Finite Group Databasebeta

← #18085426

Subgroups — #18085426

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#14574410C211yesmaximal, characteristic
2#14571974C212yesmaximal
3#14562208C212yesmaximal
4#14561503C211yesmaximal, characteristic
5C19×#1817C211yesmaximal, characteristic
6C2×#10597370C2212yes—
7#11926880—22no—
8#11926785—22no—
9#11926702—22no—
10#11926450—22no—
11#11926442—22no—
12#11926428—24no—
13#11926417—22no—
14#11926407—22no—
15#11926404C2212yes—
16#11926282—24no—
17C22×C42×C19C2211yescharacteristic
18C2×C19×C22⋊C8C2211yescharacteristic
19C2×C19×C22⋊C8C2211yescharacteristic
20C19×#336—22no—
21C23×C4×C19D411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19C2311yescharacteristic
24C22×Dic38D412yes—
25C22×C8×C19—21no—
26C22×C8×C19D412yes—
27C2×C42×C19—22no—
28C2×C42×C19—22no—
29C2×C42×C19—21no—
30C2×C42×C19—21no—
31C2×C22⋊Dic19—22no—
32C2×C22⋊Dic19—22no—
33C2×C4⋊Dic19—22no—
34C2×C4⋊Dic19D412yes—
35#10597370—22no—
36#10597370—22no—
37#10597370—22no—
38#10597370—22no—
39C2×Dic19⋊C4—24no—
40C2×Dic19⋊C4—22no—
41C2×Dic76—22no—
42C19×C22⋊C8—22no—
43C19×C22⋊C8—22no—
44C19⋊#95—24no—
45C19⋊#95—24no—
46C19⋊#95—24no—
47C19⋊#95D414yes—
48#10597275—22no—
49#10597273—24no—
50C24×C19C2×D411yescharacteristic
51C22×C4×C19—22no—
52C22×C4×C19—22no—
53C22×C4×C19—21no—
54C22×C4×C19—21no—
55C22×C4×C19—21no—
56C22×C4×C19—22no—
57C22×C4×C19—42no—
58C22×C4×C19—42no—
59C22×C4×C19Q1612yescomplemented
60C22×C4×C19C2×D412yes—
61C22×C4×C19C2×D412yes—
62C22×C4×C19C2×D411yescharacteristic
63C22×C4×C19#4111yescharacteristic
64C22×Dic19—22no—
65C22×Dic19—24no—
66C22×Dic19—22no—
67C2×Dic38—22no—
68C2×Dic38—22no—
69C2×Dic38—44no—
70C2×C8×C19—22no—
71C2×C8×C19—42no—
72C2×C8×C19—42no—
73C2×C8×C19—41no—
74C42×C19—41no—
75C42×C19—42no—
76C42×C19—41no—
77C22⋊Dic19—42no—
78C22⋊Dic19—42no—
79C22⋊Dic19—42no—
80C22⋊Dic19—42no—
81C4⋊Dic19—22no—
82C4⋊Dic19—22no—
83C4⋊Dic19—44no—
84Dic19⋊C4—48no—
85Dic19⋊C4—42no—
86Dic19⋊C4—42no—
87Dic76—82no—
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—
96C2×C4×C19—24no—
97C2×C4×C19—22no—
98C2×C4×C19—24no—
99C2×C4×C19—22no—
100C2×C4×C19—24no—
101C2×C4×C19—22no—
102C2×C4×C19—42no—
103C2×C4×C19—41no—
104C2×C4×C19—42no—
105C2×C4×C19—41no—
106C2×C4×C19—41no—
107C2×C4×C19—41no—
108C2×C4×C19—42no—
109C2×C4×C19—41no—
110C2×C4×C19#12011yescharacteristic
111C2×C4×C19#12112yes—
112C2×C4×C19#12711yescharacteristic
113C2×Dic19—44no—
114C2×Dic19—44no—
115C2×Dic19—44no—
116C2×Dic19—44no—
117C2×Dic19—42no—
118C2×Dic19—42no—
119C2×Dic19—44no—
120Dic38—44no—
121Dic38—82no—
122C8×C19—42no—
123C8×C19—81no—
124#3189—191no—
125#2855—192no—
126#1817D1911yescharacteristic
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—42no—
144C4×C19—42no—
145C4×C19#45812yes—
146Dic19—84no—
147Dic19—82no—
148Dic19—82no—
149C2×C22⋊Q8—192no—
150C22×C42C2×D1911yescharacteristic
151#484—382no—
152#467—382no—
153#451—382no—
154C2×C22⋊C8C2×D1911yescharacteristic
155C2×C22⋊C8C2×D1911yescharacteristic
156#391—382no—
157#389—382no—
158#387—384no—
159#385—382no—
160#381—382no—
161#380—192no—
162#336—22no—
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×Q8—192no—
172C23×C4D7611yescharacteristic
173C23×C4D7611yescharacteristic
174C23×C4C22×D1911yescharacteristic
175C2×Q16—382no—
176C22×C8—21no—
177C22×C8C22⋊D1912yes—
178C22⋊Q8—382no—
179C22⋊Q8—382no—
180C22⋊Q8—382no—
181C22⋊Q8—382no—
182C2×C4⋊C4—192no—
183C2×C4⋊C4—384no—
184C2×C4⋊C4—382no—
185C2×C4⋊C4—382no—
186C2×C22⋊C4—382no—
187C2×C22⋊C4—382no—
188C2×C42—21no—
189C2×C42—22no—
190C2×C42—22no—
191C2×C42—21no—
192#107—382no—
193#103—384no—
194C22⋊C8—22no—
195C22⋊C8—22no—
196#95—194no—
197#95—384no—
198#95—384no—
199#95—384no—
200C19#1032511yescharacteristic, complemented, Sylow
201C24C2×D7611yescharacteristic
202C2×Q8—382no—
203C2×Q8—382no—
204C2×Q8—764no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—21no—
210C22×C4—22no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—384no—
214C22×C4—382no—
215C22×C4—382no—
216C22×C4Dic7612yescomplemented
217C22×C4#6454111yescharacteristic
218C22×C4D4×D1912yes—
219C22×C4D4×D1912yes—
220C22×C4C2×C22⋊D1911yescharacteristic
221Q16—1522no—
222C2×C8—22no—
223C2×C8—42no—
224C2×C8—42no—
225C2×C8—41no—
226C4⋊C4—382no—
227C4⋊C4—382no—
228C4⋊C4—768no—
229C4⋊C4—764no—
230C4⋊C4—762no—
231C4⋊C4—762no—
232C22⋊C4—762no—
233C22⋊C4—762no—
234C22⋊C4—762no—
235C22⋊C4—762no—
236C42—41no—
237C42—41no—
238C42—42no—
239C23—41no—
240C23—41no—
241C23#1059732812yes—
242C23#1059735011yescharacteristic
243C23C2×Dic7611yescharacteristic
244C23#1059735512yes—
245C23#1059737611yescharacteristic
246Q8—764no—
247Q8—1522no—
248C2×C4—24no—
249C2×C4—22no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—24no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—42no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—764no—
263C2×C4—764no—
264C2×C4—764no—
265C2×C4—764no—
266C2×C4—764no—
267C2×C4—762no—
268C2×C4—762no—
269C2×C4#1059733012yes—
270C2×C4#1059738311yescharacteristic
271C2×C4#1059738611yescharacteristic
272C8—42no—
273C8—81no—
274C22—22no—
275C22—21no—
276C22—22no—
277C22—21no—
278C22—41no—
279C22—41no—
280C22—42no—
281C22#1192645311yescharacteristic
282C22#1192670212yes—
283C22#1192670812yes—
284C22#1192678511yescharacteristic
285C22#1192680211yescharacteristic
286C4—21no—
287C4—22no—
288C4—42no—
289C4—42no—
290C4—1524no—
291C4—1522no—
292C4—1522no—
293C4#1192673312yes—
294C2—22no—
295C2—21no—
296C2—21no—
297C2—22no—
298C2#1456464511yescharacteristic
299C2#1456470211yescharacteristic
300C2#1456476611yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1817C2
socleC22×C19#392
prime radicalC24×C19C2×D4
hypercenter#1817D19
hypocenterC19#10325
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1817

Complements

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

NH ≅ G/Ntype
59. C22×C4×C19Q16semidirect
200. C19#10325semidirect
216. C22×C4Dic76semidirect

Maximal subgroups

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

subgroupindex
#145744102
#145719742
#145622082
#145615032
C19×#18172
#1032519