Finite Group Databasebeta

← #11895770

Subgroups — #11895770

Order 1152.

948 conjugacy classes of subgroups.

The subgroup lattice has 585 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596189C211yesmaximal, characteristic, complemented
2#10593956C211yesmaximal, characteristic, complemented
3C3×#5072C211yesmaximal, characteristic, complemented
4C3×#5070C211yesmaximal, characteristic, complemented
5#10591480C212yesmaximal, complemented
6#10591479C212yesmaximal, complemented
7#10591436C212yesmaximal, complemented
8#10591433C212yesmaximal, complemented
9C4×#3714C211yesmaximal, characteristic, complemented
10#10590300C211yesmaximal, characteristic, complemented
11#10590296C211yesmaximal, characteristic, complemented
12#81586—31nomaximal
13#80320—31nomaximal
14C2×#3830—21no—
15C32×#127C2211yescharacteristic
16#64149C2212yes—
17#64148—22no—
18#64147—21no—
19D4×C3⋊Dic3C2212yes—
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C2×C3×#213C2212yes—
23C3×C4×D12C2211yescharacteristic
24C3×#869C2211yescharacteristic
25#63898C2212yes—
26D3×C4⋊Dic3—21no—
27#63887—22no—
28#63872C2212yes—
29#63857—21no—
30C2×#3714C2211yescharacteristic
31C3×#832C2212yes—
32C3×#832C2212yes—
33C3×#832C2212yes—
34C3×C4⋊(C3⋊C8)C2211yescharacteristic
35C3×C4×C3⋊C8C2211yescharacteristic
36#63575C2211yescharacteristic
37#63573C2212yes—
38#63572C2212yes—
39#63564C2212yes—
40#63564C2211yescharacteristic
41#63563C2211yescharacteristic
42#63555C2212yes—
43#5730—31no—
44#5718—31no—
45#5718—31no—
46#5718—61no—
47#5543—31no—
48C3×#486—31no—
49C3×#459—31no—
50#5152—32no—
51#5150—32no—
52#5084—31no—
53#5072D311yescharacteristic, complemented
54#5070D311yescharacteristic, complemented
55C4×#213—31no—
56#4842—31no—
57#4831—31no—
58#4786—32no—
59#4785—32no—
60#4766—32no—
61#4764—32no—
62#4764—32no—
63#4763—32no—
64C4×D24—31no—
65#4679—31no—
66C2×C32×D4—21no—
67C2×C32×D4—21no—
68C2×C32×D4C2312yes—
69C2×#638—22no—
70C2×#638—22no—
71C22×C3⋊Dic3—22no—
72#3830—44no—
73C2×C4⋊(C3⋊D3)C2311yescharacteristic
74C2×C4×C3⋊D3—21no—
75C2×#634D411yescharacteristic
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3—21no—
78C2×C3×Dic6—21no—
79C2×D3×Dic3—22no—
80C32×C42C2311yescharacteristic
81#3757—22no—
82#3752—21no—
83C4⋊(C3⋊Dic3)D411yescharacteristic
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85#3750D412yes—
86C4×C3⋊Dic3C2312yes—
87C3×#213—24no—
88C3×(C2×D3)⋊C4—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2312yes—
91C3×C4⋊Dic3C2311yescharacteristic
92C2×C3×C3⋊C8C2312yes—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95Dic3⋊Dic3—22no—
96Dic3⋊Dic3—22no—
97(C2×D3)⋊Dic3—22no—
98#3714—22no—
99#3366—91noSylow
100C2×#237—61no—
101C2×#237—61no—
102C2×#237—62no—
103C2×C3×D8—32no—
104C3×C4⋊Q8—31no—
105C3×#127—21no—
106C3×#127C2×D311yescharacteristic
107C3×#127C2×D311yescharacteristic
108C3×C4×D4—31no—
109#946—62no—
110#940—32no—
111#940—32no—
112#940—62no—
113#939—62no—
114#939—62no—
115#939—64no—
116#938—61no—
117#938—61no—
118#938—62no—
119D4×Dic3—32no—
120D4×Dic3—32no—
121D4×Dic3—32no—
122D4×Dic3—62no—
123C2×#213—31no—
124C2×#213C2×D312yes—
125C2×C4⋊Dic3—61no—
126#924—61no—
127C2×D24—31no—
128#897—61no—
129#893—32no—
130D3×C4⋊C4—61no—
131#890—32no—
132#890—32no—
133#878—62no—
134C4×D12—31no—
135C4×D12—31no—
136C4×D12—61no—
137C4×D12C2×D311yescharacteristic
138#869C2×D311yescharacteristic
139C4×Dic6—31no—
140C4×Dic6—31no—
141C4×Dic6—61no—
142C3×C4⋊C8—31no—
143C3×#102—32no—
144C3×#102—32no—
145C3×#102—32no—
146C3×C4×C8—31no—
147#832—31no—
148#832C2×D312yes—
149#832C2×D312yes—
150#832C2×D312yes—
151#821—31no—
152#821—32no—
153#821—31no—
154#818—31no—
155#817—32no—
156#815—32no—
157#815—32no—
158Dic3⋊C8—32no—
159Dic3⋊C8—32no—
160#809—31no—
161#809—32no—
162#808—32no—
163#807—31no—
164C4⋊(C3⋊C8)C2×D311yescharacteristic
165C4×C3⋊C8C2×D311yescharacteristic
166C23×C32—22no—
167C22×C3⋊D3—21no—
168C22×C3×D3—21no—
169C32×D4—22no—
170C32×D4—22no—
171C32×D4—42no—
172C32×D4—81no—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2411yescharacteristic
176#638—44no—
177#638—82no—
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3—44no—
180C2×C3⋊Dic3C2×D412yes—
181C2×C3⋊Dic3C2×D412yes—
182C4⋊(C3⋊D3)—21no—
183C4⋊(C3⋊D3)—21no—
184C4×C3⋊D3—42no—
185#634—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—21no—
188C3×D12—21no—
189C3×D12#4112yescomplemented
190C3×C4×D3—42no—
191C3×Dic6—81no—
192D3×Dic3—82no—
193C3×C3⋊C8—21no—
194C3×C3⋊C8—22no—
195C3×C3⋊C8—21no—
196#554—91no—
197#550—91no—
198#490—92no—
199#486—31no—
200#478—92no—
201#476—91no—
202#459—31no—
203#459—92no—
204#446—91no—
205#442—92no—
206C4×D8—91no—
207C2×C3×Q8—61no—
208C2×C3×D4—22no—
209C2×C3×D4—22no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—22no—
215C2×C3×D4—31no—
216C2×C3×D4C22×D312yes—
217C2×C3×D4C22×D312yes—
218C22×C3×C4—61no—
219C2×#67—62no—
220C2×#67—62no—
221C2×#67—62no—
222C2×#67—62no—
223C2×#67—64no—
224C2×#67—64no—
225C22×Dic3—62no—
226C22×Dic3—62no—
227C22×Dic3—62no—
228C22×Dic3—64no—
229#237—128no—
230#237—124no—
231#237—124no—
232C2×D12—31no—
233C2×D12—31no—
234C2×D12—61no—
235C2×D12C22×D311yescharacteristic
236C2×C4×D3—21no—
237C2×C4×D3—62no—
238C2×C4×D3—61no—
239C2×C4×D3—61no—
240C2×C4×D3—62no—
241C2×Dic6—21no—
242C2×Dic6—31no—
243C2×Dic6—31no—
244C2×Dic6—61no—
245C3×D8—64no—
246C2×C3×C8—31no—
247C2×C3×C8—32no—
248C2×C3×C8—31no—
249C3×C4⋊C4—31no—
250C3×C4⋊C4—32no—
251C3×C4⋊C4—61no—
252C3×C22⋊C4—61no—
253C3×C42—21no—
254C3×C42C22×D311yescharacteristic
255C3×C42C22×D311yescharacteristic
256#217—62no—
257#217—62no—
258#217—62no—
259#217—64no—
260#213—24no—
261#213—62no—
262(C2×D3)⋊C4—21no—
263(C2×D3)⋊C4—62no—
264(C2×D3)⋊C4—62no—
265(C2×D3)⋊C4—61no—
266(C2×D3)⋊C4—61no—
267C4⋊Dic3—21no—
268C4⋊Dic3—31no—
269C4⋊Dic3—31no—
270C4⋊Dic3—31no—
271C4⋊Dic3—31no—
272C4⋊Dic3—61no—
273C4⋊Dic3—61no—
274C4⋊Dic3—62no—
275C4⋊Dic3—62no—
276C4⋊Dic3C22×D312yes—
277C4⋊Dic3C22×D311yescharacteristic
278Dic3⋊C4—32no—
279Dic3⋊C4—32no—
280Dic3⋊C4—62no—
281Dic3⋊C4—62no—
282Dic3⋊C4—62no—
283C4×Dic3—32no—
284C4×Dic3—32no—
285C4×Dic3—62no—
286C2×C3⋊C8C22×D311yescharacteristic
287C2×C3⋊C8C22×D311yescharacteristic
288C2×C3⋊C8C22×D312yes—
289D24—62no—
290C22×C32—42no—
291C22×C32—42no—
292C22×C32—42no—
293C22×C32C22×D411yescharacteristic
294C2×C3⋊D3—41no—
295C2×C3⋊D3—41no—
296C2×C3⋊D3—41no—
297C2×C3×D3—22no—
298C2×C3×D3—41no—
299C2×C3×D3—41no—
300C32×C4—21no—
301C32×C4AGL(1,ℤ/8)12yes—
302C32×C4C2×#4111yescharacteristic
303C32×C42−1+411yescharacteristic
304C3⋊Dic3—22no—
305C3⋊Dic3—22no—
306C3⋊Dic3—41no—
307C3×Dic3—41no—
308C3×Dic3—42no—
309C2×#41—181no—
310C2×D8—32no—
311C2×D8—91no—
312C4⋊Q8—31no—
313#127—92no—
314#127D3211yescharacteristic
315#125—92no—
316C22⋊Q8—182no—
317C22⋊Q8—181no—
318#121—181no—
319#121—182no—
320C4×Q8—91no—
321C4×D4—31no—
322C4×D4—92no—
323C4×D4—92no—
324C4×D4—91no—
325C2×C4⋊C4—181no—
326#107—91no—
327#106—92no—
328C4⋊C8—31no—
329C4⋊C8—92no—
330#102—32no—
331#102—32no—
332#102—32no—
333#102—91no—
334#102—92no—
335#102—91no—
336#97—92no—
337C4×C8—31no—
338C23×C3—24no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—61no—
342C22×D3—21no—
343C22×D3—62no—
344C22×D3—61no—
345C22×D3—61no—
346C3×Q8—241no—
347C3×D4—22no—
348C3×D4—22no—
349C3×D4—22no—
350C3×D4—22no—
351C3×D4—32no—
352C3×D4—42no—
353C3×D4—42no—
354C3×D4—44no—
355C3×D4—42no—
356C3×D4—42no—
357C3×D4—61no—
358C3×D4—81no—
359C3×D4—81no—
360C3×D4—82no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—61no—
365C2×C3×C4—62no—
366C2×C3×C4—122no—
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4C23×D311yescharacteristic
372C2×C3×C4C23×D311yescharacteristic
373#67—128no—
374#67—124no—
375#67—124no—
376#67—242no—
377#67—242no—
378#67—244no—
379C2×Dic3—21no—
380C2×Dic3—22no—
381C2×Dic3—32no—
382C2×Dic3—32no—
383C2×Dic3—32no—
384C2×Dic3—32no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—61no—
389C2×Dic3—61no—
390C2×Dic3—128no—
391C2×Dic3—124no—
392C2×Dic3—124no—
393C2×Dic3—242no—
394D12—21no—
395D12—61no—
396D12—61no—
397D12—61no—
398D12—61no—
399D12—121no—
400D12—121no—
401D12#23712yescomplemented
402C4×D3—42no—
403C4×D3—124no—
404C4×D3—122no—
405C4×D3—122no—
406C4×D3—242no—
407Dic6—64no—
408Dic6—62no—
409Dic6—62no—
410Dic6—81no—
411C3×C8—61no—
412C3×C8—62no—
413C3×C8—61no—
414C3⋊C8—22no—
415C3⋊C8—21no—
416C3⋊C8—21no—
417C2×C32—82no—
418C2×C32#54811yescharacteristic
419C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
420C2×C32#57611yescharacteristic
421C3⋊D3—81no—
422C3×D3—42no—
423#41—364no—
424C2×Q8—61no—
425C2×Q8—91no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—31no—
429C2×D4—91no—
430C2×D4—182no—
431C2×D4—182no—
432C2×D4C2×D3212yes—
433C22×C4—61no—
434C22×C4—182no—
435C22×C4—182no—
436C22×C4—181no—
437D8—64no—
438D8—182no—
439C2×C8—31no—
440C2×C8—31no—
441C2×C8—32no—
442C4⋊C4—32no—
443C4⋊C4—31no—
444C4⋊C4—61no—
445C4⋊C4—91no—
446C4⋊C4—92no—
447C4⋊C4—91no—
448C4⋊C4—182no—
449C4⋊C4—182no—
450C22⋊C4—61no—
451C22⋊C4—182no—
452C22⋊C4—182no—
453C22⋊C4—181no—
454C42—92no—
455C42C2×D3211yescharacteristic
456C22×C3—21no—
457C22×C3—44no—
458C22×C3—44no—
459C22×C3—44no—
460C22×C3—42no—
461C22×C3—42no—
462C22×C3—42no—
463C22×C3—42no—
464C22×C3—42no—
465C22×C3—42no—
466C22×C3—62no—
467C22×C3—121no—
468C22×C3—121no—
469C22×C3C2×D3×D411yescharacteristic
470C22×C3C2×D3×D411yescharacteristic
471C2×D3—22no—
472C2×D3—41no—
473C2×D3—41no—
474C2×D3—122no—
475C2×D3—122no—
476C2×D3—122no—
477C2×D3—121no—
478C2×D3—121no—
479C2×D3—121no—
480C2×D3—121no—
481C2×D3—121no—
482C2×D3—121no—
483C3×C4—21no—
484C3×C4—21no—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—22no—
488C3×C4—41no—
489C3×C4—121no—
490C3×C4—122no—
491C3×C4#91112yes—
492C3×C4#91412yes—
493C3×C4C2×#23711yescharacteristic
494C3×C4D3×#4111yescharacteristic
495C3×C4#101011yescharacteristic
496C3×C4#101011yescharacteristic
497Dic3—41no—
498Dic3—42no—
499Dic3—64no—
500Dic3—62no—
501Dic3—62no—
502Dic3—62no—
503Dic3—62no—
504Dic3—122no—
505Dic3—122no—
506Dic3—121no—
507Dic3—121no—
508C32#336611yescharacteristic, complemented, Sylow
509C23—22no—
510C23—61no—
511C23—181no—
512Q8—182no—
513Q8—241no—
514D4—22no—
515D4—22no—
516D4—32no—
517D4—42no—
518D4—61no—
519D4—81no—
520D4—181no—
521D4—181no—
522D4—364no—
523D4—722no—
524C2×C4—61no—
525C2×C4—62no—
526C2×C4—92no—
527C2×C4—92no—
528C2×C4—122no—
529C2×C4—181no—
530C2×C4—364no—
531C2×C4—362no—
532C2×C4—722no—
533C2×C4#381111yescharacteristic
534C2×C4#381111yescharacteristic
535C2×C4C22×D3211yescharacteristic
536C8—61no—
537C8—62no—
538C8—61no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—84no—
543C2×C3—82no—
544C2×C3—82no—
545C2×C3—122no—
546C2×C3#559811yescharacteristic
547C2×C3#567711yescharacteristic
548C2×C3C2×#91111yescharacteristic
549C2×C3#575711yescharacteristic
550C2×C3C2×#91411yescharacteristic
551C2×C3#577411yescharacteristic
552D3—42no—
553D3—242no—
554D3—241no—
555D3—241no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—62no—
560C22—121no—
561C22—121no—
562C22—361no—
563C22—361no—
564C22—361no—
565C22C2×#381111yescharacteristic
566C4—21no—
567C4—122no—
568C4—121no—
569C4—182no—
570C4—182no—
571C4—361no—
572C4#6393712yes—
573C4#6430911yescharacteristic
574C4D3×#23711yescharacteristic
575C3—21no—
576C3#8032011yescharacteristic, complemented
577C3#8158611yescharacteristic, complemented
578C2—82no—
579C2—122no—
580C2—721no—
581C2#1059510211yescharacteristic
582C2C2×#6393711yescharacteristic
583C2#1059516111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
hypercenter#127D32
hypocenterC32#3366
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #10596189C2semidirect
2. #10593956C2semidirect
3. C3×#5072C2semidirect
4. C3×#5070C2semidirect
5. #10591480C2semidirect
6. #10591479C2semidirect
7. #10591436C2semidirect
8. #10591433C2semidirect
9. C4×#3714C2semidirect
10. #10590300C2semidirect
11. #10590296C2semidirect
53. #5072D3semidirect
54. #5070D3semidirect
189. C3×D12#41semidirect
401. D12#237semidirect
508. C32#3366semidirect
576. C3#80320semidirect
577. C3#81586semidirect

Maximal subgroups

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

subgroupindex
#105961892
#105939562
C3×#50722
C3×#50702
#105914802
#105914792
#105914362
#105914332
C4×#37142
#105903002
#105902962
#815863
#803203