Finite Group Databasebeta

← #11824557

Subgroups — #11824557

Order 1152.

1609 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#938C211yesmaximal, characteristic, complemented
2C2×#63971C212yesmaximal, complemented
3C2×#63904C211yesmaximal, characteristic, complemented
4#10592922C211yesmaximal, characteristic, complemented
5C3×#5222C211yesmaximal, characteristic, complemented
6#10591722C212yesmaximal, complemented
7#10591721C212yesmaximal, complemented
8#10591703C212yesmaximal, complemented
9D3×C3⋊#95C211yesmaximal, characteristic, complemented
10#10591326C211yesmaximal, characteristic, complemented
11#10591214C211yesmaximal, characteristic, complemented
12#82671—31nomaximal
13#77120—31nomaximal
14C22×C32×D4C2211yescharacteristic
15C22×#638C2212yes—
16C22×C3×#67C2212yes—
17C22×C3×C4×D3C2211yescharacteristic
18C22×#626C2211yescharacteristic
19C22×#624C2211yescharacteristic
20C22×D3×Dic3C2212yes—
21C2×#3757C2212yes—
22C2×#3752C2211yescharacteristic
23C2×C3×#217C2212yes—
24C2×C3×#217C2212yes—
25C2×C3×#217C2212yes—
26C3×#938—24no—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29#63971—28no—
30C2×#3724C2212yes—
31C2×#3722C2212yes—
32C2×(C2×D3)⋊Dic3C2211yescharacteristic
33C2×Dic32C2211yescharacteristic
34#63904—24no—
35#63658C2211yescharacteristic
36C3×C3⋊#95C2211yescharacteristic
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×#121—31no—
41C2×#939—32no—
42C2×#938D311yescharacteristic, complemented
43C2×C4×#67—31no—
44C2×#893—31no—
45C2×#884—32no—
46C3×#394—31no—
47#5223—31no—
48#5223—31no—
49#5223—61no—
50#5222D311yescharacteristic, complemented
51#5220—32no—
52C2×C3⋊#95—31no—
53#4992—31no—
54#4983—31no—
55#4981—31no—
56#4956—32no—
57#4956—32no—
58#4956—32no—
59#4945—32no—
60#4944—32no—
61#4674—31no—
62D3×#95—31no—
63C24×C32C2312yes—
64C23×C3⋊D3C2311yescharacteristic
65C23×C3×D3C2311yescharacteristic
66C2×C32×D4—22no—
67C2×C32×D4—42no—
68C22×C32×C4C2311yescharacteristic
69C2×#638—24no—
70C2×#638—24no—
71C2×#638—42no—
72C22×C3⋊Dic3C2311yescharacteristic
73C22×C3⋊Dic3C2312yes—
74C2×C3×#67—24no—
75C2×C3×#67—24no—
76C2×C3×#67—24no—
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2311yescharacteristic
81C22×C3×Dic3C2311yescharacteristic
82C2×C3×C4×D3—42no—
83C2×C3×C4×D3D414yescomplemented
84C2×#626—22no—
85C2×#626—22no—
86C2×#626D414yescomplemented
87C2×#624—22no—
88C2×#624—42no—
89C2×D3×Dic3—24no—
90C2×D3×Dic3—24no—
91C2×D3×Dic3—42no—
92#3757—24no—
93#3752—22no—
94C3×#217—24no—
95C3×#217—24no—
96C3×#217—42no—
97C3×C4⋊Dic3—22no—
98C3×Dic3⋊C4—22no—
99#3724—24no—
100#3722—24no—
101(C2×D3)⋊Dic3—22no—
102Dic32—22no—
103#2543—91noSylow
104C22×C3×D4—21no—
105C22×C3×D4—32no—
106C22×C3×D4C2×D311yescharacteristic
107C22×C3×D4C2×D311yescharacteristic
108C23×C3×C4—31no—
109C22×#67—32no—
110C22×#67—32no—
111C22×#67—31no—
112C22×#67—62no—
113C22×#67C2×D312yes—
114C23×Dic3—32no—
115C22×D12—31no—
116C22×C4×D3—32no—
117C22×C4×D3—31no—
118C22×C4×D3—31no—
119C22×C4×D3C2×D311yescharacteristic
120C3×#121—64no—
121C2×C3×C4⋊C4—31no—
122C2×C3×C4⋊C4—31no—
123C2×C3×C22⋊C4—32no—
124C2×C3×C22⋊C4—32no—
125C2×C3×C22⋊C4—32no—
126C2×#217—32no—
127C2×#217—32no—
128C2×#217—31no—
129C2×#217—62no—
130C2×#217C2×D312yes—
131C2×#217C2×D312yes—
132C2×#217C2×D312yes—
133#939—68no—
134#938—24no—
135C4×#67—64no—
136C2×(C2×D3)⋊C4—31no—
137C2×(C2×D3)⋊C4—31no—
138C2×(C2×D3)⋊C4—31no—
139C2×(C2×D3)⋊C4—32no—
140C2×(C2×D3)⋊C4—32no—
141C2×(C2×D3)⋊C4—61no—
142C2×C4⋊Dic3C2×D311yescharacteristic
143C2×Dic3⋊C4—32no—
144C2×Dic3⋊C4—32no—
145C2×Dic3⋊C4C2×D311yescharacteristic
146C2×C4×Dic3—31no—
147C2×C4×Dic3—31no—
148#893—64no—
149#884—68no—
150C3×#95—31no—
151C3⋊#95—31no—
152C3⋊#95—31no—
153C3⋊#95—32no—
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95—32no—
157C3⋊#95—32no—
158C3⋊#95—32no—
159C3⋊#95—61no—
160C3⋊#95C2×D311yescharacteristic
161C23×C32—22no—
162C23×C32—22no—
163C23×C32—22no—
164C23×C32—22no—
165C23×C32—22no—
166C23×C32—22no—
167C23×C32—22no—
168C23×C32C2411yescharacteristic
169C22×C3⋊D3—21no—
170C22×C3⋊D3—21no—
171C22×C3⋊D3—22no—
172C22×C3⋊D3—22no—
173C22×C3⋊D3C2×D412yes—
174C22×C3×D3—22no—
175C22×C3×D3—22no—
176C22×C3×D3C2×D412yes—
177C22×C3×D3C2×D412yes—
178C22×C3×D3#4112yes—
179C32×D4—44no—
180C2×C32×C4—22no—
181C2×C32×C4C2×D412yes—
182#638—48no—
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—22no—
187C2×C3⋊Dic3#4114yes—
188C3×#67—48no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3C2×D412yes—
201C2×C3×Dic3C2×D412yes—
202C3×C4×D3—44no—
203#626—28no—
204#624—44no—
205D3×Dic3—48no—
206C2×#121—31no—
207C2×#121—92no—
208C2×C4×D4—91no—
209#398—91no—
210#397—91no—
211#394—31no—
212#392—91no—
213#388—92no—
214#386—92no—
215#386—92no—
216C2×#95—91no—
217C24×C3—22no—
218C24×C3—31no—
219C24×C3C22×D312yes—
220C24×C3C22×D312yes—
221C23×D3—31no—
222C23×D3—31no—
223C23×D3—61no—
224C23×D3C22×D311yescharacteristic
225C2×C3×D4—22no—
226C2×C3×D4—22no—
227C2×C3×D4—42no—
228C2×C3×D4—42no—
229C2×C3×D4—42no—
230C2×C3×D4—44no—
231C2×C3×D4—64no—
232C2×C3×D4—64no—
233C2×C3×D4—64no—
234C22×C3×C4—21no—
235C22×C3×C4—31no—
236C22×C3×C4—31no—
237C22×C3×C4—34no—
238C22×C3×C4—32no—
239C22×C3×C4—32no—
240C22×C3×C4—31no—
241C22×C3×C4—122no—
242C22×C3×C4C22×D311yescharacteristic
243C22×C3×C4C22×D311yescharacteristic
244C2×#67—24no—
245C2×#67—24no—
246C2×#67—24no—
247C2×#67—34no—
248C2×#67—62no—
249C2×#67—62no—
250C2×#67—64no—
251C2×#67—64no—
252C2×#67—64no—
253C2×#67—64no—
254C2×#67—124no—
255C2×#67—124no—
256C2×#67—122no—
257C2×#67—122no—
258C2×#67—124no—
259C22×Dic3—32no—
260C22×Dic3—32no—
261C22×Dic3—31no—
262C22×Dic3—31no—
263C22×Dic3—62no—
264C22×Dic3—61no—
265C22×Dic3—64no—
266C22×Dic3—64no—
267C22×Dic3—122no—
268C22×Dic3C22×D312yes—
269C22×Dic3C22×D312yes—
270C22×Dic3C22×D311yescharacteristic
271C22×Dic3C22×D311yescharacteristic
272C22×Dic3C22×D311yescharacteristic
273C2×D12—34no—
274C2×D12—62no—
275C2×D12—62no—
276C2×C4×D3—42no—
277C2×C4×D3—62no—
278C2×C4×D3—64no—
279C2×C4×D3—64no—
280C2×C4×D3—62no—
281C2×C4×D3—122no—
282C2×C4×D3—122no—
283C2×C4×D3—122no—
284C2×C4×D3#6714yescomplemented
285C3×C4⋊C4—62no—
286C3×C4⋊C4—62no—
287C3×C22⋊C4—64no—
288C3×C22⋊C4—64no—
289C3×C22⋊C4—122no—
290#217—24no—
291#217—24no—
292#217—42no—
293#217—62no—
294#217—64no—
295#217—64no—
296#217—124no—
297(C2×D3)⋊C4—64no—
298(C2×D3)⋊C4—64no—
299(C2×D3)⋊C4—62no—
300(C2×D3)⋊C4—62no—
301(C2×D3)⋊C4—62no—
302(C2×D3)⋊C4—122no—
303C4⋊Dic3—22no—
304Dic3⋊C4—22no—
305Dic3⋊C4—64no—
306Dic3⋊C4—64no—
307C4×Dic3—62no—
308C4×Dic3—62no—
309C22×C32—42no—
310C22×C32—42no—
311C22×C32—42no—
312C22×C32—42no—
313C22×C32—42no—
314C22×C32—42no—
315C22×C32—42no—
316C22×C32C22×D411yescharacteristic
317C22×C32C22×D411yescharacteristic
318C22×C32C2×#4111yescharacteristic
319C22×C32C2×#4112yes—
320C22×C32H(5,𝔽2)12yes—
321C2×C3⋊D3—22no—
322C2×C3⋊D3—24no—
323C2×C3⋊D3—41no—
324C2×C3⋊D3—41no—
325C2×C3⋊D3—42no—
326C2×C3×D3—22no—
327C2×C3×D3—22no—
328C2×C3×D3—24no—
329C2×C3×D3—24no—
330C2×C3×D3#12114yes—
331C32×C4—22no—
332C3⋊Dic3—24no—
333C3⋊Dic3—41no—
334C3×Dic3—22no—
335C3×Dic3—22no—
336C3×Dic3—42no—
337C3×Dic3—41no—
338C3×Dic3—42no—
339C22×D4—32no—
340C22×D4—91no—
341C22×D4—92no—
342C22×D4D3211yescharacteristic
343C23×C4—31no—
344C23×C4—91no—
345C23×C4—92no—
346#121—64no—
347#121—188no—
348C4×D4—184no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—31no—
351C2×C4⋊C4—92no—
352C2×C22⋊C4—32no—
353C2×C22⋊C4—32no—
354C2×C22⋊C4—32no—
355C2×C22⋊C4—92no—
356C2×C22⋊C4—91no—
357C2×C22⋊C4—92no—
358C2×C22⋊C4—91no—
359C2×C42—91no—
360#95—31no—
361#95—92no—
362#95—92no—
363#95—92no—
364#95—91no—
365C23×C3—24no—
366C23×C3—22no—
367C23×C3—22no—
368C23×C3—22no—
369C23×C3—22no—
370C23×C3—22no—
371C23×C3—22no—
372C23×C3—22no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3—22no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—21no—
381C23×C3—32no—
382C23×C3—32no—
383C23×C3—32no—
384C23×C3—42no—
385C23×C3—42no—
386C23×C3—42no—
387C23×C3—42no—
388C23×C3—42no—
389C23×C3—42no—
390C23×C3—62no—
391C23×C3—62no—
392C23×C3C23×D311yescharacteristic
393C23×C3C23×D311yescharacteristic
394C22×D3—22no—
395C22×D3—22no—
396C22×D3—32no—
397C22×D3—32no—
398C22×D3—62no—
399C22×D3—61no—
400C22×D3—61no—
401C22×D3—62no—
402C22×D3—62no—
403C22×D3—61no—
404C22×D3—62no—
405C22×D3—62no—
406C22×D3—61no—
407C22×D3—121no—
408C22×D3—122no—
409C22×D3—122no—
410C22×D3—121no—
411C22×D3D3×D412yes—
412C22×D3#23712yes—
413C22×D3C2×#6712yes—
414C3×D4—44no—
415C3×D4—44no—
416C3×D4—48no—
417C3×D4—128no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—32no—
422C2×C3×C4—32no—
423C2×C3×C4—42no—
424C2×C3×C4—61no—
425C2×C3×C4—62no—
426C2×C3×C4—61no—
427C2×C3×C4—62no—
428C2×C3×C4—62no—
429C2×C3×C4—62no—
430C2×C3×C4—62no—
431C2×C3×C4—62no—
432C2×C3×C4—62no—
433C2×C3×C4—62no—
434C2×C3×C4—61no—
435C2×C3×C4—124no—
436C2×C3×C4D3×D412yes—
437C2×C3×C4C2×#6712yes—
438#67—48no—
439#67—68no—
440#67—128no—
441#67—128no—
442#67—1216no—
443C2×Dic3—21no—
444C2×Dic3—22no—
445C2×Dic3—21no—
446C2×Dic3—21no—
447C2×Dic3—22no—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—22no—
454C2×Dic3—34no—
455C2×Dic3—34no—
456C2×Dic3—64no—
457C2×Dic3—62no—
458C2×Dic3—62no—
459C2×Dic3—62no—
460C2×Dic3—62no—
461C2×Dic3—61no—
462C2×Dic3—62no—
463C2×Dic3—62no—
464C2×Dic3—61no—
465C2×Dic3—122no—
466C2×Dic3—122no—
467C2×Dic3—121no—
468C2×Dic3—122no—
469C2×Dic3—128no—
470C2×Dic3D3×D412yes—
471C2×Dic3C2×#6712yes—
472D12—68no—
473C4×D3—44no—
474C4×D3—124no—
475C4×D3—124no—
476C4×D3—128no—
477C2×C32—82no—
478C2×C32C2×#12111yescharacteristic
479C2×C32#53211yescharacteristic
480C2×C32#53411yescharacteristic
481C2×C32#54612yes—
482C2×C32#55312yes—
483C3⋊D3—42no—
484C3×D3—24no—
485C24—31no—
486C24—91no—
487C24C2×D3212yes—
488C2×D4—22no—
489C2×D4—42no—
490C2×D4—64no—
491C2×D4—64no—
492C2×D4—64no—
493C2×D4—94no—
494C2×D4—182no—
495C2×D4—182no—
496C2×D4—184no—
497C2×D4—184no—
498C2×D4—362no—
499C22×C4—31no—
500C22×C4—31no—
501C22×C4—34no—
502C22×C4—32no—
503C22×C4—31no—
504C22×C4—32no—
505C22×C4—92no—
506C22×C4—91no—
507C22×C4—122no—
508C22×C4—182no—
509C22×C4—184no—
510C22×C4—184no—
511C22×C4—362no—
512C22×C4—362no—
513C22×C4C2×D3211yescharacteristic
514C4⋊C4—62no—
515C4⋊C4—62no—
516C4⋊C4—184no—
517C22⋊C4—64no—
518C22⋊C4—64no—
519C22⋊C4—122no—
520C22⋊C4—184no—
521C22⋊C4—182no—
522C22⋊C4—184no—
523C22⋊C4—182no—
524C42—182no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—22no—
528C22×C3—21no—
529C22×C3—22no—
530C22×C3—34no—
531C22×C3—44no—
532C22×C3—44no—
533C22×C3—44no—
534C22×C3—42no—
535C22×C3—42no—
536C22×C3—42no—
537C22×C3—42no—
538C22×C3—42no—
539C22×C3—42no—
540C22×C3—42no—
541C22×C3—42no—
542C22×C3—42no—
543C22×C3—42no—
544C22×C3—42no—
545C22×C3—42no—
546C22×C3—42no—
547C22×C3—42no—
548C22×C3—64no—
549C22×C3—62no—
550C22×C3—62no—
551C22×C3—64no—
552C22×C3—82no—
553C22×C3—82no—
554C22×C3—82no—
555C22×C3—82no—
556C22×C3C2×D3×D411yescharacteristic
557C22×C3C2×D3×D411yescharacteristic
558C22×C3C2×D3×D411yescharacteristic
559C22×C3C2×#23711yescharacteristic
560C22×C3#100412yes—
561C22×C3#100412yes—
562C22×C3D3×#4111yescharacteristic
563C22×C3D3×#4112yes—
564C22×C3D3×#4112yes—
565C22×C3C22×#6711yescharacteristic
566C2×D3—22no—
567C2×D3—22no—
568C2×D3—24no—
569C2×D3—24no—
570C2×D3—62no—
571C2×D3—62no—
572C2×D3—64no—
573C2×D3—64no—
574C2×D3—124no—
575C2×D3—122no—
576C2×D3—122no—
577C2×D3—121no—
578C2×D3—121no—
579C2×D3—121no—
580C2×D3—121no—
581C2×D3—122no—
582C2×D3—241no—
583C2×D3—242no—
584C2×D3—241no—
585C2×D3#93814yes—
586C3×C4—22no—
587C3×C4—22no—
588C3×C4—42no—
589C3×C4—62no—
590C3×C4—62no—
591C3×C4—121no—
592C3×C4—122no—
593C3×C4—122no—
594Dic3—22no—
595Dic3—22no—
596Dic3—42no—
597Dic3—41no—
598Dic3—42no—
599Dic3—64no—
600Dic3—64no—
601Dic3—124no—
602Dic3—121no—
603Dic3—121no—
604Dic3—241no—
605C32#254311yescharacteristic, complemented, Sylow
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—32no—
614C23—32no—
615C23—32no—
616C23—62no—
617C23—62no—
618C23—92no—
619C23—181no—
620C23—182no—
621C23—181no—
622C23—182no—
623C23C22×D3211yescharacteristic
624D4—44no—
625D4—128no—
626D4—188no—
627D4—368no—
628C2×C4—22no—
629C2×C4—32no—
630C2×C4—32no—
631C2×C4—61no—
632C2×C4—61no—
633C2×C4—62no—
634C2×C4—62no—
635C2×C4—62no—
636C2×C4—62no—
637C2×C4—62no—
638C2×C4—62no—
639C2×C4—61no—
640C2×C4—62no—
641C2×C4—62no—
642C2×C4—94no—
643C2×C4—124no—
644C2×C4—182no—
645C2×C4—182no—
646C2×C4—182no—
647C2×C4—181no—
648C2×C4—364no—
649C2×C4—368no—
650C2×C4D3×#6712yes—
651C2×C3—21no—
652C2×C3—22no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—22no—
656C2×C3—64no—
657C2×C3—84no—
658C2×C3—82no—
659C2×C3—82no—
660C2×C3#558911yescharacteristic
661C2×C3#560112yes—
662C2×C3D3×#12111yescharacteristic
663C2×C3#561012yes—
664C2×C3#561212yes—
665C2×C3#566112yes—
666C2×C3#566811yescharacteristic
667C2×C3C2×#93811yescharacteristic
668C2×C3#580411yescharacteristic
669C2×C3#583211yescharacteristic
670D3—24no—
671D3—122no—
672D3—122no—
673D3—242no—
674C22—34no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22—62no—
683C22—64no—
684C22—62no—
685C22—64no—
686C22—182no—
687C22—184no—
688C22—361no—
689C22—362no—
690C22—361no—
691C22D32×D411yescharacteristic
692C22D3×#23711yescharacteristic
693C22#6431212yes—
694C22C2×D3×#6711yescharacteristic
695C22#6433012yes—
696C4—22no—
697C4—62no—
698C4—62no—
699C4—121no—
700C4—122no—
701C4—122no—
702C4—184no—
703C4—361no—
704C3—21no—
705C3#7712011yescharacteristic, complemented
706C3#8267111yescharacteristic, complemented
707C2—64no—
708C2—82no—
709C2—362no—
710C2#1059515311yescharacteristic
711C2#1059518312yes—
712C2D3×#93811yescharacteristic
713C2#1059529612yes—
714C2#1059552411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#2543
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#938C2semidirect
2. C2×#63971C2semidirect
3. C2×#63904C2semidirect
4. #10592922C2semidirect
5. C3×#5222C2semidirect
6. #10591722C2semidirect
7. #10591721C2semidirect
8. #10591703C2semidirect
9. D3×C3⋊#95C2semidirect
10. #10591326C2semidirect
11. #10591214C2semidirect
42. C2×#938D3semidirect
50. #5222D3semidirect
83. C2×C3×C4×D3D4semidirect
86. C2×#626D4semidirect
284. C2×C4×D3#67semidirect
605. C32#2543semidirect
705. C3#77120semidirect
706. C3#82671semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9382
C2×#639712
C2×#639042
#105929222
C3×#52222
#105917222
#105917212
#105917032
D3×C3⋊#952
#105913262
#105912142
#826713
#771203