Finite Group Databasebeta

← #49124239

Subgroups — #49124239

Order 36224.

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×#22583580C211yesmaximal, characteristic
2C2×C4×D1132C211yesmaximal, characteristic, complemented
3C2×#22583572C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D283C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D283C211yesmaximal, characteristic, complemented
6#31826365C211yesmaximal, characteristic, complemented
7#31826358C211yesmaximal, characteristic, complemented
8#31826343C211yesmaximal, characteristic, complemented
9#31826343C211yesmaximal, characteristic, complemented
10#31826341C211yesmaximal, characteristic, complemented
11#31826339C211yesmaximal, characteristic, complemented
12#31826336C211yesmaximal, characteristic, complemented
13C4×(C2×D283)⋊C4C211yesmaximal, characteristic, complemented
14#31826312C211yesmaximal, characteristic, complemented
15#388×C283C211yesmaximal, characteristic, complemented
16C24×D283C2211yescharacteristic
17C22×D1132C2211yescharacteristic
18C22×D1132C2211yescharacteristic
19C22×C22⋊D283C2211yescharacteristic
20C22×C4×D283C2211yescharacteristic
21C22×C4×D283C2211yescharacteristic
22C22×C4×D283C2211yescharacteristic
23C22×C4×D283C2211yescharacteristic
24C22×C4×D283C2211yescharacteristic, complemented
25#22583580C418yescomplemented
26C4×D1132—24no—
27#22583572—24no—
28C2×C4⋊Dic283C2211yescharacteristic, complemented
29C2×Dic283⋊C4C2211yescharacteristic, complemented
30C2×C22⋊Dic283C2211yescharacteristic
31C2×C22⋊Dic283C2211yescharacteristic
32C2×(C2×D283)⋊C4C2211yescharacteristic
33C2×(C2×D283)⋊C4C2211yescharacteristic
34C2×(C2×D283)⋊C4C2211yescharacteristic
35C2×(C2×D283)⋊C4C2211yescharacteristic
36C2×(C2×D283)⋊C4C2211yescharacteristic
37C2×(C2×D283)⋊C4C2211yescharacteristic
38C2×(C2×D283)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D283)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D283)⋊C4C2211yescharacteristic, complemented
41C22⋊C4×D283—24no—
42C22⋊C4×D283—24no—
43C2×C4×Dic283C2211yescharacteristic, complemented
44C2×C4×Dic283C2211yescharacteristic, complemented
45C283⋊#95C2211yescharacteristic, complemented
46C283⋊#95C2211yescharacteristic, complemented
47C283⋊#95C2211yescharacteristic, complemented
48C283⋊#95C2211yescharacteristic, complemented
49C2×C4⋊C4×C283C2211yescharacteristic, complemented
50C2×C22⋊C4×C283C2211yescharacteristic
51C2×C22⋊C4×C283C2211yescharacteristic
52C2×C22⋊C4×C283C2211yescharacteristic
53C2×C42×C283C2211yescharacteristic, complemented
54#95×C283C2211yescharacteristic, complemented
55#95×C283C2211yescharacteristic, complemented
56C23×D283—22no—
57C23×D283—22no—
58C23×D283—22no—
59C23×D283—22no—
60C23×D283—41no—
61C23×D283—41no—
62C23×D283C2×C414yescomplemented
63C23×D283C2311yescharacteristic
64C23×D283C2311yescharacteristic
65C23×D283C2311yescharacteristic
66C2×D1132—22no—
67C2×D1132—22no—
68C2×D1132—22no—
69C2×D1132—22no—
70C2×D1132C2×C414yescomplemented
71C2×D1132C2×C414yescomplemented
72C2×C22⋊D283—41no—
73C2×C22⋊D283—41no—
74C2×C22⋊D283C2×C414yescomplemented
75C22×Dic283C2311yescharacteristic
76C22×Dic283C2311yescharacteristic
77C22×Dic283C2311yescharacteristic
78C22×Dic283C2311yescharacteristic
79C22×Dic283C2311yescharacteristic
80C2×C4×D283—22no—
81C2×C4×D283—22no—
82C2×C4×D283—22no—
83C2×C4×D283—22no—
84C2×C4×D283—22no—
85C2×C4×D283—22no—
86C2×C4×D283—22no—
87C2×C4×D283—22no—
88C2×C4×D283—22no—
89C2×C4×D283—22no—
90C2×C4×D283—41no—
91C2×C4×D283—41no—
92C2×C4×D283—41no—
93C2×C4×D283—41no—
94C2×C4×D283—41no—
95C4⋊Dic283—22no—
96Dic283⋊C4—41no—
97C22⋊Dic283—22no—
98C22⋊Dic283—22no—
99(C2×D283)⋊C4—22no—
100(C2×D283)⋊C4—22no—
101(C2×D283)⋊C4—22no—
102(C2×D283)⋊C4—22no—
103(C2×D283)⋊C4—41no—
104(C2×D283)⋊C4C2×C414yescomplemented
105(C2×D283)⋊C4C2×C414yescomplemented
106(C2×D283)⋊C4D414yescomplemented
107(C2×D283)⋊C4D414yescomplemented
108C4×Dic283—22no—
109C4×Dic283—41no—
110C24×C283C2311yescharacteristic
111C22×C4×C283C2311yescharacteristic
112C22×C4×C283C2311yescharacteristic
113C22×C4×C283C2311yescharacteristic
114C22×C4×C283C2311yescharacteristic
115C22×C4×C283C2311yescharacteristic
116C22×C4×C283C2311yescharacteristic
117C4⋊C4×C283—22no—
118C22⋊C4×C283—22no—
119C22⋊C4×C283—22no—
120C22⋊C4×C283C2×C414yescomplemented
121C42×C283—22no—
122C22×D283—21no—
123C22×D283—21no—
124C22×D283—21no—
125C22×D283—21no—
126C22×D283—21no—
127C22×D283—21no—
128C22×D283—21no—
129C22×D283—21no—
130C22×D283—21no—
131C22×D283—21no—
132C22×D283—21no—
133C22×D283—21no—
134C22×D283—21no—
135C22×D283—21no—
136C22×D283—28no—
137C22×D283—28no—
138C22×D283—44no—
139C22×D283—44no—
140C22×D283—44no—
141C22×D283—44no—
142C22×D283—44no—
143C22×D283C22×C412yes—
144C22×D283C22×C412yes—
145C22×D283C22×C412yes—
146C22×D283C2×D412yes—
147C22×D283C2×D412yes—
148C22×D283#4112yes—
149C22×D283#4112yes—
150D1132—28no—
151D1132—28no—
152C22⋊D283—44no—
153C2×Dic283—21no—
154C2×Dic283—21no—
155C2×Dic283—21no—
156C2×Dic283—21no—
157C2×Dic283—21no—
158C2×Dic283—21no—
159C2×Dic283—21no—
160C2×Dic283—21no—
161C2×Dic283—21no—
162C2×Dic283—21no—
163C2×Dic283—21no—
164C2×Dic283—21no—
165C2×Dic283C22×C412yes—
166C2×Dic283C2×D412yes—
167C2×Dic283C2×D412yes—
168C4×D283—44no—
169C4×D283—44no—
170C4×D283—44no—
171C4×D283—44no—
172C4×D283—44no—
173C23×C283—21no—
174C23×C283—21no—
175C23×C283—21no—
176C23×C283—21no—
177C23×C283—21no—
178C23×C283—21no—
179C23×C283C22×C412yes—
180C23×C283C2411yescharacteristic
181C2×C4×C283—21no—
182C2×C4×C283—21no—
183C2×C4×C283—21no—
184C2×C4×C283—21no—
185C2×C4×C283—21no—
186C2×C4×C283—21no—
187C2×C4×C283—21no—
188C2×C4×C283—21no—
189C2×C4×C283—21no—
190C2×C4×C283—21no—
191C2×C4×C283—21no—
192C2×C4×C283—21no—
193C2×C4×C283—21no—
194C2×C4×C283—21no—
195C2×C4×C283C22×C412yes—
196C2×C4×C283C22×C412yes—
197C2×C4×C283C2×D412yes—
198C2×C4×C283C2×D412yes—
199C22×C283—22no—
200C22×C283—22no—
201C22×C283—22no—
202C22×C283—41no—
203C22×C283—41no—
204C22×C283—41no—
205C22×C283—41no—
206C22×C283C23×C411yescharacteristic
207C22×C283C22×D411yescharacteristic
208C22×C283C22×D411yescharacteristic
209C22×C283C2×#4111yescharacteristic
210C22×C283C2×#4111yescharacteristic
211C22×C283H(5,𝔽2)11yescharacteristic
212C22×C283H(5,𝔽2)11yescharacteristic
213C2×D283—22no—
214C2×D283—22no—
215C2×D283—22no—
216C2×D283—22no—
217C2×D283—22no—
218C2×D283—22no—
219C2×D283—22no—
220C2×D283—22no—
221C2×D283—22no—
222C2×D283—22no—
223C2×D283—22no—
224C2×D283—22no—
225C2×D283—22no—
226C2×D283—22no—
227C2×D283—22no—
228C2×D283—416no—
229C2×D283—41no—
230C2×D283—41no—
231C2×D283—41no—
232C2×D283—41no—
233C2×D283C4×D414yescomplemented
234C2×D283C4×D414yescomplemented
235C4×C283—22no—
236C4×C283—22no—
237C4×C283—22no—
238C4×C283—22no—
239C4×C283—41no—
240C4×C283—41no—
241Dic283—22no—
242Dic283—22no—
243Dic283—22no—
244Dic283—41no—
245Dic283—41no—
246C2×C283—42no—
247C2×C283C2×C4×D411yescharacteristic
248C2×C283C2×C4×D411yescharacteristic
249C2×C283#51811yescharacteristic
250C2×C283D4211yescharacteristic
251C2×C283#54611yescharacteristic
252C2×C283#54611yescharacteristic
253C2×C283#55111yescharacteristic
254D283—24no—
255D283—24no—
256D283—42no—
257C283#235811yescharacteristic, complemented, Sylow
258#2358—2831nomaximal, Sylow
259C2×#120—2831no—
260C2×C4×D4—2831no—
261C2×C4×D4—2831no—
262C22×C22⋊C4—2831no—
263C22×C22⋊C4—2831no—
264#390—2831no—
265#388—2831no—
266#388D28311yescharacteristic, complemented
267#386—2831no—
268#386—2831no—
269#386—2831no—
270#385—2831no—
271#385—2831no—
272C4×C22⋊C4—2831no—
273C4×C22⋊C4—2831no—
274C25—2831no—
275C22×D4—2831no—
276C22×D4—2831no—
277C22×D4—2831no—
278C23×C4—2831no—
279C23×C4—2831no—
280C23×C4—2831no—
281C23×C4—2831no—
282C23×C4—2831no—
283#120—2838no—
284C4×D4—5664no—
285C4×D4—5664no—
286C2×C4⋊C4—2831no—
287C2×C4⋊C4—2831no—
288C2×C4⋊C4C2×D28311yescharacteristic, complemented
289C2×C22⋊C4—2831no—
290C2×C22⋊C4—2831no—
291C2×C22⋊C4—2831no—
292C2×C22⋊C4—2831no—
293C2×C22⋊C4—2831no—
294C2×C22⋊C4—2831no—
295C2×C22⋊C4—2831no—
296C2×C22⋊C4—2831no—
297C2×C22⋊C4—2831no—
298C2×C22⋊C4—2831no—
299C2×C22⋊C4—2831no—
300C2×C22⋊C4—5664no—
301C2×C22⋊C4—5664no—
302C2×C22⋊C4C2×D28311yescharacteristic
303C2×C22⋊C4C2×D28311yescharacteristic
304C2×C22⋊C4C2×D28311yescharacteristic
305C2×C42—2831no—
306C2×C42—2831no—
307C2×C42C2×D28311yescharacteristic, complemented
308#95—2831no—
309#95—2831no—
310#95—2831no—
311#95—2831no—
312#95C2×D28311yescharacteristic, complemented
313#95C2×D28311yescharacteristic, complemented
314C24—2831no—
315C24—2831no—
316C24—2831no—
317C24—2834no—
318C24—5662no—
319C24—5662no—
320C24—5662no—
321C24—5662no—
322C24—11321no—
323C24—11321no—
324C24C22×D28311yescharacteristic
325C2×D4—2834no—
326C2×D4—2834no—
327C2×D4—2834no—
328C2×D4—5662no—
329C2×D4—5662no—
330C2×D4—5662no—
331C2×D4—5662no—
332C2×D4—11321no—
333C2×D4—11321no—
334C22×C4—2831no—
335C22×C4—2831no—
336C22×C4—2831no—
337C22×C4—2831no—
338C22×C4—2831no—
339C22×C4—5662no—
340C22×C4—5662no—
341C22×C4—5662no—
342C22×C4—5662no—
343C22×C4—5662no—
344C22×C4—5662no—
345C22×C4—5662no—
346C22×C4—5662no—
347C22×C4—5662no—
348C22×C4—5662no—
349C22×C4—11321no—
350C22×C4—11321no—
351C22×C4—11321no—
352C22×C4—11321no—
353C22×C4—11321no—
354C22×C4C22×D28311yescharacteristic
355C22×C4C22×D28311yescharacteristic
356C22×C4C22×D28311yescharacteristic
357C22×C4C22×D28311yescharacteristic
358C22×C4C22×D28311yescharacteristic
359C22×C4C22×D28311yescharacteristic
360C4⋊C4—22no—
361C4⋊C4—5662no—
362C4⋊C4—11321no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—2834no—
366C22⋊C4—2834no—
367C22⋊C4—2834no—
368C22⋊C4—2834no—
369C22⋊C4—5662no—
370C22⋊C4—5662no—
371C22⋊C4—5662no—
372C22⋊C4—5662no—
373C22⋊C4—5662no—
374C22⋊C4—5662no—
375C22⋊C4—11321no—
376C22⋊C4C4×D28314yescomplemented
377C42—22no—
378C42—5662no—
379C42—11321no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—2832no—
387C23—2832no—
388C23—2832no—
389C23—2832no—
390C23—2832no—
391C23—2832no—
392C23—2832no—
393C23—5668no—
394C23—5668no—
395C23—5661no—
396C23—5661no—
397C23—5661no—
398C23—5661no—
399C23—5661no—
400C23—5661no—
401C23—5661no—
402C23—5661no—
403C23—5661no—
404C23—5661no—
405C23—5661no—
406C23—5661no—
407C23—5661no—
408C23—5661no—
409C23—11324no—
410C23—11324no—
411C23—11324no—
412C23—11324no—
413C23—11324no—
414C23C2×C4×D28312yes—
415C23C23×D28311yescharacteristic
416D4—5668no—
417D4—5668no—
418D4—11324no—
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—2832no—
434C2×C4—2832no—
435C2×C4—2832no—
436C2×C4—5661no—
437C2×C4—5661no—
438C2×C4—5661no—
439C2×C4—5661no—
440C2×C4—5661no—
441C2×C4—5661no—
442C2×C4—5661no—
443C2×C4—5661no—
444C2×C4—5661no—
445C2×C4—5661no—
446C2×C4—5661no—
447C2×C4—5661no—
448C2×C4—11324no—
449C2×C4—11324no—
450C2×C4—11324no—
451C2×C4—11324no—
452C2×C4—11324no—
453C2×C4C2×C4×D28312yes—
454C2×C4C2×C4×D28312yes—
455C2×C4D4×D28312yes—
456C2×C4D4×D28312yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—2834no—
465C22—2834no—
466C22—5662no—
467C22—5662no—
468C22—5662no—
469C22—5662no—
470C22—5662no—
471C22—5662no—
472C22—5662no—
473C22—5662no—
474C22—5662no—
475C22—5662no—
476C22—5662no—
477C22—5662no—
478C22—5662no—
479C22—5662no—
480C22—5662no—
481C22—113216no—
482C22—11321no—
483C22—11321no—
484C22—11321no—
485C22—11321no—
486C22C22×C4×D28311yescharacteristic
487C22C2×D4×D28311yescharacteristic
488C22C2×D4×D28311yescharacteristic
489C22#41×D28311yescharacteristic
490C22#41×D28311yescharacteristic
491C22#2258365611yescharacteristic
492C22#2258365611yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—41no—
498C4—41no—
499C4—5662no—
500C4—5662no—
501C4—5662no—
502C4—11321no—
503C4—11321no—
504C2—42no—
505C2—5664no—
506C2—5664no—
507C2—11322no—
508C2C4×D4×D28311yescharacteristic
509C2C4×D4×D28311yescharacteristic
510C2#3182693911yescharacteristic
511C2#3182709911yescharacteristic
512C2#3182710711yescharacteristic
513C2#3182710811yescharacteristic
514C2#3182714011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
Fitting#388×C283C2
socle, cosocleC23×C283C24
prime radicalC2×#22583580C2
hypercenter#388D283
hypocenterC283#2358
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×C4×D1132C2semidirect
3. C2×#22583572C2semidirect
4. C2×C22⋊C4×D283C2semidirect
5. C2×C22⋊C4×D283C2semidirect
6. #31826365C2semidirect
7. #31826358C2semidirect
8. #31826343C2semidirect
9. #31826343C2semidirect
10. #31826341C2semidirect
11. #31826339C2semidirect
12. #31826336C2semidirect
13. C4×(C2×D283)⋊C4C2semidirect
14. #31826312C2semidirect
15. #388×C283C2semidirect
24. C22×C4×D283C22semidirect
25. #22583580C4semidirect
28. C2×C4⋊Dic283C22semidirect
29. C2×Dic283⋊C4C22semidirect
38. C2×(C2×D283)⋊C4C22semidirect
39. C2×(C2×D283)⋊C4C22semidirect
40. C2×(C2×D283)⋊C4C22semidirect
43. C2×C4×Dic283C22semidirect
44. C2×C4×Dic283C22semidirect
45. C283⋊#95C22semidirect
46. C283⋊#95C22semidirect
47. C283⋊#95C22semidirect
48. C283⋊#95C22semidirect
49. C2×C4⋊C4×C283C22semidirect
53. C2×C42×C283C22semidirect
54. #95×C283C22semidirect
55. #95×C283C22semidirect
62. C23×D283C2×C4semidirect
70. C2×D1132C2×C4semidirect
71. C2×D1132C2×C4semidirect
74. C2×C22⋊D283C2×C4semidirect
104. (C2×D283)⋊C4C2×C4semidirect
105. (C2×D283)⋊C4C2×C4semidirect
106. (C2×D283)⋊C4D4semidirect
107. (C2×D283)⋊C4D4semidirect
120. C22⋊C4×C283C2×C4semidirect
233. C2×D283C4×D4semidirect
234. C2×D283C4×D4semidirect
257. C283#2358semidirect
266. #388D283semidirect
288. C2×C4⋊C4C2×D283semidirect
307. C2×C42C2×D283semidirect
312. #95C2×D283semidirect
313. #95C2×D283semidirect
376. C22⋊C4C4×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225835802
C2×C4×D11322
C2×#225835722
C2×C22⋊C4×D2832
#318263652
#318263582
#318263432
#318263412
#318263392
#318263362
C4×(C2×D283)⋊C42
#318263122
#388×C2832
#2358283