Finite Group Databasebeta

← #11791464

Subgroups — #11791464

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 661 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#940C211yesmaximal, characteristic
2C2×#63659C211yesmaximal, characteristic, complemented
3C2×C3×#832C211yesmaximal, characteristic, complemented
4Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
5C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic, complemented
8#71761—31nomaximal
9#70161—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×C3×#67—21no—
12C22×C3×#67—21no—
13C22×C3×D12C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×#940—22no—
17C3×#940C414yescomplemented
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×Dic32—21no—
22#63659—22no—
23C3×#832—22no—
24#63579—21no—
25Dic3⋊(C3⋊C8)—22no—
26#63563—22no—
27#63562—22no—
28C2×C3×#127—31no—
29C2×#940D311yescharacteristic
30C2×C3×#102—31no—
31C2×#832—31no—
32C2×#832—31no—
33C2×#832—31no—
34C2×#832—31no—
35C2×#832—61no—
36C2×#832D311yescharacteristic, complemented
37C2×#821—31no—
38C2×Dic3⋊C8—31no—
39Dic3×C4⋊C4—31no—
40C2×#809—31no—
41C4×C4⋊Dic3—31no—
42C2×C4⋊(C3⋊C8)—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×C412yes—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C2×C3×#67—24no—
54C2×C3×#67—24no—
55C2×C3×#67—42no—
56C2×C3×#67—42no—
57C2×C3×#67—42no—
58C2×C3×#67—42no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3D411yescharacteristic
61C22×C3×Dic3D411yescharacteristic
62C2×C3×D12—21no—
63C2×C3×D12—21no—
64C2×C3×D12—21no—
65C2×C3×D12—21no—
66C2×C3×D12—21no—
67C2×C3×D12C2×C412yes—
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)D412yescomplemented
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)—21no—
72C2×C3⋊(C3⋊C8)—21no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3D412yescomplemented
75C3×C4×Dic3C2×C412yes—
76C3×C4×Dic3D412yes—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8—21no—
80Dic32—42no—
81#1982—91noSylow
82C22×C3×D4—21no—
83C22×C3×D4—31no—
84C22×C3×D4—61no—
85C22×C3×D4—61no—
86C22×C3×D4C2×D311yescharacteristic
87C22×C3×D4C2×D311yescharacteristic
88C22×#67—21no—
89C22×#67—21no—
90C22×D12C2×D311yescharacteristic
91C22×C3×C8—31no—
92C3×#127—34no—
93C3×#127—62no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C42—31no—
96#940—22no—
97#940Dic314yescomplemented
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—31no—
100C2×C4⋊Dic3—61no—
101C2×C4⋊Dic3C2×D311yescharacteristic
102C2×C4×Dic3—61no—
103C2×C4×Dic3—61no—
104C2×C4×Dic3C2×D311yescharacteristic
105C22×C3⋊C8—31no—
106C22×C3⋊C8—31no—
107C22×C3⋊C8—61no—
108C22×C3⋊C8C2×D311yescharacteristic
109C3×#102—62no—
110#832—22no—
111#832—62no—
112#832—62no—
113#832—62no—
114#832—64no—
115#832—62no—
116C3⋊#95—61no—
117C3⋊#95—61no—
118#821—62no—
119Dic3⋊C8—62no—
120#809—62no—
121C4⋊(C3⋊C8)—62no—
122C23×C32—22no—
123C23×C32—41no—
124C23×C32—41no—
125C23×C32—41no—
126C23×C32—41no—
127C23×C32—41no—
128C23×C32—41no—
129C23×C32C2×D411yescharacteristic
130C22×C3×D3—22no—
131C22×C3×D3—41no—
132C22×C3×D3—41no—
133C22×C3×D3—41no—
134C22×C3×D3—41no—
135C22×C3×D3—41no—
136C22×C3×D3—41no—
137C32×D4—22no—
138C32×D4—22no—
139C32×D4—41no—
140C32×D4—41no—
141C2×C32×C4C22×C411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4#4111yescharacteristic
146C2×C32×C4#4111yescharacteristic
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—41no—
149C2×C3⋊Dic3—41no—
150C3×#67—48no—
151C3×#67—48no—
152C2×C3×Dic3—21no—
153C2×C3×Dic3—21no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—41no—
157C2×C3×Dic3C22⋊C412yes—
158C2×C3×Dic3C22⋊C412yes—
159C2×C3×Dic3D812yes—
160C2×C3×Dic3SD1612yes—
161C3×D12—22no—
162C3×D12—22no—
163C3×D12—41no—
164C3×D12—41no—
165C3⋊(C3⋊C8)—41no—
166C3×C3⋊C8—41no—
167C2×#127—31no—
168C2×C4⋊C8—91no—
169C2×#102—31no—
170C2×#102—91no—
171C2×#102—91no—
172C2×#102—91no—
173C4×C4⋊C4—91no—
174C24×C3—21no—
175C24×C3—21no—
176C24×C3—41no—
177C24×C3—61no—
178C23×D3—21no—
179C2×C3×D4—22no—
180C2×C3×D4—22no—
181C2×C3×D4—21no—
182C2×C3×D4—21no—
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—22no—
192C2×C3×D4—32no—
193C2×C3×D4—41no—
194C2×C3×D4—41no—
195C2×C3×D4—41no—
196C2×C3×D4—64no—
197C2×C3×D4—64no—
198C2×C3×D4—61no—
199C2×C3×D4—61no—
200C2×C3×D4—61no—
201C2×C3×D4—61no—
202C2×C3×D4—61no—
203C2×C3×D4—122no—
204C2×C3×D4—122no—
205C2×C3×D4—122no—
206C2×C3×D4—122no—
207C2×C3×D4C4×D312yes—
208C2×C3×D4C2×Dic312yes—
209C22×C3×C4—21no—
210C22×C3×C4—31no—
211C22×C3×C4—31no—
212C22×C3×C4—61no—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C2×#67—24no—
216C2×#67—24no—
217C2×#67—42no—
218C2×#67—42no—
219C2×#67—42no—
220C2×#67—42no—
221C22×Dic3—21no—
222C22×Dic3—61no—
223C22×Dic3—61no—
224C22×Dic3—121no—
225C22×Dic3#6711yescharacteristic
226C22×Dic3#6711yescharacteristic
227C2×D12—21no—
228C2×D12—21no—
229C2×D12—21no—
230C2×D12—21no—
231C2×D12—21no—
232C2×D12C2×Dic312yes—
233C2×C3×C8—61no—
234C2×C3×C8—61no—
235C2×C3×C8—61no—
236C3×C4⋊C4—32no—
237C3×C4⋊C4—61no—
238C3×C42—32no—
239C3×C42—32no—
240C4⋊Dic3—21no—
241C4⋊Dic3—32no—
242C4⋊Dic3—32no—
243C4⋊Dic3—62no—
244C4⋊Dic3—61no—
245C4⋊Dic3—61no—
246C4⋊Dic3—121no—
247C4⋊Dic3#6712yescomplemented
248C4×Dic3—122no—
249C4×Dic3—122no—
250C4×Dic3C2×Dic312yes—
251C4×Dic3#6712yes—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8—62no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259C2×C3⋊C8—61no—
260C2×C3⋊C8—61no—
261C2×C3⋊C8—61no—
262C2×C3⋊C8—121no—
263C2×C3⋊C8—121no—
264C22×C32—42no—
265C22×C32—42no—
266C22×C32—42no—
267C22×C32—81no—
268C22×C32—81no—
269C22×C32—81no—
270C22×C32—81no—
271C22×C32C2×C22⋊C411yescharacteristic
272C22×C32#12111yescharacteristic
273C22×C32#12111yescharacteristic
274C22×C32C2×D811yescharacteristic
275C22×C32C2×SD1611yescharacteristic
276C22×C32AGL(1,ℤ/8)11yescharacteristic
277C22×C32AGL(1,ℤ/8)11yescharacteristic
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C2×C3×D3—42no—
281C2×C3×D3—81no—
282C2×C3×D3—81no—
283C2×C3×D3—81no—
284C2×C3×D3—81no—
285C32×C4C4×D411yescharacteristic
286C32×C4C4×D411yescharacteristic
287C32×C4#12411yescharacteristic
288C32×C4#12711yescharacteristic
289C3⋊Dic3—42no—
290C3×Dic3—22no—
291C3×Dic3—42no—
292C3×Dic3#10214yescomplemented
293C22×D4—31no—
294C22×D4—61no—
295C22×D4—61no—
296C22×D4D3211yescharacteristic
297C22×C8—31no—
298C22×C8—91no—
299#127—34no—
300#127—62no—
301C2×C4⋊C4—31no—
302C2×C4⋊C4—91no—
303C2×C42—31no—
304C2×C42—181no—
305C4⋊C8—182no—
306#102—62no—
307#102—182no—
308#102—182no—
309#102—182no—
310#95—181no—
311C23×C3—22no—
312C23×C3—22no—
313C23×C3—21no—
314C23×C3—42no—
315C23×C3—42no—
316C23×C3—42no—
317C23×C3—41no—
318C23×C3—41no—
319C23×C3—41no—
320C23×C3—41no—
321C23×C3—41no—
322C23×C3—41no—
323C23×C3—41no—
324C23×C3—41no—
325C23×C3—41no—
326C23×C3—41no—
327C23×C3—41no—
328C23×C3—41no—
329C23×C3—62no—
330C23×C3—81no—
331C23×C3—81no—
332C23×C3—81no—
333C23×C3—81no—
334C23×C3—121no—
335C23×C3—121no—
336C23×C3—121no—
337C23×C3—121no—
338C23×C3—121no—
339C23×C3—121no—
340C23×C3D3×D411yescharacteristic
341C23×C3C2×#6711yescharacteristic
342C22×D3—22no—
343C22×D3—41no—
344C22×D3—41no—
345C22×D3—41no—
346C22×D3—41no—
347C22×D3—41no—
348C22×D3—41no—
349C3×D4—24no—
350C3×D4—22no—
351C3×D4—22no—
352C3×D4—22no—
353C3×D4—22no—
354C3×D4—42no—
355C3×D4—42no—
356C3×D4—42no—
357C3×D4—41no—
358C3×D4—41no—
359C3×D4—41no—
360C3×D4—41no—
361C3×D4—62no—
362C3×D4—62no—
363C3×D4—128no—
364C3×D4—128no—
365C3×D4—121no—
366C3×D4—121no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—32no—
374C2×C3×C4—32no—
375C2×C3×C4—32no—
376C2×C3×C4—32no—
377C2×C3×C4—61no—
378C2×C3×C4—61no—
379C2×C3×C4—62no—
380C2×C3×C4—121no—
381C2×C3×C4—121no—
382C2×C3×C4C2×C4×D311yescharacteristic
383C2×C3×C4#23511yescharacteristic
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4D3×D411yescharacteristic
388C2×C3×C4#23711yescharacteristic
389C2×C3×C4#23711yescharacteristic
390C2×C3×C4#23711yescharacteristic
391C2×C3×C4C22×Dic311yescharacteristic
392C2×C3×C4C2×#6711yescharacteristic
393C2×C3×C4C2×#6711yescharacteristic
394#67—48no—
395#67—48no—
396C2×Dic3—21no—
397C2×Dic3—21no—
398C2×Dic3—22no—
399C2×Dic3—41no—
400C2×Dic3—41no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—122no—
404C2×Dic3—121no—
405C2×Dic3—121no—
406C2×Dic3—121no—
407C2×Dic3—121no—
408C2×Dic3—241no—
409C2×Dic3—241no—
410C2×Dic3#21312yes—
411C2×Dic3#21412yes—
412C2×Dic3#21712yes—
413C2×Dic3#21712yes—
414D12—22no—
415D12—22no—
416D12—41no—
417D12—41no—
418C3×C8—121no—
419C3⋊C8—41no—
420C3⋊C8—122no—
421C3⋊C8—121no—
422C3⋊C8—121no—
423C2×C32—82no—
424C2×C32#39011yescharacteristic
425C2×C32C2×#10211yescharacteristic
426C2×C32#41811yescharacteristic
427C2×C32#45911yescharacteristic
428C2×C32#45911yescharacteristic
429C2×C32#46011yescharacteristic
430C2×C32#46011yescharacteristic
431C3×D3—82no—
432C24—21no—
433C24—61no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—32no—
440C2×D4—64no—
441C2×D4—64no—
442C2×D4—61no—
443C2×D4—61no—
444C2×D4—61no—
445C2×D4—61no—
446C2×D4—61no—
447C2×D4—122no—
448C2×D4—122no—
449C2×D4—122no—
450C2×D4—122no—
451C2×D4D3×Dic312yes—
452C22×C4—31no—
453C22×C4—31no—
454C22×C4—61no—
455C22×C4—181no—
456C22×C4C2×D3211yescharacteristic
457C2×C8—61no—
458C2×C8—61no—
459C2×C8—61no—
460C2×C8—181no—
461C2×C8—181no—
462C2×C8—181no—
463C4⋊C4—32no—
464C4⋊C4—61no—
465C4⋊C4—92no—
466C4⋊C4—181no—
467C42—32no—
468C42—32no—
469C42—362no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—44no—
478C22×C3—42no—
479C22×C3—42no—
480C22×C3—42no—
481C22×C3—42no—
482C22×C3—42no—
483C22×C3—42no—
484C22×C3—82no—
485C22×C3—82no—
486C22×C3—82no—
487C22×C3—82no—
488C22×C3—82no—
489C22×C3—82no—
490C22×C3—81no—
491C22×C3—81no—
492C22×C3—81no—
493C22×C3—81no—
494C22×C3—81no—
495C22×C3—81no—
496C22×C3—81no—
497C22×C3—81no—
498C22×C3—122no—
499C22×C3—122no—
500C22×C3—122no—
501C22×C3—241no—
502C22×C3—241no—
503C22×C3—241no—
504C22×C3—241no—
505C22×C3D3×C22⋊C411yescharacteristic
506C22×C3#88411yescharacteristic
507C22×C3D3×D811yescharacteristic
508C22×C3#91111yescharacteristic
509C22×C3D3×SD1611yescharacteristic
510C22×C3#91411yescharacteristic
511C22×C3C2×#21311yescharacteristic
512C22×C3#93211yescharacteristic
513C22×C3#93211yescharacteristic
514C22×C3C2×#21411yescharacteristic
515C22×C3#93811yescharacteristic
516C22×C3#93811yescharacteristic
517C22×C3#93911yescharacteristic
518C22×C3C2×#21711yescharacteristic
519C2×D3—42no—
520C2×D3—42no—
521C2×D3—42no—
522C2×D3—81no—
523C2×D3—81no—
524C2×D3—81no—
525C2×D3—81no—
526C3×C4—21no—
527C3×C4—21no—
528C3×C4—21no—
529C3×C4—21no—
530C3×C4—34no—
531C3×C4—62no—
532C3×C4—122no—
533C3×C4#67⋊C411yescharacteristic
534C3×C4#88511yescharacteristic
535C3×C4C4×#6711yescharacteristic
536C3×C4D4×Dic311yescharacteristic
537C3×C4D4×Dic311yescharacteristic
538C3×C4#93611yescharacteristic
539C3×C4#94011yescharacteristic
540C3×C4#94011yescharacteristic
541Dic3—22no—
542Dic3—42no—
543Dic3—122no—
544Dic3—122no—
545Dic3—242no—
546Dic3#83214yescomplemented
547C32#198211yescharacteristic, complemented, Sylow
548C23—22no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—62no—
556C23—121no—
557C23—121no—
558C23—121no—
559C23—121no—
560C23—121no—
561C23—121no—
562C23D3×#6711yescharacteristic
563D4—22no—
564D4—22no—
565D4—41no—
566D4—41no—
567D4—62no—
568D4—62no—
569D4—128no—
570D4—128no—
571D4—121no—
572D4—121no—
573C2×C4—32no—
574C2×C4—32no—
575C2×C4—32no—
576C2×C4—32no—
577C2×C4—61no—
578C2×C4—61no—
579C2×C4—62no—
580C2×C4—121no—
581C2×C4—121no—
582C2×C4—182no—
583C2×C4—361no—
584C2×C4—361no—
585C2×C4C2×D3×Dic311yescharacteristic
586C2×C4#380411yescharacteristic
587C2×C4#380511yescharacteristic
588C2×C4D3×#6711yescharacteristic
589C2×C4D3×#6711yescharacteristic
590C2×C4#381111yescharacteristic
591C8—121no—
592C8—361no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—84no—
601C2×C3—82no—
602C2×C3—82no—
603C2×C3—242no—
604C2×C3#476211yescharacteristic
605C2×C3D3×#10211yescharacteristic
606C2×C3#477011yescharacteristic
607C2×C3#478611yescharacteristic
608C2×C3#495711yescharacteristic
609C2×C3#507211yescharacteristic
610C2×C3#507211yescharacteristic
611C2×C3#507511yescharacteristic
612C2×C3#507511yescharacteristic
613C2×C3#515011yescharacteristic
614C2×C3#516311yescharacteristic
615C2×C3C2×#83211yescharacteristic
616C2×C3#521511yescharacteristic
617C2×C3#522111yescharacteristic
618D3—82no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22—81no—
626C22—122no—
627C22—122no—
628C22—122no—
629C22—241no—
630C22—241no—
631C22—241no—
632C22—241no—
633C22D3×#21311yescharacteristic
634C22D3×#21411yescharacteristic
635C22#6393211yescharacteristic
636C22#6393411yescharacteristic
637C22#6395811yescharacteristic
638C22D3×#21711yescharacteristic
639C22#6397011yescharacteristic
640C4—34no—
641C4—62no—
642C4—122no—
643C4—362no—
644C4#6395911yescharacteristic
645C4Dic3×#6711yescharacteristic
646C4#67⋊Dic311yescharacteristic
647C4#6397911yescharacteristic
648C3—21no—
649C3#7016111yescharacteristic, complemented
650C3#7176111yescharacteristic, complemented
651C2—82no—
652C2—242no—
653C2D3×#83211yescharacteristic
654C2#1059142111yescharacteristic
655C2#1059142811yescharacteristic
656C2#1059142911yescharacteristic
657C2#1059143811yescharacteristic
658C2#1059143911yescharacteristic
659C2#1059170711yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC2×C3×#940C2
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1982
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×#63659C2semidirect
3. C2×C3×#832C2semidirect
4. Dic3×C4⋊Dic3C2semidirect
5. C2×Dic3⋊(C3⋊C8)C2semidirect
6. C2×#63563C2semidirect
7. C2×#63562C2semidirect
17. C3×#940C4semidirect
36. C2×#832D3semidirect
69. C4⋊(C3⋊Dic3)D4semidirect
74. C3×C4⋊Dic3D4semidirect
97. #940Dic3semidirect
247. C4⋊Dic3#67semidirect
292. C3×Dic3#102semidirect
546. Dic3#832semidirect
547. C32#1982semidirect
649. C3#70161semidirect
650. C3#71761semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9402
C2×#636592
C2×C3×#8322
Dic3×C4⋊Dic32
C2×Dic3⋊(C3⋊C8)2
C2×#635632
C2×#635622
#717613
#701613