Finite Group Databasebeta

← #11870875

Subgroups — #11870875

Order 1152.

1002 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594949C211yesmaximal, characteristic, complemented
2C2×#63894C211yesmaximal, characteristic, complemented
3#10592430C211yesmaximal, characteristic, complemented
4C3×#4735C211yesmaximal, characteristic, complemented
5C3×#4718C211yesmaximal, characteristic, complemented
6#10591168C211yesmaximal, characteristic
7#10591135C211yesmaximal, characteristic, complemented
8#10590860C212yesmaximal, complemented
9#10590769C212yesmaximal, complemented
10#10590758C212yesmaximal, complemented
11#10590745C212yesmaximal, complemented
12#81309—31nomaximal
13#79300—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×#624—21no—
16#64133C2211yescharacteristic
17C2×#3744C2212yes—
18C3×#930C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21Dic3×#67—21no—
22C2×#3722—21no—
23#63961—21no—
24#63894—21no—
25#63894—21no—
26#63894C2212yes—
27#63894C2212yes—
28Dic3×D12C2211yescharacteristic, complemented
29#63877—21no—
30#63869C2211yescharacteristic, complemented
31#63860C2211yescharacteristic, complemented
32#63859—21no—
33#63844C2211yescharacteristic, complemented
34C2×#3714C2212yes—
35C32×C22⋊C8C2211yescharacteristic
36#63648C2212yes—
37C3×#830C2211yescharacteristic
38C3×#821C2212yescomplemented
39C3×#817C2212yescomplemented
40C3×Dic3⋊C8C2212yescomplemented
41C3×C8×Dic3C2212yescomplemented
42#63575C2212yescomplemented
43#63567C2212yescomplemented
44#63564C2212yes—
45#5600—31no—
46C2×#893—31no—
47#5479—31no—
48C2×C4×D12—31no—
49C3×#481—31no—
50C3×#431—31no—
51#5036—31no—
52#4970—31no—
53#4871—32no—
54#4852—32no—
55#4847—32no—
56#4844—32no—
57#4787—32no—
58#4756—32no—
59#4735D311yescharacteristic, complemented
60#4732—31no—
61#4731—31no—
62#4731—31no—
63#4731—61no—
64#4722—31no—
65#4718D311yescharacteristic, complemented
66C4×D24—32no—
67C4×#204—32no—
68C23×C3⋊D3—21no—
69C22×C32×C4C2311yescharacteristic
70C2×C4⋊(C3⋊D3)—21no—
71C2×C4⋊(C3⋊D3)—24no—
72C2×C4⋊(C3⋊D3)C2312yes—
73C2×#634C2311yescharacteristic
74C2×C3×#67—21no—
75C22×C3×Dic3—21no—
76C22×C3×Dic3D411yescharacteristic
77C22×C3×Dic3D411yescharacteristic
78C2×C3×D12C2311yescharacteristic
79C2×#624—22no—
80C2×#624—22no—
81C2×#624—44no—
82C2×D3×Dic3—21no—
83C2×C32×C8C2312yes—
84#3757—21no—
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86#3750—21no—
87#3744—24no—
88C3×(C2×D3)⋊C4—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2312yes—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4×Dic3D411yescharacteristic
93C3×C4×Dic3D411yescharacteristic
94C3×C4×Dic3C2311yescharacteristic
95C3×C4×Dic3C2311yescharacteristic
96C2×C3×C3⋊C8C2312yes—
97#3724—21no—
98#3724—21no—
99Dic3⋊Dic3—21no—
100#3722—22no—
101#3722—22no—
102(C2×D3)⋊Dic3—21no—
103(C2×D3)⋊Dic3—21no—
104(C2×D3)⋊Dic3—21no—
105Dic32—21no—
106#3714—24no—
107#3105—91noSylow
108C22×D12—31no—
109C22×D12—31no—
110C22×D12—61no—
111C22×C4×D3—61no—
112C22×C4×D3—61no—
113C3×#121—31no—
114C2×C3×C4⋊C4—31no—
115C2×C3×C42—31no—
116#936—31no—
117#935—61no—
118D4×Dic3—31no—
119D4×Dic3—61no—
120C2×#213—32no—
121#930C2×D311yescharacteristic
122#929—61no—
123C4×#67—61no—
124C2×(C2×D3)⋊C4—61no—
125C2×(C2×D3)⋊C4—61no—
126C2×C4⋊Dic3C2×D311yescharacteristic
127#924—31no—
128#924—31no—
129#924—61no—
130C2×C4×Dic3C2×D311yescharacteristic
131C2×D24—32no—
132C2×#204—32no—
133C2×#204—32no—
134C2×#204—62no—
135#893—32no—
136#893—32no—
137#893—61no—
138#893—61no—
139#890—31no—
140#887—31no—
141#879—61no—
142#877—61no—
143#876—61no—
144#875—31no—
145C4×D12—31no—
146C4×D12—32no—
147C4×D12—32no—
148C4×D12—61no—
149C4×D12—61no—
150#872—61no—
151#870—31no—
152C4×Dic6—31no—
153C3×#106—32no—
154C3×C4⋊C8—32no—
155C3×#102—32no—
156C3×C22⋊C8—21no—
157C3×C22⋊C8—31no—
158C3×C22⋊C8C2×D311yescharacteristic
159C3×C22⋊C8C2×D311yescharacteristic
160C3×C4×C8—32no—
161#830C2×D311yescharacteristic
162#821—32no—
163#821—32no—
164#821—32no—
165#821—62no—
166#821C2×D312yescomplemented
167#818—32no—
168#817C2×D312yescomplemented
169#816—32no—
170Dic3⋊C8C2×D312yescomplemented
171C8×Dic3C2×D312yescomplemented
172#810—32no—
173#809—32no—
174#807—32no—
175C23×C32C2×D411yescharacteristic
176C22×C3⋊D3—24no—
177C22×C3⋊D3—22no—
178C22×C3⋊D3—42no—
179C22×C3⋊D3—42no—
180C22×C3×D3—21no—
181C2×C32×C4—22no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C4⋊(C3⋊D3)—24no—
187C4⋊(C3⋊D3)—22no—
188C4⋊(C3⋊D3)#4114yes—
189#634—22no—
190C3×#67—42no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—42no—
196C2×C3×Dic3C2×D411yescharacteristic
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C2×C3×Dic3C2×D411yescharacteristic
200C3×D12—22no—
201#624—44no—
202#624—44no—
203D3×Dic3—42no—
204C32×C8—22no—
205C3×C3⋊C8—22no—
206#529—91no—
207C2×C4×D4—91no—
208#484—91no—
209#481—31no—
210#478—92no—
211#463—92no—
212#450—91no—
213#447—91no—
214C4×SD16—92no—
215C4×D8—92no—
216#431—31no—
217C23×D3—61no—
218C23×D3—61no—
219C23×D3—121no—
220C2×C3×D4—31no—
221C2×C3×D4—61no—
222C22×C3×C4—21no—
223C22×C3×C4—31no—
224C22×C3×C4—31no—
225C22×C3×C4—61no—
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C2×#67—21no—
229C22×Dic3—21no—
230C22×Dic3—61no—
231C22×Dic3D1211yescharacteristic
232C22×Dic3D1211yescharacteristic
233C2×D12—32no—
234C2×D12—32no—
235C2×D12—62no—
236C2×D12—64no—
237C2×D12—64no—
238C2×D12—61no—
239C2×D12—61no—
240C2×D12—124no—
241C2×D12—121no—
242C2×D12C22×D311yescharacteristic
243C2×C4×D3—62no—
244C2×C4×D3—62no—
245C2×C4×D3—61no—
246C2×C4×D3—62no—
247C2×C4×D3—62no—
248C2×C4×D3—124no—
249C2×C4×D3—124no—
250C2×Dic6—31no—
251C2×Dic6—31no—
252C2×Dic6—61no—
253C2×C3×C8—22no—
254C2×C3×C8—32no—
255C2×C3×C8C22×D312yes—
256C2×C3×C8C22×D312yes—
257C3×C4⋊C4—32no—
258C3×C4⋊C4—31no—
259C3×C4⋊C4—61no—
260C3×C22⋊C4—61no—
261C3×C42—31no—
262C3×C42—31no—
263C3×C42—31no—
264C3×C42—31no—
265#217—61no—
266#217—61no—
267#217—61no—
268#217—61no—
269#217—61no—
270#217—121no—
271#213—64no—
272(C2×D3)⋊C4—21no—
273(C2×D3)⋊C4—62no—
274(C2×D3)⋊C4—62no—
275(C2×D3)⋊C4—61no—
276(C2×D3)⋊C4—61no—
277(C2×D3)⋊C4—61no—
278(C2×D3)⋊C4—62no—
279(C2×D3)⋊C4—62no—
280C4⋊Dic3—21no—
281C4⋊Dic3—31no—
282C4⋊Dic3—31no—
283C4⋊Dic3—61no—
284C4⋊Dic3—61no—
285C4⋊Dic3C22×D312yes—
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—64no—
303#204—64no—
304#204—64no—
305#204—124no—
306C22×C32—21no—
307C22×C32—21no—
308C22×C32#13512yes—
309C22×C32C22×D411yescharacteristic
310C2×C3⋊D3—24no—
311C2×C3⋊D3—48no—
312C2×C3⋊D3—42no—
313C2×C3⋊D3—42no—
314C2×C3×D3—41no—
315C2×C3×D3—41no—
316C2×C3×D3—41no—
317C32×C4—21no—
318C32×C4C2×#4112yes—
319C3⋊Dic3—41no—
320C3⋊Dic3—41no—
321C3×Dic3—21no—
322C3×Dic3—21no—
323C3×Dic3—21no—
324C3×Dic3—41no—
325C3×Dic3—42no—
326C3×Dic3AGL(1,ℤ/8)12yes—
327C22×D4—91no—
328C23×C4—181no—
329C2×SD16—92no—
330C2×D8—92no—
331#126—181no—
332#125—91no—
333#124—91no—
334#123—181no—
335C22⋊Q8—91no—
336#121—31no—
337C4×Q8—91no—
338C4×D4—92no—
339C4×D4—92no—
340C4×D4—91no—
341C4×D4—181no—
342C4×D4—181no—
343C4×D4—181no—
344#117—181no—
345C2×C4⋊C4—31no—
346C2×C22⋊C4—181no—
347C2×C42—31no—
348#107—92no—
349#106—32no—
350C4⋊C8—32no—
351#103—92no—
352#102—32no—
353#102—92no—
354#102—92no—
355C22⋊C8—31no—
356C22⋊C8D3211yescharacteristic
357C4×C8—32no—
358C23×C3—21no—
359C23×C3—61no—
360C23×C3C2×D1211yescharacteristic
361C23×C3D3×D411yescharacteristic
362C22×D3—21no—
363C22×D3—64no—
364C22×D3—64no—
365C22×D3—62no—
366C22×D3—62no—
367C22×D3—122no—
368C22×D3—124no—
369C22×D3—122no—
370C22×D3—122no—
371C22×D3—122no—
372C22×D3—122no—
373C22×D3—242no—
374C22×D3—242no—
375C3×D4—62no—
376C3×D4—122no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—31no—
382C2×C3×C4—31no—
383C2×C3×C4—31no—
384C2×C3×C4—31no—
385C2×C3×C4—42no—
386C2×C3×C4—62no—
387C2×C3×C4—62no—
388C2×C3×C4—61no—
389C2×C3×C4—62no—
390C2×C3×C4—122no—
391C2×C3×C4C2×D1211yescharacteristic
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4C23×D311yescharacteristic
394C2×C3×C4C23×D311yescharacteristic
395#67—42no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—21no—
399C2×Dic3—22no—
400C2×Dic3—42no—
401C2×Dic3—61no—
402C2×Dic3—61no—
403C2×Dic3—61no—
404C2×Dic3—61no—
405C2×Dic3—121no—
406C2×Dic3—121no—
407C2×Dic3—122no—
408C2×Dic3C2×D1211yescharacteristic
409C2×Dic3C2×D1211yescharacteristic
410C2×Dic3C2×D1211yescharacteristic
411C2×Dic3C2×D1211yescharacteristic
412D12—22no—
413D12—34no—
414D12—34no—
415D12—64no—
416D12—64no—
417D12—64no—
418D12—62no—
419D12—62no—
420D12—122no—
421D12—124no—
422C4×D3—124no—
423C4×D3—124no—
424C4×D3—124no—
425C4×D3—122no—
426C4×D3—124no—
427Dic6—62no—
428Dic6—62no—
429Dic6—122no—
430C3×C8—22no—
431C3×C8—22no—
432C3×C8—42no—
433C3×C8—62no—
434C3⋊C8—22no—
435C2×C32—22no—
436C2×C32#52511yescharacteristic
437C2×C32C2×#13511yescharacteristic
438C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
439C3⋊D3—44no—
440C3×D3—81no—
441C24—181no—
442C2×Q8—91no—
443C2×D4—31no—
444C2×D4—61no—
445C2×D4—92no—
446C2×D4—184no—
447C2×D4—181no—
448C22×C4—31no—
449C22×C4—31no—
450C22×C4—61no—
451C22×C4—182no—
452C22×C4—182no—
453C22×C4—181no—
454C22×C4—364no—
455C22×C4C2×D3211yescharacteristic
456SD16—184no—
457D8—184no—
458C2×C8—32no—
459C2×C8C2×D3212yes—
460C4⋊C4—32no—
461C4⋊C4—31no—
462C4⋊C4—61no—
463C4⋊C4—91no—
464C4⋊C4—181no—
465C4⋊C4—181no—
466C4⋊C4—181no—
467C4⋊C4—181no—
468C22⋊C4—61no—
469C22⋊C4—182no—
470C22⋊C4—182no—
471C22⋊C4—181no—
472C22⋊C4—181no—
473C22⋊C4—181no—
474C22⋊C4—181no—
475C42—31no—
476C42—31no—
477C42—31no—
478C42—31no—
479C42—181no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—22no—
486C22×C3—41no—
487C22×C3—41no—
488C22×C3—121no—
489C22×C3—121no—
490C22×C3—121no—
491C22×C3#90412yes—
492C22×C3#91612yes—
493C22×C3C22×D1211yescharacteristic
494C22×C3C2×D3×D411yescharacteristic
495C2×D3—41no—
496C2×D3—41no—
497C2×D3—41no—
498C2×D3—64no—
499C2×D3—64no—
500C2×D3—124no—
501C2×D3—128no—
502C2×D3—128no—
503C2×D3—122no—
504C2×D3—122no—
505C2×D3—122no—
506C2×D3—122no—
507C2×D3—242no—
508C2×D3—242no—
509C2×D3—248no—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—22no—
513C3×C4—32no—
514C3×C4—41no—
515C3×C4—61no—
516C3×C4—61no—
517C3×C4—61no—
518C3×C4—121no—
519C3×C4—122no—
520C3×C4D3×#4112yes—
521C3×C4D3×#4112yes—
522Dic3—21no—
523Dic3—21no—
524Dic3—21no—
525Dic3—41no—
526Dic3—42no—
527Dic3—121no—
528Dic3—121no—
529Dic3—121no—
530Dic3—121no—
531Dic3—241no—
532Dic3—241no—
533Dic3#90812yes—
534C32#310511yescharacteristic, complemented, Sylow
535C23—61no—
536C23—184no—
537C23—182no—
538C23—362no—
539C23—362no—
540C23D3×D1211yescharacteristic
541Q8—182no—
542D4—62no—
543D4—94no—
544D4—122no—
545D4—184no—
546D4—182no—
547C2×C4—22no—
548C2×C4—31no—
549C2×C4—31no—
550C2×C4—31no—
551C2×C4—31no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—61no—
555C2×C4—62no—
556C2×C4—122no—
557C2×C4—181no—
558C2×C4—181no—
559C2×C4—364no—
560C2×C4—362no—
561C2×C4—364no—
562C2×C4D3×D1211yescharacteristic
563C2×C4C22×D3211yescharacteristic
564C8—22no—
565C8—62no—
566C2×C3—22no—
567C2×C3—22no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—42no—
572C2×C3—241no—
573C2×C3#552411yescharacteristic
574C2×C3#565611yescharacteristic
575C2×C3C2×#90411yescharacteristic
576C2×C3C2×#90811yescharacteristic
577C2×C3C2×#91611yescharacteristic
578C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
579D3—81no—
580D3—124no—
581D3—124no—
582D3—244no—
583C22—21no—
584C22—21no—
585C22—121no—
586C22—121no—
587C22—121no—
588C22—184no—
589C22—368no—
590C22—362no—
591C22—362no—
592C22#6380612yes—
593C22C2×D3×D1211yescharacteristic
594C4—21no—
595C4—32no—
596C4—61no—
597C4—61no—
598C4—61no—
599C4—121no—
600C4—122no—
601C4—361no—
602C4—361no—
603C4#6431212yes—
604C3—21no—
605C3#7930011yescharacteristic, complemented
606C3#8130911yescharacteristic, complemented
607C2—22no—
608C2—241no—
609C2—364no—
610C2#1059407911yescharacteristic
611C2C2×#6380611yescharacteristic
612C2D3×#90811yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10591168C2
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×#63894C2semidirect
3. #10592430C2semidirect
4. C3×#4735C2semidirect
5. C3×#4718C2semidirect
7. #10591135C2semidirect
8. #10590860C2semidirect
9. #10590769C2semidirect
10. #10590758C2semidirect
11. #10590745C2semidirect
28. Dic3×D12C22semidirect
30. #63869C22semidirect
31. #63860C22semidirect
33. #63844C22semidirect
38. C3×#821C22semidirect
39. C3×#817C22semidirect
40. C3×Dic3⋊C8C22semidirect
41. C3×C8×Dic3C22semidirect
42. #63575C22semidirect
43. #63567C22semidirect
59. #4735D3semidirect
65. #4718D3semidirect
166. #821C2×D3semidirect
168. #817C2×D3semidirect
170. Dic3⋊C8C2×D3semidirect
171. C8×Dic3C2×D3semidirect
534. C32#3105semidirect
605. C3#79300semidirect
606. C3#81309semidirect

Maximal subgroups

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

subgroupindex
#105949492
C2×#638942
#105924302
C3×#47352
C3×#47182
#105911682
#105911352
#105908602
#105907692
#105907582
#105907452
#813093
#793003