Finite Group Databasebeta

← #18071561

Subgroups — #18071561

Order 4864.

682 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 87 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#14569970C211yesmaximal, characteristic
2#14565039C212yesmaximal, complemented
3#14561456C211yesmaximal, characteristic, complemented
4#14561455C212yesmaximal, complemented
5C19×#2093C211yesmaximal, characteristic, complemented
6C2×#10597328—22no—
7C2×#10597383—21no—
8C2×#10597266—22no—
9#11926461—21no—
10#11926460—22no—
11#11926446C2212yes—
12#11926306—22no—
13#11926299C2212yescomplemented
14C2×C19×#107—21no—
15C2×C19×#102—21no—
16C19×#390C2211yescharacteristic
17C19×#384C2211yescharacteristic, complemented
18C19×#336C2211yescharacteristic, complemented
19C24×D19—21no—
20C22×D4×C19D411yescharacteristic
21C22×C22⋊D19—22no—
22C22×D76—21no—
23C22×D76D412yes—
24C22×C8×C19—21no—
25C2×C4⋊C4×C19—22no—
26C2×C4⋊C4×C19—21no—
27C2×C4⋊C4×C19D411yescharacteristic
28C2×C22⋊C4×C19—22no—
29C2×C42×C19C2311yescharacteristic
30C2×C22⋊Dic19—21no—
31#10597383—42no—
32#10597383—42no—
33C2×(C2×D19)⋊C4—22no—
34C2×(C2×D19)⋊C4—22no—
35C2×(C2×D19)⋊C4—22no—
36C2×C4⋊Dic19D412yes—
37C22×C19⋊C8—22no—
38#10597328—44no—
39#10597328—44no—
40C19×#107—42no—
41C19×#102—42no—
42C19⋊#95—21no—
43#10597266—44no—
44C24×C19—21no—
45C23×D19—22no—
46C23×D19—44no—
47C23×D19—42no—
48C23×D19—81no—
49C23×D19—82no—
50C23×D19—81no—
51C2×D4×C19—21no—
52C2×D4×C19—41no—
53C2×D4×C19—41no—
54C2×D4×C19SD1612yes—
55C22×C4×C19—21no—
56C22×C4×C19—41no—
57C22×C4×C19C2×D412yes—
58C22×C4×C19C2×D411yescharacteristic
59C2×C22⋊D19—44no—
60C2×C22⋊D19—44no—
61C2×C22⋊D19—82no—
62C22×Dic19—22no—
63C2×D76—22no—
64C2×D76—42no—
65C2×D76—42no—
66C2×D76—44no—
67C2×D76—81no—
68C2×D76D814yes—
69C2×C8×C19—22no—
70C2×C8×C19—41no—
71C2×C8×C19—41no—
72C4⋊C4×C19—41no—
73C4⋊C4×C19—41no—
74C4⋊C4×C19—41no—
75C4⋊C4×C19—42no—
76C4⋊C4×C19—42no—
77C22⋊C4×C19—42no—
78C22⋊C4×C19—42no—
79C42×C19—41no—
80C22⋊Dic19—42no—
81(C2×D19)⋊C4—44no—
82(C2×D19)⋊C4—42no—
83(C2×D19)⋊C4—42no—
84(C2×D19)⋊C4—42no—
85(C2×D19)⋊C4—42no—
86C4⋊Dic19—42no—
87C2×C19⋊C8—42no—
88C2×C19⋊C8—42no—
89C2×C19⋊C8—42no—
90#7786—191nomaximal, Sylow
91C23×C19—22no—
92C23×C19—42no—
93C23×C19—41no—
94C23×C19—42no—
95C23×C19—41no—
96C23×C19#12011yescharacteristic
97C22×D19—24no—
98C22×D19—42no—
99C22×D19—42no—
100C22×D19—42no—
101C22×D19—42no—
102C22×D19—42no—
103C22×D19—42no—
104C22×D19—84no—
105C22×D19—88no—
106C22×D19—88no—
107C22×D19—84no—
108C22×D19—84no—
109D4×C19—42no—
110D4×C19—81no—
111C2×C4×C19—21no—
112C2×C4×C19—22no—
113C2×C4×C19—22no—
114C2×C4×C19—21no—
115C2×C4×C19—42no—
116C2×C4×C19—41no—
117C2×C4×C19—82no—
118C2×C4×C19—81no—
119C2×C4×C19C2×D812yes—
120C2×C4×C19C2×SD1611yescharacteristic
121C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C19AGL(1,ℤ/8)12yes—
123C22⋊D19—88no—
124C2×Dic19—42no—
125C2×Dic19—42no—
126C2×Dic19—42no—
127D76—44no—
128D76—82no—
129D76—84no—
130C8×C19—42no—
131C19⋊C8—82no—
132#2679—191no—
133#2093D1911yescharacteristic, complemented
134#2071—192no—
135#1270—191no—
136#1270—192no—
137C22×C19—42no—
138C22×C19—44no—
139C22×C19—82no—
140C22×C19—81no—
141C22×C19—81no—
142C22×C19#44712yes—
143C22×C19#45011yescharacteristic
144C22×C19#45311yescharacteristic
145C22×C19#45512yes—
146C22×C19#45811yescharacteristic
147C2×D19—44no—
148C2×D19—44no—
149C2×D19—44no—
150C2×D19—816no—
151C2×D19—82no—
152C2×D19—82no—
153C2×D19—82no—
154C2×D19—82no—
155C4×C19—22no—
156C4×C19—22no—
157C4×C19—21no—
158C4×C19—21no—
159C4×C19—81no—
160C4×C19—161no—
161Dic19—82no—
162C2×#120—382no—
163C2×#120—381no—
164C2×#107—21no—
165C2×#102—21no—
166C2×#102—382no—
167#394—382no—
168#394—381no—
169#390—192no—
170#390C2×D1911yescharacteristic
171#384C2×D1911yescharacteristic, complemented
172#340—382no—
173#336—192no—
174#336C2×D1911yescharacteristic, complemented
175C2×C19—82no—
176C2×C19#160712yes—
177C2×C19#161311yescharacteristic
178C2×C19#161911yescharacteristic
179C2×C19#163912yes—
180C2×C19#165911yescharacteristic
181D19—84no—
182C25—381no—
183C22×D4—192no—
184C22×D4—381no—
185C22×D4—382no—
186C22×D4C22⋊D1911yescharacteristic
187C22×C8—21no—
188C22×C8—382no—
189#120—764no—
190#120—764no—
191#120—762no—
192#120—762no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—192no—
196C2×C4⋊C4C22⋊D1911yescharacteristic
197C2×C22⋊C4—22no—
198C2×C22⋊C4—382no—
199C2×C22⋊C4—381no—
200C2×C22⋊C4—382no—
201C2×C22⋊C4—382no—
202C2×C42C22×D1911yescharacteristic
203#107—42no—
204#102—42no—
205#102—764no—
206#95—381no—
207C19#778611yescharacteristic, complemented, Sylow
208C24—21no—
209C24—382no—
210C24—762no—
211C24—764no—
212C24—1521no—
213C24—1522no—
214C24—1521no—
215C2×D4—21no—
216C2×D4—41no—
217C2×D4—41no—
218C2×D4—194no—
219C2×D4—382no—
220C2×D4—762no—
221C2×D4—762no—
222C2×D4—764no—
223C2×D4—764no—
224C2×D4—764no—
225C2×D4—1521no—
226C2×D4—1522no—
227C2×D4#6452712yes—
228C22×C4—21no—
229C22×C4—41no—
230C22×C4—382no—
231C22×C4D4×D1912yes—
232C22×C4C2×C22⋊D1911yescharacteristic
233C2×C8—22no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—762no—
237C2×C8—762no—
238C2×C8—762no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—762no—
245C22⋊C4—42no—
246C22⋊C4—42no—
247C22⋊C4—764no—
248C22⋊C4—762no—
249C22⋊C4—762no—
250C22⋊C4—762no—
251C22⋊C4—762no—
252C22⋊C4—762no—
253C42—41no—
254C23—22no—
255C23—42no—
256C23—41no—
257C23—42no—
258C23—41no—
259C23—384no—
260C23—762no—
261C23—762no—
262C23—762no—
263C23—762no—
264C23—762no—
265C23—762no—
266C23—1528no—
267C23—1524no—
268C23—1524no—
269C23—1528no—
270C23—1524no—
271C23#1059738311yescharacteristic
272D4—42no—
273D4—81no—
274D4—764no—
275D4—1522no—
276D4—1524no—
277D4—1528no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—82no—
285C2×C4—81no—
286C2×C4—762no—
287C2×C4—762no—
288C2×C4—762no—
289C2×C4D8×D1912yes—
290C2×C4#1059735712yes—
291C2×C4C2×#6452711yescharacteristic
292C2×C4#1059739511yescharacteristic
293C8—42no—
294C8—1522no—
295C22—42no—
296C22—44no—
297C22—82no—
298C22—81no—
299C22—81no—
300C22—764no—
301C22—764no—
302C22—764no—
303C22—15216no—
304C22—1522no—
305C22—1522no—
306C22—1522no—
307C22—1522no—
308C22#1192667612yes—
309C22#1192669411yescharacteristic
310C22#1192671111yescharacteristic
311C22#1192672012yes—
312C22#1192673311yescharacteristic
313C4—22no—
314C4—22no—
315C4—21no—
316C4—21no—
317C4—81no—
318C4—161no—
319C4—1522no—
320C2—82no—
321C2—1524no—
322C2#1456261912yes—
323C2#1456265411yescharacteristic
324C2#1456268711yescharacteristic
325C2#1456281312yes—
326C2#1456293911yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2093C2
socleC23×C19#120
prime radical#14569970C2
hypercenter#2093D19
hypocenterC19#7786
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2093

Complements

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

NH ≅ G/Ntype
2. #14565039C2semidirect
3. #14561456C2semidirect
4. #14561455C2semidirect
5. C19×#2093C2semidirect
13. #11926299C22semidirect
17. C19×#384C22semidirect
18. C19×#336C22semidirect
133. #2093D19semidirect
171. #384C2×D19semidirect
174. #336C2×D19semidirect
207. C19#7786semidirect

Maximal subgroups

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

subgroupindex
#145699702
#145650392
#145614562
#145614552
C19×#20932
#778619