Finite Group Databasebeta

← #18087037

Subgroups — #18087037

Order 4864.

406 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 97 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#14571907C211yesmaximal, characteristic
2#14563804C211yesmaximal, characteristic
3#14563803C212yesmaximal
4#14561517C212yesmaximal
5C19×#1295C211yesmaximal, characteristic
6C2×#10597275—22no—
7C2×#10597264—21no—
8C2×#10597274—22no—
9C2×#10597265—21no—
10C2×#10597260C2211yescharacteristic
11#11926486—22no—
12#11926483—21no—
13#11926465—22no—
14#11926464—21no—
15#11926414C2211yescharacteristic
16#11926410C2212yes—
17C2×C19×#97C2212yes—
18C19×#382C2211yescharacteristic
19C22×Dic38—21no—
20C22×C8×C19—22no—
21C2×C4⋊C4×C19D411yescharacteristic
22C2×C4⋊C4×C19D411yescharacteristic
23C2×C42×C19C2311yescharacteristic
24C2×C4⋊Dic19—21no—
25C2×C4⋊Dic19—22no—
26C2×C4⋊Dic19—21no—
27C2×C4⋊Dic19D412yes—
28C2×C4⋊Dic19D412yes—
29C2×Dic19⋊C4—22no—
30C22×C19⋊C8—21no—
31C19×#97—22no—
32C19×#97Q814yescomplemented
33C19×#95—22no—
34C19⋊#95—21no—
35C19⋊#95—22no—
36C19⋊#95—21no—
37C19⋊#95—22no—
38C19⋊#95—22no—
39#10597275—44no—
40#10597274—44no—
41#10597265—42no—
42#10597264—42no—
43#10597260—21no—
44#10597260Q812yescomplemented
45C22×C4×C19—21no—
46C22×C4×C19—21no—
47C22×C4×C19C2×D411yescharacteristic
48C22×C4×C19C2×D412yes—
49C22×Dic19—22no—
50C22×Dic19—22no—
51C22×Dic19—41no—
52C2×Dic38—82no—
53C2×Dic38—81no—
54C2×C8×C19—24no—
55C2×C8×C19—24no—
56C2×C8×C19—24no—
57C4⋊C4×C19—41no—
58C4⋊C4×C19—41no—
59C42×C19C2×Q812yes—
60C42×C19C2×Q811yescharacteristic
61C42×C19#4111yescharacteristic
62C4⋊Dic19—42no—
63C4⋊Dic19—42no—
64C4⋊Dic19—41no—
65C4⋊Dic19—41no—
66C4⋊Dic19—42no—
67C4⋊Dic19—42no—
68C4⋊Dic19—81no—
69Dic19⋊C4—82no—
70C2×C19⋊C8—22no—
71C2×C19⋊C8—22no—
72C2×C19⋊C8—22no—
73#10583—191nomaximal, Sylow
74C23×C19#12011yescharacteristic
75C2×C4×C19—21no—
76C2×C4×C19—22no—
77C2×C4×C19—21no—
78C2×C4×C19—22no—
79C2×C4×C19—42no—
80C2×C4×C19—41no—
81C2×C4×C19—41no—
82C2×C4×C19—42no—
83C2×C4×C19C22⋊Q812yes—
84C2×C4×C19C22⋊Q811yescharacteristic
85C2×C4×C19C4⋊Q811yescharacteristic
86C2×C4×C19C4⋊Q812yes—
87C2×Dic19—42no—
88C2×Dic19—42no—
89C2×Dic19—42no—
90C2×Dic19—42no—
91C2×Dic19—42no—
92C2×Dic19—42no—
93C2×Dic19—82no—
94C2×Dic19—81no—
95Dic38—84no—
96C8×C19—28no—
97C19⋊C8—24no—
98#2844—191no—
99#1847—192no—
100#1847—191no—
101#1295—192no—
102#1295D1911yescharacteristic
103C22×C19#39511yescharacteristic
104C22×C19#45312yes—
105C22×C19#45311yescharacteristic
106C22×C19#45612yes—
107C22×C19#45611yescharacteristic
108C4×C19—21no—
109C4×C19—22no—
110C4×C19—22no—
111C4×C19—21no—
112C4×C19—81no—
113C4×C19—81no—
114Dic19—82no—
115Dic19—82no—
116Dic19—161no—
117C2×#107—382no—
118C2×#107—381no—
119C2×#106—382no—
120C2×#106—381no—
121C2×#97—191no—
122C2×#97C2×D1912yes—
123#400—382no—
124#400—381no—
125#395—382no—
126#395—381no—
127#384—191no—
128#382—192no—
129#382C2×D1911yescharacteristic
130C2×C19#165511yescharacteristic
131C2×C19#166011yescharacteristic
132C2×C19#166012yes—
133C2×C19#206012yes—
134C2×C19#206011yescharacteristic
135C22×Q8—381no—
136C22×C8—22no—
137C22×C8—381no—
138C2×C4⋊C4—192no—
139C2×C4⋊C4—192no—
140C2×C4⋊C4—381no—
141C2×C4⋊C4—382no—
142C2×C4⋊C4—382no—
143C2×C4⋊C4—381no—
144C2×C4⋊C4D7611yescharacteristic
145C2×C4⋊C4D7611yescharacteristic
146C2×C42C22×D1911yescharacteristic
147#107—762no—
148#107—764no—
149#106—762no—
150#106—764no—
151#97—22no—
152#97—192no—
153#97—381no—
154#97Dic3814yescomplemented
155#95—22no—
156#95—382no—
157#95—381no—
158#95—381no—
159#95—382no—
160#95—382no—
161C19#1058311yescharacteristic, complemented, Sylow
162C2×Q8—1522no—
163C2×Q8—1521no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—382no—
167C22×C4—382no—
168C22×C4—761no—
169C22×C4C2×D7611yescharacteristic
170C22×C4D4×D1912yes—
171C2×C8—24no—
172C2×C8—24no—
173C2×C8—24no—
174C2×C8—382no—
175C2×C8—382no—
176C2×C8—382no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—762no—
180C4⋊C4—762no—
181C4⋊C4—762no—
182C4⋊C4—761no—
183C4⋊C4—762no—
184C4⋊C4—761no—
185C4⋊C4—1522no—
186C4⋊C4—1521no—
187C42C2×Dic3812yes—
188C42#6454311yescharacteristic
189C42Q8×D1911yescharacteristic
190C23#1059732811yescharacteristic
191Q8—1524no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—42no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—762no—
201C2×C4—762no—
202C2×C4—762no—
203C2×C4—762no—
204C2×C4—762no—
205C2×C4—762no—
206C2×C4—1522no—
207C2×C4—1521no—
208C2×C4#1059731511yescharacteristic
209C2×C4#1059732412yes—
210C2×C4#1059733412yes—
211C2×C4#1059734311yescharacteristic
212C8—28no—
213C8—384no—
214C22#1192646511yescharacteristic
215C22#1192671312yes—
216C22#1192671411yescharacteristic
217C22#1192672812yes—
218C22#1192672911yescharacteristic
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—81no—
224C4—81no—
225C4—3041no—
226C4—1522no—
227C4—1522no—
228C2#1456292511yescharacteristic
229C2#1456294711yescharacteristic
230C2#1456294812yes—
231C2#1456497912yes—
232C2#1456498111yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1295C2
socle, prime radicalC23×C19#120
hypercenter#1295D19
hypocenterC19#10583
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
32. C19×#97Q8semidirect
44. #10597260Q8semidirect
154. #97Dic38semidirect
161. C19#10583semidirect

Maximal subgroups

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

subgroupindex
#145719072
#145638042
#145638032
#145615172
C19×#12952
#1058319