Finite Group Databasebeta

← #14574900

Subgroups — #14574900

Order 2432.

308 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927174C211yesmaximal, characteristic
2#11927152C211yesmaximal, characteristic
3#11926952C211yesmaximal, characteristic, complemented
4#11926944C211yesmaximal, characteristic, complemented
5#11926911C211yesmaximal, characteristic, complemented
6#11926893C211yesmaximal, characteristic, complemented
7#11926888C211yesmaximal, characteristic
8#11926883C211yesmaximal, characteristic
9#11926881C211yesmaximal, characteristic
10#11926873C211yesmaximal, characteristic
11#11926848C211yesmaximal, characteristic, complemented
12#11926839C211yesmaximal, characteristic, complemented
13#11926830C211yesmaximal, characteristic, complemented
14#11926604C211yesmaximal, characteristic
15C19×#479C211yesmaximal, characteristic, complemented
16C19×#125C2211yescharacteristic
17C4×Q8×C19C2211yescharacteristic
18#10597392C2211yescharacteristic
19#10597390C2211yescharacteristic
20#10597344—21no—
21#10597343—21no—
22#10597343C2211yescharacteristic
23#10597342—21no—
24#10597338C2211yescharacteristic
25C4⋊C4×D19C2211yescharacteristic
26#10597336C2211yescharacteristic
27#10597336C2211yescharacteristic
28#10597335—21no—
29#10597335—21no—
30#10597334—21no—
31#10597334C2211yescharacteristic
32#10597322—21no—
33#10597318C2211yescharacteristic
34#10597316—21no—
35#10597315C2211yescharacteristic
36C4×Dic38C2211yescharacteristic
37C19×#107C2211yescharacteristic
38C19×#106C2211yescharacteristic
39C19×C4⋊C8C2211yescharacteristic
40C19×#103C2211yescharacteristic
41C19×#103C2211yescharacteristic
42#10597292C2211yescharacteristic
43#10597292C2211yescharacteristic
44(C2×D19)⋊C8C2211yescharacteristic
45(C2×D19)⋊C8C2211yescharacteristic
46#10597274C2211yescharacteristic
47#10597274C2211yescharacteristic
48#10597273C2211yescharacteristic
49#10597273C2211yescharacteristic
50#10597272C2211yescharacteristic
51C8×Dic19C2211yescharacteristic
52#10597267C2211yescharacteristic
53#10597267C2211yescharacteristic
54#10597265C2211yescharacteristic
55#10597264C2211yescharacteristic
56#10597264C2211yescharacteristic
57#10597264C2211yescharacteristic
58C4⋊(C19⋊C8)C2211yescharacteristic
59C2×Q8×C19C2311yescharacteristic
60C2×C4×D19—21no—
61C2×C4×D19C2311yescharacteristic
62C2×Dic38—21no—
63C2×Dic38—21no—
64C2×Dic38C2311yescharacteristic
65C2×C8×C19C2311yescharacteristic
66C2×C8×C19C2311yescharacteristic
67C4⋊C4×C19—21no—
68C4⋊C4×C19—21no—
69C4⋊C4×C19—21no—
70C4⋊C4×C19C2311yescharacteristic
71C4⋊C4×C19C2311yescharacteristic
72C4⋊C4×C19C2311yescharacteristic
73C42×C19—21no—
74C42×C19C2311yescharacteristic
75(C2×D19)⋊C4—21no—
76(C2×D19)⋊C4—21no—
77(C2×D19)⋊C4—21no—
78(C2×D19)⋊C4D411yescharacteristic
79(C2×D19)⋊C4D411yescharacteristic
80C4⋊Dic19—21no—
81C4⋊Dic19—21no—
82C4⋊Dic19—21no—
83C4⋊Dic19—21no—
84C4⋊Dic19C2311yescharacteristic
85C4⋊Dic19C2311yescharacteristic
86C4⋊Dic19C2311yescharacteristic
87Dic19⋊C4—21no—
88Dic19⋊C4—21no—
89Dic19⋊C4—21no—
90Dic19⋊C4—21no—
91Dic19⋊C4—21no—
92Dic19⋊C4—21no—
93Dic19⋊C4—21no—
94Dic19⋊C4—21no—
95Dic19⋊C4D411yescharacteristic
96Dic19⋊C4D411yescharacteristic
97C4×Dic19—21no—
98C4×Dic19—21no—
99C4×Dic19C2311yescharacteristic
100C2×C19⋊C8C2311yescharacteristic
101C2×C19⋊C8C2311yescharacteristic
102C22×D19C2×D411yescharacteristic
103Q8×C19—21no—
104Q8×C19—21no—
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19C2×D411yescharacteristic
110C2×C4×C19C2×D411yescharacteristic
111C2×C4×C19C2411yescharacteristic
112C2×Dic19—21no—
113C2×Dic19—21no—
114C2×Dic19—21no—
115C2×Dic19—21no—
116C2×Dic19C2×D411yescharacteristic
117C2×Dic19C2×D411yescharacteristic
118C2×Dic19C2×D411yescharacteristic
119C4×D19—21no—
120C4×D19—21no—
121C4×D19—81no—
122Dic38—21no—
123Dic38—21no—
124Dic38—81no—
125Dic38—81no—
126C8×C19—21no—
127C8×C19—21no—
128C19⋊C8—21no—
129C19⋊C8—21no—
130#3242—191nomaximal, Sylow
131C22×C19C22×D411yescharacteristic
132C2×D19—21no—
133C2×D19—21no—
134C2×D19—21no—
135C4×C19—21no—
136C4×C19—21no—
137C4×C19—41no—
138C4×C19—41no—
139C4×C19—41no—
140C4×C19—41no—
141C4×C192−1+411yescharacteristic
142C4×C192−1+411yescharacteristic
143Dic19—21no—
144Dic19—21no—
145Dic19—21no—
146Dic19—41no—
147Dic19—41no—
148Dic19—41no—
149Dic19—41no—
150#544—191no—
151#541—191no—
152#501—191no—
153#499—191no—
154#491—191no—
155#487—191no—
156#485—191no—
157#485—191no—
158#484—191no—
159#483—191no—
160#479—191no—
161#479D1911yescharacteristic, complemented
162#477—191no—
163#475—191no—
164#433—191no—
165C2×C19#53611yescharacteristic
166C2×C19#57711yescharacteristic
167C2×C19#57811yescharacteristic
168D19—41no—
169C4⋊Q8—191no—
170C4⋊Q8—191no—
171C4⋊Q8—191no—
172C4⋊Q8—381no—
173#126—381no—
174#126—381no—
175#125—191no—
176#125—191no—
177#125—381no—
178#125—381no—
179#125—381no—
180#125C2×D1911yescharacteristic
181C22⋊Q8—191no—
182C22⋊Q8—191no—
183C22⋊Q8—381no—
184C22⋊Q8—381no—
185C4×Q8—191no—
186C4×Q8C2×D1911yescharacteristic
187#117—191no—
188#117—191no—
189C2×C4⋊C4—191no—
190#107—191no—
191#107—191no—
192#107—191no—
193#107C2×D1911yescharacteristic
194#106—191no—
195#106—191no—
196#106—191no—
197#106C2×D1911yescharacteristic
198C4⋊C8—191no—
199C4⋊C8C2×D1911yescharacteristic
200#103—191no—
201#103—191no—
202#103—191no—
203#103—191no—
204#103—191no—
205#103—191no—
206#103C2×D1911yescharacteristic
207#103C2×D1911yescharacteristic
208C22⋊C8—191no—
209C22⋊C8—191no—
210#97—191no—
211C4×C8—191no—
212C19#324211yescharacteristic, complemented, Sylow
213C2×Q8—191no—
214C2×Q8—381no—
215C2×Q8—381no—
216C2×Q8C22×D1911yescharacteristic
217C22×C4—191no—
218C22×C4—381no—
219C2×C8—191no—
220C2×C8—191no—
221C2×C8C22×D1911yescharacteristic
222C2×C8C22×D1911yescharacteristic
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—21no—
226C4⋊C4—191no—
227C4⋊C4—191no—
228C4⋊C4—191no—
229C4⋊C4—191no—
230C4⋊C4—191no—
231C4⋊C4—381no—
232C4⋊C4—381no—
233C4⋊C4—381no—
234C4⋊C4—381no—
235C4⋊C4—381no—
236C4⋊C4—381no—
237C4⋊C4—381no—
238C4⋊C4—381no—
239C4⋊C4—381no—
240C4⋊C4—381no—
241C4⋊C4—381no—
242C4⋊C4—381no—
243C4⋊C4C22×D1911yescharacteristic
244C4⋊C4C22×D1911yescharacteristic
245C4⋊C4C22×D1911yescharacteristic
246C22⋊C4—191no—
247C22⋊C4—191no—
248C22⋊C4—381no—
249C22⋊C4—381no—
250C22⋊C4—381no—
251C42—21no—
252C42—191no—
253C42—381no—
254C42—381no—
255C42C22×D1911yescharacteristic
256C23—191no—
257Q8—21no—
258Q8—21no—
259Q8—381no—
260Q8—381no—
261Q8—1521no—
262Q8—1521no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—191no—
268C2×C4—191no—
269C2×C4—191no—
270C2×C4—381no—
271C2×C4—381no—
272C2×C4—381no—
273C2×C4—381no—
274C2×C4—381no—
275C2×C4—381no—
276C2×C4—1521no—
277C2×C4D4×D1911yescharacteristic
278C2×C4D4×D1911yescharacteristic
279C2×C4C23×D1911yescharacteristic
280C8—21no—
281C8—21no—
282C8—381no—
283C8—381no—
284C22—381no—
285C22—381no—
286C22—381no—
287C22C2×D4×D1911yescharacteristic
288C4—21no—
289C4—21no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—41no—
294C4—381no—
295C4—381no—
296C4—381no—
297C4—761no—
298C4—761no—
299C4—761no—
300C4—761no—
301C4#1059743311yescharacteristic
302C4#1059743611yescharacteristic
303C2—761no—
304C2#1192711711yescharacteristic
305C2#1192735111yescharacteristic
306C2#1192736011yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#479C2
socleC22×C19C22×D4
prime radicalC22×D19C2×D4
hypercenter#479D19
hypocenterC19#3242
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
3. #11926952C2semidirect
4. #11926944C2semidirect
5. #11926911C2semidirect
6. #11926893C2semidirect
11. #11926848C2semidirect
12. #11926839C2semidirect
13. #11926830C2semidirect
15. C19×#479C2semidirect
161. #479D19semidirect
212. C19#3242semidirect

Maximal subgroups

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

subgroupindex
#119271742
#119271522
#119269522
#119269442
#119269112
#119268932
#119268882
#119268832
#119268812
#119268732
#119268482
#119268392
#119268302
#119266042
C19×#4792
#324219