Finite Group Databasebeta

← #11787552

Subgroups — #11787552

Order 1152.

1005 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D12C211yesmaximal, characteristic, complemented
2C22×#3714C211yesmaximal, characteristic
3#10592638C211yesmaximal, characteristic, complemented
4C2×#63564C211yesmaximal, characteristic, complemented
5C2×#63563C211yesmaximal, characteristic, complemented
6C3×#4524C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#71613—31nomaximal
9#68673—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C3×C4×D3—21no—
13C2×C32×C42C2211yescharacteristic
14C2×#3752—21no—
15C2×#3752—21no—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×C4×D12—22no—
22C3×C4×D12—22no—
23C2×#3714—22no—
24C2×#3714—22no—
25C2×#3714C414yescomplemented
26#63564—22no—
27#63563—22no—
28C2×C3×C4×D4—31no—
29C22×#213—31no—
30C22×D24—31no—
31C2×C4×D12D311yescharacteristic, complemented
32C2×#832—31no—
33C2×#821—31no—
34C2×#821—31no—
35C2×#809—31no—
36#4939—31no—
37#4939—31no—
38#4939—61no—
39C3×#336—31no—
40#4551—31no—
41#4529—31no—
42#4524D311yescharacteristic, complemented
43C23×C3⋊D3—21no—
44C23×C3×D3—21no—
45C22×C32×C4D411yescharacteristic
46C22×C32×C4D411yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)C2×C412yescomplemented
55C22×C3×Dic3—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12C2×C412yes—
60C2×C3×D12D412yes—
61C2×C3×D12D412yes—
62C2×C3×C4×D3—24no—
63C2×C3×C4×D3—42no—
64C2×C3×C4×D3—42no—
65C32×C42—21no—
66C32×C42—21no—
67#3752—42no—
68#3752—42no—
69C4⋊(C3⋊Dic3)—21no—
70C4⋊(C3⋊Dic3)—21no—
71C3×(C2×D3)⋊C4—24no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3D412yes—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8C2×C412yescomplemented
80#3714—28no—
81#1879—91noSylow
82C22×C3×D4—31no—
83C23×C3×C4—61no—
84C22×D12—31no—
85C22×D12—31no—
86C22×D12—61no—
87C22×D12C2×D311yescharacteristic
88C22×C4×D3—21no—
89C22×C3×C8—31no—
90C22×C3×C8—31no—
91C3×C4×D4—62no—
92C3×C4×D4—62no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C22⋊C4—61no—
95C2×C3×C42—21no—
96C2×C3×C42C2×D311yescharacteristic
97C2×C3×C42C2×D311yescharacteristic
98C2×#213—34no—
99C2×#213—62no—
100C2×#213—62no—
101C2×(C2×D3)⋊C4—21no—
102C2×(C2×D3)⋊C4—62no—
103C2×(C2×D3)⋊C4—62no—
104C2×(C2×D3)⋊C4—61no—
105C2×(C2×D3)⋊C4—61no—
106C2×(C2×D3)⋊C4—61no—
107C2×(C2×D3)⋊C4—61no—
108C2×C4⋊Dic3—31no—
109C2×C4⋊Dic3—31no—
110C2×C4⋊Dic3—61no—
111C2×C4⋊Dic3C2×D311yescharacteristic
112C22×C3⋊C8C2×D311yescharacteristic
113C22×C3⋊C8C2×D311yescharacteristic
114C2×D24—34no—
115C2×D24—62no—
116C2×D24—62no—
117C4×D12—22no—
118C4×D12—22no—
119#832—62no—
120#821—62no—
121#821—62no—
122#809—62no—
123C23×C32C2×D411yescharacteristic
124C22×C3⋊D3—22no—
125C22×C3⋊D3—41no—
126C22×C3⋊D3—41no—
127C22×C3⋊D3—41no—
128C22×C3⋊D3—41no—
129C22×C3⋊D3—41no—
130C22×C3⋊D3—41no—
131C22×C3×D3—22no—
132C22×C3×D3—22no—
133C22×C3×D3—22no—
134C22×C3×D3—41no—
135C22×C3×D3—41no—
136C22×C3×D3—41no—
137C22×C3×D3—41no—
138C2×C32×C4—21no—
139C2×C32×C4—21no—
140C2×C32×C4—21no—
141C2×C32×C4—21no—
142C2×C32×C4—21no—
143C2×C32×C4D812yescomplemented
144C2×C32×C4C22×C411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4#4111yescharacteristic
149C2×C32×C4#4111yescharacteristic
150C2×C3⋊Dic3—41no—
151C2×C3⋊Dic3—41no—
152C2×C3⋊Dic3—41no—
153C4⋊(C3⋊D3)—22no—
154C4⋊(C3⋊D3)—22no—
155C4⋊(C3⋊D3)—41no—
156C4⋊(C3⋊D3)—41no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—41no—
159C2×C3×Dic3—41no—
160C3×D12—22no—
161C3×D12—22no—
162C3×D12—22no—
163C3×D12C22⋊C414yescomplemented
164C3×C4×D3—48no—
165C3×C3⋊C8—22no—
166C3×C3⋊C8—41no—
167C22×D8—91no—
168C2×C4×D4—31no—
169C2×#102—91no—
170C2×#102—91no—
171#390—91no—
172#340—91no—
173#336—31no—
174C24×C3—61no—
175C23×D3—21no—
176C23×D3—62no—
177C23×D3—61no—
178C23×D3—61no—
179C2×C3×D4—32no—
180C2×C3×D4—32no—
181C2×C3×D4—32no—
182C2×C3×D4—61no—
183C2×C3×D4—61no—
184C2×C3×D4—61no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—64no—
189C22×C3×C4—61no—
190C22×C3×C4—122no—
191C22×C3×C4—122no—
192C22×C3×C4D1211yescharacteristic
193C22×C3×C4D1211yescharacteristic
194C22×C3×C4#6711yescharacteristic
195C22×C3×C4#6711yescharacteristic
196C22×C3×C4C22×D311yescharacteristic
197C22×C3×C4C22×D311yescharacteristic
198C22×Dic3—21no—
199C22×Dic3—62no—
200C22×Dic3—61no—
201C22×Dic3—61no—
202C2×D12—21no—
203C2×D12—21no—
204C2×D12—21no—
205C2×D12—32no—
206C2×D12—32no—
207C2×D12—62no—
208C2×D12—61no—
209C2×D12—61no—
210C2×D12—61no—
211C2×D12—61no—
212C2×D12—61no—
213C2×D12—61no—
214C2×D12—61no—
215C2×D12—61no—
216C2×D12—62no—
217C2×D12—61no—
218C2×D12—61no—
219C2×D12—121no—
220C2×D12—121no—
221C2×D12—121no—
222C2×D12—121no—
223C2×D12C4×D312yes—
224C2×D12D1212yes—
225C2×D12#6712yes—
226C2×C4×D3—24no—
227C2×C4×D3—42no—
228C2×C4×D3—42no—
229C2×C3×C8—32no—
230C2×C3×C8—61no—
231C2×C3×C8—61no—
232C2×C3×C8—61no—
233C2×C3×C8—61no—
234C2×C3×C8—61no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—61no—
237C3×C22⋊C4—64no—
238C3×C42—21no—
239C3×C42—21no—
240C3×C42—21no—
241C3×C42—21no—
242C3×C42—41no—
243C3×C42—41no—
244#213—68no—
245(C2×D3)⋊C4—24no—
246(C2×D3)⋊C4—124no—
247(C2×D3)⋊C4—122no—
248(C2×D3)⋊C4—122no—
249(C2×D3)⋊C4—124no—
250(C2×D3)⋊C4—122no—
251(C2×D3)⋊C4—122no—
252C4⋊Dic3—21no—
253C4⋊Dic3—61no—
254C4⋊Dic3—61no—
255C4⋊Dic3—61no—
256C4⋊Dic3—61no—
257C4⋊Dic3—121no—
258C4⋊Dic3—121no—
259C4⋊Dic3#6712yes—
260C2×C3⋊C8—21no—
261C2×C3⋊C8—21no—
262C2×C3⋊C8—21no—
263C2×C3⋊C8—21no—
264C2×C3⋊C8—21no—
265C2×C3⋊C8C4×D312yescomplemented
266D24—68no—
267C22×C32C4×D411yescharacteristic
268C22×C32#12011yescharacteristic
269C22×C32#12111yescharacteristic
270C22×C32C2×D811yescharacteristic
271C22×C32#13511yescharacteristic
272C22×C32AGL(1,ℤ/8)11yescharacteristic
273C22×C32AGL(1,ℤ/8)11yescharacteristic
274C2×C3⋊D3—42no—
275C2×C3⋊D3—42no—
276C2×C3⋊D3—42no—
277C2×C3⋊D3—81no—
278C2×C3⋊D3—81no—
279C2×C3⋊D3—81no—
280C2×C3⋊D3—81no—
281C2×C3×D3—24no—
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C2×C3×D3—42no—
285C2×C3×D3—42no—
286C2×C3×D3—42no—
287C2×C3×D3—42no—
288C32×C4—22no—
289C32×C4—41no—
290C32×C4C2×C22⋊C411yescharacteristic
291C32×C4C4×D411yescharacteristic
292C32×C4#12111yescharacteristic
293C32×C4#12311yescharacteristic
294C3⋊Dic3—81no—
295C3×Dic3—42no—
296C22×D4—31no—
297C22×D4—91no—
298C23×C4—61no—
299C2×D8—94no—
300C2×D8—182no—
301C2×D8—182no—
302C22×C8—31no—
303C22×C8—31no—
304C4×D4—62no—
305C4×D4—62no—
306C2×C4⋊C4—31no—
307C2×C4⋊C4—91no—
308C2×C22⋊C4—61no—
309C2×C22⋊C4—181no—
310C2×C22⋊C4—181no—
311C2×C42D3211yescharacteristic
312#102—182no—
313#102—182no—
314C23×C3—21no—
315C23×C3—62no—
316C23×C3—62no—
317C23×C3—62no—
318C23×C3—121no—
319C23×C3—121no—
320C23×C3—121no—
321C23×C3—121no—
322C23×C3C2×D1211yescharacteristic
323C23×C3C2×#6711yescharacteristic
324C22×D3—22no—
325C22×D3—22no—
326C22×D3—22no—
327C22×D3—41no—
328C22×D3—41no—
329C22×D3—41no—
330C22×D3—41no—
331C22×D3—64no—
332C22×D3—62no—
333C22×D3—62no—
334C22×D3—122no—
335C22×D3—122no—
336C22×D3—122no—
337C22×D3—122no—
338C22×D3—122no—
339C22×D3—122no—
340C22×D3—121no—
341C22×D3—121no—
342C22×D3—121no—
343C22×D3—121no—
344C22×D3—121no—
345C22×D3—121no—
346C22×D3—121no—
347C22×D3—121no—
348C22×D3—121no—
349C22×D3—121no—
350C22×D3—121no—
351C22×D3—121no—
352C3×D4—34no—
353C3×D4—62no—
354C3×D4—62no—
355C3×D4—62no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—22no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—22no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—41no—
375C2×C3×C4—41no—
376C2×C3×C4—41no—
377C2×C3×C4—41no—
378C2×C3×C4—62no—
379C2×C3×C4—128no—
380C2×C3×C4—121no—
381C2×C3×C4—121no—
382C2×C3×C4D2412yescomplemented
383C2×C3×C4#21312yescomplemented
384C2×C3×C4C2×C4×D311yescharacteristic
385C2×C3×C4C2×C4×D311yescharacteristic
386C2×C3×C4C2×D1211yescharacteristic
387C2×C3×C4#23511yescharacteristic
388C2×C3×C4#23511yescharacteristic
389C2×C3×C4#23511yescharacteristic
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4#23911yescharacteristic
394C2×C3×C4C2×#6711yescharacteristic
395C2×C3×C4C2×#6711yescharacteristic
396C2×Dic3—22no—
397C2×Dic3—41no—
398C2×Dic3—41no—
399C2×Dic3—122no—
400C2×Dic3—122no—
401C2×Dic3—122no—
402C2×Dic3—121no—
403C2×Dic3—121no—
404C2×Dic3—121no—
405C2×Dic3—121no—
406C2×Dic3—121no—
407C2×Dic3—121no—
408D12—22no—
409D12—22no—
410D12—22no—
411D12—62no—
412D12—62no—
413D12—62no—
414D12—62no—
415D12—122no—
416D12—122no—
417D12—122no—
418D12—122no—
419D12—121no—
420D12—121no—
421D12—121no—
422D12—121no—
423D12(C2×D3)⋊C414yescomplemented
424C4×D3—48no—
425C3×C8—62no—
426C3×C8—121no—
427C3⋊C8—22no—
428C3⋊C8—41no—
429C2×C32#38611yescharacteristic
430C2×C32C4×D811yescharacteristic
431C2×C32#44211yescharacteristic
432C2×C32#44711yescharacteristic
433C2×C32#44911yescharacteristic
434C2×C32#45911yescharacteristic
435C2×C32#46311yescharacteristic
436C3⋊D3—82no—
437C3×D3—44no—
438C24—61no—
439C24—181no—
440C2×D4—32no—
441C2×D4—32no—
442C2×D4—32no—
443C2×D4—61no—
444C2×D4—61no—
445C2×D4—61no—
446C2×D4—92no—
447C2×D4—181no—
448C2×D4—181no—
449C2×D4—181no—
450C2×D4—181no—
451C2×D4—181no—
452C22×C4—64no—
453C22×C4—61no—
454C22×C4—122no—
455C22×C4—122no—
456C22×C4—181no—
457C22×C4#62611yescharacteristic
458C22×C4#62611yescharacteristic
459C22×C4C2×D3211yescharacteristic
460D8—188no—
461C2×C8—32no—
462C2×C8—61no—
463C2×C8—61no—
464C2×C8—61no—
465C2×C8—61no—
466C2×C8—61no—
467C4⋊C4—32no—
468C4⋊C4—61no—
469C4⋊C4—181no—
470C4⋊C4—181no—
471C22⋊C4—64no—
472C22⋊C4—362no—
473C22⋊C4—362no—
474C42—21no—
475C42—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—64no—
484C22×C3—122no—
485C22×C3—122no—
486C22×C3—122no—
487C22×C3—122no—
488C22×C3—122no—
489C22×C3—122no—
490C22×C3C4×D1211yescharacteristic
491C22×C3#88211yescharacteristic
492C22×C3#89511yescharacteristic
493C22×C3C2×D2411yescharacteristic
494C22×C3#90411yescharacteristic
495C22×C3#90811yescharacteristic
496C22×C3#90811yescharacteristic
497C22×C3C4×#6711yescharacteristic
498C22×C3#93011yescharacteristic
499C22×C3C2×#21311yescharacteristic
500C22×C3#93211yescharacteristic
501C22×C3#94911yescharacteristic
502C22×C3#95011yescharacteristic
503C22×C3#95311yescharacteristic
504C2×D3—24no—
505C2×D3—42no—
506C2×D3—42no—
507C2×D3—42no—
508C2×D3—42no—
509C2×D3—42no—
510C2×D3—42no—
511C2×D3—124no—
512C2×D3—124no—
513C2×D3—124no—
514C2×D3—122no—
515C2×D3—122no—
516C2×D3—122no—
517C2×D3—122no—
518C2×D3—122no—
519C2×D3—122no—
520C2×D3—242no—
521C2×D3—242no—
522C2×D3—242no—
523C2×D3—242no—
524C2×D3—241no—
525C2×D3—241no—
526C2×D3—241no—
527C2×D3—241no—
528C2×D3—241no—
529C2×D3—241no—
530C2×D3—241no—
531C2×D3—241no—
532C3×C4—22no—
533C3×C4—22no—
534C3×C4—21no—
535C3×C4—21no—
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—42no—
539C3×C4—42no—
540C3×C4—41no—
541C3×C4—41no—
542C3×C4—122no—
543C3×C4D3×C22⋊C411yescharacteristic
544C3×C4#88411yescharacteristic
545C3×C4#89311yescharacteristic
546C3×C4#89411yescharacteristic
547C3×C4C2×(C2×D3)⋊C411yescharacteristic
548C3×C4C4×#6711yescharacteristic
549C3×C4#92911yescharacteristic
550C3×C4#93011yescharacteristic
551Dic3—42no—
552Dic3—242no—
553Dic3—241no—
554Dic3—241no—
555C32#187911yescharacteristic, complemented, Sylow
556C23—62no—
557C23—62no—
558C23—62no—
559C23—121no—
560C23—121no—
561C23—121no—
562C23—121no—
563C23—182no—
564C23—361no—
565C23—361no—
566C23—361no—
567C23—361no—
568C23—361no—
569C23—361no—
570C23C2×#62611yescharacteristic
571D4—34no—
572D4—62no—
573D4—62no—
574D4—62no—
575D4—182no—
576D4—182no—
577D4—361no—
578D4—361no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—62no—
585C2×C4—128no—
586C2×C4—121no—
587C2×C4—121no—
588C2×C4—361no—
589C2×C4—361no—
590C2×C4—361no—
591C2×C4#371412yescomplemented
592C2×C4#379811yescharacteristic
593C2×C4#379911yescharacteristic
594C2×C4C4×D3211yescharacteristic
595C2×C4D3×D1211yescharacteristic
596C2×C4D3×#6711yescharacteristic
597C2×C4D3×#6711yescharacteristic
598C8—62no—
599C8—121no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—124no—
608C2×C3#466511yescharacteristic
609C2×C3C4×D2411yescharacteristic
610C2×C3#471111yescharacteristic
611C2×C3#473211yescharacteristic
612C2×C3#473411yescharacteristic
613C2×C3#484311yescharacteristic
614C2×C3#484411yescharacteristic
615C2×C3C4×#21311yescharacteristic
616C2×C3#501411yescharacteristic
617C2×C3#501511yescharacteristic
618C2×C3#501611yescharacteristic
619C2×C3#521311yescharacteristic
620C2×C3#521711yescharacteristic
621C2×C3#523811yescharacteristic
622D3—44no—
623D3—244no—
624D3—242no—
625D3—242no—
626C22—64no—
627C22—122no—
628C22—122no—
629C22—122no—
630C22—122no—
631C22—122no—
632C22—122no—
633C22—362no—
634C22—362no—
635C22—362no—
636C22—721no—
637C22—721no—
638C22—721no—
639C22—721no—
640C22C2×#371411yescharacteristic
641C22#6382511yescharacteristic
642C22#6382911yescharacteristic
643C22#6383011yescharacteristic
644C22C4×#62611yescharacteristic
645C22#6390911yescharacteristic
646C22#6397711yescharacteristic
647C4—22no—
648C4—41no—
649C4—122no—
650C4—721no—
651C4#6385011yescharacteristic
652C4#6390411yescharacteristic
653C4#6390611yescharacteristic
654C4D3×(C2×D3)⋊C411yescharacteristic
655C3—21no—
656C3#6867311yescharacteristic, complemented
657C3#7161311yescharacteristic, complemented
658C2—124no—
659C2—722no—
660C2C4×#371411yescharacteristic
661C2#1059034611yescharacteristic
662C2#1059034911yescharacteristic
663C2#1059036611yescharacteristic
664C2#1059116211yescharacteristic
665C2#1059116311yescharacteristic
666C2#1059138211yescharacteristic
subgroupG/H
centerC23C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×#3714C2
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1879
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×D12C2semidirect
3. #10592638C2semidirect
4. C2×#63564C2semidirect
5. C2×#63563C2semidirect
6. C3×#4524C2semidirect
7. #10589164C2semidirect
25. C2×#3714C4semidirect
31. C2×C4×D12D3semidirect
42. #4524D3semidirect
54. C2×C4⋊(C3⋊D3)C2×C4semidirect
79. C2×C3×C3⋊C8C2×C4semidirect
143. C2×C32×C4D8semidirect
163. C3×D12C22⋊C4semidirect
265. C2×C3⋊C8C4×D3semidirect
382. C2×C3×C4D24semidirect
383. C2×C3×C4#213semidirect
423. D12(C2×D3)⋊C4semidirect
555. C32#1879semidirect
591. C2×C4#3714semidirect
656. C3#68673semidirect
657. C3#71613semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D122
C22×#37142
#105926382
C2×#635642
C2×#635632
C3×#45242
#105891642
#716133
#686733