Finite Group Databasebeta

← #11792252

Subgroups — #11792252

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
1#10595043C211yesmaximal, characteristic, complemented
2C2×#63830C211yesmaximal, characteristic, complemented
3C2×#63823C211yesmaximal, characteristic, complemented
4C2×#63632C211yesmaximal, characteristic, complemented
5C3×#4939C211yesmaximal, characteristic, complemented
6C2×C3×#805C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#70392—31nomaximal
9#69664—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4—22no—
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18#63978—22no—
19#63916—21no—
20#63909—21no—
21#63871—21no—
22#63857—21no—
23#63830—22no—
24#63830—22no—
25C2×#3716—21no—
26C2×#3715—21no—
27C2×#3714—21no—
28#63823—22no—
29#63823—22no—
30C2×#3713—21no—
31#63632—22no—
32C3×#805—22no—
33#5833—31no—
34C2×#949—31no—
35C2×#932—31no—
36C2×#932—31no—
37C2×#908—31no—
38#5510—31no—
39C2×C3×#104—31no—
40C3×#390—31no—
41#4939D311yescharacteristic, complemented
42C2×#805—31no—
43C2×#805—31no—
44C2×#805—61no—
45C2×#805D311yescharacteristic, complemented
46#4554—31no—
47#4530—31no—
48C23×C3×D3—21no—
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C2×#638—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×C42—21no—
76C32×C42—21no—
77#3748—21no—
78#3748D412yescomplemented
79C2×C3⋊(C3⋊C8)—21no—
80C3×(C2×D3)⋊C4—44no—
81C3×C4⋊Dic3—21no—
82C3×C4⋊Dic3—21no—
83C3×#208—21no—
84C3×#208D412yescomplemented
85C2×C3×C3⋊C8—21no—
86Dic3⋊Dic3—22no—
87#3722—22no—
88(C2×D3)⋊Dic3—22no—
89#3716—24no—
90#3715—24no—
91#3714—24no—
92#3713—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
101C2×C3×M16—31no—
102C2×C3×C4⋊C4—31no—
103C2×C3×C22⋊C4—62no—
104C2×C3×C42—21no—
105C2×C3×C42C2×D311yescharacteristic
106C2×C3×C42C2×D311yescharacteristic
107#949—62no—
108#949—62no—
109#946—61no—
110C2×#215—61no—
111#939—62no—
112#938—61no—
113C2×#214—61no—
114C2×#214—61no—
115#932—62no—
116#932—62no—
117#932—62no—
118#932—62no—
119C2×#213—61no—
120C2×#213—61no—
121C2×#213—61no—
122#930—61no—
123#930—62no—
124C2×(C2×D3)⋊C4—22no—
125C2×C4⋊Dic3C2×D311yescharacteristic
126#924—61no—
127C2×#208—31no—
128C2×#208—31no—
129C2×#208—61no—
130C2×#208C2×D311yescharacteristic
131#908—62no—
132#908—62no—
133C2×D24—61no—
134C2×#204—61no—
135#897—61no—
136#897—61no—
137#895—61no—
138#895—61no—
139C3×#104—62no—
140#805—22no—
141#805—62no—
142#805—62no—
143#805—64no—
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×C4—22no—
153C2×C32×C4—41no—
154C2×C32×C4—41no—
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4#4111yescharacteristic
161#638—41no—
162#638—41no—
163C2×C3⋊Dic3—21no—
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—21no—
176C3×D12—22no—
177C3×D12—22no—
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—
186C3⋊(C3⋊C8)—22no—
187C3×C3⋊C8—22no—
188C2×AGL(1,ℤ/8)—91no—
189C2×AGL(1,ℤ/8)—91no—
190#537—91no—
191C2×#104—31no—
192C2×#104—91no—
193#390—31no—
194#343—91no—
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—31no—
203C2×C3×D4—32no—
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—21no—
212C22×C3×C4—21no—
213C22×C3×C4—32no—
214C22×C3×C4—41no—
215C22×C3×C4—61no—
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C22×D311yescharacteristic
218C2×#67—21no—
219C2×#67—62no—
220C2×#67—61no—
221C2×#67—61no—
222C2×#67—121no—
223C22×Dic3#6712yes—
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×D12D1211yescharacteristic
250C2×D12D1212yescomplemented
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×Dic6D1211yescharacteristic
259C3×M16—32no—
260C3×M16—61no—
261C2×C3×C8—61no—
262C3×C4⋊C4—61no—
263C3×C4⋊C4—61no—
264C3×C22⋊C4—124no—
265C3×C42—22no—
266C3×C42—21no—
267C3×C42—21no—
268C3×C42—21no—
269C3×C42—21no—
270C3×C42—41no—
271#217—62no—
272#215—64no—
273#214—64no—
274#214—64no—
275#213—64no—
276#213—64no—
277#213—64no—
278(C2×D3)⋊C4—44no—
279(C2×D3)⋊C4—62no—
280(C2×D3)⋊C4—62no—
281(C2×D3)⋊C4—62no—
282C4⋊Dic3—21no—
283C4⋊Dic3—21no—
284C4⋊Dic3—62no—
285Dic3⋊C4—62no—
286#208—21no—
287#208—32no—
288#208—32no—
289#208—62no—
290#208—61no—
291#208—61no—
292#208—121no—
293#208#6712yescomplemented
294C2×C3⋊C8—21no—
295C2×C3⋊C8—61no—
296C2×C3⋊C8—61no—
297C2×C3⋊C8—121no—
298D24—64no—
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—42no—
317C32×C4#12011yescharacteristic
318C32×C4#12011yescharacteristic
319C32×C4#12111yescharacteristic
320C32×C4#12111yescharacteristic
321C3⋊Dic3—41no—
322C3×Dic3—41no—
323C3×Dic3—42no—
324C2×#41—31no—
325C2×#41—91no—
326C22×D4—31no—
327AGL(1,ℤ/8)—182no—
328AGL(1,ℤ/8)—182no—
329AGL(1,ℤ/8)—182no—
330AGL(1,ℤ/8)—182no—
331C2×SD16—181no—
332C2×SD16—181no—
333C2×D8—181no—
334C2×D8—181no—
335C2×M16—31no—
336C2×M16—91no—
337C22⋊Q8—181no—
338C22⋊Q8—181no—
339#121—181no—
340#121—181no—
341#121—182no—
342C2×C4⋊C4—31no—
343C2×C22⋊C4—62no—
344C2×C42D3211yescharacteristic
345#104—62no—
346#104—182no—
347C23×C3—21no—
348C23×C3—62no—
349C23×C3—61no—
350C23×C3—122no—
351C23×C3—122no—
352C23×C3—121no—
353C23×C3—121no—
354C23×C3D3×D411yescharacteristic
355C23×C3C2×#6711yescharacteristic
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—61no—
368C3×D4—62no—
369C3×D4—61no—
370C3×D4—62no—
371C3×D4—121no—
372C3×D4—121no—
373C3×D4—121no—
374C3×D4—121no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—42no—
384C2×C3×C4—42no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—42no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—62no—
391C2×C3×C4—61no—
392C2×C3×C4—121no—
393C2×C3×C4—121no—
394C2×C3×C4—122no—
395C2×C3×C4C2×D1211yescharacteristic
396C2×C3×C4C2×D1211yescharacteristic
397C2×C3×C4#23511yescharacteristic
398C2×C3×C4#23511yescharacteristic
399C2×C3×C4D3×D411yescharacteristic
400C2×C3×C4D3×D411yescharacteristic
401C2×C3×C4D3×D411yescharacteristic
402C2×C3×C4D3×D411yescharacteristic
403C2×C3×C4D3×D411yescharacteristic
404C2×C3×C4D3×D411yescharacteristic
405C2×C3×C4D3×D411yescharacteristic
406C2×C3×C4C2×#6711yescharacteristic
407#67—41no—
408#67—41no—
409#67—122no—
410#67—122no—
411#67—121no—
412#67—121no—
413#67—121no—
414#67—121no—
415#67—242no—
416C2×Dic3—21no—
417C2×Dic3—22no—
418C2×Dic3—42no—
419C2×Dic3—61no—
420C2×Dic3—61no—
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—62no—
452C3⋊C8—22no—
453C3⋊C8—62no—
454C3⋊C8—62no—
455C3⋊C8—122no—
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—21no—
487C22×C4—32no—
488C22×C4—61no—
489C22×C4—181no—
490C22×C4C2×D3211yescharacteristic
491SD16—184no—
492SD16—184no—
493D8—184no—
494D8—184no—
495M16—32no—
496M16—61no—
497M16—92no—
498M16—181no—
499C2×C8—61no—
500C2×C8—181no—
501C4⋊C4—61no—
502C4⋊C4—61no—
503C4⋊C4—182no—
504C22⋊C4—124no—
505C22⋊C4—182no—
506C22⋊C4—182no—
507C42—21no—
508C42—21no—
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#88211yescharacteristic
527C22×C3#88411yescharacteristic
528C22×C3#93011yescharacteristic
529C22×C3#93711yescharacteristic
530C22×C3#94011yescharacteristic
531C22×C3#94011yescharacteristic
532C2×D3—44no—
533C2×D3—41no—
534C2×D3—42no—
535C2×D3—41no—
536C2×D3—41no—
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—42no—
554C3×C4—42no—
555C3×C4—44no—
556C3×C4—121no—
557C3×C4—122no—
558C3×C4#88211yescharacteristic
559C3×C4#88211yescharacteristic
560C3×C4#88211yescharacteristic
561C3×C4#88411yescharacteristic
562C3×C4#88411yescharacteristic
563C3×C4#88411yescharacteristic
564C3×C4#93011yescharacteristic
565C3×C4#93711yescharacteristic
566Dic3—41no—
567Dic3—42no—
568Dic3—122no—
569Dic3—121no—
570Dic3—121no—
571C32#200611yescharacteristic, complemented, Sylow
572C23—62no—
573C23—61no—
574C23—122no—
575C23—122no—
576C23—121no—
577C23—121no—
578C23—181no—
579C23D3×#6711yescharacteristic
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—22no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—62no—
601C2×C4—61no—
602C2×C4—121no—
603C2×C4—121no—
604C2×C4—122no—
605C2×C4—181no—
606C2×C4—361no—
607C2×C4—361no—
608C2×C4#379811yescharacteristic
609C2×C4D3×D1211yescharacteristic
610C2×C4D3×D1211yescharacteristic
611C2×C4#380211yescharacteristic
612C2×C4D3×#6711yescharacteristic
613C2×C4#381111yescharacteristic
614C8—62no—
615C8—182no—
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—241no—
626C2×C3—242no—
627C2×C3#482211yescharacteristic
628C2×C3#482711yescharacteristic
629C2×C3#496011yescharacteristic
630C2×C3#496011yescharacteristic
631C2×C3#506211yescharacteristic
632C2×C3#507711yescharacteristic
633D3—82no—
634D3—81no—
635D3—242no—
636D3—241no—
637D3—241no—
638C22—21no—
639C22—21no—
640C22—124no—
641C22—121no—
642C22—122no—
643C22—121no—
644C22—121no—
645C22—242no—
646C22—241no—
647C22—241no—
648C22—361no—
649C22—361no—
650C22—361no—
651C22#6390611yescharacteristic
652C22#6392211yescharacteristic
653C22#6397911yescharacteristic
654C4—42no—
655C4—121no—
656C4—122no—
657C4—361no—
658C4#6390611yescharacteristic
659C4#6391211yescharacteristic
660C4#6392211yescharacteristic
661C4#6392311yescharacteristic
662C3—21no—
663C3#6966411yescharacteristic, complemented
664C3#7039211yescharacteristic, complemented
665C2—21no—
666C2—21no—
667C2—242no—
668C2—241no—
669C2—721no—
670C2#1059039511yescharacteristic
671C2#1059040011yescharacteristic
672C2#1059139311yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32#120
hypercenterC2×C42D32
hypocenterC32#2006
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10595043C2semidirect
2. C2×#63830C2semidirect
3. C2×#63823C2semidirect
4. C2×#63632C2semidirect
5. C3×#4939C2semidirect
6. C2×C3×#805C2semidirect
7. #10589167C2semidirect
41. #4939D3semidirect
45. C2×#805D3semidirect
71. C2×C3×D12D4semidirect
78. #3748D4semidirect
84. C3×#208D4semidirect
250. C2×D12D12semidirect
293. #208#67semidirect
571. C32#2006semidirect
663. C3#69664semidirect
664. C3#70392semidirect

Maximal subgroups

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

subgroupindex
#105950432
C2×#638302
C2×#638232
C2×#636322
C3×#49392
C2×C3×#8052
#105891672
#703923
#696643