Finite Group Databasebeta

← #14572097

Subgroups — #14572097

Order 2432.

716 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 209 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×#10597436C211yesmaximal, characteristic
2#11927021C212yesmaximal, complemented
3#11926518C211yesmaximal, characteristic, complemented
4#11926517C212yesmaximal, complemented
5#11926516C218yesmaximal, complemented
6C19×#410C211yesmaximal, characteristic, complemented
7C2×#41×C19C2211yescharacteristic
8#10597436—24no—
9#10597436—24no—
10C2×Q8×D19C412yescomplemented
11C2×#64543C412yescomplemented
12C2×#64543C2214yes—
13C2×#64541C412yescomplemented
14C2×#64541C2211yescharacteristic
15C22×Dic38C412yescomplemented
16C22×Dic38C2211yescharacteristic
17C19×#117C2212yes—
18#10597372C2212yes—
19#10597333—24no—
20#10597323C2218yes—
21C4×Dic38—24no—
22C19×#99C2214yes—
23#10597291C2214yes—
24#10597263C2218yes—
25#41×C19—22no—
26#41×C19—22no—
27C2×Q8×C19C2×C411yescharacteristic
28C2×D4×C19C2×C411yescharacteristic
29C2×D4×C19C2312yes—
30C22×C4×C19C2×C412yes—
31C22×C4×C19C2311yescharacteristic
32C2×C22⋊D19C2×C414yes—
33C2×C22⋊D19C2312yes—
34C22×Dic19C2×C414yes—
35C22×Dic19C2312yes—
36Q8×D19—28no—
37#64543—216no—
38#64543—28no—
39#64541—22no—
40#64541—22no—
41#64541—24no—
42#64541—24no—
43C2×D76C2×C411yescharacteristic
44C2×C4×D19C2×C414yes—
45C2×C4×D19C2×C412yes—
46C2×Dic38—24no—
47C2×Dic38—24no—
48C2×Dic38C2×C411yescharacteristic
49C2×Dic38C2×C414yes—
50C2×Dic38C2×C412yes—
51C2×Dic38C2×C412yes—
52C2×Dic38D414yes—
53C2×Dic38D414yes—
54C4⋊C4×C19—22no—
55C22⋊C4×C19C2314yes—
56C42×C19—22no—
57C22⋊Dic19C2314yes—
58C4⋊Dic19—22no—
59Dic19⋊C4—28no—
60C4×Dic19—22no—
61C4×Dic19—28no—
62C23×C19C22×C412yes—
63C23×C19C2411yescharacteristic
64C22×D19C22×C412yes—
65Q8×C19—22no—
66D4×C19—24no—
67D4×C19—22no—
68C2×C4×C19—22no—
69C2×C4×C19—22no—
70C2×C4×C19—24no—
71C2×C4×C19C22×C412yes—
72C2×C4×C19C22×C411yescharacteristic
73C2×C4×C19C22×C411yescharacteristic
74C2×C4×C19C2×D412yes—
75C2×C4×C19C2×D412yes—
76C22⋊D19—24no—
77C22⋊D19—28no—
78C2×Dic19—28no—
79C2×Dic19—24no—
80C2×Dic19C22×C412yes—
81C2×Dic19C22×C414yes—
82C2×Dic19C2×D418yes—
83D76—21no—
84D76—21no—
85C4×D19—24no—
86C4×D19—28no—
87Dic38—21no—
88Dic38—21no—
89Dic38—28no—
90Dic38C22⋊C414yes—
91Dic38C22⋊C414yes—
92Dic38C22⋊C418yes—
93#2884—191nomaximal, Sylow
94C22×C19—22no—
95C22×C19—41no—
96C22×C19—42no—
97C22×C19C23×C411yescharacteristic
98C22×C19C22×D412yes—
99C2×D19—22no—
100C2×D19—42no—
101C4×C19—22no—
102C4×C19—44no—
103C4×C19C2×C22⋊C411yescharacteristic
104C4×C19C2×C22⋊C411yescharacteristic
105C4×C19C2×C22⋊C412yes—
106Dic19—22no—
107Dic19—44no—
108Dic19C2×C22⋊C418yes—
109C2×2−1+4—191no—
110#519—192no—
111#410—191no—
112#410—192no—
113#410—198no—
114#410D1911yescharacteristic, complemented
115C2×C19—22no—
116C2×C19—21no—
117C2×C19—42no—
118C2×C19C22×C22⋊C411yescharacteristic
119D19—42no—
1202−1+4—384no—
1212−1+4—384no—
122C2×#41—192no—
123C2×#41—194no—
124C2×#41—192no—
125C2×#41—191no—
126C2×#41C2×D1911yescharacteristic
127C22×Q8—192no—
128C22×Q8—192no—
129C22×Q8—191no—
130C4×Q8—384no—
131C4×Q8—384no—
132#117—192no—
133#117—198no—
134#117C2×D1912yes—
135#99—194no—
136#99—198no—
137#99C2×D1914yes—
138C19#288411yescharacteristic, complemented, Sylow
139#41—22no—
140#41—22no—
141#41—384no—
142#41—384no—
143#41—3816no—
144#41—388no—
145#41—382no—
146#41—382no—
147C2×Q8—192no—
148C2×Q8—192no—
149C2×Q8—194no—
150C2×Q8—191no—
151C2×Q8—194no—
152C2×Q8—194no—
153C2×Q8—384no—
154C2×Q8—384no—
155C2×Q8—388no—
156C2×Q8C4×D1911yescharacteristic
157C2×D4—194no—
158C2×D4—192no—
159C2×D4—191no—
160C2×D4C4×D1911yescharacteristic
161C2×D4C22×D1912yes—
162C22×C4—192no—
163C22×C4—194no—
164C22×C4—194no—
165C22×C4—192no—
166C22×C4C4×D1912yes—
167C22×C4C22×D1911yescharacteristic
168C4⋊C4—22no—
169C4⋊C4—388no—
170C4⋊C4—382no—
171C22⋊C4—194no—
172C22⋊C4C22×D1914yes—
173C42—22no—
174C42—388no—
175C42—382no—
176C23—192no—
177C23C2×C4×D1912yes—
178C23C23×D1911yescharacteristic
179Q8—22no—
180Q8—194no—
181Q8—194no—
182Q8—198no—
183Q8—388no—
184Q8—381no—
185Q8—381no—
186D4—24no—
187D4—22no—
188D4—388no—
189D4—384no—
190D4—381no—
191D4—381no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—24no—
195C2×C4—194no—
196C2×C4—198no—
197C2×C4—192no—
198C2×C4—388no—
199C2×C4—388no—
200C2×C4—384no—
201C2×C4—384no—
202C2×C4C2×C4×D1912yes—
203C2×C4C2×C4×D1911yescharacteristic
204C2×C4C2×C4×D1911yescharacteristic
205C2×C4D4×D1912yes—
206C2×C4D4×D1912yes—
207C22—22no—
208C22—41no—
209C22—42no—
210C22—382no—
211C22—762no—
212C22C22×C4×D1911yescharacteristic
213C22C2×D4×D1912yes—
214C4—22no—
215C4—44no—
216C4—198no—
217C4—382no—
218C4—764no—
219C4C22⋊C4×D1911yescharacteristic
220C4C22⋊C4×D1911yescharacteristic
221C4C22⋊C4×D1912yes—
222C2—22no—
223C2—21no—
224C2—42no—
225C2—762no—
226C2C2×C22⋊C4×D1911yescharacteristic
subgroupG/H
centerC2C2×C22⋊C4×D19
commutatorC22×C19C23×C4
FrattiniC23C23×D19
FittingC19×#410C2
socleC2×C19C22×C22⋊C4
prime radicalC2×#10597436C2
cosocleC23×C19C24
hypercenter#410D19
hypocenterC19#2884
LCSG ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #11927021C2semidirect
3. #11926518C2semidirect
4. #11926517C2semidirect
5. #11926516C2semidirect
6. C19×#410C2semidirect
10. C2×Q8×D19C4semidirect
11. C2×#64543C4semidirect
13. C2×#64541C4semidirect
15. C22×Dic38C4semidirect
114. #410D19semidirect
138. C19#2884semidirect

Maximal subgroups

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

subgroupindex
C2×#105974362
#119270212
#119265182
#119265172
#119265162
C19×#4102
#288419