Finite Group Databasebeta

← #18083130

Subgroups — #18083130

Order 4864.

632 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×#11926880C212yesmaximal
2#14569749C211yesmaximal, characteristic
3C2×#11926282C212yesmaximal
4#14561904C211yesmaximal, characteristic
5C19×#1280C211yesmaximal, characteristic
6C2×#10597370C2212yes—
7C22×C4⋊Dic19C2211yescharacteristic
8#11926880—24no—
9#11926880—24no—
10C2×#10597275—22no—
11C2×#10597273—22no—
12#11926476—22no—
13#11926465—22no—
14#11926404—22no—
15C2×C19⋊#95—22no—
16C2×C19⋊#95C2211yescharacteristic
17#11926282—24no—
18C2×C19×C22⋊C8C2212yes—
19C2×C19×#95C2211yescharacteristic
20C23×C4×C19D412yes—
21C23×C4×C19C2311yescharacteristic
22C23×Dic19—21no—
23C23×Dic19—21no—
24C22×Dic38D412yes—
25C22×C8×C19—22no—
26C2×C22⋊Dic19—22no—
27C2×C4⋊Dic19—22no—
28C2×C4⋊Dic19—22no—
29C2×C4⋊Dic19—21no—
30C2×C4⋊Dic19—22no—
31C2×C4⋊Dic19—22no—
32C2×C4⋊Dic19D412yes—
33C2×C4⋊Dic19D412yes—
34#10597370—22no—
35#10597370—22no—
36#10597370—22no—
37#10597370—22no—
38C2×Dic19⋊C4—22no—
39C19×C22⋊C8—22no—
40C19×C22⋊C8D414yes—
41C19×#95—22no—
42C19⋊#95—24no—
43C19⋊#95—22no—
44C19⋊#95—44no—
45#10597275—28no—
46#10597273—28no—
47C24×C19C2×D411yescharacteristic
48C22×C4×C19—22no—
49C22×C4×C19—22no—
50C22×C4×C19—42no—
51C22×C4×C19—42no—
52C22×C4×C19—42no—
53C22×C4×C19Q1614yes—
54C22×C4×C19C2×D412yes—
55C22×C4×C19C2×D412yes—
56C22×C4×C19C2×D411yescharacteristic
57C22×C4×C19#4111yescharacteristic
58C22×Dic19—22no—
59C22×Dic19—22no—
60C22×Dic19—22no—
61C22×Dic19—22no—
62C22×Dic19—41no—
63C22×Dic19—42no—
64C22×Dic19—42no—
65C22×Dic19—42no—
66C22×Dic19—41no—
67C22×Dic19—41no—
68C22×Dic19—41no—
69C22×Dic19—42no—
70C2×Dic38—22no—
71C2×Dic38—22no—
72C2×Dic38—44no—
73C2×C8×C19—24no—
74C2×C8×C19—44no—
75C22⋊Dic19—42no—
76C22⋊Dic19—42no—
77C4⋊Dic19—24no—
78C4⋊Dic19—22no—
79C4⋊Dic19—22no—
80C4⋊Dic19—42no—
81C4⋊Dic19—82no—
82C4⋊Dic19—82no—
83Dic19⋊C4—42no—
84Dic19⋊C4—42no—
85#9972—191nomaximal, Sylow
86C23×C19—21no—
87C23×C19—21no—
88C23×C19—22no—
89C23×C19#12011yescharacteristic
90C23×C19#12111yescharacteristic
91C23×C19#12711yescharacteristic
92C23×C19C2×Q1612yes—
93C23×C19#13712yes—
94C2×C4×C19—24no—
95C2×C4×C19—24no—
96C2×C4×C19—42no—
97C2×C4×C19—41no—
98C2×C4×C19—41no—
99C2×C4×C19—42no—
100C2×C4×C19—42no—
101C2×C4×C19—44no—
102C2×C4×C19—82no—
103C2×C4×C19#12012yes—
104C2×C4×C19#12112yes—
105C2×Dic19—44no—
106C2×Dic19—42no—
107C2×Dic19—44no—
108C2×Dic19—42no—
109C2×Dic19—42no—
110C2×Dic19—42no—
111C2×Dic19—42no—
112C2×Dic19—42no—
113C2×Dic19—44no—
114C2×Dic19—82no—
115C2×Dic19—81no—
116C2×Dic19—82no—
117C2×Dic19—81no—
118C2×Dic19—81no—
119C2×Dic19—81no—
120Dic38—44no—
121Dic38—82no—
122C8×C19—44no—
123C2×#484—192no—
124#2659—191no—
125C2×#328—192no—
126#1445—191no—
127#1280D1911yescharacteristic
128C22×C19—22no—
129C22×C19—22no—
130C22×C19—22no—
131C22×C19—22no—
132C22×C19—21no—
133C22×C19—21no—
134C22×C19—21no—
135C22×C19—21no—
136C22×C19#39211yescharacteristic
137C22×C19#45112yes—
138C22×C19#45311yescharacteristic
139C22×C19#45411yescharacteristic
140C22×C19#45812yes—
141C22×C19#46212yes—
142C22×C19#49411yescharacteristic
143C22×C19#49711yescharacteristic
144C4×C19—22no—
145C4×C19—22no—
146C4×C19—44no—
147Dic19—82no—
148Dic19—82no—
149Dic19—82no—
150Dic19—82no—
151C2×C22⋊Q8—192no—
152C22×C4⋊C4—191no—
153#484—384no—
154#484—384no—
155C2×#107—382no—
156C2×#103—382no—
157C2×C22⋊C8C2×D1912yes—
158#398—382no—
159#395—382no—
160#380—382no—
161C2×#95—191no—
162C2×#95—382no—
163C2×#95C2×D1911yescharacteristic
164#328—384no—
165C2×C19—21no—
166C2×C19—22no—
167C2×C19—21no—
168C2×C19#161412yes—
169C2×C19#161712yes—
170C2×C19#200611yescharacteristic
171C2×C19#201611yescharacteristic
172C2×C19#202211yescharacteristic
173C22×Q8—192no—
174C23×C4—381no—
175C23×C4—381no—
176C23×C4D7612yes—
177C23×C4C22×D1911yescharacteristic
178C22×C8—22no—
179C22⋊Q8—382no—
180C22⋊Q8—382no—
181C22⋊Q8—382no—
182C22⋊Q8—382no—
183C2×C4⋊C4—192no—
184C2×C4⋊C4—192no—
185C2×C4⋊C4—382no—
186C2×C4⋊C4—382no—
187C2×C4⋊C4—382no—
188C2×C4⋊C4—381no—
189C2×C4⋊C4—382no—
190C2×C4⋊C4—382no—
191C2×C22⋊C4—382no—
192#107—388no—
193#103—388no—
194C22⋊C8—22no—
195C22⋊C8D7614yes—
196#95—22no—
197#95—384no—
198#95—382no—
199#95—764no—
200C19#997211yescharacteristic, complemented, Sylow
201C24C2×D7611yescharacteristic
202C2×Q8—382no—
203C2×Q8—382no—
204C2×Q8—764no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—382no—
211C22×C4—382no—
212C22×C4—382no—
213C22×C4—382no—
214C22×C4—762no—
215C22×C4—761no—
216C22×C4—762no—
217C22×C4—762no—
218C22×C4—761no—
219C22×C4—761no—
220C22×C4—761no—
221C22×C4—762no—
222C22×C4Dic7614yes—
223C22×C4C2×D7612yes—
224C22×C4D4×D1912yes—
225C22×C4D4×D1911yescharacteristic
226C22×C4#6454511yescharacteristic
227C2×C8—24no—
228C2×C8—44no—
229C4⋊C4—384no—
230C4⋊C4—382no—
231C4⋊C4—382no—
232C4⋊C4—762no—
233C4⋊C4—762no—
234C4⋊C4—762no—
235C4⋊C4—1522no—
236C4⋊C4—1522no—
237C22⋊C4—762no—
238C22⋊C4—762no—
239C23—21no—
240C23—21no—
241C23—22no—
242C23#1059732011yescharacteristic
243C23#1059732811yescharacteristic
244C23#1059734111yescharacteristic
245C23C2×Dic7612yes—
246C23#1059735512yes—
247Q8—764no—
248Q8—1522no—
249C2×C4—24no—
250C2×C4—24no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—44no—
257C2×C4—82no—
258C2×C4—762no—
259C2×C4—764no—
260C2×C4—764no—
261C2×C4—762no—
262C2×C4—762no—
263C2×C4—762no—
264C2×C4—762no—
265C2×C4—762no—
266C2×C4—764no—
267C2×C4—1522no—
268C2×C4—1521no—
269C2×C4—1522no—
270C2×C4—1521no—
271C2×C4—1521no—
272C2×C4—1521no—
273C2×C4#1059732812yes—
274C2×C4#1059734112yes—
275C8—44no—
276C22—21no—
277C22—21no—
278C22—22no—
279C22—22no—
280C22—22no—
281C22—22no—
282C22—21no—
283C22—21no—
284C22#1192645411yescharacteristic
285C22#1192670212yes—
286C22#1192671411yescharacteristic
287C22#1192671911yescharacteristic
288C22#1192673512yes—
289C22#1192675512yes—
290C22#1192692411yescharacteristic
291C22#1192693811yescharacteristic
292C4—22no—
293C4—22no—
294C4—44no—
295C4—1522no—
296C4—1522no—
297C4—1522no—
298C4—1522no—
299C2—21no—
300C2—21no—
301C2—22no—
302C2#1456266212yes—
303C2#1456267912yes—
304C2#1456467911yescharacteristic
305C2#1456473711yescharacteristic
306C2#1456476711yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1280C2
socleC23×C19#120
prime radicalC24×C19C2×D4
hypercenter#1280D19
hypocenterC19#9972
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
200. C19#9972semidirect

Maximal subgroups

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

subgroupindex
C2×#119268802
#145697492
C2×#119262822
#145619042
C19×#12802
#997219