Finite Group Databasebeta

← #11885772

Subgroups — #11885772

Order 1152.

1307 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63797C211yesmaximal, characteristic, complemented
2C2×D3×D24C211yesmaximal, characteristic, complemented
3#10594621C212yesmaximal, complemented
4#10592582C211yesmaximal, characteristic, complemented
5C3×#4883C211yesmaximal, characteristic, complemented
6C3×#4872C211yesmaximal, characteristic, complemented
7#10590880C211yesmaximal, characteristic, complemented
8C8×#626C211yesmaximal, characteristic, complemented
9#10590598C212yesmaximal, complemented
10#10590595C212yesmaximal, complemented
11#10590547C212yesmaximal, complemented
12#80729—31nomaximal
13D8×D12—31nomaximal
14C2×#3802C2212yescomplemented
15C2×D3×D12—22no—
16C2×D3×D12C2212yescomplemented
17C2×#3745C2211yescharacteristic, complemented
18C2×C8×C3⋊D3C2211yescharacteristic, complemented
19#64104C2212yescomplemented
20C2×C3×D24C2211yescharacteristic
21C2×C3×D24C2211yescharacteristic, complemented
22C2×C3×D3×C8C2211yescharacteristic, complemented
23C3×#895C2212yescomplemented
24C3×#893C2212yescomplemented
25#63923—22no—
26#63922—22no—
27#63911C2212yescomplemented
28#63906—22no—
29C4×#626C2211yescharacteristic
30C2×#3714C2212yescomplemented
31C2×#3714C2212yescomplemented
32C2×#3713C2212yescomplemented
33#63797—24no—
34D3×D24—24no—
35C32×#107C2211yescharacteristic, complemented
36#63636C2212yescomplemented
37C3×C8×Dic3C2211yescharacteristic, complemented
38C3×#809C2212yescomplemented
39C3×#809C2212yescomplemented
40Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
41#63557C2211yescharacteristic, complemented
42(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
43C2×D3×D8—31no—
44C2×D3×D8—31no—
45C2×D3×D8—31no—
46C22×D24—31no—
47#5609—32no—
48D4×D12—32no—
49C3×#466—31no—
50C3×C4×D8—31no—
51#5151—31no—
52C8×#67—31no—
53#5036—32no—
54#5015—32no—
55#4883—31no—
56#4883—31no—
57#4883—61no—
58#4883D311yescharacteristic, complemented
59#4872D311yescharacteristic, complemented
60#4786—32no—
61#4773—32no—
62#4773—32no—
63#4773—32no—
64#4695—31no—
65C8×D12—31no—
66C22×D32—22no—
67C22×D32—22no—
68C2×C4⋊(C3⋊D3)—22no—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×C4×C3⋊D3C2311yescharacteristic
71C2×C3×D12—22no—
72C2×C3×D12C2312yes—
73C2×C3×D12C2312yes—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3C2311yescharacteristic
76C2×#626—22no—
77C2×#626—22no—
78C2×#626—22no—
79C2×#626D411yescharacteristic
80C2×#625—22no—
81#3802—24no—
82#3802—42no—
83D3×D12—24no—
84D3×D12—42no—
85D3×D12—48no—
86C2×C32×C8C2311yescharacteristic
87C32×C4⋊C4C2312yes—
88#3752—22no—
89C2×C3⋊(C3⋊C8)C2311yescharacteristic
90#3745—22no—
91C8×C3⋊D3—22no—
92C3×(C2×D3)⋊C4—22no—
93C3×(C2×D3)⋊C4—22no—
94C3×C4×Dic3C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2311yescharacteristic
97C3×D24—22no—
98C3×D24D414yescomplemented
99C3×D3×C8—22no—
100Dic3⋊Dic3D411yescharacteristic
101#3722D411yescharacteristic
102(C2×D3)⋊Dic3D411yescharacteristic
103#3714—24no—
104#3714—42no—
105#3713—24no—
106D4×D8—91noSylow
107C2×D3×D4—32no—
108C2×D3×D4—32no—
109C2×D3×D4—32no—
110C2×D3×D4—62no—
111C22×D12—32no—
112C22×D12—62no—
113C2×C3×D8—31no—
114C2×C3×D8—31no—
115C22×C3×C8—31no—
116C3×#121—32no—
117C3×C4×D4—32no—
118#940—32no—
119#937—62no—
120C2×#213—32no—
121C2×#213—32no—
122C2×#213—32no—
123C2×#213—32no—
124#930—62no—
125C4×#67—31no—
126D3×D8—64no—
127D3×D8—64no—
128D3×D8—64no—
129C2×D24—32no—
130C2×D24—31no—
131C2×D24—31no—
132C2×D24—32no—
133C2×D24—61no—
134C2×D24—64no—
135C2×D24C2×D311yescharacteristic
136C2×D24C2×D311yescharacteristic, complemented
137C2×D3×C8—31no—
138C2×D3×C8—31no—
139C2×D3×C8—61no—
140C2×D3×C8C2×D311yescharacteristic, complemented
141#895—32no—
142#895—32no—
143#895—62no—
144#895C2×D312yescomplemented
145#893C2×D312yescomplemented
146#884—62no—
147#882—62no—
148#882—62no—
149#882—62no—
150#874—32no—
151C4×D12—31no—
152C3×#107—21no—
153C3×#107C2×D311yescharacteristic, complemented
154C3×#107C2×D311yescharacteristic, complemented
155C3×#102—32no—
156C3×#102—32no—
157C3×C4×C8—31no—
158#830—31no—
159(C2×D3)⋊C8—31no—
160(C2×D3)⋊C8—31no—
161(C2×D3)⋊C8—31no—
162Dic3⋊C8—31no—
163C8×Dic3C2×D311yescharacteristic, complemented
164#809—32no—
165#809—32no—
166#809—62no—
167#809C2×D312yescomplemented
168#809C2×D312yescomplemented
169C4⋊(C3⋊C8)—31no—
170C22×C3⋊D3—22no—
171C22×C3⋊D3C2×D411yescharacteristic
172C22×C3×D3—22no—
173C22×C3×D3—22no—
174C22×C3×D3C2×D411yescharacteristic
175C2×D32—44no—
176C2×D32—44no—
177C2×D32—44no—
178C2×D32—44no—
179C2×D32—82no—
180C2×D32—82no—
181C2×C32×C4—22no—
182C2×C32×C4C2411yescharacteristic
183C2×C3⋊Dic3C2×D411yescharacteristic
184C4⋊(C3⋊D3)—22no—
185C4⋊(C3⋊D3)—22no—
186C4⋊(C3⋊D3)—44no—
187C4×C3⋊D3—21no—
188C4×C3⋊D3—21no—
189C2×C3×Dic3C2×D411yescharacteristic
190C2×C3×Dic3C2×D411yescharacteristic
191C2×C3×Dic3C2×D411yescharacteristic
192C3×D12—22no—
193C3×D12—22no—
194C3×D12—22no—
195C3×D12—44no—
196C3×D12C2×D414yescomplemented
197C3×C4×D3—21no—
198C3×C4×D3—21no—
199C3×C4×D3—44no—
200#626—44no—
201#626—44no—
202#626—82no—
203#626D814yescomplemented
204#625—44no—
205C32×C8C2×D412yescomplemented
206C3⋊(C3⋊C8)—21no—
207C3×C3⋊C8—21no—
208C3×C3⋊C8—21no—
209C22×D8—91no—
210C22×D8—91no—
211D42—92no—
212#493—91no—
213#466—31no—
214#466—91no—
215#459—92no—
216#447—92no—
217#447—92no—
218C4×D8—31no—
219C8×D4—91no—
220C23×D3—62no—
221C23×D3—62no—
222C23×D3—62no—
223C23×D3—62no—
224C2×C3×D4—32no—
225C2×C3×D4—32no—
226C2×C3×D4—62no—
227C22×C3×C4—31no—
228C22×C3×C4—62no—
229C2×#67—31no—
230C2×#67—62no—
231C2×#67—62no—
232C2×#67—62no—
233C2×#67—62no—
234C2×#67—62no—
235D3×D4—64no—
236D3×D4—64no—
237D3×D4—64no—
238D3×D4—122no—
239D3×D4—128no—
240D3×D4—122no—
241D3×D4—122no—
242C2×D12—22no—
243C2×D12—31no—
244C2×D12—32no—
245C2×D12—32no—
246C2×D12—62no—
247C2×D12—64no—
248C2×D12—62no—
249C2×D12—62no—
250C2×D12—62no—
251C2×D12—62no—
252C2×D12—62no—
253C2×D12—122no—
254C2×D12—122no—
255C2×D12—128no—
256C2×D12C22×D312yes—
257C2×D12C22×D312yes—
258C2×C4×D3—22no—
259C2×C4×D3—31no—
260C2×C4×D3—31no—
261C2×C4×D3—61no—
262C2×C4×D3C22×D311yescharacteristic
263C3×D8—34no—
264C3×D8—62no—
265C2×C3×C8—21no—
266C2×C3×C8—31no—
267C2×C3×C8—31no—
268C2×C3×C8—62no—
269C2×C3×C8C22×D311yescharacteristic
270C2×C3×C8C22×D311yescharacteristic
271C3×C4⋊C4—22no—
272C3×C4⋊C4C22×D312yes—
273C3×C4⋊C4C22×D312yes—
274C3×C22⋊C4—62no—
275C3×C22⋊C4—62no—
276C3×C42—31no—
277#217—31no—
278#213—64no—
279#213—64no—
280#213—64no—
281#213—122no—
282(C2×D3)⋊C4—22no—
283(C2×D3)⋊C4—22no—
284(C2×D3)⋊C4—31no—
285(C2×D3)⋊C4—31no—
286(C2×D3)⋊C4—31no—
287(C2×D3)⋊C4—62no—
288(C2×D3)⋊C4—62no—
289(C2×D3)⋊C4—122no—
290C4⋊Dic3—31no—
291Dic3⋊C4—31no—
292C4×Dic3C22×D311yescharacteristic
293C2×C3⋊C8—31no—
294C2×C3⋊C8—31no—
295C2×C3⋊C8—61no—
296C2×C3⋊C8C22×D311yescharacteristic
297C2×C3⋊C8C22×D311yescharacteristic
298D24—22no—
299D24—64no—
300D24—62no—
301D24—62no—
302D24—122no—
303D24—122no—
304D24D1214yescomplemented
305D3×C8—22no—
306D3×C8—62no—
307D3×C8—62no—
308D3×C8—122no—
309C22×C32C22×D411yescharacteristic
310C2×C3⋊D3—21no—
311C2×C3⋊D3—21no—
312C2×C3⋊D3—42no—
313C2×C3⋊D3—42no—
314C2×C3⋊D3—42no—
315C2×C3⋊D3C2×D812yescomplemented
316C2×C3×D3—21no—
317C2×C3×D3—21no—
318C2×C3×D3—24no—
319C2×C3×D3—42no—
320C2×C3×D3—42no—
321C2×C3×D3—42no—
322C2×C3×D3—42no—
323C2×C3×D3—42no—
324C2×C3×D3C2×D812yescomplemented
325D32—88no—
326D32—88no—
327C32×C4—42no—
328C32×C4C22×D411yescharacteristic
329C32×C4H(5,𝔽2)11yescharacteristic
330C3⋊Dic3—21no—
331C3×Dic3—21no—
332C3×Dic3—21no—
333C3×Dic3C2×D812yescomplemented
334C22×D4—92no—
335C22×D4—92no—
336C22×D4—182no—
337C2×D8—31no—
338C2×D8—31no—
339C2×D8—92no—
340C2×D8—92no—
341C2×D8—92no—
342C2×D8—91no—
343C2×D8—184no—
344C2×D8—184no—
345C22×C8—31no—
346C22×C8—91no—
347#127—92no—
348#121—32no—
349#121—92no—
350#121—182no—
351#120—182no—
352#120—182no—
353C4×D4—32no—
354C4×D4—91no—
355#107D3211yescharacteristic, complemented
356C4⋊C8—91no—
357#102—32no—
358#102—32no—
359#102—92no—
360C22⋊C8—91no—
361C22⋊C8—91no—
362C4×C8—31no—
363C23×C3—31no—
364C23×C3—62no—
365C23×C3—62no—
366C22×D3—22no—
367C22×D3—22no—
368C22×D3—31no—
369C22×D3—31no—
370C22×D3—61no—
371C22×D3—62no—
372C22×D3—62no—
373C22×D3—122no—
374C22×D3—124no—
375C22×D3—124no—
376C22×D3—124no—
377C22×D3—124no—
378C22×D3—124no—
379C22×D3—124no—
380C22×D3—124no—
381C22×D3—124no—
382C22×D3—242no—
383C22×D3—242no—
384C22×D3—242no—
385C22×D3—242no—
386C22×D3D3×D411yescharacteristic
387C3×D4—34no—
388C3×D4—62no—
389C3×D4—62no—
390C3×D4—62no—
391C3×D4—124no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—21no—
395C2×C3×C4—31no—
396C2×C3×C4—31no—
397C2×C3×C4—31no—
398C2×C3×C4—42no—
399C2×C3×C4—61no—
400C2×C3×C4—61no—
401C2×C3×C4—124no—
402C2×C3×C4C23×D311yescharacteristic
403C2×C3×C4C23×D311yescharacteristic
404#67—34no—
405#67—124no—
406#67—124no—
407#67—124no—
408#67—124no—
409#67—242no—
410C2×Dic3—31no—
411C2×Dic3—31no—
412C2×Dic3—61no—
413C2×Dic3D3×D411yescharacteristic
414C2×Dic3D3×D411yescharacteristic
415C2×Dic3D3×D411yescharacteristic
416D12—22no—
417D12—22no—
418D12—22no—
419D12—34no—
420D12—44no—
421D12—62no—
422D12—62no—
423D12—62no—
424D12—62no—
425D12—122no—
426D12—122no—
427D12—124no—
428D12—124no—
429D12—124no—
430D12—124no—
431D12—244no—
432D12—242no—
433D12C2×D1214yescomplemented
434C4×D3—21no—
435C4×D3—21no—
436C4×D3—44no—
437C4×D3—61no—
438C4×D3—61no—
439C4×D3—61no—
440C4×D3—61no—
441C4×D3—121no—
442C4×D3—121no—
443C3×C8—22no—
444C3×C8—61no—
445C3×C8—61no—
446C3×C8C2×D1212yescomplemented
447C3×C8D3×D412yescomplemented
448C3⋊C8—21no—
449C3⋊C8—21no—
450C3⋊C8—61no—
451C3⋊C8—61no—
452C3⋊C8—121no—
453C2×C32D4211yescharacteristic
454C2×C32C22×D811yescharacteristic
455C2×C32#57611yescharacteristic
456C3⋊D3—22no—
457C3⋊D3—82no—
458C3×D3—22no—
459C3×D3—44no—
460C3×D3—82no—
461C24—182no—
462C24—182no—
463C2×D4—32no—
464C2×D4—32no—
465C2×D4—62no—
466C2×D4—91no—
467C2×D4—92no—
468C2×D4—182no—
469C2×D4—182no—
470C2×D4—182no—
471C2×D4—182no—
472C2×D4—184no—
473C2×D4—182no—
474C2×D4—184no—
475C2×D4—362no—
476C2×D4—368no—
477C2×D4—362no—
478C22×C4—31no—
479C22×C4—62no—
480C22×C4—91no—
481D8—34no—
482D8—62no—
483D8—184no—
484D8—184no—
485D8—182no—
486D8—362no—
487C2×C8—31no—
488C2×C8—31no—
489C2×C8—62no—
490C2×C8—91no—
491C2×C8—182no—
492C2×C8C2×D3211yescharacteristic
493C4⋊C4—91no—
494C4⋊C4C2×D3212yes—
495C22⋊C4—62no—
496C22⋊C4—62no—
497C22⋊C4—91no—
498C22⋊C4—91no—
499C22⋊C4—182no—
500C42—31no—
501C22×C3—21no—
502C22×C3—32no—
503C22×C3—61no—
504C22×C3—61no—
505C22×C3—64no—
506C22×C3—122no—
507C22×C3—122no—
508C22×C3—122no—
509C22×C3—122no—
510C22×C3—122no—
511C22×C3C2×D3×D411yescharacteristic
512C22×C3C2×D3×D411yescharacteristic
513C2×D3—21no—
514C2×D3—21no—
515C2×D3—24no—
516C2×D3—32no—
517C2×D3—32no—
518C2×D3—42no—
519C2×D3—42no—
520C2×D3—42no—
521C2×D3—42no—
522C2×D3—42no—
523C2×D3—62no—
524C2×D3—61no—
525C2×D3—61no—
526C2×D3—61no—
527C2×D3—61no—
528C2×D3—121no—
529C2×D3—121no—
530C2×D3—122no—
531C2×D3—122no—
532C2×D3—122no—
533C2×D3—122no—
534C2×D3—122no—
535C2×D3—122no—
536C2×D3—242no—
537C2×D3—242no—
538C2×D3—242no—
539C2×D3—248no—
540C2×D3—248no—
541C2×D3—248no—
542C2×D3—248no—
543C2×D3D3×D812yescomplemented
544C3×C4—21no—
545C3×C4—21no—
546C3×C4—32no—
547C3×C4—42no—
548C3×C4—42no—
549C3×C4—61no—
550C3×C4—61no—
551C3×C4—82no—
552C3×C4C22×D1211yescharacteristic
553C3×C4C2×D3×D411yescharacteristic
554C3×C4#100911yescharacteristic
555C3×C4#100911yescharacteristic
556Dic3—21no—
557Dic3—21no—
558Dic3—61no—
559Dic3—61no—
560Dic3—121no—
561Dic3D3×D812yescomplemented
562C32D4×D811yescharacteristic, complemented, Sylow
563C23—31no—
564C23—62no—
565C23—62no—
566C23—91no—
567C23—182no—
568C23—364no—
569C23—364no—
570C23—364no—
571C23—364no—
572C23—722no—
573C23—722no—
574D4—34no—
575D4—62no—
576D4—62no—
577D4—62no—
578D4—94no—
579D4—124no—
580D4—182no—
581D4—182no—
582D4—364no—
583D4—364no—
584D4—364no—
585D4—364no—
586D4—722no—
587C2×C4—22no—
588C2×C4—31no—
589C2×C4—31no—
590C2×C4—31no—
591C2×C4—61no—
592C2×C4—61no—
593C2×C4—91no—
594C2×C4—124no—
595C2×C4—181no—
596C2×C4—181no—
597C2×C4C22×D3211yescharacteristic
598C8—61no—
599C8—61no—
600C8—181no—
601C8D3×D1212yescomplemented
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—62no—
606C2×C3—124no—
607C2×C3—242no—
608C2×C3D4×D1211yescharacteristic
609C2×C3#560911yescharacteristic
610C2×C3C2×D3×D811yescharacteristic
611C2×C3C2×D3×D811yescharacteristic
612C2×C3#576911yescharacteristic
613C2×C3#576911yescharacteristic
614D3—22no—
615D3—44no—
616D3—62no—
617D3—62no—
618D3—82no—
619D3—122no—
620D3—242no—
621D3—242no—
622D3—482no—
623C22—32no—
624C22—61no—
625C22—61no—
626C22—64no—
627C22—92no—
628C22—122no—
629C22—122no—
630C22—122no—
631C22—122no—
632C22—122no—
633C22—181no—
634C22—181no—
635C22—362no—
636C22—362no—
637C22—362no—
638C22—728no—
639C22—728no—
640C22D32×D411yescharacteristic
641C4—32no—
642C4—42no—
643C4—61no—
644C4—61no—
645C4—181no—
646C4C2×D3×D1211yescharacteristic
647C4#6432011yescharacteristic
648C3—21no—
649C3D8×D1211yescharacteristic, complemented
650C3#8072911yescharacteristic, complemented
651C2—62no—
652C2—124no—
653C2—182no—
654C2—242no—
655C2—722no—
656C2#1059462111yescharacteristic
657C2D32×D811yescharacteristic
658C2#1059477111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
hypercenter#107D32
hypocenterC32D4×D8
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
1. C2×#63797C2semidirect
2. C2×D3×D24C2semidirect
3. #10594621C2semidirect
4. #10592582C2semidirect
5. C3×#4883C2semidirect
6. C3×#4872C2semidirect
7. #10590880C2semidirect
8. C8×#626C2semidirect
9. #10590598C2semidirect
10. #10590595C2semidirect
11. #10590547C2semidirect
14. C2×#3802C22semidirect
16. C2×D3×D12C22semidirect
17. C2×#3745C22semidirect
18. C2×C8×C3⋊D3C22semidirect
19. #64104C22semidirect
21. C2×C3×D24C22semidirect
22. C2×C3×D3×C8C22semidirect
23. C3×#895C22semidirect
24. C3×#893C22semidirect
27. #63911C22semidirect
30. C2×#3714C22semidirect
31. C2×#3714C22semidirect
32. C2×#3713C22semidirect
35. C32×#107C22semidirect
36. #63636C22semidirect
37. C3×C8×Dic3C22semidirect
38. C3×#809C22semidirect
39. C3×#809C22semidirect
40. Dic3⋊(C3⋊C8)C22semidirect
41. #63557C22semidirect
42. (C2×D3)⋊(C3⋊C8)C22semidirect
58. #4883D3semidirect
59. #4872D3semidirect
98. C3×D24D4semidirect
136. C2×D24C2×D3semidirect
140. C2×D3×C8C2×D3semidirect
144. #895C2×D3semidirect
145. #893C2×D3semidirect
153. C3×#107C2×D3semidirect
154. C3×#107C2×D3semidirect
163. C8×Dic3C2×D3semidirect
167. #809C2×D3semidirect
168. #809C2×D3semidirect
196. C3×D12C2×D4semidirect
203. #626D8semidirect
205. C32×C8C2×D4semidirect
304. D24D12semidirect
315. C2×C3⋊D3C2×D8semidirect
324. C2×C3×D3C2×D8semidirect
333. C3×Dic3C2×D8semidirect
355. #107D32semidirect
433. D12C2×D12semidirect
446. C3×C8C2×D12semidirect
447. C3×C8D3×D4semidirect
543. C2×D3D3×D8semidirect
561. Dic3D3×D8semidirect
562. C32D4×D8semidirect
601. C8D3×D12semidirect
649. C3D8×D12semidirect
650. C3#80729semidirect

Maximal subgroups

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

subgroupindex
C2×#637972
C2×D3×D242
#105946212
#105925822
C3×#48832
C3×#48722
#105908802
C8×#6262
#105905982
#105905952
#105905472
#807293
D8×D123