Finite Group Databasebeta

← #11868685

Subgroups — #11868685

Order 1152.

943 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595050C211yesmaximal, characteristic, complemented
2C2×#63898C211yesmaximal, characteristic
3#10592817C211yesmaximal, characteristic, complemented
4C3×#5131C211yesmaximal, characteristic
5C3×#5121C211yesmaximal, characteristic, complemented
6#10591139C211yesmaximal, characteristic, complemented
7#10591085C211yesmaximal, characteristic
8#10590782C212yesmaximal, complemented
9#10590780C212yesmaximal, complemented
10#10590778C212yesmaximal, complemented
11#10590776C212yesmaximal, complemented
12#79239—31nomaximal
13#78917—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C22×D3×Dic3—21no—
16C2×C32×M16C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×#3748C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C3×#926C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22#63982—21no—
23#63982—21no—
24C2×(C2×D3)⋊Dic3—21no—
25#63919C2211yescharacteristic, complemented
26#63919C2211yescharacteristic, complemented
27C4×#627—21no—
28C4×#627—21no—
29#63898—21no—
30#63898—21no—
31#63898C2212yes—
32#63898C2212yes—
33#63872C2211yescharacteristic, complemented
34#63872C2211yescharacteristic, complemented
35#63641C2212yescomplemented
36#63641C2212yescomplemented
37C3×#821C2212yes—
38C3×#821C2212yes—
39C3×#818C2212yescomplemented
40C3×#817C2212yescomplemented
41#63576C2212yescomplemented
42#63574C2212yescomplemented
43#63562C2212yes—
44#63562C2212yes—
45C2×D4×Dic3—31no—
46#5517—31no—
47#5517—31no—
48C2×#893—31no—
49C3×#428—31no—
50C3×#418—31no—
51#5215—31no—
52#5131D311yescharacteristic
53#5121D311yescharacteristic, complemented
54#5118—31no—
55#5118—31no—
56#5118—61no—
57#5001—31no—
58#4995—31no—
59#4964—31no—
60#4891—32no—
61#4890—32no—
62#4871—32no—
63#4870—32no—
64#4766—32no—
65#4763—32no—
66#4761—32no—
67#4759—32no—
68C23×C3×D3—21no—
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3D411yescharacteristic
71C22×C3⋊Dic3D411yescharacteristic
72C22×C3×Dic3—21no—
73C2×C3×D12—21no—
74C2×C3×D12—22no—
75C2×C3×D12Q814yescomplemented
76C2×C3×D12C2312yes—
77C2×#627—21no—
78C2×#627—21no—
79C2×D3×Dic3—22no—
80C2×D3×Dic3—22no—
81C2×D3×Dic3—44no—
82C32×M16—22no—
83C2×C32×C8C2312yes—
84C4×C3⋊Dic3D411yescharacteristic
85C4×C3⋊Dic3D411yescharacteristic
86C4×C3⋊Dic3C2311yescharacteristic
87C4×C3⋊Dic3C2311yescharacteristic
88#3748—22no—
89C2×C3⋊(C3⋊C8)C2312yes—
90C3×#217—21no—
91C3×#217—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3C2312yes—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4⋊Dic3C2311yescharacteristic
96C3×C4⋊Dic3C2311yescharacteristic
97C3×C4⋊Dic3C2311yescharacteristic
98C3×C4×Dic3—21no—
99C3×C4×Dic3—21no—
100#3724—21no—
101#3724—21no—
102Dic3⋊Dic3—21no—
103Dic3⋊Dic3—21no—
104Dic3⋊Dic3—21no—
105Dic3⋊Dic3—21no—
106(C2×D3)⋊Dic3—22no—
107(C2×D3)⋊Dic3—22no—
108#3077—91noSylow
109C22×C3×D4—31no—
110C23×Dic3—61no—
111C22×D12C2×D311yescharacteristic
112C22×C4×D3—61no—
113C2×C3×M16—21no—
114C2×C3×M16C2×D311yescharacteristic
115C2×C3×M16C2×D311yescharacteristic
116C3×#117—31no—
117C3×#117—31no—
118C2×C3×C4⋊C4—31no—
119C2×#217—61no—
120D4×Dic3—32no—
121D4×Dic3—32no—
122D4×Dic3—61no—
123D4×Dic3—61no—
124C2×(C2×D3)⋊C4—61no—
125#926C2×D311yescharacteristic
126#926C2×D311yescharacteristic
127C2×C4⋊Dic3C2×D311yescharacteristic
128C2×C4×Dic3—31no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—61no—
131C2×#208—31no—
132C2×#208—31no—
133C2×#208—61no—
134#893—32no—
135#893—32no—
136#893—61no—
137#893—61no—
138#890—31no—
139#890—31no—
140#890—31no—
141#890—31no—
142#888—31no—
143#888—31no—
144#888—31no—
145#888—31no—
146#878—61no—
147#878—61no—
148#878—61no—
149#878—61no—
150C4×Dic6—61no—
151C4×Dic6—61no—
152C4×Dic6—61no—
153C4×Dic6—61no—
154C3×#107—32no—
155C3×#106—32no—
156C3×#102—32no—
157C3×#102—32no—
158#832—32no—
159#832—32no—
160#821C2×D312yes—
161#821C2×D312yes—
162#818C2×D312yescomplemented
163#817C2×D312yescomplemented
164Dic3⋊C8—32no—
165Dic3⋊C8—32no—
166Dic3⋊C8—32no—
167Dic3⋊C8—32no—
168Dic3⋊C8—62no—
169Dic3⋊C8—62no—
170#809—32no—
171#809—32no—
172#808—32no—
173#808—32no—
174#807—32no—
175#807—32no—
176C23×C32C2×D411yescharacteristic
177C22×C3×D3—24no—
178C22×C3×D3—22no—
179C22×C3×D3—42no—
180C22×C3×D3—42no—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×Q812yes—
183C2×C32×C4#4112yes—
184C2×C32×C4C2411yescharacteristic
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3—41no—
187C2×C3⋊Dic3C2×D411yescharacteristic
188C2×C3⋊Dic3C2×D411yescharacteristic
189C2×C3⋊Dic3C2×D411yescharacteristic
190C2×C3⋊Dic3C2×D411yescharacteristic
191C2×C3×Dic3—22no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—42no—
197C3×D12—24no—
198C3×D12—22no—
199C3×D12C2×Q814yes—
200#627—42no—
201#627—42no—
202D3×Dic3—44no—
203D3×Dic3—44no—
204C32×C8—22no—
205C3⋊(C3⋊C8)—22no—
206#533—91no—
207C2×C4×D4—91no—
208#478—92no—
209#478—92no—
210#476—92no—
211#474—92no—
212#428—31no—
213#428—91no—
214#423—91no—
215#418—31no—
216#418—91no—
217C24×C3—61no—
218C23×D3—21no—
219C2×C3×D4—34no—
220C2×C3×D4—32no—
221C2×C3×D4—62no—
222C2×C3×D4—61no—
223C22×C3×C4—21no—
224C22×C3×C4—61no—
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C22×Dic3—21no—
228C22×Dic3—31no—
229C22×Dic3—31no—
230C22×Dic3—31no—
231C22×Dic3—31no—
232C22×Dic3—61no—
233C22×Dic3—61no—
234C22×Dic3—62no—
235C22×Dic3—62no—
236C22×Dic3—124no—
237C2×D12—21no—
238C2×D12—22no—
239C2×D12Dic614yescomplemented
240C2×D12C22×D312yes—
241C2×C4×D3—62no—
242C2×C4×D3—62no—
243C2×C4×D3—124no—
244C2×Dic6—61no—
245C2×Dic6—61no—
246C2×Dic6—61no—
247C2×Dic6—61no—
248C3×M16—22no—
249C3×M16—22no—
250C3×M16—42no—
251C2×C3×C8—22no—
252C2×C3×C8C22×D312yes—
253C2×C3×C8C22×D312yes—
254C3×C4⋊C4—31no—
255C3×C4⋊C4—32no—
256C3×C4⋊C4—31no—
257C3×C4⋊C4—31no—
258C3×C4⋊C4—31no—
259C3×C4⋊C4—61no—
260C3×C22⋊C4—61no—
261C3×C22⋊C4—61no—
262C3×C42—61no—
263C3×C42—61no—
264#217—21no—
265#217—21no—
266#217—62no—
267#217—62no—
268(C2×D3)⋊C4—62no—
269(C2×D3)⋊C4—62no—
270C4⋊Dic3—21no—
271C4⋊Dic3—61no—
272C4⋊Dic3—61no—
273C4⋊Dic3—61no—
274C4⋊Dic3—61no—
275C4⋊Dic3C22×D311yescharacteristic
276C4⋊Dic3C22×D312yes—
277C4⋊Dic3C22×D311yescharacteristic
278C4⋊Dic3C22×D311yescharacteristic
279C4⋊Dic3C22×D311yescharacteristic
280Dic3⋊C4—61no—
281Dic3⋊C4—61no—
282Dic3⋊C4—61no—
283Dic3⋊C4—61no—
284Dic3⋊C4—61no—
285Dic3⋊C4—61no—
286Dic3⋊C4—61no—
287Dic3⋊C4—61no—
288C4×Dic3—21no—
289C4×Dic3—21no—
290C4×Dic3—31no—
291C4×Dic3—31no—
292C4×Dic3—31no—
293C4×Dic3—31no—
294C4×Dic3—31no—
295C4×Dic3—31no—
296C4×Dic3—31no—
297C4×Dic3—31no—
298C4×Dic3—61no—
299C4×Dic3—61no—
300C4×Dic3—61no—
301C4×Dic3—61no—
302#208—62no—
303#208—62no—
304#208—122no—
305C2×C3⋊C8—32no—
306C2×C3⋊C8—32no—
307C2×C3⋊C8—62no—
308C22×C32—21no—
309C22×C32—21no—
310C22×C32C22⋊Q812yes—
311C22×C32C22×D411yescharacteristic
312C2×C3×D3—24no—
313C2×C3×D3—48no—
314C2×C3×D3—42no—
315C2×C3×D3—42no—
316C32×C4C22⋊Q812yes—
317C32×C4C22×Q811yescharacteristic
318C32×C4C2×#4111yescharacteristic
319C3⋊Dic3—21no—
320C3⋊Dic3—21no—
321C3⋊Dic3—21no—
322C3⋊Dic3AGL(1,ℤ/8)12yes—
323C3×Dic3—42no—
324C3×Dic3—41no—
325C3×Dic3—41no—
326C3×Dic3—41no—
327C3×Dic3—41no—
328C22×D4—31no—
329C23×C4—181no—
330C2×M16—91no—
331C2×M16D3211yescharacteristic
332C4⋊Q8—91no—
333C4⋊Q8—91no—
334#125—91no—
335#125—91no—
336C22⋊Q8—181no—
337C22⋊Q8—181no—
338C4×Q8—181no—
339C4×Q8—181no—
340C4×D4—92no—
341C4×D4—92no—
342C4×D4—181no—
343C4×D4—181no—
344#117—31no—
345#117—31no—
346C2×C4⋊C4—31no—
347C2×C22⋊C4—181no—
348C2×C42—91no—
349#107—32no—
350#107—92no—
351#106—32no—
352#106—92no—
353C4⋊C8—92no—
354C4⋊C8—92no—
355#102—32no—
356#102—32no—
357#102—92no—
358#102—92no—
359C23×C3—21no—
360C23×C3—64no—
361C23×C3—62no—
362C23×C3—122no—
363C23×C3—122no—
364C23×C3D3×D411yescharacteristic
365C23×C3D3×D411yescharacteristic
366C22×D3—24no—
367C22×D3—22no—
368C22×D3—42no—
369C22×D3—42no—
370C3×D4—34no—
371C3×D4—64no—
372C3×D4—62no—
373C2×C3×C4—21no—
374C2×C3×C4—22no—
375C2×C3×C4—21no—
376C2×C3×C4—22no—
377C2×C3×C4—61no—
378C2×C3×C4—61no—
379C2×C3×C4—61no—
380C2×C3×C4—61no—
381C2×C3×C4—62no—
382C2×C3×C4—122no—
383C2×C3×C4C2×Dic612yes—
384C2×C3×C4#23512yes—
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4#23712yes—
388C2×C3×C4D3×Q812yes—
389C2×C3×C4C23×D311yescharacteristic
390C2×C3×C4C23×D311yescharacteristic
391C2×Dic3—21no—
392C2×Dic3—21no—
393C2×Dic3—21no—
394C2×Dic3—21no—
395C2×Dic3—22no—
396C2×Dic3—31no—
397C2×Dic3—31no—
398C2×Dic3—31no—
399C2×Dic3—31no—
400C2×Dic3—31no—
401C2×Dic3—31no—
402C2×Dic3—31no—
403C2×Dic3—31no—
404C2×Dic3—42no—
405C2×Dic3—61no—
406C2×Dic3—61no—
407C2×Dic3—61no—
408C2×Dic3—61no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—122no—
412C2×Dic3—124no—
413C2×Dic3—124no—
414C2×Dic3—121no—
415C2×Dic3—121no—
416C2×Dic3—122no—
417D12—24no—
418D12—22no—
419D12C2×Dic614yes—
420C4×D3—124no—
421C4×D3—124no—
422Dic6—122no—
423Dic6—122no—
424Dic6—122no—
425Dic6—122no—
426C3×C8—22no—
427C3×C8—22no—
428C3×C8—42no—
429C3⋊C8—62no—
430C3⋊C8—62no—
431C3⋊C8—122no—
432C2×C32—22no—
433C2×C32C2×C22⋊Q811yescharacteristic
434C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
435C2×C32#57511yescharacteristic
436C3×D3—44no—
437C24—61no—
438C2×Q8—181no—
439C2×Q8—181no—
440C2×D4—32no—
441C2×D4—34no—
442C2×D4—61no—
443C2×D4—62no—
444C22×C4—61no—
445C22×C4—91no—
446C22×C4—91no—
447C22×C4—182no—
448C22×C4—182no—
449C22×C4—364no—
450C22×C4C2×D3211yescharacteristic
451M16—22no—
452M16—182no—
453C2×C8—92no—
454C2×C8C2×D3212yes—
455C4⋊C4—31no—
456C4⋊C4—31no—
457C4⋊C4—31no—
458C4⋊C4—31no—
459C4⋊C4—32no—
460C4⋊C4—61no—
461C4⋊C4—181no—
462C4⋊C4—181no—
463C4⋊C4—181no—
464C4⋊C4—181no—
465C4⋊C4—181no—
466C4⋊C4—181no—
467C22⋊C4—61no—
468C22⋊C4—61no—
469C22⋊C4—182no—
470C22⋊C4—182no—
471C42—61no—
472C42—61no—
473C42—91no—
474C42—91no—
475C42—91no—
476C42—91no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—22no—
483C22×C3—41no—
484C22×C3—41no—
485C22×C3—64no—
486C22×C3—128no—
487C22×C3—122no—
488C22×C3—122no—
489C22×C3#87812yes—
490C22×C3#89612yes—
491C22×C3C2×D3×D411yescharacteristic
492C22×C3C2×D3×D411yescharacteristic
493C2×D3—24no—
494C2×D3—48no—
495C2×D3—42no—
496C2×D3—42no—
497C3×C4—21no—
498C3×C4—21no—
499C3×C4—22no—
500C3×C4—121no—
501C3×C4—121no—
502C3×C4—122no—
503C3×C4—121no—
504C3×C4—121no—
505C3×C4#87812yes—
506C3×C4#89612yes—
507C3×C4C22×Dic611yescharacteristic
508C3×C4C2×#23511yescharacteristic
509C3×C4C2×#23711yescharacteristic
510C3×C4C2×D3×Q811yescharacteristic
511Dic3—32no—
512Dic3—32no—
513Dic3—41no—
514Dic3—41no—
515Dic3—42no—
516Dic3—41no—
517Dic3—41no—
518Dic3—62no—
519Dic3—62no—
520Dic3—61no—
521Dic3—61no—
522Dic3—61no—
523Dic3—61no—
524Dic3—61no—
525Dic3—61no—
526Dic3—121no—
527Dic3—121no—
528C32#307711yescharacteristic, complemented, Sylow
529C23—62no—
530C23—64no—
531C23—122no—
532C23—122no—
533C23#380211yescharacteristic
534Q8—362no—
535Q8—362no—
536D4—34no—
537D4—62no—
538D4—64no—
539C2×C4—61no—
540C2×C4—61no—
541C2×C4—61no—
542C2×C4—61no—
543C2×C4—62no—
544C2×C4—91no—
545C2×C4—91no—
546C2×C4—91no—
547C2×C4—91no—
548C2×C4—122no—
549C2×C4—182no—
550C2×C4—364no—
551C2×C4—364no—
552C2×C4—361no—
553C2×C4D3×Dic612yes—
554C2×C4#380211yescharacteristic
555C2×C4#380412yes—
556C2×C4C22×D3211yescharacteristic
557C8—22no—
558C8—182no—
559C2×C3—22no—
560C2×C3—22no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—42no—
565C2×C3—124no—
566C2×C3C2×#87811yescharacteristic
567C2×C3C2×#89611yescharacteristic
568C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
569C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
570C2×C3#577311yescharacteristic
571C2×C3#577711yescharacteristic
572D3—44no—
573C22—21no—
574C22—21no—
575C22—64no—
576C22—128no—
577C22—122no—
578C22—122no—
579C22#6389912yes—
580C22C2×#380211yescharacteristic
581C4—92no—
582C4—122no—
583C4—121no—
584C4—121no—
585C4—121no—
586C4—121no—
587C4—181no—
588C4—181no—
589C4—181no—
590C4#6389912yes—
591C4C2×D3×Dic611yescharacteristic
592C4C2×#380411yescharacteristic
593C3—21no—
594C3#7891711yescharacteristic, complemented
595C3#7923911yescharacteristic, complemented
596C2—22no—
597C2—124no—
598C2#1059471611yescharacteristic
599C2#1059471811yescharacteristic
600C2C2×#6389911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
hypercenterC2×M16D32
hypocenterC32#3077
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #10595050C2semidirect
3. #10592817C2semidirect
5. C3×#5121C2semidirect
6. #10591139C2semidirect
8. #10590782C2semidirect
9. #10590780C2semidirect
10. #10590778C2semidirect
11. #10590776C2semidirect
25. #63919C22semidirect
26. #63919C22semidirect
33. #63872C22semidirect
34. #63872C22semidirect
35. #63641C22semidirect
36. #63641C22semidirect
39. C3×#818C22semidirect
40. C3×#817C22semidirect
41. #63576C22semidirect
42. #63574C22semidirect
53. #5121D3semidirect
75. C2×C3×D12Q8semidirect
162. #818C2×D3semidirect
163. #817C2×D3semidirect
239. C2×D12Dic6semidirect
528. C32#3077semidirect
594. C3#78917semidirect
595. C3#79239semidirect

Maximal subgroups

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

subgroupindex
#105950502
C2×#638982
#105928172
C3×#51312
C3×#51212
#105911392
#105910852
#105907822
#105907802
#105907782
#105907762
#792393
#789173