Finite Group Databasebeta

← #18069966

Subgroups — #18069966

Order 4864.

228 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 43 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#14563844C211yesmaximal, characteristic
2#14561567C211yesmaximal, characteristic
3C19×#1270C211yesmaximal, characteristic
4#11927019C411yescharacteristic
5#11926584—21no—
6C2×#10597290C411yescharacteristic
7#11926304—21no—
8#11926270—21no—
9C19×#390C2211yescharacteristic
10C19×#336—21no—
11C22×D4×C19C2×C411yescharacteristic
12C22×C8×C19—41no—
13C2×C4⋊C4×C19D411yescharacteristic
14C2×C22⋊C4×C19—41no—
15C2×C42×C19D411yescharacteristic
16C2×C22⋊Dic19—41no—
17D4×Dic19—41no—
18D4×Dic19—41no—
19#10597372—21no—
20C2×#64520—21no—
21#10597290—21no—
22#10597290C812yescomplemented
23C22⋊(C19⋊C8)—41no—
24#10597265—41no—
25#10597264—41no—
26C24×C19—21no—
27C2×D4×C19—21no—
28C2×D4×C19—41no—
29C2×D4×C19—41no—
30C2×D4×C19C2×C811yescharacteristic
31C2×D4×C19M1611yescharacteristic
32C22×C4×C19—21no—
33C22×C4×C19—21no—
34C22×C4×C19C22⋊C411yescharacteristic
35C22×Dic19—41no—
36C22×Dic19—41no—
37C2×C8×C19—42no—
38C2×C8×C19—81no—
39C2×C8×C19—81no—
40C4⋊C4×C19—41no—
41C22⋊C4×C19—81no—
42C22⋊C4×C19—81no—
43C42×C19—41no—
44C22⋊Dic19—42no—
45C22⋊Dic19—41no—
46C4⋊Dic19—21no—
47C4⋊Dic19—21no—
48C4×Dic19—41no—
49#64520—22no—
50#64520—41no—
51C2×C19⋊C8—41no—
52C2×C19⋊C8—81no—
53#7375—191nomaximal, Sylow
54C23×C19—21no—
55C23×C19—21no—
56C23×C19—41no—
57C23×C19—41no—
58C23×C19—81no—
59C23×C19—81no—
60C23×C19#9911yescharacteristic
61D4×C19—41no—
62D4×C19—41no—
63D4×C19—42no—
64C2×C4×C19—21no—
65C2×C4×C19—21no—
66C2×C4×C19—21no—
67C2×C4×C19—21no—
68C2×C4×C19—41no—
69C2×C4×C19—41no—
70C2×C4×C19—41no—
71C2×C4×C19—81no—
72C2×C4×C19C22⋊C811yescharacteristic
73C2×C4×C19#10111yescharacteristic
74C2×Dic19—41no—
75C2×Dic19—41no—
76C2×Dic19—161no—
77C2×Dic19—161no—
78C8×C19—82no—
79C19⋊C8—42no—
80C19⋊C8—161no—
81#1856—191no—
82#1318—191no—
83#1270D1911yescharacteristic
84C22×C19—21no—
85C22×C19—21no—
86C22×C19—41no—
87C22×C19—41no—
88C22×C19—81no—
89C22×C19—81no—
90C22×C19—81no—
91C22×C19—81no—
92C22×C19—161no—
93C22×C19#32411yescharacteristic
94C22×C19AΣL(1,𝔽16)11yescharacteristic
95C22×C19#35211yescharacteristic
96C4×C19—21no—
97C4×C19—21no—
98C4×C19—41no—
99C4×C19—41no—
100C4×C19—81no—
101Dic19—81no—
102Dic19—81no—
103#518—191no—
104#428—381no—
105C2×#100—191no—
106#390C2×D1911yescharacteristic
107#339—381no—
108#336—21no—
109#324—381no—
110C2×C19—21no—
111C2×C19—21no—
112C2×C19—81no—
113C2×C19—81no—
114C2×C19#132611yescharacteristic
115C2×C19#140211yescharacteristic
116C2×C19#140311yescharacteristic
117C22×D4C4×D1911yescharacteristic
118C2×M16—381no—
119C22×C8—41no—
120C4×D4—761no—
121C4×D4—761no—
122#117—381no—
123C2×C4⋊C4D7611yescharacteristic
124C2×C22⋊C4—41no—
125C2×C22⋊C4—761no—
126C2×C42C22⋊D1911yescharacteristic
127#107—761no—
128#106—761no—
129#100—192no—
130#100—381no—
131C22⋊C8—761no—
132C19#737511yescharacteristic, complemented, Sylow
133C24—21no—
134C2×D4—21no—
135C2×D4—41no—
136C2×D4—41no—
137C2×D4C8×D1911yescharacteristic
138C2×D4#6451511yescharacteristic
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—761no—
142C22×C4—761no—
143C22×C4(C2×D19)⋊C411yescharacteristic
144M16—382no—
145M16—761no—
146C2×C8—42no—
147C2×C8—81no—
148C2×C8—81no—
149C2×C8—761no—
150C2×C8—1521no—
151C4⋊C4—41no—
152C4⋊C4—381no—
153C4⋊C4—381no—
154C22⋊C4—81no—
155C22⋊C4—81no—
156C22⋊C4—762no—
157C22⋊C4—761no—
158C42—41no—
159C42—761no—
160C23—21no—
161C23—21no—
162C23—41no—
163C23—41no—
164C23—81no—
165C23—81no—
166C23#1059726311yescharacteristic
167D4—41no—
168D4—41no—
169D4—42no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—81no—
178C2×C4—3041no—
179C2×C4—3041no—
180C2×C4—761no—
181C2×C4—761no—
182C2×C4(C2×D19)⋊C811yescharacteristic
183C2×C4#1059728111yescharacteristic
184C8—82no—
185C8—3041no—
186C8—762no—
187C22—21no—
188C22—21no—
189C22—41no—
190C22—41no—
191C22—81no—
192C22—81no—
193C22—81no—
194C22—81no—
195C22—161no—
196C22#1192626911yescharacteristic
197C22#1192633211yescharacteristic
198C22#1192633311yescharacteristic
199C4—21no—
200C4—21no—
201C4—41no—
202C4—41no—
203C4—81no—
204C4—1521no—
205C4—1521no—
206C2—21no—
207C2—21no—
208C2—81no—
209C2—81no—
210C2#1456158411yescharacteristic
211C2#1456178111yescharacteristic
212C2#1456178411yescharacteristic
subgroupG/H
centerC22#11926332
commutatorC2×D4×C19C2×C8
Frattini#390C2×D19
FittingC19×#1270C2
socleC22×C19AΣL(1,𝔽16)
prime radicalC22×D4×C19C2×C4
cosocleC19×#390C22
hypercenter#1270D19
hypocenterC19#7375
LCSG ▷ C2×D4×C19 ▷ C2×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #390 ◁ #1270

Complements

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

NH ≅ G/Ntype
22. #10597290C8semidirect
132. C19#7375semidirect

Maximal subgroups

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

subgroupindex
#145638442
#145615672
C19×#12702
#737519