Finite Group Databasebeta

← #11864452

Subgroups — #11864452

Order 1152.

1613 conjugacy classes of subgroups.

The subgroup lattice has 645 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C2×#64158C211yesmaximal, characteristic, complemented
3#10595045C211yesmaximal, characteristic, complemented
4C22×#3717C211yesmaximal, characteristic, complemented
5C3×#5233C211yesmaximal, characteristic, complemented
6#10591584C214yesmaximal, complemented
7#10591452C214yesmaximal, complemented
8#10591099C211yesmaximal, characteristic, complemented
9#10591070C211yesmaximal, characteristic, complemented
10#84113—31nomaximal
11#78836—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C3×#1010—24no—
15C3×#1010—24no—
16C2×C3×D3×Q8C2212yescomplemented
17C2×C3×#237—22no—
18C2×C3×#237C2212yescomplemented
19C2×C3×#235—21no—
20C2×C3×#235C2211yescharacteristic
21C22×C3×Dic6—21no—
22C22×C3×Dic6C2211yescharacteristic
23#64158—24no—
24C2×#3755C2212yes—
25C2×#3753C2212yes—
26C2×#3748C2211yescharacteristic
27C3×#926C2211yescharacteristic
28C22×C3×C3⋊C8C2211yescharacteristic
29#63981—22no—
30#63911—21no—
31#63909C2214yes—
32#63864—21no—
33C2×#3717—24no—
34C2×#3717C2214yes—
35C3×#835C2212yescomplemented
36C3×#832C2212yescomplemented
37#63565C2214yescomplemented
38(C2×D3)⋊(C3⋊C8)C2214yescomplemented
39C2×C3×2−1+4—31no—
40C2×#1010D311yescharacteristic, complemented
41#5830—31no—
42C2×#949—31no—
43C2×#949—31no—
44C2×#949—61no—
45C22×#215—31no—
46C22×#204—31no—
47#5525—31no—
48C3×#416—31no—
49#5238—34no—
50#5234—31no—
51#5233D311yescharacteristic, complemented
52#5227—34no—
53#5225—31no—
54#5110—31no—
55#5004—31no—
56#4806—34no—
57#4781—34no—
58C23×C3⋊D3—21no—
59C32×#41—22no—
60C32×#41D414yescomplemented
61C2×C32×Q8C2311yescharacteristic
62C2×C32×D4—21no—
63C2×C32×D4C2311yescharacteristic
64C22×C32×C4—21no—
65C22×C32×C4C2311yescharacteristic
66C2×C4⋊(C3⋊D3)—22no—
67C2×C4⋊(C3⋊D3)—22no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×C3×#67—22no—
71C2×C3×#67D412yes—
72C22×C3×Dic3—21no—
73C22×C3×Dic3—22no—
74C3×D3×Q8—24no—
75C3×D3×Q8—24no—
76C3×#237—216no—
77C3×#237—24no—
78C3×#237—24no—
79C3×#235—28no—
80C3×#235—22no—
81C3×#235—22no—
82C2×C3×D12D411yescharacteristic
83C2×C3×C4×D3—22no—
84C2×C3×C4×D3C2312yes—
85C2×C3×Dic6—28no—
86C2×C3×Dic6—21no—
87C2×C3×Dic6—22no—
88C2×C3×Dic6—22no—
89C2×C3×Dic6D411yescharacteristic
90C2×C3×Dic6D414yescomplemented
91C2×C3×Dic6C2312yes—
92C2×#626—24no—
93#3755—24no—
94#3753—24no—
95#3748—22no—
96C2×C3⋊(C3⋊C8)C2312yes—
97C3×#217—21no—
98C3×C4⋊Dic3C2312yes—
99C3×C4×Dic3—21no—
100C2×C3×C3⋊C8—22no—
101C2×C3×C3⋊C8C2312yes—
102#3722—24no—
103#3717—28no—
104#3010—91noSylow
105C3×2−1+4—64no—
106C3×2−1+4—64no—
107C2×C3×#41—21no—
108C2×C3×#41—31no—
109C2×C3×#41—32no—
110C2×C3×#41—61no—
111C2×C3×#41—62no—
112C2×C3×#41C2×D311yescharacteristic
113C2×C3×#41C2×D311yescharacteristic
114C22×C3×Q8—32no—
115C22×C3×Q8—31no—
116C22×C3×Q8—61no—
117#1010—24no—
118#1010—24no—
119C2×D3×Q8C2×D312yescomplemented
120C2×#237—22no—
121C2×#237C2×D312yescomplemented
122C2×#235—21no—
123C2×#235C2×D311yescharacteristic
124C22×D12—31no—
125C22×D12—31no—
126C22×D12—61no—
127C22×Dic6—21no—
128C22×Dic6C2×D311yescharacteristic
129C22×C3×C8—31no—
130C3×#117—31no—
131#949—68no—
132#949—64no—
133#949—64no—
134#947—61no—
135C2×#215—32no—
136C2×#215—32no—
137C2×#215—34no—
138C2×#215—62no—
139C2×#215—64no—
140#940—61no—
141#937—62no—
142C2×#213—32no—
143C2×#213—32no—
144C2×#213—62no—
145#930—34no—
146#926C2×D311yescharacteristic
147C2×#208—31no—
148C2×#208—31no—
149C2×#208—61no—
150C22×C3⋊C8C2×D311yescharacteristic
151C2×#204—34no—
152C2×#204—64no—
153#895—34no—
154#882—62no—
155#875—61no—
156#874—61no—
157C3×#103—32no—
158C3×#102—32no—
159#835—34no—
160#835C2×D312yescomplemented
161#832C2×D312yescomplemented
162#830—34no—
163(C2×D3)⋊C8—34no—
164#810—34no—
165C23×C32—21no—
166C23×C32C2×D411yescharacteristic
167C22×C3⋊D3—22no—
168C22×C3⋊D3—42no—
169C22×C3⋊D3—82no—
170C22×C3×D3C2×D412yes—
171C32×Q8—21no—
172C32×Q8C2×D412yes—
173C32×D4—24no—
174C32×D4—21no—
175C32×D4C2×D412yes—
176C2×C32×C4—21no—
177C2×C32×C4—24no—
178C2×C32×C4C2×D412yes—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D412yes—
181C2×C32×C4C2411yescharacteristic
182C4⋊(C3⋊D3)—22no—
183C4⋊(C3⋊D3)—22no—
184C4⋊(C3⋊D3)—42no—
185C3×#67—28no—
186C3×#67—24no—
187C2×C3×Dic3—28no—
188C2×C3×Dic3—24no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3C2×D412yes—
192C3×D12—22no—
193C3×C4×D3—28no—
194C3×C4×D3—22no—
195C3×C4×D3—22no—
196C3×Dic6—28no—
197C3×Dic6—22no—
198C3×Dic6—24no—
199C3×Dic6—22no—
200C3×Dic6C2×D414yes—
201#626—84no—
202C3⋊(C3⋊C8)—22no—
203C3×C3⋊C8—22no—
204C2×2−1+4—31no—
205C2×AGL(1,ℤ/8)—91no—
206C22×SD16—91no—
207#535—91no—
208#449—94no—
209#448—94no—
210#419—91no—
211#416—31no—
212#408—91no—
213C23×D3—61no—
214C23×D3—61no—
215C23×D3—121no—
216C3×#41—22no—
217C3×#41—22no—
218C3×#41—24no—
219C3×#41—42no—
220C3×#41—68no—
221C3×#41—64no—
222C3×#41—616no—
223C3×#41—64no—
224C3×#41—62no—
225C3×#41—62no—
226C3×#41D1214yescomplemented
227C3×#41#6714yescomplemented
228C2×C3×Q8—21no—
229C2×C3×Q8—31no—
230C2×C3×Q8—34no—
231C2×C3×Q8—32no—
232C2×C3×Q8—62no—
233C2×C3×Q8—68no—
234C2×C3×Q8—64no—
235C2×C3×Q8—64no—
236C2×C3×Q8—62no—
237C2×C3×Q8—61no—
238C2×C3×Q8C22×D311yescharacteristic
239C2×C3×Q8C22×D311yescharacteristic
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—32no—
244C2×C3×D4—31no—
245C2×C3×D4—41no—
246C2×C3×D4—62no—
247C2×C3×D4C22×D311yescharacteristic
248C2×C3×D4C22×D311yescharacteristic
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—32no—
253C22×C3×C4—41no—
254C22×C3×C4—62no—
255C22×C3×C4—62no—
256C22×C3×C4—61no—
257C22×C3×C4C22×D311yescharacteristic
258C22×C3×C4C22×D311yescharacteristic
259C2×#67—22no—
260C2×#67—64no—
261C2×#67#6712yes—
262C22×Dic3—21no—
263C22×Dic3—22no—
264D3×Q8—24no—
265D3×Q8—24no—
266#237—216no—
267#237—24no—
268#237—24no—
269#235—28no—
270#235—22no—
271#235—22no—
272C2×D12—32no—
273C2×D12—32no—
274C2×D12—62no—
275C2×D12—64no—
276C2×D12—62no—
277C2×D12—62no—
278C2×D12—62no—
279C2×D12—62no—
280C2×D12—61no—
281C2×D12—61no—
282C2×D12—64no—
283C2×D12—122no—
284C2×D12—121no—
285C2×D12#6711yescharacteristic
286C2×C4×D3—22no—
287C2×C4×D3C22×D312yes—
288C2×Dic6—28no—
289C2×Dic6—21no—
290C2×Dic6—22no—
291C2×Dic6—22no—
292C2×Dic6#6711yescharacteristic
293C2×Dic6#6714yescomplemented
294C2×Dic6C22×D312yes—
295C2×C3×C8—32no—
296C2×C3×C8—62no—
297C3×C4⋊C4—32no—
298C3×C22⋊C4—61no—
299C3×C42—61no—
300#217—21no—
301#215—68no—
302#215—68no—
303#215—64no—
304#215—64no—
305#213—68no—
306#213—64no—
307#213—64no—
308(C2×D3)⋊C4—64no—
309(C2×D3)⋊C4—64no—
310C4⋊Dic3C22×D312yes—
311C4×Dic3—21no—
312#208—64no—
313#208—62no—
314#208—62no—
315C2×C3⋊C8—22no—
316C2×C3⋊C8—32no—
317C2×C3⋊C8—32no—
318C2×C3⋊C8—62no—
319C2×C3⋊C8C22×D312yes—
320#204—68no—
321C22×C32—22no—
322C22×C32—22no—
323C22×C32—42no—
324C22×C32#12012yes—
325C22×C32C22×D411yescharacteristic
326C2×C3⋊D3—42no—
327C2×C3⋊D3—44no—
328C2×C3⋊D3—84no—
329C2×C3×D3—22no—
330C2×C3×D3—24no—
331C32×C4—22no—
332C32×C4#12012yes—
333C32×C4C22×D411yescharacteristic
334C32×C4C22×D411yescharacteristic
335C3×Dic3—22no—
336C3×Dic3—24no—
337C3×Dic3—42no—
3382−1+4—64no—
3392−1+4—64no—
340C2×#41—31no—
341C2×#41—32no—
342C2×#41—61no—
343C2×#41—62no—
344C2×#41D3211yescharacteristic
345C22×Q8—32no—
346C22×Q8—31no—
347C22×Q8—61no—
348C22×D4—91no—
349AGL(1,ℤ/8)—184no—
350C2×SD16—94no—
351C2×SD16—92no—
352C2×SD16—184no—
353C2×D8—92no—
354C2×M16—91no—
355C22×C8—31no—
356#127—181no—
357#124—181no—
358#121—94no—
359#120—182no—
360#117—31no—
361#103—32no—
362#103—94no—
363#102—32no—
364C22⋊C8—94no—
365C23×C3—21no—
366C23×C3—21no—
367C23×C3—21no—
368C23×C3—32no—
369C23×C3—41no—
370C23×C3D3×D411yescharacteristic
371C23×C3C2×#6711yescharacteristic
372C22×D3—62no—
373C22×D3—62no—
374C22×D3—122no—
375C22×D3—124no—
376C22×D3—122no—
377C22×D3—122no—
378C22×D3—242no—
379C22×D3—242no—
380C22×D3—244no—
381C22×D3C2×#6712yes—
382C3×Q8—21no—
383C3×Q8—21no—
384C3×Q8—22no—
385C3×Q8—34no—
386C3×Q8—41no—
387C3×Q8—68no—
388C3×Q8—62no—
389C3×Q8—64no—
390C3×Q8—62no—
391C3×Q8C2×D1212yes—
392C3×Q8C2×#6712yes—
393C3×D4—24no—
394C3×D4—24no—
395C3×D4—21no—
396C3×D4—21no—
397C3×D4—22no—
398C3×D4—41no—
399C3×D4—44no—
400C3×D4—68no—
401C3×D4—64no—
402C3×D4—62no—
403C3×D4C2×D1212yes—
404C3×D4C2×#6712yes—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—24no—
408C2×C3×C4—24no—
409C2×C3×C4—21no—
410C2×C3×C4—22no—
411C2×C3×C4—21no—
412C2×C3×C4—22no—
413C2×C3×C4—32no—
414C2×C3×C4—44no—
415C2×C3×C4—41no—
416C2×C3×C4—68no—
417C2×C3×C4—68no—
418C2×C3×C4—64no—
419C2×C3×C4—62no—
420C2×C3×C4—62no—
421C2×C3×C4—62no—
422C2×C3×C4—62no—
423C2×C3×C4C2×D1212yes—
424C2×C3×C4D3×D411yescharacteristic
425C2×C3×C4D3×D412yes—
426C2×C3×C4C2×#6712yes—
427C2×C3×C4C2×#6711yescharacteristic
428C2×C3×C4C2×#6712yes—
429C2×C3×C4C23×D311yescharacteristic
430C2×C3×C4C23×D311yescharacteristic
431#67—28no—
432#67—24no—
433#67—244no—
434C2×Dic3—28no—
435C2×Dic3—24no—
436C2×Dic3—22no—
437C2×Dic3—22no—
438C2×Dic3C2×#6712yes—
439D12—22no—
440D12—64no—
441D12—62no—
442D12—62no—
443D12—62no—
444D12—62no—
445D12—122no—
446D12—124no—
447D12—122no—
448D12—122no—
449D12—244no—
450C4×D3—28no—
451C4×D3—22no—
452C4×D3—22no—
453Dic6—28no—
454Dic6—22no—
455Dic6—24no—
456Dic6—22no—
457Dic6C2×#6714yes—
458C3×C8—62no—
459C3⋊C8—22no—
460C3⋊C8—64no—
461C3⋊C8—62no—
462C3⋊C8—62no—
463C2×C32—22no—
464C2×C32—42no—
465C2×C32C2×#12011yescharacteristic
466C2×C32#57712yes—
467C3⋊D3—82no—
468C3×D3—42no—
469C24—181no—
470#41—22no—
471#41—68no—
472#41—64no—
473#41—616no—
474#41—64no—
475#41—62no—
476#41—62no—
477#41#62614yescomplemented
478C2×Q8—31no—
479C2×Q8—32no—
480C2×Q8—34no—
481C2×Q8—62no—
482C2×Q8—68no—
483C2×Q8—64no—
484C2×Q8—64no—
485C2×Q8—62no—
486C2×Q8—61no—
487C2×Q8C2×D3211yescharacteristic
488C2×D4—21no—
489C2×D4—32no—
490C2×D4—31no—
491C2×D4—62no—
492C2×D4—92no—
493C2×D4—184no—
494C2×D4—182no—
495C2×D4—182no—
496C2×D4—181no—
497C2×D4C2×D3211yescharacteristic
498C22×C4—21no—
499C22×C4—32no—
500C22×C4—62no—
501C22×C4—62no—
502C22×C4—61no—
503C22×C4C2×D3211yescharacteristic
504SD16—188no—
505SD16—184no—
506D8—184no—
507M16—182no—
508C2×C8—32no—
509C2×C8—62no—
510C2×C8—92no—
511C4⋊C4—32no—
512C22⋊C4—61no—
513C22⋊C4—184no—
514C42—61no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—22no—
519C22×C3—21no—
520C22×C3—22no—
521C22×C3—42no—
522C22×C3—42no—
523C22×C3—42no—
524C22×C3—42no—
525C22×C3—62no—
526C22×C3—64no—
527C22×C3—82no—
528C22×C3#88212yes—
529C22×C3#95312yes—
530C22×C3C2×D3×D411yescharacteristic
531C22×C3C22×#6711yescharacteristic
532C2×D3—24no—
533C2×D3—22no—
534C2×D3—124no—
535C2×D3—122no—
536C2×D3—124no—
537C2×D3—124no—
538C2×D3—122no—
539C2×D3—244no—
540C2×D3—244no—
541C2×D3—244no—
542C2×D3—248no—
543C3×C4—22no—
544C3×C4—22no—
545C3×C4—21no—
546C3×C4—21no—
547C3×C4—22no—
548C3×C4—42no—
549C3×C4—62no—
550C3×C4—64no—
551C3×C4—122no—
552C3×C4#88212yes—
553C3×C4#95312yes—
554C3×C4C22×D1211yescharacteristic
555C3×C4C2×D3×D411yescharacteristic
556C3×C4C22×#6711yescharacteristic
557C3×C4C22×#6711yescharacteristic
558Dic3—22no—
559Dic3—24no—
560Dic3—42no—
561C32#301011yescharacteristic, complemented, Sylow
562C23—21no—
563C23—32no—
564C23—182no—
565C23—362no—
566C23—722no—
567C23D3×#6711yescharacteristic
568Q8—21no—
569Q8—34no—
570Q8—68no—
571Q8—62no—
572Q8—62no—
573Q8—64no—
574Q8C2×#62612yes—
575D4—24no—
576D4—21no—
577D4—68no—
578D4—64no—
579D4—62no—
580D4—182no—
581D4—182no—
582D4—362no—
583D4—724no—
584D4C2×#62612yes—
585C2×C4—21no—
586C2×C4—24no—
587C2×C4—32no—
588C2×C4—68no—
589C2×C4—68no—
590C2×C4—62no—
591C2×C4—64no—
592C2×C4—62no—
593C2×C4—62no—
594C2×C4—62no—
595C2×C4C2×#62612yes—
596C2×C4D3×#6712yes—
597C2×C4D3×#6711yescharacteristic
598C2×C4C22×D3211yescharacteristic
599C8—62no—
600C8—182no—
601C2×C3—22no—
602C2×C3—22no—
603C2×C3—22no—
604C2×C3—21no—
605C2×C3—42no—
606C2×C3—42no—
607C2×C3—42no—
608C2×C3—82no—
609C2×C3—122no—
610C2×C3C2×#88211yescharacteristic
611C2×C3#577012yes—
612C2×C3#583712yes—
613C2×C3C2×#95311yescharacteristic
614D3—42no—
615D3—244no—
616D3—242no—
617D3—242no—
618C22—22no—
619C22—22no—
620C22—42no—
621C22—64no—
622C22—62no—
623C22—364no—
624C22—362no—
625C22—724no—
626C22#6397712yes—
627C22C2×D3×#6711yescharacteristic
628C4—22no—
629C4—62no—
630C4—64no—
631C4—122no—
632C4#6397712yes—
633C4C22×#62611yescharacteristic
634C4C2×D3×#6711yescharacteristic
635C3—21no—
636C3#7883611yescharacteristic, complemented
637C3#8411311yescharacteristic, complemented
638C2—22no—
639C2—42no—
640C2—122no—
641C2—722no—
642C2#1059545712yes—
643C2C2×#6397711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3010
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C2×#64158C2semidirect
3. #10595045C2semidirect
4. C22×#3717C2semidirect
5. C3×#5233C2semidirect
6. #10591584C2semidirect
7. #10591452C2semidirect
8. #10591099C2semidirect
9. #10591070C2semidirect
16. C2×C3×D3×Q8C22semidirect
18. C2×C3×#237C22semidirect
35. C3×#835C22semidirect
36. C3×#832C22semidirect
37. #63565C22semidirect
38. (C2×D3)⋊(C3⋊C8)C22semidirect
40. C2×#1010D3semidirect
51. #5233D3semidirect
60. C32×#41D4semidirect
90. C2×C3×Dic6D4semidirect
119. C2×D3×Q8C2×D3semidirect
121. C2×#237C2×D3semidirect
160. #835C2×D3semidirect
161. #832C2×D3semidirect
226. C3×#41D12semidirect
227. C3×#41#67semidirect
293. C2×Dic6#67semidirect
477. #41#626semidirect
561. C32#3010semidirect
636. C3#78836semidirect
637. C3#84113semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C2×#641582
#105950452
C22×#37172
C3×#52332
#105915842
#105914522
#105910992
#105910702
#841133
#788363