Finite Group Databasebeta

← #11860418

Subgroups — #11860418

Order 1152.

1049 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594954C211yesmaximal, characteristic
2C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
3C2×#63833C211yesmaximal, characteristic
4#10592832C211yesmaximal, characteristic
5C3×#5120C211yesmaximal, characteristic, complemented
6C3×Dic3×M16C211yesmaximal, characteristic, complemented
7#10591131C211yesmaximal, characteristic, complemented
8#10590795C212yesmaximal, complemented
9#10590794C212yesmaximal, complemented
10#10590793C212yesmaximal, complemented
11#10590792C212yesmaximal, complemented
12#78946—31nomaximal
13C4×#909—31nomaximal
14C2×#3828C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C2×C32×M16C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C2×Dic3⋊Dic3—21no—
22C2×Dic32—21no—
23#63952—21no—
24#63952—21no—
25#63894C2211yescharacteristic
26#63894C2211yescharacteristic
27C4×#624—21no—
28#63874—21no—
29#63844C2211yescharacteristic
30#63844C2211yescharacteristic
31Dic3×Dic6—21no—
32Dic3×Dic6—21no—
33Dic3×Dic6C2212yes—
34Dic3×Dic6C2212yes—
35C2×#3719C2212yes—
36#63833C418yescomplemented
37C2×#3717C2212yes—
38#63648C2212yes—
39#63643C2212yes—
40C3×#816C2212yes—
41C3×#816C2212yes—
42C3×#815C2212yes—
43C3×C8×Dic3C2212yes—
44#63575C2212yes—
45#63573C2212yes—
46C2×Q8×Dic3—31no—
47C2×#942—31no—
48C2×#909—31no—
49#5522—31no—
50C4×#235—31no—
51C2×C4×Dic6—31no—
52C3×#419—31no—
53C3×C4×M16—31no—
54#5133—31no—
55#5133—31no—
56#5133—61no—
57#5121—31no—
58#5120D311yescharacteristic, complemented
59Dic3×M16D311yescharacteristic, complemented
60#4995—31no—
61#4817—32no—
62#4790—32no—
63#4789—32no—
64#4788—32no—
65#4716—32no—
66#4710—32no—
67C4×Dic12—32no—
68C4×#204—32no—
69C22×C32×C4C2311yescharacteristic
70C2×#638—21no—
71C22×C3⋊Dic3—21no—
72#3828—22no—
73#3828C2×C414yes—
74C2×C4⋊(C3⋊D3)C2311yescharacteristic
75C2×C4×C3⋊D3—21no—
76C2×#634C2311yescharacteristic
77C22×C3×Dic3—21no—
78C22×C3×Dic3D411yescharacteristic
79C22×C3×Dic3D411yescharacteristic
80C2×C3×Dic6—21no—
81C2×C3×Dic6—22no—
82C2×C3×Dic6C2×C414yescomplemented
83C2×C3×Dic6C2312yes—
84C2×#624—21no—
85C2×#624—21no—
86C32×M16—22no—
87C2×C32×C8C2312yes—
88C4⋊(C3⋊Dic3)—21no—
89C4⋊(C3⋊Dic3)C2312yes—
90C3×#217—21no—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4⋊Dic3C2311yescharacteristic
93C3×C4×Dic3—21no—
94C3×C4×Dic3D411yescharacteristic
95C3×C4×Dic3D411yescharacteristic
96C3×C4×Dic3C2311yescharacteristic
97C3×C4×Dic3C2311yescharacteristic
98C3×#208C2×C414yescomplemented
99C2×C3×C3⋊C8C2312yes—
100#3724—21no—
101#3724—21no—
102Dic3⋊Dic3—22no—
103Dic3⋊Dic3—22no—
104#3722—21no—
105#3722—21no—
106Dic32—22no—
107Dic32—22no—
108Dic32—21no—
109Dic32—21no—
110#3719C2×C418yescomplemented
111#3717C2×C418yescomplemented
112C4×#137—91noSylow
113C22×C3×Q8—31no—
114C2×#235—31no—
115C2×#235—31no—
116C2×#235—61no—
117C22×Dic6C2×D311yescharacteristic
118C2×C3×M16—21no—
119C2×C3×M16—31no—
120C2×C3×M16C2×D311yescharacteristic
121C2×C3×M16C2×D311yescharacteristic
122C3×#117—31no—
123C2×C3×C42—31no—
124Q8×Dic3—32no—
125Q8×Dic3—32no—
126Q8×Dic3—61no—
127Q8×Dic3—61no—
128C2×#216—32no—
129#942—38no—
130C2×#215—32no—
131C4×#67—61no—
132C4×#67—61no—
133#926C2×D311yescharacteristic
134C2×C4⋊Dic3—31no—
135C2×C4⋊Dic3—31no—
136C2×C4⋊Dic3—61no—
137C2×C4⋊Dic3—61no—
138C2×Dic3⋊C4—61no—
139C2×C4×Dic3—61no—
140C2×C4×Dic3—61no—
141C2×C4×Dic3C2×D311yescharacteristic
142C2×#208C2×D311yescharacteristic
143#909—38no—
144C2×Dic12—32no—
145C2×#204—32no—
146#893—31no—
147#893—31no—
148#887—31no—
149#887—31no—
150#67⋊C4—61no—
151#67⋊C4—61no—
152C4×D12—31no—
153C4×D12—31no—
154#872—61no—
155#872—61no—
156C42×D3—61no—
157C42×D3—61no—
158C4×Dic6—32no—
159C4×Dic6—32no—
160C4×Dic6—31no—
161C4×Dic6—31no—
162C4×Dic6—61no—
163C4×Dic6—61no—
164C3×#103—32no—
165C3×#103—32no—
166C3×#97—32no—
167C3×C4×C8—32no—
168#821—32no—
169#821—32no—
170#821—62no—
171#818—32no—
172#817—32no—
173#816—32no—
174#816—32no—
175#816—62no—
176#816C2×D312yes—
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
188#638—24no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—22no—
191C2×C3⋊Dic3—42no—
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—21no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—41no—
203C2×C3×Dic3C2×D411yescharacteristic
204C2×C3×Dic3C2×D411yescharacteristic
205C2×C3×Dic3C2×D411yescharacteristic
206C2×C3×Dic3C2×D411yescharacteristic
207C3×Dic6—24no—
208C3×Dic6—22no—
209C3×Dic6C22×C414yes—
210#624—42no—
211#624—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—31no—
223#417—91no—
224C4×M16—31no—
225C2×C3×Q8—34no—
226C2×C3×Q8—32no—
227C2×C3×Q8—61no—
228C2×C3×Q8—62no—
229C22×C3×C4—21no—
230C22×C3×C4—31no—
231C22×C3×C4—31no—
232C22×C3×C4—61no—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C2×#67—61no—
236C2×#67—61no—
237C2×#67—121no—
238C22×Dic3—21no—
239C22×Dic3—61no—
240C22×Dic3—61no—
241C22×Dic3—121no—
242C22×Dic3D1211yescharacteristic
243C22×Dic3D1211yescharacteristic
244#235—34no—
245#235—34no—
246#235—64no—
247#235—62no—
248#235—62no—
249#235—122no—
250C2×D12—31no—
251C2×D12—31no—
252C2×D12—61no—
253C2×C4×D3—61no—
254C2×C4×D3—61no—
255C2×C4×D3—61no—
256C2×C4×D3—61no—
257C2×C4×D3—61no—
258C2×C4×D3—61no—
259C2×C4×D3—121no—
260C2×Dic6—21no—
261C2×Dic6—22no—
262C2×Dic6—31no—
263C2×Dic6—31no—
264C2×Dic6—61no—
265C2×Dic6C4×D314yescomplemented
266C2×Dic6C22×D312yes—
267C3×M16—22no—
268C3×M16—22no—
269C3×M16—34no—
270C3×M16—42no—
271C2×C3×C8—22no—
272C2×C3×C8—32no—
273C2×C3×C8C22×D312yes—
274C2×C3×C8C22×D312yes—
275C3×C4⋊C4—31no—
276C3×C4⋊C4—31no—
277C3×C22⋊C4—61no—
278C3×C42—31no—
279C3×C42—31no—
280C3×C42—31no—
281C3×C42—31no—
282C3×C42—61no—
283#217—21no—
284#216—38no—
285#215—38no—
286(C2×D3)⋊C4—61no—
287(C2×D3)⋊C4—61no—
288(C2×D3)⋊C4—61no—
289(C2×D3)⋊C4—61no—
290C4⋊Dic3—32no—
291C4⋊Dic3—32no—
292C4⋊Dic3—62no—
293C4⋊Dic3—61no—
294C4⋊Dic3—61no—
295C4⋊Dic3—62no—
296C4⋊Dic3—62no—
297C4⋊Dic3—121no—
298C4⋊Dic3C22×D311yescharacteristic
299C4⋊Dic3C22×D311yescharacteristic
300Dic3⋊C4—62no—
301Dic3⋊C4—62no—
302Dic3⋊C4—61no—
303Dic3⋊C4—61no—
304Dic3⋊C4—61no—
305Dic3⋊C4—61no—
306C4×Dic3—21no—
307C4×Dic3—62no—
308C4×Dic3—62no—
309C4×Dic3—61no—
310C4×Dic3—61no—
311C4×Dic3—61no—
312C4×Dic3—61no—
313C4×Dic3—62no—
314C4×Dic3—62no—
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—22no—
334C3⋊Dic3—42no—
335C3×Dic3—24no—
336C3×Dic3—21no—
337C3×Dic3—21no—
338C3×Dic3—21no—
339C3×Dic3—41no—
340C3×Dic3—41no—
341C3×Dic3#13712yescomplemented
342C2×#41—91no—
343C22×Q8—31no—
344#137—98no—
345C2×Q16—92no—
346C2×SD16—92no—
347C2×M16—31no—
348C2×M16D3211yescharacteristic
349C4×Q8—91no—
350C4×Q8—91no—
351C4×Q8—92no—
352C4×Q8—92no—
353C4×Q8—181no—
354C4×Q8—181no—
355C4×D4—91no—
356C4×D4—91no—
357C4×D4—181no—
358C4×D4—181no—
359#117—31no—
360#117—181no—
361C2×C4⋊C4—91no—
362C2×C4⋊C4—181no—
363C2×C42—31no—
364C2×C42—181no—
365C2×C42—181no—
366#107—92no—
367#106—92no—
368#103—32no—
369#103—32no—
370#103—92no—
371#102—92no—
372#97—32no—
373C4×C8—32no—
374C23×C3—21no—
375C23×C3C2×D1211yescharacteristic
376C23×C3D3×D411yescharacteristic
377C22×D3—61no—
378C22×D3—61no—
379C22×D3—121no—
380C3×Q8—34no—
381C3×Q8—64no—
382C3×Q8—62no—
383C2×C3×C4—21no—
384C2×C3×C4—22no—
385C2×C3×C4—21no—
386C2×C3×C4—22no—
387C2×C3×C4—31no—
388C2×C3×C4—31no—
389C2×C3×C4—31no—
390C2×C3×C4—31no—
391C2×C3×C4—62no—
392C2×C3×C4—64no—
393C2×C3×C4—62no—
394C2×C3×C4—61no—
395C2×C3×C4—61no—
396C2×C3×C4—121no—
397C2×C3×C4C2×C4×D312yes—
398C2×C3×C4C2×C4×D312yes—
399C2×C3×C4C2×D1211yescharacteristic
400C2×C3×C4#23512yes—
401C2×C3×C4D3×D411yescharacteristic
402C2×C3×C4#23712yes—
403C2×C3×C4C23×D311yescharacteristic
404C2×C3×C4C23×D311yescharacteristic
405#67—64no—
406#67—64no—
407#67—124no—
408C2×Dic3—24no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—21no—
412C2×Dic3—21no—
413C2×Dic3—41no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—121no—
419C2×Dic3—122no—
420C2×Dic3—122no—
421C2×Dic3—122no—
422C2×Dic3—242no—
423C2×Dic3C2×D1211yescharacteristic
424C2×Dic3C2×D1211yescharacteristic
425C2×Dic3C2×D1211yescharacteristic
426C2×Dic3C2×D1211yescharacteristic
427D12—32no—
428D12—32no—
429D12—62no—
430D12—61no—
431D12—61no—
432D12—121no—
433C4×D3—64no—
434C4×D3—64no—
435C4×D3—124no—
436C4×D3—122no—
437C4×D3—122no—
438C4×D3—122no—
439C4×D3—122no—
440Dic6—24no—
441Dic6—22no—
442Dic6—32no—
443Dic6—32no—
444Dic6—62no—
445Dic6—61no—
446Dic6—61no—
447Dic6—121no—
448Dic6C2×C4×D314yes—
449C3×C8—22no—
450C3×C8—22no—
451C3×C8—34no—
452C3×C8—42no—
453C3⋊C8C2×C4×D314yes—
454C2×C32—22no—
455C2×C32C2×C4×D411yescharacteristic
456C2×C32C2×#13711yescharacteristic
457C2×C32#57511yescharacteristic
458C3⋊D3—42no—
459#41—94no—
460#41—182no—
461C2×Q8—32no—
462C2×Q8—34no—
463C2×Q8—61no—
464C2×Q8—62no—
465C2×Q8—91no—
466C2×D4—91no—
467C2×D4—181no—
468C22×C4—31no—
469C22×C4—31no—
470C22×C4—61no—
471C22×C4—181no—
472C22×C4—181no—
473C22×C4—181no—
474C22×C4—181no—
475C22×C4C2×D3211yescharacteristic
476Q16—98no—
477SD16—98no—
478M16—22no—
479M16—34no—
480C2×C8—32no—
481C2×C8C2×D3212yes—
482C4⋊C4—31no—
483C4⋊C4—31no—
484C4⋊C4—92no—
485C4⋊C4—182no—
486C4⋊C4—182no—
487C4⋊C4—181no—
488C4⋊C4—181no—
489C4⋊C4—181no—
490C22⋊C4—61no—
491C22⋊C4—181no—
492C22⋊C4—181no—
493C42—31no—
494C42—31no—
495C42—31no—
496C42—31no—
497C42—61no—
498C42—181no—
499C42—181no—
500C42—182no—
501C42—182no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—22no—
508C22×C3—41no—
509C22×C3—41no—
510C22×C3C4×D1212yes—
511C22×C3#67⋊C412yes—
512C22×C3C22×D1211yescharacteristic
513C22×C3C2×D3×D411yescharacteristic
514C2×D3—62no—
515C2×D3—62no—
516C2×D3—122no—
517C2×D3—121no—
518C2×D3—121no—
519C2×D3—121no—
520C2×D3—121no—
521C2×D3—241no—
522C2×D3—241no—
523C3×C4—21no—
524C3×C4—21no—
525C3×C4—22no—
526C3×C4—32no—
527C3×C4—64no—
528C3×C4—61no—
529C3×C4—61no—
530C3×C4—61no—
531C3×C4—121no—
532C3×C4—121no—
533C3×C4C4×D1212yes—
534C3×C4#67⋊C412yes—
535C3×C4C22×C4×D311yescharacteristic
536C3×C4C22×C4×D311yescharacteristic
537C3×C4C2×#23511yescharacteristic
538C3×C4C2×#23711yescharacteristic
539Dic3—24no—
540Dic3—21no—
541Dic3—21no—
542Dic3—21no—
543Dic3—41no—
544Dic3—41no—
545Dic3—62no—
546Dic3—62no—
547Dic3—122no—
548Dic3—122no—
549Dic3—122no—
550Dic3—242no—
551Dic3#90912yescomplemented
552C32C4×#13711yescharacteristic, complemented, Sylow
553C23—181no—
554C23D3×D1211yescharacteristic
555Q8—34no—
556Q8—62no—
557Q8—64no—
558Q8—92no—
559Q8—181no—
560D4—92no—
561D4—184no—
562D4—181no—
563C2×C4—31no—
564C2×C4—31no—
565C2×C4—31no—
566C2×C4—31no—
567C2×C4—62no—
568C2×C4—62no—
569C2×C4—64no—
570C2×C4—61no—
571C2×C4—61no—
572C2×C4—121no—
573C2×C4—181no—
574C2×C4—184no—
575C2×C4—182no—
576C2×C4—362no—
577C2×C4—362no—
578C2×C4—362no—
579C2×C4C4×D3212yes—
580C2×C4D3×D1211yescharacteristic
581C2×C4#380412yes—
582C2×C4C22×D3211yescharacteristic
583C8—22no—
584C8—34no—
585C2×C3—22no—
586C2×C3—22no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—42no—
591C2×C3C2×C4×D1211yescharacteristic
592C2×C3C2×#67⋊C411yescharacteristic
593C2×C3C2×#90911yescharacteristic
594C2×C3#574811yescharacteristic
595C2×C3D3×#13711yescharacteristic
596C2×C3#577711yescharacteristic
597D3—122no—
598D3—122no—
599D3—242no—
600C22—21no—
601C22—21no—
602C22—182no—
603C22—361no—
604C22—361no—
605C22#6388012yes—
606C22C2×D3×D1211yescharacteristic
607C4—32no—
608C4—64no—
609C4—61no—
610C4—61no—
611C4—61no—
612C4—121no—
613C4—121no—
614C4—182no—
615C4—362no—
616C4#6388012yes—
617C4C2×C4×D3211yescharacteristic
618C4C2×#380411yescharacteristic
619C3—21no—
620C3C4×#90911yescharacteristic, complemented
621C3#7894611yescharacteristic, complemented
622C2—22no—
623C2—362no—
624C2D3×#90911yescharacteristic
625C2#1059471111yescharacteristic
626C2C2×#6388011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC2×#3828C22
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×Dic3×Dic6C2semidirect
5. C3×#5120C2semidirect
6. C3×Dic3×M16C2semidirect
7. #10591131C2semidirect
8. #10590795C2semidirect
9. #10590794C2semidirect
10. #10590793C2semidirect
11. #10590792C2semidirect
36. #63833C4semidirect
58. #5120D3semidirect
59. Dic3×M16D3semidirect
82. C2×C3×Dic6C2×C4semidirect
98. C3×#208C2×C4semidirect
110. #3719C2×C4semidirect
111. #3717C2×C4semidirect
265. C2×Dic6C4×D3semidirect
319. #208C4×D3semidirect
341. C3×Dic3#137semidirect
551. Dic3#909semidirect
552. C32C4×#137semidirect
620. C3C4×#909semidirect
621. C3#78946semidirect

Maximal subgroups

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

subgroupindex
#105949542
C2×Dic3×Dic62
C2×#638332
#105928322
C3×#51202
C3×Dic3×M162
#105911312
#105907952
#105907942
#105907932
#105907922
#789463
C4×#9093