Finite Group Databasebeta

← #18069907

Subgroups — #18069907

Order 4864.

318 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 43 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#14561573C211yesmaximal, characteristic, complemented
2#14561561C211yesmaximal, characteristic, complemented
3C19×#1794C211yesmaximal, characteristic
4#11926326—21no—
5C22⋊(C19⋊C16)—21no—
6C19×#585C411yescharacteristic
7C19×#421—21no—
8C19×#416—21no—
9C19×#410C411yescharacteristic
10C19×#408C2211yescharacteristic
11C19×2−1+4—41no—
12C19×2−1+4C812yes—
13C19×H(5,𝔽2)—21no—
14C19×H(5,𝔽2)—41no—
15C19×H(5,𝔽2)—41no—
16C2×#41×C19—21no—
17C2×#41×C19—41no—
18C2×#41×C19—42no—
19C2×#41×C19C2×C411yescharacteristic
20C2×M16×C19D411yescharacteristic
21C22×C8×C19D411yescharacteristic
22C19×#117—21no—
23C19×#104—42no—
24C19×#103—41no—
25C19×#102—41no—
26C19×#99—41no—
27C19×C22⋊C8—41no—
28#10597269—41no—
29C2×C19⋊C16—41no—
30#41×C19—22no—
31#41×C19—22no—
32#41×C19—41no—
33#41×C19—42no—
34#41×C19—41no—
35#41×C19—41no—
36#41×C19—42no—
37#41×C19—42no—
38#41×C19—44no—
39#41×C19—42no—
40#41×C19—41no—
41#41×C19—42no—
42C2×Q8×C19—21no—
43C2×Q8×C19—42no—
44C2×Q8×C19—41no—
45C2×Q8×C19C2×C811yescharacteristic
46C2×D4×C19—21no—
47C2×D4×C19—21no—
48C2×D4×C19—42no—
49C2×D4×C19—42no—
50C2×D4×C19—44no—
51C2×D4×C19—41no—
52C2×D4×C19—41no—
53C2×D4×C19M1611yescharacteristic
54C22×C4×C19—21no—
55C22×C4×C19—41no—
56C22×C4×C19—42no—
57C22×C4×C19C22⋊C411yescharacteristic
58M16×C19—41no—
59C2×C8×C19—21no—
60C2×C8×C19—21no—
61C2×C8×C19—41no—
62C4⋊C4×C19—41no—
63C22⋊C4×C19—41no—
64C42×C19—41no—
65C19⋊C16—81no—
66C19⋊C16—81no—
67#7347—191nomaximal, Sylow
68C23×C19—21no—
69C23×C19—41no—
70C23×C19—42no—
71C23×C19#10011yescharacteristic
72Q8×C19—22no—
73Q8×C19—41no—
74Q8×C19—42no—
75Q8×C19—41no—
76D4×C19—22no—
77D4×C19—41no—
78D4×C19—42no—
79D4×C19—42no—
80D4×C19—42no—
81D4×C19—44no—
82D4×C19—42no—
83D4×C19—41no—
84C2×C4×C19—21no—
85C2×C4×C19—21no—
86C2×C4×C19—21no—
87C2×C4×C19—42no—
88C2×C4×C19—41no—
89C2×C4×C19—44no—
90C2×C4×C19—42no—
91C2×C4×C19—41no—
92C2×C4×C19—41no—
93C2×C4×C19—42no—
94C2×C4×C19—81no—
95C2×C4×C19C22⋊C811yescharacteristic
96C2×C4×C19#9911yescharacteristic
97C8×C19—41no—
98C8×C19—41no—
99#1794D1911yescharacteristic
100#1321—191no—
101#1315—191no—
102C22×C19—21no—
103C22×C19—41no—
104C22×C19—42no—
105C22×C19—41no—
106C22×C19—81no—
107C22×C19—161no—
108C22×C19—162no—
109C22×C19#32311yescharacteristic
110C4×C19—21no—
111C4×C19—41no—
112C4×C19—42no—
113C4×C19—161no—
114C4×C19AΣL(1,𝔽16)11yescharacteristic
115C4×C19AΣL(1,𝔽16)11yescharacteristic
116#585Dic1911yescharacteristic
117#421—21no—
118#416—21no—
119#410Dic1911yescharacteristic
120#408C2×D1911yescharacteristic
121#349—381no—
122C22⋊C16—381no—
123C2×C19—21no—
124C2×C19—41no—
125C2×C19—81no—
126C2×C19—82no—
127C2×C19#131611yescharacteristic
1282−1+4—41no—
1292−1+4C19⋊C812yes—
130H(5,𝔽2)—21no—
131H(5,𝔽2)—41no—
132H(5,𝔽2)—41no—
133C2×#41—21no—
134C2×#41—41no—
135C2×#41—42no—
136C2×#41C2×Dic1911yescharacteristic
137C2×M16C22⋊D1911yescharacteristic
138C22×C8C22⋊D1911yescharacteristic
139#117—21no—
140M32—761no—
141C2×C16—761no—
142#104—42no—
143#103—41no—
144#102—41no—
145#99—41no—
146C22⋊C8—41no—
147C19#734711yescharacteristic, complemented, Sylow
148#41—22no—
149#41—22no—
150#41—41no—
151#41—42no—
152#41—41no—
153#41—41no—
154#41—42no—
155#41—42no—
156#41—44no—
157#41—42no—
158#41—41no—
159#41—42no—
160C2×Q8—21no—
161C2×Q8—42no—
162C2×Q8—41no—
163C2×Q8C2×C19⋊C811yescharacteristic
164C2×D4—21no—
165C2×D4—21no—
166C2×D4—42no—
167C2×D4—42no—
168C2×D4—44no—
169C2×D4—41no—
170C2×D4—41no—
171C2×D4#6452011yescharacteristic
172C22×C4—21no—
173C22×C4—41no—
174C22×C4—42no—
175C22×C4C22⋊Dic1911yescharacteristic
176M16—41no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8—41no—
180C4⋊C4—41no—
181C22⋊C4—41no—
182C42—41no—
183C16—1521no—
184C16—1521no—
185C23—21no—
186C23—41no—
187C23—42no—
188C23#1059729011yescharacteristic
189Q8—22no—
190Q8—41no—
191Q8—42no—
192Q8—41no—
193D4—22no—
194D4—41no—
195D4—42no—
196D4—42no—
197D4—42no—
198D4—44no—
199D4—42no—
200D4—41no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—42no—
205C2×C4—41no—
206C2×C4—44no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—81no—
212C2×C4C22⋊(C19⋊C8)11yescharacteristic
213C2×C4#1059729111yescharacteristic
214C8—41no—
215C8—41no—
216C22—21no—
217C22—41no—
218C22—42no—
219C22—41no—
220C22—81no—
221C22—161no—
222C22—162no—
223C22#1192626811yescharacteristic
224C4—21no—
225C4—41no—
226C4—42no—
227C4—161no—
228C4#1192633111yescharacteristic
229C4#1192633111yescharacteristic
230C2—21no—
231C2—41no—
232C2—81no—
233C2—82no—
234C2#1456156311yescharacteristic
subgroupG/H
centerC4#11926331
commutatorC2×Q8×C19C2×C8
Frattini#408C2×D19
FittingC19×#1794C2
socleC2×C19#1316
prime radicalC19×#585C4
cosocleC19×#408C22
hypercenter#1794D19
hypocenterC19#7347
LCSG ▷ C2×Q8×C19 ▷ C2×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #408 ◁ #1794

Complements

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

NH ≅ G/Ntype
1. #14561573C2semidirect
2. #14561561C2semidirect
147. C19#7347semidirect

Maximal subgroups

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

subgroupindex
#145615732
#145615612
C19×#17942
#734719