Finite Group Databasebeta

← #18070297

Subgroups — #18070297

Order 4864.

276 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C2×#11926343C211yesmaximal, characteristic
2#14564029C211yesmaximal, characteristic
3C2×C19×#333C211yesmaximal, characteristic
4#11927022C411yescharacteristic
5#11926553—21no—
6C2×#10597293—21no—
7C2×#10597293C411yescharacteristic
8#11926343—21no—
9#11926343C412yescomplemented
10#11926304—21no—
11C2×C19×C4⋊Q8C2211yescharacteristic
12C2×C19×C4⋊C8—21no—
13C19×#333—21no—
14C19×#333C412yescomplemented
15C22×Q8×C19C2×C411yescharacteristic
16C22×Q8×C19D411yescharacteristic
17C22×C8×C19—41no—
18C19×C4⋊Q8—41no—
19C19×C4⋊Q8C2×C411yescharacteristic
20C19×C4⋊Q8C2×C411yescharacteristic
21C19×C4⋊Q8D411yescharacteristic
22C19×C4⋊Q8Q811yescharacteristic
23C2×C4⋊C4×C19—41no—
24C2×C42×C19D411yescharacteristic
25Q8×Dic19—42no—
26#10597372—21no—
27#10597372—41no—
28C2×#64520—21no—
29C2×#64520—41no—
30C19×C4⋊C8—22no—
31C19×C4⋊C8—41no—
32#10597293—22no—
33#10597293—41no—
34#10597293—41no—
35#10597292—42no—
36C2×Q8×C19—21no—
37C2×Q8×C19—21no—
38C2×Q8×C19—41no—
39C2×Q8×C19—41no—
40C2×Q8×C19—41no—
41C2×Q8×C19—41no—
42C2×Q8×C19C4211yescharacteristic
43C2×Q8×C19C22⋊C411yescharacteristic
44C2×Q8×C19C4⋊C411yescharacteristic
45C2×Q8×C19C4⋊C411yescharacteristic
46C22×C4×C19—21no—
47C22×C4×C19—21no—
48C22×C4×C19—21no—
49C22×C4×C19C22⋊C411yescharacteristic
50C2×C8×C19—42no—
51C2×C8×C19—82no—
52C4⋊C4×C19—41no—
53C4⋊C4×C19—41no—
54C4⋊C4×C19—41no—
55C4⋊C4×C19—41no—
56C42×C19—21no—
57C42×C19C22⋊C411yescharacteristic
58C42×C19C4⋊C411yescharacteristic
59C22⋊Dic19—41no—
60C4⋊Dic19—22no—
61C4⋊Dic19—42no—
62C4×Dic19—41no—
63C4×Dic19—42no—
64#64520—42no—
65#64520—41no—
66#64520—41no—
67#64520—81no—
68C2×C19⋊C8—41no—
69C2×C19⋊C8—81no—
70#7491—191nomaximal, Sylow
71C23×C19#9911yescharacteristic
72Q8×C19—41no—
73Q8×C19—41no—
74Q8×C19—41no—
75Q8×C19—41no—
76Q8×C19—42no—
77Q8×C19—81no—
78C2×C4×C19—22no—
79C2×C4×C19—22no—
80C2×C4×C19—21no—
81C2×C4×C19—21no—
82C2×C4×C19—21no—
83C2×C4×C19—21no—
84C2×C4×C19—21no—
85C2×C4×C19—21no—
86C2×C4×C19—21no—
87C2×C4×C19—21no—
88C2×C4×C19—41no—
89C2×C4×C19—41no—
90C2×C4×C19—41no—
91C2×C4×C19—41no—
92C2×C4×C19#9511yescharacteristic
93C2×C4×C19#9911yescharacteristic
94C2×Dic19—42no—
95C8×C19—82no—
96C19⋊C8—81no—
97C19⋊C8—82no—
98C2×#356—191no—
99#1886—191no—
100C2×#333D1911yescharacteristic
101C22×C19—22no—
102C22×C19#34211yescharacteristic
103C22×C19AΣL(1,𝔽16)11yescharacteristic
104C22×C19#35211yescharacteristic
105C4×C19—21no—
106C4×C19—22no—
107C4×C19—21no—
108C4×C19—21no—
109C4×C19—21no—
110C4×C19—41no—
111C4×C19—41no—
112C4×C19—41no—
113C4×C19—41no—
114Dic19—82no—
115C2×C4⋊Q8C2×D1911yescharacteristic
116#519—191no—
117C2×C4⋊C8—21no—
118#419—381no—
119C2×#101—191no—
120C2×#101—381no—
121#356—192no—
122#356—381no—
123#339—381no—
124#333—21no—
125#333Dic1912yescomplemented
126C2×C19—21no—
127C2×C19—21no—
128C2×C19#139011yescharacteristic
129C2×C19#140512yes—
130C22×Q8C4×D1911yescharacteristic
131C22×Q8D7611yescharacteristic
132C2×M16—381no—
133C2×M16—761no—
134C22×C8—41no—
135C4⋊Q8—41no—
136C4⋊Q8Dic3811yescharacteristic
137C4⋊Q8C4×D1911yescharacteristic
138C4⋊Q8C2×Dic1911yescharacteristic
139C4⋊Q8C22⋊D1911yescharacteristic
140C4×Q8—762no—
141#117—381no—
142#117—761no—
143C2×C4⋊C4—41no—
144C2×C42C22⋊D1911yescharacteristic
145C4⋊C8—22no—
146C4⋊C8—41no—
147#103—762no—
148#101—382no—
149#101—761no—
150#101—761no—
151C19#749111yescharacteristic, complemented, Sylow
152C2×Q8—21no—
153C2×Q8—21no—
154C2×Q8—41no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8—41no—
158C2×Q8C4×Dic1911yescharacteristic
159C2×Q8Dic19⋊C411yescharacteristic
160C2×Q8C4⋊Dic1911yescharacteristic
161C2×Q8(C2×D19)⋊C411yescharacteristic
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4(C2×D19)⋊C411yescharacteristic
166M16—762no—
167M16—761no—
168M16—761no—
169M16—1521no—
170C2×C8—42no—
171C2×C8—82no—
172C2×C8—761no—
173C2×C8—1521no—
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C4⋊C4—382no—
179C4⋊C4—762no—
180C22⋊C4—761no—
181C42—21no—
182C42—761no—
183C42—762no—
184C42Dic19⋊C411yescharacteristic
185C42C22⋊Dic1911yescharacteristic
186C23#1059726311yescharacteristic
187Q8—41no—
188Q8—41no—
189Q8—41no—
190Q8—41no—
191Q8—42no—
192Q8—81no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—762no—
208C2×C4#1059726311yescharacteristic
209C2×C4C19⋊#9511yescharacteristic
210C8—82no—
211C8—1521no—
212C8—1522no—
213C22—22no—
214C22#1192631011yescharacteristic
215C22#1192633211yescharacteristic
216C22#1192633511yescharacteristic
217C4—21no—
218C4—22no—
219C4—21no—
220C4—21no—
221C4—21no—
222C4—41no—
223C4—41no—
224C4—41no—
225C4—41no—
226C4—1522no—
227C2—21no—
228C2—21no—
229C2#1456175411yescharacteristic
230C2#1456179012yes—
subgroupG/H
centerC22#11926332
commutatorC2×Q8×C19C42
FrattiniC2×C4⋊Q8C2×D19
FittingC2×C19×#333C2
socleC22×C19AΣL(1,𝔽16)
prime radicalC23×C19#99
cosocleC2×C19×C4⋊Q8C22
hypercenterC2×#333D19
hypocenterC19#7491
LCSG ▷ C2×Q8×C19 ▷ C2×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊Q8 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
9. #11926343C4semidirect
14. C19×#333C4semidirect
125. #333Dic19semidirect
151. C19#7491semidirect

Maximal subgroups

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

subgroupindex
C2×#119263432
#145640292
C2×C19×#3332
#749119