Finite Group Databasebeta

← #11868677

Subgroups — #11868677

Order 1152.

991 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595988C211yesmaximal, characteristic, complemented
2C2×#63898C211yesmaximal, characteristic
3C3×#5001C211yesmaximal, characteristic
4C3×#4995C211yesmaximal, characteristic, complemented
5#10591130C211yesmaximal, characteristic, complemented
6#10591120C211yesmaximal, characteristic, complemented
7#10591086C211yesmaximal, characteristic
8#10590474C212yesmaximal, complemented
9#10590473C212yesmaximal, complemented
10#10590472C212yesmaximal, complemented
11#10590471C212yesmaximal, complemented
12#79239—31nomaximal
13#78917—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C22×D3×Dic3—21no—
16C32×#117C2211yescharacteristic
17#64135C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19#64099C2211yescharacteristic, complemented
20#64099C2211yescharacteristic, complemented
21#64097C2211yescharacteristic, complemented
22#64097C2211yescharacteristic, complemented
23#64087—21no—
24#64087—21no—
25C4×#634—21no—
26C4×#634—21no—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×#208C2211yescharacteristic
29C2×C3×#208C2211yescharacteristic
30C2×(C2×D3)⋊Dic3—21no—
31#63898—21no—
32#63898—21no—
33#63898C2212yes—
34#63898C2212yes—
35C3×#809C2212yes—
36C3×#809C2212yes—
37C3×#808C2212yescomplemented
38C3×#807C2212yescomplemented
39#63575C2212yescomplemented
40#63573C2212yescomplemented
41#63572C2212yescomplemented
42#63572C2212yescomplemented
43#63563C2212yes—
44#63563C2212yes—
45C2×D4×Dic3—31no—
46#5517—31no—
47#5517—31no—
48#5517—61no—
49C2×#893—31no—
50C3×#428—31no—
51C3×#418—31no—
52#5215—31no—
53#5131—31no—
54#5121—31no—
55#5118—31no—
56#5118—31no—
57#5001D311yescharacteristic
58#4995D311yescharacteristic, complemented
59#4964—31no—
60#4891—32no—
61#4890—32no—
62#4871—32no—
63#4870—32no—
64#4766—32no—
65#4763—32no—
66#4761—32no—
67#4759—32no—
68C23×C3×D3—21no—
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3D411yescharacteristic
71C22×C3⋊Dic3D411yescharacteristic
72C2×#634—21no—
73C2×#634—21no—
74C22×C3×Dic3—21no—
75C2×C3×D12—21no—
76C2×C3×D12—22no—
77C2×C3×D12Q814yescomplemented
78C2×C3×D12C2312yes—
79C2×D3×Dic3—22no—
80C2×D3×Dic3—22no—
81C2×D3×Dic3—44no—
82C32×C4⋊C4C2311yescharacteristic
83C32×C4⋊C4C2311yescharacteristic
84C32×C22⋊C4—21no—
85C32×C42—21no—
86#3757—21no—
87C4⋊(C3⋊Dic3)—21no—
88C4⋊(C3⋊Dic3)—21no—
89C4⋊(C3⋊Dic3)C2311yescharacteristic
90C4⋊(C3⋊Dic3)C2311yescharacteristic
91#3750—21no—
92#3750—21no—
93#3750—21no—
94#3750—21no—
95C4×C3⋊Dic3—21no—
96C4×C3⋊Dic3D411yescharacteristic
97C4×C3⋊Dic3D411yescharacteristic
98C4×C3⋊Dic3C2311yescharacteristic
99C4×C3⋊Dic3C2311yescharacteristic
100C3×C4⋊Dic3—21no—
101C3×C4⋊Dic3C2312yes—
102C3×#208—22no—
103C3×#208—22no—
104C2×C3×C3⋊C8C2312yes—
105C2×C3×C3⋊C8C2312yes—
106(C2×D3)⋊Dic3—22no—
107(C2×D3)⋊Dic3—22no—
108#3077—91noSylow
109C22×C3×D4—31no—
110C23×Dic3—61no—
111C22×D12C2×D311yescharacteristic
112C22×C4×D3—61no—
113C2×C3×M16—31no—
114C2×C3×M16—31no—
115C3×#117—21no—
116C3×#117C2×D311yescharacteristic
117C3×#117C2×D311yescharacteristic
118C2×C3×C4⋊C4—31no—
119C2×#217—61no—
120D4×Dic3—32no—
121D4×Dic3—32no—
122D4×Dic3—61no—
123D4×Dic3—61no—
124C2×(C2×D3)⋊C4—61no—
125#926—31no—
126#926—31no—
127#926—61no—
128C2×C4⋊Dic3C2×D311yescharacteristic
129C2×C4×Dic3—31no—
130C2×C4×Dic3—31no—
131C2×C4×Dic3—61no—
132C2×#208C2×D311yescharacteristic
133C2×#208C2×D311yescharacteristic
134#893—32no—
135#893—32no—
136#893—61no—
137#893—61no—
138#890—31no—
139#890—31no—
140#890—31no—
141#890—31no—
142#890—61no—
143#890—61no—
144#888—31no—
145#888—31no—
146#888—31no—
147#888—31no—
148#888—61no—
149#888—61no—
150#878—61no—
151#878—61no—
152#878—61no—
153#878—61no—
154#878—62no—
155#878—62no—
156C4×Dic6—61no—
157C4×Dic6—61no—
158C4×Dic6—61no—
159C4×Dic6—61no—
160C4×Dic6—62no—
161C4×Dic6—62no—
162C3×#107—32no—
163C3×#106—32no—
164C3×#102—32no—
165C3×#102—32no—
166#832—32no—
167#832—32no—
168#821—32no—
169#821—32no—
170#818—32no—
171#817—32no—
172Dic3⋊C8—32no—
173Dic3⋊C8—32no—
174Dic3⋊C8—32no—
175Dic3⋊C8—32no—
176#809C2×D312yes—
177#809C2×D312yes—
178#808—32no—
179#808C2×D312yescomplemented
180#807—32no—
181#807C2×D312yescomplemented
182C23×C32C2×D411yescharacteristic
183C22×C3×D3—24no—
184C22×C3×D3—22no—
185C22×C3×D3—42no—
186C22×C3×D3—42no—
187C2×C32×C4—21no—
188C2×C32×C4—21no—
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2×Q812yes—
191C2×C32×C4#4112yes—
192C2×C32×C4C2411yescharacteristic
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—22no—
196C2×C3⋊Dic3—41no—
197C2×C3⋊Dic3C2×D411yescharacteristic
198C2×C3⋊Dic3C2×D411yescharacteristic
199C2×C3⋊Dic3C2×D411yescharacteristic
200C2×C3⋊Dic3C2×D411yescharacteristic
201#634—42no—
202#634—42no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—42no—
205C3×D12—24no—
206C3×D12—22no—
207C3×D12C2×Q814yes—
208D3×Dic3—44no—
209D3×Dic3—44no—
210C3×C3⋊C8—22no—
211C3×C3⋊C8—22no—
212#533—91no—
213C2×C4×D4—91no—
214#478—92no—
215#478—92no—
216#476—92no—
217#474—92no—
218#428—31no—
219#428—91no—
220#423—91no—
221#418—31no—
222#418—91no—
223C24×C3—61no—
224C23×D3—21no—
225C2×C3×D4—34no—
226C2×C3×D4—32no—
227C2×C3×D4—62no—
228C2×C3×D4—61no—
229C22×C3×C4—21no—
230C22×C3×C4—61no—
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C22×Dic3—21no—
234C22×Dic3—31no—
235C22×Dic3—31no—
236C22×Dic3—31no—
237C22×Dic3—31no—
238C22×Dic3—61no—
239C22×Dic3—61no—
240C22×Dic3—62no—
241C22×Dic3—62no—
242C22×Dic3—124no—
243C2×D12—21no—
244C2×D12—22no—
245C2×D12Dic614yescomplemented
246C2×D12C22×D312yes—
247C2×C4×D3—62no—
248C2×C4×D3—62no—
249C2×C4×D3—124no—
250C2×Dic6—61no—
251C2×Dic6—61no—
252C2×Dic6—61no—
253C2×Dic6—61no—
254C2×Dic6—62no—
255C2×Dic6—62no—
256C3×M16—62no—
257C3×M16—62no—
258C2×C3×C8—32no—
259C2×C3×C8—32no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—32no—
263C3×C4⋊C4—61no—
264C3×C4⋊C4C22×D311yescharacteristic
265C3×C4⋊C4C22×D311yescharacteristic
266C3×C4⋊C4C22×D311yescharacteristic
267C3×C4⋊C4C22×D311yescharacteristic
268C3×C22⋊C4—22no—
269C3×C22⋊C4—21no—
270C3×C22⋊C4—21no—
271C3×C42—22no—
272C3×C42—21no—
273C3×C42—21no—
274#217—62no—
275#217—62no—
276#217—62no—
277#217—61no—
278#217—61no—
279(C2×D3)⋊C4—62no—
280(C2×D3)⋊C4—62no—
281C4⋊Dic3—21no—
282C4⋊Dic3—31no—
283C4⋊Dic3—31no—
284C4⋊Dic3—31no—
285C4⋊Dic3—31no—
286C4⋊Dic3—61no—
287C4⋊Dic3—61no—
288C4⋊Dic3—61no—
289C4⋊Dic3—61no—
290C4⋊Dic3—61no—
291C4⋊Dic3—61no—
292C4⋊Dic3—62no—
293C4⋊Dic3—62no—
294C4⋊Dic3C22×D312yes—
295Dic3⋊C4—61no—
296Dic3⋊C4—61no—
297Dic3⋊C4—61no—
298Dic3⋊C4—61no—
299Dic3⋊C4—61no—
300Dic3⋊C4—61no—
301Dic3⋊C4—61no—
302Dic3⋊C4—61no—
303Dic3⋊C4—62no—
304Dic3⋊C4—62no—
305Dic3⋊C4—62no—
306Dic3⋊C4—62no—
307C4×Dic3—31no—
308C4×Dic3—31no—
309C4×Dic3—31no—
310C4×Dic3—31no—
311C4×Dic3—31no—
312C4×Dic3—31no—
313C4×Dic3—31no—
314C4×Dic3—31no—
315C4×Dic3—61no—
316C4×Dic3—61no—
317C4×Dic3—61no—
318C4×Dic3—61no—
319C4×Dic3—62no—
320C4×Dic3—61no—
321C4×Dic3—61no—
322#208—22no—
323#208—22no—
324C2×C3⋊C8C22×D312yes—
325C2×C3⋊C8C22×D312yes—
326C22×C32—21no—
327C22×C32—21no—
328C22×C32C22⋊Q812yes—
329C22×C32C22×D411yescharacteristic
330C2×C3×D3—24no—
331C2×C3×D3—48no—
332C2×C3×D3—42no—
333C2×C3×D3—42no—
334C32×C4—41no—
335C32×C4—41no—
336C32×C4C22⋊Q812yes—
337C32×C4C22×Q811yescharacteristic
338C32×C4C2×#4111yescharacteristic
339C3⋊Dic3—21no—
340C3⋊Dic3—21no—
341C3⋊Dic3—21no—
342C3⋊Dic3—41no—
343C3⋊Dic3—41no—
344C3⋊Dic3AGL(1,ℤ/8)12yes—
345C3×Dic3—42no—
346C22×D4—31no—
347C23×C4—181no—
348C2×M16—31no—
349C2×M16—31no—
350C4⋊Q8—91no—
351C4⋊Q8—91no—
352#125—91no—
353#125—91no—
354C22⋊Q8—181no—
355C22⋊Q8—181no—
356C4×Q8—181no—
357C4×Q8—181no—
358C4×D4—92no—
359C4×D4—92no—
360C4×D4—181no—
361C4×D4—181no—
362#117—91no—
363#117D3211yescharacteristic
364C2×C4⋊C4—31no—
365C2×C22⋊C4—181no—
366C2×C42—91no—
367#107—32no—
368#107—92no—
369#106—32no—
370#106—92no—
371C4⋊C8—92no—
372C4⋊C8—92no—
373#102—32no—
374#102—32no—
375#102—92no—
376#102—92no—
377C23×C3—21no—
378C23×C3—64no—
379C23×C3—62no—
380C23×C3—122no—
381C23×C3—122no—
382C23×C3D3×D411yescharacteristic
383C23×C3D3×D411yescharacteristic
384C22×D3—24no—
385C22×D3—22no—
386C22×D3—42no—
387C22×D3—42no—
388C3×D4—34no—
389C3×D4—64no—
390C3×D4—62no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—21no—
401C2×C3×C4—62no—
402C2×C3×C4—122no—
403C2×C3×C4C2×Dic612yes—
404C2×C3×C4#23512yes—
405C2×C3×C4D3×D411yescharacteristic
406C2×C3×C4D3×D411yescharacteristic
407C2×C3×C4#23712yes—
408C2×C3×C4D3×Q812yes—
409C2×C3×C4C23×D311yescharacteristic
410C2×C3×C4C23×D311yescharacteristic
411C2×Dic3—22no—
412C2×Dic3—31no—
413C2×Dic3—31no—
414C2×Dic3—31no—
415C2×Dic3—31no—
416C2×Dic3—31no—
417C2×Dic3—31no—
418C2×Dic3—31no—
419C2×Dic3—31no—
420C2×Dic3—42no—
421C2×Dic3—61no—
422C2×Dic3—61no—
423C2×Dic3—61no—
424C2×Dic3—61no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—62no—
429C2×Dic3—61no—
430C2×Dic3—61no—
431C2×Dic3—61no—
432C2×Dic3—61no—
433C2×Dic3—122no—
434C2×Dic3—124no—
435C2×Dic3—124no—
436C2×Dic3—121no—
437C2×Dic3—121no—
438C2×Dic3—122no—
439D12—24no—
440D12—22no—
441D12C2×Dic614yes—
442C4×D3—124no—
443C4×D3—124no—
444Dic6—122no—
445Dic6—122no—
446Dic6—124no—
447Dic6—124no—
448Dic6—122no—
449Dic6—122no—
450C3×C8—62no—
451C3×C8—62no—
452C3⋊C8—22no—
453C3⋊C8—22no—
454C2×C32—22no—
455C2×C32C2×C22⋊Q811yescharacteristic
456C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
457C2×C32#57511yescharacteristic
458C3×D3—44no—
459C24—61no—
460C2×Q8—181no—
461C2×Q8—181no—
462C2×D4—32no—
463C2×D4—34no—
464C2×D4—62no—
465C2×D4—61no—
466C22×C4—61no—
467C22×C4—91no—
468C22×C4—91no—
469C22×C4—182no—
470C22×C4—182no—
471C22×C4—364no—
472C22×C4C2×D3211yescharacteristic
473M16—62no—
474M16—62no—
475C2×C8—32no—
476C2×C8—32no—
477C4⋊C4—32no—
478C4⋊C4—61no—
479C4⋊C4—91no—
480C4⋊C4—91no—
481C4⋊C4—181no—
482C4⋊C4—181no—
483C4⋊C4—181no—
484C4⋊C4—181no—
485C4⋊C4—181no—
486C4⋊C4—181no—
487C4⋊C4C2×D3211yescharacteristic
488C4⋊C4C2×D3211yescharacteristic
489C22⋊C4—21no—
490C22⋊C4—182no—
491C22⋊C4—182no—
492C22⋊C4—181no—
493C42—21no—
494C42—91no—
495C42—91no—
496C42—91no—
497C42—91no—
498C42—181no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—22no—
505C22×C3—41no—
506C22×C3—41no—
507C22×C3—64no—
508C22×C3—128no—
509C22×C3—122no—
510C22×C3—122no—
511C22×C3#87812yes—
512C22×C3#89612yes—
513C22×C3C2×D3×D411yescharacteristic
514C22×C3C2×D3×D411yescharacteristic
515C2×D3—24no—
516C2×D3—48no—
517C2×D3—42no—
518C2×D3—42no—
519C3×C4—21no—
520C3×C4—21no—
521C3×C4—22no—
522C3×C4—42no—
523C3×C4—42no—
524C3×C4—41no—
525C3×C4—41no—
526C3×C4—41no—
527C3×C4—41no—
528C3×C4—122no—
529C3×C4#87812yes—
530C3×C4#89612yes—
531C3×C4C22×Dic611yescharacteristic
532C3×C4C2×#23511yescharacteristic
533C3×C4C2×#23711yescharacteristic
534C3×C4C2×D3×Q811yescharacteristic
535Dic3—32no—
536Dic3—32no—
537Dic3—42no—
538Dic3—62no—
539Dic3—62no—
540Dic3—61no—
541Dic3—61no—
542Dic3—61no—
543Dic3—61no—
544Dic3—61no—
545Dic3—61no—
546Dic3—121no—
547Dic3—121no—
548Dic3—122no—
549Dic3—122no—
550Dic3—121no—
551Dic3—121no—
552Dic3—121no—
553Dic3—121no—
554C32#307711yescharacteristic, complemented, Sylow
555C23—62no—
556C23—64no—
557C23—122no—
558C23—122no—
559C23#381111yescharacteristic
560Q8—362no—
561Q8—362no—
562D4—34no—
563D4—62no—
564D4—64no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—62no—
568C2×C4—91no—
569C2×C4—91no—
570C2×C4—91no—
571C2×C4—91no—
572C2×C4—122no—
573C2×C4—182no—
574C2×C4—181no—
575C2×C4—181no—
576C2×C4—364no—
577C2×C4—364no—
578C2×C4—361no—
579C2×C4D3×Dic612yes—
580C2×C4#379512yes—
581C2×C4#381111yescharacteristic
582C2×C4C22×D3211yescharacteristic
583C8—62no—
584C8—62no—
585C2×C3—22no—
586C2×C3—22no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—42no—
591C2×C3—124no—
592C2×C3C2×#87811yescharacteristic
593C2×C3C2×#89611yescharacteristic
594C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
595C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
596C2×C3#577311yescharacteristic
597C2×C3#577711yescharacteristic
598D3—44no—
599C22—21no—
600C22—21no—
601C22—64no—
602C22—128no—
603C22—122no—
604C22—122no—
605C22#6389612yes—
606C22C2×#381111yescharacteristic
607C4—41no—
608C4—41no—
609C4—92no—
610C4—122no—
611C4—181no—
612C4—181no—
613C4—181no—
614C4—361no—
615C4—361no—
616C4#6389612yes—
617C4C2×D3×Dic611yescharacteristic
618C4C2×#379511yescharacteristic
619C3—21no—
620C3#7891711yescharacteristic, complemented
621C3#7923911yescharacteristic, complemented
622C2—22no—
623C2—124no—
624C2C2×#6389611yescharacteristic
625C2#1059545811yescharacteristic
626C2#1059547111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
hypercenter#117D32
hypocenterC32#3077
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595988C2semidirect
4. C3×#4995C2semidirect
5. #10591130C2semidirect
6. #10591120C2semidirect
8. #10590474C2semidirect
9. #10590473C2semidirect
10. #10590472C2semidirect
11. #10590471C2semidirect
19. #64099C22semidirect
20. #64099C22semidirect
21. #64097C22semidirect
22. #64097C22semidirect
37. C3×#808C22semidirect
38. C3×#807C22semidirect
39. #63575C22semidirect
40. #63573C22semidirect
41. #63572C22semidirect
42. #63572C22semidirect
58. #4995D3semidirect
77. C2×C3×D12Q8semidirect
179. #808C2×D3semidirect
181. #807C2×D3semidirect
245. C2×D12Dic6semidirect
554. C32#3077semidirect
620. C3#78917semidirect
621. C3#79239semidirect

Maximal subgroups

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

subgroupindex
#105959882
C2×#638982
C3×#50012
C3×#49952
#105911302
#105911202
#105910862
#105904742
#105904732
#105904722
#105904712
#792393
#789173