Finite Group Databasebeta

← #11865321

Subgroups — #11865321

Order 1152.

1697 conjugacy classes of subgroups.

The subgroup lattice has 665 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5964C211yesmaximal, characteristic, complemented
2#10596299C211yesmaximal, characteristic, complemented
3#10595034C212yesmaximal, complemented
4C3×#5240C211yesmaximal, characteristic, complemented
5#10591534C214yesmaximal, complemented
6#10591531C214yesmaximal, complemented
7#10591231C212yesmaximal, complemented
8#84125—31nomaximal
9#78690—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×C4×C3⋊D3C2211yescharacteristic, complemented
12C3×#1010—22no—
13C3×#1009—22no—
14C3×D3×#41—24no—
15C3×#1007—21no—
16C3×#1004—21no—
17C3×#1004C2214yes—
18C2×C3×#235—22no—
19C2×C3×#235C2212yes—
20#64155—21no—
21#64147—21no—
22#64146C2212yescomplemented
23#64144C2212yescomplemented
24C4×#638—22no—
25#64135C2211yescharacteristic, complemented
26C3×#926C2212yescomplemented
27#63981C2214yescomplemented
28#63962C2214yescomplemented
29#63916—22no—
30C4×#626—24no—
31#63871—22no—
32C3×#834C2214yescomplemented
33#63580C2218yescomplemented
34C3×#585—31no—
35#5964D311yescharacteristic, complemented
36#5828—31no—
37#5828—31no—
38#5828—32no—
39#5828—61no—
40#5524—32no—
41C3×#410—31no—
42#5244—34no—
43#5243—34no—
44#5240—32no—
45#5240D311yescharacteristic, complemented
46#5006—32no—
47#4742—34no—
48#4741—34no—
49C23×C3⋊D3C2311yescharacteristic
50C32×#41—22no—
51C32×#41—22no—
52C2×C32×Q8D411yescharacteristic, complemented
53C2×C32×D4D411yescharacteristic, complemented
54C2×C32×D4C2312yes—
55C22×C32×C4D412yescomplemented
56C22×C32×C4C2311yescharacteristic
57C2×#638—22no—
58C22×C3⋊Dic3C2311yescharacteristic
59C2×C4×C3⋊D3—21no—
60C2×C4×C3⋊D3—21no—
61C2×C4×C3⋊D3—22no—
62C2×C4×C3⋊D3—22no—
63C2×C3×#67—24no—
64C2×C3×#67C2314yes—
65C3×#239—24no—
66C3×D3×Q8—24no—
67C3×#237—24no—
68C3×#237—28no—
69C3×D3×D4—24no—
70C3×D3×D4—28no—
71C3×#235—24no—
72C3×#235—24no—
73C3×#235—22no—
74C3×#235—24no—
75C3×#235—22no—
76C3×#235—22no—
77C3×#235—22no—
78C2×C3×D12—22no—
79C2×C3×D12D412yescomplemented
80C2×C3×C4×D3—24no—
81C2×C3×C4×D3D414yescomplemented
82C2×C3×Dic6—22no—
83C2×C3×Dic6D412yescomplemented
84C2×#626—24no—
85#3757—22no—
86#3757C2312yes—
87#3752—22no—
88C4⋊(C3⋊Dic3)—21no—
89#3750—22no—
90C4×C3⋊Dic3—21no—
91C3×#217C2314yes—
92C3×C4⋊Dic3—22no—
93C3×C4×Dic3—22no—
94Dic3⋊Dic3—24no—
95#3722—24no—
96(C2×D3)⋊Dic3—24no—
97#3025—91noSylow
98C3×2−1+4—62no—
99C3×2−1+4—61no—
100C3×H(5,𝔽2)—34no—
101C3×H(5,𝔽2)—62no—
102C3×H(5,𝔽2)—61no—
103C2×C3×#41—21no—
104C2×C3×#41—32no—
105C2×C3×#41—64no—
106C2×C3×#41—62no—
107C2×C3×#41C2×D311yescharacteristic
108C2×C3×#41C2×D311yescharacteristic
109#1010—22no—
110#1009—22no—
111D3×#41—24no—
112#1007—21no—
113#1004—21no—
114#1004C2×D314yes—
115C2×#235—22no—
116C2×#235C2×D312yes—
117C22×C4×D3—31no—
118C22×C4×D3—31no—
119C22×C4×D3—61no—
120C3×#117—32no—
121#946—62no—
122#946—62no—
123#946—61no—
124#946—61no—
125#938—62no—
126#938—62no—
127#938—61no—
128#938—61no—
129#937—32no—
130#937—32no—
131#937—34no—
132#937—62no—
133#935—32no—
134#935—32no—
135#935—34no—
136#935—62no—
137C4×#67—64no—
138C4×#67—64no—
139C4×#67—62no—
140C4×#67—62no—
141#926—31no—
142#926—31no—
143#926—61no—
144#926C2×D312yescomplemented
145#897—62no—
146#895—62no—
147#886—34no—
148#882—34no—
149C4×D12—64no—
150C3×#99—34no—
151#834—38no—
152#834C2×D314yescomplemented
153#806—38no—
154C23×C32C2×D412yes—
155C23×C32C2411yescharacteristic
156C22×C3⋊D3—21no—
157C22×C3⋊D3—22no—
158C22×C3⋊D3—42no—
159C22×C3×D3—24no—
160C22×C3×D3C2×D414yes—
161C32×Q8—22no—
162C32×D4—24no—
163C32×D4—22no—
164C2×C32×C4—22no—
165C2×C32×C4—22no—
166C2×C32×C4C2×D412yes—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D412yes—
170C2×C32×C4C2×D412yes—
171#638—44no—
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—22no—
175C4×C3⋊D3—41no—
176C4×C3⋊D3—42no—
177C4×C3⋊D3—41no—
178C3×#67—28no—
179C3×#67—24no—
180C3×#67—24no—
181C2×C3×Dic3—24no—
182C2×C3×Dic3—24no—
183C2×C3×Dic3C2×D414yes—
184C3×D12—24no—
185C3×D12—22no—
186C3×D12—22no—
187C3×C4×D3—28no—
188C3×C4×D3—24no—
189C3×C4×D3—24no—
190C3×Dic6—24no—
191C3×Dic6—22no—
192C3×Dic6—22no—
193#626—48no—
194#585—31no—
195#525—92no—
196#525—91no—
197#458—94no—
198B(4,𝔽2)—94no—
199#410—31no—
200#410—92no—
201C23×D3—31no—
202C23×D3—31no—
203C23×D3—61no—
204C3×#41—22no—
205C3×#41—22no—
206C3×#41—22no—
207C3×#41—22no—
208C3×#41—42no—
209C3×#41—42no—
210C3×#41—64no—
211C3×#41—64no—
212C3×#41—68no—
213C3×#41—64no—
214C3×#41—64no—
215C3×#41—62no—
216C3×#41—62no—
217C3×#41—64no—
218C3×#41—62no—
219C3×#41—62no—
220C2×C3×Q8—21no—
221C2×C3×Q8—32no—
222C2×C3×Q8—62no—
223C2×C3×Q8—64no—
224C2×C3×Q8D1211yescharacteristic, complemented
225C2×C3×Q8#6711yescharacteristic, complemented
226C2×C3×D4—21no—
227C2×C3×D4—22no—
228C2×C3×D4—34no—
229C2×C3×D4—32no—
230C2×C3×D4—62no—
231C2×C3×D4—68no—
232C2×C3×D4—64no—
233C2×C3×D4—64no—
234C2×C3×D4D1211yescharacteristic, complemented
235C2×C3×D4#6711yescharacteristic, complemented
236C2×C3×D4C22×D312yes—
237C2×C3×D4C22×D312yes—
238C22×C3×C4—22no—
239C22×C3×C4—21no—
240C22×C3×C4—34no—
241C22×C3×C4—64no—
242C22×C3×C4D1212yescomplemented
243C22×C3×C4#6712yescomplemented
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C2×#67—24no—
247C2×#67—64no—
248C2×#67—64no—
249C2×#67—62no—
250C2×#67—62no—
251C2×#67C22×D314yes—
252C22×Dic3—31no—
253C22×Dic3—31no—
254C22×Dic3—61no—
255#239—24no—
256D3×Q8—24no—
257#237—24no—
258#237—28no—
259D3×D4—24no—
260D3×D4—28no—
261#235—24no—
262#235—24no—
263#235—22no—
264#235—24no—
265#235—22no—
266#235—22no—
267#235—22no—
268C2×D12—22no—
269C2×D12—64no—
270C2×D12#6712yescomplemented
271C2×C4×D3—24no—
272C2×C4×D3—62no—
273C2×C4×D3—62no—
274C2×C4×D3—61no—
275C2×C4×D3—61no—
276C2×C4×D3—62no—
277C2×C4×D3—62no—
278C2×C4×D3—62no—
279C2×C4×D3—62no—
280C2×C4×D3—61no—
281C2×C4×D3—61no—
282C2×C4×D3—122no—
283C2×C4×D3—122no—
284C2×C4×D3#6714yescomplemented
285C2×Dic6—22no—
286C2×Dic6#6712yescomplemented
287C3×C4⋊C4—62no—
288C3×C22⋊C4—34no—
289C3×C42—62no—
290#217—32no—
291#217—32no—
292#217—62no—
293#217—64no—
294#217—64no—
295#217—62no—
296#217—62no—
297#217C22×D314yes—
298(C2×D3)⋊C4—64no—
299(C2×D3)⋊C4—64no—
300(C2×D3)⋊C4—64no—
301(C2×D3)⋊C4—62no—
302(C2×D3)⋊C4—62no—
303(C2×D3)⋊C4—64no—
304C4⋊Dic3—22no—
305C4⋊Dic3—62no—
306C4⋊Dic3—61no—
307C4⋊Dic3—61no—
308C4⋊Dic3—64no—
309Dic3⋊C4—64no—
310Dic3⋊C4—64no—
311Dic3⋊C4—62no—
312Dic3⋊C4—62no—
313C4×Dic3—22no—
314C4×Dic3—62no—
315C4×Dic3—61no—
316C4×Dic3—61no—
317C22×C32—22no—
318C22×C32—41no—
319C22×C32—42no—
320C22×C32C22×D411yescharacteristic
321C22×C32C22×D412yes—
322C2×C3⋊D3—22no—
323C2×C3⋊D3—24no—
324C2×C3⋊D3—41no—
325C2×C3⋊D3—42no—
326C2×C3⋊D3—41no—
327C2×C3×D3—24no—
328C2×C3×D3—44no—
329C2×C3×D3—84no—
330C32×C4—22no—
331C32×C4#12011yescharacteristic
332C32×C4#12012yes—
333C32×C4#12011yescharacteristic
334C3⋊Dic3—42no—
335C3⋊Dic3—41no—
336C3×Dic3—24no—
337C3×Dic3—44no—
3382−1+4—62no—
3392−1+4—61no—
340H(5,𝔽2)—34no—
341H(5,𝔽2)—62no—
342H(5,𝔽2)—61no—
343C2×#41—32no—
344C2×#41—64no—
345C2×#41—62no—
346C2×#41D3211yescharacteristic
347C23×C4—91no—
348#123—94no—
349#123—92no—
350C22⋊Q8—182no—
351C22⋊Q8—181no—
352#121—182no—
353#121—181no—
354#120—94no—
355#120—92no—
356C4×D4—184no—
357C4×D4—182no—
358#117—32no—
359#117—91no—
360#99—34no—
361#99—98no—
362C23×C3—21no—
363C23×C3—22no—
364C23×C3—34no—
365C23×C3—64no—
366C23×C3C2×D1212yes—
367C23×C3C2×#6712yes—
368C23×C3C23×D311yescharacteristic
369C23×C3C23×D311yescharacteristic
370C22×D3—24no—
371C22×D3—62no—
372C22×D3—61no—
373C22×D3—62no—
374C22×D3—62no—
375C22×D3—61no—
376C22×D3—122no—
377C22×D3—122no—
378C22×D3—122no—
379C22×D3—124no—
380C22×D3C2×#6714yes—
381C3×Q8—22no—
382C3×Q8—22no—
383C3×Q8—42no—
384C3×Q8—64no—
385C3×Q8—62no—
386C3×Q8—62no—
387C3×D4—24no—
388C3×D4—24no—
389C3×D4—22no—
390C3×D4—22no—
391C3×D4—42no—
392C3×D4—44no—
393C3×D4—64no—
394C3×D4—68no—
395C3×D4—64no—
396C3×D4—64no—
397C3×D4—62no—
398C3×D4—62no—
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—22no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—34no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4—68no—
412C2×C3×C4—64no—
413C2×C3×C4—64no—
414C2×C3×C4—64no—
415C2×C3×C4—64no—
416C2×C3×C4C2×D1212yes—
417C2×C3×C4C2×D1211yescharacteristic
418C2×C3×C4C2×D1211yescharacteristic
419C2×C3×C4D3×D412yes—
420C2×C3×C4D3×D412yes—
421C2×C3×C4C2×#6712yes—
422C2×C3×C4C2×#6711yescharacteristic
423C2×C3×C4C2×#6711yescharacteristic
424C2×C3×C4C2×#6712yes—
425C2×C3×C4C2×#6712yes—
426#67—28no—
427#67—24no—
428#67—24no—
429#67—128no—
430#67—124no—
431#67—124no—
432#67—128no—
433C2×Dic3—24no—
434C2×Dic3—24no—
435C2×Dic3—64no—
436C2×Dic3—62no—
437C2×Dic3—62no—
438C2×Dic3—61no—
439C2×Dic3—62no—
440C2×Dic3—62no—
441C2×Dic3—61no—
442C2×Dic3—62no—
443C2×Dic3—122no—
444C2×Dic3C2×#6714yes—
445D12—24no—
446D12—22no—
447D12—22no—
448D12—128no—
449C4×D3—28no—
450C4×D3—24no—
451C4×D3—24no—
452C4×D3—122no—
453C4×D3—124no—
454C4×D3—122no—
455C4×D3—121no—
456C4×D3—122no—
457C4×D3—121no—
458C4×D3—121no—
459C4×D3—122no—
460C4×D3—121no—
461Dic6—24no—
462Dic6—22no—
463Dic6—22no—
464C2×C32—21no—
465C2×C32—22no—
466C2×C32—42no—
467C2×C32C2×#12011yescharacteristic
468C3⋊D3—42no—
469C3×D3—44no—
470C24—91no—
471#41—22no—
472#41—22no—
473#41—64no—
474#41—64no—
475#41—68no—
476#41—64no—
477#41—64no—
478#41—62no—
479#41—62no—
480#41—64no—
481#41—62no—
482#41—62no—
483C2×Q8—32no—
484C2×Q8—62no—
485C2×Q8—64no—
486C2×Q8#62611yescharacteristic, complemented
487C2×D4—34no—
488C2×D4—32no—
489C2×D4—62no—
490C2×D4—68no—
491C2×D4—64no—
492C2×D4—64no—
493C2×D4—184no—
494C2×D4—182no—
495C2×D4#62611yescharacteristic, complemented
496C2×D4C2×D3212yes—
497C22×C4—34no—
498C22×C4—64no—
499C22×C4—91no—
500C22×C4—181no—
501C22×C4—181no—
502C22×C4—182no—
503C22×C4—182no—
504C22×C4#62612yescomplemented
505C22×C4C2×D3211yescharacteristic
506C4⋊C4—62no—
507C4⋊C4—184no—
508C4⋊C4—181no—
509C4⋊C4—182no—
510C22⋊C4—34no—
511C22⋊C4—92no—
512C22⋊C4—184no—
513C22⋊C4—184no—
514C22⋊C4—182no—
515C22⋊C4—182no—
516C42—62no—
517C42—181no—
518C22×C3—22no—
519C22×C3—22no—
520C22×C3—21no—
521C22×C3—22no—
522C22×C3—42no—
523C22×C3—41no—
524C22×C3—41no—
525C22×C3—42no—
526C22×C3—42no—
527C22×C3—42no—
528C22×C3—44no—
529C22×C3—64no—
530C22×C3—124no—
531C22×C3—244no—
532C22×C3C22×D1211yescharacteristic
533C22×C3C2×D3×D412yes—
534C22×C3C22×#6711yescharacteristic
535C22×C3C22×#6712yes—
536C2×D3—24no—
537C2×D3—44no—
538C2×D3—64no—
539C2×D3—64no—
540C2×D3—62no—
541C2×D3—62no—
542C2×D3—64no—
543C2×D3—84no—
544C2×D3—124no—
545C2×D3—122no—
546C2×D3—122no—
547C2×D3—122no—
548C2×D3—121no—
549C2×D3—121no—
550C2×D3—122no—
551C2×D3—124no—
552C2×D3—121no—
553C2×D3—121no—
554C3×C4—22no—
555C3×C4—22no—
556C3×C4—21no—
557C3×C4—22no—
558C3×C4—21no—
559C3×C4—42no—
560C3×C4—64no—
561C3×C4—124no—
562C3×C4#88211yescharacteristic
563C3×C4#88212yes—
564C3×C4#88211yescharacteristic
565C3×C4#95311yescharacteristic
566C3×C4#95312yes—
567C3×C4#95311yescharacteristic
568Dic3—24no—
569Dic3—44no—
570Dic3—122no—
571Dic3—124no—
572Dic3—122no—
573Dic3—122no—
574Dic3—121no—
575Dic3—121no—
576C32#302511yescharacteristic, complemented, Sylow
577C23—34no—
578C23—64no—
579C23—181no—
580C23—182no—
581C23—362no—
582C23C2×#62612yes—
583C23C22×D3211yescharacteristic
584Q8—22no—
585Q8—64no—
586Q8—62no—
587Q8—62no—
588D4—24no—
589D4—22no—
590D4—64no—
591D4—68no—
592D4—64no—
593D4—64no—
594D4—62no—
595D4—62no—
596D4—368no—
597D4—364no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—34no—
601C2×C4—68no—
602C2×C4—64no—
603C2×C4—64no—
604C2×C4—64no—
605C2×C4—64no—
606C2×C4—182no—
607C2×C4—181no—
608C2×C4—182no—
609C2×C4—361no—
610C2×C4—362no—
611C2×C4—361no—
612C2×C4C2×#62612yes—
613C2×C4C2×#62611yescharacteristic
614C2×C4C2×#62611yescharacteristic
615C2×C4D3×#6712yes—
616C2×C4D3×#6712yes—
617C2×C3—22no—
618C2×C3—22no—
619C2×C3—21no—
620C2×C3—21no—
621C2×C3—22no—
622C2×C3—21no—
623C2×C3—42no—
624C2×C3—42no—
625C2×C3—42no—
626C2×C3—82no—
627C2×C3—124no—
628C2×C3C2×#88211yescharacteristic
629C2×C3C2×#95311yescharacteristic
630D3—44no—
631D3—124no—
632D3—122no—
633D3—122no—
634C22—22no—
635C22—41no—
636C22—42no—
637C22—64no—
638C22—124no—
639C22—182no—
640C22—184no—
641C22—244no—
642C22—362no—
643C22—361no—
644C22—361no—
645C22C22×#62611yescharacteristic
646C22C2×D3×#6712yes—
647C4—22no—
648C4—64no—
649C4—124no—
650C4—362no—
651C4—361no—
652C4#6397711yescharacteristic
653C4#6397712yes—
654C4#6397711yescharacteristic
655C3—21no—
656C3#7869011yescharacteristic, complemented
657C3#8412511yescharacteristic, complemented
658C2—22no—
659C2—21no—
660C2—42no—
661C2—124no—
662C2—362no—
663C2C2×#6397711yescharacteristic
subgroupG/H
centerC4#63977
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×#120
hypercenterC2×#41D32
hypocenterC32#3025
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C3×#5964C2semidirect
2. #10596299C2semidirect
3. #10595034C2semidirect
4. C3×#5240C2semidirect
5. #10591534C2semidirect
6. #10591531C2semidirect
7. #10591231C2semidirect
11. C22×C4×C3⋊D3C22semidirect
22. #64146C22semidirect
23. #64144C22semidirect
25. #64135C22semidirect
26. C3×#926C22semidirect
27. #63981C22semidirect
28. #63962C22semidirect
32. C3×#834C22semidirect
33. #63580C22semidirect
35. #5964D3semidirect
45. #5240D3semidirect
52. C2×C32×Q8D4semidirect
53. C2×C32×D4D4semidirect
55. C22×C32×C4D4semidirect
79. C2×C3×D12D4semidirect
81. C2×C3×C4×D3D4semidirect
83. C2×C3×Dic6D4semidirect
144. #926C2×D3semidirect
152. #834C2×D3semidirect
224. C2×C3×Q8D12semidirect
225. C2×C3×Q8#67semidirect
234. C2×C3×D4D12semidirect
235. C2×C3×D4#67semidirect
242. C22×C3×C4D12semidirect
243. C22×C3×C4#67semidirect
270. C2×D12#67semidirect
284. C2×C4×D3#67semidirect
286. C2×Dic6#67semidirect
486. C2×Q8#626semidirect
495. C2×D4#626semidirect
504. C22×C4#626semidirect
576. C32#3025semidirect
656. C3#78690semidirect
657. C3#84125semidirect

Maximal subgroups

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

subgroupindex
C3×#59642
#105962992
#105950342
C3×#52402
#105915342
#105915312
#105912312
#841253
#786903