Finite Group Databasebeta

← #11787978

Subgroups — #11787978

Order 1152.

881 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#929C211yesmaximal, characteristic
2#10595506C211yesmaximal, characteristic
3#10592910C211yesmaximal, characteristic, complemented
4C3×#5211C211yesmaximal, characteristic, complemented
5C2×#63580C211yesmaximal, characteristic
6#10589187C211yesmaximal, characteristic, complemented
7#10589186C211yesmaximal, characteristic, complemented
8#71704—31nomaximal
9#69538—31nomaximal
10C23×C32×C4C2211yescharacteristic
11C22×C3×#67C2211yescharacteristic
12C2×#3757C2211yescharacteristic
13C2×#3757C2211yescharacteristic
14C2×C3×#217C2211yescharacteristic
15C2×C3×#217C2211yescharacteristic
16C2×C3×#217C2211yescharacteristic
17C3×#929—22no—
18C3×#929C414yescomplemented
19C2×C3×(C2×D3)⋊C4—21no—
20C2×C3×Dic3⋊C4—21no—
21#67⋊Dic3—22no—
22Dic3×#67—22no—
23D3×#217—21no—
24#63955—21no—
25#63658—22no—
26C3×C3⋊#95—22no—
27#63580—22no—
28C2×C3×#123—31no—
29#5798—31no—
30C2×#929D311yescharacteristic
31#5486—31no—
32C3×#381—31no—
33C2×#834—31no—
34#5211—31no—
35#5211—31no—
36#5211—61no—
37#5211D311yescharacteristic, complemented
38C2×#806—31no—
39#4527—31no—
40#4527—31no—
41#4527—31no—
42#4526—31no—
43C24×C32C2311yescharacteristic
44C23×C3×D3D411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4—21no—
47C22×C32×C4—21no—
48C22×C32×C4—21no—
49C22×C32×C4—21no—
50C22×C32×C4—21no—
51C22×C32×C4C2×C412yescomplemented
52C22×C3⋊Dic3—21no—
53C22×C3⋊Dic3D412yes—
54C2×C3×#67—21no—
55C2×C3×#67—21no—
56C2×C3×#67—21no—
57C2×C3×#67—21no—
58C2×C3×#67C2×C412yes—
59C2×C3×#67D412yes—
60C22×C3×Dic3—21no—
61C22×C3×Dic3—21no—
62C22×C3×Dic3D411yescharacteristic
63C22×C3×Dic3D412yes—
64C2×D3×Dic3—22no—
65#3757—21no—
66#3757—21no—
67#3757—21no—
68#3757—21no—
69C3×#217—21no—
70C3×#217—21no—
71C3×#217—21no—
72C3×#217—21no—
73C3×#217—21no—
74C3×#217C2×C412yescomplemented
75C3×(C2×D3)⋊C4—24no—
76C3×Dic3⋊C4—24no—
77Dic3⋊Dic3—22no—
78(C2×D3)⋊Dic3—22no—
79Dic32—22no—
80#1890—91noSylow
81C22×C3×D4—31no—
82C23×C3×C4—21no—
83C23×C3×C4C2×D311yescharacteristic
84C23×C3×C4C2×D311yescharacteristic
85C22×#67C2×D311yescharacteristic
86C3×#123—34no—
87C3×#123—62no—
88C2×C3×C4⋊C4—61no—
89C2×C3×C22⋊C4—31no—
90C2×C3×C22⋊C4—31no—
91C2×C3×C22⋊C4—31no—
92C2×C3×C22⋊C4—61no—
93C2×#217—31no—
94C2×#217—31no—
95C2×#217—31no—
96C2×#217—31no—
97C2×#217—61no—
98C2×#217—61no—
99C2×#217—61no—
100C2×#217C2×D311yescharacteristic
101C2×#217C2×D311yescharacteristic
102C2×#217C2×D311yescharacteristic
103D4×Dic3—62no—
104D4×Dic3—62no—
105#929—22no—
106#929Dic314yescomplemented
107C4×#67—62no—
108C2×(C2×D3)⋊C4—21no—
109#926—61no—
110C2×Dic3⋊C4—21no—
111#67⋊C4—62no—
112D3×C22⋊C4—61no—
113#877—61no—
114C3×#95—62no—
115#834—62no—
116C3⋊#95—22no—
117C3⋊#95—62no—
118C3⋊#95—62no—
119C3⋊#95—64no—
120#806—62no—
121C23×C32—42no—
122C23×C32C22×C411yescharacteristic
123C23×C32C2×D411yescharacteristic
124C23×C32C2×D411yescharacteristic
125C23×C32C2×D411yescharacteristic
126C23×C32C2×D411yescharacteristic
127C23×C32#4111yescharacteristic
128C23×C32#4111yescharacteristic
129C22×C3×D3—21no—
130C22×C3×D3—21no—
131C22×C3×D3—42no—
132C22×C3×D3C22⋊C412yes—
133C2×C32×C4—22no—
134C2×C32×C4—22no—
135C2×C32×C4—22no—
136C2×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C32×C4—41no—
139C2×C32×C4—41no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—42no—
142C2×C3⋊Dic3—42no—
143C2×C3⋊Dic3—41no—
144C3×#67—22no—
145C3×#67—22no—
146C3×#67—22no—
147C3×#67—22no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—42no—
153C2×C3×Dic3—42no—
154C2×C3×Dic3—42no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3C22⋊C412yes—
157D3×Dic3—82no—
158C2×#123—31no—
159#518—91no—
160C2×#99—91no—
161#381—31no—
162#381—91no—
163#342—91no—
164#342—91no—
165C24×C3—21no—
166C24×C3—31no—
167C24×C3C22×D311yescharacteristic
168C24×C3C22×D311yescharacteristic
169C23×D3#6711yescharacteristic
170C2×C3×D4—32no—
171C2×C3×D4—32no—
172C2×C3×D4—61no—
173C2×C3×D4—61no—
174C2×C3×D4—61no—
175C2×C3×D4—61no—
176C22×C3×C4—22no—
177C22×C3×C4—22no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—22no—
191C22×C3×C4—31no—
192C22×C3×C4—32no—
193C22×C3×C4—41no—
194C22×C3×C4—41no—
195C22×C3×C4—41no—
196C22×C3×C4—41no—
197C22×C3×C4—61no—
198C22×C3×C4—61no—
199C22×C3×C4C4×D312yescomplemented
200C22×C3×C4C2×Dic312yescomplemented
201C2×#67—21no—
202C2×#67—21no—
203C2×#67—21no—
204C2×#67—21no—
205C2×#67C2×Dic312yes—
206C2×#67#6712yes—
207C22×Dic3—21no—
208C22×Dic3—21no—
209C22×Dic3—32no—
210C22×Dic3—32no—
211C22×Dic3—62no—
212C22×Dic3—62no—
213C22×Dic3—62no—
214C22×Dic3—61no—
215C22×Dic3—61no—
216C22×Dic3#6711yescharacteristic
217C22×Dic3#6712yes—
218C2×C4×D3—62no—
219C3×C4⋊C4—64no—
220C3×C22⋊C4—32no—
221C3×C22⋊C4—64no—
222C3×C22⋊C4—61no—
223C3×C22⋊C4—61no—
224C3×C22⋊C4—61no—
225C3×C22⋊C4—61no—
226C3×C22⋊C4—61no—
227#217—21no—
228#217—21no—
229#217—21no—
230#217—21no—
231#217—21no—
232#217—62no—
233#217—61no—
234#217—61no—
235#217—61no—
236#217—61no—
237#217—61no—
238#217—61no—
239#217—61no—
240#217—61no—
241#217—121no—
242#217—121no—
243#217—121no—
244#217—121no—
245#217C2×Dic312yescomplemented
246(C2×D3)⋊C4—24no—
247(C2×D3)⋊C4—62no—
248C4⋊Dic3—62no—
249Dic3⋊C4—24no—
250Dic3⋊C4—62no—
251C4×Dic3—62no—
252C4×Dic3—62no—
253C22×C32—22no—
254C22×C32—22no—
255C22×C32—22no—
256C22×C32—41no—
257C22×C32—41no—
258C22×C32—41no—
259C22×C32—41no—
260C22×C32C2×C22⋊C411yescharacteristic
261C22×C32C4×D411yescharacteristic
262C22×C32C4×D411yescharacteristic
263C22×C32#12011yescharacteristic
264C22×C32#12111yescharacteristic
265C22×C32#12111yescharacteristic
266C22×C32#12311yescharacteristic
267C2×C3×D3—22no—
268C2×C3×D3—42no—
269C2×C3×D3—42no—
270C2×C3×D3—81no—
271C32×C4—42no—
272C3⋊Dic3—42no—
273C3⋊Dic3—81no—
274C3×Dic3—22no—
275C3×Dic3—42no—
276C3×Dic3—42no—
277C3×Dic3—81no—
278C22×D4—31no—
279C23×C4D3211yescharacteristic
280#123—34no—
281#123—62no—
282C4×D4—182no—
283C4×D4—182no—
284#117—181no—
285C2×C4⋊C4—61no—
286C2×C22⋊C4—31no—
287C2×C22⋊C4—31no—
288C2×C22⋊C4—31no—
289C2×C22⋊C4—61no—
290C2×C22⋊C4—91no—
291C2×C22⋊C4—91no—
292C2×C22⋊C4—181no—
293#99—182no—
294#95—62no—
295#95—182no—
296C23×C3—21no—
297C23×C3—21no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—21no—
302C23×C3—21no—
303C23×C3—32no—
304C23×C3—42no—
305C23×C3—42no—
306C23×C3—44no—
307C23×C3—61no—
308C23×C3—61no—
309C23×C3—122no—
310C23×C3C2×C4×D311yescharacteristic
311C23×C3#23511yescharacteristic
312C23×C3D3×D411yescharacteristic
313C23×C3D3×D411yescharacteristic
314C23×C3D3×D411yescharacteristic
315C23×C3D3×D411yescharacteristic
316C23×C3D3×D411yescharacteristic
317C23×C3#23711yescharacteristic
318C23×C3#23711yescharacteristic
319C23×C3#23711yescharacteristic
320C23×C3C22×Dic311yescharacteristic
321C23×C3C2×#6711yescharacteristic
322C23×C3C2×#6711yescharacteristic
323C23×C3C2×#6711yescharacteristic
324C22×D3—21no—
325C22×D3—21no—
326C22×D3—42no—
327C22×D3#21712yes—
328C3×D4—62no—
329C3×D4—62no—
330C3×D4—62no—
331C3×D4—62no—
332C2×C3×C4—24no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—32no—
340C2×C3×C4—42no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4—42no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—41no—
353C2×C3×C4—41no—
354C2×C3×C4—61no—
355C2×C3×C4—61no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—122no—
359C2×C3×C4—122no—
360C2×C3×C4—122no—
361C2×C3×C4—121no—
362#67—22no—
363#67—22no—
364#67—22no—
365#67—22no—
366C2×Dic3—21no—
367C2×Dic3—21no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—42no—
371C2×Dic3—42no—
372C2×Dic3—42no—
373C2×Dic3—41no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—122no—
377C2×Dic3—122no—
378C2×Dic3—122no—
379C2×Dic3—122no—
380C2×Dic3—124no—
381C2×Dic3—124no—
382C2×Dic3—122no—
383C2×Dic3—122no—
384C2×Dic3—121no—
385C2×Dic3—121no—
386C2×Dic3—242no—
387C2×Dic3#21712yes—
388C4×D3—242no—
389C2×C32—21no—
390C2×C32—21no—
391C2×C32—21no—
392C2×C32—21no—
393C2×C32—21no—
394C2×C32—21no—
395C2×C32#38611yescharacteristic
396C2×C32#45812yes—
397C3×D3—42no—
398C24—31no—
399C24C2×D3211yescharacteristic
400C2×D4—32no—
401C2×D4—32no—
402C2×D4—61no—
403C2×D4—61no—
404C2×D4—61no—
405C2×D4—61no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—31no—
413C22×C4—32no—
414C22×C4—61no—
415C22×C4—61no—
416C22×C4—92no—
417C22×C4—182no—
418C22×C4—181no—
419C22×C4D3×Dic312yescomplemented
420C4⋊C4—64no—
421C4⋊C4—182no—
422C22⋊C4—32no—
423C22⋊C4—64no—
424C22⋊C4—61no—
425C22⋊C4—61no—
426C22⋊C4—61no—
427C22⋊C4—61no—
428C22⋊C4—61no—
429C22⋊C4—182no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C22⋊C4—181no—
434C42—182no—
435C22×C3—24no—
436C22×C3—22no—
437C22×C3—22no—
438C22×C3—22no—
439C22×C3—22no—
440C22×C3—22no—
441C22×C3—22no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—42no—
450C22×C3—42no—
451C22×C3—41no—
452C22×C3—41no—
453C22×C3—41no—
454C22×C3—41no—
455C22×C3—41no—
456C22×C3—41no—
457C22×C3—41no—
458C22×C3—41no—
459C22×C3—42no—
460C22×C3—42no—
461C22×C3—42no—
462C22×C3—42no—
463C22×C3—62no—
464C22×C3—122no—
465C22×C3—122no—
466C22×C3—241no—
467C22×C3D3×C22⋊C411yescharacteristic
468C22×C3#67⋊C411yescharacteristic
469C22×C3#88311yescharacteristic
470C22×C3#88411yescharacteristic
471C22×C3C4×#6711yescharacteristic
472C22×C3D4×Dic311yescharacteristic
473C22×C3D4×Dic311yescharacteristic
474C22×C3#93511yescharacteristic
475C22×C3#93711yescharacteristic
476C22×C3#93711yescharacteristic
477C22×C3#93811yescharacteristic
478C22×C3#93911yescharacteristic
479C22×C3#93911yescharacteristic
480C22×C3C2×#21711yescharacteristic
481C2×D3—22no—
482C2×D3—42no—
483C2×D3—42no—
484C2×D3—81no—
485C3×C4—44no—
486C3×C4—42no—
487C3×C4—42no—
488C3×C4—62no—
489C3×C4—122no—
490C3×C4—122no—
491C3×C4—241no—
492Dic3—22no—
493Dic3—42no—
494Dic3—42no—
495Dic3—81no—
496Dic3—122no—
497Dic3—122no—
498Dic3—242no—
499Dic3—242no—
500Dic3—241no—
501Dic3—241no—
502C32#189011yescharacteristic, complemented, Sylow
503C23—32no—
504C23—42no—
505C23—61no—
506C23—61no—
507C23—122no—
508C23C2×D3×Dic311yescharacteristic
509C23#380411yescharacteristic
510C23#380511yescharacteristic
511C23D3×#6711yescharacteristic
512C23D3×#6711yescharacteristic
513C23D3×#6711yescharacteristic
514C23#381111yescharacteristic
515D4—62no—
516D4—62no—
517D4—62no—
518D4—62no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—32no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—61no—
528C2×C4—61no—
529C2×C4—62no—
530C2×C4—62no—
531C2×C4—122no—
532C2×C4—122no—
533C2×C4—122no—
534C2×C4—121no—
535C2×C4—182no—
536C2×C4—362no—
537C2×C4—362no—
538C2×C4—361no—
539C2×C4—722no—
540C2×C3—22no—
541C2×C3—22no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—22no—
555C2×C3—21no—
556C2×C3—41no—
557C2×C3—41no—
558C2×C3—41no—
559C2×C3—41no—
560C2×C3—122no—
561C2×C3#495611yescharacteristic
562C2×C3#505312yes—
563C2×C3#505312yes—
564C2×C3#522011yescharacteristic
565D3—42no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—62no—
574C22—122no—
575C22—122no—
576C22—241no—
577C22D3×#21711yescharacteristic
578C22#6396911yescharacteristic
579C22#6397011yescharacteristic
580C22#6397111yescharacteristic
581C22Dic3×#6711yescharacteristic
582C22#67⋊Dic311yescharacteristic
583C22#6398311yescharacteristic
584C4—42no—
585C4—62no—
586C4—122no—
587C4—122no—
588C4—241no—
589C4—362no—
590C4—721no—
591C3—21no—
592C3#6953811yescharacteristic, complemented
593C3#7170411yescharacteristic, complemented
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—122no—
601C2#1059139812yes—
602C2#1059172111yescharacteristic
subgroupG/H
centerC22#63983
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC23×C32×C4C22
socleC22×C32#120
prime radicalC22×C3×#67C22
cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32#1890
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. #10592910C2semidirect
4. C3×#5211C2semidirect
6. #10589187C2semidirect
7. #10589186C2semidirect
18. C3×#929C4semidirect
37. #5211D3semidirect
51. C22×C32×C4C2×C4semidirect
74. C3×#217C2×C4semidirect
106. #929Dic3semidirect
199. C22×C3×C4C4×D3semidirect
200. C22×C3×C4C2×Dic3semidirect
245. #217C2×Dic3semidirect
419. C22×C4D3×Dic3semidirect
502. C32#1890semidirect
592. C3#69538semidirect
593. C3#71704semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9292
#105955062
#105929102
C3×#52112
C2×#635802
#105891872
#105891862
#717043
#695383