Finite Group Databasebeta

← #11773338

Subgroups — #11773338

Order 1152.

1809 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3757C211yesmaximal, characteristic
2C22×C3×#217C211yesmaximal, characteristic
3C22×C3×#217C211yesmaximal, characteristic
4C2×#63579C212yesmaximal, complemented
5C2×#63579C212yesmaximal, complemented
6#71549—31nomaximal
7#71548—31nomaximal
8C25×C32C2211yescharacteristic
9C23×C3⋊Dic3C2212yes—
10C23×C3×Dic3C2211yescharacteristic
11C23×C3×Dic3C2211yescharacteristic
12C23×C3×Dic3C2212yes—
13C2×#3757—24no—
14C2×#3757—22no—
15C2×C3×#217—24no—
16C2×C3×#217—22no—
17C2×C3×#217—22no—
18C2×C3×#217—22no—
19C2×C3×#217C414yescomplemented
20#63579—24no—
21#63579—24no—
22C22×C3×C22⋊C4—31no—
23C22×C3×C22⋊C4—31no—
24C22×#217—31no—
25C22×#217—31no—
26C22×#217—61no—
27C22×#217D311yescharacteristic
28C22×#217D311yescharacteristic
29C2×C3⋊#95—32no—
30C2×C3⋊#95—32no—
31C2×C3⋊#95—32no—
32C2×C3⋊#95—32no—
33C24×C32—22no—
34C24×C32—22no—
35C24×C32—22no—
36C24×C32—22no—
37C24×C32—22no—
38C24×C32—22no—
39C24×C32C2×C412yes—
40C24×C32D412yes—
41C24×C32D412yes—
42C24×C32C2311yescharacteristic
43C22×C3⋊Dic3—22no—
44C22×C3⋊Dic3—22no—
45C22×C3⋊Dic3—22no—
46C22×C3⋊Dic3—22no—
47C22×C3⋊Dic3—22no—
48C22×C3⋊Dic3—22no—
49C22×C3⋊Dic3D414yes—
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
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×Dic3C2×C412yes—
65C22×C3×Dic3C2×C412yes—
66C22×C3×Dic3D414yes—
67#3757—28no—
68C3×#217—28no—
69C3×#217—28no—
70#1440—91noSylow
71C25×C3—21no—
72C25×C3C2×D311yescharacteristic
73C25×C3C2×D311yescharacteristic
74C23×C3×C4—31no—
75C23×C3×C4—31no—
76C23×C3×C4—32no—
77C23×Dic3—32no—
78C23×Dic3—32no—
79C23×Dic3—62no—
80C23×Dic3C2×D311yescharacteristic
81C23×Dic3C2×D311yescharacteristic
82C23×Dic3C2×D312yes—
83C2×C3×C22⋊C4—34no—
84C2×C3×C22⋊C4—64no—
85C2×C3×C22⋊C4—62no—
86C2×C3×C22⋊C4—62no—
87C2×C3×C22⋊C4—62no—
88C2×#217—22no—
89C2×#217—22no—
90C2×#217—22no—
91C2×#217—24no—
92C2×#217—64no—
93C2×#217—64no—
94C2×#217—68no—
95C2×#217—64no—
96C2×#217—62no—
97C2×#217—62no—
98C2×#217Dic314yescomplemented
99C3⋊#95—64no—
100C3⋊#95—64no—
101C3⋊#95—64no—
102C3⋊#95—64no—
103C23×C32—24no—
104C23×C32—22no—
105C23×C32—24no—
106C23×C32—22no—
107C23×C32—22no—
108C23×C32—22no—
109C23×C32—24no—
110C23×C32—22no—
111C23×C32—24no—
112C23×C32—24no—
113C23×C32—24no—
114C23×C32—22no—
115C23×C32—42no—
116C23×C32—42no—
117C23×C32—42no—
118C23×C32—42no—
119C23×C32—42no—
120C23×C32—42no—
121C23×C32—42no—
122C23×C32—42no—
123C23×C32C22⋊C414yes—
124C23×C32C22×C411yescharacteristic
125C23×C32C2×D411yescharacteristic
126C23×C32C2×D412yes—
127C23×C32C2×D412yes—
128C23×C32C2×D411yescharacteristic
129C23×C32#4112yes—
130C23×C32#4112yes—
131C23×C32#4112yes—
132C23×C32#4112yes—
133C2×C3⋊Dic3—24no—
134C2×C3⋊Dic3—24no—
135C2×C3⋊Dic3—24no—
136C2×C3⋊Dic3—42no—
137C2×C3⋊Dic3—42no—
138C2×C3⋊Dic3—42no—
139C2×C3⋊Dic3—42no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—24no—
143C2×C3×Dic3—24no—
144C2×C3×Dic3—24no—
145C2×C3×Dic3—24no—
146C2×C3×Dic3—24no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—42no—
150C2×C3×Dic3—42no—
151C2×C3×Dic3—42no—
152C2×C3×Dic3—42no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—42no—
156C2×C3×Dic3—42no—
157C22×C22⋊C4—31no—
158C22×C22⋊C4—31no—
159C22×C22⋊C4—91no—
160C2×#95—92no—
161C2×#95—92no—
162C24×C3—24no—
163C24×C3—24no—
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—21no—
180C24×C3—42no—
181C24×C3—42no—
182C24×C3—42no—
183C24×C3—42no—
184C24×C3C4×D312yes—
185C24×C3D1212yes—
186C24×C3C2×Dic312yes—
187C24×C3#6712yes—
188C24×C3#6712yes—
189C24×C3#6712yes—
190C24×C3C22×D311yescharacteristic
191C24×C3C22×D311yescharacteristic
192C22×C3×C4—32no—
193C22×C3×C4—32no—
194C22×C3×C4—34no—
195C22×C3×C4—61no—
196C22×C3×C4—61no—
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×C3×C4—62no—
204C22×C3×C4—62no—
205C22×C3×C4—62no—
206C22×C3×C4—61no—
207C22×C3×C4—61no—
208C22×C3×C4—62no—
209C22×Dic3—22no—
210C22×Dic3—22no—
211C22×Dic3—22no—
212C22×Dic3—22no—
213C22×Dic3—22no—
214C22×Dic3—22no—
215C22×Dic3—22no—
216C22×Dic3—22no—
217C22×Dic3—21no—
218C22×Dic3—21no—
219C22×Dic3—22no—
220C22×Dic3—21no—
221C22×Dic3—21no—
222C22×Dic3—22no—
223C22×Dic3—34no—
224C22×Dic3—34no—
225C22×Dic3—64no—
226C22×Dic3—64no—
227C22×Dic3—64no—
228C22×Dic3—62no—
229C22×Dic3—62no—
230C22×Dic3—62no—
231C22×Dic3—62no—
232C22×Dic3—62no—
233C22×Dic3—62no—
234C22×Dic3—62no—
235C22×Dic3—62no—
236C22×Dic3—62no—
237C22×Dic3—62no—
238C22×Dic3—62no—
239C22×Dic3—62no—
240C22×Dic3—122no—
241C22×Dic3—122no—
242C22×Dic3—122no—
243C22×Dic3—122no—
244C22×Dic3C2×Dic312yes—
245C22×Dic3C2×Dic312yes—
246C22×Dic3#6714yes—
247C3×C22⋊C4—68no—
248C3×C22⋊C4—68no—
249#217—28no—
250#217—28no—
251#217—616no—
252#217—68no—
253#217—68no—
254C22×C32—24no—
255C22×C32—24no—
256C22×C32—24no—
257C22×C32—44no—
258C22×C32—44no—
259C22×C32—44no—
260C22×C32—44no—
261C22×C32—44no—
262C22×C32—44no—
263C22×C32C2×C22⋊C411yescharacteristic
264C22×C32#11711yescharacteristic
265C22×C32#11711yescharacteristic
266C22×C32C4×D412yes—
267C22×C32C4×D412yes—
268C22×C32#12011yescharacteristic
269C22×C32#12011yescharacteristic
270C22×C32#12112yes—
271C22×C32#12112yes—
272C22×C32#12112yes—
273C22×C32#12112yes—
274C22×C32#12312yes—
275C22×C32#12312yes—
276C22×C32#12312yes—
277C22×C32#12311yescharacteristic
278C22×C32#12312yes—
279C22×C32#12311yescharacteristic
280C22×C32#12412yes—
281C22×C32#12412yes—
282C22×C32#12612yes—
283C22×C32#12612yes—
284C3⋊Dic3—44no—
285C3×Dic3—42no—
286C3×Dic3—42no—
287C3×Dic3—44no—
288C25D3211yescharacteristic
289C23×C4—31no—
290C23×C4—31no—
291C23×C4—32no—
292C23×C4—92no—
293C2×C22⋊C4—34no—
294C2×C22⋊C4—64no—
295C2×C22⋊C4—62no—
296C2×C22⋊C4—62no—
297C2×C22⋊C4—62no—
298C2×C22⋊C4—184no—
299C2×C22⋊C4—182no—
300#95—184no—
301#95—184no—
302C23×C3—24no—
303C23×C3—24no—
304C23×C3—28no—
305C23×C3—28no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—24no—
309C23×C3—22no—
310C23×C3—22no—
311C23×C3—24no—
312C23×C3—22no—
313C23×C3—22no—
314C23×C3—24no—
315C23×C3—24no—
316C23×C3—22no—
317C23×C3—24no—
318C23×C3—24no—
319C23×C3—24no—
320C23×C3—24no—
321C23×C3—24no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—24no—
327C23×C3—24no—
328C23×C3—24no—
329C23×C3—22no—
330C23×C3—24no—
331C23×C3—21no—
332C23×C3—22no—
333C23×C3—22no—
334C23×C3—22no—
335C23×C3—22no—
336C23×C3—21no—
337C23×C3—21no—
338C23×C3—22no—
339C23×C3—22no—
340C23×C3—42no—
341C23×C3—42no—
342C23×C3—44no—
343C23×C3—42no—
344C23×C3—44no—
345C23×C3—44no—
346C23×C3—42no—
347C23×C3—44no—
348C23×C3—44no—
349C23×C3—44no—
350C23×C3—44no—
351C23×C3—44no—
352C23×C3—44no—
353C23×C3—44no—
354C23×C3—44no—
355C23×C3—44no—
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×C3—42no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—42no—
371C23×C3—42no—
372C23×C3(C2×D3)⋊C414yes—
373C23×C3#21714yes—
374C23×C3C2×C4×D311yescharacteristic
375C23×C3C2×D1211yescharacteristic
376C23×C3#23512yes—
377C23×C3#23512yes—
378C23×C3#23512yes—
379C23×C3D3×D412yes—
380C23×C3D3×D412yes—
381C23×C3D3×D412yes—
382C23×C3#23712yes—
383C23×C3#23712yes—
384C23×C3#23712yes—
385C23×C3#23712yes—
386C23×C3#23712yes—
387C23×C3C22×Dic311yescharacteristic
388C23×C3C2×#6711yescharacteristic
389C23×C3C2×#6711yescharacteristic
390C23×C3C2×#6711yescharacteristic
391C23×C3C2×#6712yes—
392C2×C3×C4—64no—
393C2×C3×C4—64no—
394C2×C3×C4—64no—
395C2×C3×C4—62no—
396C2×C3×C4—62no—
397C2×C3×C4—64no—
398C2×C3×C4—64no—
399C2×C3×C4—121no—
400C2×C3×C4—122no—
401C2×C3×C4—122no—
402C2×C3×C4—121no—
403C2×C3×C4—121no—
404C2×C3×C4—122no—
405C2×C3×C4—122no—
406C2×C3×C4—122no—
407C2×C3×C4—122no—
408C2×C3×C4—121no—
409C2×Dic3—24no—
410C2×Dic3—24no—
411C2×Dic3—24no—
412C2×Dic3—24no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—24no—
416C2×Dic3—41no—
417C2×Dic3—42no—
418C2×Dic3—41no—
419C2×Dic3—42no—
420C2×Dic3—41no—
421C2×Dic3—41no—
422C2×Dic3—42no—
423C2×Dic3—42no—
424C2×Dic3—42no—
425C2×Dic3—42no—
426C2×Dic3—68no—
427C2×Dic3—64no—
428C2×Dic3—64no—
429C2×Dic3—64no—
430C2×Dic3—64no—
431C2×Dic3—64no—
432C2×Dic3—64no—
433C2×Dic3—124no—
434C2×Dic3—124no—
435C2×Dic3—124no—
436C2×Dic3—124no—
437C2×Dic3—124no—
438C2×Dic3—124no—
439C2×Dic3—122no—
440C2×Dic3—122no—
441C2×Dic3—122no—
442C2×Dic3—122no—
443C2×Dic3—122no—
444C2×Dic3—122no—
445C2×Dic3—122no—
446C2×Dic3—122no—
447C2×C32—44no—
448C2×C32#38111yescharacteristic
449C2×C32#38611yescharacteristic
450C2×C32#38611yescharacteristic
451C2×C32#38812yes—
452C2×C32#38812yes—
453C2×C32#39412yes—
454C2×C32#39412yes—
455C2×C32#39712yes—
456C2×C32#39712yes—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24D3×Dic312yes—
464C24#62512yes—
465C24#62612yes—
466C24C2×D3211yescharacteristic
467C22×C4—32no—
468C22×C4—32no—
469C22×C4—34no—
470C22×C4—62no—
471C22×C4—62no—
472C22×C4—62no—
473C22×C4—62no—
474C22×C4—62no—
475C22×C4—61no—
476C22×C4—61no—
477C22×C4—62no—
478C22×C4—61no—
479C22×C4—61no—
480C22×C4—62no—
481C22×C4—62no—
482C22×C4—62no—
483C22×C4—62no—
484C22×C4—94no—
485C22×C4—182no—
486C22×C4—182no—
487C22×C4—182no—
488C22×C4—182no—
489C22×C4—182no—
490C22×C4—182no—
491C22⋊C4—68no—
492C22⋊C4—68no—
493C22⋊C4—188no—
494C22×C3—28no—
495C22×C3—24no—
496C22×C3—24no—
497C22×C3—24no—
498C22×C3—24no—
499C22×C3—24no—
500C22×C3—24no—
501C22×C3—22no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—22no—
511C22×C3—21no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—21no—
519C22×C3—22no—
520C22×C3—22no—
521C22×C3—21no—
522C22×C3—44no—
523C22×C3—44no—
524C22×C3—48no—
525C22×C3—48no—
526C22×C3—48no—
527C22×C3—48no—
528C22×C3—48no—
529C22×C3—48no—
530C22×C3—44no—
531C22×C3—44no—
532C22×C3—44no—
533C22×C3—44no—
534C22×C3—44no—
535C22×C3—44no—
536C22×C3—44no—
537C22×C3—44no—
538C22×C3—44no—
539C22×C3—44no—
540C22×C3—44no—
541C22×C3—44no—
542C22×C3#87711yescharacteristic
543C22×C3#87711yescharacteristic
544C22×C3#87912yes—
545C22×C3#87912yes—
546C22×C3#87912yes—
547C22×C3#87912yes—
548C22×C3#67⋊C412yes—
549C22×C3#88211yescharacteristic
550C22×C3#88312yes—
551C22×C3#88312yes—
552C22×C3#88312yes—
553C22×C3#88412yes—
554C22×C3#88412yes—
555C22×C3#88512yes—
556C22×C3#88512yes—
557C22×C3#88512yes—
558C22×C3#88611yescharacteristic
559C22×C3#88612yes—
560C22×C3#92611yescharacteristic
561C22×C3#92611yescharacteristic
562C22×C3C2×(C2×D3)⋊C411yescharacteristic
563C22×C3C4×#6712yes—
564C22×C3#92911yescharacteristic
565C22×C3#92912yes—
566C22×C3#92912yes—
567C22×C3#93012yes—
568C22×C3D4×Dic312yes—
569C22×C3D4×Dic312yes—
570C22×C3#93512yes—
571C22×C3#93511yescharacteristic
572C22×C3#93511yescharacteristic
573C22×C3#93512yes—
574C22×C3#93612yes—
575C22×C3#93711yescharacteristic
576C22×C3#93711yescharacteristic
577C22×C3#93812yes—
578C22×C3#93912yes—
579C22×C3#93912yes—
580C22×C3#93912yes—
581C22×C3#93912yes—
582C22×C3C2×#21711yescharacteristic
583C22×C3#95311yescharacteristic
584C3×C4—122no—
585C3×C4—122no—
586C3×C4—124no—
587Dic3—42no—
588Dic3—42no—
589Dic3—44no—
590Dic3—128no—
591Dic3—124no—
592Dic3—124no—
593C32#144011yescharacteristic, complemented, Sylow
594C23—22no—
595C23—22no—
596C23—24no—
597C23—22no—
598C23—22no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—22no—
603C23—24no—
604C23—24no—
605C23—22no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23(C2×D3)⋊Dic314yes—
615C23C2×D3×Dic311yescharacteristic
616C23#380412yes—
617C23#380412yes—
618C23#380412yes—
619C23#380512yes—
620C23C2×#62511yescharacteristic
621C23C2×#62611yescharacteristic
622C23D3×#6712yes—
623C23#381112yes—
624C2×C4—62no—
625C2×C4—62no—
626C2×C4—64no—
627C2×C4—64no—
628C2×C4—64no—
629C2×C4—64no—
630C2×C4—64no—
631C2×C4—122no—
632C2×C4—122no—
633C2×C4—122no—
634C2×C4—121no—
635C2×C4—121no—
636C2×C4—121no—
637C2×C4—122no—
638C2×C4—122no—
639C2×C4—122no—
640C2×C4—121no—
641C2×C4—184no—
642C2×C4—184no—
643C2×C4—184no—
644C2×C4—362no—
645C2×C4—362no—
646C2×C4—362no—
647C2×C4—362no—
648C2×C3—22no—
649C2×C3—21no—
650C2×C3—22no—
651C2×C3—22no—
652C2×C3—22no—
653C2×C3—21no—
654C2×C3—22no—
655C2×C3—21no—
656C2×C3—22no—
657C2×C3—48no—
658C2×C3—44no—
659C2×C3—44no—
660C2×C3#494311yescharacteristic
661C2×C3#494412yes—
662C2×C3#494512yes—
663C2×C3#495112yes—
664C2×C3#495112yes—
665C2×C3#495212yes—
666C2×C3#495212yes—
667C2×C3#495212yes—
668C2×C3#495312yes—
669C2×C3#495811yescharacteristic
670C2×C3#495912yes—
671C2×C3#495912yes—
672C2×C3#496112yes—
673C2×C3#521111yescharacteristic
674C2×C3#521311yescharacteristic
675C2×C3#522011yescharacteristic
676C2×C3#522011yescharacteristic
677C2×C3#522212yes—
678C22—24no—
679C22—24no—
680C22—24no—
681C22—44no—
682C22—44no—
683C22—44no—
684C22—44no—
685C22—44no—
686C22—44no—
687C22#6395312yes—
688C22#6395511yescharacteristic
689C22#6395511yescharacteristic
690C22#6395612yes—
691C22#6395612yes—
692C22#6395812yes—
693C22#6395912yes—
694C22C2×(C2×D3)⋊Dic311yescharacteristic
695C22#6396111yescharacteristic
696C22#6396112yes—
697C22#6396211yescharacteristic
698C22#6396612yes—
699C22#6396912yes—
700C22#6397112yes—
701C22Dic3×#6712yes—
702C22#67⋊Dic312yes—
703C22#6397512yes—
704C22#6397611yescharacteristic
705C22#6397812yes—
706C22#6398012yes—
707C22#6398111yescharacteristic
708C4—124no—
709C4—122no—
710C4—122no—
711C4—364no—
712C3—21no—
713C3#7154811yescharacteristic, complemented
714C3#7154911yescharacteristic, complemented
715C2—44no—
716C2#1059169412yes—
717C2#1059169611yescharacteristic
718C2#1059170112yes—
719C2#1059170212yes—
720C2#1059170812yes—
721C2#1059171011yescharacteristic
722C2#1059171212yes—
723C2#1059171311yescharacteristic
724C2#1059171712yes—
subgroupG/H
center, FrattiniC24C2×D32
commutatorC23×C32C22×C4
Fitting, prime radicalC25×C32C22
socle, cosocleC24×C32C23
hypercenterC25D32
hypocenterC32#1440
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C25

Complements

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

NH ≅ G/Ntype
4. C2×#63579C2semidirect
5. C2×#63579C2semidirect
19. C2×C3×#217C4semidirect
98. C2×#217Dic3semidirect
593. C32#1440semidirect
713. C3#71548semidirect
714. C3#71549semidirect

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
C2×#635792
#715493
#715483