Finite Group Databasebeta

← #11792408

Subgroups — #11792408

Order 1152.

953 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596299C211yesmaximal, characteristic, complemented
2C3×#5822C211yesmaximal, characteristic, complemented
3#10595034C211yesmaximal, characteristic, complemented
4C3×#5236C211yesmaximal, characteristic, complemented
5#10591110C211yesmaximal, characteristic, complemented
6#10591074C211yesmaximal, characteristic, complemented
7#10589158C211yesmaximal, characteristic, complemented
8#72118—31nomaximal
9#70406—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×C4×C3⋊D3C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13#64155—21no—
14#64147—21no—
15#64146—21no—
16#64144—21no—
17C4×#638—22no—
18#64135C2211yescharacteristic
19C3×#951—21no—
20C3×#950—22no—
21C3×#949—21no—
22C3×#942—21no—
23C3×#932—21no—
24C3×#926C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27#63981—21no—
28#63962—21no—
29#63916—21no—
30C4×#626—22no—
31#63871—21no—
32C3×#837—22no—
33#63568—22no—
34#63557—22no—
35C3×#575—31no—
36#5828—31no—
37#5828—31no—
38#5828—31no—
39#5828—61no—
40#5822D311yescharacteristic, complemented
41#5524—31no—
42C3×#421—31no—
43#5236—31no—
44#5236D311yescharacteristic, complemented
45#5139—31no—
46#5126—31no—
47#5126—31no—
48#4557—31no—
49#4531—31no—
50C23×C3⋊D3D411yescharacteristic
51C32×#41—21no—
52C32×#41—21no—
53C32×#41—21no—
54C32×#41—21no—
55C2×C32×Q8D411yescharacteristic, complemented
56C2×C32×D4—21no—
57C2×C32×D4D411yescharacteristic, complemented
58C22×C32×C4—21no—
59C22×C32×C4C2311yescharacteristic
60C2×#638—22no—
61C22×C3⋊Dic3D411yescharacteristic
62C2×C4×C3⋊D3—21no—
63C2×C4×C3⋊D3—21no—
64C2×C4×C3⋊D3—21no—
65C2×C4×C3⋊D3—21no—
66C2×C4×C3⋊D3—21no—
67C2×C4×C3⋊D3—21no—
68C2×C3×#67—21no—
69C3×#235—21no—
70C3×#235—21no—
71C3×#235—21no—
72C3×#235—21no—
73C2×C3×D12D411yescharacteristic, complemented
74C2×C3×C4×D3—21no—
75C2×C3×Dic6D411yescharacteristic, complemented
76C2×#626—22no—
77#3757—22no—
78#3757—21no—
79#3752—22no—
80C4⋊(C3⋊Dic3)—21no—
81#3750—22no—
82C4×C3⋊Dic3D412yescomplemented
83C3×#217—21no—
84C3×#216—22no—
85C3×#215—22no—
86C3×#214—22no—
87C3×#213—22no—
88C3×C4⋊Dic3—21no—
89C3×C4×Dic3D412yescomplemented
90C3×#208—21no—
91C3×#208—21no—
92C3×#208—21no—
93C3×#208—21no—
94C2×C3×C3⋊C8—21no—
95C2×C3×C3⋊C8D412yescomplemented
96Dic3⋊Dic3—22no—
97#3722—22no—
98(C2×D3)⋊Dic3—22no—
99#2010—91noSylow
100C2×C3×#41—21no—
101C2×C3×#41—31no—
102C2×C3×#41C2×D311yescharacteristic
103C2×C3×#41C2×D311yescharacteristic
104C2×#235C2×D311yescharacteristic
105C22×C4×D3—31no—
106C22×C4×D3—31no—
107C22×C4×D3—61no—
108C3×#137—61no—
109C3×#137—61no—
110C3×AGL(1,ℤ/8)—61no—
111C3×AGL(1,ℤ/8)—61no—
112C3×#135—62no—
113C2×C3×M16—31no—
114C2×C3×M16—31no—
115C3×#117—31no—
116#951—21no—
117#950—22no—
118#949—21no—
119#946—61no—
120#946—62no—
121#946—61no—
122#946—61no—
123#942—21no—
124#938—61no—
125#938—62no—
126#938—61no—
127#938—61no—
128#937—61no—
129#937—61no—
130#937—61no—
131#937—62no—
132#935—61no—
133#935—61no—
134#935—61no—
135#935—62no—
136#932—21no—
137C4×#67—62no—
138C4×#67—62no—
139C4×#67—64no—
140C4×#67—62no—
141#926—31no—
142#926—31no—
143#926—61no—
144#926C2×D311yescharacteristic
145C2×#208C2×D311yescharacteristic
146C2×#208C2×D311yescharacteristic
147#897—61no—
148#895—61no—
149#886—61no—
150#882—61no—
151C4×D12—62no—
152C3×#104—62no—
153#837—22no—
154#837—62no—
155#825—62no—
156(C2×D3)⋊C8—62no—
157(C2×D3)⋊C8—62no—
158C23×C32—21no—
159C23×C32C2×D411yescharacteristic
160C22×C3⋊D3—21no—
161C22×C3⋊D3—21no—
162C22×C3⋊D3—21no—
163C22×C3⋊D3—42no—
164C22×C3×D3—21no—
165C32×Q8—21no—
166C32×Q8—21no—
167C32×D4—21no—
168C32×D4—21no—
169C32×D4—41no—
170C32×D4—41no—
171C2×C32×C4—21no—
172C2×C32×C4—41no—
173C2×C32×C4—41no—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4#4111yescharacteristic
180#638—44no—
181C2×C3⋊Dic3—22no—
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3—21no—
185C4×C3⋊D3—41no—
186C4×C3⋊D3—41no—
187C4×C3⋊D3—41no—
188C4×C3⋊D3—41no—
189C3×#67—41no—
190C3×#67—41no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—21no—
193C3×D12—21no—
194C3×D12—21no—
195C3×C4×D3—41no—
196C3×C4×D3—41no—
197C3×Dic6—21no—
198C3×Dic6—21no—
199#626—44no—
200C3×C3⋊C8—22no—
201C3×C3⋊C8—41no—
202#575—31no—
203#525—91no—
204#525—91no—
205#421—31no—
206#421—91no—
207#407—91no—
208H(3,ℤ/4)—91no—
209C23×D3—31no—
210C23×D3—31no—
211C23×D3—61no—
212C3×#41—21no—
213C3×#41—21no—
214C3×#41—21no—
215C3×#41—21no—
216C3×#41—21no—
217C3×#41—21no—
218C3×#41—21no—
219C3×#41—21no—
220C3×#41—41no—
221C3×#41—41no—
222C3×#41—41no—
223C3×#41—41no—
224C3×#41—61no—
225C3×#41—61no—
226C3×#41—61no—
227C3×#41—61no—
228C2×C3×Q8—21no—
229C2×C3×Q8—31no—
230C2×C3×Q8D1211yescharacteristic, complemented
231C2×C3×Q8#6711yescharacteristic, complemented
232C2×C3×D4—22no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—31no—
237C2×C3×D4—61no—
238C2×C3×D4D1211yescharacteristic, complemented
239C2×C3×D4#6711yescharacteristic, complemented
240C22×C3×C4—22no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—61no—
245C22×C3×C4C22×D311yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C2×#67—21no—
248C2×#67—62no—
249C2×#67—64no—
250C2×#67—62no—
251C2×#67—62no—
252C22×Dic3—31no—
253C22×Dic3—31no—
254C22×Dic3—61no—
255#235—21no—
256#235—21no—
257#235—21no—
258#235—21no—
259C2×D12—62no—
260C2×D12#6711yescharacteristic, complemented
261C2×C4×D3—21no—
262C2×C4×D3—62no—
263C2×C4×D3—62no—
264C2×C4×D3—61no—
265C2×C4×D3—61no—
266C2×C4×D3—61no—
267C2×C4×D3—61no—
268C2×C4×D3—61no—
269C2×C4×D3—61no—
270C2×C4×D3—61no—
271C2×C4×D3—61no—
272C2×C4×D3—61no—
273C2×C4×D3—61no—
274C2×C4×D3—61no—
275C2×C4×D3—61no—
276C2×C4×D3—121no—
277C2×C4×D3—121no—
278C2×C4×D3—121no—
279C2×C4×D3—121no—
280C2×Dic6#6711yescharacteristic, complemented
281C3×Q16—62no—
282C3×SD16—62no—
283C3×SD16—62no—
284C3×D8—62no—
285C3×M16—61no—
286C3×M16—61no—
287C3×M16—61no—
288C3×M16—61no—
289C2×C3×C8—32no—
290C2×C3×C8—61no—
291C3×C4⋊C4—61no—
292C3×C22⋊C4—61no—
293C3×C42—32no—
294#217—21no—
295#217—62no—
296#217—62no—
297#217—64no—
298#217—62no—
299#217—62no—
300#217—61no—
301#217—61no—
302#216—22no—
303#215—22no—
304#214—22no—
305#213—22no—
306(C2×D3)⋊C4—62no—
307(C2×D3)⋊C4—62no—
308(C2×D3)⋊C4—64no—
309(C2×D3)⋊C4—62no—
310(C2×D3)⋊C4—62no—
311(C2×D3)⋊C4—62no—
312C4⋊Dic3—21no—
313C4⋊Dic3—62no—
314C4⋊Dic3—62no—
315C4⋊Dic3—61no—
316C4⋊Dic3—61no—
317Dic3⋊C4—62no—
318Dic3⋊C4—64no—
319Dic3⋊C4—62no—
320Dic3⋊C4—62no—
321C4×Dic3—32no—
322C4×Dic3—32no—
323C4×Dic3—62no—
324C4×Dic3#6712yescomplemented
325#208—21no—
326#208—21no—
327#208—21no—
328#208—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8#6712yescomplemented
331C22×C32—41no—
332C22×C32—42no—
333C22×C32—41no—
334C22×C32#12011yescharacteristic
335C22×C32#12011yescharacteristic
336C22×C32#12111yescharacteristic
337C2×C3⋊D3—22no—
338C2×C3⋊D3—22no—
339C2×C3⋊D3—22no—
340C2×C3⋊D3—41no—
341C2×C3⋊D3—41no—
342C2×C3⋊D3—41no—
343C2×C3⋊D3—41no—
344C2×C3×D3—42no—
345C2×C3×D3—41no—
346C32×C4—41no—
347C32×C4#12011yescharacteristic
348C32×C4#12111yescharacteristic
349C32×C4#12111yescharacteristic
350C32×C4#12711yescharacteristic
351C3⋊Dic3—42no—
352C3⋊Dic3—41no—
353C3×Dic3—42no—
354C3×Dic3—41no—
355C2×#41—31no—
356C2×#41D3211yescharacteristic
357C23×C4—91no—
358#137—61no—
359#137—61no—
360AGL(1,ℤ/8)—61no—
361AGL(1,ℤ/8)—61no—
362#135—62no—
363C2×M16—31no—
364C2×M16—31no—
365#123—181no—
366#123—181no—
367C22⋊Q8—181no—
368C22⋊Q8—181no—
369#121—181no—
370#121—181no—
371#120—181no—
372#120—181no—
373C4×D4—182no—
374C4×D4—182no—
375#117—31no—
376#117—91no—
377#104—62no—
378#104—182no—
379C22⋊C8—182no—
380C23×C3—22no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—61no—
385C23×C3D3×D411yescharacteristic
386C23×C3D3×D411yescharacteristic
387C22×D3—21no—
388C22×D3—62no—
389C22×D3—61no—
390C22×D3—61no—
391C22×D3—61no—
392C22×D3—61no—
393C22×D3—61no—
394C22×D3—61no—
395C22×D3—121no—
396C22×D3—121no—
397C22×D3—122no—
398C22×D3—122no—
399C22×D3—124no—
400C3×Q8—21no—
401C3×Q8—21no—
402C3×Q8—21no—
403C3×Q8—21no—
404C3×Q8—41no—
405C3×Q8—41no—
406C3×Q8—61no—
407C3×Q8—61no—
408C3×D4—21no—
409C3×D4—21no—
410C3×D4—21no—
411C3×D4—21no—
412C3×D4—41no—
413C3×D4—41no—
414C3×D4—42no—
415C3×D4—42no—
416C3×D4—41no—
417C3×D4—41no—
418C3×D4—41no—
419C3×D4—41no—
420C3×D4—61no—
421C3×D4—61no—
422C3×D4—121no—
423C3×D4—121no—
424C2×C3×C4—22no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—42no—
434C2×C3×C4—42no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—61no—
440C2×C3×C4—62no—
441C2×C3×C4—121no—
442C2×C3×C4—121no—
443C2×C3×C4C2×D1211yescharacteristic
444C2×C3×C4#23511yescharacteristic
445C2×C3×C4D3×D411yescharacteristic
446C2×C3×C4D3×D411yescharacteristic
447C2×C3×C4D3×D411yescharacteristic
448C2×C3×C4D3×D411yescharacteristic
449C2×C3×C4D3×D411yescharacteristic
450C2×C3×C4#23711yescharacteristic
451C2×C3×C4C2×#6711yescharacteristic
452C2×C3×C4C2×#6711yescharacteristic
453C2×C3×C4C2×#6711yescharacteristic
454C2×C3×C4C2×#6711yescharacteristic
455#67—41no—
456#67—41no—
457#67—124no—
458#67—128no—
459#67—124no—
460#67—124no—
461C2×Dic3—22no—
462C2×Dic3—21no—
463C2×Dic3—64no—
464C2×Dic3—62no—
465C2×Dic3—62no—
466C2×Dic3—61no—
467C2×Dic3—61no—
468C2×Dic3—62no—
469C2×Dic3—61no—
470C2×Dic3—61no—
471C2×Dic3—61no—
472C2×Dic3—61no—
473C2×Dic3—121no—
474C2×Dic3—121no—
475D12—21no—
476D12—21no—
477D12—124no—
478C4×D3—41no—
479C4×D3—41no—
480C4×D3—122no—
481C4×D3—122no—
482C4×D3—122no—
483C4×D3—122no—
484C4×D3—121no—
485C4×D3—121no—
486C4×D3—121no—
487C4×D3—121no—
488C4×D3—121no—
489C4×D3—121no—
490C4×D3—121no—
491C4×D3—121no—
492Dic6—21no—
493Dic6—21no—
494C3×C8—62no—
495C3×C8—121no—
496C3⋊C8—22no—
497C3⋊C8—41no—
498C2×C32—21no—
499C2×C32—21no—
500C2×C32—21no—
501C2×C32—81no—
502C2×C32#39211yescharacteristic
503C3⋊D3—42no—
504C3×D3—81no—
505C24—91no—
506#41—21no—
507#41—21no—
508#41—21no—
509#41—21no—
510#41—61no—
511#41—61no—
512#41—61no—
513#41—61no—
514C2×Q8—31no—
515C2×Q8#62611yescharacteristic, complemented
516C2×D4—21no—
517C2×D4—31no—
518C2×D4—61no—
519C2×D4—182no—
520C2×D4—182no—
521C2×D4#62611yescharacteristic, complemented
522C22×C4—21no—
523C22×C4—61no—
524C22×C4—91no—
525C22×C4—181no—
526C22×C4—181no—
527C22×C4—181no—
528C22×C4—181no—
529C22×C4—181no—
530C22×C4—181no—
531C22×C4C2×D3211yescharacteristic
532Q16—62no—
533SD16—62no—
534SD16—62no—
535D8—62no—
536M16—61no—
537M16—61no—
538M16—61no—
539M16—61no—
540C2×C8—32no—
541C2×C8—61no—
542C4⋊C4—61no—
543C4⋊C4—182no—
544C4⋊C4—182no—
545C4⋊C4—181no—
546C22⋊C4—61no—
547C22⋊C4—182no—
548C22⋊C4—182no—
549C22⋊C4—182no—
550C22⋊C4—182no—
551C22⋊C4—181no—
552C42—32no—
553C42—92no—
554C22×C3—21no—
555C22×C3—21no—
556C22×C3—21no—
557C22×C3—41no—
558C22×C3—41no—
559C22×C3—42no—
560C22×C3—44no—
561C22×C3—42no—
562C22×C3—42no—
563C22×C3—42no—
564C22×C3—41no—
565C22×C3—41no—
566C22×C3—122no—
567C22×C3—121no—
568C22×C3#88211yescharacteristic
569C22×C3#88411yescharacteristic
570C22×C3#93711yescharacteristic
571C22×C3#93711yescharacteristic
572C22×C3#93711yescharacteristic
573C22×C3#93811yescharacteristic
574C2×D3—42no—
575C2×D3—41no—
576C2×D3—62no—
577C2×D3—64no—
578C2×D3—62no—
579C2×D3—62no—
580C2×D3—62no—
581C2×D3—62no—
582C2×D3—62no—
583C2×D3—122no—
584C2×D3—122no—
585C2×D3—122no—
586C2×D3—122no—
587C2×D3—121no—
588C2×D3—121no—
589C2×D3—121no—
590C2×D3—121no—
591C2×D3—121no—
592C2×D3—121no—
593C2×D3—122no—
594C2×D3—122no—
595C2×D3—121no—
596C2×D3—121no—
597C3×C4—21no—
598C3×C4—21no—
599C3×C4—21no—
600C3×C4—21no—
601C3×C4—42no—
602C3×C4—41no—
603C3×C4—41no—
604C3×C4—122no—
605C3×C4—121no—
606C3×C4#88211yescharacteristic
607C3×C4#88411yescharacteristic
608C3×C4#93011yescharacteristic
609C3×C4#93911yescharacteristic
610C3×C4#93911yescharacteristic
611C3×C4#94011yescharacteristic
612C3×C4#94011yescharacteristic
613C3×C4#95311yescharacteristic
614Dic3—42no—
615Dic3—41no—
616Dic3—122no—
617Dic3—124no—
618Dic3—122no—
619Dic3—122no—
620Dic3—121no—
621Dic3—121no—
622C32#201011yescharacteristic, complemented, Sylow
623C23—21no—
624C23—61no—
625C23—181no—
626C23—181no—
627C23—181no—
628C23—362no—
629C23#381111yescharacteristic
630Q8—21no—
631Q8—21no—
632Q8—61no—
633Q8—61no—
634D4—21no—
635D4—21no—
636D4—41no—
637D4—41no—
638D4—61no—
639D4—61no—
640D4—121no—
641D4—121no—
642D4—364no—
643D4—364no—
644C2×C4—21no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—62no—
648C2×C4—61no—
649C2×C4—121no—
650C2×C4—121no—
651C2×C4—181no—
652C2×C4—182no—
653C2×C4—181no—
654C2×C4—181no—
655C2×C4—361no—
656C2×C4—361no—
657C2×C4—361no—
658C2×C4—361no—
659C2×C4#380411yescharacteristic
660C2×C4C2×#62611yescharacteristic
661C2×C4D3×#6711yescharacteristic
662C2×C4D3×#6711yescharacteristic
663C2×C4D3×#6711yescharacteristic
664C2×C4#381111yescharacteristic
665C8—62no—
666C8—121no—
667C2×C3—22no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—41no—
676C2×C3—41no—
677C2×C3—82no—
678C2×C3—81no—
679C2×C3—81no—
680C2×C3—241no—
681C2×C3#496011yescharacteristic
682C2×C3#522311yescharacteristic
683D3—81no—
684D3—124no—
685D3—122no—
686D3—122no—
687C22—41no—
688C22—42no—
689C22—41no—
690C22—122no—
691C22—121no—
692C22—182no—
693C22—182no—
694C22—182no—
695C22—361no—
696C22—361no—
697C22—361no—
698C22—361no—
699C22#6395811yescharacteristic
700C22#6398111yescharacteristic
701C22#6398311yescharacteristic
702C4—41no—
703C4—122no—
704C4—121no—
705C4—362no—
706C4—361no—
707C4#6397111yescharacteristic
708C4#6397711yescharacteristic
709C4#6397811yescharacteristic
710C4#6397911yescharacteristic
711C3—21no—
712C3#7040611yescharacteristic, complemented
713C3#7211811yescharacteristic, complemented
714C2—21no—
715C2—21no—
716C2—21no—
717C2—81no—
718C2—241no—
719C2—362no—
720C2#1059172411yescharacteristic
subgroupG/H
centerC4#63979
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC2×C32#392
hypercenterC2×#41D32
hypocenterC32#2010
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #10596299C2semidirect
2. C3×#5822C2semidirect
3. #10595034C2semidirect
4. C3×#5236C2semidirect
5. #10591110C2semidirect
6. #10591074C2semidirect
7. #10589158C2semidirect
40. #5822D3semidirect
44. #5236D3semidirect
55. C2×C32×Q8D4semidirect
57. C2×C32×D4D4semidirect
73. C2×C3×D12D4semidirect
75. C2×C3×Dic6D4semidirect
82. C4×C3⋊Dic3D4semidirect
89. C3×C4×Dic3D4semidirect
95. C2×C3×C3⋊C8D4semidirect
230. C2×C3×Q8D12semidirect
231. C2×C3×Q8#67semidirect
238. C2×C3×D4D12semidirect
239. C2×C3×D4#67semidirect
260. C2×D12#67semidirect
280. C2×Dic6#67semidirect
324. C4×Dic3#67semidirect
330. C2×C3⋊C8#67semidirect
515. C2×Q8#626semidirect
521. C2×D4#626semidirect
622. C32#2010semidirect
712. C3#70406semidirect
713. C3#72118semidirect

Maximal subgroups

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

subgroupindex
#105962992
C3×#58222
#105950342
C3×#52362
#105911102
#105910742
#105891582
#721183
#704063