Finite Group Databasebeta

← #18078558

Subgroups — #18078558

Order 4864.

458 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 119 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#14572273C211yesmaximal, characteristic
2#14562320C212yesmaximal, complemented
3#14561949C211yesmaximal, characteristic
4#14561493C212yesmaximal, complemented
5C19×#2628C211yesmaximal, characteristic
6#11926605—24no—
7#11926597C2212yes—
8#11926568C2212yes—
9#11926508—21no—
10C4×#64520—21no—
11#11926290—24no—
12#11926270—21no—
13#11926268—21no—
14C2×C19×C4⋊Q8C2211yescharacteristic
15C2×C19×#117C2211yescharacteristic
16C19×#400C412yes—
17C19×#399C412yes—
18C19×#395—21no—
19C19×#393—21no—
20C19×#389—21no—
21C19×#382C2211yescharacteristic
22C19×#380—21no—
23C22×Q8×C19—21no—
24C23×C4×C19D411yescharacteristic
25C19×C4⋊Q8—22no—
26C19×C4⋊Q8—22no—
27C19×#117—22no—
28C19×#117—22no—
29C2×C4⋊C4×C19—21no—
30C2×C4⋊C4×C19—21no—
31C2×C4⋊C4×C19—22no—
32C2×C4⋊C4×C19C2×C412yes—
33C2×C4⋊C4×C19C2×C411yescharacteristic
34C2×C4⋊C4×C19D411yescharacteristic
35C2×C22⋊C4×C19—22no—
36C2×C22⋊C4×C19C2×C411yescharacteristic
37C2×C22⋊C4×C19D411yescharacteristic
38C2×C42×C19D411yescharacteristic
39C2×C42×C19C2311yescharacteristic
40C2×#64520—22no—
41C19×#95—22no—
42C19×#95—22no—
43C19×#95—21no—
44C19×#95C2×C412yes—
45C22⋊(C19⋊C8)—24no—
46C22⋊(C19⋊C8)—22no—
47C4⋊(C19⋊C8)—22no—
48C4⋊(C19⋊C8)—22no—
49C4⋊(C19⋊C8)D414yes—
50#10597260—22no—
51C4×C19⋊C8—22no—
52C4×C19⋊C8—22no—
53C24×C19C22⋊C411yescharacteristic
54C2×Q8×C19—42no—
55C2×Q8×C19—82no—
56C22×C4×C19—21no—
57C22×C4×C19—21no—
58C22×C4×C19—22no—
59C22×C4×C19—22no—
60C22×C4×C19—22no—
61C22×C4×C19—22no—
62C22×C4×C19C22⋊C411yescharacteristic
63C22×C4×C19C22⋊C411yescharacteristic
64C22×C4×C19C22⋊C411yescharacteristic
65C22×C4×C19C22×C411yescharacteristic
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19C2×D411yescharacteristic
68C4⋊C4×C19—22no—
69C4⋊C4×C19—22no—
70C4⋊C4×C19—24no—
71C4⋊C4×C19—41no—
72C4⋊C4×C19—41no—
73C4⋊C4×C19—42no—
74C4⋊C4×C19—82no—
75C22⋊C4×C19—22no—
76C22⋊C4×C19—22no—
77C22⋊C4×C19—82no—
78C42×C19—21no—
79C42×C19—21no—
80C42×C19C2×D412yes—
81C42×C19#4112yes—
82#64520—42no—
83#64520—42no—
84C2×C19⋊C8—24no—
85C2×C19⋊C8—42no—
86#9194—191nomaximal, Sylow
87C23×C19—21no—
88C23×C19—21no—
89C23×C19—21no—
90C23×C19—41no—
91C23×C19—41no—
92C23×C19C2×C22⋊C411yescharacteristic
93Q8×C19—84no—
94C2×C4×C19—21no—
95C2×C4×C19—21no—
96C2×C4×C19—21no—
97C2×C4×C19—21no—
98C2×C4×C19—21no—
99C2×C4×C19—41no—
100C2×C4×C19—41no—
101C2×C4×C19—42no—
102C2×C4×C19—42no—
103C2×C4×C19—41no—
104C2×C4×C19—41no—
105C2×C4×C19—42no—
106C2×C4×C19—42no—
107C2×C4×C19—42no—
108C2×C4×C19—42no—
109C2×C4×C19—42no—
110C2×C4×C19—42no—
111C2×C4×C19C4×D412yes—
112C2×C4×C19#12011yescharacteristic
113C2×C4×C19#12112yes—
114C2×C4×C19#12311yescharacteristic
115C2×C4×C19#13512yes—
116C2×C4×C19#13712yes—
117C19⋊C8—44no—
118C19⋊C8—82no—
119#2921—191no—
120#2628D1911yescharacteristic
121#1549—192no—
122#1458—191no—
123#1286—192no—
124C22×C19—21no—
125C22×C19—21no—
126C22×C19—42no—
127C22×C19—41no—
128C22×C19—41no—
129C22×C19—41no—
130C22×C19—81no—
131C22×C19#38611yescharacteristic
132C22×C19#41611yescharacteristic
133C22×C19#41911yescharacteristic
134C4×C19—22no—
135C4×C19—22no—
136C4×C19—41no—
137C4×C19—41no—
138C4×C19—41no—
139C4×C19—82no—
140C4×C19—82no—
141C4×C19#45212yes—
142C4×C19#48512yes—
143C2×C4⋊Q8C2×D1911yescharacteristic
144C2×#117C2×D1911yescharacteristic
145#433—384no—
146#431—192no—
147#423—192no—
148#407—381no—
149C4×M16—381no—
150#400Dic1912yes—
151#399Dic1912yes—
152#395—21no—
153#393—21no—
154#389—21no—
155#382C2×D1911yescharacteristic
156#380—21no—
157#332—384no—
158#324—381no—
159#323—381no—
160C2×C19—21no—
161C2×C19—21no—
162C2×C19—81no—
163C2×C19#187311yescharacteristic
164C2×C19#191011yescharacteristic
165C2×C19#191511yescharacteristic
166C22×Q8—21no—
167C23×C4C22⋊D1911yescharacteristic
168C2×M16—382no—
169C4⋊Q8—22no—
170C4⋊Q8—22no—
171#117—22no—
172#117—22no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4C2×Dic1912yes—
177C2×C4⋊C4C2×Dic1911yescharacteristic
178C2×C4⋊C4C22⋊D1911yescharacteristic
179C2×C22⋊C4—22no—
180C2×C22⋊C4C2×Dic1911yescharacteristic
181C2×C22⋊C4C22⋊D1911yescharacteristic
182C2×C42C22⋊D1911yescharacteristic
183C2×C42C22×D1911yescharacteristic
184C4⋊C8—194no—
185C4⋊C8—382no—
186C4⋊C8—382no—
187C22⋊C8—384no—
188C22⋊C8—382no—
189#97—382no—
190C4×C8—382no—
191C4×C8—382no—
192#95—22no—
193#95—22no—
194#95—21no—
195#95C2×Dic1912yes—
196C19#919411yescharacteristic, complemented, Sylow
197C24C22⋊Dic1911yescharacteristic
198C2×Q8—42no—
199C2×Q8—82no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4C22⋊Dic1911yescharacteristic
207C22×C4C22⋊Dic1911yescharacteristic
208C22×C4C22⋊Dic1911yescharacteristic
209C22×C4C22×Dic1911yescharacteristic
210C22×C4C2×C22⋊D1911yescharacteristic
211C22×C4C2×C22⋊D1911yescharacteristic
212M16—762no—
213M16—762no—
214C2×C8—384no—
215C2×C8—762no—
216C4⋊C4—22no—
217C4⋊C4—22no—
218C4⋊C4—24no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—42no—
222C4⋊C4—82no—
223C22⋊C4—22no—
224C22⋊C4—22no—
225C22⋊C4—82no—
226C42—21no—
227C42—21no—
228C42D4×D1912yes—
229C42#6454312yes—
230C23—21no—
231C23—21no—
232C23—21no—
233C23—41no—
234C23—41no—
235C23C2×C22⋊Dic1911yescharacteristic
236Q8—84no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4D4×Dic1912yes—
255C2×C4#1059738111yescharacteristic
256C2×C4#1059738311yescharacteristic
257C2×C4#1059738512yes—
258C2×C4#1059738812yes—
259C2×C4#1059739612yes—
260C8—764no—
261C8—1522no—
262C22—21no—
263C22—21no—
264C22—42no—
265C22—41no—
266C22—41no—
267C22—41no—
268C22—81no—
269C22#1192642411yescharacteristic
270C22#1192654011yescharacteristic
271C22#1192655311yescharacteristic
272C4—22no—
273C4—22no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—82no—
278C4—82no—
279C4#1192670412yes—
280C4#1192688212yes—
281C2—21no—
282C2—21no—
283C2—81no—
284C2#1456394811yescharacteristic
285C2#1456416311yescharacteristic
286C2#1456418811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2628C2
socleC22×C19#386
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#2628D19
hypocenterC19#9194
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2628

Complements

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

NH ≅ G/Ntype
2. #14562320C2semidirect
4. #14561493C2semidirect
196. C19#9194semidirect

Maximal subgroups

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

subgroupindex
#145722732
#145623202
#145619492
#145614932
C19×#26282
#919419