Finite Group Databasebeta

← #18087040

Subgroups — #18087040

Order 4864.

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

normal subgroups only

This group has 374 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#14563769C212yesmaximal
4#14561517C212yesmaximal
5C19×#1295C211yesmaximal, characteristic
6C2×#10597264—21no—
7C2×#10597265—21no—
8C2×#10597260C2211yescharacteristic
9#11926486—22no—
10#11926483—21no—
11#11926465—22no—
12#11926464—21no—
13#11926414C2211yescharacteristic
14#11926410C2212yes—
15#11926307—22no—
16#11926307—22no—
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—22no—
25C2×C4⋊Dic19—21no—
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#10597265—42no—
40#10597264—42no—
41#10597260—21no—
42#10597260Q812yescomplemented
43C22×C4×C19—21no—
44C22×C4×C19—21no—
45C22×C4×C19C2×D411yescharacteristic
46C22×C4×C19C2×D412yes—
47C22×Dic19—22no—
48C22×Dic19—22no—
49C22×Dic19—41no—
50C2×Dic38—81no—
51C2×Dic38—82no—
52C2×C8×C19—24no—
53C2×C8×C19—42no—
54C2×C8×C19—42no—
55C4⋊C4×C19—41no—
56C4⋊C4×C19—41no—
57C42×C19C2×Q812yes—
58C42×C19C2×Q811yescharacteristic
59C42×C19#4111yescharacteristic
60C4⋊Dic19—42no—
61C4⋊Dic19—42no—
62C4⋊Dic19—41no—
63C4⋊Dic19—41no—
64C4⋊Dic19—44no—
65C4⋊Dic19—81no—
66Dic19⋊C4—82no—
67C2×C19⋊C8—22no—
68C2×C19⋊C8—22no—
69C2×C19⋊C8—22no—
70#10584—191nomaximal, Sylow
71C23×C19#12011yescharacteristic
72C2×C4×C19—21no—
73C2×C4×C19—22no—
74C2×C4×C19—22no—
75C2×C4×C19—21no—
76C2×C4×C19—41no—
77C2×C4×C19—41no—
78C2×C4×C19—42no—
79C2×C4×C19—42no—
80C2×C4×C19C22⋊Q812yes—
81C2×C4×C19C22⋊Q811yescharacteristic
82C2×C4×C19C4⋊Q811yescharacteristic
83C2×C4×C19C4⋊Q812yes—
84C2×Dic19—42no—
85C2×Dic19—42no—
86C2×Dic19—42no—
87C2×Dic19—42no—
88C2×Dic19—42no—
89C2×Dic19—42no—
90C2×Dic19—81no—
91C2×Dic19—82no—
92Dic38—84no—
93C8×C19—44no—
94C19⋊C8—24no—
95#2844—191no—
96#1847—191no—
97#1836—192no—
98#1295—192no—
99#1295D1911yescharacteristic
100C22×C19#39511yescharacteristic
101C22×C19#45311yescharacteristic
102C22×C19#45412yes—
103C22×C19#45512yes—
104C22×C19#45611yescharacteristic
105C4×C19—21no—
106C4×C19—21no—
107C4×C19—22no—
108C4×C19—22no—
109C4×C19—81no—
110C4×C19—81no—
111Dic19—82no—
112Dic19—82no—
113Dic19—161no—
114C2×#107—381no—
115C2×#106—381no—
116C2×#97—191no—
117C2×#97C2×D1912yes—
118#400—382no—
119#400—381no—
120#395—382no—
121#395—381no—
122#384—191no—
123#382—192no—
124#382C2×D1911yescharacteristic
125#340—382no—
126#340—382no—
127C2×C19#165711yescharacteristic
128C2×C19#165911yescharacteristic
129C2×C19#166412yes—
130C2×C19#206011yescharacteristic
131C2×C19#206112yes—
132C22×Q8—381no—
133C22×C8—22no—
134C22×C8—381no—
135C2×C4⋊C4—192no—
136C2×C4⋊C4—192no—
137C2×C4⋊C4—381no—
138C2×C4⋊C4—382no—
139C2×C4⋊C4—382no—
140C2×C4⋊C4—381no—
141C2×C4⋊C4D7611yescharacteristic
142C2×C4⋊C4D7611yescharacteristic
143C2×C42C22×D1911yescharacteristic
144#107—762no—
145#106—762no—
146#97—22no—
147#97—192no—
148#97—381no—
149#97Dic3814yescomplemented
150#95—22no—
151#95—382no—
152#95—381no—
153#95—381no—
154#95—382no—
155#95—382no—
156C19#1058411yescharacteristic, complemented, Sylow
157C2×Q8—1521no—
158C2×Q8—1522no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—382no—
162C22×C4—382no—
163C22×C4—761no—
164C22×C4C2×D7611yescharacteristic
165C22×C4D4×D1912yes—
166C2×C8—24no—
167C2×C8—42no—
168C2×C8—42no—
169C2×C8—382no—
170C2×C8—382no—
171C2×C8—382no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—762no—
175C4⋊C4—762no—
176C4⋊C4—761no—
177C4⋊C4—761no—
178C4⋊C4—764no—
179C4⋊C4—1522no—
180C4⋊C4—1521no—
181C42C2×Dic3812yes—
182C42#6454311yescharacteristic
183C42Q8×D1911yescharacteristic
184C23#1059732811yescharacteristic
185Q8—1524no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—762no—
195C2×C4—762no—
196C2×C4—762no—
197C2×C4—762no—
198C2×C4—762no—
199C2×C4—762no—
200C2×C4—1521no—
201C2×C4—1522no—
202C2×C4#1059731511yescharacteristic
203C2×C4#1059732412yes—
204C2×C4#1059733412yes—
205C2×C4#1059734311yescharacteristic
206C8—44no—
207C8—384no—
208C22#1192646511yescharacteristic
209C22#1192671411yescharacteristic
210C22#1192671812yes—
211C22#1192672312yes—
212C22#1192672911yescharacteristic
213C4—21no—
214C4—21no—
215C4—22no—
216C4—22no—
217C4—81no—
218C4—81no—
219C4—3041no—
220C4—1522no—
221C4—1522no—
222C2#1456293411yescharacteristic
223C2#1456294211yescharacteristic
224C2#1456297112yes—
225C2#1456498111yescharacteristic
226C2#1456498412yes—
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1295C2
socle, prime radicalC23×C19#120
hypercenter#1295D19
hypocenterC19#10584
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
42. #10597260Q8semidirect
149. #97Dic38semidirect
156. C19#10584semidirect

Maximal subgroups

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

subgroupindex
#145719072
#145638042
#145637692
#145615172
C19×#12952
#1058419