Finite Group Databasebeta

← #44487396

Subgroups — #44487396

Order 30592.

792 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#21439918C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D239C211yesmaximal, characteristic
3C2×C22⋊C4×D239C211yesmaximal, characteristic
4#29504666C211yesmaximal, characteristic, complemented
5#29504665C211yesmaximal, characteristic, complemented
6#29504660C211yesmaximal, characteristic, complemented
7#29504646C211yesmaximal, characteristic, complemented
8#29504643C211yesmaximal, characteristic, complemented
9#29504634C211yesmaximal, characteristic, complemented
10#29504631C211yesmaximal, characteristic, complemented
11#29504627C211yesmaximal, characteristic
12C4×(C2×D239)⋊C4C211yesmaximal, characteristic, complemented
13C4×(C2×D239)⋊C4C211yesmaximal, characteristic, complemented
14#29504619C211yesmaximal, characteristic, complemented
15#388×C239C211yesmaximal, characteristic, complemented
16C24×D239C2211yescharacteristic
17C22×C4×D239C2211yescharacteristic
18C22×C4×D239C2211yescharacteristic
19C22×C4×D239C2211yescharacteristic
20C22×C4×D239C2211yescharacteristic
21#21439918—24no—
22C2×C4⋊Dic239C2211yescharacteristic, complemented
23C2×Dic239⋊C4C2211yescharacteristic, complemented
24C2×Dic239⋊C4C2211yescharacteristic, complemented
25C2×C22⋊Dic239C2211yescharacteristic
26C2×C22⋊Dic239C2211yescharacteristic
27C2×C22⋊Dic239C2211yescharacteristic
28C2×(C2×D239)⋊C4C2211yescharacteristic
29C2×(C2×D239)⋊C4C2211yescharacteristic
30C2×(C2×D239)⋊C4C2211yescharacteristic
31C2×(C2×D239)⋊C4C2211yescharacteristic
32C2×(C2×D239)⋊C4C2211yescharacteristic
33C2×(C2×D239)⋊C4C2211yescharacteristic
34C2×(C2×D239)⋊C4C2211yescharacteristic
35C2×(C2×D239)⋊C4C2211yescharacteristic
36C22⋊C4×D239—24no—
37C22⋊C4×D239C418yescomplemented
38C2×C4×Dic239C2211yescharacteristic, complemented
39C2×C4×Dic239C2211yescharacteristic, complemented
40C2×C4×Dic239C2211yescharacteristic, complemented
41C239⋊#95C2211yescharacteristic, complemented
42C239⋊#95C2211yescharacteristic, complemented
43C239⋊#95C2211yescharacteristic, complemented
44C239⋊#95C2211yescharacteristic, complemented
45C239⋊#95C2211yescharacteristic, complemented
46C239⋊#95C2211yescharacteristic, complemented
47C2×C4⋊C4×C239C2211yescharacteristic, complemented
48C2×C22⋊C4×C239C2211yescharacteristic
49C2×C22⋊C4×C239C2211yescharacteristic
50C2×C22⋊C4×C239C2211yescharacteristic
51C2×C42×C239C2211yescharacteristic, complemented
52#95×C239C2211yescharacteristic, complemented
53#95×C239C2211yescharacteristic, complemented
54C23×D239—22no—
55C23×D239—22no—
56C23×D239—22no—
57C23×D239—22no—
58C23×D239—41no—
59C23×D239—41no—
60C23×D239C2×C414yes—
61C23×D239C2311yescharacteristic
62C23×D239C2311yescharacteristic
63C22×Dic239C2311yescharacteristic
64C22×Dic239C2311yescharacteristic
65C22×Dic239C2311yescharacteristic
66C22×Dic239C2311yescharacteristic
67C22×Dic239C2311yescharacteristic
68C22×Dic239C2311yescharacteristic
69C2×C4×D239—22no—
70C2×C4×D239—22no—
71C2×C4×D239—22no—
72C2×C4×D239—22no—
73C2×C4×D239—22no—
74C2×C4×D239—22no—
75C2×C4×D239—41no—
76C2×C4×D239—41no—
77C2×C4×D239—41no—
78C2×C4×D239—41no—
79C2×C4×D239C2×C414yescomplemented
80C2×C4×D239C2×C414yescomplemented
81C4⋊Dic239—22no—
82Dic239⋊C4—41no—
83Dic239⋊C4—41no—
84C22⋊Dic239—22no—
85C22⋊Dic239—41no—
86C22⋊Dic239C2×C414yescomplemented
87(C2×D239)⋊C4—22no—
88(C2×D239)⋊C4—22no—
89(C2×D239)⋊C4—22no—
90(C2×D239)⋊C4—22no—
91(C2×D239)⋊C4—22no—
92(C2×D239)⋊C4C2×C414yes—
93(C2×D239)⋊C4C2×C414yes—
94(C2×D239)⋊C4D414yes—
95C4×Dic239—22no—
96C4×Dic239—22no—
97C4×Dic239—41no—
98C24×C239C2311yescharacteristic
99C22×C4×C239C2311yescharacteristic
100C22×C4×C239C2311yescharacteristic
101C22×C4×C239C2311yescharacteristic
102C22×C4×C239C2311yescharacteristic
103C22×C4×C239C2311yescharacteristic
104C22×C4×C239C2311yescharacteristic
105C4⋊C4×C239—22no—
106C22⋊C4×C239—22no—
107C22⋊C4×C239—41no—
108C22⋊C4×C239C2×C414yescomplemented
109C42×C239—41no—
110C22×D239—21no—
111C22×D239—21no—
112C22×D239—21no—
113C22×D239—21no—
114C22×D239—21no—
115C22×D239—21no—
116C22×D239—21no—
117C22×D239—21no—
118C22×D239—28no—
119C22×D239—28no—
120C22×D239—44no—
121C22×D239—44no—
122C22×D239—44no—
123C22×D239—44no—
124C22×D239—44no—
125C22×D239C22×C412yes—
126C22×D239C22×C412yes—
127C22×D239C2×D412yes—
128C22×D239#4112yes—
129C22×D239#4112yes—
130C22×D239#4112yes—
131C2×Dic239—21no—
132C2×Dic239—21no—
133C2×Dic239—21no—
134C2×Dic239—21no—
135C2×Dic239—21no—
136C2×Dic239—21no—
137C2×Dic239—21no—
138C2×Dic239—21no—
139C2×Dic239—21no—
140C2×Dic239—21no—
141C2×Dic239—21no—
142C2×Dic239—21no—
143C2×Dic239—21no—
144C2×Dic239—21no—
145C2×Dic239—21no—
146C2×Dic239C22×C412yes—
147C2×Dic239C22×C412yes—
148C2×Dic239C2×D412yes—
149C4×D239—28no—
150C4×D239—44no—
151C4×D239—44no—
152C4×D239—44no—
153C23×C239—21no—
154C23×C239—21no—
155C23×C239—21no—
156C23×C239—21no—
157C23×C239—21no—
158C23×C239—21no—
159C23×C239C22×C412yes—
160C23×C239C2411yescharacteristic
161C2×C4×C239—21no—
162C2×C4×C239—21no—
163C2×C4×C239—21no—
164C2×C4×C239—21no—
165C2×C4×C239—21no—
166C2×C4×C239—21no—
167C2×C4×C239—21no—
168C2×C4×C239—21no—
169C2×C4×C239—21no—
170C2×C4×C239—21no—
171C2×C4×C239—21no—
172C2×C4×C239—21no—
173C2×C4×C239—21no—
174C2×C4×C239—21no—
175C2×C4×C239—21no—
176C2×C4×C239C22×C412yes—
177C2×C4×C239C22×C412yes—
178C2×C4×C239C2×D412yes—
179C22×C239—22no—
180C22×C239—22no—
181C22×C239—22no—
182C22×C239—41no—
183C22×C239—41no—
184C22×C239—41no—
185C22×C239—41no—
186C22×C239C23×C411yescharacteristic
187C22×C239C22×D411yescharacteristic
188C22×C239C2×#4111yescharacteristic
189C22×C239C2×#4111yescharacteristic
190C22×C239C2×#4111yescharacteristic
191C22×C239H(5,𝔽2)11yescharacteristic
192C22×C239H(5,𝔽2)11yescharacteristic
193C2×D239—22no—
194C2×D239—22no—
195C2×D239—22no—
196C2×D239—22no—
197C2×D239—22no—
198C2×D239—22no—
199C2×D239—22no—
200C2×D239—22no—
201C2×D239—22no—
202C2×D239—22no—
203C2×D239—22no—
204C2×D239—22no—
205C2×D239—416no—
206C2×D239#11714yescomplemented
207C2×D239C4×D414yes—
208C4×C239—22no—
209C4×C239—22no—
210C4×C239—22no—
211C4×C239—41no—
212C4×C239—41no—
213C4×C239—41no—
214Dic239—22no—
215Dic239—22no—
216Dic239—22no—
217Dic239—41no—
218Dic239—41no—
219Dic239—41no—
220C2×C239—42no—
221C2×C239C2×#11711yescharacteristic
222C2×C239C2×C4×D411yescharacteristic
223C2×C239#51811yescharacteristic
224C2×C239#54611yescharacteristic
225C2×C239#54611yescharacteristic
226C2×C239#55111yescharacteristic
227C2×C239#55111yescharacteristic
228D239—24no—
229D239—24no—
230C239#234211yescharacteristic, complemented, Sylow
231#2342—2391nomaximal, Sylow
232C2×#117—2391no—
233C22×C22⋊C4—2391no—
234C22×C22⋊C4—2391no—
235#388—2391no—
236#388—2391no—
237#388—2391no—
238#388D23911yescharacteristic, complemented
239#385—2391no—
240#385—2391no—
241#381—2391no—
242#380—2391no—
243#379—2391no—
244C4×C22⋊C4—2391no—
245C4×C22⋊C4—2391no—
246C4×C22⋊C4—2391no—
247C25—2391no—
248C23×C4—2391no—
249C23×C4—2391no—
250C23×C4—2391no—
251C23×C4—2391no—
252#117—4784no—
253C2×C4⋊C4—2391no—
254C2×C4⋊C4—2391no—
255C2×C4⋊C4—2391no—
256C2×C4⋊C4C2×D23911yescharacteristic, complemented
257C2×C22⋊C4—4784no—
258C2×C22⋊C4—2391no—
259C2×C22⋊C4—2391no—
260C2×C22⋊C4—2391no—
261C2×C22⋊C4—2391no—
262C2×C22⋊C4—2391no—
263C2×C22⋊C4—2391no—
264C2×C22⋊C4—2391no—
265C2×C22⋊C4—2391no—
266C2×C22⋊C4—2391no—
267C2×C22⋊C4—2391no—
268C2×C22⋊C4—2391no—
269C2×C22⋊C4—2398no—
270C2×C22⋊C4C2×D23911yescharacteristic
271C2×C22⋊C4C2×D23911yescharacteristic
272C2×C22⋊C4C2×D23911yescharacteristic
273C2×C42—2391no—
274C2×C42—2391no—
275C2×C42—2391no—
276C2×C42C2×D23911yescharacteristic, complemented
277#95—2391no—
278#95—2391no—
279#95—2391no—
280#95—2391no—
281#95—2391no—
282#95—2391no—
283#95C2×D23911yescharacteristic, complemented
284#95C2×D23911yescharacteristic, complemented
285C24—9561no—
286C24—9561no—
287C24—4782no—
288C24—4782no—
289C24—4782no—
290C24—4782no—
291C24—2394no—
292C24—2391no—
293C24—2391no—
294C24C22×D23911yescharacteristic
295C22×C4—9561no—
296C22×C4—9561no—
297C22×C4—9561no—
298C22×C4—9561no—
299C22×C4—4782no—
300C22×C4—4782no—
301C22×C4—4782no—
302C22×C4—4782no—
303C22×C4—4782no—
304C22×C4—4782no—
305C22×C4—2394no—
306C22×C4—2391no—
307C22×C4—2391no—
308C22×C4—2391no—
309C22×C4—2391no—
310C22×C4—2391no—
311C22×C4—2391no—
312C22×C4—2394no—
313C22×C4C22×D23911yescharacteristic
314C22×C4C22×D23911yescharacteristic
315C22×C4C22×D23911yescharacteristic
316C22×C4C22×D23911yescharacteristic
317C22×C4C22×D23911yescharacteristic
318C22×C4C22×D23911yescharacteristic
319C4⋊C4—22no—
320C4⋊C4—9561no—
321C4⋊C4—9561no—
322C4⋊C4—4782no—
323C22⋊C4—22no—
324C22⋊C4—41no—
325C22⋊C4—9561no—
326C22⋊C4—4782no—
327C22⋊C4—4782no—
328C22⋊C4—4782no—
329C22⋊C4—4782no—
330C22⋊C4—4782no—
331C22⋊C4—4782no—
332C22⋊C4—2394no—
333C22⋊C4—2394no—
334C22⋊C4—2394no—
335C22⋊C4—2394no—
336C22⋊C4C4×D23914yescomplemented
337C42—41no—
338C42—9561no—
339C42—4782no—
340C42—4782no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—9564no—
348C23—9564no—
349C23—9564no—
350C23—9564no—
351C23—9564no—
352C23—4788no—
353C23—4788no—
354C23—4781no—
355C23—4781no—
356C23—4781no—
357C23—4781no—
358C23—4781no—
359C23—4781no—
360C23—4781no—
361C23—4781no—
362C23—2392no—
363C23—2392no—
364C23—2392no—
365C23—2392no—
366C23—2392no—
367C23—2392no—
368C23C2×C4×D23912yes—
369C23C23×D23911yescharacteristic
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—9564no—
386C2×C4—9564no—
387C2×C4—9564no—
388C2×C4—4788no—
389C2×C4—4781no—
390C2×C4—4781no—
391C2×C4—4781no—
392C2×C4—4781no—
393C2×C4—4781no—
394C2×C4—4781no—
395C2×C4—4781no—
396C2×C4—4781no—
397C2×C4—4781no—
398C2×C4—4781no—
399C2×C4—4781no—
400C2×C4—4781no—
401C2×C4—4781no—
402C2×C4—4781no—
403C2×C4—4781no—
404C2×C4—2392no—
405C2×C4—2392no—
406C2×C4—2392no—
407C2×C4C2×C4×D23912yes—
408C2×C4C2×C4×D23912yes—
409C2×C4D4×D23912yes—
410C22—22no—
411C22—22no—
412C22—22no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—95616no—
418C22—4782no—
419C22—4782no—
420C22—4782no—
421C22—4782no—
422C22—4782no—
423C22—4782no—
424C22—4782no—
425C22—4782no—
426C22—4782no—
427C22—4782no—
428C22—4782no—
429C22—4782no—
430C22—2394no—
431C22—2394no—
432C22C22×C4×D23911yescharacteristic
433C22C2×D4×D23911yescharacteristic
434C22#41×D23911yescharacteristic
435C22#41×D23911yescharacteristic
436C22#41×D23911yescharacteristic
437C22#2144000511yescharacteristic
438C22#2144000611yescharacteristic
439C4—22no—
440C4—22no—
441C4—22no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—9561no—
446C4—9561no—
447C4—9561no—
448C4—4782no—
449C4—4782no—
450C4—4782no—
451C2—42no—
452C2—4784no—
453C2—4784no—
454C2#117×D23911yescharacteristic
455C2C4×D4×D23911yescharacteristic
456C2#2950524411yescharacteristic
457C2#2950541111yescharacteristic
458C2#2950541511yescharacteristic
459C2#2950544711yescharacteristic
460C2#2950545011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D239
commutatorC22×C239C23×C4
Fitting#388×C239C2
socle, cosocleC23×C239C24
prime radicalC24×D239C22
hypercenter#388D239
hypocenterC239#2342
LCSG ▷ C22×C239 ▷ C239
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#21439918C2semidirect
4. #29504666C2semidirect
5. #29504665C2semidirect
6. #29504660C2semidirect
7. #29504646C2semidirect
8. #29504643C2semidirect
9. #29504634C2semidirect
10. #29504631C2semidirect
12. C4×(C2×D239)⋊C4C2semidirect
13. C4×(C2×D239)⋊C4C2semidirect
14. #29504619C2semidirect
15. #388×C239C2semidirect
22. C2×C4⋊Dic239C22semidirect
23. C2×Dic239⋊C4C22semidirect
24. C2×Dic239⋊C4C22semidirect
37. C22⋊C4×D239C4semidirect
38. C2×C4×Dic239C22semidirect
39. C2×C4×Dic239C22semidirect
40. C2×C4×Dic239C22semidirect
41. C239⋊#95C22semidirect
42. C239⋊#95C22semidirect
43. C239⋊#95C22semidirect
44. C239⋊#95C22semidirect
45. C239⋊#95C22semidirect
46. C239⋊#95C22semidirect
47. C2×C4⋊C4×C239C22semidirect
51. C2×C42×C239C22semidirect
52. #95×C239C22semidirect
53. #95×C239C22semidirect
79. C2×C4×D239C2×C4semidirect
80. C2×C4×D239C2×C4semidirect
86. C22⋊Dic239C2×C4semidirect
108. C22⋊C4×C239C2×C4semidirect
206. C2×D239#117semidirect
230. C239#2342semidirect
238. #388D239semidirect
256. C2×C4⋊C4C2×D239semidirect
276. C2×C42C2×D239semidirect
283. #95C2×D239semidirect
284. #95C2×D239semidirect
336. C22⋊C4C4×D239semidirect

Maximal subgroups

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

subgroupindex
C2×#214399182
C2×C22⋊C4×D2392
#295046662
#295046652
#295046602
#295046462
#295046432
#295046342
#295046312
#295046272
C4×(C2×D239)⋊C42
#295046192
#388×C2392
#2342239