Finite Group Databasebeta

← #44487525

Subgroups — #44487525

Order 30592.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#21439928C211yesmaximal, characteristic
2C2×C4×C22⋊D239C211yesmaximal, characteristic, complemented
3C22×(C2×D239)⋊C4C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D239C211yesmaximal, characteristic, complemented
5#29504672C211yesmaximal, characteristic, complemented
6#29504663C211yesmaximal, characteristic, complemented
7#29504662C211yesmaximal, characteristic, complemented
8#29504652C211yesmaximal, characteristic, complemented
9#29504651C211yesmaximal, characteristic, complemented
10#29504648C211yesmaximal, characteristic, complemented
11#29504645C211yesmaximal, characteristic, complemented
12#29504643C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic239C211yesmaximal, characteristic, complemented
14C4×(C2×D239)⋊C4C211yesmaximal, characteristic, complemented
15C2×C4×D4×C239C211yesmaximal, characteristic, complemented
16C24×D239C2211yescharacteristic
17C22×C22⋊D239C2211yescharacteristic
18C22×C22⋊D239C2211yescharacteristic
19C23×Dic239C2211yescharacteristic
20C22×C4×D239C2211yescharacteristic
21C22×C4×D239C2211yescharacteristic
22#21439928C418yescomplemented
23C4×C22⋊D239—24no—
24C2×Dic239⋊C4C2211yescharacteristic, complemented
25C2×Dic239⋊C4C2211yescharacteristic, complemented
26C2×C22⋊Dic239C2211yescharacteristic
27C2×C22⋊Dic239C2211yescharacteristic
28C2×C22⋊Dic239C2211yescharacteristic, complemented
29C2×C22⋊Dic239C2211yescharacteristic, complemented
30C2×(C2×D239)⋊C4—24no—
31C2×(C2×D239)⋊C4C2211yescharacteristic
32C2×(C2×D239)⋊C4C2211yescharacteristic
33C2×(C2×D239)⋊C4C2211yescharacteristic
34C2×(C2×D239)⋊C4C2211yescharacteristic
35C2×(C2×D239)⋊C4C2211yescharacteristic
36C2×(C2×D239)⋊C4C2211yescharacteristic
37C2×(C2×D239)⋊C4C2211yescharacteristic
38C2×(C2×D239)⋊C4C2211yescharacteristic
39C22⋊C4×D239—24no—
40C2×C4×Dic239C2211yescharacteristic, complemented
41C2×C4×Dic239C2211yescharacteristic, complemented
42C239⋊#95C2211yescharacteristic, complemented
43C239⋊#95C2211yescharacteristic, complemented
44C239⋊#95C2211yescharacteristic, complemented
45C239⋊#95C2211yescharacteristic, complemented
46C239⋊#95C2211yescharacteristic, complemented
47C239⋊#95C2211yescharacteristic, complemented
48C22×D4×C239C2211yescharacteristic
49C23×C4×C239C2211yescharacteristic
50C23×C4×C239C2211yescharacteristic, complemented
51C4×D4×C239—24no—
52C2×C4⋊C4×C239C2211yescharacteristic, complemented
53C2×C22⋊C4×C239C2211yescharacteristic
54C2×C22⋊C4×C239C2211yescharacteristic, complemented
55C2×C42×C239C2211yescharacteristic, complemented
56C23×D239—22no—
57C23×D239—22no—
58C23×D239—22no—
59C23×D239—22no—
60C23×D239—41no—
61C23×D239—41no—
62C23×D239C2×C414yescomplemented
63C23×D239C2311yescharacteristic
64C23×D239C2311yescharacteristic
65C2×C22⋊D239—22no—
66C2×C22⋊D239—22no—
67C2×C22⋊D239—41no—
68C2×C22⋊D239—41no—
69C2×C22⋊D239C2×C414yescomplemented
70C2×C22⋊D239C2×C414yescomplemented
71C22×Dic239—22no—
72C22×Dic239—22no—
73C22×Dic239—41no—
74C22×Dic239C2311yescharacteristic
75C22×Dic239C2311yescharacteristic
76C22×Dic239C2311yescharacteristic
77C22×Dic239C2311yescharacteristic
78C22×Dic239C2311yescharacteristic
79C22×Dic239C2311yescharacteristic
80C2×C4×D239—22no—
81C2×C4×D239—22no—
82C2×C4×D239—22no—
83C2×C4×D239—22no—
84C2×C4×D239—41no—
85C2×C4×D239—41no—
86Dic239⋊C4—22no—
87Dic239⋊C4—41no—
88C22⋊Dic239—22no—
89C22⋊Dic239—22no—
90C22⋊Dic239—41no—
91C22⋊Dic239C2×C414yescomplemented
92(C2×D239)⋊C4—22no—
93(C2×D239)⋊C4—22no—
94(C2×D239)⋊C4—22no—
95(C2×D239)⋊C4—22no—
96(C2×D239)⋊C4—22no—
97(C2×D239)⋊C4C2×C414yescomplemented
98(C2×D239)⋊C4C2×C414yescomplemented
99(C2×D239)⋊C4D414yescomplemented
100C4×Dic239—22no—
101C4×Dic239—41no—
102C24×C239C2311yescharacteristic
103C24×C239C2311yescharacteristic
104C2×D4×C239—22no—
105C2×D4×C239—22no—
106C2×D4×C239C2×C414yescomplemented
107C22×C4×C239—22no—
108C22×C4×C239—22no—
109C22×C4×C239—22no—
110C22×C4×C239—22no—
111C22×C4×C239—41no—
112C22×C4×C239—41no—
113C22×C4×C239C2311yescharacteristic
114C22×C4×C239C2311yescharacteristic
115C22×C4×C239C2311yescharacteristic
116C22×C4×C239C2311yescharacteristic
117C22×C4×C239C2311yescharacteristic
118C4⋊C4×C239—22no—
119C22⋊C4×C239—22no—
120C22⋊C4×C239D414yescomplemented
121C42×C239—22no—
122C22×D239—21no—
123C22×D239—21no—
124C22×D239—21no—
125C22×D239—21no—
126C22×D239—28no—
127C22×D239—21no—
128C22×D239—21no—
129C22×D239—21no—
130C22×D239—21no—
131C22×D239—21no—
132C22×D239—21no—
133C22×D239—28no—
134C22×D239—44no—
135C22×D239—44no—
136C22×D239—44no—
137C22×D239—44no—
138C22×D239—44no—
139C22×D239C22×C412yes—
140C22×D239C22×C412yes—
141C22×D239C2×D412yes—
142C22×D239#4112yes—
143C22⋊D239—28no—
144C22⋊D239—44no—
145C2×Dic239—21no—
146C2×Dic239—21no—
147C2×Dic239—21no—
148C2×Dic239—21no—
149C2×Dic239—21no—
150C2×Dic239—21no—
151C2×Dic239—21no—
152C2×Dic239—21no—
153C2×Dic239—21no—
154C2×Dic239—21no—
155C2×Dic239—21no—
156C2×Dic239—21no—
157C2×Dic239—21no—
158C2×Dic239—21no—
159C2×Dic239—21no—
160C2×Dic239—44no—
161C2×Dic239C22×C412yes—
162C2×Dic239C22×C412yes—
163C2×Dic239C2×D412yes—
164C4×D239—44no—
165C4×D239—44no—
166C23×C239—21no—
167C23×C239—21no—
168C23×C239—21no—
169C23×C239—21no—
170C23×C239—21no—
171C23×C239—21no—
172C23×C239—21no—
173C23×C239—21no—
174C23×C239—21no—
175C23×C239—21no—
176C23×C239C22×C412yes—
177C23×C239C22×C412yes—
178C23×C239C2×D412yes—
179C23×C239#4112yes—
180C23×C239C2411yescharacteristic
181D4×C239—28no—
182C2×C4×C239—21no—
183C2×C4×C239—21no—
184C2×C4×C239—21no—
185C2×C4×C239—21no—
186C2×C4×C239—21no—
187C2×C4×C239—21no—
188C2×C4×C239—21no—
189C2×C4×C239—21no—
190C2×C4×C239—21no—
191C2×C4×C239—21no—
192C2×C4×C239—21no—
193C2×C4×C239—44no—
194C2×C4×C239—44no—
195C2×C4×C239C22×C412yes—
196C2×C4×C239C2×D412yes—
197C2×C4×C239C2×D412yes—
198C2×C4×C239C2×D412yes—
199C22×C239—22no—
200C22×C239—22no—
201C22×C239—22no—
202C22×C239—22no—
203C22×C239—22no—
204C22×C239—22no—
205C22×C239—22no—
206C22×C239—22no—
207C22×C239—22no—
208C22×C239—41no—
209C22×C239—41no—
210C22×C239—41no—
211C22×C239—41no—
212C22×C239C4×D414yescomplemented
213C22×C239C23×C411yescharacteristic
214C22×C239C22×D411yescharacteristic
215C22×C239C22×D411yescharacteristic
216C22×C239C2×#4111yescharacteristic
217C22×C239C2×#4111yescharacteristic
218C22×C239H(5,𝔽2)11yescharacteristic
219C22×C239H(5,𝔽2)11yescharacteristic
220C2×D239—22no—
221C2×D239—22no—
222C2×D239—22no—
223C2×D239—22no—
224C2×D239—22no—
225C2×D239—22no—
226C2×D239—22no—
227C2×D239—22no—
228C2×D239—22no—
229C2×D239—416no—
230C2×D239—41no—
231C2×D239—41no—
232C2×D239—41no—
233C2×D239—41no—
234C2×D239C4×D414yescomplemented
235C4×C239—22no—
236C4×C239—22no—
237C4×C239—22no—
238C4×C239—22no—
239C4×C239—41no—
240Dic239—22no—
241Dic239—22no—
242Dic239—22no—
243Dic239—41no—
244Dic239—41no—
245Dic239—41no—
246C2×C239—24no—
247C2×C239—42no—
248C2×C239C2×C4×D411yescharacteristic
249C2×C239C2×C4×D411yescharacteristic
250C2×C239#51811yescharacteristic
251C2×C239D4211yescharacteristic
252C2×C239#54611yescharacteristic
253C2×C239#54611yescharacteristic
254C2×C239#55111yescharacteristic
255D239—24no—
256D239—42no—
257C239#235811yescharacteristic, complemented, Sylow
258#2358—2391nomaximal, Sylow
259C2×#120—2391no—
260C2×C4×D4—2391no—
261C2×C4×D4D23911yescharacteristic, complemented
262C22×C22⋊C4—2391no—
263C22×C22⋊C4—2391no—
264#390—2391no—
265#388—2391no—
266#388—2391no—
267#386—2391no—
268#386—2391no—
269#386—2391no—
270#385—2391no—
271#385—2391no—
272C4×C22⋊C4—2391no—
273C4×C22⋊C4—2391no—
274C25—2391no—
275C22×D4—2391no—
276C22×D4—2391no—
277C22×D4C2×D23911yescharacteristic
278C23×C4—2391no—
279C23×C4—2391no—
280C23×C4—2391no—
281C23×C4C2×D23911yescharacteristic
282C23×C4C2×D23911yescharacteristic, complemented
283#120—2398no—
284C4×D4—24no—
285C4×D4—4784no—
286C2×C4⋊C4—2391no—
287C2×C4⋊C4—2391no—
288C2×C4⋊C4C2×D23911yescharacteristic, complemented
289C2×C22⋊C4—4784no—
290C2×C22⋊C4—4784no—
291C2×C22⋊C4—2391no—
292C2×C22⋊C4—2391no—
293C2×C22⋊C4—2391no—
294C2×C22⋊C4—2391no—
295C2×C22⋊C4—2391no—
296C2×C22⋊C4—2391no—
297C2×C22⋊C4—2391no—
298C2×C22⋊C4—2391no—
299C2×C22⋊C4—2391no—
300C2×C22⋊C4—2391no—
301C2×C22⋊C4—2391no—
302C2×C22⋊C4—2391no—
303C2×C22⋊C4C2×D23911yescharacteristic
304C2×C22⋊C4C2×D23911yescharacteristic, complemented
305C2×C42—2391no—
306C2×C42—2391no—
307C2×C42C2×D23911yescharacteristic, complemented
308#95—2391no—
309#95—2391no—
310#95—2391no—
311#95—2391no—
312#95—2391no—
313#95—2391no—
314C24—9561no—
315C24—9561no—
316C24—4782no—
317C24—4782no—
318C24—4782no—
319C24—4782no—
320C24—2394no—
321C24—2391no—
322C24—2391no—
323C24C22×D23911yescharacteristic
324C24C22×D23911yescharacteristic
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—9561no—
328C2×D4—9561no—
329C2×D4—4782no—
330C2×D4—4782no—
331C2×D4—2394no—
332C2×D4—2394no—
333C2×D4C4×D23914yescomplemented
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—9561no—
341C22×C4—9561no—
342C22×C4—9561no—
343C22×C4—4782no—
344C22×C4—4782no—
345C22×C4—4782no—
346C22×C4—4782no—
347C22×C4—4782no—
348C22×C4—4782no—
349C22×C4—2391no—
350C22×C4—2391no—
351C22×C4—2391no—
352C22×C4—2391no—
353C22×C4—2391no—
354C22×C4—2391no—
355C22×C4C22×D23911yescharacteristic
356C22×C4C22×D23911yescharacteristic
357C22×C4C22×D23911yescharacteristic
358C22×C4C22×D23911yescharacteristic
359C22×C4C22×D23911yescharacteristic
360C4⋊C4—22no—
361C4⋊C4—9561no—
362C4⋊C4—4782no—
363C22⋊C4—22no—
364C22⋊C4—9561no—
365C22⋊C4—4782no—
366C22⋊C4—4782no—
367C22⋊C4—4782no—
368C22⋊C4—4782no—
369C22⋊C4—4782no—
370C22⋊C4—4782no—
371C22⋊C4—4782no—
372C22⋊C4—2394no—
373C22⋊C4—2394no—
374C22⋊C4—2394no—
375C22⋊C4—2394no—
376C22⋊C4C22⋊D23914yescomplemented
377C42—22no—
378C42—9561no—
379C42—4782no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—9564no—
391C23—9564no—
392C23—9564no—
393C23—9564no—
394C23—9564no—
395C23—4788no—
396C23—4781no—
397C23—4781no—
398C23—4781no—
399C23—4781no—
400C23—4788no—
401C23—4781no—
402C23—4781no—
403C23—4781no—
404C23—4781no—
405C23—4781no—
406C23—4781no—
407C23—2392no—
408C23—2392no—
409C23—2392no—
410C23—2392no—
411C23C2×C4×D23912yes—
412C23C2×C4×D23912yes—
413C23C2×C22⋊D23912yes—
414C23#1683854812yes—
415C23C23×D23911yescharacteristic
416D4—28no—
417D4—9564no—
418D4—4788no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—44no—
431C2×C4—44no—
432C2×C4—9564no—
433C2×C4—9564no—
434C2×C4—9564no—
435C2×C4—4781no—
436C2×C4—4781no—
437C2×C4—4781no—
438C2×C4—4781no—
439C2×C4—4781no—
440C2×C4—4781no—
441C2×C4—4781no—
442C2×C4—4781no—
443C2×C4—4781no—
444C2×C4—4781no—
445C2×C4—4781no—
446C2×C4—4781no—
447C2×C4—4781no—
448C2×C4—4781no—
449C2×C4—4781no—
450C2×C4—2392no—
451C2×C4—2392no—
452C2×C4—2392no—
453C2×C4C2×C4×D23912yes—
454C2×C4D4×D23912yes—
455C2×C4C2×C22⋊D23912yes—
456C2×C4C2×C22⋊D23912yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—95616no—
471C22—9561no—
472C22—9561no—
473C22—9561no—
474C22—9561no—
475C22—4782no—
476C22—4782no—
477C22—4782no—
478C22—4782no—
479C22—4782no—
480C22—4782no—
481C22—4782no—
482C22—4782no—
483C22—4782no—
484C22—2394no—
485C22C4×C22⋊D23914yescomplemented
486C22C22×C4×D23911yescharacteristic
487C22C2×D4×D23911yescharacteristic
488C22C22×C22⋊D23911yescharacteristic
489C22#41×D23911yescharacteristic
490C22C2×#1683854811yescharacteristic
491C22#2144000511yescharacteristic
492C22#2144000611yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—41no—
498C4—9561no—
499C4—9561no—
500C4—9561no—
501C4—4782no—
502C4—4782no—
503C4—4782no—
504C2—24no—
505C2—42no—
506C2—9562no—
507C2—4784no—
508C2C4×D4×D23911yescharacteristic
509C2C2×C4×C22⋊D23911yescharacteristic
510C2#2950524411yescharacteristic
511C2D4×C22⋊D23911yescharacteristic
512C2#2950541011yescharacteristic
513C2#2950541811yescharacteristic
514C2#2950545111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D239
commutatorC22×C239C23×C4
FittingC2×C4×D4×C239C2
socle, cosocleC23×C239C24
prime radicalC2×#21439928C2
hypercenterC2×C4×D4D239
hypocenterC239#2358
LCSG ▷ C22×C239 ▷ C239
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D239C2semidirect
3. C22×(C2×D239)⋊C4C2semidirect
4. C2×C22⋊C4×D239C2semidirect
5. #29504672C2semidirect
6. #29504663C2semidirect
7. #29504662C2semidirect
8. #29504652C2semidirect
9. #29504651C2semidirect
10. #29504648C2semidirect
11. #29504645C2semidirect
12. #29504643C2semidirect
13. C22⋊C4×Dic239C2semidirect
14. C4×(C2×D239)⋊C4C2semidirect
15. C2×C4×D4×C239C2semidirect
22. #21439928C4semidirect
24. C2×Dic239⋊C4C22semidirect
25. C2×Dic239⋊C4C22semidirect
28. C2×C22⋊Dic239C22semidirect
29. C2×C22⋊Dic239C22semidirect
40. C2×C4×Dic239C22semidirect
41. C2×C4×Dic239C22semidirect
42. C239⋊#95C22semidirect
43. C239⋊#95C22semidirect
44. C239⋊#95C22semidirect
45. C239⋊#95C22semidirect
46. C239⋊#95C22semidirect
47. C239⋊#95C22semidirect
50. C23×C4×C239C22semidirect
52. C2×C4⋊C4×C239C22semidirect
54. C2×C22⋊C4×C239C22semidirect
55. C2×C42×C239C22semidirect
62. C23×D239C2×C4semidirect
69. C2×C22⋊D239C2×C4semidirect
70. C2×C22⋊D239C2×C4semidirect
91. C22⋊Dic239C2×C4semidirect
97. (C2×D239)⋊C4C2×C4semidirect
98. (C2×D239)⋊C4C2×C4semidirect
99. (C2×D239)⋊C4D4semidirect
106. C2×D4×C239C2×C4semidirect
120. C22⋊C4×C239D4semidirect
212. C22×C239C4×D4semidirect
234. C2×D239C4×D4semidirect
257. C239#2358semidirect
261. C2×C4×D4D239semidirect
282. C23×C4C2×D239semidirect
288. C2×C4⋊C4C2×D239semidirect
304. C2×C22⋊C4C2×D239semidirect
307. C2×C42C2×D239semidirect
333. C2×D4C4×D239semidirect
376. C22⋊C4C22⋊D239semidirect
485. C22C4×C22⋊D239semidirect

Maximal subgroups

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

subgroupindex
C2×#214399282
C2×C4×C22⋊D2392
C22×(C2×D239)⋊C42
C2×C22⋊C4×D2392
#295046722
#295046632
#295046622
#295046522
#295046512
#295046482
#295046452
#295046432
C22⋊C4×Dic2392
C4×(C2×D239)⋊C42
C2×C4×D4×C2392
#2358239