Finite Group Databasebeta

← #14568547

Subgroups — #14568547

Order 2432.

788 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 788 conjugacy classes of subgroups — too many to draw. Only its 161 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×#10597330C212yesmaximal, complemented
2C2×#10597385C212yesmaximal, complemented
3C2×(C22⋊D19)⋊C4C212yesmaximal, complemented
4#11926461C211yesmaximal, characteristic, complemented
5#11926460C212yesmaximal, complemented
6#11926413C211yesmaximal, characteristic, complemented
7#11926403C212yesmaximal, complemented
8#11926402C212yesmaximal, complemented
9C19×#394C211yesmaximal, characteristic, complemented
10C22×D4×C19C2211yescharacteristic
11C22×C22⋊D19C2212yes—
12C22×C22⋊D19C2212yes—
13C23×Dic19C2212yes—
14C22×D76C2211yescharacteristic
15C22×C4×D19C2212yes—
16C2×C4⋊C4×C19C2211yescharacteristic
17C2×C22⋊C4×C19C2212yes—
18C2×C22⋊C4×C19C2212yes—
19C2×C22⋊Dic19C2212yes—
20#10597385—28no—
21C2×(C2×D19)⋊C4C2212yes—
22C2×(C2×D19)⋊C4C2212yes—
23C2×(C2×D19)⋊C4C2212yes—
24C2×C4⋊Dic19C2211yescharacteristic
25C2×Dic19⋊C4C2212yes—
26C2×Dic19⋊C4C2212yes—
27C2×Dic19⋊C4C2212yes—
28C2×C4×Dic19C2211yescharacteristic
29#10597330—28no—
30(C22⋊D19)⋊C4—28no—
31C19×#95C2211yescharacteristic
32C19⋊#95C2211yescharacteristic
33C19⋊#95C2212yes—
34C24×C19C2312yes—
35C23×D19C2312yes—
36C2×D4×C19—24no—
37C2×D4×C19—41no—
38C22×C4×C19C2311yescharacteristic
39C22×C4×C19C2312yes—
40C22×C4×C19C2311yescharacteristic
41C22×C4×C19C2311yescharacteristic
42C2×C22⋊D19—24no—
43C2×C22⋊D19—24no—
44C2×C22⋊D19—24no—
45C2×C22⋊D19—24no—
46C2×C22⋊D19—42no—
47C2×C22⋊D19D418yescomplemented
48C22×Dic19—24no—
49C22×Dic19—24no—
50C22×Dic19—24no—
51C22×Dic19C2312yes—
52C22×Dic19C2312yes—
53C22×Dic19C2312yes—
54C2×D76—24no—
55C2×D76—41no—
56C2×C4×D19—24no—
57C2×C4×D19—24no—
58C2×C4×D19—24no—
59C4⋊C4×C19—41no—
60C22⋊C4×C19—24no—
61C22⋊C4×C19—24no—
62C22⋊Dic19—24no—
63(C2×D19)⋊C4—24no—
64(C2×D19)⋊C4—24no—
65(C2×D19)⋊C4—24no—
66C4⋊Dic19—41no—
67Dic19⋊C4—24no—
68Dic19⋊C4—24no—
69Dic19⋊C4—24no—
70C4×Dic19D414yescomplemented
71C23×C19—22no—
72C23×C19—22no—
73C23×C19—22no—
74C23×C19—22no—
75C23×C19—22no—
76C23×C19—22no—
77C23×C19C2×D414yes—
78C23×C19C2411yescharacteristic
79C22×D19—22no—
80C22×D19—22no—
81C22×D19—22no—
82C22×D19—22no—
83C22×D19—22no—
84C22×D19—22no—
85C22×D19C2×D414yes—
86D4×C19—44no—
87C2×C4×C19—21no—
88C2×C4×C19—21no—
89C2×C4×C19—22no—
90C2×C4×C19—22no—
91C2×C4×C19—22no—
92C2×C4×C19—22no—
93C2×C4×C19—22no—
94C2×C4×C19—21no—
95C2×C4×C19—21no—
96C2×C4×C19C2×D412yes—
97C22⋊D19—216no—
98C22⋊D19—48no—
99C2×Dic19—22no—
100C2×Dic19—22no—
101C2×Dic19—22no—
102C2×Dic19—22no—
103C2×Dic19—22no—
104C2×Dic19—22no—
105C2×Dic19—48no—
106C2×Dic19C2×D414yes—
107C2×Dic19C2×D414yes—
108C2×Dic19#4114yes—
109D76—44no—
110C4×D19—48no—
111#2537—191nomaximal, Sylow
112C22×C19—24no—
113C22×C19—24no—
114C22×C19—24no—
115C22×C19—42no—
116C22×C19—42no—
117C22×C19—42no—
118C22×C19—42no—
119C22×C19C22×D411yescharacteristic
120C22×C19C22×D412yes—
121C22×C19C2×#4112yes—
122C22×C19H(5,𝔽2)11yescharacteristic
123C22×C192−1+411yescharacteristic
124C2×D19—24no—
125C2×D19—24no—
126C2×D19—24no—
127C2×D19—42no—
128C2×D19—42no—
129C2×D19—42no—
130C2×D19—42no—
131C4×C19—22no—
132C4×C19—42no—
133C4×C19—41no—
134C4×C19—41no—
135Dic19—42no—
136Dic19—42no—
137Dic19#12118yescomplemented
138C2×#121—192no—
139C2×#121—192no—
140C2×C4×D4—192no—
141#394—191no—
142#394—192no—
143#394D1911yescharacteristic, complemented
144#384—191no—
145#380—192no—
146#380—192no—
147C2×C19—44no—
148C2×C19C2×#12112yes—
149C2×C19#53711yescharacteristic
150C2×C19D4211yescharacteristic
151C2×C19#54712yes—
152C2×C19#55511yescharacteristic
153D19—44no—
154C22×D4—192no—
155C22×D4—192no—
156C22×D4—191no—
157C22×D4C2×D1911yescharacteristic
158C23×C4—192no—
159C23×C4—192no—
160#121—388no—
161#121—388no—
162C4×D4—388no—
163C2×C4⋊C4—192no—
164C2×C4⋊C4—192no—
165C2×C4⋊C4—192no—
166C2×C4⋊C4—191no—
167C2×C4⋊C4C2×D1911yescharacteristic
168C2×C22⋊C4—192no—
169C2×C22⋊C4—192no—
170C2×C22⋊C4—192no—
171C2×C22⋊C4—192no—
172C2×C22⋊C4C2×D1912yes—
173C2×C22⋊C4C2×D1912yes—
174C2×C42—191no—
175#95—191no—
176#95—192no—
177#95C2×D1911yescharacteristic
178C19#253711yescharacteristic, complemented, Sylow
179C24—192no—
180C24C22×D1912yes—
181C2×D4—24no—
182C2×D4—41no—
183C2×D4—198no—
184C2×D4—384no—
185C2×D4—384no—
186C2×D4—384no—
187C2×D4—384no—
188C2×D4—384no—
189C2×D4—761no—
190C2×D4—762no—
191C22×C4—192no—
192C22×C4—192no—
193C22×C4—192no—
194C22×C4—384no—
195C22×C4—384no—
196C22×C4—384no—
197C22×C4—384no—
198C22×C4—384no—
199C22×C4—384no—
200C22×C4C22×D1912yes—
201C22×C4C22×D1911yescharacteristic
202C22×C4C22×D1911yescharacteristic
203C22×C4C22×D1911yescharacteristic
204C4⋊C4—41no—
205C4⋊C4—384no—
206C4⋊C4—384no—
207C4⋊C4—384no—
208C4⋊C4—761no—
209C22⋊C4—24no—
210C22⋊C4—24no—
211C22⋊C4—384no—
212C22⋊C4—384no—
213C22⋊C4—384no—
214C22⋊C4—384no—
215C42—194no—
216C23—22no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—194no—
223C23—382no—
224C23—382no—
225C23—382no—
226C23—382no—
227C23—382no—
228C23—382no—
229C23D4×D1914yes—
230C23C23×D1911yescharacteristic
231D4—44no—
232D4—3816no—
233D4—764no—
234D4—768no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—194no—
245C2×C4—194no—
246C2×C4—194no—
247C2×C4—382no—
248C2×C4—382no—
249C2×C4—382no—
250C2×C4—382no—
251C2×C4—382no—
252C2×C4—382no—
253C2×C4—768no—
254C2×C4—768no—
255C2×C4D4×D1912yes—
256C22—24no—
257C22—24no—
258C22—24no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—384no—
264C22—384no—
265C22—384no—
266C22—762no—
267C22—762no—
268C22—762no—
269C22—762no—
270C22C2×D4×D1911yescharacteristic
271C22C2×D4×D1912yes—
272C22#1059743011yescharacteristic
273C22#41×D1912yes—
274C22#1059743611yescharacteristic
275C4—22no—
276C4—41no—
277C4—41no—
278C4—42no—
279C4—198no—
280C4—762no—
281C4—762no—
282C2—44no—
283C2—764no—
284C2#121×D1912yes—
285C2#1192712111yescharacteristic
286C2#1192717611yescharacteristic
287C2#1192719212yes—
288C2#1192725611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#394C2
hypercenter#394D19
hypocenterC19#2537
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#10597330C2semidirect
2. C2×#10597385C2semidirect
3. C2×(C22⋊D19)⋊C4C2semidirect
4. #11926461C2semidirect
5. #11926460C2semidirect
6. #11926413C2semidirect
7. #11926403C2semidirect
8. #11926402C2semidirect
9. C19×#394C2semidirect
47. C2×C22⋊D19D4semidirect
70. C4×Dic19D4semidirect
137. Dic19#121semidirect
143. #394D19semidirect
178. C19#2537semidirect

Maximal subgroups

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

subgroupindex
C2×#105973302
C2×#105973852
C2×(C22⋊D19)⋊C42
#119264612
#119264602
#119264132
#119264032
#119264022
C19×#3942
#253719