Finite Group Databasebeta

← #11773341

Subgroups — #11773341

Order 1152.

1809 conjugacy classes of subgroups.

The subgroup lattice has 677 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3752C211yesmaximal, characteristic
2C22×#3722C211yesmaximal, characteristic
3C22×#3722C211yesmaximal, characteristic
4C2×C3×C3⋊#95C212yesmaximal, complemented
5C2×#63579C212yesmaximal, complemented
6#69429—32nomaximal
7C24×C3⋊D3C2211yescharacteristic
8C23×C32×C4C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C23×C3×Dic3C2212yes—
11C23×C3×Dic3C2212yes—
12C2×#3752—22no—
13C2×#3752—22no—
14C2×#3752C414yescomplemented
15C2×#3722—24no—
16C2×#3722—24no—
17C2×#3722—22no—
18C2×#3722—22no—
19C3×C3⋊#95—24no—
20#63579—24no—
21C22×(C2×D3)⋊C4—32no—
22C22×(C2×D3)⋊C4—32no—
23C22×(C2×D3)⋊C4—32no—
24C22×(C2×D3)⋊C4—61no—
25C2×C3×#95—32no—
26C2×C3⋊#95—32no—
27C2×C3⋊#95—32no—
28C2×C3⋊#95D312yescomplemented
29C24×C32C2311yescharacteristic
30C23×C3⋊D3—22no—
31C23×C3⋊D3—22no—
32C23×C3⋊D3—22no—
33C23×C3⋊D3—22no—
34C23×C3⋊D3—22no—
35C23×C3⋊D3—22no—
36C23×C3⋊D3C2×C412yes—
37C23×C3⋊D3D412yes—
38C23×C3⋊D3D412yes—
39C22×C32×C4—21no—
40C22×C32×C4—21no—
41C22×C32×C4—22no—
42C22×C32×C4—22no—
43C22×C32×C4C2×C412yes—
44C22×C3⋊Dic3—21no—
45C22×C3⋊Dic3—21no—
46C22×C3⋊Dic3—22no—
47C22×C3⋊Dic3—22no—
48C22×C3⋊Dic3C2×C412yes—
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×Dic3—22no—
59C22×C3×Dic3—22no—
60C22×C3×Dic3—22no—
61C22×C3×Dic3D414yes—
62C22×C3×Dic3D414yes—
63#3752—28no—
64#3722—28no—
65#3722—28no—
66#1440—91noSylow
67C24×D3—32no—
68C24×D3—61no—
69C23×C3×C4—21no—
70C23×C3×C4—32no—
71C23×C3×C4—32no—
72C23×C3×C4C2×D312yes—
73C23×Dic3—32no—
74C23×Dic3—61no—
75C23×Dic3C2×D312yes—
76C23×Dic3C2×D312yes—
77C2×(C2×D3)⋊C4—38no—
78C2×(C2×D3)⋊C4—64no—
79C2×(C2×D3)⋊C4—64no—
80C2×(C2×D3)⋊C4—64no—
81C2×(C2×D3)⋊C4—64no—
82C2×(C2×D3)⋊C4—64no—
83C2×(C2×D3)⋊C4—64no—
84C2×(C2×D3)⋊C4—64no—
85C2×(C2×D3)⋊C4—64no—
86C2×(C2×D3)⋊C4—64no—
87C2×(C2×D3)⋊C4—64no—
88C2×(C2×D3)⋊C4—64no—
89C3×#95—64no—
90C3⋊#95—24no—
91C3⋊#95—64no—
92C3⋊#95—64no—
93C23×C32C22×C411yescharacteristic
94C23×C32C2×D412yes—
95C23×C32C2×D411yescharacteristic
96C23×C32C2×D411yescharacteristic
97C23×C32C2×D412yes—
98C23×C32#4112yes—
99C23×C32#4112yes—
100C23×C32#4112yes—
101C23×C32#4112yes—
102C22×C3⋊D3—22no—
103C22×C3⋊D3—22no—
104C22×C3⋊D3—24no—
105C22×C3⋊D3—24no—
106C22×C3⋊D3—24no—
107C22×C3⋊D3—24no—
108C22×C3⋊D3—22no—
109C22×C3⋊D3—22no—
110C22×C3⋊D3—24no—
111C22×C3⋊D3—24no—
112C22×C3⋊D3—22no—
113C22×C3⋊D3—22no—
114C22×C3⋊D3—42no—
115C22×C3⋊D3—42no—
116C22×C3⋊D3—42no—
117C22×C3⋊D3—42no—
118C22×C3⋊D3—42no—
119C22×C3⋊D3—42no—
120C22×C3⋊D3—42no—
121C22×C3⋊D3—42no—
122C22×C3⋊D3C22⋊C414yes—
123C2×C32×C4—22no—
124C2×C32×C4—24no—
125C2×C32×C4—41no—
126C2×C32×C4—42no—
127C2×C32×C4—41no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—24no—
130C2×C3⋊Dic3—41no—
131C2×C3⋊Dic3—42no—
132C2×C3⋊Dic3—41no—
133C2×C3×Dic3—24no—
134C2×C3×Dic3—24no—
135C2×C3×Dic3—24no—
136C2×C3×Dic3—24no—
137C2×C3×Dic3—24no—
138C2×C3×Dic3—24no—
139C2×C3×Dic3—42no—
140C2×C3×Dic3—42no—
141C2×C3×Dic3—42no—
142C2×C3×Dic3—42no—
143C2×C3×Dic3—42no—
144C2×C3×Dic3—42no—
145C2×C3×Dic3—42no—
146C2×C3×Dic3—42no—
147C22×C22⋊C4—91no—
148C22×C22⋊C4—91no—
149C22×C22⋊C4—91no—
150C2×#95—32no—
151C2×#95—92no—
152C24×C3—21no—
153C24×C3C22×D312yes—
154C23×D3—34no—
155C23×D3—34no—
156C23×D3—34no—
157C23×D3—62no—
158C23×D3—62no—
159C23×D3—62no—
160C23×D3—64no—
161C23×D3—64no—
162C23×D3—62no—
163C23×D3—62no—
164C23×D3—62no—
165C23×D3—62no—
166C23×D3—62no—
167C23×D3—62no—
168C23×D3—62no—
169C23×D3—62no—
170C23×D3—62no—
171C23×D3—62no—
172C23×D3—62no—
173C23×D3—62no—
174C23×D3—122no—
175C23×D3—122no—
176C23×D3—122no—
177C23×D3—122no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—34no—
188C22×C3×C4—34no—
189C22×C3×C4—42no—
190C22×C3×C4—42no—
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×C3×C4C4×D314yes—
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—22no—
216C22×Dic3—34no—
217C22×Dic3—62no—
218C22×Dic3—62no—
219C22×Dic3—62no—
220C22×Dic3—62no—
221C22×Dic3—62no—
222C22×Dic3—62no—
223C22×Dic3—62no—
224C22×Dic3—62no—
225C22×Dic3—62no—
226C22×Dic3—122no—
227C22×Dic3—122no—
228C22×Dic3D1214yes—
229C22×Dic3#6714yes—
230(C2×D3)⋊C4—616no—
231(C2×D3)⋊C4—616no—
232(C2×D3)⋊C4—616no—
233(C2×D3)⋊C4—616no—
234C22×C32C2×C22⋊C411yescharacteristic
235C22×C32#11711yescharacteristic
236C22×C32#11711yescharacteristic
237C22×C32C4×D412yes—
238C22×C32C4×D412yes—
239C22×C32#12011yescharacteristic
240C22×C32#12011yescharacteristic
241C22×C32#12112yes—
242C22×C32#12112yes—
243C22×C32#12112yes—
244C22×C32#12112yes—
245C22×C32#12311yescharacteristic
246C22×C32#12312yes—
247C22×C32#12312yes—
248C22×C32#12312yes—
249C22×C32#12311yescharacteristic
250C22×C32#12312yes—
251C22×C32#12412yes—
252C22×C32#12412yes—
253C22×C32#12612yes—
254C22×C32#12612yes—
255C2×C3⋊D3—24no—
256C2×C3⋊D3—24no—
257C2×C3⋊D3—24no—
258C2×C3⋊D3—44no—
259C2×C3⋊D3—44no—
260C2×C3⋊D3—44no—
261C2×C3⋊D3—44no—
262C2×C3⋊D3—44no—
263C2×C3⋊D3—44no—
264C32×C4—42no—
265C3⋊Dic3—42no—
266C3×Dic3—44no—
267C3×Dic3—44no—
268C25—91no—
269C23×C4—32no—
270C23×C4—32no—
271C23×C4—91no—
272C23×C4D3211yescharacteristic
273C2×C22⋊C4—94no—
274C2×C22⋊C4—182no—
275C2×C22⋊C4—182no—
276C2×C22⋊C4—184no—
277C2×C22⋊C4—184no—
278C2×C22⋊C4—182no—
279C2×C22⋊C4—182no—
280#95—64no—
281#95—184no—
282C23×C3—22no—
283C23×C3—22no—
284C23×C3—22no—
285C23×C3—22no—
286C23×C3—22no—
287C23×C3—21no—
288C23×C3—22no—
289C23×C3—21no—
290C23×C3—21no—
291C23×C3C2×C4×D312yes—
292C23×C3C2×D1212yes—
293C23×C3#23512yes—
294C23×C3#23512yes—
295C23×C3#23512yes—
296C23×C3#23512yes—
297C23×C3D3×D412yes—
298C23×C3D3×D412yes—
299C23×C3D3×D412yes—
300C23×C3D3×D412yes—
301C23×C3#23712yes—
302C23×C3#23712yes—
303C23×C3#23912yes—
304C23×C3#23912yes—
305C23×C3C2×#6712yes—
306C22×D3—38no—
307C22×D3—64no—
308C22×D3—64no—
309C22×D3—68no—
310C22×D3—68no—
311C22×D3—64no—
312C22×D3—64no—
313C22×D3—64no—
314C22×D3—64no—
315C22×D3—64no—
316C22×D3—64no—
317C22×D3—64no—
318C22×D3—64no—
319C22×D3—64no—
320C22×D3—64no—
321C22×D3—64no—
322C22×D3—64no—
323C22×D3—64no—
324C22×D3—64no—
325C22×D3—64no—
326C22×D3—64no—
327C22×D3—64no—
328C22×D3—64no—
329C22×D3—64no—
330C22×D3—124no—
331C22×D3—122no—
332C22×D3—124no—
333C22×D3—122no—
334C22×D3—124no—
335C22×D3—124no—
336C22×D3—122no—
337C22×D3—122no—
338C22×D3—124no—
339C22×D3—124no—
340C22×D3—124no—
341C22×D3—124no—
342C22×D3—124no—
343C22×D3—124no—
344C22×D3—124no—
345C22×D3—124no—
346C22×D3—122no—
347C22×D3—122no—
348C22×D3—122no—
349C22×D3—122no—
350C22×D3—122no—
351C22×D3—122no—
352C22×D3—122no—
353C22×D3—122no—
354C22×D3—122no—
355C22×D3—122no—
356C22×D3—122no—
357C22×D3—122no—
358C22×D3—122no—
359C22×D3—122no—
360C22×D3—122no—
361C22×D3—122no—
362C2×C3×C4—24no—
363C2×C3×C4—24no—
364C2×C3×C4—24no—
365C2×C3×C4—24no—
366C2×C3×C4—44no—
367C2×C3×C4—44no—
368C2×C3×C4—42no—
369C2×C3×C4—42no—
370C2×C3×C4—42no—
371C2×C3×C4—42no—
372C2×C3×C4—42no—
373C2×C3×C4—42no—
374C2×C3×C4—64no—
375C2×C3×C4—64no—
376C2×C3×C4—64no—
377C2×C3×C4—64no—
378C2×C3×C4—64no—
379C2×C3×C4—64no—
380C2×C3×C4—122no—
381C2×C3×C4—122no—
382C2×C3×C4—122no—
383C2×C3×C4—122no—
384C2×C3×C4—122no—
385C2×C3×C4—122no—
386C2×C3×C4—122no—
387C2×C3×C4—122no—
388C2×Dic3—24no—
389C2×Dic3—24no—
390C2×Dic3—24no—
391C2×Dic3—24no—
392C2×Dic3—24no—
393C2×Dic3—24no—
394C2×Dic3—42no—
395C2×Dic3—42no—
396C2×Dic3—42no—
397C2×Dic3—42no—
398C2×Dic3—42no—
399C2×Dic3—42no—
400C2×Dic3—42no—
401C2×Dic3—42no—
402C2×Dic3—64no—
403C2×Dic3—64no—
404C2×Dic3—64no—
405C2×Dic3—64no—
406C2×Dic3—124no—
407C2×Dic3—122no—
408C2×Dic3—124no—
409C2×Dic3—122no—
410C2×Dic3—122no—
411C2×Dic3—122no—
412C2×Dic3—122no—
413C2×Dic3—122no—
414C2×C32#38111yescharacteristic
415C2×C32#38611yescharacteristic
416C2×C32#38611yescharacteristic
417C2×C32#38812yes—
418C2×C32#38812yes—
419C2×C32#39412yes—
420C2×C32#39412yes—
421C2×C32#39712yes—
422C2×C32#39712yes—
423C3⋊D3—44no—
424C24—92no—
425C24—92no—
426C24—92no—
427C24—182no—
428C24—182no—
429C24—182no—
430C24—182no—
431C24—182no—
432C24—182no—
433C24C2×D3211yescharacteristic
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—34no—
439C22×C4—34no—
440C22×C4—62no—
441C22×C4—62no—
442C22×C4—62no—
443C22×C4—62no—
444C22×C4—62no—
445C22×C4—62no—
446C22×C4—62no—
447C22×C4—62no—
448C22×C4—62no—
449C22×C4—62no—
450C22×C4—62no—
451C22×C4—62no—
452C22×C4—92no—
453C22×C4—182no—
454C22×C4—182no—
455C22×C4—181no—
456C22×C4—181no—
457C22×C4#62412yes—
458C22⋊C4—188no—
459C22⋊C4—188no—
460C22⋊C4—188no—
461C22×C3—22no—
462C22×C3—21no—
463C22×C3—22no—
464C22×C3—22no—
465C22×C3—22no—
466C22×C3—22no—
467C22×C3—22no—
468C22×C3—21no—
469C22×C3—22no—
470C22×C3—22no—
471C22×C3—22no—
472C22×C3—21no—
473C22×C3—22no—
474C22×C3—22no—
475C22×C3—22no—
476C22×C3—21no—
477C22×C3—22no—
478C22×C3—22no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3#87212yes—
483C22×C3C4×D1212yes—
484C22×C3#87512yes—
485C22×C3#87612yes—
486C22×C3D3×C22⋊C412yes—
487C22×C3#67⋊C412yes—
488C22×C3#88212yes—
489C22×C3#88312yes—
490C22×C3#88312yes—
491C22×C3#88312yes—
492C22×C3#88412yes—
493C22×C3#88412yes—
494C22×C3#88412yes—
495C22×C3#88512yes—
496C22×C3#88512yes—
497C22×C3#88612yes—
498C22×C3#89212yes—
499C22×C3#89312yes—
500C22×C3#89412yes—
501C22×C3#89412yes—
502C22×C3#89412yes—
503C22×C3#89412yes—
504C22×C3#89412yes—
505C22×C3#89512yes—
506C22×C3#89512yes—
507C22×C3#89812yes—
508C22×C3#89812yes—
509C22×C3#89812yes—
510C22×C3C4×#6712yes—
511C22×C3#92912yes—
512C22×C3#93012yes—
513C22×C3#93712yes—
514C22×C3#93812yes—
515C22×C3#93912yes—
516C22×C3#94712yes—
517C2×D3—68no—
518C2×D3—68no—
519C2×D3—68no—
520C2×D3—68no—
521C2×D3—124no—
522C2×D3—124no—
523C2×D3—128no—
524C2×D3—128no—
525C2×D3—128no—
526C2×D3—128no—
527C2×D3—128no—
528C2×D3—128no—
529C2×D3—124no—
530C2×D3—124no—
531C2×D3—124no—
532C2×D3—124no—
533C2×D3—124no—
534C2×D3—124no—
535C2×D3—124no—
536C2×D3—124no—
537C2×D3—124no—
538C2×D3—124no—
539C2×D3—124no—
540C2×D3—124no—
541C3×C4—44no—
542C3×C4—44no—
543C3×C4—124no—
544C3×C4—124no—
545Dic3—44no—
546Dic3—44no—
547Dic3—124no—
548Dic3—124no—
549C32#144011yescharacteristic, complemented, Sylow
550C23—94no—
551C23—182no—
552C23—184no—
553C23—184no—
554C23—182no—
555C23—184no—
556C23—182no—
557C23—184no—
558C23—182no—
559C23—184no—
560C23—184no—
561C23—182no—
562C23—182no—
563C23—362no—
564C23—362no—
565C23—362no—
566C23—362no—
567C23—362no—
568C23—362no—
569C23—362no—
570C23—362no—
571C23#379612yes—
572C23#379812yes—
573C23#379912yes—
574C23D3×D1212yes—
575C23#380412yes—
576C23C2×#62411yescharacteristic
577C23D3×#6712yes—
578C23#381111yescharacteristic
579C23#381111yescharacteristic
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—64no—
586C2×C4—64no—
587C2×C4—64no—
588C2×C4—64no—
589C2×C4—64no—
590C2×C4—64no—
591C2×C4—122no—
592C2×C4—122no—
593C2×C4—122no—
594C2×C4—122no—
595C2×C4—122no—
596C2×C4—122no—
597C2×C4—122no—
598C2×C4—122no—
599C2×C4—184no—
600C2×C4—182no—
601C2×C4—361no—
602C2×C4—362no—
603C2×C4—361no—
604C2×C3—22no—
605C2×C3—22no—
606C2×C3—22no—
607C2×C3—21no—
608C2×C3—22no—
609C2×C3—22no—
610C2×C3—22no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3#466412yes—
614C2×C3#466512yes—
615C2×C3#466912yes—
616C2×C3#467012yes—
617C2×C3#467212yes—
618C2×C3#467412yes—
619C2×C3#467512yes—
620C2×C3#467512yes—
621C2×C3#494012yes—
622C2×C3#495612yes—
623C2×C3#495912yes—
624C2×C3#496112yes—
625C2×C3#499012yes—
626C2×C3#499112yes—
627C2×C3#499212yes—
628D3—128no—
629D3—128no—
630C22—184no—
631C22—184no—
632C22—184no—
633C22—364no—
634C22—364no—
635C22—364no—
636C22—364no—
637C22—364no—
638C22—364no—
639C22#6384812yes—
640C22#6384911yescharacteristic
641C22#6385012yes—
642C22#6385212yes—
643C22#6385312yes—
644C22#6385312yes—
645C22#6386812yes—
646C22#6387411yescharacteristic
647C22#6388612yes—
648C22#6389012yes—
649C22#6389412yes—
650C22#6389711yescharacteristic
651C22#6390612yes—
652C22#6390712yes—
653C22#6391012yes—
654C22#6392311yescharacteristic
655C22#6395212yes—
656C22#6395812yes—
657C22#6397411yescharacteristic
658C22#6397511yescharacteristic
659C22#6398311yescharacteristic
660C4—42no—
661C4—124no—
662C4—124no—
663C4—362no—
664C3—21no—
665C3#6942912yescomplemented
666C2—364no—
667C2#1059120212yes—
668C2#1059120412yes—
669C2#1059120812yes—
670C2#1059121911yescharacteristic
671C2#1059126612yes—
672C2#1059129112yes—
673C2#1059131212yes—
674C2#1059138011yescharacteristic
675C2#1059172211yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC23×C32C22×C4
FittingC23×C32×C4C22
socle, cosocleC24×C32C23
prime radicalC24×C3⋊D3C22
hypercenterC23×C4D32
hypocenterC32#1440
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. C2×C3×C3⋊#95C2semidirect
5. C2×#63579C2semidirect
14. C2×#3752C4semidirect
28. C2×C3⋊#95D3semidirect
549. C32#1440semidirect
665. C3#69429semidirect

Maximal subgroups

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

subgroupindex
C22×#37522
C22×#37222
C2×C3×C3⋊#952
C2×#635792
#694293