Finite Group Databasebeta

← #11791853

Subgroups — #11791853

Order 1152.

719 conjugacy classes of subgroups.

The subgroup lattice has 649 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#878C211yesmaximal, characteristic
2#10591716C211yesmaximal, characteristic
3Dic3×#217C211yesmaximal, characteristic
4#10589392C211yesmaximal, characteristic
5C3×#4526C211yesmaximal, characteristic
6#10589186C211yesmaximal, characteristic
7#10589186C211yesmaximal, characteristic
8#71701—31nomaximal
9#68955—31nomaximal
10C23×C3×Dic3C2211yescharacteristic
11C22×C3×Dic6C411yescharacteristic, complemented
12C2×C32×C22⋊C4C2211yescharacteristic
13C2×#3757C2211yescharacteristic
14C2×#3757C2211yescharacteristic
15C2×C3×#217C2211yescharacteristic
16C2×C3×#217C2211yescharacteristic
17C2×C3×#217C2211yescharacteristic
18C2×C3×C4⋊Dic3C411yescharacteristic, complemented
19C2×C3×Dic3⋊C4C411yescharacteristic, complemented
20C2×C3×Dic3⋊C4C411yescharacteristic, complemented
21C3×#878—21no—
22C3×#878—21no—
23C3×#878—21no—
24C3×#878—21no—
25C2×Dic3⋊Dic3—21no—
26C2×Dic32—21no—
27#63579—21no—
28#63579—21no—
29C2×C3×C22⋊Q8—31no—
30C2×#878D311yescharacteristic
31#5212—31no—
32C4×#217—31no—
33#4942—31no—
34Dic3×C22⋊C4—31no—
35C3×#342—31no—
36#4527—31no—
37#4527—31no—
38#4526—31no—
39#4526—31no—
40#4526—31no—
41#4526—31no—
42#4526—61no—
43#4526D311yescharacteristic
44C24×C32C2311yescharacteristic
45C22×C32×C4C2×C411yescharacteristic
46C22×C32×C4C2×C411yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3—21no—
51C22×C3×Dic3—42no—
52C22×C3×Dic3C2×C411yescharacteristic
53C22×C3×Dic3C2×C411yescharacteristic
54C22×C3×Dic3C2×C411yescharacteristic
55C22×C3×Dic3C2×C411yescharacteristic
56C22×C3×Dic3D411yescharacteristic
57C22×C3×Dic3D411yescharacteristic
58C22×C3×Dic3D411yescharacteristic
59C22×C3×Dic3D411yescharacteristic
60C2×C3×Dic6—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—42no—
63C32×C22⋊C4—21no—
64C32×C22⋊C4—21no—
65#3757—21no—
66#3757—21no—
67#3757—21no—
68#3757Q812yescomplemented
69C3×#217—21no—
70C3×#217—21no—
71C3×#217—21no—
72C3×#217—21no—
73C3×#217—21no—
74C3×#217Q812yescomplemented
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3—21no—
77C3×Dic3⋊C4—21no—
78C3×Dic3⋊C4—21no—
79C3×Dic3⋊C4—21no—
80C3×Dic3⋊C4—21no—
81Dic3⋊Dic3—42no—
82Dic32—42no—
83#1996—91noSylow
84C22×C3×Q8—31no—
85C23×C3×C4—31no—
86C23×Dic3C2×D311yescharacteristic
87C22×Dic6Dic311yescharacteristic, complemented
88C3×C22⋊Q8—61no—
89C3×C22⋊Q8—61no—
90C3×C22⋊Q8—61no—
91C3×C22⋊Q8—61no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C22⋊C4—21no—
96C2×C3×C22⋊C4—31no—
97C2×C3×C22⋊C4—31no—
98C2×C3×C22⋊C4—31no—
99C2×C3×C22⋊C4C2×D311yescharacteristic
100C2×C3×C22⋊C4C2×D311yescharacteristic
101C2×#217—31no—
102C2×#217—31no—
103C2×#217—31no—
104C2×#217—31no—
105C2×#217—61no—
106C2×#217—61no—
107C2×#217C2×D311yescharacteristic
108C2×#217C2×D311yescharacteristic
109C2×#217C2×D311yescharacteristic
110C2×C4⋊Dic3—61no—
111C2×C4⋊Dic3Dic311yescharacteristic, complemented
112C2×Dic3⋊C4—61no—
113C2×Dic3⋊C4Dic311yescharacteristic, complemented
114C2×Dic3⋊C4Dic311yescharacteristic, complemented
115C2×C4×Dic3—61no—
116C2×C4×Dic3—61no—
117#878—21no—
118#878—21no—
119#878—21no—
120#878—21no—
121C3⋊#95—61no—
122C3⋊#95—61no—
123C3⋊#95—61no—
124C3⋊#95—61no—
125C23×C32—41no—
126C23×C32—41no—
127C23×C32C22×C411yescharacteristic
128C23×C32C2×D411yescharacteristic
129C23×C32C2×D411yescharacteristic
130C23×C32C2×Q811yescharacteristic
131C23×C32C2×Q811yescharacteristic
132C23×C32#4111yescharacteristic
133C23×C32#4111yescharacteristic
134C2×C32×C4—21no—
135C2×C32×C4—21no—
136C2×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—41no—
140C2×C3⋊Dic3—41no—
141C2×C3⋊Dic3—41no—
142C2×C3⋊Dic3—41no—
143C2×C3⋊Dic3—41no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—41no—
157C2×C3×Dic3—41no—
158C2×C3×Dic3—41no—
159C2×C3×Dic3—41no—
160C2×C3×Dic3C22⋊C411yescharacteristic
161C2×C3×Dic3C22⋊C411yescharacteristic
162C2×C3×Dic3C22⋊C411yescharacteristic
163C2×C3×Dic3C22⋊C411yescharacteristic
164C3×Dic6—42no—
165C3×Dic6—42no—
166C2×C22⋊Q8—31no—
167#380—91no—
168C4×C22⋊C4—91no—
169#342—31no—
170#342—91no—
171#342—91no—
172#342—91no—
173C24×C3—21no—
174C24×C3C22×D311yescharacteristic
175C24×C3C22×D311yescharacteristic
176C2×C3×Q8—61no—
177C2×C3×Q8—61no—
178C2×C3×Q8—122no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—31no—
182C22×C3×C4—31no—
183C22×C3×C4—31no—
184C22×C3×C4—31no—
185C22×C3×C4—31no—
186C22×C3×C4—31no—
187C22×C3×C4—31no—
188C22×C3×C4—31no—
189C22×C3×C4—61no—
190C22×C3×C4—61no—
191C22×C3×C4—122no—
192C22×C3×C4C4×D311yescharacteristic
193C22×C3×C4C4×D311yescharacteristic
194C22×C3×C4C2×Dic311yescharacteristic
195C22×C3×C4C2×Dic311yescharacteristic
196C22×Dic3—21no—
197C22×Dic3—21no—
198C22×Dic3—42no—
199C22×Dic3—61no—
200C22×Dic3—61no—
201C22×Dic3—61no—
202C22×Dic3—61no—
203C22×Dic3—121no—
204C22×Dic3—121no—
205C22×Dic3C2×Dic311yescharacteristic
206C22×Dic3C2×Dic311yescharacteristic
207C22×Dic3C2×Dic311yescharacteristic
208C22×Dic3C2×Dic311yescharacteristic
209C22×Dic3#6711yescharacteristic
210C22×Dic3#6711yescharacteristic
211C22×Dic3#6711yescharacteristic
212C22×Dic3#6711yescharacteristic
213C2×Dic6—21no—
214C2×Dic6—21no—
215C2×Dic6—42no—
216C3×C4⋊C4—61no—
217C3×C4⋊C4—61no—
218C3×C4⋊C4—61no—
219C3×C4⋊C4—61no—
220C3×C4⋊C4—61no—
221C3×C4⋊C4—61no—
222C3×C22⋊C4—21no—
223C3×C22⋊C4—21no—
224C3×C22⋊C4—21no—
225C3×C22⋊C4—21no—
226C3×C22⋊C4—32no—
227C3×C22⋊C4—41no—
228C3×C22⋊C4—41no—
229C3×C22⋊C4—61no—
230C3×C22⋊C4—61no—
231C3×C22⋊C4—61no—
232C3×C22⋊C4—61no—
233C3×C22⋊C4—61no—
234#217—21no—
235#217—21no—
236#217—21no—
237#217—21no—
238#217—21no—
239#217—32no—
240#217—32no—
241#217—62no—
242#217—61no—
243#217—61no—
244#217—62no—
245#217—61no—
246#217—61no—
247#217—61no—
248#217—61no—
249#217—121no—
250#217—121no—
251#217Dic612yescomplemented
252C4⋊Dic3—21no—
253C4⋊Dic3—21no—
254C4⋊Dic3—122no—
255Dic3⋊C4—21no—
256Dic3⋊C4—21no—
257Dic3⋊C4—21no—
258Dic3⋊C4—21no—
259Dic3⋊C4—122no—
260C4×Dic3—122no—
261C4×Dic3—122no—
262C22×C32—21no—
263C22×C32—21no—
264C22×C32—21no—
265C22×C32—21no—
266C22×C32—21no—
267C22×C32—21no—
268C22×C32—41no—
269C22×C32—41no—
270C22×C32—41no—
271C22×C32—41no—
272C22×C32C2×C22⋊C411yescharacteristic
273C22×C32C4×Q811yescharacteristic
274C22×C32C4×Q811yescharacteristic
275C22×C32C22⋊Q811yescharacteristic
276C22×C32C22⋊Q811yescharacteristic
277C22×C32#12411yescharacteristic
278C22×C32C4⋊Q811yescharacteristic
279C32×C4—41no—
280C32×C4—41no—
281C3⋊Dic3—42no—
282C3⋊Dic3—81no—
283C3×Dic3—21no—
284C3×Dic3—21no—
285C3×Dic3—21no—
286C3×Dic3—42no—
287C3×Dic3—41no—
288C3×Dic3—41no—
289C3×Dic3—81no—
290C3×Dic3#9912yes—
291C22×Q8—31no—
292C23×C4—31no—
293C22⋊Q8—61no—
294C22⋊Q8—61no—
295C22⋊Q8—61no—
296C22⋊Q8—61no—
297C2×C4⋊C4—31no—
298C2×C4⋊C4—31no—
299C2×C4⋊C4—31no—
300C2×C4⋊C4—181no—
301C2×C22⋊C4—31no—
302C2×C22⋊C4—31no—
303C2×C22⋊C4—31no—
304C2×C22⋊C4—91no—
305C2×C22⋊C4—91no—
306C2×C22⋊C4D3211yescharacteristic
307C2×C42—181no—
308#95—181no—
309#95—181no—
310C23×C3—21no—
311C23×C3—21no—
312C23×C3—21no—
313C23×C3—21no—
314C23×C3—21no—
315C23×C3—21no—
316C23×C3—21no—
317C23×C3—41no—
318C23×C3—41no—
319C23×C3—41no—
320C23×C3—41no—
321C23×C3—81no—
322C23×C3—81no—
323C23×C3C2×Dic611yescharacteristic
324C23×C3C2×C4×D311yescharacteristic
325C23×C3#23511yescharacteristic
326C23×C3D3×D411yescharacteristic
327C23×C3D3×D411yescharacteristic
328C23×C3#23711yescharacteristic
329C23×C3D3×Q811yescharacteristic
330C23×C3D3×Q811yescharacteristic
331C23×C3D3×Q811yescharacteristic
332C23×C3#23911yescharacteristic
333C23×C3#23911yescharacteristic
334C23×C3C22×Dic311yescharacteristic
335C23×C3C2×#6711yescharacteristic
336C23×C3C2×#6711yescharacteristic
337C3×Q8—122no—
338C3×Q8—122no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—31no—
344C2×C3×C4—31no—
345C2×C3×C4—31no—
346C2×C3×C4—31no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—41no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—61no—
357C2×C3×C4—61no—
358C2×C3×C4—62no—
359C2×C3×C4—81no—
360C2×C3×C4—81no—
361C2×C3×C4—121no—
362C2×C3×C4—121no—
363C2×C3×C4—121no—
364C2×C3×C4—121no—
365C2×C3×C4—121no—
366C2×C3×C4—121no—
367C2×C3×C4—121no—
368C2×C3×C4—121no—
369C2×C3×C4—121no—
370C2×C3×C4—121no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—21no—
376C2×Dic3—21no—
377C2×Dic3—41no—
378C2×Dic3—41no—
379C2×Dic3—41no—
380C2×Dic3—41no—
381C2×Dic3—41no—
382C2×Dic3—41no—
383C2×Dic3—41no—
384C2×Dic3—41no—
385C2×Dic3—41no—
386C2×Dic3—41no—
387C2×Dic3—62no—
388C2×Dic3—62no—
389C2×Dic3—122no—
390C2×Dic3—121no—
391C2×Dic3—121no—
392C2×Dic3—121no—
393C2×Dic3—121no—
394C2×Dic3—121no—
395C2×Dic3—121no—
396C2×Dic3—122no—
397C2×Dic3—121no—
398C2×Dic3—121no—
399C2×Dic3—121no—
400C2×Dic3—121no—
401C2×Dic3—241no—
402C2×Dic3—241no—
403C2×Dic3—241no—
404C2×Dic3—241no—
405C2×Dic3#21711yescharacteristic
406C2×Dic3#21711yescharacteristic
407C2×Dic3#21711yescharacteristic
408C2×Dic3#21711yescharacteristic
409Dic6—42no—
410Dic6—42no—
411C2×C32—21no—
412C2×C32—21no—
413C2×C32—21no—
414C2×C32—21no—
415C2×C32—21no—
416C2×C32—21no—
417C2×C32#39111yescharacteristic
418C2×C32C2×#9911yescharacteristic
419C2×C32#41011yescharacteristic
420C24C2×D3211yescharacteristic
421C2×Q8—61no—
422C2×Q8—61no—
423C2×Q8—122no—
424C22×C4—31no—
425C22×C4—31no—
426C22×C4—31no—
427C22×C4—31no—
428C22×C4—31no—
429C22×C4—31no—
430C22×C4—31no—
431C22×C4—31no—
432C22×C4—61no—
433C22×C4—61no—
434C22×C4—122no—
435C22×C4—181no—
436C22×C4—181no—
437C22×C4D3×Dic311yescharacteristic
438C22×C4D3×Dic311yescharacteristic
439C4⋊C4—61no—
440C4⋊C4—61no—
441C4⋊C4—61no—
442C4⋊C4—61no—
443C4⋊C4—61no—
444C4⋊C4—61no—
445C4⋊C4—362no—
446C22⋊C4—21no—
447C22⋊C4—21no—
448C22⋊C4—32no—
449C22⋊C4—61no—
450C22⋊C4—61no—
451C22⋊C4—61no—
452C22⋊C4—61no—
453C22⋊C4—61no—
454C22⋊C4—92no—
455C22⋊C4—181no—
456C22⋊C4—181no—
457C22⋊C4—181no—
458C42—362no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—41no—
479C22×C3—41no—
480C22×C3—41no—
481C22×C3—41no—
482C22×C3—41no—
483C22×C3—41no—
484C22×C3—41no—
485C22×C3—41no—
486C22×C3—41no—
487C22×C3—41no—
488C22×C3—41no—
489C22×C3—41no—
490C22×C3—41no—
491C22×C3—41no—
492C22×C3—81no—
493C22×C3—81no—
494C22×C3—81no—
495C22×C3—81no—
496C22×C3C4×Dic611yescharacteristic
497C22×C3#87811yescharacteristic
498C22×C3D3×C22⋊C411yescharacteristic
499C22×C3#88511yescharacteristic
500C22×C3#88711yescharacteristic
501C22×C3#88811yescharacteristic
502C22×C3#89611yescharacteristic
503C22×C3#94411yescharacteristic
504C22×C3Q8×Dic311yescharacteristic
505C22×C3Q8×Dic311yescharacteristic
506C22×C3#94611yescharacteristic
507C22×C3#94611yescharacteristic
508C22×C3#94711yescharacteristic
509C22×C3C2×#21711yescharacteristic
510C3×C4—32no—
511C3×C4—41no—
512C3×C4—41no—
513C3×C4—41no—
514C3×C4—41no—
515C3×C4—61no—
516C3×C4—61no—
517C3×C4—61no—
518C3×C4—81no—
519C3×C4—81no—
520C3×C4—122no—
521C3×C4—121no—
522C3×C4—121no—
523C3×C4—241no—
524Dic3—21no—
525Dic3—21no—
526Dic3—21no—
527Dic3—42no—
528Dic3—41no—
529Dic3—41no—
530Dic3—81no—
531Dic3—122no—
532Dic3—122no—
533Dic3—242no—
534Dic3—241no—
535Dic3—241no—
536Dic3—242no—
537Dic3#83412yes—
538C32#199611yescharacteristic, complemented, Sylow
539C23—41no—
540C23—41no—
541C23D3×Dic611yescharacteristic
542C23#379611yescharacteristic
543C23#379711yescharacteristic
544C23#379911yescharacteristic
545C23C2×D3×Dic311yescharacteristic
546C23D3×#6711yescharacteristic
547C23D3×#6711yescharacteristic
548Q8—122no—
549Q8—122no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—31no—
553C2×C4—31no—
554C2×C4—31no—
555C2×C4—31no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—62no—
559C2×C4—62no—
560C2×C4—62no—
561C2×C4—62no—
562C2×C4—61no—
563C2×C4—61no—
564C2×C4—121no—
565C2×C4—121no—
566C2×C4—121no—
567C2×C4—121no—
568C2×C4—121no—
569C2×C4—121no—
570C2×C4—121no—
571C2×C4—121no—
572C2×C4—121no—
573C2×C4—121no—
574C2×C4—182no—
575C2×C4—361no—
576C2×C4—361no—
577C2×C4—361no—
578C2×C4—361no—
579C2×C4—361no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—41no—
596C2×C3—41no—
597C2×C3—41no—
598C2×C3—41no—
599C2×C3—41no—
600C2×C3—41no—
601C2×C3#464611yescharacteristic
602C2×C3#474011yescharacteristic
603C2×C3D3×#9911yescharacteristic
604C2×C3C2×#83411yescharacteristic
605C2×C3#522911yescharacteristic
606C2×C3#524011yescharacteristic
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22#6383911yescharacteristic
618C22Dic3×Dic611yescharacteristic
619C22#6384311yescharacteristic
620C22#6388711yescharacteristic
621C22#6388811yescharacteristic
622C22#6390711yescharacteristic
623C22D3×#21711yescharacteristic
624C4—32no—
625C4—41no—
626C4—41no—
627C4—61no—
628C4—61no—
629C4—61no—
630C4—122no—
631C4—121no—
632C4—121no—
633C4—241no—
634C4—362no—
635C4—721no—
636C3—21no—
637C3#6895511yescharacteristic, complemented
638C3#7170111yescharacteristic, complemented
639C2—21no—
640C2—21no—
641C2—21no—
642C2—21no—
643C2—21no—
644C2—21no—
645C2#1059126111yescharacteristic
646C2D3×#83411yescharacteristic
647C2#1059152811yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32C2×C22⋊C4
prime radical, cosocleC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#1996
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
11. C22×C3×Dic6C4semidirect
18. C2×C3×C4⋊Dic3C4semidirect
19. C2×C3×Dic3⋊C4C4semidirect
20. C2×C3×Dic3⋊C4C4semidirect
68. #3757Q8semidirect
74. C3×#217Q8semidirect
87. C22×Dic6Dic3semidirect
111. C2×C4⋊Dic3Dic3semidirect
113. C2×Dic3⋊C4Dic3semidirect
114. C2×Dic3⋊C4Dic3semidirect
251. #217Dic6semidirect
538. C32#1996semidirect
637. C3#68955semidirect
638. C3#71701semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8782
#105917162
Dic3×#2172
#105893922
C3×#45262
#105891862
#717013
#689553