Finite Group Databasebeta

← #14571636

Subgroups — #14571636

Order 2432.

578 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 125 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×#10597340C211yesmaximal, characteristic, complemented
2C2×#10597384C211yesmaximal, characteristic, complemented
3#11926483C211yesmaximal, characteristic, complemented
4#11926481C211yesmaximal, characteristic, complemented
5#11926467C212yesmaximal, complemented
6#11926460C212yesmaximal, complemented
7#11926459C212yesmaximal, complemented
8#11926453C212yesmaximal, complemented
9#11926452C211yesmaximal, characteristic, complemented
10#11926403C211yesmaximal, characteristic, complemented
11C19×#394C211yesmaximal, characteristic, complemented
12C22×D4×C19C2211yescharacteristic
13C22×C22⋊D19C2212yes—
14C22×C22⋊D19C2212yes—
15C22×D76C2211yescharacteristic
16C22×C4×D19C2211yescharacteristic
17C2×C4⋊C4×C19C2211yescharacteristic
18C2×C22⋊C4×C19C2212yes—
19C2×C22⋊C4×C19C2212yes—
20C2×C22⋊Dic19C2212yes—
21C2×C22⋊Dic19C2212yes—
22#10597384—24no—
23C2×(C2×D19)⋊C4C2211yescharacteristic
24C2×(C2×D19)⋊C4C2211yescharacteristic
25C2×(C2×D19)⋊C4C2211yescharacteristic
26C2×(C2×D19)⋊C4C2212yes—
27C2×(C2×D19)⋊C4C2212yes—
28C2×C4⋊Dic19C2211yescharacteristic
29C2×C4⋊Dic19C2212yes—
30C2×Dic19⋊C4C2211yescharacteristic
31C2×Dic19⋊C4C2212yes—
32#10597340—24no—
33C19×#95C2211yescharacteristic
34C19⋊#95C2211yescharacteristic
35C19⋊#95C2212yes—
36C19⋊#95C2212yes—
37C24×C19C2312yes—
38C23×D19C2311yescharacteristic
39C23×D19C2311yescharacteristic
40C2×D4×C19—22no—
41C2×D4×C19—42no—
42C22×C4×C19C2311yescharacteristic
43C22×C4×C19C2311yescharacteristic
44C22×C4×C19C2312yes—
45C22×C4×C19C2311yescharacteristic
46C2×C22⋊D19—24no—
47C2×C22⋊D19—42no—
48C2×C22⋊D19—42no—
49C2×C22⋊D19—42no—
50C2×C22⋊D19—42no—
51C2×C22⋊D19—42no—
52C22×Dic19C2311yescharacteristic
53C22×Dic19C2312yes—
54C22×Dic19C2312yes—
55C22×Dic19C2311yescharacteristic
56C2×D76—22no—
57C2×D76—42no—
58C2×C4×D19—42no—
59C2×C4×D19D414yescomplemented
60C4⋊C4×C19—22no—
61C22⋊C4×C19—42no—
62C22⋊C4×C19—42no—
63C22⋊Dic19—24no—
64C22⋊Dic19—42no—
65(C2×D19)⋊C4—22no—
66(C2×D19)⋊C4—22no—
67(C2×D19)⋊C4—22no—
68(C2×D19)⋊C4—42no—
69(C2×D19)⋊C4—42no—
70C4⋊Dic19—22no—
71C4⋊Dic19—42no—
72Dic19⋊C4—22no—
73Dic19⋊C4—42no—
74C23×C19—22no—
75C23×C19—22no—
76C23×C19—22no—
77C23×C19—22no—
78C23×C19—22no—
79C23×C19—22no—
80C23×C19—22no—
81C23×C19C2411yescharacteristic
82C22×D19—21no—
83C22×D19—22no—
84C22×D19—22no—
85C22×D19—21no—
86C22×D19—21no—
87C22×D19—22no—
88C22×D19—22no—
89C22×D19—21no—
90C22×D19—21no—
91C22×D19C2×D412yes—
92D4×C19—44no—
93C2×C4×C19—22no—
94C2×C4×C19—21no—
95C2×C4×C19—21no—
96C2×C4×C19—22no—
97C2×C4×C19—22no—
98C2×C4×C19—22no—
99C2×C4×C19—21no—
100C2×C4×C19—22no—
101C2×C4×C19—21no—
102C2×C4×C19C2×D412yes—
103C22⋊D19—48no—
104C22⋊D19—48no—
105C2×Dic19—22no—
106C2×Dic19—21no—
107C2×Dic19—22no—
108C2×Dic19—22no—
109C2×Dic19—22no—
110C2×Dic19—22no—
111C2×Dic19—22no—
112C2×Dic19—22no—
113C2×Dic19—22no—
114C2×Dic19C2×D412yes—
115D76—44no—
116C4×D19—44no—
117#2813—191nomaximal, Sylow
118C22×C19—42no—
119C22×C19—42no—
120C22×C19—42no—
121C22×C19—42no—
122C22×C19—42no—
123C22×C19—42no—
124C22×C19—42no—
125C22×C19C22×D411yescharacteristic
126C22×C19H(5,𝔽2)12yes—
127C22×C19H(5,𝔽2)11yescharacteristic
128C22×C19H(5,𝔽2)12yes—
129C22×C192−1+411yescharacteristic
130C2×D19—22no—
131C2×D19—22no—
132C2×D19—22no—
133C2×D19—42no—
134C2×D19—42no—
135C2×D19—41no—
136C2×D19—41no—
137C2×D19—41no—
138C2×D19—42no—
139C2×D19—42no—
140C4×C19—22no—
141C4×C19—41no—
142C4×C19—41no—
143C4×C19—42no—
144Dic19—22no—
145Dic19—41no—
146Dic19—42no—
147Dic19—42no—
148C2×#123—191no—
149C2×#121—191no—
150#400—191no—
151#399—191no—
152#396—192no—
153#394—192no—
154#394—192no—
155#394D1911yescharacteristic, complemented
156#392—191no—
157#392—192no—
158#380—191no—
159C2×C19—82no—
160C2×C19#53411yescharacteristic
161C2×C19#53511yescharacteristic
162C2×C19#53711yescharacteristic
163C2×C19#56012yes—
164C2×C19#56212yes—
165D19—42no—
166D19—81no—
167C22×D4—192no—
168C22×D4—192no—
169C22×D4—191no—
170C22×D4C2×D1911yescharacteristic
171C23×C4—191no—
172#123—384no—
173#121—384no—
174C2×C4⋊C4—191no—
175C2×C4⋊C4—191no—
176C2×C4⋊C4—192no—
177C2×C4⋊C4—192no—
178C2×C4⋊C4C2×D1911yescharacteristic
179C2×C22⋊C4—192no—
180C2×C22⋊C4—191no—
181C2×C22⋊C4—191no—
182C2×C22⋊C4—191no—
183C2×C22⋊C4—192no—
184C2×C22⋊C4—192no—
185C2×C22⋊C4—192no—
186C2×C22⋊C4C2×D1912yes—
187C2×C22⋊C4C2×D1912yes—
188#95—191no—
189#95—192no—
190#95—192no—
191#95C2×D1911yescharacteristic
192C19#281311yescharacteristic, complemented, Sylow
193C24—191no—
194C24—191no—
195C24C22×D1912yes—
196C2×D4—22no—
197C2×D4—42no—
198C2×D4—382no—
199C2×D4—384no—
200C2×D4—762no—
201C2×D4—762no—
202C2×D4—762no—
203C2×D4—762no—
204C2×D4—762no—
205C2×D4—762no—
206C22×C4—191no—
207C22×C4—194no—
208C22×C4—192no—
209C22×C4—192no—
210C22×C4—191no—
211C22×C4—762no—
212C22×C4C22×D1911yescharacteristic
213C22×C4C22×D1911yescharacteristic
214C22×C4C22×D1912yes—
215C22×C4C22×D1911yescharacteristic
216C4⋊C4—22no—
217C4⋊C4—382no—
218C4⋊C4—382no—
219C4⋊C4—762no—
220C4⋊C4—762no—
221C22⋊C4—42no—
222C22⋊C4—42no—
223C22⋊C4—382no—
224C22⋊C4—382no—
225C22⋊C4—384no—
226C22⋊C4—382no—
227C22⋊C4—762no—
228C22⋊C4—762no—
229C22⋊C4—762no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23—22no—
235C23—22no—
236C23—22no—
237C23—192no—
238C23—381no—
239C23—382no—
240C23—382no—
241C23—381no—
242C23—381no—
243C23—382no—
244C23—381no—
245C23—382no—
246C23—381no—
247C23C23×D1911yescharacteristic
248D4—44no—
249D4—764no—
250D4—768no—
251D4—768no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—192no—
262C2×C4—382no—
263C2×C4—381no—
264C2×C4—382no—
265C2×C4—382no—
266C2×C4—382no—
267C2×C4—382no—
268C2×C4—382no—
269C2×C4—382no—
270C2×C4—382no—
271C2×C4—764no—
272C2×C4D4×D1912yes—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—382no—
281C22—382no—
282C22—382no—
283C22—762no—
284C22—762no—
285C22—761no—
286C22—761no—
287C22—761no—
288C22—762no—
289C22—762no—
290C22C2×D4×D1911yescharacteristic
291C22#1059743012yes—
292C22#1059743011yescharacteristic
293C22#1059743512yes—
294C22#1059743611yescharacteristic
295C4—22no—
296C4—41no—
297C4—41no—
298C4—42no—
299C4—382no—
300C4—762no—
301C4—761no—
302C4—762no—
303C2—82no—
304C2—762no—
305C2—1521no—
306C2#1192710411yescharacteristic
307C2#1192711211yescharacteristic
308C2#1192712311yescharacteristic
309C2#1192728212yes—
310C2#1192729112yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#394C2
hypercenter#394D19
hypocenterC19#2813
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#10597340C2semidirect
2. C2×#10597384C2semidirect
3. #11926483C2semidirect
4. #11926481C2semidirect
5. #11926467C2semidirect
6. #11926460C2semidirect
7. #11926459C2semidirect
8. #11926453C2semidirect
9. #11926452C2semidirect
10. #11926403C2semidirect
11. C19×#394C2semidirect
59. C2×C4×D19D4semidirect
155. #394D19semidirect
192. C19#2813semidirect

Maximal subgroups

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

subgroupindex
C2×#105973402
C2×#105973842
#119264832
#119264812
#119264672
#119264602
#119264592
#119264532
#119264522
#119264032
C19×#3942
#281319