Finite Group Databasebeta

← #11792247

Subgroups — #11792247

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#908C211yesmaximal, characteristic, complemented
2#10595043C211yesmaximal, characteristic, complemented
3C2×#63830C211yesmaximal, characteristic, complemented
4C2×#63652C211yesmaximal, characteristic, complemented
5#10591323C211yesmaximal, characteristic, complemented
6C2×#63568C211yesmaximal, characteristic, complemented
7C3×#4554C211yesmaximal, characteristic, complemented
8#72098—31nomaximal
9#69008—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#908—22no—
18C3×#908—22no—
19C2×C3×D24—21no—
20C2×C3×#204—21no—
21#63978—22no—
22C2×(C2×D3)⋊Dic3—22no—
23#63916—21no—
24#63909—21no—
25#63871—21no—
26#63857—21no—
27#63830—22no—
28#63830—22no—
29C2×#3716—21no—
30C2×#3714—21no—
31#63652—22no—
32#63568—22no—
33C2×C3×AGL(1,ℤ/8)—31no—
34#5833—31no—
35C2×#932—31no—
36C2×#908—31no—
37C2×#908D311yescharacteristic, complemented
38#5510—31no—
39C2×#837—31no—
40#5221—31no—
41C2×#825—31no—
42C2×#825—31no—
43C2×#825—31no—
44C2×#825—61no—
45#4988—31no—
46C3×#343—31no—
47#4554D311yescharacteristic, complemented
48C23×C3×D3—21no—
49C22×C32×C4C2311yescharacteristic
50C2×#638—21no—
51C22×C3⋊Dic3—21no—
52#3828—21no—
53#3828—21no—
54#3828—21no—
55#3828—21no—
56C2×C4⋊(C3⋊D3)D411yescharacteristic
57C2×C4×C3⋊D3—21no—
58C2×#634D411yescharacteristic
59C2×C3×#67—21no—
60C22×C3×Dic3D412yes—
61C3×#235—21no—
62C3×#235—21no—
63C3×#235—21no—
64C3×#235—21no—
65C2×C3×D12—21no—
66C2×C3×D12—21no—
67C2×C3×D12—21no—
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12D411yescharacteristic
71C2×C3×D12D412yescomplemented
72C2×C3×C4×D3—21no—
73C2×C3×Dic6D411yescharacteristic
74C2×#626—22no—
75C32×M16—21no—
76C32×M16D412yescomplemented
77C2×C32×C8—21no—
78C4×C3⋊Dic3—21no—
79C4×C3⋊Dic3—21no—
80C3×C4⋊Dic3—21no—
81C3×C4⋊Dic3—21no—
82C3×#208—21no—
83C3×#208D412yescomplemented
84C2×C3×C3⋊C8—21no—
85C3×D24—24no—
86C3×#204—24no—
87Dic3⋊Dic3—22no—
88#3722—22no—
89(C2×D3)⋊Dic3—22no—
90(C2×D3)⋊Dic3—44no—
91#3716—24no—
92#3714—24no—
93#2006—91noSylow
94C2×C3×#41—31no—
95C22×C3×D4—31no—
96C2×#235—31no—
97C2×#235—31no—
98C2×#235—61no—
99C2×#235C2×D311yescharacteristic
100C22×D12C2×D311yescharacteristic
101C3×AGL(1,ℤ/8)—62no—
102C3×AGL(1,ℤ/8)—62no—
103C2×C3×SD16—61no—
104C2×C3×D8—61no—
105C2×C3×M16—21no—
106C2×C3×M16—31no—
107C2×C3×M16C2×D311yescharacteristic
108C2×C3×M16C2×D311yescharacteristic
109C2×C3×C4⋊C4—31no—
110C2×#217—62no—
111#946—61no—
112#939—62no—
113#938—61no—
114C2×#214—61no—
115#932—62no—
116#932—62no—
117C2×#213—61no—
118#930—61no—
119#930—62no—
120C2×(C2×D3)⋊C4—62no—
121C2×C4⋊Dic3C2×D311yescharacteristic
122#924—61no—
123C2×C4×Dic3—31no—
124C2×C4×Dic3—31no—
125C2×C4×Dic3—61no—
126C2×#208C2×D311yescharacteristic
127#908—22no—
128#908—22no—
129#908—62no—
130#908—62no—
131C2×D24—21no—
132C2×D24—61no—
133C2×#204—21no—
134C2×#204—61no—
135#897—61no—
136#897—61no—
137#895—61no—
138#895—61no—
139#837—62no—
140#825—64no—
141#825—62no—
142#825—62no—
143#825—62no—
144C23×C32C2×D411yescharacteristic
145C22×C3⋊D3—21no—
146C22×C3×D3—21no—
147C22×C3×D3—22no—
148C22×C3×D3—42no—
149C22×C3×D3—42no—
150C22×C3×D3—41no—
151C22×C3×D3—41no—
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4#4111yescharacteristic
158#638—41no—
159#638—41no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3—41no—
163C2×C3⋊Dic3—41no—
164C4⋊(C3⋊D3)—21no—
165C4⋊(C3⋊D3)—21no—
166C4×C3⋊D3—41no—
167C4×C3⋊D3—41no—
168#634—21no—
169#634—21no—
170C3×#67—41no—
171C3×#67—41no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—42no—
175C3×D12—22no—
176C3×D12—22no—
177C3×D12—21no—
178C3×D12—21no—
179C3×D12—41no—
180C3×D12—41no—
181C3×C4×D3—41no—
182C3×C4×D3—41no—
183C3×Dic6—21no—
184C3×Dic6—21no—
185#626—82no—
186C32×C8—22no—
187C3×C3⋊C8—22no—
188C2×AGL(1,ℤ/8)—31no—
189C2×AGL(1,ℤ/8)—91no—
190#537—91no—
191C2×#104—91no—
192C2×#104—91no—
193#390—91no—
194#343—31no—
195C24×C3—61no—
196C23×D3—21no—
197C3×#41—61no—
198C3×#41—61no—
199C3×#41—61no—
200C3×#41—61no—
201C2×C3×Q8—31no—
202C2×C3×D4—32no—
203C2×C3×D4—31no—
204C2×C3×D4—61no—
205C2×C3×D4—61no—
206C2×C3×D4—61no—
207C2×C3×D4—61no—
208C2×C3×D4—61no—
209C2×C3×D4—61no—
210C22×C3×C4—21no—
211C22×C3×C4—32no—
212C22×C3×C4—61no—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C2×#67—21no—
216C2×#67—62no—
217C2×#67—61no—
218C2×#67—61no—
219C2×#67—121no—
220C22×Dic3—61no—
221C22×Dic3—61no—
222C22×Dic3—121no—
223C22×Dic3D1212yes—
224#235—21no—
225#235—21no—
226#235—21no—
227#235—21no—
228#235—62no—
229#235—62no—
230#235—61no—
231#235—61no—
232#235—61no—
233#235—61no—
234#235—61no—
235#235—61no—
236#235—61no—
237#235—61no—
238#235—121no—
239#235—121no—
240C2×D12—21no—
241C2×D12—21no—
242C2×D12—21no—
243C2×D12—21no—
244C2×D12—21no—
245C2×D12—31no—
246C2×D12—31no—
247C2×D12—61no—
248C2×D12—62no—
249C2×D12#6711yescharacteristic
250C2×D12#6712yescomplemented
251C2×C4×D3—21no—
252C2×C4×D3—61no—
253C2×C4×D3—61no—
254C2×C4×D3—121no—
255C2×Dic6—31no—
256C2×Dic6—31no—
257C2×Dic6—61no—
258C2×Dic6#6711yescharacteristic
259C3×SD16—64no—
260C3×D8—64no—
261C3×M16—21no—
262C3×M16—21no—
263C3×M16—22no—
264C3×M16—32no—
265C3×M16—41no—
266C3×M16—61no—
267C3×M16D1212yescomplemented
268C3×M16#6712yescomplemented
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—41no—
272C2×C3×C8—61no—
273C3×C4⋊C4—61no—
274C3×C4⋊C4—61no—
275#217—62no—
276#217—124no—
277#214—64no—
278#213—64no—
279(C2×D3)⋊C4—62no—
280(C2×D3)⋊C4—62no—
281(C2×D3)⋊C4—62no—
282(C2×D3)⋊C4—124no—
283C4⋊Dic3—21no—
284C4⋊Dic3—21no—
285C4⋊Dic3—62no—
286Dic3⋊C4—62no—
287C4×Dic3—62no—
288C4×Dic3—61no—
289C4×Dic3—61no—
290C4×Dic3—61no—
291C4×Dic3—61no—
292C4×Dic3—121no—
293#208—21no—
294#208D1212yescomplemented
295C2×C3⋊C8—21no—
296D24—24no—
297D24—64no—
298#204—24no—
299#204—64no—
300C22×C32—21no—
301C22×C32—21no—
302C22×C32#12011yescharacteristic
303C22×C32#12111yescharacteristic
304C22×C32#12711yescharacteristic
305C2×C3⋊D3—41no—
306C2×C3⋊D3—41no—
307C2×C3⋊D3—41no—
308C2×C3×D3—44no—
309C2×C3×D3—41no—
310C2×C3×D3—42no—
311C2×C3×D3—41no—
312C2×C3×D3—41no—
313C2×C3×D3—82no—
314C2×C3×D3—81no—
315C2×C3×D3—81no—
316C32×C4#12011yescharacteristic
317C32×C4#12011yescharacteristic
318C32×C4#12111yescharacteristic
319C32×C4#12111yescharacteristic
320C3⋊Dic3—42no—
321C3⋊Dic3—41no—
322C3×Dic3—41no—
323C3×Dic3—42no—
324C2×#41—31no—
325C2×#41—91no—
326C22×D4—31no—
327AGL(1,ℤ/8)—62no—
328AGL(1,ℤ/8)—62no—
329AGL(1,ℤ/8)—182no—
330AGL(1,ℤ/8)—182no—
331C2×SD16—61no—
332C2×SD16—181no—
333C2×D8—61no—
334C2×D8—181no—
335C2×M16—31no—
336C2×M16D3211yescharacteristic
337C22⋊Q8—181no—
338C22⋊Q8—181no—
339#121—181no—
340#121—181no—
341#121—182no—
342C2×C4⋊C4—31no—
343C2×C22⋊C4—182no—
344C2×C42—91no—
345#104—182no—
346#104—182no—
347C23×C3—21no—
348C23×C3—61no—
349C23×C3—62no—
350C23×C3—122no—
351C23×C3—122no—
352C23×C3—121no—
353C23×C3—121no—
354C23×C3C2×D1211yescharacteristic
355C23×C3D3×D411yescharacteristic
356C22×D3—21no—
357C22×D3—22no—
358C22×D3—42no—
359C22×D3—42no—
360C22×D3—41no—
361C22×D3—41no—
362C22×D3—61no—
363C22×D3—61no—
364C22×D3—121no—
365C3×Q8—61no—
366C3×Q8—61no—
367C3×D4—62no—
368C3×D4—61no—
369C3×D4—62no—
370C3×D4—61no—
371C3×D4—121no—
372C3×D4—121no—
373C3×D4—121no—
374C3×D4—121no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—61no—
382C2×C3×C4—62no—
383C2×C3×C4—121no—
384C2×C3×C4—121no—
385C2×C3×C4—122no—
386C2×C3×C4C2×D1211yescharacteristic
387C2×C3×C4C2×D1211yescharacteristic
388C2×C3×C4D3×D411yescharacteristic
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4#23711yescharacteristic
394C2×C3×C4#23911yescharacteristic
395C2×C3×C4C2×#6711yescharacteristic
396C2×C3×C4C2×#6711yescharacteristic
397C2×C3×C4C2×#6711yescharacteristic
398#67—41no—
399#67—41no—
400#67—122no—
401#67—122no—
402#67—121no—
403#67—121no—
404#67—121no—
405#67—121no—
406#67—242no—
407C2×Dic3—22no—
408C2×Dic3—21no—
409C2×Dic3—42no—
410C2×Dic3—62no—
411C2×Dic3—62no—
412C2×Dic3—61no—
413C2×Dic3—61no—
414C2×Dic3—121no—
415C2×Dic3—122no—
416C2×Dic3—122no—
417C2×Dic3—121no—
418C2×Dic3—121no—
419C2×Dic3—122no—
420C2×Dic3—121no—
421C2×Dic3—121no—
422D12—22no—
423D12—21no—
424D12—22no—
425D12—21no—
426D12—41no—
427D12—41no—
428D12—62no—
429D12—61no—
430D12—61no—
431D12—61no—
432D12—61no—
433D12—121no—
434D12—242no—
435C4×D3—41no—
436C4×D3—41no—
437C4×D3—122no—
438C4×D3—122no—
439C4×D3—121no—
440C4×D3—121no—
441C4×D3—121no—
442C4×D3—121no—
443Dic6—21no—
444Dic6—21no—
445Dic6—62no—
446Dic6—61no—
447Dic6—61no—
448Dic6—61no—
449Dic6—61no—
450Dic6—121no—
451C3×C8—22no—
452C3×C8—22no—
453C3×C8—42no—
454C3×C8—62no—
455C3⋊C8—22no—
456C2×C32—21no—
457C2×C32—21no—
458C2×C32#39211yescharacteristic
459C2×C32#45311yescharacteristic
460C2×C32#45411yescharacteristic
461C3⋊D3—81no—
462C3×D3—81no—
463C3×D3—82no—
464C24—61no—
465#41—61no—
466#41—61no—
467#41—61no—
468#41—61no—
469#41—181no—
470#41—181no—
471#41—181no—
472#41—181no—
473C2×Q8—31no—
474C2×Q8—91no—
475C2×D4—31no—
476C2×D4—32no—
477C2×D4—61no—
478C2×D4—61no—
479C2×D4—61no—
480C2×D4—61no—
481C2×D4—61no—
482C2×D4—61no—
483C2×D4—91no—
484C2×D4—182no—
485C2×D4—181no—
486C22×C4—32no—
487C22×C4—61no—
488C22×C4—181no—
489C22×C4—181no—
490C22×C4C2×D3211yescharacteristic
491SD16—64no—
492SD16—184no—
493D8—64no—
494D8—184no—
495M16—21no—
496M16—32no—
497M16—61no—
498M16#62612yescomplemented
499C2×C8—21no—
500C2×C8—61no—
501C4⋊C4—61no—
502C4⋊C4—61no—
503C4⋊C4—182no—
504C22⋊C4—182no—
505C22⋊C4—182no—
506C22⋊C4—364no—
507C42—181no—
508C42—181no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—41no—
517C22×C3—41no—
518C22×C3—124no—
519C22×C3—121no—
520C22×C3—122no—
521C22×C3—121no—
522C22×C3—121no—
523C22×C3—242no—
524C22×C3—241no—
525C22×C3—241no—
526C22×C3#87411yescharacteristic
527C22×C3#88211yescharacteristic
528C22×C3#89511yescharacteristic
529C22×C3#93711yescharacteristic
530C22×C3#93911yescharacteristic
531C22×C3#94011yescharacteristic
532C2×D3—44no—
533C2×D3—41no—
534C2×D3—41no—
535C2×D3—41no—
536C2×D3—42no—
537C2×D3—82no—
538C2×D3—81no—
539C2×D3—81no—
540C2×D3—122no—
541C2×D3—121no—
542C2×D3—121no—
543C2×D3—121no—
544C2×D3—121no—
545C2×D3—121no—
546C2×D3—121no—
547C2×D3—241no—
548C2×D3—241no—
549C3×C4—21no—
550C3×C4—21no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—121no—
554C3×C4—122no—
555C3×C4#88211yescharacteristic
556C3×C4#88211yescharacteristic
557C3×C4#89511yescharacteristic
558C3×C4#89511yescharacteristic
559C3×C4#93711yescharacteristic
560C3×C4#93811yescharacteristic
561C3×C4#93911yescharacteristic
562C3×C4#95311yescharacteristic
563Dic3—41no—
564Dic3—42no—
565Dic3—122no—
566Dic3—122no—
567Dic3—122no—
568Dic3—124no—
569Dic3—121no—
570Dic3—121no—
571C32#200611yescharacteristic, complemented, Sylow
572C23—62no—
573C23—61no—
574C23—122no—
575C23—122no—
576C23—121no—
577C23—121no—
578C23—181no—
579C23D3×D1211yescharacteristic
580Q8—61no—
581Q8—61no—
582Q8—181no—
583Q8—181no—
584D4—61no—
585D4—62no—
586D4—61no—
587D4—62no—
588D4—121no—
589D4—121no—
590D4—121no—
591D4—121no—
592D4—181no—
593D4—181no—
594D4—361no—
595D4—361no—
596D4—722no—
597C2×C4—62no—
598C2×C4—61no—
599C2×C4—121no—
600C2×C4—121no—
601C2×C4—122no—
602C2×C4—182no—
603C2×C4—181no—
604C2×C4—361no—
605C2×C4—361no—
606C2×C4—361no—
607C2×C4—361no—
608C2×C4#379611yescharacteristic
609C2×C4D3×D1211yescharacteristic
610C2×C4#380211yescharacteristic
611C2×C4C2×#62611yescharacteristic
612C2×C4D3×#6711yescharacteristic
613C2×C4D3×#6711yescharacteristic
614C8—22no—
615C8—62no—
616C2×C3—21no—
617C2×C3—21no—
618C2×C3—21no—
619C2×C3—21no—
620C2×C3—21no—
621C2×C3—21no—
622C2×C3—21no—
623C2×C3—41no—
624C2×C3—41no—
625C2×C3—242no—
626C2×C3—241no—
627C2×C3#467111yescharacteristic
628C2×C3#474711yescharacteristic
629C2×C3#475311yescharacteristic
630C2×C3#519811yescharacteristic
631C2×C3#520111yescharacteristic
632C2×C3#522311yescharacteristic
633D3—82no—
634D3—81no—
635D3—242no—
636D3—241no—
637D3—241no—
638C22—21no—
639C22—21no—
640C22—124no—
641C22—121no—
642C22—121no—
643C22—121no—
644C22—122no—
645C22—242no—
646C22—241no—
647C22—241no—
648C22—361no—
649C22—361no—
650C22—361no—
651C22#6388611yescharacteristic
652C22#6391111yescharacteristic
653C22#6392211yescharacteristic
654C4—122no—
655C4—121no—
656C4—362no—
657C4—361no—
658C4#6388611yescharacteristic
659C4#6391611yescharacteristic
660C4#6392211yescharacteristic
661C4#6397711yescharacteristic
662C3—21no—
663C3#6900811yescharacteristic, complemented
664C3#7209811yescharacteristic, complemented
665C2—21no—
666C2—21no—
667C2—242no—
668C2—241no—
669C2—721no—
670C2#1059101411yescharacteristic
671C2#1059102011yescharacteristic
672C2#1059139111yescharacteristic
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. #10595043C2semidirect
3. C2×#63830C2semidirect
4. C2×#63652C2semidirect
5. #10591323C2semidirect
6. C2×#63568C2semidirect
7. C3×#4554C2semidirect
37. C2×#908D3semidirect
47. #4554D3semidirect
71. C2×C3×D12D4semidirect
76. C32×M16D4semidirect
83. C3×#208D4semidirect
250. C2×D12#67semidirect
267. C3×M16D12semidirect
268. C3×M16#67semidirect
294. #208D12semidirect
498. M16#626semidirect
571. C32#2006semidirect
663. C3#69008semidirect
664. 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
#105950432
C2×#638302
C2×#636522
#105913232
C2×#635682
C3×#45542
#720983
#690083