Finite Group Databasebeta

← #14574516

Subgroups — #14574516

Order 2432.

390 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927122C211yesmaximal, characteristic
2#11927117C211yesmaximal, characteristic, complemented
3#11926884C211yesmaximal, characteristic, complemented
4#11926880C211yesmaximal, characteristic, complemented
5#11926872C211yesmaximal, characteristic, complemented
6#11926866C211yesmaximal, characteristic, complemented
7#11926801C211yesmaximal, characteristic, complemented
8#11926787C211yesmaximal, characteristic, complemented
9#11926782C211yesmaximal, characteristic, complemented
10#11926772C211yesmaximal, characteristic, complemented
11#11926706C211yesmaximal, characteristic, complemented
12#11926698C211yesmaximal, characteristic, complemented
13#11926681C211yesmaximal, characteristic, complemented
14#11926509C211yesmaximal, characteristic, complemented
15C19×#452C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C2×Q8×D19C2211yescharacteristic
18C2×#64541C2211yescharacteristic
19C2×Q16×C19C2211yescharacteristic
20C2×SD16×C19C2211yescharacteristic
21C19×C22⋊Q8C2211yescharacteristic
22#10597392C2211yescharacteristic
23#10597392C2211yescharacteristic
24#10597392C2211yescharacteristic
25C2×#64528C2211yescharacteristic
26#10597385—21no—
27#10597385—21no—
28#10597384C2211yescharacteristic
29#10597384C2211yescharacteristic
30C2×#64526C2211yescharacteristic
31#10597376—21no—
32C2×C4⋊Dic19C2211yescharacteristic
33#10597370—21no—
34#10597370C2211yescharacteristic
35C2×#64515C2211yescharacteristic
36C2×C8×D19C2211yescharacteristic
37#10597343C2211yescharacteristic
38#10597340—21no—
39#10597338C2211yescharacteristic
40#10597334—21no—
41#10597331—21no—
42#10597329—21no—
43C19×#103C2211yescharacteristic
44C19×#102C2211yescharacteristic
45C19×C22⋊C8C2211yescharacteristic
46#10597292C2211yescharacteristic
47#10597292C2211yescharacteristic
48#10597292C2211yescharacteristic
49#10597289C2211yescharacteristic
50C22⋊(C19⋊C8)C2211yescharacteristic
51(C2×D19)⋊C8C2211yescharacteristic
52(C2×D19)⋊C8C2211yescharacteristic
53#10597275C2211yescharacteristic
54#10597275C2211yescharacteristic
55#10597273C2211yescharacteristic
56#10597273C2211yescharacteristic
57#10597265C2211yescharacteristic
58#10597265C2211yescharacteristic
59#41×C19—41no—
60#41×C19—41no—
61C2×Q8×C19C2311yescharacteristic
62C2×Q8×C19C2311yescharacteristic
63C2×D4×C19—21no—
64C2×D4×C19C2311yescharacteristic
65C22×C4×C19—21no—
66C22×C4×C19C2311yescharacteristic
67C2×C22⋊D19—21no—
68C2×C22⋊D19—21no—
69C2×C22⋊D19D411yescharacteristic
70C2×C22⋊D19D411yescharacteristic
71C22×Dic19—21no—
72Q8×D19—41no—
73Q8×D19—41no—
74#64541—41no—
75#64541—41no—
76C2×D76D411yescharacteristic
77C2×C4×D19—21no—
78C2×C4×D19C2311yescharacteristic
79C2×C4×D19C2311yescharacteristic
80C2×Dic38—21no—
81C2×Dic38D411yescharacteristic
82C2×Dic38C2311yescharacteristic
83Q16×C19—41no—
84SD16×C19—41no—
85C2×C8×C19C2311yescharacteristic
86C2×C8×C19C2311yescharacteristic
87C4⋊C4×C19—21no—
88C4⋊C4×C19C2311yescharacteristic
89C22⋊C4×C19—21no—
90C22⋊Dic19—21no—
91C22⋊Dic19—21no—
92C22⋊Dic19—21no—
93#64528—41no—
94#64526—41no—
95(C2×D19)⋊C4—21no—
96(C2×D19)⋊C4—21no—
97(C2×D19)⋊C4—21no—
98(C2×D19)⋊C4—21no—
99(C2×D19)⋊C4—21no—
100C4⋊Dic19—21no—
101C4⋊Dic19—21no—
102C4⋊Dic19C2311yescharacteristic
103C4⋊Dic19C2311yescharacteristic
104C4⋊Dic19C2311yescharacteristic
105Dic19⋊C4—21no—
106Dic19⋊C4—21no—
107Dic19⋊C4—21no—
108Dic19⋊C4—21no—
109C4×Dic19—21no—
110C2×C19⋊C8C2311yescharacteristic
111C2×C19⋊C8C2311yescharacteristic
112#64515—41no—
113C8×D19—41no—
114C23×C19—21no—
115C23×C19C2×D411yescharacteristic
116C22×D19C2×D411yescharacteristic
117C22×D19C2×D411yescharacteristic
118Q8×C19—21no—
119Q8×C19—21no—
120Q8×C19—21no—
121Q8×C19—21no—
122D4×C19—21no—
123D4×C19—21no—
124D4×C19—42no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—42no—
131C2×C4×C19C2×D411yescharacteristic
132C2×C4×C19C2411yescharacteristic
133C22⋊D19—41no—
134C22⋊D19—41no—
135C22⋊D19—81no—
136C22⋊D19—81no—
137C2×Dic19—21no—
138C2×Dic19—21no—
139C2×Dic19—21no—
140C2×Dic19—21no—
141C2×Dic19—81no—
142C2×Dic19C2×D411yescharacteristic
143C2×Dic19C2×D411yescharacteristic
144D76—41no—
145C4×D19—21no—
146C4×D19—21no—
147C4×D19—21no—
148C4×D19—21no—
149C4×D19—42no—
150Dic38—21no—
151Dic38—21no—
152Dic38—41no—
153Dic38—42no—
154C8×C19—21no—
155C8×C19—21no—
156C19⋊C8—21no—
157C19⋊C8—21no—
158#3201—191nomaximal, Sylow
159C22×C19—21no—
160C22×C19—21no—
161C22×C19—21no—
162C22×C19—41no—
163C22×C19—41no—
164C22×C19—41no—
165C22×C19C22×D411yescharacteristic
166C2×D19—21no—
167C2×D19—21no—
168C2×D19—21no—
169C2×D19—21no—
170C2×D19—21no—
171C2×D19—21no—
172C4×C19—21no—
173C4×C19—41no—
174C4×C19—41no—
175C4×C19—41no—
176C4×C19H(5,𝔽2)11yescharacteristic
177C4×C19H(5,𝔽2)11yescharacteristic
178Dic19—21no—
179Dic19—21no—
180Dic19—41no—
181Dic19—41no—
182Dic19—41no—
183Dic19—41no—
184#537—191no—
185#536—191no—
186#485—191no—
187#484—191no—
188#483—191no—
189#482—191no—
190#470—191no—
191#468—191no—
192#467—191no—
193#465—191no—
194#452—191no—
195#452D1911yescharacteristic, complemented
196#451—191no—
197#448—191no—
198#408—191no—
199C2×C19—41no—
200C2×C19—81no—
201C2×C19#53411yescharacteristic
202C2×C19#57711yescharacteristic
203C2×C19#57811yescharacteristic
204D19—41no—
205D19—41no—
206C2×#41—191no—
207C2×#41C2×D1911yescharacteristic
208C22×Q8—191no—
209C2×Q16—191no—
210C2×Q16C2×D1911yescharacteristic
211C2×SD16—191no—
212C2×SD16C2×D1911yescharacteristic
213C2×M16—191no—
214C22×C8—191no—
215C4⋊Q8—381no—
216#124—381no—
217#123—381no—
218#123—381no—
219C22⋊Q8—191no—
220C22⋊Q8—191no—
221C22⋊Q8—191no—
222C22⋊Q8—191no—
223C22⋊Q8—191no—
224C22⋊Q8—381no—
225C22⋊Q8C2×D1911yescharacteristic
226#121—191no—
227#121—191no—
228#121—381no—
229#121—381no—
230#121—381no—
231#117—191no—
232C2×C4⋊C4—191no—
233#107—191no—
234#107—191no—
235#106—191no—
236#106—191no—
237#103—191no—
238#103—191no—
239#103—191no—
240#103—191no—
241#103—191no—
242#103C2×D1911yescharacteristic
243#102—191no—
244#102C2×D1911yescharacteristic
245C22⋊C8—191no—
246C22⋊C8—191no—
247C22⋊C8—191no—
248C22⋊C8C2×D1911yescharacteristic
249C19#320111yescharacteristic, complemented, Sylow
250#41—41no—
251#41—41no—
252#41—761no—
253#41—761no—
254C2×Q8—191no—
255C2×Q8—191no—
256C2×Q8—381no—
257C2×Q8—761no—
258C2×Q8—761no—
259C2×Q8C22×D1911yescharacteristic
260C2×Q8C22×D1911yescharacteristic
261C2×D4—21no—
262C2×D4—191no—
263C2×D4—191no—
264C2×D4—191no—
265C2×D4—381no—
266C2×D4—381no—
267C2×D4C22×D1911yescharacteristic
268C22×C4—21no—
269C22×C4—191no—
270C22×C4—191no—
271C22×C4—381no—
272C22×C4—381no—
273C22×C4C22×D1911yescharacteristic
274Q16—41no—
275Q16—761no—
276SD16—41no—
277SD16—761no—
278M16—761no—
279C2×C8—191no—
280C2×C8—191no—
281C2×C8—761no—
282C2×C8C22×D1911yescharacteristic
283C2×C8C22×D1911yescharacteristic
284C4⋊C4—21no—
285C4⋊C4—191no—
286C4⋊C4—191no—
287C4⋊C4—191no—
288C4⋊C4—381no—
289C4⋊C4—381no—
290C4⋊C4—381no—
291C4⋊C4—381no—
292C4⋊C4—381no—
293C4⋊C4—381no—
294C4⋊C4C22×D1911yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—381no—
297C22⋊C4—381no—
298C22⋊C4—381no—
299C22⋊C4—381no—
300C22⋊C4—381no—
301C22⋊C4—381no—
302C22⋊C4—381no—
303C22⋊C4—381no—
304C42—381no—
305C23—21no—
306C23—191no—
307C23—191no—
308C23D4×D1911yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—21no—
313Q8—381no—
314Q8—381no—
315Q8—761no—
316Q8—762no—
317D4—21no—
318D4—21no—
319D4—42no—
320D4—761no—
321D4—761no—
322D4—761no—
323D4—1521no—
324D4—1521no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—191no—
332C2×C4—191no—
333C2×C4—381no—
334C2×C4—381no—
335C2×C4—381no—
336C2×C4—381no—
337C2×C4—381no—
338C2×C4—381no—
339C2×C4—381no—
340C2×C4—381no—
341C2×C4—762no—
342C2×C4—1521no—
343C2×C4D4×D1911yescharacteristic
344C2×C4C23×D1911yescharacteristic
345C8—21no—
346C8—21no—
347C8—381no—
348C8—381no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—381no—
356C22—381no—
357C22—381no—
358C22—381no—
359C22—381no—
360C22—381no—
361C22C2×D4×D1911yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—381no—
367C4—381no—
368C4—761no—
369C4—761no—
370C4—761no—
371C4—761no—
372C4#1059743011yescharacteristic
373C4#1059743011yescharacteristic
374C2—41no—
375C2—81no—
376C2—761no—
377C2—761no—
378C2#1192710411yescharacteristic
379C2#1192735311yescharacteristic
380C2#1192735811yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#452C2
socleC22×C19C22×D4
prime radical#11927122C2
hypercenter#452D19
hypocenterC19#3201
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. #11927117C2semidirect
3. #11926884C2semidirect
4. #11926880C2semidirect
5. #11926872C2semidirect
6. #11926866C2semidirect
7. #11926801C2semidirect
8. #11926787C2semidirect
9. #11926782C2semidirect
10. #11926772C2semidirect
11. #11926706C2semidirect
12. #11926698C2semidirect
13. #11926681C2semidirect
14. #11926509C2semidirect
15. C19×#452C2semidirect
195. #452D19semidirect
249. C19#3201semidirect

Maximal subgroups

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

subgroupindex
#119271222
#119271172
#119268842
#119268802
#119268722
#119268662
#119268012
#119267872
#119267822
#119267722
#119267062
#119266982
#119266812
#119265092
C19×#4522
#320119