Finite Group Databasebeta

← #11865838

Subgroups — #11865838

Order 1152.

1644 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64123C211yesmaximal, characteristic, complemented
2C2×#64120C211yesmaximal, characteristic, complemented
3#10596139C211yesmaximal, characteristic, complemented
4C4×D4×C3⋊D3C211yesmaximal, characteristic, complemented
5C32×#463C211yesmaximal, characteristic, complemented
6#10592861C211yesmaximal, characteristic, complemented
7#10592849C211yesmaximal, characteristic, complemented
8#10592756C211yesmaximal, characteristic, complemented
9#10592715C211yesmaximal, characteristic, complemented
10#10592543C211yesmaximal, characteristic, complemented
11#10592536C211yesmaximal, characteristic, complemented
12#10592517C211yesmaximal, characteristic, complemented
13#10592502C211yesmaximal, characteristic, complemented
14#10592485C211yesmaximal, characteristic, complemented
15#10592470C211yesmaximal, characteristic, complemented
16#80534—34nomaximal
17C2×#3832C2211yescharacteristic
18C2×#3830C2211yescharacteristic
19C2×D4×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3—21no—
21C2×C32×SD16C2211yescharacteristic
22C2×C32×D8C2211yescharacteristic
23C32×#124C2211yescharacteristic, complemented
24C32×C4×D4C2211yescharacteristic
25#64153C2211yescharacteristic, complemented
26C2×#3755C2211yescharacteristic
27#64149C2211yescharacteristic, complemented
28D4×C3⋊Dic3C2211yescharacteristic
29C2×#3754C2211yescharacteristic
30C2×#3753C2211yescharacteristic
31C2×#3753C2211yescharacteristic
32C4×#638—21no—
33#64123—24no—
34#64120—24no—
35C2×#3745C2211yescharacteristic
36C2×#3744C2211yescharacteristic
37C2×#3743C2211yescharacteristic
38C2×#3743C2211yescharacteristic
39#64102C2211yescharacteristic
40C4⋊C4×C3⋊D3C2211yescharacteristic
41#64093—21no—
42#64093—21no—
43#64090—21no—
44#64090—21no—
45#64090—21no—
46C22⋊C4×C3⋊D3—21no—
47#64084C2211yescharacteristic, complemented
48C4×C4⋊(C3⋊D3)C2211yescharacteristic
49C42×C3⋊D3C2211yescharacteristic
50C32×C4⋊C8C2211yescharacteristic, complemented
51C32×#103C2211yescharacteristic, complemented
52C32×#102C2211yescharacteristic, complemented
53#63662C2211yescharacteristic, complemented
54#63659C2211yescharacteristic, complemented
55#63648C2211yescharacteristic, complemented
56#63643C2211yescharacteristic, complemented
57#63641C2211yescharacteristic, complemented
58#63641C2211yescharacteristic, complemented
59#63637C2211yescharacteristic, complemented
60#63636C2211yescharacteristic, complemented
61C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
62C2×#914—34no—
63C2×#911—34no—
64#5668—34no—
65C4×D3×D4—34no—
66C3×#463D314yescomplemented
67#5162—34no—
68#5150—34no—
69#5057—34no—
70#5016—34no—
71#4844—34no—
72#4837—34no—
73#4818—34no—
74#4803—34no—
75#4786—34no—
76#4771—34no—
77C23×C3⋊D3—21no—
78C2×C32×Q8C2311yescharacteristic
79C2×C32×D4C2311yescharacteristic
80C2×C32×D4C2311yescharacteristic
81C22×C32×C4—21no—
82C2×#638—21no—
83C2×#638—21no—
84C2×#638—21no—
85C2×#638—21no—
86C22×C3⋊Dic3—21no—
87C22×C3⋊Dic3—21no—
88#3832—22no—
89#3832—22no—
90#3830—22no—
91#3830—22no—
92D4×C3⋊D3—22no—
93D4×C3⋊D3D414yescomplemented
94C2×C4⋊(C3⋊D3)—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3—44no—
102C2×C4×C3⋊D3D411yescharacteristic
103C2×C4×C3⋊D3D411yescharacteristic
104C2×C4×C3⋊D3C2311yescharacteristic
105C2×#634C2311yescharacteristic
106C32×SD16—22no—
107C32×D8—22no—
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112C32×C22⋊C4—21no—
113C32×C22⋊C4—21no—
114C32×C42C2311yescharacteristic
115#3757—21no—
116#3755—22no—
117#3754—22no—
118#3753—22no—
119#3753—22no—
120#3752—21no—
121#3752—21no—
122#3752—21no—
123#3752—21no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125#3750—21no—
126#3750—21no—
127#3750—21no—
128C4×C3⋊Dic3D411yescharacteristic
129C4×C3⋊Dic3D411yescharacteristic
130C4×C3⋊Dic3C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133#3745—22no—
134#3744—22no—
135#3743—22no—
136#3743—22no—
137#3036—91noSylow
138C2×#239—34no—
139C2×#237—34no—
140C2×D3×D4—34no—
141C22×C4×D3—64no—
142C2×C3×SD16C2×D314yes—
143C2×C3×D8C2×D314yes—
144C3×#124C2×D314yescomplemented
145C3×C4×D4C2×D314yes—
146#944—34no—
147C2×#215—34no—
148#940—34no—
149D4×Dic3—34no—
150C2×#214—34no—
151C2×#213—34no—
152C2×#213—34no—
153C4×#67—64no—
154#914—616no—
155#911—616no—
156C2×D24—34no—
157C2×#204—34no—
158C2×ΓL(1,𝔽25)—34no—
159C2×ΓL(1,𝔽25)—34no—
160#893—34no—
161D3×C4⋊C4—34no—
162#884—64no—
163#884—64no—
164#67⋊C4—64no—
165#67⋊C4—64no—
166#67⋊C4—64no—
167D3×C22⋊C4—64no—
168#875—34no—
169C4×D12—34no—
170C42×D3—34no—
171C3×C4⋊C8C2×D314yescomplemented
172C3×#103C2×D314yescomplemented
173C3×#102C2×D314yescomplemented
174#835—34no—
175#832—34no—
176#821—34no—
177#816—34no—
178Dic3⋊C8—34no—
179Dic3⋊C8—34no—
180#810—34no—
181#809—34no—
182C4⋊(C3⋊C8)—34no—
183C23×C32—21no—
184C23×C32—21no—
185C22×C3⋊D3—21no—
186C22×C3⋊D3—24no—
187C22×C3⋊D3—21no—
188C22×C3⋊D3—42no—
189C22×C3⋊D3—42no—
190C22×C3⋊D3C2×D411yescharacteristic
191C32×Q8—21no—
192C32×Q8—21no—
193C32×D4—21no—
194C32×D4—21no—
195C32×D4—21no—
196C32×D4C2×D412yes—
197C2×C32×C4—21no—
198C2×C32×C4—21no—
199C2×C32×C4—42no—
200C2×C32×C4C2×D411yescharacteristic
201C2×C32×C4C2×D411yescharacteristic
202C2×C32×C4C2411yescharacteristic
203#638—24no—
204#638—42no—
205#638—42no—
206#638—42no—
207C2×C3⋊Dic3—21no—
208C2×C3⋊Dic3—21no—
209C2×C3⋊Dic3—42no—
210C2×C3⋊Dic3—42no—
211C2×C3⋊Dic3C2×D411yescharacteristic
212C2×C3⋊Dic3C2×D411yescharacteristic
213C2×C3⋊Dic3C2×D411yescharacteristic
214C4⋊(C3⋊D3)—21no—
215C4⋊(C3⋊D3)—21no—
216C4⋊(C3⋊D3)—21no—
217C4⋊(C3⋊D3)—42no—
218C4⋊(C3⋊D3)C2×D412yes—
219C4×C3⋊D3—22no—
220C4×C3⋊D3—41no—
221C4×C3⋊D3—42no—
222C4×C3⋊D3—42no—
223C4×C3⋊D3—42no—
224C4×C3⋊D3—42no—
225C4×C3⋊D3C2×D412yes—
226C4×C3⋊D3#4112yes—
227#634—21no—
228#634—21no—
229C32×C8—21no—
230C32×C8—21no—
231C3⋊(C3⋊C8)—21no—
232C3⋊(C3⋊C8)—21no—
233C2×AGL(1,ℤ/8)—91no—
234C2×AGL(1,ℤ/8)—91no—
235#532—91no—
236C2×C4×D4—91no—
237#463—91no—
238#463—91no—
239#463—91no—
240#463C3⋊D311yescharacteristic, complemented
241#461—91no—
242#461—91no—
243#459—91no—
244#459—91no—
245#423—91no—
246#417—91no—
247#417—91no—
248C23×D3—64no—
249C2×C3×Q8C22×D314yes—
250C2×C3×D4C22×D314yes—
251C2×C3×D4C22×D314yes—
252C22×C3×C4—24no—
253C2×#67—64no—
254C2×#67—64no—
255C2×#67—64no—
256C2×#67—64no—
257C22×Dic3—64no—
258C22×Dic3—64no—
259#239—68no—
260#239—68no—
261#237—68no—
262#237—68no—
263D3×D4—316no—
264D3×D4—68no—
265C2×D12—34no—
266C2×D12—34no—
267C2×D12—64no—
268C2×C4×D3—34no—
269C2×C4×D3—34no—
270C2×C4×D3—34no—
271C2×C4×D3—64no—
272C2×C4×D3—64no—
273C2×C4×D3—64no—
274C2×C4×D3—64no—
275C2×C4×D3—1216no—
276C2×Dic6—34no—
277C3×SD16—28no—
278C3×D8—28no—
279C2×C3×C8C22×D314yes—
280C2×C3×C8C22×D314yes—
281C3×C4⋊C4C22×D314yes—
282C3×C22⋊C4—24no—
283C3×C22⋊C4—24no—
284C3×C22⋊C4—24no—
285C3×C42C22×D314yes—
286#217—64no—
287#215—68no—
288#214—68no—
289#213—68no—
290#213—68no—
291(C2×D3)⋊C4—64no—
292(C2×D3)⋊C4—64no—
293(C2×D3)⋊C4—64no—
294(C2×D3)⋊C4—64no—
295C4⋊Dic3—34no—
296Dic3⋊C4—64no—
297Dic3⋊C4—64no—
298Dic3⋊C4—64no—
299C4×Dic3—34no—
300C4×Dic3—34no—
301C4×Dic3—34no—
302C2×C3⋊C8—34no—
303C2×C3⋊C8—34no—
304D24—68no—
305#204—68no—
306ΓL(1,𝔽25)—68no—
307ΓL(1,𝔽25)—68no—
308C22×C32—22no—
309C22×C32—41no—
310C22×C32—41no—
311C22×C32—41no—
312C22×C32—41no—
313C22×C32—41no—
314C22×C32C22×D411yescharacteristic
315C2×C3⋊D3—21no—
316C2×C3⋊D3—21no—
317C2×C3⋊D3—22no—
318C2×C3⋊D3—48no—
319C2×C3⋊D3—41no—
320C2×C3⋊D3—41no—
321C2×C3⋊D3—41no—
322C2×C3⋊D3—41no—
323C2×C3⋊D3—41no—
324C2×C3⋊D3#12112yes—
325C32×C4—21no—
326C32×C4—21no—
327C32×C4—41no—
328C32×C4—41no—
329C32×C4C22×D411yescharacteristic
330C32×C4C2×#4111yescharacteristic
331C3⋊Dic3—21no—
332C3⋊Dic3—41no—
333C3⋊Dic3—41no—
334C3⋊Dic3#12112yes—
335C3⋊Dic3AGL(1,ℤ/8)12yescomplemented
336C2×#41—91no—
337C2×#41—91no—
338C22×D4—91no—
339C23×C4—181no—
340AGL(1,ℤ/8)—184no—
341AGL(1,ℤ/8)—184no—
342C2×SD16—91no—
343C2×SD16—91no—
344C2×SD16—91no—
345C2×SD16C2×C3⋊D311yescharacteristic
346C2×D8—91no—
347C2×D8—91no—
348C2×D8—91no—
349C2×D8C2×C3⋊D311yescharacteristic
350C2×M16—91no—
351C2×M16—91no—
352C4⋊Q8—91no—
353#127—91no—
354#124—91no—
355#124C2×C3⋊D311yescharacteristic, complemented
356#121—181no—
357#121—181no—
358C4×D4—91no—
359C4×D4—91no—
360C4×D4—91no—
361C4×D4—181no—
362C4×D4—181no—
363C4×D4—181no—
364C4×D4—181no—
365C4×D4C2×C3⋊D311yescharacteristic
366C2×C4⋊C4—91no—
367C2×C22⋊C4—181no—
368C2×C42—91no—
369C4⋊C8—91no—
370C4⋊C8—91no—
371C4⋊C8—91no—
372C4⋊C8C2×C3⋊D311yescharacteristic, complemented
373#103—91no—
374#103—91no—
375#103—91no—
376#103C2×C3⋊D311yescharacteristic, complemented
377#102—91no—
378#102—91no—
379#102—91no—
380#102C2×C3⋊D311yescharacteristic, complemented
381C23×C3—24no—
382C23×C3—24no—
383C22×D3—34no—
384C22×D3—616no—
385C22×D3—64no—
386C22×D3—64no—
387C22×D3—128no—
388C22×D3—128no—
389C3×Q8—24no—
390C3×Q8—24no—
391C3×D4—24no—
392C3×D4—24no—
393C3×D4—24no—
394C3×D4D3×D418yes—
395C2×C3×C4—24no—
396C2×C3×C4—24no—
397C2×C3×C4—48no—
398C2×C3×C4D3×D414yes—
399C2×C3×C4D3×D414yes—
400C2×C3×C4C23×D314yes—
401#67—616no—
402#67—128no—
403#67—128no—
404#67—128no—
405C2×Dic3—34no—
406C2×Dic3—34no—
407C2×Dic3—34no—
408C2×Dic3—64no—
409C2×Dic3—64no—
410C2×Dic3—128no—
411C2×Dic3—128no—
412D12—38no—
413D12—64no—
414D12—64no—
415D12—64no—
416D12—128no—
417C4×D3—38no—
418C4×D3—38no—
419C4×D3—68no—
420C4×D3—128no—
421C4×D3—128no—
422C4×D3—124no—
423C4×D3—128no—
424C4×D3—128no—
425Dic6—64no—
426Dic6—64no—
427C3×C8—24no—
428C3×C8—24no—
429C3⋊C8—64no—
430C3⋊C8—64no—
431C2×C32—42no—
432C2×C32—81no—
433C2×C32C2×#12111yescharacteristic
434C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
435C2×C32#57511yescharacteristic
436C3⋊D3—22no—
437C3⋊D3—42no—
438C3⋊D3—81no—
439C24—181no—
440#41—182no—
441#41—182no—
442#41—182no—
443#41—182no—
444C2×Q8—91no—
445C2×Q8C22×C3⋊D311yescharacteristic
446C2×D4—94no—
447C2×D4—91no—
448C2×D4—91no—
449C2×D4—181no—
450C2×D4—182no—
451C2×D4—181no—
452C2×D4—181no—
453C2×D4—181no—
454C2×D4—181no—
455C2×D4C22×C3⋊D311yescharacteristic
456C2×D4C22×C3⋊D311yescharacteristic
457C22×C4—21no—
458C22×C4—91no—
459C22×C4—91no—
460C22×C4—91no—
461C22×C4—181no—
462C22×C4—181no—
463C22×C4—181no—
464C22×C4—181no—
465C22×C4—181no—
466C22×C4—181no—
467C22×C4—364no—
468SD16—22no—
469SD16—182no—
470SD16—182no—
471SD16—182no—
472D8—22no—
473D8—182no—
474D8—182no—
475D8—182no—
476M16—182no—
477M16—182no—
478C2×C8—91no—
479C2×C8—91no—
480C2×C8C22×C3⋊D311yescharacteristic
481C2×C8C22×C3⋊D311yescharacteristic
482C4⋊C4—91no—
483C4⋊C4—181no—
484C4⋊C4—181no—
485C4⋊C4—181no—
486C4⋊C4C22×C3⋊D311yescharacteristic
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—181no—
491C22⋊C4—181no—
492C22⋊C4—181no—
493C22⋊C4—181no—
494C22⋊C4—181no—
495C42—91no—
496C42—91no—
497C42—91no—
498C42C22×C3⋊D311yescharacteristic
499C22×C3—28no—
500C22×C3—44no—
501C22×C3—44no—
502C22×C3—44no—
503C22×C3—44no—
504C22×C3—44no—
505C22×C3C2×D3×D414yes—
506C2×D3—38no—
507C2×D3—64no—
508C2×D3—64no—
509C2×D3—68no—
510C2×D3—1232no—
511C2×D3—124no—
512C2×D3—124no—
513C2×D3—124no—
514C2×D3—124no—
515C2×D3—124no—
516C3×C4—24no—
517C3×C4—24no—
518C3×C4—44no—
519C3×C4—44no—
520C3×C4C2×D3×D414yes—
521C3×C4D3×#4114yes—
522Dic3—38no—
523Dic3—38no—
524Dic3—64no—
525Dic3—124no—
526Dic3—124no—
527C32#303611yescharacteristic, complemented, Sylow
528C23—21no—
529C23—21no—
530C23—91no—
531C23—184no—
532C23—181no—
533C23—181no—
534C23—362no—
535C23—362no—
536Q8—21no—
537Q8—21no—
538Q8—181no—
539Q8—181no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—92no—
544D4—184no—
545D4—181no—
546D4—181no—
547D4—181no—
548D4—362no—
549D4—362no—
550D4—362no—
551D4—362no—
552D4D4×C3⋊D312yes—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—42no—
556C2×C4—91no—
557C2×C4—91no—
558C2×C4—92no—
559C2×C4—92no—
560C2×C4—91no—
561C2×C4—182no—
562C2×C4—181no—
563C2×C4—181no—
564C2×C4—361no—
565C2×C4—362no—
566C2×C4—362no—
567C2×C4—362no—
568C2×C4—362no—
569C2×C4—362no—
570C2×C4—362no—
571C2×C4D4×C3⋊D311yescharacteristic
572C2×C4D4×C3⋊D311yescharacteristic
573C2×C4C23×C3⋊D311yescharacteristic
574C8—21no—
575C8—21no—
576C8—181no—
577C8—181no—
578C2×C3—48no—
579C2×C3—84no—
580C2×C3D3×#12114yes—
581C2×C3#576814yes—
582C2×C3D3×AGL(1,ℤ/8)14yes—
583D3—68no—
584D3—128no—
585D3—244no—
586C22—22no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—92no—
593C22—181no—
594C22—181no—
595C22—182no—
596C22—368no—
597C22—361no—
598C22—361no—
599C22—361no—
600C22—361no—
601C22—361no—
602C22C2×D4×C3⋊D311yescharacteristic
603C4—21no—
604C4—21no—
605C4—41no—
606C4—41no—
607C4—92no—
608C4—92no—
609C4—181no—
610C4—361no—
611C4—361no—
612C4C2×D4×C3⋊D311yescharacteristic
613C4#41×C3⋊D311yescharacteristic
614C3#8053414yescomplemented
615C2—42no—
616C2—81no—
617C2—182no—
618C2—362no—
619C2—721no—
620C2C3⋊D3×#12111yescharacteristic
621C2#1059623911yescharacteristic
622C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#463C2
socleC22×C32C22×D4
hypercenter#463C3⋊D3
hypocenterC32#3036
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#64123C2semidirect
2. C2×#64120C2semidirect
3. #10596139C2semidirect
4. C4×D4×C3⋊D3C2semidirect
5. C32×#463C2semidirect
6. #10592861C2semidirect
7. #10592849C2semidirect
8. #10592756C2semidirect
9. #10592715C2semidirect
10. #10592543C2semidirect
11. #10592536C2semidirect
12. #10592517C2semidirect
13. #10592502C2semidirect
14. #10592485C2semidirect
15. #10592470C2semidirect
23. C32×#124C22semidirect
25. #64153C22semidirect
27. #64149C22semidirect
47. #64084C22semidirect
50. C32×C4⋊C8C22semidirect
51. C32×#103C22semidirect
52. C32×#102C22semidirect
53. #63662C22semidirect
54. #63659C22semidirect
55. #63648C22semidirect
56. #63643C22semidirect
57. #63641C22semidirect
58. #63641C22semidirect
59. #63637C22semidirect
60. #63636C22semidirect
61. C4⋊(C3⋊(C3⋊C8))C22semidirect
66. C3×#463D3semidirect
93. D4×C3⋊D3D4semidirect
144. C3×#124C2×D3semidirect
171. C3×C4⋊C8C2×D3semidirect
172. C3×#103C2×D3semidirect
173. C3×#102C2×D3semidirect
240. #463C3⋊D3semidirect
335. C3⋊Dic3AGL(1,ℤ/8)semidirect
355. #124C2×C3⋊D3semidirect
372. C4⋊C8C2×C3⋊D3semidirect
376. #103C2×C3⋊D3semidirect
380. #102C2×C3⋊D3semidirect
527. C32#3036semidirect
614. C3#80534semidirect

Maximal subgroups

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

subgroupindex
C2×#641232
C2×#641202
#105961392
C4×D4×C3⋊D32
C32×#4632
#105928612
#105928492
#105927562
#105927152
#105925432
#105925362
#105925172
#105925022
#105924852
#105924702
#805343