Finite Group Databasebeta

← #11887367

Subgroups — #11887367

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#10596029C211yesmaximal, characteristic, complemented
2#10596025C211yesmaximal, characteristic, complemented
3C32×C4×D8C211yesmaximal, characteristic, complemented
4#10592857C211yesmaximal, characteristic, complemented
5#10592855C211yesmaximal, characteristic, complemented
6#10592715C211yesmaximal, characteristic, complemented
7#10592708C211yesmaximal, characteristic, complemented
8#10592584C211yesmaximal, characteristic, complemented
9#10592583C211yesmaximal, characteristic, complemented
10#10592477C211yesmaximal, characteristic, complemented
11#10592474C211yesmaximal, characteristic, complemented
12#10592471C211yesmaximal, characteristic, complemented
13C3⋊D3×#102C211yesmaximal, characteristic, complemented
14#10592396C211yesmaximal, characteristic, complemented
15C8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
16#79609—34nomaximal
17C2×#3830C2211yescharacteristic
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C32×D8C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic, complemented
22#64147C2211yescharacteristic
23#64147C2211yescharacteristic, complemented
24C2×#3754C2211yescharacteristic, complemented
25C2×#3753C2211yescharacteristic
26#64139—21no—
27#64138—21no—
28C4×#638—21no—
29C2×#3752—21no—
30C2×C8×C3⋊D3C2211yescharacteristic
31C2×C8×C3⋊D3C2211yescharacteristic, complemented
32#64106C2211yescharacteristic
33#64104C2211yescharacteristic
34#64101C2211yescharacteristic, complemented
35C4⋊C4×C3⋊D3C2211yescharacteristic
36#64095—21no—
37#64093—21no—
38#64091—21no—
39#64088—21no—
40#64084C2211yescharacteristic
41C4×C4⋊(C3⋊D3)C2211yescharacteristic
42#64079C2211yescharacteristic, complemented
43C32×#107C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45C32×#102C2211yescharacteristic, complemented
46C32×C4×C8C2211yescharacteristic, complemented
47#63659C2211yescharacteristic
48#63659C2211yescharacteristic
49#63648C2211yescharacteristic
50#63648C2211yescharacteristic
51#63647C2211yescharacteristic
52#63647C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54#63643C2211yescharacteristic, complemented
55#63637C2211yescharacteristic, complemented
56#63636C2211yescharacteristic
57#63635C2211yescharacteristic, complemented
58#63634C2211yescharacteristic, complemented
59C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
60#5558—34no—
61#5554—34no—
62C3×C4×D8D314yescomplemented
63#5158—34no—
64#5156—34no—
65#5016—34no—
66#5009—34no—
67#4885—34no—
68#4884—34no—
69#4778—34no—
70#4775—34no—
71#4772—34no—
72D3×#102—34no—
73#4697—34no—
74C8×D12—34no—
75C23×C3⋊D3—21no—
76C2×C32×D4C2311yescharacteristic
77C2×C32×D4C2311yescharacteristic
78C22×C32×C4—21no—
79C22×C32×C4—21no—
80C2×#638—21no—
81C2×#638—21no—
82C2×#638—21no—
83C2×#638—21no—
84C22×C3⋊Dic3—21no—
85#3830—22no—
86#3830—41no—
87D4×C3⋊D3—22no—
88D4×C3⋊D3—41no—
89C2×C4⋊(C3⋊D3)—21no—
90C2×C4⋊(C3⋊D3)D411yescharacteristic
91C2×C4⋊(C3⋊D3)C2311yescharacteristic
92C2×C4×C3⋊D3—21no—
93C2×C4×C3⋊D3C2311yescharacteristic
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C32×D8—22no—
97C2×C32×C8C2311yescharacteristic
98C2×C32×C8C2311yescharacteristic
99C32×C4⋊C4C2311yescharacteristic
100C32×C4⋊C4C2311yescharacteristic
101C32×C22⋊C4—21no—
102C32×C22⋊C4—21no—
103C32×C42C2311yescharacteristic
104#3757—21no—
105#3757—21no—
106#3754—41no—
107#3753—41no—
108#3752—21no—
109#3752—21no—
110#3752—21no—
111#3752—21no—
112#3752—21no—
113#3752D411yescharacteristic
114#3752D411yescharacteristic
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)D411yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
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#3297—91noSylow
128C2×#237—34no—
129C2×D3×D4—34no—
130C2×C3×D8C2×D314yes—
131C3×C4×D4C2×D314yes—
132C3×C4×D4C2×D314yescomplemented
133#938—34no—
134#938—34no—
135C2×#214—34no—
136C2×#213—34no—
137#930—64no—
138#929—64no—
139C4×#67—64no—
140C2×(C2×D3)⋊C4—64no—
141C2×D3×C8—34no—
142C2×D3×C8—34no—
143#897—34no—
144#895—34no—
145#892—34no—
146D3×C4⋊C4—34no—
147#886—64no—
148#884—64no—
149#882—64no—
150#879—64no—
151#875—34no—
152C4×D12—34no—
153#870—34no—
154C3×#107C2×D314yescomplemented
155C3×#102C2×D314yes—
156C3×#102C2×D314yescomplemented
157C3×C4×C8C2×D314yescomplemented
158#832—34no—
159#832—34no—
160#821—34no—
161#821—34no—
162(C2×D3)⋊C8—34no—
163(C2×D3)⋊C8—34no—
164#816—34no—
165#816—34no—
166#810—34no—
167#809—34no—
168#808—34no—
169#807—34no—
170C4⋊(C3⋊C8)—34no—
171C23×C32—21no—
172C23×C32—21no—
173C22×C3⋊D3—21no—
174C22×C3⋊D3—42no—
175C22×C3⋊D3—42no—
176C22×C3⋊D3—81no—
177C22×C3⋊D3C2×D411yescharacteristic
178C22×C3⋊D3C2×D411yescharacteristic
179C32×D4—21no—
180C32×D4—21no—
181C32×D4—21no—
182C32×D4#4112yes—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—81no—
186C2×C32×C4—81no—
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2411yescharacteristic
190#638—42no—
191#638—42no—
192#638—42no—
193#638—81no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—42no—
198C2×C3⋊Dic3C2×D411yescharacteristic
199C2×C3⋊Dic3C2×D411yescharacteristic
200C4⋊(C3⋊D3)—22no—
201C4⋊(C3⋊D3)—21no—
202C4⋊(C3⋊D3)—21no—
203C4⋊(C3⋊D3)—81no—
204C4×C3⋊D3—21no—
205C4×C3⋊D3—21no—
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×D8C3⋊D311yescharacteristic, complemented
227C8×D4—91no—
228#416—91no—
229C2×#102—91no—
230C23×D3—64no—
231C2×C3×D4C22×D314yes—
232C2×C3×D4C22×D314yes—
233C22×C3×C4—24no—
234C22×C3×C4—24no—
235C2×#67—64no—
236C2×#67—64no—
237C2×#67—64no—
238C2×#67—64no—
239C22×Dic3—64no—
240#237—68no—
241#237—124no—
242D3×D4—68no—
243D3×D4—124no—
244C2×D12—34no—
245C2×D12—34no—
246C2×D12—64no—
247C2×C4×D3—34no—
248C2×C4×D3—34no—
249C2×C4×D3—64no—
250C2×Dic6—34no—
251C3×D8—28no—
252C2×C3×C8C22×D314yes—
253C2×C3×C8C22×D314yes—
254C3×C4⋊C4C22×D314yes—
255C3×C4⋊C4C22×D314yes—
256C3×C22⋊C4—24no—
257C3×C22⋊C4—24no—
258C3×C42C22×D314yes—
259#217—64no—
260#217—64no—
261#214—124no—
262#213—124no—
263(C2×D3)⋊C4—34no—
264(C2×D3)⋊C4—34no—
265(C2×D3)⋊C4—64no—
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—34no—
273C4⋊Dic3—64no—
274Dic3⋊C4—64no—
275Dic3⋊C4—64no—
276Dic3⋊C4—64no—
277C4×Dic3—64no—
278C2×C3⋊C8—34no—
279C2×C3⋊C8—34no—
280D3×C8—124no—
281D3×C8—124no—
282C22×C32—22no—
283C22×C32—41no—
284C22×C32—41no—
285C22×C32—41no—
286C22×C32—41no—
287C22×C32—41no—
288C22×C32C22×D411yescharacteristic
289C2×C3⋊D3—21no—
290C2×C3⋊D3—21no—
291C2×C3⋊D3—21no—
292C2×C3⋊D3—21no—
293C2×C3⋊D3—21no—
294C2×C3⋊D3—41no—
295C2×C3⋊D3—41no—
296C2×C3⋊D3—41no—
297C2×C3⋊D3—84no—
298C2×C3⋊D3#13512yes—
299C32×C4—21no—
300C32×C4—21no—
301C32×C4—41no—
302C32×C4—41no—
303C32×C4C2×#4111yescharacteristic
304C32×C4H(5,𝔽2)11yescharacteristic
305C3⋊Dic3—21no—
306C3⋊Dic3—21no—
307C3⋊Dic3—41no—
308C3⋊Dic3—41no—
309C3⋊Dic3—41no—
310C2×#41—91no—
311C22×D4—91no—
312C2×SD16—91no—
313C2×D8—91no—
314C2×D8C2×C3⋊D311yescharacteristic
315C22×C8—91no—
316C22×C8—91no—
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—181no—
331C4×D4C2×C3⋊D311yescharacteristic
332C4×D4C2×C3⋊D311yescharacteristic, complemented
333#117—91no—
334C2×C4⋊C4—91no—
335C2×C22⋊C4—181no—
336#107—91no—
337#107C2×C3⋊D311yescharacteristic, complemented
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#102—91no—
347#102—91no—
348#102C2×C3⋊D311yescharacteristic
349#102C2×C3⋊D311yescharacteristic, complemented
350C22⋊C8—91no—
351C22⋊C8—91no—
352C4×C8C2×C3⋊D311yescharacteristic, complemented
353C23×C3—24no—
354C23×C3—24no—
355C22×D3—34no—
356C22×D3—34no—
357C22×D3—64no—
358C22×D3—128no—
359C22×D3—128no—
360C22×D3—244no—
361C3×D4—24no—
362C3×D4—24no—
363C3×D4—24no—
364C3×D4#23518yes—
365C2×C3×C4—24no—
366C2×C3×C4—24no—
367C2×C3×C4—84no—
368C2×C3×C4—84no—
369C2×C3×C4D3×D414yes—
370C2×C3×C4D3×D414yes—
371C2×C3×C4C23×D314yes—
372#67—128no—
373#67—128no—
374#67—128no—
375#67—244no—
376C2×Dic3—34no—
377C2×Dic3—34no—
378C2×Dic3—64no—
379C2×Dic3—64no—
380C2×Dic3—64no—
381C2×Dic3—128no—
382D12—68no—
383D12—64no—
384D12—64no—
385D12—244no—
386C4×D3—64no—
387C4×D3—64no—
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—42no—
398C2×C32—81no—
399C2×C32#54611yescharacteristic
400C2×C32C2×#13511yescharacteristic
401C2×C32#57611yescharacteristic
402C3⋊D3—22no—
403C3⋊D3—41no—
404C3⋊D3—81no—
405C24—181no—
406#41—182no—
407#41—361no—
408C2×Q8—91no—
409C2×D4—91no—
410C2×D4—91no—
411C2×D4—181no—
412C2×D4—181no—
413C2×D4—182no—
414C2×D4—181no—
415C2×D4—181no—
416C2×D4—181no—
417C2×D4—361no—
418C2×D4C22×C3⋊D311yescharacteristic
419C2×D4C22×C3⋊D311yescharacteristic
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—91no—
423C22×C4—91no—
424C22×C4—181no—
425C22×C4—181no—
426SD16—361no—
427D8—22no—
428D8—361no—
429C2×C8—91no—
430C2×C8—91no—
431C2×C8—361no—
432C2×C8—361no—
433C2×C8C22×C3⋊D311yescharacteristic
434C2×C8C22×C3⋊D311yescharacteristic
435C4⋊C4—91no—
436C4⋊C4—91no—
437C4⋊C4—91no—
438C4⋊C4—181no—
439C4⋊C4—181no—
440C4⋊C4—181no—
441C4⋊C4—181no—
442C4⋊C4C22×C3⋊D311yescharacteristic
443C4⋊C4C22×C3⋊D311yescharacteristic
444C22⋊C4—21no—
445C22⋊C4—21no—
446C22⋊C4—91no—
447C22⋊C4—91no—
448C22⋊C4—181no—
449C22⋊C4—181no—
450C22⋊C4—181no—
451C22⋊C4—181no—
452C22⋊C4—181no—
453C22⋊C4—181no—
454C22⋊C4—181no—
455C42—181no—
456C42C22×C3⋊D311yescharacteristic
457C22×C3—28no—
458C22×C3—44no—
459C22×C3—44no—
460C22×C3—44no—
461C22×C3—44no—
462C22×C3—44no—
463C22×C3C2×D3×D414yes—
464C2×D3—38no—
465C2×D3—64no—
466C2×D3—64no—
467C2×D3—64no—
468C2×D3—64no—
469C2×D3—64no—
470C2×D3—124no—
471C2×D3—124no—
472C2×D3—124no—
473C2×D3—2416no—
474C3×C4—24no—
475C3×C4—24no—
476C3×C4—44no—
477C3×C4—44no—
478C3×C4C2×#23514yes—
479C3×C4#100914yes—
480Dic3—64no—
481Dic3—64no—
482Dic3—124no—
483Dic3—124no—
484Dic3—124no—
485C32#329711yescharacteristic, complemented, Sylow
486C23—21no—
487C23—21no—
488C23—91no—
489C23—91no—
490C23—181no—
491C23—362no—
492C23—362no—
493C23—721no—
494Q8—181no—
495Q8—181no—
496D4—21no—
497D4—21no—
498D4—21no—
499D4—182no—
500D4—181no—
501D4—181no—
502D4—362no—
503D4—362no—
504D4—362no—
505D4—721no—
506D4—721no—
507D4#382812yes—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—81no—
511C2×C4—81no—
512C2×C4—91no—
513C2×C4—91no—
514C2×C4—181no—
515C2×C4—181no—
516C2×C4—181no—
517C2×C4—181no—
518C2×C4—181no—
519C2×C4—181no—
520C2×C4—181no—
521C2×C4—362no—
522C2×C4—721no—
523C2×C4D4×C3⋊D311yescharacteristic
524C2×C4D4×C3⋊D311yescharacteristic
525C2×C4C23×C3⋊D311yescharacteristic
526C8—21no—
527C8—21no—
528C8—181no—
529C8—181no—
530C2×C3—48no—
531C2×C3—84no—
532C2×C3#555014yes—
533C2×C3#575714yes—
534C2×C3D3×#13514yes—
535D3—68no—
536D3—124no—
537D3—244no—
538C22—22no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—92no—
545C22—181no—
546C22—181no—
547C22—181no—
548C22—181no—
549C22—181no—
550C22—361no—
551C22—361no—
552C22—361no—
553C22—724no—
554C22C2×D4×C3⋊D311yescharacteristic
555C4—21no—
556C4—21no—
557C4—41no—
558C4—41no—
559C4—181no—
560C4—181no—
561C4—361no—
562C4—361no—
563C4—361no—
564C4C2×#382811yescharacteristic
565C4#6436611yescharacteristic
566C3#7960914yescomplemented
567C2—42no—
568C2—81no—
569C2—182no—
570C2—361no—
571C2—721no—
572C2#1059602111yescharacteristic
573C2#1059622811yescharacteristic
574C2C3⋊D3×#13511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×D8C2
socleC22×C32C22×D4
hypercenterC4×D8C3⋊D3
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #10596029C2semidirect
2. #10596025C2semidirect
3. C32×C4×D8C2semidirect
4. #10592857C2semidirect
5. #10592855C2semidirect
6. #10592715C2semidirect
7. #10592708C2semidirect
8. #10592584C2semidirect
9. #10592583C2semidirect
10. #10592477C2semidirect
11. #10592474C2semidirect
12. #10592471C2semidirect
13. C3⋊D3×#102C2semidirect
14. #10592396C2semidirect
15. C8×C4⋊(C3⋊D3)C2semidirect
21. C32×C4×D4C22semidirect
23. #64147C22semidirect
24. C2×#3754C22semidirect
31. C2×C8×C3⋊D3C22semidirect
34. #64101C22semidirect
42. #64079C22semidirect
43. C32×#107C22semidirect
45. C32×#102C22semidirect
46. C32×C4×C8C22semidirect
52. #63647C22semidirect
53. #63643C22semidirect
54. #63643C22semidirect
55. #63637C22semidirect
57. #63635C22semidirect
58. #63634C22semidirect
59. C4⋊(C3⋊(C3⋊C8))C22semidirect
62. C3×C4×D8D3semidirect
132. C3×C4×D4C2×D3semidirect
154. C3×#107C2×D3semidirect
156. C3×#102C2×D3semidirect
157. C3×C4×C8C2×D3semidirect
226. C4×D8C3⋊D3semidirect
332. C4×D4C2×C3⋊D3semidirect
337. #107C2×C3⋊D3semidirect
349. #102C2×C3⋊D3semidirect
352. C4×C8C2×C3⋊D3semidirect
485. C32#3297semidirect
566. C3#79609semidirect

Maximal subgroups

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

subgroupindex
#105960292
#105960252
C32×C4×D82
#105928572
#105928552
#105927152
#105927082
#105925842
#105925832
#105924772
#105924742
#105924712
C3⋊D3×#1022
#105923962
C8×C4⋊(C3⋊D3)2
#796093