Finite Group Databasebeta

← #11860227

Subgroups — #11860227

Order 1152.

1139 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#41×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#950C211yesmaximal, characteristic
3#10594958C211yesmaximal, characteristic, complemented
4C3×#5233C211yesmaximal, characteristic, complemented
5#10591582C212yesmaximal, complemented
6#10591572C212yesmaximal, complemented
7#10591446C212yesmaximal, complemented
8#10591436C212yesmaximal, complemented
9#10591122C211yesmaximal, characteristic, complemented
10#10591084C211yesmaximal, characteristic, complemented
11C2×#63555C211yesmaximal, characteristic, complemented
12#83897—31nomaximal
13#78819—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16Q8×C3⋊Dic3C2212yes—
17D4×C3⋊Dic3—22no—
18D4×C3⋊Dic3C2212yes—
19#64135—21no—
20#64135C2211yescharacteristic
21C2×C4×C3⋊Dic3—21no—
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C3×#950C418yescomplemented
24C2×C3×#216C2211yescharacteristic
25C2×C3×#215C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27C2×C3×#213C2211yescharacteristic
28C3×#926C2211yescharacteristic
29C22×C3×C3⋊C8C2211yescharacteristic
30C22×C3×C3⋊C8C2211yescharacteristic
31#67⋊Dic3—22no—
32#63898C2212yes—
33C4×D3×Dic3—21no—
34#63855—21no—
35#63843C2212yes—
36C3×#835C2212yes—
37C3×#832C2212yes—
38#63575C2212yes—
39#63573C2212yes—
40#63566C2212yes—
41#63563C2212yes—
42#63555C2212yes—
43#63555C2212yes—
44C2×C3×#135—31no—
45Dic3×#41—31no—
46Dic3×#41—31no—
47Dic3×#41—31no—
48Dic3×#41—61no—
49C2×#950D311yescharacteristic
50#5522—31no—
51C3×#416—31no—
52#5233—31no—
53#5233D311yescharacteristic, complemented
54#5184—32no—
55#5164—32no—
56#5164—32no—
57#5152—32no—
58#5113—31no—
59#5106—31no—
60C2×#815—31no—
61C2×#815—31no—
62#4998—31no—
63#4817—32no—
64#4789—32no—
65#4785—32no—
66#4757—32no—
67C32×#41—22no—
68C32×#41C2×C414yescomplemented
69C2×C32×Q8C2311yescharacteristic
70C2×C32×D4—21no—
71C2×C32×D4C2311yescharacteristic
72C22×C32×C4—21no—
73C22×C32×C4C2311yescharacteristic
74C22×C3⋊Dic3—22no—
75C22×C3⋊Dic3D412yes—
76C2×C3×#67—21no—
77C3×#235—22no—
78C3×#235C2×C414yescomplemented
79C2×C3×D12C2311yescharacteristic
80C2×C3×C4×D3—21no—
81C2×C3×Dic6C2311yescharacteristic
82C2×D3×Dic3—22no—
83#3757—21no—
84#3757—22no—
85C4⋊(C3⋊Dic3)—22no—
86C4⋊(C3⋊Dic3)C2312yes—
87C4×C3⋊Dic3—21no—
88C4×C3⋊Dic3—22no—
89C4×C3⋊Dic3D411yescharacteristic
90C4×C3⋊Dic3D411yescharacteristic
91C4×C3⋊Dic3C2312yes—
92C3×#217—21no—
93C3×#216C2×C414yescomplemented
94C3×#215C2×C414yescomplemented
95C3×#214C2×C414yescomplemented
96C3×#213C2×C414yescomplemented
97C3×C4⋊Dic3C2312yes—
98C3×C4×Dic3—21no—
99C2×C3×C3⋊C8—22no—
100C2×C3×C3⋊C8C2×C414yescomplemented
101C2×C3×C3⋊C8C2312yes—
102C2×C3×C3⋊C8C2311yescharacteristic
103C2×C3×C3⋊C8C2311yescharacteristic
104Dic3⋊Dic3—22no—
105(C2×D3)⋊Dic3—22no—
106Dic32—22no—
107#2943—91noSylow
108C2×C3×#41—21no—
109C2×C3×#41—31no—
110C2×C3×#41C2×D311yescharacteristic
111C2×C3×#41C2×D311yescharacteristic
112C2×#235C2×D311yescharacteristic
113C3×#135—38no—
114C2×C3×Q16—31no—
115C2×C3×SD16—31no—
116C2×C3×SD16—31no—
117C2×C3×D8—31no—
118C22×C3×C8—31no—
119C22×C3×C8—31no—
120C3×#117—31no—
121#950Dic318yescomplemented
122Q8×Dic3—32no—
123Q8×Dic3—32no—
124Q8×Dic3—32no—
125Q8×Dic3—62no—
126C2×#216C2×D311yescharacteristic
127C2×#215C2×D311yescharacteristic
128D4×Dic3—32no—
129D4×Dic3—32no—
130D4×Dic3—32no—
131D4×Dic3—62no—
132D4×Dic3—62no—
133D4×Dic3—62no—
134D4×Dic3—62no—
135D4×Dic3—64no—
136C2×#214C2×D311yescharacteristic
137C2×#213C2×D311yescharacteristic
138#926—31no—
139#926—31no—
140#926—61no—
141#926—61no—
142#926—61no—
143#926—61no—
144#926—62no—
145#926C2×D311yescharacteristic
146C2×C4×Dic3—31no—
147C2×C4×Dic3—31no—
148C2×C4×Dic3—61no—
149C2×C4×Dic3—61no—
150C2×C4×Dic3—61no—
151C2×C4×Dic3—61no—
152C2×C4×Dic3—62no—
153C22×C3⋊C8C2×D311yescharacteristic
154C22×C3⋊C8C2×D311yescharacteristic
155#893—32no—
156#887—32no—
157#67⋊C4—62no—
158#872—61no—
159C42×D3—61no—
160C3×#103—32no—
161C3×#102—32no—
162#835—32no—
163#835C2×D312yes—
164#832—32no—
165#832C2×D312yes—
166#821—32no—
167#818—32no—
168#817—32no—
169#816—32no—
170#815—32no—
171#815—32no—
172#815—32no—
173#815—32no—
174#808—32no—
175#807—32no—
176C23×C32—21no—
177C23×C32C2×D411yescharacteristic
178C22×C3×D3—21no—
179C32×Q8—21no—
180C32×Q8C22×C412yes—
181C32×D4—24no—
182C32×D4—21no—
183C32×D4C22×C412yes—
184C2×C32×C4—21no—
185C2×C32×C4—24no—
186C2×C32×C4C22×C412yes—
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4#4112yes—
189C2×C32×C4C2411yescharacteristic
190C2×C3⋊Dic3—22no—
191C2×C3⋊Dic3—42no—
192C2×C3⋊Dic3—44no—
193C2×C3⋊Dic3C2×D412yes—
194C2×C3⋊Dic3C2×D412yes—
195C3×#67—24no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—22no—
198C3×D12—21no—
199C3×D12C22×C412yes—
200C3×C4×D3—24no—
201C3×Dic6—21no—
202C3×Dic6C22×C412yes—
203D3×Dic3—44no—
204C3×C3⋊C8—22no—
205C3×C3⋊C8C22×C412yes—
206C3×C3⋊C8C22×C412yes—
207C2×#135—31no—
208C4×#41—91no—
209C4×#41—91no—
210#442—92no—
211#441—92no—
212#440—92no—
213#440—92no—
214#427—91no—
215#416—31no—
216#416—91no—
217C2×#97—91no—
218C3×#41—24no—
219C3×#41—22no—
220C3×#41—22no—
221C3×#41—24no—
222C3×#41—34no—
223C3×#41—62no—
224C3×#41C4×D314yescomplemented
225C3×#41C2×Dic314yescomplemented
226C2×C3×Q8—21no—
227C2×C3×Q8—31no—
228C2×C3×Q8C22×D311yescharacteristic
229C2×C3×Q8C22×D311yescharacteristic
230C2×C3×D4—22no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—31no—
235C2×C3×D4—61no—
236C2×C3×D4C22×D311yescharacteristic
237C2×C3×D4C22×D311yescharacteristic
238C22×C3×C4—22no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—61no—
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C2×#67—21no—
246C22×Dic3—32no—
247C22×Dic3—32no—
248C22×Dic3—62no—
249C22×Dic3—62no—
250C22×Dic3—62no—
251C22×Dic3—62no—
252C22×Dic3—64no—
253#235—22no—
254#235C2×Dic314yescomplemented
255C2×D12C22×D311yescharacteristic
256C2×C4×D3—21no—
257C2×C4×D3—62no—
258C2×Dic6C22×D311yescharacteristic
259C3×Q16—34no—
260C3×SD16—34no—
261C3×SD16—34no—
262C3×D8—34no—
263C2×C3×C8—34no—
264C2×C3×C8—31no—
265C2×C3×C8—31no—
266C2×C3×C8—32no—
267C2×C3×C8—62no—
268C3×C4⋊C4—32no—
269C3×C22⋊C4—61no—
270C3×C42—61no—
271#217—21no—
272#217—62no—
273#217—62no—
274#217—62no—
275#217—64no—
276#217—62no—
277#217—61no—
278#217—61no—
279#216C2×Dic314yescomplemented
280#215C2×Dic314yescomplemented
281#214C2×Dic314yescomplemented
282#213C2×Dic314yescomplemented
283(C2×D3)⋊C4—62no—
284C4⋊Dic3—32no—
285C4⋊Dic3—32no—
286C4⋊Dic3—62no—
287C4⋊Dic3—62no—
288C4⋊Dic3—62no—
289C4⋊Dic3—62no—
290C4⋊Dic3—64no—
291C4⋊Dic3C22×D312yes—
292Dic3⋊C4—62no—
293C4×Dic3—21no—
294C4×Dic3—31no—
295C4×Dic3—31no—
296C4×Dic3—31no—
297C4×Dic3—31no—
298C4×Dic3—32no—
299C4×Dic3—32no—
300C4×Dic3—61no—
301C4×Dic3—61no—
302C4×Dic3—62no—
303C4×Dic3—62no—
304C4×Dic3—62no—
305C4×Dic3—62no—
306C4×Dic3—62no—
307C4×Dic3—62no—
308C4×Dic3—64no—
309C4×Dic3—61no—
310C4×Dic3—61no—
311C2×C3⋊C8—22no—
312C2×C3⋊C8C2×Dic314yescomplemented
313C2×C3⋊C8C22×D312yes—
314C2×C3⋊C8C22×D311yescharacteristic
315C2×C3⋊C8C22×D311yescharacteristic
316C22×C32—22no—
317C22×C32—22no—
318C22×C32—42no—
319C22×C32C4×D412yes—
320C22×C32C22×D411yescharacteristic
321C2×C3×D3—22no—
322C2×C3×D3—42no—
323C32×C4—22no—
324C32×C4C4×D412yes—
325C32×C4C23×C411yescharacteristic
326C32×C4C2×#4111yescharacteristic
327C3⋊Dic3—22no—
328C3⋊Dic3—22no—
329C3⋊Dic3—42no—
330C3×Dic3—22no—
331C3×Dic3—42no—
332C2×#41—31no—
333C2×#41D3211yescharacteristic
334#135—38no—
335C2×Q16—31no—
336C2×SD16—31no—
337C2×SD16—31no—
338C2×D8—31no—
339C22×C8—31no—
340C22×C8—31no—
341C4×Q8—92no—
342C4×Q8—92no—
343C4×D4—92no—
344C4×D4—92no—
345C4×D4—182no—
346C4×D4—182no—
347#117—31no—
348#117—91no—
349#117—181no—
350#117—181no—
351C2×C42—91no—
352C2×C42—181no—
353C2×C42—181no—
354#107—92no—
355#106—92no—
356#103—32no—
357#103—92no—
358#102—32no—
359#102—92no—
360#97—92no—
361#97—92no—
362C23×C3—22no—
363C23×C3—21no—
364C23×C3—21no—
365C23×C3—21no—
366C23×C3—61no—
367C23×C3D3×D411yescharacteristic
368C23×C3D3×D411yescharacteristic
369C22×D3—21no—
370C3×Q8—22no—
371C3×Q8—21no—
372C3×Q8—21no—
373C3×Q8—22no—
374C3×Q8—32no—
375C3×Q8—61no—
376C3×Q8C2×C4×D312yes—
377C3×Q8C22×Dic312yes—
378C3×D4—28no—
379C3×D4—22no—
380C3×D4—24no—
381C3×D4—24no—
382C3×D4—21no—
383C3×D4—21no—
384C3×D4—22no—
385C3×D4—32no—
386C3×D4—64no—
387C3×D4—61no—
388C3×D4C2×C4×D312yes—
389C3×D4C22×Dic312yes—
390C2×C3×C4—22no—
391C2×C3×C4—28no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—24no—
395C2×C3×C4—24no—
396C2×C3×C4—21no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—21no—
400C2×C3×C4—61no—
401C2×C3×C4—64no—
402C2×C3×C4—62no—
403C2×C3×C4C2×C4×D312yes—
404C2×C3×C4D3×D411yescharacteristic
405C2×C3×C4D3×D411yescharacteristic
406C2×C3×C4#23712yes—
407C2×C3×C4#23712yes—
408C2×C3×C4C22×Dic312yes—
409C2×C3×C4C23×D311yescharacteristic
410C2×C3×C4C23×D311yescharacteristic
411#67—24no—
412C2×Dic3—21no—
413C2×Dic3—22no—
414C2×Dic3—32no—
415C2×Dic3—32no—
416C2×Dic3—32no—
417C2×Dic3—32no—
418C2×Dic3—62no—
419C2×Dic3—62no—
420C2×Dic3—64no—
421C2×Dic3—62no—
422C2×Dic3—62no—
423C2×Dic3—124no—
424C2×Dic3—122no—
425C2×Dic3—122no—
426C2×Dic3—124no—
427C2×Dic3—128no—
428C2×Dic3—124no—
429C2×Dic3—124no—
430D12—21no—
431D12C22×Dic312yes—
432C4×D3—24no—
433C4×D3—124no—
434Dic6—21no—
435Dic6C22×Dic312yes—
436C3×C8—32no—
437C3×C8—32no—
438C3×C8—62no—
439C3⋊C8—22no—
440C3⋊C8C22×Dic312yes—
441C3⋊C8C22×Dic312yes—
442C2×C32—22no—
443C2×C32—42no—
444C2×C32C2×C4×D411yescharacteristic
445C2×C32#57512yes—
446C3×D3—42no—
447#41—22no—
448#41—34no—
449#41—62no—
450#41D3×Dic314yescomplemented
451C2×Q8—31no—
452C2×Q8C2×D3211yescharacteristic
453C2×D4—21no—
454C2×D4—31no—
455C2×D4—61no—
456C2×D4C2×D3211yescharacteristic
457C22×C4—21no—
458C22×C4—61no—
459C22×C4—92no—
460C22×C4—182no—
461C22×C4—182no—
462C22×C4C2×D3211yescharacteristic
463Q16—34no—
464SD16—34no—
465SD16—34no—
466D8—34no—
467C2×C8—31no—
468C2×C8—31no—
469C2×C8—34no—
470C2×C8—32no—
471C2×C8—62no—
472C4⋊C4—32no—
473C4⋊C4—92no—
474C4⋊C4—182no—
475C4⋊C4—182no—
476C22⋊C4—61no—
477C22⋊C4—182no—
478C22⋊C4—182no—
479C22⋊C4—181no—
480C42—61no—
481C42—92no—
482C42—91no—
483C42—91no—
484C42—182no—
485C42—182no—
486C42—181no—
487C22×C3—22no—
488C22×C3—22no—
489C22×C3—24no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—21no—
493C22×C3—22no—
494C22×C3—42no—
495C22×C3—44no—
496C22×C3—42no—
497C22×C3—42no—
498C22×C3—62no—
499C22×C3—122no—
500C22×C3#67⋊C412yes—
501C22×C3D4×Dic312yes—
502C22×C3C2×D3×D411yescharacteristic
503C22×C3C2×D3×D411yescharacteristic
504C2×D3—22no—
505C2×D3—42no—
506C3×C4—24no—
507C3×C4—22no—
508C3×C4—22no—
509C3×C4—21no—
510C3×C4—21no—
511C3×C4—22no—
512C3×C4—62no—
513C3×C4—122no—
514C3×C4#67⋊C412yes—
515C3×C4D4×Dic312yes—
516C3×C4C22×C4×D311yescharacteristic
517C3×C4C2×#23711yescharacteristic
518C3×C4C2×#23711yescharacteristic
519C3×C4C23×Dic311yescharacteristic
520Dic3—22no—
521Dic3—42no—
522Dic3—64no—
523Dic3—62no—
524Dic3—62no—
525Dic3—62no—
526Dic3—62no—
527Dic3—122no—
528Dic3—124no—
529Dic3—122no—
530Dic3—122no—
531C32#294311yescharacteristic, complemented, Sylow
532C23—21no—
533C23—61no—
534C23#381111yescharacteristic
535Q8—21no—
536Q8—32no—
537Q8—61no—
538Q8C2×D3×Dic312yes—
539D4—24no—
540D4—21no—
541D4—32no—
542D4—64no—
543D4—61no—
544D4C2×D3×Dic312yes—
545C2×C4—21no—
546C2×C4—24no—
547C2×C4—61no—
548C2×C4—64no—
549C2×C4—62no—
550C2×C4—92no—
551C2×C4—92no—
552C2×C4—182no—
553C2×C4—364no—
554C2×C4—362no—
555C2×C4—364no—
556C2×C4C2×D3×Dic312yes—
557C2×C4#380512yes—
558C2×C4#381111yescharacteristic
559C2×C4C22×D3211yescharacteristic
560C8—32no—
561C8—32no—
562C8—62no—
563C2×C3—22no—
564C2×C3—22no—
565C2×C3—22no—
566C2×C3—21no—
567C2×C3—42no—
568C2×C3—44no—
569C2×C3—42no—
570C2×C3—42no—
571C2×C3—122no—
572C2×C3C2×#67⋊C411yescharacteristic
573C2×C3#576812yes—
574C2×C3#576812yes—
575C2×C3C2×D4×Dic311yescharacteristic
576D3—42no—
577C22—22no—
578C22—22no—
579C22—42no—
580C22—62no—
581C22—122no—
582C22#67⋊Dic312yes—
583C22C2×#381111yescharacteristic
584C4—22no—
585C4—62no—
586C4—122no—
587C4—182no—
588C4—182no—
589C4—362no—
590C4#67⋊Dic312yes—
591C4C22×D3×Dic311yescharacteristic
592C4C2×#380511yescharacteristic
593C3—21no—
594C3#7881911yescharacteristic, complemented
595C3#8389711yescharacteristic, complemented
596C2—22no—
597C2—42no—
598C2—122no—
599C2#1059546012yes—
600C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC2×C3×#950C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2943
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #41×C3⋊Dic3C2semidirect
3. #10594958C2semidirect
4. C3×#5233C2semidirect
5. #10591582C2semidirect
6. #10591572C2semidirect
7. #10591446C2semidirect
8. #10591436C2semidirect
9. #10591122C2semidirect
10. #10591084C2semidirect
11. C2×#63555C2semidirect
23. C3×#950C4semidirect
53. #5233D3semidirect
68. C32×#41C2×C4semidirect
78. C3×#235C2×C4semidirect
93. C3×#216C2×C4semidirect
94. C3×#215C2×C4semidirect
95. C3×#214C2×C4semidirect
96. C3×#213C2×C4semidirect
100. C2×C3×C3⋊C8C2×C4semidirect
121. #950Dic3semidirect
224. C3×#41C4×D3semidirect
225. C3×#41C2×Dic3semidirect
254. #235C2×Dic3semidirect
279. #216C2×Dic3semidirect
280. #215C2×Dic3semidirect
281. #214C2×Dic3semidirect
282. #213C2×Dic3semidirect
312. C2×C3⋊C8C2×Dic3semidirect
450. #41D3×Dic3semidirect
531. C32#2943semidirect
594. C3#78819semidirect
595. C3#83897semidirect

Maximal subgroups

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

subgroupindex
#41×C3⋊Dic32
C2×C3×#9502
#105949582
C3×#52332
#105915822
#105915722
#105914462
#105914362
#105911222
#105910842
C2×#635552
#838973
#788193