Finite Group Databasebeta

← #11864215

Subgroups — #11864215

Order 1152.

1669 conjugacy classes of subgroups.

The subgroup lattice has 663 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic
2C2×#64133C211yesmaximal, characteristic, complemented
3C2×#63831C212yesmaximal, complemented
4C3×#5207C211yesmaximal, characteristic, complemented
5#10591186C212yesmaximal, complemented
6#10591173C214yesmaximal, complemented
7#10591172C212yesmaximal, complemented
8#10591088C212yesmaximal, complemented
9#84084—31nomaximal
10#78640—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×#634C2211yescharacteristic, complemented
13C22×C3×#67—21no—
14C2×C3×#235—21no—
15C2×C3×#235—21no—
16C2×C3×#235—28no—
17C2×C3×#235C2212yes—
18C2×C3×#235C2212yes—
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3—21no—
21C22×C3×Dic6C2211yescharacteristic
22C2×#3757—21no—
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
24#64133—21no—
25#64133—21no—
26#64133C2212yes—
27#64133C2212yescomplemented
28C2×#3750—21no—
29C2×C3×#208C2212yescomplemented
30C2×#3719C2214yescomplemented
31#63831—28no—
32C2×#3716C2214yescomplemented
33C3×#830C2212yes—
34C3×#830C2212yescomplemented
35#63566C2214yescomplemented
36#63563C2214yescomplemented
37C22×C3×#41—31no—
38C22×#235D311yescharacteristic
39C2×#951—32no—
40C2×#924—31no—
41C2×#924—31no—
42C2×#924—61no—
43C2×#909—32no—
44C3×#407—31no—
45#5239—34no—
46#5232—32no—
47#5228—32no—
48#5218—32no—
49#5207D311yescharacteristic, complemented
50#5133—32no—
51#4739—32no—
52#4733—34no—
53#4731—32no—
54C24×C32D411yescharacteristic
55C23×C3×D3—21no—
56C22×C32×C4—24no—
57C22×C32×C4D411yescharacteristic
58C22×C32×C4D411yescharacteristic
59C22×C32×C4D411yescharacteristic
60C22×C32×C4C2311yescharacteristic
61C22×C32×C4C2311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C3⋊Dic3—21no—
64C22×C3⋊Dic3—21no—
65C2×#634—24no—
66C2×#634—21no—
67C2×#634C2312yes—
68C2×C3×#67—28no—
69C2×C3×#67—22no—
70C2×C3×#67—22no—
71C22×C3×Dic3—21no—
72C3×#235—28no—
73C3×#235—28no—
74C3×#235—24no—
75C3×#235—24no—
76C3×#235—24no—
77C3×#235D418yes—
78C2×C3×D12—21no—
79C2×C3×D12—24no—
80C2×C3×D12C2312yes—
81C2×C3×C4×D3—28no—
82C2×C3×C4×D3—22no—
83C2×C3×C4×D3—22no—
84C2×C3×Dic6—21no—
85C2×C3×Dic6—24no—
86C2×C3×Dic6C2312yes—
87#3757—22no—
88#3757—22no—
89C4⋊(C3⋊Dic3)—21no—
90C4⋊(C3⋊Dic3)C2312yes—
91#3750—22no—
92#3750—22no—
93C3×#208—24no—
94C2×C3×C3⋊C8C2314yes—
95#3719—28no—
96#3716—28no—
97#3007—91noSylow
98C2×C3×#41—32no—
99C2×C3×#41—32no—
100C2×C3×#41—68no—
101C2×C3×#41—61no—
102C2×C3×#41—61no—
103C22×C3×Q8—31no—
104C22×C3×D4—31no—
105C22×C3×D4—61no—
106C23×C3×C4—21no—
107C23×C3×C4—61no—
108C23×C3×C4C2×D311yescharacteristic
109C23×C3×C4C2×D311yescharacteristic
110C22×#67—21no—
111C2×#235—21no—
112C2×#235—21no—
113C2×#235—28no—
114C2×#235C2×D312yes—
115C2×#235C2×D312yes—
116C22×D12C2×D311yescharacteristic
117C22×C4×D3—21no—
118C22×Dic6—31no—
119C22×Dic6—31no—
120C22×Dic6—61no—
121C22×Dic6C2×D311yescharacteristic
122C2×C3×M16—32no—
123C2×#217—62no—
124C2×#217—61no—
125C2×#217—61no—
126#951—68no—
127C2×#216—34no—
128C2×#214—34no—
129C2×C4⋊Dic3—31no—
130C2×C4⋊Dic3—31no—
131C2×C4⋊Dic3—61no—
132#924—32no—
133#924—32no—
134#924—32no—
135#924—32no—
136#924—62no—
137#924—62no—
138#924—62no—
139#924—62no—
140#924—61no—
141#924—61no—
142#924—61no—
143#924—61no—
144C2×Dic3⋊C4—62no—
145C2×Dic3⋊C4—61no—
146C2×Dic3⋊C4—61no—
147C2×#208C2×D312yescomplemented
148#909—68no—
149C2×Dic12—34no—
150C2×#204—34no—
151C3×C22⋊C8—32no—
152C3×C22⋊C8—32no—
153#835—34no—
154#832—34no—
155#830C2×D312yes—
156#830C2×D312yescomplemented
157#821—34no—
158#816—34no—
159C23×C32—22no—
160C23×C32—22no—
161C23×C32—41no—
162C23×C32C2×D411yescharacteristic
163C23×C32C2×D411yescharacteristic
164C23×C32C2×D411yescharacteristic
165C22×C3×D3—24no—
166C22×C3×D3—22no—
167C22×C3×D3—42no—
168C22×C3×D3—42no—
169C2×C32×C4—22no—
170C2×C32×C4—22no—
171C2×C32×C4—22no—
172C2×C32×C4—22no—
173C2×C32×C4—22no—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D414yes—
178C2×C32×C4C2411yescharacteristic
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—22no—
181C2×C3⋊Dic3—42no—
182C2×C3⋊Dic3—42no—
183#634—24no—
184#634—42no—
185C3×#67—28no—
186C3×#67—28no—
187C2×C3×Dic3—24no—
188C2×C3×Dic3—22no—
189C3×D12—24no—
190C3×D12—22no—
191C3×D12C2×D414yes—
192C3×C4×D3—28no—
193C3×C4×D3—28no—
194C3×Dic6—24no—
195C3×Dic6—22no—
196C3×Dic6C2×D414yes—
197C3×C3⋊C8—24no—
198C22×#41—31no—
199C2×#137—92no—
200C2×C22⋊Q8—91no—
201#452—94no—
202#451—92no—
203#450—92no—
204#417—92no—
205#407—31no—
206C24×C3—21no—
207C24×C3—61no—
208C24×C3D1211yescharacteristic
209C24×C3#6711yescharacteristic
210C23×D3—21no—
211C3×#41—38no—
212C3×#41—64no—
213C3×#41—64no—
214C3×#41—68no—
215C3×#41—68no—
216C3×#41—64no—
217C2×C3×Q8—32no—
218C2×C3×Q8—64no—
219C2×C3×Q8—61no—
220C2×C3×D4—32no—
221C2×C3×D4—64no—
222C2×C3×D4—68no—
223C2×C3×D4—62no—
224C2×C3×D4—62no—
225C2×C3×D4—61no—
226C22×C3×C4—24no—
227C22×C3×C4—24no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—44no—
235C22×C3×C4—68no—
236C22×C3×C4—61no—
237C22×C3×C4—62no—
238C22×C3×C4—62no—
239C22×C3×C4D1211yescharacteristic
240C22×C3×C4D1211yescharacteristic
241C22×C3×C4D1211yescharacteristic
242C22×C3×C4#6711yescharacteristic
243C22×C3×C4#6711yescharacteristic
244C22×C3×C4#6711yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C22×C3×C4C22×D311yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C2×#67—28no—
252C2×#67—22no—
253C2×#67—22no—
254C22×Dic3—21no—
255C22×Dic3—62no—
256C22×Dic3—62no—
257C22×Dic3—61no—
258C22×Dic3—61no—
259C22×Dic3—61no—
260C22×Dic3—61no—
261#235—28no—
262#235—28no—
263#235—24no—
264#235—24no—
265#235—24no—
266#235#6718yes—
267C2×D12—21no—
268C2×D12—24no—
269C2×D12C22×D312yes—
270C2×C4×D3—28no—
271C2×C4×D3—22no—
272C2×C4×D3—22no—
273C2×Dic6—21no—
274C2×Dic6—24no—
275C2×Dic6—32no—
276C2×Dic6—32no—
277C2×Dic6—62no—
278C2×Dic6—64no—
279C2×Dic6—64no—
280C2×Dic6—62no—
281C2×Dic6—61no—
282C2×Dic6—61no—
283C2×Dic6—124no—
284C2×Dic6C22×D312yes—
285C3×M16—64no—
286C2×C3×C8—34no—
287#217—64no—
288#217—64no—
289#217—62no—
290#217—62no—
291#217—62no—
292#217—62no—
293#216—68no—
294#214—68no—
295C4⋊Dic3—32no—
296C4⋊Dic3—32no—
297C4⋊Dic3—62no—
298C4⋊Dic3—62no—
299C4⋊Dic3—61no—
300C4⋊Dic3—61no—
301Dic3⋊C4—64no—
302Dic3⋊C4—64no—
303Dic3⋊C4—62no—
304Dic3⋊C4—62no—
305Dic3⋊C4—62no—
306Dic3⋊C4—62no—
307#208—24no—
308C2×C3⋊C8C22×D314yes—
309Dic12—68no—
310#204—68no—
311C22×C32—21no—
312C22×C32—21no—
313C22×C32—21no—
314C22×C32—21no—
315C22×C32—21no—
316C22×C32—21no—
317C22×C32—21no—
318C22×C32—44no—
319C22×C32#12012yes—
320C22×C32#13712yescomplemented
321C22×C32C22×D411yescharacteristic
322C2×C3×D3—24no—
323C2×C3×D3—48no—
324C2×C3×D3—42no—
325C2×C3×D3—42no—
326C32×C4—21no—
327C32×C4—21no—
328C32×C4#12012yes—
329C32×C4C22×D412yes—
330C3⋊Dic3—42no—
331C3⋊Dic3—42no—
332C3×Dic3—24no—
333C2×#41—32no—
334C2×#41—32no—
335C2×#41—68no—
336C2×#41—61no—
337C2×#41—61no—
338C22×Q8—31no—
339C22×Q8—91no—
340C22×D4—31no—
341C22×D4—61no—
342C23×C4—61no—
343C23×C4D3211yescharacteristic
344#137—188no—
345C2×Q16—94no—
346C2×SD16—94no—
347C2×M16—32no—
348C22⋊Q8—92no—
349C22⋊Q8—92no—
350C22⋊Q8—181no—
351C22⋊Q8—181no—
352C2×C4⋊C4—91no—
353C2×C4⋊C4—181no—
354C2×C22⋊C4—181no—
355#103—94no—
356#102—94no—
357C22⋊C8—32no—
358C22⋊C8—32no—
359C23×C3—24no—
360C23×C3—22no—
361C23×C3—22no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—21no—
365C23×C3—21no—
366C23×C3—21no—
367C23×C3—42no—
368C23×C3—41no—
369C23×C3—41no—
370C23×C3—42no—
371C23×C3—64no—
372C23×C3—62no—
373C23×C3—122no—
374C23×C3—122no—
375C23×C3C2×D1211yescharacteristic
376C23×C3C2×D1211yescharacteristic
377C23×C3C2×D1211yescharacteristic
378C23×C3C2×#6711yescharacteristic
379C23×C3C2×#6711yescharacteristic
380C23×C3C2×#6711yescharacteristic
381C22×D3—24no—
382C22×D3—22no—
383C22×D3—42no—
384C22×D3—42no—
385C3×Q8—34no—
386C3×Q8—64no—
387C3×Q8—62no—
388C3×D4—34no—
389C3×D4—64no—
390C3×D4—68no—
391C3×D4—68no—
392C3×D4—62no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—24no—
408C2×C3×C4—42no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4—42no—
412C2×C3×C4—42no—
413C2×C3×C4—68no—
414C2×C3×C4—64no—
415C2×C3×C4—62no—
416C2×C3×C4—68no—
417C2×C3×C4C2×D1211yescharacteristic
418C2×C3×C4C2×D1211yescharacteristic
419C2×C3×C4C2×D1211yescharacteristic
420C2×C3×C4D3×D414yes—
421C2×C3×C4C2×#6711yescharacteristic
422C2×C3×C4C2×#6711yescharacteristic
423C2×C3×C4C2×#6711yescharacteristic
424C2×C3×C4C2×#6714yes—
425C2×C3×C4C23×D311yescharacteristic
426C2×C3×C4C23×D311yescharacteristic
427#67—28no—
428#67—28no—
429C2×Dic3—24no—
430C2×Dic3—22no—
431C2×Dic3—64no—
432C2×Dic3—64no—
433C2×Dic3—62no—
434C2×Dic3—62no—
435C2×Dic3—62no—
436C2×Dic3—62no—
437C2×Dic3—124no—
438C2×Dic3—124no—
439C2×Dic3—122no—
440C2×Dic3—122no—
441C2×Dic3—122no—
442C2×Dic3—122no—
443D12—24no—
444D12—22no—
445D12C2×#6714yes—
446C4×D3—28no—
447C4×D3—28no—
448Dic6—24no—
449Dic6—22no—
450Dic6—64no—
451Dic6—64no—
452Dic6—124no—
453Dic6—124no—
454Dic6—122no—
455Dic6—122no—
456Dic6C2×#6714yes—
457C3×C8—64no—
458C3⋊C8—24no—
459C2×C32—22no—
460C2×C32—22no—
461C2×C32—41no—
462C2×C32C2×#12011yescharacteristic
463C2×C32C2×#13711yescharacteristic
464C2×C32#57511yescharacteristic
465C3×D3—44no—
466C24—61no—
467C24#62611yescharacteristic
468#41—38no—
469#41—64no—
470#41—64no—
471#41—68no—
472#41—68no—
473#41—64no—
474C2×Q8—32no—
475C2×Q8—64no—
476C2×Q8—61no—
477C2×Q8—92no—
478C2×Q8—181no—
479C2×Q8—184no—
480C2×D4—32no—
481C2×D4—64no—
482C2×D4—68no—
483C2×D4—62no—
484C2×D4—62no—
485C2×D4—61no—
486C22×C4—24no—
487C22×C4—68no—
488C22×C4—61no—
489C22×C4—62no—
490C22×C4—62no—
491C22×C4—181no—
492C22×C4—181no—
493C22×C4#62611yescharacteristic
494C22×C4#62611yescharacteristic
495C22×C4#62611yescharacteristic
496C22×C4C2×D3211yescharacteristic
497C22×C4C2×D3211yescharacteristic
498C22×C4C2×D3211yescharacteristic
499Q16—188no—
500SD16—188no—
501M16—64no—
502C2×C8—34no—
503C4⋊C4—92no—
504C4⋊C4—181no—
505C4⋊C4—182no—
506C4⋊C4—182no—
507C22⋊C4—182no—
508C22⋊C4—182no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—22no—
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—21no—
523C22×C3—21no—
524C22×C3—21no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—22no—
528C22×C3—22no—
529C22×C3—41no—
530C22×C3—41no—
531C22×C3—41no—
532C22×C3—41no—
533C22×C3—44no—
534C22×C3—44no—
535C22×C3—48no—
536C22×C3—64no—
537C22×C3—128no—
538C22×C3—122no—
539C22×C3—122no—
540C22×C3#88212yes—
541C22×C3#90912yescomplemented
542C22×C3#95112yescomplemented
543C22×C3#95312yes—
544C22×C3C22×D1211yescharacteristic
545C22×C3C22×#6711yescharacteristic
546C2×D3—24no—
547C2×D3—48no—
548C2×D3—42no—
549C2×D3—42no—
550C3×C4—21no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—21no—
554C3×C4—22no—
555C3×C4—22no—
556C3×C4—41no—
557C3×C4—41no—
558C3×C4—64no—
559C3×C4#88212yes—
560C3×C4#95312yes—
561C3×C4C2×D3×D412yes—
562C3×C4C22×#6712yes—
563Dic3—24no—
564Dic3—124no—
565Dic3—124no—
566Dic3—122no—
567Dic3—122no—
568Dic3—122no—
569Dic3—122no—
570C32#300711yescharacteristic, complemented, Sylow
571C23—22no—
572C23—22no—
573C23—41no—
574C23—64no—
575C23—62no—
576C23—122no—
577C23—122no—
578C23C2×#62611yescharacteristic
579C23C2×#62611yescharacteristic
580C23C2×#62611yescharacteristic
581Q8—34no—
582Q8—64no—
583Q8—62no—
584Q8—184no—
585Q8—362no—
586D4—34no—
587D4—64no—
588D4—68no—
589D4—68no—
590D4—62no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—68no—
597C2×C4—64no—
598C2×C4—62no—
599C2×C4—68no—
600C2×C4—182no—
601C2×C4—182no—
602C2×C4—362no—
603C2×C4—362no—
604C2×C4C2×#62611yescharacteristic
605C2×C4C2×#62611yescharacteristic
606C2×C4C2×#62611yescharacteristic
607C2×C4D3×#6714yes—
608C2×C4C22×D3211yescharacteristic
609C8—64no—
610C2×C3—24no—
611C2×C3—22no—
612C2×C3—22no—
613C2×C3—22no—
614C2×C3—22no—
615C2×C3—21no—
616C2×C3—21no—
617C2×C3—21no—
618C2×C3—42no—
619C2×C3—42no—
620C2×C3—41no—
621C2×C3—41no—
622C2×C3—124no—
623C2×C3C2×#88211yescharacteristic
624C2×C3C2×#90911yescharacteristic
625C2×C3#574811yescharacteristic
626C2×C3#582211yescharacteristic
627C2×C3C2×#95111yescharacteristic
628C2×C3C2×#95311yescharacteristic
629D3—44no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22—21no—
635C22—21no—
636C22—21no—
637C22—44no—
638C22—64no—
639C22—128no—
640C22—122no—
641C22—122no—
642C22#6383112yescomplemented
643C22#6397712yes—
644C22C22×#62611yescharacteristic
645C4—21no—
646C4—21no—
647C4—64no—
648C4—362no—
649C4—362no—
650C4#6397712yes—
651C4C2×D3×#6712yes—
652C3—21no—
653C3#7864011yescharacteristic, complemented
654C3#8408411yescharacteristic, complemented
655C2—22no—
656C2—22no—
657C2—41no—
658C2—124no—
659C2C2×#6383111yescharacteristic
660C2#1059479511yescharacteristic
661C2C2×#6397711yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC22×C32C22×D4
prime radicalC22×C3×#235C2
hypercenterC23×C4D32
hypocenterC32#3007
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×#64133C2semidirect
3. C2×#63831C2semidirect
4. C3×#5207C2semidirect
5. #10591186C2semidirect
6. #10591173C2semidirect
7. #10591172C2semidirect
8. #10591088C2semidirect
12. C22×#634C22semidirect
23. C2×C4⋊(C3⋊Dic3)C22semidirect
27. #64133C22semidirect
29. C2×C3×#208C22semidirect
30. C2×#3719C22semidirect
32. C2×#3716C22semidirect
34. C3×#830C22semidirect
35. #63566C22semidirect
36. #63563C22semidirect
49. #5207D3semidirect
147. C2×#208C2×D3semidirect
156. #830C2×D3semidirect
320. C22×C32#137semidirect
541. C22×C3#909semidirect
542. C22×C3#951semidirect
570. C32#3007semidirect
642. C22#63831semidirect
653. C3#78640semidirect
654. C3#84084semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C2×#641332
C2×#638312
C3×#52072
#105911862
#105911732
#105911722
#105910882
#840843
#786403