Finite Group Databasebeta

← #14574517

Subgroups — #14574517

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#11926885C211yesmaximal, characteristic, complemented
3#11926877C211yesmaximal, characteristic, complemented
4#11926872C211yesmaximal, characteristic, complemented
5#11926868C211yesmaximal, characteristic, complemented
6#11926800C211yesmaximal, characteristic, complemented
7#11926792C211yesmaximal, characteristic, complemented
8#11926783C211yesmaximal, characteristic, complemented
9#11926775C211yesmaximal, characteristic, complemented
10#11926704C211yesmaximal, characteristic, complemented
11#11926704C211yesmaximal, characteristic, complemented
12#11926700C211yesmaximal, characteristic, complemented
13#11926683C211yesmaximal, characteristic, complemented
14#11926511C211yesmaximal, characteristic, complemented
15C19×#536C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C22×Q8×C19C2211yescharacteristic
18C2×#64541C2211yescharacteristic
19C19×C4⋊Q8—21no—
20C19×#124—21no—
21C19×#123—21no—
22C19×#123—21no—
23C19×C22⋊Q8C2211yescharacteristic
24C19×C22⋊Q8C2211yescharacteristic
25C19×C22⋊Q8C2211yescharacteristic
26C19×C22⋊Q8C2211yescharacteristic
27C19×#117C2211yescharacteristic
28#10597392—21no—
29C2×#64528C2211yescharacteristic
30C2×#64528C2211yescharacteristic
31C2×#64527C2211yescharacteristic
32C2×#64527C2211yescharacteristic
33#10597385—21no—
34#10597385—21no—
35#10597384—21no—
36#10597376C2211yescharacteristic
37#10597376C2211yescharacteristic
38C2×C4⋊Dic19C2211yescharacteristic
39#10597370C2211yescharacteristic
40#10597370C2211yescharacteristic
41C2×#64520C2211yescharacteristic
42C22×C19⋊C8C2211yescharacteristic
43#10597292C2211yescharacteristic
44#10597292C2211yescharacteristic
45#10597292C2211yescharacteristic
46#10597292C2211yescharacteristic
47C22⋊(C19⋊C8)C2211yescharacteristic
48C22⋊(C19⋊C8)C2211yescharacteristic
49C22⋊(C19⋊C8)C2211yescharacteristic
50C22⋊(C19⋊C8)C2211yescharacteristic
51#10597267C2211yescharacteristic
52#10597267C2211yescharacteristic
53#10597266C2211yescharacteristic
54#10597266C2211yescharacteristic
55#10597265C2211yescharacteristic
56#10597265C2211yescharacteristic
57#10597264C2211yescharacteristic
58#10597264C2211yescharacteristic
59#41×C19—41no—
60#41×C19—41no—
61C2×Q8×C19—21no—
62C2×Q8×C19—41no—
63C2×Q8×C19—41no—
64C2×Q8×C19D411yescharacteristic
65C2×Q8×C19C2311yescharacteristic
66C2×Q8×C19C2311yescharacteristic
67C2×D4×C19D411yescharacteristic
68C2×D4×C19D411yescharacteristic
69C2×D4×C19D411yescharacteristic
70C22×C4×C19—21no—
71C22×C4×C19C2311yescharacteristic
72C22×C4×C19C2311yescharacteristic
73C22×C4×C19C2311yescharacteristic
74C2×C22⋊D19—21no—
75C2×C22⋊D19—21no—
76C2×C22⋊D19—21no—
77C22×Dic19—21no—
78#64541—41no—
79#64541—41no—
80C2×D76C2311yescharacteristic
81C2×C4×D19—21no—
82C2×Dic38C2311yescharacteristic
83C4⋊C4×C19—21no—
84C4⋊C4×C19—21no—
85C4⋊C4×C19—21no—
86C4⋊C4×C19—21no—
87C4⋊C4×C19C2311yescharacteristic
88C4⋊C4×C19C2311yescharacteristic
89C22⋊C4×C19—21no—
90C22⋊C4×C19—21no—
91C22⋊C4×C19—21no—
92C22⋊C4×C19—21no—
93C22⋊C4×C19—21no—
94C42×C19—21no—
95C22⋊Dic19—21no—
96C22⋊Dic19—21no—
97#64528—41no—
98#64528—41no—
99#64527—41no—
100#64527—41no—
101(C2×D19)⋊C4—21no—
102(C2×D19)⋊C4—21no—
103C4⋊Dic19—21no—
104C4⋊Dic19C2311yescharacteristic
105C4⋊Dic19C2311yescharacteristic
106Dic19⋊C4—21no—
107Dic19⋊C4—21no—
108#64520—41no—
109C2×C19⋊C8—41no—
110C2×C19⋊C8C2311yescharacteristic
111C2×C19⋊C8C2311yescharacteristic
112C2×C19⋊C8C2311yescharacteristic
113C2×C19⋊C8C2311yescharacteristic
114C23×C19C2×D411yescharacteristic
115C23×C19C2×D411yescharacteristic
116C23×C19C2×D411yescharacteristic
117C22×D19—21no—
118Q8×C19—21no—
119Q8×C19—21no—
120Q8×C19—21no—
121Q8×C19—21no—
122Q8×C19—41no—
123Q8×C19—42no—
124D4×C19—41no—
125D4×C19—41no—
126D4×C19—41no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19—42no—
138C2×C4×C19C2×D411yescharacteristic
139C2×C4×C19C2×D411yescharacteristic
140C2×C4×C19C2×D411yescharacteristic
141C2×C4×C19C2411yescharacteristic
142C22⋊D19—42no—
143C22⋊D19—81no—
144C22⋊D19—81no—
145C2×Dic19—21no—
146C2×Dic19—21no—
147C2×Dic19—21no—
148C2×Dic19—81no—
149D76—21no—
150D76—21no—
151C4×D19—42no—
152Dic38—21no—
153Dic38—21no—
154C19⋊C8—21no—
155C19⋊C8—21no—
156C19⋊C8—21no—
157C19⋊C8—21no—
158#3201—191nomaximal, Sylow
159C22×C19—21no—
160C22×C19—21no—
161C22×C19—21no—
162C22×C19—21no—
163C22×C19—21no—
164C22×C19—21no—
165C22×C19—21no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19C22×D411yescharacteristic
169C2×D19—41no—
170C2×D19—41no—
171C2×D19—41no—
172C4×C19—21no—
173C4×C19—21no—
174C4×C19—21no—
175C4×C19—41no—
176C4×C19—41no—
177C4×C19—41no—
178C4×C19—41no—
179C4×C19H(5,𝔽2)11yescharacteristic
180C4×C19H(5,𝔽2)11yescharacteristic
181Dic19—41no—
182Dic19—41no—
183Dic19—41no—
184#537—191no—
185#536D1911yescharacteristic, complemented
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#452—191no—
196#451—191no—
197#448—191no—
198#408—191no—
199C2×C19—41no—
200C2×C19—41no—
201C2×C19—41no—
202C2×C19#53411yescharacteristic
203C2×C19#57711yescharacteristic
204C2×C19#57811yescharacteristic
205D19—81no—
206C2×#41—191no—
207C2×#41C2×D1911yescharacteristic
208C22×Q8C2×D1911yescharacteristic
209C2×Q16—191no—
210C2×Q16—191no—
211C2×SD16—191no—
212C2×SD16—191no—
213C2×M16—191no—
214C22×C8—191no—
215C4⋊Q8—21no—
216#124—21no—
217#123—21no—
218#123—21no—
219C22⋊Q8—191no—
220C22⋊Q8—191no—
221C22⋊Q8—381no—
222C22⋊Q8C2×D1911yescharacteristic
223C22⋊Q8C2×D1911yescharacteristic
224C22⋊Q8C2×D1911yescharacteristic
225C22⋊Q8C2×D1911yescharacteristic
226#121—191no—
227#121—191no—
228#121—381no—
229#121—381no—
230#121—381no—
231#117C2×D1911yescharacteristic
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#103—191no—
243#102—191no—
244#102—191no—
245C22⋊C8—191no—
246C22⋊C8—191no—
247C22⋊C8—191no—
248C22⋊C8—191no—
249C19#320111yescharacteristic, complemented, Sylow
250#41—41no—
251#41—41no—
252#41—761no—
253#41—761no—
254C2×Q8—21no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—191no—
258C2×Q8C22⋊D1911yescharacteristic
259C2×Q8C22×D1911yescharacteristic
260C2×Q8C22×D1911yescharacteristic
261C2×D4—191no—
262C2×D4—381no—
263C2×D4—381no—
264C2×D4—381no—
265C2×D4C22⋊D1911yescharacteristic
266C2×D4C22⋊D1911yescharacteristic
267C2×D4C22⋊D1911yescharacteristic
268C22×C4—21no—
269C22×C4—381no—
270C22×C4—381no—
271C22×C4C22×D1911yescharacteristic
272C22×C4C22×D1911yescharacteristic
273C22×C4C22×D1911yescharacteristic
274Q16—761no—
275Q16—761no—
276SD16—761no—
277SD16—761no—
278M16—761no—
279C2×C8—191no—
280C2×C8—191no—
281C2×C8—191no—
282C2×C8—191no—
283C2×C8—761no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—191no—
289C4⋊C4—191no—
290C4⋊C4—381no—
291C4⋊C4—381no—
292C4⋊C4—381no—
293C4⋊C4C22×D1911yescharacteristic
294C4⋊C4C22×D1911yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—381no—
301C22⋊C4—381no—
302C22⋊C4—381no—
303C22⋊C4—381no—
304C42—21no—
305C23—381no—
306C23C2×C22⋊D1911yescharacteristic
307C23C2×C22⋊D1911yescharacteristic
308C23C2×C22⋊D1911yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—21no—
313Q8—41no—
314Q8—42no—
315Q8—381no—
316Q8—381no—
317D4—41no—
318D4—41no—
319D4—41no—
320D4—381no—
321D4—381no—
322D4—762no—
323D4—1521no—
324D4—1521no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—381no—
337C2×C4—381no—
338C2×C4—381no—
339C2×C4—762no—
340C2×C4—1521no—
341C2×C4C2×C22⋊D1911yescharacteristic
342C2×C4C2×C22⋊D1911yescharacteristic
343C2×C4C2×C22⋊D1911yescharacteristic
344C2×C4C23×D1911yescharacteristic
345C8—381no—
346C8—381no—
347C8—381no—
348C8—381no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—761no—
359C22—761no—
360C22—761no—
361C22C22×C22⋊D1911yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—761no—
370C4—761no—
371C4—761no—
372C4#1059743011yescharacteristic
373C4#1059743011yescharacteristic
374C2—41no—
375C2—41no—
376C2—41no—
377C2—1521no—
378C2#1192710311yescharacteristic
379C2#1192735211yescharacteristic
380C2#1192735911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#536C2
socleC22×C19C22×D4
prime radical#11927122C2
hypercenter#536D19
hypocenterC19#3201
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #11926885C2semidirect
3. #11926877C2semidirect
4. #11926872C2semidirect
5. #11926868C2semidirect
6. #11926800C2semidirect
7. #11926792C2semidirect
8. #11926783C2semidirect
9. #11926775C2semidirect
10. #11926704C2semidirect
11. #11926704C2semidirect
12. #11926700C2semidirect
13. #11926683C2semidirect
14. #11926511C2semidirect
15. C19×#536C2semidirect
185. #536D19semidirect
249. C19#3201semidirect

Maximal subgroups

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

subgroupindex
#119271222
#119268852
#119268772
#119268722
#119268682
#119268002
#119267922
#119267832
#119267752
#119267042
#119267002
#119266832
#119265112
C19×#5362
#320119