Finite Group Databasebeta

← #11895772

Subgroups — #11895772

Order 1152.

851 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×#5718C211yesmaximal, characteristic, complemented
2#10593960C211yesmaximal, characteristic, complemented
3#10592769C211yesmaximal, characteristic, complemented
4C3×#5072C211yesmaximal, characteristic, complemented
5#10591477C212yesmaximal, complemented
6#10591430C212yesmaximal, complemented
7#10591428C212yesmaximal, complemented
8#10591409C212yesmaximal, complemented
9C4×#3713C211yesmaximal, characteristic, complemented
10#10590268C211yesmaximal, characteristic, complemented
11#10590259C211yesmaximal, characteristic, complemented
12#83581—31nomaximal
13#80320—31nomaximal
14C2×C3×#237—21no—
15C32×#127C2211yescharacteristic
16#64078C2211yescharacteristic
17C3×#940C2212yes—
18C3×#939—22no—
19C3×#938—21no—
20C3×D4×Dic3C2212yes—
21C2×C3×#213C2212yes—
22C3×C4×D12C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63896—22no—
26Dic3×D12C2212yes—
27D3×C4⋊Dic3—21no—
28#63869C2212yes—
29#63856—21no—
30C2×#3713C2211yescharacteristic
31#63659C2212yes—
32#63659C2212yes—
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C3×#832C2212yes—
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36#63576C2211yescharacteristic
37#63573C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63563C2212yes—
40#63562C2211yescharacteristic
41#63562C2211yescharacteristic
42#63554C2212yes—
43C3×#550—31no—
44#5718D311yescharacteristic, complemented
45#5579—31no—
46#5543—31no—
47C3×#459—31no—
48#5152—32no—
49#5150—32no—
50#5072—32no—
51#5072D311yescharacteristic, complemented
52#5071—32no—
53#5070—31no—
54#5070—31no—
55#5070—61no—
56#5024—31no—
57#5014—32no—
58C4×#213—31no—
59C4×#213—31no—
60#5009—32no—
61#5008—31no—
62#4842—31no—
63#4831—31no—
64#4764—32no—
65#4763—32no—
66C2×C32×D4—21no—
67C2×C32×D4—21no—
68C2×C32×D4C2312yes—
69C2×#634—21no—
70C2×C3×#67—22no—
71C2×C3×#67—22no—
72C22×C3×Dic3—22no—
73C3×#237—44no—
74C2×C3×D12C2311yescharacteristic
75C2×C3×D12C2311yescharacteristic
76C2×C3×C4×D3—21no—
77C2×C3×C4×D3—21no—
78C2×C3×Dic6D411yescharacteristic
79C2×D3×Dic3—22no—
80C32×C42C2311yescharacteristic
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)C2312yes—
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C3×#217—22no—
86C3×#213—24no—
87C3×(C2×D3)⋊C4—21no—
88C3×(C2×D3)⋊C4—21no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2311yescharacteristic
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4D412yes—
93C3×C4×Dic3C2312yes—
94C2×C3×C3⋊C8C2312yes—
95#3724—22no—
96Dic3⋊Dic3—22no—
97(C2×D3)⋊Dic3—22no—
98#3713—22no—
99#3366—91noSylow
100C2×C3×#41—61no—
101C2×#237—21no—
102C2×C3×D8—32no—
103C3×#127—21no—
104C3×#127—32no—
105C3×#127C2×D311yescharacteristic
106C3×#127C2×D311yescharacteristic
107C3×#121—61no—
108C3×#121—62no—
109C3×C4×Q8—31no—
110C3×C4×D4—32no—
111C3×C4×D4—31no—
112C3×C4×D4—31no—
113#946—61no—
114#940C2×D312yes—
115#939—22no—
116#938—21no—
117D4×Dic3—32no—
118D4×Dic3C2×D312yes—
119C2×#213—31no—
120C2×#213—31no—
121C2×#213C2×D312yes—
122C2×C4⋊Dic3—61no—
123#924—61no—
124#896—62no—
125D3×C4⋊C4—61no—
126#890—32no—
127#878—62no—
128C4×D12—32no—
129C4×D12C2×D311yescharacteristic
130C4×D12C2×D311yescharacteristic
131#870—32no—
132#869—31no—
133#869—31no—
134#869—61no—
135C4×Dic6C2×D311yescharacteristic
136C3×C4⋊C8—31no—
137C3×#102—32no—
138#832—32no—
139#832—32no—
140#832—32no—
141#832—32no—
142#832—31no—
143#832—31no—
144#832—32no—
145#832—62no—
146#832—62no—
147#832C2×D312yes—
148#821—32no—
149#817—32no—
150#815—32no—
151Dic3⋊C8—32no—
152#809—31no—
153#809—31no—
154#808—32no—
155#807—31no—
156#807—31no—
157C4⋊(C3⋊C8)—32no—
158C4⋊(C3⋊C8)C2×D311yescharacteristic
159#803—32no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—31no—
162C4×C3⋊C8—61no—
163C23×C32—22no—
164C22×C3×D3—21no—
165C22×C3×D3—21no—
166C32×D4—22no—
167C32×D4—22no—
168C32×D4—42no—
169C32×D4—81no—
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×Dic3—21no—
179C2×C3×Dic3—44no—
180C2×C3×Dic3C2×D412yes—
181C2×C3×Dic3C2×D412yes—
182C3×D12—21no—
183C3×D12—21no—
184C3×D12—21no—
185C3×D12#4112yescomplemented
186C3×C4×D3—42no—
187C3×C4×D3—42no—
188C3×Dic6—22no—
189D3×Dic3—82no—
190C3⋊(C3⋊C8)—21no—
191C3⋊(C3⋊C8)—21no—
192C3×C3⋊C8—22no—
193#554—91no—
194#550—31no—
195#490—92no—
196#486—91no—
197#478—92no—
198#476—91no—
199#459—31no—
200#459—92no—
201#446—91no—
202#442—92no—
203C4×D8—91no—
204C3×#41—124no—
205C2×C3×Q8—31no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—22no—
211C2×C3×D4—31no—
212C2×C3×D4—31no—
213C2×C3×D4—41no—
214C2×C3×D4—41no—
215C2×C3×D4—62no—
216C2×C3×D4—62no—
217C2×C3×D4C22×D312yes—
218C2×C3×D4C22×D312yes—
219C22×C3×C4—62no—
220C22×C3×C4—61no—
221C22×C3×C4—61no—
222C2×#67—22no—
223C2×#67—22no—
224C22×Dic3—22no—
225C22×Dic3—62no—
226#237—44no—
227C2×D12C22×D311yescharacteristic
228C2×D12C22×D311yescharacteristic
229C2×C4×D3—21no—
230C2×C4×D3—21no—
231C2×C4×D3—62no—
232C2×Dic6—61no—
233C2×Dic6—61no—
234C2×Dic6—121no—
235C2×Dic6#6711yescharacteristic
236C3×D8—64no—
237C2×C3×C8—32no—
238C3×C4⋊C4—31no—
239C3×C4⋊C4—32no—
240C3×C4⋊C4—31no—
241C3×C4⋊C4—31no—
242C3×C22⋊C4—62no—
243C3×C22⋊C4—61no—
244C3×C22⋊C4—61no—
245C3×C42—21no—
246C3×C42—32no—
247C3×C42C22×D311yescharacteristic
248C3×C42C22×D311yescharacteristic
249#217—22no—
250#217—62no—
251#213—24no—
252#213—62no—
253#213—62no—
254(C2×D3)⋊C4—21no—
255(C2×D3)⋊C4—21no—
256(C2×D3)⋊C4—62no—
257C4⋊Dic3—32no—
258C4⋊Dic3—32no—
259C4⋊Dic3—62no—
260C4⋊Dic3—61no—
261C4⋊Dic3—61no—
262C4⋊Dic3—62no—
263C4⋊Dic3—121no—
264C4⋊Dic3#6711yescharacteristic
265C4⋊Dic3C22×D311yescharacteristic
266C4⋊Dic3C22×D311yescharacteristic
267Dic3⋊C4—62no—
268Dic3⋊C4—62no—
269Dic3⋊C4—62no—
270Dic3⋊C4#6712yes—
271C4×Dic3C22×D312yes—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—31no—
275C2×C3⋊C8—31no—
276C2×C3⋊C8—61no—
277C2×C3⋊C8—61no—
278C2×C3⋊C8C22×D312yes—
279C22×C32—42no—
280C22×C32—42no—
281C22×C32—42no—
282C22×C32C22×D411yescharacteristic
283C2×C3×D3—22no—
284C2×C3×D3—41no—
285C2×C3×D3—41no—
286C2×C3×D3—41no—
287C2×C3×D3—41no—
288C2×C3×D3—41no—
289C32×C4—21no—
290C32×C4AGL(1,ℤ/8)12yes—
291C32×C4C2×#4111yescharacteristic
292C32×C42−1+411yescharacteristic
293C3⋊Dic3—42no—
294C3×Dic3—22no—
295C3×Dic3—22no—
296C3×Dic3—41no—
297C3×Dic3—41no—
298C2×#41—61no—
299C2×D8—32no—
300C2×D8—91no—
301C4⋊Q8—91no—
302#127—32no—
303#127D3211yescharacteristic
304#125—92no—
305C22⋊Q8—182no—
306C22⋊Q8—181no—
307#121—61no—
308#121—62no—
309C4×Q8—31no—
310C4×D4—32no—
311C4×D4—31no—
312C4×D4—31no—
313C4×D4—92no—
314C2×C4⋊C4—181no—
315#107—91no—
316#106—92no—
317C4⋊C8—31no—
318C4⋊C8—92no—
319#102—32no—
320#102—91no—
321#102—91no—
322#102—92no—
323#102—92no—
324#102—92no—
325#97—92no—
326C4×C8—91no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—42no—
330C23×C3—61no—
331C23×C3—61no—
332C22×D3—21no—
333C22×D3—21no—
334C3×Q8—62no—
335C3×D4—22no—
336C3×D4—22no—
337C3×D4—22no—
338C3×D4—22no—
339C3×D4—32no—
340C3×D4—42no—
341C3×D4—42no—
342C3×D4—42no—
343C3×D4—42no—
344C3×D4—61no—
345C3×D4—61no—
346C3×D4—61no—
347C3×D4—82no—
348C3×D4—81no—
349C3×D4—81no—
350C3×D4—82no—
351C3×D4—124no—
352C3×D4—242no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—32no—
357C2×C3×C4—32no—
358C2×C3×C4—61no—
359C2×C3×C4—61no—
360C2×C3×C4—124no—
361C2×C3×C4—122no—
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—21no—
373C2×Dic3—44no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—122no—
377C2×Dic3—242no—
378C2×Dic3C2×#6712yes—
379C2×Dic3C2×#6712yes—
380D12—21no—
381D12—21no—
382D12—21no—
383D12#23712yescomplemented
384C4×D3—42no—
385C4×D3—42no—
386C4×D3—242no—
387Dic6—22no—
388Dic6—241no—
389Dic6—241no—
390Dic6—242no—
391C3×C8—62no—
392C3⋊C8—22no—
393C3⋊C8—61no—
394C3⋊C8—61no—
395C3⋊C8—61no—
396C3⋊C8—61no—
397C3⋊C8—121no—
398C3⋊C8—121no—
399C2×C32—82no—
400C2×C32#54811yescharacteristic
401C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
402C2×C32#57611yescharacteristic
403C3×D3—42no—
404C3×D3—81no—
405#41—124no—
406C2×Q8—31no—
407C2×Q8—181no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—31no—
411C2×D4—31no—
412C2×D4—62no—
413C2×D4—62no—
414C2×D4C2×D3212yes—
415C22×C4—62no—
416C22×C4—61no—
417C22×C4—61no—
418C22×C4—182no—
419D8—64no—
420D8—182no—
421C2×C8—32no—
422C2×C8—91no—
423C2×C8—91no—
424C4⋊C4—31no—
425C4⋊C4—32no—
426C4⋊C4—31no—
427C4⋊C4—31no—
428C4⋊C4—92no—
429C4⋊C4—182no—
430C4⋊C4—182no—
431C4⋊C4—181no—
432C22⋊C4—62no—
433C22⋊C4—61no—
434C22⋊C4—61no—
435C22⋊C4—182no—
436C42—32no—
437C42C2×D3211yescharacteristic
438C22×C3—21no—
439C22×C3—42no—
440C22×C3—42no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—42no—
444C22×C3—42no—
445C22×C3—62no—
446C22×C3—82no—
447C22×C3—82no—
448C22×C3—82no—
449C22×C3—121no—
450C22×C3—121no—
451C22×C3—121no—
452C22×C3—121no—
453C22×C3—121no—
454C22×C3C2×D3×D411yescharacteristic
455C22×C3C22×#6711yescharacteristic
456C2×D3—22no—
457C2×D3—41no—
458C2×D3—41no—
459C2×D3—41no—
460C2×D3—41no—
461C2×D3—41no—
462C3×C4—22no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—22no—
468C3×C4—62no—
469C3×C4—62no—
470C3×C4—121no—
471C3×C4—121no—
472C3×C4#91112yes—
473C3×C4#93212yes—
474C3×C4C2×#23711yescharacteristic
475C3×C4D3×#4111yescharacteristic
476C3×C4#101011yescharacteristic
477C3×C4#101011yescharacteristic
478Dic3—22no—
479Dic3—22no—
480Dic3—41no—
481Dic3—41no—
482Dic3—122no—
483Dic3—122no—
484Dic3—242no—
485C32#336611yescharacteristic, complemented, Sylow
486C23—22no—
487C23—61no—
488C23—61no—
489Q8—62no—
490Q8—721no—
491D4—22no—
492D4—22no—
493D4—32no—
494D4—42no—
495D4—61no—
496D4—61no—
497D4—61no—
498D4—81no—
499D4—124no—
500D4—242no—
501C2×C4—32no—
502C2×C4—32no—
503C2×C4—61no—
504C2×C4—61no—
505C2×C4—124no—
506C2×C4—122no—
507C2×C4—122no—
508C2×C4—182no—
509C2×C4—722no—
510C2×C4D3×#6711yescharacteristic
511C2×C4D3×#6711yescharacteristic
512C2×C4C22×D3211yescharacteristic
513C8—62no—
514C8—181no—
515C8—181no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—82no—
520C2×C3—82no—
521C2×C3—122no—
522C2×C3—162no—
523C2×C3—241no—
524C2×C3#559811yescharacteristic
525C2×C3C2×#91111yescharacteristic
526C2×C3#577411yescharacteristic
527C2×C3C2×#93211yescharacteristic
528C2×C3#583111yescharacteristic
529C2×C3#583511yescharacteristic
530D3—42no—
531D3—81no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—62no—
536C22—121no—
537C22—121no—
538C22—121no—
539C22—121no—
540C22—121no—
541C22C2×D3×#6711yescharacteristic
542C4—21no—
543C4—62no—
544C4—62no—
545C4—121no—
546C4—121no—
547C4—362no—
548C4#6393212yes—
549C4#6430911yescharacteristic
550C4D3×#23711yescharacteristic
551C3—21no—
552C3#8032011yescharacteristic, complemented
553C3#8358111yescharacteristic, complemented
554C2—82no—
555C2—122no—
556C2—241no—
557C2#1059509711yescharacteristic
558C2C2×#6393211yescharacteristic
559C2#1059515711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
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. C3×#5718C2semidirect
2. #10593960C2semidirect
3. #10592769C2semidirect
4. C3×#5072C2semidirect
5. #10591477C2semidirect
6. #10591430C2semidirect
7. #10591428C2semidirect
8. #10591409C2semidirect
9. C4×#3713C2semidirect
10. #10590268C2semidirect
11. #10590259C2semidirect
44. #5718D3semidirect
51. #5072D3semidirect
185. C3×D12#41semidirect
383. D12#237semidirect
485. C32#3366semidirect
552. C3#80320semidirect
553. C3#83581semidirect

Maximal subgroups

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

subgroupindex
C3×#57182
#105939602
#105927692
C3×#50722
#105914772
#105914302
#105914282
#105914092
C4×#37132
#105902682
#105902592
#835813
#803203