Finite Group Databasebeta

← #14564765

Subgroups — #14564765

Order 2432.

430 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 73 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
1#11927103C211yesmaximal, characteristic
2C2×#10597332C211yesmaximal, characteristic, complemented
3C2×#10597381C211yesmaximal, characteristic, complemented
4C2×#10597263C211yesmaximal, characteristic, complemented
5#11926405C211yesmaximal, characteristic, complemented
6#11926310C211yesmaximal, characteristic, complemented
7C2×C19×#99C211yesmaximal, characteristic, complemented
8C22×D4×C19C2211yescharacteristic
9C22×C22⋊D19C2211yescharacteristic
10C23×Dic19C2211yescharacteristic
11C2×C22⋊C4×C19C2211yescharacteristic
12C2×C22⋊C4×C19C2211yescharacteristic
13#10597399—21no—
14C2×C22⋊Dic19—21no—
15C2×C22⋊Dic19C2211yescharacteristic
16C2×C22⋊Dic19C2211yescharacteristic
17#10597385—22no—
18#10597383—21no—
19#10597381—21no—
20#10597381—22no—
21#10597381—22no—
22#10597375—21no—
23C2×(C2×D19)⋊C4—21no—
24C2×C4⋊Dic19—21no—
25C2×Dic19⋊C4—21no—
26#10597332—22no—
27#10597332—22no—
28C19×#99—22no—
29C19⋊#95—22no—
30#10597263—22no—
31C24×C19D411yescharacteristic
32C24×C19C2311yescharacteristic
33C23×D19D411yescharacteristic
34C2×D4×C19—21no—
35C2×D4×C19—21no—
36C2×D4×C19—21no—
37C2×D4×C19—21no—
38C2×D4×C19—21no—
39C2×D4×C19—21no—
40C22×C4×C19—21no—
41C22×C4×C19—21no—
42C22×C4×C19D411yescharacteristic
43C2×C22⋊D19—21no—
44C2×C22⋊D19—21no—
45C2×C22⋊D19—21no—
46C2×C22⋊D19—21no—
47C2×C22⋊D19—21no—
48C2×C22⋊D19—21no—
49C2×C22⋊D19—22no—
50C22×Dic19—21no—
51C22×Dic19—21no—
52C22×Dic19—21no—
53C22×Dic19—21no—
54C22×Dic19—21no—
55C22×Dic19—21no—
56C22×Dic19—21no—
57C22×Dic19D411yescharacteristic
58C22×Dic19D412yes—
59C22×Dic19D412yescomplemented
60C22⋊C4×C19—21no—
61C22⋊C4×C19—21no—
62C22⋊C4×C19—21no—
63C22⋊C4×C19D412yescomplemented
64C22⋊Dic19—24no—
65C22⋊Dic19—22no—
66C22⋊Dic19—21no—
67C22⋊Dic19—21no—
68C22⋊Dic19—21no—
69C22⋊Dic19D412yescomplemented
70(C2×D19)⋊C4—22no—
71(C2×D19)⋊C4—24no—
72C4⋊Dic19—24no—
73Dic19⋊C4—24no—
74Dic19⋊C4—22no—
75C23×C19—21no—
76C23×C19—21no—
77C23×C19—21no—
78C23×C19—42no—
79C23×C19—42no—
80C23×C19C2×D411yescharacteristic
81C23×C19C2×D411yescharacteristic
82C23×C19C2×D411yescharacteristic
83C23×C19C2×D411yescharacteristic
84C23×C19C2×D411yescharacteristic
85C23×C19C2×D411yescharacteristic
86C23×C19#4111yescharacteristic
87C22×D19—21no—
88C22×D19—21no—
89C22×D19—21no—
90C22×D19—42no—
91D4×C19—41no—
92D4×C19—41no—
93D4×C19—41no—
94D4×C19—41no—
95C2×C4×C19—21no—
96C2×C4×C19—21no—
97C2×C4×C19—22no—
98C2×C4×C19—21no—
99C2×C4×C19—42no—
100C2×C4×C19—42no—
101C2×C4×C19—41no—
102C22⋊D19—41no—
103C22⋊D19—41no—
104C22⋊D19—41no—
105C22⋊D19—41no—
106C22⋊D19—82no—
107C2×Dic19—22no—
108C2×Dic19—22no—
109C2×Dic19—21no—
110C2×Dic19—22no—
111C2×Dic19—21no—
112C2×Dic19—22no—
113C2×Dic19—22no—
114C2×Dic19—21no—
115C2×Dic19—42no—
116C2×Dic19—41no—
117C2×Dic19—41no—
118C2×Dic19—41no—
119C2×Dic19—41no—
120C2×Dic19—42no—
121#2022—191nomaximal, Sylow
122C22×C19—22no—
123C22×C19—22no—
124C22×C19—22no—
125C22×C19—41no—
126C22×C19—41no—
127C22×C19—41no—
128C22×C19—41no—
129C22×C19—42no—
130C22×C19—41no—
131C22×C19—42no—
132C22×C19—81no—
133C22×C19#12011yescharacteristic
134C22×C19#12011yescharacteristic
135C22×C19#12011yescharacteristic
136C22×C19#12111yescharacteristic
137C22×C19#12111yescharacteristic
138C22×C19#12111yescharacteristic
139C22×C19#12711yescharacteristic
140C2×D19—42no—
141C2×D19—41no—
142C2×D19—42no—
143C2×D19—81no—
144C4×C19—42no—
145C4×C19—41no—
146C4×C19—81no—
147Dic19—42no—
148Dic19—42no—
149Dic19—41no—
150Dic19—42no—
151#534—191no—
152C2×#123—191no—
153C2×#123—191no—
154C2×#99—191no—
155C2×#99D1911yescharacteristic, complemented
156#381—191no—
157#342—191no—
158C2×C19—21no—
159C2×C19—21no—
160C2×C19—21no—
161C2×C19—21no—
162C2×C19—21no—
163C2×C19—21no—
164C2×C19—81no—
165C2×C19#39211yescharacteristic
166C2×C19#45812yes—
167D19—81no—
168C22×D4—191no—
169C22×D4C2×D1911yescharacteristic
170C23×C4—191no—
171#123—382no—
172#123—382no—
173#123—382no—
174#123—381no—
175#123—381no—
176#123—382no—
177#121—382no—
178#120—381no—
179#120—381no—
180C2×C4⋊C4—381no—
181C2×C4⋊C4—381no—
182C2×C22⋊C4—191no—
183C2×C22⋊C4—191no—
184C2×C22⋊C4—381no—
185C2×C22⋊C4—381no—
186C2×C22⋊C4C2×D1911yescharacteristic
187C2×C22⋊C4C2×D1911yescharacteristic
188#99—22no—
189#99—382no—
190#95—382no—
191C19#202211yescharacteristic, complemented, Sylow
192C24—191no—
193C24D7611yescharacteristic
194C24C22×D1911yescharacteristic
195C2×D4—21no—
196C2×D4—21no—
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—21no—
201C2×D4—381no—
202C2×D4—381no—
203C2×D4—381no—
204C2×D4—381no—
205C2×D4—381no—
206C2×D4—381no—
207C2×D4—382no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—191no—
211C22×C4—192no—
212C22×C4—192no—
213C22×C4—381no—
214C22×C4—381no—
215C22×C4—381no—
216C22×C4—381no—
217C22×C4—381no—
218C22×C4—381no—
219C22×C4—381no—
220C22×C4D7611yescharacteristic
221C4⋊C4—384no—
222C4⋊C4—382no—
223C4⋊C4—384no—
224C22⋊C4—21no—
225C22⋊C4—21no—
226C22⋊C4—21no—
227C22⋊C4—192no—
228C22⋊C4—384no—
229C22⋊C4—382no—
230C22⋊C4—384no—
231C22⋊C4—382no—
232C22⋊C4—381no—
233C22⋊C4—381no—
234C22⋊C4—381no—
235C22⋊C4C22⋊D1912yescomplemented
236C23—21no—
237C23—21no—
238C23—21no—
239C23—42no—
240C23—42no—
241C23—381no—
242C23—381no—
243C23—381no—
244C23—762no—
245C23C2×D7611yescharacteristic
246C23#6454111yescharacteristic
247C23D4×D1911yescharacteristic
248C23D4×D1911yescharacteristic
249C23D4×D1911yescharacteristic
250C23D4×D1911yescharacteristic
251C23C2×C22⋊D1911yescharacteristic
252D4—41no—
253D4—41no—
254D4—41no—
255D4—41no—
256D4—761no—
257D4—761no—
258D4—761no—
259D4—761no—
260D4—1522no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—382no—
269C2×C4—381no—
270C2×C4—382no—
271C2×C4—382no—
272C2×C4—382no—
273C2×C4—381no—
274C2×C4—382no—
275C2×C4—381no—
276C2×C4—762no—
277C2×C4—761no—
278C2×C4—761no—
279C2×C4—761no—
280C2×C4—761no—
281C2×C4—762no—
282C22—22no—
283C22—22no—
284C22—22no—
285C22—41no—
286C22—41no—
287C22—41no—
288C22—41no—
289C22—42no—
290C22—41no—
291C22—42no—
292C22—81no—
293C22—762no—
294C22—761no—
295C22—762no—
296C22—1521no—
297C22#1059732811yescharacteristic
298C22#1059732811yescharacteristic
299C22#1059733011yescharacteristic
300C22#1059733011yescharacteristic
301C22#1059737611yescharacteristic
302C22#1059738311yescharacteristic
303C22#1059738611yescharacteristic
304C4—42no—
305C4—41no—
306C4—81no—
307C4—762no—
308C4—762no—
309C4—761no—
310C4—762no—
311C2—21no—
312C2—21no—
313C2—21no—
314C2—21no—
315C2—21no—
316C2—21no—
317C2—81no—
318C2—1521no—
319C2#1192645311yescharacteristic
320C2#1192673512yes—
subgroupG/H
centerC22#10597328
commutator, cosocleC24×C19C23
FrattiniC24C22×D19
FittingC2×C19×#99C2
socleC22×C19#120
prime radical#11927103C2
hypercenterC2×#99D19
hypocenterC19#2022
LCSG ▷ C24×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#10597332C2semidirect
3. C2×#10597381C2semidirect
4. C2×#10597263C2semidirect
5. #11926405C2semidirect
6. #11926310C2semidirect
7. C2×C19×#99C2semidirect
59. C22×Dic19D4semidirect
63. C22⋊C4×C19D4semidirect
69. C22⋊Dic19D4semidirect
155. C2×#99D19semidirect
191. C19#2022semidirect
235. C22⋊C4C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
#119271032
C2×#105973322
C2×#105973812
C2×#105972632
#119264052
#119263102
C2×C19×#992
#202219