Finite Group Databasebeta

← #14569212

Subgroups — #14569212

Order 2432.

492 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 145 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×C4×Dic38C211yesmaximal, characteristic, complemented
2#11926474C211yesmaximal, characteristic, complemented
3#11926469C211yesmaximal, characteristic
4#11926464C211yesmaximal, characteristic, complemented
5#11926456C211yesmaximal, characteristic
6#11926432C212yesmaximal
7#11926428C212yesmaximal, complemented
8#11926425C212yesmaximal, complemented
9#11926417C212yesmaximal
10#11926412C211yesmaximal, characteristic, complemented
11C2×C19×#117C211yesmaximal, characteristic
12C23×C4×C19C2211yescharacteristic
13C22×Dic38C2211yescharacteristic
14C19×#117—24no—
15C2×C4⋊C4×C19C2211yescharacteristic
16C2×C4⋊C4×C19C2211yescharacteristic
17C2×C22⋊C4×C19C2211yescharacteristic
18C2×C22⋊C4×C19C2211yescharacteristic
19C2×C42×C19C2211yescharacteristic
20C2×C42×C19C2211yescharacteristic
21C2×C22⋊Dic19C2212yes—
22C2×C22⋊Dic19C2212yes—
23C2×C4⋊Dic19C2211yescharacteristic
24C2×Dic19⋊C4C2212yes—
25C2×Dic19⋊C4C2212yes—
26C2×Dic19⋊C4C2212yes—
27C2×C4×Dic19C2212yes—
28C4×Dic38—24no—
29C19⋊#95C2212yes—
30C19⋊#95C2212yes—
31C19⋊#95C2211yescharacteristic
32C19⋊#95C2211yescharacteristic
33C19⋊#95C2212yes—
34C19⋊#95C2212yes—
35C19⋊#95C2212yes—
36C19⋊#95C2212yes—
37C24×C19C2311yescharacteristic
38C22×C4×C19—22no—
39C22×C4×C19—22no—
40C22×C4×C19—22no—
41C22×C4×C19C2311yescharacteristic
42C22×C4×C19C2311yescharacteristic
43C22×C4×C19C2311yescharacteristic
44C22×C4×C19C2311yescharacteristic
45C22×C4×C19C2311yescharacteristic
46C22×C4×C19C2311yescharacteristic
47C22×Dic19C2312yes—
48C22×Dic19C2312yes—
49C22×Dic19C2312yes—
50C22×Dic19C2312yes—
51C2×Dic38—22no—
52C2×Dic38—24no—
53C4⋊C4×C19—22no—
54C4⋊C4×C19—22no—
55C22⋊C4×C19—22no—
56C22⋊C4×C19—22no—
57C42×C19—22no—
58C42×C19D414yes—
59C22⋊Dic19—24no—
60C22⋊Dic19—24no—
61C4⋊Dic19—22no—
62Dic19⋊C4—24no—
63Dic19⋊C4—24no—
64Dic19⋊C4—24no—
65C4×Dic19—24no—
66C23×C19—21no—
67C23×C19—22no—
68C23×C19—21no—
69C23×C19—22no—
70C23×C19#4112yes—
71C23×C19C2411yescharacteristic
72C2×C4×C19—28no—
73C2×C4×C19—21no—
74C2×C4×C19—22no—
75C2×C4×C19—21no—
76C2×C4×C19—21no—
77C2×C4×C19—21no—
78C2×C4×C19—22no—
79C2×C4×C19—21no—
80C2×C4×C19—21no—
81C2×C4×C19—22no—
82C2×C4×C19—22no—
83C2×C4×C19C2×D412yes—
84C2×C4×C19C2×D412yes—
85C2×C4×C19C2×D412yes—
86C2×C4×C19#4112yes—
87C2×Dic19—22no—
88C2×Dic19—22no—
89C2×Dic19—22no—
90C2×Dic19—22no—
91C2×Dic19—22no—
92C2×Dic19—22no—
93C2×Dic19—22no—
94C2×Dic19—22no—
95C2×Dic19—22no—
96C2×Dic19—22no—
97C2×Dic19—22no—
98C2×Dic19#4114yes—
99Dic38—28no—
100#2599—191nomaximal, Sylow
101C22×C19—22no—
102C22×C19—24no—
103C22×C19—41no—
104C22×C19—41no—
105C22×C19—42no—
106C22×C19C22×D411yescharacteristic
107C22×C19C2×#4111yescharacteristic
108C22×C19C2×#4111yescharacteristic
109C22×C19C2×#4112yes—
110C22×C192−1+412yes—
111C4×C19—22no—
112C4×C19—22no—
113C4×C19—22no—
114C4×C19—22no—
115C4×C19—41no—
116C4×C19—41no—
117Dic19—24no—
118Dic19—42no—
119Dic19—42no—
120Dic19—42no—
121C2×C4×Q8—191no—
122C2×#117D1911yescharacteristic
123#398—191no—
124#397—191no—
125#395—191no—
126#393—191no—
127#388—192no—
128#387—192no—
129#387—192no—
130#385—192no—
131#383—191no—
132C2×C19—42no—
133C2×C19#52511yescharacteristic
134C2×C19#52511yescharacteristic
135C2×C19#53611yescharacteristic
136C2×C19#55212yes—
137C2×C19#55612yes—
138C22×Q8—191no—
139C23×C4C2×D1911yescharacteristic
140C4×Q8—384no—
141#117—24no—
142C2×C4⋊C4—192no—
143C2×C4⋊C4—191no—
144C2×C4⋊C4—192no—
145C2×C4⋊C4—192no—
146C2×C4⋊C4C2×D1911yescharacteristic
147C2×C4⋊C4C2×D1911yescharacteristic
148C2×C22⋊C4—192no—
149C2×C22⋊C4—192no—
150C2×C22⋊C4C2×D1911yescharacteristic
151C2×C22⋊C4C2×D1911yescharacteristic
152C2×C42—192no—
153C2×C42C2×D1911yescharacteristic
154C2×C42C2×D1911yescharacteristic
155#95—192no—
156#95—192no—
157#95—191no—
158#95—191no—
159#95—192no—
160#95—192no—
161#95—192no—
162#95—192no—
163C19#259911yescharacteristic, complemented, Sylow
164C24C22×D1911yescharacteristic
165C2×Q8—384no—
166C2×Q8—382no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—192no—
171C22×C4—192no—
172C22×C4—192no—
173C22×C4—192no—
174C22×C4C22×D1911yescharacteristic
175C22×C4C22×D1911yescharacteristic
176C22×C4C22×D1911yescharacteristic
177C22×C4C22×D1911yescharacteristic
178C22×C4C22×D1911yescharacteristic
179C22×C4C22×D1911yescharacteristic
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—384no—
183C4⋊C4—384no—
184C4⋊C4—384no—
185C4⋊C4—382no—
186C22⋊C4—22no—
187C22⋊C4—22no—
188C22⋊C4—384no—
189C22⋊C4—384no—
190C42—22no—
191C42—384no—
192C42C22⋊D1914yes—
193C23—21no—
194C23—22no—
195C23—22no—
196C23—21no—
197C23#6454112yes—
198C23C23×D1911yescharacteristic
199Q8—388no—
200C2×C4—28no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—194no—
212C2×C4—382no—
213C2×C4—382no—
214C2×C4—382no—
215C2×C4—382no—
216C2×C4—382no—
217C2×C4—382no—
218C2×C4—382no—
219C2×C4—382no—
220C2×C4—382no—
221C2×C4—382no—
222C2×C4—382no—
223C2×C4#6454112yes—
224C2×C4C2×C22⋊D1912yes—
225C2×C4C2×C22⋊D1912yes—
226C2×C4C2×C22⋊D1912yes—
227C22—22no—
228C22—24no—
229C22—41no—
230C22—41no—
231C22—42no—
232C22C2×#6454111yescharacteristic
233C22C2×#6454111yescharacteristic
234C22#41×D1912yes—
235C22#1059743612yes—
236C22C22×C22⋊D1911yescharacteristic
237C4—22no—
238C4—22no—
239C4—22no—
240C4—22no—
241C4—41no—
242C4—41no—
243C4—384no—
244C4—762no—
245C4—762no—
246C4—762no—
247C2—42no—
248C2#1192705111yescharacteristic
249C2#1192705511yescharacteristic
250C2#1192711511yescharacteristic
251C2#1192722712yes—
252C2#1192726212yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#117C2
prime radicalC24×C19C23
hypercenterC2×#117D19
hypocenterC19#2599
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×C4×Dic38C2semidirect
2. #11926474C2semidirect
4. #11926464C2semidirect
7. #11926428C2semidirect
8. #11926425C2semidirect
10. #11926412C2semidirect
163. C19#2599semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic382
#119264742
#119264692
#119264642
#119264562
#119264322
#119264282
#119264252
#119264172
#119264122
C2×C19×#1172
#259919