Finite Group Databasebeta

← #11860416

Subgroups — #11860416

Order 1152.

1043 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic3×#235C211yesmaximal, characteristic
2C2×#63844C211yesmaximal, characteristic, complemented
3C2×#63831C211yesmaximal, characteristic
4#10592819C211yesmaximal, characteristic, complemented
5C3×#5133C211yesmaximal, characteristic
6C3×Dic3×M16C211yesmaximal, characteristic, complemented
7#10591130C211yesmaximal, characteristic, complemented
8#10590794C212yesmaximal, complemented
9#10590793C212yesmaximal, complemented
10#10590747C212yesmaximal, complemented
11#10590744C212yesmaximal, complemented
12#78867—31nomaximal
13C4×#909—31nomaximal
14C22×#634C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×C32×M16C2211yescharacteristic
17#64135C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21Dic3×#67—21no—
22Dic3×#67—21no—
23C2×#3724—21no—
24C2×Dic32—21no—
25Dic3×D12C2211yescharacteristic
26Dic3×D12C2211yescharacteristic
27C4×D3×Dic3—21no—
28#63855—21no—
29#63844—21no—
30#63844—21no—
31#63844C2212yes—
32#63844C2212yes—
33Dic3×Dic6C2211yescharacteristic
34Dic3×Dic6C2211yescharacteristic
35C2×#3719C2212yes—
36#63831C418yescomplemented
37C2×#3716C2212yes—
38#63643C2212yes—
39#63643C2212yes—
40C3×#821C2212yes—
41C3×#816C2212yes—
42C3×#815C2212yes—
43C3×C8×Dic3C2212yes—
44#63575C2212yes—
45#63573C2212yes—
46Dic3×#41—31no—
47C2×#951—31no—
48C2×#909—31no—
49C2×#887—31no—
50C4×#235—31no—
51C2×C4×Dic6—31no—
52C3×#417—31no—
53C3×C4×M16—31no—
54#5133D311yescharacteristic
55#5121—31no—
56#5120—31no—
57#5120—31no—
58#5120—61no—
59Dic3×M16D311yescharacteristic, complemented
60#4964—31no—
61#4790—32no—
62#4789—32no—
63#4758—32no—
64#4757—32no—
65#4716—32no—
66#4710—32no—
67C4×Dic12—32no—
68C4×#204—32no—
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3—21no—
71C2×#634—21no—
72C2×#634—22no—
73C2×#634C2×C414yescomplemented
74C2×#634C2312yes—
75C2×C3×#67—21no—
76C22×C3×Dic3—21no—
77C22×C3×Dic3D411yescharacteristic
78C22×C3×Dic3D411yescharacteristic
79C3×#235—22no—
80C3×#235C2×C414yes—
81C2×C3×D12C2311yescharacteristic
82C2×C3×C4×D3—21no—
83C2×C3×Dic6C2311yescharacteristic
84C2×D3×Dic3—21no—
85C2×D3×Dic3—21no—
86C32×M16—22no—
87C2×C32×C8C2312yes—
88#3757—21no—
89C4⋊(C3⋊Dic3)C2311yescharacteristic
90C4⋊(C3⋊Dic3)C2311yescharacteristic
91C4×C3⋊Dic3—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3C2312yes—
94C3×C4×Dic3D411yescharacteristic
95C3×C4×Dic3D411yescharacteristic
96C3×C4×Dic3C2311yescharacteristic
97C3×C4×Dic3C2311yescharacteristic
98C3×#208C2×C414yescomplemented
99C2×C3×C3⋊C8C2312yes—
100#3724—22no—
101#3724—22no—
102Dic3⋊Dic3—21no—
103Dic3⋊Dic3—21no—
104(C2×D3)⋊Dic3—21no—
105(C2×D3)⋊Dic3—21no—
106Dic32—21no—
107Dic32—21no—
108Dic32—22no—
109Dic32—22no—
110#3719C2×C418yescomplemented
111#3716C2×C418yescomplemented
112C4×#137—91noSylow
113C2×C3×#41—31no—
114C2×#235C2×D311yescharacteristic
115C22×Dic6—31no—
116C22×Dic6—31no—
117C22×Dic6—61no—
118C2×C3×M16—21no—
119C2×C3×M16—31no—
120C2×C3×M16C2×D311yescharacteristic
121C2×C3×M16C2×D311yescharacteristic
122C2×C3×C4⋊C4—31no—
123C2×C3×C42—31no—
124#951—38no—
125Q8×Dic3—31no—
126Q8×Dic3—31no—
127C2×#216—32no—
128D4×Dic3—31no—
129D4×Dic3—31no—
130D4×Dic3—61no—
131D4×Dic3—61no—
132C2×#214—32no—
133C4×#67—61no—
134C4×#67—61no—
135#926—31no—
136#926—31no—
137#926—61no—
138#926—61no—
139C2×C4⋊Dic3C2×D311yescharacteristic
140C2×Dic3⋊C4—61no—
141C2×Dic3⋊C4—61no—
142C2×C4×Dic3—61no—
143C2×C4×Dic3—61no—
144C2×C4×Dic3—61no—
145C2×C4×Dic3C2×D311yescharacteristic
146C2×#208C2×D311yescharacteristic
147#909—38no—
148C2×Dic12—32no—
149C2×#204—32no—
150#887—32no—
151#887—32no—
152#887—61no—
153#887—61no—
154C4×D12—31no—
155C4×D12—31no—
156#872—61no—
157C42×D3—61no—
158C4×Dic6—31no—
159C4×Dic6—31no—
160C4×Dic6—32no—
161C4×Dic6—32no—
162C4×Dic6—61no—
163C4×Dic6—61no—
164C3×#103—32no—
165C3×#102—32no—
166C3×#97—32no—
167C3×C4×C8—32no—
168#821C2×D312yes—
169#818—32no—
170#817—32no—
171#816—32no—
172#816—32no—
173#816—32no—
174#816—32no—
175#816—62no—
176#816—62no—
177#816C2×D312yes—
178#815C2×D312yes—
179C8×Dic3C2×D312yes—
180#808—32no—
181#807—32no—
182C23×C32C2×D411yescharacteristic
183C22×C3×D3—21no—
184C2×C32×C4C22×C412yes—
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4#4112yes—
187C2×C32×C4C2411yescharacteristic
188C2×C3⋊Dic3—24no—
189C2×C3⋊Dic3—22no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192#634—24no—
193#634—22no—
194#634C22×C414yes—
195C3×#67—24no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—41no—
200C2×C3×Dic3—42no—
201C2×C3×Dic3C2×D411yescharacteristic
202C2×C3×Dic3C2×D411yescharacteristic
203C2×C3×Dic3C2×D411yescharacteristic
204C2×C3×Dic3C2×D411yescharacteristic
205C3×D12—21no—
206C3×D12C22×C412yes—
207C3×C4×D3—24no—
208C3×Dic6—21no—
209C3×Dic6C22×C412yes—
210D3×Dic3—42no—
211D3×Dic3—42no—
212C32×C8—22no—
213C3×C3⋊C8C22×C414yes—
214C2×#137—91no—
215C4×#41—91no—
216C2×C4×Q8—91no—
217#441—92no—
218#440—92no—
219C4×Q16—92no—
220C4×SD16—92no—
221#428—91no—
222#419—91no—
223#417—31no—
224C4×M16—31no—
225C3×#41—34no—
226C3×#41—62no—
227C2×C3×Q8—31no—
228C2×C3×D4—31no—
229C2×C3×D4—61no—
230C22×C3×C4—21no—
231C22×C3×C4—31no—
232C22×C3×C4—31no—
233C22×C3×C4—61no—
234C22×C3×C4—61no—
235C22×C3×C4C22×D311yescharacteristic
236C22×C3×C4C22×D311yescharacteristic
237C2×#67—21no—
238C22×Dic3—21no—
239C22×Dic3—61no—
240C22×Dic3—61no—
241C22×Dic3—61no—
242C22×Dic3—61no—
243C22×Dic3—121no—
244C22×Dic3D1211yescharacteristic
245C22×Dic3D1211yescharacteristic
246#235—22no—
247#235C4×D314yes—
248C2×D12C22×D311yescharacteristic
249C2×C4×D3—21no—
250C2×C4×D3—61no—
251C2×C4×D3—61no—
252C2×Dic6—34no—
253C2×Dic6—34no—
254C2×Dic6—32no—
255C2×Dic6—32no—
256C2×Dic6—62no—
257C2×Dic6—64no—
258C2×Dic6—61no—
259C2×Dic6—62no—
260C2×Dic6—61no—
261C2×Dic6—62no—
262C2×Dic6—121no—
263C2×Dic6—122no—
264C2×Dic6C22×D311yescharacteristic
265C3×M16—22no—
266C3×M16—22no—
267C3×M16—34no—
268C3×M16—42no—
269C2×C3×C8—22no—
270C2×C3×C8—32no—
271C2×C3×C8C22×D312yes—
272C2×C3×C8C22×D312yes—
273C3×C4⋊C4—32no—
274C3×C4⋊C4—61no—
275C3×C42—31no—
276C3×C42—31no—
277C3×C42—31no—
278C3×C42—31no—
279#217—61no—
280#217—61no—
281#217—61no—
282#217—61no—
283#217—121no—
284#216—38no—
285#214—38no—
286(C2×D3)⋊C4—61no—
287(C2×D3)⋊C4—61no—
288C4⋊Dic3—21no—
289C4⋊Dic3—31no—
290C4⋊Dic3—31no—
291C4⋊Dic3—31no—
292C4⋊Dic3—31no—
293C4⋊Dic3—61no—
294C4⋊Dic3—61no—
295C4⋊Dic3—61no—
296C4⋊Dic3—61no—
297C4⋊Dic3C22×D312yes—
298Dic3⋊C4—62no—
299Dic3⋊C4—62no—
300Dic3⋊C4—61no—
301Dic3⋊C4—61no—
302Dic3⋊C4—62no—
303Dic3⋊C4—62no—
304C4×Dic3—62no—
305C4×Dic3—62no—
306C4×Dic3—61no—
307C4×Dic3—61no—
308C4×Dic3—61no—
309C4×Dic3—61no—
310C4×Dic3—62no—
311C4×Dic3—62no—
312C4×Dic3—61no—
313C4×Dic3—61no—
314C4×Dic3—121no—
315C4×Dic3D1211yescharacteristic
316C4×Dic3D1211yescharacteristic
317C4×Dic3C22×D311yescharacteristic
318C4×Dic3C22×D311yescharacteristic
319#208C4×D314yescomplemented
320C2×C3⋊C8C22×D312yes—
321Dic12—38no—
322#204—38no—
323C22×C32—21no—
324C22×C32—21no—
325C22×C32C4×D412yes—
326C22×C32C22×D411yescharacteristic
327C2×C3×D3—22no—
328C2×C3×D3—41no—
329C2×C3×D3—41no—
330C32×C4C4×D412yes—
331C32×C4C23×C411yescharacteristic
332C32×C4C2×#4111yescharacteristic
333C3⋊Dic3—24no—
334C3⋊Dic3—41no—
335C3⋊Dic3—41no—
336C3×Dic3—22no—
337C3×Dic3—21no—
338C3×Dic3—21no—
339C3×Dic3—21no—
340C3×Dic3—42no—
341C3×Dic3#13712yescomplemented
342C2×#41—31no—
343C22×Q8—91no—
344#137—98no—
345C2×Q16—92no—
346C2×SD16—92no—
347C2×M16—31no—
348C2×M16D3211yescharacteristic
349C4×Q8—92no—
350C4×Q8—92no—
351C4×Q8—91no—
352C4×Q8—91no—
353C4×Q8—181no—
354C4×Q8—181no—
355C4×D4—91no—
356C4×D4—91no—
357C4×D4—181no—
358C4×D4—181no—
359#117—91no—
360#117—181no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—181no—
363C2×C42—31no—
364C2×C42—181no—
365C2×C42—181no—
366#107—92no—
367#106—92no—
368#103—32no—
369#103—92no—
370#103—92no—
371#102—32no—
372#97—32no—
373C4×C8—32no—
374C23×C3—21no—
375C23×C3—61no—
376C23×C3C2×D1211yescharacteristic
377C23×C3D3×D411yescharacteristic
378C22×D3—21no—
379C3×Q8—32no—
380C3×Q8—61no—
381C3×D4—32no—
382C3×D4—64no—
383C3×D4—61no—
384C2×C3×C4—21no—
385C2×C3×C4—22no—
386C2×C3×C4—21no—
387C2×C3×C4—22no—
388C2×C3×C4—31no—
389C2×C3×C4—31no—
390C2×C3×C4—31no—
391C2×C3×C4—31no—
392C2×C3×C4—62no—
393C2×C3×C4—61no—
394C2×C3×C4—64no—
395C2×C3×C4—62no—
396C2×C3×C4—121no—
397C2×C3×C4—122no—
398C2×C3×C4C2×C4×D312yes—
399C2×C3×C4C2×C4×D312yes—
400C2×C3×C4C2×D1211yescharacteristic
401C2×C3×C4#23512yes—
402C2×C3×C4D3×D411yescharacteristic
403C2×C3×C4#23712yes—
404C2×C3×C4C23×D311yescharacteristic
405C2×C3×C4C23×D311yescharacteristic
406#67—24no—
407C2×Dic3—21no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—41no—
411C2×Dic3—42no—
412C2×Dic3—64no—
413C2×Dic3—64no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416C2×Dic3—61no—
417C2×Dic3—61no—
418C2×Dic3—61no—
419C2×Dic3—61no—
420C2×Dic3—122no—
421C2×Dic3—124no—
422C2×Dic3—121no—
423C2×Dic3—121no—
424C2×Dic3—122no—
425C2×Dic3—122no—
426C2×Dic3C2×D1211yescharacteristic
427C2×Dic3C2×D1211yescharacteristic
428C2×Dic3C2×D1211yescharacteristic
429C2×Dic3C2×D1211yescharacteristic
430D12—21no—
431D12C2×C4×D312yes—
432C4×D3—24no—
433C4×D3—122no—
434C4×D3—122no—
435Dic6—21no—
436Dic6—34no—
437Dic6—34no—
438Dic6—64no—
439Dic6—64no—
440Dic6—64no—
441Dic6—62no—
442Dic6—62no—
443Dic6—122no—
444Dic6—124no—
445Dic6C2×C4×D312yes—
446C3×C8—22no—
447C3×C8—22no—
448C3×C8—34no—
449C3×C8—42no—
450C3⋊C8C2×C4×D314yes—
451C2×C32—22no—
452C2×C32C2×C4×D411yescharacteristic
453C2×C32C2×#13711yescharacteristic
454C2×C32#57511yescharacteristic
455C3×D3—42no—
456#41—34no—
457#41—62no—
458C2×Q8—31no—
459C2×Q8—92no—
460C2×Q8—94no—
461C2×Q8—181no—
462C2×Q8—182no—
463C2×D4—31no—
464C2×D4—61no—
465C22×C4—31no—
466C22×C4—31no—
467C22×C4—61no—
468C22×C4—61no—
469C22×C4—181no—
470C22×C4—181no—
471C22×C4—181no—
472C22×C4C2×D3211yescharacteristic
473Q16—98no—
474SD16—98no—
475M16—22no—
476M16—34no—
477C2×C8—32no—
478C2×C8C2×D3212yes—
479C4⋊C4—32no—
480C4⋊C4—61no—
481C4⋊C4—91no—
482C4⋊C4—91no—
483C4⋊C4—182no—
484C4⋊C4—182no—
485C4⋊C4—181no—
486C4⋊C4—181no—
487C22⋊C4—181no—
488C22⋊C4—181no—
489C22⋊C4—181no—
490C42—31no—
491C42—31no—
492C42—31no—
493C42—31no—
494C42—181no—
495C42—181no—
496C42—182no—
497C42—182no—
498C42—181no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—22no—
505C22×C3—41no—
506C22×C3—41no—
507C22×C3—62no—
508C22×C3—121no—
509C22×C3—121no—
510C22×C3C4×D1212yes—
511C22×C3#67⋊C412yes—
512C22×C3C22×D1211yescharacteristic
513C22×C3C2×D3×D411yescharacteristic
514C2×D3—22no—
515C2×D3—41no—
516C2×D3—41no—
517C3×C4—21no—
518C3×C4—21no—
519C3×C4—22no—
520C3×C4—32no—
521C3×C4—62no—
522C3×C4—61no—
523C3×C4—61no—
524C3×C4—61no—
525C3×C4—122no—
526C3×C4C4×D1212yes—
527C3×C4#67⋊C412yes—
528C3×C4C22×C4×D311yescharacteristic
529C3×C4C22×C4×D311yescharacteristic
530C3×C4C2×#23511yescharacteristic
531C3×C4C2×#23711yescharacteristic
532Dic3—22no—
533Dic3—21no—
534Dic3—21no—
535Dic3—21no—
536Dic3—42no—
537Dic3—64no—
538Dic3—64no—
539Dic3—124no—
540Dic3—121no—
541Dic3—121no—
542Dic3—121no—
543Dic3—121no—
544Dic3—241no—
545Dic3—241no—
546Dic3#90912yescomplemented
547C32C4×#13711yescharacteristic, complemented, Sylow
548C23—61no—
549C23D3×D1211yescharacteristic
550Q8—32no—
551Q8—61no—
552Q8—94no—
553Q8—182no—
554Q8—184no—
555D4—32no—
556D4—64no—
557D4—61no—
558C2×C4—31no—
559C2×C4—31no—
560C2×C4—31no—
561C2×C4—31no—
562C2×C4—62no—
563C2×C4—61no—
564C2×C4—64no—
565C2×C4—62no—
566C2×C4—121no—
567C2×C4—122no—
568C2×C4—182no—
569C2×C4—184no—
570C2×C4—181no—
571C2×C4—181no—
572C2×C4—362no—
573C2×C4—362no—
574C2×C4C4×D3212yes—
575C2×C4D3×D1211yescharacteristic
576C2×C4#380412yes—
577C2×C4C22×D3211yescharacteristic
578C8—22no—
579C8—34no—
580C2×C3—22no—
581C2×C3—22no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—42no—
586C2×C3—122no—
587C2×C3C2×C4×D1211yescharacteristic
588C2×C3C2×#67⋊C411yescharacteristic
589C2×C3C2×#90911yescharacteristic
590C2×C3#574811yescharacteristic
591C2×C3#577311yescharacteristic
592C2×C3D3×#13711yescharacteristic
593D3—42no—
594C22—21no—
595C22—21no—
596C22—62no—
597C22—121no—
598C22—121no—
599C22#6388012yes—
600C22C2×D3×D1211yescharacteristic
601C4—32no—
602C4—62no—
603C4—61no—
604C4—61no—
605C4—61no—
606C4—122no—
607C4—184no—
608C4—361no—
609C4—361no—
610C4#6388012yes—
611C4C2×C4×D3211yescharacteristic
612C4C2×#380411yescharacteristic
613C3—21no—
614C3C4×#90911yescharacteristic, complemented
615C3#7886711yescharacteristic, complemented
616C2—22no—
617C2—122no—
618C2D3×#90911yescharacteristic
619C2#1059471211yescharacteristic
620C2C2×#6388011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32C4×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#63844C2semidirect
4. #10592819C2semidirect
6. C3×Dic3×M16C2semidirect
7. #10591130C2semidirect
8. #10590794C2semidirect
9. #10590793C2semidirect
10. #10590747C2semidirect
11. #10590744C2semidirect
36. #63831C4semidirect
59. Dic3×M16D3semidirect
73. C2×#634C2×C4semidirect
98. C3×#208C2×C4semidirect
110. #3719C2×C4semidirect
111. #3716C2×C4semidirect
319. #208C4×D3semidirect
341. C3×Dic3#137semidirect
546. Dic3#909semidirect
547. C32C4×#137semidirect
614. C3C4×#909semidirect
615. C3#78867semidirect

Maximal subgroups

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

subgroupindex
Dic3×#2352
C2×#638442
C2×#638312
#105928192
C3×#51332
C3×Dic3×M162
#105911302
#105907942
#105907932
#105907472
#105907442
#788673
C4×#9093