Finite Group Databasebeta

← #11860008

Subgroups — #11860008

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64159C211yesmaximal, characteristic
2C3×Dic3×#41C211yesmaximal, characteristic, complemented
3#10594954C211yesmaximal, characteristic, complemented
4C3×#5233C211yesmaximal, characteristic, complemented
5#10591537C212yesmaximal, complemented
6#10591536C212yesmaximal, complemented
7#10591401C212yesmaximal, complemented
8#10591400C212yesmaximal, complemented
9#10591138C211yesmaximal, characteristic, complemented
10#10591105C211yesmaximal, characteristic, complemented
11C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
12C4×#950—31nomaximal
13#78818—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C2×#3828C2211yescharacteristic
16#64159C418yescomplemented
17C2×#3756C2211yescharacteristic
18C2×#3755C2211yescharacteristic
19C2×#3754C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×Q8×Dic3C2212yes—
23C3×D4×Dic3—22no—
24C3×D4×Dic3C2212yes—
25C3×#926—21no—
26C3×#926C2211yescharacteristic
27C3×#926C2211yescharacteristic
28C2×C3×C4×Dic3—21no—
29C2×C3×C4×Dic3C2211yescharacteristic
30C22×C3×C3⋊C8C2211yescharacteristic
31#63952—22no—
32#63894C2212yes—
33C4×#624—21no—
34#63874—21no—
35#63844C2212yes—
36C3×#835C2212yes—
37C3×#832C2212yes—
38#63576C2212yes—
39#63574C2212yes—
40#63567C2212yes—
41#63564C2212yes—
42Dic3×C3⋊C8C2212yes—
43Dic3×C3⋊C8C2212yes—
44C3×C4×#41—31no—
45Dic3×#41D311yescharacteristic, complemented
46C2×#950—31no—
47C2×#950—31no—
48C2×#950—61no—
49#5522—31no—
50C4×#235—31no—
51C3×#416—31no—
52#5233D311yescharacteristic, complemented
53#5113—31no—
54C2×C8×Dic3—31no—
55C4×#216—32no—
56C4×#215—32no—
57C4×#214—32no—
58C4×#213—32no—
59#5002—31no—
60#4998—31no—
61#4998—31no—
62C2×C4×C3⋊C8—31no—
63#4790—32no—
64#4788—32no—
65#4758—32no—
66#4756—32no—
67C32×#41—22no—
68C32×#41C2×C414yescomplemented
69C2×C32×Q8C2311yescharacteristic
70C2×C32×D4—21no—
71C2×C32×D4C2311yescharacteristic
72C22×C32×C4—21no—
73C22×C32×C4C2311yescharacteristic
74C2×#638—21no—
75#3828—22no—
76#3828C2×C414yescomplemented
77C2×C4⋊(C3⋊D3)C2311yescharacteristic
78C2×C4×C3⋊D3—21no—
79C2×#634C2311yescharacteristic
80C22×C3×Dic3—22no—
81C22×C3×Dic3D412yes—
82C2×#624—22no—
83#3756C2×C414yescomplemented
84#3755C2×C414yescomplemented
85#3754C2×C414yescomplemented
86#3753C2×C414yescomplemented
87C2×C3⋊(C3⋊C8)C2×C414yescomplemented
88C2×C3⋊(C3⋊C8)C2311yescharacteristic
89C2×C3⋊(C3⋊C8)C2311yescharacteristic
90C3×#217—21no—
91C3×#217—21no—
92C3×#217—22no—
93C3×C4⋊Dic3—22no—
94C3×C4⋊Dic3C2312yes—
95C3×C4⋊Dic3C2312yes—
96C3×C4×Dic3—21no—
97C3×C4×Dic3—21no—
98C3×C4×Dic3—22no—
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3C2312yes—
102C2×C3×C3⋊C8—22no—
103C2×C3×C3⋊C8C2312yes—
104#3724—22no—
105#3722—22no—
106Dic32—22no—
107C4×#135—91noSylow
108C2×C3×#41—21no—
109C2×C3×#41C2×D311yescharacteristic
110C2×C3×#41C2×D311yescharacteristic
111C2×#235—31no—
112C2×#235—31no—
113C2×#235—61no—
114C22×C3×C8—31no—
115C3×C4×Q8—32no—
116C3×C4×D4—32no—
117C3×C4×D4—62no—
118C3×#117—31no—
119C3×#117—31no—
120C3×#117—61no—
121C2×C3×C42—31no—
122C2×C3×C42—61no—
123#950—38no—
124#950—38no—
125#950—68no—
126Q8×Dic3C2×D312yes—
127C2×#216—31no—
128C2×#216—31no—
129C2×#216—61no—
130C2×#215—31no—
131C2×#215—31no—
132C2×#215—61no—
133D4×Dic3—22no—
134D4×Dic3C2×D312yes—
135C2×#214—31no—
136C2×#214—31no—
137C2×#214—61no—
138C2×#213—31no—
139C2×#213—31no—
140C2×#213—61no—
141C4×#67—62no—
142#926—21no—
143#926C2×D311yescharacteristic
144#926C2×D311yescharacteristic
145C2×C4×Dic3—21no—
146C2×C4×Dic3C2×D311yescharacteristic
147C22×C3⋊C8—31no—
148C22×C3⋊C8—31no—
149C22×C3⋊C8—61no—
150C22×C3⋊C8C2×D311yescharacteristic
151#893—32no—
152#887—32no—
153#67⋊C4—62no—
154C4×D12—32no—
155#872—61no—
156#872—61no—
157C42×D3—61no—
158C42×D3—61no—
159C4×Dic6—32no—
160C3×#103—32no—
161C3×#102—32no—
162#835C2×D312yes—
163#832C2×D312yes—
164#821—32no—
165#816—32no—
166C8×Dic3—32no—
167C8×Dic3—32no—
168#810—32no—
169#809—32no—
170#808—32no—
171#808—32no—
172#807—32no—
173#807—32no—
174C4×C3⋊C8—32no—
175C4×C3⋊C8—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
190#638—24no—
191C2×C3⋊Dic3—21no—
192C4⋊(C3⋊D3)—21no—
193C4⋊(C3⋊D3)C22×C412yes—
194C4×C3⋊D3—24no—
195#634—21no—
196#634C22×C412yes—
197C2×C3×Dic3—24no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—44no—
201C2×C3×Dic3C2×D412yes—
202C2×C3×Dic3C2×D412yes—
203#624—44no—
204C3⋊(C3⋊C8)C22×C412yes—
205C3⋊(C3⋊C8)C22×C412yes—
206C3×C3⋊C8—22no—
207C2×#135—91no—
208C4×#41—31no—
209C4×#41—91no—
210C4×Q16—92no—
211C4×SD16—92no—
212C4×SD16—92no—
213C4×D8—92no—
214#427—91no—
215#416—31no—
216#416—91no—
217C2×C4×C8—91no—
218C3×#41—22no—
219C3×#41—22no—
220C3×#41—24no—
221C3×#41—42no—
222C3×#41C4×D314yescomplemented
223C3×#41C4×D314yescomplemented
224C2×C3×Q8—21no—
225C2×C3×Q8C22×D311yescharacteristic
226C2×C3×Q8C22×D311yescharacteristic
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—41no—
231C2×C3×D4C22×D311yescharacteristic
232C2×C3×D4C22×D311yescharacteristic
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—32no—
237C22×C3×C4—41no—
238C22×C3×C4—62no—
239C22×C3×C4C22×D311yescharacteristic
240C22×C3×C4C22×D311yescharacteristic
241C2×#67—61no—
242C2×#67—61no—
243C2×#67—121no—
244C22×Dic3—22no—
245C22×Dic3#6712yes—
246#235—34no—
247#235—34no—
248#235—64no—
249#235—62no—
250#235—62no—
251#235—122no—
252C2×D12—31no—
253C2×D12—31no—
254C2×D12—61no—
255C2×C4×D3—61no—
256C2×C4×D3—61no—
257C2×C4×D3—62no—
258C2×C4×D3—62no—
259C2×C4×D3—121no—
260C2×Dic6—31no—
261C2×Dic6—31no—
262C2×Dic6—61no—
263C2×C3×C8—32no—
264C2×C3×C8—62no—
265C3×C4⋊C4—32no—
266C3×C4⋊C4—32no—
267C3×C4⋊C4—62no—
268C3×C22⋊C4—62no—
269C3×C22⋊C4—61no—
270C3×C22⋊C4—61no—
271C3×C42—31no—
272C3×C42—31no—
273C3×C42—32no—
274C3×C42—62no—
275C3×C42—61no—
276C3×C42—61no—
277#217—21no—
278#217—21no—
279#217—22no—
280#216—34no—
281#216—34no—
282#216—64no—
283#215—34no—
284#215—34no—
285#215—64no—
286#214—34no—
287#214—34no—
288#214—64no—
289#213—34no—
290#213—34no—
291#213—64no—
292(C2×D3)⋊C4—62no—
293(C2×D3)⋊C4—62no—
294C4⋊Dic3—22no—
295C4⋊Dic3C22×D312yes—
296C4⋊Dic3C22×D312yes—
297Dic3⋊C4—62no—
298Dic3⋊C4—62no—
299C4×Dic3—21no—
300C4×Dic3—21no—
301C4×Dic3—22no—
302C4×Dic3—62no—
303C4×Dic3—62no—
304C4×Dic3#6711yescharacteristic
305C4×Dic3#6711yescharacteristic
306C4×Dic3C22×D312yes—
307C2×C3⋊C8—22no—
308C2×C3⋊C8—34no—
309C2×C3⋊C8—34no—
310C2×C3⋊C8—31no—
311C2×C3⋊C8—31no—
312C2×C3⋊C8—31no—
313C2×C3⋊C8—31no—
314C2×C3⋊C8—61no—
315C2×C3⋊C8—64no—
316C2×C3⋊C8—61no—
317C2×C3⋊C8C22×D312yes—
318C22×C32—22no—
319C22×C32—22no—
320C22×C32—42no—
321C22×C32C4×D412yes—
322C22×C32C22×D411yescharacteristic
323C2×C3⋊D3—22no—
324C2×C3⋊D3—42no—
325C32×C4—22no—
326C32×C4C4×D412yes—
327C32×C4C23×C411yescharacteristic
328C32×C4C2×#4111yescharacteristic
329C3⋊Dic3—22no—
330C3×Dic3—22no—
331C3×Dic3—42no—
332C3×Dic3—42no—
333C3×Dic3#13514yescomplemented
334C2×#41—91no—
335C2×#41D3211yescharacteristic
336#135—98no—
337C2×Q16—91no—
338C2×SD16—91no—
339C2×SD16—91no—
340C2×D8—91no—
341C22×C8—31no—
342C22×C8—91no—
343C4×Q8—32no—
344C4×Q8—92no—
345C4×D4—32no—
346C4×D4—62no—
347C4×D4—92no—
348C4×D4—182no—
349#117—31no—
350#117—31no—
351#117—61no—
352#117—181no—
353C2×C42—31no—
354C2×C42—61no—
355C2×C42—181no—
356#107—92no—
357#106—92no—
358#103—32no—
359#103—92no—
360#102—32no—
361#102—92no—
362C4×C8—92no—
363C4×C8—92no—
364C23×C3—21no—
365C23×C3—21no—
366C23×C3—21no—
367C23×C3—41no—
368C23×C3D3×D411yescharacteristic
369C23×C3C2×#6711yescharacteristic
370C22×D3—61no—
371C22×D3—61no—
372C22×D3—121no—
373C3×Q8—21no—
374C3×Q8—21no—
375C3×Q8—22no—
376C3×Q8—41no—
377C3×Q8C2×C4×D312yes—
378C3×Q8C2×C4×D312yes—
379C3×D4—24no—
380C3×D4—24no—
381C3×D4—21no—
382C3×D4—21no—
383C3×D4—22no—
384C3×D4—41no—
385C3×D4—44no—
386C3×D4C2×C4×D312yes—
387C3×D4C2×C4×D312yes—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—24no—
391C2×C3×C4—24no—
392C2×C3×C4—21no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—21no—
396C2×C3×C4—32no—
397C2×C3×C4—32no—
398C2×C3×C4—44no—
399C2×C3×C4—41no—
400C2×C3×C4—64no—
401C2×C3×C4—62no—
402C2×C3×C4—62no—
403C2×C3×C4—124no—
404C2×C3×C4C2×C4×D312yes—
405C2×C3×C4C2×C4×D312yes—
406C2×C3×C4#23512yes—
407C2×C3×C4D3×D411yescharacteristic
408C2×C3×C4#23712yes—
409C2×C3×C4C2×#6711yescharacteristic
410C2×C3×C4C23×D311yescharacteristic
411C2×C3×C4C23×D311yescharacteristic
412#67—64no—
413#67—64no—
414#67—124no—
415C2×Dic3—24no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—44no—
419C2×Dic3—61no—
420C2×Dic3—61no—
421C2×Dic3—121no—
422C2×Dic3C2×#6712yes—
423C2×Dic3C2×#6712yes—
424D12—32no—
425D12—32no—
426D12—62no—
427D12—61no—
428D12—61no—
429D12—121no—
430C4×D3—64no—
431C4×D3—64no—
432C4×D3—124no—
433C4×D3—124no—
434C4×D3—124no—
435Dic6—32no—
436Dic6—32no—
437Dic6—62no—
438Dic6—61no—
439Dic6—61no—
440Dic6—121no—
441C3×C8—62no—
442C3⋊C8—22no—
443C3⋊C8—32no—
444C3⋊C8—32no—
445C3⋊C8—32no—
446C3⋊C8—32no—
447C3⋊C8—62no—
448C3⋊C8—62no—
449C2×C32—22no—
450C2×C32—42no—
451C2×C32C2×C4×D411yescharacteristic
452C2×C32C2×#13512yes—
453C3⋊D3—42no—
454#41—22no—
455#41—94no—
456#41—182no—
457#41#62414yescomplemented
458C2×Q8—91no—
459C2×Q8C2×D3211yescharacteristic
460C2×D4—21no—
461C2×D4—91no—
462C2×D4—181no—
463C2×D4C2×D3211yescharacteristic
464C22×C4—21no—
465C22×C4—32no—
466C22×C4—62no—
467C22×C4—182no—
468C22×C4—181no—
469C22×C4C2×D3211yescharacteristic
470Q16—94no—
471SD16—94no—
472SD16—94no—
473D8—94no—
474C2×C8—32no—
475C2×C8—62no—
476C2×C8—91no—
477C2×C8—91no—
478C2×C8—94no—
479C4⋊C4—32no—
480C4⋊C4—32no—
481C4⋊C4—62no—
482C4⋊C4—182no—
483C22⋊C4—62no—
484C22⋊C4—61no—
485C22⋊C4—61no—
486C22⋊C4—182no—
487C42—32no—
488C42—31no—
489C42—31no—
490C42—62no—
491C42—61no—
492C42—61no—
493C42—182no—
494C22×C3—22no—
495C22×C3—22no—
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—21no—
499C22×C3—22no—
500C22×C3—42no—
501C22×C3—42no—
502C22×C3—42no—
503C22×C3—42no—
504C22×C3—82no—
505C22×C3#67⋊C412yes—
506C22×C3C4×#6712yes—
507C22×C3C2×D3×D411yescharacteristic
508C22×C3C22×#6711yescharacteristic
509C2×D3—62no—
510C2×D3—62no—
511C2×D3—122no—
512C2×D3—122no—
513C2×D3—122no—
514C2×D3—242no—
515C3×C4—22no—
516C3×C4—22no—
517C3×C4—21no—
518C3×C4—21no—
519C3×C4—22no—
520C3×C4—34no—
521C3×C4—42no—
522C3×C4—62no—
523C3×C4—122no—
524C3×C4—122no—
525C3×C4#67⋊C412yes—
526C3×C4C4×#6712yes—
527C3×C4C22×C4×D311yescharacteristic
528C3×C4C22×C4×D311yescharacteristic
529C3×C4C2×#23511yescharacteristic
530C3×C4C2×#23711yescharacteristic
531Dic3—22no—
532Dic3—42no—
533Dic3—42no—
534Dic3—62no—
535Dic3—62no—
536Dic3—122no—
537Dic3#95014yescomplemented
538C32C4×#13511yescharacteristic, complemented, Sylow
539C23—21no—
540C23—181no—
541C23D3×#6711yescharacteristic
542Q8—21no—
543Q8—92no—
544Q8—181no—
545Q8C2×#62412yes—
546D4—24no—
547D4—21no—
548D4—92no—
549D4—184no—
550D4—181no—
551D4C2×#62412yes—
552C2×C4—21no—
553C2×C4—24no—
554C2×C4—32no—
555C2×C4—32no—
556C2×C4—64no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—124no—
560C2×C4—181no—
561C2×C4—184no—
562C2×C4—364no—
563C2×C4#380412yes—
564C2×C4C2×#62412yes—
565C2×C4D3×#6711yescharacteristic
566C2×C4C22×D3211yescharacteristic
567C8—62no—
568C8—92no—
569C8—92no—
570C2×C3—22no—
571C2×C3—22no—
572C2×C3—22no—
573C2×C3—21no—
574C2×C3—42no—
575C2×C3—42no—
576C2×C3—42no—
577C2×C3—82no—
578C2×C3C2×#67⋊C411yescharacteristic
579C2×C3D3×#13512yes—
580C2×C3C2×C4×#6711yescharacteristic
581C2×C3C2×#95012yes—
582D3—122no—
583D3—122no—
584D3—242no—
585C22—22no—
586C22—22no—
587C22—42no—
588C22—182no—
589C22—362no—
590C22#6395212yes—
591C22C2×D3×#6711yescharacteristic
592C4—22no—
593C4—34no—
594C4—62no—
595C4—122no—
596C4—122no—
597C4—182no—
598C4#6395212yes—
599C4C2×#380411yescharacteristic
600C4C22×#62411yescharacteristic
601C3—21no—
602C3#7881811yescharacteristic, complemented
603C3C4×#95011yescharacteristic, complemented
604C2—22no—
605C2—42no—
606C2—362no—
607C2D3×#95012yes—
608C2C2×#6395211yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC2×#64159C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32C4×#135
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
2. C3×Dic3×#41C2semidirect
3. #10594954C2semidirect
4. C3×#5233C2semidirect
5. #10591537C2semidirect
6. #10591536C2semidirect
7. #10591401C2semidirect
8. #10591400C2semidirect
9. #10591138C2semidirect
10. #10591105C2semidirect
11. C2×Dic3×C3⋊C8C2semidirect
16. #64159C4semidirect
45. Dic3×#41D3semidirect
52. #5233D3semidirect
68. C32×#41C2×C4semidirect
76. #3828C2×C4semidirect
83. #3756C2×C4semidirect
84. #3755C2×C4semidirect
85. #3754C2×C4semidirect
86. #3753C2×C4semidirect
87. C2×C3⋊(C3⋊C8)C2×C4semidirect
222. C3×#41C4×D3semidirect
223. C3×#41C4×D3semidirect
333. C3×Dic3#135semidirect
457. #41#624semidirect
537. Dic3#950semidirect
538. C32C4×#135semidirect
602. C3#78818semidirect
603. C3C4×#950semidirect

Maximal subgroups

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

subgroupindex
C2×#641592
C3×Dic3×#412
#105949542
C3×#52332
#105915372
#105915362
#105914012
#105914002
#105911382
#105911052
C2×Dic3×C3⋊C82
C4×#9503
#788183