Finite Group Databasebeta

← #11788850

Subgroups — #11788850

Order 1152.

865 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595519C211yesmaximal, characteristic
2#10595510C211yesmaximal, characteristic, complemented
3C2×#63633C211yesmaximal, characteristic, complemented
4C2×C3×#806C211yesmaximal, characteristic, complemented
5C2×#63580C211yesmaximal, characteristic, complemented
6C3×#4526C211yesmaximal, characteristic, complemented
7#10589187C211yesmaximal, characteristic, complemented
8#70034—31nomaximal
9#68964—31nomaximal
10C22×#638C2211yescharacteristic
11C22×C3×#67C2211yescharacteristic
12C2×C32×C22⋊C4C2211yescharacteristic
13C2×#3757C2211yescharacteristic
14C2×C3×#217C2211yescharacteristic
15C2×C3×#217C2211yescharacteristic
16C2×C3×#217C2211yescharacteristic
17#63981—21no—
18#63978—22no—
19#63977C412yescomplemented
20#63974—21no—
21#63966C412yescomplemented
22#63962—21no—
23#63957—21no—
24#63952—22no—
25#63952—22no—
26#63633—22no—
27C3×#806—22no—
28#63580—22no—
29#5804—31no—
30#5493—31no—
31#5486—31no—
32#5486—31no—
33C2×C3×#99—31no—
34C2×#834—31no—
35C2×#806—31no—
36C2×#806—31no—
37C2×#806—31no—
38C2×#806—61no—
39C2×#806D311yescharacteristic, complemented
40C3×#342—31no—
41#4527—31no—
42#4527—31no—
43#4526D311yescharacteristic, complemented
44C24×C32C2311yescharacteristic
45C23×C3⋊D3D411yescharacteristic
46C23×C3×D3C2×C411yescharacteristic, complemented
47C22×C32×C4—21no—
48C2×#638—21no—
49C2×#638—21no—
50C2×#638—21no—
51C2×#638—21no—
52C2×#638C2×C412yes—
53C2×#638D412yes—
54C22×C3⋊Dic3—21no—
55C22×C3⋊Dic3D411yescharacteristic
56C2×C3×#67—21no—
57C2×C3×#67—21no—
58C2×C3×#67—21no—
59C2×C3×#67—21no—
60C2×C3×#67—21no—
61C2×C3×#67—21no—
62C22×C3×Dic3—21no—
63C22×C3×Dic3—21no—
64C22×C3×Dic3—21no—
65C22×C3×Dic3C2×C411yescharacteristic, complemented
66C2×#626—22no—
67C2×#624—22no—
68C32×C22⋊C4—21no—
69C32×C22⋊C4—21no—
70#3757—21no—
71#3757—21no—
72C3×#217—21no—
73C3×#217—21no—
74C3×#217—21no—
75C3×#217C2×C412yescomplemented
76C3×#217D412yescomplemented
77C3×#217D412yescomplemented
78#3724—22no—
79Dic3⋊Dic3—22no—
80#3722—22no—
81#3722—22no—
82(C2×D3)⋊Dic3—22no—
83Dic32—22no—
84#1913—91noSylow
85C22×C3×D4—31no—
86C22×#67—31no—
87C22×#67—31no—
88C22×#67—61no—
89C22×#67C2×D311yescharacteristic
90C2×C3×C22⋊C4—21no—
91C2×C3×C22⋊C4—31no—
92C2×C3×C22⋊C4—31no—
93C2×C3×C22⋊C4—31no—
94C2×C3×C22⋊C4C2×D311yescharacteristic
95C2×C3×C22⋊C4C2×D311yescharacteristic
96#953—32no—
97C2×#217—31no—
98C2×#217—31no—
99C2×#217—61no—
100C2×#217C2×D311yescharacteristic
101C2×#217C2×D311yescharacteristic
102C2×#217C2×D311yescharacteristic
103#939—62no—
104#937—61no—
105#935—61no—
106#930—62no—
107#929—32no—
108C4×#67—62no—
109C4×#67—62no—
110#886—32no—
111#886—61no—
112#882—32no—
113#882—61no—
114#67⋊C4—62no—
115#67⋊C4—62no—
116D3×C22⋊C4—61no—
117D3×C22⋊C4—61no—
118#877—61no—
119#877—61no—
120C3×#99—62no—
121#834—62no—
122#806—22no—
123#806—62no—
124#806—62no—
125#806—64no—
126#806—62no—
127C23×C32—81no—
128C23×C32C22×C411yescharacteristic
129C23×C32C2×D411yescharacteristic
130C23×C32C2×D411yescharacteristic
131C23×C32C2×D411yescharacteristic
132C23×C32C2×D411yescharacteristic
133C23×C32#4111yescharacteristic
134C23×C32#4111yescharacteristic
135C22×C3⋊D3—21no—
136C22×C3⋊D3—21no—
137C22×C3⋊D3—81no—
138C22×C3⋊D3C22⋊C412yes—
139C22×C3×D3—21no—
140C22×C3×D3—21no—
141C22×C3×D3—21no—
142C22×C3×D3—81no—
143C2×C32×C4—41no—
144C2×C32×C4—81no—
145#638—22no—
146#638—22no—
147#638—22no—
148#638—22no—
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3—21no—
151C2×C3⋊Dic3—41no—
152C2×C3⋊Dic3—81no—
153C2×C3⋊Dic3C22⋊C412yes—
154C3×#67—41no—
155C3×#67—41no—
156C3×#67—41no—
157C3×#67—41no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—21no—
160C2×C3×Dic3—21no—
161C2×C3×Dic3—21no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—81no—
165C2×C3×Dic3—81no—
166C2×C3×Dic3—81no—
167#626—82no—
168#624—82no—
169#534—91no—
170#518—91no—
171C2×#99—31no—
172C2×#99—91no—
173C2×#99—91no—
174#342—31no—
175#342—91no—
176C24×C3—21no—
177C24×C3—31no—
178C24×C3C22×D311yescharacteristic
179C24×C3C22×D311yescharacteristic
180C23×D3—31no—
181C23×D3—31no—
182C23×D3—61no—
183C23×D3C4×D311yescharacteristic, complemented
184C2×C3×D4—61no—
185C2×C3×D4—61no—
186C2×C3×D4—61no—
187C2×C3×D4—61no—
188C2×C3×D4—61no—
189C2×C3×D4—61no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—31no—
193C22×C3×C4—41no—
194C22×C3×C4—61no—
195C22×C3×C4—61no—
196C22×C3×C4—61no—
197C2×#67—21no—
198C2×#67—21no—
199C2×#67—21no—
200C2×#67—21no—
201C2×#67—21no—
202C2×#67—21no—
203C2×#67—32no—
204C2×#67—32no—
205C2×#67—32no—
206C2×#67—32no—
207C2×#67—62no—
208C2×#67—62no—
209C2×#67—62no—
210C2×#67—61no—
211C2×#67—61no—
212C2×#67—61no—
213C2×#67—61no—
214C2×#67—61no—
215C2×#67—61no—
216C2×#67—61no—
217C2×#67—61no—
218C2×#67—121no—
219C2×#67—121no—
220C2×#67—121no—
221C2×#67—121no—
222C22×Dic3—21no—
223C22×Dic3—21no—
224C22×Dic3—21no—
225C22×Dic3—31no—
226C22×Dic3—31no—
227C22×Dic3—61no—
228C22×Dic3—61no—
229C22×Dic3—61no—
230C22×Dic3—121no—
231C22×Dic3C4×D311yescharacteristic, complemented
232C2×D12—62no—
233C2×C4×D3—62no—
234C2×C4×D3—62no—
235C3×C22⋊C4—22no—
236C3×C22⋊C4—21no—
237C3×C22⋊C4—21no—
238C3×C22⋊C4—21no—
239C3×C22⋊C4—21no—
240C3×C22⋊C4—32no—
241C3×C22⋊C4—32no—
242C3×C22⋊C4—32no—
243C3×C22⋊C4—41no—
244C3×C22⋊C4—61no—
245C3×C22⋊C4—61no—
246C3×C22⋊C4—61no—
247#217—21no—
248#217—21no—
249#217—21no—
250#217—62no—
251#217—62no—
252#217—61no—
253#217—61no—
254#217—61no—
255#217—61no—
256#217—121no—
257#217C4×D312yescomplemented
258#217D1212yescomplemented
259#217#6712yescomplemented
260(C2×D3)⋊C4—62no—
261(C2×D3)⋊C4—62no—
262(C2×D3)⋊C4—62no—
263(C2×D3)⋊C4—62no—
264(C2×D3)⋊C4—62no—
265C4⋊Dic3—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4—62no—
268Dic3⋊C4—62no—
269C4×Dic3—62no—
270C4×Dic3—62no—
271C22×C32—41no—
272C22×C32—41no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32—41no—
276C22×C32—41no—
277C22×C32—41no—
278C22×C32C2×C22⋊C411yescharacteristic
279C22×C32C4×D411yescharacteristic
280C22×C32C4×D411yescharacteristic
281C22×C32#12011yescharacteristic
282C22×C32#12111yescharacteristic
283C22×C32#12111yescharacteristic
284C22×C32#12311yescharacteristic
285C2×C3⋊D3—22no—
286C2×C3⋊D3—42no—
287C2×C3⋊D3—42no—
288C2×C3⋊D3—81no—
289C2×C3×D3—42no—
290C2×C3×D3—41no—
291C2×C3×D3—81no—
292C2×C3×D3—81no—
293C32×C4—81no—
294C3⋊Dic3—22no—
295C3⋊Dic3—81no—
296C3×Dic3—42no—
297C3×Dic3—42no—
298C3×Dic3—42no—
299C3×Dic3—41no—
300C22×D4—31no—
301C22×D4—91no—
302#123—92no—
303#123—181no—
304#121—182no—
305#120—92no—
306#120—181no—
307C4×D4—182no—
308C4×D4—182no—
309#117—181no—
310C2×C22⋊C4—31no—
311C2×C22⋊C4—31no—
312C2×C22⋊C4—31no—
313C2×C22⋊C4—91no—
314C2×C22⋊C4—181no—
315C2×C22⋊C4D3211yescharacteristic
316#99—62no—
317#99—182no—
318#99—182no—
319C23×C3—21no—
320C23×C3—21no—
321C23×C3—21no—
322C23×C3—21no—
323C23×C3—21no—
324C23×C3—21no—
325C23×C3—21no—
326C23×C3—61no—
327C23×C3—61no—
328C23×C3—61no—
329C23×C3—81no—
330C23×C3—81no—
331C23×C3—82no—
332C23×C3—241no—
333C23×C3C2×C4×D311yescharacteristic
334C23×C3C2×C4×D311yescharacteristic
335C23×C3C2×D1211yescharacteristic
336C23×C3#23511yescharacteristic
337C23×C3#23511yescharacteristic
338C23×C3D3×D411yescharacteristic
339C23×C3D3×D411yescharacteristic
340C23×C3D3×D411yescharacteristic
341C23×C3D3×D411yescharacteristic
342C23×C3D3×D411yescharacteristic
343C23×C3D3×D411yescharacteristic
344C23×C3#23711yescharacteristic
345C23×C3#23911yescharacteristic
346C23×C3C2×#6711yescharacteristic
347C22×D3—21no—
348C22×D3—21no—
349C22×D3—21no—
350C22×D3—32no—
351C22×D3—32no—
352C22×D3—62no—
353C22×D3—61no—
354C22×D3—61no—
355C22×D3—61no—
356C22×D3—61no—
357C22×D3—81no—
358C22×D3—121no—
359C22×D3—121no—
360C22×D3—241no—
361C22×D3—241no—
362C22×D3—242no—
363C3×D4—121no—
364C3×D4—121no—
365C3×D4—121no—
366C3×D4—121no—
367C2×C3×C4—42no—
368C2×C3×C4—41no—
369C2×C3×C4—41no—
370C2×C3×C4—61no—
371C2×C3×C4—61no—
372C2×C3×C4—62no—
373C2×C3×C4—62no—
374C2×C3×C4—61no—
375C2×C3×C4—62no—
376C2×C3×C4—82no—
377C2×C3×C4—81no—
378C2×C3×C4—81no—
379C2×C3×C4—241no—
380C2×C3×C4—241no—
381C2×C3×C4—241no—
382#67—41no—
383#67—41no—
384#67—41no—
385#67—41no—
386#67—62no—
387#67—62no—
388#67—62no—
389#67—62no—
390#67—62no—
391#67—62no—
392#67—62no—
393#67—62no—
394#67—122no—
395#67—122no—
396#67—122no—
397#67—122no—
398#67—242no—
399C2×Dic3—22no—
400C2×Dic3—21no—
401C2×Dic3—21no—
402C2×Dic3—22no—
403C2×Dic3—21no—
404C2×Dic3—22no—
405C2×Dic3—32no—
406C2×Dic3—32no—
407C2×Dic3—62no—
408C2×Dic3—61no—
409C2×Dic3—61no—
410C2×Dic3—61no—
411C2×Dic3—61no—
412C2×Dic3—81no—
413C2×Dic3—81no—
414C2×Dic3—81no—
415C2×Dic3—121no—
416C2×Dic3—121no—
417C2×Dic3—122no—
418C2×Dic3—121no—
419C2×Dic3—121no—
420C2×Dic3—242no—
421C2×Dic3—241no—
422C2×Dic3—241no—
423D12—242no—
424C4×D3—242no—
425C4×D3—242no—
426C2×C32—21no—
427C2×C32—21no—
428C2×C32—21no—
429C2×C32—21no—
430C2×C32—21no—
431C2×C32—21no—
432C2×C32—21no—
433C2×C32#38611yescharacteristic
434C3⋊D3—42no—
435C3×D3—81no—
436C24—31no—
437C24—91no—
438C24C2×D3211yescharacteristic
439C2×D4—61no—
440C2×D4—61no—
441C2×D4—61no—
442C2×D4—61no—
443C2×D4—61no—
444C2×D4—61no—
445C2×D4—92no—
446C2×D4—92no—
447C2×D4—182no—
448C2×D4—181no—
449C2×D4—181no—
450C2×D4—181no—
451C2×D4—181no—
452C22×C4—21no—
453C22×C4—31no—
454C22×C4—61no—
455C22×C4—61no—
456C22×C4—61no—
457C22×C4—91no—
458C22×C4—182no—
459C22×C4—181no—
460C4⋊C4—182no—
461C4⋊C4—182no—
462C22⋊C4—21no—
463C22⋊C4—21no—
464C22⋊C4—32no—
465C22⋊C4—32no—
466C22⋊C4—32no—
467C22⋊C4—61no—
468C22⋊C4—61no—
469C22⋊C4—61no—
470C22⋊C4—182no—
471C22⋊C4—182no—
472C22⋊C4—182no—
473C22⋊C4—181no—
474C22⋊C4—181no—
475C42—182no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—41no—
484C22×C3—41no—
485C22×C3—41no—
486C22×C3—41no—
487C22×C3—41no—
488C22×C3—41no—
489C22×C3—41no—
490C22×C3—41no—
491C22×C3—41no—
492C22×C3—41no—
493C22×C3—41no—
494C22×C3—41no—
495C22×C3—41no—
496C22×C3—41no—
497C22×C3—42no—
498C22×C3—42no—
499C22×C3—42no—
500C22×C3—81no—
501C22×C3—81no—
502C22×C3—81no—
503C22×C3—81no—
504C22×C3—122no—
505C22×C3—121no—
506C22×C3—241no—
507C22×C3—241no—
508C22×C3C4×D1211yescharacteristic
509C22×C3D3×C22⋊C411yescharacteristic
510C22×C3D3×C22⋊C411yescharacteristic
511C22×C3#67⋊C411yescharacteristic
512C22×C3#88211yescharacteristic
513C22×C3#88311yescharacteristic
514C22×C3#88411yescharacteristic
515C22×C3#88411yescharacteristic
516C22×C3#89311yescharacteristic
517C22×C3#89411yescharacteristic
518C22×C3#89511yescharacteristic
519C22×C3C4×#6711yescharacteristic
520C22×C3#93711yescharacteristic
521C22×C3#93811yescharacteristic
522C2×D3—42no—
523C2×D3—41no—
524C2×D3—62no—
525C2×D3—62no—
526C2×D3—81no—
527C2×D3—81no—
528C2×D3—122no—
529C2×D3—122no—
530C2×D3—122no—
531C2×D3—122no—
532C2×D3—122no—
533C2×D3—242no—
534C2×D3—242no—
535C2×D3—241no—
536C2×D3—241no—
537C2×D3—242no—
538C3×C4—81no—
539C3×C4—81no—
540C3×C4—82no—
541C3×C4—122no—
542C3×C4—122no—
543C3×C4—122no—
544C3×C4—121no—
545Dic3—42no—
546Dic3—42no—
547Dic3—42no—
548Dic3—41no—
549Dic3—62no—
550Dic3—62no—
551Dic3—122no—
552Dic3—241no—
553Dic3—241no—
554Dic3—242no—
555C32#191311yescharacteristic, complemented, Sylow
556C23—61no—
557C23—61no—
558C23—61no—
559C23—81no—
560C23—92no—
561C23—181no—
562C23—181no—
563C23—241no—
564C23—721no—
565C23#379911yescharacteristic
566C23C4×D3211yescharacteristic
567C23D3×D1211yescharacteristic
568C23#380211yescharacteristic
569C23#380411yescharacteristic
570C23D3×#6711yescharacteristic
571C23#381111yescharacteristic
572D4—121no—
573D4—121no—
574D4—121no—
575D4—121no—
576D4—182no—
577D4—182no—
578D4—182no—
579D4—182no—
580D4—722no—
581C2×C4—41no—
582C2×C4—61no—
583C2×C4—61no—
584C2×C4—62no—
585C2×C4—61no—
586C2×C4—62no—
587C2×C4—62no—
588C2×C4—81no—
589C2×C4—92no—
590C2×C4—181no—
591C2×C4—181no—
592C2×C4—241no—
593C2×C4—241no—
594C2×C4—241no—
595C2×C4—361no—
596C2×C4—722no—
597C2×C4—721no—
598C2×C3—22no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—41no—
615C2×C3—41no—
616C2×C3—41no—
617C2×C3—41no—
618C2×C3—41no—
619C2×C3—41no—
620C2×C3—241no—
621C2×C3#466511yescharacteristic
622C2×C3#495611yescharacteristic
623D3—81no—
624D3—122no—
625D3—122no—
626D3—242no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—122no—
635C22—121no—
636C22—182no—
637C22—241no—
638C22—241no—
639C22—362no—
640C22—362no—
641C22—721no—
642C22#6385411yescharacteristic
643C22#6388011yescharacteristic
644C22#6390411yescharacteristic
645C22#6391011yescharacteristic
646C22#6392111yescharacteristic
647C22#6392211yescharacteristic
648C22#6395811yescharacteristic
649C4—81no—
650C4—122no—
651C4—122no—
652C4—122no—
653C4—121no—
654C4—182no—
655C4—721no—
656C3—21no—
657C3#6896411yescharacteristic, complemented
658C3#7003411yescharacteristic, complemented
659C2—21no—
660C2—21no—
661C2—21no—
662C2—21no—
663C2—21no—
664C2—21no—
665C2—21no—
666C2—241no—
667C2—362no—
668C2#1059127511yescharacteristic
subgroupG/H
centerC2#10591275
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC2×C32#386
prime radical#10595519C2
cosocleC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#1913
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10595510C2semidirect
3. C2×#63633C2semidirect
4. C2×C3×#806C2semidirect
5. C2×#63580C2semidirect
6. C3×#4526C2semidirect
7. #10589187C2semidirect
19. #63977C4semidirect
21. #63966C4semidirect
39. C2×#806D3semidirect
43. #4526D3semidirect
46. C23×C3×D3C2×C4semidirect
65. C22×C3×Dic3C2×C4semidirect
75. C3×#217C2×C4semidirect
76. C3×#217D4semidirect
77. C3×#217D4semidirect
183. C23×D3C4×D3semidirect
231. C22×Dic3C4×D3semidirect
257. #217C4×D3semidirect
258. #217D12semidirect
259. #217#67semidirect
555. C32#1913semidirect
657. C3#68964semidirect
658. C3#70034semidirect

Maximal subgroups

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

subgroupindex
#105955192
#105955102
C2×#636332
C2×C3×#8062
C2×#635802
C3×#45262
#105891872
#700343
#689643