Finite Group Databasebeta

← #11787438

Subgroups — #11787438

Order 1152.

885 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic3×D12C211yesmaximal, characteristic
2C22×#3716C211yesmaximal, characteristic
3C2×#63643C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic
5#10591213C211yesmaximal, characteristic, complemented
6C3×#4550C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#70171—31nomaximal
9#68672—31nomaximal
10C22×#634C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×D3×Dic3—21no—
13C22×C32×C8C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×(C2×D3)⋊Dic3—21no—
19Dic3×D12—22no—
20Dic3×D12—22no—
21C2×#3716—22no—
22C2×#3716—22no—
23C2×#3716C414yescomplemented
24#63643—22no—
25C3×#821—22no—
26#63579—21no—
27#63579—21no—
28C2×D4×Dic3—31no—
29C22×#214—31no—
30C22×#204—31no—
31C2×C4×D12—31no—
32C2×C3×#102—31no—
33C2×#821D311yescharacteristic
34C2×#816—31no—
35C2×#816—31no—
36C2×#816—61no—
37#4973—31no—
38#4929—31no—
39C3×#336—31no—
40#4551—31no—
41#4550D311yescharacteristic, complemented
42#4529—31no—
43C23×C3×D3—21no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C22×C3⋊Dic3—21no—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634C2×C412yescomplemented
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C22×C3×Dic3D411yescharacteristic
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12C2×C412yes—
60C2×C3×D12D412yes—
61C2×C3×D12D412yes—
62C2×D3×Dic3—24no—
63C2×D3×Dic3—42no—
64C2×D3×Dic3—42no—
65C2×C32×C8—21no—
66C2×C32×C8—21no—
67C2×C32×C8—21no—
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)D412yes—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4×Dic3—21no—
73C3×C4×Dic3—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8C2×C412yescomplemented
77(C2×D3)⋊Dic3—24no—
78#3716—28no—
79#1877—91noSylow
80C22×C3×D4—31no—
81C23×Dic3—61no—
82C22×D12C2×D311yescharacteristic
83C22×C4×D3—61no—
84C22×Dic6—31no—
85C22×Dic6—31no—
86C22×Dic6—61no—
87C22×C3×C8—21no—
88C22×C3×C8—31no—
89C22×C3×C8C2×D311yescharacteristic
90C22×C3×C8C2×D311yescharacteristic
91C2×C3×C4⋊C4—31no—
92C2×C3×C42—31no—
93C2×#217—61no—
94D4×Dic3—62no—
95D4×Dic3—62no—
96C2×#214—34no—
97C2×#214—62no—
98C2×#214—62no—
99C2×(C2×D3)⋊C4—61no—
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—31no—
102C2×C4⋊Dic3—61no—
103C2×C4⋊Dic3C2×D311yescharacteristic
104C2×C4×Dic3C2×D311yescharacteristic
105C22×C3⋊C8C2×D311yescharacteristic
106C2×#204—34no—
107C2×#204—62no—
108C2×#204—62no—
109C4×D12—62no—
110C4×D12—62no—
111C3×#102—62no—
112C3⋊#95—61no—
113C3⋊#95—61no—
114C3⋊#95—61no—
115C3⋊#95—61no—
116#821—22no—
117#816—62no—
118#816—62no—
119#816—64no—
120C23×C32C2×D411yescharacteristic
121C22×C3×D3—22no—
122C22×C3×D3—22no—
123C22×C3×D3—22no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—41no—
137C2×C3⋊Dic3—41no—
138C2×C3⋊Dic3—41no—
139C2×C3⋊Dic3—41no—
140#634—22no—
141#634—22no—
142#634—41no—
143#634—41no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3SD1612yescomplemented
153C3×D12—22no—
154C3×D12—22no—
155C3×D12—22no—
156C3×D12C22⋊C414yes—
157D3×Dic3—48no—
158C32×C8—41no—
159C3×C3⋊C8—22no—
160C22×SD16—91no—
161C2×C4×D4—91no—
162C2×#103—91no—
163C2×#102—31no—
164#391—91no—
165#340—91no—
166#336—31no—
167C24×C3—61no—
168C23×D3—21no—
169C2×C3×D4—32no—
170C2×C3×D4—32no—
171C2×C3×D4—32no—
172C2×C3×D4—61no—
173C2×C3×D4—61no—
174C2×C3×D4—61no—
175C22×C3×C4—21no—
176C22×C3×C4—31no—
177C22×C3×C4—31no—
178C22×C3×C4—61no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C22×Dic3—21no—
182C22×Dic3—64no—
183C22×Dic3—61no—
184C22×Dic3—61no—
185C22×Dic3—61no—
186C22×Dic3—61no—
187C22×Dic3—121no—
188C22×Dic3—121no—
189C22×Dic3—122no—
190C22×Dic3—122no—
191C22×Dic3D1211yescharacteristic
192C22×Dic3D1211yescharacteristic
193C2×D12—21no—
194C2×D12—21no—
195C2×D12—21no—
196C2×D12C4×D312yes—
197C2×D12D1212yes—
198C2×D12#6712yes—
199C2×C4×D3—64no—
200C2×C4×D3—122no—
201C2×C4×D3—122no—
202C2×Dic6—32no—
203C2×Dic6—32no—
204C2×Dic6—62no—
205C2×Dic6—62no—
206C2×Dic6—62no—
207C2×Dic6—61no—
208C2×Dic6—61no—
209C2×Dic6—61no—
210C2×Dic6—61no—
211C2×Dic6—61no—
212C2×Dic6—61no—
213C2×Dic6—61no—
214C2×Dic6—61no—
215C2×Dic6—61no—
216C2×Dic6—61no—
217C2×Dic6—121no—
218C2×Dic6—121no—
219C2×Dic6—121no—
220C2×C3×C8—22no—
221C2×C3×C8—21no—
222C2×C3×C8—21no—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8—21no—
226C2×C3×C8—21no—
227C2×C3×C8—32no—
228C2×C3×C8—41no—
229C2×C3×C8—41no—
230C2×C3×C8—61no—
231C2×C3×C8—61no—
232C3×C4⋊C4—61no—
233C3×C4⋊C4—61no—
234C3×C42—61no—
235C3×C42—61no—
236#217—64no—
237#214—68no—
238(C2×D3)⋊C4—64no—
239C4⋊Dic3—21no—
240C4⋊Dic3—21no—
241C4⋊Dic3—32no—
242C4⋊Dic3—32no—
243C4⋊Dic3—62no—
244C4⋊Dic3—61no—
245C4⋊Dic3—61no—
246C4⋊Dic3—121no—
247C4×Dic3—21no—
248C4×Dic3—21no—
249C2×C3⋊C8—21no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8C4×D312yescomplemented
252#204—68no—
253C22×C32C4×D411yescharacteristic
254C22×C32#12011yescharacteristic
255C22×C32#12111yescharacteristic
256C22×C32C2×SD1611yescharacteristic
257C22×C32#13511yescharacteristic
258C22×C32AGL(1,ℤ/8)11yescharacteristic
259C22×C32#13711yescharacteristic
260C2×C3×D3—24no—
261C2×C3×D3—42no—
262C2×C3×D3—42no—
263C2×C3×D3—42no—
264C2×C3×D3—42no—
265C2×C3×D3—42no—
266C2×C3×D3—42no—
267C32×C4C2×C22⋊C411yescharacteristic
268C32×C4C4×D411yescharacteristic
269C32×C4#12111yescharacteristic
270C32×C4#12311yescharacteristic
271C3⋊Dic3—42no—
272C3⋊Dic3—42no—
273C3×Dic3—22no—
274C3×Dic3—41no—
275C3×Dic3—81no—
276C22×Q8—91no—
277C22×D4—31no—
278C23×C4—181no—
279C2×SD16—94no—
280C2×SD16—182no—
281C2×SD16—182no—
282C22×C8—31no—
283C22×C8D3211yescharacteristic
284C4×D4—182no—
285C4×D4—182no—
286C2×C4⋊C4—31no—
287C2×C4⋊C4—91no—
288C2×C22⋊C4—181no—
289C2×C42—31no—
290#103—182no—
291#102—62no—
292#95—181no—
293#95—181no—
294C23×C3—21no—
295C23×C3—62no—
296C23×C3—62no—
297C23×C3—62no—
298C23×C3—121no—
299C23×C3—121no—
300C23×C3—121no—
301C23×C3—121no—
302C23×C3C2×D1211yescharacteristic
303C23×C3D3×D411yescharacteristic
304C22×D3—22no—
305C22×D3—22no—
306C22×D3—22no—
307C22×D3—41no—
308C22×D3—41no—
309C22×D3—41no—
310C22×D3—41no—
311C3×D4—34no—
312C3×D4—62no—
313C3×D4—62no—
314C3×D4—62no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—32no—
322C2×C3×C4—61no—
323C2×C3×C4—61no—
324C2×C3×C4—61no—
325C2×C3×C4—61no—
326C2×C3×C4—61no—
327C2×C3×C4—121no—
328C2×C3×C4—121no—
329C2×C3×C4—121no—
330C2×C3×C4C2×C4×D311yescharacteristic
331C2×C3×C4C2×C4×D311yescharacteristic
332C2×C3×C4C2×D1211yescharacteristic
333C2×C3×C4#23511yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4#23711yescharacteristic
339C2×C3×C4#23711yescharacteristic
340C2×C3×C4#23911yescharacteristic
341C2×C3×C4C2×#6711yescharacteristic
342C2×Dic3—21no—
343C2×Dic3—21no—
344C2×Dic3—21no—
345C2×Dic3—21no—
346C2×Dic3—21no—
347C2×Dic3—41no—
348C2×Dic3—41no—
349C2×Dic3—41no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—122no—
355C2×Dic3—122no—
356C2×Dic3—128no—
357C2×Dic3—122no—
358C2×Dic3—122no—
359C2×Dic3—121no—
360C2×Dic3—121no—
361C2×Dic3—121no—
362C2×Dic3—121no—
363C2×Dic3—121no—
364C2×Dic3—121no—
365C2×Dic3—121no—
366C2×Dic3—121no—
367C2×Dic3—241no—
368C2×Dic3—241no—
369C2×Dic3#20412yescomplemented
370D12—22no—
371D12—22no—
372D12—22no—
373D12(C2×D3)⋊C414yes—
374C4×D3—128no—
375Dic6—64no—
376Dic6—62no—
377Dic6—62no—
378Dic6—62no—
379Dic6—62no—
380Dic6—122no—
381Dic6—122no—
382Dic6—122no—
383Dic6—121no—
384Dic6—121no—
385Dic6—121no—
386Dic6—121no—
387C3×C8—42no—
388C3×C8—41no—
389C3×C8—41no—
390C3×C8—62no—
391C3⋊C8—22no—
392C2×C32#38611yescharacteristic
393C2×C32C4×SD1611yescharacteristic
394C2×C32#44011yescharacteristic
395C2×C32#45011yescharacteristic
396C2×C32#45211yescharacteristic
397C2×C32#46111yescharacteristic
398C2×C32#46311yescharacteristic
399C3×D3—44no—
400C24—61no—
401C2×Q8—92no—
402C2×Q8—181no—
403C2×Q8—181no—
404C2×Q8—181no—
405C2×Q8—181no—
406C2×Q8—181no—
407C2×D4—32no—
408C2×D4—32no—
409C2×D4—32no—
410C2×D4—61no—
411C2×D4—61no—
412C2×D4—61no—
413C22×C4—31no—
414C22×C4—31no—
415C22×C4—61no—
416C22×C4—184no—
417C22×C4—181no—
418C22×C4—181no—
419C22×C4—362no—
420C22×C4—362no—
421C22×C4C2×D3211yescharacteristic
422SD16—188no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—32no—
427C2×C8—61no—
428C2×C8—61no—
429C4⋊C4—61no—
430C4⋊C4—61no—
431C4⋊C4—92no—
432C4⋊C4—181no—
433C22⋊C4—184no—
434C42—61no—
435C42—61no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—64no—
444C22×C3—122no—
445C22×C3—122no—
446C22×C3—122no—
447C22×C3—122no—
448C22×C3—122no—
449C22×C3—122no—
450C22×C3C4×D1211yescharacteristic
451C22×C3#67⋊C411yescharacteristic
452C22×C3#88211yescharacteristic
453C22×C3#88211yescharacteristic
454C22×C3#89511yescharacteristic
455C22×C3C2×#20411yescharacteristic
456C22×C3#90411yescharacteristic
457C22×C3#90811yescharacteristic
458C22×C3#90911yescharacteristic
459C22×C3#91111yescharacteristic
460C22×C3#91211yescharacteristic
461C22×C3D3×SD1611yescharacteristic
462C22×C3#91511yescharacteristic
463C22×C3#93911yescharacteristic
464C2×D3—24no—
465C2×D3—42no—
466C2×D3—42no—
467C2×D3—42no—
468C2×D3—42no—
469C2×D3—42no—
470C2×D3—42no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—62no—
476C3×C4—121no—
477C3×C4—241no—
478C3×C4D3×C22⋊C411yescharacteristic
479C3×C4#67⋊C411yescharacteristic
480C3×C4#88411yescharacteristic
481C3×C4#88611yescharacteristic
482C3×C4#89311yescharacteristic
483C3×C4#89411yescharacteristic
484C3×C4C2×(C2×D3)⋊C411yescharacteristic
485C3×C4#93911yescharacteristic
486Dic3—22no—
487Dic3—41no—
488Dic3—81no—
489Dic3—124no—
490Dic3—122no—
491Dic3—122no—
492Dic3—122no—
493Dic3—122no—
494Dic3—242no—
495C32#187711yescharacteristic, complemented, Sylow
496C23—62no—
497C23—62no—
498C23—62no—
499C23—121no—
500C23—121no—
501C23—121no—
502C23—121no—
503C23D3×D1211yescharacteristic
504Q8—182no—
505Q8—182no—
506Q8—361no—
507Q8—361no—
508D4—34no—
509D4—62no—
510D4—62no—
511D4—62no—
512C2×C4—32no—
513C2×C4—61no—
514C2×C4—61no—
515C2×C4—61no—
516C2×C4—61no—
517C2×C4—61no—
518C2×C4—121no—
519C2×C4—121no—
520C2×C4—121no—
521C2×C4—182no—
522C2×C4—182no—
523C2×C4—368no—
524C2×C4—361no—
525C2×C4—361no—
526C2×C4—361no—
527C2×C4—361no—
528C2×C4#379611yescharacteristic
529C2×C4C4×D3211yescharacteristic
530C2×C4D3×D1211yescharacteristic
531C2×C4#380411yescharacteristic
532C2×C4D3×#6711yescharacteristic
533C2×C4#381111yescharacteristic
534C8—41no—
535C8—62no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—124no—
544C2×C3#466511yescharacteristic
545C2×C3C4×#20411yescharacteristic
546C2×C3#471011yescharacteristic
547C2×C3#473111yescharacteristic
548C2×C3#473311yescharacteristic
549C2×C3#475711yescharacteristic
550C2×C3#475811yescharacteristic
551C2×C3#477611yescharacteristic
552C2×C3#478311yescharacteristic
553C2×C3#484111yescharacteristic
554C2×C3#484411yescharacteristic
555C2×C3#495811yescharacteristic
556C2×C3#515311yescharacteristic
557C2×C3#516211yescharacteristic
558D3—44no—
559C22—64no—
560C22—122no—
561C22—122no—
562C22—122no—
563C22—122no—
564C22—122no—
565C22—122no—
566C22D3×#20411yescharacteristic
567C22#6379511yescharacteristic
568C22#6380011yescharacteristic
569C22#6380711yescharacteristic
570C22#6388011yescharacteristic
571C22#6388611yescharacteristic
572C22#6392311yescharacteristic
573C4—62no—
574C4—121no—
575C4—241no—
576C4—362no—
577C4—362no—
578C4#6388111yescharacteristic
579C4#6389011yescharacteristic
580C4D3×(C2×D3)⋊C411yescharacteristic
581C4#6397111yescharacteristic
582C3—21no—
583C3#6867211yescharacteristic, complemented
584C3#7017111yescharacteristic, complemented
585C2—124no—
586C2#1059074411yescharacteristic
587C2#1059074711yescharacteristic
588C2#1059075211yescharacteristic
589C2#1059075511yescharacteristic
590C2#1059094611yescharacteristic
591C2#1059096911yescharacteristic
592C2#1059136411yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1877
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. C2×#63643C2semidirect
5. #10591213C2semidirect
6. C3×#4550C2semidirect
7. #10589164C2semidirect
23. C2×#3716C4semidirect
41. #4550D3semidirect
52. C2×#634C2×C4semidirect
76. C2×C3×C3⋊C8C2×C4semidirect
152. C2×C3×Dic3SD16semidirect
251. C2×C3⋊C8C4×D3semidirect
369. C2×Dic3#204semidirect
495. C32#1877semidirect
583. C3#68672semidirect
584. C3#70171semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3×D122
C22×#37162
C2×#636432
C2×C3×#8212
#105912132
C3×#45502
#105891642
#701713
#686723