Finite Group Databasebeta

← #44487526

Subgroups — #44487526

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×#21439922C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D239C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D239C211yesmaximal, characteristic, complemented
6#29504672C211yesmaximal, characteristic, complemented
7#29504665C211yesmaximal, characteristic, complemented
8#29504650C211yesmaximal, characteristic, complemented
9#29504650C211yesmaximal, characteristic, complemented
10#29504648C211yesmaximal, characteristic, complemented
11#29504646C211yesmaximal, characteristic, complemented
12#29504643C211yesmaximal, characteristic, complemented
13C4×(C2×D239)⋊C4C211yesmaximal, characteristic, complemented
14#29504619C211yesmaximal, characteristic, complemented
15#388×C239C211yesmaximal, characteristic, complemented
16C24×D239C2211yescharacteristic
17C22×D956C2211yescharacteristic
18C22×D956C2211yescharacteristic
19C22×C22⋊D239C2211yescharacteristic
20C22×C4×D239C2211yescharacteristic
21C22×C4×D239C2211yescharacteristic
22C22×C4×D239C2211yescharacteristic
23C22×C4×D239C2211yescharacteristic
24C22×C4×D239C2211yescharacteristic, complemented
25#21439930C418yescomplemented
26C4×D956—24no—
27#21439922—24no—
28C2×C4⋊Dic239C2211yescharacteristic, complemented
29C2×Dic239⋊C4C2211yescharacteristic, complemented
30C2×C22⋊Dic239C2211yescharacteristic
31C2×C22⋊Dic239C2211yescharacteristic
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—
42C22⋊C4×D239—24no—
43C2×C4×Dic239C2211yescharacteristic, complemented
44C2×C4×Dic239C2211yescharacteristic, complemented
45C239⋊#95C2211yescharacteristic, complemented
46C239⋊#95C2211yescharacteristic, complemented
47C239⋊#95C2211yescharacteristic, complemented
48C239⋊#95C2211yescharacteristic, complemented
49C2×C4⋊C4×C239C2211yescharacteristic, complemented
50C2×C22⋊C4×C239C2211yescharacteristic
51C2×C22⋊C4×C239C2211yescharacteristic
52C2×C22⋊C4×C239C2211yescharacteristic
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—22no—
69C2×D956—22no—
70C2×D956C2×C414yescomplemented
71C2×D956C2×C414yescomplemented
72C2×C22⋊D239—41no—
73C2×C22⋊D239—41no—
74C2×C22⋊D239C2×C414yescomplemented
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—22no—
85C2×C4×D239—22no—
86C2×C4×D239—22no—
87C2×C4×D239—22no—
88C2×C4×D239—22no—
89C2×C4×D239—22no—
90C2×C4×D239—41no—
91C2×C4×D239—41no—
92C2×C4×D239—41no—
93C2×C4×D239—41no—
94C2×C4×D239—41no—
95C4⋊Dic239—22no—
96Dic239⋊C4—41no—
97C22⋊Dic239—22no—
98C22⋊Dic239—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
107(C2×D239)⋊C4D414yescomplemented
108C4×Dic239—22no—
109C4×Dic239—41no—
110C24×C239C2311yescharacteristic
111C22×C4×C239C2311yescharacteristic
112C22×C4×C239C2311yescharacteristic
113C22×C4×C239C2311yescharacteristic
114C22×C4×C239C2311yescharacteristic
115C22×C4×C239C2311yescharacteristic
116C22×C4×C239C2311yescharacteristic
117C4⋊C4×C239—22no—
118C22⋊C4×C239—22no—
119C22⋊C4×C239—22no—
120C22⋊C4×C239C2×C414yescomplemented
121C42×C239—22no—
122C22×D239—21no—
123C22×D239—21no—
124C22×D239—21no—
125C22×D239—21no—
126C22×D239—21no—
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—28no—
137C22×D239—28no—
138C22×D239—44no—
139C22×D239—44no—
140C22×D239—44no—
141C22×D239—44no—
142C22×D239—44no—
143C22×D239C22×C412yes—
144C22×D239C22×C412yes—
145C22×D239C22×C412yes—
146C22×D239C2×D412yes—
147C22×D239C2×D412yes—
148C22×D239#4112yes—
149C22×D239#4112yes—
150D956—28no—
151D956—28no—
152C22⋊D239—44no—
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×Dic239C22×C412yes—
166C2×Dic239C2×D412yes—
167C2×Dic239C2×D412yes—
168C4×D239—44no—
169C4×D239—44no—
170C4×D239—44no—
171C4×D239—44no—
172C4×D239—44no—
173C23×C239—21no—
174C23×C239—21no—
175C23×C239—21no—
176C23×C239—21no—
177C23×C239—21no—
178C23×C239—21no—
179C23×C239C22×C412yes—
180C23×C239C2411yescharacteristic
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×C239C22×C412yes—
196C2×C4×C239C22×C412yes—
197C2×C4×C239C2×D412yes—
198C2×C4×C239C2×D412yes—
199C22×C239—22no—
200C22×C239—22no—
201C22×C239—22no—
202C22×C239—41no—
203C22×C239—41no—
204C22×C239—41no—
205C22×C239—41no—
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—22no—
226C2×D239—22no—
227C2×D239—22no—
228C2×D239—416no—
229C2×D239—41no—
230C2×D239—41no—
231C2×D239—41no—
232C2×D239—41no—
233C2×D239C4×D414yescomplemented
234C2×D239C4×D414yescomplemented
235C4×C239—22no—
236C4×C239—22no—
237C4×C239—22no—
238C4×C239—22no—
239C4×C239—41no—
240C4×C239—41no—
241Dic239—22no—
242Dic239—22no—
243Dic239—22no—
244Dic239—41no—
245Dic239—41no—
246C2×C239—42no—
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—24no—
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#388D23911yescharacteristic, complemented
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×D4—2391no—
278C23×C4—2391no—
279C23×C4—2391no—
280C23×C4—2391no—
281C23×C4—2391no—
282C23×C4—2391no—
283#120—2398no—
284C4×D4—4784no—
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⋊C4C2×D23911yescharacteristic
303C2×C22⋊C4C2×D23911yescharacteristic
304C2×C22⋊C4C2×D23911yescharacteristic
305C2×C42—2391no—
306C2×C42—2391no—
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—9561no—
335C22×C4—9561no—
336C22×C4—9561no—
337C22×C4—9561no—
338C22×C4—9561no—
339C22×C4—4782no—
340C22×C4—4782no—
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—9561no—
362C4⋊C4—4782no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—9561no—
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—22no—
378C42—9561no—
379C42—4782no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—9564no—
387C23—9564no—
388C23—9564no—
389C23—9564no—
390C23—9564no—
391C23—4788no—
392C23—4788no—
393C23—4781no—
394C23—4781no—
395C23—4781no—
396C23—4781no—
397C23—4781no—
398C23—4781no—
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—
412C23—2392no—
413C23—2392no—
414C23C2×C4×D23912yes—
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—9564no—
434C2×C4—9564no—
435C2×C4—9564no—
436C2×C4—9564no—
437C2×C4—9564no—
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×C4C2×C4×D23912yes—
455C2×C4D4×D23912yes—
456C2×C4D4×D23912yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—95616no—
465C22—9561no—
466C22—9561no—
467C22—9561no—
468C22—9561no—
469C22—4782no—
470C22—4782no—
471C22—4782no—
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—2394no—
486C22C22×C4×D23911yescharacteristic
487C22C2×D4×D23911yescharacteristic
488C22C2×D4×D23911yescharacteristic
489C22#41×D23911yescharacteristic
490C22#41×D23911yescharacteristic
491C22#2144000611yescharacteristic
492C22#2144000611yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—41no—
498C4—41no—
499C4—9561no—
500C4—9561no—
501C4—4782no—
502C4—4782no—
503C4—4782no—
504C2—42no—
505C2—9562no—
506C2—4784no—
507C2—4784no—
508C2C4×D4×D23911yescharacteristic
509C2C4×D4×D23911yescharacteristic
510C2#2950524611yescharacteristic
511C2#2950540611yescharacteristic
512C2#2950541411yescharacteristic
513C2#2950541511yescharacteristic
514C2#2950544711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D239
commutatorC22×C239C23×C4
Fitting#388×C239C2
socle, cosocleC23×C239C24
prime radicalC2×#21439930C2
hypercenter#388D239
hypocenterC239#2358
LCSG ▷ C22×C239 ▷ C239
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×C4×D956C2semidirect
3. C2×#21439922C2semidirect
4. C2×C22⋊C4×D239C2semidirect
5. C2×C22⋊C4×D239C2semidirect
6. #29504672C2semidirect
7. #29504665C2semidirect
8. #29504650C2semidirect
9. #29504650C2semidirect
10. #29504648C2semidirect
11. #29504646C2semidirect
12. #29504643C2semidirect
13. C4×(C2×D239)⋊C4C2semidirect
14. #29504619C2semidirect
15. #388×C239C2semidirect
24. C22×C4×D239C22semidirect
25. #21439930C4semidirect
28. C2×C4⋊Dic239C22semidirect
29. C2×Dic239⋊C4C22semidirect
38. C2×(C2×D239)⋊C4C22semidirect
39. C2×(C2×D239)⋊C4C22semidirect
40. C2×(C2×D239)⋊C4C22semidirect
43. C2×C4×Dic239C22semidirect
44. C2×C4×Dic239C22semidirect
45. C239⋊#95C22semidirect
46. C239⋊#95C22semidirect
47. C239⋊#95C22semidirect
48. C239⋊#95C22semidirect
49. C2×C4⋊C4×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
107. (C2×D239)⋊C4D4semidirect
120. C22⋊C4×C239C2×C4semidirect
233. C2×D239C4×D4semidirect
234. C2×D239C4×D4semidirect
257. C239#2358semidirect
266. #388D239semidirect
288. C2×C4⋊C4C2×D239semidirect
307. C2×C42C2×D239semidirect
312. #95C2×D239semidirect
313. #95C2×D239semidirect
376. C22⋊C4C4×D239semidirect

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×#214399222
C2×C22⋊C4×D2392
#295046722
#295046652
#295046502
#295046482
#295046462
#295046432
C4×(C2×D239)⋊C42
#295046192
#388×C2392
#2358239