Finite Group Databasebeta

← #11898274

Subgroups — #11898274

Order 1152.

1001 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595143C212yesmaximal, complemented
2#10592850C211yesmaximal, characteristic, complemented
3C3×#5151C211yesmaximal, characteristic, complemented
4C3×Dic3×D8C211yesmaximal, characteristic, complemented
5#10591481C212yesmaximal, complemented
6#10591433C212yesmaximal, complemented
7#10591429C212yesmaximal, complemented
8#10590880C211yesmaximal, characteristic, complemented
9C8×#627C211yesmaximal, characteristic, complemented
10#10590777C211yesmaximal, characteristic, complemented
11#10590763C211yesmaximal, characteristic, complemented
12#81778—31nomaximal
13#79578—31nomaximal
14C2×#3804—22no—
15C2×C32×D8C2211yescharacteristic
16#64149C2212yes—
17C2×#3753C2212yes—
18C2×#3745C2211yescharacteristic
19C3×#940C2212yes—
20C3×D4×Dic3C2212yes—
21C2×C3×#213C2212yes—
22C2×C3×D24C2211yescharacteristic
23#63978—22no—
24#63971—22no—
25#63958—22no—
26C4×#627C2211yescharacteristic
27#63911C2212yes—
28#63898C2212yes—
29#63894C2212yes—
30C2×#3714C2212yes—
31C8×C3⋊Dic3C2211yescharacteristic
32C3×#832C2212yes—
33C3×#818C2211yescharacteristic
34C3×C8×Dic3C2211yescharacteristic
35C3×C8×Dic3C2211yescharacteristic
36#63572C2211yescharacteristic
37Dic3⋊(C3⋊C8)C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2211yescharacteristic
39#63564C2212yes—
40#63562C2212yes—
41#5718—32no—
42#5553—32no—
43C3×#493—31no—
44C3×C4×D8—31no—
45#5151—31no—
46#5151—31no—
47#5151—31no—
48#5151—61no—
49#5151D311yescharacteristic, complemented
50#5150—32no—
51#5150—32no—
52Dic3×D8—31no—
53Dic3×D8D311yescharacteristic, complemented
54#5072—32no—
55#5015—32no—
56#4872—31no—
57#4872—31no—
58#4786—32no—
59#4786—32no—
60#4695—31no—
61C4×D24—31no—
62C8×Dic6—31no—
63C8×Dic6—31no—
64C2×C32×D4C2312yes—
65C2×#638—22no—
66C2×#638—22no—
67C2×C4⋊(C3⋊D3)C2312yes—
68C2×C3×#67—22no—
69C2×C3×#67—22no—
70C22×C3×Dic3—22no—
71C2×C3×D12C2312yes—
72C2×#627D411yescharacteristic
73C2×#626—22no—
74C2×#626—22no—
75C2×#624—22no—
76#3804—48no—
77C2×D3×Dic3—22no—
78C32×D8—22no—
79C2×C32×C8C2311yescharacteristic
80#3753—42no—
81C4×C3⋊Dic3C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83#3745—22no—
84C3×#217—22no—
85C3×#213—42no—
86C3×C4⋊Dic3C2312yes—
87C3×C4×Dic3C2311yescharacteristic
88C3×C4×Dic3C2311yescharacteristic
89C2×C3×C3⋊C8C2311yescharacteristic
90C2×C3×C3⋊C8C2311yescharacteristic
91C3×D24—22no—
92#3724D411yescharacteristic
93Dic3⋊Dic3D411yescharacteristic
94Dic3⋊Dic3D411yescharacteristic
95#3722—22no—
96(C2×D3)⋊Dic3—22no—
97#3714—42no—
98#3391—91noSylow
99C2×#237—62no—
100C2×#235—62no—
101C2×C3×D8—21no—
102C2×C3×D8—32no—
103C2×C3×D8—31no—
104C2×C3×D8C2×D311yescharacteristic
105C2×C3×D8C2×D311yescharacteristic
106C3×#127—32no—
107C3×C4×D4—32no—
108#940—32no—
109#940—32no—
110#940—32no—
111#940—62no—
112#940C2×D312yes—
113#939—62no—
114#939—62no—
115#938—62no—
116D4×Dic3—32no—
117D4×Dic3C2×D312yes—
118C2×#213—32no—
119C2×#213—32no—
120C2×#213—32no—
121C2×#213—62no—
122C2×#213C2×D312yes—
123#930—62no—
124C2×D24—31no—
125C2×D24—31no—
126C2×D24—32no—
127C2×D24—61no—
128C2×D24C2×D311yescharacteristic
129#893—32no—
130#893—32no—
131#884—62no—
132#884—62no—
133#874—32no—
134C4×D12—32no—
135C4×Dic6—31no—
136C4×Dic6—31no—
137C3×#107—31no—
138C3×#102—32no—
139C3×C4×C8—31no—
140C3×C4×C8—31no—
141#832—32no—
142#832C2×D312yes—
143#821—32no—
144#818C2×D311yescharacteristic
145Dic3⋊C8—31no—
146Dic3⋊C8—31no—
147Dic3⋊C8—31no—
148Dic3⋊C8—31no—
149C8×Dic3—31no—
150C8×Dic3—31no—
151C8×Dic3—61no—
152C8×Dic3C2×D311yescharacteristic
153C8×Dic3C2×D311yescharacteristic
154#809—32no—
155#809—32no—
156C4⋊(C3⋊C8)—31no—
157C4⋊(C3⋊C8)—31no—
158C23×C32—22no—
159C22×C3⋊D3—22no—
160C22×C3×D3—22no—
161C32×D4—22no—
162C32×D4—22no—
163C2×C32×C4C2411yescharacteristic
164#638—44no—
165#638—82no—
166C2×C3⋊Dic3C2×D411yescharacteristic
167C2×C3⋊Dic3C2×D411yescharacteristic
168C4⋊(C3⋊D3)—22no—
169C4⋊(C3⋊D3)—22no—
170C3×#67—44no—
171C3×#67—82no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—44no—
174C2×C3×Dic3C2×D411yescharacteristic
175C2×C3×Dic3C2×D411yescharacteristic
176C2×C3×Dic3C2×D411yescharacteristic
177C2×C3×Dic3C2×D411yescharacteristic
178C3×D12—22no—
179C3×D12—22no—
180#627D814yescomplemented
181#626—44no—
182#626—82no—
183#624—44no—
184D3×Dic3—44no—
185C32×C8#4112yescomplemented
186C3⋊(C3⋊C8)—21no—
187C3×C3⋊C8—21no—
188C3×C3⋊C8—21no—
189#550—92no—
190#493—31no—
191#493—91no—
192#493—91no—
193#459—92no—
194#459—92no—
195#459—92no—
196C8×Q8—91no—
197C4×D8—31no—
198C4×D8—91no—
199C4×D8—91no—
200C2×C3×D4—22no—
201C2×C3×D4—32no—
202C2×C3×D4—62no—
203C2×C3×D4—62no—
204C2×C3×D4C22×D312yes—
205C2×C3×D4C22×D312yes—
206C22×C3×C4—62no—
207C2×#67—22no—
208C2×#67—22no—
209C2×#67—62no—
210C2×#67—62no—
211C2×#67—62no—
212C2×#67—62no—
213C2×#67—62no—
214C2×#67—62no—
215C2×#67—122no—
216C2×#67—122no—
217C22×Dic3—22no—
218C22×Dic3—62no—
219#237—128no—
220#235—128no—
221C2×D12—32no—
222C2×D12—32no—
223C2×D12—62no—
224C2×D12—62no—
225C2×D12—62no—
226C2×D12C22×D312yes—
227C2×C4×D3—62no—
228C2×C4×D3—62no—
229C2×C4×D3—62no—
230C2×Dic6—31no—
231C2×Dic6—31no—
232C3×D8—22no—
233C3×D8—22no—
234C3×D8—42no—
235C3×D8—62no—
236C3×D8—122no—
237C2×C3×C8—21no—
238C2×C3×C8—31no—
239C2×C3×C8—31no—
240C2×C3×C8C22×D311yescharacteristic
241C2×C3×C8C22×D311yescharacteristic
242C3×C4⋊C4—32no—
243C3×C22⋊C4—62no—
244C3×C42—31no—
245C3×C42—31no—
246#217—22no—
247#217—62no—
248#213—42no—
249#213—122no—
250#213—122no—
251#213—122no—
252#213—124no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—62no—
255(C2×D3)⋊C4—62no—
256C4⋊Dic3—31no—
257C4⋊Dic3—31no—
258C4⋊Dic3C22×D312yes—
259Dic3⋊C4—31no—
260Dic3⋊C4—31no—
261Dic3⋊C4—31no—
262Dic3⋊C4—31no—
263C4×Dic3—31no—
264C4×Dic3—31no—
265C4×Dic3—61no—
266C4×Dic3C22×D311yescharacteristic
267C4×Dic3C22×D311yescharacteristic
268C2×C3⋊C8—31no—
269C2×C3⋊C8—31no—
270C2×C3⋊C8—61no—
271C2×C3⋊C8C22×D311yescharacteristic
272C2×C3⋊C8C22×D311yescharacteristic
273D24—22no—
274D24—62no—
275D24—62no—
276D24—122no—
277D24—122no—
278C22×C32—42no—
279C22×C32—42no—
280C22×C32—42no—
281C22×C32C22×D411yescharacteristic
282C2×C3⋊D3—42no—
283C2×C3⋊D3—42no—
284C2×C3⋊D3—42no—
285C2×C3×D3—42no—
286C2×C3×D3—42no—
287C2×C3×D3—42no—
288C32×C4C2×#4111yescharacteristic
289C32×C4H(5,𝔽2)11yescharacteristic
290C3⋊Dic3—21no—
291C3⋊Dic3C2×D812yes—
292C3×Dic3—21no—
293C3×Dic3—21no—
294C3×Dic3—42no—
295C3×Dic3C2×D812yes—
296C3×Dic3C2×D812yes—
297C2×#41—182no—
298C2×D8—32no—
299C2×D8—31no—
300C2×D8—92no—
301C2×D8—92no—
302C2×D8—91no—
303C2×D8D3211yescharacteristic
304#127—32no—
305#127—92no—
306#127—92no—
307#121—182no—
308#121—182no—
309#121—182no—
310C4×Q8—91no—
311C4×D4—32no—
312C4×D4—92no—
313C4×D4—92no—
314#107—31no—
315C4⋊C8—91no—
316C4⋊C8—91no—
317C4⋊C8—91no—
318#102—32no—
319#102—92no—
320#102—92no—
321C4×C8—31no—
322C4×C8—31no—
323C4×C8—91no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—42no—
327C23×C3—62no—
328C22×D3—22no—
329C22×D3—62no—
330C22×D3—62no—
331C22×D3—122no—
332C3×D4—22no—
333C3×D4—22no—
334C3×D4—22no—
335C3×D4—22no—
336C3×D4—42no—
337C3×D4—42no—
338C3×D4—62no—
339C3×D4—62no—
340C3×D4—124no—
341C3×D4—242no—
342C2×C3×C4—21no—
343C2×C3×C4—31no—
344C2×C3×C4—31no—
345C2×C3×C4—31no—
346C2×C3×C4—31no—
347C2×C3×C4—62no—
348C2×C3×C4—124no—
349C2×C3×C4C23×D311yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351#67—44no—
352#67—82no—
353#67—124no—
354#67—124no—
355#67—124no—
356#67—244no—
357#67—242no—
358#67—242no—
359#67—242no—
360#67—244no—
361C2×Dic3—22no—
362C2×Dic3—31no—
363C2×Dic3—31no—
364C2×Dic3—31no—
365C2×Dic3—31no—
366C2×Dic3—44no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—124no—
370C2×Dic3D3×D411yescharacteristic
371C2×Dic3D3×D411yescharacteristic
372C2×Dic3D3×D411yescharacteristic
373C2×Dic3D3×D411yescharacteristic
374D12—22no—
375D12—22no—
376D12—62no—
377D12—62no—
378D12—62no—
379D12—62no—
380D12—122no—
381D12—122no—
382D12—124no—
383D12—242no—
384C4×D3—124no—
385C4×D3—124no—
386C4×D3—124no—
387Dic6—34no—
388Dic6—34no—
389C3×C8—22no—
390C3×C8—61no—
391C3×C8—61no—
392C3×C8#23512yescomplemented
393C3×C8#23712yescomplemented
394C3⋊C8—21no—
395C3⋊C8—21no—
396C3⋊C8—62no—
397C3⋊C8—61no—
398C3⋊C8—61no—
399C2×C32—82no—
400C2×C32#55011yescharacteristic
401C2×C32C22×D811yescharacteristic
402C2×C32#57611yescharacteristic
403C3⋊D3—82no—
404C3×D3—82no—
405#41—368no—
406C2×Q8—91no—
407C2×D4—32no—
408C2×D4—62no—
409C2×D4—62no—
410C2×D4—92no—
411C2×D4—182no—
412C2×D4—182no—
413C2×D4—182no—
414C2×D4—182no—
415C2×D4C2×D3212yes—
416C22×C4—62no—
417C22×C4—182no—
418C22×C4—182no—
419D8—22no—
420D8—62no—
421D8—122no—
422D8—182no—
423D8—362no—
424D8—362no—
425C2×C8—31no—
426C2×C8—31no—
427C2×C8—91no—
428C2×C8C2×D3211yescharacteristic
429C4⋊C4—32no—
430C4⋊C4—91no—
431C4⋊C4—91no—
432C4⋊C4—91no—
433C22⋊C4—62no—
434C22⋊C4—182no—
435C22⋊C4—182no—
436C42—31no—
437C42—31no—
438C42—91no—
439C22×C3—21no—
440C22×C3—42no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—42no—
444C22×C3—42no—
445C22×C3—42no—
446C22×C3—82no—
447C22×C3—82no—
448C22×C3—82no—
449C22×C3—122no—
450C22×C3—122no—
451C22×C3—122no—
452C22×C3C2×D3×D411yescharacteristic
453C22×C3C2×D3×D411yescharacteristic
454C2×D3—42no—
455C2×D3—42no—
456C2×D3—42no—
457C2×D3—122no—
458C2×D3—122no—
459C2×D3—122no—
460C2×D3—122no—
461C2×D3—122no—
462C2×D3—122no—
463C2×D3—242no—
464C2×D3—242no—
465C2×D3—242no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—32no—
469C3×C4—32no—
470C3×C4—61no—
471C3×C4—61no—
472C3×C4—122no—
473C3×C4C2×#23511yescharacteristic
474C3×C4C2×#23711yescharacteristic
475C3×C4#100411yescharacteristic
476C3×C4#100911yescharacteristic
477Dic3—21no—
478Dic3—21no—
479Dic3—32no—
480Dic3—32no—
481Dic3—42no—
482Dic3—62no—
483Dic3—62no—
484Dic3—61no—
485Dic3—61no—
486Dic3D3×D812yes—
487Dic3D3×D812yes—
488C32#339111yescharacteristic, complemented, Sylow
489C23—22no—
490C23—62no—
491C23—182no—
492Q8—94no—
493D4—22no—
494D4—22no—
495D4—62no—
496D4—62no—
497D4—124no—
498D4—182no—
499D4—182no—
500D4—242no—
501D4—364no—
502D4—364no—
503D4—722no—
504D4—722no—
505C2×C4—31no—
506C2×C4—31no—
507C2×C4—31no—
508C2×C4—31no—
509C2×C4—62no—
510C2×C4—91no—
511C2×C4—91no—
512C2×C4—124no—
513C2×C4—364no—
514C2×C4—364no—
515C2×C4C22×D3211yescharacteristic
516C8—61no—
517C8—61no—
518C8—181no—
519C8#380412yescomplemented
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—82no—
524C2×C3—82no—
525C2×C3—162no—
526C2×C3—242no—
527C2×C3#555311yescharacteristic
528C2×C3#571811yescharacteristic
529C2×C3C2×D3×D811yescharacteristic
530C2×C3C2×D3×D811yescharacteristic
531C2×C3#575711yescharacteristic
532C2×C3#576911yescharacteristic
533D3—82no—
534D3—242no—
535D3—242no—
536D3—482no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—122no—
541C22—122no—
542C22—122no—
543C22—362no—
544C22—362no—
545C22—362no—
546C22D32×D411yescharacteristic
547C4—32no—
548C4—32no—
549C4—61no—
550C4—61no—
551C4—92no—
552C4—122no—
553C4—181no—
554C4#6431411yescharacteristic
555C4C2×#380411yescharacteristic
556C3—21no—
557C3#7957811yescharacteristic, complemented
558C3#8177811yescharacteristic, complemented
559C2—82no—
560C2—242no—
561C2—722no—
562C2D32×D811yescharacteristic
563C2#1059473411yescharacteristic
564C2#1059514311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3391
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #10595143C2semidirect
2. #10592850C2semidirect
3. C3×#5151C2semidirect
4. C3×Dic3×D8C2semidirect
5. #10591481C2semidirect
6. #10591433C2semidirect
7. #10591429C2semidirect
8. #10590880C2semidirect
9. C8×#627C2semidirect
10. #10590777C2semidirect
11. #10590763C2semidirect
49. #5151D3semidirect
53. Dic3×D8D3semidirect
180. #627D8semidirect
185. C32×C8#41semidirect
392. C3×C8#235semidirect
393. C3×C8#237semidirect
488. C32#3391semidirect
519. C8#3804semidirect
557. C3#79578semidirect
558. C3#81778semidirect

Maximal subgroups

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

subgroupindex
#105951432
#105928502
C3×#51512
C3×Dic3×D82
#105914812
#105914332
#105914292
#105908802
C8×#6272
#105907772
#105907632
#817783
#795783