Finite Group Databasebeta

← #11895779

Subgroups — #11895779

Order 1152.

839 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593956C211yesmaximal, characteristic, complemented
2#10593906C211yesmaximal, characteristic, complemented
3#10592530C211yesmaximal, characteristic, complemented
4C3×#4843C211yesmaximal, characteristic, complemented
5C3×#4842C211yesmaximal, characteristic, complemented
6#10590888C212yesmaximal, complemented
7#10590782C212yesmaximal, complemented
8#10590781C212yesmaximal, complemented
9#10590749C212yesmaximal, complemented
10C4×#3713C211yesmaximal, characteristic, complemented
11#10590277C211yesmaximal, characteristic, complemented
12#81088—31nomaximal
13#80320—31nomaximal
14C2×#3795—21no—
15C4×#634C2211yescharacteristic
16C2×C3×D24C2212yes—
17C3×#874C2211yescharacteristic
18C3×C4×D12C2211yescharacteristic
19C3×C4×D12C2211yescharacteristic
20C3×#869C2211yescharacteristic
21#63914C2212yes—
22#63908—21no—
23#63898C2212yes—
24#63898C2212yes—
25D3×C4⋊Dic3—21no—
26#63887—22no—
27#63885—22no—
28#63872C2212yes—
29#63857—21no—
30C2×#3713C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32#63642C2212yes—
33#63641C2212yes—
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#821C2212yes—
36C3×#821C2212yes—
37C3×#817C2212yes—
38#63576C2211yescharacteristic
39#63562C2212yes—
40#63562C2211yescharacteristic
41#63562C2212yes—
42#63562C2211yescharacteristic
43#5730—31no—
44#5718—31no—
45#5553—31no—
46#5543—31no—
47C3×#476—31no—
48C3×#459—31no—
49#5152—32no—
50#5150—32no—
51#5088—31no—
52#5070—31no—
53C4×#213—31no—
54C4×#213—31no—
55#4871—32no—
56#4869—32no—
57#4843D311yescharacteristic, complemented
58#4842D311yescharacteristic, complemented
59#4831—31no—
60#4831—31no—
61#4831—61no—
62#4786—32no—
63#4764—32no—
64#4764—32no—
65#4763—32no—
66C2×#634D411yescharacteristic
67C2×C3×D12—21no—
68C2×C3×D12—21no—
69C2×C3×D12C2312yes—
70C2×C3×D12C2311yescharacteristic
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×C4×D3—21no—
74C2×C3×Dic6—21no—
75C2×#625—22no—
76C2×#625—22no—
77C2×D3×Dic3—22no—
78C2×D3×Dic3—22no—
79#3795—44no—
80C2×C32×C8C2312yes—
81C32×C42C2311yescharacteristic
82C4⋊(C3⋊Dic3)D411yescharacteristic
83#3750D412yes—
84C4×C3⋊Dic3C2312yes—
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C3×(C2×D3)⋊C4—21no—
88C3×(C2×D3)⋊C4—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2312yes—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4⋊Dic3C2311yescharacteristic
93C3×D24—24no—
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97(C2×D3)⋊Dic3—22no—
98#3713—22no—
99#3366—91noSylow
100C2×#237—61no—
101C2×#235—61no—
102C2×C3×D8—32no—
103C3×C4⋊Q8—31no—
104C3×#127—31no—
105C3×C4×D4—31no—
106C3×C4×D4—31no—
107#946—62no—
108#940—32no—
109#940—32no—
110#939—62no—
111#938—61no—
112D4×Dic3—32no—
113D4×Dic3—32no—
114C2×#213—31no—
115C2×#213—31no—
116#930—61no—
117C2×C4⋊Dic3—61no—
118#924—61no—
119C2×D24C2×D312yes—
120#897—61no—
121#893—32no—
122#893—32no—
123D3×C4⋊C4—61no—
124#890—32no—
125#890—32no—
126#884—62no—
127#878—62no—
128#874C2×D311yescharacteristic
129C4×D12C2×D311yescharacteristic
130C4×D12C2×D311yescharacteristic
131#869C2×D311yescharacteristic
132C4×Dic6—31no—
133C4×Dic6—31no—
134C4×Dic6—61no—
135C3×#106—32no—
136C3×C4⋊C8—21no—
137C3×C4⋊C8C2×D311yescharacteristic
138C3×C4⋊C8C2×D311yescharacteristic
139C3×#102—32no—
140C3×#102—32no—
141#832—32no—
142#832—31no—
143#832—32no—
144#832—31no—
145#821C2×D312yes—
146#821C2×D312yes—
147#817C2×D312yes—
148#815—32no—
149#815—32no—
150#815—62no—
151Dic3⋊C8—32no—
152Dic3⋊C8—32no—
153Dic3⋊C8—62no—
154#809—31no—
155#809—32no—
156#809—32no—
157#809—31no—
158#807—31no—
159#807—31no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—31no—
162C4×C3⋊C8—61no—
163C22×C3×D3—21no—
164C22×C3×D3—22no—
165C22×C3×D3—21no—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3C2×D412yes—
170C2×C3⋊Dic3C2×D412yes—
171#634—22no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—21no—
175C3×D12—21no—
176C3×D12—22no—
177C3×D12—21no—
178C3×D12—21no—
179C3×D12—22no—
180C3×D12—42no—
181C3×D12—81no—
182C3×D12#4112yescomplemented
183C3×C4×D3—42no—
184C3×C4×D3—42no—
185C3×Dic6—81no—
186#625—44no—
187#625—82no—
188D3×Dic3—44no—
189D3×Dic3—82no—
190C32×C8—22no—
191C3⋊(C3⋊C8)—21no—
192C3⋊(C3⋊C8)—21no—
193#554—91no—
194#550—91no—
195#490—92no—
196#486—91no—
197#478—92no—
198#476—31no—
199#459—31no—
200#459—92no—
201#446—91no—
202#442—92no—
203C4×D8—91no—
204C2×C3×Q8—61no—
205C2×C3×D4—31no—
206C2×C3×D4—32no—
207C2×C3×D4—31no—
208C2×C3×D4—61no—
209C2×C3×D4—61no—
210C22×C3×C4—61no—
211C22×C3×C4—61no—
212C2×#67—62no—
213C2×#67—62no—
214C2×#67—62no—
215C2×#67—62no—
216C22×Dic3—62no—
217C22×Dic3—62no—
218#237—124no—
219#235—124no—
220C2×D12—21no—
221C2×D12—21no—
222C2×D12C22×D312yes—
223C2×D12C22×D311yescharacteristic
224C2×D12C22×D311yescharacteristic
225C2×C4×D3—21no—
226C2×C4×D3—21no—
227C2×C4×D3—62no—
228C2×C4×D3—62no—
229C2×Dic6—21no—
230C2×Dic6—31no—
231C2×Dic6—31no—
232C2×Dic6—61no—
233C3×D8—64no—
234C2×C3×C8—22no—
235C2×C3×C8C22×D312yes—
236C2×C3×C8C22×D312yes—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—31no—
239C3×C4⋊C4—32no—
240C3×C4⋊C4—61no—
241C3×C22⋊C4—61no—
242C3×C22⋊C4—61no—
243C3×C42—21no—
244C3×C42C22×D311yescharacteristic
245C3×C42C22×D311yescharacteristic
246#217—62no—
247#217—62no—
248#213—62no—
249#213—62no—
250(C2×D3)⋊C4—21no—
251(C2×D3)⋊C4—21no—
252(C2×D3)⋊C4—62no—
253(C2×D3)⋊C4—62no—
254C4⋊Dic3—21no—
255C4⋊Dic3—31no—
256C4⋊Dic3—31no—
257C4⋊Dic3—61no—
258C4⋊Dic3—62no—
259C4⋊Dic3—62no—
260C4⋊Dic3C22×D311yescharacteristic
261C4⋊Dic3C22×D311yescharacteristic
262C4⋊Dic3C22×D312yes—
263Dic3⋊C4—32no—
264Dic3⋊C4—32no—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4—62no—
268C4×Dic3—32no—
269C4×Dic3—32no—
270C4×Dic3—62no—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—31no—
275C2×C3⋊C8—61no—
276C2×C3⋊C8—61no—
277D24—24no—
278C22×C32C22×D411yescharacteristic
279C2×C3×D3—22no—
280C2×C3×D3—41no—
281C2×C3×D3—41no—
282C2×C3×D3—41no—
283C2×C3×D3—42no—
284C2×C3×D3—42no—
285C2×C3×D3—41no—
286C2×C3×D3—41no—
287C2×C3×D3—42no—
288C32×C4—21no—
289C32×C4AGL(1,ℤ/8)12yes—
290C32×C4C2×#4111yescharacteristic
291C32×C42−1+411yescharacteristic
292C3⋊Dic3—22no—
293C3⋊Dic3—22no—
294C3×Dic3—41no—
295C3×Dic3—41no—
296C3×Dic3—42no—
297C2×#41—181no—
298C2×D8—32no—
299C2×D8—91no—
300C4⋊Q8—31no—
301#127—31no—
302#127—92no—
303#125—92no—
304C22⋊Q8—182no—
305C22⋊Q8—181no—
306#121—182no—
307#121—181no—
308C4×Q8—91no—
309C4×D4—31no—
310C4×D4—31no—
311C4×D4—92no—
312C4×D4—92no—
313C2×C4⋊C4—181no—
314#107—91no—
315#106—32no—
316C4⋊C8—92no—
317C4⋊C8D3211yescharacteristic
318#102—32no—
319#102—32no—
320#102—91no—
321#102—91no—
322#102—92no—
323#102—92no—
324#97—92no—
325C4×C8—91no—
326C23×C3—61no—
327C23×C3—62no—
328C23×C3—61no—
329C22×D3—21no—
330C22×D3—21no—
331C22×D3—22no—
332C3×Q8—241no—
333C3×D4—32no—
334C3×D4—61no—
335C3×D4—61no—
336C3×D4—62no—
337C3×D4—62no—
338C3×D4—61no—
339C3×D4—122no—
340C3×D4—241no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—61no—
345C2×C3×C4—62no—
346C2×C3×C4—61no—
347C2×C3×C4—122no—
348C2×C3×C4—122no—
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354C2×C3×C4C23×D311yescharacteristic
355#67—124no—
356#67—124no—
357#67—242no—
358#67—242no—
359C2×Dic3—21no—
360C2×Dic3—22no—
361C2×Dic3—21no—
362C2×Dic3—32no—
363C2×Dic3—32no—
364C2×Dic3—32no—
365C2×Dic3—32no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—124no—
369C2×Dic3—242no—
370D12—22no—
371D12—21no—
372D12—21no—
373D12—21no—
374D12—22no—
375D12—42no—
376D12—81no—
377D12#23712yescomplemented
378C4×D3—42no—
379C4×D3—42no—
380C4×D3—124no—
381C4×D3—242no—
382Dic6—62no—
383Dic6—62no—
384Dic6—81no—
385Dic6—122no—
386C3×C8—22no—
387C3×C8—22no—
388C3×C8—42no—
389C3⋊C8—62no—
390C3⋊C8—61no—
391C3⋊C8—61no—
392C3⋊C8—61no—
393C3⋊C8—61no—
394C3⋊C8—121no—
395C2×C32#54811yescharacteristic
396C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
397C2×C32#57611yescharacteristic
398C3×D3—42no—
399C3×D3—82no—
400C3×D3—81no—
401#41—364no—
402C2×Q8—61no—
403C2×Q8—91no—
404C2×D4—31no—
405C2×D4—31no—
406C2×D4—32no—
407C2×D4—61no—
408C2×D4—61no—
409C2×D4—182no—
410C2×D4—182no—
411C22×C4—61no—
412C22×C4—61no—
413C22×C4—182no—
414C22×C4—182no—
415D8—64no—
416D8—182no—
417C2×C8—91no—
418C2×C8—91no—
419C2×C8C2×D3212yes—
420C4⋊C4—31no—
421C4⋊C4—32no—
422C4⋊C4—31no—
423C4⋊C4—61no—
424C4⋊C4—91no—
425C4⋊C4—92no—
426C4⋊C4—182no—
427C4⋊C4—182no—
428C22⋊C4—61no—
429C22⋊C4—61no—
430C22⋊C4—182no—
431C22⋊C4—182no—
432C42—92no—
433C42C2×D3211yescharacteristic
434C22×C3—21no—
435C22×C3—62no—
436C22×C3—121no—
437C22×C3—121no—
438C22×C3—122no—
439C22×C3—121no—
440C22×C3—122no—
441C22×C3—121no—
442C22×C3—122no—
443C22×C3—121no—
444C22×C3C2×D3×D411yescharacteristic
445C22×C3C2×D3×D411yescharacteristic
446C2×D3—22no—
447C2×D3—41no—
448C2×D3—41no—
449C2×D3—41no—
450C2×D3—42no—
451C2×D3—41no—
452C2×D3—42no—
453C2×D3—41no—
454C2×D3—42no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—22no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—41no—
461C3×C4—121no—
462C3×C4—121no—
463C3×C4—122no—
464C3×C4#91112yes—
465C3×C4#91412yes—
466C3×C4C2×#23711yescharacteristic
467C3×C4#100711yescharacteristic
468C3×C4D3×#4111yescharacteristic
469C3×C4#101011yescharacteristic
470Dic3—41no—
471Dic3—41no—
472Dic3—42no—
473Dic3—62no—
474Dic3—62no—
475Dic3—62no—
476Dic3—62no—
477Dic3—122no—
478Dic3—122no—
479C32#336611yescharacteristic, complemented, Sylow
480C23—61no—
481C23—61no—
482C23—62no—
483Q8—182no—
484Q8—241no—
485D4—32no—
486D4—62no—
487D4—61no—
488D4—61no—
489D4—61no—
490D4—62no—
491D4—122no—
492D4—241no—
493D4—364no—
494D4—722no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—62no—
498C2×C4—92no—
499C2×C4—92no—
500C2×C4—122no—
501C2×C4—122no—
502C2×C4—364no—
503C2×C4—722no—
504C2×C4#380211yescharacteristic
505C2×C4#380211yescharacteristic
506C2×C4C22×D3211yescharacteristic
507C8—22no—
508C8—181no—
509C8—181no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—122no—
514C2×C3—241no—
515C2×C3—242no—
516C2×C3#559811yescharacteristic
517C2×C3#563311yescharacteristic
518C2×C3C2×#91111yescharacteristic
519C2×C3C2×#91411yescharacteristic
520C2×C3#577411yescharacteristic
521C2×C3#577411yescharacteristic
522D3—42no—
523D3—82no—
524D3—81no—
525C22—62no—
526C22—121no—
527C22—121no—
528C22—121no—
529C22—122no—
530C22—122no—
531C22—121no—
532C22—122no—
533C22—121no—
534C22C2×#380211yescharacteristic
535C4—21no—
536C4—121no—
537C4—121no—
538C4—122no—
539C4—182no—
540C4—182no—
541C4#6379812yes—
542C4D3×#23711yescharacteristic
543C4#6431511yescharacteristic
544C3—21no—
545C3#8032011yescharacteristic, complemented
546C3#8108811yescharacteristic, complemented
547C2—122no—
548C2—241no—
549C2—242no—
550C2#1059452511yescharacteristic
551C2C2×#6379811yescharacteristic
552C2#1059472011yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3366
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #10593956C2semidirect
2. #10593906C2semidirect
3. #10592530C2semidirect
4. C3×#4843C2semidirect
5. C3×#4842C2semidirect
6. #10590888C2semidirect
7. #10590782C2semidirect
8. #10590781C2semidirect
9. #10590749C2semidirect
10. C4×#3713C2semidirect
11. #10590277C2semidirect
57. #4843D3semidirect
58. #4842D3semidirect
182. C3×D12#41semidirect
377. D12#237semidirect
479. C32#3366semidirect
545. C3#80320semidirect
546. C3#81088semidirect

Maximal subgroups

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

subgroupindex
#105939562
#105939062
#105925302
C3×#48432
C3×#48422
#105908882
#105907822
#105907812
#105907492
C4×#37132
#105902772
#810883
#803203