindex
#145716282
#145651782
#145650452
#145614602
C19×#12722
#781219