Finite Group Databasebeta

← #11868659

Subgroups — #11868659

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×#5728C211yesmaximal, characteristic, complemented
2C4×D3×D12C211yesmaximal, characteristic
3#10592786C211yesmaximal, characteristic, complemented
4C3×#5087C211yesmaximal, characteristic, complemented
5#10590592C212yesmaximal
6#10590468C212yesmaximal, complemented
7#10590467C212yesmaximal, complemented
8#10590436C212yesmaximal, complemented
9#10590336C211yesmaximal, characteristic, complemented
10#10590300C211yesmaximal, characteristic, complemented
11#10590266C211yesmaximal, characteristic, complemented
12#83350—31nomaximal
13#80965—31nomaximal
14C2×D3×D12C2211yescharacteristic
15C2×C4×D32—21no—
16C32×C4⋊Q8C2211yescharacteristic, complemented
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C3×#946—21no—
19C3×Q8×Dic3—21no—
20C3×#897—21no—
21C3×#892C2212yes—
22C3×#890C2212yescomplemented
23C3×#887—21no—
24C3×C4×D12C2211yescharacteristic
25C3×C42×D3C2211yescharacteristic
26C3×#869C2211yescharacteristic, complemented
27D3×(C2×D3)⋊C4—21no—
28C4×#626—21no—
29#63894C2211yescharacteristic
30Dic3×D12C2211yescharacteristic
31D3×C4⋊Dic3C2211yescharacteristic
32#63880—21no—
33C2×#3711C2212yes—
34#63636C2212yes—
35#63634C2212yescomplemented
36C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
37C3×#809C2212yes—
38C3×#807C2212yescomplemented
39C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
40#63574C2212yescomplemented
41#63573C2212yescomplemented
42Dic3⋊(C3⋊C8)C2212yescomplemented
43#63564C2212yes—
44#63562C2212yes—
45C3×#533—31no—
46#5728D311yescharacteristic, complemented
47C4×D3×D4—31no—
48C2×C4×D12—31no—
49C3×#474—31no—
50#5087—31no—
51#5087—31no—
52#5087—61no—
53#5087D311yescharacteristic, complemented
54#5084—31no—
55#5084—31no—
56#5066—32no—
57#5066—32no—
58#5008—31no—
59#5001—32no—
60#4995—32no—
61#4924—31no—
62#4891—32no—
63#4881—32no—
64#4842—31no—
65#4837—31no—
66#4770—32no—
67#4763—32no—
68C22×D32—21no—
69C2×C32×Q8—21no—
70C2×C4⋊(C3⋊D3)C2311yescharacteristic
71C2×C4×C3⋊D3—21no—
72C2×C3×D12C2311yescharacteristic
73C2×C3×C4×D3—21no—
74C2×C3×C4×D3D411yescharacteristic
75C2×C3×C4×D3D411yescharacteristic
76C2×C3×C4×D3C2311yescharacteristic
77C2×C3×Dic6—21no—
78C2×#626—21no—
79C2×#624—21no—
80C2×D3×Dic3—21no—
81C2×D3×Dic3—21no—
82D3×D12—22no—
83D3×D12Q814yescomplemented
84C4×D32—44no—
85C32×C4⋊C4—21no—
86C32×C4⋊C4C2312yes—
87C32×C42C2311yescharacteristic
88#3752—21no—
89C4⋊(C3⋊Dic3)C2311yescharacteristic
90C2×C3⋊(C3⋊C8)C2312yes—
91C3×(C2×D3)⋊C4—22no—
92C3×(C2×D3)⋊C4—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3—22no—
95C3×C4⋊Dic3C2312yes—
96C3×C4⋊Dic3C2311yescharacteristic
97C3×Dic3⋊C4—22no—
98C3×C4×Dic3—22no—
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3C2311yescharacteristic
102C2×C3×C3⋊C8C2312yes—
103Dic3⋊Dic3—21no—
104#3722—21no—
105(C2×D3)⋊Dic3—21no—
106#3711—24no—
107#3077—91noSylow
108C2×D3×D4—31no—
109C22×D12—31no—
110C22×C4×D3—61no—
111C22×C4×D3—61no—
112C3×C4⋊Q8—21no—
113C3×C4⋊Q8—31no—
114C3×C4⋊Q8C2×D311yescharacteristic, complemented
115C3×C4⋊Q8C2×D311yescharacteristic, complemented
116C3×#125—32no—
117C3×C22⋊Q8—61no—
118C3×C22⋊Q8—61no—
119C3×C4×Q8—61no—
120C3×C4×Q8—61no—
121C3×C4×D4—31no—
122C3×#117—32no—
123C2×C3×C42—31no—
124#946—21no—
125Q8×Dic3—21no—
126D4×Dic3—31no—
127C4×#67—61no—
128C2×(C2×D3)⋊C4—61no—
129C2×C4⋊Dic3—31no—
130C2×#208—32no—
131C2×ΓL(1,𝔽25)—32no—
132#897—21no—
133#893—31no—
134#892C2×D312yes—
135D3×C4⋊C4—31no—
136#890C2×D312yescomplemented
137#887—21no—
138#67⋊C4—61no—
139D3×C22⋊C4—61no—
140C4×D12—31no—
141C4×D12—31no—
142C4×D12—31no—
143C4×D12—31no—
144C4×D12—61no—
145C4×D12—61no—
146C4×D12—61no—
147C4×D12C2×D311yescharacteristic
148C42×D3C2×D311yescharacteristic
149#869C2×D311yescharacteristic, complemented
150C3×#107—32no—
151C3×C4⋊C8—31no—
152C3×#102—32no—
153#832—32no—
154#821—32no—
155#817—32no—
156Dic3⋊C8—32no—
157#809—32no—
158#809—32no—
159#809—32no—
160#809—32no—
161#809—62no—
162#809C2×D312yes—
163#808—32no—
164#808—32no—
165#808—32no—
166#807—32no—
167#807—32no—
168#807—62no—
169#807C2×D312yescomplemented
170C4⋊(C3⋊C8)—31no—
171C4⋊(C3⋊C8)—31no—
172C4⋊(C3⋊C8)—32no—
173C4⋊(C3⋊C8)—61no—
174C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
175C22×C3⋊D3—21no—
176C22×C3×D3—21no—
177C22×C3×D3C2×D411yescharacteristic
178C2×D32—24no—
179C2×D32—42no—
180C2×D32—42no—
181C32×Q8—42no—
182C2×C32×C4—22no—
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2411yescharacteristic
186C2×C3⋊Dic3—21no—
187C4⋊(C3⋊D3)—21no—
188C4⋊(C3⋊D3)C2×Q812yes—
189C4×C3⋊D3—42no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3C2×D411yescharacteristic
193C2×C3×Dic3C2×D411yescharacteristic
194C2×C3×Dic3C2×D411yescharacteristic
195C3×D12—21no—
196C3×D12C2×Q812yes—
197C3×C4×D3—22no—
198C3×C4×D3—41no—
199C3×C4×D3—42no—
200C3×C4×D3C2×Q812yes—
201C3×C4×D3#4112yes—
202C3×Dic6—42no—
203#626—24no—
204#624—42no—
205D3×Dic3—42no—
206D3×Dic3—42no—
207C3⋊(C3⋊C8)—22no—
208C3×C3⋊C8—22no—
209#533—31no—
210C2×C4×D4—91no—
211#478—92no—
212#478—92no—
213#476—91no—
214#476—91no—
215#474—31no—
216#474—91no—
217#428—92no—
218#423—91no—
219#418—92no—
220C23×D3—61no—
221C23×D3—61no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—41no—
225C2×C3×Q8—61no—
226C2×C3×D4—31no—
227C22×C3×C4—31no—
228C22×C3×C4—31no—
229C22×C3×C4—31no—
230C22×C3×C4—61no—
231C2×#67—61no—
232C22×Dic3—61no—
233C22×Dic3—61no—
234D3×D4—34no—
235D3×D4—62no—
236C2×D12—31no—
237C2×D12—31no—
238C2×D12—34no—
239C2×D12—61no—
240C2×D12—62no—
241C2×D12—61no—
242C2×D12C22×D311yescharacteristic
243C2×C4×D3—21no—
244C2×C4×D3—61no—
245C2×C4×D3—61no—
246C2×C4×D3—61no—
247C2×C4×D3—61no—
248C2×C4×D3—61no—
249C2×C4×D3—61no—
250C2×C4×D3—121no—
251C2×C4×D3—124no—
252C2×C4×D3—124no—
253C2×C4×D3#6711yescharacteristic
254C2×C4×D3#6711yescharacteristic
255C2×C4×D3C22×D311yescharacteristic
256C2×Dic6—21no—
257C2×C3×C8—32no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—22no—
261C3×C4⋊C4—32no—
262C3×C4⋊C4—31no—
263C3×C4⋊C4—41no—
264C3×C4⋊C4—62no—
265C3×C4⋊C4—62no—
266C3×C4⋊C4—61no—
267C3×C4⋊C4C22×D312yes—
268C3×C4⋊C4C22×D312yes—
269C3×C22⋊C4—62no—
270C3×C22⋊C4—61no—
271C3×C42—21no—
272C3×C42—31no—
273C3×C42—31no—
274C3×C42—31no—
275C3×C42—62no—
276C3×C42C22×D311yescharacteristic
277C3×C42C22×D311yescharacteristic
278#217—61no—
279(C2×D3)⋊C4—22no—
280(C2×D3)⋊C4—21no—
281(C2×D3)⋊C4—61no—
282(C2×D3)⋊C4—61no—
283(C2×D3)⋊C4—61no—
284(C2×D3)⋊C4—61no—
285(C2×D3)⋊C4—61no—
286(C2×D3)⋊C4—121no—
287C4⋊Dic3—21no—
288C4⋊Dic3—22no—
289C4⋊Dic3—31no—
290C4⋊Dic3—31no—
291C4⋊Dic3—61no—
292C4⋊Dic3—61no—
293C4⋊Dic3C22×D311yescharacteristic
294C4⋊Dic3C22×D312yes—
295Dic3⋊C4—22no—
296Dic3⋊C4—61no—
297C4×Dic3—22no—
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×C32C22×D411yescharacteristic
308C2×C3⋊D3—22no—
309C2×C3⋊D3—41no—
310C2×C3⋊D3—41no—
311C2×C3×D3—21no—
312C2×C3×D3—21no—
313C2×C3×D3—22no—
314C2×C3×D3—41no—
315C2×C3×D3—41no—
316C2×C3×D3C22⋊Q812yes—
317D32—48no—
318C32×C4—21no—
319C32×C4—42no—
320C32×C4AGL(1,ℤ/8)12yes—
321C32×C4C22×Q811yescharacteristic
322C32×C4C2×#4111yescharacteristic
323C3⋊Dic3—41no—
324C3×Dic3—21no—
325C3×Dic3—21no—
326C3×Dic3—41no—
327C3×Dic3—42no—
328C3×Dic3C22⋊Q812yes—
329C22×D4—91no—
330C23×C4—181no—
331C2×M16—92no—
332C4⋊Q8—31no—
333C4⋊Q8D3211yescharacteristic, complemented
334#125—32no—
335C22⋊Q8—61no—
336C22⋊Q8—61no—
337C4×Q8—61no—
338C4×Q8—61no—
339C4×D4—31no—
340C4×D4—91no—
341C4×D4—91no—
342C4×D4—91no—
343C4×D4—181no—
344C4×D4—181no—
345#117—32no—
346C2×C4⋊C4—91no—
347C2×C22⋊C4—181no—
348C2×C42—31no—
349#107—32no—
350#107—92no—
351#106—92no—
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—31no—
361C23×C3—61no—
362C22×D3—21no—
363C22×D3—64no—
364C22×D3—61no—
365C22×D3—61no—
366C22×D3—64no—
367C22×D3—121no—
368C22×D3—122no—
369C22×D3—122no—
370C22×D3—122no—
371C22×D3—122no—
372C22×D3C2×#6711yescharacteristic
373C3×Q8—42no—
374C3×Q8—42no—
375C3×Q8—82no—
376C3×Q8—122no—
377C3×D4—32no—
378C3×D4—61no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—31no—
385C2×C3×C4—32no—
386C2×C3×C4—32no—
387C2×C3×C4—31no—
388C2×C3×C4—31no—
389C2×C3×C4—42no—
390C2×C3×C4—62no—
391C2×C3×C4—62no—
392C2×C3×C4—61no—
393C2×C3×C4—121no—
394C2×C3×C4—122no—
395C2×C3×C4D3×D411yescharacteristic
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4C2×#6711yescharacteristic
398C2×C3×C4C2×#6711yescharacteristic
399C2×C3×C4C23×D311yescharacteristic
400C2×C3×C4C23×D311yescharacteristic
401#67—64no—
402C2×Dic3—21no—
403C2×Dic3—22no—
404C2×Dic3—61no—
405C2×Dic3—61no—
406C2×Dic3—121no—
407C2×Dic3—122no—
408C2×Dic3—122no—
409C2×Dic3C2×#6711yescharacteristic
410C2×Dic3C2×#6711yescharacteristic
411C2×Dic3C2×#6711yescharacteristic
412D12—21no—
413D12—32no—
414D12—32no—
415D12—62no—
416D12—64no—
417D12—61no—
418D12—61no—
419D12—121no—
420D12D3×Q812yes—
421C4×D3—22no—
422C4×D3—41no—
423C4×D3—42no—
424C4×D3—122no—
425C4×D3—122no—
426C4×D3—122no—
427C4×D3—122no—
428C4×D3—122no—
429C4×D3—122no—
430C4×D3—242no—
431C4×D3D3×Q812yes—
432C4×D3#23912yes—
433Dic6—42no—
434C3×C8—62no—
435C3⋊C8—22no—
436C3⋊C8—62no—
437C3⋊C8—62no—
438C3⋊C8—122no—
439C2×C32C2×C22⋊Q811yescharacteristic
440C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
441C2×C32#57511yescharacteristic
442C3⋊D3—42no—
443C3×D3—22no—
444C3×D3—42no—
445C24—181no—
446C2×Q8—21no—
447C2×Q8—61no—
448C2×D4—31no—
449C2×D4—94no—
450C2×D4—91no—
451C2×D4—182no—
452C2×D4—181no—
453C22×C4—31no—
454C22×C4—31no—
455C22×C4—31no—
456C22×C4—61no—
457C22×C4—181no—
458C22×C4—181no—
459C22×C4—181no—
460C22×C4—181no—
461C22×C4—364no—
462M16—184no—
463C2×C8—32no—
464C2×C8—92no—
465C4⋊C4—21no—
466C4⋊C4—32no—
467C4⋊C4—31no—
468C4⋊C4—62no—
469C4⋊C4—62no—
470C4⋊C4—61no—
471C4⋊C4—91no—
472C4⋊C4—181no—
473C4⋊C4C2×D3212yes—
474C22⋊C4—62no—
475C22⋊C4—61no—
476C22⋊C4—181no—
477C22⋊C4—181no—
478C22⋊C4—181no—
479C42—31no—
480C42—31no—
481C42—31no—
482C42—62no—
483C42C2×D3211yescharacteristic
484C22×C3—21no—
485C22×C3—32no—
486C22×C3—61no—
487C22×C3—61no—
488C22×C3—62no—
489C22×C3—121no—
490C22×C3—121no—
491C22×C3C2×D3×D411yescharacteristic
492C22×C3C22×#6711yescharacteristic
493C2×D3—21no—
494C2×D3—21no—
495C2×D3—22no—
496C2×D3—41no—
497C2×D3—41no—
498C2×D3—62no—
499C2×D3—62no—
500C2×D3—122no—
501C2×D3—128no—
502C2×D3—128no—
503C2×D3—121no—
504C2×D3—121no—
505C2×D3—121no—
506C2×D3—121no—
507C2×D3—241no—
508C2×D3—241no—
509C2×D3#94612yes—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—21no—
513C3×C4—21no—
514C3×C4—22no—
515C3×C4—32no—
516C3×C4—41no—
517C3×C4—42no—
518C3×C4—42no—
519C3×C4—61no—
520C3×C4—61no—
521C3×C4—82no—
522C3×C4—122no—
523C3×C4—121no—
524C3×C4#91112yes—
525C3×C4#94912yes—
526C3×C4C2×D3×Q811yescharacteristic
527C3×C4C2×D3×Q811yescharacteristic
528C3×C4C2×#23911yescharacteristic
529C3×C4D3×#4111yescharacteristic
530Dic3—21no—
531Dic3—21no—
532Dic3—41no—
533Dic3—42no—
534Dic3—121no—
535Dic3—121no—
536Dic3—241no—
537Dic3#94612yes—
538C32#307711yescharacteristic, complemented, Sylow
539C23—31no—
540C23—61no—
541C23—184no—
542C23—181no—
543C23—362no—
544C23—362no—
545Q8—42no—
546Q8—122no—
547D4—32no—
548D4—61no—
549D4—92no—
550D4—184no—
551D4—181no—
552C2×C4—22no—
553C2×C4—31no—
554C2×C4—32no—
555C2×C4—32no—
556C2×C4—31no—
557C2×C4—31no—
558C2×C4—62no—
559C2×C4—62no—
560C2×C4—61no—
561C2×C4—121no—
562C2×C4—122no—
563C2×C4—181no—
564C2×C4—362no—
565C2×C4—362no—
566C2×C4—362no—
567C2×C4—362no—
568C2×C4D3×#6711yescharacteristic
569C2×C4D3×#6711yescharacteristic
570C2×C4C22×D3211yescharacteristic
571C8—62no—
572C8—182no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—62no—
577C2×C3—122no—
578C2×C3D3×C22⋊Q811yescharacteristic
579C2×C3C2×#91111yescharacteristic
580C2×C3#577711yescharacteristic
581C2×C3C2×#94611yescharacteristic
582C2×C3C2×#94911yescharacteristic
583C2×C3#582211yescharacteristic
584D3—22no—
585D3—42no—
586D3—122no—
587D3—122no—
588D3—242no—
589C22—32no—
590C22—61no—
591C22—61no—
592C22—62no—
593C22—121no—
594C22—121no—
595C22—182no—
596C22—368no—
597C22—361no—
598C22—361no—
599C22C2×D3×#6711yescharacteristic
600C4—21no—
601C4—32no—
602C4—42no—
603C4—61no—
604C4—61no—
605C4—121no—
606C4—122no—
607C4—361no—
608C4#6392512yes—
609C4D32×Q811yescharacteristic
610C4D3×#23911yescharacteristic
611C3—21no—
612C3#8096511yescharacteristic, complemented
613C3#8335011yescharacteristic, complemented
614C2—62no—
615C2—122no—
616C2—362no—
617C2C2×#6392511yescharacteristic
618C2#1059531711yescharacteristic
619C2D3×#94611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
hypercenterC4⋊Q8D32
hypocenterC32#3077
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5728C2semidirect
3. #10592786C2semidirect
4. C3×#5087C2semidirect
6. #10590468C2semidirect
7. #10590467C2semidirect
8. #10590436C2semidirect
9. #10590336C2semidirect
10. #10590300C2semidirect
11. #10590266C2semidirect
16. C32×C4⋊Q8C22semidirect
22. C3×#890C22semidirect
26. C3×#869C22semidirect
35. #63634C22semidirect
36. C4⋊(C3⋊(C3⋊C8))C22semidirect
38. C3×#807C22semidirect
39. C3×C4⋊(C3⋊C8)C22semidirect
40. #63574C22semidirect
41. #63573C22semidirect
42. Dic3⋊(C3⋊C8)C22semidirect
46. #5728D3semidirect
53. #5087D3semidirect
83. D3×D12Q8semidirect
114. C3×C4⋊Q8C2×D3semidirect
115. C3×C4⋊Q8C2×D3semidirect
136. #890C2×D3semidirect
149. #869C2×D3semidirect
169. #807C2×D3semidirect
174. C4⋊(C3⋊C8)C2×D3semidirect
333. C4⋊Q8D32semidirect
538. C32#3077semidirect
612. C3#80965semidirect
613. C3#83350semidirect

Maximal subgroups

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

subgroupindex
C3×#57282
C4×D3×D122
#105927862
C3×#50872
#105905922
#105904682
#105904672
#105904362
#105903362
#105903002
#105902662
#833503
#809653