Finite Group Databasebeta

← #14567945

Subgroups — #14567945

Order 2432.

584 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 151 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×(C22⋊D19)⋊C4C211yesmaximal, characteristic
2C2×C4⋊C4×D19C211yesmaximal, characteristic, complemented
3#11926484C211yesmaximal, characteristic, complemented
4#11926482C211yesmaximal, characteristic, complemented
5#11926480C211yesmaximal, characteristic, complemented
6#11926439C212yesmaximal, complemented
7#11926420C212yesmaximal
8#11926415C212yesmaximal, complemented
9#11926403C211yesmaximal, characteristic, complemented
10#11926402C212yesmaximal, complemented
11C19×#399C211yesmaximal, characteristic, complemented
12C22×C22⋊D19C2211yescharacteristic
13C23×Dic19C2211yescharacteristic
14C22×C4×D19C2211yescharacteristic
15C22×C4×D19C2212yes—
16C2×C4⋊C4×C19C2211yescharacteristic
17C2×C4⋊C4×C19C2212yes—
18C2×C22⋊C4×C19C2211yescharacteristic
19C2×C22⋊C4×C19C2212yes—
20C2×C22⋊Dic19C2212yes—
21C2×(C2×D19)⋊C4C2212yes—
22C2×(C2×D19)⋊C4C2211yescharacteristic
23C2×C4⋊Dic19C2211yescharacteristic
24C2×Dic19⋊C4C2212yes—
25C2×Dic19⋊C4C2212yes—
26C2×Dic19⋊C4C2211yescharacteristic
27C2×Dic19⋊C4C2212yes—
28C2×C4×Dic19C2211yescharacteristic
29C4⋊C4×D19—24no—
30(C22⋊D19)⋊C4—24no—
31C19×#95C2211yescharacteristic
32C19⋊#95C2212yes—
33C19⋊#95C2212yes—
34C19⋊#95C2211yescharacteristic
35C19⋊#95C2212yes—
36C19⋊#95C2212yes—
37C24×C19C2311yescharacteristic
38C23×D19C2311yescharacteristic
39C22×C4×C19C2312yes—
40C22×C4×C19C2311yescharacteristic
41C22×C4×C19C2312yes—
42C22×C4×C19C2311yescharacteristic
43C2×C22⋊D19—22no—
44C2×C22⋊D19—22no—
45C2×C22⋊D19Q814yes—
46C22×Dic19—22no—
47C22×Dic19—24no—
48C22×Dic19C2312yes—
49C22×Dic19C2312yes—
50C22×Dic19C2311yescharacteristic
51C22×Dic19C2311yescharacteristic
52C22×Dic19C2311yescharacteristic
53C2×C4×D19—24no—
54C2×C4×D19—24no—
55C2×C4×D19—42no—
56C2×C4×D19—42no—
57C2×C4×D19D414yes—
58C4⋊C4×C19—22no—
59C4⋊C4×C19—42no—
60C22⋊C4×C19—22no—
61C22⋊C4×C19—42no—
62C22⋊Dic19—42no—
63(C2×D19)⋊C4—22no—
64(C2×D19)⋊C4—24no—
65C4⋊Dic19—22no—
66Dic19⋊C4—22no—
67Dic19⋊C4—24no—
68Dic19⋊C4—24no—
69Dic19⋊C4—42no—
70C4×Dic19—22no—
71C23×C19—21no—
72C23×C19—22no—
73C23×C19—21no—
74C23×C19—22no—
75C23×C19C2×Q812yes—
76C23×C19C2411yescharacteristic
77C22×D19—22no—
78C22×D19—22no—
79C22×D19C2×D412yes—
80C22×D19C2×Q812yes—
81C22×D19#4112yes—
82C2×C4×C19—22no—
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—22no—
90C2×C4×C19—22no—
91C2×C4×C19C2×D412yes—
92C22⋊D19—28no—
93C2×Dic19—21no—
94C2×Dic19—21no—
95C2×Dic19—22no—
96C2×Dic19—21no—
97C2×Dic19—22no—
98C2×Dic19—22no—
99C2×Dic19—22no—
100C2×Dic19—22no—
101C2×Dic19—22no—
102C2×Dic19—22no—
103C2×Dic19—44no—
104C2×Dic19C2×D412yes—
105C2×Dic19C2×Q812yes—
106C2×Dic19#4114yes—
107C4×D19—28no—
108C4×D19—48no—
109#2487—191nomaximal, Sylow
110C22×C19—22no—
111C22×C19—24no—
112C22×C19—41no—
113C22×C19—41no—
114C22×C19—42no—
115C22×C19C22×D411yescharacteristic
116C22×C19C22×Q811yescharacteristic
117C22×C19C2×#4111yescharacteristic
118C22×C19C2×#4112yes—
119C22×C19H(5,𝔽2)12yes—
120C2×D19—22no—
121C2×D19—22no—
122C2×D19—24no—
123C2×D19—24no—
124C2×D19C22⋊Q814yes—
125C4×C19—22no—
126C4×C19—42no—
127C4×C19—41no—
128C4×C19—42no—
129Dic19—22no—
130Dic19—41no—
131Dic19—42no—
132Dic19—42no—
133Dic19#12314yes—
134C2×C4×D4—191no—
135C22×C4⋊C4—191no—
136#400—191no—
137#400—191no—
138#399—191no—
139#399D1911yescharacteristic, complemented
140#389—192no—
141#386—192no—
142#385—192no—
143#380—192no—
144#380—191no—
145C2×C19—42no—
146C2×C19C2×C22⋊Q811yescharacteristic
147C2×C19C2×#12311yescharacteristic
148C2×C19#53511yescharacteristic
149C2×C19#55312yes—
150C2×C19#55412yes—
151D19—24no—
152C22×D4—191no—
153C23×C4—191no—
154C23×C4—191no—
155C23×C4—192no—
156C4×D4—384no—
157C2×C4⋊C4—192no—
158C2×C4⋊C4—191no—
159C2×C4⋊C4—191no—
160C2×C4⋊C4—192no—
161C2×C4⋊C4—192no—
162C2×C4⋊C4—384no—
163C2×C4⋊C4C2×D1911yescharacteristic
164C2×C4⋊C4C2×D1912yes—
165C2×C22⋊C4—191no—
166C2×C22⋊C4—192no—
167C2×C22⋊C4—192no—
168C2×C22⋊C4C2×D1911yescharacteristic
169C2×C22⋊C4C2×D1912yes—
170C2×C42—191no—
171#95—192no—
172#95—192no—
173#95—191no—
174#95—192no—
175#95—192no—
176#95C2×D1911yescharacteristic
177C19#248711yescharacteristic, complemented, Sylow
178C24—191no—
179C24C22×D1911yescharacteristic
180C2×D4—194no—
181C2×D4—382no—
182C2×D4—382no—
183C22×C4—191no—
184C22×C4—191no—
185C22×C4—194no—
186C22×C4—191no—
187C22×C4—192no—
188C22×C4—192no—
189C22×C4—384no—
190C22×C4—384no—
191C22×C4—382no—
192C22×C4—384no—
193C22×C4—762no—
194C22×C4—762no—
195C22×C4C22×D1912yes—
196C22×C4C22×D1912yes—
197C22×C4C22×D1911yescharacteristic
198C22×C4C22×D1911yescharacteristic
199C4⋊C4—22no—
200C4⋊C4—42no—
201C4⋊C4—384no—
202C4⋊C4—384no—
203C4⋊C4—382no—
204C4⋊C4—382no—
205C4⋊C4—762no—
206C22⋊C4—22no—
207C22⋊C4—42no—
208C22⋊C4—384no—
209C22⋊C4—382no—
210C22⋊C4—762no—
211C42—382no—
212C23—21no—
213C23—22no—
214C23—22no—
215C23—21no—
216C23—192no—
217C23—192no—
218C23—192no—
219C23—382no—
220C23—382no—
221C23Q8×D1912yes—
222C23C23×D1911yescharacteristic
223D4—388no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—192no—
234C2×C4—194no—
235C2×C4—192no—
236C2×C4—388no—
237C2×C4—381no—
238C2×C4—381no—
239C2×C4—381no—
240C2×C4—382no—
241C2×C4—382no—
242C2×C4—382no—
243C2×C4—382no—
244C2×C4—382no—
245C2×C4—382no—
246C2×C4—382no—
247C2×C4—768no—
248C2×C4—764no—
249C2×C4D4×D1912yes—
250C22—24no—
251C22—22no—
252C22—41no—
253C22—41no—
254C22—42no—
255C22—194no—
256C22—382no—
257C22—382no—
258C22—384no—
259C22—384no—
260C22C2×D4×D1911yescharacteristic
261C22#1059743012yes—
262C22C2×Q8×D1911yescharacteristic
263C22#41×D1912yes—
264C22#41×D1911yescharacteristic
265C4—22no—
266C4—42no—
267C4—41no—
268C4—42no—
269C4—194no—
270C4—382no—
271C4—761no—
272C4—762no—
273C4—762no—
274C2—42no—
275C2—384no—
276C2C22⋊Q8×D1911yescharacteristic
277C2#123×D1911yescharacteristic
278C2#1192710711yescharacteristic
279C2#1192723912yes—
280C2#1192724812yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#399C2
prime radicalC22×C22⋊D19C22
hypercenter#399D19
hypocenterC19#2487
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D19C2semidirect
3. #11926484C2semidirect
4. #11926482C2semidirect
5. #11926480C2semidirect
6. #11926439C2semidirect
8. #11926415C2semidirect
9. #11926403C2semidirect
10. #11926402C2semidirect
11. C19×#399C2semidirect
139. #399D19semidirect
177. C19#2487semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D19)⋊C42
C2×C4⋊C4×D192
#119264842
#119264822
#119264802
#119264392
#119264202
#119264152
#119264032
#119264022
C19×#3992
#248719