Finite Group Databasebeta

← #14574706

Subgroups — #14574706

Order 2432.

396 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#11927152C211yesmaximal, characteristic, complemented
2#11927107C211yesmaximal, characteristic
3#11926935C211yesmaximal, characteristic, complemented
4#11926915C211yesmaximal, characteristic, complemented
5#11926907C211yesmaximal, characteristic, complemented
6#11926897C211yesmaximal, characteristic, complemented
7#11926767C211yesmaximal, characteristic, complemented
8#11926766C211yesmaximal, characteristic, complemented
9#11926741C211yesmaximal, characteristic, complemented
10#11926707C211yesmaximal, characteristic, complemented
11#11926703C211yesmaximal, characteristic, complemented
12#11926696C211yesmaximal, characteristic, complemented
13#11926693C211yesmaximal, characteristic, complemented
14#11926604C211yesmaximal, characteristic, complemented
15C19×#460C211yesmaximal, characteristic, complemented
16C2×#64543C2211yescharacteristic
17C2×D4×D19C2211yescharacteristic
18C2×SD16×C19C2211yescharacteristic
19C2×SD16×C19C2211yescharacteristic, complemented
20C19×#127C2211yescharacteristic
21C4×Q8×C19C2211yescharacteristic, complemented
22#10597392C2211yescharacteristic
23#10597390C2211yescharacteristic, complemented
24C2×#64528C2211yescharacteristic, complemented
25C2×#64527C2211yescharacteristic
26#10597386C2211yescharacteristic
27#10597385—21no—
28#10597385—21no—
29#10597383—21no—
30#10597383—21no—
31#10597382C2211yescharacteristic
32C2×#64526C2211yescharacteristic
33C2×#64526C2211yescharacteristic, complemented
34C2×Dic76C2211yescharacteristic, complemented
35C2×#64516C2211yescharacteristic
36#10597344—21no—
37#10597343C2211yescharacteristic
38#10597336C2211yescharacteristic, complemented
39#10597335—21no—
40#10597322—21no—
41#10597321C2211yescharacteristic
42#10597318C2211yescharacteristic
43#10597316—21no—
44C4×Dic38C2211yescharacteristic, complemented
45C19×C4⋊C8C2211yescharacteristic, complemented
46C19×#102C2211yescharacteristic
47C19×#102C2211yescharacteristic, complemented
48#10597289C2211yescharacteristic
49#10597289C2211yescharacteristic, complemented
50#10597278C2211yescharacteristic
51(C2×D19)⋊C8C2211yescharacteristic
52(C2×D19)⋊C8C2211yescharacteristic
53#10597273C2211yescharacteristic, complemented
54#10597272C2211yescharacteristic, complemented
55C8×Dic19C2211yescharacteristic, complemented
56#10597267C2211yescharacteristic, complemented
57#10597266C2211yescharacteristic
58C4⋊(C19⋊C8)C2211yescharacteristic, complemented
59C23×D19—21no—
60C2×Q8×C19C2311yescharacteristic
61C2×D4×C19—21no—
62C2×D4×C19—21no—
63C2×D4×C19C2311yescharacteristic
64C2×D4×C19C2311yescharacteristic
65C2×C22⋊D19—21no—
66C2×C22⋊D19—21no—
67C2×C22⋊D19—21no—
68C2×C22⋊D19—21no—
69C22×Dic19—21no—
70#64543—41no—
71#64543—41no—
72D4×D19—41no—
73D4×D19—41no—
74C2×D76C2311yescharacteristic
75C2×C4×D19C2311yescharacteristic
76C2×Dic38C2311yescharacteristic
77C2×Dic38C2311yescharacteristic
78SD16×C19—41no—
79SD16×C19—41no—
80C2×C8×C19C2311yescharacteristic
81C2×C8×C19C2311yescharacteristic
82C4⋊C4×C19—21no—
83C4⋊C4×C19C2311yescharacteristic
84C42×C19—21no—
85C42×C19C2311yescharacteristic
86C22⋊Dic19—21no—
87C22⋊Dic19—21no—
88#64528—41no—
89#64527—41no—
90#64526—41no—
91#64526—41no—
92(C2×D19)⋊C4—21no—
93(C2×D19)⋊C4—21no—
94(C2×D19)⋊C4—21no—
95(C2×D19)⋊C4—21no—
96(C2×D19)⋊C4D411yescharacteristic
97(C2×D19)⋊C4D411yescharacteristic
98C4⋊Dic19—21no—
99C4⋊Dic19—21no—
100C4⋊Dic19C2311yescharacteristic
101Dic19⋊C4—21no—
102Dic19⋊C4—21no—
103Dic19⋊C4—21no—
104Dic19⋊C4—21no—
105Dic19⋊C4—21no—
106Dic19⋊C4D411yescharacteristic
107Dic19⋊C4D411yescharacteristic
108C4×Dic19—21no—
109C4×Dic19C2311yescharacteristic
110C2×C19⋊C8C2311yescharacteristic
111C2×C19⋊C8C2311yescharacteristic
112Dic76—41no—
113#64516—41no—
114C23×C19—21no—
115C23×C19—21no—
116C22×D19—21no—
117C22×D19—42no—
118C22×D19—81no—
119C22×D19—81no—
120C22×D19C2×D411yescharacteristic
121Q8×C19—21no—
122Q8×C19—21no—
123D4×C19—21no—
124D4×C19—21no—
125D4×C19—21no—
126D4×C19—21no—
127D4×C19—81no—
128D4×C19—81no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19C2×D411yescharacteristic
132C2×C4×C19C2×D411yescharacteristic
133C2×C4×C19C2411yescharacteristic
134C22⋊D19—42no—
135C22⋊D19—42no—
136C22⋊D19—81no—
137C22⋊D19—81no—
138C2×Dic19—21no—
139C2×Dic19—21no—
140C2×Dic19—21no—
141C2×Dic19—42no—
142C2×Dic19C2×D411yescharacteristic
143C2×Dic19C2×D411yescharacteristic
144C2×Dic19C2×D411yescharacteristic
145D76—21no—
146D76—21no—
147C4×D19—21no—
148C4×D19—21no—
149Dic38—21no—
150Dic38—21no—
151Dic38—21no—
152Dic38—21no—
153C8×C19—21no—
154C8×C19—21no—
155C19⋊C8—21no—
156C19⋊C8—21no—
157#3222—191nomaximal, Sylow
158C22×C19—41no—
159C22×C19—41no—
160C22×C19—41no—
161C22×C19—41no—
162C22×C19—41no—
163C22×C19—41no—
164C22×C19C22×D411yescharacteristic
165C2×D19—21no—
166C2×D19—21no—
167C2×D19—21no—
168C2×D19—41no—
169C2×D19—41no—
170C2×D19—41no—
171C2×D19—84no—
172C4×C19—21no—
173C4×C19—21no—
174C4×C19—41no—
175C4×C19—41no—
176C4×C19H(5,𝔽2)11yescharacteristic
177C4×C19H(5,𝔽2)11yescharacteristic
178Dic19—21no—
179Dic19—21no—
180Dic19—21no—
181Dic19—41no—
182Dic19—41no—
183Dic19—41no—
184#541—191no—
185#535—191no—
186#497—191no—
187#492—191no—
188#490—191no—
189#488—191no—
190#464—191no—
191#464—191no—
192#460—191no—
193#460D1911yescharacteristic, complemented
194#452—191no—
195#452—191no—
196#450—191no—
197#450—191no—
198#433—191no—
199C2×C19—81no—
200C2×C19—81no—
201C2×C19#53511yescharacteristic
202C2×C19#57711yescharacteristic
203C2×C19#57711yescharacteristic
204D19—41no—
205D19—81no—
206C2×#41—191no—
207C22×D4—191no—
208C2×Q16—191no—
209C2×Q16—191no—
210C2×SD16—191no—
211C2×SD16—191no—
212C2×SD16—191no—
213C2×SD16—191no—
214C2×SD16C2×D1911yescharacteristic
215C2×SD16C2×D1911yescharacteristic, complemented
216C4⋊Q8—191no—
217#127—191no—
218#127C2×D1911yescharacteristic
219#126—381no—
220#126—381no—
221#125—191no—
222#125—381no—
223#125—381no—
224#124—191no—
225#124—191no—
226C22⋊Q8—191no—
227C22⋊Q8—191no—
228#121—381no—
229#121—381no—
230#120—381no—
231#120—381no—
232C4×Q8—191no—
233C4×Q8C2×D1911yescharacteristic, complemented
234#117—191no—
235C4⋊C8—191no—
236C4⋊C8C2×D1911yescharacteristic, complemented
237#103—191no—
238#103—191no—
239#102—191no—
240#102—191no—
241#102—191no—
242#102—191no—
243#102C2×D1911yescharacteristic
244#102C2×D1911yescharacteristic, complemented
245C22⋊C8—191no—
246C22⋊C8—191no—
247#97—191no—
248C4×C8—191no—
249C19#322211yescharacteristic, complemented, Sylow
250C24—381no—
251#41—761no—
252#41—761no—
253C2×Q8—191no—
254C2×Q8—191no—
255C2×Q8C22×D1911yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—191no—
259C2×D4—381no—
260C2×D4—381no—
261C2×D4—381no—
262C2×D4—381no—
263C2×D4—761no—
264C2×D4—761no—
265C2×D4C22×D1911yescharacteristic
266C2×D4C22×D1911yescharacteristic
267C22×C4—191no—
268C22×C4—381no—
269Q16—761no—
270Q16—761no—
271SD16—41no—
272SD16—41no—
273SD16—761no—
274SD16—761no—
275SD16—761no—
276SD16—761no—
277C2×C8—191no—
278C2×C8—191no—
279C2×C8C22×D1911yescharacteristic
280C2×C8C22×D1911yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—191no—
283C4⋊C4—191no—
284C4⋊C4—191no—
285C4⋊C4—381no—
286C4⋊C4—381no—
287C4⋊C4—381no—
288C4⋊C4—381no—
289C4⋊C4—381no—
290C4⋊C4—381no—
291C4⋊C4—381no—
292C4⋊C4C22×D1911yescharacteristic
293C22⋊C4—191no—
294C22⋊C4—191no—
295C22⋊C4—381no—
296C22⋊C4—381no—
297C22⋊C4—381no—
298C22⋊C4—381no—
299C22⋊C4—381no—
300C22⋊C4—381no—
301C42—21no—
302C42—191no—
303C42—381no—
304C42C22×D1911yescharacteristic
305C23—21no—
306C23—21no—
307C23—191no—
308C23—381no—
309C23—762no—
310C23—1521no—
311C23—1521no—
312Q8—21no—
313Q8—21no—
314Q8—381no—
315Q8—381no—
316Q8—381no—
317Q8—381no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—81no—
323D4—81no—
324D4—381no—
325D4—381no—
326D4—762no—
327D4—762no—
328D4—1521no—
329D4—1521no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—191no—
333C2×C4—191no—
334C2×C4—191no—
335C2×C4—381no—
336C2×C4—381no—
337C2×C4—381no—
338C2×C4—381no—
339C2×C4—381no—
340C2×C4—762no—
341C2×C4D4×D1911yescharacteristic
342C2×C4D4×D1911yescharacteristic
343C2×C4C23×D1911yescharacteristic
344C8—21no—
345C8—21no—
346C8—381no—
347C8—381no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—381no—
355C22—381no—
356C22—381no—
357C22—761no—
358C22—761no—
359C22—761no—
360C22—1524no—
361C22C2×D4×D1911yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—381no—
367C4—381no—
368C4—381no—
369C4—761no—
370C4—761no—
371C4—761no—
372C4#1059743011yescharacteristic
373C4#1059743511yescharacteristic
374C2—81no—
375C2—81no—
376C2—761no—
377C2—1521no—
378C2#1192711011yescharacteristic
379C2#1192735011yescharacteristic
380C2#1192735411yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#460C2
socleC22×C19C22×D4
prime radical#11927107C2
hypercenter#460D19
hypocenterC19#3222
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #11927152C2semidirect
3. #11926935C2semidirect
4. #11926915C2semidirect
5. #11926907C2semidirect
6. #11926897C2semidirect
7. #11926767C2semidirect
8. #11926766C2semidirect
9. #11926741C2semidirect
10. #11926707C2semidirect
11. #11926703C2semidirect
12. #11926696C2semidirect
13. #11926693C2semidirect
14. #11926604C2semidirect
15. C19×#460C2semidirect
19. C2×SD16×C19C22semidirect
21. C4×Q8×C19C22semidirect
23. #10597390C22semidirect
24. C2×#64528C22semidirect
33. C2×#64526C22semidirect
34. C2×Dic76C22semidirect
38. #10597336C22semidirect
44. C4×Dic38C22semidirect
45. C19×C4⋊C8C22semidirect
47. C19×#102C22semidirect
49. #10597289C22semidirect
53. #10597273C22semidirect
54. #10597272C22semidirect
55. C8×Dic19C22semidirect
56. #10597267C22semidirect
58. C4⋊(C19⋊C8)C22semidirect
193. #460D19semidirect
215. C2×SD16C2×D19semidirect
233. C4×Q8C2×D19semidirect
236. C4⋊C8C2×D19semidirect
244. #102C2×D19semidirect
249. C19#3222semidirect

Maximal subgroups

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

subgroupindex
#119271522
#119271072
#119269352
#119269152
#119269072
#119268972
#119267672
#119267662
#119267412
#119267072
#119267032
#119266962
#119266932
#119266042
C19×#4602
#322219