Finite Group Databasebeta

← #11895763

Subgroups — #11895763

Order 1152.

846 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5553C211yesmaximal, characteristic, complemented
2#10593960C211yesmaximal, characteristic, complemented
3#10592707C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic, complemented
5#10591477C212yesmaximal, complemented
6#10591428C212yesmaximal, complemented
7#10590542C212yesmaximal, complemented
8#10590455C212yesmaximal, complemented
9#10590347C211yesmaximal, characteristic, complemented
10#10590273C211yesmaximal, characteristic, complemented
11#10590258C211yesmaximal, characteristic, complemented
12#83581—31nomaximal
13#79570—31nomaximal
14C2×C3×#235—21no—
15C32×C4×D4C2211yescharacteristic
16#64078C2211yescharacteristic
17C3×#940C2212yes—
18C2×C3×#213C2211yescharacteristic
19C3×#930—21no—
20C3×#893C2212yes—
21C3×#884—22no—
22C3×#874C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63896—22no—
26Dic3×D12C2212yes—
27D3×C4⋊Dic3—21no—
28#63869C2212yes—
29#63856—21no—
30C2×#3713C2212yes—
31#63659C2212yes—
32#63635C2212yes—
33C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
34C3×#832C2211yescharacteristic
35C3×#809C2211yescharacteristic
36C3×#807C2211yescharacteristic
37C3×C4×C3⋊C8C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63563C2212yes—
40#63563C2212yes—
41#63562C2212yes—
42#63554C2212yes—
43C3×#550—31no—
44#5579—31no—
45#5553D311yescharacteristic, complemented
46#5543—31no—
47C3×C4×D8—31no—
48#5150—32no—
49#5072—32no—
50#5072—31no—
51#5071—32no—
52#5070—31no—
53#5024—31no—
54#5015—31no—
55#5014—32no—
56C4×#213D311yescharacteristic, complemented
57#5009—32no—
58#5008—31no—
59#5008—31no—
60#5008—61no—
61#4891—32no—
62#4785—32no—
63#4764—32no—
64#4694—31no—
65#4679—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#634—21no—
69C2×C3×#67—22no—
70C2×C3×#67—22no—
71C3×#235—44no—
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12C2312yes—
75C2×C3×D12C2311yescharacteristic
76C2×C3×C4×D3—21no—
77C2×C3×C4×D3—22no—
78C2×C3×Dic6D411yescharacteristic
79C2×D3×Dic3—22no—
80C32×C4⋊C4C2311yescharacteristic
81C32×C22⋊C4—21no—
82C32×C42C2311yescharacteristic
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)C2312yes—
85C2×C3⋊(C3⋊C8)C2312yes—
86C3×#213—22no—
87C3×(C2×D3)⋊C4—21no—
88C3×(C2×D3)⋊C4—22no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4D412yes—
92C3×C4×Dic3C2312yes—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95#3724—22no—
96Dic3⋊Dic3—22no—
97(C2×D3)⋊Dic3—22no—
98#3713—24no—
99#3366—91noSylow
100C2×C3×#41—61no—
101C2×#235—21no—
102C2×C3×D8—31no—
103C3×#127—32no—
104C3×#127—31no—
105C3×#121—62no—
106C3×#121—61no—
107C3×C4×Q8—31no—
108C3×C4×D4—21no—
109C3×C4×D4—32no—
110C3×C4×D4—31no—
111C3×C4×D4C2×D311yescharacteristic
112C3×C4×D4C2×D311yescharacteristic
113#946—61no—
114#940C2×D312yes—
115D4×Dic3—32no—
116C2×#213—32no—
117C2×#213—32no—
118C2×#213C2×D311yescharacteristic
119#930—21no—
120C2×C4⋊Dic3—61no—
121#924—61no—
122#896—62no—
123#893C2×D312yes—
124D3×C4⋊C4—61no—
125#890—32no—
126#884—22no—
127#878—62no—
128#874C2×D311yescharacteristic
129C4×D12—32no—
130C4×D12C2×D311yescharacteristic
131#870—32no—
132#869—31no—
133#869—31no—
134#869—61no—
135C4×Dic6C2×D311yescharacteristic
136C3×#107—31no—
137C3×#102—31no—
138C3×#102—31no—
139C3×C4×C8—31no—
140#832—32no—
141#832—32no—
142#832—32no—
143#832—32no—
144#832—32no—
145#832—62no—
146#832C2×D311yescharacteristic
147#821—32no—
148#821—32no—
149#815—32no—
150Dic3⋊C8—32no—
151#809—32no—
152#809C2×D311yescharacteristic
153#808—32no—
154#808—32no—
155#808—62no—
156#807C2×D311yescharacteristic
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—31no—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)—61no—
161#803—32no—
162C4×C3⋊C8C2×D311yescharacteristic
163C23×C32—21no—
164C22×C3×D3—21no—
165C22×C3×D3—22no—
166C32×D4—21no—
167C32×D4—21no—
168C2×C32×C4—21no—
169C2×C32×C4—42no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—22no—
174#634—81no—
175C3×#67—44no—
176C3×#67—82no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C3×D12—22no—
181C3×D12—21no—
182C3×D12—22no—
183C3×D12—42no—
184C3×D12—81no—
185C3×D12#4112yescomplemented
186C3×C4×D3—44no—
187C3×C4×D3—42no—
188C3×Dic6—22no—
189D3×Dic3—82no—
190C3⋊(C3⋊C8)—22no—
191C3×C3⋊C8—21no—
192C3×C3⋊C8—21no—
193#554—91no—
194#550—31no—
195#490—92no—
196#486—91no—
197#478—92no—
198#476—91no—
199#459—91no—
200#459—92no—
201#446—91no—
202#442—92no—
203C4×D8—31no—
204C3×#41—124no—
205C2×C3×Q8—31no—
206C2×C3×D4—21no—
207C2×C3×D4—31no—
208C2×C3×D4—32no—
209C2×C3×D4—62no—
210C2×C3×D4—62no—
211C2×C3×D4—61no—
212C2×C3×D4—61no—
213C2×C3×D4C22×D311yescharacteristic
214C2×C3×D4C22×D311yescharacteristic
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—41no—
218C22×C3×C4—62no—
219C22×C3×C4—61no—
220C2×#67—22no—
221C2×#67—22no—
222C22×Dic3—62no—
223#235—44no—
224C2×D12—21no—
225C2×D12—21no—
226C2×D12C22×D312yes—
227C2×D12C22×D311yescharacteristic
228C2×C4×D3—21no—
229C2×C4×D3—22no—
230C2×C4×D3—62no—
231C2×Dic6—61no—
232C2×Dic6—61no—
233C2×Dic6—121no—
234C2×Dic6#6711yescharacteristic
235C3×D8—62no—
236C2×C3×C8—31no—
237C2×C3×C8—31no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—31no—
240C3×C4⋊C4—32no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4C22×D311yescharacteristic
243C3×C4⋊C4C22×D311yescharacteristic
244C3×C22⋊C4—21no—
245C3×C22⋊C4—21no—
246C3×C22⋊C4—41no—
247C3×C22⋊C4—62no—
248C3×C22⋊C4—61no—
249C3×C42—21no—
250C3×C42—32no—
251C3×C42C22×D311yescharacteristic
252C3×C42C22×D311yescharacteristic
253#217—62no—
254#213—22no—
255#213—64no—
256#213—64no—
257(C2×D3)⋊C4—21no—
258(C2×D3)⋊C4—22no—
259(C2×D3)⋊C4—62no—
260C4⋊Dic3—32no—
261C4⋊Dic3—32no—
262C4⋊Dic3—62no—
263C4⋊Dic3—61no—
264C4⋊Dic3—61no—
265C4⋊Dic3—62no—
266C4⋊Dic3—121no—
267C4⋊Dic3#6711yescharacteristic
268C4⋊Dic3C22×D311yescharacteristic
269Dic3⋊C4—62no—
270Dic3⋊C4—62no—
271Dic3⋊C4—62no—
272Dic3⋊C4#6712yes—
273C4×Dic3C22×D312yes—
274C2×C3⋊C8—32no—
275C2×C3⋊C8—32no—
276C2×C3⋊C8—62no—
277C2×C3⋊C8C22×D311yescharacteristic
278C2×C3⋊C8C22×D311yescharacteristic
279C22×C32—41no—
280C22×C32—41no—
281C22×C32—41no—
282C22×C32C22×D411yescharacteristic
283C2×C3×D3—22no—
284C2×C3×D3—41no—
285C2×C3×D3—41no—
286C2×C3×D3—42no—
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C32×C4—21no—
290C32×C4—41no—
291C32×C4AGL(1,ℤ/8)12yes—
292C32×C4C2×#4111yescharacteristic
293C32×C42−1+411yescharacteristic
294C3⋊Dic3—42no—
295C3×Dic3—22no—
296C3×Dic3—22no—
297C3×Dic3—41no—
298C2×#41—61no—
299C2×D8—31no—
300C2×D8—92no—
301C4⋊Q8—91no—
302#127—32no—
303#127—31no—
304#125—92no—
305C22⋊Q8—182no—
306C22⋊Q8—181no—
307#121—62no—
308#121—61no—
309C4×Q8—31no—
310C4×D4—32no—
311C4×D4—31no—
312C4×D4—92no—
313C4×D4D3211yescharacteristic
314C2×C4⋊C4—181no—
315#107—31no—
316#106—92no—
317C4⋊C8—92no—
318C4⋊C8—91no—
319#102—31no—
320#102—31no—
321#102—92no—
322#102—92no—
323#102—92no—
324#102—92no—
325#97—92no—
326C4×C8—31no—
327C23×C3—21no—
328C23×C3—21no—
329C23×C3—41no—
330C23×C3—61no—
331C23×C3—62no—
332C22×D3—21no—
333C22×D3—22no—
334C3×Q8—62no—
335C3×D4—22no—
336C3×D4—21no—
337C3×D4—21no—
338C3×D4—21no—
339C3×D4—21no—
340C3×D4—32no—
341C3×D4—41no—
342C3×D4—62no—
343C3×D4—61no—
344C3×D4—62no—
345C3×D4—124no—
346C3×D4—122no—
347C3×D4—241no—
348C3×D4—242no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—32no—
355C2×C3×C4—32no—
356C2×C3×C4—41no—
357C2×C3×C4—42no—
358C2×C3×C4—42no—
359C2×C3×C4—61no—
360C2×C3×C4—82no—
361C2×C3×C4—124no—
362C2×C3×C4—122no—
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C2×#6711yescharacteristic
367C2×C3×C4C23×D311yescharacteristic
368C2×C3×C4C23×D311yescharacteristic
369#67—44no—
370#67—82no—
371C2×Dic3—21no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—122no—
375C2×Dic3—242no—
376C2×Dic3C2×#6712yes—
377C2×Dic3C2×#6712yes—
378D12—22no—
379D12—21no—
380D12—22no—
381D12—42no—
382D12—81no—
383D12#23512yescomplemented
384C4×D3—44no—
385C4×D3—42no—
386C4×D3—242no—
387Dic6—22no—
388Dic6—241no—
389Dic6—241no—
390Dic6—242no—
391C3×C8—61no—
392C3×C8—61no—
393C3⋊C8—21no—
394C3⋊C8—21no—
395C3⋊C8—62no—
396C3⋊C8—62no—
397C3⋊C8—122no—
398C2×C32—81no—
399C2×C32#54811yescharacteristic
400C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
401C2×C32#57611yescharacteristic
402C3×D3—42no—
403C3×D3—82no—
404#41—124no—
405C2×Q8—31no—
406C2×Q8—181no—
407C2×D4—31no—
408C2×D4—32no—
409C2×D4—62no—
410C2×D4—62no—
411C2×D4—61no—
412C2×D4—61no—
413C2×D4C2×D3211yescharacteristic
414C22×C4—21no—
415C22×C4—62no—
416C22×C4—61no—
417C22×C4—182no—
418D8—62no—
419D8—184no—
420C2×C8—31no—
421C2×C8—31no—
422C2×C8—92no—
423C4⋊C4—31no—
424C4⋊C4—32no—
425C4⋊C4—31no—
426C4⋊C4—92no—
427C4⋊C4—182no—
428C4⋊C4—182no—
429C4⋊C4—181no—
430C4⋊C4C2×D3211yescharacteristic
431C22⋊C4—21no—
432C22⋊C4—62no—
433C22⋊C4—61no—
434C22⋊C4—182no—
435C42—32no—
436C42C2×D3211yescharacteristic
437C22×C3—21no—
438C22×C3—42no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3—62no—
446C22×C3—81no—
447C22×C3—81no—
448C22×C3—121no—
449C22×C3—121no—
450C22×C3—122no—
451C22×C3—122no—
452C22×C3—122no—
453C22×C3C2×D3×D411yescharacteristic
454C22×C3C22×#6711yescharacteristic
455C2×D3—22no—
456C2×D3—41no—
457C2×D3—41no—
458C2×D3—42no—
459C2×D3—42no—
460C2×D3—42no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—22no—
466C3×C4—41no—
467C3×C4—41no—
468C3×C4—41no—
469C3×C4—62no—
470C3×C4—62no—
471C3×C4—81no—
472C3×C4—121no—
473C3×C4#91112yes—
474C3×C4#93212yes—
475C3×C4C2×#23511yescharacteristic
476C3×C4D3×#4111yescharacteristic
477C3×C4#101011yescharacteristic
478C3×C4#101011yescharacteristic
479Dic3—22no—
480Dic3—22no—
481Dic3—41no—
482Dic3—122no—
483Dic3—122no—
484Dic3—242no—
485C32#336611yescharacteristic, complemented, Sylow
486C23—21no—
487C23—61no—
488C23—62no—
489Q8—62no—
490Q8—721no—
491D4—21no—
492D4—21no—
493D4—32no—
494D4—61no—
495D4—62no—
496D4—62no—
497D4—124no—
498D4—122no—
499D4—241no—
500D4—242no—
501C2×C4—21no—
502C2×C4—32no—
503C2×C4—32no—
504C2×C4—42no—
505C2×C4—61no—
506C2×C4—124no—
507C2×C4—122no—
508C2×C4—182no—
509C2×C4—722no—
510C2×C4D3×#6711yescharacteristic
511C2×C4D3×#6711yescharacteristic
512C2×C4C22×D3211yescharacteristic
513C8—61no—
514C8—61no—
515C8—182no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—82no—
520C2×C3—81no—
521C2×C3—81no—
522C2×C3—122no—
523C2×C3—242no—
524C2×C3#555211yescharacteristic
525C2×C3C2×#91111yescharacteristic
526C2×C3#576911yescharacteristic
527C2×C3C2×#93211yescharacteristic
528C2×C3#583111yescharacteristic
529C2×C3#583511yescharacteristic
530D3—42no—
531D3—82no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—62no—
536C22—121no—
537C22—121no—
538C22—122no—
539C22—122no—
540C22—122no—
541C22C2×D3×#6711yescharacteristic
542C4—21no—
543C4—41no—
544C4—62no—
545C4—62no—
546C4—121no—
547C4—362no—
548C4#6393212yes—
549C4#6429811yescharacteristic
550C4D3×#23511yescharacteristic
551C3—21no—
552C3#7957011yescharacteristic, complemented
553C3#8358111yescharacteristic, complemented
554C2—81no—
555C2—122no—
556C2—242no—
557C2#1059489911yescharacteristic
558C2C2×#6393211yescharacteristic
559C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3366
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5553C2semidirect
2. #10593960C2semidirect
3. #10592707C2semidirect
4. C3×C4×#213C2semidirect
5. #10591477C2semidirect
6. #10591428C2semidirect
7. #10590542C2semidirect
8. #10590455C2semidirect
9. #10590347C2semidirect
10. #10590273C2semidirect
11. #10590258C2semidirect
45. #5553D3semidirect
56. C4×#213D3semidirect
185. C3×D12#41semidirect
383. D12#235semidirect
485. C32#3366semidirect
552. C3#79570semidirect
553. C3#83581semidirect

Maximal subgroups

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

subgroupindex
C3×#55532
#105939602
#105927072
C3×C4×#2132
#105914772
#105914282
#105905422
#105904552
#105903472
#105902732
#105902582
#835813
#795703