Finite Group Databasebeta

← #18076576

Subgroups — #18076576

Order 4864.

418 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 107 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#14564434C211yesmaximal, characteristic
2#14562421C212yesmaximal, complemented
3#14561956C211yesmaximal, characteristic
4#14561533C212yesmaximal, complemented
5C19×#2973C211yesmaximal, characteristic
6#11926597C2212yes—
7C2×C4⋊(C19⋊C8)C2211yescharacteristic
8C2×C22⋊(C19⋊C8)—21no—
9C2×C22⋊(C19⋊C8)—21no—
10C2×#10597260C2211yescharacteristic
11#11926296—22no—
12#11926294—22no—
13#11926268C412yes—
14#11926268C412yes—
15C2×C4×D4×C19C2211yescharacteristic
16C19×#435—22no—
17C19×#435—22no—
18C19×#432C2212yes—
19C19×#407—21no—
20C2×C19×C22⋊C8—21no—
21C22×D4×C19Q811yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19D411yescharacteristic
24C2×M16×C19—21no—
25C2×M16×C19—21no—
26C22×C8×C19—21no—
27C22×C8×C19—21no—
28C4×D4×C19—22no—
29C4×D4×C19—22no—
30C2×C4⋊C4×C19Q811yescharacteristic
31C2×C22⋊C4×C19C2×C411yescharacteristic
32C2×C22⋊C4×C19C2×C411yescharacteristic
33C2×C42×C19C2311yescharacteristic
34C22×C19⋊C8—21no—
35C22×C19⋊C8—21no—
36C19×C4⋊C8D412yes—
37C19×C4⋊C8D412yes—
38C19×C22⋊C8—22no—
39C19×C22⋊C8—22no—
40C19×C22⋊C8—22no—
41C19×#97—22no—
42C22⋊(C19⋊C8)—42no—
43C22⋊(C19⋊C8)—42no—
44C22⋊(C19⋊C8)C2×C414yes—
45C4⋊(C19⋊C8)—22no—
46C4⋊(C19⋊C8)—22no—
47#10597260—22no—
48C4×C19⋊C8—22no—
49C24×C19C4⋊C411yescharacteristic
50C24×C19C4⋊C411yescharacteristic
51C2×D4×C19—22no—
52C2×D4×C19—22no—
53C2×D4×C19—41no—
54C22×C4×C19—21no—
55C22×C4×C19—21no—
56C22×C4×C19—21no—
57C22×C4×C19—21no—
58C22×C4×C19—41no—
59C22×C4×C19—41no—
60C22×C4×C19—41no—
61C22×C4×C19—41no—
62C22×C4×C19C4⋊C411yescharacteristic
63C22×C4×C19C4⋊C411yescharacteristic
64C22×C4×C19C22×C411yescharacteristic
65C22×C4×C19C2×D411yescharacteristic
66C22×C4×C19C2×Q811yescharacteristic
67M16×C19—81no—
68M16×C19—81no—
69C2×C8×C19—22no—
70C2×C8×C19—22no—
71C2×C8×C19—81no—
72C2×C8×C19—81no—
73C4⋊C4×C19—22no—
74C22⋊C4×C19—22no—
75C22⋊C4×C19—22no—
76C42×C19C2×D412yes—
77C42×C19#4112yes—
78C2×C19⋊C8—22no—
79C2×C19⋊C8—24no—
80C2×C19⋊C8—41no—
81C2×C19⋊C8—41no—
82C2×C19⋊C8—41no—
83C2×C19⋊C8—41no—
84C2×C19⋊C8—41no—
85#8864—191nomaximal, Sylow
86C23×C19—21no—
87C23×C19—21no—
88C23×C19—21no—
89C23×C19—21no—
90C23×C19—21no—
91C23×C19—41no—
92C23×C19—41no—
93C23×C19—41no—
94C23×C19—41no—
95C23×C19#10812yes—
96C23×C19C2×C4⋊C411yescharacteristic
97D4×C19—44no—
98C2×C4×C19—21no—
99C2×C4×C19—21no—
100C2×C4×C19—21no—
101C2×C4×C19—21no—
102C2×C4×C19—21no—
103C2×C4×C19—21no—
104C2×C4×C19—41no—
105C2×C4×C19—41no—
106C2×C4×C19—41no—
107C2×C4×C19—41no—
108C2×C4×C19—41no—
109C2×C4×C19—41no—
110C2×C4×C19—41no—
111C2×C4×C19—81no—
112C2×C4×C19—81no—
113C2×C4×C19C4×D412yes—
114C2×C4×C19#12011yescharacteristic
115C2×C4×C19C22⋊Q812yes—
116C2×C4×C19#12311yescharacteristic
117C8×C19—42no—
118C8×C19—42no—
119C19⋊C8—44no—
120C19⋊C8—42no—
121C19⋊C8—81no—
122#2973D1911yescharacteristic
123#1955—191no—
124#1573—192no—
125#1460—191no—
126#1302—192no—
127C22×C19—21no—
128C22×C19—21no—
129C22×C19—22no—
130C22×C19—42no—
131C22×C19—42no—
132C22×C19—41no—
133C22×C19—41no—
134C22×C19—41no—
135C22×C19—41no—
136C22×C19—41no—
137C22×C19—81no—
138C22×C19—81no—
139C22×C19#38511yescharacteristic
140C22×C19C2×#10811yescharacteristic
141C22×C19#43011yescharacteristic
142C4×C19—22no—
143C4×C19—21no—
144C4×C19—22no—
145C4×C19—41no—
146C4×C19—41no—
147C4×C19#45311yescharacteristic
148C4×C19#45511yescharacteristic
149C2×C4×D4C2×D1911yescharacteristic
150#435—22no—
151#435—22no—
152#432C2×D1912yes—
153#431—192no—
154C2×C4⋊C8—191no—
155#407—21no—
156C2×C22⋊C8—21no—
157C2×C22⋊C8—381no—
158C2×C22⋊C8—381no—
159C2×#97—191no—
160#335—382no—
161#334—382no—
162#323—192no—
163#323—192no—
164C2×C19—21no—
165C2×C19—21no—
166C2×C19—42no—
167C2×C19—81no—
168C2×C19#185511yescharacteristic
169C2×C19#185611yescharacteristic
170C2×C19#186811yescharacteristic
171C22×D4Dic3811yescharacteristic
172C23×C4C22⋊D1911yescharacteristic
173C23×C4C22⋊D1911yescharacteristic
174C2×M16—21no—
175C2×M16—21no—
176C22×C8—21no—
177C22×C8—21no—
178C22×C8—381no—
179C22×C8—381no—
180C4×D4—22no—
181C4×D4—22no—
182C2×C4⋊C4Dic3811yescharacteristic
183C2×C22⋊C4C4×D1911yescharacteristic
184C2×C22⋊C4C4×D1911yescharacteristic
185C2×C42C22×D1911yescharacteristic
186C4⋊C8—382no—
187C4⋊C8—382no—
188C4⋊C8C22⋊D1912yes—
189C4⋊C8C22⋊D1912yes—
190C22⋊C8—22no—
191C22⋊C8—22no—
192C22⋊C8—22no—
193C22⋊C8—194no—
194C22⋊C8—762no—
195C22⋊C8—762no—
196#97—22no—
197#97—382no—
198C4×C8—382no—
199C19#886411yescharacteristic, complemented, Sylow
200C24Dic19⋊C411yescharacteristic
201C24Dic19⋊C411yescharacteristic
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—41no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4Dic19⋊C411yescharacteristic
214C22×C4Dic19⋊C411yescharacteristic
215C22×C4C2×Dic3811yescharacteristic
216C22×C4C2×C4×D1911yescharacteristic
217C22×C4C2×C22⋊D1911yescharacteristic
218M16—81no—
219M16—81no—
220C2×C8—22no—
221C2×C8—22no—
222C2×C8—81no—
223C2×C8—81no—
224C2×C8—382no—
225C2×C8—384no—
226C2×C8—761no—
227C2×C8—761no—
228C2×C8—761no—
229C2×C8—761no—
230C2×C8—761no—
231C4⋊C4—22no—
232C22⋊C4—22no—
233C22⋊C4—22no—
234C42#6454112yes—
235C42C2×C22⋊D1912yes—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23—41no—
242C23—41no—
243C23—41no—
244C23—41no—
245C23#1059727912yes—
246C23C2×Dic19⋊C411yescharacteristic
247D4—44no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4#1059737012yes—
264C2×C4C4×C22⋊D1912yes—
265C2×C4#1059737511yescharacteristic
266C2×C4#1059739911yescharacteristic
267C8—42no—
268C8—42no—
269C8—762no—
270C8—764no—
271C8—1521no—
272C22—21no—
273C22—21no—
274C22—22no—
275C22—42no—
276C22—42no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—81no—
283C22—81no—
284C22#1192641711yescharacteristic
285C22C2×#1059727911yescharacteristic
286C22#1192659211yescharacteristic
287C4—22no—
288C4—21no—
289C4—22no—
290C4—41no—
291C4—41no—
292C4#1192671211yescharacteristic
293C4#1192672211yescharacteristic
294C2—21no—
295C2—21no—
296C2—42no—
297C2—81no—
298C2#1456384011yescharacteristic
299C2#1456384511yescharacteristic
300C2#1456392111yescharacteristic
subgroupG/H
centerC2×C4#10597399
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2973C2
socleC22×C19#385
prime radicalC22×D4×C19Q8
cosocleC2×C42×C19C23
hypercenter#2973D19
hypocenterC19#8864
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #14562421C2semidirect
4. #14561533C2semidirect
199. C19#8864semidirect

Maximal subgroups

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

subgroupindex
#145644342
#145624212
#145619562
#145615332
C19×#29732
#886419