Finite Group Databasebeta

← #11788174

Subgroups — #11788174

Order 1152.

969 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C42×D3C211yesmaximal, characteristic, complemented
2#10595023C211yesmaximal, characteristic
3C2×#63632C211yesmaximal, characteristic, complemented
4C2×#63570C211yesmaximal, characteristic, complemented
5#10591069C211yesmaximal, characteristic, complemented
6C3×#4523C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#71532—31nomaximal
9#68756—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C3×C4×D3—21no—
12C22×C3×C4×D3C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×C4×Dic3—21no—
17C2×C3×C4×Dic3C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C3×C42×D3—22no—
20C3×C42×D3—22no—
21#63977—21no—
22#63966—21no—
23#63909C412yescomplemented
24C4×#626—22no—
25#63857C412yescomplemented
26#63632—22no—
27#63570—22no—
28(C2×D3)⋊(C3⋊C8)—22no—
29C22×C3×C42—31no—
30#5791—31no—
31#5524—31no—
32C2×C42×D3D311yescharacteristic, complemented
33#5207—31no—
34C2×#825—31no—
35#5126—31no—
36C2×#805—31no—
37C2×#805—31no—
38C2×#805—31no—
39C2×#805—61no—
40C3×#339—31no—
41#4532—31no—
42#4523—31no—
43#4523D311yescharacteristic, complemented
44C23×C3×D3D411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48#3828—21no—
49#3828—21no—
50#3828—21no—
51#3828—21no—
52C2×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
53C2×C4×C3⋊D3—21no—
54C2×#634C2×C411yescharacteristic, complemented
55C22×C3×Dic3—21no—
56C22×C3×Dic3D411yescharacteristic
57C2×C3×C4×D3—28no—
58C2×C3×C4×D3—24no—
59C2×C3×C4×D3—21no—
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3—21no—
62C2×C3×C4×D3—21no—
63C2×C3×C4×D3C2×C412yes—
64C2×C3×C4×D3D412yes—
65C2×#626—22no—
66C32×C42—21no—
67C32×C42D412yescomplemented
68#3748—21no—
69#3748—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C3×#217—21no—
72C3×C4⋊Dic3C2×C412yescomplemented
73C3×C4×Dic3—24no—
74C3×C4×Dic3—21no—
75C3×C4×Dic3—21no—
76C3×C4×Dic3D412yescomplemented
77C3×#208—21no—
78C3×#208—21no—
79C2×C3×C3⋊C8—21no—
80Dic3⋊Dic3—22no—
81#3722—22no—
82(C2×D3)⋊Dic3—22no—
83#1896—91noSylow
84C23×C3×C4—31no—
85C23×C3×C4—61no—
86C2×#235—31no—
87C2×#235—31no—
88C2×#235—61no—
89C22×C4×D3—21no—
90C22×C4×D3C2×D311yescharacteristic
91C2×C3×M16—31no—
92C3×#117—31no—
93C2×C3×C42—21no—
94C2×C3×C42—31no—
95C2×C3×C42—62no—
96C2×C3×C42—61no—
97C2×C3×C42—62no—
98C2×C3×C42C2×D311yescharacteristic
99C2×C3×C42C2×D311yescharacteristic
100#953—61no—
101#930—32no—
102#929—61no—
103C4×#67—62no—
104#926C2×D311yescharacteristic
105#924—32no—
106C2×C4×Dic3—21no—
107C2×C4×Dic3C2×D311yescharacteristic
108C2×#208—31no—
109C2×#208—31no—
110C2×#208—61no—
111C2×#208C2×D311yescharacteristic
112#897—32no—
113#895—32no—
114#886—61no—
115#882—61no—
116C4×D12—62no—
117C42×D3—22no—
118C42×D3—22no—
119#830—62no—
120#825—62no—
121(C2×D3)⋊C8—62no—
122#805—62no—
123#805—64no—
124#805—62no—
125#805—62no—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—21no—
128C22×C3×D3—21no—
129C22×C3×D3—21no—
130C22×C3×D3—24no—
131C22×C3×D3C22⋊C412yes—
132C2×C32×C4—24no—
133C2×C32×C4—22no—
134C2×C32×C4C22×C411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4#4111yescharacteristic
139C2×C32×C4#4111yescharacteristic
140#638—41no—
141#638—41no—
142C2×C3⋊Dic3—21no—
143C4⋊(C3⋊D3)—21no—
144C4⋊(C3⋊D3)—21no—
145C4×C3⋊D3—41no—
146C4×C3⋊D3—41no—
147#634—21no—
148#634—21no—
149C2×C3×Dic3—24no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—21no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3C22⋊C412yes—
155C3×C4×D3—216no—
156C3×C4×D3—22no—
157C3×C4×D3—22no—
158C3×C4×D3—22no—
159C3×C4×D3—22no—
160#626—44no—
161C3⋊(C3⋊C8)—41no—
162C3×C3⋊C8—41no—
163#525—91no—
164C22×C42—31no—
165C2×#104—91no—
166C2×#104—91no—
167#407—91no—
168#339—31no—
169#339—91no—
170C24×C3—31no—
171C23×D3#6711yescharacteristic
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—31no—
176C22×C3×C4—32no—
177C22×C3×C4—32no—
178C22×C3×C4—41no—
179C22×C3×C4—64no—
180C22×C3×C4—68no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4—61no—
184C22×C3×C4—61no—
185C22×C3×C4—61no—
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C2×#67—62no—
189C2×#67—61no—
190C2×#67—61no—
191C2×#67—121no—
192C22×Dic3—21no—
193C22×Dic3#6711yescharacteristic
194#235—62no—
195#235—62no—
196#235—61no—
197#235—61no—
198#235—61no—
199#235—61no—
200#235—61no—
201#235—61no—
202#235—61no—
203#235—61no—
204#235—121no—
205#235—121no—
206C2×D12—31no—
207C2×D12—31no—
208C2×D12—61no—
209C2×D12—62no—
210C2×C4×D3—24no—
211C2×C4×D3—28no—
212C2×C4×D3—21no—
213C2×C4×D3—21no—
214C2×C4×D3—21no—
215C2×C4×D3—21no—
216C2×C4×D3—61no—
217C2×C4×D3—61no—
218C2×C4×D3—121no—
219C2×C4×D3C4×D312yes—
220C2×C4×D3D1212yes—
221C2×Dic6—31no—
222C2×Dic6—31no—
223C2×Dic6—61no—
224C3×M16—61no—
225C3×M16—61no—
226C2×C3×C8—61no—
227C3×C4⋊C4—32no—
228C3×C22⋊C4—61no—
229C3×C42—21no—
230C3×C42—21no—
231C3×C42—22no—
232C3×C42—32no—
233C3×C42—41no—
234C3×C42—64no—
235C3×C42—61no—
236C3×C42—61no—
237C3×C42D1212yescomplemented
238C3×C42#6712yescomplemented
239#217—21no—
240#217—62no—
241(C2×D3)⋊C4—62no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—62no—
244C4⋊Dic3—62no—
245C4⋊Dic3C4×D312yescomplemented
246Dic3⋊C4—62no—
247C4×Dic3—24no—
248C4×Dic3—21no—
249C4×Dic3—21no—
250C4×Dic3#6712yescomplemented
251#208—21no—
252#208—21no—
253#208—62no—
254#208—61no—
255#208—61no—
256#208—61no—
257#208—61no—
258#208—121no—
259C2×C3⋊C8—21no—
260C2×C3⋊C8—61no—
261C2×C3⋊C8—61no—
262C2×C3⋊C8—121no—
263C22×C32—22no—
264C22×C32C2×C22⋊C411yescharacteristic
265C22×C32#12011yescharacteristic
266C22×C32#12311yescharacteristic
267C2×C3⋊D3—41no—
268C2×C3⋊D3—42no—
269C2×C3×D3—24no—
270C2×C3×D3—24no—
271C2×C3×D3—22no—
272C2×C3×D3—22no—
273C2×C3×D3#10414yescomplemented
274C32×C4—24no—
275C32×C4C4×D411yescharacteristic
276C32×C4C4×D411yescharacteristic
277C32×C4#12111yescharacteristic
278C32×C4#12111yescharacteristic
279C3⋊Dic3—41no—
280C3×Dic3—24no—
281C3×Dic3—22no—
282C3×Dic3—42no—
283C2×#41—91no—
284C23×C4—31no—
285C23×C4—61no—
286C2×M16—31no—
287C2×M16—91no—
288#123—181no—
289C22⋊Q8—92no—
290#121—92no—
291#120—181no—
292C4×D4—182no—
293#117—31no—
294C2×C42—31no—
295C2×C42—62no—
296C2×C42—61no—
297C2×C42—62no—
298C2×C42D3211yescharacteristic
299#104—182no—
300#104—182no—
301C22⋊C8—182no—
302C23×C3—21no—
303C23×C3—32no—
304C23×C3—64no—
305C23×C3—61no—
306C23×C3—61no—
307C23×C3D3×D411yescharacteristic
308C23×C3C2×#6711yescharacteristic
309C22×D3—21no—
310C22×D3—21no—
311C22×D3—24no—
312C22×D3—61no—
313C22×D3—61no—
314C22×D3—121no—
315C22×D3(C2×D3)⋊C412yes—
316C2×C3×C4—24no—
317C2×C3×C4—24no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—32no—
327C2×C3×C4—42no—
328C2×C3×C4—44no—
329C2×C3×C4—616no—
330C2×C3×C4—64no—
331C2×C3×C4—62no—
332C2×C3×C4—61no—
333C2×C3×C4—61no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4C2×C4×D311yescharacteristic
340C2×C3×C4C2×C4×D311yescharacteristic
341C2×C3×C4C2×D1211yescharacteristic
342C2×C3×C4C2×D1211yescharacteristic
343C2×C3×C4#23511yescharacteristic
344C2×C3×C4#23511yescharacteristic
345C2×C3×C4#23511yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4#23911yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351#67—124no—
352#67—122no—
353#67—122no—
354#67—121no—
355#67—121no—
356#67—121no—
357#67—121no—
358C2×Dic3—24no—
359C2×Dic3—21no—
360C2×Dic3—21no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—121no—
366C2×Dic3(C2×D3)⋊C412yes—
367D12—62no—
368D12—61no—
369D12—61no—
370D12—61no—
371D12—61no—
372D12—121no—
373D12—124no—
374C4×D3—216no—
375C4×D3—22no—
376C4×D3—22no—
377C4×D3—22no—
378C4×D3—22no—
379C4×D3—122no—
380C4×D3—122no—
381C4×D3—121no—
382C4×D3—121no—
383C4×D3—121no—
384C4×D3—121no—
385Dic6—62no—
386Dic6—61no—
387Dic6—61no—
388Dic6—61no—
389Dic6—61no—
390Dic6—121no—
391C3×C8—121no—
392C3⋊C8—41no—
393C3⋊C8—122no—
394C3⋊C8—121no—
395C3⋊C8—121no—
396C2×C32—21no—
397C2×C32—21no—
398C2×C32#38611yescharacteristic
399C2×C32C2×#10412yes—
400C3⋊D3—81no—
401C3×D3—24no—
402C24—31no—
403#41—181no—
404#41—181no—
405#41—181no—
406#41—181no—
407C2×Q8—91no—
408C2×D4—91no—
409C2×D4—182no—
410C2×D4—181no—
411C22×C4—21no—
412C22×C4—31no—
413C22×C4—32no—
414C22×C4—32no—
415C22×C4—64no—
416C22×C4—68no—
417C22×C4—61no—
418C22×C4—61no—
419C22×C4—61no—
420C22×C4—61no—
421C22×C4—61no—
422C22×C4—181no—
423C22×C4C2×D3211yescharacteristic
424M16—61no—
425M16—61no—
426M16—181no—
427M16—181no—
428C2×C8—61no—
429C2×C8—181no—
430C4⋊C4—32no—
431C4⋊C4—182no—
432C22⋊C4—61no—
433C22⋊C4—182no—
434C22⋊C4—182no—
435C42—21no—
436C42—32no—
437C42—64no—
438C42—61no—
439C42—61no—
440C42#62612yescomplemented
441C22×C3—22no—
442C22×C3—22no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—34no—
447C22×C3—42no—
448C22×C3—64no—
449C22×C3—64no—
450C22×C3—62no—
451C22×C3—62no—
452C22×C3D3×C22⋊C411yescharacteristic
453C22×C3#88211yescharacteristic
454C22×C3#89411yescharacteristic
455C22×C3C2×(C2×D3)⋊C411yescharacteristic
456C22×C3#92911yescharacteristic
457C22×C3#95311yescharacteristic
458C2×D3—24no—
459C2×D3—24no—
460C2×D3—22no—
461C2×D3—22no—
462C2×D3—122no—
463C2×D3—121no—
464C2×D3—122no—
465C2×D3—121no—
466C2×D3—122no—
467C2×D3—242no—
468C2×D3#80514yescomplemented
469C3×C4—24no—
470C3×C4—24no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—44no—
476C3×C4—64no—
477C3×C4—62no—
478C3×C4—122no—
479C3×C4C4×D1211yescharacteristic
480C3×C4#88411yescharacteristic
481C3×C4#89311yescharacteristic
482C3×C4#89511yescharacteristic
483C3×C4C4×#6711yescharacteristic
484C3×C4C4×#6711yescharacteristic
485C3×C4#93011yescharacteristic
486C3×C4#93011yescharacteristic
487Dic3—24no—
488Dic3—22no—
489Dic3—42no—
490Dic3—122no—
491Dic3—121no—
492Dic3—121no—
493C32#189611yescharacteristic, complemented, Sylow
494C23—32no—
495C23—64no—
496C23—61no—
497C23—61no—
498C23—181no—
499C23D3×#6711yescharacteristic
500Q8—181no—
501Q8—181no—
502D4—181no—
503D4—181no—
504D4—364no—
505D4—361no—
506D4—361no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—32no—
510C2×C4—616no—
511C2×C4—64no—
512C2×C4—61no—
513C2×C4—62no—
514C2×C4—61no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—181no—
521C2×C4—361no—
522C2×C4—361no—
523C2×C4#379811yescharacteristic
524C2×C4#379911yescharacteristic
525C2×C4C4×D3211yescharacteristic
526C2×C4D3×D1211yescharacteristic
527C2×C4C2×#62611yescharacteristic
528C2×C4D3×#6711yescharacteristic
529C8—121no—
530C8—361no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—22no—
537C2×C3—41no—
538C2×C3—41no—
539C2×C3—64no—
540C2×C3#466511yescharacteristic
541C2×C3D3×#10412yes—
542C2×C3C2×#80512yes—
543C2×C3#521311yescharacteristic
544D3—24no—
545D3—242no—
546D3—241no—
547D3—241no—
548C22—22no—
549C22—34no—
550C22—64no—
551C22—64no—
552C22—62no—
553C22—62no—
554C22—361no—
555C22—362no—
556C22#6385011yescharacteristic
557C22D3×(C2×D3)⋊C411yescharacteristic
558C22#6397711yescharacteristic
559C4—24no—
560C4—64no—
561C4—62no—
562C4—122no—
563C4—361no—
564C4C4×#62611yescharacteristic
565C4#6390411yescharacteristic
566C4#6390611yescharacteristic
567C4#6390911yescharacteristic
568C3—21no—
569C3#6875611yescharacteristic, complemented
570C3#7153211yescharacteristic, complemented
571C2—21no—
572C2—21no—
573C2—64no—
574C2—721no—
575C2D3×#80512yes—
576C2#1059138211yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radical#10595023C2
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1896
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C3×C42×D3C2semidirect
3. C2×#63632C2semidirect
4. C2×#63570C2semidirect
5. #10591069C2semidirect
6. C3×#4523C2semidirect
7. #10589161C2semidirect
23. #63909C4semidirect
25. #63857C4semidirect
32. C2×C42×D3D3semidirect
43. #4523D3semidirect
52. C2×C4⋊(C3⋊D3)C2×C4semidirect
54. C2×#634C2×C4semidirect
67. C32×C42D4semidirect
72. C3×C4⋊Dic3C2×C4semidirect
76. C3×C4×Dic3D4semidirect
237. C3×C42D12semidirect
238. C3×C42#67semidirect
245. C4⋊Dic3C4×D3semidirect
250. C4×Dic3#67semidirect
273. C2×C3×D3#104semidirect
440. C42#626semidirect
468. C2×D3#805semidirect
493. C32#1896semidirect
569. C3#68756semidirect
570. C3#71532semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C42×D32
#105950232
C2×#636322
C2×#635702
#105910692
C3×#45232
#105891612
#715323
#687563