Finite Group Databasebeta

← #14568539

Subgroups — #14568539

Order 2432.

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

normal subgroups only

This group has 604 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×#10597324C212yesmaximal, complemented
2C2×#10597333C211yesmaximal, characteristic, complemented
3C2×D4×Dic19C211yesmaximal, characteristic
4#11926476C211yesmaximal, characteristic, complemented
5#11926474C211yesmaximal, characteristic, complemented
6#11926458C211yesmaximal, characteristic
7#11926438C212yesmaximal, complemented
8#11926437C212yesmaximal, complemented
9#11926408C211yesmaximal, characteristic, complemented
10#11926402C212yesmaximal, complemented
11C19×#394C211yesmaximal, characteristic
12C22×D4×C19C2211yescharacteristic
13C23×Dic19C2212yes—
14C22×Dic38C2211yescharacteristic
15C2×C4⋊C4×C19C2211yescharacteristic
16C2×C22⋊C4×C19C2212yes—
17C2×C22⋊C4×C19C2212yes—
18C2×C22⋊Dic19C2212yes—
19C2×C22⋊Dic19C2212yes—
20C2×C22⋊Dic19C2212yes—
21D4×Dic19—24no—
22C2×C4⋊Dic19C2212yes—
23C2×C4⋊Dic19C2211yescharacteristic
24C2×Dic19⋊C4C2212yes—
25C2×Dic19⋊C4C2212yes—
26C2×Dic19⋊C4C2211yescharacteristic
27C2×Dic19⋊C4C2211yescharacteristic
28C2×C4×Dic19C2211yescharacteristic
29C2×C4×Dic19C2211yescharacteristic
30C2×C4×Dic19C2211yescharacteristic
31#10597333—24no—
32#10597324—28no—
33C19×#95C2211yescharacteristic
34C19⋊#95C2212yes—
35C19⋊#95C2212yes—
36C19⋊#95C2212yes—
37C19⋊#95C2211yescharacteristic
38C24×C19C2312yes—
39C2×D4×C19—24no—
40C2×D4×C19—22no—
41C22×C4×C19C2311yescharacteristic
42C22×C4×C19C2312yes—
43C22×C4×C19C2311yescharacteristic
44C22×C4×C19C2311yescharacteristic
45C22×Dic19—24no—
46C22×Dic19—24no—
47C22×Dic19—24no—
48C22×Dic19C2312yes—
49C22×Dic19C2311yescharacteristic
50C22×Dic19C2312yes—
51C22×Dic19C2311yescharacteristic
52C22×Dic19C2311yescharacteristic
53C22×Dic19C2311yescharacteristic
54C2×Dic38—22no—
55C2×Dic38—22no—
56C2×Dic38D414yescomplemented
57C4⋊C4×C19—22no—
58C22⋊C4×C19—24no—
59C22⋊C4×C19—24no—
60C22⋊Dic19—24no—
61C22⋊Dic19—24no—
62C22⋊Dic19—24no—
63C4⋊Dic19—22no—
64C4⋊Dic19—24no—
65Dic19⋊C4—24no—
66Dic19⋊C4—22no—
67Dic19⋊C4—24no—
68Dic19⋊C4—22no—
69C4×Dic19—22no—
70C4×Dic19—22no—
71C4×Dic19D414yes—
72C23×C19—22no—
73C23×C19—22no—
74C23×C19—22no—
75C23×C19—22no—
76C23×C19—22no—
77C23×C19—22no—
78C23×C19#4114yes—
79C23×C19C2411yescharacteristic
80D4×C19—28no—
81C2×C4×C19—21no—
82C2×C4×C19—21no—
83C2×C4×C19—22no—
84C2×C4×C19—21no—
85C2×C4×C19—22no—
86C2×C4×C19—22no—
87C2×C4×C19—22no—
88C2×C4×C19—22no—
89C2×C4×C19C2×D412yes—
90C2×C4×C19C2×D412yes—
91C2×Dic19—21no—
92C2×Dic19—21no—
93C2×Dic19—22no—
94C2×Dic19—21no—
95C2×Dic19—22no—
96C2×Dic19—22no—
97C2×Dic19—22no—
98C2×Dic19—22no—
99C2×Dic19—22no—
100C2×Dic19—22no—
101C2×Dic19—22no—
102C2×Dic19—48no—
103C2×Dic19C2×D412yes—
104C2×Dic19C2×D412yes—
105C2×Dic19C2×D412yes—
106C2×Dic19C2×D412yes—
107C2×Dic19#4112yes—
108Dic38—28no—
109#2536—191nomaximal, Sylow
110C22×C19—24no—
111C22×C19—24no—
112C22×C19—24no—
113C22×C19—42no—
114C22×C19—42no—
115C22×C19—42no—
116C22×C19—42no—
117C22×C19C22×D411yescharacteristic
118C22×C19C22×D411yescharacteristic
119C22×C19C2×#4112yes—
120C22×C19C2×#4111yescharacteristic
121C22×C192−1+412yes—
122C4×C19—22no—
123C4×C19—22no—
124C4×C19—41no—
125C4×C19—42no—
126Dic19—22no—
127Dic19—22no—
128Dic19—42no—
129Dic19—41no—
130Dic19—42no—
131Dic19#12114yes—
132C2×C22⋊Q8—192no—
133C2×C4×Q8—191no—
134C2×C4×D4—191no—
135#398—191no—
136#398—191no—
137#394—191no—
138#394D1911yescharacteristic
139#388—192no—
140#388—192no—
141#382—191no—
142#380—192no—
143C2×C19—44no—
144C2×C19C2×#12111yescharacteristic
145C2×C19#52511yescharacteristic
146C2×C19#53611yescharacteristic
147C2×C19#54812yes—
148C2×C19#55212yes—
149C22×Q8—191no—
150C22×D4C2×D1911yescharacteristic
151C23×C4—192no—
152C22⋊Q8—388no—
153C4×Q8—384no—
154C4×D4—384no—
155C2×C4⋊C4—191no—
156C2×C4⋊C4—191no—
157C2×C4⋊C4—191no—
158C2×C4⋊C4—192no—
159C2×C4⋊C4—192no—
160C2×C4⋊C4—192no—
161C2×C4⋊C4C2×D1911yescharacteristic
162C2×C22⋊C4—192no—
163C2×C22⋊C4—192no—
164C2×C22⋊C4—192no—
165C2×C22⋊C4C2×D1912yes—
166C2×C22⋊C4C2×D1912yes—
167C2×C42—191no—
168C2×C42—191no—
169C2×C42—191no—
170#95—192no—
171#95—192no—
172#95—192no—
173#95—191no—
174#95C2×D1911yescharacteristic
175C19#253611yescharacteristic, complemented, Sylow
176C24C22×D1912yes—
177C2×Q8—194no—
178C2×Q8—382no—
179C2×Q8—382no—
180C2×D4—24no—
181C2×D4—22no—
182C22×C4—191no—
183C22×C4—191no—
184C22×C4—191no—
185C22×C4—192no—
186C22×C4—191no—
187C22×C4—192no—
188C22×C4—384no—
189C22×C4—384no—
190C22×C4—384no—
191C22×C4C22×D1912yes—
192C22×C4C22×D1911yescharacteristic
193C22×C4C22×D1911yescharacteristic
194C22×C4C22×D1911yescharacteristic
195C4⋊C4—22no—
196C4⋊C4—382no—
197C4⋊C4—384no—
198C4⋊C4—384no—
199C4⋊C4—382no—
200C4⋊C4—384no—
201C4⋊C4—382no—
202C22⋊C4—24no—
203C22⋊C4—24no—
204C22⋊C4—384no—
205C22⋊C4—384no—
206C22⋊C4—384no—
207C42—194no—
208C42—382no—
209C42—382no—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—22no—
214C23—22no—
215C23—22no—
216C23#6454314yes—
217C23C23×D1911yescharacteristic
218Q8—388no—
219D4—28no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—192no—
229C2×C4—192no—
230C2×C4—192no—
231C2×C4—192no—
232C2×C4—192no—
233C2×C4—381no—
234C2×C4—381no—
235C2×C4—382no—
236C2×C4—381no—
237C2×C4—382no—
238C2×C4—382no—
239C2×C4—382no—
240C2×C4—382no—
241C2×C4—382no—
242C2×C4—382no—
243C2×C4—382no—
244C2×C4—768no—
245C2×C4D4×D1912yes—
246C2×C4D4×D1912yes—
247C22—24no—
248C22—24no—
249C22—24no—
250C22—42no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22C2×D4×D1911yescharacteristic
255C22C2×D4×D1911yescharacteristic
256C22C2×#6454312yes—
257C22#41×D1911yescharacteristic
258C22#1059743612yes—
259C4—22no—
260C4—22no—
261C4—41no—
262C4—42no—
263C4—194no—
264C4—382no—
265C4—382no—
266C4—761no—
267C4—762no—
268C4—762no—
269C2—44no—
270C2#121×D1911yescharacteristic
271C2#1192705011yescharacteristic
272C2#1192711411yescharacteristic
273C2#1192720012yes—
274C2#1192723112yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#394C2
prime radicalC22×D4×C19C22
hypercenter#394D19
hypocenterC19#2536
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#10597324C2semidirect
2. C2×#10597333C2semidirect
4. #11926476C2semidirect
5. #11926474C2semidirect
7. #11926438C2semidirect
8. #11926437C2semidirect
9. #11926408C2semidirect
10. #11926402C2semidirect
56. C2×Dic38D4semidirect
175. C19#2536semidirect

Maximal subgroups

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

subgroupindex
C2×#105973242
C2×#105973332
C2×D4×Dic192
#119264762
#119264742
#119264582
#119264382
#119264372
#119264082
#119264022
C19×#3942
#253619