Finite Group Databasebeta

← #11792248

Subgroups — #11792248

Order 1152.

861 conjugacy classes of subgroups.

The subgroup lattice has 653 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#908C211yesmaximal, characteristic, complemented
2#10595044C211yesmaximal, characteristic, complemented
3C2×#63823C211yesmaximal, characteristic, complemented
4C2×C3×#825C211yesmaximal, characteristic, complemented
5#10591318C211yesmaximal, characteristic, complemented
6C2×#63569C211yesmaximal, characteristic, complemented
7#10589420C211yesmaximal, characteristic, complemented
8#72098—31nomaximal
9#70392—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C3×#908—22no—
18C3×#908—22no—
19C2×C3×D24—21no—
20C2×C3×#204—21no—
21#63980—22no—
22C2×(C2×D3)⋊Dic3—22no—
23#63908—21no—
24#63908—21no—
25#63856—21no—
26#63856—21no—
27C2×#3715—21no—
28#63823—22no—
29#63823—22no—
30C2×#3713—21no—
31C3×#825—22no—
32#63569—22no—
33C2×C3×AGL(1,ℤ/8)—31no—
34#5833—31no—
35#5833—31no—
36C2×#949—31no—
37C2×#932—31no—
38C2×#908D311yescharacteristic, complemented
39C2×C3×#104—31no—
40C2×#837—31no—
41#5221—31no—
42C2×#825D311yescharacteristic, complemented
43#4939—31no—
44C2×#805—31no—
45#4554—31no—
46#4554—31no—
47#4554—61no—
48C23×C3×D3—21no—
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3D412yes—
51C2×C3×#67—21no—
52C2×C3×#67—21no—
53C22×C3×Dic3—21no—
54C3×#235—21no—
55C3×#235—21no—
56C3×#235—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C3×#235—21no—
62C2×C3×D12—21no—
63C2×C3×D12—21no—
64C2×C3×D12—21no—
65C2×C3×D12—21no—
66C2×C3×D12—21no—
67C2×C3×D12D411yescharacteristic
68C2×C3×D12D411yescharacteristic
69C2×C3×D12D412yescomplemented
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×C3×Dic6D411yescharacteristic
74C2×#625—22no—
75C32×M16—21no—
76C32×M16D412yescomplemented
77C2×C32×C8—21no—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)—21no—
80#3748—21no—
81#3748D412yescomplemented
82C2×C3⋊(C3⋊C8)—21no—
83C3×C4×Dic3—21no—
84C3×C4×Dic3—21no—
85C3×D24—24no—
86C3×#204—24no—
87#3724—22no—
88(C2×D3)⋊Dic3—22no—
89(C2×D3)⋊Dic3—22no—
90(C2×D3)⋊Dic3—44no—
91#3715—24no—
92#3713—24no—
93#2006—91noSylow
94C2×C3×#41—31no—
95C2×C3×#41—31no—
96C22×C3×D4—31no—
97C2×#235C2×D311yescharacteristic
98C2×#235C2×D311yescharacteristic
99C22×D12C2×D311yescharacteristic
100C3×AGL(1,ℤ/8)—62no—
101C3×AGL(1,ℤ/8)—62no—
102C2×C3×SD16—61no—
103C2×C3×D8—61no—
104C2×C3×M16—21no—
105C2×C3×M16C2×D311yescharacteristic
106C2×C3×M16C2×D311yescharacteristic
107C2×C3×C42—31no—
108C2×#217—62no—
109#949—62no—
110#949—62no—
111#946—61no—
112#946—61no—
113C2×#215—61no—
114#939—62no—
115#939—62no—
116#938—61no—
117#938—61no—
118C2×#214—61no—
119#932—62no—
120#932—62no—
121C2×#213—61no—
122C2×#213—61no—
123#930—61no—
124#930—61no—
125C2×(C2×D3)⋊C4—62no—
126C2×C4⋊Dic3—31no—
127C2×C4⋊Dic3—31no—
128C2×C4⋊Dic3—61no—
129#924—61no—
130#924—61no—
131C2×C4×Dic3C2×D311yescharacteristic
132C2×#208—31no—
133C2×#208—31no—
134C2×#208—61no—
135#908—22no—
136#908—22no—
137C2×D24—21no—
138C2×#204—21no—
139C3×#104—62no—
140#837—62no—
141#825—22no—
142#805—62no—
143C23×C32C2×D411yescharacteristic
144C22×C3×D3—21no—
145C22×C3×D3—21no—
146C22×C3×D3—22no—
147C22×C3×D3—42no—
148C22×C3×D3—42no—
149C22×C3×D3—41no—
150C22×C3×D3—41no—
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4#4111yescharacteristic
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—42no—
159C3×#67—41no—
160C3×#67—41no—
161C3×#67—41no—
162C3×#67—41no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—41no—
167C2×C3×Dic3—41no—
168C3×D12—21no—
169C3×D12—22no—
170C3×D12—22no—
171C3×D12—21no—
172C3×D12—21no—
173C3×D12—21no—
174C3×D12—41no—
175C3×D12—41no—
176C3×C4×D3—41no—
177C3×C4×D3—41no—
178C3×C4×D3—41no—
179C3×C4×D3—41no—
180C3×Dic6—21no—
181C3×Dic6—21no—
182C3×Dic6—21no—
183C3×Dic6—21no—
184#625—82no—
185C32×C8—22no—
186C3⋊(C3⋊C8)—22no—
187C2×AGL(1,ℤ/8)—31no—
188C2×AGL(1,ℤ/8)—91no—
189#537—91no—
190C2×#104—31no—
191C2×#104—91no—
192#390—91no—
193#343—91no—
194C24×C3—61no—
195C23×D3—21no—
196C3×#41—61no—
197C3×#41—61no—
198C3×#41—61no—
199C3×#41—61no—
200C3×#41—61no—
201C3×#41—61no—
202C3×#41—61no—
203C3×#41—61no—
204C2×C3×Q8—31no—
205C2×C3×Q8—31no—
206C2×C3×D4—31no—
207C2×C3×D4—32no—
208C2×C3×D4—31no—
209C2×C3×D4—61no—
210C2×C3×D4—61no—
211C2×C3×D4—61no—
212C2×C3×D4—61no—
213C2×C3×D4—61no—
214C2×C3×D4—61no—
215C2×C3×D4—61no—
216C22×C3×C4—21no—
217C22×C3×C4—61no—
218C22×C3×C4—61no—
219C22×C3×C4—61no—
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C2×#67—21no—
223C2×#67—21no—
224C2×#67—62no—
225C2×#67—62no—
226C22×Dic3—21no—
227C22×Dic3—32no—
228C22×Dic3—32no—
229C22×Dic3—62no—
230#235—21no—
231#235—21no—
232#235—21no—
233#235—21no—
234#235—21no—
235#235—21no—
236#235—21no—
237#235—21no—
238C2×D12—21no—
239C2×D12—21no—
240C2×D12—21no—
241C2×D12—21no—
242C2×D12—21no—
243C2×D12D1211yescharacteristic
244C2×D12#6711yescharacteristic
245C2×D12#6712yescomplemented
246C2×C4×D3—21no—
247C2×C4×D3—21no—
248C2×Dic6D1211yescharacteristic
249C2×Dic6#6711yescharacteristic
250C3×SD16—64no—
251C3×D8—64no—
252C3×M16—21no—
253C3×M16—21no—
254C3×M16—22no—
255C3×M16—41no—
256C3×M16#6712yescomplemented
257C3×M16#6712yescomplemented
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8—41no—
261C3×C42—61no—
262C3×C42—61no—
263#217—62no—
264#217—62no—
265#217—124no—
266#215—64no—
267#214—64no—
268#213—64no—
269#213—64no—
270(C2×D3)⋊C4—62no—
271(C2×D3)⋊C4—62no—
272(C2×D3)⋊C4—124no—
273C4⋊Dic3—61no—
274C4⋊Dic3—61no—
275C4⋊Dic3—61no—
276C4⋊Dic3—61no—
277C4⋊Dic3—121no—
278C4⋊Dic3—121no—
279Dic3⋊C4—62no—
280Dic3⋊C4—62no—
281C4×Dic3—21no—
282C4×Dic3—21no—
283#208—32no—
284#208—32no—
285#208—62no—
286#208—61no—
287#208—61no—
288#208—121no—
289C2×C3⋊C8—61no—
290C2×C3⋊C8—61no—
291C2×C3⋊C8—121no—
292D24—24no—
293#204—24no—
294C22×C32—21no—
295C22×C32—21no—
296C22×C32#12011yescharacteristic
297C22×C32#12111yescharacteristic
298C22×C32#12711yescharacteristic
299C2×C3×D3—44no—
300C2×C3×D3—41no—
301C2×C3×D3—41no—
302C2×C3×D3—42no—
303C2×C3×D3—41no—
304C2×C3×D3—41no—
305C2×C3×D3—41no—
306C2×C3×D3—41no—
307C2×C3×D3—82no—
308C2×C3×D3—81no—
309C2×C3×D3—81no—
310C32×C4#12011yescharacteristic
311C32×C4#12011yescharacteristic
312C32×C4#12111yescharacteristic
313C32×C4#12111yescharacteristic
314C3⋊Dic3—42no—
315C3×Dic3—42no—
316C3×Dic3—41no—
317C3×Dic3—41no—
318C2×#41—31no—
319C2×#41—31no—
320C22×D4—31no—
321AGL(1,ℤ/8)—62no—
322AGL(1,ℤ/8)—62no—
323AGL(1,ℤ/8)—182no—
324AGL(1,ℤ/8)—182no—
325C2×SD16—61no—
326C2×SD16—181no—
327C2×D8—61no—
328C2×D8—181no—
329C2×M16—91no—
330C2×M16D3211yescharacteristic
331C22⋊Q8—181no—
332C22⋊Q8—181no—
333#121—181no—
334#121—181no—
335#121—182no—
336C2×C4⋊C4—91no—
337C2×C22⋊C4—182no—
338C2×C42—31no—
339#104—62no—
340#104—182no—
341C23×C3—21no—
342C23×C3—61no—
343C23×C3—62no—
344C23×C3—61no—
345C23×C3—122no—
346C23×C3—122no—
347C23×C3—121no—
348C23×C3—121no—
349C23×C3D3×D411yescharacteristic
350C23×C3D3×D411yescharacteristic
351C22×D3—21no—
352C22×D3—21no—
353C22×D3—22no—
354C22×D3—42no—
355C22×D3—42no—
356C22×D3—41no—
357C22×D3—41no—
358C3×Q8—61no—
359C3×Q8—61no—
360C3×Q8—61no—
361C3×Q8—61no—
362C3×D4—62no—
363C3×D4—61no—
364C3×D4—61no—
365C3×D4—61no—
366C3×D4—62no—
367C3×D4—61no—
368C3×D4—121no—
369C3×D4—121no—
370C3×D4—121no—
371C3×D4—121no—
372C3×D4—121no—
373C3×D4—121no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—62no—
381C2×C3×C4—61no—
382C2×C3×C4—61no—
383C2×C3×C4—121no—
384C2×C3×C4—121no—
385C2×C3×C4—121no—
386C2×C3×C4—121no—
387C2×C3×C4—121no—
388C2×C3×C4—121no—
389C2×C3×C4C2×D1211yescharacteristic
390C2×C3×C4#23511yescharacteristic
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4D3×D411yescharacteristic
394C2×C3×C4D3×D411yescharacteristic
395C2×C3×C4D3×D411yescharacteristic
396C2×C3×C4#23711yescharacteristic
397C2×C3×C4C2×#6711yescharacteristic
398C2×C3×C4C2×#6711yescharacteristic
399C2×C3×C4C2×#6711yescharacteristic
400C2×C3×C4C2×#6711yescharacteristic
401#67—41no—
402#67—41no—
403#67—41no—
404#67—41no—
405#67—242no—
406#67—242no—
407C2×Dic3—22no—
408C2×Dic3—21no—
409C2×Dic3—21no—
410C2×Dic3—41no—
411C2×Dic3—41no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—122no—
415C2×Dic3—122no—
416C2×Dic3—122no—
417C2×Dic3—242no—
418D12—21no—
419D12—21no—
420D12—22no—
421D12—21no—
422D12—22no—
423D12—21no—
424D12—41no—
425D12—41no—
426C4×D3—41no—
427C4×D3—41no—
428C4×D3—41no—
429C4×D3—41no—
430Dic6—21no—
431Dic6—21no—
432Dic6—21no—
433Dic6—21no—
434C3×C8—22no—
435C3×C8—22no—
436C3×C8—42no—
437C3⋊C8—62no—
438C3⋊C8—62no—
439C3⋊C8—122no—
440C2×C32—21no—
441C2×C32—21no—
442C2×C32#39211yescharacteristic
443C2×C32#45311yescharacteristic
444C2×C32#45411yescharacteristic
445C3×D3—81no—
446C3×D3—81no—
447C3×D3—82no—
448C24—61no—
449#41—61no—
450#41—61no—
451#41—61no—
452#41—61no—
453#41—61no—
454#41—61no—
455#41—61no—
456#41—61no—
457C2×Q8—31no—
458C2×Q8—31no—
459C2×D4—31no—
460C2×D4—31no—
461C2×D4—32no—
462C2×D4—61no—
463C2×D4—61no—
464C2×D4—61no—
465C2×D4—61no—
466C2×D4—61no—
467C2×D4—61no—
468C2×D4—61no—
469C2×D4—182no—
470C22×C4—61no—
471C22×C4—61no—
472C22×C4—61no—
473C22×C4—92no—
474C22×C4C2×D3211yescharacteristic
475SD16—64no—
476SD16—184no—
477D8—64no—
478D8—184no—
479M16—21no—
480M16—92no—
481M16—181no—
482M16#62512yescomplemented
483C2×C8—21no—
484C2×C8—181no—
485C4⋊C4—182no—
486C4⋊C4—181no—
487C4⋊C4—181no—
488C22⋊C4—182no—
489C22⋊C4—182no—
490C22⋊C4—364no—
491C42—61no—
492C42—61no—
493C22×C3—21no—
494C22×C3—21no—
495C22×C3—21no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—41no—
501C22×C3—41no—
502C22×C3—124no—
503C22×C3—121no—
504C22×C3—121no—
505C22×C3—121no—
506C22×C3—122no—
507C22×C3—121no—
508C22×C3—121no—
509C22×C3—121no—
510C22×C3—242no—
511C22×C3—241no—
512C22×C3—241no—
513C22×C3#88211yescharacteristic
514C22×C3#88411yescharacteristic
515C22×C3#93711yescharacteristic
516C22×C3#93911yescharacteristic
517C22×C3#94011yescharacteristic
518C22×C3#94011yescharacteristic
519C2×D3—44no—
520C2×D3—41no—
521C2×D3—41no—
522C2×D3—41no—
523C2×D3—41no—
524C2×D3—42no—
525C2×D3—41no—
526C2×D3—41no—
527C2×D3—82no—
528C2×D3—81no—
529C2×D3—81no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—21no—
534C3×C4—122no—
535C3×C4—121no—
536C3×C4—121no—
537C3×C4#88211yescharacteristic
538C3×C4#88411yescharacteristic
539C3×C4#93011yescharacteristic
540C3×C4#93711yescharacteristic
541C3×C4#93711yescharacteristic
542C3×C4#93811yescharacteristic
543C3×C4#93911yescharacteristic
544C3×C4#95311yescharacteristic
545Dic3—42no—
546Dic3—41no—
547Dic3—41no—
548Dic3—122no—
549Dic3—122no—
550Dic3—242no—
551C32#200611yescharacteristic, complemented, Sylow
552C23—62no—
553C23—61no—
554C23—61no—
555C23—122no—
556C23—122no—
557C23—121no—
558C23—121no—
559C23#380211yescharacteristic
560Q8—61no—
561Q8—61no—
562Q8—61no—
563Q8—61no—
564D4—61no—
565D4—61no—
566D4—61no—
567D4—62no—
568D4—61no—
569D4—62no—
570D4—121no—
571D4—121no—
572D4—121no—
573D4—121no—
574D4—121no—
575D4—121no—
576D4—722no—
577C2×C4—62no—
578C2×C4—61no—
579C2×C4—61no—
580C2×C4—121no—
581C2×C4—121no—
582C2×C4—121no—
583C2×C4—121no—
584C2×C4—121no—
585C2×C4—121no—
586C2×C4—182no—
587C2×C4—362no—
588C2×C4#379511yescharacteristic
589C2×C4D3×D1211yescharacteristic
590C2×C4#380211yescharacteristic
591C2×C4C2×#62511yescharacteristic
592C2×C4D3×#6711yescharacteristic
593C2×C4D3×#6711yescharacteristic
594C8—22no—
595C8—182no—
596C2×C3—21no—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—41no—
604C2×C3—41no—
605C2×C3—241no—
606C2×C3—242no—
607C2×C3—241no—
608C2×C3#482211yescharacteristic
609C2×C3#482711yescharacteristic
610C2×C3#496011yescharacteristic
611C2×C3#519811yescharacteristic
612C2×C3#520111yescharacteristic
613C2×C3#522311yescharacteristic
614D3—82no—
615D3—81no—
616D3—81no—
617C22—21no—
618C22—21no—
619C22—124no—
620C22—121no—
621C22—121no—
622C22—121no—
623C22—121no—
624C22—121no—
625C22—121no—
626C22—122no—
627C22—242no—
628C22—241no—
629C22—241no—
630C22#6388511yescharacteristic
631C22#6391411yescharacteristic
632C22#6392211yescharacteristic
633C4—122no—
634C4—121no—
635C4—121no—
636C4—362no—
637C4#6388511yescharacteristic
638C4#6390811yescharacteristic
639C4#6392211yescharacteristic
640C4#6397611yescharacteristic
641C3—21no—
642C3#7039211yescharacteristic, complemented
643C3#7209811yescharacteristic, complemented
644C2—21no—
645C2—21no—
646C2—242no—
647C2—241no—
648C2—241no—
649C2#1059101311yescharacteristic
650C2#1059101911yescharacteristic
651C2#1059138911yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#120
hypercenterC2×M16D32
hypocenterC32#2006
LCSG ▷ C22×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
1. C2×C3×#908C2semidirect
2. #10595044C2semidirect
3. C2×#63823C2semidirect
4. C2×C3×#825C2semidirect
5. #10591318C2semidirect
6. C2×#63569C2semidirect
7. #10589420C2semidirect
38. C2×#908D3semidirect
42. C2×#825D3semidirect
69. C2×C3×D12D4semidirect
76. C32×M16D4semidirect
81. #3748D4semidirect
245. C2×D12#67semidirect
256. C3×M16#67semidirect
257. C3×M16#67semidirect
482. M16#625semidirect
551. C32#2006semidirect
642. C3#70392semidirect
643. C3#72098semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9082
#105950442
C2×#638232
C2×C3×#8252
#105913182
C2×#635692
#105894202
#720983
#703923