Finite Group Databasebeta

← #11869664

Subgroups — #11869664

Order 1152.

892 conjugacy classes of subgroups.

The subgroup lattice has 615 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594892C211yesmaximal, characteristic
2C2×#63841C211yesmaximal, characteristic, complemented
3#10592420C211yesmaximal, characteristic, complemented
4C3×#4735C211yesmaximal, characteristic, complemented
5C3×D3×C22⋊C8C211yesmaximal, characteristic, complemented
6#10591135C211yesmaximal, characteristic, complemented
7#10591094C211yesmaximal, characteristic, complemented
8#10590954C212yesmaximal, complemented
9#10590837C212yesmaximal, complemented
10#10590709C212yesmaximal, complemented
11#10590706C212yesmaximal, complemented
12#81324—31nomaximal
13#78591—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C2×#3795C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17#64133C2211yescharacteristic
18C3×#930C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×D3×C8C2212yes—
21#63976—21no—
22Dic3×#67—21no—
23C2×(C2×D3)⋊Dic3—21no—
24C2×Dic32—21no—
25#63908C2211yescharacteristic
26#63905—21no—
27#63879—21no—
28#63857C2211yescharacteristic
29#63841—21no—
30#63841—21no—
31#63841C2211yescharacteristic
32#63841C2212yes—
33#63841C2212yes—
34C32×C22⋊C8C2211yescharacteristic
35#63644C2212yescomplemented
36#63643C2212yescomplemented
37C3×#830C2211yescharacteristic
38C3×#821C2212yescomplemented
39C3×(C2×D3)⋊C8C2212yes—
40C3×#817C2212yescomplemented
41#63575C2212yescomplemented
42#63575C2212yescomplemented
43#63567C2212yescomplemented
44#63563C2212yescomplemented
45#5791—31no—
46C2×#926—31no—
47#5606—31no—
48C2×#892—31no—
49C3×#481—31no—
50C2×C3×C22⋊C8—31no—
51#5113—32no—
52#5106—32no—
53#5033—31no—
54#4970—31no—
55#4868—32no—
56#4860—32no—
57#4779—32no—
58#4772—32no—
59#4737—32no—
60#4736—31no—
61#4735D311yescharacteristic, complemented
62D3×C22⋊C8D311yescharacteristic, complemented
63#4723—32no—
64#4722—31no—
65#4721—31no—
66#4721—31no—
67#4721—61no—
68C23×C3×D3D411yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3—21no—
71C2×#634C2311yescharacteristic
72C2×C3×#67—21no—
73C22×C3×Dic3—21no—
74C22×C3×Dic3D411yescharacteristic
75C2×C3×D12C2311yescharacteristic
76C2×C3×C4×D3—24no—
77C2×C3×C4×D3D411yescharacteristic
78C2×C3×C4×D3D411yescharacteristic
79C2×C3×C4×D3C2311yescharacteristic
80C2×C3×C4×D3C2311yescharacteristic
81C2×#625—21no—
82C2×#625—21no—
83C2×D3×Dic3—21no—
84#3795—24no—
85C2×C32×C8C2312yes—
86#3757—21no—
87C4⋊(C3⋊Dic3)—21no—
88C4⋊(C3⋊Dic3)C2312yes—
89C4⋊(C3⋊Dic3)C2311yescharacteristic
90#3750—21no—
91C3×(C2×D3)⋊C4—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3C2312yes—
94C3×C4⋊Dic3C2311yescharacteristic
95C2×C3×C3⋊C8C2312yes—
96C3×D3×C8—24no—
97Dic3⋊Dic3—21no—
98(C2×D3)⋊Dic3—22no—
99(C2×D3)⋊Dic3—22no—
100(C2×D3)⋊Dic3—21no—
101(C2×D3)⋊Dic3—21no—
102(C2×D3)⋊Dic3—21no—
103Dic32—22no—
104Dic32—22no—
105Dic32—21no—
106#3091—91noSylow
107C23×C3×C4—31no—
108C2×#237—31no—
109C2×#235—31no—
110C22×C4×D3C2×D311yescharacteristic
111C22×C3×C8—32no—
112C3×#121—31no—
113C2×C3×C4⋊C4—31no—
114#953—61no—
115C2×#217—61no—
116#938—31no—
117#937—61no—
118D4×Dic3—61no—
119#930—31no—
120#930C2×D311yescharacteristic
121#929—61no—
122C4×#67—61no—
123C4×#67—61no—
124C2×(C2×D3)⋊C4—61no—
125#926—32no—
126#926—32no—
127#926—31no—
128#926—61no—
129#926—61no—
130C2×C4⋊Dic3—31no—
131C2×C4⋊Dic3—31no—
132C2×C4⋊Dic3—61no—
133C2×C4⋊Dic3C2×D311yescharacteristic
134#924—31no—
135#924—31no—
136#924—31no—
137#924—61no—
138C2×C4×Dic3—61no—
139C2×C4×Dic3—61no—
140C2×D3×C8C2×D312yes—
141#897—31no—
142#892—32no—
143#892—32no—
144#892—31no—
145#892—61no—
146#892—61no—
147#883—61no—
148#67⋊C4—61no—
149C3×#106—32no—
150C3×#102—32no—
151C3×C22⋊C8—21no—
152C3×C22⋊C8—31no—
153C3×C22⋊C8—32no—
154C3×C22⋊C8C2×D311yescharacteristic
155C3×C22⋊C8C2×D311yescharacteristic
156#832—32no—
157#830C2×D311yescharacteristic
158#821—32no—
159#821C2×D312yescomplemented
160(C2×D3)⋊C8C2×D312yes—
161#818—32no—
162#818—32no—
163#817—32no—
164#817—32no—
165#817—62no—
166#817C2×D312yescomplemented
167#816—32no—
168#816—32no—
169#816—32no—
170#816—62no—
171#810—32no—
172#807—32no—
173#807—32no—
174C23×C32C2×D411yescharacteristic
175C22×C3×D3—22no—
176C22×C3×D3—22no—
177C22×C3×D3—21no—
178C22×C3×D3—41no—
179C22×C3×D3C2×D411yescharacteristic
180C22×C3×D3C2×D411yescharacteristic
181C2×C32×C4—22no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—21no—
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×Dic3—42no—
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C3×D12—22no—
197C3×C4×D3—22no—
198C3×C4×D3—22no—
199C3×C4×D3—22no—
200C3×C4×D3#4114yes—
201#625—42no—
202#625—42no—
203D3×Dic3—42no—
204C32×C8—22no—
205C3×C3⋊C8—22no—
206#525—91no—
207C2×#117—91no—
208#485—92no—
209#484—91no—
210#483—91no—
211#482—92no—
212#481—31no—
213#480—91no—
214#427—92no—
215#416—92no—
216C2×C22⋊C8—31no—
217C24×C3—31no—
218C23×D3D1211yescharacteristic
219C2×C3×D4—31no—
220C2×C3×D4—61no—
221C22×C3×C4—21no—
222C22×C3×C4—31no—
223C22×C3×C4—31no—
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4—31no—
227C22×C3×C4—64no—
228C22×C3×C4—61no—
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C2×#67—21no—
232C2×#67—61no—
233C2×#67—61no—
234C2×#67—61no—
235C2×#67—61no—
236C22×Dic3—21no—
237C22×Dic3—61no—
238C22×Dic3—61no—
239C22×Dic3—61no—
240C22×Dic3—121no—
241C22×Dic3D1211yescharacteristic
242#237—64no—
243#235—64no—
244C2×D12C22×D311yescharacteristic
245C2×C4×D3—24no—
246C2×C4×D3—61no—
247C2×C4×D3D1211yescharacteristic
248C2×C4×D3D1211yescharacteristic
249C2×C4×D3C22×D311yescharacteristic
250C2×C4×D3C22×D311yescharacteristic
251C2×Dic6—31no—
252C2×Dic6—31no—
253C2×Dic6—61no—
254C2×C3×C8—22no—
255C2×C3×C8—32no—
256C2×C3×C8—64no—
257C2×C3×C8C22×D312yes—
258C2×C3×C8C22×D312yes—
259C3×C4⋊C4—31no—
260C3×C4⋊C4—32no—
261C3×C4⋊C4—61no—
262C3×C22⋊C4—61no—
263#217—61no—
264#217—62no—
265#217—62no—
266#217—61no—
267#217—61no—
268#217—61no—
269#217—61no—
270#217—121no—
271(C2×D3)⋊C4—21no—
272(C2×D3)⋊C4—61no—
273(C2×D3)⋊C4—61no—
274(C2×D3)⋊C4—61no—
275(C2×D3)⋊C4—62no—
276(C2×D3)⋊C4—62no—
277C4⋊Dic3—21no—
278C4⋊Dic3—31no—
279C4⋊Dic3—32no—
280C4⋊Dic3—32no—
281C4⋊Dic3—31no—
282C4⋊Dic3—62no—
283C4⋊Dic3—61no—
284C4⋊Dic3—61no—
285C4⋊Dic3—61no—
286C4⋊Dic3—61no—
287C4⋊Dic3—121no—
288C4⋊Dic3C22×D312yes—
289C4⋊Dic3C22×D311yescharacteristic
290Dic3⋊C4—61no—
291Dic3⋊C4—61no—
292Dic3⋊C4—61no—
293Dic3⋊C4—121no—
294C4×Dic3—62no—
295C4×Dic3—62no—
296C4×Dic3—61no—
297C4×Dic3—61no—
298C4×Dic3—62no—
299C4×Dic3—62no—
300C2×C3⋊C8C22×D312yes—
301D3×C8—24no—
302C22×C32—21no—
303C22×C32—21no—
304C22×C32#13512yes—
305C22×C32C22×D411yescharacteristic
306C2×C3×D3—21no—
307C2×C3×D3—21no—
308C2×C3×D3—21no—
309C2×C3×D3—21no—
310C2×C3×D3—21no—
311C2×C3×D3—44no—
312C2×C3×D3—41no—
313C2×C3×D3—41no—
314C2×C3×D3—41no—
315C2×C3×D3#12312yes—
316C32×C4—21no—
317C32×C4C2×#4112yes—
318C3⋊Dic3—41no—
319C3⋊Dic3—42no—
320C3⋊Dic3—41no—
321C3×Dic3—21no—
322C3×Dic3—41no—
323C3×Dic3—42no—
324C3×Dic3#12312yes—
325C2×#41—91no—
326C23×C4—31no—
327C22×C8—32no—
328#123—181no—
329C22⋊Q8—91no—
330C22⋊Q8—91no—
331#121—31no—
332#121—91no—
333#120—181no—
334C4×D4—181no—
335C4×D4—181no—
336#117—92no—
337#117—92no—
338#117—91no—
339#117—181no—
340#117—181no—
341C2×C4⋊C4—31no—
342C2×C4⋊C4—91no—
343C2×C22⋊C4—181no—
344C2×C42—181no—
345#107—92no—
346#107—92no—
347#106—32no—
348#106—92no—
349#103—92no—
350#103—92no—
351#102—32no—
352#102—92no—
353C22⋊C8—31no—
354C22⋊C8—32no—
355C22⋊C8D3211yescharacteristic
356C23×C3—21no—
357C23×C3—31no—
358C23×C3—31no—
359C23×C3—62no—
360C23×C3—62no—
361C23×C3—61no—
362C23×C3—121no—
363C23×C3C2×D1211yescharacteristic
364C23×C3D3×D411yescharacteristic
365C22×D3—22no—
366C22×D3—22no—
367C22×D3—21no—
368C22×D3—41no—
369C22×D3C2×D1211yescharacteristic
370C22×D3C2×D1211yescharacteristic
371C3×D4—62no—
372C3×D4—122no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—31no—
378C2×C3×C4—34no—
379C2×C3×C4—31no—
380C2×C3×C4—42no—
381C2×C3×C4—62no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—61no—
387C2×C3×C4—122no—
388C2×C3×C4C2×D1211yescharacteristic
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4C23×D311yescharacteristic
391C2×C3×C4C23×D311yescharacteristic
392#67—42no—
393#67—122no—
394#67—122no—
395#67—122no—
396#67—122no—
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—21no—
400C2×Dic3—42no—
401C2×Dic3—62no—
402C2×Dic3—61no—
403C2×Dic3—61no—
404C2×Dic3—62no—
405C2×Dic3—61no—
406C2×Dic3—61no—
407C2×Dic3—121no—
408C2×Dic3—121no—
409C2×Dic3—122no—
410C2×Dic3—122no—
411C2×Dic3—122no—
412C2×Dic3—122no—
413C2×Dic3—242no—
414C2×Dic3C2×D1211yescharacteristic
415C2×Dic3C2×D1211yescharacteristic
416D12—22no—
417C4×D3—22no—
418C4×D3—22no—
419C4×D3—22no—
420C4×D3—122no—
421C4×D3#23714yes—
422Dic6—62no—
423Dic6—62no—
424Dic6—122no—
425C3×C8—22no—
426C3×C8—22no—
427C3×C8—42no—
428C3×C8—62no—
429C3⋊C8—22no—
430C2×C32—22no—
431C2×C32C2×#12311yescharacteristic
432C2×C32C2×#13511yescharacteristic
433C2×C32#57511yescharacteristic
434C3×D3—22no—
435C3×D3—41no—
436C3×D3—81no—
437C24—31no—
438#41—184no—
439C2×Q8—91no—
440C2×D4—31no—
441C2×D4—61no—
442C2×D4—181no—
443C2×D4—181no—
444C22×C4—31no—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—31no—
448C22×C4—31no—
449C22×C4—64no—
450C22×C4—61no—
451C22×C4—181no—
452C22×C4—181no—
453C22×C4C2×D3211yescharacteristic
454C2×C8—32no—
455C2×C8—64no—
456C2×C8C2×D3212yes—
457C4⋊C4—32no—
458C4⋊C4—31no—
459C4⋊C4—61no—
460C4⋊C4—92no—
461C4⋊C4—91no—
462C4⋊C4—181no—
463C4⋊C4—181no—
464C4⋊C4—181no—
465C22⋊C4—61no—
466C22⋊C4—181no—
467C22⋊C4—182no—
468C22⋊C4—182no—
469C22⋊C4—181no—
470C22⋊C4—181no—
471C22⋊C4—181no—
472C42—182no—
473C42—182no—
474C42—181no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—22no—
481C22×C3—32no—
482C22×C3—41no—
483C22×C3—41no—
484C22×C3—61no—
485C22×C3—61no—
486C22×C3—61no—
487C22×C3—61no—
488C22×C3—61no—
489C22×C3—124no—
490C22×C3—121no—
491C22×C3—121no—
492C22×C3—121no—
493C22×C3#90412yes—
494C22×C3#91612yes—
495C22×C3C22×D1211yescharacteristic
496C22×C3C2×D3×D411yescharacteristic
497C2×D3—21no—
498C2×D3—21no—
499C2×D3—21no—
500C2×D3—21no—
501C2×D3—21no—
502C2×D3—44no—
503C2×D3—41no—
504C2×D3—41no—
505C2×D3—41no—
506C2×D3#88612yes—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—22no—
510C3×C4—32no—
511C3×C4—41no—
512C3×C4—61no—
513C3×C4—121no—
514C3×C4—122no—
515C3×C4C2×#23712yes—
516C3×C4D3×#4112yes—
517Dic3—21no—
518Dic3—41no—
519Dic3—42no—
520Dic3—121no—
521Dic3—122no—
522Dic3—121no—
523Dic3—121no—
524Dic3—122no—
525Dic3—121no—
526Dic3—241no—
527Dic3—242no—
528Dic3—241no—
529Dic3#88612yes—
530C32#309111yescharacteristic, complemented, Sylow
531C23—31no—
532C23—31no—
533C23—62no—
534C23—62no—
535C23—61no—
536C23—121no—
537C23D3×D1211yescharacteristic
538Q8—182no—
539D4—62no—
540D4—122no—
541D4—362no—
542D4—362no—
543C2×C4—22no—
544C2×C4—31no—
545C2×C4—34no—
546C2×C4—31no—
547C2×C4—62no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—61no—
553C2×C4—122no—
554C2×C4—182no—
555C2×C4—181no—
556C2×C4—181no—
557C2×C4—362no—
558C2×C4—362no—
559C2×C4D3×D1211yescharacteristic
560C2×C4C22×D3211yescharacteristic
561C8—22no—
562C8—62no—
563C2×C3—22no—
564C2×C3—22no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—42no—
569C2×C3—62no—
570C2×C3—121no—
571C2×C3—241no—
572C2×C3C2×#88611yescharacteristic
573C2×C3D3×#12311yescharacteristic
574C2×C3C2×#90411yescharacteristic
575C2×C3#574811yescharacteristic
576C2×C3C2×#91611yescharacteristic
577C2×C3#577311yescharacteristic
578D3—22no—
579D3—41no—
580D3—81no—
581C22—21no—
582C22—21no—
583C22—32no—
584C22—61no—
585C22—61no—
586C22—61no—
587C22—61no—
588C22—61no—
589C22—124no—
590C22—121no—
591C22—121no—
592C22—121no—
593C22#6380612yes—
594C22C2×D3×D1211yescharacteristic
595C4—21no—
596C4—32no—
597C4—61no—
598C4—121no—
599C4—122no—
600C4—362no—
601C4—361no—
602C4—361no—
603C4D3×#23712yes—
604C3—21no—
605C3#7859111yescharacteristic, complemented
606C3#8132411yescharacteristic, complemented
607C2—22no—
608C2—62no—
609C2—121no—
610C2—241no—
611C2D3×#88611yescharacteristic
612C2C2×#6380611yescharacteristic
613C2#1059471211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10594892C2
hypercenterC22⋊C8D32
hypocenterC32#3091
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
2. C2×#63841C2semidirect
3. #10592420C2semidirect
4. C3×#4735C2semidirect
5. C3×D3×C22⋊C8C2semidirect
6. #10591135C2semidirect
7. #10591094C2semidirect
8. #10590954C2semidirect
9. #10590837C2semidirect
10. #10590709C2semidirect
11. #10590706C2semidirect
35. #63644C22semidirect
36. #63643C22semidirect
38. C3×#821C22semidirect
40. C3×#817C22semidirect
41. #63575C22semidirect
42. #63575C22semidirect
43. #63567C22semidirect
44. #63563C22semidirect
61. #4735D3semidirect
62. D3×C22⋊C8D3semidirect
159. #821C2×D3semidirect
166. #817C2×D3semidirect
530. C32#3091semidirect
605. C3#78591semidirect
606. C3#81324semidirect

Maximal subgroups

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

subgroupindex
#105948922
C2×#638412
#105924202
C3×#47352
C3×D3×C22⋊C82
#105911352
#105910942
#105909542
#105908372
#105907092
#105907062
#813243
#785913