Finite Group Databasebeta

← #18083411

Subgroups — #18083411

Order 4864.

528 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 105 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#14573675C212yesmaximal
2#14566928C211yesmaximal, characteristic
3#14564616C211yesmaximal, characteristic
4#14562065C212yesmaximal
5C19×#1274C211yesmaximal, characteristic
6#11927101C2211yescharacteristic
7C2×C4×Dic38C2212yes—
8#11926880—22no—
9#11926840—22no—
10#11926755—22no—
11#11926702—22no—
12C4×Dic76—24no—
13#11926568C2211yescharacteristic
14#11926476—22no—
15#11926465—22no—
16C4×C4⋊Dic19—22no—
17#11926304—22no—
18#11926276—24no—
19C19×#431C2212yes—
20C19×#376C2211yescharacteristic
21C22×Dic38D412yes—
22C2×C42×C19D412yes—
23C2×C42×C19C2311yescharacteristic
24#10597372—21no—
25C2×C4⋊Dic19—24no—
26C2×C4⋊Dic19D412yes—
27#10597370—22no—
28C2×Dic19⋊C4—22no—
29C2×C4×Dic19—22no—
30C2×#64520—21no—
31C2×Dic76—24no—
32#10597316—21no—
33#10597315D412yes—
34C4×Dic38—22no—
35C4×Dic38—22no—
36C4×Dic38—22no—
37C4×Dic38—22no—
38C4×Dic38—22no—
39C19×C4⋊C8—22no—
40C19×C22⋊C8—22no—
41C4×C8×C19D414yes—
42C19×#95—22no—
43C19⋊#95—22no—
44C19⋊#95—22no—
45#10597275—24no—
46#10597273—24no—
47#10597273—24no—
48C4⋊(C19⋊C8)—22no—
49C22×C4×C19—22no—
50C22×C4×C19C2×D411yescharacteristic
51C22×C4×C19C2×D412yes—
52C22×Dic19—22no—
53C22×Dic19—22no—
54C2×Dic38—22no—
55C2×Dic38—22no—
56C2×Dic38—22no—
57C2×Dic38—44no—
58C2×C8×C19—24no—
59C42×C19—22no—
60C42×C19Q1614yescomplemented
61C42×C19C2×D412yes—
62C42×C19C2×D411yescharacteristic
63C42×C19#4111yescharacteristic
64C22⋊Dic19—41no—
65C4⋊Dic19—22no—
66C4⋊Dic19—22no—
67C4⋊Dic19—22no—
68C4⋊Dic19—22no—
69C4⋊Dic19—48no—
70Dic19⋊C4—42no—
71Dic19⋊C4—42no—
72Dic19⋊C4—42no—
73C4×Dic19—42no—
74C4×Dic19—42no—
75C4×Dic19—41no—
76#64520—42no—
77C2×C19⋊C8—41no—
78Dic76—48no—
79#10017—191nomaximal, Sylow
80C23×C19#12011yescharacteristic
81C2×C4×C19—24no—
82C2×C4×C19—42no—
83C2×C4×C19—44no—
84C2×C4×C19#12012yes—
85C2×C4×C19#12112yes—
86C2×C4×C19#12111yescharacteristic
87C2×C4×C19#12711yescharacteristic
88C2×C4×C19C2×Q1612yes—
89C2×C4×C19#13712yes—
90C2×Dic19—24no—
91C2×Dic19—42no—
92C2×Dic19—42no—
93C2×Dic19—44no—
94C2×Dic19—42no—
95C2×Dic19—42no—
96Dic38—24no—
97Dic38—24no—
98Dic38—42no—
99Dic38—42no—
100Dic38—44no—
101C8×C19—44no—
102C19⋊C8—81no—
103#3104—192no—
104#2399—191no—
105#1995—191no—
106#1487—192no—
107#1274D1911yescharacteristic
108C22×C19—22no—
109C22×C19#39211yescharacteristic
110C22×C19#45112yes—
111C4×C19—22no—
112C4×C19—22no—
113C4×C19—44no—
114C4×C19#46212yes—
115C4×C19#49411yescharacteristic
116C4×C19#49711yescharacteristic
117Dic19—44no—
118Dic19—82no—
119Dic19—82no—
120#533—191no—
121C2×C4×Q8—192no—
122#484—382no—
123#477—382no—
124#462—382no—
125#451—382no—
126C4×Q16—384no—
127#431C2×D1912yes—
128#423—191no—
129#398—382no—
130#395—382no—
131C4×C4⋊C4—382no—
132#376C2×D1911yescharacteristic
133#339—382no—
134Q8⋊C8—384no—
135C2×C19—22no—
136C2×C19#201012yes—
137C2×C19#201611yescharacteristic
138C22×Q8—192no—
139C2×Q16—384no—
140C2×M16—381no—
141C4⋊Q8—192no—
142#125—381no—
143C22⋊Q8—382no—
144C4×Q8—382no—
145C4×Q8—382no—
146C4×Q8—382no—
147C4×Q8—382no—
148C4×Q8—382no—
149#117—381no—
150C2×C4⋊C4—192no—
151C2×C4⋊C4—384no—
152C2×C4⋊C4—382no—
153C2×C42—382no—
154C2×C42D7612yes—
155C2×C42C22×D1911yescharacteristic
156#107—384no—
157C4⋊C8—22no—
158C4⋊C8—382no—
159#103—384no—
160#103—384no—
161C22⋊C8—22no—
162C4×C8D7614yes—
163#95—22no—
164#95—382no—
165#95—382no—
166C19#1001711yescharacteristic, complemented, Sylow
167C2×Q8—382no—
168C2×Q8—382no—
169C2×Q8—382no—
170C2×Q8—764no—
171C22×C4—22no—
172C22×C4—382no—
173C22×C4—382no—
174C22×C4C2×D7611yescharacteristic
175C22×C4D4×D1912yes—
176Q16—768no—
177M16—762no—
178C2×C8—24no—
179C2×C8—761no—
180C4⋊C4—382no—
181C4⋊C4—382no—
182C4⋊C4—382no—
183C4⋊C4—382no—
184C4⋊C4—768no—
185C4⋊C4—762no—
186C4⋊C4—762no—
187C4⋊C4—762no—
188C22⋊C4—761no—
189C42—22no—
190C42—762no—
191C42—761no—
192C42—762no—
193C42Dic7614yescomplemented
194C42C2×D7612yes—
195C42D4×D1911yescharacteristic
196C42#6454511yescharacteristic
197C23#1059732811yescharacteristic
198Q8—384no—
199Q8—384no—
200Q8—762no—
201Q8—762no—
202Q8—764no—
203C2×C4—24no—
204C2×C4—42no—
205C2×C4—44no—
206C2×C4—384no—
207C2×C4—762no—
208C2×C4—762no—
209C2×C4—764no—
210C2×C4—762no—
211C2×C4—762no—
212C2×C4#1059732011yescharacteristic
213C2×C4#1059732812yes—
214C2×C4#1059734112yes—
215C2×C4#1059734111yescharacteristic
216C2×C4C2×Dic7612yes—
217C2×C4#1059735512yes—
218C8—44no—
219C8—1521no—
220C22—22no—
221C22#1192645411yescharacteristic
222C22#1192670212yes—
223C4—22no—
224C4—22no—
225C4—44no—
226C4—764no—
227C4—1522no—
228C4—1522no—
229C4#1192675512yes—
230C4#1192692411yescharacteristic
231C4#1192693811yescharacteristic
232C2—22no—
233C2#1456470312yes—
234C2#1456473711yescharacteristic
subgroupG/H
centerC2×C4#10597320
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1274C2
socleC22×C19#392
prime radicalC23×C19#120
hypercenter#1274D19
hypocenterC19#10017
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
60. C42×C19Q16semidirect
166. C19#10017semidirect
193. C42Dic76semidirect

Maximal subgroups

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

subgroupindex
#145736752
#145669282
#145646162
#145620652
C19×#12742
#1001719