Finite Group Databasebeta

← #11864216

Subgroups — #11864216

Order 1152.

1953 conjugacy classes of subgroups.

The subgroup lattice has 687 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic
2C2×C3×#924C211yesmaximal, characteristic, complemented
3C2×#63833C212yesmaximal, complemented
4C3×#5207C211yesmaximal, characteristic, complemented
5#10591190C212yesmaximal, complemented
6#10591184C214yesmaximal, complemented
7#10591183C212yesmaximal, complemented
8#10591106C212yesmaximal, complemented
9#82735—31nomaximal
10#78640—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×#638—21no—
13C2×#3828—21no—
14C2×#3828—21no—
15C2×#3828—28no—
16C2×#3828C2212yes—
17C2×#3828C2212yes—
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4×C3⋊D3—21no—
20C22×#634C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic, complemented
22C2×C3×#217—21no—
23C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
24C3×#924—21no—
25C3×#924—21no—
26C3×#924C2212yes—
27C3×#924C2212yescomplemented
28C2×C3×Dic3⋊C4—21no—
29C2×C3×#208C2212yescomplemented
30C2×#3719C2214yescomplemented
31#63833—28no—
32C2×#3717C2214yescomplemented
33C3×#830C2212yes—
34C3×#830C2212yescomplemented
35#63567C2214yescomplemented
36#63564C2214yescomplemented
37C22×#235—31no—
38C22×#235—31no—
39C22×#235—61no—
40C2×C3×C22⋊Q8—31no—
41C2×#942—32no—
42C2×#924D311yescharacteristic, complemented
43C2×#909—32no—
44C3×#407—31no—
45#5207D311yescharacteristic, complemented
46#5133—32no—
47#5050—32no—
48#5047—34no—
49#5046—32no—
50#4966—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
63C2×#638—28no—
64C2×#638—22no—
65C2×#638—22no—
66C22×C3⋊Dic3—21no—
67#3828—28no—
68#3828—28no—
69#3828—24no—
70#3828—24no—
71#3828—24no—
72#3828D418yes—
73C2×C4⋊(C3⋊D3)—21no—
74C2×C4⋊(C3⋊D3)—24no—
75C2×C4⋊(C3⋊D3)C2312yes—
76C2×C4×C3⋊D3—28no—
77C2×C4×C3⋊D3—22no—
78C2×C4×C3⋊D3—22no—
79C2×#634—21no—
80C2×#634—24no—
81C2×#634C2312yes—
82C22×C3×Dic3—21no—
83C22×C3×Dic3—21no—
84C2×C3×Dic6—24no—
85C2×C3×Dic6—21no—
86C2×C3×Dic6C2312yes—
87C3×#217—22no—
88C3×#217—22no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2312yes—
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4—22no—
93C3×#208—24no—
94C2×C3×C3⋊C8C2314yes—
95#3719—28no—
96#3717—28no—
97#3007—91noSylow
98C22×C3×Q8—31no—
99C23×C3×C4—21no—
100C23×C3×C4C2×D311yescharacteristic
101C23×C3×C4C2×D311yescharacteristic
102C22×#67—62no—
103C22×#67—61no—
104C22×#67—61no—
105C2×#235—32no—
106C2×#235—32no—
107C2×#235—32no—
108C2×#235—32no—
109C2×#235—62no—
110C2×#235—62no—
111C2×#235—68no—
112C2×#235—68no—
113C2×#235—616no—
114C2×#235—62no—
115C2×#235—62no—
116C2×#235—61no—
117C2×#235—61no—
118C2×#235—61no—
119C2×#235—61no—
120C22×D12—31no—
121C22×D12—31no—
122C22×D12—61no—
123C22×C4×D3—62no—
124C22×C4×D3—61no—
125C22×C4×D3—61no—
126C22×Dic6—31no—
127C22×Dic6—31no—
128C22×Dic6—61no—
129C22×Dic6C2×D311yescharacteristic, complemented
130C2×C3×M16—32no—
131C3×C22⋊Q8—32no—
132C3×C22⋊Q8—32no—
133C3×C22⋊Q8—61no—
134C3×C22⋊Q8—61no—
135C2×C3×C4⋊C4—31no—
136C2×C3×C4⋊C4—61no—
137C2×C3×C22⋊C4—61no—
138C2×#217—21no—
139C2×#216—34no—
140#942—68no—
141C2×#215—34no—
142C2×C4⋊Dic3C2×D311yescharacteristic, complemented
143#924—21no—
144#924—21no—
145#924C2×D312yes—
146#924C2×D312yescomplemented
147C2×Dic3⋊C4—21no—
148C2×#208C2×D312yescomplemented
149#909—68no—
150C2×Dic12—34no—
151C2×#204—34no—
152C3×C22⋊C8—32no—
153C3×C22⋊C8—32no—
154#830C2×D312yes—
155#830C2×D312yescomplemented
156#821—34no—
157#816—34no—
158#810—34no—
159#809—34no—
160C23×C32—22no—
161C23×C32—22no—
162C23×C32—41no—
163C23×C32C2×D411yescharacteristic
164C23×C32C2×D411yescharacteristic
165C23×C32C2×D411yescharacteristic
166C22×C3⋊D3—24no—
167C22×C3⋊D3—22no—
168C22×C3⋊D3—42no—
169C22×C3⋊D3—42no—
170C2×C32×C4—22no—
171C2×C32×C4—22no—
172C2×C32×C4—22no—
173C2×C32×C4—22no—
174C2×C32×C4—22no—
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D414yes—
179C2×C32×C4C2411yescharacteristic
180#638—28no—
181#638—28no—
182C2×C3⋊Dic3—24no—
183C2×C3⋊Dic3—22no—
184C4⋊(C3⋊D3)—24no—
185C4⋊(C3⋊D3)—22no—
186C4⋊(C3⋊D3)C2×D414yes—
187C4×C3⋊D3—28no—
188C4×C3⋊D3—28no—
189#634—24no—
190#634—22no—
191#634C2×D414yes—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—42no—
195C2×C3×Dic3—42no—
196C3×Dic6—24no—
197C3×Dic6—42no—
198C3×C3⋊C8—24no—
199C22×#41—91no—
200C2×#137—92no—
201C2×C22⋊Q8—31no—
202#452—94no—
203#451—92no—
204#450—92no—
205#417—92no—
206#407—31no—
207C24×C3—21no—
208C24×C3D1211yescharacteristic
209C24×C3#6711yescharacteristic
210C23×D3—62no—
211C23×D3—61no—
212C23×D3—61no—
213C2×C3×Q8—32no—
214C2×C3×Q8—61no—
215C2×C3×Q8—64no—
216C22×C3×C4—28no—
217C22×C3×C4—24no—
218C22×C3×C4—24no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—61no—
226C22×C3×C4—61no—
227C22×C3×C4D1211yescharacteristic
228C22×C3×C4D1211yescharacteristic
229C22×C3×C4D1211yescharacteristic
230C22×C3×C4#6711yescharacteristic
231C22×C3×C4#6711yescharacteristic
232C22×C3×C4#6711yescharacteristic
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C22×C3×C4C22×D311yescharacteristic
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C22×C3×C4C22×D311yescharacteristic
239C2×#67—616no—
240C2×#67—68no—
241C2×#67—68no—
242C2×#67—64no—
243C2×#67—64no—
244C2×#67—62no—
245C2×#67—62no—
246C2×#67—62no—
247C2×#67—62no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—62no—
251C22×Dic3—61no—
252C22×Dic3—61no—
253#235—38no—
254#235—38no—
255#235—68no—
256#235—64no—
257#235—64no—
258#235—64no—
259#235—64no—
260#235—68no—
261#235—68no—
262#235—616no—
263#235—616no—
264#235—68no—
265#235—68no—
266#235—68no—
267#235—68no—
268#235—68no—
269#235—64no—
270#235—64no—
271C2×D12—32no—
272C2×D12—32no—
273C2×D12—62no—
274C2×D12—64no—
275C2×D12—64no—
276C2×D12—68no—
277C2×D12—62no—
278C2×D12—61no—
279C2×D12—61no—
280C2×C4×D3—616no—
281C2×C4×D3—68no—
282C2×C4×D3—68no—
283C2×C4×D3—64no—
284C2×C4×D3—64no—
285C2×C4×D3—62no—
286C2×C4×D3—62no—
287C2×C4×D3—62no—
288C2×C4×D3—62no—
289C2×Dic6—24no—
290C2×Dic6—21no—
291C2×Dic6—32no—
292C2×Dic6—32no—
293C2×Dic6—62no—
294C2×Dic6—64no—
295C2×Dic6—64no—
296C2×Dic6—68no—
297C2×Dic6—62no—
298C2×Dic6—61no—
299C2×Dic6—61no—
300C2×Dic6C22×D312yes—
301C3×M16—64no—
302C2×C3×C8—34no—
303C3×C4⋊C4—32no—
304C3×C4⋊C4—62no—
305C3×C4⋊C4—62no—
306C3×C4⋊C4—61no—
307C3×C22⋊C4—62no—
308C3×C22⋊C4—62no—
309#217—22no—
310#217—22no—
311#216—68no—
312#215—68no—
313C4⋊Dic3—21no—
314C4⋊Dic3C22×D312yes—
315Dic3⋊C4—22no—
316Dic3⋊C4—22no—
317#208—24no—
318C2×C3⋊C8C22×D314yes—
319Dic12—68no—
320#204—68no—
321C22×C32—21no—
322C22×C32—21no—
323C22×C32—21no—
324C22×C32—21no—
325C22×C32—21no—
326C22×C32—21no—
327C22×C32—21no—
328C22×C32—44no—
329C22×C32#12012yes—
330C22×C32#13712yescomplemented
331C22×C32C22×D411yescharacteristic
332C2×C3⋊D3—24no—
333C2×C3⋊D3—48no—
334C2×C3⋊D3—42no—
335C2×C3⋊D3—42no—
336C32×C4—21no—
337C32×C4—21no—
338C32×C4#12012yes—
339C32×C4C22×D412yes—
340C3⋊Dic3—24no—
341C3×Dic3—42no—
342C3×Dic3—42no—
343C2×#41—92no—
344C2×#41—92no—
345C2×#41—188no—
346C2×#41—181no—
347C2×#41—181no—
348C22×Q8—31no—
349C22×Q8—91no—
350C22×D4—91no—
351C22×D4—181no—
352C23×C4—181no—
353C23×C4D3211yescharacteristic
354#137—188no—
355C2×Q16—94no—
356C2×SD16—94no—
357C2×M16—32no—
358C22⋊Q8—32no—
359C22⋊Q8—32no—
360C22⋊Q8—61no—
361C22⋊Q8—61no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—61no—
364C2×C22⋊C4—61no—
365#103—94no—
366#102—94no—
367C22⋊C8—32no—
368C22⋊C8—32no—
369C23×C3—24no—
370C23×C3—22no—
371C23×C3—22no—
372C23×C3—22no—
373C23×C3—22no—
374C23×C3—21no—
375C23×C3—21no—
376C23×C3—21no—
377C23×C3—42no—
378C23×C3—41no—
379C23×C3—41no—
380C23×C3—42no—
381C23×C3C2×D1211yescharacteristic
382C23×C3C2×D1211yescharacteristic
383C23×C3C2×D1211yescharacteristic
384C23×C3C2×#6711yescharacteristic
385C23×C3C2×#6711yescharacteristic
386C23×C3C2×#6711yescharacteristic
387C22×D3—68no—
388C22×D3—64no—
389C22×D3—64no—
390C22×D3—64no—
391C22×D3—62no—
392C22×D3—62no—
393C22×D3—124no—
394C22×D3—122no—
395C22×D3—122no—
396C22×D3—124no—
397C22×D3—122no—
398C22×D3—122no—
399C3×Q8—64no—
400C3×Q8—122no—
401C2×C3×C4—24no—
402C2×C3×C4—24no—
403C2×C3×C4—24no—
404C2×C3×C4—24no—
405C2×C3×C4—24no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—24no—
421C2×C3×C4—62no—
422C2×C3×C4—62no—
423C2×C3×C4—122no—
424C2×C3×C4—122no—
425C2×C3×C4C2×D1211yescharacteristic
426C2×C3×C4C2×D1211yescharacteristic
427C2×C3×C4C2×D1211yescharacteristic
428C2×C3×C4D3×D414yes—
429C2×C3×C4D3×D414yes—
430C2×C3×C4C2×#6711yescharacteristic
431C2×C3×C4C2×#6711yescharacteristic
432C2×C3×C4C2×#6711yescharacteristic
433C2×C3×C4C23×D311yescharacteristic
434C2×C3×C4C23×D311yescharacteristic
435#67—616no—
436#67—68no—
437#67—68no—
438#67—616no—
439#67—68no—
440#67—68no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—42no—
444C2×Dic3—42no—
445C2×Dic3—68no—
446C2×Dic3—64no—
447C2×Dic3—64no—
448C2×Dic3—64no—
449C2×Dic3—62no—
450C2×Dic3—62no—
451D12—34no—
452D12—34no—
453D12—64no—
454D12—68no—
455D12—64no—
456D12—64no—
457D12—64no—
458D12—62no—
459D12—62no—
460C4×D3—616no—
461C4×D3—68no—
462C4×D3—68no—
463C4×D3—616no—
464C4×D3—68no—
465C4×D3—68no—
466Dic6—24no—
467Dic6—34no—
468Dic6—34no—
469Dic6—42no—
470Dic6—64no—
471Dic6—68no—
472Dic6—64no—
473Dic6—64no—
474Dic6—64no—
475Dic6—62no—
476Dic6—62no—
477C3×C8—64no—
478C3⋊C8—24no—
479C2×C32—22no—
480C2×C32—22no—
481C2×C32—41no—
482C2×C32C2×#12011yescharacteristic
483C2×C32C2×#13711yescharacteristic
484C2×C32#57511yescharacteristic
485C3⋊D3—44no—
486C24—181no—
487C24#62611yescharacteristic
488#41—98no—
489#41—184no—
490#41—184no—
491#41—188no—
492#41—188no—
493#41—184no—
494C2×Q8—32no—
495C2×Q8—61no—
496C2×Q8—64no—
497C2×Q8—92no—
498C2×Q8—184no—
499C2×Q8—181no—
500C2×D4—92no—
501C2×D4—184no—
502C2×D4—188no—
503C2×D4—182no—
504C2×D4—182no—
505C2×D4—181no—
506C22×C4—24no—
507C22×C4—61no—
508C22×C4—61no—
509C22×C4—188no—
510C22×C4—181no—
511C22×C4—182no—
512C22×C4—182no—
513C22×C4#62611yescharacteristic
514C22×C4#62611yescharacteristic
515C22×C4#62611yescharacteristic
516C22×C4C2×D3211yescharacteristic
517C22×C4C2×D3211yescharacteristic
518C22×C4C2×D3211yescharacteristic
519Q16—188no—
520SD16—188no—
521M16—64no—
522C2×C8—34no—
523C4⋊C4—32no—
524C4⋊C4—61no—
525C4⋊C4—62no—
526C4⋊C4—62no—
527C22⋊C4—62no—
528C22⋊C4—62no—
529C22×C3—22no—
530C22×C3—22no—
531C22×C3—21no—
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—21no—
537C22×C3—21no—
538C22×C3—21no—
539C22×C3—22no—
540C22×C3—21no—
541C22×C3—21no—
542C22×C3—21no—
543C22×C3—21no—
544C22×C3—21no—
545C22×C3—21no—
546C22×C3—21no—
547C22×C3—22no—
548C22×C3—22no—
549C22×C3—41no—
550C22×C3—41no—
551C22×C3—41no—
552C22×C3—41no—
553C22×C3—44no—
554C22×C3—44no—
555C22×C3—48no—
556C22×C3#88212yes—
557C22×C3#90912yescomplemented
558C22×C3#93712yes—
559C22×C3#94212yescomplemented
560C22×C3C22×D1211yescharacteristic
561C22×C3C22×#6711yescharacteristic
562C2×D3—68no—
563C2×D3—64no—
564C2×D3—64no—
565C2×D3—1216no—
566C2×D3—128no—
567C2×D3—128no—
568C2×D3—124no—
569C2×D3—124no—
570C2×D3—122no—
571C2×D3—122no—
572C2×D3—122no—
573C2×D3—122no—
574C3×C4—22no—
575C3×C4—22no—
576C3×C4—21no—
577C3×C4—21no—
578C3×C4—21no—
579C3×C4—21no—
580C3×C4—22no—
581C3×C4—22no—
582C3×C4—122no—
583C3×C4—122no—
584C3×C4#88212yes—
585C3×C4#93712yes—
586C3×C4C2×D3×D412yes—
587C3×C4C2×D3×D412yes—
588Dic3—42no—
589Dic3—42no—
590Dic3—68no—
591Dic3—64no—
592Dic3—64no—
593C32#300711yescharacteristic, complemented, Sylow
594C23—22no—
595C23—22no—
596C23—41no—
597C23—184no—
598C23—182no—
599C23—362no—
600C23—362no—
601C23C2×#62611yescharacteristic
602C23C2×#62611yescharacteristic
603C23C2×#62611yescharacteristic
604Q8—64no—
605Q8—94no—
606Q8—122no—
607Q8—184no—
608Q8—182no—
609D4—94no—
610D4—184no—
611D4—188no—
612D4—188no—
613D4—182no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—62no—
620C2×C4—62no—
621C2×C4—122no—
622C2×C4—122no—
623C2×C4—188no—
624C2×C4—184no—
625C2×C4—182no—
626C2×C4—188no—
627C2×C4C2×#62611yescharacteristic
628C2×C4C2×#62611yescharacteristic
629C2×C4C2×#62611yescharacteristic
630C2×C4#381114yes—
631C2×C4C22×D3211yescharacteristic
632C8—64no—
633C2×C3—24no—
634C2×C3—22no—
635C2×C3—22no—
636C2×C3—22no—
637C2×C3—22no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—21no—
641C2×C3—42no—
642C2×C3—42no—
643C2×C3—41no—
644C2×C3—41no—
645C2×C3C2×#88211yescharacteristic
646C2×C3C2×#90911yescharacteristic
647C2×C3#574811yescharacteristic
648C2×C3C2×#93711yescharacteristic
649C2×C3C2×#94211yescharacteristic
650C2×C3#582211yescharacteristic
651D3—128no—
652D3—124no—
653D3—124no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—44no—
662C22—184no—
663C22—368no—
664C22—362no—
665C22—362no—
666C22#6383312yescomplemented
667C22#6398112yes—
668C22C22×#62611yescharacteristic
669C4—21no—
670C4—21no—
671C4—122no—
672C4—122no—
673C4—184no—
674C4#6398112yes—
675C4C2×#381112yes—
676C3—21no—
677C3#7864011yescharacteristic, complemented
678C3#8273511yescharacteristic, complemented
679C2—22no—
680C2—22no—
681C2—41no—
682C2—364no—
683C2#1059479511yescharacteristic
684C2C2×#6383311yescharacteristic
685C2C2×#6398111yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC22×C32C22×D4
prime radicalC22×#3828C2
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×C3×#924C2semidirect
3. C2×#63833C2semidirect
4. C3×#5207C2semidirect
5. #10591190C2semidirect
6. #10591184C2semidirect
7. #10591183C2semidirect
8. #10591106C2semidirect
21. C22×C3×Dic6C22semidirect
23. C2×C3×C4⋊Dic3C22semidirect
27. C3×#924C22semidirect
29. C2×C3×#208C22semidirect
30. C2×#3719C22semidirect
32. C2×#3717C22semidirect
34. C3×#830C22semidirect
35. #63567C22semidirect
36. #63564C22semidirect
42. C2×#924D3semidirect
45. #5207D3semidirect
129. C22×Dic6C2×D3semidirect
142. C2×C4⋊Dic3C2×D3semidirect
146. #924C2×D3semidirect
148. C2×#208C2×D3semidirect
155. #830C2×D3semidirect
330. C22×C32#137semidirect
557. C22×C3#909semidirect
559. C22×C3#942semidirect
593. C32#3007semidirect
666. C22#63833semidirect
677. C3#78640semidirect
678. C3#82735semidirect

Maximal subgroups

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

subgroupindex
C22×#38282
C2×C3×#9242
C2×#638332
C3×#52072
#105911902
#105911842
#105911832
#105911062
#827353
#786403