Finite Group Databasebeta

← #44487524

Subgroups — #44487524

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×#21439922C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D239C211yesmaximal, characteristic, complemented
4C22×(C2×D239)⋊C4C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D239C211yesmaximal, characteristic, complemented
6#29504673C211yesmaximal, characteristic, complemented
7#29504662C211yesmaximal, characteristic, complemented
8#29504661C211yesmaximal, characteristic, complemented
9#29504650C211yesmaximal, characteristic, complemented
10#29504650C211yesmaximal, characteristic, complemented
11#29504649C211yesmaximal, characteristic, complemented
12#29504643C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic239C211yesmaximal, characteristic, complemented
14#29504619C211yesmaximal, characteristic, complemented
15#385×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
25#21439922—24no—
26C4×C22⋊D239—24no—
27C2×Dic239⋊C4C2211yescharacteristic, complemented
28C2×C22⋊Dic239C2211yescharacteristic
29C2×(C2×D239)⋊C4—24no—
30C2×(C2×D239)⋊C4C2211yescharacteristic
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, complemented
39C2×(C2×D239)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D239)⋊C4C2211yescharacteristic, complemented
41C22⋊C4×D239—24no—
42C2×C4×Dic239C2211yescharacteristic, complemented
43C2×C4×Dic239C2211yescharacteristic, complemented
44C2×C4×Dic239C2211yescharacteristic, complemented
45C239⋊#95C2211yescharacteristic, complemented
46C239⋊#95C2211yescharacteristic, complemented
47C239⋊#95C2211yescharacteristic, complemented
48C239⋊#95C2211yescharacteristic, complemented
49C23×C4×C239C2211yescharacteristic
50C2×C4⋊C4×C239C2211yescharacteristic, complemented
51C2×C4⋊C4×C239C2211yescharacteristic, complemented
52C2×C22⋊C4×C239C2211yescharacteristic
53C2×C22⋊C4×C239C2211yescharacteristic
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—
92Dic239⋊C4—22no—
93C22⋊Dic239D414yescomplemented
94(C2×D239)⋊C4—22no—
95(C2×D239)⋊C4—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—41no—
102(C2×D239)⋊C4C2×C414yescomplemented
103(C2×D239)⋊C4C2×C414yescomplemented
104(C2×D239)⋊C4D414yescomplemented
105C4×Dic239—22no—
106C4×Dic239—22no—
107C4×Dic239—41no—
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
118C4⋊C4×C239—22no—
119C4⋊C4×C239—41no—
120C22⋊C4×C239—22no—
121C22⋊C4×C239C2×C414yescomplemented
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—44no—
165C2×Dic239C22×C412yes—
166C2×Dic239C2×D412yes—
167C2×Dic239C2×D412yes—
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—21no—
194C2×C4×C239—21no—
195C2×C4×C239—44no—
196C2×C4×C239C22×C412yes—
197C2×C4×C239C22×C412yes—
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—41no—
239C4×C239—41no—
240C4×C239—41no—
241Dic239—22no—
242Dic239—22no—
243Dic239—22no—
244Dic239—22no—
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#385D23911yescharacteristic, complemented
272C4×C22⋊C4—2391no—
273C4×C22⋊C4—2391no—
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⋊C4C2×D23911yescharacteristic, complemented
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
305C2×C42—2391no—
306C2×C42—2391no—
307C2×C42—2391no—
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—22no—
361C4⋊C4—41no—
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⋊C4C4×D23914yescomplemented
377C42—9561no—
378C42—4782no—
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—
413C23D4×D23912yes—
414C23#1683854912yes—
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—21no—
433C2×C4—21no—
434C2×C4—44no—
435C2×C4—9564no—
436C2×C4—9564no—
437C2×C4—9564no—
438C2×C4—9564no—
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×C4—2392no—
454C2×C4C2×C4×D23912yes—
455C2×C4C2×C4×D23912yes—
456C2×C4D4×D23912yes—
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—
485C22#2143992214yescomplemented
486C22C22×C4×D23911yescharacteristic
487C22C2×D4×D23911yescharacteristic
488C22C2×D4×D23911yescharacteristic
489C22#41×D23911yescharacteristic
490C22C2×#1683854911yescharacteristic
491C22#2144000511yescharacteristic
492C22#2144000611yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—41no—
497C4—41no—
498C4—41no—
499C4—9561no—
500C4—4782no—
501C4—4782no—
502C4—4782no—
503C4—4782no—
504C2—24no—
505C2—9562no—
506C2—9562no—
507C2—4784no—
508C2C4×D4×D23911yescharacteristic
509C2C2×#2143992211yescharacteristic
510C2#2950524411yescharacteristic
511C2#2950540411yescharacteristic
512C2#2950541311yescharacteristic
513C2#2950541411yescharacteristic
514C2#2950544911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D239
commutatorC22×C239C23×C4
Fitting#385×C239C2
socle, cosocleC23×C239C24
prime radicalC2×#21439930C2
hypercenter#385D239
hypocenterC239#2358
LCSG ▷ C22×C239 ▷ C239
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#21439922C2semidirect
3. C2×C4×C22⋊D239C2semidirect
4. C22×(C2×D239)⋊C4C2semidirect
5. C2×C22⋊C4×D239C2semidirect
6. #29504673C2semidirect
7. #29504662C2semidirect
8. #29504661C2semidirect
9. #29504650C2semidirect
10. #29504650C2semidirect
11. #29504649C2semidirect
12. #29504643C2semidirect
13. C22⋊C4×Dic239C2semidirect
14. #29504619C2semidirect
15. #385×C239C2semidirect
23. C22×C4×D239C22semidirect
24. #21439930C4semidirect
27. C2×Dic239⋊C4C22semidirect
38. C2×(C2×D239)⋊C4C22semidirect
39. C2×(C2×D239)⋊C4C22semidirect
40. C2×(C2×D239)⋊C4C22semidirect
42. C2×C4×Dic239C22semidirect
43. C2×C4×Dic239C22semidirect
44. C2×C4×Dic239C22semidirect
45. C239⋊#95C22semidirect
46. C239⋊#95C22semidirect
47. C239⋊#95C22semidirect
48. C239⋊#95C22semidirect
50. C2×C4⋊C4×C239C22semidirect
51. C2×C4⋊C4×C239C22semidirect
54. #95×C239C22semidirect
55. #95×C239C22semidirect
62. C23×D239C2×C4semidirect
70. C2×D956C2×C4semidirect
71. C2×D956C2×C4semidirect
74. C2×C22⋊D239C2×C4semidirect
93. C22⋊Dic239D4semidirect
102. (C2×D239)⋊C4C2×C4semidirect
103. (C2×D239)⋊C4C2×C4semidirect
104. (C2×D239)⋊C4D4semidirect
121. C22⋊C4×C239C2×C4semidirect
205. C22×C239C4×D4semidirect
234. C2×D239C4×D4semidirect
257. C239#2358semidirect
271. #385D239semidirect
287. C2×C4⋊C4C2×D239semidirect
288. C2×C4⋊C4C2×D239semidirect
312. #95C2×D239semidirect
313. #95C2×D239semidirect
376. C22⋊C4C4×D239semidirect
485. C22#21439922semidirect

Maximal subgroups

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

subgroupindex
C2×#214399302
C2×#214399222
C2×C4×C22⋊D2392
C22×(C2×D239)⋊C42
C2×C22⋊C4×D2392
#295046732
#295046622
#295046612
#295046502
#295046492
#295046432
C22⋊C4×Dic2392
#295046192
#385×C2392
#2358239