Finite Group Databasebeta

← #18070271

Subgroups — #18070271

Order 4864.

262 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 59 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#14564029C211yesmaximal, characteristic
2#14562361C211yesmaximal, characteristic
3C2×C19×#356C211yesmaximal, characteristic
4#11927022C411yescharacteristic
5#11926601—21no—
6#11926553—21no—
7C2×#10597293C411yescharacteristic
8#11926304—21no—
9#11926293—21no—
10#11926293C412yescomplemented
11C2×C19×C4⋊Q8C2211yescharacteristic
12C2×C19×#101—21no—
13C19×#356—21no—
14C19×#356C412yescomplemented
15C22×Q8×C19C2×C411yescharacteristic
16C22×Q8×C19D411yescharacteristic
17C2×M16×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—
29C19×#101—22no—
30C19×#101—41no—
31#10597293—41no—
32#10597292—42no—
33C22⋊(C19⋊C8)—41no—
34C4⋊(C19⋊C8)—22no—
35#10597260—41no—
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
50M16×C19—42no—
51M16×C19—81no—
52C2×C8×C19—81no—
53C4⋊C4×C19—41no—
54C4⋊C4×C19—41no—
55C4⋊C4×C19—41no—
56C4⋊C4×C19—41no—
57C42×C19—21no—
58C42×C19C22⋊C411yescharacteristic
59C42×C19C4⋊C411yescharacteristic
60C22⋊Dic19—41no—
61C4⋊Dic19—22no—
62C4⋊Dic19—42no—
63C4×Dic19—41no—
64C4×Dic19—42no—
65#64520—41no—
66#64520—41no—
67C2×C19⋊C8—42no—
68C2×C19⋊C8—41no—
69#7483—191nomaximal, Sylow
70C23×C19#9911yescharacteristic
71Q8×C19—41no—
72Q8×C19—41no—
73Q8×C19—41no—
74Q8×C19—41no—
75Q8×C19—42no—
76Q8×C19—81no—
77C2×C4×C19—21no—
78C2×C4×C19—21no—
79C2×C4×C19—21no—
80C2×C4×C19—21no—
81C2×C4×C19—21no—
82C2×C4×C19—21no—
83C2×C4×C19—21no—
84C2×C4×C19—21no—
85C2×C4×C19—42no—
86C2×C4×C19—41no—
87C2×C4×C19—41no—
88C2×C4×C19—41no—
89C2×C4×C19—41no—
90C2×C4×C19#9511yescharacteristic
91C2×C4×C19#9911yescharacteristic
92C2×Dic19—42no—
93C8×C19—82no—
94C19⋊C8—82no—
95C19⋊C8—81no—
96C2×#356D1911yescharacteristic
97#1886—191no—
98#1558—191no—
99C22×C19—41no—
100C22×C19#34211yescharacteristic
101C22×C19AΣL(1,𝔽16)11yescharacteristic
102C22×C19#35211yescharacteristic
103C4×C19—22no—
104C4×C19—21no—
105C4×C19—21no—
106C4×C19—41no—
107C4×C19—41no—
108C4×C19—41no—
109C4×C19—41no—
110C4×C19—41no—
111Dic19—82no—
112C2×C4⋊Q8C2×D1911yescharacteristic
113#519—191no—
114#432—381no—
115#419—381no—
116C2×#101—21no—
117C2×#101—191no—
118#356—21no—
119#356Dic1912yescomplemented
120#339—381no—
121#333—192no—
122#333—381no—
123C2×C19—21no—
124C2×C19—21no—
125C2×C19—21no—
126C2×C19#139011yescharacteristic
127C22×Q8C4×D1911yescharacteristic
128C22×Q8C22⋊D1911yescharacteristic
129C2×M16—41no—
130C2×M16—381no—
131C4⋊Q8—41no—
132C4⋊Q8Dic3811yescharacteristic
133C4⋊Q8C4×D1911yescharacteristic
134C4⋊Q8C2×Dic1911yescharacteristic
135C4⋊Q8C22⋊D1911yescharacteristic
136C4×Q8—762no—
137#117—381no—
138#117—761no—
139C2×C4⋊C4—41no—
140C2×C42D7611yescharacteristic
141C4⋊C8—382no—
142#103—762no—
143#101—22no—
144#101—41no—
145#101—761no—
146C22⋊C8—761no—
147#97—761no—
148C19#748311yescharacteristic, complemented, Sylow
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—41no—
152C2×Q8—41no—
153C2×Q8—41no—
154C2×Q8—41no—
155C2×Q8C4×Dic1911yescharacteristic
156C2×Q8Dic19⋊C411yescharacteristic
157C2×Q8Dic19⋊C411yescharacteristic
158C2×Q8C22⋊Dic1911yescharacteristic
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4(C2×D19)⋊C411yescharacteristic
163M16—42no—
164M16—81no—
165M16—761no—
166M16—761no—
167C2×C8—81no—
168C2×C8—762no—
169C2×C8—761no—
170C4⋊C4—41no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—382no—
175C4⋊C4—762no—
176C22⋊C4—761no—
177C42—21no—
178C42—761no—
179C42—762no—
180C42C4⋊Dic1911yescharacteristic
181C42(C2×D19)⋊C411yescharacteristic
182C23#1059726311yescharacteristic
183Q8—41no—
184Q8—41no—
185Q8—41no—
186Q8—41no—
187Q8—42no—
188Q8—81no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—42no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—762no—
203C2×C4#1059726311yescharacteristic
204C2×C4C19⋊#9511yescharacteristic
205C8—82no—
206C8—1521no—
207C8—1522no—
208C22—41no—
209C22#1192631011yescharacteristic
210C22#1192633011yescharacteristic
211C22#1192633311yescharacteristic
212C4—22no—
213C4—21no—
214C4—21no—
215C4—41no—
216C4—41no—
217C4—41no—
218C4—41no—
219C4—41no—
220C4—1522no—
221C2—21no—
222C2—21no—
223C2—21no—
224C2#1456175211yescharacteristic
subgroupG/H
centerC2#14561752
commutatorC2×Q8×C19C42
FrattiniC2×C4⋊Q8C2×D19
FittingC2×C19×#356C2
socleC2×C19#1390
prime radicalC23×C19#99
cosocleC2×C19×C4⋊Q8C22
hypercenterC2×#356D19
hypocenterC19#7483
LCSG ▷ C2×Q8×C19 ▷ C2×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊Q8 ◁ C2×#356

Complements

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

NH ≅ G/Ntype
10. #11926293C4semidirect
14. C19×#356C4semidirect
119. #356Dic19semidirect
148. C19#7483semidirect

Maximal subgroups

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

subgroupindex
#145640292
#145623612
C2×C19×#3562
#748319