Finite Group Databasebeta

← #11870871

Subgroups — #11870871

Order 1152.

960 conjugacy classes of subgroups.

The subgroup lattice has 603 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594949C211yesmaximal, characteristic, complemented
2C2×Dic3×D12C211yesmaximal, characteristic, complemented
3#10592421C211yesmaximal, characteristic, complemented
4C3×#4732C211yesmaximal, characteristic
5C3×#4718C211yesmaximal, characteristic, complemented
6#10591172C211yesmaximal, characteristic, complemented
7#10591092C211yesmaximal, characteristic, complemented
8#10590767C212yesmaximal, complemented
9Dic3×D24C212yesmaximal, complemented
10#10590755C212yesmaximal, complemented
11#10590744C212yesmaximal, complemented
12#79989—31nomaximal
13#79300—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C22×D3×Dic3—21no—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17#64133C2211yescharacteristic
18C3×#930C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×C3×D24C2212yes—
21Dic3×#67—21no—
22#63961—21no—
23C2×(C2×D3)⋊Dic3—21no—
24Dic3×D12—21no—
25Dic3×D12—21no—
26Dic3×D12C2212yes—
27Dic3×D12C2212yes—
28Dic3×D12C2211yescharacteristic, complemented
29#63877—21no—
30#63869C2211yescharacteristic, complemented
31#63860C2211yescharacteristic, complemented
32#63859—21no—
33#63844C2211yescharacteristic, complemented
34C2×#3716C2212yes—
35C32×C22⋊C8C2211yescharacteristic
36#63645C2212yescomplemented
37#63643C2212yescomplemented
38C3×#830C2211yescharacteristic
39C3×#821C2212yes—
40C3×Dic3⋊C8C2212yescomplemented
41C3×C8×Dic3C2212yescomplemented
42#63573C2212yescomplemented
43#63563C2212yes—
44#63563C2212yescomplemented
45C2×D4×Dic3—31no—
46#5600—31no—
47#5479—31no—
48C2×C4×D12—31no—
49C3×#447—31no—
50C3×#431—31no—
51#5218—31no—
52#5153—32no—
53Dic3×D8—32no—
54#5034—31no—
55#4847—32no—
56#4844—32no—
57#4766—32no—
58#4758—32no—
59#4735—31no—
60#4732D311yescharacteristic
61#4731—31no—
62#4722—31no—
63#4722—31no—
64#4722—61no—
65#4718D311yescharacteristic, complemented
66C4×D24—32no—
67C4×#204—32no—
68C23×C3×D3—21no—
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3—21no—
71C2×#634C2311yescharacteristic
72C2×C3×#67—21no—
73C22×C3×Dic3D411yescharacteristic
74C22×C3×Dic3D411yescharacteristic
75C2×C3×D12—21no—
76C2×C3×D12—24no—
77C2×C3×D12C2311yescharacteristic
78C2×C3×D12C2312yes—
79C2×D3×Dic3—22no—
80C2×D3×Dic3—22no—
81C2×D3×Dic3—21no—
82C2×D3×Dic3—44no—
83C2×C32×C8C2312yes—
84#3757—21no—
85C4⋊(C3⋊Dic3)—21no—
86C4⋊(C3⋊Dic3)C2311yescharacteristic
87C4⋊(C3⋊Dic3)C2312yes—
88#3750—21no—
89C3×(C2×D3)⋊C4—21no—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×C4×Dic3D411yescharacteristic
92C3×C4×Dic3D411yescharacteristic
93C3×C4×Dic3C2311yescharacteristic
94C3×C4×Dic3C2311yescharacteristic
95C2×C3×C3⋊C8C2312yes—
96C3×D24—24no—
97#3724—21no—
98#3724—21no—
99Dic3⋊Dic3—21no—
100(C2×D3)⋊Dic3—21no—
101(C2×D3)⋊Dic3—21no—
102(C2×D3)⋊Dic3—21no—
103(C2×D3)⋊Dic3—22no—
104(C2×D3)⋊Dic3—22no—
105Dic32—21no—
106#3716—24no—
107#3105—91noSylow
108C22×C3×D4—31no—
109C23×Dic3—61no—
110C22×D12C2×D311yescharacteristic
111C22×C4×D3—61no—
112C2×C3×D8—32no—
113C3×#121—31no—
114C2×C3×C42—31no—
115C2×#217—61no—
116#936—31no—
117#935—61no—
118D4×Dic3—31no—
119D4×Dic3—32no—
120D4×Dic3—32no—
121D4×Dic3—61no—
122D4×Dic3—61no—
123D4×Dic3—61no—
124C2×#214—32no—
125#930C2×D311yescharacteristic
126#929—61no—
127C4×#67—61no—
128C2×(C2×D3)⋊C4—61no—
129C2×C4⋊Dic3—31no—
130C2×C4⋊Dic3—31no—
131C2×C4⋊Dic3—61no—
132#924—31no—
133#924—31no—
134#924—61no—
135C2×C4×Dic3C2×D311yescharacteristic
136C2×D24C2×D312yes—
137C2×#204—32no—
138#890—31no—
139#887—31no—
140#879—61no—
141#877—61no—
142#876—61no—
143#875—31no—
144C4×D12—32no—
145C4×D12—31no—
146C4×D12—32no—
147C4×D12—61no—
148C4×D12—61no—
149#872—61no—
150#870—31no—
151C4×Dic6—31no—
152C3×C4⋊C8—32no—
153C3×#102—32no—
154C3×C22⋊C8—21no—
155C3×C22⋊C8—31no—
156C3×C22⋊C8C2×D311yescharacteristic
157C3×C22⋊C8C2×D311yescharacteristic
158C3×C4×C8—32no—
159#832—32no—
160#832—32no—
161#830C2×D311yescharacteristic
162#821—32no—
163#821—32no—
164#821C2×D312yes—
165#818—32no—
166#818—32no—
167#818—62no—
168#817—32no—
169#816—32no—
170#816—32no—
171#816—62no—
172Dic3⋊C8C2×D312yescomplemented
173C8×Dic3C2×D312yescomplemented
174#808—32no—
175C23×C32C2×D411yescharacteristic
176C22×C3×D3—24no—
177C22×C3×D3—22no—
178C22×C3×D3—21no—
179C22×C3×D3—42no—
180C22×C3×D3—42no—
181C2×C32×C4—22no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—42no—
188#634—22no—
189C3×#67—42no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3C2×D411yescharacteristic
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C2×C3×Dic3C2×D411yescharacteristic
197C3×D12—24no—
198C3×D12—22no—
199C3×D12—22no—
200C3×D12#4114yes—
201D3×Dic3—44no—
202D3×Dic3—42no—
203D3×Dic3—44no—
204C32×C8—22no—
205C3×C3⋊C8—22no—
206#529—91no—
207C2×C4×D4—91no—
208#484—91no—
209#481—91no—
210#478—92no—
211#463—92no—
212#450—91no—
213#447—31no—
214C4×SD16—92no—
215C4×D8—92no—
216#431—31no—
217C24×C3—61no—
218C23×D3—21no—
219C2×C3×D4—32no—
220C2×C3×D4—31no—
221C2×C3×D4—64no—
222C2×C3×D4—61no—
223C2×C3×D4—61no—
224C22×C3×C4—21no—
225C22×C3×C4—31no—
226C22×C3×C4—31no—
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C2×#67—21no—
230C22×Dic3—61no—
231C22×Dic3—61no—
232C22×Dic3—61no—
233C22×Dic3—62no—
234C22×Dic3—62no—
235C22×Dic3—121no—
236C22×Dic3—124no—
237C22×Dic3D1211yescharacteristic
238C22×Dic3D1211yescharacteristic
239C2×D12—21no—
240C2×D12—24no—
241C2×D12C22×D311yescharacteristic
242C2×D12C22×D312yes—
243C2×C4×D3—61no—
244C2×C4×D3—62no—
245C2×C4×D3—62no—
246C2×C4×D3—124no—
247C2×Dic6—31no—
248C2×Dic6—31no—
249C2×Dic6—61no—
250C3×D8—64no—
251C2×C3×C8—22no—
252C2×C3×C8—32no—
253C2×C3×C8C22×D312yes—
254C2×C3×C8C22×D312yes—
255C3×C4⋊C4—31no—
256C3×C22⋊C4—61no—
257C3×C42—31no—
258C3×C42—31no—
259C3×C42—31no—
260C3×C42—31no—
261#217—61no—
262#217—61no—
263#217—61no—
264#217—61no—
265#217—61no—
266#217—62no—
267#217—62no—
268#217—121no—
269#214—64no—
270(C2×D3)⋊C4—21no—
271(C2×D3)⋊C4—61no—
272(C2×D3)⋊C4—62no—
273(C2×D3)⋊C4—62no—
274(C2×D3)⋊C4—61no—
275(C2×D3)⋊C4—61no—
276C4⋊Dic3—32no—
277C4⋊Dic3—32no—
278C4⋊Dic3—31no—
279C4⋊Dic3—31no—
280C4⋊Dic3—62no—
281C4⋊Dic3—61no—
282C4⋊Dic3—61no—
283C4⋊Dic3—61no—
284C4⋊Dic3—61no—
285C4⋊Dic3—121no—
286C4⋊Dic3C22×D311yescharacteristic
287Dic3⋊C4—61no—
288Dic3⋊C4—61no—
289Dic3⋊C4—61no—
290Dic3⋊C4—61no—
291Dic3⋊C4—61no—
292Dic3⋊C4—61no—
293Dic3⋊C4—61no—
294Dic3⋊C4—121no—
295C4×Dic3—61no—
296C4×Dic3—61no—
297C4×Dic3D1211yescharacteristic
298C4×Dic3D1211yescharacteristic
299C4×Dic3C22×D311yescharacteristic
300C4×Dic3C22×D311yescharacteristic
301C2×C3⋊C8C22×D312yes—
302D24—24no—
303#204—64no—
304C22×C32—21no—
305C22×C32—21no—
306C22×C32#13512yes—
307C22×C32C22×D411yescharacteristic
308C2×C3×D3—24no—
309C2×C3×D3—48no—
310C2×C3×D3—42no—
311C2×C3×D3—42no—
312C2×C3×D3—41no—
313C2×C3×D3—41no—
314C2×C3×D3—41no—
315C32×C4—21no—
316C32×C4C2×#4112yes—
317C3⋊Dic3—41no—
318C3⋊Dic3—42no—
319C3⋊Dic3—41no—
320C3×Dic3—21no—
321C3×Dic3—21no—
322C3×Dic3—21no—
323C3×Dic3—41no—
324C3×Dic3AGL(1,ℤ/8)12yes—
325C22×D4—31no—
326C23×C4—181no—
327C2×SD16—92no—
328C2×D8—32no—
329#126—181no—
330#125—91no—
331#124—91no—
332#123—181no—
333C22⋊Q8—91no—
334#121—31no—
335C4×Q8—91no—
336C4×D4—92no—
337C4×D4—92no—
338C4×D4—91no—
339C4×D4—181no—
340C4×D4—181no—
341C4×D4—181no—
342#117—181no—
343C2×C4⋊C4—91no—
344C2×C22⋊C4—181no—
345C2×C42—31no—
346#107—92no—
347#106—92no—
348C4⋊C8—32no—
349#103—92no—
350#102—32no—
351#102—92no—
352#102—92no—
353C22⋊C8—31no—
354C22⋊C8D3211yescharacteristic
355C4×C8—32no—
356C23×C3—21no—
357C23×C3—64no—
358C23×C3—62no—
359C23×C3—61no—
360C23×C3—122no—
361C23×C3—122no—
362C23×C3C2×D1211yescharacteristic
363C23×C3D3×D411yescharacteristic
364C22×D3—24no—
365C22×D3—22no—
366C22×D3—21no—
367C22×D3—42no—
368C22×D3—42no—
369C3×D4—34no—
370C3×D4—64no—
371C3×D4—62no—
372C3×D4—62no—
373C3×D4—122no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—31no—
379C2×C3×C4—31no—
380C2×C3×C4—31no—
381C2×C3×C4—31no—
382C2×C3×C4—42no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—61no—
386C2×C3×C4C2×D1211yescharacteristic
387C2×C3×C4D3×D411yescharacteristic
388C2×C3×C4C23×D311yescharacteristic
389C2×C3×C4C23×D311yescharacteristic
390#67—42no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—21no—
394C2×Dic3—61no—
395C2×Dic3—61no—
396C2×Dic3—62no—
397C2×Dic3—61no—
398C2×Dic3—61no—
399C2×Dic3—62no—
400C2×Dic3—121no—
401C2×Dic3—121no—
402C2×Dic3—122no—
403C2×Dic3—124no—
404C2×Dic3—122no—
405C2×Dic3—122no—
406C2×Dic3—122no—
407C2×Dic3—124no—
408C2×Dic3—242no—
409C2×Dic3C2×D1211yescharacteristic
410C2×Dic3C2×D1211yescharacteristic
411C2×Dic3C2×D1211yescharacteristic
412C2×Dic3C2×D1211yescharacteristic
413D12—24no—
414D12—22no—
415D12—22no—
416D12#23714yes—
417C4×D3—122no—
418C4×D3—124no—
419C4×D3—124no—
420Dic6—62no—
421Dic6—62no—
422Dic6—122no—
423C3×C8—22no—
424C3×C8—22no—
425C3×C8—42no—
426C3×C8—62no—
427C3⋊C8—22no—
428C2×C32—22no—
429C2×C32#52511yescharacteristic
430C2×C32C2×#13511yescharacteristic
431C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
432C3×D3—44no—
433C3×D3—81no—
434C24—61no—
435C2×Q8—91no—
436C2×D4—32no—
437C2×D4—31no—
438C2×D4—64no—
439C2×D4—61no—
440C2×D4—61no—
441C22×C4—31no—
442C22×C4—31no—
443C22×C4—181no—
444C22×C4—182no—
445C22×C4—182no—
446C22×C4—181no—
447C22×C4—364no—
448C22×C4C2×D3211yescharacteristic
449SD16—184no—
450D8—64no—
451C2×C8—32no—
452C2×C8C2×D3212yes—
453C4⋊C4—31no—
454C4⋊C4—91no—
455C4⋊C4—92no—
456C4⋊C4—181no—
457C4⋊C4—181no—
458C4⋊C4—181no—
459C4⋊C4—181no—
460C4⋊C4—181no—
461C22⋊C4—61no—
462C22⋊C4—182no—
463C22⋊C4—182no—
464C22⋊C4—181no—
465C22⋊C4—181no—
466C22⋊C4—181no—
467C22⋊C4—181no—
468C42—31no—
469C42—31no—
470C42—31no—
471C42—31no—
472C42—181no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—22no—
479C22×C3—41no—
480C22×C3—41no—
481C22×C3—64no—
482C22×C3—128no—
483C22×C3—122no—
484C22×C3—122no—
485C22×C3—121no—
486C22×C3—121no—
487C22×C3—121no—
488C22×C3#90412yes—
489C22×C3#91212yes—
490C22×C3C22×D1211yescharacteristic
491C22×C3C2×D3×D411yescharacteristic
492C2×D3—24no—
493C2×D3—48no—
494C2×D3—42no—
495C2×D3—42no—
496C2×D3—41no—
497C2×D3—41no—
498C2×D3—41no—
499C3×C4—21no—
500C3×C4—21no—
501C3×C4—22no—
502C3×C4—32no—
503C3×C4—41no—
504C3×C4—61no—
505C3×C4—61no—
506C3×C4—61no—
507C3×C4—121no—
508C3×C4C2×#23712yes—
509C3×C4D3×#4112yes—
510Dic3—21no—
511Dic3—21no—
512Dic3—21no—
513Dic3—41no—
514Dic3—122no—
515Dic3—121no—
516Dic3—122no—
517Dic3—121no—
518Dic3—121no—
519Dic3—121no—
520Dic3—241no—
521Dic3—242no—
522Dic3—241no—
523Dic3#90812yes—
524C32#310511yescharacteristic, complemented, Sylow
525C23—64no—
526C23—62no—
527C23—61no—
528C23—122no—
529C23—122no—
530C23D3×D1211yescharacteristic
531Q8—182no—
532D4—34no—
533D4—64no—
534D4—62no—
535D4—62no—
536D4—122no—
537C2×C4—22no—
538C2×C4—31no—
539C2×C4—31no—
540C2×C4—31no—
541C2×C4—31no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—61no—
545C2×C4—181no—
546C2×C4—181no—
547C2×C4—182no—
548C2×C4—364no—
549C2×C4—362no—
550C2×C4—364no—
551C2×C4—362no—
552C2×C4D3×D1211yescharacteristic
553C2×C4C22×D3211yescharacteristic
554C8—22no—
555C8—62no—
556C2×C3—22no—
557C2×C3—22no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—42no—
562C2×C3—124no—
563C2×C3—241no—
564C2×C3#552411yescharacteristic
565C2×C3#558611yescharacteristic
566C2×C3C2×#90411yescharacteristic
567C2×C3C2×#90811yescharacteristic
568C2×C3C2×#91211yescharacteristic
569C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
570D3—44no—
571D3—81no—
572C22—21no—
573C22—21no—
574C22—64no—
575C22—128no—
576C22—122no—
577C22—122no—
578C22—121no—
579C22—121no—
580C22—121no—
581C22#6380712yes—
582C22C2×D3×D1211yescharacteristic
583C4—21no—
584C4—32no—
585C4—61no—
586C4—61no—
587C4—61no—
588C4—121no—
589C4—361no—
590C4—362no—
591C4—361no—
592C4D3×#23712yes—
593C3—21no—
594C3#7930011yescharacteristic, complemented
595C3#7998911yescharacteristic, complemented
596C2—22no—
597C2—124no—
598C2—241no—
599C2#1059407811yescharacteristic
600C2C2×#6380711yescharacteristic
601C2D3×#90811yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radicalC3×#4732C2
hypercenterC22⋊C8D32
hypocenterC32#3105
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10594949C2semidirect
2. C2×Dic3×D12C2semidirect
3. #10592421C2semidirect
5. C3×#4718C2semidirect
6. #10591172C2semidirect
7. #10591092C2semidirect
8. #10590767C2semidirect
9. Dic3×D24C2semidirect
10. #10590755C2semidirect
11. #10590744C2semidirect
28. Dic3×D12C22semidirect
30. #63869C22semidirect
31. #63860C22semidirect
33. #63844C22semidirect
36. #63645C22semidirect
37. #63643C22semidirect
40. C3×Dic3⋊C8C22semidirect
41. C3×C8×Dic3C22semidirect
42. #63573C22semidirect
44. #63563C22semidirect
65. #4718D3semidirect
172. Dic3⋊C8C2×D3semidirect
173. C8×Dic3C2×D3semidirect
524. C32#3105semidirect
594. C3#79300semidirect
595. C3#79989semidirect

Maximal subgroups

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

subgroupindex
#105949492
C2×Dic3×D122
#105924212
C3×#47322
C3×#47182
#105911722
#105910922
#105907672
Dic3×D242
#105907552
#105907442
#799893
#793003