Finite Group Databasebeta

← #11787547

Subgroups — #11787547

Order 1152.

933 conjugacy classes of subgroups.

The subgroup lattice has 637 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic3×D12C211yesmaximal, characteristic, complemented
2C22×#3713C211yesmaximal, characteristic
3C3×#4988C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5C2×#63563C211yesmaximal, characteristic, complemented
6#10589395C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#70172—31nomaximal
9#69657—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×D3×Dic3—21no—
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×(C2×D3)⋊C4—21no—
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C2×(C2×D3)⋊Dic3—21no—
21Dic3×D12—22no—
22Dic3×D12—22no—
23C2×#3713—22no—
24C2×#3713—22no—
25C2×#3713C414yescomplemented
26C3×#809—22no—
27#63563—22no—
28C2×D4×Dic3—31no—
29C22×#213—31no—
30C22×#213—31no—
31C2×C4×D12—31no—
32C2×C3×#102—31no—
33C3×#390—31no—
34C2×#832—31no—
35C2×#821—31no—
36#4988D311yescharacteristic, complemented
37C2×#809D311yescharacteristic, complemented
38#4550—31no—
39#4529—31no—
40#4529—31no—
41#4529—61no—
42#4524—31no—
43C23×C3×D3—21no—
44C23×C3×D3—21no—
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3×Dic3D411yescharacteristic
49C22×C3×Dic3D411yescharacteristic
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12C2×C412yes—
59C2×C3×D12C2×C412yescomplemented
60C2×C3×D12D412yes—
61C2×C3×D12D412yes—
62C2×D3×Dic3—24no—
63C2×D3×Dic3—42no—
64C2×D3×Dic3—42no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4—21no—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)D412yes—
69C2×C3⋊(C3⋊C8)—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)C2×C412yescomplemented
72C3×(C2×D3)⋊C4—42no—
73C3×(C2×D3)⋊C4—42no—
74C3×C4×Dic3—21no—
75C3×C4×Dic3—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79(C2×D3)⋊Dic3—24no—
80#3713—28no—
81#1879—91noSylow
82C22×C3×D4—31no—
83C22×C3×D4—31no—
84C23×Dic3—61no—
85C22×D12C2×D311yescharacteristic
86C22×D12C2×D311yescharacteristic
87C22×C4×D3—61no—
88C22×C3×C8—31no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4C2×D311yescharacteristic
91C2×C3×C4⋊C4C2×D311yescharacteristic
92C2×C3×C22⋊C4—61no—
93C2×C3×C22⋊C4—61no—
94C2×C3×C42—31no—
95C2×#217—61no—
96D4×Dic3—62no—
97D4×Dic3—62no—
98C2×#213—34no—
99C2×#213—34no—
100C2×#213—62no—
101C2×#213—62no—
102C2×#213—62no—
103C2×#213—62no—
104C2×(C2×D3)⋊C4—21no—
105C2×(C2×D3)⋊C4—21no—
106C2×(C2×D3)⋊C4—61no—
107C2×C4⋊Dic3—31no—
108C2×C4⋊Dic3—31no—
109C2×C4⋊Dic3—61no—
110C2×C4×Dic3C2×D311yescharacteristic
111C22×C3⋊C8—31no—
112C22×C3⋊C8—31no—
113C22×C3⋊C8—61no—
114C22×C3⋊C8C2×D311yescharacteristic
115C4×D12—62no—
116C4×D12—62no—
117C3×#102—62no—
118#832—62no—
119#821—62no—
120#809—22no—
121C23×C32C2×D411yescharacteristic
122C22×C3×D3—22no—
123C22×C3×D3—22no—
124C22×C3×D3—22no—
125C22×C3×D3—22no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C22×C3×D3—41no—
131C22×C3×D3—41no—
132C22×C3×D3—41no—
133C22×C3×D3—41no—
134C22×C3×D3—41no—
135C22×C3×D3—41no—
136C2×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C32×C4—41no—
139C2×C32×C4C22×C411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C32×C4#4111yescharacteristic
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—41no—
147C2×C3⋊Dic3—41no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—21no—
153C2×C3×Dic3D812yescomplemented
154C3×D12—22no—
155C3×D12—22no—
156C3×D12—22no—
157C3×D12—22no—
158C3×D12—22no—
159C3×D12—41no—
160C3×D12—41no—
161C3×D12C22⋊C414yescomplemented
162D3×Dic3—48no—
163C3⋊(C3⋊C8)—22no—
164C3×C3⋊C8—41no—
165C22×D8—91no—
166C2×C4×D4—91no—
167C2×#102—31no—
168C2×#102—91no—
169#390—31no—
170#340—91no—
171#336—91no—
172C24×C3—61no—
173C24×C3—61no—
174C23×D3—21no—
175C23×D3—21no—
176C2×C3×D4—32no—
177C2×C3×D4—32no—
178C2×C3×D4—32no—
179C2×C3×D4—32no—
180C2×C3×D4—61no—
181C2×C3×D4—61no—
182C2×C3×D4—61no—
183C2×C3×D4—61no—
184C2×C3×D4—61no—
185C2×C3×D4—61no—
186C2×C3×D4—61no—
187C2×C3×D4—61no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—31no—
192C22×C3×C4—31no—
193C22×C3×C4—41no—
194C22×C3×C4C22×D311yescharacteristic
195C22×C3×C4C22×D311yescharacteristic
196C22×Dic3—64no—
197C22×Dic3—61no—
198C22×Dic3—61no—
199C22×Dic3—121no—
200C22×Dic3—122no—
201C22×Dic3—122no—
202C22×Dic3#6711yescharacteristic
203C22×Dic3#6711yescharacteristic
204C2×D12—21no—
205C2×D12—21no—
206C2×D12—21no—
207C2×D12—21no—
208C2×D12—21no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12—21no—
212C2×D12C4×D312yes—
213C2×D12C4×D312yescomplemented
214C2×D12D1212yes—
215C2×D12#6712yes—
216C2×C4×D3—64no—
217C2×C4×D3—122no—
218C2×C4×D3—122no—
219C2×C3×C8—61no—
220C2×C3×C8—61no—
221C2×C3×C8—61no—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—41no—
228C3×C22⋊C4—122no—
229C3×C22⋊C4—122no—
230C3×C42—61no—
231C3×C42—61no—
232#217—64no—
233#213—68no—
234#213—68no—
235(C2×D3)⋊C4—42no—
236(C2×D3)⋊C4—42no—
237(C2×D3)⋊C4—64no—
238C4⋊Dic3—32no—
239C4⋊Dic3—32no—
240C4⋊Dic3—62no—
241C4⋊Dic3—61no—
242C4⋊Dic3—61no—
243C4⋊Dic3—121no—
244C4×Dic3—21no—
245C4×Dic3—21no—
246C2×C3⋊C8—21no—
247C2×C3⋊C8—21no—
248C2×C3⋊C8—21no—
249C2×C3⋊C8—32no—
250C2×C3⋊C8—32no—
251C2×C3⋊C8—62no—
252C2×C3⋊C8—61no—
253C2×C3⋊C8—61no—
254C2×C3⋊C8—61no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8—121no—
257C2×C3⋊C8—121no—
258C22×C32C4×D411yescharacteristic
259C22×C32#12011yescharacteristic
260C22×C32#12111yescharacteristic
261C22×C32C2×D811yescharacteristic
262C22×C32#13511yescharacteristic
263C22×C32AGL(1,ℤ/8)11yescharacteristic
264C22×C32AGL(1,ℤ/8)11yescharacteristic
265C2×C3×D3—24no—
266C2×C3×D3—42no—
267C2×C3×D3—42no—
268C2×C3×D3—42no—
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—42no—
273C2×C3×D3—42no—
274C2×C3×D3—42no—
275C2×C3×D3—81no—
276C2×C3×D3—81no—
277C2×C3×D3—81no—
278C2×C3×D3—81no—
279C32×C4—81no—
280C32×C4C2×C22⋊C411yescharacteristic
281C32×C4C4×D411yescharacteristic
282C32×C4#12111yescharacteristic
283C32×C4#12311yescharacteristic
284C3⋊Dic3—42no—
285C3×Dic3—22no—
286C3×Dic3—41no—
287C22×D4—31no—
288C22×D4—31no—
289C23×C4—181no—
290C2×D8—94no—
291C2×D8—182no—
292C2×D8—182no—
293C22×C8—31no—
294C22×C8—91no—
295C4×D4—182no—
296C4×D4—182no—
297C2×C4⋊C4—91no—
298C2×C4⋊C4D3211yescharacteristic
299C2×C22⋊C4—61no—
300C2×C22⋊C4—61no—
301C2×C22⋊C4—181no—
302C2×C42—31no—
303#102—62no—
304#102—182no—
305C23×C3—21no—
306C23×C3—62no—
307C23×C3—62no—
308C23×C3—62no—
309C23×C3—62no—
310C23×C3—121no—
311C23×C3—121no—
312C23×C3—121no—
313C23×C3—121no—
314C23×C3—121no—
315C23×C3—121no—
316C23×C3—121no—
317C23×C3—121no—
318C23×C3—121no—
319C23×C3—121no—
320C23×C3D3×D411yescharacteristic
321C23×C3C2×#6711yescharacteristic
322C22×D3—22no—
323C22×D3—22no—
324C22×D3—22no—
325C22×D3—22no—
326C22×D3—41no—
327C22×D3—41no—
328C22×D3—41no—
329C22×D3—41no—
330C22×D3—41no—
331C22×D3—41no—
332C22×D3—41no—
333C22×D3—41no—
334C22×D3—41no—
335C22×D3—41no—
336C3×D4—34no—
337C3×D4—62no—
338C3×D4—62no—
339C3×D4—62no—
340C3×D4—62no—
341C3×D4—62no—
342C3×D4—121no—
343C3×D4—121no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—32no—
351C2×C3×C4—42no—
352C2×C3×C4—41no—
353C2×C3×C4—41no—
354C2×C3×C4—41no—
355C2×C3×C4—41no—
356C2×C3×C4—41no—
357C2×C3×C4—41no—
358C2×C3×C4—61no—
359C2×C3×C4—61no—
360C2×C3×C4—61no—
361C2×C3×C4—61no—
362C2×C3×C4—61no—
363C2×C3×C4—81no—
364C2×C3×C4—81no—
365C2×C3×C4C2×C4×D311yescharacteristic
366C2×C3×C4C2×C4×D311yescharacteristic
367C2×C3×C4C2×D1211yescharacteristic
368C2×C3×C4#23511yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4#23711yescharacteristic
374C2×C3×C4#23711yescharacteristic
375C2×C3×C4#23711yescharacteristic
376C2×C3×C4C2×#6711yescharacteristic
377C2×Dic3—21no—
378C2×Dic3—21no—
379C2×Dic3—21no—
380C2×Dic3—21no—
381C2×Dic3—21no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—122no—
385C2×Dic3—128no—
386C2×Dic3—121no—
387C2×Dic3—121no—
388C2×Dic3—121no—
389C2×Dic3—121no—
390C2×Dic3—241no—
391C2×Dic3—241no—
392C2×Dic3#21312yescomplemented
393D12—22no—
394D12—22no—
395D12—22no—
396D12—22no—
397D12—22no—
398D12—41no—
399D12—41no—
400D12(C2×D3)⋊C414yescomplemented
401C4×D3—128no—
402C3×C8—121no—
403C3⋊C8—41no—
404C3⋊C8—62no—
405C3⋊C8—62no—
406C3⋊C8—122no—
407C2×C32#38611yescharacteristic
408C2×C32C4×D811yescharacteristic
409C2×C32#44211yescharacteristic
410C2×C32#44711yescharacteristic
411C2×C32#44911yescharacteristic
412C2×C32#45911yescharacteristic
413C2×C32#46311yescharacteristic
414C3×D3—44no—
415C3×D3—82no—
416C24—61no—
417C24—61no—
418C2×D4—32no—
419C2×D4—32no—
420C2×D4—32no—
421C2×D4—32no—
422C2×D4—61no—
423C2×D4—61no—
424C2×D4—61no—
425C2×D4—61no—
426C2×D4—61no—
427C2×D4—61no—
428C2×D4—61no—
429C2×D4—61no—
430C22×C4—21no—
431C22×C4—31no—
432C22×C4—31no—
433C22×C4—184no—
434C22×C4—181no—
435C22×C4—362no—
436C22×C4—362no—
437C22×C4C2×D3211yescharacteristic
438D8—188no—
439C2×C8—61no—
440C2×C8—61no—
441C2×C8—61no—
442C2×C8—92no—
443C2×C8—181no—
444C2×C8—181no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—92no—
448C4⋊C4—181no—
449C22⋊C4—122no—
450C22⋊C4—122no—
451C22⋊C4—184no—
452C42—61no—
453C42—61no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—64no—
462C22×C3—122no—
463C22×C3—122no—
464C22×C3—122no—
465C22×C3—122no—
466C22×C3—122no—
467C22×C3—122no—
468C22×C3—122no—
469C22×C3—122no—
470C22×C3—122no—
471C22×C3—241no—
472C22×C3—241no—
473C22×C3—241no—
474C22×C3—241no—
475C22×C3#67⋊C411yescharacteristic
476C22×C3#88211yescharacteristic
477C22×C3D3×D811yescharacteristic
478C22×C3#91111yescharacteristic
479C22×C3#91411yescharacteristic
480C22×C3#91611yescharacteristic
481C22×C3C4×#6711yescharacteristic
482C22×C3C2×#21311yescharacteristic
483C22×C3#93211yescharacteristic
484C22×C3#93711yescharacteristic
485C22×C3#93811yescharacteristic
486C22×C3#93911yescharacteristic
487C22×C3#94911yescharacteristic
488C22×C3#95011yescharacteristic
489C2×D3—24no—
490C2×D3—42no—
491C2×D3—42no—
492C2×D3—42no—
493C2×D3—42no—
494C2×D3—42no—
495C2×D3—42no—
496C2×D3—42no—
497C2×D3—42no—
498C2×D3—42no—
499C2×D3—81no—
500C2×D3—81no—
501C2×D3—81no—
502C2×D3—81no—
503C3×C4—21no—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—62no—
508C3×C4—82no—
509C3×C4—81no—
510C3×C4—81no—
511C3×C4—121no—
512C3×C4D3×C22⋊C411yescharacteristic
513C3×C4#67⋊C411yescharacteristic
514C3×C4#67⋊C411yescharacteristic
515C3×C4#88311yescharacteristic
516C3×C4#88411yescharacteristic
517C3×C4#88611yescharacteristic
518C3×C4C2×(C2×D3)⋊C411yescharacteristic
519C3×C4#93911yescharacteristic
520Dic3—22no—
521Dic3—41no—
522Dic3—122no—
523Dic3—122no—
524Dic3—242no—
525C32#187911yescharacteristic, complemented, Sylow
526C23—62no—
527C23—62no—
528C23—62no—
529C23—62no—
530C23—121no—
531C23—121no—
532C23—121no—
533C23—121no—
534C23—121no—
535C23—121no—
536C23—121no—
537C23—121no—
538C23—121no—
539C23—121no—
540C23D3×#6711yescharacteristic
541D4—34no—
542D4—62no—
543D4—62no—
544D4—62no—
545D4—62no—
546D4—62no—
547D4—121no—
548D4—121no—
549C2×C4—32no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—61no—
554C2×C4—61no—
555C2×C4—61no—
556C2×C4—61no—
557C2×C4—61no—
558C2×C4—182no—
559C2×C4—368no—
560C2×C4—361no—
561C2×C4—361no—
562C2×C4#379511yescharacteristic
563C2×C4C4×D3211yescharacteristic
564C2×C4D3×D1211yescharacteristic
565C2×C4#380211yescharacteristic
566C2×C4#380511yescharacteristic
567C2×C4D3×#6711yescharacteristic
568C8—121no—
569C8—182no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—124no—
578C2×C3—242no—
579C2×C3#475611yescharacteristic
580C2×C3#477311yescharacteristic
581C2×C3#478111yescharacteristic
582C2×C3#478511yescharacteristic
583C2×C3#495611yescharacteristic
584C2×C3#495811yescharacteristic
585C2×C3C4×#21311yescharacteristic
586C2×C3#501411yescharacteristic
587C2×C3#503611yescharacteristic
588C2×C3#503711yescharacteristic
589C2×C3#505711yescharacteristic
590C2×C3#507211yescharacteristic
591C2×C3#515011yescharacteristic
592C2×C3#516511yescharacteristic
593D3—44no—
594D3—82no—
595C22—64no—
596C22—122no—
597C22—122no—
598C22—122no—
599C22—122no—
600C22—122no—
601C22—122no—
602C22—122no—
603C22—122no—
604C22—122no—
605C22—241no—
606C22—241no—
607C22—241no—
608C22—241no—
609C22#6387911yescharacteristic
610C22#6392211yescharacteristic
611C22D3×#21311yescharacteristic
612C22#6393211yescharacteristic
613C22#6393911yescharacteristic
614C22#6394711yescharacteristic
615C22#6397011yescharacteristic
616C4—62no—
617C4—81no—
618C4—121no—
619C4—362no—
620C4#6388511yescharacteristic
621C4#6389111yescharacteristic
622C4#6390211yescharacteristic
623C4D3×(C2×D3)⋊C411yescharacteristic
624C3—21no—
625C3#6965711yescharacteristic, complemented
626C3#7017211yescharacteristic, complemented
627C2—124no—
628C2—242no—
629C2#1059045211yescharacteristic
630C2#1059045511yescharacteristic
631C2#1059059511yescharacteristic
632C2#1059061311yescharacteristic
633C2#1059136311yescharacteristic
634C2#1059142811yescharacteristic
635C2#1059156711yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×#3713C2
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1879
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×Dic3×D12C2semidirect
3. C3×#4988C2semidirect
4. C2×C3×#809C2semidirect
5. C2×#63563C2semidirect
6. #10589395C2semidirect
7. #10589155C2semidirect
25. C2×#3713C4semidirect
36. #4988D3semidirect
37. C2×#809D3semidirect
59. C2×C3×D12C2×C4semidirect
71. C2×C3⋊(C3⋊C8)C2×C4semidirect
153. C2×C3×Dic3D8semidirect
161. C3×D12C22⋊C4semidirect
213. C2×D12C4×D3semidirect
392. C2×Dic3#213semidirect
400. D12(C2×D3)⋊C4semidirect
525. C32#1879semidirect
625. C3#69657semidirect
626. C3#70172semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3×D122
C22×#37132
C3×#49882
C2×C3×#8092
C2×#635632
#105893952
#105891552
#701723
#696573