Finite Group Databasebeta

← #11870430

Subgroups — #11870430

Order 1152.

1041 conjugacy classes of subgroups.

The subgroup lattice has 643 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594910C211yesmaximal, characteristic, complemented
2C2×Dic3×D12C211yesmaximal, characteristic, complemented
3#10592435C211yesmaximal, characteristic, complemented
4C3×#4732C211yesmaximal, characteristic, complemented
5C3×#4718C211yesmaximal, characteristic, complemented
6#10591162C211yesmaximal, characteristic, complemented
7#10591094C211yesmaximal, characteristic, complemented
8#10590762C212yesmaximal, complemented
9Dic3×D24C212yesmaximal, complemented
10#10590753C212yesmaximal, complemented
11#10590745C212yesmaximal, complemented
12#79988—31nomaximal
13#79297—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C2×#3804—21no—
16C22×D3×Dic3—21no—
17#64139C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C3×#930C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×D24C2212yes—
22#63978—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63918C2211yescharacteristic, complemented
25#63911C2211yescharacteristic, complemented
26#63894C2211yescharacteristic, complemented
27Dic3×D12—21no—
28Dic3×D12—21no—
29Dic3×D12C2212yes—
30Dic3×D12C2212yes—
31Dic3×D12C2211yescharacteristic, complemented
32#63880—21no—
33#63852—21no—
34C2×#3714C2212yes—
35C32×C22⋊C8C2211yescharacteristic
36#63648C2212yescomplemented
37#63645C2212yescomplemented
38C3×#830C2211yescharacteristic
39C3×#821C2212yes—
40C3×Dic3⋊C8C2212yescomplemented
41C3×C8×Dic3C2212yescomplemented
42#63575C2212yescomplemented
43#63563C2212yes—
44#63563C2212yescomplemented
45C2×D4×Dic3—31no—
46#5596—31no—
47#5477—31no—
48C2×C4×D12—31no—
49C3×#447—31no—
50C3×#431—31no—
51#5217—31no—
52#5150—32no—
53Dic3×D8—32no—
54#5033—31no—
55#4846—32no—
56#4843—32no—
57#4759—32no—
58#4756—32no—
59#4736—31no—
60#4736—31no—
61#4736—31no—
62#4736—61no—
63#4732—31no—
64#4732D311yescharacteristic, complemented
65#4718D311yescharacteristic, complemented
66C4×D24—32no—
67C4×D24—32no—
68C23×C3×D3—21no—
69C22×C32×C4C2311yescharacteristic
70C2×#638—21no—
71C22×C3⋊Dic3—21no—
72C2×C4⋊(C3⋊D3)C2311yescharacteristic
73C2×C3×#67—21no—
74C22×C3×Dic3D411yescharacteristic
75C22×C3×Dic3D411yescharacteristic
76C2×C3×D12—21no—
77C2×C3×D12—24no—
78C2×C3×D12C2311yescharacteristic
79C2×C3×D12C2312yes—
80C2×#627—21no—
81C2×#626—21no—
82C2×#626—21no—
83C2×#624—21no—
84#3804—44no—
85C2×D3×Dic3—22no—
86C2×D3×Dic3—22no—
87C2×D3×Dic3—21no—
88C2×D3×Dic3—44no—
89C2×C32×C8C2312yes—
90#3752—21no—
91C4⋊(C3⋊Dic3)—21no—
92C4⋊(C3⋊Dic3)C2311yescharacteristic
93C4⋊(C3⋊Dic3)C2312yes—
94C3×(C2×D3)⋊C4—21no—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×C4×Dic3D411yescharacteristic
97C3×C4×Dic3D411yescharacteristic
98C3×C4×Dic3C2311yescharacteristic
99C3×C4×Dic3C2311yescharacteristic
100C2×C3×C3⋊C8C2312yes—
101C3×D24—24no—
102Dic3⋊Dic3—21no—
103#3722—21no—
104(C2×D3)⋊Dic3—21no—
105(C2×D3)⋊Dic3—22no—
106(C2×D3)⋊Dic3—22no—
107#3714—24no—
108#3100—91noSylow
109C22×C3×D4—31no—
110C23×Dic3—61no—
111C2×#237—61no—
112C2×#235—61no—
113C22×D12C2×D311yescharacteristic
114C22×C4×D3—61no—
115C2×C3×D8—32no—
116C3×#121—31no—
117C2×C3×C42—31no—
118C2×#217—61no—
119#940—31no—
120#939—61no—
121D4×Dic3—31no—
122D4×Dic3—32no—
123D4×Dic3—32no—
124D4×Dic3—61no—
125D4×Dic3—61no—
126C2×#213—32no—
127#930—31no—
128#930—31no—
129#930—61no—
130#930—61no—
131#930C2×D311yescharacteristic
132C2×(C2×D3)⋊C4—61no—
133C2×C4⋊Dic3—31no—
134C2×C4⋊Dic3—31no—
135C2×C4⋊Dic3—61no—
136C2×C4×Dic3C2×D311yescharacteristic
137C2×D24—32no—
138C2×D24C2×D312yes—
139#893—31no—
140#888—31no—
141#885—61no—
142#67⋊C4—61no—
143#875—61no—
144#874—31no—
145C4×D12—32no—
146C4×D12—31no—
147C4×D12—32no—
148C4×D12—31no—
149C4×D12—61no—
150C4×D12—61no—
151C4×D12—61no—
152#869—31no—
153C3×C4⋊C8—32no—
154C3×#102—32no—
155C3×C22⋊C8—21no—
156C3×C22⋊C8—31no—
157C3×C22⋊C8C2×D311yescharacteristic
158C3×C22⋊C8C2×D311yescharacteristic
159C3×C4×C8—32no—
160#832—32no—
161#832—32no—
162#830C2×D311yescharacteristic
163#821—32no—
164#821—32no—
165#821—32no—
166#821—32no—
167#821—62no—
168#821C2×D312yes—
169#818—32no—
170#818—32no—
171#818—32no—
172#818—62no—
173Dic3⋊C8C2×D312yescomplemented
174C8×Dic3C2×D312yescomplemented
175#807—32no—
176C23×C32C2×D411yescharacteristic
177C22×C3⋊D3—21no—
178C22×C3×D3—24no—
179C22×C3×D3—22no—
180C22×C3×D3—21no—
181C22×C3×D3—42no—
182C22×C3×D3—42no—
183C2×C32×C4—22no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2411yescharacteristic
186#638—42no—
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—42no—
190C4⋊(C3⋊D3)—22no—
191C3×#67—42no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—41no—
194C2×C3×Dic3D814yescomplemented
195C2×C3×Dic3C2×D411yescharacteristic
196C2×C3×Dic3C2×D411yescharacteristic
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C3×D12—24no—
200C3×D12—22no—
201C3×D12—22no—
202C3×D12#4114yescomplemented
203#627—42no—
204#626—42no—
205#626—42no—
206#624—42no—
207D3×Dic3—44no—
208D3×Dic3—44no—
209D3×Dic3—42no—
210C32×C8—22no—
211C3×C3⋊C8—22no—
212#532—91no—
213C2×C4×D4—91no—
214#480—91no—
215#480—91no—
216#474—92no—
217#459—92no—
218#447—31no—
219#447—91no—
220C4×D8—92no—
221C4×D8—92no—
222#431—31no—
223C24×C3—61no—
224C23×D3—21no—
225C2×C3×D4—32no—
226C2×C3×D4—31no—
227C2×C3×D4—64no—
228C2×C3×D4—61no—
229C2×C3×D4—61no—
230C22×C3×C4—21no—
231C22×C3×C4—31no—
232C22×C3×C4—31no—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C2×#67—21no—
236C2×#67—61no—
237C2×#67—61no—
238C2×#67—61no—
239C2×#67—61no—
240C2×#67—121no—
241C22×Dic3—61no—
242C22×Dic3—61no—
243C22×Dic3—61no—
244C22×Dic3—62no—
245C22×Dic3—62no—
246C22×Dic3—121no—
247C22×Dic3—124no—
248C22×Dic3D1211yescharacteristic
249C22×Dic3D1211yescharacteristic
250#237—124no—
251#235—124no—
252C2×D12—21no—
253C2×D12—24no—
254C2×D12—31no—
255C2×D12—31no—
256C2×D12—61no—
257C2×D12—61no—
258C2×D12—61no—
259C2×D12C22×D311yescharacteristic
260C2×D12C22×D312yes—
261C2×C4×D3—61no—
262C2×C4×D3—62no—
263C2×C4×D3—62no—
264C2×C4×D3—61no—
265C2×C4×D3—61no—
266C2×C4×D3—124no—
267C2×Dic6—61no—
268C2×Dic6—61no—
269C3×D8—64no—
270C2×C3×C8—22no—
271C2×C3×C8—32no—
272C2×C3×C8C22×D312yes—
273C2×C3×C8C22×D312yes—
274C3×C4⋊C4—31no—
275C3×C22⋊C4—61no—
276C3×C42—31no—
277C3×C42—31no—
278C3×C42—31no—
279C3×C42—31no—
280#217—61no—
281#217—62no—
282#217—62no—
283#213—64no—
284(C2×D3)⋊C4—21no—
285(C2×D3)⋊C4—61no—
286(C2×D3)⋊C4—62no—
287(C2×D3)⋊C4—62no—
288(C2×D3)⋊C4—61no—
289(C2×D3)⋊C4—61no—
290(C2×D3)⋊C4—61no—
291(C2×D3)⋊C4—61no—
292(C2×D3)⋊C4—121no—
293C4⋊Dic3—32no—
294C4⋊Dic3—31no—
295C4⋊Dic3—32no—
296C4⋊Dic3—31no—
297C4⋊Dic3—61no—
298C4⋊Dic3—62no—
299C4⋊Dic3—61no—
300C4⋊Dic3—61no—
301C4⋊Dic3—61no—
302C4⋊Dic3—121no—
303C4⋊Dic3C22×D311yescharacteristic
304Dic3⋊C4—61no—
305C4×Dic3D1211yescharacteristic
306C4×Dic3D1211yescharacteristic
307C4×Dic3C22×D311yescharacteristic
308C4×Dic3C22×D311yescharacteristic
309C2×C3⋊C8C22×D312yes—
310D24—24no—
311D24—64no—
312C22×C32—21no—
313C22×C32—21no—
314C22×C32C2×D812yes—
315C22×C32C22×D411yescharacteristic
316C2×C3⋊D3—41no—
317C2×C3⋊D3—41no—
318C2×C3⋊D3—41no—
319C2×C3×D3—24no—
320C2×C3×D3—48no—
321C2×C3×D3—42no—
322C2×C3×D3—42no—
323C2×C3×D3—41no—
324C2×C3×D3—41no—
325C2×C3×D3—41no—
326C32×C4—21no—
327C32×C4C2×#4112yes—
328C3⋊Dic3—42no—
329C3⋊Dic3—41no—
330C3×Dic3—21no—
331C3×Dic3—21no—
332C3×Dic3—41no—
333C3×Dic3C2×D812yes—
334C3×Dic3C2×D812yes—
335C2×#41—181no—
336C22×D4—31no—
337C23×C4—181no—
338C2×D8—32no—
339C2×D8—92no—
340C4⋊Q8—91no—
341#127—91no—
342#124—181no—
343#121—31no—
344#121—91no—
345#121—181no—
346C4×D4—91no—
347C4×D4—92no—
348C4×D4—92no—
349C4×D4—91no—
350C4×D4—181no—
351C4×D4—181no—
352C4×D4—181no—
353C2×C4⋊C4—91no—
354C2×C22⋊C4—181no—
355C2×C42—31no—
356#107—92no—
357#107—92no—
358C4⋊C8—32no—
359#102—32no—
360#102—92no—
361#102—92no—
362#102—92no—
363C22⋊C8—31no—
364C22⋊C8D3211yescharacteristic
365C4×C8—32no—
366C23×C3—21no—
367C23×C3—64no—
368C23×C3—62no—
369C23×C3—61no—
370C23×C3—122no—
371C23×C3—122no—
372C23×C3C2×D1211yescharacteristic
373C23×C3D3×D411yescharacteristic
374C22×D3—24no—
375C22×D3—22no—
376C22×D3—21no—
377C22×D3—42no—
378C22×D3—42no—
379C22×D3—61no—
380C22×D3—61no—
381C22×D3—121no—
382C3×D4—34no—
383C3×D4—64no—
384C3×D4—62no—
385C3×D4—62no—
386C3×D4—122no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—34no—
392C2×C3×C4—31no—
393C2×C3×C4—31no—
394C2×C3×C4—31no—
395C2×C3×C4—31no—
396C2×C3×C4—42no—
397C2×C3×C4—61no—
398C2×C3×C4—121no—
399C2×C3×C4C2×D1211yescharacteristic
400C2×C3×C4D3×D411yescharacteristic
401C2×C3×C4C23×D311yescharacteristic
402C2×C3×C4C23×D311yescharacteristic
403#67—42no—
404#67—122no—
405#67—122no—
406#67—122no—
407#67—122no—
408#67—242no—
409C2×Dic3—21no—
410C2×Dic3—41no—
411C2×Dic3—61no—
412C2×Dic3—62no—
413C2×Dic3—61no—
414C2×Dic3—62no—
415C2×Dic3—122no—
416C2×Dic3—121no—
417C2×Dic3—122no—
418C2×Dic3—122no—
419C2×Dic3—122no—
420C2×Dic3—124no—
421C2×Dic3—124no—
422C2×Dic3—242no—
423C2×Dic3D2414yescomplemented
424C2×Dic3C2×D1211yescharacteristic
425C2×Dic3C2×D1211yescharacteristic
426C2×Dic3C2×D1211yescharacteristic
427C2×Dic3C2×D1211yescharacteristic
428D12—24no—
429D12—22no—
430D12—22no—
431D12—62no—
432D12—62no—
433D12—122no—
434D12—122no—
435D12—122no—
436D12#23714yescomplemented
437C4×D3—122no—
438C4×D3—124no—
439C4×D3—124no—
440C4×D3—122no—
441C4×D3—122no—
442Dic6—122no—
443Dic6—122no—
444C3×C8—22no—
445C3×C8—22no—
446C3×C8—42no—
447C3×C8—62no—
448C3⋊C8—22no—
449C2×C32—22no—
450C2×C32#52511yescharacteristic
451C2×C32C22×D811yescharacteristic
452C2×C32#57511yescharacteristic
453C3⋊D3—81no—
454C3×D3—44no—
455C3×D3—81no—
456C24—61no—
457#41—364no—
458C2×Q8—181no—
459C2×D4—32no—
460C2×D4—31no—
461C2×D4—64no—
462C2×D4—61no—
463C2×D4—61no—
464C2×D4—91no—
465C2×D4—181no—
466C2×D4—181no—
467C2×D4—181no—
468C22×C4—31no—
469C22×C4—31no—
470C22×C4—181no—
471C22×C4—182no—
472C22×C4—182no—
473C22×C4—181no—
474C22×C4—181no—
475C22×C4—364no—
476C22×C4C2×D3211yescharacteristic
477D8—64no—
478D8—184no—
479C2×C8—32no—
480C2×C8C2×D3212yes—
481C4⋊C4—31no—
482C4⋊C4—92no—
483C4⋊C4—91no—
484C4⋊C4—181no—
485C4⋊C4—181no—
486C22⋊C4—61no—
487C22⋊C4—181no—
488C22⋊C4—182no—
489C22⋊C4—182no—
490C22⋊C4—181no—
491C22⋊C4—181no—
492C42—31no—
493C42—31no—
494C42—31no—
495C42—31no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—22no—
502C22×C3—41no—
503C22×C3—41no—
504C22×C3—64no—
505C22×C3—128no—
506C22×C3—122no—
507C22×C3—122no—
508C22×C3—121no—
509C22×C3—121no—
510C22×C3—121no—
511C22×C3C2×D2412yes—
512C22×C3D3×D812yes—
513C22×C3C22×D1211yescharacteristic
514C22×C3C2×D3×D411yescharacteristic
515C2×D3—24no—
516C2×D3—48no—
517C2×D3—42no—
518C2×D3—42no—
519C2×D3—41no—
520C2×D3—41no—
521C2×D3—41no—
522C2×D3—121no—
523C2×D3—121no—
524C2×D3—121no—
525C2×D3—121no—
526C2×D3—121no—
527C2×D3—121no—
528C2×D3—241no—
529C2×D3—241no—
530C2×D3—241no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—22no—
534C3×C4—32no—
535C3×C4—32no—
536C3×C4—41no—
537C3×C4—61no—
538C3×C4—61no—
539C3×C4—121no—
540C3×C4C2×#23712yes—
541C3×C4D3×#4112yes—
542Dic3—21no—
543Dic3—21no—
544Dic3—41no—
545Dic3—121no—
546Dic3—122no—
547Dic3—121no—
548Dic3—122no—
549Dic3—242no—
550Dic3—241no—
551Dic3C2×D2412yes—
552Dic3C2×D2412yes—
553C32#310011yescharacteristic, complemented, Sylow
554C23—64no—
555C23—62no—
556C23—61no—
557C23—122no—
558C23—122no—
559C23—181no—
560C23D3×D1211yescharacteristic
561Q8—362no—
562D4—34no—
563D4—64no—
564D4—62no—
565D4—62no—
566D4—122no—
567D4—182no—
568D4—362no—
569D4—362no—
570D4—362no—
571C2×C4—22no—
572C2×C4—31no—
573C2×C4—31no—
574C2×C4—34no—
575C2×C4—31no—
576C2×C4—31no—
577C2×C4—61no—
578C2×C4—121no—
579C2×C4—182no—
580C2×C4—181no—
581C2×C4—362no—
582C2×C4—364no—
583C2×C4—364no—
584C2×C4—362no—
585C2×C4—362no—
586C2×C4D3×D1211yescharacteristic
587C2×C4C22×D3211yescharacteristic
588C8—22no—
589C8—62no—
590C2×C3—22no—
591C2×C3—22no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—42no—
596C2×C3—124no—
597C2×C3—241no—
598C2×C3#552411yescharacteristic
599C2×C3#558611yescharacteristic
600C2×C3C22×D2411yescharacteristic
601C2×C3#574811yescharacteristic
602C2×C3C2×D3×D811yescharacteristic
603C2×C3#577311yescharacteristic
604D3—44no—
605D3—81no—
606D3—241no—
607D3—241no—
608D3—481no—
609C22—21no—
610C22—21no—
611C22—64no—
612C22—128no—
613C22—122no—
614C22—122no—
615C22—121no—
616C22—121no—
617C22—121no—
618C22—361no—
619C22—361no—
620C22—361no—
621C22D3×D2412yes—
622C22C2×D3×D1211yescharacteristic
623C4—21no—
624C4—32no—
625C4—32no—
626C4—61no—
627C4—61no—
628C4—121no—
629C4—362no—
630C4—361no—
631C4D3×#23712yes—
632C3—21no—
633C3#7929711yescharacteristic, complemented
634C3#7998811yescharacteristic, complemented
635C2—22no—
636C2—124no—
637C2—241no—
638C2—721no—
639C2#1059407811yescharacteristic
640C2C2×D3×D2411yescharacteristic
641C2#1059471211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3100
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10594910C2semidirect
2. C2×Dic3×D12C2semidirect
3. #10592435C2semidirect
4. C3×#4732C2semidirect
5. C3×#4718C2semidirect
6. #10591162C2semidirect
7. #10591094C2semidirect
8. #10590762C2semidirect
9. Dic3×D24C2semidirect
10. #10590753C2semidirect
11. #10590745C2semidirect
24. #63918C22semidirect
25. #63911C22semidirect
26. #63894C22semidirect
31. Dic3×D12C22semidirect
36. #63648C22semidirect
37. #63645C22semidirect
40. C3×Dic3⋊C8C22semidirect
41. C3×C8×Dic3C22semidirect
42. #63575C22semidirect
44. #63563C22semidirect
64. #4732D3semidirect
65. #4718D3semidirect
173. Dic3⋊C8C2×D3semidirect
174. C8×Dic3C2×D3semidirect
194. C2×C3×Dic3D8semidirect
202. C3×D12#41semidirect
423. C2×Dic3D24semidirect
436. D12#237semidirect
553. C32#3100semidirect
633. C3#79297semidirect
634. C3#79988semidirect

Maximal subgroups

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

subgroupindex
#105949102
C2×Dic3×D122
#105924352
C3×#47322
C3×#47182
#105911622
#105910942
#105907622
Dic3×D242
#105907532
#105907452
#799883
#792973