Finite Group Databasebeta

← #14565629

Subgroups — #14565629

Order 2432.

246 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 41 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#11927278C211yesmaximal, characteristic, complemented
2#11926734C211yesmaximal, characteristic, complemented
3#11926712C211yesmaximal, characteristic
4#11926336C211yesmaximal, characteristic, complemented
5#11926334C211yesmaximal, characteristic, complemented
6#11926333C211yesmaximal, characteristic, complemented
7C19×#458C211yesmaximal, characteristic, complemented
8C19×H(5,𝔽2)C2211yescharacteristic
9C19×#123—21no—
10C19×#123C2211yescharacteristic
11#10597395—21no—
12#10597386C2211yescharacteristic
13#10597381—21no—
14#10597381C2211yescharacteristic
15C4×C22⋊D19—21no—
16#10597340—21no—
17#10597333—21no—
18#10597331—21no—
19#10597331—21no—
20(C22⋊D19)⋊C4—21no—
21C19×#99—21no—
22C19×#99C2211yescharacteristic
23#10597294—21no—
24#10597291—21no—
25#10597291C2211yescharacteristic
26#10597290C2211yescharacteristic
27#41×C19—21no—
28#41×C19—41no—
29C2×D4×C19—21no—
30C2×D4×C19—21no—
31C2×D4×C19—41no—
32C2×D4×C19C2311yescharacteristic
33C22×C4×C19D411yescharacteristic
34C2×C22⋊D19—21no—
35C2×C22⋊D19—21no—
36C22×Dic19D411yescharacteristic
37C2×D76D411yescharacteristic
38C2×C4×D19—21no—
39C2×Dic38—21no—
40C4⋊C4×C19—21no—
41C4⋊C4×C19—41no—
42C22⋊C4×C19—21no—
43C22⋊C4×C19—21no—
44C22⋊C4×C19—41no—
45C22⋊C4×C19D411yescharacteristic
46C22⋊Dic19—21no—
47C22⋊Dic19—21no—
48C22⋊Dic19—41no—
49C22⋊Dic19D411yescharacteristic
50#64527—41no—
51#64525—41no—
52(C2×D19)⋊C4—21no—
53(C2×D19)⋊C4—21no—
54(C2×D19)⋊C4—21no—
55Dic19⋊C4—21no—
56Dic19⋊C4—21no—
57Dic19⋊C4—41no—
58C4×Dic19—21no—
59C4×Dic19—21no—
60C4×Dic19D411yescharacteristic
61#64520—21no—
62C23×C19—21no—
63C23×C19—21no—
64C23×C19C2×D411yescharacteristic
65C23×C19C2×D411yescharacteristic
66C22×D19—21no—
67Q8×C19—21no—
68D4×C19—21no—
69D4×C19—41no—
70D4×C19—41no—
71D4×C19—41no—
72D4×C19—41no—
73C2×C4×C19—21no—
74C2×C4×C19—21no—
75C2×C4×C19—21no—
76C2×C4×C19—21no—
77C2×C4×C19—41no—
78C2×C4×C19—41no—
79C2×C4×C19—41no—
80C2×C4×C19C2×D411yescharacteristic
81C22⋊D19—42no—
82C22⋊D19—42no—
83C2×Dic19—21no—
84C2×Dic19—21no—
85C2×Dic19—21no—
86C2×Dic19—41no—
87C2×Dic19—41no—
88D76—41no—
89C4×D19—81no—
90Dic38—42no—
91C19⋊C8—41no—
92#2198—191nomaximal, Sylow
93C22×C19—21no—
94C22×C19—21no—
95C22×C19—41no—
96C22×C19—41no—
97C22×C19—41no—
98C22×C19—81no—
99C22×C19—81no—
100C22×C19#12011yescharacteristic
101C2×D19—41no—
102C2×D19—41no—
103C2×D19—41no—
104C4×C19—21no—
105C4×C19—41no—
106C4×C19—41no—
107C4×C19—41no—
108C4×C19—81no—
109Dic19—22no—
110Dic19—41no—
111Dic19—41no—
112Dic19—81no—
113#559—191no—
114#458—191no—
115#458D1911yescharacteristic, complemented
116#453—191no—
117#353—191no—
118#352—191no—
119#352—191no—
120C2×C19—21no—
121C2×C19—41no—
122C2×C19—41no—
123C2×C19—81no—
124C2×C19B(4,𝔽2)11yescharacteristic
125D19—81no—
126H(5,𝔽2)C2×D1911yescharacteristic
127AGL(1,ℤ/8)—381no—
128#127—191no—
129#124—381no—
130#124—381no—
131#123—21no—
132#123—191no—
133#123—381no—
134#123—381no—
135#123C2×D1911yescharacteristic
136C4×Q8—381no—
137C4×D4—381no—
138C4×D4—381no—
139#104—381no—
140#100—191no—
141#99—21no—
142#99—191no—
143#99—381no—
144#99C2×D1911yescharacteristic
145C19#219811yescharacteristic, complemented, Sylow
146#41—21no—
147#41—41no—
148C2×Q8—381no—
149C2×D4—21no—
150C2×D4—21no—
151C2×D4—41no—
152C2×D4—191no—
153C2×D4—381no—
154C2×D4—381no—
155C2×D4C22×D1911yescharacteristic
156C22×C4—191no—
157C22×C4—381no—
158C22×C4C22⋊D1911yescharacteristic
159SD16—761no—
160D8—761no—
161M16—381no—
162C4⋊C4—21no—
163C4⋊C4—41no—
164C4⋊C4—381no—
165C4⋊C4—381no—
166C4⋊C4—761no—
167C22⋊C4—21no—
168C22⋊C4—21no—
169C22⋊C4—41no—
170C22⋊C4—191no—
171C22⋊C4—381no—
172C22⋊C4—381no—
173C22⋊C4—381no—
174C22⋊C4—381no—
175C22⋊C4—381no—
176C22⋊C4—761no—
177C22⋊C4C22⋊D1911yescharacteristic
178C42—191no—
179C42—381no—
180C42—381no—
181C23—21no—
182C23—21no—
183C23—381no—
184C23D4×D1911yescharacteristic
185C23C2×C22⋊D1911yescharacteristic
186Q8—21no—
187Q8—762no—
188D4—21no—
189D4—41no—
190D4—41no—
191D4—41no—
192D4—41no—
193D4—761no—
194D4—762no—
195D4—762no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—381no—
204C2×C4—381no—
205C2×C4—381no—
206C2×C4—761no—
207C2×C4—761no—
208C2×C4—1521no—
209C2×C4D4×D1911yescharacteristic
210C8—761no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—81no—
217C22—81no—
218C22—761no—
219C22—761no—
220C22—761no—
221C22#1059738311yescharacteristic
222C4—21no—
223C4—41no—
224C4—41no—
225C4—41no—
226C4—81no—
227C4—382no—
228C4—761no—
229C4—761no—
230C4—1521no—
231C2—21no—
232C2—41no—
233C2—41no—
234C2—81no—
235C2—1521no—
236C2#1192673011yescharacteristic
subgroupG/H
centerC2#11926730
commutator, cosocleC2×D4×C19C23
FrattiniC2×D4C22×D19
FittingC19×#458C2
socleC2×C19B(4,𝔽2)
prime radical#11926712C2
hypercenter#458D19
hypocenterC19#2198
LCSG ▷ C2×D4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #458

Complements

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

NH ≅ G/Ntype
1. #11927278C2semidirect
2. #11926734C2semidirect
4. #11926336C2semidirect
5. #11926334C2semidirect
6. #11926333C2semidirect
7. C19×#458C2semidirect
115. #458D19semidirect
145. C19#2198semidirect

Maximal subgroups

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

subgroupindex
#119272782
#119267342
#119267122
#119263362
#119263342
#119263332
C19×#4582
#219819