Finite Group Databasebeta

← #11870451

Subgroups — #11870451

Order 1152.

1054 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5716C211yesmaximal, characteristic, complemented
2C4×D3×D12C211yesmaximal, characteristic, complemented
3#10592771C211yesmaximal, characteristic, complemented
4C3×#5072C211yesmaximal, characteristic, complemented
5#10591515C212yesmaximal, complemented
6Dic3×#213C212yesmaximal, complemented
7#10591413C212yesmaximal, complemented
8#10591400C212yesmaximal, complemented
9#10590313C211yesmaximal, characteristic, complemented
10#10590269C211yesmaximal, characteristic, complemented
11#10590248C211yesmaximal, characteristic, complemented
12#83298—31nomaximal
13#80312—31nomaximal
14C2×C3×#237—21no—
15C2×D3×D12C2211yescharacteristic
16C2×C4×D32—21no—
17C32×#127C2211yescharacteristic, complemented
18C2×#3753C2212yes—
19C4×C4⋊(C3⋊D3)C2211yescharacteristic
20C3×#938—21no—
21C3×#938C2212yes—
22C3×#936—21no—
23C3×D4×Dic3—21no—
24C3×D4×Dic3C2212yescomplemented
25C2×C3×#213C2212yes—
26C3×C4×D12C2211yescharacteristic
27C3×C42×D3C2211yescharacteristic
28C3×#869C2211yescharacteristic, complemented
29D3×(C2×D3)⋊C4—21no—
30C4×#626—21no—
31#63894C2211yescharacteristic
32Dic3×D12C2211yescharacteristic
33D3×C4⋊Dic3C2211yescharacteristic
34#63880—21no—
35#63659C2212yescomplemented
36C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
37C3×#832C2212yescomplemented
38C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
39#63576C2212yescomplemented
40#63575C2212yescomplemented
41#63564C2212yes—
42#63562C2212yes—
43(C2×D3)⋊(C3⋊C8)C2212yes—
44Dic3×C3⋊C8C2212yescomplemented
45C3×#532—31no—
46#5716D311yescharacteristic, complemented
47C4×D3×D4—31no—
48C2×C4×D12—31no—
49C3×#459—31no—
50#5156—32no—
51Dic3×D8—32no—
52#5087—31no—
53#5087—31no—
54#5072—31no—
55#5072—31no—
56#5072—61no—
57#5072D311yescharacteristic, complemented
58#5036—32no—
59#5033—32no—
60C4×#213—32no—
61C4×#213—32no—
62#5007—31no—
63#4925—31no—
64#4846—31no—
65#4833—31no—
66#4774—32no—
67#4756—32no—
68C22×D32—21no—
69C2×C32×D4—21no—
70C2×C32×D4—21no—
71C2×C32×D4C2312yes—
72C2×C4⋊(C3⋊D3)C2311yescharacteristic
73C2×C4×C3⋊D3—21no—
74C2×C3×#67—22no—
75C22×C3×Dic3—22no—
76C3×#237—44no—
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3D411yescharacteristic
80C2×C3×C4×D3D411yescharacteristic
81C2×C3×C4×D3C2311yescharacteristic
82C2×C3×Dic6—21no—
83C2×#626—21no—
84C2×#624—21no—
85C2×D3×Dic3—21no—
86C2×D3×Dic3—21no—
87D3×D12—22no—
88D3×D12—22no—
89C4×D32—44no—
90C32×C42C2311yescharacteristic
91#3753—24no—
92#3752—21no—
93C4⋊(C3⋊Dic3)C2311yescharacteristic
94C2×C3⋊(C3⋊C8)C2312yes—
95C3×#217—22no—
96C3×#217—22no—
97C3×#213—24no—
98C3×(C2×D3)⋊C4—21no—
99C3×C4⋊Dic3—21no—
100C3×C4⋊Dic3C2312yes—
101C3×C4⋊Dic3C2311yescharacteristic
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3D411yescharacteristic
104C3×C4×Dic3C2311yescharacteristic
105C2×C3×C3⋊C8C2312yes—
106Dic3⋊Dic3—21no—
107#3722—21no—
108(C2×D3)⋊Dic3—21no—
109#3100—91noSylow
110C2×C3×#41—61no—
111C2×#237—21no—
112C2×D3×D4—31no—
113C22×D12—31no—
114C22×C4×D3—61no—
115C22×C4×D3—61no—
116C2×C3×D8—32no—
117C3×C4⋊Q8—31no—
118C3×#127—21no—
119C3×#127C2×D311yescharacteristic, complemented
120C3×#127C2×D311yescharacteristic, complemented
121C3×#124—61no—
122C3×#121—32no—
123C3×#121—61no—
124C3×C4×D4—32no—
125C3×C4×D4—31no—
126C3×C4×D4—61no—
127C2×C3×C42—31no—
128#938—21no—
129#938C2×D312yes—
130#936—21no—
131D4×Dic3—21no—
132D4×Dic3—31no—
133D4×Dic3C2×D312yescomplemented
134C2×#213—32no—
135C2×#213—32no—
136C2×#213—62no—
137C2×#213C2×D312yes—
138C4×#67—61no—
139C2×(C2×D3)⋊C4—61no—
140C2×C4⋊Dic3—31no—
141#893—31no—
142D3×C4⋊C4—31no—
143#67⋊C4—61no—
144D3×C22⋊C4—61no—
145C4×D12—31no—
146C4×D12—31no—
147C4×D12—31no—
148C4×D12—31no—
149C4×D12—61no—
150C4×D12—61no—
151C4×D12—61no—
152C4×D12C2×D311yescharacteristic
153C42×D3C2×D311yescharacteristic
154#869C2×D311yescharacteristic, complemented
155C3×C4⋊C8—31no—
156C3×#102—32no—
157#832—32no—
158#832—32no—
159#832—32no—
160#832—62no—
161#832C2×D312yescomplemented
162#830—32no—
163#821—32no—
164(C2×D3)⋊C8—32no—
165#818—32no—
166C8×Dic3—32no—
167#809—32no—
168#809—32no—
169#807—32no—
170#807—32no—
171#807—32no—
172C4⋊(C3⋊C8)—31no—
173C4⋊(C3⋊C8)—31no—
174C4⋊(C3⋊C8)—61no—
175C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
176C4×C3⋊C8—32no—
177C23×C32—22no—
178C22×C3⋊D3—21no—
179C22×C3×D3—21no—
180C22×C3×D3C2×D411yescharacteristic
181C2×D32—24no—
182C2×D32—42no—
183C2×D32—42no—
184C32×D4—22no—
185C32×D4—22no—
186C32×D4—42no—
187C32×D4—42no—
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2411yescharacteristic
191C2×C3⋊Dic3—21no—
192C4⋊(C3⋊D3)—21no—
193C4⋊(C3⋊D3)#4112yescomplemented
194C4×C3⋊D3—42no—
195C3×#67—44no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—44no—
199C2×C3×Dic3C2×D411yescharacteristic
200C2×C3×Dic3C2×D411yescharacteristic
201C2×C3×Dic3C2×D411yescharacteristic
202C3×D12—21no—
203C3×D12#4112yescomplemented
204C3×C4×D3—21no—
205C3×C4×D3—21no—
206C3×C4×D3—41no—
207C3×C4×D3—42no—
208C3×C4×D3D814yescomplemented
209C3×Dic6—42no—
210#626—24no—
211#624—42no—
212D3×Dic3—42no—
213D3×Dic3—42no—
214C3⋊(C3⋊C8)—22no—
215C3×C3⋊C8—22no—
216#532—31no—
217C2×C4×D4—91no—
218#480—92no—
219#474—91no—
220#474—91no—
221#459—31no—
222#459—91no—
223#447—92no—
224C4×D8—92no—
225C4×D8—92no—
226#431—91no—
227C23×D3—61no—
228C23×D3—61no—
229C3×#41—124no—
230C2×C3×Q8—61no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—22no—
236C2×C3×D4—31no—
237C2×C3×D4—41no—
238C2×C3×D4—41no—
239C2×C3×D4—62no—
240C2×C3×D4C22×D312yes—
241C2×C3×D4C22×D312yes—
242C22×C3×C4—31no—
243C22×C3×C4—31no—
244C22×C3×C4—31no—
245C22×C3×C4—62no—
246C22×C3×C4—61no—
247C2×#67—22no—
248C2×#67—61no—
249C22×Dic3—22no—
250C22×Dic3—61no—
251C22×Dic3—61no—
252#237—44no—
253D3×D4—62no—
254D3×D4—62no—
255C2×D12—31no—
256C2×D12—31no—
257C2×D12—61no—
258C2×D12—62no—
259C2×D12—61no—
260C2×D12—62no—
261C2×D12C22×D311yescharacteristic
262C2×C4×D3—21no—
263C2×C4×D3—61no—
264C2×C4×D3—61no—
265C2×C4×D3—61no—
266C2×C4×D3—61no—
267C2×C4×D3—61no—
268C2×C4×D3—61no—
269C2×C4×D3—121no—
270C2×C4×D3—124no—
271C2×C4×D3—124no—
272C2×C4×D3#6711yescharacteristic
273C2×C4×D3#6711yescharacteristic
274C2×C4×D3C22×D311yescharacteristic
275C2×Dic6—21no—
276C3×D8—64no—
277C2×C3×C8—32no—
278C3×C4⋊C4—32no—
279C3×C4⋊C4—31no—
280C3×C4⋊C4—61no—
281C3×C22⋊C4—62no—
282C3×C22⋊C4—62no—
283C3×C22⋊C4—61no—
284C3×C42—21no—
285C3×C42—31no—
286C3×C42—31no—
287C3×C42—31no—
288C3×C42C22×D311yescharacteristic
289C3×C42C22×D311yescharacteristic
290#217—22no—
291#217—22no—
292#217—61no—
293#213—24no—
294#213—64no—
295#213—64no—
296#213—124no—
297(C2×D3)⋊C4—21no—
298(C2×D3)⋊C4—61no—
299(C2×D3)⋊C4—61no—
300(C2×D3)⋊C4—61no—
301(C2×D3)⋊C4—61no—
302(C2×D3)⋊C4—61no—
303(C2×D3)⋊C4—121no—
304C4⋊Dic3—21no—
305C4⋊Dic3—31no—
306C4⋊Dic3—31no—
307C4⋊Dic3—61no—
308C4⋊Dic3—61no—
309C4⋊Dic3C22×D311yescharacteristic
310C4⋊Dic3C22×D312yes—
311Dic3⋊C4—61no—
312C4×Dic3#6711yescharacteristic
313C4×Dic3#6711yescharacteristic
314C4×Dic3C22×D311yescharacteristic
315C2×C3⋊C8—32no—
316C2×C3⋊C8—32no—
317C2×C3⋊C8—62no—
318C2×C3⋊C8C22×D312yes—
319C22×C32—42no—
320C22×C32—42no—
321C22×C32—42no—
322C22×C32C22×D411yescharacteristic
323C2×C3⋊D3—22no—
324C2×C3⋊D3—41no—
325C2×C3⋊D3—41no—
326C2×C3×D3—21no—
327C2×C3×D3—21no—
328C2×C3×D3—22no—
329C2×C3×D3—41no—
330C2×C3×D3—41no—
331C2×C3×D3C2×D812yes—
332D32—48no—
333C32×C4—21no—
334C32×C4C2×D812yes—
335C32×C4C2×#4111yescharacteristic
336C32×C4C2×#4111yescharacteristic
337C3⋊Dic3—41no—
338C3×Dic3—21no—
339C3×Dic3—21no—
340C3×Dic3—41no—
341C3×Dic3—42no—
342C3×Dic3C2×D812yes—
343C2×#41—61no—
344C22×D4—91no—
345C23×C4—181no—
346C2×D8—32no—
347C2×D8—92no—
348C4⋊Q8—31no—
349#127D3211yescharacteristic, complemented
350#124—61no—
351#121—32no—
352#121—61no—
353C4×D4—32no—
354C4×D4—31no—
355C4×D4—61no—
356C4×D4—91no—
357C4×D4—91no—
358C4×D4—91no—
359C4×D4—181no—
360C4×D4—181no—
361C2×C4⋊C4—91no—
362C2×C22⋊C4—181no—
363C2×C42—31no—
364#107—92no—
365#107—92no—
366C4⋊C8—31no—
367C4⋊C8—91no—
368#102—32no—
369#102—92no—
370#102—92no—
371#102—92no—
372C22⋊C8—92no—
373C4×C8—92no—
374C23×C3—22no—
375C23×C3—22no—
376C23×C3—31no—
377C23×C3—42no—
378C23×C3—61no—
379C22×D3—21no—
380C22×D3—64no—
381C22×D3—64no—
382C22×D3—61no—
383C22×D3—61no—
384C22×D3—121no—
385C22×D3—122no—
386C22×D3—122no—
387C22×D3—122no—
388C22×D3—122no—
389C22×D3C2×#6711yescharacteristic
390C3×Q8—122no—
391C3×D4—22no—
392C3×D4—22no—
393C3×D4—22no—
394C3×D4—22no—
395C3×D4—32no—
396C3×D4—42no—
397C3×D4—42no—
398C3×D4—42no—
399C3×D4—42no—
400C3×D4—42no—
401C3×D4—42no—
402C3×D4—61no—
403C3×D4—82no—
404C3×D4—82no—
405C3×D4—124no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—31no—
410C2×C3×C4—34no—
411C2×C3×C4—31no—
412C2×C3×C4—31no—
413C2×C3×C4—61no—
414C2×C3×C4—61no—
415C2×C3×C4—62no—
416C2×C3×C4—61no—
417C2×C3×C4—121no—
418C2×C3×C4—124no—
419C2×C3×C4—122no—
420C2×C3×C4D3×D411yescharacteristic
421C2×C3×C4D3×D411yescharacteristic
422C2×C3×C4C2×#6711yescharacteristic
423C2×C3×C4C2×#6711yescharacteristic
424C2×C3×C4C23×D311yescharacteristic
425C2×C3×C4C23×D311yescharacteristic
426#67—44no—
427#67—64no—
428C2×Dic3—21no—
429C2×Dic3—22no—
430C2×Dic3—44no—
431C2×Dic3—61no—
432C2×Dic3—61no—
433C2×Dic3—121no—
434C2×Dic3—122no—
435C2×Dic3—122no—
436C2×Dic3C2×#6711yescharacteristic
437C2×Dic3C2×#6711yescharacteristic
438C2×Dic3C2×#6711yescharacteristic
439D12—21no—
440D12—32no—
441D12—32no—
442D12—62no—
443D12—64no—
444D12—61no—
445D12—61no—
446D12—121no—
447D12#23712yescomplemented
448C4×D3—21no—
449C4×D3—21no—
450C4×D3—41no—
451C4×D3—42no—
452C4×D3—122no—
453C4×D3—122no—
454C4×D3—122no—
455C4×D3—122no—
456C4×D3—122no—
457C4×D3—122no—
458C4×D3—242no—
459C4×D3#21314yescomplemented
460Dic6—42no—
461C3×C8—62no—
462C3⋊C8—22no—
463C3⋊C8—62no—
464C3⋊C8—62no—
465C3⋊C8—122no—
466C2×C32—82no—
467C2×C32#52511yescharacteristic
468C2×C32C22×D811yescharacteristic
469C2×C32#57511yescharacteristic
470C3⋊D3—42no—
471C3×D3—22no—
472C3×D3—42no—
473C24—181no—
474#41—124no—
475C2×Q8—61no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—31no—
479C2×D4—62no—
480C2×D4—91no—
481C2×D4—181no—
482C2×D4—182no—
483C2×D4—182no—
484C2×D4C2×D3212yes—
485C22×C4—31no—
486C22×C4—31no—
487C22×C4—31no—
488C22×C4—62no—
489C22×C4—61no—
490C22×C4—181no—
491C22×C4—181no—
492C22×C4—181no—
493C22×C4—181no—
494C22×C4—364no—
495D8—64no—
496D8—184no—
497C2×C8—32no—
498C2×C8—92no—
499C4⋊C4—31no—
500C4⋊C4—32no—
501C4⋊C4—61no—
502C4⋊C4—91no—
503C4⋊C4—181no—
504C22⋊C4—62no—
505C22⋊C4—62no—
506C22⋊C4—61no—
507C22⋊C4—181no—
508C22⋊C4—181no—
509C22⋊C4—181no—
510C42—31no—
511C42—31no—
512C42—31no—
513C42C2×D3211yescharacteristic
514C22×C3—21no—
515C22×C3—32no—
516C22×C3—42no—
517C22×C3—42no—
518C22×C3—42no—
519C22×C3—42no—
520C22×C3—42no—
521C22×C3—42no—
522C22×C3—61no—
523C22×C3—61no—
524C22×C3—62no—
525C22×C3—82no—
526C22×C3—82no—
527C22×C3—82no—
528C22×C3—121no—
529C22×C3—121no—
530C22×C3C2×D3×D411yescharacteristic
531C22×C3C22×#6711yescharacteristic
532C2×D3—21no—
533C2×D3—21no—
534C2×D3—22no—
535C2×D3—41no—
536C2×D3—41no—
537C2×D3—62no—
538C2×D3—62no—
539C2×D3—122no—
540C2×D3—128no—
541C2×D3—128no—
542C2×D3—121no—
543C2×D3—121no—
544C2×D3—121no—
545C2×D3—121no—
546C2×D3—241no—
547C2×D3—241no—
548C2×D3C2×#21312yes—
549C3×C4—21no—
550C3×C4—21no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—22no—
554C3×C4—32no—
555C3×C4—41no—
556C3×C4—61no—
557C3×C4—61no—
558C3×C4—122no—
559C3×C4—121no—
560C3×C4D3×D812yes—
561C3×C4C2×#21312yes—
562C3×C4C2×#23711yescharacteristic
563C3×C4D3×#4111yescharacteristic
564C3×C4D3×#4111yescharacteristic
565C3×C4D3×#4111yescharacteristic
566Dic3—21no—
567Dic3—21no—
568Dic3—41no—
569Dic3—42no—
570Dic3—121no—
571Dic3—121no—
572Dic3—241no—
573Dic3C2×#21312yes—
574C32#310011yescharacteristic, complemented, Sylow
575C23—22no—
576C23—31no—
577C23—61no—
578C23—184no—
579C23—181no—
580C23—362no—
581C23—362no—
582Q8—122no—
583D4—22no—
584D4—22no—
585D4—32no—
586D4—42no—
587D4—42no—
588D4—61no—
589D4—92no—
590D4—124no—
591D4—184no—
592D4—181no—
593C2×C4—31no—
594C2×C4—34no—
595C2×C4—31no—
596C2×C4—31no—
597C2×C4—61no—
598C2×C4—61no—
599C2×C4—62no—
600C2×C4—61no—
601C2×C4—121no—
602C2×C4—124no—
603C2×C4—122no—
604C2×C4—181no—
605C2×C4—362no—
606C2×C4—362no—
607C2×C4—362no—
608C2×C4—362no—
609C2×C4D3×#6711yescharacteristic
610C2×C4D3×#6711yescharacteristic
611C2×C4C22×D3211yescharacteristic
612C8—62no—
613C8—182no—
614C2×C3—21no—
615C2×C3—21no—
616C2×C3—21no—
617C2×C3—62no—
618C2×C3—82no—
619C2×C3—82no—
620C2×C3—122no—
621C2×C3—162no—
622C2×C3#560611yescharacteristic
623C2×C3C2×D3×D811yescharacteristic
624C2×C3#577311yescharacteristic
625C2×C3C22×#21311yescharacteristic
626C2×C3#582211yescharacteristic
627C2×C3#582811yescharacteristic
628D3—22no—
629D3—42no—
630D3—122no—
631D3—122no—
632D3—242no—
633C22—32no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—61no—
638C22—61no—
639C22—62no—
640C22—121no—
641C22—121no—
642C22—182no—
643C22—368no—
644C22—361no—
645C22—361no—
646C22C2×D3×#6711yescharacteristic
647C4—21no—
648C4—32no—
649C4—61no—
650C4—61no—
651C4—121no—
652C4—122no—
653C4—361no—
654C4D3×#21312yes—
655C4D3×#23711yescharacteristic
656C4#6431211yescharacteristic
657C3—21no—
658C3#8031211yescharacteristic, complemented
659C3#8329811yescharacteristic, complemented
660C2—62no—
661C2—82no—
662C2—122no—
663C2—362no—
664C2C2×D3×#21311yescharacteristic
665C2#1059509511yescharacteristic
666C2#1059530111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
hypercenter#127D32
hypocenterC32#3100
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C3×#5716C2semidirect
2. C4×D3×D12C2semidirect
3. #10592771C2semidirect
4. C3×#5072C2semidirect
5. #10591515C2semidirect
6. Dic3×#213C2semidirect
7. #10591413C2semidirect
8. #10591400C2semidirect
9. #10590313C2semidirect
10. #10590269C2semidirect
11. #10590248C2semidirect
17. C32×#127C22semidirect
24. C3×D4×Dic3C22semidirect
28. C3×#869C22semidirect
35. #63659C22semidirect
36. C4⋊(C3⋊(C3⋊C8))C22semidirect
37. C3×#832C22semidirect
38. C3×C4⋊(C3⋊C8)C22semidirect
39. #63576C22semidirect
40. #63575C22semidirect
44. Dic3×C3⋊C8C22semidirect
46. #5716D3semidirect
57. #5072D3semidirect
119. C3×#127C2×D3semidirect
120. C3×#127C2×D3semidirect
133. D4×Dic3C2×D3semidirect
154. #869C2×D3semidirect
161. #832C2×D3semidirect
175. C4⋊(C3⋊C8)C2×D3semidirect
193. C4⋊(C3⋊D3)#41semidirect
203. C3×D12#41semidirect
208. C3×C4×D3D8semidirect
349. #127D32semidirect
447. D12#237semidirect
459. C4×D3#213semidirect
574. C32#3100semidirect
658. C3#80312semidirect
659. C3#83298semidirect

Maximal subgroups

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

subgroupindex
C3×#57162
C4×D3×D122
#105927712
C3×#50722
#105915152
Dic3×#2132
#105914132
#105914002
#105903132
#105902692
#105902482
#832983
#803123