Finite Group Databasebeta

← #11870453

Subgroups — #11870453

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
1C4×D3×D12C211yesmaximal, characteristic, complemented
2#10593970C211yesmaximal, characteristic, complemented
3#10592542C211yesmaximal, characteristic, complemented
4C3×#4846C211yesmaximal, characteristic, complemented
5C3×#4833C211yesmaximal, characteristic, complemented
6#10590947C212yesmaximal, complemented
7#10590763C212yesmaximal, complemented
8#10590745C212yesmaximal, complemented
9#10590679C212yesmaximal, complemented
10#10590349C211yesmaximal, characteristic, complemented
11#10590313C211yesmaximal, characteristic, complemented
12#80948—31nomaximal
13#79297—31nomaximal
14C2×D3×D12C2211yescharacteristic
15C2×C4×D32—21no—
16C2×#3799—21no—
17C2×#3745C2212yes—
18#64083C2211yescharacteristic, complemented
19C4×C4⋊(C3⋊D3)C2211yescharacteristic
20C3×C4×D12C2211yescharacteristic
21C3×C42×D3C2211yescharacteristic
22C3×#869C2211yescharacteristic, complemented
23D3×(C2×D3)⋊C4—21no—
24#63909—21no—
25#63909C2212yes—
26C4×#626—21no—
27#63894—21no—
28#63894C2211yescharacteristic
29#63894C2212yescomplemented
30Dic3×D12C2211yescharacteristic
31D3×C4⋊Dic3C2211yescharacteristic
32#63880—21no—
33#63864—21no—
34C2×#3714C2212yes—
35C32×C4⋊C8C2211yescharacteristic, complemented
36#63648C2212yescomplemented
37C3×#821C2212yes—
38C3×(C2×D3)⋊C8C2212yes—
39C3×#818C2212yescomplemented
40C3×C8×Dic3C2212yescomplemented
41C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
42#63575C2212yescomplemented
43#63564C2212yes—
44#63564C2212yescomplemented
45#5725—31no—
46C4×D3×D4—31no—
47#5477—31no—
48C2×C4×D12—31no—
49C3×#474—31no—
50C3×#431—31no—
51#5087—31no—
52#5015—31no—
53#4882—32no—
54#4872—32no—
55#4846—31no—
56#4846D311yescharacteristic, complemented
57#4843—31no—
58#4843—31no—
59#4843—31no—
60#4843—61no—
61#4833D311yescharacteristic, complemented
62#4773—32no—
63#4756—32no—
64#4736—32no—
65#4732—32no—
66C4×D24—32no—
67C4×D24—32no—
68C22×D32—21no—
69C2×C4⋊(C3⋊D3)—21no—
70C2×C4⋊(C3⋊D3)—21no—
71C2×C4⋊(C3⋊D3)C2312yes—
72C2×C4⋊(C3⋊D3)C2311yescharacteristic
73C2×C4×C3⋊D3—21no—
74C2×C3×D12C2311yescharacteristic
75C2×C3×C4×D3—21no—
76C2×C3×C4×D3D411yescharacteristic
77C2×C3×C4×D3D411yescharacteristic
78C2×C3×C4×D3C2311yescharacteristic
79C2×C3×Dic6—21no—
80C2×#626—21no—
81C2×#626—22no—
82C2×#624—22no—
83C2×#624—21no—
84C2×D3×Dic3—21no—
85C2×D3×Dic3—21no—
86D3×D12—22no—
87D3×D12—22no—
88C4×D32—44no—
89#3799—44no—
90C2×C32×C8C2312yes—
91C32×C42C2311yescharacteristic
92#3752—21no—
93C4⋊(C3⋊Dic3)C2311yescharacteristic
94#3745—24no—
95C3×(C2×D3)⋊C4—21no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3C2312yes—
98C3×C4⋊Dic3C2311yescharacteristic
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3C2311yescharacteristic
102C2×C3×C3⋊C8C2312yes—
103Dic3⋊Dic3—21no—
104#3722—22no—
105#3722—22no—
106#3722—21no—
107(C2×D3)⋊Dic3—21no—
108#3714—24no—
109#3100—91noSylow
110C2×#239—61no—
111C2×D3×D4—31no—
112C2×#235—61no—
113C22×D12—31no—
114C22×C4×D3—61no—
115C22×C4×D3—61no—
116C3×C4⋊Q8—31no—
117C3×C4×D4—31no—
118C2×C3×C42—31no—
119#947—61no—
120D4×Dic3—31no—
121C2×#213—32no—
122#930—32no—
123#930—61no—
124C4×#67—61no—
125C2×(C2×D3)⋊C4—61no—
126C2×C4⋊Dic3—31no—
127C2×D24—32no—
128C2×D24—32no—
129C2×D24—32no—
130C2×D24—62no—
131#895—32no—
132#895—61no—
133#893—31no—
134#893—32no—
135#893—61no—
136D3×C4⋊C4—31no—
137#67⋊C4—61no—
138D3×C22⋊C4—61no—
139#875—61no—
140#874—31no—
141#874—31no—
142#874—61no—
143C4×D12—31no—
144C4×D12—31no—
145C4×D12—31no—
146C4×D12—31no—
147C4×D12—32no—
148C4×D12—61no—
149C4×D12—61no—
150C4×D12—61no—
151C4×D12—61no—
152C4×D12C2×D311yescharacteristic
153C42×D3C2×D311yescharacteristic
154#869C2×D311yescharacteristic, complemented
155C3×#107—32no—
156C3×C4⋊C8—21no—
157C3×C4⋊C8—31no—
158C3×C4⋊C8C2×D311yescharacteristic, complemented
159C3×C4⋊C8C2×D311yescharacteristic, complemented
160C3×#102—32no—
161C3×C22⋊C8—32no—
162C3×C4×C8—32no—
163#821—32no—
164#821—32no—
165#821—32no—
166#821—32no—
167#821—62no—
168#821C2×D312yes—
169(C2×D3)⋊C8C2×D312yes—
170#818—32no—
171#818C2×D312yescomplemented
172C8×Dic3C2×D312yescomplemented
173#809—32no—
174#809—32no—
175#807—32no—
176C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
177C22×C3⋊D3—21no—
178C22×C3⋊D3—22no—
179C22×C3×D3—21no—
180C22×C3×D3C2×D411yescharacteristic
181C2×D32—24no—
182C2×D32—42no—
183C2×D32—42no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2411yescharacteristic
187C2×C3⋊Dic3—21no—
188C4⋊(C3⋊D3)—21no—
189C4⋊(C3⋊D3)—22no—
190C4⋊(C3⋊D3)—22no—
191C4⋊(C3⋊D3)—42no—
192C4⋊(C3⋊D3)—42no—
193C4⋊(C3⋊D3)#4112yescomplemented
194C4×C3⋊D3—42no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C2×C3×Dic3C2×D411yescharacteristic
200C3×D12—21no—
201C3×D12#4112yescomplemented
202C3×C4×D3—21no—
203C3×C4×D3—21no—
204C3×C4×D3—41no—
205C3×C4×D3—42no—
206C3×C4×D3D814yescomplemented
207C3×Dic6—42no—
208#626—24no—
209#626—44no—
210#624—44no—
211#624—42no—
212D3×Dic3—42no—
213D3×Dic3—42no—
214C32×C8—22no—
215C3×C3⋊C8—22no—
216#532—91no—
217C2×C4×D4—91no—
218#480—92no—
219#474—31no—
220#474—91no—
221#459—91no—
222#459—91no—
223#447—92no—
224C4×D8—92no—
225C4×D8—92no—
226#431—31no—
227C23×D3—61no—
228C23×D3—61no—
229C2×C3×Q8—61no—
230C2×C3×D4—31no—
231C22×C3×C4—31no—
232C22×C3×C4—31no—
233C22×C3×C4—31no—
234C22×C3×C4—61no—
235C2×#67—62no—
236C2×#67—61no—
237C22×Dic3—61no—
238C22×Dic3—61no—
239#239—124no—
240D3×D4—62no—
241D3×D4—62no—
242#235—124no—
243C2×D12—31no—
244C2×D12—31no—
245C2×D12—32no—
246C2×D12—32no—
247C2×D12—61no—
248C2×D12—62no—
249C2×D12—62no—
250C2×D12—61no—
251C2×D12—62no—
252C2×D12—62no—
253C2×D12—61no—
254C2×D12—61no—
255C2×D12—61no—
256C2×D12—61no—
257C2×D12—121no—
258C2×D12—121no—
259C2×D12C22×D311yescharacteristic
260C2×C4×D3—21no—
261C2×C4×D3—61no—
262C2×C4×D3—62no—
263C2×C4×D3—61no—
264C2×C4×D3—61no—
265C2×C4×D3—61no—
266C2×C4×D3—61no—
267C2×C4×D3—61no—
268C2×C4×D3—62no—
269C2×C4×D3—121no—
270C2×C4×D3—124no—
271C2×C4×D3—124no—
272C2×C4×D3D1211yescharacteristic
273C2×C4×D3D1211yescharacteristic
274C2×C4×D3C22×D311yescharacteristic
275C2×Dic6—21no—
276C2×C3×C8—22no—
277C2×C3×C8—32no—
278C2×C3×C8C22×D312yes—
279C2×C3×C8C22×D312yes—
280C3×C4⋊C4—32no—
281C3×C4⋊C4—31no—
282C3×C4⋊C4—61no—
283C3×C22⋊C4—61no—
284C3×C42—21no—
285C3×C42—31no—
286C3×C42—31no—
287C3×C42—31no—
288C3×C42C22×D311yescharacteristic
289C3×C42C22×D311yescharacteristic
290#217—61no—
291#213—64no—
292(C2×D3)⋊C4—21no—
293(C2×D3)⋊C4—61no—
294(C2×D3)⋊C4—62no—
295(C2×D3)⋊C4—62no—
296(C2×D3)⋊C4—61no—
297(C2×D3)⋊C4—61no—
298(C2×D3)⋊C4—61no—
299(C2×D3)⋊C4—61no—
300(C2×D3)⋊C4—62no—
301(C2×D3)⋊C4—62no—
302(C2×D3)⋊C4—121no—
303C4⋊Dic3—21no—
304C4⋊Dic3—31no—
305C4⋊Dic3—31no—
306C4⋊Dic3—61no—
307C4⋊Dic3—61no—
308C4⋊Dic3C22×D312yes—
309C4⋊Dic3C22×D311yescharacteristic
310Dic3⋊C4—61no—
311C4×Dic3D1211yescharacteristic
312C4×Dic3D1211yescharacteristic
313C4×Dic3C22×D311yescharacteristic
314C2×C3⋊C8C22×D312yes—
315D24—64no—
316D24—64no—
317D24—64no—
318D24—124no—
319C22×C32C22×D411yescharacteristic
320C2×C3⋊D3—22no—
321C2×C3⋊D3—41no—
322C2×C3⋊D3—41no—
323C2×C3⋊D3—42no—
324C2×C3⋊D3—42no—
325C2×C3⋊D3—42no—
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—181no—
344C22×D4—91no—
345C23×C4—181no—
346C2×D8—92no—
347C2×D8—92no—
348C4⋊Q8—31no—
349#127—91no—
350#124—181no—
351#121—92no—
352#121—181no—
353C4×D4—31no—
354C4×D4—91no—
355C4×D4—92no—
356C4×D4—91no—
357C4×D4—91no—
358C4×D4—181no—
359C4×D4—181no—
360C4×D4—181no—
361C2×C4⋊C4—91no—
362C2×C22⋊C4—181no—
363C2×C42—31no—
364#107—32no—
365#107—92no—
366C4⋊C8—31no—
367C4⋊C8D3211yescharacteristic, complemented
368#102—32no—
369#102—92no—
370#102—92no—
371#102—92no—
372C22⋊C8—32no—
373C4×C8—32no—
374C23×C3—31no—
375C23×C3—61no—
376C22×D3—21no—
377C22×D3—64no—
378C22×D3—64no—
379C22×D3—61no—
380C22×D3—61no—
381C22×D3—62no—
382C22×D3—62no—
383C22×D3—121no—
384C22×D3—122no—
385C22×D3—122no—
386C22×D3—122no—
387C22×D3—122no—
388C22×D3—122no—
389C22×D3C2×D1211yescharacteristic
390C3×Q8—122no—
391C3×D4—32no—
392C3×D4—61no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—31no—
397C2×C3×C4—34no—
398C2×C3×C4—31no—
399C2×C3×C4—31no—
400C2×C3×C4—61no—
401C2×C3×C4—61no—
402C2×C3×C4—61no—
403C2×C3×C4—62no—
404C2×C3×C4—121no—
405C2×C3×C4—122no—
406C2×C3×C4C2×D1211yescharacteristic
407C2×C3×C4C2×D1211yescharacteristic
408C2×C3×C4D3×D411yescharacteristic
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4C23×D311yescharacteristic
411C2×C3×C4C23×D311yescharacteristic
412#67—64no—
413#67—124no—
414C2×Dic3—22no—
415C2×Dic3—21no—
416C2×Dic3—61no—
417C2×Dic3—61no—
418C2×Dic3—121no—
419C2×Dic3—122no—
420C2×Dic3—122no—
421C2×Dic3C2×D1211yescharacteristic
422C2×Dic3C2×D1211yescharacteristic
423C2×Dic3C2×D1211yescharacteristic
424D12—21no—
425D12—32no—
426D12—32no—
427D12—62no—
428D12—64no—
429D12—61no—
430D12—62no—
431D12—61no—
432D12—62no—
433D12—62no—
434D12—62no—
435D12—121no—
436D12—122no—
437D12—122no—
438D12—122no—
439D12—122no—
440D12—124no—
441D12—122no—
442D12—122no—
443D12—242no—
444D12—242no—
445D12#23912yescomplemented
446C4×D3—21no—
447C4×D3—21no—
448C4×D3—41no—
449C4×D3—42no—
450C4×D3—122no—
451C4×D3—124no—
452C4×D3—122no—
453C4×D3—122no—
454C4×D3—122no—
455C4×D3—122no—
456C4×D3—122no—
457C4×D3—124no—
458C4×D3—242no—
459C4×D3D2414yescomplemented
460Dic6—42no—
461C3×C8—22no—
462C3×C8—22no—
463C3×C8—42no—
464C3×C8—62no—
465C3⋊C8—22no—
466C2×C32#52511yescharacteristic
467C2×C32C22×D811yescharacteristic
468C2×C32#57511yescharacteristic
469C3⋊D3—42no—
470C3⋊D3—82no—
471C3×D3—22no—
472C3×D3—42no—
473C24—181no—
474#41—364no—
475C2×Q8—61no—
476C2×D4—31no—
477C2×D4—91no—
478C2×D4—92no—
479C2×D4—181no—
480C2×D4—182no—
481C2×D4—182no—
482C2×D4—182no—
483C2×D4—181no—
484C2×D4—181no—
485C22×C4—31no—
486C22×C4—31no—
487C22×C4—31no—
488C22×C4—61no—
489C22×C4—181no—
490C22×C4—182no—
491C22×C4—181no—
492C22×C4—181no—
493C22×C4—181no—
494C22×C4—364no—
495D8—184no—
496D8—184no—
497C2×C8—32no—
498C2×C8C2×D3212yes—
499C4⋊C4—32no—
500C4⋊C4—31no—
501C4⋊C4—61no—
502C4⋊C4—91no—
503C4⋊C4—181no—
504C22⋊C4—61no—
505C22⋊C4—181no—
506C22⋊C4—182no—
507C22⋊C4—182no—
508C22⋊C4—181no—
509C22⋊C4—181no—
510C42—31no—
511C42—31no—
512C42—31no—
513C42C2×D3211yescharacteristic
514C22×C3—21no—
515C22×C3—32no—
516C22×C3—61no—
517C22×C3—61no—
518C22×C3—62no—
519C22×C3—121no—
520C22×C3—121no—
521C22×C3C22×D1211yescharacteristic
522C22×C3C2×D3×D411yescharacteristic
523C2×D3—21no—
524C2×D3—21no—
525C2×D3—22no—
526C2×D3—41no—
527C2×D3—41no—
528C2×D3—62no—
529C2×D3—62no—
530C2×D3—122no—
531C2×D3—128no—
532C2×D3—128no—
533C2×D3—121no—
534C2×D3—121no—
535C2×D3—121no—
536C2×D3—121no—
537C2×D3—122no—
538C2×D3—122no—
539C2×D3—122no—
540C2×D3—122no—
541C2×D3—122no—
542C2×D3—122no—
543C2×D3—241no—
544C2×D3—241no—
545C2×D3—242no—
546C2×D3—242no—
547C2×D3—242no—
548C2×D3C2×D2412yes—
549C3×C4—21no—
550C3×C4—21no—
551C3×C4—22no—
552C3×C4—21no—
553C3×C4—21no—
554C3×C4—32no—
555C3×C4—41no—
556C3×C4—61no—
557C3×C4—61no—
558C3×C4—121no—
559C3×C4—122no—
560C3×C4C2×D2412yes—
561C3×C4D3×D812yes—
562C3×C4C2×#23911yescharacteristic
563C3×C4D3×#4111yescharacteristic
564C3×C4D3×#4111yescharacteristic
565C3×C4D3×#4111yescharacteristic
566Dic3—21no—
567Dic3—21no—
568Dic3—42no—
569Dic3—41no—
570Dic3—121no—
571Dic3—121no—
572Dic3—241no—
573Dic3C2×D2412yes—
574C32#310011yescharacteristic, complemented, Sylow
575C23—31no—
576C23—61no—
577C23—184no—
578C23—181no—
579C23—182no—
580C23—362no—
581C23—362no—
582Q8—122no—
583D4—32no—
584D4—61no—
585D4—92no—
586D4—184no—
587D4—182no—
588D4—181no—
589D4—182no—
590D4—362no—
591D4—364no—
592D4—362no—
593C2×C4—31no—
594C2×C4—34no—
595C2×C4—31no—
596C2×C4—31no—
597C2×C4—61no—
598C2×C4—61no—
599C2×C4—61no—
600C2×C4—62no—
601C2×C4—121no—
602C2×C4—122no—
603C2×C4—181no—
604C2×C4—362no—
605C2×C4—364no—
606C2×C4—362no—
607C2×C4—362no—
608C2×C4—362no—
609C2×C4D3×D1211yescharacteristic
610C2×C4D3×D1211yescharacteristic
611C2×C4C22×D3211yescharacteristic
612C8—22no—
613C8—62no—
614C2×C3—21no—
615C2×C3—21no—
616C2×C3—21no—
617C2×C3—62no—
618C2×C3—122no—
619C2×C3#552411yescharacteristic
620C2×C3#562711yescharacteristic
621C2×C3C22×D2411yescharacteristic
622C2×C3#574811yescharacteristic
623C2×C3C2×D3×D811yescharacteristic
624C2×C3#577711yescharacteristic
625D3—22no—
626D3—42no—
627D3—122no—
628D3—122no—
629D3—242no—
630D3—242no—
631D3—242no—
632D3—482no—
633C22—32no—
634C22—61no—
635C22—61no—
636C22—62no—
637C22—121no—
638C22—121no—
639C22—182no—
640C22—368no—
641C22—361no—
642C22—361no—
643C22—362no—
644C22—362no—
645C22—362no—
646C22C2×D3×D1211yescharacteristic
647C4—21no—
648C4—32no—
649C4—61no—
650C4—61no—
651C4—121no—
652C4—122no—
653C4—361no—
654C4D3×D2412yes—
655C4#6431211yescharacteristic
656C4D3×#23911yescharacteristic
657C3—21no—
658C3#7929711yescharacteristic, complemented
659C3#8094811yescharacteristic, complemented
660C2—62no—
661C2—122no—
662C2—362no—
663C2—722no—
664C2#1059462711yescharacteristic
665C2C2×D3×D2411yescharacteristic
666C2#1059471111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3100
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C4×D3×D12C2semidirect
2. #10593970C2semidirect
3. #10592542C2semidirect
4. C3×#4846C2semidirect
5. C3×#4833C2semidirect
6. #10590947C2semidirect
7. #10590763C2semidirect
8. #10590745C2semidirect
9. #10590679C2semidirect
10. #10590349C2semidirect
11. #10590313C2semidirect
18. #64083C22semidirect
22. C3×#869C22semidirect
29. #63894C22semidirect
35. C32×C4⋊C8C22semidirect
36. #63648C22semidirect
39. C3×#818C22semidirect
40. C3×C8×Dic3C22semidirect
41. C3×C4⋊(C3⋊C8)C22semidirect
42. #63575C22semidirect
44. #63564C22semidirect
56. #4846D3semidirect
61. #4833D3semidirect
154. #869C2×D3semidirect
158. C3×C4⋊C8C2×D3semidirect
159. C3×C4⋊C8C2×D3semidirect
171. #818C2×D3semidirect
172. C8×Dic3C2×D3semidirect
176. C4⋊(C3⋊C8)C2×D3semidirect
193. C4⋊(C3⋊D3)#41semidirect
201. C3×D12#41semidirect
206. C3×C4×D3D8semidirect
367. C4⋊C8D32semidirect
445. D12#239semidirect
459. C4×D3D24semidirect
574. C32#3100semidirect
658. C3#79297semidirect
659. C3#80948semidirect

Maximal subgroups

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

subgroupindex
C4×D3×D122
#105939702
#105925422
C3×#48462
C3×#48332
#105909472
#105907632
#105907452
#105906792
#105903492
#105903132
#809483
#792973