Finite Group Databasebeta

← #11787545

Subgroups — #11787545

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 679 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3753C211yesmaximal, characteristic
2C2×#63894C211yesmaximal, characteristic, complemented
3C3×#5221C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5C2×#63564C211yesmaximal, characteristic, complemented
6#10589163C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#70208—31nomaximal
9#69657—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×#624—21no—
13C2×#3753—22no—
14C2×#3753—22no—
15C2×#3753C414yescomplemented
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×#217—21no—
18C2×C3×#217—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4×Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×#3722—21no—
24#63894—22no—
25#63894—22no—
26C3×#832—22no—
27#63564—22no—
28C22×#213—31no—
29C22×#213—31no—
30C22×#213—61no—
31C2×#893—31no—
32C2×C4×D12—31no—
33C2×C3×#102—31no—
34C3×#390—31no—
35#5221D311yescharacteristic, complemented
36C2×#832D311yescharacteristic, complemented
37C2×#821—31no—
38C2×#809—31no—
39#4550—31no—
40#4529—31no—
41#4529—31no—
42#4524—31no—
43C24×C32—21no—
44C23×C3⋊D3—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4—21no—
50C2×C32×D4C2×C412yescomplemented
51C22×C32×C4C2311yescharacteristic
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)C2×C412yes—
56C2×C4⋊(C3⋊D3)D412yes—
57C2×C4⋊(C3⋊D3)D412yes—
58C22×C3×Dic3—21no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3D411yescharacteristic
61C22×C3×Dic3D411yescharacteristic
62C2×#624—24no—
63C2×#624—42no—
64C2×#624—42no—
65#3753—28no—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)C2×C412yescomplemented
69C3×#217—42no—
70C3×#217—42no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3D412yes—
75C3×C4×Dic3—21no—
76C3×C4×Dic3—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8—21no—
80#3722—24no—
81#1879—91noSylow
82C22×C3×D4—21no—
83C22×C3×D4C2×D311yescharacteristic
84C22×C3×D4C2×D311yescharacteristic
85C22×D12—31no—
86C22×D12—31no—
87C22×D12—61no—
88C22×C4×D3—61no—
89C22×C4×D3—61no—
90C22×C3×C8—31no—
91C2×C3×C4⋊C4—31no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C22⋊C4—61no—
94C2×C3×C22⋊C4—61no—
95C2×C3×C42—31no—
96C2×#217—21no—
97C2×#217—21no—
98C2×#213—34no—
99C2×#213—34no—
100C2×#213—64no—
101C2×#213—62no—
102C2×#213—62no—
103C2×#213—62no—
104C2×#213—62no—
105C2×#213—64no—
106C2×#213—64no—
107C2×(C2×D3)⋊C4—61no—
108C2×(C2×D3)⋊C4—61no—
109C2×C4⋊Dic3C2×D311yescharacteristic
110C2×C4⋊Dic3C2×D311yescharacteristic
111C2×C4×Dic3C2×D311yescharacteristic
112C22×C3⋊C8—31no—
113C22×C3⋊C8—31no—
114C22×C3⋊C8—61no—
115C22×C3⋊C8C2×D311yescharacteristic
116#893—62no—
117#893—62no—
118C4×D12—62no—
119C4×D12—62no—
120C3×#102—62no—
121#832—22no—
122#821—62no—
123#809—62no—
124C23×C32—22no—
125C23×C32—41no—
126C23×C32—41no—
127C23×C32—41no—
128C23×C32—41no—
129C23×C32—41no—
130C23×C32—41no—
131C23×C32C2×D411yescharacteristic
132C22×C3⋊D3—22no—
133C22×C3⋊D3—22no—
134C22×C3⋊D3—22no—
135C22×C3⋊D3—41no—
136C22×C3⋊D3—41no—
137C22×C3⋊D3—41no—
138C22×C3⋊D3—41no—
139C32×D4—22no—
140C32×D4—22no—
141C32×D4—41no—
142C32×D4—41no—
143C2×C32×C4C22×C411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4#4111yescharacteristic
148C2×C32×C4#4111yescharacteristic
149C4⋊(C3⋊D3)—22no—
150C4⋊(C3⋊D3)—22no—
151C4⋊(C3⋊D3)—22no—
152C4⋊(C3⋊D3)C22⋊C414yescomplemented
153C2×C3×Dic3—21no—
154C2×C3×Dic3—21no—
155C2×C3×Dic3—21no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—21no—
158C2×C3×Dic3—21no—
159C2×C3×Dic3—41no—
160C2×C3×Dic3—41no—
161C2×C3×Dic3—41no—
162C2×C3×Dic3—41no—
163C2×C3×Dic3—41no—
164C2×C3×Dic3D812yescomplemented
165#624—48no—
166C3⋊(C3⋊C8)—22no—
167C3×C3⋊C8—41no—
168C22×D8—91no—
169C2×C4×D4—91no—
170C2×#102—31no—
171C2×#102—91no—
172#390—31no—
173#340—91no—
174#336—91no—
175C24×C3—21no—
176C24×C3—21no—
177C24×C3—41no—
178C23×D3—61no—
179C23×D3—61no—
180C23×D3—121no—
181C2×C3×D4—22no—
182C2×C3×D4—22no—
183C2×C3×D4—21no—
184C2×C3×D4—21no—
185C2×C3×D4—21no—
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—21no—
193C2×C3×D4—22no—
194C2×C3×D4—41no—
195C2×C3×D4—41no—
196C2×C3×D4—41no—
197C2×C3×D4C4×D312yescomplemented
198C2×C3×D4C4×D312yescomplemented
199C22×C3×C4—21no—
200C22×C3×C4—31no—
201C22×C3×C4—31no—
202C22×C3×C4—61no—
203C22×C3×C4—61no—
204C22×C3×C4C22×D311yescharacteristic
205C22×C3×C4C22×D311yescharacteristic
206C22×Dic3—21no—
207C22×Dic3—21no—
208C22×Dic3#6711yescharacteristic
209C22×Dic3#6711yescharacteristic
210C2×D12—32no—
211C2×D12—32no—
212C2×D12—32no—
213C2×D12—32no—
214C2×D12—32no—
215C2×D12—32no—
216C2×D12—62no—
217C2×D12—62no—
218C2×D12—62no—
219C2×D12—61no—
220C2×D12—61no—
221C2×D12—61no—
222C2×D12—61no—
223C2×D12—61no—
224C2×D12—61no—
225C2×D12—121no—
226C2×D12—121no—
227C2×D12—121no—
228C2×C4×D3—64no—
229C2×C4×D3—64no—
230C2×C4×D3—122no—
231C2×C4×D3—122no—
232C2×C4×D3—122no—
233C2×C4×D3—122no—
234C2×C3×C8—61no—
235C2×C3×C8—61no—
236C2×C3×C8—61no—
237C3×C4⋊C4—32no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4—61no—
241C3×C22⋊C4—122no—
242C3×C22⋊C4—122no—
243C3×C42—61no—
244C3×C42—61no—
245#217—42no—
246#217—42no—
247#213—68no—
248#213—68no—
249#213—616no—
250(C2×D3)⋊C4—64no—
251(C2×D3)⋊C4—64no—
252C4⋊Dic3—21no—
253C4⋊Dic3—21no—
254C4⋊Dic3—21no—
255C4⋊Dic3#6712yes—
256C4×Dic3—21no—
257C4×Dic3—21no—
258C2×C3⋊C8—21no—
259C2×C3⋊C8—21no—
260C2×C3⋊C8—21no—
261C2×C3⋊C8—32no—
262C2×C3⋊C8—32no—
263C2×C3⋊C8—62no—
264C2×C3⋊C8—62no—
265C2×C3⋊C8—62no—
266C2×C3⋊C8—61no—
267C2×C3⋊C8—61no—
268C2×C3⋊C8—61no—
269C2×C3⋊C8—61no—
270C22×C32—42no—
271C22×C32—42no—
272C22×C32—42no—
273C22×C32—81no—
274C22×C32—81no—
275C22×C32—81no—
276C22×C32—81no—
277C22×C32C4×D411yescharacteristic
278C22×C32#12011yescharacteristic
279C22×C32#12111yescharacteristic
280C22×C32C2×D811yescharacteristic
281C22×C32#13511yescharacteristic
282C22×C32AGL(1,ℤ/8)11yescharacteristic
283C22×C32AGL(1,ℤ/8)11yescharacteristic
284C2×C3⋊D3—24no—
285C2×C3⋊D3—42no—
286C2×C3⋊D3—42no—
287C2×C3⋊D3—42no—
288C2×C3⋊D3—42no—
289C2×C3⋊D3—42no—
290C2×C3⋊D3—42no—
291C32×C4C2×C22⋊C411yescharacteristic
292C32×C4C4×D411yescharacteristic
293C32×C4#12111yescharacteristic
294C32×C4#12311yescharacteristic
295C3×Dic3—22no—
296C3×Dic3—42no—
297C3×Dic3—41no—
298C3×Dic3—81no—
299C22×D4—91no—
300C22×D4D3211yescharacteristic
301C23×C4—181no—
302C2×D8—94no—
303C2×D8—182no—
304C2×D8—182no—
305C22×C8—31no—
306C22×C8—91no—
307C4×D4—182no—
308C4×D4—182no—
309C2×C4⋊C4—31no—
310C2×C4⋊C4—31no—
311C2×C22⋊C4—61no—
312C2×C22⋊C4—61no—
313C2×C22⋊C4—181no—
314C2×C42—31no—
315#102—62no—
316#102—182no—
317C23×C3—22no—
318C23×C3—22no—
319C23×C3—21no—
320C23×C3—42no—
321C23×C3—42no—
322C23×C3—42no—
323C23×C3—41no—
324C23×C3—41no—
325C23×C3—41no—
326C23×C3—41no—
327C23×C3—41no—
328C23×C3—41no—
329C23×C3—41no—
330C23×C3—41no—
331C23×C3—41no—
332C23×C3—41no—
333C23×C3—41no—
334C23×C3—41no—
335C23×C3—81no—
336C23×C3—81no—
337C23×C3—81no—
338C23×C3—81no—
339C23×C3D3×D411yescharacteristic
340C23×C3C2×#6711yescharacteristic
341C22×D3—62no—
342C22×D3—62no—
343C22×D3—62no—
344C22×D3—62no—
345C22×D3—62no—
346C22×D3—62no—
347C22×D3—122no—
348C22×D3—122no—
349C22×D3—122no—
350C22×D3—121no—
351C22×D3—121no—
352C22×D3—121no—
353C22×D3—121no—
354C22×D3—121no—
355C22×D3—121no—
356C22×D3—121no—
357C22×D3—121no—
358C22×D3—241no—
359C22×D3—241no—
360C22×D3—241no—
361C22×D3—241no—
362C3×D4—24no—
363C3×D4—22no—
364C3×D4—22no—
365C3×D4—22no—
366C3×D4—22no—
367C3×D4—42no—
368C3×D4—42no—
369C3×D4—42no—
370C3×D4—41no—
371C3×D4—41no—
372C3×D4—41no—
373C3×D4—41no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—32no—
381C2×C3×C4—61no—
382C2×C3×C4—61no—
383C2×C3×C4—61no—
384C2×C3×C4—61no—
385C2×C3×C4—61no—
386C2×C3×C4—62no—
387C2×C3×C4—121no—
388C2×C3×C4—121no—
389C2×C3×C4—121no—
390C2×C3×C4—121no—
391C2×C3×C4—121no—
392C2×C3×C4C2×C4×D311yescharacteristic
393C2×C3×C4C2×C4×D311yescharacteristic
394C2×C3×C4#23511yescharacteristic
395C2×C3×C4#23511yescharacteristic
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4D3×D411yescharacteristic
400C2×C3×C4D3×D411yescharacteristic
401C2×C3×C4#23711yescharacteristic
402C2×C3×C4#23711yescharacteristic
403C2×C3×C4C2×#6711yescharacteristic
404C2×Dic3—21no—
405C2×Dic3—21no—
406C2×Dic3—21no—
407C2×Dic3—21no—
408C2×Dic3—22no—
409C2×Dic3—21no—
410C2×Dic3—41no—
411C2×Dic3—41no—
412C2×Dic3—41no—
413C2×Dic3—41no—
414C2×Dic3—41no—
415C2×Dic3#21312yescomplemented
416D12—34no—
417D12—34no—
418D12—64no—
419D12—62no—
420D12—62no—
421D12—62no—
422D12—62no—
423D12—62no—
424D12—62no—
425D12—122no—
426D12—122no—
427D12—122no—
428C4×D3—128no—
429C4×D3—128no—
430C3×C8—121no—
431C3⋊C8—41no—
432C3⋊C8—64no—
433C3⋊C8—62no—
434C3⋊C8—62no—
435C2×C32—82no—
436C2×C32#38611yescharacteristic
437C2×C32C4×D811yescharacteristic
438C2×C32#44211yescharacteristic
439C2×C32#44711yescharacteristic
440C2×C32#44911yescharacteristic
441C2×C32#45911yescharacteristic
442C2×C32#46311yescharacteristic
443C3⋊D3—44no—
444C24—21no—
445C24—181no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—92no—
452C2×D4—92no—
453C2×D4—92no—
454C2×D4—181no—
455C2×D4—181no—
456C2×D4—181no—
457C2×D4#62412yescomplemented
458C22×C4—31no—
459C22×C4—31no—
460C22×C4—61no—
461C22×C4—61no—
462C22×C4—184no—
463C22×C4—362no—
464C22×C4—362no—
465C22×C4C2×D3211yescharacteristic
466D8—188no—
467C2×C8—61no—
468C2×C8—61no—
469C2×C8—61no—
470C2×C8—92no—
471C2×C8—181no—
472C2×C8—181no—
473C4⋊C4—32no—
474C4⋊C4—61no—
475C4⋊C4—61no—
476C4⋊C4—61no—
477C22⋊C4—122no—
478C22⋊C4—122no—
479C22⋊C4—184no—
480C42—61no—
481C42—61no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3—21no—
489C22×C3—44no—
490C22×C3—42no—
491C22×C3—42no—
492C22×C3—42no—
493C22×C3—42no—
494C22×C3—42no—
495C22×C3—42no—
496C22×C3—82no—
497C22×C3—82no—
498C22×C3—82no—
499C22×C3—82no—
500C22×C3—82no—
501C22×C3—82no—
502C22×C3—81no—
503C22×C3—81no—
504C22×C3—81no—
505C22×C3—81no—
506C22×C3—81no—
507C22×C3—81no—
508C22×C3—81no—
509C22×C3—81no—
510C22×C3#67⋊C411yescharacteristic
511C22×C3#88411yescharacteristic
512C22×C3D3×D811yescharacteristic
513C22×C3#91111yescharacteristic
514C22×C3#91411yescharacteristic
515C22×C3#91611yescharacteristic
516C22×C3C4×#6711yescharacteristic
517C22×C3C2×#21311yescharacteristic
518C22×C3#93211yescharacteristic
519C22×C3#93711yescharacteristic
520C22×C3#93711yescharacteristic
521C22×C3#93811yescharacteristic
522C22×C3#94911yescharacteristic
523C22×C3#95011yescharacteristic
524C2×D3—64no—
525C2×D3—64no—
526C2×D3—124no—
527C2×D3—122no—
528C2×D3—122no—
529C2×D3—122no—
530C2×D3—122no—
531C2×D3—122no—
532C2×D3—122no—
533C2×D3—122no—
534C2×D3—122no—
535C2×D3—122no—
536C2×D3—122no—
537C2×D3—122no—
538C2×D3—122no—
539C2×D3—242no—
540C2×D3—242no—
541C2×D3—242no—
542C2×D3—242no—
543C2×D3—242no—
544C2×D3—242no—
545C3×C4—21no—
546C3×C4—21no—
547C3×C4—21no—
548C3×C4—21no—
549C3×C4—62no—
550C3×C4—121no—
551C3×C4—122no—
552C3×C4—241no—
553C3×C4D3×C22⋊C411yescharacteristic
554C3×C4D3×C22⋊C411yescharacteristic
555C3×C4#67⋊C411yescharacteristic
556C3×C4#88311yescharacteristic
557C3×C4#88311yescharacteristic
558C3×C4#88411yescharacteristic
559C3×C4C4×#6711yescharacteristic
560C3×C4#93811yescharacteristic
561Dic3—22no—
562Dic3—42no—
563Dic3—41no—
564Dic3—81no—
565C32#187911yescharacteristic, complemented, Sylow
566C23—22no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—182no—
574C23—182no—
575C23—182no—
576C23—361no—
577C23—361no—
578C23—361no—
579C23—361no—
580C23D3×#6711yescharacteristic
581D4—22no—
582D4—22no—
583D4—41no—
584D4—41no—
585D4—94no—
586D4—182no—
587D4—182no—
588D4—182no—
589C2×C4—32no—
590C2×C4—61no—
591C2×C4—61no—
592C2×C4—61no—
593C2×C4—61no—
594C2×C4—61no—
595C2×C4—62no—
596C2×C4—121no—
597C2×C4—121no—
598C2×C4—121no—
599C2×C4—121no—
600C2×C4—121no—
601C2×C4—368no—
602C2×C4#380411yescharacteristic
603C2×C4#380411yescharacteristic
604C2×C4C2×#62411yescharacteristic
605C2×C4D3×#6711yescharacteristic
606C2×C4#381111yescharacteristic
607C2×C4#381111yescharacteristic
608C8—121no—
609C8—182no—
610C2×C3—21no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—21no—
616C2×C3—21no—
617C2×C3—84no—
618C2×C3—82no—
619C2×C3—82no—
620C2×C3#475611yescharacteristic
621C2×C3#478511yescharacteristic
622C2×C3#478611yescharacteristic
623C2×C3#478711yescharacteristic
624C2×C3#495611yescharacteristic
625C2×C3#495611yescharacteristic
626C2×C3C4×#21311yescharacteristic
627C2×C3#501411yescharacteristic
628C2×C3#503611yescharacteristic
629C2×C3#503711yescharacteristic
630C2×C3#505711yescharacteristic
631C2×C3#507211yescharacteristic
632C2×C3#515611yescharacteristic
633C2×C3#517211yescharacteristic
634D3—124no—
635D3—124no—
636D3—244no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—184no—
645C22—362no—
646C22—362no—
647C22—362no—
648C22—362no—
649C22—362no—
650C22—362no—
651C22D3×#21311yescharacteristic
652C22#6392511yescharacteristic
653C22#6393411yescharacteristic
654C22#6393511yescharacteristic
655C22#6395211yescharacteristic
656C22#6395811yescharacteristic
657C22#6398311yescharacteristic
658C4—62no—
659C4—122no—
660C4—121no—
661C4—241no—
662C4#6395211yescharacteristic
663C4#6395811yescharacteristic
664C4#6397411yescharacteristic
665C4#6397511yescharacteristic
666C3—21no—
667C3#6965711yescharacteristic, complemented
668C3#7020811yescharacteristic, complemented
669C2—82no—
670C2—364no—
671C2#1059140011yescharacteristic
672C2#1059140411yescharacteristic
673C2#1059142911yescharacteristic
674C2#1059143211yescharacteristic
675C2#1059151511yescharacteristic
676C2#1059152111yescharacteristic
677C2#1059172211yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC22×#3753C2
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1879
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63894C2semidirect
3. C3×#5221C2semidirect
4. C2×C3×#832C2semidirect
5. C2×#63564C2semidirect
6. #10589163C2semidirect
7. #10589155C2semidirect
15. C2×#3753C4semidirect
35. #5221D3semidirect
36. C2×#832D3semidirect
50. C2×C32×D4C2×C4semidirect
68. C2×C3⋊(C3⋊C8)C2×C4semidirect
152. C4⋊(C3⋊D3)C22⋊C4semidirect
164. C2×C3×Dic3D8semidirect
197. C2×C3×D4C4×D3semidirect
198. C2×C3×D4C4×D3semidirect
415. C2×Dic3#213semidirect
457. C2×D4#624semidirect
565. C32#1879semidirect
667. C3#69657semidirect
668. C3#70208semidirect

Maximal subgroups

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

subgroupindex
C22×#37532
C2×#638942
C3×#52212
C2×C3×#8322
C2×#635642
#105891632
#105891552
#702083
#696573