Finite Group Databasebeta

← #18078537

Subgroups — #18078537

Order 4864.

436 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 103 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#14569511C211yesmaximal, characteristic
2C4×#10597293C211yesmaximal, characteristic
3#14562238C212yesmaximal
4#14561501C212yesmaximal
5C19×#2983C211yesmaximal, characteristic
6C2×#10597316C2211yescharacteristic
7C2×#10597293—21no—
8C4×#64520C2212yes—
9#11926483C411yescharacteristic
10#11926483C411yescharacteristic
11#11926482—21no—
12#11926474C411yescharacteristic
13#11926474C411yescharacteristic
14#11926463—21no—
15#11926428—21no—
16#11926428—21no—
17#11926412C2211yescharacteristic
18#11926313—21no—
19#11926285—24no—
20C2×C4×Q8×C19C2211yescharacteristic
21C19×#446—24no—
22C19×#432—21no—
23C19×#432C2212yes—
24C19×#431—21no—
25C22×Q8×C19D411yescharacteristic
26C4×Q8×C19—22no—
27C4×Q8×C19—22no—
28C2×C4⋊C4×C19C2×C411yescharacteristic
29C2×C4⋊C4×C19C2×C411yescharacteristic
30C2×C4⋊C4×C19D411yescharacteristic
31C2×C42×C19D411yescharacteristic
32C2×C42×C19D411yescharacteristic
33C2×C42×C19C2311yescharacteristic
34C2×C4⋊Dic19C2×C411yescharacteristic
35C2×C4⋊Dic19C2×C411yescharacteristic
36C2×Dic19⋊C4—21no—
37C2×Dic19⋊C4—21no—
38C2×Dic19⋊C4—21no—
39C2×Dic19⋊C4—21no—
40C2×#64520—22no—
41#10597316—22no—
42#10597316—22no—
43C19×C4⋊C8—22no—
44C19×C4⋊C8—22no—
45C19×C4⋊C8—22no—
46C19×C22⋊C8—22no—
47C19×#97—22no—
48C19×#97D414yes—
49C4×C8×C19—22no—
50#10597293—24no—
51C19⋊#95—21no—
52C19⋊#95—21no—
53C19⋊#95—21no—
54C19⋊#95—21no—
55C19⋊#95—21no—
56C19⋊#95—21no—
57C19⋊#95—21no—
58C19⋊#95—21no—
59C19⋊#95C2×C411yescharacteristic
60C19⋊#95C2×C411yescharacteristic
61#10597260—22no—
62C4×C19⋊C8—22no—
63C2×Q8×C19—22no—
64C2×Q8×C19—22no—
65C2×Q8×C19—41no—
66C22×C4×C19C22⋊C411yescharacteristic
67C22×C4×C19C22⋊C411yescharacteristic
68C22×C4×C19C22⋊C411yescharacteristic
69C22×C4×C19C22⋊C411yescharacteristic
70C22×C4×C19C22×C411yescharacteristic
71C22×C4×C19C2×D411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C22×Dic19—21no—
74C22×Dic19—21no—
75C22×Dic19—21no—
76C22×Dic19—21no—
77C2×C8×C19—24no—
78C4⋊C4×C19—22no—
79C4⋊C4×C19—22no—
80C4⋊C4×C19—22no—
81C42×C19—21no—
82C42×C19—21no—
83C42×C19—21no—
84C42×C19—21no—
85C42×C19C2×D412yes—
86C42×C19#4112yes—
87C4⋊Dic19—22no—
88C4⋊Dic19—22no—
89Dic19⋊C4—42no—
90Dic19⋊C4—42no—
91Dic19⋊C4—41no—
92Dic19⋊C4—42no—
93Dic19⋊C4—41no—
94#64520—24no—
95#64520—42no—
96C2×C19⋊C8—42no—
97#9190—191nomaximal, Sylow
98C23×C19C2×C22⋊C411yescharacteristic
99Q8×C19—44no—
100C2×C4×C19—21no—
101C2×C4×C19—21no—
102C2×C4×C19—21no—
103C2×C4×C19—21no—
104C2×C4×C19—21no—
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—41no—
110C2×C4×C19—41no—
111C2×C4×C19—41no—
112C2×C4×C19—41no—
113C2×C4×C19#10412yes—
114C2×C4×C19C4×D412yes—
115C2×C4×C19#12011yescharacteristic
116C2×C4×C19#12112yes—
117C2×C4×C19#12311yescharacteristic
118C2×Dic19—41no—
119C2×Dic19—41no—
120C2×Dic19—41no—
121C2×Dic19—41no—
122C2×Dic19—42no—
123C2×Dic19—41no—
124C2×Dic19—41no—
125C2×Dic19—41no—
126C2×Dic19—41no—
127C2×Dic19—41no—
128C2×Dic19—41no—
129C8×C19—44no—
130C19⋊C8—44no—
131#2983D1911yescharacteristic
132#2634—191no—
133C4×#101—191no—
134#1528—192no—
135#1288—192no—
136C22×C19—21no—
137C22×C19—21no—
138C22×C19#38611yescharacteristic
139C22×C19C2×#10411yescharacteristic
140C22×C19#42111yescharacteristic
141C4×C19—22no—
142C4×C19—22no—
143C4×C19—21no—
144C4×C19—21no—
145C4×C19—22no—
146C4×C19—41no—
147C4×C19—41no—
148C4×C19—41no—
149Dic19—81no—
150Dic19—81no—
151Dic19—81no—
152Dic19—81no—
153C2×#125—191no—
154C2×C4×Q8C2×D1911yescharacteristic
155#446—24no—
156#432—21no—
157#432C2×D1912yes—
158#431—21no—
159C2×#101—381no—
160C4×M16—192no—
161#400—191no—
162#400—191no—
163#400—381no—
164#398—191no—
165#398—191no—
166#395—381no—
167#387—381no—
168#387—381no—
169#383—191no—
170#343—381no—
171#330—384no—
172C2×C19—21no—
173C2×C19—21no—
174C2×C19#187111yescharacteristic
175C2×C19#191211yescharacteristic
176C2×C19#191511yescharacteristic
177C22×Q8D7611yescharacteristic
178C2×M16—382no—
179#125—382no—
180#125—382no—
181C4×Q8—22no—
182C4×Q8—22no—
183C2×C4⋊C4—191no—
184C2×C4⋊C4—191no—
185C2×C4⋊C4—381no—
186C2×C4⋊C4—381no—
187C2×C4⋊C4—381no—
188C2×C4⋊C4—381no—
189C2×C4⋊C4C4×D1911yescharacteristic
190C2×C4⋊C4C4×D1911yescharacteristic
191C2×C4⋊C4D7611yescharacteristic
192C2×C42C22⋊D1911yescharacteristic
193C2×C42C22⋊D1911yescharacteristic
194C2×C42C22×D1911yescharacteristic
195C4⋊C8—22no—
196C4⋊C8—22no—
197C4⋊C8—22no—
198#101—384no—
199C22⋊C8—22no—
200#97—22no—
201#97—382no—
202#97C22⋊D1914yes—
203C4×C8—22no—
204C4×C8—382no—
205#95—191no—
206#95—191no—
207#95—381no—
208#95—381no—
209#95—381no—
210#95—381no—
211#95—381no—
212#95—381no—
213#95—381no—
214#95—381no—
215C19#919011yescharacteristic, complemented, Sylow
216C2×Q8—22no—
217C2×Q8—22no—
218C2×Q8—41no—
219C22×C4—381no—
220C22×C4—381no—
221C22×C4—381no—
222C22×C4—381no—
223C22×C4(C2×D19)⋊C411yescharacteristic
224C22×C4(C2×D19)⋊C411yescharacteristic
225C22×C4(C2×D19)⋊C411yescharacteristic
226C22×C4(C2×D19)⋊C411yescharacteristic
227C22×C4C2×C4×D1911yescharacteristic
228C22×C4C2×D7611yescharacteristic
229C22×C4C2×C22⋊D1911yescharacteristic
230M16—384no—
231M16—762no—
232C2×C8—24no—
233C2×C8—762no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—382no—
238C4⋊C4—382no—
239C4⋊C4—762no—
240C4⋊C4—762no—
241C4⋊C4—761no—
242C4⋊C4—762no—
243C4⋊C4—761no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42#6454112yes—
249C42C2×C22⋊D1912yes—
250C23C2×(C2×D19)⋊C411yescharacteristic
251Q8—44no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—761no—
266C2×C4—761no—
267C2×C4—761no—
268C2×C4—761no—
269C2×C4—762no—
270C2×C4—761no—
271C2×C4—761no—
272C2×C4—761no—
273C2×C4—761no—
274C2×C4—761no—
275C2×C4—761no—
276C2×C4#1059728212yes—
277C2×C4C4×C22⋊D1912yes—
278C2×C4#1059737511yescharacteristic
279C2×C4#1059737612yes—
280C2×C4#1059739911yescharacteristic
281C8—44no—
282C8—764no—
283C22—21no—
284C22—21no—
285C22#1192642311yescharacteristic
286C22C2×#1059728211yescharacteristic
287C22#1192656011yescharacteristic
288C4—21no—
289C4—21no—
290C4—22no—
291C4—22no—
292C4—22no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—1521no—
297C4—1521no—
298C4—1521no—
299C4—1521no—
300C2—21no—
301C2—21no—
302C2#1456393711yescharacteristic
303C2#1456417211yescharacteristic
304C2#1456418711yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2983C2
socleC22×C19#386
prime radicalC23×C19C2×C22⋊C4
cosocleC2×C42×C19C23
hypercenter#2983D19
hypocenterC19#9190
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
215. C19#9190semidirect

Maximal subgroups

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

subgroupindex
#145695112
C4×#105972932
#145622382
#145615012
C19×#29832
#919019