Finite Group Databasebeta

← #11868669

Subgroups — #11868669

Order 1152.

934 conjugacy classes of subgroups.

The subgroup lattice has 621 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×D3×D4C211yesmaximal, characteristic
2#10593859C211yesmaximal, characteristic, complemented
3#10592706C211yesmaximal, characteristic, complemented
4C3×#5008C211yesmaximal, characteristic, complemented
5#10591421C212yesmaximal
6#10591411C212yesmaximal, complemented
7#10590581C212yesmaximal, complemented
8#10590545C212yesmaximal, complemented
9#10590336C211yesmaximal, characteristic, complemented
10#10590272C211yesmaximal, characteristic, complemented
11#10590266C211yesmaximal, characteristic, complemented
12#82296—31nomaximal
13#81060—31nomaximal
14C2×C3×D3×D4C2211yescharacteristic
15C22×C3×C4×D3—21no—
16C32×C4×D4C2211yescharacteristic
17#64078C2211yescharacteristic, complemented
18C3×D4×Dic3C2211yescharacteristic
19C3×C4×#67—21no—
20C3×#893C2211yescharacteristic
21C3×D3×C4⋊C4C2211yescharacteristic
22C3×#67⋊C4—21no—
23C3×D3×C22⋊C4—21no—
24C3×C4×D12C2211yescharacteristic
25C3×C42×D3C2211yescharacteristic
26C3×#869C2211yescharacteristic, complemented
27#63869C2212yescomplemented
28#63857—21no—
29#63856—21no—
30#63844—21no—
31Dic3×Dic6—21no—
32#63841C2212yes—
33C2×#3711C2212yes—
34#63659C2212yes—
35#63634C2212yescomplemented
36C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
37C3×#832C2212yes—
38C3×#808C2212yescomplemented
39C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
40#63575C2212yescomplemented
41#63574C2212yescomplemented
42Dic3⋊(C3⋊C8)C2212yescomplemented
43#63563C2212yes—
44#63562C2212yes—
45C2×C3×C4×D4—31no—
46#5728—31no—
47C4×D3×D4D311yescharacteristic
48#5470—31no—
49C3×#476—31no—
50#5215—32no—
51#5084—31no—
52#5009—32no—
53#5009—32no—
54#5008—31no—
55#5008D311yescharacteristic, complemented
56#5007—31no—
57#5007—31no—
58#5007—31no—
59#5007—61no—
60#4964—32no—
61#4924—31no—
62#4871—32no—
63#4861—32no—
64#4846—31no—
65#4837—31no—
66#4770—32no—
67#4766—32no—
68C23×C3×D3—21no—
69C2×C32×D4C2311yescharacteristic
70C22×C32×C4—21no—
71C2×#634—21no—
72C2×C3×#67—21no—
73C22×C3×Dic3—21no—
74C3×D3×D4—22no—
75C3×D3×D4Q814yescomplemented
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3—21no—
80C2×C3×C4×D3—44no—
81C2×C3×C4×D3D411yescharacteristic
82C2×C3×C4×D3D411yescharacteristic
83C2×C3×C4×D3C2311yescharacteristic
84C2×C3×Dic6—21no—
85C32×C4⋊C4C2311yescharacteristic
86C32×C22⋊C4—21no—
87C32×C42C2311yescharacteristic
88C4⋊(C3⋊Dic3)—21no—
89C4⋊(C3⋊Dic3)C2312yes—
90C2×C3⋊(C3⋊C8)C2312yes—
91C3×#217—21no—
92C3×(C2×D3)⋊C4—21no—
93C3×(C2×D3)⋊C4—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×C4⋊Dic3C2312yes—
97C3×Dic3⋊C4—21no—
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3C2311yescharacteristic
101C2×C3×C3⋊C8C2312yes—
102#3724—22no—
103Dic3⋊Dic3—22no—
104(C2×D3)⋊Dic3—22no—
105Dic32—22no—
106#3711—24no—
107#3077—91noSylow
108C22×C3×D4—31no—
109C23×C3×C4—61no—
110C2×D3×D4C2×D311yescharacteristic
111C22×C4×D3—21no—
112C3×C4⋊Q8—31no—
113C3×C4×D4—21no—
114C3×C4×D4—31no—
115C3×C4×D4—31no—
116C3×C4×D4—31no—
117C3×C4×D4—61no—
118C3×C4×D4—61no—
119C3×C4×D4C2×D311yescharacteristic
120C3×C4×D4C2×D311yescharacteristic
121C2×C3×C4⋊C4—31no—
122C2×C3×C22⋊C4—61no—
123C2×C3×C42—31no—
124#946—61no—
125Q8×Dic3—61no—
126D4×Dic3C2×D311yescharacteristic
127C4×#67—21no—
128#926—32no—
129#924—61no—
130#924—61no—
131C2×#208—32no—
132C2×ΓL(1,𝔽25)—32no—
133#897—61no—
134#893C2×D311yescharacteristic
135#892—32no—
136D3×C4⋊C4C2×D311yescharacteristic
137#890—32no—
138#887—61no—
139#67⋊C4—21no—
140D3×C22⋊C4—21no—
141C4×D12C2×D311yescharacteristic
142C42×D3C2×D311yescharacteristic
143#870—32no—
144#869—31no—
145#869—31no—
146#869—61no—
147#869C2×D311yescharacteristic, complemented
148C4×Dic6—61no—
149C4×Dic6—61no—
150C3×#106—32no—
151C3×C4⋊C8—31no—
152C3×#102—32no—
153#832—32no—
154#832—32no—
155#832—32no—
156#832—32no—
157#832—62no—
158#832C2×D312yes—
159#821—32no—
160#818—32no—
161Dic3⋊C8—32no—
162#809—32no—
163#808—32no—
164#808—32no—
165#808C2×D312yescomplemented
166#807—32no—
167#807—32no—
168#807—32no—
169#807—62no—
170C4⋊(C3⋊C8)—31no—
171C4⋊(C3⋊C8)—31no—
172C4⋊(C3⋊C8)—32no—
173C4⋊(C3⋊C8)—61no—
174C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
175C23×C32—21no—
176C22×C3×D3—21no—
177C22×C3×D3—24no—
178C22×C3×D3—42no—
179C22×C3×D3—42no—
180C22×C3×D3C2×D411yescharacteristic
181C32×D4—21no—
182C32×D4C2×Q812yes—
183C2×C32×C4—21no—
184C2×C32×C4—42no—
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2411yescharacteristic
188C2×C3⋊Dic3—22no—
189#634—42no—
190C3×#67—24no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—42no—
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C2×C3×Dic3C2×D411yescharacteristic
197C3×D12—21no—
198C3×D12C2×Q812yes—
199C3×C4×D3—22no—
200C3×C4×D3—41no—
201C3×C4×D3—42no—
202C3×C4×D3—42no—
203C3×C4×D3—42no—
204C3×C4×D3C2×Q812yes—
205C3×C4×D3#4112yes—
206C3×Dic6—42no—
207C3⋊(C3⋊C8)—22no—
208C3×C3⋊C8—22no—
209#533—91no—
210C2×C4×D4—31no—
211#478—92no—
212#478—92no—
213#476—31no—
214#476—91no—
215#474—91no—
216#474—91no—
217#428—92no—
218#423—91no—
219#418—92no—
220C24×C3—61no—
221C23×D3—21no—
222C2×C3×Q8—61no—
223C2×C3×D4—21no—
224C2×C3×D4—34no—
225C2×C3×D4—31no—
226C2×C3×D4—62no—
227C2×C3×D4—61no—
228C2×C3×D4C22×D311yescharacteristic
229C2×C3×D4C22×D311yescharacteristic
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—31no—
233C22×C3×C4—31no—
234C22×C3×C4—31no—
235C22×C3×C4—41no—
236C22×C3×C4—61no—
237C22×C3×C4—61no—
238C22×C3×C4—61no—
239C22×C3×C4—61no—
240C22×C3×C4—124no—
241C2×#67—21no—
242C22×Dic3—21no—
243D3×D4—22no—
244D3×D4Dic614yescomplemented
245C2×D12C22×D311yescharacteristic
246C2×C4×D3—21no—
247C2×C4×D3—21no—
248C2×C4×D3—21no—
249C2×C4×D3—44no—
250C2×C4×D3#6711yescharacteristic
251C2×C4×D3#6711yescharacteristic
252C2×C4×D3C22×D311yescharacteristic
253C2×Dic6—21no—
254C2×Dic6—61no—
255C2×Dic6—61no—
256C2×Dic6—121no—
257C2×C3×C8—32no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—31no—
260C3×C4⋊C4—32no—
261C3×C4⋊C4—61no—
262C3×C4⋊C4—61no—
263C3×C4⋊C4C22×D311yescharacteristic
264C3×C4⋊C4C22×D311yescharacteristic
265C3×C22⋊C4—21no—
266C3×C22⋊C4—21no—
267C3×C22⋊C4—41no—
268C3×C22⋊C4—61no—
269C3×C22⋊C4—61no—
270C3×C22⋊C4—61no—
271C3×C42—21no—
272C3×C42—31no—
273C3×C42—31no—
274C3×C42—31no—
275C3×C42C22×D311yescharacteristic
276C3×C42C22×D311yescharacteristic
277#217—21no—
278#217—62no—
279(C2×D3)⋊C4—21no—
280(C2×D3)⋊C4—21no—
281(C2×D3)⋊C4—62no—
282C4⋊Dic3—21no—
283C4⋊Dic3—32no—
284C4⋊Dic3—32no—
285C4⋊Dic3—62no—
286C4⋊Dic3—61no—
287C4⋊Dic3—61no—
288C4⋊Dic3—62no—
289C4⋊Dic3—121no—
290C4⋊Dic3C22×D311yescharacteristic
291C4⋊Dic3C22×D312yes—
292Dic3⋊C4—21no—
293Dic3⋊C4—62no—
294Dic3⋊C4—62no—
295Dic3⋊C4—62no—
296C4×Dic3—62no—
297C4×Dic3—62no—
298C4×Dic3#6711yescharacteristic
299C4×Dic3#6711yescharacteristic
300C4×Dic3C22×D311yescharacteristic
301#208—64no—
302C2×C3⋊C8—32no—
303C2×C3⋊C8—32no—
304C2×C3⋊C8—62no—
305C2×C3⋊C8C22×D312yes—
306ΓL(1,𝔽25)—64no—
307C22×C32—22no—
308C22×C32—41no—
309C22×C32—41no—
310C22×C32C22×D411yescharacteristic
311C2×C3×D3—21no—
312C2×C3×D3—21no—
313C2×C3×D3—22no—
314C2×C3×D3—48no—
315C2×C3×D3—41no—
316C2×C3×D3—41no—
317C2×C3×D3C22⋊Q812yes—
318C32×C4—21no—
319C32×C4—41no—
320C32×C4AGL(1,ℤ/8)12yes—
321C32×C4C22×Q811yescharacteristic
322C32×C4C2×#4111yescharacteristic
323C3⋊Dic3—42no—
324C3×Dic3—21no—
325C3×Dic3—21no—
326C3×Dic3—41no—
327C3×Dic3—42no—
328C3×Dic3C22⋊Q812yes—
329C22×D4—31no—
330C23×C4—61no—
331C2×M16—92no—
332C4⋊Q8—31no—
333C4⋊Q8—91no—
334#125—92no—
335C22⋊Q8—181no—
336C22⋊Q8—181no—
337C4×Q8—181no—
338C4×Q8—181no—
339C4×D4—31no—
340C4×D4—31no—
341C4×D4—31no—
342C4×D4—61no—
343C4×D4—61no—
344C4×D4D3211yescharacteristic
345#117—92no—
346C2×C4⋊C4—31no—
347C2×C22⋊C4—61no—
348C2×C42—31no—
349#107—92no—
350#107—92no—
351#106—32no—
352#106—92no—
353C4⋊C8—31no—
354C4⋊C8—92no—
355C4⋊C8—91no—
356#102—32no—
357#102—92no—
358#102—92no—
359#102—92no—
360C23×C3—21no—
361C23×C3—21no—
362C23×C3—31no—
363C23×C3—41no—
364C23×C3—64no—
365C23×C3—61no—
366C23×C3—122no—
367C23×C3—122no—
368C22×D3—21no—
369C22×D3—24no—
370C22×D3—42no—
371C22×D3—42no—
372C22×D3C2×#6711yescharacteristic
373C3×Q8—122no—
374C3×D4—21no—
375C3×D4—21no—
376C3×D4—22no—
377C3×D4—32no—
378C3×D4—41no—
379C3×D4—64no—
380C3×D4—61no—
381C3×D4C2×Dic612yes—
382C3×D4D3×Q812yes—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—31no—
389C2×C3×C4—32no—
390C2×C3×C4—32no—
391C2×C3×C4—31no—
392C2×C3×C4—31no—
393C2×C3×C4—41no—
394C2×C3×C4—42no—
395C2×C3×C4—42no—
396C2×C3×C4—62no—
397C2×C3×C4—61no—
398C2×C3×C4—62no—
399C2×C3×C4—82no—
400C2×C3×C4—121no—
401C2×C3×C4—122no—
402C2×C3×C4—122no—
403C2×C3×C4—122no—
404C2×C3×C4—122no—
405C2×C3×C4D3×D411yescharacteristic
406C2×C3×C4D3×D411yescharacteristic
407C2×C3×C4C2×#6711yescharacteristic
408C2×C3×C4C2×#6711yescharacteristic
409C2×C3×C4C23×D311yescharacteristic
410C2×C3×C4C23×D311yescharacteristic
411#67—24no—
412C2×Dic3—22no—
413C2×Dic3—21no—
414C2×Dic3—42no—
415C2×Dic3—62no—
416C2×Dic3—62no—
417C2×Dic3—122no—
418C2×Dic3C2×#6711yescharacteristic
419C2×Dic3C2×#6711yescharacteristic
420C2×Dic3C2×#6711yescharacteristic
421D12—21no—
422D12C2×Dic612yes—
423C4×D3—22no—
424C4×D3—41no—
425C4×D3—42no—
426C4×D3—42no—
427C4×D3—42no—
428C4×D3C2×Dic612yes—
429C4×D3#23512yes—
430Dic6—42no—
431Dic6—122no—
432Dic6—122no—
433Dic6—242no—
434C3×C8—62no—
435C3⋊C8—22no—
436C3⋊C8—62no—
437C3⋊C8—62no—
438C3⋊C8—122no—
439C2×C32—42no—
440C2×C32C2×C22⋊Q811yescharacteristic
441C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
442C2×C32#57511yescharacteristic
443C3×D3—22no—
444C3×D3—42no—
445C24—61no—
446C2×Q8—61no—
447C2×Q8—181no—
448C2×D4—34no—
449C2×D4—31no—
450C2×D4—62no—
451C2×D4—61no—
452C2×D4C2×D3211yescharacteristic
453C22×C4—21no—
454C22×C4—31no—
455C22×C4—31no—
456C22×C4—31no—
457C22×C4—61no—
458C22×C4—61no—
459C22×C4—61no—
460C22×C4—61no—
461C22×C4—124no—
462M16—184no—
463C2×C8—32no—
464C2×C8—92no—
465C4⋊C4—32no—
466C4⋊C4—31no—
467C4⋊C4—61no—
468C4⋊C4—61no—
469C4⋊C4—92no—
470C4⋊C4—182no—
471C4⋊C4—182no—
472C4⋊C4—181no—
473C4⋊C4C2×D3211yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—61no—
476C22⋊C4—61no—
477C22⋊C4—61no—
478C22⋊C4—182no—
479C42—31no—
480C42—31no—
481C42—31no—
482C42—182no—
483C42C2×D3211yescharacteristic
484C22×C3—22no—
485C22×C3—22no—
486C22×C3—21no—
487C22×C3—32no—
488C22×C3—42no—
489C22×C3—41no—
490C22×C3—41no—
491C22×C3—41no—
492C22×C3—41no—
493C22×C3—61no—
494C22×C3—61no—
495C22×C3—62no—
496C22×C3—81no—
497C22×C3—81no—
498C22×C3—128no—
499C22×C3—121no—
500C22×C3—121no—
501C22×C3C2×D3×D411yescharacteristic
502C22×C3C22×#6711yescharacteristic
503C2×D3—21no—
504C2×D3—21no—
505C2×D3—22no—
506C2×D3—48no—
507C2×D3—41no—
508C2×D3—41no—
509C2×D3#92412yes—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—21no—
513C3×C4—21no—
514C3×C4—22no—
515C3×C4—32no—
516C3×C4—41no—
517C3×C4—41no—
518C3×C4—41no—
519C3×C4—61no—
520C3×C4—61no—
521C3×C4—81no—
522C3×C4—121no—
523C3×C4—122no—
524C3×C4#91412yes—
525C3×C4#93212yes—
526C3×C4C22×Dic611yescharacteristic
527C3×C4C2×#23511yescharacteristic
528C3×C4C2×D3×Q811yescharacteristic
529C3×C4D3×#4111yescharacteristic
530Dic3—21no—
531Dic3—21no—
532Dic3—42no—
533Dic3—41no—
534Dic3—122no—
535Dic3—122no—
536Dic3—242no—
537Dic3#92412yes—
538C32#307711yescharacteristic, complemented, Sylow
539C23—21no—
540C23—31no—
541C23—64no—
542C23—61no—
543C23—122no—
544C23—122no—
545Q8—122no—
546Q8—362no—
547D4—21no—
548D4—32no—
549D4—64no—
550D4—61no—
551D4D3×Dic612yes—
552C2×C4—21no—
553C2×C4—31no—
554C2×C4—32no—
555C2×C4—32no—
556C2×C4—31no—
557C2×C4—31no—
558C2×C4—42no—
559C2×C4—62no—
560C2×C4—62no—
561C2×C4—61no—
562C2×C4—121no—
563C2×C4—122no—
564C2×C4—122no—
565C2×C4—122no—
566C2×C4—122no—
567C2×C4—182no—
568C2×C4D3×#6711yescharacteristic
569C2×C4D3×#6711yescharacteristic
570C2×C4C22×D3211yescharacteristic
571C8—62no—
572C8—182no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—42no—
577C2×C3—42no—
578C2×C3—62no—
579C2×C3—82no—
580C2×C3—122no—
581C2×C3D3×C22⋊Q811yescharacteristic
582C2×C3C2×#91411yescharacteristic
583C2×C3#577311yescharacteristic
584C2×C3C2×#92411yescharacteristic
585C2×C3C2×#93211yescharacteristic
586C2×C3#582211yescharacteristic
587D3—22no—
588D3—42no—
589C22—22no—
590C22—32no—
591C22—41no—
592C22—41no—
593C22—61no—
594C22—61no—
595C22—62no—
596C22—128no—
597C22—121no—
598C22—121no—
599C22C2×D3×#6711yescharacteristic
600C4—21no—
601C4—32no—
602C4—41no—
603C4—61no—
604C4—61no—
605C4—121no—
606C4—122no—
607C4—362no—
608C4#6393412yes—
609C4C2×D3×Dic611yescharacteristic
610C4D3×#23511yescharacteristic
611C3—21no—
612C3#8106011yescharacteristic, complemented
613C3#8229611yescharacteristic, complemented
614C2—42no—
615C2—62no—
616C2—122no—
617C2D3×#92411yescharacteristic
618C2C2×#6393411yescharacteristic
619C2#1059546911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
hypercenterC4×D4D32
hypocenterC32#3077
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593859C2semidirect
3. #10592706C2semidirect
4. C3×#5008C2semidirect
6. #10591411C2semidirect
7. #10590581C2semidirect
8. #10590545C2semidirect
9. #10590336C2semidirect
10. #10590272C2semidirect
11. #10590266C2semidirect
17. #64078C22semidirect
26. C3×#869C22semidirect
27. #63869C22semidirect
35. #63634C22semidirect
36. C4⋊(C3⋊(C3⋊C8))C22semidirect
38. C3×#808C22semidirect
39. C3×C4⋊(C3⋊C8)C22semidirect
40. #63575C22semidirect
41. #63574C22semidirect
42. Dic3⋊(C3⋊C8)C22semidirect
55. #5008D3semidirect
75. C3×D3×D4Q8semidirect
147. #869C2×D3semidirect
165. #808C2×D3semidirect
174. C4⋊(C3⋊C8)C2×D3semidirect
244. D3×D4Dic6semidirect
538. C32#3077semidirect
612. C3#81060semidirect
613. C3#82296semidirect

Maximal subgroups

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

subgroupindex
C3×C4×D3×D42
#105938592
#105927062
C3×#50082
#105914212
#105914112
#105905812
#105905452
#105903362
#105902722
#105902662
#822963
#810603