Finite Group Databasebeta

← #18069211

Subgroups — #18069211

Order 4864.

338 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 49 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#14564633C211yesmaximal, characteristic
2#14561559C211yesmaximal, characteristic, complemented
3C19×#1289C211yesmaximal, characteristic, complemented
4C22×D152C411yescharacteristic, complemented
5C2×#10597376—21no—
6C2×#10597278—21no—
7C22⋊(C19⋊C16)—21no—
8#11926307C411yescharacteristic, complemented
9C2×C19×C22⋊C8C2211yescharacteristic
10C19×#380—21no—
11C23×C4×C19D411yescharacteristic
12C22×C22⋊D19—41no—
13C22×D76—21no—
14C22×C8×C19C2×C411yescharacteristic
15C22×C8×C19D411yescharacteristic
16C2×C4⋊C4×C19—41no—
17C2×C22⋊C4×C19—41no—
18#10597376—42no—
19#10597376—42no—
20C2×(C2×D19)⋊C4—41no—
21C2×C4⋊Dic19—21no—
22C2×D152—41no—
23C2×D152—42no—
24C19×C22⋊C8—41no—
25C19×#95—22no—
26#10597278—42no—
27C2×C19⋊C16—41no—
28C24×C19D811yescharacteristic
29C23×D19—41no—
30C22×C4×C19—21no—
31C22×C4×C19—21no—
32C22×C4×C19—41no—
33C22×C4×C19—41no—
34C22×C4×C19—42no—
35C22×C4×C19C22⋊C411yescharacteristic
36C22×C4×C19SD1611yescharacteristic
37C2×C22⋊D19—44no—
38C2×C22⋊D19—82no—
39C2×C22⋊D19—81no—
40C2×C22⋊D19—81no—
41C22×Dic19—41no—
42C2×D76—22no—
43C2×D76—41no—
44C2×D76—41no—
45C2×D76—41no—
46C2×D76—41no—
47C2×D76—41no—
48C2×C8×C19—21no—
49C2×C8×C19—21no—
50C2×C8×C19—41no—
51C2×C8×C19—41no—
52C4⋊C4×C19—81no—
53C4⋊C4×C19—81no—
54C22⋊C4×C19—81no—
55C22⋊C4×C19—81no—
56(C2×D19)⋊C4—44no—
57C4⋊Dic19—22no—
58C4⋊Dic19—41no—
59D152—42no—
60D152—42no—
61C19⋊C16—81no—
62#7076—191nomaximal, Sylow
63C23×C19—21no—
64C23×C19—21no—
65C23×C19—41no—
66C23×C19—41no—
67C23×C19#10211yescharacteristic
68C23×C19D1611yescharacteristic
69C23×C19SD3211yescharacteristic
70C22×D19—42no—
71C22×D19—81no—
72C22×D19—81no—
73C22×D19—81no—
74C22×D19—81no—
75C22×D19—81no—
76C22×D19—81no—
77C2×C4×C19—21no—
78C2×C4×C19—21no—
79C2×C4×C19—21no—
80C2×C4×C19—41no—
81C2×C4×C19—41no—
82C2×C4×C19—41no—
83C2×C4×C19—81no—
84C2×C4×C19—82no—
85C2×C4×C19—82no—
86C2×C4×C19—82no—
87C2×C4×C19#9911yescharacteristic
88C2×C4×C19#10411yescharacteristic
89C22⋊D19—84no—
90C22⋊D19—84no—
91C2×Dic19—42no—
92C2×Dic19—81no—
93C2×Dic19—81no—
94D76—42no—
95D76—42no—
96D76—81no—
97D76—81no—
98C8×C19—41no—
99C8×C19—41no—
100#1999—191no—
101#1314—191no—
102#1289D1911yescharacteristic, complemented
103C22×C19—21no—
104C22×C19—21no—
105C22×C19—21no—
106C22×C19—21no—
107C22×C19—41no—
108C22×C19—41no—
109C22×C19—41no—
110C22×C19—41no—
111C22×C19—81no—
112C22×C19#32711yescharacteristic
113C22×C19#35711yescharacteristic
114C22×C19#36011yescharacteristic
115C2×D19—82no—
116C2×D19—82no—
117C2×D19—82no—
118C2×D19—161no—
119C2×D19—161no—
120C2×D19—161no—
121C2×D19—161no—
122C4×C19—21no—
123C4×C19—41no—
124C4×C19—162no—
125C4×C19AΣL(1,𝔽16)11yescharacteristic
126C4×C19#35311yescharacteristic
127Dic19—82no—
128C22×D8—191no—
129C2×#121—381no—
130C2×#102—381no—
131C2×C22⋊C8C2×D1911yescharacteristic
132#380—21no—
133C22⋊C16—381no—
134#340—191no—
135C2×C19—21no—
136C2×C19—21no—
137C2×C19—41no—
138C2×C19—41no—
139C2×C19#133911yescharacteristic
140C2×C19#134311yescharacteristic
141C2×C19#134711yescharacteristic
142D19—162no—
143C22×D4—381no—
144C22×D4—761no—
145C23×C4C22⋊D1911yescharacteristic
146C2×D8—761no—
147C2×D8—762no—
148C22×C8C4×D1911yescharacteristic
149C22×C8D7611yescharacteristic
150#121—762no—
151#121—762no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—381no—
154C2×C22⋊C4—41no—
155C2×C22⋊C4—761no—
156C2×C16—761no—
157#102—762no—
158C22⋊C8—41no—
159#95—22no—
160C19#707611yescharacteristic, complemented, Sylow
161C24—761no—
162C24#6452511yescharacteristic
163C2×D4—382no—
164C2×D4—761no—
165C2×D4—761no—
166C2×D4—761no—
167C2×D4—764no—
168C2×D4—761no—
169C2×D4—761no—
170C2×D4—1522no—
171C2×D4—1521no—
172C2×D4—1521no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—42no—
178C22×C4—761no—
179C22×C4(C2×D19)⋊C411yescharacteristic
180C22×C4#6452711yescharacteristic
181D8—762no—
182D8—762no—
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—41no—
186C2×C8—41no—
187C4⋊C4—81no—
188C4⋊C4—81no—
189C4⋊C4—382no—
190C4⋊C4—761no—
191C22⋊C4—81no—
192C22⋊C4—81no—
193C22⋊C4—764no—
194C16—1521no—
195C23—21no—
196C23—21no—
197C23—41no—
198C23—41no—
199C23—762no—
200C23—1521no—
201C23—1521no—
202C23—1521no—
203C23—1521no—
204C23—1521no—
205C23—1521no—
206C23#1059726611yescharacteristic
207C23#1059728311yescharacteristic
208C23#1059728511yescharacteristic
209D4—762no—
210D4—762no—
211D4—1521no—
212D4—1524no—
213D4—1524no—
214D4—1521no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—81no—
222C2×C4—82no—
223C2×C4—82no—
224C2×C4—82no—
225C2×C4—762no—
226C2×C4—1521no—
227C2×C4—1521no—
228C2×C4#1059726211yescharacteristic
229C2×C4#1059726311yescharacteristic
230C8—41no—
231C8—41no—
232C22—21no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—41no—
237C22—41no—
238C22—41no—
239C22—41no—
240C22—81no—
241C22—3041no—
242C22—3041no—
243C22—3041no—
244C22—3041no—
245C22—1522no—
246C22—1522no—
247C22—1522no—
248C22#1192627711yescharacteristic
249C22#1192634411yescharacteristic
250C22#1192635311yescharacteristic
251C4—21no—
252C4—41no—
253C4—162no—
254C4—1522no—
255C4#1192633011yescharacteristic
256C4#1192633611yescharacteristic
257C2—21no—
258C2—21no—
259C2—41no—
260C2—41no—
261C2—3042no—
262C2#1456161911yescharacteristic
263C2#1456163111yescharacteristic
264C2#1456164311yescharacteristic
subgroupG/H
centerC22#11926277
commutatorC22×C8×C19C2×C4
FrattiniC2×C22⋊C8C2×D19
FittingC19×#1289C2
socleC22×C19#327
prime radical#14564633C2
cosocleC2×C19×C22⋊C8C22
hypercenter#1289D19
hypocenterC19#7076
LCSG ▷ C22×C8×C19 ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1289

Complements

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

NH ≅ G/Ntype
2. #14561559C2semidirect
3. C19×#1289C2semidirect
4. C22×D152C4semidirect
8. #11926307C4semidirect
102. #1289D19semidirect
160. C19#7076semidirect

Maximal subgroups

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

subgroupindex
#145646332
#145615592
C19×#12892
#707619