Finite Group Databasebeta

← #14570658

Subgroups — #14570658

Order 2432.

592 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 129 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×#10597331C212yesmaximal, complemented
2#11926461C211yesmaximal, characteristic, complemented
3#11926453C212yesmaximal, complemented
4#11926452C212yesmaximal, complemented
5#11926449C211yesmaximal, characteristic, complemented
6#11926444C212yesmaximal, complemented
7#11926438C212yesmaximal, complemented
8#11926433C212yesmaximal, complemented
9C19×#394C211yesmaximal, characteristic, complemented
10C22×D4×C19C2211yescharacteristic
11C22×C22⋊D19C2212yes—
12C22×C22⋊D19C2212yes—
13C22×D76C2211yescharacteristic
14C22×Dic38C2211yescharacteristic
15C2×C4⋊C4×C19C2211yescharacteristic
16C2×C22⋊C4×C19C2212yes—
17C2×C22⋊C4×C19C2212yes—
18C2×C22⋊Dic19C2212yes—
19C2×C22⋊Dic19C2212yes—
20C2×(C2×D19)⋊C4C2212yes—
21C2×(C2×D19)⋊C4C2212yes—
22C2×(C2×D19)⋊C4C2212yes—
23C2×(C2×D19)⋊C4C2212yes—
24C2×Dic19⋊C4C2212yes—
25C2×C4×Dic19C2212yes—
26C2×C4×Dic19C2211yescharacteristic
27#10597331—28no—
28C19×#95C2211yescharacteristic
29C19⋊#95C2212yes—
30C19⋊#95C2211yescharacteristic
31C19⋊#95C2212yes—
32C24×C19C2312yes—
33C23×D19C2312yes—
34C2×D4×C19—42no—
35C2×D4×C19—41no—
36C22×C4×C19C2311yescharacteristic
37C22×C4×C19C2312yes—
38C22×C4×C19C2311yescharacteristic
39C22×C4×C19C2311yescharacteristic
40C2×C22⋊D19—24no—
41C2×C22⋊D19—24no—
42C2×C22⋊D19—42no—
43C2×C22⋊D19—42no—
44C2×C22⋊D19—42no—
45C2×C22⋊D19—42no—
46C22×Dic19C2312yes—
47C22×Dic19C2312yes—
48C22×Dic19C2312yes—
49C2×D76—42no—
50C2×D76—41no—
51C2×Dic38—41no—
52C2×Dic38—41no—
53C2×Dic38D414yescomplemented
54C4⋊C4×C19—41no—
55C22⋊C4×C19—24no—
56C22⋊C4×C19—42no—
57C22⋊Dic19—24no—
58C22⋊Dic19—24no—
59(C2×D19)⋊C4—24no—
60(C2×D19)⋊C4—24no—
61(C2×D19)⋊C4—24no—
62(C2×D19)⋊C4—42no—
63Dic19⋊C4—42no—
64C4×Dic19—24no—
65C4×Dic19—41no—
66C23×C19—22no—
67C23×C19—22no—
68C23×C19—22no—
69C23×C19—22no—
70C23×C19—22no—
71C23×C19—22no—
72C23×C19—22no—
73C23×C19C2411yescharacteristic
74C22×D19—22no—
75C22×D19—22no—
76C22×D19—22no—
77C22×D19—22no—
78C22×D19—22no—
79C22×D19—22no—
80C22×D19—22no—
81D4×C19—44no—
82C2×C4×C19—21no—
83C2×C4×C19—21no—
84C2×C4×C19—22no—
85C2×C4×C19—22no—
86C2×C4×C19—22no—
87C2×C4×C19—22no—
88C2×C4×C19—22no—
89C2×C4×C19—21no—
90C2×C4×C19—21no—
91C2×C4×C19C2×D412yes—
92C22⋊D19—48no—
93C22⋊D19—48no—
94C2×Dic19—22no—
95C2×Dic19—22no—
96C2×Dic19—22no—
97C2×Dic19—22no—
98C2×Dic19—22no—
99C2×Dic19—22no—
100C2×Dic19—22no—
101C2×Dic19C2×D414yes—
102C2×Dic19#4114yes—
103D76—44no—
104Dic38—44no—
105#2733—191nomaximal, Sylow
106C22×C19—42no—
107C22×C19—42no—
108C22×C19—42no—
109C22×C19—42no—
110C22×C19—42no—
111C22×C19—42no—
112C22×C19—42no—
113C22×C19C22×D411yescharacteristic
114C22×C19C2×#4112yes—
115C22×C19H(5,𝔽2)11yescharacteristic
116C22×C19H(5,𝔽2)12yes—
117C22×C19H(5,𝔽2)11yescharacteristic
118C2×D19—42no—
119C2×D19—42no—
120C2×D19—42no—
121C2×D19—42no—
122C2×D19—42no—
123C2×D19—42no—
124C2×D19—42no—
125C4×C19—22no—
126C4×C19—42no—
127C4×C19—41no—
128C4×C19—41no—
129Dic19—24no—
130Dic19—24no—
131Dic19—42no—
132C2×#124—192no—
133#394—191no—
134#394D1911yescharacteristic, complemented
135#392—192no—
136#392—192no—
137#391—191no—
138#390—192no—
139#388—192no—
140#388—192no—
141C2×C19—82no—
142C2×C19#53411yescharacteristic
143C2×C19#53812yes—
144C2×C19#55012yes—
145C2×C19#55511yescharacteristic
146C2×C19H(3,𝔽4)11yescharacteristic
147D19—82no—
148C22×Q8—191no—
149C22×D4—192no—
150C22×D4—192no—
151C22×D4—191no—
152C22×D4C2×D1911yescharacteristic
153#124—388no—
154C2×C4⋊C4—192no—
155C2×C4⋊C4C2×D1911yescharacteristic
156C2×C22⋊C4—192no—
157C2×C22⋊C4—192no—
158C2×C22⋊C4—192no—
159C2×C22⋊C4—192no—
160C2×C22⋊C4—192no—
161C2×C22⋊C4—192no—
162C2×C22⋊C4C2×D1912yes—
163C2×C22⋊C4C2×D1912yes—
164C2×C42—192no—
165C2×C42—191no—
166#95—191no—
167#95—192no—
168#95—192no—
169#95C2×D1911yescharacteristic
170C19#273311yescharacteristic, complemented, Sylow
171C24—192no—
172C24C22×D1912yes—
173C2×Q8—194no—
174C2×Q8—761no—
175C2×Q8—761no—
176C2×D4—42no—
177C2×D4—41no—
178C2×D4—384no—
179C2×D4—384no—
180C2×D4—762no—
181C2×D4—761no—
182C2×D4—762no—
183C2×D4—762no—
184C2×D4—762no—
185C2×D4—762no—
186C22×C4—192no—
187C22×C4—192no—
188C22×C4—192no—
189C22×C4C22×D1911yescharacteristic
190C22×C4C22×D1911yescharacteristic
191C22×C4C22×D1912yes—
192C22×C4C22×D1911yescharacteristic
193C4⋊C4—41no—
194C4⋊C4—762no—
195C22⋊C4—24no—
196C22⋊C4—42no—
197C22⋊C4—384no—
198C22⋊C4—384no—
199C22⋊C4—384no—
200C22⋊C4—384no—
201C22⋊C4—384no—
202C22⋊C4—762no—
203C42—384no—
204C42—761no—
205C23—22no—
206C23—22no—
207C23—22no—
208C23—22no—
209C23—22no—
210C23—22no—
211C23—22no—
212C23—382no—
213C23—382no—
214C23—382no—
215C23—382no—
216C23—382no—
217C23—382no—
218C23—382no—
219C23C23×D1911yescharacteristic
220Q8—764no—
221D4—44no—
222D4—764no—
223D4—768no—
224D4—768no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—194no—
235C2×C4—194no—
236C2×C4—382no—
237C2×C4—382no—
238C2×C4—382no—
239C2×C4—382no—
240C2×C4—382no—
241C2×C4—382no—
242C2×C4—382no—
243C2×C4D4×D1912yes—
244C22—42no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—42no—
249C22—42no—
250C22—42no—
251C22—762no—
252C22—762no—
253C22—762no—
254C22—762no—
255C22—762no—
256C22—762no—
257C22—762no—
258C22C2×D4×D1911yescharacteristic
259C22#1059743011yescharacteristic
260C22#1059743012yes—
261C22#41×D1912yes—
262C22#1059743511yescharacteristic
263C4—22no—
264C4—42no—
265C4—41no—
266C4—41no—
267C4—384no—
268C4—384no—
269C4—762no—
270C2—82no—
271C2—1522no—
272C2#1192710211yescharacteristic
273C2#1192713012yes—
274C2#1192721212yes—
275C2#1192725611yescharacteristic
276C2#1192728711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#394C2
hypercenter#394D19
hypocenterC19#2733
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#10597331C2semidirect
2. #11926461C2semidirect
3. #11926453C2semidirect
4. #11926452C2semidirect
5. #11926449C2semidirect
6. #11926444C2semidirect
7. #11926438C2semidirect
8. #11926433C2semidirect
9. C19×#394C2semidirect
53. C2×Dic38D4semidirect
134. #394D19semidirect
170. C19#2733semidirect

Maximal subgroups

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

subgroupindex
C2×#105973312
#119264612
#119264532
#119264522
#119264492
#119264442
#119264382
#119264332
C19×#3942
#273319