Finite Group Databasebeta

← #18085504

Subgroups — #18085504

Order 4864.

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

normal subgroups only

This group has 738 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#14567916C211yesmaximal, characteristic
2#14567913C212yesmaximal
3#14563707C212yesmaximal
4C19⋊#1304C211yesmaximal, characteristic
5C19×#1819C211yesmaximal, characteristic
6C22×C22⋊Dic19C2212yes—
7#11926472—24no—
8#11926469—22no—
9#11926419—22no—
10#11926417—22no—
11#11926416—22no—
12#11926407—22no—
13#11926405—22no—
14#11926405—22no—
15#11926400C2212yes—
16#11926310—24no—
17C22×C22⋊C4×C19C2211yescharacteristic
18C19×#379C2211yescharacteristic
19C19×#379C2211yescharacteristic
20C19×#342—22no—
21C25×C19C2311yescharacteristic
22C23×C4×C19D412yes—
23C23×Dic19D412yes—
24C23×Dic19D412yes—
25C2×C22⋊C4×C19—21no—
26C2×C22⋊C4×C19—22no—
27C2×C22⋊C4×C19—22no—
28C2×C22⋊C4×C19—22no—
29C2×C22⋊C4×C19—21no—
30C2×C22⋊C4×C19—21no—
31C2×C22⋊C4×C19—22no—
32C2×C22⋊C4×C19D412yes—
33C2×C22⋊Dic19—22no—
34C2×C22⋊Dic19—22no—
35C2×C22⋊Dic19—22no—
36C2×C22⋊Dic19—22no—
37C2×C22⋊Dic19—22no—
38C2×C22⋊Dic19—22no—
39C2×C22⋊Dic19—22no—
40C2×C22⋊Dic19—22no—
41C2×C22⋊Dic19D414yes—
42C2×C4⋊Dic19—22no—
43C2×Dic19⋊C4—24no—
44C19⋊#95—22no—
45C19⋊#95—24no—
46C19⋊#95—24no—
47C19⋊#95—24no—
48C19⋊#95—24no—
49C24×C19—42no—
50C24×C19—44no—
51C24×C19C2×D411yescharacteristic
52C24×C19C2×D412yes—
53C24×C19C2×D412yes—
54C24×C19C2×D411yescharacteristic
55C24×C19#4111yescharacteristic
56C22×C4×C19—22no—
57C22×C4×C19—22no—
58C22×C4×C19—22no—
59C22×C4×C19—22no—
60C22×C4×C19—44no—
61C22×C4×C19—41no—
62C22×Dic19—24no—
63C22×Dic19—22no—
64C22×Dic19—22no—
65C22×Dic19—22no—
66C22×Dic19—22no—
67C22×Dic19—22no—
68C22×Dic19—22no—
69C22×Dic19—44no—
70C22×Dic19—44no—
71C22⋊C4×C19—44no—
72C22⋊C4×C19—41no—
73C22⋊C4×C19—42no—
74C22⋊C4×C19—41no—
75C22⋊C4×C19—42no—
76C22⋊C4×C19—44no—
77C22⋊C4×C19—42no—
78C22⋊Dic19—44no—
79C22⋊Dic19—44no—
80C22⋊Dic19—42no—
81C22⋊Dic19—42no—
82C22⋊Dic19—42no—
83C22⋊Dic19—42no—
84C22⋊Dic19—44no—
85C4⋊Dic19—82no—
86Dic19⋊C4—84no—
87#10339—191nomaximal, Sylow
88C23×C19—24no—
89C23×C19—24no—
90C23×C19—24no—
91C23×C19—24no—
92C23×C19—22no—
93C23×C19—41no—
94C23×C19—42no—
95C23×C19—42no—
96C23×C19—42no—
97C23×C19—42no—
98C23×C19—41no—
99C23×C19—42no—
100C23×C19—88no—
101C23×C19#12011yescharacteristic
102C23×C19#12012yes—
103C23×C19#12111yescharacteristic
104C23×C19#12112yes—
105C23×C19#12711yescharacteristic
106C2×C4×C19—44no—
107C2×C4×C19—44no—
108C2×C4×C19—42no—
109C2×C4×C19—44no—
110C2×C4×C19—42no—
111C2×C4×C19—82no—
112C2×C4×C19—82no—
113C2×C4×C19—81no—
114C2×Dic19—44no—
115C2×Dic19—44no—
116C2×Dic19—44no—
117C2×Dic19—44no—
118C2×Dic19—42no—
119C2×Dic19—42no—
120C2×Dic19—44no—
121C2×Dic19—44no—
122C2×Dic19—44no—
123C2×Dic19—82no—
124C2×Dic19—82no—
125#2483—191no—
126#2483—192no—
127#1819—192no—
128#1819D1911yescharacteristic
129#1304—191no—
130C22×C19—22no—
131C22×C19—22no—
132C22×C19—22no—
133C22×C19—22no—
134C22×C19—22no—
135C22×C19—22no—
136C22×C19—22no—
137C22×C19—21no—
138C22×C19—22no—
139C22×C19—21no—
140C22×C19—44no—
141C22×C19—48no—
142C22×C19—84no—
143C22×C19—82no—
144C22×C19—82no—
145C22×C19#39211yescharacteristic
146C22×C19#45812yes—
147C22×C19#45814yes—
148C4×C19—82no—
149C4×C19—82no—
150C4×C19—161no—
151Dic19—84no—
152Dic19—82no—
153Dic19—82no—
154C22×C22⋊C4—192no—
155C22×C22⋊C4C2×D1911yescharacteristic
156#397—384no—
157#397—382no—
158#385—382no—
159#385—382no—
160#385—382no—
161#381—382no—
162#381—382no—
163#381—382no—
164#379—192no—
165#379C2×D1911yescharacteristic
166#379C2×D1911yescharacteristic
167#342—22no—
168#342—384no—
169C2×C19—24no—
170C2×C19—22no—
171C2×C19—41no—
172C2×C19—42no—
173C2×C19—41no—
174C2×C19#202212yes—
175C2×C19#202211yescharacteristic
176C25C22×D1911yescharacteristic
177C23×C4—192no—
178C23×C4—192no—
179C23×C4D7612yes—
180C2×C4⋊C4—384no—
181C2×C4⋊C4—382no—
182C2×C22⋊C4—21no—
183C2×C22⋊C4—22no—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—21no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—21no—
189C2×C22⋊C4—194no—
190C2×C22⋊C4—382no—
191C2×C22⋊C4—382no—
192C2×C22⋊C4—382no—
193C2×C22⋊C4—382no—
194C2×C22⋊C4—382no—
195C2×C22⋊C4—382no—
196C2×C22⋊C4—382no—
197C2×C22⋊C4—382no—
198C2×C22⋊C4C22⋊D1912yes—
199#95—382no—
200#95—384no—
201#95—384no—
202#95—384no—
203#95—384no—
204C19#1033911yescharacteristic, complemented, Sylow
205C24—42no—
206C24—44no—
207C24C2×D7611yescharacteristic
208C24#6454111yescharacteristic
209C24D4×D1912yes—
210C24D4×D1912yes—
211C24C2×C22⋊D1911yescharacteristic
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—44no—
217C22×C4—41no—
218C22×C4—382no—
219C22×C4—382no—
220C22×C4—382no—
221C22×C4—384no—
222C22×C4—382no—
223C22×C4—382no—
224C22×C4—382no—
225C22×C4—764no—
226C22×C4—764no—
227C4⋊C4—1524no—
228C4⋊C4—1522no—
229C22⋊C4—44no—
230C22⋊C4—41no—
231C22⋊C4—41no—
232C22⋊C4—42no—
233C22⋊C4—42no—
234C22⋊C4—42no—
235C22⋊C4—44no—
236C22⋊C4—764no—
237C22⋊C4—764no—
238C22⋊C4—762no—
239C22⋊C4—762no—
240C22⋊C4—762no—
241C22⋊C4—762no—
242C22⋊C4—764no—
243C23—24no—
244C23—24no—
245C23—24no—
246C23—22no—
247C23—24no—
248C23—41no—
249C23—42no—
250C23—42no—
251C23—41no—
252C23—42no—
253C23—42no—
254C23—42no—
255C23—88no—
256C23#1059732812yes—
257C23#1059733012yes—
258C23#1059737611yescharacteristic
259C23#1059738311yescharacteristic
260C23#1059738611yescharacteristic
261C2×C4—44no—
262C2×C4—44no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—44no—
266C2×C4—82no—
267C2×C4—82no—
268C2×C4—81no—
269C2×C4—764no—
270C2×C4—764no—
271C2×C4—764no—
272C2×C4—764no—
273C2×C4—762no—
274C2×C4—762no—
275C2×C4—764no—
276C2×C4—764no—
277C2×C4—764no—
278C2×C4—1522no—
279C2×C4—1522no—
280C22—22no—
281C22—22no—
282C22—22no—
283C22—22no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—21no—
288C22—22no—
289C22—21no—
290C22—48no—
291C22—44no—
292C22—82no—
293C22—84no—
294C22—82no—
295C22#1192645311yescharacteristic
296C22#1192673312yes—
297C22#1192673514yes—
298C4—82no—
299C4—82no—
300C4—161no—
301C4—1524no—
302C4—1522no—
303C4—1522no—
304C2—22no—
305C2—24no—
306C2—41no—
307C2—41no—
308C2—42no—
309C2#1456476512yes—
310C2#1456476611yescharacteristic
subgroupG/H
centerC22#11926453
commutator, prime radical, cosocleC25×C19C23
FrattiniC25C22×D19
FittingC19×#1819C2
socleC22×C19#392
hypercenter#1819D19
hypocenterC19#10339
LCSG ▷ C25×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C25 ◁ #1819

Complements

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

NH ≅ G/Ntype
204. C19#10339semidirect

Maximal subgroups

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

subgroupindex
#145679162
#145679132
#145637072
C19⋊#13042
C19×#18192
#1033919