Finite Group Databasebeta

← #11887340

Subgroups — #11887340

Order 1152.

1260 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596277C211yesmaximal, characteristic, complemented
2#10595985C211yesmaximal, characteristic, complemented
3C2×C32×#102C211yesmaximal, characteristic, complemented
4#10592916C211yesmaximal, characteristic, complemented
5#10592813C211yesmaximal, characteristic, complemented
6C8×#638C211yesmaximal, characteristic, complemented
7#10592669C211yesmaximal, characteristic, complemented
8#10592486C211yesmaximal, characteristic, complemented
9#10592480C211yesmaximal, characteristic, complemented
10#10592478C211yesmaximal, characteristic, complemented
11#10592474C211yesmaximal, characteristic, complemented
12#10592471C211yesmaximal, characteristic, complemented
13#10592467C211yesmaximal, characteristic, complemented
14#10592462C211yesmaximal, characteristic, complemented
15#10592455C211yesmaximal, characteristic, complemented
16#78760—34nomaximal
17C22×C32×D4C2211yescharacteristic
18C2×#3830C2211yescharacteristic
19C22×C32×C8C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21#64162—21no—
22C2×#3757—21no—
23#64148—21no—
24#64147C2211yescharacteristic
25#64145C2211yescharacteristic
26#64144—21no—
27D4×C3⋊Dic3C2211yescharacteristic
28C2×#3753C2211yescharacteristic
29C2×#3753C2211yescharacteristic
30#64139—21no—
31#64139C2211yescharacteristic
32C4×#638—21no—
33C4×#638C2211yescharacteristic
34#64133C2211yescharacteristic
35C2×#3744C2211yescharacteristic, complemented
36C2×C8×C3⋊D3C2211yescharacteristic, complemented
37#64107—21no—
38#64104C2211yescharacteristic, complemented
39#64103—21no—
40#64102C2211yescharacteristic, complemented
41#64101C2211yescharacteristic, complemented
42#64099C2211yescharacteristic, complemented
43C32×#102C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×#102C2211yescharacteristic
47#63659C2211yescharacteristic
48#63659C2211yescharacteristic
49#63657C2211yescharacteristic
50#63648C2211yescharacteristic, complemented
51#63647C2211yescharacteristic, complemented
52#63644C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54#63641C2211yescharacteristic, complemented
55C8×C3⋊Dic3C2211yescharacteristic, complemented
56#63637C2211yescharacteristic, complemented
57#63637C2211yescharacteristic, complemented
58#63634C2211yescharacteristic, complemented
59#63634C2211yescharacteristic, complemented
60#5806—34no—
61#5514—34no—
62C2×C3×#102D314yescomplemented
63#5217—34no—
64#5114—34no—
65C8×#67—34no—
66#4970—34no—
67#4787—34no—
68#4781—34no—
69#4779—34no—
70#4775—34no—
71#4772—34no—
72#4768—34no—
73#4763—34no—
74#4756—34no—
75C24×C32—21no—
76C2×C32×D4—22no—
77C2×C32×D4—21no—
78C2×C32×D4—41no—
79C2×C32×D4C2311yescharacteristic
80C2×C32×D4C2311yescharacteristic
81C22×C32×C4—21no—
82C22×C32×C4C2311yescharacteristic
83C2×#638—21no—
84C2×#638—21no—
85C2×#638—21no—
86C2×#638D411yescharacteristic
87C22×C3⋊Dic3—21no—
88C22×C3⋊Dic3—21no—
89#3830—22no—
90#3830—41no—
91C2×C4⋊(C3⋊D3)—21no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C32×C8—41no—
97C2×C32×C8C2311yescharacteristic
98C2×C32×C8C2311yescharacteristic
99C32×C4⋊C4—21no—
100C32×C4⋊C4C2311yescharacteristic
101C32×C4⋊C4C2311yescharacteristic
102#3757—21no—
103#3757—21no—
104#3757—21no—
105#3757—21no—
106#3757—21no—
107#3757D411yescharacteristic
108#3753—22no—
109#3753—41no—
110#3752—21no—
111#3752—21no—
112#3752—21no—
113#3752—21no—
114#3752D411yescharacteristic
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119#3750—21no—
120#3750D411yescharacteristic
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125#3744—41no—
126C8×C3⋊D3—41no—
127#3297—91noSylow
128C22×C3×D4C2×D314yes—
129C2×#237—34no—
130C22×C3×C8C2×D314yes—
131C2×C3×C4⋊C4C2×D314yes—
132#953—64no—
133C2×#217—64no—
134#939—64no—
135#938—34no—
136#936—34no—
137#935—64no—
138D4×Dic3—34no—
139C2×#213—34no—
140C2×#213—34no—
141#930—34no—
142#930—64no—
143C4×#67—34no—
144C4×#67—64no—
145#924—34no—
146C2×#204—34no—
147C2×D3×C8—34no—
148#898—64no—
149#895—34no—
150#894—64no—
151#893—34no—
152#892—34no—
153#890—34no—
154C3×#102C2×D314yes—
155C3×#102C2×D314yes—
156C3×#102C2×D314yes—
157C3×#102C2×D314yes—
158#832—34no—
159#832—34no—
160#830—34no—
161#821—34no—
162(C2×D3)⋊C8—34no—
163#817—34no—
164#816—34no—
165Dic3⋊C8—34no—
166C8×Dic3—34no—
167#810—34no—
168#810—34no—
169#807—34no—
170#807—34no—
171C23×C32—21no—
172C23×C32—21no—
173C23×C32—42no—
174C23×C32—42no—
175C23×C32—81no—
176C23×C32C2×D411yescharacteristic
177C22×C3⋊D3—21no—
178C22×C3⋊D3C2×D411yescharacteristic
179C32×D4—21no—
180C32×D4—21no—
181C32×D4—21no—
182C32×D4—42no—
183C32×D4#4112yes—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4—81no—
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2411yescharacteristic
191#638—22no—
192#638—42no—
193#638—42no—
194#638—81no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—21no—
198C2×C3⋊Dic3—42no—
199C2×C3⋊Dic3—81no—
200C2×C3⋊Dic3C2×D411yescharacteristic
201C2×C3⋊Dic3C2×D411yescharacteristic
202C2×C3⋊Dic3C2×D411yescharacteristic
203C4⋊(C3⋊D3)—21no—
204C4⋊(C3⋊D3)—21no—
205C4⋊(C3⋊D3)—81no—
206C4×C3⋊D3—21no—
207C4×C3⋊D3—21no—
208C4×C3⋊D3—81no—
209#634—21no—
210#634—21no—
211C32×C8—21no—
212C32×C8—21no—
213C3⋊(C3⋊C8)—21no—
214C3⋊(C3⋊C8)—21no—
215#553—91no—
216#546—91no—
217#488—91no—
218#484—91no—
219#482—91no—
220#478—91no—
221#466—91no—
222#465—91no—
223#463—91no—
224#449—91no—
225#447—91no—
226C4×D8—91no—
227C8×D4—91no—
228#416—91no—
229C2×#102C3⋊D311yescharacteristic, complemented
230C24×C3—24no—
231C2×C3×D4—28no—
232C2×C3×D4—24no—
233C2×C3×D4—44no—
234C2×C3×D4C22×D314yes—
235C2×C3×D4C22×D314yes—
236C22×C3×C4—24no—
237C22×C3×C4C22×D314yes—
238C2×#67—34no—
239C2×#67—64no—
240C2×#67—64no—
241C2×#67—64no—
242C22×Dic3—64no—
243C22×Dic3—64no—
244#237—68no—
245#237—124no—
246C2×D12—34no—
247C2×D12—64no—
248C2×C4×D3—34no—
249C2×C4×D3—64no—
250C2×Dic6—34no—
251C2×C3×C8—44no—
252C2×C3×C8C22×D314yes—
253C2×C3×C8C22×D314yes—
254C3×C4⋊C4—24no—
255C3×C4⋊C4C22×D314yes—
256C3×C4⋊C4C22×D314yes—
257#217—34no—
258#217—64no—
259#217—64no—
260#217—64no—
261#217—64no—
262#217—64no—
263#213—68no—
264#213—124no—
265(C2×D3)⋊C4—34no—
266(C2×D3)⋊C4—64no—
267(C2×D3)⋊C4—64no—
268(C2×D3)⋊C4—64no—
269(C2×D3)⋊C4—64no—
270C4⋊Dic3—34no—
271C4⋊Dic3—34no—
272C4⋊Dic3—64no—
273Dic3⋊C4—34no—
274Dic3⋊C4—64no—
275Dic3⋊C4—64no—
276C4×Dic3—34no—
277C4×Dic3—64no—
278C2×C3⋊C8—34no—
279C2×C3⋊C8—34no—
280#204—124no—
281D3×C8—124no—
282C22×C32—21no—
283C22×C32—21no—
284C22×C32—22no—
285C22×C32—41no—
286C22×C32—41no—
287C22×C32—41no—
288C22×C32—41no—
289C22×C32—41no—
290C22×C32—84no—
291C22×C32#13512yes—
292C22×C32C22×D411yescharacteristic
293C2×C3⋊D3—21no—
294C2×C3⋊D3—21no—
295C2×C3⋊D3—21no—
296C2×C3⋊D3—41no—
297C2×C3⋊D3—41no—
298C2×C3⋊D3—41no—
299C32×C4—21no—
300C32×C4—41no—
301C32×C4—41no—
302C32×C4C2×#4111yescharacteristic
303C32×C4H(5,𝔽2)11yescharacteristic
304C3⋊Dic3—21no—
305C3⋊Dic3—21no—
306C3⋊Dic3—21no—
307C3⋊Dic3—41no—
308C3⋊Dic3—41no—
309C3⋊Dic3—41no—
310C2×#41—91no—
311C22×D4C2×C3⋊D311yescharacteristic
312C2×SD16—91no—
313C2×D8—91no—
314C2×D8—91no—
315C22×C8—91no—
316C22×C8C2×C3⋊D311yescharacteristic
317#126—181no—
318#125—91no—
319#124—91no—
320#123—181no—
321#123—181no—
322C22⋊Q8—91no—
323#121—91no—
324#121—91no—
325#121—91no—
326#121—181no—
327#121—181no—
328#120—181no—
329C4×D4—91no—
330C4×D4—91no—
331C4×D4—91no—
332C4×D4—181no—
333#117—91no—
334C2×C4⋊C4C2×C3⋊D311yescharacteristic
335C2×C22⋊C4—181no—
336#107—91no—
337#107—91no—
338#106—91no—
339C4⋊C8—91no—
340#103—91no—
341#103—91no—
342#103—91no—
343#102—91no—
344#102—91no—
345#102—91no—
346#102C2×C3⋊D311yescharacteristic
347#102C2×C3⋊D311yescharacteristic
348#102C2×C3⋊D311yescharacteristic
349#102C2×C3⋊D311yescharacteristic
350C22⋊C8—91no—
351C22⋊C8—91no—
352C4×C8—91no—
353C23×C3—24no—
354C23×C3—24no—
355C23×C3—48no—
356C23×C3—48no—
357C23×C3—84no—
358C23×C3D3×D414yes—
359C22×D3—34no—
360C22×D3—64no—
361C3×D4—24no—
362C3×D4—24no—
363C3×D4—24no—
364C3×D4—48no—
365C3×D4#23518yes—
366C2×C3×C4—24no—
367C2×C3×C4—24no—
368C2×C3×C4—24no—
369C2×C3×C4—24no—
370C2×C3×C4—84no—
371C2×C3×C4D3×D414yes—
372C2×C3×C4C23×D314yes—
373#67—68no—
374#67—128no—
375#67—128no—
376#67—244no—
377C2×Dic3—34no—
378C2×Dic3—34no—
379C2×Dic3—34no—
380C2×Dic3—64no—
381C2×Dic3—64no—
382C2×Dic3—64no—
383C2×Dic3—128no—
384C2×Dic3—244no—
385D12—64no—
386D12—64no—
387D12—244no—
388C4×D3—64no—
389C4×D3—64no—
390C4×D3—244no—
391Dic6—64no—
392Dic6—64no—
393C3×C8—24no—
394C3×C8—24no—
395C3⋊C8—64no—
396C3⋊C8—64no—
397C2×C32—22no—
398C2×C32—42no—
399C2×C32—81no—
400C2×C32#54611yescharacteristic
401C2×C32C2×#13511yescharacteristic
402C2×C32#57611yescharacteristic
403C3⋊D3—41no—
404C3⋊D3—81no—
405C24—21no—
406#41—182no—
407#41—361no—
408C2×Q8—91no—
409C2×D4—22no—
410C2×D4—21no—
411C2×D4—41no—
412C2×D4—91no—
413C2×D4—91no—
414C2×D4—181no—
415C2×D4—181no—
416C2×D4—181no—
417C2×D4—181no—
418C2×D4C22×C3⋊D311yescharacteristic
419C2×D4C22×C3⋊D311yescharacteristic
420C22×C4—21no—
421C22×C4—91no—
422C22×C4—181no—
423C22×C4—181no—
424C22×C4—181no—
425C22×C4C22×C3⋊D311yescharacteristic
426SD16—361no—
427D8—182no—
428D8—361no—
429C2×C8—41no—
430C2×C8—91no—
431C2×C8—91no—
432C2×C8—361no—
433C2×C8C22×C3⋊D311yescharacteristic
434C2×C8C22×C3⋊D311yescharacteristic
435C4⋊C4—21no—
436C4⋊C4—91no—
437C4⋊C4—91no—
438C4⋊C4—91no—
439C4⋊C4—181no—
440C4⋊C4—181no—
441C4⋊C4—181no—
442C4⋊C4C22×C3⋊D311yescharacteristic
443C4⋊C4C22×C3⋊D311yescharacteristic
444C22⋊C4—91no—
445C22⋊C4—91no—
446C22⋊C4—181no—
447C22⋊C4—181no—
448C22⋊C4—181no—
449C22⋊C4—181no—
450C22⋊C4—181no—
451C22⋊C4—181no—
452C22⋊C4—181no—
453C22⋊C4—181no—
454C22⋊C4—181no—
455C42—91no—
456C42—181no—
457C22×C3—24no—
458C22×C3—24no—
459C22×C3—28no—
460C22×C3—44no—
461C22×C3—44no—
462C22×C3—44no—
463C22×C3—44no—
464C22×C3—44no—
465C22×C3—816no—
466C22×C3#91618yes—
467C22×C3C2×D3×D414yes—
468C2×D3—64no—
469C2×D3—64no—
470C2×D3—64no—
471C2×D3—124no—
472C2×D3—124no—
473C2×D3—124no—
474C3×C4—24no—
475C3×C4—44no—
476C3×C4—44no—
477C3×C4C2×#23514yes—
478C3×C4#100414yes—
479Dic3—64no—
480Dic3—64no—
481Dic3—64no—
482Dic3—124no—
483Dic3—124no—
484Dic3—124no—
485C32#329711yescharacteristic, complemented, Sylow
486C23—21no—
487C23—21no—
488C23—42no—
489C23—42no—
490C23—81no—
491C23—91no—
492C23—181no—
493C23D4×C3⋊D311yescharacteristic
494Q8—181no—
495Q8—181no—
496D4—21no—
497D4—21no—
498D4—21no—
499D4—42no—
500D4—182no—
501D4—181no—
502D4—181no—
503D4—362no—
504D4—362no—
505D4—721no—
506D4—721no—
507D4#382812yes—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—81no—
513C2×C4—91no—
514C2×C4—91no—
515C2×C4—91no—
516C2×C4—181no—
517C2×C4—181no—
518C2×C4—181no—
519C2×C4—181no—
520C2×C4—181no—
521C2×C4—362no—
522C2×C4—721no—
523C2×C4—721no—
524C2×C4D4×C3⋊D311yescharacteristic
525C2×C4C23×C3⋊D311yescharacteristic
526C8—21no—
527C8—21no—
528C8—181no—
529C8—181no—
530C2×C3—28no—
531C2×C3—48no—
532C2×C3—84no—
533C2×C3#549014yes—
534C2×C3#575714yes—
535C2×C3C2×#91614yes—
536D3—124no—
537D3—244no—
538C22—21no—
539C22—21no—
540C22—22no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—84no—
547C22—181no—
548C22—181no—
549C22—181no—
550C22—361no—
551C22—361no—
552C22—361no—
553C22#6412512yes—
554C22C2×D4×C3⋊D311yescharacteristic
555C4—21no—
556C4—41no—
557C4—41no—
558C4—181no—
559C4—181no—
560C4—181no—
561C4—361no—
562C4—361no—
563C4—361no—
564C4C2×#382811yescharacteristic
565C4#6436111yescharacteristic
566C3#7876014yescomplemented
567C2—22no—
568C2—42no—
569C2—81no—
570C2—361no—
571C2—721no—
572C2#1059596111yescharacteristic
573C2#1059622811yescharacteristic
574C2C2×#6412511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#102C2
socleC22×C32C22×D4
hypercenterC2×#102C3⋊D3
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #10596277C2semidirect
2. #10595985C2semidirect
3. C2×C32×#102C2semidirect
4. #10592916C2semidirect
5. #10592813C2semidirect
6. C8×#638C2semidirect
7. #10592669C2semidirect
8. #10592486C2semidirect
9. #10592480C2semidirect
10. #10592478C2semidirect
11. #10592474C2semidirect
12. #10592471C2semidirect
13. #10592467C2semidirect
14. #10592462C2semidirect
15. #10592455C2semidirect
35. C2×#3744C22semidirect
36. C2×C8×C3⋊D3C22semidirect
38. #64104C22semidirect
40. #64102C22semidirect
41. #64101C22semidirect
42. #64099C22semidirect
50. #63648C22semidirect
51. #63647C22semidirect
52. #63644C22semidirect
53. #63643C22semidirect
54. #63641C22semidirect
55. C8×C3⋊Dic3C22semidirect
56. #63637C22semidirect
57. #63637C22semidirect
58. #63634C22semidirect
59. #63634C22semidirect
62. C2×C3×#102D3semidirect
229. C2×#102C3⋊D3semidirect
485. C32#3297semidirect
566. C3#78760semidirect

Maximal subgroups

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

subgroupindex
#105962772
#105959852
C2×C32×#1022
#105929162
#105928132
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