Finite Group Databasebeta

← #18070328

Subgroups — #18070328

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#14565300C211yesmaximal, characteristic
3C19×#1963C211yesmaximal, characteristic
4#11926528—21no—
5#11926518—21no—
6#11926343C412yescomplemented
7#11926341—21no—
8#11926339—21no—
9#11926337C412yescomplemented
10C19×#532C2211yescharacteristic
11C19×#423C411yescharacteristic, complemented
12C2×C19×#104—21no—
13C2×C19×#104—21no—
14C19×#376C411yescharacteristic, complemented
15C2×#41×C19D411yescharacteristic
16C2×#41×C19D411yescharacteristic
17C2×M16×C19—21no—
18C19×C4⋊Q8C2×C411yescharacteristic
19C19×#127C2×C411yescharacteristic
20C19×#124D411yescharacteristic
21C19×#124Q811yescharacteristic
22C19×#121—41no—
23C4×D4×C19—41no—
24C2×C42×C19—21no—
25C2×C42×C19C2×C411yescharacteristic
26#10597372—41no—
27C2×#64520—41no—
28C19×C4⋊C8—41no—
29C19×#104—42no—
30C19×#104—42no—
31C19×#95—41no—
32#10597293—22no—
33#10597291—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×C19C22⋊C411yescharacteristic
46C2×D4×C19C4⋊C411yescharacteristic
47C22×C4×C19—21no—
48C22×C4×C19—21no—
49C22×C4×C19—21no—
50C22×C4×C19—41no—
51C22×C4×C19C22⋊C411yescharacteristic
52M16×C19—41no—
53M16×C19—41no—
54C2×C8×C19—41no—
55C4⋊C4×C19—41no—
56C22⋊C4×C19—41no—
57C22⋊C4×C19—41no—
58C42×C19—21no—
59C42×C19—22no—
60C42×C19—41no—
61C42×C19C4211yescharacteristic
62C42×C19C4⋊C411yescharacteristic
63C22⋊Dic19—42no—
64C4⋊Dic19—81no—
65C4×Dic19—81no—
66#64520—42no—
67#64520—81no—
68C2×C19⋊C8—81no—
69#7503—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—81no—
78D4×C19—81no—
79D4×C19—82no—
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—41no—
87C2×C4×C19—41no—
88C2×C4×C19—41no—
89C2×C4×C19—41no—
90C2×C4×C19—42no—
91C2×C4×C19—81no—
92C2×C4×C19—82no—
93C2×C4×C19#9511yescharacteristic
94C2×C4×C19#9911yescharacteristic
95C2×Dic19—82no—
96C8×C19—81no—
97C19⋊C8—82no—
98#2132—191no—
99#2126—191no—
100#1963D1911yescharacteristic
101C22×C19—21no—
102C22×C19—41no—
103C22×C19—41no—
104C22×C19—41no—
105C22×C19—81no—
106C22×C19—81no—
107C22×C19#34211yescharacteristic
108C4×C19—21no—
109C4×C19—41no—
110C4×C19—41no—
111C4×C19—41no—
112C4×C19—41no—
113C4×C19—82no—
114C4×C19#35311yescharacteristic
115C4×C19#35411yescharacteristic
116Dic19—162no—
117#532C2×D1911yescharacteristic
118#423Dic1911yescharacteristic, complemented
119C2×#104—21no—
120C2×#104—21no—
121#413—381no—
122#410—381no—
123#376Dic1911yescharacteristic, complemented
124#356—192no—
125#355—381no—
126#354—381no—
127#353—192no—
128C2×C19—21no—
129C2×C19—41no—
130C2×C19—81no—
131C2×C19—81no—
132C2×C19#139311yescharacteristic
133C2×#41C22⋊D1911yescharacteristic
134C2×#41C22⋊D1911yescharacteristic
135C2×M16—21no—
136C2×M16—761no—
137C4⋊Q8C4×D1911yescharacteristic
138#127C4×D1911yescharacteristic
139#124Dic3811yescharacteristic
140#124D7611yescharacteristic
141#121—41no—
142C4×D4—41no—
143#117—761no—
144C2×C42—21no—
145C2×C42C2×Dic1911yescharacteristic
146C4⋊C8—41no—
147#104—42no—
148#104—42no—
149#101—382no—
150#100—761no—
151#99—382no—
152#99—761no—
153#95—41no—
154C19#750311yescharacteristic, complemented, Sylow
155#41—41no—
156#41—41no—
157#41—41no—
158#41—41no—
159C2×Q8Dic19⋊C411yescharacteristic
160C2×Q8(C2×D19)⋊C411yescharacteristic
161C2×D4—21no—
162C2×D4—21no—
163C2×D4—41no—
164C2×D4Dic19⋊C411yescharacteristic
165C2×D4(C2×D19)⋊C411yescharacteristic
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—41no—
170C22×C4C22⋊Dic1911yescharacteristic
171M16—41no—
172M16—41no—
173M16—762no—
174M16—1521no—
175C2×C8—41no—
176C2×C8—1521no—
177C4⋊C4—41no—
178C4⋊C4—1521no—
179C22⋊C4—41no—
180C22⋊C4—41no—
181C22⋊C4—762no—
182C42—21no—
183C42—22no—
184C42—41no—
185C42—1521no—
186C42C4×Dic1911yescharacteristic
187C42C4⋊Dic1911yescharacteristic
188C23—21no—
189C23—21no—
190C23#1059729111yescharacteristic
191Q8—41no—
192Q8—41no—
193D4—41no—
194D4—41no—
195D4—81no—
196D4—81no—
197D4—82no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—81no—
210C2×C4—82no—
211C2×C4—1522no—
212C2×C4C19⋊#9511yescharacteristic
213C2×C4#1059729111yescharacteristic
214C8—81no—
215C8—1522no—
216C22—21no—
217C22—41no—
218C22—41no—
219C22—41no—
220C22—81no—
221C22—81no—
222C22#1192631111yescharacteristic
223C4—21no—
224C4—41no—
225C4—41no—
226C4—41no—
227C4—41no—
228C4—82no—
229C4—3042no—
230C4#1192633711yescharacteristic
231C4#1192633911yescharacteristic
232C2—21no—
233C2—41no—
234C2—81no—
235C2—81no—
236C2#1456176011yescharacteristic
subgroupG/H
centerC4#11926339
commutatorC42×C19C42
Frattini#532C2×D19
FittingC19×#1963C2
socleC2×C19#1393
prime radical, cosocleC19×#532C22
hypercenter#1963D19
hypocenterC19#7503
LCSG ▷ C42×C19 ▷ C2×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #1963

Complements

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

NH ≅ G/Ntype
6. #11926343C4semidirect
9. #11926337C4semidirect
11. C19×#423C4semidirect
14. C19×#376C4semidirect
118. #423Dic19semidirect
123. #376Dic19semidirect
154. C19#7503semidirect

Maximal subgroups

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

subgroupindex
#145653202
#145653002
C19×#19632
#750319