Finite Group Databasebeta

← #14576964

Subgroups — #14576964

Order 2432.

1556 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#64541C211yesmaximal, characteristic, complemented
2#11927122C214yesmaximal, complemented
3#11927118C212yesmaximal, complemented
4#11927115C212yesmaximal, complemented
5#11927111C212yesmaximal, complemented
6#11927108C212yesmaximal, complemented
7#11927103C214yesmaximal, complemented
8#11927090C214yesmaximal, complemented
9#11927055C214yesmaximal, complemented
10#11927051C214yesmaximal, complemented
11C2×#10597372C211yesmaximal, characteristic, complemented
12C22×#41×C19C211yesmaximal, characteristic, complemented
13C2×#41×C19—28no—
14C2×#41×C19C2212yes—
15C2×#41×C19C2212yes—
16C2×#41×C19C2212yescomplemented
17C2×#41×C19C2212yescomplemented
18C22×Q8×C19C2211yescharacteristic, complemented
19C22×D4×C19C2212yes—
20C22×D4×C19C2211yescharacteristic, complemented
21C23×C4×C19C2211yescharacteristic
22C23×C4×C19C2212yescomplemented
23C22×C22⋊D19C2212yes—
24C2×#64541—28no—
25C2×#64541C2212yes—
26C2×#64541C2212yes—
27C2×#64541C2212yescomplemented
28C2×#64541C2212yescomplemented
29C22×D76C2211yescharacteristic, complemented
30C22×C4×D19C2212yescomplemented
31C22×Dic38C2211yescharacteristic, complemented
32#10597399C2218yescomplemented
33C2×C22⋊Dic19C2212yes—
34#10597393C2214yescomplemented
35#10597392C2218yescomplemented
36#10597390C2214yescomplemented
37#10597386C2214yescomplemented
38#10597385C22116yescomplemented
39#10597384C2218yescomplemented
40#10597383C2218yescomplemented
41#10597382C2214yescomplemented
42#10597381C2218yescomplemented
43#10597376C2218yescomplemented
44#10597375C2218yescomplemented
45C4×C22⋊D19C22116yescomplemented
46#10597372C2212yescomplemented
47#10597372C2212yescomplemented
48#10597372C2212yescomplemented
49#10597372C2212yescomplemented
50C2×C4⋊Dic19C2212yescomplemented
51#10597370C2218yescomplemented
52C2×C4×Dic19C2212yescomplemented
53C24×C19C2312yes—
54C24×C19C2311yescharacteristic
55C23×D19C2312yes—
56#41×C19—28no—
57#41×C19—28no—
58#41×C19—28no—
59#41×C19—28no—
60C2×Q8×C19—24no—
61C2×Q8×C19C2312yes—
62C2×Q8×C19C2312yes—
63C2×D4×C19—28no—
64C2×D4×C19—24no—
65C2×D4×C19C2314yes—
66C2×D4×C19C2312yes—
67C2×D4×C19C2312yes—
68C2×D4×C19C2314yes—
69C22×C4×C19—28no—
70C22×C4×C19D418yescomplemented
71C22×C4×C19C2314yes—
72C22×C4×C19C2312yes—
73C22×C4×C19C2314yes—
74C22×C4×C19C2311yescharacteristic
75C22×C4×C19C2311yescharacteristic
76C22×C4×C19C2311yescharacteristic
77C22×C4×C19C2311yescharacteristic
78C22×C4×C19C2311yescharacteristic
79C22×C4×C19C2311yescharacteristic
80C2×C22⋊D19—28no—
81C2×C22⋊D19C2314yes—
82C2×C22⋊D19C2314yes—
83C2×C22⋊D19C23116yes—
84C22×Dic19C2312yes—
85C22×Dic19C2314yes—
86#64541—28no—
87#64541—28no—
88#64541—28no—
89#64541—28no—
90C2×D76—24no—
91C2×D76C2312yes—
92C2×D76C2312yes—
93C2×C4×D19—28no—
94C2×C4×D19C2314yes—
95C2×C4×D19C2314yes—
96C2×Dic38—24no—
97C2×Dic38C2312yes—
98C2×Dic38C2312yes—
99C22⋊Dic19C2314yes—
100C22⋊Dic19C23116yes—
101C22⋊Dic19C2314yes—
102(C2×D19)⋊C4C23116yes—
103C4⋊Dic19C2314yes—
104C4⋊Dic19C2314yes—
105Dic19⋊C4C23116yes—
106C4×Dic19C2314yes—
107C4×Dic19C2314yes—
108C23×C19—24no—
109C23×C19—42no—
110C23×C19—44no—
111C23×C19C2×D414yes—
112C23×C19C2414yes—
113C23×C19C2411yescharacteristic
114C23×C19C2411yescharacteristic
115C23×C19C2411yescharacteristic
116C22×D19—24no—
117C22×D19—44no—
118C22×D19C2414yes—
119Q8×C19—24no—
120Q8×C19—24no—
121D4×C19—28no—
122D4×C19—28no—
123D4×C19—24no—
124D4×C19—24no—
125C2×C4×C19—24no—
126C2×C4×C19—28no—
127C2×C4×C19—28no—
128C2×C4×C19C2×D414yes—
129C2×C4×C19C2×D414yes—
130C2×C4×C19C2×D414yes—
131C2×C4×C19C2×D414yes—
132C2×C4×C19C2×D414yes—
133C2×C4×C19C2×D414yes—
134C2×C4×C19C2414yes—
135C2×C4×C19C2411yescharacteristic
136C2×C4×C19C2411yescharacteristic
137C2×C4×C19C2411yescharacteristic
138C2×C4×C19C2411yescharacteristic
139C22⋊D19—28no—
140C22⋊D19—28no—
141C22⋊D19—416no—
142C2×Dic19—24no—
143C2×Dic19—44no—
144C2×Dic19C2418yes—
145C2×Dic19C2414yes—
146D76—24no—
147D76—24no—
148C4×D19—28no—
149C4×D19—28no—
150Dic38—24no—
151Dic38—24no—
152#3449—191nomaximal, Sylow
153C22×C19—22no—
154C22×C19—22no—
155C22×C19—22no—
156C22×C19—24no—
157C22×C19—28no—
158C22×C19—44no—
159C22×C19—48no—
160C22×C19C22×D412yes—
161C22×C19C22×D412yes—
162C22×C19C22×D412yes—
163C22×C19C2511yescharacteristic
164C2×D19—24no—
165C2×D19—28no—
166C2×D19—48no—
167C4×C19—24no—
168C4×C19C22×D412yes—
169C4×C19C22×D412yes—
170C4×C19C22×D412yes—
171C4×C19C22×D412yes—
172Dic19—24no—
173Dic19—28no—
174C22×#41—191no—
175C22×#41D1911yescharacteristic, complemented
176#537—194no—
177#536—192no—
178#536—192no—
179#535—192no—
180#535—192no—
181#534—194no—
182#532—194no—
183#525—194no—
184#525—194no—
185C2×#117—191no—
186C2×C19—22no—
187C2×C19—22no—
188C2×C19—22no—
189C2×C19—44no—
190C2×C19C23×D411yescharacteristic
191C2×C19#58512yes—
192D19—44no—
193C2×#41—28no—
194C2×#41—192no—
195C2×#41—192no—
196C2×#41—192no—
197C2×#41—192no—
198C2×#41—388no—
199C2×#41C2×D1912yes—
200C2×#41C2×D1912yes—
201C2×#41C2×D1912yescomplemented
202C2×#41C2×D1912yescomplemented
203C22×Q8—191no—
204C22×Q8C2×D1911yescharacteristic, complemented
205C22×D4—192no—
206C22×D4—191no—
207C22×D4C2×D1912yes—
208C22×D4C2×D1911yescharacteristic, complemented
209C23×C4—192no—
210C23×C4C2×D1911yescharacteristic
211C23×C4C2×D1912yescomplemented
212C4⋊Q8—194no—
213#127—194no—
214#124—194no—
215#124—194no—
216#123—198no—
217#123—198no—
218C22⋊Q8—198no—
219C22⋊Q8—198no—
220#121—198no—
221#121—1916no—
222#121—198no—
223#120—198no—
224#120—198no—
225C4×D4—1916no—
226#117—192no—
227#117—192no—
228#117—192no—
229#117—192no—
230C2×C4⋊C4—192no—
231C2×C22⋊C4—192no—
232C2×C42—192no—
233C19#344911yescharacteristic, complemented, Sylow
234C24—192no—
235C24C22×D1912yes—
236C24C22×D1911yescharacteristic
237#41—28no—
238#41—28no—
239#41—28no—
240#41—28no—
241#41—388no—
242#41—388no—
243#41—388no—
244#41—388no—
245C2×Q8—24no—
246C2×Q8—192no—
247C2×Q8—192no—
248C2×Q8—384no—
249C2×Q8C22×D1912yes—
250C2×Q8C22×D1912yes—
251C2×D4—28no—
252C2×D4—24no—
253C2×D4—194no—
254C2×D4—194no—
255C2×D4—1916no—
256C2×D4—192no—
257C2×D4—192no—
258C2×D4—388no—
259C2×D4—384no—
260C2×D4C22×D1914yes—
261C2×D4C22×D1914yes—
262C2×D4C22×D1912yes—
263C2×D4C22×D1912yes—
264C22×C4—28no—
265C22×C4—192no—
266C22×C4—194no—
267C22×C4—194no—
268C22×C4—194no—
269C22×C4—388no—
270C22×C4C22⋊D1918yescomplemented
271C22×C4C22×D1914yes—
272C22×C4C22×D1912yes—
273C22×C4C22×D1914yes—
274C22×C4C22×D1911yescharacteristic
275C22×C4C22×D1911yescharacteristic
276C22×C4C22×D1911yescharacteristic
277C22×C4C22×D1911yescharacteristic
278C22×C4C22×D1911yescharacteristic
279C22×C4C22×D1911yescharacteristic
280C4⋊C4—1916no—
281C4⋊C4—194no—
282C4⋊C4—194no—
283C22⋊C4—194no—
284C22⋊C4—194no—
285C22⋊C4—1916no—
286C22⋊C4—1916no—
287C42—194no—
288C42—194no—
289C23—24no—
290C23—42no—
291C23—44no—
292C23—194no—
293C23—384no—
294C23—764no—
295C23C2×C22⋊D1914yes—
296C23C23×D1914yes—
297C23C23×D1911yescharacteristic
298C23C23×D1911yescharacteristic
299C23C23×D1911yescharacteristic
300Q8—24no—
301Q8—24no—
302Q8—384no—
303Q8—384no—
304D4—28no—
305D4—28no—
306D4—24no—
307D4—24no—
308D4—388no—
309D4—388no—
310D4—384no—
311D4—384no—
312D4—7616no—
313C2×C4—24no—
314C2×C4—28no—
315C2×C4—28no—
316C2×C4—198no—
317C2×C4—194no—
318C2×C4—384no—
319C2×C4—388no—
320C2×C4—388no—
321C2×C4—764no—
322C2×C4C2×C22⋊D1914yes—
323C2×C4C2×C22⋊D1914yes—
324C2×C4C2×C22⋊D1914yes—
325C2×C4C2×C22⋊D1914yes—
326C2×C4C2×C22⋊D1914yes—
327C2×C4C2×C22⋊D1914yes—
328C2×C4C23×D1914yes—
329C2×C4C23×D1911yescharacteristic
330C2×C4C23×D1911yescharacteristic
331C2×C4C23×D1911yescharacteristic
332C2×C4C23×D1911yescharacteristic
333C22—22no—
334C22—22no—
335C22—22no—
336C22—24no—
337C22—28no—
338C22—44no—
339C22—48no—
340C22—384no—
341C22—388no—
342C22—768no—
343C22C22×C22⋊D1912yes—
344C22C22×C22⋊D1912yes—
345C22C22×C22⋊D1912yes—
346C22C24×D1911yescharacteristic
347C4—24no—
348C4—384no—
349C4—388no—
350C4C22×C22⋊D1912yes—
351C4C22×C22⋊D1912yes—
352C4C22×C22⋊D1912yes—
353C4C22×C22⋊D1912yes—
354C2—22no—
355C2—22no—
356C2—22no—
357C2—44no—
358C2—764no—
359C2C23×C22⋊D1911yescharacteristic
360C2#1192738012yes—
subgroupG/H
centerC2×C4C23×D19
commutator, socle, cosocleC22×C19C25
FrattiniC22C24×D19
FittingC22×#41×C19C2
hypercenterC22×#41D19
hypocenterC19#3449
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×#64541C2semidirect
2. #11927122C2semidirect
3. #11927118C2semidirect
4. #11927115C2semidirect
5. #11927111C2semidirect
6. #11927108C2semidirect
7. #11927103C2semidirect
8. #11927090C2semidirect
9. #11927055C2semidirect
10. #11927051C2semidirect
11. C2×#10597372C2semidirect
12. C22×#41×C19C2semidirect
16. C2×#41×C19C22semidirect
17. C2×#41×C19C22semidirect
18. C22×Q8×C19C22semidirect
20. C22×D4×C19C22semidirect
22. C23×C4×C19C22semidirect
27. C2×#64541C22semidirect
28. C2×#64541C22semidirect
29. C22×D76C22semidirect
30. C22×C4×D19C22semidirect
31. C22×Dic38C22semidirect
32. #10597399C22semidirect
34. #10597393C22semidirect
35. #10597392C22semidirect
36. #10597390C22semidirect
37. #10597386C22semidirect
38. #10597385C22semidirect
39. #10597384C22semidirect
40. #10597383C22semidirect
41. #10597382C22semidirect
42. #10597381C22semidirect
43. #10597376C22semidirect
44. #10597375C22semidirect
45. C4×C22⋊D19C22semidirect
46. #10597372C22semidirect
47. #10597372C22semidirect
48. #10597372C22semidirect
49. #10597372C22semidirect
50. C2×C4⋊Dic19C22semidirect
51. #10597370C22semidirect
52. C2×C4×Dic19C22semidirect
70. C22×C4×C19D4semidirect
175. C22×#41D19semidirect
201. C2×#41C2×D19semidirect
202. C2×#41C2×D19semidirect
204. C22×Q8C2×D19semidirect
208. C22×D4C2×D19semidirect
211. C23×C4C2×D19semidirect
233. C19#3449semidirect
270. C22×C4C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
C22×#645412
#119271222
#119271182
#119271152
#119271112
#119271082
#119271032
#119270902
#119270552
#119270512
C2×#105973722
C22×#41×C192
#344919