Finite Group Databasebeta

← #14568101

Subgroups — #14568101

Order 2432.

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

normal subgroups only

This group has 708 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×#10597340C212yesmaximal, complemented
2C2×#10597329C212yesmaximal, complemented
3C2×#10597330C211yesmaximal, characteristic
4C2×C4⋊C4×D19C211yesmaximal, characteristic, complemented
5#11926481C211yesmaximal, characteristic, complemented
6#11926480C211yesmaximal, characteristic, complemented
7#11926479C211yesmaximal, characteristic, complemented
8#11926444C212yesmaximal, complemented
9#11926413C212yesmaximal, complemented
10#11926391C211yesmaximal, characteristic, complemented
11C19×#399C211yesmaximal, characteristic, complemented
12C22×C22⋊D19C2211yescharacteristic
13C22×C22⋊D19C2211yescharacteristic
14C22×D76C2211yescharacteristic
15C22×C4×D19C2212yes—
16C22×C4×D19C2211yescharacteristic
17C2×C4⋊C4×C19C2212yes—
18C2×C4⋊C4×C19C2211yescharacteristic
19C2×C22⋊C4×C19C2212yes—
20C2×C22⋊C4×C19C2211yescharacteristic
21C2×C22⋊Dic19C2212yes—
22C2×(C2×D19)⋊C4C2212yes—
23C2×(C2×D19)⋊C4C2212yes—
24C2×(C2×D19)⋊C4C2211yescharacteristic
25C2×(C2×D19)⋊C4C2212yes—
26C2×C4⋊Dic19C2212yes—
27C2×C4⋊Dic19C2211yescharacteristic
28C2×Dic19⋊C4C2212yes—
29C2×Dic19⋊C4C2212yes—
30C2×Dic19⋊C4C2211yescharacteristic
31C2×Dic19⋊C4C2212yes—
32C2×C4×Dic19C2212yes—
33#10597340—28no—
34C4⋊C4×D19—24no—
35#10597330—24no—
36#10597329—28no—
37C19×#95C2211yescharacteristic
38C19⋊#95C2211yescharacteristic
39C24×C19C2311yescharacteristic
40C23×D19C2311yescharacteristic
41C23×D19C2311yescharacteristic
42C22×C4×C19C2312yes—
43C22×C4×C19C2311yescharacteristic
44C22×C4×C19C2311yescharacteristic
45C22×C4×C19C2312yes—
46C2×C22⋊D19—24no—
47C2×C22⋊D19—22no—
48C2×C22⋊D19—22no—
49C2×C22⋊D19—24no—
50C22×Dic19C2312yes—
51C22×Dic19C2311yescharacteristic
52C22×Dic19C2312yes—
53C22×Dic19C2311yescharacteristic
54C2×D76—22no—
55C2×D76—24no—
56C2×C4×D19—24no—
57C2×C4×D19—24no—
58C2×C4×D19—24no—
59C2×C4×D19—24no—
60C2×C4×D19D414yes—
61C4⋊C4×C19—22no—
62C4⋊C4×C19—24no—
63C22⋊C4×C19—24no—
64C22⋊C4×C19—22no—
65C22⋊Dic19—24no—
66(C2×D19)⋊C4—22no—
67(C2×D19)⋊C4—24no—
68(C2×D19)⋊C4—24no—
69(C2×D19)⋊C4D418yescomplemented
70C4⋊Dic19—24no—
71C4⋊Dic19—22no—
72Dic19⋊C4—24no—
73Dic19⋊C4—22no—
74Dic19⋊C4—24no—
75Dic19⋊C4—24no—
76C4×Dic19—24no—
77C23×C19—22no—
78C23×C19—21no—
79C23×C19—22no—
80C23×C19—21no—
81C23×C19—21no—
82C23×C19C2411yescharacteristic
83C22×D19—22no—
84C22×D19—21no—
85C22×D19—21no—
86C22×D19—22no—
87C22×D19—21no—
88C22×D19—22no—
89C22×D19—21no—
90C22×D19—21no—
91C22×D19C2×D414yes—
92C22×D19C2×D412yes—
93C2×C4×C19—22no—
94C2×C4×C19—22no—
95C2×C4×C19—22no—
96C2×C4×C19—22no—
97C2×C4×C19—21no—
98C2×C4×C19—22no—
99C2×C4×C19—22no—
100C2×C4×C19—22no—
101C2×C4×C19C2×D414yes—
102C2×C4×C19C2×D412yes—
103C22⋊D19—44no—
104C22⋊D19—44no—
105C2×Dic19—22no—
106C2×Dic19—22no—
107C2×Dic19—22no—
108C2×Dic19—22no—
109C2×Dic19—22no—
110C2×Dic19—21no—
111C2×Dic19—22no—
112C2×Dic19C2×D414yes—
113C2×Dic19C2×D412yes—
114C2×Dic19#4114yes—
115D76—44no—
116C4×D19—28no—
117C4×D19—48no—
118#2501—191nomaximal, Sylow
119C22×C19—41no—
120C22×C19—41no—
121C22×C19—41no—
122C22×C19—42no—
123C22×C19—42no—
124C22×C19C22×D411yescharacteristic
125C22×C19C22×D412yes—
126C22×C19C2×#4112yes—
127C22×C192−1+411yescharacteristic
128C22×C192−1+411yescharacteristic
129C2×D19—22no—
130C2×D19—22no—
131C2×D19—24no—
132C2×D19—24no—
133C2×D19—41no—
134C2×D19—41no—
135C2×D19—41no—
136C2×D19—42no—
137C2×D19—42no—
138C2×D19#12714yes—
139C4×C19—22no—
140C4×C19—24no—
141C4×C19—42no—
142C4×C19—41no—
143Dic19—24no—
144Dic19—42no—
145Dic19—41no—
146Dic19#12314yescomplemented
147C2×#123—192no—
148C2×#123—192no—
149C2×#121—191no—
150C22×C4⋊C4—191no—
151#399—191no—
152#399—191no—
153#399—191no—
154#399D1911yescharacteristic, complemented
155#390—192no—
156#384—192no—
157C4×C22⋊C4—191no—
158C2×C19—81no—
159C2×C19C2×#12311yescharacteristic
160C2×C19C2×#12711yescharacteristic
161C2×C19#53611yescharacteristic
162C2×C19#54712yes—
163C2×C19#54712yes—
164D19—24no—
165D19—81no—
166C22×D4—191no—
167C22×D4—191no—
168C22×D4—191no—
169C23×C4—191no—
170C23×C4—192no—
171#123—388no—
172#123—388no—
173#121—384no—
174C2×C4⋊C4—192no—
175C2×C4⋊C4—191no—
176C2×C4⋊C4—191no—
177C2×C4⋊C4—192no—
178C2×C4⋊C4—192no—
179C2×C4⋊C4—192no—
180C2×C4⋊C4—384no—
181C2×C4⋊C4C2×D1911yescharacteristic
182C2×C4⋊C4C2×D1912yes—
183C2×C22⋊C4—192no—
184C2×C22⋊C4—192no—
185C2×C22⋊C4—191no—
186C2×C22⋊C4—192no—
187C2×C22⋊C4—192no—
188C2×C22⋊C4C2×D1911yescharacteristic
189C2×C22⋊C4C2×D1912yes—
190C2×C42—192no—
191#95—191no—
192#95C2×D1911yescharacteristic
193C19#250111yescharacteristic, complemented, Sylow
194C24—191no—
195C24—191no—
196C24C22×D1911yescharacteristic
197C2×D4—382no—
198C2×D4—384no—
199C2×D4—382no—
200C2×D4—384no—
201C2×D4—382no—
202C2×D4—384no—
203C22×C4—191no—
204C22×C4—192no—
205C22×C4—194no—
206C22×C4—192no—
207C22×C4—191no—
208C22×C4—384no—
209C22×C4—384no—
210C22×C4—384no—
211C22×C4—384no—
212C22×C4C22×D1912yes—
213C22×C4C22×D1911yescharacteristic
214C22×C4C22×D1911yescharacteristic
215C22×C4C22×D1912yes—
216C4⋊C4—22no—
217C4⋊C4—24no—
218C4⋊C4—384no—
219C4⋊C4—382no—
220C4⋊C4—384no—
221C4⋊C4—384no—
222C4⋊C4—382no—
223C4⋊C4—384no—
224C22⋊C4—22no—
225C22⋊C4—24no—
226C22⋊C4—198no—
227C22⋊C4—384no—
228C22⋊C4—384no—
229C22⋊C4—382no—
230C22⋊C4—384no—
231C42—384no—
232C23—22no—
233C23—21no—
234C23—21no—
235C23—22no—
236C23—21no—
237C23—194no—
238C23—192no—
239C23—381no—
240C23—382no—
241C23—381no—
242C23—382no—
243C23—381no—
244C23—381no—
245C23—382no—
246C23—381no—
247C23C23×D1911yescharacteristic
248D4—764no—
249D4—764no—
250D4—764no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—192no—
260C2×C4—194no—
261C2×C4—194no—
262C2×C4—388no—
263C2×C4—382no—
264C2×C4—382no—
265C2×C4—382no—
266C2×C4—382no—
267C2×C4—381no—
268C2×C4—382no—
269C2×C4—382no—
270C2×C4—768no—
271C2×C4D4×D1914yes—
272C2×C4D4×D1912yes—
273C22—41no—
274C22—41no—
275C22—41no—
276C22—42no—
277C22—42no—
278C22—194no—
279C22—382no—
280C22—382no—
281C22—384no—
282C22—384no—
283C22—761no—
284C22—761no—
285C22—761no—
286C22—762no—
287C22—762no—
288C22C2×D4×D1911yescharacteristic
289C22C2×D4×D1912yes—
290C22#1059743311yescharacteristic
291C22#41×D1912yes—
292C22#1059743611yescharacteristic
293C4—22no—
294C4—24no—
295C4—42no—
296C4—41no—
297C4—194no—
298C4—384no—
299C4—762no—
300C4—761no—
301C2—81no—
302C2—384no—
303C2—1521no—
304C2#123×D1911yescharacteristic
305C2#127×D1911yescharacteristic
306C2#1192711711yescharacteristic
307C2#1192719212yes—
308C2#1192719612yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#399C2
prime radicalC2×#10597330C2
hypercenter#399D19
hypocenterC19#2501
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#10597340C2semidirect
2. C2×#10597329C2semidirect
4. C2×C4⋊C4×D19C2semidirect
5. #11926481C2semidirect
6. #11926480C2semidirect
7. #11926479C2semidirect
8. #11926444C2semidirect
9. #11926413C2semidirect
10. #11926391C2semidirect
11. C19×#399C2semidirect
69. (C2×D19)⋊C4D4semidirect
146. Dic19#123semidirect
154. #399D19semidirect
193. C19#2501semidirect

Maximal subgroups

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

subgroupindex
C2×#105973402
C2×#105973292
C2×#105973302
C2×C4⋊C4×D192
#119264812
#119264802
#119264792
#119264442
#119264132
#119263912
C19×#3992
#250119