Finite Group Databasebeta

← #49124238

Subgroups — #49124238

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×#22583578C211yesmaximal, characteristic
2C2×C4×C22⋊D283C211yesmaximal, characteristic, complemented
3C22×(C2×D283)⋊C4C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D283C211yesmaximal, characteristic, complemented
5#31826365C211yesmaximal, characteristic, complemented
6#31826356C211yesmaximal, characteristic, complemented
7#31826355C211yesmaximal, characteristic, complemented
8#31826345C211yesmaximal, characteristic, complemented
9#31826344C211yesmaximal, characteristic, complemented
10#31826341C211yesmaximal, characteristic, complemented
11#31826338C211yesmaximal, characteristic, complemented
12#31826336C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic283C211yesmaximal, characteristic, complemented
14C4×(C2×D283)⋊C4C211yesmaximal, characteristic, complemented
15C2×C4×D4×C283C211yesmaximal, characteristic, complemented
16C24×D283C2211yescharacteristic
17C22×C22⋊D283C2211yescharacteristic
18C22×C22⋊D283C2211yescharacteristic
19C23×Dic283C2211yescharacteristic
20C22×C4×D283C2211yescharacteristic
21C22×C4×D283C2211yescharacteristic
22#22583578C418yescomplemented
23C4×C22⋊D283—24no—
24C2×Dic283⋊C4C2211yescharacteristic, complemented
25C2×Dic283⋊C4C2211yescharacteristic, complemented
26C2×C22⋊Dic283C2211yescharacteristic
27C2×C22⋊Dic283C2211yescharacteristic
28C2×C22⋊Dic283C2211yescharacteristic, complemented
29C2×C22⋊Dic283C2211yescharacteristic, complemented
30C2×(C2×D283)⋊C4—24no—
31C2×(C2×D283)⋊C4C2211yescharacteristic
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
39C22⋊C4×D283—24no—
40C2×C4×Dic283C2211yescharacteristic, complemented
41C2×C4×Dic283C2211yescharacteristic, complemented
42C283⋊#95C2211yescharacteristic, complemented
43C283⋊#95C2211yescharacteristic, complemented
44C283⋊#95C2211yescharacteristic, complemented
45C283⋊#95C2211yescharacteristic, complemented
46C283⋊#95C2211yescharacteristic, complemented
47C283⋊#95C2211yescharacteristic, complemented
48C22×D4×C283C2211yescharacteristic
49C23×C4×C283C2211yescharacteristic
50C23×C4×C283C2211yescharacteristic, complemented
51C4×D4×C283—24no—
52C2×C4⋊C4×C283C2211yescharacteristic, complemented
53C2×C22⋊C4×C283C2211yescharacteristic
54C2×C22⋊C4×C283C2211yescharacteristic, complemented
55C2×C42×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
65C2×C22⋊D283—22no—
66C2×C22⋊D283—22no—
67C2×C22⋊D283—41no—
68C2×C22⋊D283—41no—
69C2×C22⋊D283C2×C414yescomplemented
70C2×C22⋊D283C2×C414yescomplemented
71C22×Dic283—22no—
72C22×Dic283—22no—
73C22×Dic283—41no—
74C22×Dic283C2311yescharacteristic
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—41no—
85C2×C4×D283—41no—
86Dic283⋊C4—22no—
87Dic283⋊C4—41no—
88C22⋊Dic283—22no—
89C22⋊Dic283—22no—
90C22⋊Dic283—41no—
91C22⋊Dic283C2×C414yescomplemented
92(C2×D283)⋊C4—22no—
93(C2×D283)⋊C4—22no—
94(C2×D283)⋊C4—22no—
95(C2×D283)⋊C4—22no—
96(C2×D283)⋊C4—22no—
97(C2×D283)⋊C4C2×C414yescomplemented
98(C2×D283)⋊C4C2×C414yescomplemented
99(C2×D283)⋊C4D414yescomplemented
100C4×Dic283—22no—
101C4×Dic283—41no—
102C24×C283C2311yescharacteristic
103C24×C283C2311yescharacteristic
104C2×D4×C283—22no—
105C2×D4×C283—22no—
106C2×D4×C283C2×C414yescomplemented
107C22×C4×C283—22no—
108C22×C4×C283—22no—
109C22×C4×C283—22no—
110C22×C4×C283—22no—
111C22×C4×C283—41no—
112C22×C4×C283—41no—
113C22×C4×C283C2311yescharacteristic
114C22×C4×C283C2311yescharacteristic
115C22×C4×C283C2311yescharacteristic
116C22×C4×C283C2311yescharacteristic
117C22×C4×C283C2311yescharacteristic
118C4⋊C4×C283—22no—
119C22⋊C4×C283—22no—
120C22⋊C4×C283D414yescomplemented
121C42×C283—22no—
122C22×D283—21no—
123C22×D283—21no—
124C22×D283—21no—
125C22×D283—21no—
126C22×D283—28no—
127C22×D283—21no—
128C22×D283—21no—
129C22×D283—21no—
130C22×D283—21no—
131C22×D283—21no—
132C22×D283—21no—
133C22×D283—28no—
134C22×D283—44no—
135C22×D283—44no—
136C22×D283—44no—
137C22×D283—44no—
138C22×D283—44no—
139C22×D283C22×C412yes—
140C22×D283C22×C412yes—
141C22×D283C2×D412yes—
142C22×D283#4112yes—
143C22⋊D283—28no—
144C22⋊D283—44no—
145C2×Dic283—21no—
146C2×Dic283—21no—
147C2×Dic283—21no—
148C2×Dic283—21no—
149C2×Dic283—21no—
150C2×Dic283—21no—
151C2×Dic283—21no—
152C2×Dic283—21no—
153C2×Dic283—21no—
154C2×Dic283—21no—
155C2×Dic283—21no—
156C2×Dic283—21no—
157C2×Dic283—21no—
158C2×Dic283—21no—
159C2×Dic283—21no—
160C2×Dic283—44no—
161C2×Dic283C22×C412yes—
162C2×Dic283C22×C412yes—
163C2×Dic283C2×D412yes—
164C4×D283—44no—
165C4×D283—44no—
166C23×C283—21no—
167C23×C283—21no—
168C23×C283—21no—
169C23×C283—21no—
170C23×C283—21no—
171C23×C283—21no—
172C23×C283—21no—
173C23×C283—21no—
174C23×C283—21no—
175C23×C283—21no—
176C23×C283C22×C412yes—
177C23×C283C22×C412yes—
178C23×C283C2×D412yes—
179C23×C283#4112yes—
180C23×C283C2411yescharacteristic
181D4×C283—28no—
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—44no—
194C2×C4×C283—44no—
195C2×C4×C283C22×C412yes—
196C2×C4×C283C2×D412yes—
197C2×C4×C283C2×D412yes—
198C2×C4×C283C2×D412yes—
199C22×C283—22no—
200C22×C283—22no—
201C22×C283—22no—
202C22×C283—22no—
203C22×C283—22no—
204C22×C283—22no—
205C22×C283—22no—
206C22×C283—22no—
207C22×C283—22no—
208C22×C283—41no—
209C22×C283—41no—
210C22×C283—41no—
211C22×C283—41no—
212C22×C283C4×D414yescomplemented
213C22×C283C23×C411yescharacteristic
214C22×C283C22×D411yescharacteristic
215C22×C283C22×D411yescharacteristic
216C22×C283C2×#4111yescharacteristic
217C22×C283C2×#4111yescharacteristic
218C22×C283H(5,𝔽2)11yescharacteristic
219C22×C283H(5,𝔽2)11yescharacteristic
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—22no—
229C2×D283—416no—
230C2×D283—41no—
231C2×D283—41no—
232C2×D283—41no—
233C2×D283—41no—
234C2×D283C4×D414yescomplemented
235C4×C283—22no—
236C4×C283—22no—
237C4×C283—22no—
238C4×C283—22no—
239C4×C283—41no—
240Dic283—22no—
241Dic283—22no—
242Dic283—22no—
243Dic283—41no—
244Dic283—41no—
245Dic283—41no—
246C2×C283—24no—
247C2×C283—42no—
248C2×C283C2×C4×D411yescharacteristic
249C2×C283C2×C4×D411yescharacteristic
250C2×C283#51811yescharacteristic
251C2×C283D4211yescharacteristic
252C2×C283#54611yescharacteristic
253C2×C283#54611yescharacteristic
254C2×C283#55111yescharacteristic
255D283—24no—
256D283—42no—
257C283#235811yescharacteristic, complemented, Sylow
258#2358—2831nomaximal, Sylow
259C2×#120—2831no—
260C2×C4×D4—2831no—
261C2×C4×D4D28311yescharacteristic, complemented
262C22×C22⋊C4—2831no—
263C22×C22⋊C4—2831no—
264#390—2831no—
265#388—2831no—
266#388—2831no—
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×D4C2×D28311yescharacteristic
278C23×C4—2831no—
279C23×C4—2831no—
280C23×C4—2831no—
281C23×C4C2×D28311yescharacteristic
282C23×C4C2×D28311yescharacteristic, complemented
283#120—2838no—
284C4×D4—24no—
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—2831no—
301C2×C22⋊C4—5664no—
302C2×C22⋊C4—5664no—
303C2×C22⋊C4C2×D28311yescharacteristic
304C2×C22⋊C4C2×D28311yescharacteristic, complemented
305C2×C42—2831no—
306C2×C42—2831no—
307C2×C42C2×D28311yescharacteristic, complemented
308#95—2831no—
309#95—2831no—
310#95—2831no—
311#95—2831no—
312#95—2831no—
313#95—2831no—
314C24—2831no—
315C24—2831no—
316C24—2834no—
317C24—5662no—
318C24—5662no—
319C24—5662no—
320C24—5662no—
321C24—11321no—
322C24—11321no—
323C24C22×D28311yescharacteristic
324C24C22×D28311yescharacteristic
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—2834no—
328C2×D4—2834no—
329C2×D4—5662no—
330C2×D4—5662no—
331C2×D4—11321no—
332C2×D4—11321no—
333C2×D4C4×D28314yescomplemented
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—2831no—
341C22×C4—2831no—
342C22×C4—2831no—
343C22×C4—2831no—
344C22×C4—2831no—
345C22×C4—2831no—
346C22×C4—5662no—
347C22×C4—5662no—
348C22×C4—5662no—
349C22×C4—5662no—
350C22×C4—5662no—
351C22×C4—5662no—
352C22×C4—11321no—
353C22×C4—11321no—
354C22×C4—11321no—
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—2834no—
365C22⋊C4—2834no—
366C22⋊C4—2834no—
367C22⋊C4—2834no—
368C22⋊C4—5662no—
369C22⋊C4—5662no—
370C22⋊C4—5662no—
371C22⋊C4—5662no—
372C22⋊C4—5662no—
373C22⋊C4—5662no—
374C22⋊C4—5662no—
375C22⋊C4—11321no—
376C22⋊C4C22⋊D28314yescomplemented
377C42—22no—
378C42—5662no—
379C42—11321no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—2832no—
391C23—2832no—
392C23—2832no—
393C23—2832no—
394C23—5668no—
395C23—5661no—
396C23—5661no—
397C23—5661no—
398C23—5661no—
399C23—5668no—
400C23—5661no—
401C23—5661no—
402C23—5661no—
403C23—5661no—
404C23—5661no—
405C23—5661no—
406C23—11324no—
407C23—11324no—
408C23—11324no—
409C23—11324no—
410C23—11324no—
411C23C2×C4×D28312yes—
412C23C2×C4×D28312yes—
413C23C2×C22⋊D28312yes—
414C23#1798539212yes—
415C23C23×D28311yescharacteristic
416D4—28no—
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—44no—
431C2×C4—44no—
432C2×C4—2832no—
433C2×C4—2832no—
434C2×C4—2832no—
435C2×C4—5661no—
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—5661no—
449C2×C4—5661no—
450C2×C4—11324no—
451C2×C4—11324no—
452C2×C4—11324no—
453C2×C4C2×C4×D28312yes—
454C2×C4D4×D28312yes—
455C2×C4C2×C22⋊D28312yes—
456C2×C4C2×C22⋊D28312yes—
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—2834no—
471C22—5662no—
472C22—5662no—
473C22—5662no—
474C22—5662no—
475C22—5662no—
476C22—5662no—
477C22—5662no—
478C22—5662no—
479C22—5662no—
480C22—113216no—
481C22—11321no—
482C22—11321no—
483C22—11321no—
484C22—11321no—
485C22C4×C22⋊D28314yescomplemented
486C22C22×C4×D28311yescharacteristic
487C22C2×D4×D28311yescharacteristic
488C22C22×C22⋊D28311yescharacteristic
489C22#41×D28311yescharacteristic
490C22C2×#1798539211yescharacteristic
491C22#2258365511yescharacteristic
492C22#2258365611yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—41no—
498C4—5662no—
499C4—5662no—
500C4—5662no—
501C4—11321no—
502C4—11321no—
503C4—11321no—
504C2—24no—
505C2—42no—
506C2—5664no—
507C2—11322no—
508C2C4×D4×D28311yescharacteristic
509C2C2×C4×C22⋊D28311yescharacteristic
510C2#3182693711yescharacteristic
511C2D4×C22⋊D28311yescharacteristic
512C2#3182710311yescharacteristic
513C2#3182711111yescharacteristic
514C2#3182714411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
FittingC2×C4×D4×C283C2
socle, cosocleC23×C283C24
prime radicalC2×#22583578C2
hypercenterC2×C4×D4D283
hypocenterC283#2358
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D283C2semidirect
3. C22×(C2×D283)⋊C4C2semidirect
4. C2×C22⋊C4×D283C2semidirect
5. #31826365C2semidirect
6. #31826356C2semidirect
7. #31826355C2semidirect
8. #31826345C2semidirect
9. #31826344C2semidirect
10. #31826341C2semidirect
11. #31826338C2semidirect
12. #31826336C2semidirect
13. C22⋊C4×Dic283C2semidirect
14. C4×(C2×D283)⋊C4C2semidirect
15. C2×C4×D4×C283C2semidirect
22. #22583578C4semidirect
24. C2×Dic283⋊C4C22semidirect
25. C2×Dic283⋊C4C22semidirect
28. C2×C22⋊Dic283C22semidirect
29. C2×C22⋊Dic283C22semidirect
40. C2×C4×Dic283C22semidirect
41. C2×C4×Dic283C22semidirect
42. C283⋊#95C22semidirect
43. C283⋊#95C22semidirect
44. C283⋊#95C22semidirect
45. C283⋊#95C22semidirect
46. C283⋊#95C22semidirect
47. C283⋊#95C22semidirect
50. C23×C4×C283C22semidirect
52. C2×C4⋊C4×C283C22semidirect
54. C2×C22⋊C4×C283C22semidirect
55. C2×C42×C283C22semidirect
62. C23×D283C2×C4semidirect
69. C2×C22⋊D283C2×C4semidirect
70. C2×C22⋊D283C2×C4semidirect
91. C22⋊Dic283C2×C4semidirect
97. (C2×D283)⋊C4C2×C4semidirect
98. (C2×D283)⋊C4C2×C4semidirect
99. (C2×D283)⋊C4D4semidirect
106. C2×D4×C283C2×C4semidirect
120. C22⋊C4×C283D4semidirect
212. C22×C283C4×D4semidirect
234. C2×D283C4×D4semidirect
257. C283#2358semidirect
261. C2×C4×D4D283semidirect
282. C23×C4C2×D283semidirect
288. C2×C4⋊C4C2×D283semidirect
304. C2×C22⋊C4C2×D283semidirect
307. C2×C42C2×D283semidirect
333. C2×D4C4×D283semidirect
376. C22⋊C4C22⋊D283semidirect
485. C22C4×C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225835782
C2×C4×C22⋊D2832
C22×(C2×D283)⋊C42
C2×C22⋊C4×D2832
#318263652
#318263562
#318263552
#318263452
#318263442
#318263412
#318263382
#318263362
C22⋊C4×Dic2832
C4×(C2×D283)⋊C42
C2×C4×D4×C2832
#2358283