Finite Group Databasebeta

← #11806915

Subgroups — #11806915

Order 1152.

1807 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#940C211yesmaximal, characteristic
2C2×#67⋊Dic3C212yesmaximal, complemented
3C2×Dic3×#67C212yesmaximal, complemented
4#10592919C211yesmaximal, characteristic, complemented
5C3×#5220C211yesmaximal, characteristic, complemented
6#10591707C212yesmaximal, complemented
7#10591707C212yesmaximal, complemented
8#10591376C212yesmaximal, complemented
9#10591242C212yesmaximal, complemented
10#83173—31nomaximal
11#74679—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C23×C3⋊Dic3C2211yescharacteristic
14C22×C3×#67C2212yes—
15C22×C3×#67C2212yes—
16C23×C3×Dic3C2211yescharacteristic
17C22×C3×D12C2211yescharacteristic
18C22×D3×Dic3C2212yes—
19C2×#3757C2212yes—
20C2×#3757C2211yescharacteristic
21C2×C3×#217C2212yes—
22C2×C3×#217C2211yescharacteristic
23C3×#940C418yescomplemented
24C2×C3×C4×Dic3C2211yescharacteristic
25#67⋊Dic3—28no—
26Dic3×#67—28no—
27C2×Dic3⋊Dic3C2212yes—
28C2×Dic3⋊Dic3C2212yes—
29C2×(C2×D3)⋊Dic3C2212yes—
30C2×(C2×D3)⋊Dic3C2212yes—
31C2×(C2×D3)⋊Dic3C2212yes—
32C2×Dic32C2212yes—
33C2×Dic32C2212yes—
34#63658C2212yes—
35C3×C3⋊#95C2212yes—
36C2×C3×#127—31no—
37C2×#940D311yescharacteristic
38C2×D4×Dic3—32no—
39C2×D4×Dic3—32no—
40C2×C4×#67—32no—
41C2×#67⋊C4—32no—
42C3×#386—31no—
43#5221—32no—
44#5221—32no—
45#5220—31no—
46#5220—31no—
47#5220—32no—
48#5220—61no—
49#5220D311yescharacteristic, complemented
50#4957—32no—
51#4957—32no—
52C4×C4⋊Dic3—32no—
53#4665—32no—
54#4649—32no—
55C24×C32C2311yescharacteristic
56C24×C32C2311yescharacteristic
57C23×C3×D3C2312yes—
58C2×C32×D4—41no—
59C2×C32×D4—41no—
60C2×C32×D4C2×C414yescomplemented
61C22×C32×C4C2311yescharacteristic
62C22×C3⋊Dic3—24no—
63C22×C3⋊Dic3—41no—
64C22×C3⋊Dic3C2312yes—
65C22×C3⋊Dic3C2312yes—
66C2×C3×#67—24no—
67C2×C3×#67—24no—
68C2×C3×#67—24no—
69C2×C3×#67—24no—
70C2×C3×#67C2×C418yescomplemented
71C2×C3×#67C2×C418yescomplemented
72C22×C3×Dic3—24no—
73C22×C3×Dic3—41no—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C2×C3×D12—41no—
78C2×C3×D12—41no—
79C2×C3×D12C2×C414yescomplemented
80C2×D3×Dic3—24no—
81C2×D3×Dic3—24no—
82C2×D3×Dic3—42no—
83#3757—24no—
84#3757—41no—
85C3×#217—24no—
86C3×#217—41no—
87C3×C4×Dic3C2×C414yescomplemented
88Dic3⋊Dic3—24no—
89Dic3⋊Dic3D418yescomplemented
90(C2×D3)⋊Dic3—24no—
91(C2×D3)⋊Dic3—24no—
92(C2×D3)⋊Dic3—42no—
93Dic32—24no—
94Dic32—24no—
95#2366—91noSylow
96C22×C3×D4—21no—
97C22×C3×D4—32no—
98C22×C3×D4—32no—
99C22×C3×D4—31no—
100C22×C3×D4C2×D311yescharacteristic
101C22×C3×D4C2×D311yescharacteristic
102C23×C3×C4—31no—
103C22×#67C2×D312yes—
104C22×#67C2×D312yes—
105C23×Dic3—31no—
106C23×Dic3—31no—
107C23×Dic3—32no—
108C23×Dic3—61no—
109C23×Dic3C2×D311yescharacteristic
110C22×D12C2×D311yescharacteristic
111C22×C4×D3—32no—
112C3×#127—38no—
113C2×C3×C22⋊C4—32no—
114C2×C3×C22⋊C4—31no—
115C2×C3×C42—31no—
116C2×#217—32no—
117C2×#217—32no—
118C2×#217—32no—
119C2×#217—32no—
120C2×#217—31no—
121C2×#217—31no—
122C2×#217—32no—
123C2×#217—62no—
124C2×#217—61no—
125C2×#217C2×D312yes—
126C2×#217C2×D311yescharacteristic
127#940Dic318yescomplemented
128D4×Dic3—68no—
129D4×Dic3—68no—
130C4×#67—68no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—32no—
134C2×C4⋊Dic3—32no—
135C2×C4⋊Dic3—32no—
136C2×Dic3⋊C4—32no—
137C2×Dic3⋊C4—32no—
138C2×C4×Dic3—32no—
139C2×C4×Dic3—32no—
140C2×C4×Dic3—32no—
141C2×C4×Dic3—32no—
142C2×C4×Dic3C2×D311yescharacteristic
143#67⋊C4—68no—
144C3×#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—62no—
148C3⋊#95C2×D312yes—
149C23×C32—21no—
150C23×C32—21no—
151C23×C32—22no—
152C23×C32—22no—
153C23×C32—22no—
154C23×C32—22no—
155C23×C32—21no—
156C23×C32—21no—
157C23×C32C22×C412yes—
158C23×C32C22×C412yes—
159C23×C32C2411yescharacteristic
160C22×C3×D3—22no—
161C22×C3×D3—22no—
162C22×C3×D3—22no—
163C22×C3×D3—22no—
164C22×C3×D3—22no—
165C22×C3×D3—22no—
166C22×C3×D3C22×C414yes—
167C32×D4—44no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4C22×C412yes—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3—22no—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3—44no—
177C2×C3⋊Dic3C2×D414yes—
178C3×#67—216no—
179C3×#67—216no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—44no—
186C2×C3×Dic3C22×C414yes—
187C2×C3×Dic3C2×D414yes—
188C2×C3×Dic3C2×D414yes—
189C2×C3×Dic3#4114yes—
190C3×D12—44no—
191D3×Dic3—48no—
192C2×#127—31no—
193C2×C4×D4—92no—
194C2×C4×D4—92no—
195#390—92no—
196#390—92no—
197#386—31no—
198#386—92no—
199#386—91no—
200C4×C4⋊C4—92no—
201C24×C3—21no—
202C24×C3—21no—
203C24×C3—32no—
204C24×C3C22×D311yescharacteristic
205C24×C3C22×D311yescharacteristic
206C24×C3C22×D311yescharacteristic
207C24×C3C22×D311yescharacteristic
208C23×D3C22×D312yes—
209C2×C3×D4—24no—
210C2×C3×D4—38no—
211C2×C3×D4—38no—
212C2×C3×D4—34no—
213C2×C3×D4—41no—
214C2×C3×D4—41no—
215C2×C3×D4—41no—
216C2×C3×D4—41no—
217C2×C3×D4—42no—
218C2×C3×D4—42no—
219C2×C3×D4—64no—
220C2×C3×D4—64no—
221C2×C3×D4—64no—
222C2×C3×D4—64no—
223C2×C3×D4—121no—
224C2×C3×D4—121no—
225C2×C3×D4C4×D314yescomplemented
226C2×C3×D4C2×Dic314yescomplemented
227C22×C3×C4—21no—
228C22×C3×C4—32no—
229C22×C3×C4—32no—
230C22×C3×C4—32no—
231C22×C3×C4—64no—
232C22×C3×C4—121no—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C2×#67—24no—
236C2×#67—24no—
237C2×#67—24no—
238C2×#67—24no—
239C2×#67C2×Dic318yescomplemented
240C2×#67C2×Dic318yescomplemented
241C22×Dic3—24no—
242C22×Dic3—32no—
243C22×Dic3—32no—
244C22×Dic3—32no—
245C22×Dic3—32no—
246C22×Dic3—41no—
247C22×Dic3—62no—
248C22×Dic3—62no—
249C22×Dic3—64no—
250C22×Dic3—64no—
251C22×Dic3—64no—
252C22×Dic3—64no—
253C22×Dic3—124no—
254C22×Dic3—122no—
255C22×Dic3—121no—
256C22×Dic3—121no—
257C22×Dic3—122no—
258C22×Dic3C22×D312yes—
259C22×Dic3C22×D312yes—
260C22×Dic3C22×D312yes—
261C2×D12—41no—
262C2×D12—41no—
263C2×D12C2×Dic314yescomplemented
264C2×C4×D3—64no—
265C2×C4×D3—64no—
266C2×C4×D3—122no—
267C3×C22⋊C4—64no—
268C3×C22⋊C4—121no—
269C3×C42—34no—
270#217—24no—
271#217—41no—
272#217—64no—
273#217—64no—
274#217—64no—
275#217—64no—
276#217—124no—
277#217—122no—
278#217—121no—
279#217—121no—
280#217—122no—
281(C2×D3)⋊C4—64no—
282(C2×D3)⋊C4—64no—
283(C2×D3)⋊C4—122no—
284C4⋊Dic3—38no—
285C4⋊Dic3—64no—
286Dic3⋊C4—38no—
287Dic3⋊C4—64no—
288C4×Dic3—64no—
289C4×Dic3—64no—
290C4×Dic3—64no—
291C4×Dic3—64no—
292C4×Dic3C2×Dic314yescomplemented
293C22×C32—22no—
294C22×C32—24no—
295C22×C32—24no—
296C22×C32—22no—
297C22×C32—41no—
298C22×C32—42no—
299C22×C32—41no—
300C22×C32—41no—
301C22×C32—42no—
302C22×C32—41no—
303C22×C32C23×C411yescharacteristic
304C22×C32C22×D412yes—
305C22×C32C2×#4112yes—
306C22×C32H(5,𝔽2)11yescharacteristic
307C22×C32H(5,𝔽2)11yescharacteristic
308C2×C3×D3—24no—
309C2×C3×D3—24no—
310C2×C3×D3—24no—
311C2×C3×D3—42no—
312C2×C3×D3—42no—
313C2×C3×D3—42no—
314C2×C3×D3—42no—
315C32×C4—22no—
316C3⋊Dic3—24no—
317C3⋊Dic3—42no—
318C3×Dic3—24no—
319C3×Dic3—42no—
320C3×Dic3C4×D418yescomplemented
321C22×D4—32no—
322C22×D4—32no—
323C22×D4—31no—
324C22×D4D3211yescharacteristic
325C23×C4—31no—
326C23×C4—92no—
327C23×C4—91no—
328#127—38no—
329C4×D4—188no—
330C4×D4—188no—
331C2×C4⋊C4—92no—
332C2×C4⋊C4—92no—
333C2×C22⋊C4—32no—
334C2×C22⋊C4—31no—
335C2×C22⋊C4—92no—
336C2×C22⋊C4—92no—
337C2×C22⋊C4—92no—
338C2×C22⋊C4—92no—
339C2×C22⋊C4—91no—
340C2×C42—31no—
341C2×C42—92no—
342C2×C42—92no—
343#95—32no—
344#95—92no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—22no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3—21no—
354C23×C3—21no—
355C23×C3—21no—
356C23×C3—21no—
357C23×C3—21no—
358C23×C3—21no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—22no—
362C23×C3—22no—
363C23×C3—21no—
364C23×C3—22no—
365C23×C3—22no—
366C23×C3—34no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—41no—
371C23×C3—41no—
372C23×C3—42no—
373C23×C3—62no—
374C23×C3—62no—
375C23×C3—62no—
376C23×C3—62no—
377C23×C3—62no—
378C23×C3—62no—
379C23×C3C2×C4×D312yes—
380C23×C3C2×C4×D312yes—
381C23×C3C22×Dic312yes—
382C23×C3C22×Dic312yes—
383C23×C3C23×D311yescharacteristic
384C23×C3C23×D311yescharacteristic
385C22×D3—22no—
386C22×D3—22no—
387C22×D3—22no—
388C22×D3—22no—
389C22×D3—22no—
390C22×D3—22no—
391C22×D3C22×Dic314yes—
392C3×D4—44no—
393C3×D4—44no—
394C3×D4—48no—
395C3×D4—616no—
396C3×D4—616no—
397C3×D4—124no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—22no—
403C2×C3×C4—34no—
404C2×C3×C4—34no—
405C2×C3×C4—34no—
406C2×C3×C4—34no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—62no—
410C2×C3×C4—62no—
411C2×C3×C4—62no—
412C2×C3×C4—62no—
413C2×C3×C4—62no—
414C2×C3×C4—124no—
415C2×C3×C4C2×C4×D312yes—
416C2×C3×C4C22×Dic312yes—
417#67—216no—
418#67—216no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—22no—
424C2×Dic3—34no—
425C2×Dic3—34no—
426C2×Dic3—44no—
427C2×Dic3—64no—
428C2×Dic3—62no—
429C2×Dic3—62no—
430C2×Dic3—62no—
431C2×Dic3—62no—
432C2×Dic3—62no—
433C2×Dic3—62no—
434C2×Dic3—62no—
435C2×Dic3—62no—
436C2×Dic3—62no—
437C2×Dic3—62no—
438C2×Dic3—122no—
439C2×Dic3—122no—
440C2×Dic3—122no—
441C2×Dic3—122no—
442C2×Dic3—122no—
443C2×Dic3—128no—
444C2×Dic3—124no—
445C2×Dic3—124no—
446C2×Dic3—128no—
447C2×Dic3D3×D414yes—
448C2×Dic3D3×D414yes—
449C2×Dic3#23714yes—
450C2×Dic3C22×Dic314yes—
451D12—44no—
452C4×D3—128no—
453C2×C32—42no—
454C2×C32—42no—
455C2×C32C2×C4×D412yes—
456C2×C32#51811yescharacteristic
457C2×C32D4211yescharacteristic
458C2×C32#55012yes—
459C2×C32#55911yescharacteristic
460C3×D3—44no—
461C24—32no—
462C24C2×D3211yescharacteristic
463C24C2×D3211yescharacteristic
464C2×D4—38no—
465C2×D4—38no—
466C2×D4—34no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—64no—
470C2×D4—64no—
471C2×D4—64no—
472C2×D4—64no—
473C2×D4—121no—
474C2×D4—121no—
475C2×D4D3×Dic314yescomplemented
476C22×C4—32no—
477C22×C4—32no—
478C22×C4—32no—
479C22×C4—64no—
480C22×C4—92no—
481C22×C4—92no—
482C22×C4—121no—
483C22×C4—184no—
484C22×C4—184no—
485C22×C4—184no—
486C22×C4—362no—
487C22×C4—361no—
488C22×C4C2×D3211yescharacteristic
489C4⋊C4—98no—
490C4⋊C4—184no—
491C22⋊C4—64no—
492C22⋊C4—121no—
493C22⋊C4—184no—
494C22⋊C4—184no—
495C22⋊C4—184no—
496C22⋊C4—362no—
497C22⋊C4—361no—
498C42—34no—
499C42—184no—
500C42—184no—
501C22×C3—24no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—24no—
505C22×C3—24no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—24no—
509C22×C3—24no—
510C22×C3—22no—
511C22×C3—22no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—44no—
516C22×C3—42no—
517C22×C3—44no—
518C22×C3—42no—
519C22×C3—42no—
520C22×C3—44no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3—41no—
524C22×C3—41no—
525C22×C3—41no—
526C22×C3—41no—
527C22×C3—42no—
528C22×C3—42no—
529C22×C3—41no—
530C22×C3—41no—
531C22×C3—42no—
532C22×C3—42no—
533C22×C3—64no—
534C22×C3—64no—
535C22×C3—64no—
536C22×C3—81no—
537C22×C3—82no—
538C22×C3—81no—
539C22×C3—122no—
540C22×C3—122no—
541C22×C3—122no—
542C22×C3—122no—
543C22×C3C22×C4×D311yescharacteristic
544C22×C3C2×D3×D412yes—
545C22×C3C2×D3×D412yes—
546C22×C3C2×#23712yes—
547C22×C3#100411yescharacteristic
548C22×C3#100411yescharacteristic
549C22×C3#100411yescharacteristic
550C22×C3#100411yescharacteristic
551C22×C3D3×#4112yes—
552C22×C3C23×Dic311yescharacteristic
553C2×D3—24no—
554C2×D3—24no—
555C2×D3—24no—
556C2×D3—42no—
557C2×D3—42no—
558C2×D3—42no—
559C2×D3—42no—
560C3×C4—22no—
561C3×C4—22no—
562C3×C4—38no—
563C3×C4—42no—
564C3×C4—64no—
565C3×C4—122no—
566Dic3—24no—
567Dic3—42no—
568Dic3—64no—
569Dic3—64no—
570Dic3—124no—
571Dic3—122no—
572Dic3—122no—
573Dic3—242no—
574Dic3D4×Dic318yescomplemented
575C32#236611yescharacteristic, complemented, Sylow
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—34no—
585C23—62no—
586C23—62no—
587C23—62no—
588C23—62no—
589C23—62no—
590C23—62no—
591C23C2×D3×Dic312yes—
592C23C2×D3×Dic312yes—
593C23C22×D3211yescharacteristic
594D4—44no—
595D4—616no—
596D4—616no—
597D4—124no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—34no—
601C2×C4—34no—
602C2×C4—34no—
603C2×C4—34no—
604C2×C4—62no—
605C2×C4—62no—
606C2×C4—62no—
607C2×C4—62no—
608C2×C4—62no—
609C2×C4—94no—
610C2×C4—124no—
611C2×C4—182no—
612C2×C4—182no—
613C2×C4—182no—
614C2×C4—182no—
615C2×C4—182no—
616C2×C4—368no—
617C2×C4—364no—
618C2×C4C2×D3×Dic312yes—
619C2×C3—22no—
620C2×C3—21no—
621C2×C3—22no—
622C2×C3—21no—
623C2×C3—21no—
624C2×C3—44no—
625C2×C3—42no—
626C2×C3—42no—
627C2×C3—42no—
628C2×C3—42no—
629C2×C3—82no—
630C2×C3—124no—
631C2×C3#548611yescharacteristic
632C2×C3C4×D3×D412yes—
633C2×C3#559011yescharacteristic
634C2×C3#559912yes—
635C2×C3#566411yescharacteristic
636C2×C3#571311yescharacteristic
637C2×C3#571711yescharacteristic
638C2×C3#571812yes—
639C2×C3C2×D4×Dic312yes—
640C2×C3#579811yescharacteristic
641D3—44no—
642C22—24no—
643C22—24no—
644C22—22no—
645C22—22no—
646C22—41no—
647C22—41no—
648C22—42no—
649C22—42no—
650C22—41no—
651C22—41no—
652C22—64no—
653C22—64no—
654C22—64no—
655C22—122no—
656C22—122no—
657C22—122no—
658C22—122no—
659C22D32×D412yes—
660C22D3×#23712yes—
661C22C22×D3×Dic311yescharacteristic
662C22#6433011yescharacteristic
663C22#6433011yescharacteristic
664C4—22no—
665C4—38no—
666C4—64no—
667C4—122no—
668C4—184no—
669C4—362no—
670C3—21no—
671C3#7467911yescharacteristic, complemented
672C3#8317311yescharacteristic, complemented
673C2—42no—
674C2—42no—
675C2—124no—
676C2D3×D4×Dic312yes—
677C2#1059520011yescharacteristic
678C2#1059522712yes—
679C2#1059529511yescharacteristic
680C2#1059550611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×D4C22
socle, cosocleC23×C32C24
prime radicalC2×C3×#940C2
hypercenterC22×D4D32
hypocenterC32#2366
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#67⋊Dic3C2semidirect
3. C2×Dic3×#67C2semidirect
4. #10592919C2semidirect
5. C3×#5220C2semidirect
6. #10591707C2semidirect
7. #10591707C2semidirect
8. #10591376C2semidirect
9. #10591242C2semidirect
23. C3×#940C4semidirect
49. #5220D3semidirect
60. C2×C32×D4C2×C4semidirect
70. C2×C3×#67C2×C4semidirect
71. C2×C3×#67C2×C4semidirect
79. C2×C3×D12C2×C4semidirect
87. C3×C4×Dic3C2×C4semidirect
89. Dic3⋊Dic3D4semidirect
127. #940Dic3semidirect
225. C2×C3×D4C4×D3semidirect
226. C2×C3×D4C2×Dic3semidirect
239. C2×#67C2×Dic3semidirect
240. C2×#67C2×Dic3semidirect
263. C2×D12C2×Dic3semidirect
292. C4×Dic3C2×Dic3semidirect
320. C3×Dic3C4×D4semidirect
475. C2×D4D3×Dic3semidirect
574. Dic3D4×Dic3semidirect
575. C32#2366semidirect
671. C3#74679semidirect
672. C3#83173semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9402
C2×#67⋊Dic32
C2×Dic3×#672
#105929192
C3×#52202
#105917072
#105913762
#105912422
#831733
#746793