Finite Group Databasebeta

← #11860417

Subgroups — #11860417

Order 1152.

1039 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
1#10594958C211yesmaximal, characteristic
2C2×#63843C211yesmaximal, characteristic, complemented
3C2×#63827C211yesmaximal, characteristic
4M16×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C3×#5133C211yesmaximal, characteristic
6C3×#5120C211yesmaximal, characteristic, complemented
7#10591139C211yesmaximal, characteristic, complemented
8#10590791C212yesmaximal, complemented
9#10590790C212yesmaximal, complemented
10#10590743C212yesmaximal, complemented
11#10590742C212yesmaximal, complemented
12#78946—31nomaximal
13#78867—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C2×C32×M16C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×#3748C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21#67⋊Dic3—21no—
22#67⋊Dic3—21no—
23C2×Dic3⋊Dic3—21no—
24C2×Dic32—21no—
25#63898C2211yescharacteristic
26#63898C2211yescharacteristic
27C4×D3×Dic3—21no—
28#63855—21no—
29#63843—21no—
30#63843—21no—
31#63843C2212yes—
32#63843C2212yes—
33#63843C2211yescharacteristic
34#63843C2211yescharacteristic
35C2×#3718C2212yes—
36#63827C418yescomplemented
37C2×#3715C2212yes—
38#63642C2212yes—
39C8×C3⋊Dic3C2212yes—
40C3×#821C2212yes—
41C3×#816C2212yes—
42C3×#816C2212yes—
43C3×#816C2212yes—
44#63576C2212yes—
45#63574C2212yes—
46Dic3×#41—31no—
47C2×#951—31no—
48C2×Q8×Dic3—31no—
49C2×#942—31no—
50#5522—31no—
51C2×#887—31no—
52C3×#419—31no—
53C3×#417—31no—
54#5133D311yescharacteristic
55#5120D311yescharacteristic, complemented
56Dic3×M16—31no—
57Dic3×M16—31no—
58Dic3×M16—61no—
59#4995—31no—
60#4964—31no—
61#4817—32no—
62#4790—32no—
63#4790—32no—
64#4789—32no—
65#4789—32no—
66#4788—32no—
67#4758—32no—
68#4757—32no—
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3D411yescharacteristic
71C22×C3⋊Dic3D411yescharacteristic
72C2×C3×#67—21no—
73C22×C3×Dic3—21no—
74C22×C3×Dic3—21no—
75C3×#235—22no—
76C3×#235C2×C414yes—
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×Dic6—21no—
80C2×C3×Dic6—22no—
81C2×C3×Dic6C2×C414yescomplemented
82C2×C3×Dic6C2312yes—
83C2×C3×Dic6C2311yescharacteristic
84C2×D3×Dic3—21no—
85C2×D3×Dic3—21no—
86C32×M16—22no—
87C2×C32×C8C2312yes—
88C4×C3⋊Dic3D411yescharacteristic
89C4×C3⋊Dic3D411yescharacteristic
90C4×C3⋊Dic3C2311yescharacteristic
91C4×C3⋊Dic3C2311yescharacteristic
92#3748C2×C414yescomplemented
93C2×C3⋊(C3⋊C8)C2312yes—
94C3×#217—21no—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3C2312yes—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×C4⋊Dic3C2311yescharacteristic
99C3×C4×Dic3—21no—
100Dic3⋊Dic3—22no—
101Dic3⋊Dic3—22no—
102Dic3⋊Dic3—21no—
103Dic3⋊Dic3—21no—
104(C2×D3)⋊Dic3—21no—
105(C2×D3)⋊Dic3—21no—
106Dic32—22no—
107Dic32—22no—
108Dic32—21no—
109Dic32—21no—
110#3718C2×C418yescomplemented
111#3715C2×C418yescomplemented
112C4×#137—91noSylow
113C2×C3×#41—31no—
114C22×C3×Q8—31no—
115C2×#235C2×D311yescharacteristic
116C22×Dic6C2×D311yescharacteristic
117C2×C3×M16—21no—
118C2×C3×M16C2×D311yescharacteristic
119C2×C3×M16C2×D311yescharacteristic
120C3×#117—31no—
121C2×C3×C4⋊C4—31no—
122#951—38no—
123Q8×Dic3—32no—
124Q8×Dic3—32no—
125Q8×Dic3—31no—
126Q8×Dic3—31no—
127Q8×Dic3—61no—
128Q8×Dic3—61no—
129C2×#216—32no—
130C2×#216—32no—
131#942—38no—
132C2×#215—32no—
133D4×Dic3—31no—
134D4×Dic3—31no—
135D4×Dic3—61no—
136D4×Dic3—61no—
137C2×#214—32no—
138#926—61no—
139#926C2×D311yescharacteristic
140C2×C4⋊Dic3—61no—
141C2×C4⋊Dic3C2×D311yescharacteristic
142C2×Dic3⋊C4—61no—
143C2×C4×Dic3—31no—
144C2×C4×Dic3—31no—
145C2×C4×Dic3—61no—
146C2×C4×Dic3—61no—
147C2×C4×Dic3—61no—
148C2×C4×Dic3—61no—
149C2×#208—31no—
150C2×#208—31no—
151C2×#208—61no—
152#893—31no—
153#893—31no—
154#887—32no—
155#887—32no—
156#887—31no—
157#887—31no—
158#887—61no—
159#887—61no—
160#67⋊C4—61no—
161#67⋊C4—61no—
162#872—61no—
163C42×D3—61no—
164C3×#103—32no—
165C3×#103—32no—
166C3×#103—32no—
167C3×#102—32no—
168#821C2×D312yes—
169#816C2×D312yes—
170#816C2×D312yes—
171#816C2×D312yes—
172#815—32no—
173#815—32no—
174#815—62no—
175C8×Dic3—32no—
176C8×Dic3—32no—
177C8×Dic3—62no—
178#808—32no—
179#808—32no—
180#807—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—22no—
189C2×C3⋊Dic3—41no—
190C2×C3⋊Dic3C2×D411yescharacteristic
191C2×C3⋊Dic3C2×D411yescharacteristic
192C2×C3⋊Dic3C2×D411yescharacteristic
193C2×C3⋊Dic3C2×D411yescharacteristic
194C3×#67—24no—
195C2×C3×Dic3—24no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3—42no—
202C3×D12—21no—
203C3×D12C22×C412yes—
204C3×C4×D3—24no—
205C3×Dic6—24no—
206C3×Dic6—22no—
207C3×Dic6—21no—
208C3×Dic6C22×C414yes—
209C3×Dic6C22×C412yes—
210D3×Dic3—42no—
211D3×Dic3—42no—
212C32×C8—22no—
213C3⋊(C3⋊C8)C22×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—31no—
224C4×M16—91no—
225C3×#41—34no—
226C3×#41—62no—
227C2×C3×Q8—34no—
228C2×C3×Q8—32no—
229C2×C3×Q8—31no—
230C2×C3×Q8—61no—
231C2×C3×Q8—62no—
232C2×C3×D4—31no—
233C2×C3×D4—61no—
234C22×C3×C4—21no—
235C22×C3×C4—61no—
236C22×C3×C4—61no—
237C22×C3×C4—61no—
238C22×C3×C4C22×D311yescharacteristic
239C22×C3×C4C22×D311yescharacteristic
240C2×#67—21no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3—31no—
244C22×Dic3—31no—
245C22×Dic3—31no—
246C22×Dic3—31no—
247C22×Dic3—61no—
248C22×Dic3—61no—
249C22×Dic3—61no—
250C22×Dic3—61no—
251#235—22no—
252#235C4×D314yes—
253C2×D12C22×D311yescharacteristic
254C2×C4×D3—21no—
255C2×C4×D3—61no—
256C2×C4×D3—61no—
257C2×Dic6—21no—
258C2×Dic6—22no—
259C2×Dic6C4×D314yescomplemented
260C2×Dic6C22×D312yes—
261C2×Dic6C22×D311yescharacteristic
262C3×M16—24no—
263C3×M16—22no—
264C3×M16—22no—
265C2×C3×C8—22no—
266C2×C3×C8C22×D312yes—
267C2×C3×C8C22×D312yes—
268C3×C4⋊C4—31no—
269C3×C4⋊C4—32no—
270C3×C4⋊C4—31no—
271C3×C4⋊C4—61no—
272C3×C22⋊C4—61no—
273C3×C42—61no—
274#217—21no—
275#217—61no—
276#217—61no—
277#216—38no—
278#216—38no—
279#215—38no—
280#214—38no—
281(C2×D3)⋊C4—61no—
282(C2×D3)⋊C4—61no—
283C4⋊Dic3—21no—
284C4⋊Dic3—62no—
285C4⋊Dic3—62no—
286C4⋊Dic3—61no—
287C4⋊Dic3—61no—
288C4⋊Dic3C22×D311yescharacteristic
289C4⋊Dic3C22×D312yes—
290C4⋊Dic3C22×D311yescharacteristic
291Dic3⋊C4—61no—
292Dic3⋊C4—61no—
293Dic3⋊C4—62no—
294Dic3⋊C4—62no—
295C4×Dic3—21no—
296C4×Dic3—31no—
297C4×Dic3—31no—
298C4×Dic3—31no—
299C4×Dic3—31no—
300C4×Dic3—31no—
301C4×Dic3—31no—
302C4×Dic3—31no—
303C4×Dic3—31no—
304C4×Dic3—61no—
305C4×Dic3—61no—
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—62no—
315C4×Dic3—62no—
316#208—34no—
317#208—34no—
318#208—64no—
319C2×C3⋊C8—32no—
320C2×C3⋊C8—32no—
321C2×C3⋊C8—62no—
322C22×C32—21no—
323C22×C32—21no—
324C22×C32C4×D412yes—
325C22×C32C22×D411yescharacteristic
326C2×C3×D3—22no—
327C2×C3×D3—41no—
328C2×C3×D3—41no—
329C32×C4C4×D412yes—
330C32×C4C23×C411yescharacteristic
331C32×C4C2×#4111yescharacteristic
332C3⋊Dic3—21no—
333C3⋊Dic3—21no—
334C3⋊Dic3—21no—
335C3⋊Dic3#13712yescomplemented
336C3×Dic3—24no—
337C3×Dic3—22no—
338C3×Dic3—41no—
339C3×Dic3—41no—
340C3×Dic3—42no—
341C2×#41—31no—
342C22×Q8—31no—
343#137—98no—
344C2×Q16—92no—
345C2×SD16—92no—
346C2×M16—91no—
347C2×M16D3211yescharacteristic
348C4×Q8—92no—
349C4×Q8—92no—
350C4×Q8—91no—
351C4×Q8—91no—
352C4×Q8—181no—
353C4×Q8—181no—
354C4×D4—91no—
355C4×D4—91no—
356C4×D4—181no—
357C4×D4—181no—
358#117—31no—
359#117—181no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—181no—
362C2×C42—91no—
363C2×C42—181no—
364C2×C42—181no—
365#107—92no—
366#106—92no—
367#103—32no—
368#103—32no—
369#103—32no—
370#102—32no—
371#97—92no—
372C4×C8—92no—
373C23×C3—21no—
374C23×C3—61no—
375C23×C3D3×D411yescharacteristic
376C23×C3D3×D411yescharacteristic
377C22×D3—21no—
378C3×Q8—34no—
379C3×Q8—32no—
380C3×Q8—64no—
381C3×Q8—62no—
382C3×Q8—61no—
383C3×D4—32no—
384C3×D4—64no—
385C3×D4—61no—
386C2×C3×C4—21no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—22no—
390C2×C3×C4—64no—
391C2×C3×C4—61no—
392C2×C3×C4—62no—
393C2×C3×C4—64no—
394C2×C3×C4—62no—
395C2×C3×C4—61no—
396C2×C3×C4—61no—
397C2×C3×C4—122no—
398C2×C3×C4C2×C4×D312yes—
399C2×C3×C4C2×C4×D312yes—
400C2×C3×C4D3×D411yescharacteristic
401C2×C3×C4D3×D411yescharacteristic
402C2×C3×C4#23712yes—
403C2×C3×C4#23712yes—
404C2×C3×C4C23×D311yescharacteristic
405C2×C3×C4C23×D311yescharacteristic
406#67—24no—
407C2×Dic3—24no—
408C2×Dic3—22no—
409C2×Dic3—21no—
410C2×Dic3—21no—
411C2×Dic3—21no—
412C2×Dic3—22no—
413C2×Dic3—31no—
414C2×Dic3—31no—
415C2×Dic3—31no—
416C2×Dic3—31no—
417C2×Dic3—31no—
418C2×Dic3—31no—
419C2×Dic3—31no—
420C2×Dic3—31no—
421C2×Dic3—42no—
422C2×Dic3—61no—
423C2×Dic3—61no—
424C2×Dic3—61no—
425C2×Dic3—61no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—122no—
429C2×Dic3—122no—
430C2×Dic3—122no—
431C2×Dic3—121no—
432C2×Dic3—121no—
433C2×Dic3—122no—
434D12—21no—
435D12C2×C4×D312yes—
436C4×D3—24no—
437C4×D3—122no—
438C4×D3—122no—
439Dic6—24no—
440Dic6—22no—
441Dic6—21no—
442Dic6C2×C4×D314yes—
443Dic6C2×C4×D312yes—
444C3×C8—24no—
445C3×C8—22no—
446C3×C8—22no—
447C3⋊C8—34no—
448C3⋊C8—34no—
449C3⋊C8—64no—
450C2×C32—22no—
451C2×C32C2×C4×D411yescharacteristic
452C2×C32C2×#13711yescharacteristic
453C2×C32#57511yescharacteristic
454C3×D3—42no—
455#41—34no—
456#41—62no—
457C2×Q8—32no—
458C2×Q8—31no—
459C2×Q8—34no—
460C2×Q8—61no—
461C2×Q8—62no—
462C2×D4—31no—
463C2×D4—61no—
464C22×C4—61no—
465C22×C4—61no—
466C22×C4—61no—
467C22×C4—91no—
468C22×C4—91no—
469C22×C4—181no—
470C22×C4—181no—
471C22×C4C2×D3211yescharacteristic
472Q16—98no—
473SD16—98no—
474M16—22no—
475M16—94no—
476C2×C8—92no—
477C2×C8C2×D3212yes—
478C4⋊C4—32no—
479C4⋊C4—31no—
480C4⋊C4—31no—
481C4⋊C4—61no—
482C4⋊C4—182no—
483C4⋊C4—182no—
484C4⋊C4—181no—
485C4⋊C4—181no—
486C22⋊C4—61no—
487C22⋊C4—181no—
488C22⋊C4—181no—
489C42—61no—
490C42—91no—
491C42—91no—
492C42—91no—
493C42—91no—
494C42—181no—
495C42—181no—
496C42—182no—
497C42—182no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—22no—
504C22×C3—41no—
505C22×C3—41no—
506C22×C3—62no—
507C22×C3—121no—
508C22×C3—121no—
509C22×C3#67⋊C412yes—
510C22×C3#67⋊C412yes—
511C22×C3C2×D3×D411yescharacteristic
512C22×C3C2×D3×D411yescharacteristic
513C2×D3—22no—
514C2×D3—41no—
515C2×D3—41no—
516C3×C4—21no—
517C3×C4—21no—
518C3×C4—22no—
519C3×C4—62no—
520C3×C4—64no—
521C3×C4—121no—
522C3×C4—121no—
523C3×C4—122no—
524C3×C4#67⋊C412yes—
525C3×C4#67⋊C412yes—
526C3×C4C22×C4×D311yescharacteristic
527C3×C4C22×C4×D311yescharacteristic
528C3×C4C2×#23711yescharacteristic
529C3×C4C2×#23711yescharacteristic
530Dic3—24no—
531Dic3—22no—
532Dic3—32no—
533Dic3—32no—
534Dic3—42no—
535Dic3—41no—
536Dic3—41no—
537Dic3—62no—
538Dic3—62no—
539Dic3—61no—
540Dic3—61no—
541Dic3—61no—
542Dic3—61no—
543Dic3—61no—
544Dic3—61no—
545Dic3—121no—
546Dic3—121no—
547C32C4×#13711yescharacteristic, complemented, Sylow
548C23—61no—
549C23#380211yescharacteristic
550Q8—34no—
551Q8—32no—
552Q8—62no—
553Q8—61no—
554Q8—64no—
555D4—32no—
556D4—64no—
557D4—61no—
558C2×C4—61no—
559C2×C4—62no—
560C2×C4—64no—
561C2×C4—64no—
562C2×C4—61no—
563C2×C4—61no—
564C2×C4—62no—
565C2×C4—91no—
566C2×C4—91no—
567C2×C4—91no—
568C2×C4—91no—
569C2×C4—122no—
570C2×C4—182no—
571C2×C4—362no—
572C2×C4—362no—
573C2×C4—361no—
574C2×C4C4×D3212yes—
575C2×C4#380211yescharacteristic
576C2×C4#380512yes—
577C2×C4C22×D3211yescharacteristic
578C8—22no—
579C8—94no—
580C2×C3—22no—
581C2×C3—22no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—42no—
586C2×C3—122no—
587C2×C3C2×#67⋊C411yescharacteristic
588C2×C3C2×#67⋊C411yescharacteristic
589C2×C3#577311yescharacteristic
590C2×C3D3×#13711yescharacteristic
591C2×C3D3×#13711yescharacteristic
592C2×C3#577711yescharacteristic
593D3—42no—
594C22—21no—
595C22—21no—
596C22—62no—
597C22—121no—
598C22—121no—
599C22#6390212yes—
600C22C2×#380211yescharacteristic
601C4—62no—
602C4—64no—
603C4—92no—
604C4—121no—
605C4—122no—
606C4—121no—
607C4—181no—
608C4—181no—
609C4—181no—
610C4#6390212yes—
611C4C2×C4×D3211yescharacteristic
612C4C2×#380511yescharacteristic
613C3—21no—
614C3#7886711yescharacteristic, complemented
615C3#7894611yescharacteristic, complemented
616C2—22no—
617C2—122no—
618C2#1059471711yescharacteristic
619C2#1059471811yescharacteristic
620C2C2×#6390211yescharacteristic
subgroupG/H
centerC22C2×#3802
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×#63843C2semidirect
4. M16×C3⋊Dic3C2semidirect
6. C3×#5120C2semidirect
7. #10591139C2semidirect
8. #10590791C2semidirect
9. #10590790C2semidirect
10. #10590743C2semidirect
11. #10590742C2semidirect
36. #63827C4semidirect
55. #5120D3semidirect
81. C2×C3×Dic6C2×C4semidirect
92. #3748C2×C4semidirect
110. #3718C2×C4semidirect
111. #3715C2×C4semidirect
259. C2×Dic6C4×D3semidirect
335. C3⋊Dic3#137semidirect
547. C32C4×#137semidirect
614. C3#78867semidirect
615. C3#78946semidirect

Maximal subgroups

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

subgroupindex
#105949582
C2×#638432
C2×#638272
M16×C3⋊Dic32
C3×#51332
C3×#51202
#105911392
#105907912
#105907902
#105907432
#105907422
#789463
#788673