Finite Group Databasebeta

← #11773446

Subgroups — #11773446

Order 1152.

1381 conjugacy classes of subgroups.

The subgroup lattice has 609 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊Dic3C211yesmaximal, characteristic
2C22×Dic3⋊Dic3C212yesmaximal
3C2×#63658C211yesmaximal, characteristic
4C2×C3×C3⋊#95C211yesmaximal, characteristic
5C2×#63579C212yesmaximal
6#71568—31nomaximal
7#69419—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C23×C3⋊Dic3C2211yescharacteristic
11C23×C3×Dic3C2212yes—
12C23×C3×Dic3C2212yes—
13C2×C3×C4⋊Dic3—22no—
14C2×C3×C4⋊Dic3—24no—
15C2×Dic3⋊Dic3—24no—
16C2×Dic3⋊Dic3—24no—
17C2×Dic3⋊Dic3—24no—
18#63658—22no—
19C3×C3⋊#95C414yescomplemented
20#63579—24no—
21C22×C3×C4⋊C4—31no—
22C22×C4⋊Dic3—32no—
23C22×C4⋊Dic3D311yescharacteristic
24C22×Dic3⋊C4—32no—
25C2×C3×#95—31no—
26C2×C3⋊#95—31no—
27C2×C3⋊#95—31no—
28C2×C3⋊#95—32no—
29C2×C3⋊#95—32no—
30C2×C3⋊#95—61no—
31C2×C3⋊#95D311yescharacteristic
32C24×C32C2311yescharacteristic
33C22×C32×C4—22no—
34C22×C32×C4—22no—
35C22×C32×C4C2×C412yes—
36C22×C32×C4D412yes—
37C22×C32×C4Q812yes—
38C22×C3⋊Dic3—21no—
39C22×C3⋊Dic3—21no—
40C22×C3⋊Dic3—22no—
41C22×C3⋊Dic3—22no—
42C22×C3⋊Dic3—22no—
43C22×C3⋊Dic3—21no—
44C22×C3⋊Dic3—21no—
45C22×C3⋊Dic3—22no—
46C22×C3⋊Dic3D412yes—
47C22×C3⋊Dic3Q812yes—
48C22×C3×Dic3—22no—
49C22×C3×Dic3—22no—
50C22×C3×Dic3—22no—
51C22×C3×Dic3—22no—
52C22×C3×Dic3—22no—
53C22×C3×Dic3—22no—
54C22×C3×Dic3—22no—
55C22×C3×Dic3—22no—
56C22×C3×Dic3—22no—
57C22×C3×Dic3—22no—
58C22×C3×Dic3C2×C414yes—
59C22×C3×Dic3D414yes—
60C22×C3×Dic3D414yes—
61C22×C3×Dic3Q814yes—
62C3×C4⋊Dic3—28no—
63Dic3⋊Dic3—216no—
64#1444—91noSylow
65C23×C3×C4—21no—
66C23×C3×C4—32no—
67C23×C3×C4—32no—
68C23×C3×C4C2×D311yescharacteristic
69C23×C3×C4C2×D311yescharacteristic
70C23×Dic3—31no—
71C23×Dic3—31no—
72C23×Dic3—31no—
73C23×Dic3—31no—
74C23×Dic3—61no—
75C23×Dic3—61no—
76C23×Dic3C2×D312yes—
77C23×Dic3C2×D312yes—
78C2×C3×C4⋊C4—64no—
79C2×C3×C4⋊C4—62no—
80C2×C4⋊Dic3—22no—
81C2×C4⋊Dic3—24no—
82C2×C4⋊Dic3—64no—
83C2×C4⋊Dic3—64no—
84C2×C4⋊Dic3—64no—
85C2×Dic3⋊C4—64no—
86C2×Dic3⋊C4—64no—
87C2×Dic3⋊C4—64no—
88C3×#95—34no—
89C3⋊#95—64no—
90C3⋊#95—64no—
91C3⋊#95—62no—
92C3⋊#95—62no—
93C3⋊#95—64no—
94C3⋊#95Dic314yescomplemented
95C23×C32C22×C411yescharacteristic
96C23×C32C2×D412yes—
97C23×C32C2×D411yescharacteristic
98C23×C32C2×D411yescharacteristic
99C23×C32C2×D412yes—
100C23×C32C2×Q811yescharacteristic
101C23×C32C2×Q812yes—
102C23×C32C2×Q811yescharacteristic
103C23×C32#4112yes—
104C23×C32#4111yescharacteristic
105C23×C32#4111yescharacteristic
106C2×C32×C4—24no—
107C2×C32×C4—22no—
108C2×C32×C4—24no—
109C2×C32×C4—22no—
110C2×C32×C4C4⋊C414yescomplemented
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3—24no—
114C2×C3⋊Dic3—24no—
115C2×C3⋊Dic3—41no—
116C2×C3⋊Dic3—42no—
117C2×C3⋊Dic3—42no—
118C2×C3⋊Dic3—41no—
119C2×C3⋊Dic3—41no—
120C2×C3⋊Dic3—41no—
121C2×C3×Dic3—24no—
122C2×C3×Dic3—24no—
123C2×C3×Dic3—24no—
124C2×C3×Dic3—24no—
125C2×C3×Dic3—24no—
126C2×C3×Dic3—24no—
127C2×C3×Dic3—24no—
128C2×C3×Dic3—24no—
129C2×C3×Dic3—24no—
130C2×C3×Dic3—42no—
131C2×C3×Dic3—42no—
132C2×C3×Dic3—42no—
133C2×C3×Dic3—42no—
134C2×C3×Dic3C4⋊C418yescomplemented
135C22×C4⋊C4—31no—
136C22×C4⋊C4—92no—
137C2×#95—31no—
138C2×#95—92no—
139C2×#95—91no—
140C24×C3—21no—
141C24×C3C22×D311yescharacteristic
142C24×C3C22×D311yescharacteristic
143C22×C3×C4—22no—
144C22×C3×C4—22no—
145C22×C3×C4—22no—
146C22×C3×C4—22no—
147C22×C3×C4—22no—
148C22×C3×C4—22no—
149C22×C3×C4—22no—
150C22×C3×C4—34no—
151C22×C3×C4—34no—
152C22×C3×C4—34no—
153C22×C3×C4—34no—
154C22×C3×C4—42no—
155C22×C3×C4—42no—
156C22×C3×C4—62no—
157C22×C3×C4—62no—
158C22×C3×C4—62no—
159C22×C3×C4—62no—
160C22×C3×C4—62no—
161C22×C3×C4—62no—
162C22×C3×C4—62no—
163C22×C3×C4—62no—
164C22×C3×C4—62no—
165C22×C3×C4—62no—
166C22×C3×C4Dic612yes—
167C22×C3×C4Dic612yes—
168C22×C3×C4C4×D312yes—
169C22×C3×C4D1212yes—
170C22×C3×C4C2×Dic312yes—
171C22×C3×C4#6712yes—
172C22×Dic3—22no—
173C22×Dic3—22no—
174C22×Dic3—22no—
175C22×Dic3—22no—
176C22×Dic3—22no—
177C22×Dic3—22no—
178C22×Dic3—22no—
179C22×Dic3—22no—
180C22×Dic3—22no—
181C22×Dic3—22no—
182C22×Dic3—32no—
183C22×Dic3—32no—
184C22×Dic3—32no—
185C22×Dic3—32no—
186C22×Dic3—62no—
187C22×Dic3—62no—
188C22×Dic3—62no—
189C22×Dic3—62no—
190C22×Dic3—62no—
191C22×Dic3—62no—
192C22×Dic3—62no—
193C22×Dic3—61no—
194C22×Dic3—61no—
195C22×Dic3—62no—
196C22×Dic3—62no—
197C22×Dic3—62no—
198C22×Dic3—62no—
199C22×Dic3—62no—
200C22×Dic3—61no—
201C22×Dic3—61no—
202C22×Dic3—62no—
203C22×Dic3—61no—
204C22×Dic3—61no—
205C22×Dic3—61no—
206C22×Dic3—61no—
207C22×Dic3—62no—
208C22×Dic3—122no—
209C22×Dic3—122no—
210C22×Dic3—122no—
211C22×Dic3—122no—
212C22×Dic3Dic614yes—
213C22×Dic3D1214yes—
214C22×Dic3C2×Dic314yes—
215C22×Dic3#6714yes—
216C3×C4⋊C4—68no—
217C4⋊Dic3—28no—
218C4⋊Dic3—616no—
219Dic3⋊C4—616no—
220C22×C32C2×C4⋊C412yes—
221C22×C32C2×C4⋊C411yescharacteristic
222C22×C32C4×D411yescharacteristic
223C22×C32C4×D412yes—
224C22×C32C4×Q811yescharacteristic
225C22×C32#12012yes—
226C22×C32#12011yescharacteristic
227C22×C32#12111yescharacteristic
228C22×C32#12112yes—
229C22×C32C22⋊Q812yes—
230C22×C32C22⋊Q812yes—
231C22×C32C22⋊Q812yes—
232C22×C32C22⋊Q812yes—
233C22×C32C22⋊Q811yescharacteristic
234C22×C32#12312yes—
235C22×C32#12311yescharacteristic
236C22×C32#12512yes—
237C22×C32#12511yescharacteristic
238C22×C32#12711yescharacteristic
239C22×C32C4⋊Q812yes—
240C22×C32C4⋊Q811yescharacteristic
241C22×C32C4⋊Q811yescharacteristic
242C22×C32C4⋊Q812yes—
243C32×C4—24no—
244C3⋊Dic3—42no—
245C3⋊Dic3—42no—
246C3×Dic3—28no—
247C3×Dic3—44no—
248C23×C4—32no—
249C23×C4—32no—
250C23×C4—91no—
251C23×C4—91no—
252C23×C4D3211yescharacteristic
253C2×C4⋊C4—64no—
254C2×C4⋊C4—62no—
255C2×C4⋊C4—184no—
256C2×C4⋊C4—184no—
257C2×C4⋊C4—184no—
258#95—34no—
259#95—184no—
260#95—182no—
261C23×C3—22no—
262C23×C3—21no—
263C23×C3—21no—
264C23×C3—21no—
265C23×C3—22no—
266C23×C3—21no—
267C23×C3—21no—
268C23×C3—22no—
269C23×C3—21no—
270C23×C3—21no—
271C23×C3—22no—
272C23×C3C2×Dic612yes—
273C23×C3C2×Dic611yescharacteristic
274C23×C3C2×Dic611yescharacteristic
275C23×C3C2×C4×D311yescharacteristic
276C23×C3C2×D1212yes—
277C23×C3C2×D1211yescharacteristic
278C23×C3#23512yes—
279C23×C3D3×D412yes—
280C23×C3D3×D411yescharacteristic
281C23×C3D3×D411yescharacteristic
282C23×C3D3×D412yes—
283C23×C3#23711yescharacteristic
284C23×C3#23711yescharacteristic
285C23×C3#23712yes—
286C23×C3D3×Q812yes—
287C23×C3D3×Q811yescharacteristic
288C23×C3D3×Q811yescharacteristic
289C23×C3#23911yescharacteristic
290C23×C3#23911yescharacteristic
291C23×C3C22×Dic311yescharacteristic
292C23×C3C2×#6711yescharacteristic
293C23×C3C2×#6712yes—
294C2×C3×C4—24no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—24no—
298C2×C3×C4—24no—
299C2×C3×C4—22no—
300C2×C3×C4—24no—
301C2×C3×C4—22no—
302C2×C3×C4—24no—
303C2×C3×C4—38no—
304C2×C3×C4—44no—
305C2×C3×C4—42no—
306C2×C3×C4—44no—
307C2×C3×C4—42no—
308C2×C3×C4—64no—
309C2×C3×C4—64no—
310C2×C3×C4—64no—
311C2×C3×C4—64no—
312C2×C3×C4—64no—
313C2×C3×C4—64no—
314C2×C3×C4—64no—
315C2×C3×C4—64no—
316C2×C3×C4—64no—
317C2×C3×C4—122no—
318C2×C3×C4—122no—
319C2×C3×C4—122no—
320C2×C3×C4—122no—
321C2×C3×C4Dic3⋊C414yescomplemented
322C2×C3×C4C4⋊Dic314yescomplemented
323C2×Dic3—24no—
324C2×Dic3—24no—
325C2×Dic3—24no—
326C2×Dic3—24no—
327C2×Dic3—24no—
328C2×Dic3—24no—
329C2×Dic3—24no—
330C2×Dic3—24no—
331C2×Dic3—24no—
332C2×Dic3—42no—
333C2×Dic3—42no—
334C2×Dic3—42no—
335C2×Dic3—42no—
336C2×Dic3—64no—
337C2×Dic3—64no—
338C2×Dic3—64no—
339C2×Dic3—62no—
340C2×Dic3—64no—
341C2×Dic3—62no—
342C2×Dic3—64no—
343C2×Dic3—64no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—124no—
347C2×Dic3—124no—
348C2×Dic3—124no—
349C2×Dic3—124no—
350C2×Dic3—122no—
351C2×Dic3—122no—
352C2×Dic3—122no—
353C2×Dic3—122no—
354C2×Dic3—121no—
355C2×Dic3—121no—
356C2×Dic3—121no—
357C2×Dic3—122no—
358C2×Dic3—121no—
359C2×Dic3—122no—
360C2×Dic3—122no—
361C2×Dic3—121no—
362C2×Dic3—122no—
363C2×Dic3—121no—
364C2×Dic3—121no—
365C2×Dic3—121no—
366C2×Dic3C4⋊Dic318yescomplemented
367C2×C32#38411yescharacteristic
368C2×C32#38511yescharacteristic
369C2×C32#38512yes—
370C2×C32#38911yescharacteristic
371C2×C32#38912yes—
372C2×C32#39211yescharacteristic
373C2×C32#39511yescharacteristic
374C2×C32#39512yes—
375C2×C32#39812yes—
376C2×C32#39811yescharacteristic
377C2×C32#39911yescharacteristic
378C24C2×D3211yescharacteristic
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—34no—
382C22×C4—34no—
383C22×C4—34no—
384C22×C4—34no—
385C22×C4—62no—
386C22×C4—62no—
387C22×C4—62no—
388C22×C4—62no—
389C22×C4—62no—
390C22×C4—62no—
391C22×C4—62no—
392C22×C4—62no—
393C22×C4—62no—
394C22×C4—62no—
395C22×C4—92no—
396C22×C4—92no—
397C22×C4—181no—
398C22×C4—181no—
399C22×C4—182no—
400C22×C4—182no—
401C22×C4—182no—
402C22×C4—181no—
403C22×C4—181no—
404C22×C4—182no—
405C22×C4D3×Dic312yes—
406C22×C4#62612yes—
407C22×C4#62712yes—
408C4⋊C4—68no—
409C4⋊C4—1816no—
410C22×C3—22no—
411C22×C3—21no—
412C22×C3—22no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—22no—
417C22×C3—22no—
418C22×C3—22no—
419C22×C3—22no—
420C22×C3—22no—
421C22×C3—21no—
422C22×C3—22no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—22no—
426C22×C3—21no—
427C22×C3—22no—
428C22×C3—22no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—22no—
432C22×C3—21no—
433C22×C3#86911yescharacteristic
434C22×C3#86912yes—
435C22×C3#87411yescharacteristic
436C22×C3#87812yes—
437C22×C3#87812yes—
438C22×C3#87812yes—
439C22×C3#88212yes—
440C22×C3#88211yescharacteristic
441C22×C3#88612yes—
442C22×C3#88611yescharacteristic
443C22×C3#88711yescharacteristic
444C22×C3#88812yes—
445C22×C3#88812yes—
446C22×C3#88811yescharacteristic
447C22×C3#88811yescharacteristic
448C22×C3#88912yes—
449C22×C3#89012yes—
450C22×C3#89011yescharacteristic
451C22×C3#89011yescharacteristic
452C22×C3D3×C4⋊C412yes—
453C22×C3#89311yescharacteristic
454C22×C3#89412yes—
455C22×C3#89512yes—
456C22×C3#89511yescharacteristic
457C22×C3#89612yes—
458C22×C3#89612yes—
459C22×C3#89711yescharacteristic
460C22×C3#89712yes—
461C22×C3C2×Dic3⋊C411yescharacteristic
462C22×C3#92412yes—
463C22×C3C2×C4⋊Dic312yes—
464C22×C3C2×C4⋊Dic311yescharacteristic
465C22×C3C4×#6712yes—
466C22×C3#92911yescharacteristic
467C22×C3D4×Dic311yescharacteristic
468C22×C3D4×Dic312yes—
469C22×C3#93712yes—
470C22×C3#93811yescharacteristic
471C22×C3#93912yes—
472C22×C3#94011yescharacteristic
473C22×C3#94412yes—
474C22×C3#94411yescharacteristic
475C22×C3Q8×Dic311yescharacteristic
476C22×C3#94611yescharacteristic
477C22×C3#94612yes—
478C22×C3#95311yescharacteristic
479C3×C4—24no—
480C3×C4—24no—
481C3×C4—44no—
482C3×C4—68no—
483C3×C4—124no—
484Dic3—28no—
485Dic3—44no—
486Dic3—124no—
487Dic3—124no—
488Dic3—122no—
489Dic3—122no—
490Dic3—122no—
491Dic3—122no—
492C32#144411yescharacteristic, complemented, Sylow
493C23D3×Dic612yes—
494C23#379611yescharacteristic
495C23#379611yescharacteristic
496C23#379711yescharacteristic
497C23D3×D1212yes—
498C23#380211yescharacteristic
499C23C2×D3×Dic311yescharacteristic
500C23#380412yes—
501C23C2×#62611yescharacteristic
502C23C2×#62711yescharacteristic
503C23D3×#6712yes—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—38no—
509C2×C4—64no—
510C2×C4—64no—
511C2×C4—64no—
512C2×C4—64no—
513C2×C4—64no—
514C2×C4—64no—
515C2×C4—64no—
516C2×C4—64no—
517C2×C4—64no—
518C2×C4—122no—
519C2×C4—122no—
520C2×C4—122no—
521C2×C4—122no—
522C2×C4—182no—
523C2×C4—184no—
524C2×C4—182no—
525C2×C4—184no—
526C2×C4—362no—
527C2×C4—362no—
528C2×C4—361no—
529C2×C4—361no—
530C2×C4—361no—
531C2×C4—361no—
532C2×C4Dic3⋊Dic314yescomplemented
533C2×C3—22no—
534C2×C3—22no—
535C2×C3—21no—
536C2×C3—22no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—22no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3#465612yes—
545C2×C3#465611yescharacteristic
546C2×C3#466112yes—
547C2×C3#466111yescharacteristic
548C2×C3#467111yescharacteristic
549C2×C3#467711yescharacteristic
550C2×C3#493511yescharacteristic
551C2×C3#495012yes—
552C2×C3#495011yescharacteristic
553C2×C3#497211yescharacteristic
554C2×C3#497511yescharacteristic
555C2×C3#497612yes—
556C2×C3#497912yes—
557C2×C3#498212yes—
558C2×C3#498311yescharacteristic
559C2×C3#498412yes—
560C2×C3#498411yescharacteristic
561C2×C3#498912yes—
562C2×C3#499311yescharacteristic
563C2×C3#521011yescharacteristic
564C2×C3#522311yescharacteristic
565C2×C3#523011yescharacteristic
566C22#6383912yes—
567C22#6384311yescharacteristic
568C22#6384612yes—
569C22#6386611yescharacteristic
570C22#6387111yescharacteristic
571C22#6387211yescharacteristic
572C22#6388612yes—
573C22#6388712yes—
574C22D3×C4⋊Dic312yes—
575C22#6389012yes—
576C22#6389512yes—
577C22#6389811yescharacteristic
578C22#6389912yes—
579C22#6391111yescharacteristic
580C22#6391611yescharacteristic
581C22#6391812yes—
582C22#6391911yescharacteristic
583C22#6392212yes—
584C22#6396412yes—
585C22C2×Dic3⋊Dic311yescharacteristic
586C22#6396611yescharacteristic
587C22Dic3×#6712yes—
588C22#6397711yescharacteristic
589C4—24no—
590C4—68no—
591C4—124no—
592C4—362no—
593C4—362no—
594C3—21no—
595C3#6941911yescharacteristic, complemented
596C3#7156811yescharacteristic, complemented
597C2#1059126512yes—
598C2#1059133812yes—
599C2#1059134611yescharacteristic
600C2#1059134812yes—
601C2#1059134911yescharacteristic
602C2#1059135011yescharacteristic
603C2#1059135711yescharacteristic
604C2#1059135811yescharacteristic
605C2#1059137712yes—
606C2#1059139111yescharacteristic
607C2#1059171811yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC23×C32C22×C4
FittingC23×C32×C4C22
socle, prime radical, cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32#1444
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
19. C3×C3⋊#95C4semidirect
94. C3⋊#95Dic3semidirect
110. C2×C32×C4C4⋊C4semidirect
134. C2×C3×Dic3C4⋊C4semidirect
321. C2×C3×C4Dic3⋊C4semidirect
322. C2×C3×C4C4⋊Dic3semidirect
366. C2×Dic3C4⋊Dic3semidirect
492. C32#1444semidirect
532. C2×C4Dic3⋊Dic3semidirect
595. C3#69419semidirect
596. C3#71568semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊Dic32
C22×Dic3⋊Dic32
C2×#636582
C2×C3×C3⋊#952
C2×#635792
#715683
#694193