Finite Group Databasebeta

← #18069908

Subgroups — #18069908

Order 4864.

318 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 39 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#14563598C211yesmaximal, characteristic
2#14561573C211yesmaximal, characteristic, complemented
3C19×#1315C211yesmaximal, characteristic, complemented
4#11927380C411yescharacteristic
5#11926560—21no—
6#11926541—21no—
7#11926518C411yescharacteristic
8#11926326—21no—
9C19×#408C2211yescharacteristic
10C19×C22⋊C16—21no—
11C2×#41×C19C2×C411yescharacteristic
12#10597436—41no—
13#10597435—41no—
14#41×D19—42no—
15#10597433C812yes—
16#10597430—21no—
17#10597430—41no—
18C2×#64541—21no—
19C2×#64541—41no—
20C2×M16×C19D411yescharacteristic
21C22×C8×C19D411yescharacteristic
22#10597372—21no—
23C2×C16×C19—41no—
24C19×C22⋊C8—41no—
25#10597291—41no—
26#10597282—42no—
27#10597278—41no—
28#10597273—41no—
29#10597269—41no—
30#41×C19—41no—
31#41×C19—41no—
32C2×Q8×C19C2×C811yescharacteristic
33C2×D4×C19—21no—
34C2×D4×C19M1611yescharacteristic
35C22×C4×C19—21no—
36C22×C4×C19C22⋊C411yescharacteristic
37C2×C22⋊D19—42no—
38C2×C22⋊D19—41no—
39#64545—42no—
40Q8×D19—42no—
41#64543—42no—
42#64543—44no—
43D4×D19—42no—
44D4×D19—44no—
45#64541—22no—
46#64541—22no—
47#64541—41no—
48#64541—42no—
49#64541—41no—
50#64541—42no—
51#64541—42no—
52C2×D76—21no—
53C2×D76—41no—
54C2×C4×D19—41no—
55C2×C4×D19—42no—
56C2×Dic38—21no—
57C2×Dic38—41no—
58M16×C19—41no—
59C2×C8×C19—21no—
60C2×C8×C19—21no—
61C2×C8×C19—41no—
62C22⋊Dic19—41no—
63C4⋊Dic19—41no—
64C4×Dic19—41no—
65C16×C19—81no—
66C19⋊C16—81no—
67#7347—191nomaximal, Sylow
68C23×C19—21no—
69C23×C19#10011yescharacteristic
70C22×D19—41no—
71C22×D19—42no—
72Q8×C19—41no—
73D4×C19—41no—
74D4×C19—42no—
75C2×C4×C19—21no—
76C2×C4×C19—21no—
77C2×C4×C19—21no—
78C2×C4×C19—41no—
79C2×C4×C19—41no—
80C2×C4×C19C22⋊C811yescharacteristic
81C2×C4×C19#9911yescharacteristic
82C22⋊D19—42no—
83C22⋊D19—44no—
84C22⋊D19—42no—
85C2×Dic19—41no—
86C2×Dic19—42no—
87C2×Dic19—81no—
88D76—22no—
89D76—42no—
90D76—41no—
91C4×D19—42no—
92C4×D19—44no—
93C4×D19—42no—
94Dic38—22no—
95Dic38—41no—
96Dic38—42no—
97C8×C19—41no—
98C8×C19—41no—
99#1794—191no—
100#1321—191no—
101#1315D1911yescharacteristic, complemented
102C22×C19—21no—
103C22×C19—41no—
104C22×C19—41no—
105C22×C19—81no—
106C22×C19#32311yescharacteristic
107C2×D19—42no—
108C2×D19—161no—
109C2×D19—162no—
110C4×C19—21no—
111C4×C19—41no—
112C4×C19AΣL(1,𝔽16)11yescharacteristic
113C4×C19AΣL(1,𝔽16)11yescharacteristic
114Dic19—42no—
115Dic19—161no—
116#585—191no—
117#421—381no—
118#416—381no—
119#410—191no—
120#408C2×D1911yescharacteristic
121#349—381no—
122C22⋊C16—21no—
123C2×C19—21no—
124C2×C19—41no—
125C2×C19—81no—
126C2×C19#131611yescharacteristic
127D19—82no—
1282−1+4—192no—
1292−1+4—761no—
130H(5,𝔽2)—381no—
131H(5,𝔽2)—761no—
132H(5,𝔽2)—761no—
133C2×#41—381no—
134C2×#41—761no—
135C2×#41—762no—
136C2×#41C4×D1911yescharacteristic
137C2×M16D7611yescharacteristic
138C22×C8C22⋊D1911yescharacteristic
139#117—381no—
140M32—761no—
141C2×C16—41no—
142#104—762no—
143#103—761no—
144#102—761no—
145#99—761no—
146C22⋊C8—41no—
147C19#734711yescharacteristic, complemented, Sylow
148#41—41no—
149#41—41no—
150#41—382no—
151#41—382no—
152#41—761no—
153#41—762no—
154#41—762no—
155#41—762no—
156#41—762no—
157#41—764no—
158#41—762no—
159#41—761no—
160C2×Q8—381no—
161C2×Q8—761no—
162C2×Q8—762no—
163C2×Q8C8×D1911yescharacteristic
164C2×D4—21no—
165C2×D4—381no—
166C2×D4—761no—
167C2×D4—762no—
168C2×D4—764no—
169C2×D4—762no—
170C2×D4—761no—
171C2×D4#6451511yescharacteristic
172C22×C4—21no—
173C22×C4—761no—
174C22×C4—762no—
175C22×C4(C2×D19)⋊C411yescharacteristic
176M16—41no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8—41no—
180C4⋊C4—761no—
181C22⋊C4—761no—
182C42—761no—
183C16—81no—
184C16—1521no—
185C23—21no—
186C23—761no—
187C23—762no—
188C23#1059728011yescharacteristic
189Q8—41no—
190Q8—382no—
191Q8—762no—
192Q8—761no—
193D4—41no—
194D4—42no—
195D4—382no—
196D4—762no—
197D4—762no—
198D4—764no—
199D4—762no—
200D4—761no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—762no—
207C2×C4—764no—
208C2×C4—761no—
209C2×C4—762no—
210C2×C4—762no—
211C2×C4—1521no—
212C2×C4#1059726311yescharacteristic
213C2×C4(C2×D19)⋊C811yescharacteristic
214C8—41no—
215C8—41no—
216C22—21no—
217C22—41no—
218C22—41no—
219C22—81no—
220C22—3041no—
221C22—3042no—
222C22—762no—
223C22#1192626711yescharacteristic
224C4—21no—
225C4—41no—
226C4—3041no—
227C4—762no—
228C4#1192633011yescharacteristic
229C4#1192633211yescharacteristic
230C2—21no—
231C2—41no—
232C2—81no—
233C2—1522no—
234C2#1456156211yescharacteristic
subgroupG/H
centerC4#11926332
commutatorC2×Q8×C19C2×C8
Frattini#408C2×D19
FittingC19×#1315C2
socleC2×C19#1316
prime radical#11927380C4
cosocleC19×#408C22
hypercenter#1315D19
hypocenterC19#7347
LCSG ▷ C2×Q8×C19 ▷ C2×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #408 ◁ #1315

Complements

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

NH ≅ G/Ntype
2. #14561573C2semidirect
3. C19×#1315C2semidirect
101. #1315D19semidirect
147. C19#7347semidirect

Maximal subgroups

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

subgroupindex
#145635982
#145615732
C19×#13152
#734719