Finite Group Databasebeta

← #14571635

Subgroups — #14571635

Order 2432.

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

normal subgroups only

This group has 578 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×#10597375C211yesmaximal, characteristic, complemented
2#11926482C211yesmaximal, characteristic, complemented
3#11926479C211yesmaximal, characteristic, complemented
4#11926467C212yesmaximal, complemented
5#11926460C212yesmaximal, complemented
6#11926458C212yesmaximal, complemented
7#11926458C211yesmaximal, characteristic, complemented
8#11926452C212yesmaximal, complemented
9#11926452C211yesmaximal, characteristic, complemented
10#11926404C211yesmaximal, characteristic, complemented
11C2×C19×#121C211yesmaximal, characteristic, complemented
12C22×D4×C19C2212yes—
13C22×D4×C19C2211yescharacteristic
14C23×C4×C19C2211yescharacteristic
15C22×C22⋊D19C2211yescharacteristic
16C22×C22⋊D19C2212yes—
17C19×#121—24no—
18C2×C4⋊C4×C19C2211yescharacteristic
19C2×C22⋊C4×C19C2212yes—
20C2×C22⋊Dic19C2211yescharacteristic
21C2×C22⋊Dic19C2212yes—
22C2×C22⋊Dic19C2212yes—
23C2×C22⋊Dic19C2212yes—
24C2×C22⋊Dic19C2212yes—
25#10597375—24no—
26C2×(C2×D19)⋊C4C2211yescharacteristic
27C2×(C2×D19)⋊C4C2211yescharacteristic
28C2×(C2×D19)⋊C4C2212yes—
29C2×C4⋊Dic19C2212yes—
30C2×Dic19⋊C4C2211yescharacteristic
31C2×Dic19⋊C4C2211yescharacteristic
32C2×Dic19⋊C4C2212yes—
33C19⋊#95C2211yescharacteristic
34C19⋊#95C2211yescharacteristic
35C19⋊#95C2212yes—
36C19⋊#95C2212yes—
37C24×C19C2312yes—
38C24×C19C2311yescharacteristic
39C23×D19C2311yescharacteristic
40C2×D4×C19—24no—
41C2×D4×C19—22no—
42C2×D4×C19—42no—
43C2×D4×C19—42no—
44C2×D4×C19—42no—
45C22×C4×C19—42no—
46C22×C4×C19D414yescomplemented
47C22×C4×C19C2312yes—
48C22×C4×C19C2311yescharacteristic
49C22×C4×C19C2311yescharacteristic
50C2×C22⋊D19—22no—
51C2×C22⋊D19—42no—
52C2×C22⋊D19—42no—
53C2×C22⋊D19—42no—
54C2×C22⋊D19—42no—
55C22×Dic19C2311yescharacteristic
56C22×Dic19C2312yes—
57C22×Dic19C2311yescharacteristic
58C22×Dic19C2312yes—
59C22×Dic19C2311yescharacteristic
60C4⋊C4×C19—22no—
61C22⋊C4×C19—24no—
62C22⋊Dic19—22no—
63C22⋊Dic19—42no—
64C22⋊Dic19—42no—
65C22⋊Dic19—42no—
66C22⋊Dic19—42no—
67(C2×D19)⋊C4—22no—
68(C2×D19)⋊C4—22no—
69(C2×D19)⋊C4—42no—
70C4⋊Dic19—42no—
71Dic19⋊C4—22no—
72Dic19⋊C4—22no—
73Dic19⋊C4—42no—
74C23×C19—21no—
75C23×C19—22no—
76C23×C19—22no—
77C23×C19—21no—
78C23×C19—22no—
79C23×C19—22no—
80C23×C19—22no—
81C23×C19—22no—
82C23×C19—22no—
83C23×C19—22no—
84C23×C19—22no—
85C23×C19C2×D412yes—
86C23×C19C2411yescharacteristic
87C22×D19—21no—
88C22×D19—22no—
89C22×D19—22no—
90C22×D19—21no—
91C22×D19—21no—
92D4×C19—44no—
93D4×C19—48no—
94C2×C4×C19—22no—
95C2×C4×C19—22no—
96C2×C4×C19—22no—
97C2×C4×C19—22no—
98C2×C4×C19—22no—
99C2×C4×C19—44no—
100C2×C4×C19C2×D412yes—
101C2×C4×C19C2×D412yes—
102C22⋊D19—44no—
103C22⋊D19—48no—
104C2×Dic19—21no—
105C2×Dic19—21no—
106C2×Dic19—21no—
107C2×Dic19—22no—
108C2×Dic19—22no—
109C2×Dic19—22no—
110C2×Dic19—22no—
111C2×Dic19—21no—
112C2×Dic19—22no—
113C2×Dic19—22no—
114C2×Dic19—22no—
115C2×Dic19—22no—
116C2×Dic19—21no—
117#2813—191nomaximal, Sylow
118C22×C19—22no—
119C22×C19—22no—
120C22×C19—22no—
121C22×C19—42no—
122C22×C19—42no—
123C22×C19—42no—
124C22×C19—42no—
125C22×C19—42no—
126C22×C19—42no—
127C22×C19—42no—
128C22×C19—42no—
129C22×C19—42no—
130C22×C19C22×D411yescharacteristic
131C22×C19H(5,𝔽2)12yes—
132C22×C19H(5,𝔽2)12yes—
133C22×C19H(5,𝔽2)11yescharacteristic
134C22×C192−1+411yescharacteristic
135C2×D19—41no—
136C2×D19—41no—
137C2×D19—41no—
138C2×D19—42no—
139C2×D19—42no—
140C4×C19—22no—
141C4×C19—22no—
142C4×C19—42no—
143Dic19—41no—
144Dic19—41no—
145Dic19—41no—
146Dic19—42no—
147Dic19—42no—
148C2×#123—191no—
149C2×#121D1911yescharacteristic, complemented
150#400—191no—
151#399—191no—
152#396—192no—
153#394—191no—
154#394—192no—
155#394—192no—
156#392—191no—
157#392—192no—
158#380—191no—
159C2×C19—42no—
160C2×C19—82no—
161C2×C19#53411yescharacteristic
162C2×C19#53511yescharacteristic
163C2×C19#53711yescharacteristic
164C2×C19#56012yes—
165C2×C19#56212yes—
166D19—81no—
167C22×D4—191no—
168C22×D4—192no—
169C22×D4C2×D1912yes—
170C22×D4C2×D1911yescharacteristic
171C23×C4C2×D1911yescharacteristic
172#123—384no—
173#121—24no—
174C2×C4⋊C4—191no—
175C2×C4⋊C4—191no—
176C2×C4⋊C4—192no—
177C2×C4⋊C4—192no—
178C2×C4⋊C4C2×D1911yescharacteristic
179C2×C22⋊C4—191no—
180C2×C22⋊C4—191no—
181C2×C22⋊C4—191no—
182C2×C22⋊C4—192no—
183C2×C22⋊C4—192no—
184C2×C22⋊C4—192no—
185C2×C22⋊C4—192no—
186C2×C22⋊C4—192no—
187C2×C22⋊C4C2×D1912yes—
188#95—191no—
189#95—191no—
190#95—192no—
191#95—192no—
192C19#281311yescharacteristic, complemented, Sylow
193C24—191no—
194C24C22×D1912yes—
195C24C22×D1911yescharacteristic
196C2×D4—24no—
197C2×D4—22no—
198C2×D4—42no—
199C2×D4—42no—
200C2×D4—42no—
201C2×D4—382no—
202C2×D4—762no—
203C2×D4—762no—
204C2×D4—762no—
205C2×D4—762no—
206C22×C4—42no—
207C22×C4—192no—
208C22×C4—191no—
209C22×C4—191no—
210C22×C4—192no—
211C22×C4—191no—
212C22×C4C22⋊D1914yescomplemented
213C22×C4C22×D1912yes—
214C22×C4C22×D1911yescharacteristic
215C22×C4C22×D1911yescharacteristic
216C4⋊C4—22no—
217C4⋊C4—382no—
218C4⋊C4—382no—
219C4⋊C4—762no—
220C4⋊C4—762no—
221C22⋊C4—24no—
222C22⋊C4—382no—
223C22⋊C4—382no—
224C22⋊C4—382no—
225C22⋊C4—762no—
226C22⋊C4—762no—
227C22⋊C4—762no—
228C22⋊C4—762no—
229C22⋊C4—762no—
230C23—22no—
231C23—22no—
232C23—21no—
233C23—21no—
234C23—22no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—22no—
241C23—382no—
242C23—382no—
243C23—381no—
244C23—381no—
245C23—381no—
246C23C2×C22⋊D1912yes—
247C23C23×D1911yescharacteristic
248D4—44no—
249D4—48no—
250D4—764no—
251D4—768no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—44no—
258C2×C4—382no—
259C2×C4—382no—
260C2×C4—382no—
261C2×C4—382no—
262C2×C4—382no—
263C2×C4—382no—
264C2×C4—381no—
265C2×C4—382no—
266C2×C4—382no—
267C2×C4—381no—
268C2×C4—381no—
269C2×C4—381no—
270C2×C4—381no—
271C2×C4C2×C22⋊D1912yes—
272C2×C4C2×C22⋊D1912yes—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—761no—
286C22—761no—
287C22—761no—
288C22—762no—
289C22—762no—
290C22#1059743012yes—
291C22#1059743012yes—
292C22#1059743511yescharacteristic
293C22#1059743611yescharacteristic
294C22C22×C22⋊D1911yescharacteristic
295C4—22no—
296C4—22no—
297C4—42no—
298C4—761no—
299C4—761no—
300C4—761no—
301C4—762no—
302C4—762no—
303C2—42no—
304C2—82no—
305C2—1521no—
306C2#1192710311yescharacteristic
307C2#1192711111yescharacteristic
308C2#1192712211yescharacteristic
309C2#1192728212yes—
310C2#1192728912yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#121C2
hypercenterC2×#121D19
hypocenterC19#2813
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10597375C2semidirect
2. #11926482C2semidirect
3. #11926479C2semidirect
4. #11926467C2semidirect
5. #11926460C2semidirect
6. #11926458C2semidirect
7. #11926458C2semidirect
8. #11926452C2semidirect
9. #11926452C2semidirect
10. #11926404C2semidirect
11. C2×C19×#121C2semidirect
46. C22×C4×C19D4semidirect
149. C2×#121D19semidirect
192. C19#2813semidirect
212. C22×C4C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
C2×#105973752
#119264822
#119264792
#119264672
#119264602
#119264582
#119264522
#119264042
C2×C19×#1212
#281319