Finite Group Databasebeta

← #18070288

Subgroups — #18070288

Order 4864.

270 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 59 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#14565320C211yesmaximal, characteristic
2#14564019C211yesmaximal, characteristic
3C19×#1543C211yesmaximal, characteristic
4#11927311C411yescharacteristic
5#11926561—21no—
6#11926528—21no—
7#11926518C411yescharacteristic
8#11926343—21no—
9#11926341C412yescomplemented
10#11926304—21no—
11C19×#532C2211yescharacteristic
12C19×#431—21no—
13C19×#333—21no—
14C19×#331C412yescomplemented
15C2×#41×C19C2×C411yescharacteristic
16C2×#41×C19D411yescharacteristic
17C19×C4⋊Q8D411yescharacteristic
18C19×#127C2×C411yescharacteristic
19C19×#124C2×C411yescharacteristic
20C19×#124Q811yescharacteristic
21C19×#121—41no—
22C4×D4×C19—41no—
23C2×C42×C19D411yescharacteristic
24#10597394—42no—
25#10597372—21no—
26C2×#64520—21no—
27C2×#64520—41no—
28C2×#64520—41no—
29C19×C4⋊C8—22no—
30C19×C22⋊C8—41no—
31C4×C8×C19—41no—
32#10597294—42no—
33#10597293—22no—
34#10597291—41no—
35#10597290—41no—
36#41×C19—41no—
37#41×C19—41no—
38#41×C19—41no—
39#41×C19—41no—
40C2×Q8×C19C22⋊C411yescharacteristic
41C2×Q8×C19C4⋊C411yescharacteristic
42C2×D4×C19—21no—
43C2×D4×C19—21no—
44C2×D4×C19—41no—
45C2×D4×C19C4211yescharacteristic
46C2×D4×C19C4⋊C411yescharacteristic
47C22×C4×C19—21no—
48C22×C4×C19—21no—
49C22×C4×C19—21no—
50C22×C4×C19C22⋊C411yescharacteristic
51C2×C8×C19—42no—
52C4⋊C4×C19—41no—
53C22⋊C4×C19—41no—
54C22⋊C4×C19—41no—
55C42×C19—21no—
56C42×C19C22⋊C411yescharacteristic
57C42×C19C4⋊C411yescharacteristic
58C22⋊Dic19—41no—
59C4⋊Dic19—41no—
60C4×Dic19—41no—
61#64520—22no—
62#64520—42no—
63#64520—41no—
64#64520—42no—
65#64520—81no—
66C2×C19⋊C8—41no—
67C2×C19⋊C8—42no—
68C2×C19⋊C8—81no—
69#7488—191nomaximal, Sylow
70C23×C19—21no—
71C23×C19—21no—
72C23×C19#9911yescharacteristic
73Q8×C19—41no—
74Q8×C19—41no—
75D4×C19—41no—
76D4×C19—41no—
77D4×C19—42no—
78D4×C19—82no—
79D4×C19—81no—
80C2×C4×C19—21no—
81C2×C4×C19—21no—
82C2×C4×C19—21no—
83C2×C4×C19—21no—
84C2×C4×C19—21no—
85C2×C4×C19—21no—
86C2×C4×C19—42no—
87C2×C4×C19—41no—
88C2×C4×C19—41no—
89C2×C4×C19—41no—
90C2×C4×C19—41no—
91C2×C4×C19#9511yescharacteristic
92C2×C4×C19#9911yescharacteristic
93C2×Dic19—81no—
94C8×C19—82no—
95C19⋊C8—42no—
96C19⋊C8—82no—
97#2132—191no—
98#1884—191no—
99#1543D1911yescharacteristic
100C22×C19—21no—
101C22×C19—41no—
102C22×C19—41no—
103C22×C19—41no—
104C22×C19—81no—
105C22×C19—81no—
106C22×C19#34211yescharacteristic
107C4×C19—22no—
108C4×C19—21no—
109C4×C19—41no—
110C4×C19—41no—
111C4×C19—41no—
112C4×C19AΣL(1,𝔽16)11yescharacteristic
113C4×C19#35211yescharacteristic
114Dic19—161no—
115#568—191no—
116#532C2×D1911yescharacteristic
117#431—21no—
118#421—381no—
119#413—381no—
120#410—191no—
121#356—381no—
122#355—192no—
123#339—381no—
124#333—21no—
125#331Dic1912yescomplemented
126C2×C19—21no—
127C2×C19—41no—
128C2×C19—81no—
129C2×C19—81no—
130C2×C19#139011yescharacteristic
131C2×#41C4×D1911yescharacteristic
132C2×#41D7611yescharacteristic
133#131—762no—
134C2×M16—381no—
135C2×M16—761no—
136C2×M16—761no—
137C4⋊Q8C22⋊D1911yescharacteristic
138#127C2×Dic1911yescharacteristic
139#124Dic3811yescharacteristic
140#124C4×D1911yescharacteristic
141#121—41no—
142C4×D4—41no—
143#117—381no—
144C2×C42C22⋊D1911yescharacteristic
145C4⋊C8—22no—
146#104—762no—
147#101—382no—
148#100—761no—
149#99—761no—
150C22⋊C8—41no—
151C4×C8—41no—
152C19#748811yescharacteristic, complemented, Sylow
153#41—41no—
154#41—41no—
155#41—41no—
156#41—41no—
157C2×Q8Dic19⋊C411yescharacteristic
158C2×Q8(C2×D19)⋊C411yescharacteristic
159C2×D4—21no—
160C2×D4—21no—
161C2×D4—41no—
162C2×D4C4×Dic1911yescharacteristic
163C2×D4C4⋊Dic1911yescharacteristic
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4(C2×D19)⋊C411yescharacteristic
168M16—382no—
169M16—762no—
170M16—761no—
171M16—762no—
172M16—1521no—
173C2×C8—42no—
174C2×C8—761no—
175C2×C8—762no—
176C2×C8—1521no—
177C4⋊C4—41no—
178C4⋊C4—761no—
179C22⋊C4—41no—
180C22⋊C4—41no—
181C22⋊C4—761no—
182C42—21no—
183C42—761no—
184C42Dic19⋊C411yescharacteristic
185C42C22⋊Dic1911yescharacteristic
186C23—21no—
187C23—21no—
188C23#1059726311yescharacteristic
189Q8—41no—
190Q8—41no—
191D4—41no—
192D4—41no—
193D4—42no—
194D4—82no—
195D4—81no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—42no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—1521no—
208C2×C4#1059726311yescharacteristic
209C2×C4C19⋊#9511yescharacteristic
210C8—82no—
211C8—762no—
212C8—1522no—
213C22—21no—
214C22—41no—
215C22—41no—
216C22—41no—
217C22—81no—
218C22—81no—
219C22#1192631011yescharacteristic
220C4—22no—
221C4—21no—
222C4—41no—
223C4—41no—
224C4—41no—
225C4—3041no—
226C4#1192633211yescharacteristic
227C4#1192633511yescharacteristic
228C2—21no—
229C2—41no—
230C2—81no—
231C2—81no—
232C2#1456175411yescharacteristic
subgroupG/H
centerC4#11926332
commutatorC2×D4×C19C42
Frattini#532C2×D19
FittingC19×#1543C2
socleC2×C19#1390
prime radical, cosocleC19×#532C22
hypercenter#1543D19
hypocenterC19#7488
LCSG ▷ C2×D4×C19 ▷ C2×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #1543

Complements

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

NH ≅ G/Ntype
9. #11926341C4semidirect
14. C19×#331C4semidirect
125. #331Dic19semidirect
152. C19#7488semidirect

Maximal subgroups

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

subgroupindex
#145653202
#145640192
C19×#15432
#748819