Finite Group Databasebeta

← #11868813

Subgroups — #11868813

Order 1152.

886 conjugacy classes of subgroups.

The subgroup lattice has 593 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#237C211yesmaximal, characteristic
2D3×#869C211yesmaximal, characteristic, complemented
3#10592707C211yesmaximal, characteristic, complemented
4C3×#5008C211yesmaximal, characteristic, complemented
5#10591414C212yesmaximal
6#10591410C212yesmaximal, complemented
7#10590556C212yesmaximal, complemented
8#10590437C212yesmaximal, complemented
9#10590336C211yesmaximal, characteristic, complemented
10#10590310C211yesmaximal, characteristic, complemented
11#10590283C211yesmaximal, characteristic, complemented
12#82508—31nomaximal
13#81061—31nomaximal
14C2×C3×#237C2211yescharacteristic
15C2×D3×Dic6—21no—
16C32×C4×D4C2211yescharacteristic
17#64078C2211yescharacteristic
18C3×D4×Dic3C2211yescharacteristic
19C3×C4×#67—21no—
20C2×C3×C4×Dic3—21no—
21C3×#892C2211yescharacteristic
22C3×#887C2211yescharacteristic
23C3×#67⋊C4—21no—
24C3×#877—21no—
25C3×C42×D3C2211yescharacteristic
26C3×#869C2211yescharacteristic
27C3×C4×Dic6C2211yescharacteristic
28#63918—21no—
29#63918C2212yes—
30D3×C4⋊Dic3—21no—
31D3×C4⋊Dic3C2212yes—
32#63866—21no—
33C2×#3711C2212yes—
34#63659C2212yes—
35#63635C2212yes—
36C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
37C3×#832C2212yes—
38C3×#808C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63576C2212yes—
41#63575C2212yes—
42Dic3⋊(C3⋊C8)C2212yes—
43#63566C2212yes—
44#63565C2212yes—
45C3×C4×#41—31no—
46D3×C4⋊Q8—31no—
47C4×#237D311yescharacteristic
48C2×#869—31no—
49C3×#476—31no—
50#5232—32no—
51#5091—31no—
52#5021—31no—
53#5021—31no—
54#5020—32no—
55#5008—31no—
56#5008—31no—
57#5008—61no—
58#5008D311yescharacteristic, complemented
59#5007—32no—
60#4995—32no—
61#4924—31no—
62#4861—32no—
63#4854—32no—
64#4850—31no—
65#4837—31no—
66#4771—32no—
67#4759—32no—
68C2×C32×D4C2311yescharacteristic
69C22×C32×C4—21no—
70C2×#634—21no—
71C2×C3×#67—21no—
72C22×C3×Dic3—21no—
73C22×C3×Dic3—21no—
74C3×#237—22no—
75C3×#237Q814yescomplemented
76C2×C3×C4×D3D411yescharacteristic
77C2×C3×C4×D3D411yescharacteristic
78C2×C3×C4×D3C2311yescharacteristic
79C2×C3×Dic6—21no—
80C2×C3×Dic6C2311yescharacteristic
81C2×#627—22no—
82C2×D3×Dic3—22no—
83D3×Dic6—44no—
84C32×C4⋊C4C2311yescharacteristic
85C32×C22⋊C4—21no—
86C32×C42C2311yescharacteristic
87C4⋊(C3⋊Dic3)—21no—
88C4⋊(C3⋊Dic3)C2312yes—
89C2×C3⋊(C3⋊C8)C2312yes—
90C3×#217—21no—
91C3×(C2×D3)⋊C4—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×C4⋊Dic3C2312yes—
95C3×Dic3⋊C4—21no—
96C3×Dic3⋊C4—21no—
97C3×C4×Dic3—21no—
98C3×C4×Dic3—21no—
99C3×C4×Dic3—21no—
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3C2311yescharacteristic
103C2×C3×C3⋊C8C2312yes—
104Dic3⋊Dic3—22no—
105Dic3⋊Dic3—22no—
106#3711—24no—
107#3079—91noSylow
108C2×C3×#41—31no—
109C2×D3×Q8—61no—
110C2×#237C2×D311yescharacteristic
111C22×Dic6—61no—
112C3×C4⋊Q8—31no—
113C3×C4×Q8—31no—
114C3×C4×Q8—31no—
115C3×C4×D4—21no—
116C3×C4×D4—31no—
117C3×C4×D4—61no—
118C3×C4×D4—61no—
119C3×C4×D4C2×D311yescharacteristic
120C3×C4×D4C2×D311yescharacteristic
121C3×#117—31no—
122C3×#117—61no—
123C2×C3×C42—31no—
124C2×C3×C42—61no—
125#944—61no—
126D4×Dic3C2×D311yescharacteristic
127C4×#67—21no—
128C2×C4⋊Dic3—32no—
129C2×C4⋊Dic3—61no—
130C2×C4×Dic3—21no—
131C2×#208—32no—
132C2×ΓL(1,𝔽25)—32no—
133#892C2×D311yescharacteristic
134D3×C4⋊C4—32no—
135D3×C4⋊C4—61no—
136#888—32no—
137#888—61no—
138#887C2×D311yescharacteristic
139#67⋊C4—21no—
140#877—21no—
141C42×D3C2×D311yescharacteristic
142#869—31no—
143#869—31no—
144#869—32no—
145#869—61no—
146#869—61no—
147#869—61no—
148#869C2×D311yescharacteristic
149C4×Dic6C2×D311yescharacteristic
150C3×#106—32no—
151C3×C4⋊C8—31no—
152C3×#102—32no—
153#835—32no—
154#835—32no—
155#832—32no—
156#832—32no—
157#832—62no—
158#832C2×D312yes—
159#818—32no—
160#816—32no—
161Dic3⋊C8—32no—
162#810—32no—
163#808—32no—
164#808—32no—
165#808—62no—
166#808C2×D312yes—
167#807—32no—
168#807—32no—
169#807—32no—
170C4⋊(C3⋊C8)—31no—
171C4⋊(C3⋊C8)—31no—
172C4⋊(C3⋊C8)—32no—
173C4⋊(C3⋊C8)—61no—
174C4⋊(C3⋊C8)C2×D311yescharacteristic
175C23×C32—21no—
176C22×C3×D3C2×D411yescharacteristic
177C32×D4—21no—
178C32×D4C2×Q812yescomplemented
179C2×C32×C4—21no—
180C2×C32×C4—42no—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3—22no—
185#634—42no—
186C3×#67—24no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—24no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—42no—
192C2×C3×Dic3C2×D411yescharacteristic
193C2×C3×Dic3C2×D411yescharacteristic
194C2×C3×Dic3C2×D411yescharacteristic
195C3×C4×D3—22no—
196C3×C4×D3—22no—
197C3×C4×D3C2×Q812yes—
198C3×C4×D3#4112yes—
199C3×Dic6—21no—
200C3×Dic6—42no—
201C3×Dic6C2×Q812yescomplemented
202#627—44no—
203D3×Dic3—44no—
204C3⋊(C3⋊C8)—22no—
205C3×C3⋊C8—22no—
206C2×C4⋊Q8—91no—
207C4×#41—31no—
208#477—91no—
209#477—91no—
210#476—31no—
211#476—91no—
212#475—92no—
213#474—92no—
214#428—92no—
215#423—91no—
216#417—92no—
217C3×#41—34no—
218C3×#41—62no—
219C2×C3×Q8—31no—
220C2×C3×Q8—61no—
221C2×C3×D4—21no—
222C2×C3×D4—61no—
223C2×C3×D4C22×D311yescharacteristic
224C2×C3×D4C22×D311yescharacteristic
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—31no—
228C22×C3×C4—31no—
229C22×C3×C4—31no—
230C22×C3×C4—41no—
231C22×C3×C4—61no—
232C22×C3×C4—61no—
233C2×#67—21no—
234C22×Dic3—21no—
235C22×Dic3—21no—
236C22×Dic3—62no—
237D3×Q8—124no—
238#237—22no—
239#237Dic614yescomplemented
240C2×C4×D3—62no—
241C2×C4×D3#6711yescharacteristic
242C2×C4×D3#6711yescharacteristic
243C2×C4×D3C22×D311yescharacteristic
244C2×Dic6—21no—
245C2×Dic6—62no—
246C2×Dic6—61no—
247C2×Dic6—61no—
248C2×Dic6—62no—
249C2×Dic6—121no—
250C2×Dic6—124no—
251C2×Dic6C22×D311yescharacteristic
252C2×C3×C8—32no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—31no—
255C3×C4⋊C4—32no—
256C3×C4⋊C4—61no—
257C3×C4⋊C4—61no—
258C3×C4⋊C4—61no—
259C3×C4⋊C4C22×D311yescharacteristic
260C3×C4⋊C4C22×D311yescharacteristic
261C3×C22⋊C4—21no—
262C3×C22⋊C4—21no—
263C3×C22⋊C4—41no—
264C3×C22⋊C4—61no—
265C3×C22⋊C4—61no—
266C3×C42—21no—
267C3×C42—31no—
268C3×C42—31no—
269C3×C42—31no—
270C3×C42—61no—
271C3×C42—61no—
272C3×C42—61no—
273C3×C42C22×D311yescharacteristic
274C3×C42C22×D311yescharacteristic
275#217—21no—
276(C2×D3)⋊C4—21no—
277C4⋊Dic3—21no—
278C4⋊Dic3—32no—
279C4⋊Dic3—32no—
280C4⋊Dic3—62no—
281C4⋊Dic3—62no—
282C4⋊Dic3—62no—
283C4⋊Dic3—61no—
284C4⋊Dic3—61no—
285C4⋊Dic3—121no—
286C4⋊Dic3C22×D311yescharacteristic
287C4⋊Dic3C22×D312yes—
288Dic3⋊C4—21no—
289Dic3⋊C4—21no—
290Dic3⋊C4—62no—
291Dic3⋊C4—62no—
292C4×Dic3—21no—
293C4×Dic3—21no—
294C4×Dic3—21no—
295C4×Dic3#6711yescharacteristic
296C4×Dic3#6711yescharacteristic
297C4×Dic3C22×D311yescharacteristic
298#208—64no—
299C2×C3⋊C8—32no—
300C2×C3⋊C8—32no—
301C2×C3⋊C8—62no—
302C2×C3⋊C8C22×D312yes—
303ΓL(1,𝔽25)—64no—
304C22×C32—22no—
305C22×C32—41no—
306C22×C32—41no—
307C22×C32C22×D411yescharacteristic
308C2×C3×D3—21no—
309C2×C3×D3—21no—
310C2×C3×D3C22⋊Q812yes—
311C32×C4—21no—
312C32×C4—41no—
313C32×C4#13712yes—
314C32×C4C22×Q811yescharacteristic
315C32×C4C2×#4111yescharacteristic
316C3⋊Dic3—42no—
317C3×Dic3—22no—
318C3×Dic3—21no—
319C3×Dic3—42no—
320C3×Dic3—41no—
321C3×Dic3C22⋊Q812yes—
322C3×Dic3AGL(1,ℤ/8)12yes—
323C2×#41—31no—
324C22×Q8—181no—
325C2×M16—92no—
326C4⋊Q8—31no—
327C4⋊Q8—92no—
328C4⋊Q8—91no—
329C4⋊Q8—181no—
330C4⋊Q8—181no—
331C4×Q8—31no—
332C4×Q8—31no—
333C4×D4—31no—
334C4×D4—61no—
335C4×D4—61no—
336C4×D4D3211yescharacteristic
337#117—31no—
338#117—61no—
339C2×C4⋊C4—92no—
340C2×C4⋊C4—181no—
341C2×C42—31no—
342C2×C42—61no—
343#107—92no—
344#107—92no—
345#106—32no—
346#106—92no—
347C4⋊C8—31no—
348C4⋊C8—92no—
349C4⋊C8—91no—
350#103—92no—
351#103—92no—
352#102—32no—
353#102—92no—
354C23×C3—21no—
355C23×C3—21no—
356C23×C3—31no—
357C23×C3—41no—
358C22×D3C2×#6711yescharacteristic
359C3×Q8—32no—
360C3×Q8—61no—
361C3×Q8—122no—
362C3×D4—21no—
363C3×D4—21no—
364C3×D4—22no—
365C3×D4—41no—
366C3×D4—64no—
367C3×D4C2×Dic612yescomplemented
368C3×D4D3×Q812yescomplemented
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—31no—
375C2×C3×C4—31no—
376C2×C3×C4—32no—
377C2×C3×C4—32no—
378C2×C3×C4—31no—
379C2×C3×C4—41no—
380C2×C3×C4—42no—
381C2×C3×C4—42no—
382C2×C3×C4—62no—
383C2×C3×C4—64no—
384C2×C3×C4—61no—
385C2×C3×C4—62no—
386C2×C3×C4—61no—
387C2×C3×C4—62no—
388C2×C3×C4—82no—
389C2×C3×C4—122no—
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4C2×#6711yescharacteristic
393C2×C3×C4C2×#6711yescharacteristic
394C2×C3×C4C23×D311yescharacteristic
395C2×C3×C4C23×D311yescharacteristic
396#67—24no—
397C2×Dic3—21no—
398C2×Dic3—24no—
399C2×Dic3—22no—
400C2×Dic3—21no—
401C2×Dic3—42no—
402C2×Dic3—62no—
403C2×Dic3—62no—
404C2×Dic3—122no—
405C2×Dic3—124no—
406C2×Dic3C2×#6711yescharacteristic
407C2×Dic3C2×#6711yescharacteristic
408C2×Dic3C2×#6711yescharacteristic
409C4×D3—22no—
410C4×D3—22no—
411C4×D3—124no—
412C4×D3C2×Dic612yes—
413C4×D3#23512yes—
414Dic6—21no—
415Dic6—42no—
416Dic6—124no—
417Dic6—122no—
418Dic6—122no—
419Dic6—124no—
420Dic6—242no—
421Dic6C2×Dic612yescomplemented
422C3×C8—62no—
423C3⋊C8—22no—
424C3⋊C8—62no—
425C3⋊C8—62no—
426C3⋊C8—122no—
427C2×C32—42no—
428C2×C32C2×C22⋊Q811yescharacteristic
429C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
430C2×C32C2×#13711yescharacteristic
431C3×D3—22no—
432#41—34no—
433#41—62no—
434C2×Q8—31no—
435C2×Q8—61no—
436C2×Q8—182no—
437C2×Q8—181no—
438C2×Q8—364no—
439C2×D4—61no—
440C2×D4C2×D3211yescharacteristic
441C22×C4—21no—
442C22×C4—31no—
443C22×C4—31no—
444C22×C4—31no—
445C22×C4—61no—
446C22×C4—61no—
447C22×C4—182no—
448M16—184no—
449C2×C8—32no—
450C2×C8—92no—
451C4⋊C4—32no—
452C4⋊C4—31no—
453C4⋊C4—61no—
454C4⋊C4—61no—
455C4⋊C4—61no—
456C4⋊C4—92no—
457C4⋊C4—182no—
458C4⋊C4—182no—
459C4⋊C4—181no—
460C4⋊C4C2×D3211yescharacteristic
461C22⋊C4—21no—
462C22⋊C4—61no—
463C22⋊C4—61no—
464C42—31no—
465C42—31no—
466C42—31no—
467C42—61no—
468C42—61no—
469C42—61no—
470C42C2×D3211yescharacteristic
471C22×C3—22no—
472C22×C3—22no—
473C22×C3—21no—
474C22×C3—32no—
475C22×C3—42no—
476C22×C3—41no—
477C22×C3—41no—
478C22×C3—41no—
479C22×C3—41no—
480C22×C3—61no—
481C22×C3—61no—
482C22×C3—81no—
483C22×C3—81no—
484C22×C3C2×D3×D411yescharacteristic
485C22×C3C22×#6711yescharacteristic
486C2×D3—21no—
487C2×D3—21no—
488C2×D3#92412yes—
489C3×C4—21no—
490C3×C4—21no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—22no—
494C3×C4—32no—
495C3×C4—32no—
496C3×C4—41no—
497C3×C4—41no—
498C3×C4—41no—
499C3×C4—61no—
500C3×C4—62no—
501C3×C4—81no—
502C3×C4—121no—
503C3×C4—122no—
504C3×C4#91512yes—
505C3×C4#95112yes—
506C3×C4C22×Dic611yescharacteristic
507C3×C4C2×#23511yescharacteristic
508C3×C4C2×D3×Q811yescharacteristic
509C3×C4D3×#4111yescharacteristic
510Dic3—22no—
511Dic3—21no—
512Dic3—42no—
513Dic3—41no—
514Dic3—122no—
515Dic3—122no—
516Dic3—242no—
517Dic3#92412yes—
518Dic3#94912yes—
519C32#307911yescharacteristic, complemented, Sylow
520C23—21no—
521C23—31no—
522Q8—32no—
523Q8—61no—
524Q8—122no—
525Q8—362no—
526Q8—364no—
527D4—21no—
528D4—64no—
529D4D3×Dic612yescomplemented
530C2×C4—21no—
531C2×C4—31no—
532C2×C4—31no—
533C2×C4—32no—
534C2×C4—32no—
535C2×C4—31no—
536C2×C4—42no—
537C2×C4—62no—
538C2×C4—64no—
539C2×C4—61no—
540C2×C4—62no—
541C2×C4—61no—
542C2×C4—62no—
543C2×C4—122no—
544C2×C4—182no—
545C2×C4—364no—
546C2×C4D3×#6711yescharacteristic
547C2×C4D3×#6711yescharacteristic
548C2×C4C22×D3211yescharacteristic
549C8—62no—
550C8—182no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—42no—
555C2×C3—42no—
556C2×C3—62no—
557C2×C3—82no—
558C2×C3D3×C22⋊Q811yescharacteristic
559C2×C3C2×#91511yescharacteristic
560C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
561C2×C3C2×#92411yescharacteristic
562C2×C3C2×#94911yescharacteristic
563C2×C3C2×#95111yescharacteristic
564D3—22no—
565C22—22no—
566C22—32no—
567C22—41no—
568C22—41no—
569C22—61no—
570C22—61no—
571C22C2×D3×#6711yescharacteristic
572C4—21no—
573C4—32no—
574C4—32no—
575C4—41no—
576C4—61no—
577C4—62no—
578C4—121no—
579C4—122no—
580C4—362no—
581C4#6392912yes—
582C4C2×D3×Dic611yescharacteristic
583C4D3×#23511yescharacteristic
584C3—21no—
585C3#8106111yescharacteristic, complemented
586C3#8250811yescharacteristic, complemented
587C2—42no—
588C2—62no—
589C2D3×#92411yescharacteristic
590C2C2×#6392911yescharacteristic
591C2D3×#94911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×#237C22
hypercenterC4×D4D32
hypocenterC32#3079
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. D3×#869C2semidirect
3. #10592707C2semidirect
4. C3×#5008C2semidirect
6. #10591410C2semidirect
7. #10590556C2semidirect
8. #10590437C2semidirect
9. #10590336C2semidirect
10. #10590310C2semidirect
11. #10590283C2semidirect
58. #5008D3semidirect
75. C3×#237Q8semidirect
178. C32×D4C2×Q8semidirect
201. C3×Dic6C2×Q8semidirect
239. #237Dic6semidirect
367. C3×D4C2×Dic6semidirect
368. C3×D4D3×Q8semidirect
421. Dic6C2×Dic6semidirect
519. C32#3079semidirect
529. D4D3×Dic6semidirect
585. C3#81061semidirect
586. C3#82508semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2372
D3×#8692
#105927072
C3×#50082
#105914142
#105914102
#105905562
#105904372
#105903362
#105903102
#105902832
#825083
#810613