Finite Group Databasebeta

← #11887219

Subgroups — #11887219

Order 1152.

1224 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596147C211yesmaximal, characteristic
2#10596052C211yesmaximal, characteristic, complemented
3C32×#464C211yesmaximal, characteristic, complemented
4#10592887C211yesmaximal, characteristic, complemented
5#10592886C211yesmaximal, characteristic, complemented
6#10592870C211yesmaximal, characteristic, complemented
7#10592868C211yesmaximal, characteristic, complemented
8#10592755C211yesmaximal, characteristic, complemented
9C4×#3755C211yesmaximal, characteristic, complemented
10#10592546C211yesmaximal, characteristic, complemented
11#10592533C211yesmaximal, characteristic, complemented
12#10592504C211yesmaximal, characteristic, complemented
13#10592503C211yesmaximal, characteristic, complemented
14#10592483C211yesmaximal, characteristic, complemented
15C3⋊D3×#102C211yesmaximal, characteristic, complemented
16#80615—34nomaximal
17C2×#3832C2211yescharacteristic
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic, complemented
20C2×C32×SD16C2211yescharacteristic
21C32×#124C2211yescharacteristic
22C32×C4×Q8C2211yescharacteristic, complemented
23#64155C2211yescharacteristic
24#64155C2211yescharacteristic
25#64155C2211yescharacteristic, complemented
26C2×#3755C2211yescharacteristic
27#64147C2211yescharacteristic
28C2×C8×C3⋊D3C2211yescharacteristic
29C2×C8×C3⋊D3C2211yescharacteristic, complemented
30#64103—21no—
31#64101C2211yescharacteristic, complemented
32C4⋊C4×C3⋊D3C2211yescharacteristic
33#64098—21no—
34#64093—21no—
35#64092—21no—
36#64091—21no—
37C22⋊C4×C3⋊D3—21no—
38#64085—21no—
39C4×C4⋊(C3⋊D3)C2211yescharacteristic
40C4×C4⋊(C3⋊D3)C2211yescharacteristic
41#64081—21no—
42#64079C2211yescharacteristic, complemented
43C32×C4⋊C8C2211yescharacteristic, complemented
44C32×#103C2211yescharacteristic, complemented
45C32×#102C2211yescharacteristic
46#63662C2211yescharacteristic, complemented
47#63662C2211yescharacteristic, complemented
48#63662C2211yescharacteristic, complemented
49#63659C2211yescharacteristic
50#63659C2211yescharacteristic
51#63648C2211yescharacteristic
52#63648C2211yescharacteristic
53#63647C2211yescharacteristic
54#63647C2211yescharacteristic, complemented
55#63645C2211yescharacteristic, complemented
56#63644C2211yescharacteristic, complemented
57#63636C2211yescharacteristic
58#63635C2211yescharacteristic, complemented
59C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
60#5676—34no—
61#5581—34no—
62C3×#464D314yescomplemented
63#5188—34no—
64#5187—34no—
65#5171—34no—
66#5169—34no—
67#5056—34no—
68C4×#215—34no—
69#4847—34no—
70#4834—34no—
71#4805—34no—
72#4804—34no—
73#4784—34no—
74D3×#102—34no—
75C23×C3⋊D3—21no—
76C2×C32×Q8C2311yescharacteristic
77C2×C32×Q8C2311yescharacteristic
78C2×C32×D4C2311yescharacteristic
79C2×#638—21no—
80C2×#638—21no—
81#3832—22no—
82#3832—41no—
83D4×C3⋊D3—22no—
84D4×C3⋊D3—41no—
85C2×C4⋊(C3⋊D3)—21no—
86C2×C4⋊(C3⋊D3)D411yescharacteristic
87C2×C4⋊(C3⋊D3)C2311yescharacteristic
88C2×C4×C3⋊D3—21no—
89C2×C4×C3⋊D3—21no—
90C2×C4×C3⋊D3—21no—
91C2×C4×C3⋊D3C2311yescharacteristic
92C2×C4×C3⋊D3C2311yescharacteristic
93C32×Q16—41no—
94C32×SD16—41no—
95C2×C32×C8C2311yescharacteristic
96C2×C32×C8C2311yescharacteristic
97C32×C4⋊C4—21no—
98C32×C4⋊C4C2311yescharacteristic
99C32×C22⋊C4—21no—
100C32×C22⋊C4—21no—
101C32×C42—21no—
102C32×C42C2311yescharacteristic
103#3757—21no—
104#3755—22no—
105#3752—21no—
106#3752—21no—
107#3752—21no—
108#3752—21no—
109#3752—21no—
110#3752D411yescharacteristic
111#3752D411yescharacteristic
112C4⋊(C3⋊Dic3)D411yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117#3750—21no—
118#3750—21no—
119#3750—21no—
120#3750—21no—
121#3750—21no—
122C4×C3⋊Dic3—21no—
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C8×C3⋊D3—41no—
126C8×C3⋊D3—41no—
127#3296—91noSylow
128C2×#239—34no—
129C2×D3×D4—34no—
130C2×C3×Q16C2×D314yescomplemented
131C2×C3×SD16C2×D314yes—
132C3×#124C2×D314yes—
133C3×C4×Q8C2×D314yescomplemented
134#946—34no—
135#946—34no—
136#946—34no—
137C2×#215—34no—
138#938—34no—
139C2×D3×C8—34no—
140C2×D3×C8—34no—
141#894—64no—
142#892—34no—
143D3×C4⋊C4—34no—
144#889—64no—
145#884—64no—
146#883—64no—
147#882—64no—
148D3×C22⋊C4—64no—
149#876—64no—
150C4×D12—34no—
151C4×D12—34no—
152#872—64no—
153#870—34no—
154C3×C4⋊C8C2×D314yescomplemented
155C3×#103C2×D314yescomplemented
156C3×#102C2×D314yes—
157#835—34no—
158#835—34no—
159#835—34no—
160#832—34no—
161#832—34no—
162#821—34no—
163#821—34no—
164(C2×D3)⋊C8—34no—
165(C2×D3)⋊C8—34no—
166#818—34no—
167#817—34no—
168#809—34no—
169#808—34no—
170C4×C3⋊C8—34no—
171C23×C32—21no—
172C22×C3⋊D3—21no—
173C22×C3⋊D3—42no—
174C22×C3⋊D3—42no—
175C22×C3⋊D3—81no—
176C22×C3⋊D3C2×D411yescharacteristic
177C22×C3⋊D3C2×D411yescharacteristic
178C32×Q8—21no—
179C32×Q8—21no—
180C32×Q8—21no—
181C32×Q8—21no—
182C32×D4—21no—
183C32×D4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2411yescharacteristic
190#638—42no—
191#638—81no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3C2×D411yescharacteristic
196C2×C3⋊Dic3C2×D411yescharacteristic
197C4⋊(C3⋊D3)—22no—
198C4⋊(C3⋊D3)—21no—
199C4⋊(C3⋊D3)—42no—
200C4⋊(C3⋊D3)#4112yes—
201C4×C3⋊D3—21no—
202C4×C3⋊D3—21no—
203C4×C3⋊D3—21no—
204C4×C3⋊D3—21no—
205C4×C3⋊D3—42no—
206C4×C3⋊D3—42no—
207C4×C3⋊D3—81no—
208C32×C8—21no—
209C32×C8—21no—
210C3⋊(C3⋊C8)—21no—
211C3⋊(C3⋊C8)—21no—
212#552—91no—
213#546—91no—
214#488—91no—
215#483—91no—
216#482—91no—
217#478—91no—
218#467—91no—
219#465—91no—
220#464C3⋊D311yescharacteristic, complemented
221#452—91no—
222#450—91no—
223C4×SD16—91no—
224C8×D4—91no—
225#416—91no—
226C2×#102—91no—
227C23×D3—64no—
228C2×C3×Q8C22×D314yes—
229C2×C3×Q8C22×D314yes—
230C2×C3×D4C22×D314yes—
231C2×#67—64no—
232C2×#67—64no—
233#239—68no—
234#239—124no—
235D3×D4—68no—
236D3×D4—124no—
237C2×D12—34no—
238C2×D12—34no—
239C2×D12—64no—
240C2×C4×D3—34no—
241C2×C4×D3—34no—
242C2×C4×D3—64no—
243C2×C4×D3—64no—
244C2×C4×D3—64no—
245C3×Q16—44no—
246C3×SD16—44no—
247C2×C3×C8C22×D314yes—
248C2×C3×C8C22×D314yes—
249C3×C4⋊C4—24no—
250C3×C4⋊C4C22×D314yes—
251C3×C22⋊C4—24no—
252C3×C22⋊C4—24no—
253C3×C42—24no—
254C3×C42C22×D314yes—
255#217—64no—
256#215—68no—
257(C2×D3)⋊C4—34no—
258(C2×D3)⋊C4—34no—
259(C2×D3)⋊C4—64no—
260(C2×D3)⋊C4—64no—
261(C2×D3)⋊C4—64no—
262(C2×D3)⋊C4—64no—
263(C2×D3)⋊C4—64no—
264C4⋊Dic3—34no—
265C4⋊Dic3—34no—
266C4⋊Dic3—34no—
267C4⋊Dic3—34no—
268Dic3⋊C4—64no—
269Dic3⋊C4—64no—
270Dic3⋊C4—64no—
271Dic3⋊C4—64no—
272Dic3⋊C4—64no—
273Dic3⋊C4—64no—
274C4×Dic3—64no—
275C2×C3⋊C8—34no—
276C2×C3⋊C8—34no—
277D3×C8—124no—
278D3×C8—124no—
279C22×C32—41no—
280C22×C32—41no—
281C22×C32—41no—
282C22×C32C22×D411yescharacteristic
283C2×C3⋊D3—21no—
284C2×C3⋊D3—21no—
285C2×C3⋊D3—21no—
286C2×C3⋊D3—22no—
287C2×C3⋊D3—21no—
288C2×C3⋊D3—21no—
289C2×C3⋊D3—41no—
290C2×C3⋊D3—41no—
291C2×C3⋊D3—84no—
292C2×C3⋊D3#13512yes—
293C32×C4—21no—
294C32×C4—21no—
295C32×C4—41no—
296C32×C4—41no—
297C32×C4—41no—
298C32×C4C2×#4111yescharacteristic
299C32×C4H(5,𝔽2)11yescharacteristic
300C3⋊Dic3—21no—
301C3⋊Dic3—21no—
302C3⋊Dic3—41no—
303C3⋊Dic3—41no—
304C3⋊Dic3—41no—
305C2×#41—91no—
306C22×D4—91no—
307C2×Q16C2×C3⋊D311yescharacteristic, complemented
308C2×SD16—91no—
309C2×SD16C2×C3⋊D311yescharacteristic
310C22×C8—91no—
311C22×C8—91no—
312#126—181no—
313#125—91no—
314#125—181no—
315#124C2×C3⋊D311yescharacteristic
316#123—181no—
317#123—181no—
318C22⋊Q8—91no—
319C22⋊Q8—91no—
320C22⋊Q8—91no—
321#121—91no—
322#121—181no—
323#120—181no—
324C4×Q8C2×C3⋊D311yescharacteristic, complemented
325C4×D4—91no—
326C4×D4—91no—
327#117—91no—
328#117—181no—
329C2×C4⋊C4—91no—
330C2×C22⋊C4—181no—
331#107—91no—
332#106—91no—
333#106—91no—
334C4⋊C8C2×C3⋊D311yescharacteristic, complemented
335#103—91no—
336#103—91no—
337#103—91no—
338#103C2×C3⋊D311yescharacteristic, complemented
339#102—91no—
340#102—91no—
341#102—91no—
342#102—91no—
343#102—91no—
344#102C2×C3⋊D311yescharacteristic
345C22⋊C8—91no—
346C22⋊C8—91no—
347C4×C8—91no—
348C23×C3—24no—
349C22×D3—34no—
350C22×D3—34no—
351C22×D3—64no—
352C22×D3—128no—
353C22×D3—128no—
354C22×D3—244no—
355C3×Q8—24no—
356C3×Q8—24no—
357C3×Q8—24no—
358C3×Q8—24no—
359C3×D4—24no—
360C3×D4—24no—
361C2×C3×C4—24no—
362C2×C3×C4—24no—
363C2×C3×C4—24no—
364C2×C3×C4D3×D414yes—
365C2×C3×C4D3×D414yes—
366C2×C3×C4C23×D314yes—
367#67—128no—
368#67—244no—
369C2×Dic3—34no—
370C2×Dic3—34no—
371C2×Dic3—64no—
372C2×Dic3—64no—
373C2×Dic3—64no—
374D12—38no—
375D12—68no—
376D12—64no—
377D12—128no—
378C4×D3—64no—
379C4×D3—64no—
380C4×D3—64no—
381C4×D3—64no—
382C4×D3—128no—
383C4×D3—128no—
384C4×D3—244no—
385C3×C8—24no—
386C3×C8—24no—
387C3⋊C8—64no—
388C3⋊C8—64no—
389C2×C32—81no—
390C2×C32#54611yescharacteristic
391C2×C32C2×#13511yescharacteristic
392C2×C32#57711yescharacteristic
393C3⋊D3—22no—
394C3⋊D3—41no—
395C3⋊D3—42no—
396C24—181no—
397#41—182no—
398#41—361no—
399C2×Q8C22×C3⋊D311yescharacteristic
400C2×Q8C22×C3⋊D311yescharacteristic
401C2×D4—91no—
402C2×D4—91no—
403C2×D4—181no—
404C2×D4—181no—
405C2×D4—182no—
406C2×D4—181no—
407C2×D4—361no—
408C2×D4C22×C3⋊D311yescharacteristic
409C22×C4—91no—
410C22×C4—91no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4—181no—
414Q16—41no—
415SD16—41no—
416SD16—182no—
417C2×C8—91no—
418C2×C8—91no—
419C2×C8—361no—
420C2×C8—361no—
421C2×C8C22×C3⋊D311yescharacteristic
422C2×C8C22×C3⋊D311yescharacteristic
423C4⋊C4—21no—
424C4⋊C4—91no—
425C4⋊C4—91no—
426C4⋊C4—91no—
427C4⋊C4—91no—
428C4⋊C4—181no—
429C4⋊C4—181no—
430C4⋊C4—181no—
431C4⋊C4—181no—
432C4⋊C4—181no—
433C4⋊C4—181no—
434C4⋊C4C22×C3⋊D311yescharacteristic
435C22⋊C4—21no—
436C22⋊C4—21no—
437C22⋊C4—91no—
438C22⋊C4—91no—
439C22⋊C4—181no—
440C22⋊C4—181no—
441C22⋊C4—181no—
442C22⋊C4—181no—
443C22⋊C4—181no—
444C22⋊C4—181no—
445C42—21no—
446C42—181no—
447C42C22×C3⋊D311yescharacteristic
448C22×C3—44no—
449C22×C3—44no—
450C22×C3—44no—
451C22×C3C2×D3×D414yes—
452C2×D3—38no—
453C2×D3—64no—
454C2×D3—64no—
455C2×D3—64no—
456C2×D3—64no—
457C2×D3—64no—
458C2×D3—68no—
459C2×D3—124no—
460C2×D3—124no—
461C2×D3—2416no—
462C3×C4—24no—
463C3×C4—24no—
464C3×C4—44no—
465C3×C4—44no—
466C3×C4—44no—
467C3×C4#100414yes—
468C3×C4D3×#4114yes—
469Dic3—64no—
470Dic3—64no—
471Dic3—124no—
472Dic3—124no—
473Dic3—124no—
474C32#329611yescharacteristic, complemented, Sylow
475C23—21no—
476C23—91no—
477C23—91no—
478C23—181no—
479C23—362no—
480C23—362no—
481C23—721no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—21no—
486D4—21no—
487D4—21no—
488D4—92no—
489D4—182no—
490D4—181no—
491D4—362no—
492D4—362no—
493D4—721no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—91no—
498C2×C4—91no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4—181no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—181no—
506C2×C4—362no—
507C2×C4—362no—
508C2×C4—721no—
509C2×C4D4×C3⋊D311yescharacteristic
510C2×C4D4×C3⋊D311yescharacteristic
511C2×C4C23×C3⋊D311yescharacteristic
512C8—21no—
513C8—21no—
514C8—181no—
515C8—181no—
516C2×C3—84no—
517C2×C3#561214yes—
518C2×C3D3×#13514yes—
519C2×C3#577814yes—
520D3—68no—
521D3—124no—
522D3—128no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22—92no—
527C22—181no—
528C22—181no—
529C22—181no—
530C22—181no—
531C22—181no—
532C22—182no—
533C22—361no—
534C22—361no—
535C22—724no—
536C22C2×D4×C3⋊D311yescharacteristic
537C4—21no—
538C4—21no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—181no—
543C4—181no—
544C4—361no—
545C4—361no—
546C4—361no—
547C4#6436111yescharacteristic
548C4#41×C3⋊D311yescharacteristic
549C3#8061514yescomplemented
550C2—81no—
551C2—182no—
552C2—361no—
553C2—362no—
554C2#1059608311yescharacteristic
555C2C3⋊D3×#13511yescharacteristic
556C2#1059624911yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#464C2
socleC22×C32C22×D4
prime radical#10596147C2
hypercenter#464C3⋊D3
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. #10596052C2semidirect
3. C32×#464C2semidirect
4. #10592887C2semidirect
5. #10592886C2semidirect
6. #10592870C2semidirect
7. #10592868C2semidirect
8. #10592755C2semidirect
9. C4×#3755C2semidirect
10. #10592546C2semidirect
11. #10592533C2semidirect
12. #10592504C2semidirect
13. #10592503C2semidirect
14. #10592483C2semidirect
15. C3⋊D3×#102C2semidirect
19. C2×C32×Q16C22semidirect
22. C32×C4×Q8C22semidirect
25. #64155C22semidirect
29. C2×C8×C3⋊D3C22semidirect
31. #64101C22semidirect
42. #64079C22semidirect
43. C32×C4⋊C8C22semidirect
44. C32×#103C22semidirect
46. #63662C22semidirect
47. #63662C22semidirect
48. #63662C22semidirect
54. #63647C22semidirect
55. #63645C22semidirect
56. #63644C22semidirect
58. #63635C22semidirect
59. C4×C3⋊(C3⋊C8)C22semidirect
62. C3×#464D3semidirect
130. C2×C3×Q16C2×D3semidirect
133. C3×C4×Q8C2×D3semidirect
154. C3×C4⋊C8C2×D3semidirect
155. C3×#103C2×D3semidirect
220. #464C3⋊D3semidirect
307. C2×Q16C2×C3⋊D3semidirect
324. C4×Q8C2×C3⋊D3semidirect
334. C4⋊C8C2×C3⋊D3semidirect
338. #103C2×C3⋊D3semidirect
474. C32#3296semidirect
549. C3#80615semidirect

Maximal subgroups

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

subgroupindex
#105961472
#105960522
C32×#4642
#105928872
#105928862
#105928702
#105928682
#105927552
C4×#37552
#105925462
#105925332
#105925042
#105925032
#105924832
C3⋊D3×#1022
#806153