Finite Group Databasebeta

← #18078538

Subgroups — #18078538

Order 4864.

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

normal subgroups only

This group has 436 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#14572720C211yesmaximal, characteristic
2C4×#10597293C211yesmaximal, characteristic
3#14562237C212yesmaximal
4#14561499C212yesmaximal
5C19×#2634C211yesmaximal, characteristic
6#11926675—24no—
7#11926601—21no—
8#11926601C2212yes—
9#11926597—21no—
10C2×#10597293—21no—
11C4×#64520C2212yes—
12#11926313—21no—
13#11926286—24no—
14C2×C19×#125C2211yescharacteristic
15C2×C4×Q8×C19C2211yescharacteristic
16C19×#400—21no—
17C19×#400C411yescharacteristic
18C19×#400C411yescharacteristic
19C19×#398C411yescharacteristic
20C19×#398C411yescharacteristic
21C19×#395—21no—
22C19×#387—21no—
23C19×#387—21no—
24C19×#383C2211yescharacteristic
25C22×Q8×C19D411yescharacteristic
26C19×#125—22no—
27C19×#125—22no—
28C4×Q8×C19—22no—
29C4×Q8×C19—22no—
30C2×C4⋊C4×C19—21no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19C2×C411yescharacteristic
35C2×C4⋊C4×C19C2×C411yescharacteristic
36C2×C4⋊C4×C19C2×C411yescharacteristic
37C2×C4⋊C4×C19C2×C411yescharacteristic
38C2×C4⋊C4×C19D411yescharacteristic
39C2×C42×C19D411yescharacteristic
40C2×C42×C19D411yescharacteristic
41C2×C42×C19C2311yescharacteristic
42C2×#64520—22no—
43C19×#95—21no—
44C19×#95—21no—
45C19×#95—21no—
46C19×#95—21no—
47C19×#95—21no—
48C19×#95—21no—
49C19×#95—21no—
50C19×#95—21no—
51C19×#95C2×C411yescharacteristic
52C19×#95C2×C411yescharacteristic
53#10597293—24no—
54C22⋊(C19⋊C8)—22no—
55C4⋊(C19⋊C8)—22no—
56C4⋊(C19⋊C8)—22no—
57C4⋊(C19⋊C8)—22no—
58#10597260—22no—
59#10597260—22no—
60#10597260D414yes—
61C4×C19⋊C8—22no—
62C4×C19⋊C8—22no—
63C2×Q8×C19—22no—
64C2×Q8×C19—22no—
65C2×Q8×C19—41no—
66C22×C4×C19—21no—
67C22×C4×C19—21no—
68C22×C4×C19—21no—
69C22×C4×C19—21no—
70C22×C4×C19C22⋊C411yescharacteristic
71C22×C4×C19C22⋊C411yescharacteristic
72C22×C4×C19C22⋊C411yescharacteristic
73C22×C4×C19C22⋊C411yescharacteristic
74C22×C4×C19C22×C411yescharacteristic
75C22×C4×C19C2×D411yescharacteristic
76C22×C4×C19C2×D411yescharacteristic
77C4⋊C4×C19—22no—
78C4⋊C4×C19—22no—
79C4⋊C4×C19—22no—
80C4⋊C4×C19—22no—
81C4⋊C4×C19—22no—
82C4⋊C4×C19—42no—
83C4⋊C4×C19—42no—
84C4⋊C4×C19—41no—
85C4⋊C4×C19—42no—
86C4⋊C4×C19—41no—
87C42×C19—21no—
88C42×C19—21no—
89C42×C19—21no—
90C42×C19—21no—
91C42×C19C2×D412yes—
92C42×C19#4112yes—
93#64520—24no—
94#64520—42no—
95C2×C19⋊C8—24no—
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—41no—
114C2×C4×C19—41no—
115C2×C4×C19—41no—
116C2×C4×C19—41no—
117C2×C4×C19—42no—
118C2×C4×C19—41no—
119C2×C4×C19—41no—
120C2×C4×C19—41no—
121C2×C4×C19—41no—
122C2×C4×C19—41no—
123C2×C4×C19—41no—
124C2×C4×C19#10412yes—
125C2×C4×C19C4×D412yes—
126C2×C4×C19#12011yescharacteristic
127C2×C4×C19#12112yes—
128C2×C4×C19#12311yescharacteristic
129C19⋊C8—44no—
130C19⋊C8—44no—
131#2983—191no—
132#2634D1911yescharacteristic
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—
149C4×C19—81no—
150C4×C19—81no—
151C4×C19—81no—
152C4×C19—81no—
153C2×#125C2×D1911yescharacteristic
154C2×C4×Q8C2×D1911yescharacteristic
155#446—384no—
156#432—192no—
157#432—381no—
158#431—381no—
159C2×#101—381no—
160C4×M16—192no—
161#400—21no—
162#400Dic1911yescharacteristic
163#400Dic1911yescharacteristic
164#398Dic1911yescharacteristic
165#398Dic1911yescharacteristic
166#395—21no—
167#387—21no—
168#387—21no—
169#383C2×D1911yescharacteristic
170#343—381no—
171#330—384no—
172C2×C19—21no—
173C2×C19—21no—
174C2×C19#187111yescharacteristic
175C2×C19#191211yescharacteristic
176C2×C19#191511yescharacteristic
177C22×Q8C22⋊D1911yescharacteristic
178C2×M16—382no—
179#125—22no—
180#125—22no—
181C4×Q8—22no—
182C4×Q8—22no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4C2×Dic1911yescharacteristic
188C2×C4⋊C4C2×Dic1911yescharacteristic
189C2×C4⋊C4C2×Dic1911yescharacteristic
190C2×C4⋊C4C2×Dic1911yescharacteristic
191C2×C4⋊C4C22⋊D1911yescharacteristic
192C2×C42C22⋊D1911yescharacteristic
193C2×C42C22⋊D1911yescharacteristic
194C2×C42C22×D1911yescharacteristic
195C4⋊C8—382no—
196C4⋊C8—382no—
197C4⋊C8—382no—
198#101—384no—
199C22⋊C8—382no—
200#97—194no—
201#97—382no—
202#97—382no—
203C4×C8—382no—
204C4×C8—382no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95C2×Dic1911yescharacteristic
214#95C2×Dic1911yescharacteristic
215C19#919011yescharacteristic, complemented, Sylow
216C2×Q8—22no—
217C2×Q8—22no—
218C2×Q8—41no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4C22⋊Dic1911yescharacteristic
224C22×C4C22⋊Dic1911yescharacteristic
225C22×C4C22⋊Dic1911yescharacteristic
226C22×C4C22⋊Dic1911yescharacteristic
227C22×C4C22×Dic1911yescharacteristic
228C22×C4C2×C22⋊D1911yescharacteristic
229C22×C4C2×C22⋊D1911yescharacteristic
230M16—384no—
231M16—762no—
232C2×C8—384no—
233C2×C8—762no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—22no—
238C4⋊C4—22no—
239C4⋊C4—42no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42D4×D1912yes—
249C42#6454312yes—
250C23C2×C22⋊Dic1911yescharacteristic
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—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4#1059729412yes—
277C2×C4D4×Dic1912yes—
278C2×C4#1059738111yescharacteristic
279C2×C4#1059738311yescharacteristic
280C2×C4#1059738512yes—
281C8—764no—
282C8—764no—
283C22—21no—
284C22—21no—
285C22#1192642411yescharacteristic
286C22C2×#1059729411yescharacteristic
287C22#1192656111yescharacteristic
288C4—21no—
289C4—21no—
290C4—22no—
291C4—22no—
292C4—22no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—81no—
297C4—81no—
298C4—81no—
299C4—81no—
300C2—21no—
301C2—21no—
302C2#1456393811yescharacteristic
303C2#1456417311yescharacteristic
304C2#1456418811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2634C2
socleC22×C19#386
prime radicalC23×C19C2×C22⋊C4
cosocleC2×C42×C19C23
hypercenter#2634D19
hypocenterC19#9190
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2634

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
#145727202
C4×#105972932
#145622372
#145614992
C19×#26342
#919019