Finite Group Databasebeta

← #44487530

Subgroups — #44487530

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×#21439930C211yesmaximal, characteristic
2C2×C4×D956C211yesmaximal, characteristic, complemented
3C2×(C22⋊D239)⋊C4C211yesmaximal, characteristic, complemented
4C22×(C2×D239)⋊C4C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D239C211yesmaximal, characteristic, complemented
6#29504674C211yesmaximal, characteristic, complemented
7#29504664C211yesmaximal, characteristic, complemented
8#29504663C211yesmaximal, characteristic, complemented
9#29504651C211yesmaximal, characteristic, complemented
10#29504650C211yesmaximal, characteristic, complemented
11#29504650C211yesmaximal, characteristic, complemented
12#29504647C211yesmaximal, characteristic, complemented
13#29504646C211yesmaximal, characteristic, complemented
14C4×(C2×D239)⋊C4C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C239C211yesmaximal, characteristic, complemented
16C24×D239C2211yescharacteristic
17C22×D956C2211yescharacteristic
18C22×D956C2211yescharacteristic
19C22×C22⋊D239C2211yescharacteristic
20C23×Dic239C2211yescharacteristic
21C22×C4×D239C2211yescharacteristic
22C22×C4×D239C2211yescharacteristic
23C22×C4×D239C2211yescharacteristic, complemented
24#21439930C418yescomplemented
25C4×D956—24no—
26(C22⋊D239)⋊C4—24no—
27C2×C4⋊Dic239C2211yescharacteristic, complemented
28C2×C4⋊Dic239C2211yescharacteristic, complemented
29C2×Dic239⋊C4C2211yescharacteristic, complemented
30C2×C22⋊Dic239C2211yescharacteristic
31C2×(C2×D239)⋊C4—24no—
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
39C2×(C2×D239)⋊C4C2211yescharacteristic
40C2×(C2×D239)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D239)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D239)⋊C4C2211yescharacteristic, complemented
43C22⋊C4×D239—24no—
44C2×C4×Dic239C2211yescharacteristic, complemented
45C239⋊#95C2211yescharacteristic, complemented
46C239⋊#95C2211yescharacteristic, complemented
47C239⋊#95C2211yescharacteristic, complemented
48C239⋊#95C2211yescharacteristic, complemented
49C23×C4×C239C2211yescharacteristic
50C2×C22⋊C4×C239C2211yescharacteristic
51C2×C22⋊C4×C239C2211yescharacteristic
52C2×C42×C239C2211yescharacteristic, complemented
53C2×C42×C239C2211yescharacteristic, complemented
54#95×C239C2211yescharacteristic, complemented
55#95×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
65C23×D239C2311yescharacteristic
66C2×D956—22no—
67C2×D956—22no—
68C2×D956—41no—
69C2×D956—41no—
70C2×D956C2×C414yescomplemented
71C2×D956C2×C414yescomplemented
72C2×C22⋊D239—22no—
73C2×C22⋊D239—22no—
74C2×C22⋊D239C2×C414yescomplemented
75C22×Dic239—22no—
76C22×Dic239—22no—
77C22×Dic239—41no—
78C22×Dic239C2311yescharacteristic
79C22×Dic239C2311yescharacteristic
80C22×Dic239C2311yescharacteristic
81C22×Dic239C2311yescharacteristic
82C22×Dic239C2311yescharacteristic
83C2×C4×D239—22no—
84C2×C4×D239—22no—
85C2×C4×D239—22no—
86C2×C4×D239—22no—
87C2×C4×D239—22no—
88C2×C4×D239—22no—
89C2×C4×D239—41no—
90C2×C4×D239—41no—
91C2×C4×D239—41no—
92C4⋊Dic239—22no—
93C4⋊Dic239—41no—
94Dic239⋊C4—22no—
95C22⋊Dic239—22no—
96(C2×D239)⋊C4—22no—
97(C2×D239)⋊C4—22no—
98(C2×D239)⋊C4—22no—
99(C2×D239)⋊C4—22no—
100(C2×D239)⋊C4—22no—
101(C2×D239)⋊C4—22no—
102(C2×D239)⋊C4—22no—
103(C2×D239)⋊C4—41no—
104(C2×D239)⋊C4C2×C414yescomplemented
105(C2×D239)⋊C4C2×C414yescomplemented
106(C2×D239)⋊C4D414yescomplemented
107C4×Dic239—22no—
108C24×C239C2311yescharacteristic
109C22×C4×C239—22no—
110C22×C4×C239—22no—
111C22×C4×C239—41no—
112C22×C4×C239C2311yescharacteristic
113C22×C4×C239C2311yescharacteristic
114C22×C4×C239C2311yescharacteristic
115C22×C4×C239C2311yescharacteristic
116C22×C4×C239C2311yescharacteristic
117C22×C4×C239C2311yescharacteristic
118C22⋊C4×C239C2×C414yescomplemented
119C22⋊C4×C239D414yescomplemented
120C42×C239—22no—
121C42×C239—41no—
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—21no—
134C22×D239—21no—
135C22×D239—21no—
136C22×D239—21no—
137C22×D239—21no—
138C22×D239—21no—
139C22×D239—28no—
140C22×D239—44no—
141C22×D239—44no—
142C22×D239—44no—
143C22×D239—44no—
144C22×D239—44no—
145C22×D239C22×C412yes—
146C22×D239C22×C412yes—
147C22×D239C22×C412yes—
148C22×D239C2×D412yes—
149C22×D239#4112yes—
150D956—28no—
151D956—44no—
152C22⋊D239—28no—
153C2×Dic239—21no—
154C2×Dic239—21no—
155C2×Dic239—21no—
156C2×Dic239—21no—
157C2×Dic239—21no—
158C2×Dic239—21no—
159C2×Dic239—21no—
160C2×Dic239—21no—
161C2×Dic239—21no—
162C2×Dic239—21no—
163C2×Dic239—21no—
164C2×Dic239—21no—
165C2×Dic239—21no—
166C2×Dic239—44no—
167C2×Dic239C22×C412yes—
168C2×Dic239C2×D412yes—
169C4×D239—44no—
170C4×D239—44no—
171C4×D239—44no—
172C23×C239—21no—
173C23×C239—21no—
174C23×C239—21no—
175C23×C239—21no—
176C23×C239C22×C412yes—
177C23×C239C2×D412yes—
178C23×C239#4112yes—
179C23×C239C2411yescharacteristic
180C2×C4×C239—21no—
181C2×C4×C239—21no—
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×C239C22×C412yes—
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×C239C4×D414yescomplemented
206C22×C239C23×C411yescharacteristic
207C22×C239C22×D411yescharacteristic
208C22×C239C22×D411yescharacteristic
209C22×C239C2×#4111yescharacteristic
210C22×C239C2×#4111yescharacteristic
211C22×C239H(5,𝔽2)11yescharacteristic
212C22×C239H(5,𝔽2)11yescharacteristic
213C2×D239—22no—
214C2×D239—22no—
215C2×D239—22no—
216C2×D239—22no—
217C2×D239—22no—
218C2×D239—22no—
219C2×D239—22no—
220C2×D239—22no—
221C2×D239—22no—
222C2×D239—22no—
223C2×D239—22no—
224C2×D239—22no—
225C2×D239—416no—
226C2×D239—41no—
227C2×D239—41no—
228C2×D239—41no—
229C2×D239—41no—
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—22no—
240C4×C239—41no—
241Dic239—22no—
242Dic239—22no—
243Dic239—41no—
244Dic239—41no—
245Dic239—41no—
246C2×C239—24no—
247C2×C239C2×C4×D411yescharacteristic
248C2×C239C2×C4×D411yescharacteristic
249C2×C239#51811yescharacteristic
250C2×C239D4211yescharacteristic
251C2×C239#54611yescharacteristic
252C2×C239#54611yescharacteristic
253C2×C239#55111yescharacteristic
254D239—24no—
255D239—42no—
256D239—42no—
257C239#235811yescharacteristic, complemented, Sylow
258#2358—2391nomaximal, Sylow
259C2×#120—2391no—
260C2×C4×D4—2391no—
261C2×C4×D4—2391no—
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⋊C4D23911yescharacteristic, complemented
274C25—2391no—
275C22×D4—2391no—
276C22×D4—2391no—
277C22×D4—2391no—
278C23×C4—2391no—
279C23×C4—2391no—
280C23×C4—2391no—
281C23×C4—2391no—
282C23×C4C2×D23911yescharacteristic
283#120—2398no—
284C4×D4—4784no—
285C4×D4—4784no—
286C2×C4⋊C4—2391no—
287C2×C4⋊C4—2391no—
288C2×C4⋊C4—2391no—
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
305C2×C42—2391no—
306C2×C42C2×D23911yescharacteristic, complemented
307C2×C42C2×D23911yescharacteristic, complemented
308#95—2391no—
309#95—2391no—
310#95—2391no—
311#95—2391no—
312#95C2×D23911yescharacteristic, complemented
313#95C2×D23911yescharacteristic, complemented
314C24—9561no—
315C24—9561no—
316C24—4782no—
317C24—4782no—
318C24—4782no—
319C24—4782no—
320C24—2394no—
321C24—2391no—
322C24—2391no—
323C24—2391no—
324C24C22×D23911yescharacteristic
325C2×D4—9561no—
326C2×D4—9561no—
327C2×D4—4782no—
328C2×D4—4782no—
329C2×D4—4782no—
330C2×D4—4782no—
331C2×D4—2394no—
332C2×D4—2394no—
333C2×D4—2394no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—41no—
337C22×C4—9561no—
338C22×C4—9561no—
339C22×C4—9561no—
340C22×C4—9561no—
341C22×C4—4782no—
342C22×C4—4782no—
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×C4C22×D23911yescharacteristic
355C22×C4C22×D23911yescharacteristic
356C22×C4C22×D23911yescharacteristic
357C22×C4C22×D23911yescharacteristic
358C22×C4C22×D23911yescharacteristic
359C22×C4C22×D23911yescharacteristic
360C4⋊C4—9561no—
361C4⋊C4—4782no—
362C4⋊C4—4782no—
363C22⋊C4—9561no—
364C22⋊C4—4782no—
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⋊C4C4×D23914yescomplemented
376C22⋊C4D95614yescomplemented
377C42—22no—
378C42—41no—
379C42—4782no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—9564no—
385C23—9564no—
386C23—9564no—
387C23—9564no—
388C23—9564no—
389C23—4788no—
390C23—4781no—
391C23—4781no—
392C23—4781no—
393C23—4781no—
394C23—4781no—
395C23—4781no—
396C23—4781no—
397C23—4781no—
398C23—4788no—
399C23—4781no—
400C23—4781no—
401C23—4781no—
402C23—4781no—
403C23—4781no—
404C23—4781no—
405C23—4781no—
406C23—4781no—
407C23—2392no—
408C23—2392no—
409C23—2392no—
410C23—2392no—
411C23—2392no—
412C23C2×C4×D23912yes—
413C23C2×D95612yes—
414C23#1683854812yes—
415C23C23×D23911yescharacteristic
416D4—9564no—
417D4—4788no—
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—21no—
431C2×C4—21no—
432C2×C4—44no—
433C2×C4—9564no—
434C2×C4—9564no—
435C2×C4—9564no—
436C2×C4—9564no—
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×C4C2×C4×D23912yes—
453C2×C4C2×C4×D23912yes—
454C2×C4D4×D23912yes—
455C2×C4C2×D95612yes—
456C2×C4C2×D95612yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—95616no—
464C22—9561no—
465C22—9561no—
466C22—9561no—
467C22—9561no—
468C22—9561no—
469C22—9561no—
470C22—9561no—
471C22—9561no—
472C22—4782no—
473C22—4782no—
474C22—4782no—
475C22—4782no—
476C22—4782no—
477C22—4782no—
478C22—4782no—
479C22—4782no—
480C22—4782no—
481C22—4782no—
482C22—4782no—
483C22—4782no—
484C22—2394no—
485C22C4×D95614yescomplemented
486C22C22×C4×D23911yescharacteristic
487C22C2×D4×D23911yescharacteristic
488C22C22×D95611yescharacteristic
489C22#41×D23911yescharacteristic
490C22C2×#1683854811yescharacteristic
491C22#2144000511yescharacteristic
492C22#2144000611yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—22no—
498C4—41no—
499C4—9561no—
500C4—9561no—
501C4—9561no—
502C4—4782no—
503C4—4782no—
504C2—24no—
505C2—9562no—
506C2—9562no—
507C2—4784no—
508C2C4×D4×D23911yescharacteristic
509C2C2×C4×D95611yescharacteristic
510C2#2950524411yescharacteristic
511C2D4×D95611yescharacteristic
512C2#2950541211yescharacteristic
513C2#2950541711yescharacteristic
514C2#2950544611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D239
commutatorC22×C239C23×C4
FittingC4×C22⋊C4×C239C2
socle, cosocleC23×C239C24
prime radicalC2×#21439930C2
hypercenterC4×C22⋊C4D239
hypocenterC239#2358
LCSG ▷ C22×C239 ▷ C239
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D956C2semidirect
3. C2×(C22⋊D239)⋊C4C2semidirect
4. C22×(C2×D239)⋊C4C2semidirect
5. C2×C22⋊C4×D239C2semidirect
6. #29504674C2semidirect
7. #29504664C2semidirect
8. #29504663C2semidirect
9. #29504651C2semidirect
10. #29504650C2semidirect
11. #29504650C2semidirect
12. #29504647C2semidirect
13. #29504646C2semidirect
14. C4×(C2×D239)⋊C4C2semidirect
15. C4×C22⋊C4×C239C2semidirect
23. C22×C4×D239C22semidirect
24. #21439930C4semidirect
27. C2×C4⋊Dic239C22semidirect
28. C2×C4⋊Dic239C22semidirect
29. C2×Dic239⋊C4C22semidirect
40. C2×(C2×D239)⋊C4C22semidirect
41. C2×(C2×D239)⋊C4C22semidirect
42. C2×(C2×D239)⋊C4C22semidirect
44. C2×C4×Dic239C22semidirect
45. C239⋊#95C22semidirect
46. C239⋊#95C22semidirect
47. C239⋊#95C22semidirect
48. C239⋊#95C22semidirect
52. C2×C42×C239C22semidirect
53. C2×C42×C239C22semidirect
54. #95×C239C22semidirect
55. #95×C239C22semidirect
62. C23×D239C2×C4semidirect
70. C2×D956C2×C4semidirect
71. C2×D956C2×C4semidirect
74. C2×C22⋊D239C2×C4semidirect
104. (C2×D239)⋊C4C2×C4semidirect
105. (C2×D239)⋊C4C2×C4semidirect
106. (C2×D239)⋊C4D4semidirect
118. C22⋊C4×C239C2×C4semidirect
119. C22⋊C4×C239D4semidirect
205. C22×C239C4×D4semidirect
234. C2×D239C4×D4semidirect
257. C239#2358semidirect
273. C4×C22⋊C4D239semidirect
306. C2×C42C2×D239semidirect
307. C2×C42C2×D239semidirect
312. #95C2×D239semidirect
313. #95C2×D239semidirect
375. C22⋊C4C4×D239semidirect
376. C22⋊C4D956semidirect
485. C22C4×D956semidirect

Maximal subgroups

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

subgroupindex
C2×#214399302
C2×C4×D9562
C2×(C22⋊D239)⋊C42
C22×(C2×D239)⋊C42
C2×C22⋊C4×D2392
#295046742
#295046642
#295046632
#295046512
#295046502
#295046472
#295046462
C4×(C2×D239)⋊C42
C4×C22⋊C4×C2392
#2358239