Finite Group Databasebeta

← #11895775

Subgroups — #11895775

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
1#10593960C211yesmaximal, characteristic, complemented
2#10593902C211yesmaximal, characteristic, complemented
3#10592393C211yesmaximal, characteristic, complemented
4C3×C4×D24C211yesmaximal, characteristic, complemented
5C3×#4679C211yesmaximal, characteristic, complemented
6#10590882C212yesmaximal, complemented
7#10590774C212yesmaximal, complemented
8#10590753C212yesmaximal, complemented
9#10590746C212yesmaximal, complemented
10#10590349C211yesmaximal, characteristic, complemented
11#10590268C211yesmaximal, characteristic, complemented
12#79969—31nomaximal
13#79570—31nomaximal
14C2×#3799—21no—
15#64083C2211yescharacteristic
16#64078C2211yescharacteristic
17C2×C3×D24C2211yescharacteristic
18C3×C4×D12C2211yescharacteristic
19C3×C4×D12C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21#63911C2212yes—
22#63910—22no—
23#63909—21no—
24#63896—22no—
25#63894C2212yes—
26Dic3×D12C2212yes—
27D3×C4⋊Dic3—21no—
28#63869C2212yes—
29#63856—21no—
30C2×#3714C2212yes—
31C32×C4×C8C2211yescharacteristic
32#63648C2212yes—
33#63648C2212yes—
34C3×#821C2211yescharacteristic
35C3×#821C2211yescharacteristic
36C3×#818C2211yescharacteristic
37C3×#815C2212yes—
38C3×Dic3⋊C8C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63573C2212yes—
41#63564C2212yes—
42#63563C2212yes—
43#5579—31no—
44#5577—31no—
45#5553—31no—
46#5543—31no—
47C3×#446—31no—
48C3×C4×D8—31no—
49#5150—32no—
50#5015—31no—
51#5008—31no—
52#4891—32no—
53#4847—32no—
54#4843—32no—
55#4843—31no—
56#4842—31no—
57#4785—32no—
58#4764—32no—
59#4713—32no—
60#4711—32no—
61#4694—31no—
62#4694—31no—
63#4694—61no—
64C4×D24D311yescharacteristic, complemented
65#4679D311yescharacteristic, complemented
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)C2312yes—
69C2×#634—21no—
70C2×C3×D12C2311yescharacteristic
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×C4×D3—21no—
74C2×C3×Dic6D411yescharacteristic
75C2×#626—22no—
76C2×#626—22no—
77C2×#624—22no—
78C2×D3×Dic3—22no—
79#3799—44no—
80C2×C32×C8C2311yescharacteristic
81C2×C32×C8C2311yescharacteristic
82C32×C42C2311yescharacteristic
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)C2312yes—
85C3×(C2×D3)⋊C4—21no—
86C3×(C2×D3)⋊C4—21no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2311yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4D412yes—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2312yes—
93C3×D24—22no—
94#3724—22no—
95Dic3⋊Dic3—22no—
96#3722—22no—
97(C2×D3)⋊Dic3—22no—
98#3714—24no—
99#3366—91noSylow
100C2×#239—61no—
101C2×#235—61no—
102C2×C3×D8—31no—
103C3×C4×Q8—31no—
104C3×C4×D4—31no—
105C3×C4×D4—31no—
106#946—61no—
107#940—32no—
108D4×Dic3—32no—
109C2×#213—32no—
110#930—61no—
111C2×C4⋊Dic3—61no—
112#924—61no—
113C2×D24—32no—
114C2×D24C2×D311yescharacteristic
115#896—62no—
116#895—62no—
117#895—61no—
118#893—32no—
119D3×C4⋊C4—61no—
120#890—32no—
121#884—62no—
122#878—62no—
123#874—32no—
124#874—31no—
125#874—31no—
126#874—61no—
127C4×D12—32no—
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×#107—31no—
137C3×C4⋊C8—32no—
138C3×C4⋊C8—31no—
139C3×#102—31no—
140C3×#102—31no—
141C3×#97—32no—
142C3×C4×C8—21no—
143C3×C4×C8C2×D311yescharacteristic
144C3×C4×C8C2×D311yescharacteristic
145#832—32no—
146#821—32no—
147#821—32no—
148#821—32no—
149#821—32no—
150#821—32no—
151#821—32no—
152#821—62no—
153#821—62no—
154#821C2×D311yescharacteristic
155#821C2×D311yescharacteristic
156#818C2×D311yescharacteristic
157#817—32no—
158#815C2×D312yes—
159Dic3⋊C8C2×D312yes—
160#809—32no—
161#808—32no—
162C4⋊(C3⋊C8)C2×D311yescharacteristic
163C22×C3⋊D3—22no—
164C22×C3×D3—21no—
165C22×C3×D3—21no—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3—22no—
170C4⋊(C3⋊D3)—22no—
171C4⋊(C3⋊D3)—22no—
172C4⋊(C3⋊D3)—42no—
173C4⋊(C3⋊D3)—81no—
174#634—81no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×D412yes—
179C3×D12—21no—
180C3×D12—21no—
181C3×D12—21no—
182C3×D12#4112yescomplemented
183C3×C4×D3—42no—
184C3×C4×D3—42no—
185C3×Dic6—22no—
186#626—44no—
187#626—82no—
188#624—44no—
189D3×Dic3—82no—
190C32×C8—21no—
191C32×C8—21no—
192C3×C3⋊C8—22no—
193#554—91no—
194#550—91no—
195#490—92no—
196#486—91no—
197#478—92no—
198#476—91no—
199#459—91no—
200#459—92no—
201#446—31no—
202#442—92no—
203C4×D8—31no—
204C2×C3×Q8—31no—
205C2×C3×D4—31no—
206C2×C3×D4—31no—
207C22×C3×C4—61no—
208C22×C3×C4—61no—
209C2×#67—62no—
210C2×#67—62no—
211C22×Dic3—62no—
212#239—124no—
213#235—124no—
214C2×D12—32no—
215C2×D12—32no—
216C2×D12—62no—
217C2×D12—62no—
218C2×D12—61no—
219C2×D12—61no—
220C2×D12—62no—
221C2×D12—61no—
222C2×D12—61no—
223C2×D12—121no—
224C2×D12—121no—
225C2×D12C22×D311yescharacteristic
226C2×D12C22×D311yescharacteristic
227C2×C4×D3—21no—
228C2×C4×D3—21no—
229C2×C4×D3—62no—
230C2×C4×D3—62no—
231C2×C4×D3—62no—
232C2×Dic6—61no—
233C2×Dic6—61no—
234C2×Dic6—121no—
235C2×Dic6D1211yescharacteristic
236C3×D8—62no—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—32no—
240C2×C3×C8C22×D311yescharacteristic
241C2×C3×C8C22×D311yescharacteristic
242C2×C3×C8C22×D311yescharacteristic
243C2×C3×C8C22×D311yescharacteristic
244C3×C4⋊C4—31no—
245C3×C4⋊C4—32no—
246C3×C4⋊C4—31no—
247C3×C4⋊C4—31no—
248C3×C22⋊C4—61no—
249C3×C22⋊C4—61no—
250C3×C42—21no—
251C3×C42—32no—
252C3×C42C22×D311yescharacteristic
253C3×C42C22×D311yescharacteristic
254#217—62no—
255#213—64no—
256(C2×D3)⋊C4—21no—
257(C2×D3)⋊C4—21no—
258(C2×D3)⋊C4—62no—
259(C2×D3)⋊C4—62no—
260(C2×D3)⋊C4—62no—
261C4⋊Dic3—32no—
262C4⋊Dic3—32no—
263C4⋊Dic3—62no—
264C4⋊Dic3—61no—
265C4⋊Dic3—61no—
266C4⋊Dic3—62no—
267C4⋊Dic3—121no—
268C4⋊Dic3D1211yescharacteristic
269C4⋊Dic3C22×D311yescharacteristic
270C4⋊Dic3C22×D311yescharacteristic
271Dic3⋊C4—62no—
272Dic3⋊C4—62no—
273Dic3⋊C4—62no—
274Dic3⋊C4D1212yes—
275C4×Dic3C22×D312yes—
276C2×C3⋊C8C22×D312yes—
277D24—22no—
278D24—64no—
279C22×C32C22×D411yescharacteristic
280C2×C3⋊D3—42no—
281C2×C3⋊D3—42no—
282C2×C3⋊D3—42no—
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—181no—
299C2×D8—31no—
300C2×D8—92no—
301C4⋊Q8—91no—
302#127—92no—
303#127—91no—
304#125—92no—
305C22⋊Q8—182no—
306C22⋊Q8—181no—
307#121—182no—
308#121—181no—
309C4×Q8—31no—
310C4×D4—31no—
311C4×D4—31no—
312C4×D4—92no—
313C4×D4—92no—
314C2×C4⋊C4—181no—
315#107—31no—
316#106—92no—
317C4⋊C8—32no—
318C4⋊C8—31no—
319#102—31no—
320#102—31no—
321#102—92no—
322#102—92no—
323#102—92no—
324#102—92no—
325#97—32no—
326C4×C8D3211yescharacteristic
327C23×C3—61no—
328C23×C3—61no—
329C22×D3—21no—
330C22×D3—21no—
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—122no—
334C3×Q8—62no—
335C3×D4—32no—
336C3×D4—61no—
337C3×D4—61no—
338C3×D4—61no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—32no—
343C2×C3×C4—32no—
344C2×C3×C4—61no—
345C2×C3×C4—61no—
346C2×C3×C4—122no—
347C2×C3×C4—122no—
348C2×C3×C4C2×D1211yescharacteristic
349C2×C3×C4C2×D1211yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4C23×D311yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354#67—124no—
355#67—242no—
356C2×Dic3—21no—
357C2×Dic3—21no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—122no—
361C2×Dic3—242no—
362C2×Dic3C2×D1212yes—
363C2×Dic3C2×D1212yes—
364D12—21no—
365D12—21no—
366D12—21no—
367D12—62no—
368D12—62no—
369D12—62no—
370D12—62no—
371D12—122no—
372D12—122no—
373D12—124no—
374D12—122no—
375D12—122no—
376D12—242no—
377D12—241no—
378D12—241no—
379D12—242no—
380D12—242no—
381D12#23512yescomplemented
382C4×D3—42no—
383C4×D3—42no—
384C4×D3—124no—
385C4×D3—124no—
386C4×D3—242no—
387Dic6—22no—
388Dic6—241no—
389Dic6—241no—
390Dic6—242no—
391C3×C8—21no—
392C3×C8—21no—
393C3×C8—21no—
394C3×C8—21no—
395C3×C8—41no—
396C3×C8—41no—
397C3×C8—62no—
398C3⋊C8—22no—
399C2×C32#54811yescharacteristic
400C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
401C2×C32#57611yescharacteristic
402C3⋊D3—82no—
403C3×D3—42no—
404C3×D3—81no—
405#41—364no—
406C2×Q8—31no—
407C2×Q8—181no—
408C2×D4—31no—
409C2×D4—31no—
410C2×D4—92no—
411C2×D4—182no—
412C2×D4—182no—
413C2×D4—181no—
414C2×D4—181no—
415C22×C4—61no—
416C22×C4—61no—
417C22×C4—182no—
418C22×C4—182no—
419D8—62no—
420D8—184no—
421C2×C8—32no—
422C2×C8C2×D3211yescharacteristic
423C2×C8C2×D3211yescharacteristic
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—61no—
433C22⋊C4—61no—
434C22⋊C4—182no—
435C22⋊C4—182no—
436C42—32no—
437C42C2×D3211yescharacteristic
438C22×C3—21no—
439C22×C3—62no—
440C22×C3—121no—
441C22×C3—121no—
442C22×C3—121no—
443C22×C3—121no—
444C22×C3—121no—
445C22×C3C22×D1211yescharacteristic
446C22×C3C2×D3×D411yescharacteristic
447C2×D3—22no—
448C2×D3—41no—
449C2×D3—41no—
450C2×D3—41no—
451C2×D3—41no—
452C2×D3—41no—
453C2×D3—122no—
454C2×D3—122no—
455C2×D3—122no—
456C2×D3—122no—
457C2×D3—122no—
458C2×D3—122no—
459C2×D3—242no—
460C2×D3—242no—
461C2×D3—242no—
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#90812yes—
473C3×C4#91112yes—
474C3×C4C2×#23511yescharacteristic
475C3×C4#100711yescharacteristic
476C3×C4D3×#4111yescharacteristic
477C3×C4#101011yescharacteristic
478Dic3—22no—
479Dic3—22no—
480Dic3—41no—
481Dic3—41no—
482Dic3—122no—
483Dic3—122no—
484Dic3—242no—
485C32#336611yescharacteristic, complemented, Sylow
486C23—61no—
487C23—61no—
488C23—182no—
489Q8—62no—
490Q8—721no—
491D4—32no—
492D4—61no—
493D4—61no—
494D4—61no—
495D4—182no—
496D4—182no—
497D4—364no—
498D4—362no—
499D4—721no—
500D4—722no—
501C2×C4—32no—
502C2×C4—32no—
503C2×C4—61no—
504C2×C4—61no—
505C2×C4—122no—
506C2×C4—122no—
507C2×C4—182no—
508C2×C4—364no—
509C2×C4—722no—
510C2×C4D3×D1211yescharacteristic
511C2×C4D3×D1211yescharacteristic
512C2×C4C22×D3211yescharacteristic
513C8—21no—
514C8—21no—
515C8—62no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—122no—
520C2×C3—241no—
521C2×C3#555211yescharacteristic
522C2×C3#557611yescharacteristic
523C2×C3C2×#90811yescharacteristic
524C2×C3#575211yescharacteristic
525C2×C3C2×#91111yescharacteristic
526C2×C3#576911yescharacteristic
527D3—42no—
528D3—81no—
529D3—242no—
530D3—242no—
531D3—482no—
532C22—62no—
533C22—121no—
534C22—121no—
535C22—121no—
536C22—121no—
537C22—121no—
538C22—362no—
539C22—362no—
540C22—362no—
541C22C2×D3×D1211yescharacteristic
542C4—21no—
543C4—62no—
544C4—62no—
545C4—121no—
546C4—121no—
547C4—362no—
548C4#6379512yes—
549C4#6429711yescharacteristic
550C4D3×#23511yescharacteristic
551C3—21no—
552C3#7957011yescharacteristic, complemented
553C3#7996911yescharacteristic, complemented
554C2—122no—
555C2—241no—
556C2—722no—
557C2#1059389911yescharacteristic
558C2C2×#6379511yescharacteristic
559C2#1059468011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
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. #10593960C2semidirect
2. #10593902C2semidirect
3. #10592393C2semidirect
4. C3×C4×D24C2semidirect
5. C3×#4679C2semidirect
6. #10590882C2semidirect
7. #10590774C2semidirect
8. #10590753C2semidirect
9. #10590746C2semidirect
10. #10590349C2semidirect
11. #10590268C2semidirect
64. C4×D24D3semidirect
65. #4679D3semidirect
182. C3×D12#41semidirect
381. D12#235semidirect
485. C32#3366semidirect
552. C3#79570semidirect
553. C3#79969semidirect

Maximal subgroups

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

subgroupindex
#105939602
#105939022
#105923932
C3×C4×D242
C3×#46792
#105908822
#105907742
#105907532
#105907462
#105903492
#105902682
#799693
#795703