Finite Group Databasebeta

← #18085423

Subgroups — #18085423

Order 4864.

602 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 103 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#14571969C212yesmaximal
2#14563701C211yesmaximal, characteristic
3#14562207C212yesmaximal
4#14561503C211yesmaximal, characteristic
5C19×#3189C211yesmaximal, characteristic
6C22×C4×Dic19C2211yescharacteristic
7C2×C22⋊(C19⋊C8)C2211yescharacteristic
8#11926451—22no—
9#11926440—22no—
10#11926425—24no—
11#11926416—22no—
12#11926405—22no—
13#11926404C2212yes—
14#11926298—22no—
15#11926281—24no—
16C2×C19×C22⋊Q8C2212yes—
17C19×#484—22no—
18C19×#467—22no—
19C19×#451—22no—
20C2×C19×C22⋊C8C2211yescharacteristic
21C22×Q8×C19D412yes—
22C23×C4×C19C2311yescharacteristic
23C23×Dic19D411yescharacteristic
24C23×Dic19D411yescharacteristic
25C2×Q16×C19—22no—
26C22×C8×C19D412yes—
27C19×C22⋊Q8—22no—
28C19×C22⋊Q8—22no—
29C19×C22⋊Q8—22no—
30C19×C22⋊Q8—22no—
31C2×C4⋊C4×C19—22no—
32C2×C4⋊C4×C19D412yes—
33C2×C22⋊C4×C19—22no—
34C2×C22⋊Dic19—22no—
35C2×C4⋊Dic19—22no—
36C2×Dic19⋊C4—24no—
37C2×C4×Dic19—21no—
38C2×C4×Dic19—22no—
39C2×C4×Dic19—22no—
40C2×C4×Dic19—21no—
41C22×C19⋊C8—21no—
42C19×#107—22no—
43C19×#103—24no—
44C19×C22⋊C8—22no—
45C19⋊#95—24no—
46C19⋊#95—24no—
47C19⋊#95—24no—
48C19⋊#95D414yes—
49C22⋊(C19⋊C8)—22no—
50C24×C19C2×D411yescharacteristic
51C2×Q8×C19—22no—
52C2×Q8×C19—22no—
53C2×Q8×C19—44no—
54C22×C4×C19—22no—
55C22×C4×C19—22no—
56C22×C4×C19—42no—
57C22×C4×C19C2×D412yes—
58C22×C4×C19C2×D412yes—
59C22×C4×C19C2×D411yescharacteristic
60C22×C4×C19#4111yescharacteristic
61C22×Dic19—22no—
62C22×Dic19—22no—
63C22×Dic19—21no—
64C22×Dic19—21no—
65C22×Dic19—21no—
66C22×Dic19—22no—
67C22×Dic19—24no—
68C22×Dic19—42no—
69C22×Dic19Q1612yescomplemented
70Q16×C19—82no—
71C2×C8×C19—22no—
72C2×C8×C19—42no—
73C4⋊C4×C19—22no—
74C4⋊C4×C19—22no—
75C4⋊C4×C19—42no—
76C4⋊C4×C19—42no—
77C22⋊C4×C19—42no—
78C22⋊C4×C19—42no—
79C22⋊Dic19—42no—
80C22⋊Dic19—42no—
81C4⋊Dic19—44no—
82Dic19⋊C4—48no—
83C4×Dic19—41no—
84C4×Dic19—42no—
85C4×Dic19—41no—
86C2×C19⋊C8—42no—
87C2×C19⋊C8—41no—
88#10325—191nomaximal, Sylow
89C23×C19—41no—
90C23×C19—41no—
91C23×C19#12012yes—
92C23×C19#12111yescharacteristic
93C23×C19C2×Q1611yescharacteristic
94C23×C19#13511yescharacteristic
95C23×C19#13712yes—
96Q8×C19—44no—
97Q8×C19—82no—
98C2×C4×C19—22no—
99C2×C4×C19—24no—
100C2×C4×C19—42no—
101C2×C4×C19—41no—
102C2×C4×C19—44no—
103C2×C4×C19—44no—
104C2×C4×C19—42no—
105C2×C4×C19—42no—
106C2×C4×C19#12011yescharacteristic
107C2×C4×C19#12112yes—
108C2×C4×C19#12711yescharacteristic
109C2×Dic19—24no—
110C2×Dic19—22no—
111C2×Dic19—24no—
112C2×Dic19—22no—
113C2×Dic19—42no—
114C2×Dic19—41no—
115C2×Dic19—41no—
116C2×Dic19—41no—
117C2×Dic19—42no—
118C2×Dic19—41no—
119C2×Dic19—44no—
120C2×Dic19—44no—
121C2×Dic19—44no—
122C8×C19—42no—
123C19⋊C8—81no—
124#3189D1911yescharacteristic
125#2855—192no—
126#1817—191no—
127#1520—192no—
128#1289—191no—
129C22×C19—22no—
130C22×C19—21no—
131C22×C19—22no—
132C22×C19—21no—
133C22×C19—41no—
134C22×C19—41no—
135C22×C19—42no—
136C22×C19#39211yescharacteristic
137C22×C19#45112yes—
138C22×C19#45212yes—
139C22×C19#46711yescharacteristic
140C22×C19#47011yescharacteristic
141C4×C19—21no—
142C4×C19—22no—
143C4×C19—82no—
144C4×C19—82no—
145C4×C19#45812yes—
146Dic19—42no—
147Dic19—42no—
148Dic19—84no—
149C2×C22⋊Q8C2×D1912yes—
150C22×C42—191no—
151#484—22no—
152#467—22no—
153#451—22no—
154C2×C22⋊C8—191no—
155C2×C22⋊C8C2×D1911yescharacteristic
156#391—382no—
157#389—382no—
158#387—384no—
159#385—382no—
160#381—382no—
161#380—192no—
162#336—382no—
163#328—384no—
164C2×C19—22no—
165C2×C19—22no—
166C2×C19—21no—
167C2×C19—21no—
168C2×C19#200111yescharacteristic
169C2×C19#201011yescharacteristic
170C2×C19#202211yescharacteristic
171C22×Q8C22⋊D1912yes—
172C23×C4—191no—
173C23×C4—191no—
174C23×C4C22×D1911yescharacteristic
175C2×Q16—22no—
176C22×C8—381no—
177C22×C8C22⋊D1912yes—
178C22⋊Q8—22no—
179C22⋊Q8—22no—
180C22⋊Q8—22no—
181C22⋊Q8—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—384no—
184C2×C4⋊C4—382no—
185C2×C4⋊C4C22⋊D1912yes—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—382no—
188C2×C42—382no—
189C2×C42—381no—
190C2×C42—381no—
191C2×C42—382no—
192#107—22no—
193#103—24no—
194C22⋊C8—22no—
195C22⋊C8—382no—
196#95—194no—
197#95—384no—
198#95—384no—
199#95—384no—
200C19#1032511yescharacteristic, complemented, Sylow
201C24D4×D1911yescharacteristic
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—44no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—42no—
208C22×C4—192no—
209C22×C4—382no—
210C22×C4—382no—
211C22×C4—381no—
212C22×C4—381no—
213C22×C4—382no—
214C22×C4—381no—
215C22×C4—384no—
216C22×C4—762no—
217C22×C4D4×D1912yes—
218C22×C4#6454311yescharacteristic
219C22×C4C2×C22⋊D1912yes—
220C22×C4C2×C22⋊D1911yescharacteristic
221Q16—82no—
222C2×C8—22no—
223C2×C8—42no—
224C2×C8—762no—
225C2×C8—761no—
226C4⋊C4—22no—
227C4⋊C4—22no—
228C4⋊C4—42no—
229C4⋊C4—42no—
230C4⋊C4—764no—
231C4⋊C4—768no—
232C22⋊C4—42no—
233C22⋊C4—42no—
234C22⋊C4—762no—
235C22⋊C4—762no—
236C42—762no—
237C42—761no—
238C42—761no—
239C23—41no—
240C23—41no—
241C23Q16×D1911yescharacteristic
242C23#1059736412yes—
243C23#1059736511yescharacteristic
244C23#1059738312yes—
245C23#1059738411yescharacteristic
246Q8—44no—
247Q8—82no—
248C2×C4—24no—
249C2×C4—22no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—44no—
253C2×C4—44no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—384no—
257C2×C4—382no—
258C2×C4—384no—
259C2×C4—382no—
260C2×C4—762no—
261C2×C4—761no—
262C2×C4—761no—
263C2×C4—762no—
264C2×C4—761no—
265C2×C4—761no—
266C2×C4—764no—
267C2×C4—764no—
268C2×C4—764no—
269C2×C4#1059738512yes—
270C2×C4#1059738611yescharacteristic
271C2×C4#1059739911yescharacteristic
272C8—42no—
273C8—1521no—
274C22—22no—
275C22—21no—
276C22—22no—
277C22—21no—
278C22—41no—
279C22—42no—
280C22—41no—
281C22#1192645211yescharacteristic
282C22#1192669812yes—
283C22#1192670512yes—
284C22#1192678211yescharacteristic
285C22#1192679911yescharacteristic
286C4—21no—
287C4—22no—
288C4—82no—
289C4—82no—
290C4—762no—
291C4—762no—
292C4—1524no—
293C4#1192673412yes—
294C2—22no—
295C2—21no—
296C2—22no—
297C2—21no—
298C2#1456464211yescharacteristic
299C2#1456469911yescharacteristic
300C2#1456476411yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#3189C2
socleC22×C19#392
prime radicalC24×C19C2×D4
hypercenter#3189D19
hypocenterC19#10325
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3189

Complements

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

NH ≅ G/Ntype
69. C22×Dic19Q16semidirect
200. C19#10325semidirect

Maximal subgroups

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

subgroupindex
#145719692
#145637012
#145622072
#145615032
C19×#31892
#1032519