Finite Group Databasebeta

← #18087039

Subgroups — #18087039

Order 4864.

374 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 95 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#14563770C212yesmaximal
3#14561517C212yesmaximal
4#14561516C211yesmaximal, characteristic
5C19×#1847C211yesmaximal, characteristic
6C2×#10597260C2212yes—
7#11926486—22no—
8#11926483—21no—
9#11926465—22no—
10#11926464—21no—
11#11926410C2212yes—
12#11926306—22no—
13#11926306—22no—
14C2×C19×#107—21no—
15C2×C19×#106—21no—
16C2×C19×#97C2211yescharacteristic
17C19×#384C2211yescharacteristic
18C19×#382C2211yescharacteristic
19C22×Dic38—21no—
20C22×C8×C19—21no—
21C2×C4⋊C4×C19—22no—
22C2×C4⋊C4×C19—21no—
23C2×C4⋊C4×C19D411yescharacteristic
24C2×C4⋊C4×C19D411yescharacteristic
25C2×C42×C19C2311yescharacteristic
26C2×C4⋊Dic19—21no—
27C2×C4⋊Dic19D412yes—
28C2×C4⋊Dic19D412yes—
29C2×Dic19⋊C4—22no—
30C22×C19⋊C8—22no—
31C19×#107—42no—
32C19×#106—42no—
33C19×#97—21no—
34C19×#97Q812yescomplemented
35C19×#95—22no—
36C19⋊#95—21no—
37C19⋊#95—22no—
38C19⋊#95—21no—
39C19⋊#95—22no—
40C19⋊#95—22no—
41#10597260—22no—
42#10597260Q814yescomplemented
43C22×C4×C19—21no—
44C22×C4×C19—21no—
45C22×C4×C19—41no—
46C22×C4×C19C2×D412yes—
47C22×C4×C19C2×D411yescharacteristic
48C22×Dic19—22no—
49C22×Dic19—22no—
50C2×Dic38—81no—
51C2×Dic38—82no—
52C2×C8×C19—22no—
53C2×C8×C19—22no—
54C2×C8×C19—22no—
55C4⋊C4×C19—41no—
56C4⋊C4×C19—41no—
57C4⋊C4×C19—44no—
58C4⋊C4×C19—41no—
59C4⋊C4×C19—41no—
60C42×C19C2×Q811yescharacteristic
61C42×C19C2×Q812yes—
62C42×C19#4111yescharacteristic
63C4⋊Dic19—42no—
64C4⋊Dic19—42no—
65C4⋊Dic19—81no—
66Dic19⋊C4—82no—
67C2×C19⋊C8—24no—
68C2×C19⋊C8—42no—
69C2×C19⋊C8—42no—
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×C19—81no—
81C2×C4×C19—82no—
82C2×C4×C19C22⋊Q812yes—
83C2×C4×C19C22⋊Q811yescharacteristic
84C2×C4×C19C4⋊Q811yescharacteristic
85C2×C4×C19C4⋊Q812yes—
86C2×Dic19—42no—
87C2×Dic19—42no—
88C2×Dic19—42no—
89C2×Dic19—42no—
90C2×Dic19—42no—
91C2×Dic19—42no—
92Dic38—84no—
93C8×C19—24no—
94C19⋊C8—44no—
95#2844—191no—
96#1847D1911yescharacteristic
97#1836—192no—
98#1295—192no—
99#1295—191no—
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—
111C4×C19—161no—
112Dic19—82no—
113Dic19—82no—
114C2×#107—21no—
115C2×#106—21no—
116C2×#97—192no—
117C2×#97C2×D1911yescharacteristic
118#400—382no—
119#400—381no—
120#395—382no—
121#395—381no—
122#384C2×D1911yescharacteristic
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—21no—
134C22×C8—382no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—192no—
138C2×C4⋊C4—192no—
139C2×C4⋊C4—382no—
140C2×C4⋊C4—381no—
141C2×C4⋊C4C22⋊D1911yescharacteristic
142C2×C4⋊C4C22⋊D1911yescharacteristic
143C2×C42C22×D1911yescharacteristic
144#107—42no—
145#106—42no—
146#97—21no—
147#97—194no—
148#97—382no—
149#97Dic3812yescomplemented
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—41no—
162C22×C4—382no—
163C22×C4—382no—
164C22×C4D4×D1912yes—
165C22×C4C2×C22⋊D1911yescharacteristic
166C2×C8—22no—
167C2×C8—22no—
168C2×C8—22no—
169C2×C8—384no—
170C2×C8—762no—
171C2×C8—762no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—44no—
177C4⋊C4—762no—
178C4⋊C4—762no—
179C4⋊C4—1522no—
180C4⋊C4—1521no—
181C42C2×Dic3811yescharacteristic
182C42#6454111yescharacteristic
183C42Q8×D1912yes—
184C23#1059738311yescharacteristic
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—81no—
195C2×C4—82no—
196C2×C4—762no—
197C2×C4—762no—
198C2×C4—762no—
199C2×C4—762no—
200C2×C4—762no—
201C2×C4—762no—
202C2×C4#1059733412yes—
203C2×C4#1059734212yes—
204C2×C4#1059737011yescharacteristic
205C2×C4#1059739011yescharacteristic
206C8—24no—
207C8—764no—
208C22#1192646411yescharacteristic
209C22#1192671111yescharacteristic
210C22#1192671512yes—
211C22#1192672012yes—
212C22#1192672611yescharacteristic
213C4—21no—
214C4—21no—
215C4—22no—
216C4—22no—
217C4—81no—
218C4—81no—
219C4—161no—
220C4—1522no—
221C4—1522no—
222C2#1456293111yescharacteristic
223C2#1456293911yescharacteristic
224C2#1456296712yes—
225C2#1456498011yescharacteristic
226C2#1456498312yes—
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1847C2
socle, prime radicalC23×C19#120
hypercenter#1847D19
hypocenterC19#10584
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
34. 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
#145637702
#145615172
#145615162
C19×#18472
#1058419