Finite Group Databasebeta

← #14575060

Subgroups — #14575060

Order 2432.

334 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927168C211yesmaximal, characteristic
2#11927152C211yesmaximal, characteristic, complemented
3#11926850C211yesmaximal, characteristic, complemented
4#11926847C211yesmaximal, characteristic, complemented
5#11926826C211yesmaximal, characteristic, complemented
6#11926801C211yesmaximal, characteristic, complemented
7#11926791C211yesmaximal, characteristic
8#11926786C211yesmaximal, characteristic, complemented
9#11926776C211yesmaximal, characteristic
10#11926767C211yesmaximal, characteristic, complemented
11#11926766C211yesmaximal, characteristic, complemented
12#11926753C211yesmaximal, characteristic, complemented
13#11926748C211yesmaximal, characteristic, complemented
14#11926569C211yesmaximal, characteristic, complemented
15C19×#477C211yesmaximal, characteristic, complemented
16C19×C4⋊Q8C2211yescharacteristic
17C4×Q8×C19C2211yescharacteristic
18#10597393—21no—
19#10597392—21no—
20#10597392C2211yescharacteristic
21#10597390C2211yescharacteristic
22C2×#64528C2211yescharacteristic
23C2×#64527C2211yescharacteristic
24C2×Dic76C2211yescharacteristic
25C2×#64516C2211yescharacteristic
26C2×#64515C2211yescharacteristic
27C2×C8×D19C2211yescharacteristic
28#10597344—21no—
29#10597344—21no—
30#10597343C2211yescharacteristic
31#10597343C2211yescharacteristic
32#10597341C2211yescharacteristic
33#10597340—21no—
34#10597339C2211yescharacteristic
35#10597336C2211yescharacteristic
36#10597335—21no—
37#10597333C2211yescharacteristic
38#10597322—21no—
39#10597321C2211yescharacteristic
40#10597318C2211yescharacteristic
41#10597316—21no—
42C4×Dic38C2211yescharacteristic
43C19×#107C2211yescharacteristic
44C19×#107C2211yescharacteristic
45C19×C4⋊C8C2211yescharacteristic
46C19×#103C2211yescharacteristic
47C19×#103C2211yescharacteristic
48#10597278C2211yescharacteristic
49#10597273C2211yescharacteristic
50Dic19⋊C8C2211yescharacteristic
51Dic19⋊C8C2211yescharacteristic
52#10597267C2211yescharacteristic
53#10597267C2211yescharacteristic
54#10597267C2211yescharacteristic
55#10597266C2211yescharacteristic
56#10597265C2211yescharacteristic
57#10597265C2211yescharacteristic
58C4⋊(C19⋊C8)C2211yescharacteristic
59C2×Q8×C19—21no—
60C2×Q8×C19C2311yescharacteristic
61C2×D76—21no—
62C2×D76C2311yescharacteristic
63C2×C4×D19—21no—
64C2×C4×D19C2311yescharacteristic
65C2×Dic38C2311yescharacteristic
66C2×Dic38C2311yescharacteristic
67C2×C8×C19C2311yescharacteristic
68C2×C8×C19C2311yescharacteristic
69C4⋊C4×C19—21no—
70C4⋊C4×C19—21no—
71C4⋊C4×C19C2311yescharacteristic
72C4⋊C4×C19C2311yescharacteristic
73C4⋊C4×C19C2311yescharacteristic
74C42×C19—21no—
75C42×C19C2311yescharacteristic
76#64528—41no—
77#64527—41no—
78(C2×D19)⋊C4—21no—
79(C2×D19)⋊C4—21no—
80(C2×D19)⋊C4—21no—
81(C2×D19)⋊C4—21no—
82(C2×D19)⋊C4—21no—
83(C2×D19)⋊C4—21no—
84(C2×D19)⋊C4—21no—
85(C2×D19)⋊C4D411yescharacteristic
86(C2×D19)⋊C4D411yescharacteristic
87C4⋊Dic19—21no—
88C4⋊Dic19—21no—
89C4⋊Dic19—21no—
90C4⋊Dic19C2311yescharacteristic
91Dic19⋊C4—21no—
92Dic19⋊C4—21no—
93Dic19⋊C4—21no—
94Dic19⋊C4—21no—
95Dic19⋊C4—21no—
96Dic19⋊C4—21no—
97Dic19⋊C4D411yescharacteristic
98Dic19⋊C4D411yescharacteristic
99C4×Dic19—21no—
100C4×Dic19—21no—
101C4×Dic19C2311yescharacteristic
102C2×C19⋊C8C2311yescharacteristic
103C2×C19⋊C8C2311yescharacteristic
104Dic76—41no—
105#64516—41no—
106#64515—41no—
107C8×D19—41no—
108C22×D19—21no—
109C22×D19C2×D411yescharacteristic
110Q8×C19—21no—
111Q8×C19—21no—
112Q8×C19—81no—
113C2×C4×C19—21no—
114C2×C4×C19—21no—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19C2×D411yescharacteristic
118C2×C4×C19C2×D411yescharacteristic
119C2×C4×C19C2411yescharacteristic
120C2×Dic19—21no—
121C2×Dic19—21no—
122C2×Dic19—21no—
123C2×Dic19C2×D411yescharacteristic
124C2×Dic19C2×D411yescharacteristic
125C2×Dic19C2×D411yescharacteristic
126D76—21no—
127D76—21no—
128D76—81no—
129C4×D19—21no—
130C4×D19—21no—
131C4×D19—81no—
132Dic38—21no—
133Dic38—21no—
134Dic38—21no—
135Dic38—21no—
136C8×C19—21no—
137C8×C19—21no—
138C19⋊C8—21no—
139C19⋊C8—21no—
140#3258—191nomaximal, Sylow
141C22×C19C22×D411yescharacteristic
142C2×D19—21no—
143C2×D19—21no—
144C2×D19—21no—
145C2×D19—41no—
146C2×D19—41no—
147C2×D19—41no—
148C4×C19—21no—
149C4×C19—21no—
150C4×C19—41no—
151C4×C19—41no—
152C4×C19—41no—
153C4×C19—41no—
154C4×C19H(5,𝔽2)11yescharacteristic
155C4×C192−1+411yescharacteristic
156Dic19—21no—
157Dic19—21no—
158Dic19—21no—
159Dic19—41no—
160Dic19—41no—
161Dic19—41no—
162#542—191no—
163#541—191no—
164#479—191no—
165#478—191no—
166#477D1911yescharacteristic, complemented
167#475—191no—
168#470—191no—
169#468—191no—
170#467—191no—
171#465—191no—
172#464—191no—
173#464—191no—
174#462—191no—
175#461—191no—
176#424—191no—
177C2×C19#53711yescharacteristic
178C2×C19#57711yescharacteristic
179C2×C19#57811yescharacteristic
180D19—41no—
181D19—81no—
182C2×Q16—191no—
183C2×Q16—191no—
184C2×SD16—191no—
185C2×SD16—191no—
186C2×M16—191no—
187C22×C8—191no—
188C4⋊Q8—191no—
189C4⋊Q8C2×D1911yescharacteristic
190#126—381no—
191#126—381no—
192#126—381no—
193#125—191no—
194#125—381no—
195#125—381no—
196#124—191no—
197#124—381no—
198#123—381no—
199C22⋊Q8—191no—
200C22⋊Q8—191no—
201C22⋊Q8—191no—
202C22⋊Q8—381no—
203#121—191no—
204C4×Q8—191no—
205C4×Q8—191no—
206C4×Q8C2×D1911yescharacteristic
207C4×D4—191no—
208#117—191no—
209#107C2×D1911yescharacteristic
210#107C2×D1911yescharacteristic
211#106—191no—
212#106—191no—
213C4⋊C8—191no—
214C4⋊C8—191no—
215C4⋊C8—191no—
216C4⋊C8C2×D1911yescharacteristic
217#103—191no—
218#103—191no—
219#103—191no—
220#103—191no—
221#103C2×D1911yescharacteristic
222#103C2×D1911yescharacteristic
223#102—191no—
224#102—191no—
225C19#325811yescharacteristic, complemented, Sylow
226C2×Q8—21no—
227C2×Q8—191no—
228C2×Q8—191no—
229C2×Q8C22×D1911yescharacteristic
230C2×D4—191no—
231C2×D4—381no—
232C22×C4—191no—
233C22×C4—381no—
234Q16—761no—
235Q16—761no—
236SD16—761no—
237SD16—761no—
238M16—761no—
239C2×C8—191no—
240C2×C8—191no—
241C2×C8—761no—
242C2×C8C22×D1911yescharacteristic
243C2×C8C22×D1911yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—191no—
247C4⋊C4—191no—
248C4⋊C4—191no—
249C4⋊C4—381no—
250C4⋊C4—381no—
251C4⋊C4—381no—
252C4⋊C4—381no—
253C4⋊C4—381no—
254C4⋊C4—381no—
255C4⋊C4—381no—
256C4⋊C4—381no—
257C4⋊C4—381no—
258C4⋊C4C22×D1911yescharacteristic
259C4⋊C4C22×D1911yescharacteristic
260C4⋊C4C22×D1911yescharacteristic
261C22⋊C4—191no—
262C22⋊C4—191no—
263C22⋊C4—381no—
264C22⋊C4—381no—
265C22⋊C4—381no—
266C22⋊C4—381no—
267C22⋊C4—381no—
268C22⋊C4—381no—
269C22⋊C4—381no—
270C42—21no—
271C42—191no—
272C42—381no—
273C42—381no—
274C42C22×D1911yescharacteristic
275C23—191no—
276C23—381no—
277Q8—21no—
278Q8—21no—
279Q8—81no—
280Q8—381no—
281Q8—381no—
282Q8—381no—
283Q8—381no—
284D4—381no—
285D4—381no—
286D4—1521no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—191no—
292C2×C4—191no—
293C2×C4—191no—
294C2×C4—381no—
295C2×C4—381no—
296C2×C4—381no—
297C2×C4—381no—
298C2×C4—381no—
299C2×C4—1521no—
300C2×C4D4×D1911yescharacteristic
301C2×C4D4×D1911yescharacteristic
302C2×C4C23×D1911yescharacteristic
303C8—21no—
304C8—21no—
305C8—381no—
306C8—381no—
307C22—381no—
308C22—381no—
309C22—381no—
310C22—761no—
311C22—761no—
312C22—761no—
313C22C2×D4×D1911yescharacteristic
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—381no—
321C4—381no—
322C4—381no—
323C4—761no—
324C4—761no—
325C4—761no—
326C4#1059743311yescharacteristic
327C4#1059743511yescharacteristic
328C2—761no—
329C2—1521no—
330C2#1192712411yescharacteristic
331C2#1192735411yescharacteristic
332C2#1192735711yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#477C2
socleC22×C19C22×D4
prime radical#10597341C22
hypercenter#477D19
hypocenterC19#3258
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. #11927152C2semidirect
3. #11926850C2semidirect
4. #11926847C2semidirect
5. #11926826C2semidirect
6. #11926801C2semidirect
8. #11926786C2semidirect
10. #11926767C2semidirect
11. #11926766C2semidirect
12. #11926753C2semidirect
13. #11926748C2semidirect
14. #11926569C2semidirect
15. C19×#477C2semidirect
166. #477D19semidirect
225. C19#3258semidirect

Maximal subgroups

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

subgroupindex
#119271682
#119271522
#119268502
#119268472
#119268262
#119268012
#119267912
#119267862
#119267762
#119267672
#119267662
#119267532
#119267482
#119265692
C19×#4772
#325819