Finite Group Databasebeta

← #11860423

Subgroups — #11860423

Order 1152.

1117 conjugacy classes of subgroups.

The subgroup lattice has 641 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic, complemented
2#10594958C211yesmaximal, characteristic
3C2×#63831C211yesmaximal, characteristic
4C3×#4966C211yesmaximal, characteristic
5C3×#4964C211yesmaximal, characteristic, complemented
6#10591107C211yesmaximal, characteristic, complemented
7#10591060C211yesmaximal, characteristic, complemented
8#10590485C212yesmaximal, complemented
9#10590482C212yesmaximal, complemented
10#10590461C212yesmaximal, complemented
11#10590460C212yesmaximal, complemented
12#79200—31nomaximal
13#78867—31nomaximal
14C22×#634C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×#3750—21no—
18C2×C4×C3⋊Dic3—21no—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20#64096—21no—
21#64096—21no—
22#64096C2212yes—
23#64096C2212yes—
24C3×#926C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27#67⋊Dic3—21no—
28#67⋊Dic3—21no—
29#63898C2211yescharacteristic
30#63898C2211yescharacteristic
31C4×D3×Dic3—21no—
32#63855—21no—
33#63843C2211yescharacteristic
34#63843C2211yescharacteristic
35C2×#3719C2212yes—
36#63831C418yescomplemented
37C2×#3716C2212yes—
38C3×#810C2212yes—
39C3×#809C2212yes—
40C3×#808C2212yes—
41C3×#807C2212yes—
42#63567C2212yes—
43#63567C2212yes—
44#63555C2212yes—
45#63553C2212yes—
46Dic3×#41—31no—
47C2×#951—31no—
48C2×#909—31no—
49#5522—31no—
50C2×#887—31no—
51C2×#887—31no—
52C2×#887—61no—
53C3×#428—31no—
54C3×#417—31no—
55#5120—31no—
56Dic3×M16—31no—
57Dic3×M16—31no—
58#5004—31no—
59#4966D311yescharacteristic
60#4964D311yescharacteristic, complemented
61#4889—32no—
62#4873—32no—
63#4853—32no—
64#4852—32no—
65#4790—32no—
66#4789—32no—
67#4758—32no—
68#4757—32no—
69C22×C32×C4—21no—
70C22×C32×C4C2311yescharacteristic
71C22×C3⋊Dic3—21no—
72C22×C3⋊Dic3D411yescharacteristic
73C22×C3⋊Dic3D411yescharacteristic
74C2×#634—21no—
75C2×#634—22no—
76C2×#634C2×C414yescomplemented
77C2×#634C2312yes—
78C2×C3×#67—21no—
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×C4⋊C4—21no—
87C32×C4⋊C4C2312yes—
88#3750—22no—
89#3750—22no—
90C4×C3⋊Dic3—22no—
91C4×C3⋊Dic3—22no—
92C4×C3⋊Dic3D411yescharacteristic
93C4×C3⋊Dic3D411yescharacteristic
94C4×C3⋊Dic3C2311yescharacteristic
95C4×C3⋊Dic3C2311yescharacteristic
96C3×#217—21no—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×C4⋊Dic3C2311yescharacteristic
99C3×C4×Dic3—21no—
100C3×#208—22no—
101C3×#208C2×C414yescomplemented
102C2×C3×C3⋊C8C2312yes—
103C2×C3×C3⋊C8C2312yes—
104Dic3⋊Dic3—21no—
105Dic3⋊Dic3—21no—
106(C2×D3)⋊Dic3—21no—
107(C2×D3)⋊Dic3—21no—
108Dic32—21no—
109Dic32—21no—
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—31no—
119C2×C3×M16—31no—
120C3×#117—31no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4C2×D311yescharacteristic
123C2×C3×C4⋊C4C2×D311yescharacteristic
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—
133#926—61no—
134#926C2×D311yescharacteristic
135C2×Dic3⋊C4—61no—
136C2×Dic3⋊C4—61no—
137C2×Dic3⋊C4—62no—
138C2×C4×Dic3—31no—
139C2×C4×Dic3—31no—
140C2×C4×Dic3—61no—
141C2×C4×Dic3—61no—
142C2×C4×Dic3—61no—
143C2×C4×Dic3—61no—
144C2×C4×Dic3—62no—
145C2×#208C2×D311yescharacteristic
146C2×#208C2×D311yescharacteristic
147#909—38no—
148C2×Dic12—32no—
149C2×#204—32no—
150#893—31no—
151#893—31no—
152#887—31no—
153#887—31no—
154#887—32no—
155#887—32no—
156#887—32no—
157#887—32no—
158#887—62no—
159#887—62no—
160#887—61no—
161#887—61no—
162#887—61no—
163#887—61no—
164#887—62no—
165#887—62no—
166#67⋊C4—61no—
167#67⋊C4—61no—
168#872—61no—
169C42×D3—61no—
170C3×#107—32no—
171C3×#106—32no—
172C3×#103—32no—
173C3×#102—32no—
174#816—32no—
175#816—32no—
176#815—32no—
177#815—32no—
178C8×Dic3—32no—
179C8×Dic3—32no—
180#810—32no—
181#810—32no—
182#810C2×D312yes—
183#809C2×D312yes—
184#808C2×D312yes—
185#807C2×D312yes—
186C23×C32C2×D411yescharacteristic
187C22×C3×D3—21no—
188C2×C32×C4—22no—
189C2×C32×C4—42no—
190C2×C32×C4C22×C412yes—
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4#4112yes—
193C2×C32×C4C2411yescharacteristic
194C2×C3⋊Dic3—24no—
195C2×C3⋊Dic3—22no—
196C2×C3⋊Dic3—22no—
197C2×C3⋊Dic3—41no—
198C2×C3⋊Dic3C2×D411yescharacteristic
199C2×C3⋊Dic3C2×D411yescharacteristic
200C2×C3⋊Dic3C2×D411yescharacteristic
201C2×C3⋊Dic3C2×D411yescharacteristic
202#634—24no—
203#634—22no—
204#634C22×C414yes—
205C3×#67—24no—
206C2×C3×Dic3—21no—
207C2×C3×Dic3—21no—
208C2×C3×Dic3—21no—
209C3×D12—21no—
210C3×D12C22×C412yes—
211C3×C4×D3—24no—
212C3×Dic6—21no—
213C3×Dic6C22×C412yes—
214D3×Dic3—42no—
215D3×Dic3—42no—
216C3×C3⋊C8—22no—
217C3×C3⋊C8C22×C414yes—
218C2×#137—91no—
219C4×#41—91no—
220C2×C4×Q8—91no—
221#441—92no—
222#440—92no—
223C4×Q16—92no—
224C4×SD16—92no—
225#428—31no—
226#419—91no—
227#417—31no—
228C4×M16—91no—
229C3×#41—34no—
230C3×#41—62no—
231C2×C3×Q8—31no—
232C2×C3×D4—31no—
233C2×C3×D4—61no—
234C22×C3×C4—22no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—61no—
239C22×C3×C4C22×D311yescharacteristic
240C22×C3×C4C22×D311yescharacteristic
241C2×#67—21no—
242C22×Dic3—31no—
243C22×Dic3—31no—
244C22×Dic3—31no—
245C22×Dic3—31no—
246C22×Dic3—61no—
247C22×Dic3—61no—
248C22×Dic3—61no—
249C22×Dic3—61no—
250C22×Dic3—62no—
251C22×Dic3—61no—
252C22×Dic3—61no—
253#235—22no—
254#235C4×D314yes—
255C2×D12C22×D311yescharacteristic
256C2×C4×D3—21no—
257C2×C4×D3—61no—
258C2×C4×D3—61no—
259C2×Dic6—34no—
260C2×Dic6—34no—
261C2×Dic6—32no—
262C2×Dic6—32no—
263C2×Dic6—62no—
264C2×Dic6—64no—
265C2×Dic6—62no—
266C2×Dic6—64no—
267C2×Dic6—61no—
268C2×Dic6—61no—
269C2×Dic6—62no—
270C2×Dic6—62no—
271C2×Dic6C22×D311yescharacteristic
272C3×M16—34no—
273C3×M16—62no—
274C2×C3×C8—32no—
275C2×C3×C8—32no—
276C3×C4⋊C4—22no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—22no—
280C3×C4⋊C4—31no—
281C3×C4⋊C4—31no—
282C3×C4⋊C4C22×D312yes—
283C3×C4⋊C4C22×D312yes—
284C3×C22⋊C4—61no—
285C3×C42—61no—
286#217—21no—
287#217—61no—
288#217—61no—
289#216—38no—
290#214—38no—
291(C2×D3)⋊C4—61no—
292(C2×D3)⋊C4—61no—
293C4⋊Dic3—61no—
294C4⋊Dic3—61no—
295C4⋊Dic3C22×D311yescharacteristic
296C4⋊Dic3C22×D311yescharacteristic
297Dic3⋊C4—61no—
298Dic3⋊C4—61no—
299Dic3⋊C4—62no—
300Dic3⋊C4—62no—
301Dic3⋊C4—62no—
302Dic3⋊C4—62no—
303Dic3⋊C4—64no—
304Dic3⋊C4—64no—
305C4×Dic3—21no—
306C4×Dic3—31no—
307C4×Dic3—31no—
308C4×Dic3—31no—
309C4×Dic3—31no—
310C4×Dic3—31no—
311C4×Dic3—31no—
312C4×Dic3—31no—
313C4×Dic3—31no—
314C4×Dic3—61no—
315C4×Dic3—61no—
316C4×Dic3—61no—
317C4×Dic3—61no—
318C4×Dic3—61no—
319C4×Dic3—61no—
320C4×Dic3—61no—
321C4×Dic3—61no—
322C4×Dic3—62no—
323C4×Dic3—62no—
324C4×Dic3—62no—
325C4×Dic3—62no—
326C4×Dic3—64no—
327C4×Dic3—64no—
328#208—22no—
329#208C4×D314yescomplemented
330C2×C3⋊C8C22×D312yes—
331C2×C3⋊C8C22×D312yes—
332Dic12—38no—
333#204—38no—
334C22×C32—21no—
335C22×C32—21no—
336C22×C32C4×D412yes—
337C22×C32C22×D411yescharacteristic
338C2×C3×D3—22no—
339C2×C3×D3—41no—
340C2×C3×D3—41no—
341C32×C4—42no—
342C32×C4C4×D412yes—
343C32×C4C23×C411yescharacteristic
344C32×C4C2×#4111yescharacteristic
345C3⋊Dic3—24no—
346C3⋊Dic3—21no—
347C3⋊Dic3—21no—
348C3⋊Dic3—21no—
349C3⋊Dic3#13712yescomplemented
350C3×Dic3—22no—
351C3×Dic3—41no—
352C3×Dic3—41no—
353C2×#41—31no—
354C22×Q8—91no—
355#137—98no—
356C2×Q16—92no—
357C2×SD16—92no—
358C2×M16—31no—
359C2×M16—31no—
360C4×Q8—91no—
361C4×Q8—91no—
362C4×Q8—92no—
363C4×Q8—92no—
364C4×Q8—181no—
365C4×Q8—181no—
366C4×D4—91no—
367C4×D4—91no—
368C4×D4—181no—
369C4×D4—181no—
370#117—31no—
371#117—181no—
372C2×C4⋊C4—181no—
373C2×C4⋊C4D3211yescharacteristic
374C2×C42—91no—
375C2×C42—181no—
376C2×C42—181no—
377#107—32no—
378#106—32no—
379#103—32no—
380#103—92no—
381#103—92no—
382#102—32no—
383#97—92no—
384C4×C8—92no—
385C23×C3—21no—
386C23×C3—61no—
387C23×C3D3×D411yescharacteristic
388C23×C3D3×D411yescharacteristic
389C22×D3—21no—
390C3×Q8—32no—
391C3×Q8—61no—
392C3×D4—32no—
393C3×D4—64no—
394C3×D4—61no—
395C2×C3×C4—24no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—21no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—21no—
402C2×C3×C4—44no—
403C2×C3×C4—42no—
404C2×C3×C4—42no—
405C2×C3×C4—61no—
406C2×C3×C4—64no—
407C2×C3×C4—61no—
408C2×C3×C4—61no—
409C2×C3×C4C2×C4×D312yes—
410C2×C3×C4C2×C4×D312yes—
411C2×C3×C4D3×D411yescharacteristic
412C2×C3×C4D3×D411yescharacteristic
413C2×C3×C4#23712yes—
414C2×C3×C4#23912yes—
415C2×C3×C4C23×D311yescharacteristic
416C2×C3×C4C23×D311yescharacteristic
417#67—24no—
418C2×Dic3—21no—
419C2×Dic3—21no—
420C2×Dic3—21no—
421C2×Dic3—31no—
422C2×Dic3—31no—
423C2×Dic3—31no—
424C2×Dic3—31no—
425C2×Dic3—31no—
426C2×Dic3—31no—
427C2×Dic3—31no—
428C2×Dic3—31no—
429C2×Dic3—61no—
430C2×Dic3—61no—
431C2×Dic3—61no—
432C2×Dic3—61no—
433C2×Dic3—62no—
434C2×Dic3—62no—
435C2×Dic3—64no—
436C2×Dic3—68no—
437C2×Dic3—64no—
438C2×Dic3—64no—
439C2×Dic3—64no—
440C2×Dic3—62no—
441C2×Dic3—62no—
442C2×Dic3—122no—
443C2×Dic3—122no—
444C2×Dic3—121no—
445C2×Dic3—121no—
446C2×Dic3—122no—
447D12—21no—
448D12C2×C4×D312yes—
449C4×D3—24no—
450C4×D3—122no—
451C4×D3—122no—
452Dic6—21no—
453Dic6—34no—
454Dic6—34no—
455Dic6—64no—
456Dic6—64no—
457Dic6—68no—
458Dic6—64no—
459Dic6—64no—
460Dic6—62no—
461Dic6—62no—
462Dic6C2×C4×D312yes—
463C3×C8—34no—
464C3×C8—62no—
465C3⋊C8—22no—
466C3⋊C8C2×C4×D314yes—
467C2×C32—22no—
468C2×C32C2×C4×D411yescharacteristic
469C2×C32C2×#13711yescharacteristic
470C2×C32#57511yescharacteristic
471C3×D3—42no—
472#41—34no—
473#41—62no—
474C2×Q8—31no—
475C2×Q8—92no—
476C2×Q8—94no—
477C2×Q8—182no—
478C2×Q8—181no—
479C2×D4—31no—
480C2×D4—61no—
481C22×C4—21no—
482C22×C4—61no—
483C22×C4—91no—
484C22×C4—91no—
485C22×C4—181no—
486C22×C4—181no—
487C22×C4—181no—
488C22×C4C2×D3211yescharacteristic
489Q16—98no—
490SD16—98no—
491M16—34no—
492M16—62no—
493C2×C8—32no—
494C2×C8—32no—
495C4⋊C4—21no—
496C4⋊C4—31no—
497C4⋊C4—31no—
498C4⋊C4—182no—
499C4⋊C4—182no—
500C4⋊C4—181no—
501C4⋊C4—181no—
502C4⋊C4C2×D3212yes—
503C22⋊C4—61no—
504C22⋊C4—181no—
505C22⋊C4—181no—
506C42—61no—
507C42—91no—
508C42—91no—
509C42—91no—
510C42—91no—
511C42—182no—
512C42—182no—
513C42—181no—
514C42—181no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—21no—
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—22no—
523C22×C3—62no—
524C22×C3—121no—
525C22×C3—121no—
526C22×C3#67⋊C412yes—
527C22×C3#89312yes—
528C22×C3C2×D3×D411yescharacteristic
529C22×C3C2×D3×D411yescharacteristic
530C2×D3—22no—
531C2×D3—41no—
532C2×D3—41no—
533C3×C4—21no—
534C3×C4—21no—
535C3×C4—22no—
536C3×C4—44no—
537C3×C4—42no—
538C3×C4—42no—
539C3×C4—62no—
540C3×C4—121no—
541C3×C4—121no—
542C3×C4#67⋊C412yes—
543C3×C4#89312yes—
544C3×C4C22×C4×D311yescharacteristic
545C3×C4C22×C4×D311yescharacteristic
546C3×C4C2×#23711yescharacteristic
547C3×C4C2×#23911yescharacteristic
548Dic3—22no—
549Dic3—32no—
550Dic3—32no—
551Dic3—41no—
552Dic3—41no—
553Dic3—62no—
554Dic3—68no—
555Dic3—62no—
556Dic3—64no—
557Dic3—64no—
558Dic3—61no—
559Dic3—61no—
560Dic3—61no—
561Dic3—61no—
562Dic3—61no—
563Dic3—61no—
564Dic3—121no—
565Dic3—121no—
566C32C4×#13711yescharacteristic, complemented, Sylow
567C23—61no—
568C23#381111yescharacteristic
569Q8—32no—
570Q8—61no—
571Q8—94no—
572Q8—182no—
573Q8—184no—
574D4—32no—
575D4—64no—
576D4—61no—
577C2×C4—22no—
578C2×C4—42no—
579C2×C4—61no—
580C2×C4—64no—
581C2×C4—61no—
582C2×C4—61no—
583C2×C4—91no—
584C2×C4—91no—
585C2×C4—91no—
586C2×C4—91no—
587C2×C4—182no—
588C2×C4—182no—
589C2×C4—184no—
590C2×C4—362no—
591C2×C4—362no—
592C2×C4—361no—
593C2×C4#379612yes—
594C2×C4C4×D3212yes—
595C2×C4#381111yescharacteristic
596C2×C4C22×D3211yescharacteristic
597C8—34no—
598C8—62no—
599C2×C3—24no—
600C2×C3—22no—
601C2×C3—22no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—122no—
606C2×C3C2×#67⋊C411yescharacteristic
607C2×C3C2×#89311yescharacteristic
608C2×C3#577311yescharacteristic
609C2×C3#577311yescharacteristic
610C2×C3D3×#13711yescharacteristic
611C2×C3D3×#13711yescharacteristic
612D3—42no—
613C22—21no—
614C22—21no—
615C22—62no—
616C22—121no—
617C22—121no—
618C22#6388112yes—
619C22C2×#381111yescharacteristic
620C4—42no—
621C4—62no—
622C4—92no—
623C4—121no—
624C4—121no—
625C4—181no—
626C4—181no—
627C4—184no—
628C4—181no—
629C4#6388112yes—
630C4C2×#379611yescharacteristic
631C4C2×C4×D3211yescharacteristic
632C3—21no—
633C3#7886711yescharacteristic, complemented
634C3#7920011yescharacteristic, complemented
635C2—22no—
636C2—122no—
637C2C2×#6388111yescharacteristic
638C2#1059510111yescharacteristic
639C2#1059532211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32C4×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64096C2semidirect
5. C3×#4964C2semidirect
6. #10591107C2semidirect
7. #10591060C2semidirect
8. #10590485C2semidirect
9. #10590482C2semidirect
10. #10590461C2semidirect
11. #10590460C2semidirect
36. #63831C4semidirect
60. #4964D3semidirect
76. C2×#634C2×C4semidirect
101. C3×#208C2×C4semidirect
110. #3719C2×C4semidirect
111. #3716C2×C4semidirect
329. #208C4×D3semidirect
349. C3⋊Dic3#137semidirect
566. C32C4×#137semidirect
633. C3#78867semidirect
634. C3#79200semidirect

Maximal subgroups

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

subgroupindex
C2×#640962
#105949582
C2×#638312
C3×#49662
C3×#49642
#105911072
#105910602
#105904852
#105904822
#105904612
#105904602
#792003
#788673