Finite Group Databasebeta

← #49124243

Subgroups — #49124243

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×(C22⋊D283)⋊C4C211yesmaximal, characteristic, complemented
4C22×(C2×D283)⋊C4C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D283C211yesmaximal, characteristic, complemented
6#31826367C211yesmaximal, characteristic, complemented
7#31826357C211yesmaximal, characteristic, complemented
8#31826356C211yesmaximal, characteristic, complemented
9#31826344C211yesmaximal, characteristic, complemented
10#31826343C211yesmaximal, characteristic, complemented
11#31826343C211yesmaximal, characteristic, complemented
12#31826340C211yesmaximal, characteristic, complemented
13#31826339C211yesmaximal, characteristic, complemented
14C4×(C2×D283)⋊C4C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C283C211yesmaximal, characteristic, complemented
16C24×D283C2211yescharacteristic
17C22×D1132C2211yescharacteristic
18C22×D1132C2211yescharacteristic
19C22×C22⋊D283C2211yescharacteristic
20C23×Dic283C2211yescharacteristic
21C22×C4×D283C2211yescharacteristic
22C22×C4×D283C2211yescharacteristic
23C22×C4×D283C2211yescharacteristic, complemented
24#22583580C418yescomplemented
25C4×D1132—24no—
26(C22⋊D283)⋊C4—24no—
27C2×C4⋊Dic283C2211yescharacteristic, complemented
28C2×C4⋊Dic283C2211yescharacteristic, complemented
29C2×Dic283⋊C4C2211yescharacteristic, complemented
30C2×C22⋊Dic283C2211yescharacteristic
31C2×(C2×D283)⋊C4—24no—
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
39C2×(C2×D283)⋊C4C2211yescharacteristic
40C2×(C2×D283)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D283)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D283)⋊C4C2211yescharacteristic, complemented
43C22⋊C4×D283—24no—
44C2×C4×Dic283C2211yescharacteristic, complemented
45C283⋊#95C2211yescharacteristic, complemented
46C283⋊#95C2211yescharacteristic, complemented
47C283⋊#95C2211yescharacteristic, complemented
48C283⋊#95C2211yescharacteristic, complemented
49C23×C4×C283C2211yescharacteristic
50C2×C22⋊C4×C283C2211yescharacteristic
51C2×C22⋊C4×C283C2211yescharacteristic
52C2×C42×C283C2211yescharacteristic, complemented
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—41no—
69C2×D1132—41no—
70C2×D1132C2×C414yescomplemented
71C2×D1132C2×C414yescomplemented
72C2×C22⋊D283—22no—
73C2×C22⋊D283—22no—
74C2×C22⋊D283C2×C414yescomplemented
75C22×Dic283—22no—
76C22×Dic283—22no—
77C22×Dic283—41no—
78C22×Dic283C2311yescharacteristic
79C22×Dic283C2311yescharacteristic
80C22×Dic283C2311yescharacteristic
81C22×Dic283C2311yescharacteristic
82C22×Dic283C2311yescharacteristic
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—41no—
90C2×C4×D283—41no—
91C2×C4×D283—41no—
92C4⋊Dic283—22no—
93C4⋊Dic283—41no—
94Dic283⋊C4—22no—
95C22⋊Dic283—22no—
96(C2×D283)⋊C4—22no—
97(C2×D283)⋊C4—22no—
98(C2×D283)⋊C4—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
107C4×Dic283—22no—
108C24×C283C2311yescharacteristic
109C22×C4×C283—22no—
110C22×C4×C283—22no—
111C22×C4×C283—41no—
112C22×C4×C283C2311yescharacteristic
113C22×C4×C283C2311yescharacteristic
114C22×C4×C283C2311yescharacteristic
115C22×C4×C283C2311yescharacteristic
116C22×C4×C283C2311yescharacteristic
117C22×C4×C283C2311yescharacteristic
118C22⋊C4×C283C2×C414yescomplemented
119C22⋊C4×C283D414yescomplemented
120C42×C283—22no—
121C42×C283—41no—
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—21no—
134C22×D283—21no—
135C22×D283—21no—
136C22×D283—21no—
137C22×D283—21no—
138C22×D283—21no—
139C22×D283—28no—
140C22×D283—44no—
141C22×D283—44no—
142C22×D283—44no—
143C22×D283—44no—
144C22×D283—44no—
145C22×D283C22×C412yes—
146C22×D283C22×C412yes—
147C22×D283C22×C412yes—
148C22×D283C2×D412yes—
149C22×D283#4112yes—
150D1132—28no—
151D1132—44no—
152C22⋊D283—28no—
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×Dic283—21no—
166C2×Dic283—44no—
167C2×Dic283C22×C412yes—
168C2×Dic283C2×D412yes—
169C4×D283—44no—
170C4×D283—44no—
171C4×D283—44no—
172C23×C283—21no—
173C23×C283—21no—
174C23×C283—21no—
175C23×C283—21no—
176C23×C283C22×C412yes—
177C23×C283C2×D412yes—
178C23×C283#4112yes—
179C23×C283C2411yescharacteristic
180C2×C4×C283—21no—
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—44no—
194C2×C4×C283C22×C412yes—
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×C283C4×D414yescomplemented
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—416no—
226C2×D283—41no—
227C2×D283—41no—
228C2×D283—41no—
229C2×D283—41no—
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—22no—
240C4×C283—41no—
241Dic283—22no—
242Dic283—22no—
243Dic283—41no—
244Dic283—41no—
245Dic283—41no—
246C2×C283—24no—
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—42no—
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#388—2831no—
267#386—2831no—
268#386—2831no—
269#386—2831no—
270#385—2831no—
271#385—2831no—
272C4×C22⋊C4—2831no—
273C4×C22⋊C4D28311yescharacteristic, complemented
274C25—2831no—
275C22×D4—2831no—
276C22×D4—2831no—
277C22×D4—2831no—
278C23×C4—2831no—
279C23×C4—2831no—
280C23×C4—2831no—
281C23×C4—2831no—
282C23×C4C2×D28311yescharacteristic
283#120—2838no—
284C4×D4—5664no—
285C4×D4—5664no—
286C2×C4⋊C4—2831no—
287C2×C4⋊C4—2831no—
288C2×C4⋊C4—2831no—
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
305C2×C42—2831no—
306C2×C42C2×D28311yescharacteristic, complemented
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—22no—
335C22×C4—22no—
336C22×C4—41no—
337C22×C4—2831no—
338C22×C4—2831no—
339C22×C4—2831no—
340C22×C4—2831no—
341C22×C4—2831no—
342C22×C4—5662no—
343C22×C4—5662no—
344C22×C4—5662no—
345C22×C4—5662no—
346C22×C4—5662no—
347C22×C4—5662no—
348C22×C4—5662no—
349C22×C4—5662no—
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—5662no—
361C4⋊C4—5662no—
362C4⋊C4—11321no—
363C22⋊C4—2834no—
364C22⋊C4—2834no—
365C22⋊C4—2834no—
366C22⋊C4—5662no—
367C22⋊C4—5662no—
368C22⋊C4—5662no—
369C22⋊C4—5662no—
370C22⋊C4—5662no—
371C22⋊C4—5662no—
372C22⋊C4—5662no—
373C22⋊C4—5662no—
374C22⋊C4—11321no—
375C22⋊C4C4×D28314yescomplemented
376C22⋊C4D113214yescomplemented
377C42—22no—
378C42—41no—
379C42—5662no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—2832no—
385C23—2832no—
386C23—2832no—
387C23—2832no—
388C23—2832no—
389C23—5668no—
390C23—5661no—
391C23—5661no—
392C23—5661no—
393C23—5661no—
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—11324no—
408C23—11324no—
409C23—11324no—
410C23—11324no—
411C23—11324no—
412C23C2×C4×D28312yes—
413C23C2×D113212yes—
414C23#1798539212yes—
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—44no—
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—11324no—
449C2×C4—11324no—
450C2×C4—11324no—
451C2×C4—11324no—
452C2×C4C2×C4×D28312yes—
453C2×C4C2×C4×D28312yes—
454C2×C4D4×D28312yes—
455C2×C4C2×D113212yes—
456C2×C4C2×D113212yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—2834no—
464C22—5662no—
465C22—5662no—
466C22—5662no—
467C22—5662no—
468C22—5662no—
469C22—5662no—
470C22—5662no—
471C22—5662no—
472C22—5662no—
473C22—5662no—
474C22—5662no—
475C22—5662no—
476C22—113216no—
477C22—11321no—
478C22—11321no—
479C22—11321no—
480C22—11321no—
481C22—11321no—
482C22—11321no—
483C22—11321no—
484C22—11321no—
485C22C4×D113214yescomplemented
486C22C22×C4×D28311yescharacteristic
487C22C2×D4×D28311yescharacteristic
488C22C22×D113211yescharacteristic
489C22#41×D28311yescharacteristic
490C22C2×#1798539211yescharacteristic
491C22#2258365511yescharacteristic
492C22#2258365611yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—22no—
498C4—41no—
499C4—5662no—
500C4—5662no—
501C4—11321no—
502C4—11321no—
503C4—11321no—
504C2—24no—
505C2—5664no—
506C2—11322no—
507C2—11322no—
508C2C4×D4×D28311yescharacteristic
509C2C2×C4×D113211yescharacteristic
510C2#3182693711yescharacteristic
511C2D4×D113211yescharacteristic
512C2#3182710511yescharacteristic
513C2#3182711011yescharacteristic
514C2#3182713911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
FittingC4×C22⋊C4×C283C2
socle, cosocleC23×C283C24
prime radicalC2×#22583580C2
hypercenterC4×C22⋊C4D283
hypocenterC283#2358
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D1132C2semidirect
3. C2×(C22⋊D283)⋊C4C2semidirect
4. C22×(C2×D283)⋊C4C2semidirect
5. C2×C22⋊C4×D283C2semidirect
6. #31826367C2semidirect
7. #31826357C2semidirect
8. #31826356C2semidirect
9. #31826344C2semidirect
10. #31826343C2semidirect
11. #31826343C2semidirect
12. #31826340C2semidirect
13. #31826339C2semidirect
14. C4×(C2×D283)⋊C4C2semidirect
15. C4×C22⋊C4×C283C2semidirect
23. C22×C4×D283C22semidirect
24. #22583580C4semidirect
27. C2×C4⋊Dic283C22semidirect
28. C2×C4⋊Dic283C22semidirect
29. C2×Dic283⋊C4C22semidirect
40. C2×(C2×D283)⋊C4C22semidirect
41. C2×(C2×D283)⋊C4C22semidirect
42. C2×(C2×D283)⋊C4C22semidirect
44. C2×C4×Dic283C22semidirect
45. C283⋊#95C22semidirect
46. C283⋊#95C22semidirect
47. C283⋊#95C22semidirect
48. C283⋊#95C22semidirect
52. C2×C42×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
118. C22⋊C4×C283C2×C4semidirect
119. C22⋊C4×C283D4semidirect
205. C22×C283C4×D4semidirect
234. C2×D283C4×D4semidirect
257. C283#2358semidirect
273. C4×C22⋊C4D283semidirect
306. C2×C42C2×D283semidirect
307. C2×C42C2×D283semidirect
312. #95C2×D283semidirect
313. #95C2×D283semidirect
375. C22⋊C4C4×D283semidirect
376. C22⋊C4D1132semidirect
485. C22C4×D1132semidirect

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×(C22⋊D283)⋊C42
C22×(C2×D283)⋊C42
C2×C22⋊C4×D2832
#318263672
#318263572
#318263562
#318263442
#318263432
#318263402
#318263392
C4×(C2×D283)⋊C42
C4×C22⋊C4×C2832
#2358283