Finite Group Databasebeta

← #11792241

Subgroups — #11792241

Order 1152.

961 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64141C211yesmaximal, characteristic, complemented
2C2×C3×#932C211yesmaximal, characteristic, complemented
3#10595043C211yesmaximal, characteristic, complemented
4C3×#5221C211yesmaximal, characteristic, complemented
5C2×#63570C211yesmaximal, characteristic, complemented
6C2×#63569C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#72098—31nomaximal
9#69664—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13C2×#3754—21no—
14#64141—22no—
15#64141—22no—
16C2×#3753—21no—
17C2×#3748C2211yescharacteristic
18C2×C3×#217—22no—
19C2×C3×#214—21no—
20C3×#932—22no—
21C3×#932—22no—
22C2×C3×#213—21no—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26#63978—22no—
27#63916—21no—
28#63909—21no—
29#63871—21no—
30#63857—21no—
31#63570—22no—
32#63569—22no—
33C2×C3×AGL(1,ℤ/8)—31no—
34#5833—31no—
35C2×#932—31no—
36C2×#932—31no—
37C2×#932—61no—
38C2×#932D311yescharacteristic, complemented
39#5510—31no—
40C3×#390—31no—
41C2×#837—31no—
42#5221D311yescharacteristic, complemented
43C2×#825—31no—
44C2×#805—31no—
45C2×#805—31no—
46#4554—31no—
47#4530—31no—
48C24×C32—21no—
49C2×C32×D4—21no—
50C2×C32×D4—21no—
51C2×C32×D4—21no—
52C2×C32×D4—21no—
53C2×C32×D4—21no—
54C2×C32×D4D412yescomplemented
55C22×C32×C4C2311yescharacteristic
56C2×#638—21no—
57#3828—21no—
58#3828—21no—
59#3828—21no—
60#3828—21no—
61C2×C4⋊(C3⋊D3)D411yescharacteristic
62C2×C4×C3⋊D3—21no—
63C2×#634D411yescharacteristic
64C2×C3×#67—21no—
65C22×C3×Dic3—21no—
66C22×C3×Dic3D412yes—
67C3×#235—21no—
68C3×#235—21no—
69C3×#235—21no—
70C3×#235—21no—
71C2×C3×D12D411yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×Dic6D411yescharacteristic
74C2×#626—22no—
75#3754—24no—
76#3753—24no—
77#3748—21no—
78#3748D412yescomplemented
79C2×C3⋊(C3⋊C8)—21no—
80C3×#217—44no—
81C3×#214—24no—
82C3×#213—24no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3—21no—
85C3×C4×Dic3—21no—
86C3×C4×Dic3—21no—
87C3×#208—21no—
88C3×#208D412yescomplemented
89C2×C3×C3⋊C8—21no—
90Dic3⋊Dic3—22no—
91#3722—22no—
92(C2×D3)⋊Dic3—22no—
93#2006—91noSylow
94C2×C3×#41—31no—
95C22×C3×D4—21no—
96C22×C3×D4C2×D311yescharacteristic
97C22×C3×D4C2×D311yescharacteristic
98C2×#235—31no—
99C2×#235—31no—
100C2×#235—61no—
101C2×#235C2×D311yescharacteristic
102C3×AGL(1,ℤ/8)—62no—
103C3×AGL(1,ℤ/8)—62no—
104C2×C3×SD16—61no—
105C2×C3×D8—61no—
106C2×C3×M16—31no—
107C2×C3×C4⋊C4—31no—
108C2×C3×C22⋊C4—62no—
109C2×C3×C42—31no—
110C2×#217—22no—
111#946—61no—
112#939—62no—
113#938—61no—
114C2×#214—21no—
115C2×#214—61no—
116C2×#214—61no—
117C2×#214—62no—
118#932—22no—
119#932—22no—
120#932—62no—
121#932—62no—
122#932—64no—
123#932—64no—
124#932—62no—
125#932—62no—
126C2×#213—21no—
127C2×#213—61no—
128C2×#213—61no—
129C2×#213—62no—
130#930—61no—
131#930—62no—
132C2×C4⋊Dic3C2×D311yescharacteristic
133#924—61no—
134C2×C4×Dic3C2×D311yescharacteristic
135C2×#208—31no—
136C2×#208—31no—
137C2×#208—61no—
138C2×#208C2×D311yescharacteristic
139#897—61no—
140#897—61no—
141#895—61no—
142#895—61no—
143#837—62no—
144#825—62no—
145#805—62no—
146#805—62no—
147C23×C32—22no—
148C23×C32—41no—
149C23×C32—41no—
150C23×C32—42no—
151C23×C32—42no—
152C23×C32C2×D411yescharacteristic
153C22×C3⋊D3—21no—
154C22×C3×D3—21no—
155C32×D4—22no—
156C32×D4—22no—
157C32×D4—41no—
158C32×D4—41no—
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4#4111yescharacteristic
165#638—41no—
166#638—41no—
167C2×C3⋊Dic3—21no—
168C4⋊(C3⋊D3)—21no—
169C4⋊(C3⋊D3)—21no—
170C4×C3⋊D3—41no—
171C4×C3⋊D3—41no—
172#634—21no—
173#634—21no—
174C3×#67—41no—
175C3×#67—41no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—41no—
180C2×C3×Dic3—41no—
181C2×C3×Dic3—42no—
182C3×D12—21no—
183C3×D12—21no—
184C3×C4×D3—41no—
185C3×C4×D3—41no—
186C3×Dic6—21no—
187C3×Dic6—21no—
188#626—82no—
189C3⋊(C3⋊C8)—22no—
190C3×C3⋊C8—22no—
191C2×AGL(1,ℤ/8)—31no—
192C2×AGL(1,ℤ/8)—91no—
193#537—91no—
194C2×#104—91no—
195C2×#104—91no—
196#390—31no—
197#343—91no—
198C24×C3—21no—
199C24×C3—21no—
200C24×C3—41no—
201C3×#41—61no—
202C3×#41—61no—
203C3×#41—61no—
204C3×#41—61no—
205C2×C3×Q8—31no—
206C2×C3×D4—22no—
207C2×C3×D4—22no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—22no—
219C2×C3×D4—31no—
220C2×C3×D4—41no—
221C2×C3×D4—41no—
222C2×C3×D4—41no—
223C2×C3×D4—61no—
224C2×C3×D4D1212yescomplemented
225C2×C3×D4#6712yescomplemented
226C22×C3×C4—21no—
227C22×C3×C4—32no—
228C22×C3×C4—61no—
229C22×C3×C4—61no—
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C2×#67—21no—
233C2×#67—62no—
234C2×#67—61no—
235C2×#67—61no—
236C2×#67—121no—
237C22×Dic3—21no—
238C22×Dic3#6712yes—
239#235—21no—
240#235—21no—
241#235—21no—
242#235—21no—
243#235—62no—
244#235—62no—
245#235—61no—
246#235—61no—
247#235—61no—
248#235—61no—
249#235—61no—
250#235—61no—
251#235—61no—
252#235—61no—
253#235—121no—
254#235—121no—
255C2×D12—31no—
256C2×D12—31no—
257C2×D12—61no—
258C2×D12—62no—
259C2×D12#6711yescharacteristic
260C2×C4×D3—21no—
261C2×C4×D3—61no—
262C2×C4×D3—61no—
263C2×C4×D3—121no—
264C2×Dic6—31no—
265C2×Dic6—31no—
266C2×Dic6—61no—
267C2×Dic6#6711yescharacteristic
268C3×SD16—64no—
269C3×D8—64no—
270C3×M16—32no—
271C3×M16—61no—
272C2×C3×C8—61no—
273C3×C4⋊C4—61no—
274C3×C4⋊C4—61no—
275C3×C22⋊C4—124no—
276C3×C42—61no—
277C3×C42—61no—
278#217—44no—
279#217—62no—
280#214—24no—
281#214—68no—
282#214—64no—
283#214—64no—
284#213—24no—
285#213—68no—
286#213—64no—
287#213—64no—
288(C2×D3)⋊C4—62no—
289(C2×D3)⋊C4—62no—
290(C2×D3)⋊C4—62no—
291C4⋊Dic3—21no—
292C4⋊Dic3—21no—
293C4⋊Dic3—62no—
294Dic3⋊C4—62no—
295C4×Dic3—21no—
296C4×Dic3—21no—
297#208—21no—
298#208—32no—
299#208—32no—
300#208—62no—
301#208—62no—
302#208—61no—
303#208—61no—
304#208#6712yescomplemented
305C2×C3⋊C8—21no—
306C2×C3⋊C8—62no—
307C2×C3⋊C8—61no—
308C2×C3⋊C8—61no—
309C22×C32—21no—
310C22×C32—21no—
311C22×C32—42no—
312C22×C32—44no—
313C22×C32—82no—
314C22×C32—81no—
315C22×C32—81no—
316C22×C32#12011yescharacteristic
317C22×C32#12111yescharacteristic
318C22×C32#12711yescharacteristic
319C2×C3⋊D3—41no—
320C2×C3⋊D3—41no—
321C2×C3⋊D3—41no—
322C2×C3×D3—41no—
323C2×C3×D3—41no—
324C2×C3×D3—41no—
325C32×C4#12011yescharacteristic
326C32×C4#12011yescharacteristic
327C32×C4#12111yescharacteristic
328C32×C4#12111yescharacteristic
329C3⋊Dic3—41no—
330C3×Dic3—42no—
331C3×Dic3—41no—
332C3×Dic3—42no—
333C2×#41—31no—
334C2×#41—91no—
335C22×D4D3211yescharacteristic
336AGL(1,ℤ/8)—62no—
337AGL(1,ℤ/8)—62no—
338AGL(1,ℤ/8)—182no—
339AGL(1,ℤ/8)—182no—
340C2×SD16—61no—
341C2×SD16—181no—
342C2×D8—61no—
343C2×D8—181no—
344C2×M16—31no—
345C2×M16—91no—
346C22⋊Q8—181no—
347C22⋊Q8—181no—
348#121—181no—
349#121—181no—
350#121—182no—
351C2×C4⋊C4—31no—
352C2×C22⋊C4—62no—
353C2×C42—31no—
354#104—182no—
355#104—182no—
356C23×C3—22no—
357C23×C3—22no—
358C23×C3—21no—
359C23×C3—42no—
360C23×C3—42no—
361C23×C3—42no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—41no—
367C23×C3—41no—
368C23×C3—41no—
369C23×C3—41no—
370C23×C3—61no—
371C23×C3—82no—
372C23×C3—82no—
373C23×C3D3×D411yescharacteristic
374C23×C3C2×#6711yescharacteristic
375C22×D3—21no—
376C22×D3—61no—
377C22×D3—61no—
378C22×D3—121no—
379C3×Q8—61no—
380C3×Q8—61no—
381C3×D4—24no—
382C3×D4—22no—
383C3×D4—22no—
384C3×D4—22no—
385C3×D4—22no—
386C3×D4—42no—
387C3×D4—42no—
388C3×D4—42no—
389C3×D4—41no—
390C3×D4—41no—
391C3×D4—41no—
392C3×D4—41no—
393C3×D4—61no—
394C3×D4—61no—
395C3×D4—121no—
396C3×D4—121no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—62no—
404C2×C3×C4—61no—
405C2×C3×C4—62no—
406C2×C3×C4—121no—
407C2×C3×C4—121no—
408C2×C3×C4—121no—
409C2×C3×C4—121no—
410C2×C3×C4—122no—
411C2×C3×C4C2×D1211yescharacteristic
412C2×C3×C4#23511yescharacteristic
413C2×C3×C4D3×D411yescharacteristic
414C2×C3×C4D3×D411yescharacteristic
415C2×C3×C4D3×D411yescharacteristic
416C2×C3×C4D3×D411yescharacteristic
417C2×C3×C4D3×D411yescharacteristic
418C2×C3×C4D3×D411yescharacteristic
419C2×C3×C4#23711yescharacteristic
420C2×C3×C4C2×#6711yescharacteristic
421C2×C3×C4C2×#6711yescharacteristic
422C2×C3×C4C2×#6711yescharacteristic
423#67—41no—
424#67—41no—
425#67—122no—
426#67—122no—
427#67—121no—
428#67—121no—
429#67—121no—
430#67—121no—
431#67—242no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—21no—
435C2×Dic3—41no—
436C2×Dic3—41no—
437C2×Dic3—42no—
438C2×Dic3—61no—
439C2×Dic3—61no—
440C2×Dic3—121no—
441D12—21no—
442D12—21no—
443D12—62no—
444D12—61no—
445D12—61no—
446D12—61no—
447D12—61no—
448D12—121no—
449D12—242no—
450C4×D3—41no—
451C4×D3—41no—
452C4×D3—122no—
453C4×D3—122no—
454C4×D3—121no—
455C4×D3—121no—
456C4×D3—121no—
457C4×D3—121no—
458Dic6—21no—
459Dic6—21no—
460Dic6—62no—
461Dic6—61no—
462Dic6—61no—
463Dic6—61no—
464Dic6—61no—
465Dic6—121no—
466C3×C8—62no—
467C3⋊C8—22no—
468C3⋊C8—64no—
469C3⋊C8—62no—
470C3⋊C8—62no—
471C2×C32—21no—
472C2×C32—21no—
473C2×C32—82no—
474C2×C32#39211yescharacteristic
475C2×C32#45311yescharacteristic
476C2×C32#45411yescharacteristic
477C3⋊D3—81no—
478C3×D3—81no—
479C24—21no—
480#41—61no—
481#41—61no—
482#41—61no—
483#41—61no—
484#41—181no—
485#41—181no—
486#41—181no—
487#41—181no—
488C2×Q8—31no—
489C2×Q8—91no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—31no—
496C2×D4—61no—
497C2×D4—91no—
498C2×D4—182no—
499C2×D4—181no—
500C2×D4#62612yescomplemented
501C22×C4—32no—
502C22×C4—61no—
503C22×C4—61no—
504C22×C4—181no—
505C22×C4C2×D3211yescharacteristic
506SD16—64no—
507SD16—184no—
508D8—64no—
509D8—184no—
510M16—32no—
511M16—61no—
512M16—92no—
513M16—181no—
514C2×C8—61no—
515C2×C8—181no—
516C4⋊C4—61no—
517C4⋊C4—61no—
518C4⋊C4—182no—
519C22⋊C4—124no—
520C22⋊C4—182no—
521C22⋊C4—182no—
522C42—61no—
523C42—61no—
524C22×C3—21no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—21no—
528C22×C3—21no—
529C22×C3—21no—
530C22×C3—21no—
531C22×C3—41no—
532C22×C3—41no—
533C22×C3—44no—
534C22×C3—44no—
535C22×C3—44no—
536C22×C3—42no—
537C22×C3—42no—
538C22×C3—84no—
539C22×C3—82no—
540C22×C3—82no—
541C22×C3—82no—
542C22×C3—82no—
543C22×C3—84no—
544C22×C3—81no—
545C22×C3—81no—
546C22×C3—81no—
547C22×C3—81no—
548C22×C3—121no—
549C22×C3—121no—
550C22×C3—121no—
551C22×C3#93011yescharacteristic
552C22×C3#93711yescharacteristic
553C22×C3#93711yescharacteristic
554C22×C3#93911yescharacteristic
555C22×C3#94011yescharacteristic
556C22×C3#94011yescharacteristic
557C2×D3—41no—
558C2×D3—41no—
559C2×D3—41no—
560C2×D3—122no—
561C2×D3—121no—
562C2×D3—121no—
563C2×D3—121no—
564C2×D3—121no—
565C2×D3—121no—
566C2×D3—121no—
567C2×D3—241no—
568C2×D3—241no—
569C3×C4—21no—
570C3×C4—21no—
571C3×C4—21no—
572C3×C4—21no—
573C3×C4—122no—
574C3×C4—122no—
575C3×C4—121no—
576C3×C4#88211yescharacteristic
577C3×C4#88211yescharacteristic
578C3×C4#88411yescharacteristic
579C3×C4#88411yescharacteristic
580C3×C4#93711yescharacteristic
581C3×C4#93811yescharacteristic
582C3×C4#93911yescharacteristic
583C3×C4#95311yescharacteristic
584Dic3—42no—
585Dic3—41no—
586Dic3—42no—
587Dic3—122no—
588Dic3—121no—
589Dic3—121no—
590C32#200611yescharacteristic, complemented, Sylow
591C23—22no—
592C23—42no—
593C23—42no—
594C23—41no—
595C23—41no—
596C23—61no—
597C23—181no—
598C23D3×#6711yescharacteristic
599Q8—61no—
600Q8—61no—
601Q8—181no—
602Q8—181no—
603D4—22no—
604D4—22no—
605D4—41no—
606D4—41no—
607D4—61no—
608D4—61no—
609D4—121no—
610D4—121no—
611D4—181no—
612D4—181no—
613D4—361no—
614D4—361no—
615D4—722no—
616C2×C4—62no—
617C2×C4—62no—
618C2×C4—61no—
619C2×C4—121no—
620C2×C4—121no—
621C2×C4—121no—
622C2×C4—121no—
623C2×C4—122no—
624C2×C4—181no—
625C2×C4—361no—
626C2×C4—361no—
627C2×C4#380411yescharacteristic
628C2×C4C2×#62611yescharacteristic
629C2×C4D3×#6711yescharacteristic
630C2×C4D3×#6711yescharacteristic
631C2×C4#381111yescharacteristic
632C2×C4#381111yescharacteristic
633C8—62no—
634C8—182no—
635C2×C3—21no—
636C2×C3—21no—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—21no—
641C2×C3—21no—
642C2×C3—41no—
643C2×C3—41no—
644C2×C3—84no—
645C2×C3—82no—
646C2×C3—82no—
647C2×C3—241no—
648C2×C3#496011yescharacteristic
649C2×C3#506211yescharacteristic
650C2×C3#507711yescharacteristic
651C2×C3#519811yescharacteristic
652C2×C3#520111yescharacteristic
653C2×C3#522311yescharacteristic
654D3—81no—
655D3—242no—
656D3—241no—
657D3—241no—
658C22—21no—
659C22—21no—
660C22—44no—
661C22—42no—
662C22—82no—
663C22—81no—
664C22—81no—
665C22—121no—
666C22—121no—
667C22—121no—
668C22—361no—
669C22—361no—
670C22—361no—
671C22#6397811yescharacteristic
672C22#6397911yescharacteristic
673C22#6398311yescharacteristic
674C4—122no—
675C4—122no—
676C4—121no—
677C4—361no—
678C4#6395811yescharacteristic
679C4#6397111yescharacteristic
680C4#6397711yescharacteristic
681C4#6398111yescharacteristic
682C3—21no—
683C3#6966411yescharacteristic, complemented
684C3#7209811yescharacteristic, complemented
685C2—21no—
686C2—21no—
687C2—82no—
688C2—241no—
689C2—721no—
690C2#1059152311yescharacteristic
691C2#1059152511yescharacteristic
692C2#1059172411yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC22×C32#120
hypercenterC22×D4D32
hypocenterC32#2006
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64141C2semidirect
2. C2×C3×#932C2semidirect
3. #10595043C2semidirect
4. C3×#5221C2semidirect
5. C2×#63570C2semidirect
6. C2×#63569C2semidirect
7. #10589167C2semidirect
38. C2×#932D3semidirect
42. #5221D3semidirect
54. C2×C32×D4D4semidirect
78. #3748D4semidirect
88. C3×#208D4semidirect
224. C2×C3×D4D12semidirect
225. C2×C3×D4#67semidirect
304. #208#67semidirect
500. C2×D4#626semidirect
590. C32#2006semidirect
683. C3#69664semidirect
684. C3#72098semidirect

Maximal subgroups

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

subgroupindex
C2×#641412
C2×C3×#9322
#105950432
C3×#52212
C2×#635702
C2×#635692
#105891672
#720983
#696643