Finite Group Databasebeta

← #11773313

Subgroups — #11773313

Order 1152.

1897 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3757C211yesmaximal, characteristic
2C22×C3×#217C212yesmaximal
3C22×#3724C211yesmaximal, characteristic, complemented
4C2×#63579C211yesmaximal, characteristic, complemented
5C2×#63579C212yesmaximal, complemented
6#71547—32nomaximal
7C25×C32C2211yescharacteristic
8C23×C3⋊Dic3C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C23×C3×Dic3C2212yes—
11C23×C3×Dic3C2212yes—
12C2×#3757—22no—
13C2×#3757—22no—
14C2×#3757C414yescomplemented
15C2×C3×#217—24no—
16C2×C3×#217—24no—
17C2×C3×#217—24no—
18C2×#3724—22no—
19C2×#3724—24no—
20#63579—22no—
21#63579—24no—
22C22×C3×C22⋊C4—32no—
23C22×#217—32no—
24C22×#217—61no—
25C22×#217D312yes—
26C22×Dic3⋊C4—32no—
27C2×C3⋊#95—32no—
28C2×C3⋊#95—32no—
29C2×C3⋊#95—32no—
30C24×C32—21no—
31C24×C32—21no—
32C24×C32—22no—
33C24×C32—22no—
34C24×C32—21no—
35C24×C32—21no—
36C24×C32—22no—
37C24×C32—22no—
38C24×C32C2×C412yes—
39C24×C32D412yes—
40C24×C32Q812yes—
41C24×C32C2311yescharacteristic
42C22×C3⋊Dic3—22no—
43C22×C3⋊Dic3—22no—
44C22×C3⋊Dic3—21no—
45C22×C3⋊Dic3—21no—
46C22×C3⋊Dic3—22no—
47C22×C3⋊Dic3—22no—
48C22×C3⋊Dic3C2×C412yes—
49C22×C3⋊Dic3C2×C412yes—
50C22×C3⋊Dic3D412yes—
51C22×C3⋊Dic3D412yes—
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×Dic3—22no—
59C22×C3×Dic3—22no—
60C22×C3×Dic3—22no—
61C22×C3×Dic3—22no—
62C22×C3×Dic3—22no—
63C22×C3×Dic3—22no—
64C22×C3×Dic3D414yes—
65C22×C3×Dic3D414yes—
66#3757—28no—
67C3×#217—216no—
68#3724—28no—
69#1439—91noSylow
70C25×C3—21no—
71C25×C3C2×D312yes—
72C23×C3×C4—32no—
73C23×C3×C4—32no—
74C23×Dic3—32no—
75C23×Dic3—32no—
76C23×Dic3—61no—
77C23×Dic3—61no—
78C23×Dic3C2×D312yes—
79C23×Dic3C2×D312yes—
80C2×C3×C22⋊C4—64no—
81C2×C3×C22⋊C4—64no—
82C2×C3×C22⋊C4—64no—
83C2×#217—24no—
84C2×#217—24no—
85C2×#217—24no—
86C2×#217—38no—
87C2×#217—64no—
88C2×#217—64no—
89C2×#217—64no—
90C2×#217—64no—
91C2×#217—64no—
92C2×Dic3⋊C4—64no—
93C2×Dic3⋊C4—64no—
94C2×Dic3⋊C4—64no—
95C3⋊#95—64no—
96C3⋊#95—64no—
97C3⋊#95—64no—
98C23×C32—22no—
99C23×C32—22no—
100C23×C32—22no—
101C23×C32—22no—
102C23×C32—22no—
103C23×C32—22no—
104C23×C32—24no—
105C23×C32—24no—
106C23×C32—24no—
107C23×C32—24no—
108C23×C32—24no—
109C23×C32—24no—
110C23×C32—41no—
111C23×C32—42no—
112C23×C32—42no—
113C23×C32—42no—
114C23×C32—41no—
115C23×C32—42no—
116C23×C32—41no—
117C23×C32—42no—
118C23×C32—42no—
119C23×C32—41no—
120C23×C32C4⋊C414yescomplemented
121C23×C32C22×C411yescharacteristic
122C23×C32C2×D411yescharacteristic
123C23×C32C2×D411yescharacteristic
124C23×C32C2×D412yes—
125C23×C32C2×D412yes—
126C23×C32C2×D411yescharacteristic
127C23×C32C2×Q811yescharacteristic
128C23×C32#4112yes—
129C23×C32#4112yes—
130C23×C32#4111yescharacteristic
131C23×C32#4111yescharacteristic
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—24no—
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—24no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—24no—
138C2×C3⋊Dic3—42no—
139C2×C3⋊Dic3—41no—
140C2×C3⋊Dic3—41no—
141C2×C3⋊Dic3C22⋊C414yescomplemented
142C2×C3×Dic3—24no—
143C2×C3×Dic3—24no—
144C2×C3×Dic3—24no—
145C2×C3×Dic3—24no—
146C2×C3×Dic3—24no—
147C2×C3×Dic3—24no—
148C2×C3×Dic3—42no—
149C2×C3×Dic3—42no—
150C2×C3×Dic3—42no—
151C2×C3×Dic3—42no—
152C2×C3×Dic3—42no—
153C2×C3×Dic3—42no—
154C2×C3×Dic3—42no—
155C2×C3×Dic3—42no—
156C22×C4⋊C4—91no—
157C22×C22⋊C4—32no—
158C22×C22⋊C4—91no—
159C2×#95—92no—
160C2×#95—91no—
161C24×C3—22no—
162C24×C3—22no—
163C24×C3—22no—
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3—22no—
171C24×C3—22no—
172C24×C3—22no—
173C24×C3—22no—
174C24×C3—22no—
175C24×C3—22no—
176C24×C3—22no—
177C24×C3—22no—
178C24×C3—22no—
179C24×C3—22no—
180C24×C3—21no—
181C24×C3—42no—
182C24×C3—42no—
183C24×C3—42no—
184C24×C3—42no—
185C24×C3Dic614yes—
186C24×C3C4×D314yes—
187C24×C3#6714yes—
188C24×C3C22×D312yes—
189C22×C3×C4—34no—
190C22×C3×C4—34no—
191C22×C3×C4—62no—
192C22×C3×C4—62no—
193C22×C3×C4—62no—
194C22×C3×C4—62no—
195C22×C3×C4—62no—
196C22×C3×C4—62no—
197C22×C3×C4—62no—
198C22×C3×C4—62no—
199C22×C3×C4—62no—
200C22×C3×C4—62no—
201C22×C3×C4—62no—
202C22×C3×C4—62no—
203C22×Dic3—22no—
204C22×Dic3—22no—
205C22×Dic3—22no—
206C22×Dic3—22no—
207C22×Dic3—22no—
208C22×Dic3—22no—
209C22×Dic3—22no—
210C22×Dic3—22no—
211C22×Dic3—22no—
212C22×Dic3—22no—
213C22×Dic3—22no—
214C22×Dic3—22no—
215C22×Dic3—34no—
216C22×Dic3—34no—
217C22×Dic3—34no—
218C22×Dic3—34no—
219C22×Dic3—62no—
220C22×Dic3—62no—
221C22×Dic3—62no—
222C22×Dic3—62no—
223C22×Dic3—62no—
224C22×Dic3—62no—
225C22×Dic3—62no—
226C22×Dic3—62no—
227C22×Dic3—62no—
228C22×Dic3—62no—
229C22×Dic3—62no—
230C22×Dic3—62no—
231C22×Dic3—62no—
232C22×Dic3—62no—
233C22×Dic3—62no—
234C22×Dic3—62no—
235C22×Dic3—122no—
236C22×Dic3—122no—
237C22×Dic3—122no—
238C22×Dic3—122no—
239C22×Dic3#6714yes—
240C22×Dic3#6714yes—
241C3×C22⋊C4—616no—
242#217—216no—
243#217—616no—
244#217—616no—
245Dic3⋊C4—616no—
246C22×C32—24no—
247C22×C32—28no—
248C22×C32—42no—
249C22×C32—44no—
250C22×C32—42no—
251C22×C32—42no—
252C22×C32—42no—
253C22×C32—44no—
254C22×C32—44no—
255C22×C32—42no—
256C22×C32—42no—
257C22×C32C2×C22⋊C411yescharacteristic
258C22×C32C2×C4⋊C411yescharacteristic
259C22×C32#11711yescharacteristic
260C22×C32C4×D412yes—
261C22×C32C4×D412yes—
262C22×C32#12011yescharacteristic
263C22×C32#12012yes—
264C22×C32#12112yes—
265C22×C32#12112yes—
266C22×C32#12112yes—
267C22×C32#12111yescharacteristic
268C22×C32#12111yescharacteristic
269C22×C32C22⋊Q811yescharacteristic
270C22×C32C22⋊Q811yescharacteristic
271C22×C32C22⋊Q812yes—
272C22×C32C22⋊Q812yes—
273C22×C32#12311yescharacteristic
274C22×C32#12312yes—
275C22×C32#12312yes—
276C22×C32#12411yescharacteristic
277C22×C32#12412yes—
278C22×C32#12612yes—
279C22×C32#12711yescharacteristic
280C3⋊Dic3—24no—
281C3⋊Dic3—42no—
282C3×Dic3—44no—
283C3×Dic3—44no—
284C25D3211yescharacteristic
285C23×C4—32no—
286C23×C4—32no—
287C23×C4—91no—
288C23×C4—91no—
289C2×C4⋊C4—184no—
290C2×C4⋊C4—182no—
291C2×C22⋊C4—64no—
292C2×C22⋊C4—64no—
293C2×C22⋊C4—64no—
294C2×C22⋊C4—94no—
295C2×C22⋊C4—182no—
296C2×C22⋊C4—182no—
297#95—184no—
298#95—182no—
299C23×C3—24no—
300C23×C3—24no—
301C23×C3—24no—
302C23×C3—24no—
303C23×C3—24no—
304C23×C3—24no—
305C23×C3—24no—
306C23×C3—24no—
307C23×C3—24no—
308C23×C3—24no—
309C23×C3—24no—
310C23×C3—24no—
311C23×C3—24no—
312C23×C3—24no—
313C23×C3—24no—
314C23×C3—24no—
315C23×C3—24no—
316C23×C3—24no—
317C23×C3—24no—
318C23×C3—24no—
319C23×C3—24no—
320C23×C3—24no—
321C23×C3—24no—
322C23×C3—24no—
323C23×C3—24no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—21no—
327C23×C3—21no—
328C23×C3—21no—
329C23×C3—21no—
330C23×C3—21no—
331C23×C3—22no—
332C23×C3—22no—
333C23×C3—21no—
334C23×C3—21no—
335C23×C3—44no—
336C23×C3—44no—
337C23×C3—44no—
338C23×C3—44no—
339C23×C3—44no—
340C23×C3—44no—
341C23×C3—42no—
342C23×C3—44no—
343C23×C3—44no—
344C23×C3—44no—
345C23×C3—44no—
346C23×C3—44no—
347C23×C3—44no—
348C23×C3—42no—
349C23×C3—42no—
350C23×C3—42no—
351C23×C3—42no—
352C23×C3—42no—
353C23×C3—42no—
354C23×C3—42no—
355C23×C3—42no—
356C23×C3—42no—
357C23×C3—42no—
358C23×C3—42no—
359C23×C3—42no—
360C23×C3—42no—
361C23×C3—42no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—42no—
367C23×C3Dic3⋊C418yescomplemented
368C23×C3C2×Dic612yes—
369C23×C3C2×C4×D312yes—
370C23×C3#23512yes—
371C23×C3#23512yes—
372C23×C3D3×D412yes—
373C23×C3D3×D412yes—
374C23×C3D3×D412yes—
375C23×C3D3×D412yes—
376C23×C3#23712yes—
377C23×C3#23712yes—
378C23×C3#23712yes—
379C23×C3#23712yes—
380C23×C3C2×#6712yes—
381C23×C3C2×#6712yes—
382C23×C3C2×#6712yes—
383C2×C3×C4—64no—
384C2×C3×C4—64no—
385C2×C3×C4—64no—
386C2×C3×C4—64no—
387C2×C3×C4—64no—
388C2×C3×C4—64no—
389C2×C3×C4—122no—
390C2×C3×C4—122no—
391C2×C3×C4—122no—
392C2×C3×C4—122no—
393C2×C3×C4—122no—
394C2×C3×C4—122no—
395C2×C3×C4—122no—
396C2×C3×C4—122no—
397C2×Dic3—24no—
398C2×Dic3—24no—
399C2×Dic3—24no—
400C2×Dic3—24no—
401C2×Dic3—24no—
402C2×Dic3—24no—
403C2×Dic3—38no—
404C2×Dic3—42no—
405C2×Dic3—42no—
406C2×Dic3—42no—
407C2×Dic3—42no—
408C2×Dic3—42no—
409C2×Dic3—42no—
410C2×Dic3—42no—
411C2×Dic3—42no—
412C2×Dic3—64no—
413C2×Dic3—64no—
414C2×Dic3—64no—
415C2×Dic3—64no—
416C2×Dic3—64no—
417C2×Dic3—64no—
418C2×Dic3—64no—
419C2×Dic3—64no—
420C2×Dic3—64no—
421C2×Dic3—64no—
422C2×Dic3—64no—
423C2×Dic3—124no—
424C2×Dic3—124no—
425C2×Dic3—122no—
426C2×Dic3—122no—
427C2×Dic3—124no—
428C2×Dic3—122no—
429C2×Dic3—124no—
430C2×Dic3—122no—
431C2×Dic3—122no—
432C2×Dic3—122no—
433C2×Dic3—122no—
434C2×Dic3—122no—
435C2×C32—44no—
436C2×C32#38011yescharacteristic
437C2×C32#38512yes—
438C2×C32#38611yescharacteristic
439C2×C32#38812yes—
440C2×C32#39011yescharacteristic
441C2×C32#39211yescharacteristic
442C2×C32#39311yescharacteristic
443C2×C32#39412yes—
444C2×C32#39612yes—
445C2×C32#39711yescharacteristic
446C2×C32#39911yescharacteristic
447C24—22no—
448C24—22no—
449C24—21no—
450C24—21no—
451C24—22no—
452C24—22no—
453C24—21no—
454C24—21no—
455C24#62412yes—
456C24#62512yes—
457C24#62712yes—
458C24C2×D3211yescharacteristic
459C22×C4—34no—
460C22×C4—34no—
461C22×C4—62no—
462C22×C4—62no—
463C22×C4—62no—
464C22×C4—62no—
465C22×C4—62no—
466C22×C4—62no—
467C22×C4—62no—
468C22×C4—62no—
469C22×C4—62no—
470C22×C4—62no—
471C22×C4—62no—
472C22×C4—62no—
473C22×C4—92no—
474C22×C4—92no—
475C22×C4—92no—
476C22×C4—92no—
477C22×C4—182no—
478C22×C4—182no—
479C22×C4—182no—
480C22×C4—182no—
481C22×C4—181no—
482C22×C4—181no—
483C4⋊C4—188no—
484C22⋊C4—616no—
485C22⋊C4—188no—
486C22×C3—28no—
487C22×C3—28no—
488C22×C3—28no—
489C22×C3—28no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—21no—
493C22×C3—22no—
494C22×C3—21no—
495C22×C3—22no—
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—21no—
501C22×C3—22no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—22no—
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—48no—
514C22×C3—48no—
515C22×C3—44no—
516C22×C3—44no—
517C22×C3—48no—
518C22×C3—44no—
519C22×C3—48no—
520C22×C3—44no—
521C22×C3—44no—
522C22×C3—44no—
523C22×C3—44no—
524C22×C3—44no—
525C22×C3—44no—
526C22×C3—44no—
527C22×C3—44no—
528C22×C3—44no—
529C22×C3—44no—
530C22×C3—44no—
531C22×C3—44no—
532C22×C3—44no—
533C22×C3—44no—
534C22×C3—44no—
535C22×C3#87712yes—
536C22×C3#87812yes—
537C22×C3#87812yes—
538C22×C3#87812yes—
539C22×C3#87812yes—
540C22×C3#87912yes—
541C22×C3#87912yes—
542C22×C3D3×C22⋊C412yes—
543C22×C3#67⋊C412yes—
544C22×C3#67⋊C412yes—
545C22×C3#88312yes—
546C22×C3#88312yes—
547C22×C3#88412yes—
548C22×C3#88412yes—
549C22×C3#88512yes—
550C22×C3#88512yes—
551C22×C3C2×Dic3⋊C412yes—
552C22×C3#92412yes—
553C22×C3#92412yes—
554C22×C3C4×#6712yes—
555C22×C3C4×#6712yes—
556C22×C3#92912yes—
557C22×C3#93512yes—
558C22×C3#93512yes—
559C22×C3#93612yes—
560C22×C3#93712yes—
561C22×C3#93712yes—
562C22×C3#93812yes—
563C22×C3#93812yes—
564C22×C3#93912yes—
565C22×C3#93912yes—
566C22×C3#93912yes—
567C22×C3#93912yes—
568C22×C3#94012yes—
569C22×C3#95312yes—
570C3×C4—124no—
571C3×C4—124no—
572Dic3—44no—
573Dic3—44no—
574Dic3—68no—
575Dic3—124no—
576Dic3—124no—
577Dic3—124no—
578C32#143911yescharacteristic, complemented, Sylow
579C23—24no—
580C23—24no—
581C23—22no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—22no—
586C23—24no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—41no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23#372414yescomplemented
602C23#380412yes—
603C23#380412yes—
604C23#380511yescharacteristic
605C23#380511yescharacteristic
606C23C2×#62411yescharacteristic
607C23C2×#62511yescharacteristic
608C23C2×#62711yescharacteristic
609C23D3×#6712yes—
610C23D3×#6712yes—
611C23#381111yescharacteristic
612C23#381111yescharacteristic
613C2×C4—64no—
614C2×C4—64no—
615C2×C4—64no—
616C2×C4—64no—
617C2×C4—64no—
618C2×C4—64no—
619C2×C4—94no—
620C2×C4—122no—
621C2×C4—122no—
622C2×C4—122no—
623C2×C4—122no—
624C2×C4—122no—
625C2×C4—122no—
626C2×C4—122no—
627C2×C4—122no—
628C2×C4—184no—
629C2×C4—184no—
630C2×C4—182no—
631C2×C4—182no—
632C2×C4—184no—
633C2×C4—182no—
634C2×C4—361no—
635C2×C4—362no—
636C2×C4—361no—
637C2×C3—22no—
638C2×C3—21no—
639C2×C3—22no—
640C2×C3—21no—
641C2×C3—22no—
642C2×C3—21no—
643C2×C3—22no—
644C2×C3—21no—
645C2×C3—21no—
646C2×C3—21no—
647C2×C3—21no—
648C2×C3—48no—
649C2×C3—48no—
650C2×C3#494212yes—
651C2×C3#494412yes—
652C2×C3#494512yes—
653C2×C3#494612yes—
654C2×C3#494712yes—
655C2×C3#494812yes—
656C2×C3#494812yes—
657C2×C3#494912yes—
658C2×C3#495212yes—
659C2×C3#495612yes—
660C2×C3#495712yes—
661C2×C3#495912yes—
662C2×C3#521012yes—
663C2×C3#522212yes—
664C2×C3#522312yes—
665C22—28no—
666C22—24no—
667C22—44no—
668C22—42no—
669C22—42no—
670C22—44no—
671C22—42no—
672C22—44no—
673C22—42no—
674C22—42no—
675C22—42no—
676C22#6395212yes—
677C22#6395212yes—
678C22#6395311yescharacteristic
679C22#6395612yes—
680C22#6395711yescharacteristic
681C22#6395812yes—
682C22#6395912yes—
683C22#6396112yes—
684C22#6396412yes—
685C22#6396412yes—
686C22C2×#372411yescharacteristic
687C22#6396912yes—
688C22#6397012yes—
689C22#6397112yes—
690C22#6397411yescharacteristic
691C22#6397511yescharacteristic
692C22#6397612yes—
693C22#6397911yescharacteristic
694C22#6398011yescharacteristic
695C22#6398011yescharacteristic
696C22#6398211yescharacteristic
697C22#6398211yescharacteristic
698C22#6398311yescharacteristic
699C4—124no—
700C4—124no—
701C4—184no—
702C4—362no—
703C3—21no—
704C3#7154712yescomplemented
705C2—44no—
706C2#1059169112yes—
707C2#1059169211yescharacteristic
708C2#1059169312yes—
709C2#1059169411yescharacteristic
710C2#1059170312yes—
711C2#1059170411yescharacteristic
712C2#1059170812yes—
713C2#1059171511yescharacteristic
714C2#1059172011yescharacteristic
715C2#1059172211yescharacteristic
716C2#1059172311yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC23×C32C22×C4
Fitting, prime radicalC25×C32C22
socle, cosocleC24×C32C23
hypercenterC25D32
hypocenterC32#1439
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C25

Complements

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

NH ≅ G/Ntype
3. C22×#3724C2semidirect
4. C2×#63579C2semidirect
5. C2×#63579C2semidirect
14. C2×#3757C4semidirect
120. C23×C32C4⋊C4semidirect
141. C2×C3⋊Dic3C22⋊C4semidirect
367. C23×C3Dic3⋊C4semidirect
578. C32#1439semidirect
601. C23#3724semidirect
704. C3#71547semidirect

Maximal subgroups

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

subgroupindex
C22×#37572
C22×C3×#2172
C22×#37242
C2×#635792
#715473