Finite Group Databasebeta

← #14569777

Subgroups — #14569777

Order 2432.

534 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10597325C211yesmaximal, characteristic, complemented
2C2×#10597382C211yesmaximal, characteristic, complemented
3#11926467C212yesmaximal, complemented
4#11926465C211yesmaximal, characteristic, complemented
5#11926458C212yesmaximal, complemented
6#11926458C211yesmaximal, characteristic, complemented
7#11926456C211yesmaximal, characteristic, complemented
8#11926447C212yesmaximal, complemented
9#11926437C212yesmaximal, complemented
10#11926395C211yesmaximal, characteristic, complemented
11C19×#392C211yesmaximal, characteristic
12C22×D4×C19C2211yescharacteristic
13C22×D4×C19C2212yes—
14C22×Dic38C2211yescharacteristic
15C2×C22⋊C4×C19C2211yescharacteristic
16C2×C22⋊C4×C19C2212yes—
17C2×C22⋊Dic19C2212yes—
18C2×C22⋊Dic19C2212yes—
19C2×C22⋊Dic19C2211yescharacteristic
20C2×C22⋊Dic19C2211yescharacteristic
21C2×C22⋊Dic19C2212yes—
22C2×C22⋊Dic19C2212yes—
23C2×C22⋊Dic19C2212yes—
24#10597382—24no—
25C2×C4⋊Dic19C2211yescharacteristic
26C2×C4⋊Dic19C2212yes—
27C2×Dic19⋊C4C2211yescharacteristic
28C2×Dic19⋊C4C2211yescharacteristic
29C2×Dic19⋊C4C2212yes—
30C2×C4×Dic19C2212yes—
31C2×C4×Dic19C2211yescharacteristic
32#10597325—24no—
33C19×#95C2211yescharacteristic
34C19⋊#95C2211yescharacteristic
35C19⋊#95C2212yes—
36C19⋊#95C2212yes—
37C24×C19C2311yescharacteristic
38C24×C19C2312yes—
39C2×D4×C19—22no—
40C2×D4×C19—24no—
41C2×D4×C19—42no—
42C2×D4×C19—42no—
43C2×D4×C19—42no—
44C22×C4×C19C2311yescharacteristic
45C22×C4×C19C2311yescharacteristic
46C22×C4×C19C2312yes—
47C22×Dic19C2312yes—
48C22×Dic19C2312yes—
49C22×Dic19C2311yescharacteristic
50C22×Dic19C2311yescharacteristic
51C22×Dic19C2311yescharacteristic
52C22×Dic19C2311yescharacteristic
53C2×Dic38—22no—
54C2×Dic38—42no—
55C22⋊C4×C19—22no—
56C22⋊C4×C19—24no—
57C22⋊Dic19—24no—
58C22⋊Dic19—24no—
59C22⋊Dic19—22no—
60C22⋊Dic19—22no—
61C22⋊Dic19—42no—
62C22⋊Dic19—42no—
63C22⋊Dic19—42no—
64C4⋊Dic19—22no—
65C4⋊Dic19—42no—
66Dic19⋊C4—22no—
67Dic19⋊C4—24no—
68Dic19⋊C4—22no—
69C4×Dic19—42no—
70C4×Dic19D414yescomplemented
71C23×C19—21no—
72C23×C19—22no—
73C23×C19—22no—
74C23×C19—22no—
75C23×C19—22no—
76C23×C19—22no—
77C23×C19—22no—
78C23×C19—22no—
79C23×C19—22no—
80C23×C19—21no—
81C23×C19—21no—
82C23×C19—22no—
83C23×C19C2411yescharacteristic
84D4×C19—44no—
85D4×C19—48no—
86C2×C4×C19—22no—
87C2×C4×C19—22no—
88C2×C4×C19—22no—
89C2×C4×C19—21no—
90C2×C4×C19—22no—
91C2×C4×C19C2×D412yes—
92C2×C4×C19#4114yes—
93C2×Dic19—22no—
94C2×Dic19—21no—
95C2×Dic19—21no—
96C2×Dic19—21no—
97C2×Dic19—21no—
98C2×Dic19—22no—
99C2×Dic19—22no—
100C2×Dic19—22no—
101C2×Dic19—22no—
102C2×Dic19—22no—
103C2×Dic19—21no—
104C2×Dic19—22no—
105C2×Dic19—22no—
106C2×Dic19—21no—
107C2×Dic19C2×D412yes—
108C2×Dic19C2×D412yes—
109Dic38—44no—
110#2662—191nomaximal, Sylow
111C22×C19—41no—
112C22×C19—42no—
113C22×C19—42no—
114C22×C19—41no—
115C22×C19—41no—
116C22×C19—42no—
117C22×C19—42no—
118C22×C19—42no—
119C22×C19—42no—
120C22×C19—42no—
121C22×C19—42no—
122C22×C19—42no—
123C22×C19C22×D411yescharacteristic
124C22×C19C2×#4112yes—
125C22×C19H(5,𝔽2)12yes—
126C22×C19H(5,𝔽2)11yescharacteristic
127C22×C192−1+411yescharacteristic
128C4×C19—22no—
129C4×C19—24no—
130C4×C19—41no—
131Dic19—22no—
132Dic19—22no—
133Dic19—42no—
134Dic19—41no—
135Dic19—41no—
136Dic19—42no—
137C2×#126—191no—
138C2×#124—191no—
139#396—192no—
140#395—191no—
141#394—191no—
142#394—192no—
143#393—191no—
144#392D1911yescharacteristic
145#390—192no—
146#388—192no—
147C4×C4⋊C4—191no—
148C2×C19—82no—
149C2×C19—81no—
150C2×C19#53211yescharacteristic
151C2×C19#53511yescharacteristic
152C2×C19#53711yescharacteristic
153C2×C19#53812yes—
154C2×C19#54212yes—
155C22×Q8—191no—
156C22×D4C2×D1911yescharacteristic
157C22×D4C2×D1912yes—
158#126—384no—
159#124—384no—
160C2×C4⋊C4—191no—
161C2×C4⋊C4—191no—
162C2×C4⋊C4—191no—
163C2×C4⋊C4—192no—
164C2×C4⋊C4—192no—
165C2×C22⋊C4—192no—
166C2×C22⋊C4—192no—
167C2×C22⋊C4—191no—
168C2×C22⋊C4—191no—
169C2×C22⋊C4—192no—
170C2×C22⋊C4—192no—
171C2×C22⋊C4—192no—
172C2×C22⋊C4C2×D1911yescharacteristic
173C2×C22⋊C4C2×D1912yes—
174C2×C42—191no—
175C2×C42—192no—
176#95—191no—
177#95—192no—
178#95—192no—
179#95C2×D1911yescharacteristic
180C19#266211yescharacteristic, complemented, Sylow
181C24C22×D1911yescharacteristic
182C24C22×D1912yes—
183C2×Q8—382no—
184C2×Q8—762no—
185C2×D4—22no—
186C2×D4—24no—
187C2×D4—42no—
188C2×D4—42no—
189C2×D4—42no—
190C22×C4—191no—
191C22×C4—191no—
192C22×C4—192no—
193C22×C4—191no—
194C22×C4—192no—
195C22×C4—191no—
196C22×C4C22×D1911yescharacteristic
197C22×C4C22×D1911yescharacteristic
198C22×C4C22×D1912yes—
199C4⋊C4—382no—
200C4⋊C4—382no—
201C4⋊C4—382no—
202C4⋊C4—384no—
203C4⋊C4—762no—
204C22⋊C4—22no—
205C22⋊C4—24no—
206C22⋊C4—384no—
207C22⋊C4—384no—
208C22⋊C4—382no—
209C22⋊C4—382no—
210C22⋊C4—762no—
211C22⋊C4—762no—
212C22⋊C4—762no—
213C42—194no—
214C42—762no—
215C23—21no—
216C23—22no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—22no—
223C23—22no—
224C23—21no—
225C23—21no—
226C23—22no—
227C23C23×D1911yescharacteristic
228Q8—764no—
229D4—44no—
230D4—48no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—192no—
237C2×C4—192no—
238C2×C4—382no—
239C2×C4—381no—
240C2×C4—381no—
241C2×C4—382no—
242C2×C4—381no—
243C2×C4—381no—
244C2×C4—382no—
245C2×C4—382no—
246C2×C4—381no—
247C2×C4—382no—
248C2×C4—382no—
249C2×C4—382no—
250C2×C4—382no—
251C2×C4—381no—
252C2×C4D4×D1912yes—
253C2×C4#6454314yes—
254C22—41no—
255C22—42no—
256C22—42no—
257C22—41no—
258C22—41no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—42no—
266C22C2×D4×D1911yescharacteristic
267C22C2×#6454312yes—
268C22#1059743012yes—
269C22#1059743011yescharacteristic
270C22#1059743611yescharacteristic
271C4—22no—
272C4—24no—
273C4—41no—
274C4—382no—
275C4—382no—
276C4—762no—
277C4—761no—
278C4—761no—
279C4—762no—
280C2—82no—
281C2—81no—
282C2#1192709211yescharacteristic
283C2#1192710911yescharacteristic
284C2#1192712311yescharacteristic
285C2#1192712912yes—
286C2#1192716112yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
Fitting, prime radicalC19×#392C2
hypercenter#392D19
hypocenterC19#2662
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#10597325C2semidirect
2. C2×#10597382C2semidirect
3. #11926467C2semidirect
4. #11926465C2semidirect
5. #11926458C2semidirect
6. #11926458C2semidirect
7. #11926456C2semidirect
8. #11926447C2semidirect
9. #11926437C2semidirect
10. #11926395C2semidirect
70. C4×Dic19D4semidirect
180. C19#2662semidirect

Maximal subgroups

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

subgroupindex
C2×#105973252
C2×#105973822
#119264672
#119264652
#119264582
#119264562
#119264472
#119264372
#119263952
C19×#3922
#266219