Finite Group Databasebeta

← #11868815

Subgroups — #11868815

Order 1152.

977 conjugacy classes of subgroups.

The subgroup lattice has 619 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64097C211yesmaximal, characteristic, complemented
2#10594958C211yesmaximal, characteristic
3C3×#4966C211yesmaximal, characteristic
4C3×#4964C211yesmaximal, characteristic, complemented
5#10591131C211yesmaximal, characteristic, complemented
6#10591120C211yesmaximal, characteristic, complemented
7#10591088C211yesmaximal, characteristic
8#10590497C212yesmaximal, complemented
9#10590496C212yesmaximal, complemented
10#10590472C212yesmaximal, complemented
11#10590471C212yesmaximal, complemented
12#79240—31nomaximal
13#78870—31nomaximal
14C22×#634—21no—
15C2×C3×#235C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×#3750—21no—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20#64097—21no—
21#64097—21no—
22#64097C2212yes—
23#64097C2212yes—
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
35C3×#810C2212yes—
36C3×#809C2212yes—
37C3×#808C2212yes—
38C3×#807C2212yes—
39#63575C2212yes—
40#63573C2212yes—
41#63572C2212yes—
42#63572C2212yes—
43#63566C2212yes—
44#63563C2212yes—
45Dic3×#41—31no—
46#5522—31no—
47C2×#888—31no—
48C2×#888—31no—
49C2×#888—61no—
50C3×#428—31no—
51C3×#417—31no—
52#5232—31no—
53#5133—31no—
54#5121—31no—
55#5118—31no—
56#5118—31no—
57#4995—31no—
58#4966D311yescharacteristic
59#4964D311yescharacteristic, complemented
60#4890—32no—
61#4875—32no—
62#4870—32no—
63#4854—32no—
64#4793—32no—
65#4791—32no—
66#4761—32no—
67#4759—32no—
68C22×C32×C4—21no—
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3—21no—
71C22×C3⋊Dic3D411yescharacteristic
72C22×C3⋊Dic3D411yescharacteristic
73C2×#634—22no—
74C2×#634—22no—
75C2×#634—44no—
76C2×C3×#67—21no—
77C3×#235—22no—
78C3×#235Q814yescomplemented
79C2×C3×D12C2311yescharacteristic
80C2×C3×C4×D3—21no—
81C2×C3×Dic6C2311yescharacteristic
82C2×D3×Dic3—21no—
83C2×D3×Dic3—21no—
84C32×C4⋊C4—21no—
85C32×C4⋊C4C2312yes—
86C4⋊(C3⋊Dic3)—21no—
87C4⋊(C3⋊Dic3)C2312yes—
88#3750—22no—
89#3750—22no—
90C4×C3⋊Dic3D411yescharacteristic
91C4×C3⋊Dic3D411yescharacteristic
92C4×C3⋊Dic3C2311yescharacteristic
93C4×C3⋊Dic3C2311yescharacteristic
94C3×#217—21no—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×C4⋊Dic3C2311yescharacteristic
97C3×C4×Dic3—21no—
98C3×#208—22no—
99C3×#208—22no—
100C2×C3×C3⋊C8C2312yes—
101C2×C3×C3⋊C8C2312yes—
102Dic3⋊Dic3—21no—
103Dic3⋊Dic3—21no—
104(C2×D3)⋊Dic3—21no—
105(C2×D3)⋊Dic3—21no—
106Dic32—21no—
107Dic32—21no—
108#3079—91noSylow
109C2×C3×#41—31no—
110C2×#235C2×D311yescharacteristic
111C22×Dic6—61no—
112C22×Dic6—61no—
113C22×Dic6—62no—
114C2×C3×M16—31no—
115C2×C3×M16—31no—
116C3×#117—31no—
117C2×C3×C4⋊C4—21no—
118C2×C3×C4⋊C4C2×D311yescharacteristic
119C2×C3×C4⋊C4C2×D311yescharacteristic
120Q8×Dic3—31no—
121Q8×Dic3—31no—
122D4×Dic3—31no—
123D4×Dic3—31no—
124D4×Dic3—61no—
125D4×Dic3—61no—
126#926—61no—
127#926C2×D311yescharacteristic
128C2×C4⋊Dic3—31no—
129C2×C4⋊Dic3—31no—
130C2×C4⋊Dic3—61no—
131C2×Dic3⋊C4—61no—
132C2×Dic3⋊C4—61no—
133C2×Dic3⋊C4—62no—
134C2×C4×Dic3—31no—
135C2×C4×Dic3—31no—
136C2×C4×Dic3—61no—
137C2×C4×Dic3—61no—
138C2×#208C2×D311yescharacteristic
139C2×#208C2×D311yescharacteristic
140#893—31no—
141#893—31no—
142#888—32no—
143#888—32no—
144#888—32no—
145#888—32no—
146#888—62no—
147#888—62no—
148#888—61no—
149#888—61no—
150#888—61no—
151#888—61no—
152#888—62no—
153#888—62no—
154#887—31no—
155#887—31no—
156#67⋊C4—61no—
157#67⋊C4—61no—
158#872—61no—
159C42×D3—61no—
160C3×#107—32no—
161C3×#106—32no—
162C3×#103—32no—
163C3×#102—32no—
164#835—32no—
165#832—32no—
166#821—32no—
167#818—32no—
168#817—32no—
169#816—32no—
170Dic3⋊C8—32no—
171Dic3⋊C8—32no—
172Dic3⋊C8—32no—
173Dic3⋊C8—32no—
174#810C2×D312yes—
175#809C2×D312yes—
176#808—32no—
177#808C2×D312yes—
178#807—32no—
179#807C2×D312yes—
180C23×C32C2×D411yescharacteristic
181C22×C3×D3—21no—
182C2×C32×C4—22no—
183C2×C32×C4—42no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2×Q812yes—
186C2×C32×C4#4112yes—
187C2×C32×C4C2411yescharacteristic
188C2×C3⋊Dic3—22no—
189C2×C3⋊Dic3—22no—
190C2×C3⋊Dic3—22no—
191C2×C3⋊Dic3—42no—
192C2×C3⋊Dic3C2×D411yescharacteristic
193C2×C3⋊Dic3C2×D411yescharacteristic
194C2×C3⋊Dic3C2×D411yescharacteristic
195C2×C3⋊Dic3C2×D411yescharacteristic
196#634—44no—
197#634—44no—
198C3×#67—24no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3—21no—
202C3×D12—21no—
203C3×D12C2×Q812yescomplemented
204C3×C4×D3—24no—
205C3×Dic6—21no—
206C3×Dic6C2×Q812yescomplemented
207D3×Dic3—42no—
208D3×Dic3—42no—
209C3×C3⋊C8—22no—
210C3×C3⋊C8—22no—
211C2×C4⋊Q8—91no—
212C4×#41—91no—
213#477—92no—
214#476—92no—
215#475—92no—
216#474—92no—
217#428—31no—
218#428—91no—
219#423—91no—
220#417—31no—
221#417—91no—
222C3×#41—34no—
223C3×#41—62no—
224C2×C3×Q8—31no—
225C2×C3×D4—31no—
226C2×C3×D4—61no—
227C22×C3×C4—22no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—61no—
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C22×D311yescharacteristic
234C2×#67—21no—
235C22×Dic3—31no—
236C22×Dic3—31no—
237C22×Dic3—31no—
238C22×Dic3—31no—
239C22×Dic3—61no—
240C22×Dic3—61no—
241C22×Dic3—61no—
242C22×Dic3—61no—
243C22×Dic3—62no—
244C22×Dic3—61no—
245C22×Dic3—61no—
246#235—22no—
247#235Dic614yescomplemented
248C2×D12C22×D311yescharacteristic
249C2×C4×D3—21no—
250C2×C4×D3—61no—
251C2×C4×D3—61no—
252C2×Dic6—62no—
253C2×Dic6—62no—
254C2×Dic6—62no—
255C2×Dic6—62no—
256C2×Dic6—64no—
257C2×Dic6—64no—
258C2×Dic6—124no—
259C2×Dic6—124no—
260C2×Dic6—128no—
261C2×Dic6C22×D311yescharacteristic
262C3×M16—62no—
263C3×M16—62no—
264C2×C3×C8—32no—
265C2×C3×C8—32no—
266C3×C4⋊C4—22no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—22no—
270C3×C4⋊C4—31no—
271C3×C4⋊C4—31no—
272C3×C4⋊C4C22×D312yes—
273C3×C4⋊C4C22×D312yes—
274C3×C22⋊C4—61no—
275C3×C42—61no—
276#217—21no—
277#217—61no—
278#217—61no—
279(C2×D3)⋊C4—61no—
280(C2×D3)⋊C4—61no—
281C4⋊Dic3—32no—
282C4⋊Dic3—32no—
283C4⋊Dic3—62no—
284C4⋊Dic3—61no—
285C4⋊Dic3—61no—
286C4⋊Dic3—62no—
287C4⋊Dic3—61no—
288C4⋊Dic3—61no—
289C4⋊Dic3C22×D311yescharacteristic
290C4⋊Dic3C22×D311yescharacteristic
291Dic3⋊C4—61no—
292Dic3⋊C4—61no—
293Dic3⋊C4—62no—
294Dic3⋊C4—62no—
295Dic3⋊C4—62no—
296Dic3⋊C4—62no—
297Dic3⋊C4—64no—
298Dic3⋊C4—64no—
299C4×Dic3—21no—
300C4×Dic3—31no—
301C4×Dic3—31no—
302C4×Dic3—31no—
303C4×Dic3—31no—
304C4×Dic3—31no—
305C4×Dic3—31no—
306C4×Dic3—31no—
307C4×Dic3—31no—
308C4×Dic3—61no—
309C4×Dic3—61no—
310C4×Dic3—61no—
311C4×Dic3—61no—
312C4×Dic3—61no—
313C4×Dic3—61no—
314C4×Dic3—61no—
315C4×Dic3—61no—
316#208—22no—
317#208—22no—
318C2×C3⋊C8C22×D312yes—
319C2×C3⋊C8C22×D312yes—
320C22×C32—21no—
321C22×C32—21no—
322C22×C32C22⋊Q812yes—
323C22×C32C22×D411yescharacteristic
324C2×C3×D3—22no—
325C2×C3×D3—41no—
326C2×C3×D3—41no—
327C32×C4—42no—
328C32×C4C22⋊Q812yes—
329C32×C4C22×Q811yescharacteristic
330C32×C4C2×#4111yescharacteristic
331C3⋊Dic3—21no—
332C3⋊Dic3—21no—
333C3⋊Dic3—42no—
334C3⋊Dic3AGL(1,ℤ/8)12yes—
335C3⋊Dic3#13712yes—
336C3×Dic3—22no—
337C3×Dic3—41no—
338C3×Dic3—41no—
339C2×#41—31no—
340C22×Q8—181no—
341C2×M16—31no—
342C2×M16—31no—
343C4⋊Q8—92no—
344C4⋊Q8—92no—
345C4⋊Q8—181no—
346C4⋊Q8—181no—
347C4×Q8—91no—
348C4×Q8—91no—
349C4×D4—91no—
350C4×D4—91no—
351C4×D4—181no—
352C4×D4—181no—
353#117—31no—
354#117—181no—
355C2×C4⋊C4—91no—
356C2×C4⋊C4—181no—
357C2×C4⋊C4D3211yescharacteristic
358C2×C42—91no—
359C2×C42—181no—
360#107—32no—
361#107—92no—
362#106—32no—
363#106—92no—
364C4⋊C8—92no—
365C4⋊C8—92no—
366#103—32no—
367#103—92no—
368#102—32no—
369#102—92no—
370C23×C3—21no—
371C23×C3—61no—
372C23×C3D3×D411yescharacteristic
373C23×C3D3×D411yescharacteristic
374C22×D3—21no—
375C3×Q8—32no—
376C3×Q8—61no—
377C3×D4—32no—
378C3×D4—64no—
379C3×D4—61no—
380C2×C3×C4—24no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—21no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—21no—
387C2×C3×C4—44no—
388C2×C3×C4—42no—
389C2×C3×C4—42no—
390C2×C3×C4—61no—
391C2×C3×C4—64no—
392C2×C3×C4—61no—
393C2×C3×C4—61no—
394C2×C3×C4C2×Dic612yes—
395C2×C3×C4#23512yes—
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4#23712yes—
399C2×C3×C4D3×Q812yes—
400C2×C3×C4C23×D311yescharacteristic
401C2×C3×C4C23×D311yescharacteristic
402#67—24no—
403C2×Dic3—21no—
404C2×Dic3—21no—
405C2×Dic3—21no—
406C2×Dic3—31no—
407C2×Dic3—31no—
408C2×Dic3—31no—
409C2×Dic3—31no—
410C2×Dic3—31no—
411C2×Dic3—31no—
412C2×Dic3—31no—
413C2×Dic3—31no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416C2×Dic3—61no—
417C2×Dic3—61no—
418C2×Dic3—62no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—62no—
422C2×Dic3—64no—
423C2×Dic3—64no—
424C2×Dic3—64no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—122no—
428C2×Dic3—122no—
429C2×Dic3—124no—
430C2×Dic3—122no—
431C2×Dic3—122no—
432D12—21no—
433D12C2×Dic612yescomplemented
434C4×D3—24no—
435C4×D3—122no—
436C4×D3—122no—
437Dic6—21no—
438Dic6—124no—
439Dic6—124no—
440Dic6—128no—
441Dic6—128no—
442Dic6—124no—
443Dic6—124no—
444Dic6C2×Dic612yescomplemented
445C3×C8—62no—
446C3×C8—62no—
447C3⋊C8—22no—
448C3⋊C8—22no—
449C2×C32—22no—
450C2×C32C2×C22⋊Q811yescharacteristic
451C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
452C2×C32C2×#13711yescharacteristic
453C3×D3—42no—
454#41—34no—
455#41—62no—
456C2×Q8—31no—
457C2×Q8—182no—
458C2×Q8—182no—
459C2×Q8—364no—
460C2×D4—31no—
461C2×D4—61no—
462C22×C4—21no—
463C22×C4—61no—
464C22×C4—91no—
465C22×C4—91no—
466C22×C4—181no—
467C22×C4—181no—
468C22×C4—181no—
469C22×C4C2×D3211yescharacteristic
470M16—62no—
471M16—62no—
472C2×C8—32no—
473C2×C8—32no—
474C4⋊C4—21no—
475C4⋊C4—31no—
476C4⋊C4—31no—
477C4⋊C4—92no—
478C4⋊C4—182no—
479C4⋊C4—182no—
480C4⋊C4—181no—
481C4⋊C4—181no—
482C4⋊C4—181no—
483C4⋊C4C2×D3212yes—
484C22⋊C4—61no—
485C22⋊C4—181no—
486C22⋊C4—181no—
487C42—61no—
488C42—91no—
489C42—91no—
490C42—91no—
491C42—91no—
492C42—181no—
493C42—181no—
494C22×C3—22no—
495C22×C3—22no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—22no—
502C22×C3—62no—
503C22×C3—121no—
504C22×C3—121no—
505C22×C3#87812yes—
506C22×C3#89612yes—
507C22×C3C2×D3×D411yescharacteristic
508C22×C3C2×D3×D411yescharacteristic
509C2×D3—22no—
510C2×D3—41no—
511C2×D3—41no—
512C3×C4—21no—
513C3×C4—21no—
514C3×C4—22no—
515C3×C4—44no—
516C3×C4—42no—
517C3×C4—42no—
518C3×C4—62no—
519C3×C4—121no—
520C3×C4—121no—
521C3×C4#87812yes—
522C3×C4#89612yes—
523C3×C4C22×Dic611yescharacteristic
524C3×C4C2×#23511yescharacteristic
525C3×C4C2×#23711yescharacteristic
526C3×C4C2×D3×Q811yescharacteristic
527Dic3—22no—
528Dic3—32no—
529Dic3—32no—
530Dic3—32no—
531Dic3—32no—
532Dic3—41no—
533Dic3—41no—
534Dic3—62no—
535Dic3—62no—
536Dic3—62no—
537Dic3—62no—
538Dic3—61no—
539Dic3—61no—
540Dic3—61no—
541Dic3—61no—
542Dic3—124no—
543Dic3—122no—
544Dic3—122no—
545C32#307911yescharacteristic, complemented, Sylow
546C23—61no—
547C23#381111yescharacteristic
548Q8—32no—
549Q8—61no—
550Q8—364no—
551Q8—364no—
552D4—32no—
553D4—64no—
554D4—61no—
555C2×C4—22no—
556C2×C4—42no—
557C2×C4—61no—
558C2×C4—64no—
559C2×C4—61no—
560C2×C4—61no—
561C2×C4—91no—
562C2×C4—91no—
563C2×C4—91no—
564C2×C4—91no—
565C2×C4—182no—
566C2×C4—182no—
567C2×C4—182no—
568C2×C4—362no—
569C2×C4—362no—
570C2×C4—362no—
571C2×C4D3×Dic612yes—
572C2×C4#379512yes—
573C2×C4#381111yescharacteristic
574C2×C4C22×D3211yescharacteristic
575C8—62no—
576C8—62no—
577C2×C3—24no—
578C2×C3—22no—
579C2×C3—22no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—122no—
584C2×C3C2×#87811yescharacteristic
585C2×C3C2×#89611yescharacteristic
586C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
587C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
588C2×C3D3×#13711yescharacteristic
589C2×C3D3×#13711yescharacteristic
590D3—42no—
591C22—21no—
592C22—21no—
593C22—62no—
594C22—121no—
595C22—121no—
596C22#6389612yes—
597C22C2×#381111yescharacteristic
598C4—42no—
599C4—62no—
600C4—92no—
601C4—92no—
602C4—121no—
603C4—121no—
604C4—181no—
605C4—181no—
606C4—362no—
607C4#6389612yes—
608C4C2×D3×Dic611yescharacteristic
609C4C2×#379511yescharacteristic
610C3—21no—
611C3#7887011yescharacteristic, complemented
612C3#7924011yescharacteristic, complemented
613C2—22no—
614C2—122no—
615C2C2×#6389611yescharacteristic
616C2#1059510011yescharacteristic
617C2#1059532211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
hypercenterC2×C4⋊C4D32
hypocenterC32#3079
LCSG ▷ C2×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×#64097C2semidirect
4. C3×#4964C2semidirect
5. #10591131C2semidirect
6. #10591120C2semidirect
8. #10590497C2semidirect
9. #10590496C2semidirect
10. #10590472C2semidirect
11. #10590471C2semidirect
59. #4964D3semidirect
78. C3×#235Q8semidirect
203. C3×D12C2×Q8semidirect
206. C3×Dic6C2×Q8semidirect
247. #235Dic6semidirect
433. D12C2×Dic6semidirect
444. Dic6C2×Dic6semidirect
545. C32#3079semidirect
611. C3#78870semidirect
612. C3#79240semidirect

Maximal subgroups

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

subgroupindex
C2×#640972
#105949582
C3×#49662
C3×#49642
#105911312
#105911202
#105910882
#105904972
#105904962
#105904722
#105904712
#792403
#788703