Finite Group Databasebeta

← #14574407

Subgroups — #14574407

Order 2432.

416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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×#10597370C211yesmaximal, characteristic
2#11926879C212yesmaximal, complemented
3#11926877C212yesmaximal, complemented
4#11926783C214yesmaximal, complemented
5#11926700C212yesmaximal, complemented
6#11926699C212yesmaximal, complemented
7C2×C22⋊(C19⋊C8)C211yesmaximal, characteristic
8C2×C19×C22⋊Q8C211yesmaximal, characteristic
9C22×Q8×C19C2211yescharacteristic
10C23×C4×C19C2211yescharacteristic
11C22×Dic38C2211yescharacteristic
12C19×C22⋊Q8—21no—
13C19×C22⋊Q8—21no—
14C19×C22⋊Q8C2212yes—
15C19×C22⋊Q8C2212yes—
16C2×C4⋊C4×C19—21no—
17C2×C4⋊C4×C19C2211yescharacteristic
18C2×C22⋊C4×C19—21no—
19C2×C22⋊Dic19—21no—
20C2×#64528C2214yescomplemented
21C2×C4⋊Dic19C2211yescharacteristic
22#10597370—21no—
23#10597370—21no—
24#10597370C2212yes—
25#10597370C2212yes—
26C2×Dic19⋊C4—21no—
27C22×C19⋊C8C2212yes—
28#10597292C2214yescomplemented
29C22⋊(C19⋊C8)C2212yes—
30C22⋊(C19⋊C8)C2212yes—
31#10597267C2214yescomplemented
32#10597264C2214yescomplemented
33C24×C19D411yescharacteristic
34C2×Q8×C19—21no—
35C2×Q8×C19—42no—
36C2×Q8×C19C2312yes—
37C22×C4×C19—21no—
38C22×C4×C19—21no—
39C22×C4×C19—42no—
40C22×C4×C19D411yescharacteristic
41C22×C4×C19D411yescharacteristic
42C22×C4×C19D411yescharacteristic
43C22×C4×C19C2311yescharacteristic
44C22×C4×C19C2311yescharacteristic
45C22×C4×C19C2311yescharacteristic
46C22×Dic19—21no—
47C22×Dic19—21no—
48C2×Dic38—21no—
49C2×Dic38—42no—
50C2×Dic38C2312yes—
51C4⋊C4×C19—22no—
52C4⋊C4×C19—22no—
53C4⋊C4×C19—21no—
54C4⋊C4×C19C2312yes—
55C22⋊C4×C19—22no—
56C22⋊C4×C19—22no—
57C22⋊Dic19—22no—
58C22⋊Dic19—22no—
59#64528—44no—
60C4⋊Dic19—21no—
61C4⋊Dic19C2312yes—
62Dic19⋊C4—22no—
63Dic19⋊C4—22no—
64C2×C19⋊C8—42no—
65C2×C19⋊C8C2314yes—
66C23×C19—41no—
67C23×C19—41no—
68C23×C19Q1614yescomplemented
69C23×C19C2×D411yescharacteristic
70C23×C19C2×D411yescharacteristic
71C23×C19C2×D411yescharacteristic
72Q8×C19—24no—
73Q8×C19—42no—
74C2×C4×C19—22no—
75C2×C4×C19—22no—
76C2×C4×C19—22no—
77C2×C4×C19—22no—
78C2×C4×C19—22no—
79C2×C4×C19—41no—
80C2×C4×C19—41no—
81C2×C4×C19—41no—
82C2×C4×C19—42no—
83C2×C4×C19—42no—
84C2×C4×C19C2×D411yescharacteristic
85C2×C4×C19C2×D411yescharacteristic
86C2×C4×C19C2×D411yescharacteristic
87C2×C4×C19C2411yescharacteristic
88C2×Dic19—22no—
89C2×Dic19—22no—
90C2×Dic19—42no—
91C2×Dic19—42no—
92Dic38—24no—
93Dic38—42no—
94C19⋊C8—24no—
95#3189—191nomaximal, Sylow
96C22×C19—21no—
97C22×C19—21no—
98C22×C19—21no—
99C22×C19—21no—
100C22×C19—21no—
101C22×C19—21no—
102C22×C19—44no—
103C22×C19C2×Q1612yes—
104C22×C19C2×Q1612yes—
105C22×C19C2×Q1612yes—
106C22×C19C22×D411yescharacteristic
107C4×C19—21no—
108C4×C19—21no—
109C4×C19—21no—
110C4×C19—42no—
111C4×C19—42no—
112C4×C19H(5,𝔽2)12yes—
113Dic19—42no—
114Dic19—42no—
115C2×C22⋊Q8—191no—
116C2×C22⋊Q8D1911yescharacteristic
117#484—192no—
118#484—192no—
119#467—194no—
120#451—192no—
121#451—192no—
122C2×C22⋊C8—191no—
123C2×C19—22no—
124C2×C19—22no—
125C2×C19—22no—
126C2×C19#53411yescharacteristic
127C2×C19C22×Q1611yescharacteristic
128C2×C19#57511yescharacteristic
129C22×Q8—191no—
130C22×Q8C2×D1911yescharacteristic
131C23×C4C2×D1911yescharacteristic
132C2×Q16—194no—
133C22×C8—192no—
134C22⋊Q8—21no—
135C22⋊Q8—21no—
136C22⋊Q8—192no—
137C22⋊Q8—192no—
138C22⋊Q8—381no—
139C22⋊Q8—381no—
140C22⋊Q8C2×D1912yes—
141C22⋊Q8C2×D1912yes—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—191no—
144C2×C4⋊C4—381no—
145C2×C4⋊C4C2×D1911yescharacteristic
146C2×C22⋊C4—21no—
147C2×C22⋊C4—381no—
148#107—194no—
149#103—194no—
150#103—194no—
151C22⋊C8—192no—
152C22⋊C8—192no—
153C19#318911yescharacteristic, complemented, Sylow
154C24C22⋊D1911yescharacteristic
155C2×Q8—21no—
156C2×Q8—42no—
157C2×Q8—192no—
158C2×Q8—381no—
159C2×Q8—762no—
160C2×Q8C22×D1912yes—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—42no—
164C22×C4—381no—
165C22×C4—381no—
166C22×C4C22⋊D1911yescharacteristic
167C22×C4C22⋊D1911yescharacteristic
168C22×C4C22⋊D1911yescharacteristic
169C22×C4C22×D1911yescharacteristic
170C22×C4C22×D1911yescharacteristic
171C22×C4C22×D1911yescharacteristic
172Q16—764no—
173C2×C8—194no—
174C2×C8—762no—
175C4⋊C4—22no—
176C4⋊C4—22no—
177C4⋊C4—21no—
178C4⋊C4—192no—
179C4⋊C4—382no—
180C4⋊C4—382no—
181C4⋊C4—381no—
182C4⋊C4C22×D1912yes—
183C22⋊C4—22no—
184C22⋊C4—22no—
185C22⋊C4—382no—
186C22⋊C4—382no—
187C23—41no—
188C23—41no—
189C23#6452814yescomplemented
190C23C2×C22⋊D1911yescharacteristic
191C23C2×C22⋊D1911yescharacteristic
192C23C2×C22⋊D1911yescharacteristic
193Q8—24no—
194Q8—42no—
195Q8—384no—
196Q8—762no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—382no—
208C2×C4—382no—
209C2×C4—762no—
210C2×C4—762no—
211C2×C4C2×C22⋊D1911yescharacteristic
212C2×C4C2×C22⋊D1911yescharacteristic
213C2×C4C2×C22⋊D1911yescharacteristic
214C2×C4C23×D1911yescharacteristic
215C8—384no—
216C22—21no—
217C22—21no—
218C22—21no—
219C22—21no—
220C22—21no—
221C22—21no—
222C22—44no—
223C22C2×#6452812yes—
224C22C2×#6452812yes—
225C22C2×#6452812yes—
226C22C22×C22⋊D1911yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—42no—
231C4—42no—
232C4—762no—
233C4—762no—
234C4#1059743012yes—
235C2—22no—
236C2—22no—
237C2—22no—
238C2#1192710311yescharacteristic
239C2C22×#6452811yescharacteristic
240C2#1192734211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC2×C19×C22⋊Q8C2
socleC22×C19C22×D4
prime radicalC24×C19D4
hypercenterC2×C22⋊Q8D19
hypocenterC19#3189
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11926879C2semidirect
3. #11926877C2semidirect
4. #11926783C2semidirect
5. #11926700C2semidirect
6. #11926699C2semidirect
20. C2×#64528C22semidirect
28. #10597292C22semidirect
31. #10597267C22semidirect
32. #10597264C22semidirect
68. C23×C19Q16semidirect
153. C19#3189semidirect
189. C23#64528semidirect

Maximal subgroups

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

subgroupindex
C2×#105973702
#119268792
#119268772
#119267832
#119267002
#119266992
C2×C22⋊(C19⋊C8)2
C2×C19×C22⋊Q82
#318919