Finite Group Databasebeta

← #18080224

Subgroups — #18080224

Order 4864.

468 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 111 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#14572720C211yesmaximal, characteristic
2#14562361C212yesmaximal
3#14561979C211yesmaximal, characteristic
4#14561491C212yesmaximal
5C19×#2546C211yesmaximal, characteristic
6#11926675—24no—
7#11926601—21no—
8#11926601C2212yes—
9#11926601C2212yes—
10#11926597—21no—
11#11926293—24no—
12#11926270—21no—
13#11926270—21no—
14C2×C19×C4⋊Q8C412yes—
15C2×C19×C4⋊Q8C2211yescharacteristic
16C2×C4×Q8×C19C2211yescharacteristic
17C19×#398—21no—
18C19×#398—21no—
19C19×#391C412yes—
20C19×#389—21no—
21C19×#389—21no—
22C4×C4⋊C4×C19C2211yescharacteristic
23C22×Q8×C19C2×C412yes—
24C22×Q8×C19C2×C411yescharacteristic
25C19×C4⋊Q8—22no—
26C19×C4⋊Q8—22no—
27C19×C4⋊Q8—44no—
28C4×Q8×C19—22no—
29C4×Q8×C19—22no—
30C2×C4⋊C4×C19—21no—
31C2×C4⋊C4×C19—22no—
32C2×C4⋊C4×C19—22no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19C2×C411yescharacteristic
36C2×C4⋊C4×C19D411yescharacteristic
37C2×C4⋊C4×C19D411yescharacteristic
38C2×C42×C19C2×C412yes—
39C2×C42×C19D411yescharacteristic
40C2×C42×C19D411yescharacteristic
41C2×C42×C19C2311yescharacteristic
42C19×#95—22no—
43C19×#95—22no—
44C19×#95—21no—
45C22⋊(C19⋊C8)—22no—
46C22⋊(C19⋊C8)—22no—
47C4⋊(C19⋊C8)—22no—
48C4⋊(C19⋊C8)—22no—
49C4⋊(C19⋊C8)—22no—
50C4⋊(C19⋊C8)D414yes—
51#10597260—22no—
52#10597260—22no—
53#10597260—22no—
54C4×C19⋊C8—22no—
55C2×Q8×C19—22no—
56C2×Q8×C19—22no—
57C2×Q8×C19—24no—
58C2×Q8×C19—41no—
59C2×Q8×C19—42no—
60C2×Q8×C19—42no—
61C22×C4×C19—22no—
62C22×C4×C19—22no—
63C22×C4×C19C22⋊C411yescharacteristic
64C22×C4×C19C22⋊C411yescharacteristic
65C22×C4×C19C22⋊C411yescharacteristic
66C22×C4×C19C22⋊C411yescharacteristic
67C22×C4×C19C22×C411yescharacteristic
68C22×C4×C19C2×D411yescharacteristic
69C22×C4×C19C2×D411yescharacteristic
70C4⋊C4×C19—24no—
71C4⋊C4×C19—22no—
72C4⋊C4×C19—22no—
73C4⋊C4×C19—22no—
74C4⋊C4×C19—44no—
75C4⋊C4×C19—44no—
76C4⋊C4×C19—41no—
77C4⋊C4×C19—42no—
78C4⋊C4×C19—41no—
79C42×C19—21no—
80C42×C19—21no—
81C42×C19—21no—
82C42×C19—21no—
83C42×C19—42no—
84C42×C19C2×D412yes—
85C42×C19#4112yes—
86C2×C19⋊C8—24no—
87C2×C19⋊C8—42no—
88#9452—191nomaximal, Sylow
89C23×C19C2×C22⋊C411yescharacteristic
90Q8×C19—44no—
91Q8×C19—84no—
92C2×C4×C19—21no—
93C2×C4×C19—21no—
94C2×C4×C19—21no—
95C2×C4×C19—21no—
96C2×C4×C19—22no—
97C2×C4×C19—24no—
98C2×C4×C19—21no—
99C2×C4×C19—21no—
100C2×C4×C19—21no—
101C2×C4×C19—21no—
102C2×C4×C19—21no—
103C2×C4×C19—41no—
104C2×C4×C19—42no—
105C2×C4×C19—42no—
106C2×C4×C19—41no—
107C2×C4×C19—41no—
108C2×C4×C19—42no—
109C2×C4×C19—42no—
110C2×C4×C19—42no—
111C2×C4×C19#10012yes—
112C2×C4×C19C4×D412yes—
113C2×C4×C19#12011yescharacteristic
114C2×C4×C19#12112yes—
115C2×C4×C19#12311yescharacteristic
116C19⋊C8—44no—
117C19⋊C8—82no—
118#2983—191no—
119#2546D1911yescharacteristic
120#1558—192no—
121#1467—191no—
122#1285—192no—
123C22×C19—21no—
124C22×C19—21no—
125C22×C19#38611yescharacteristic
126C22×C19C2×#10011yescharacteristic
127C22×C19#41311yescharacteristic
128C4×C19—21no—
129C4×C19—22no—
130C4×C19—22no—
131C4×C19—22no—
132C4×C19—44no—
133C4×C19—41no—
134C4×C19—41no—
135C4×C19—41no—
136C4×C19—82no—
137C4×C19#45612yes—
138C2×C4⋊Q8Dic1912yes—
139C2×C4⋊Q8C2×D1911yescharacteristic
140C2×C4×Q8C2×D1911yescharacteristic
141#446—384no—
142#432—192no—
143#432—192no—
144#432—381no—
145#431—381no—
146#398—21no—
147#398—21no—
148#391Dic1912yes—
149#389—21no—
150#389—21no—
151C4×C4⋊C4C2×D1911yescharacteristic
152#333—384no—
153#324—381no—
154#324—381no—
155C2×C19—21no—
156C2×C19—21no—
157C2×C19#188611yescharacteristic
158C2×C19#190011yescharacteristic
159C2×C19#190911yescharacteristic
160C22×Q8C2×Dic1912yes—
161C22×Q8C2×Dic1911yescharacteristic
162C4⋊Q8—22no—
163C4⋊Q8—22no—
164C4⋊Q8—44no—
165C4×Q8—22no—
166C4×Q8—22no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4C2×Dic1911yescharacteristic
173C2×C4⋊C4C22⋊D1911yescharacteristic
174C2×C4⋊C4C22⋊D1911yescharacteristic
175C2×C42C2×Dic1912yes—
176C2×C42C22⋊D1911yescharacteristic
177C2×C42C22⋊D1911yescharacteristic
178C2×C42C22×D1911yescharacteristic
179C4⋊C8—194no—
180C4⋊C8—382no—
181C4⋊C8—382no—
182C4⋊C8—382no—
183C22⋊C8—382no—
184C22⋊C8—382no—
185#97—382no—
186#97—382no—
187#97—382no—
188C4×C8—382no—
189#95—22no—
190#95—22no—
191#95—21no—
192C19#945211yescharacteristic, complemented, Sylow
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—24no—
196C2×Q8—41no—
197C2×Q8—42no—
198C2×Q8—42no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4C22⋊Dic1911yescharacteristic
202C22×C4C22⋊Dic1911yescharacteristic
203C22×C4C22⋊Dic1911yescharacteristic
204C22×C4C22⋊Dic1911yescharacteristic
205C22×C4C22×Dic1911yescharacteristic
206C22×C4C2×C22⋊D1911yescharacteristic
207C22×C4C2×C22⋊D1911yescharacteristic
208C2×C8—384no—
209C2×C8—762no—
210C4⋊C4—24no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—22no—
214C4⋊C4—44no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—42no—
218C4⋊C4—44no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—42no—
224C42D4×D1912yes—
225C42#6454312yes—
226C23C2×C22⋊Dic1911yescharacteristic
227Q8—44no—
228Q8—84no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—24no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4#1059729012yes—
249C2×C4D4×Dic1912yes—
250C2×C4#1059738111yescharacteristic
251C2×C4#1059738311yescharacteristic
252C2×C4#1059738512yes—
253C8—764no—
254C8—1522no—
255C22—21no—
256C22—21no—
257C22#1192642411yescharacteristic
258C22C2×#1059729011yescharacteristic
259C22#1192652811yescharacteristic
260C4—22no—
261C4—22no—
262C4—22no—
263C4—21no—
264C4—44no—
265C4—41no—
266C4—41no—
267C4—41no—
268C4—82no—
269C4#1192672612yes—
270C2—21no—
271C2—21no—
272C2#1456402911yescharacteristic
273C2#1456409911yescharacteristic
274C2#1456415811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2546C2
socleC22×C19#386
prime radicalC23×C19C2×C22⋊C4
cosocleC2×C42×C19C23
hypercenter#2546D19
hypocenterC19#9452
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2546

Complements

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

NH ≅ G/Ntype
192. C19#9452semidirect

Maximal subgroups

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

subgroupindex
#145727202
#145623612
#145619792
#145614912
C19×#25462
#945219