Finite Group Databasebeta

← #11865057

Subgroups — #11865057

Order 1152.

1601 conjugacy classes of subgroups.

The subgroup lattice has 833 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1009C211yesmaximal, characteristic, complemented
2C3×#5822C211yesmaximal, characteristic, complemented
3#10595040C211yesmaximal, characteristic, complemented
4#10594786C211yesmaximal, characteristic, complemented
5#10592935C211yesmaximal, characteristic, complemented
6#10591665C214yesmaximal, complemented
7#10591664C214yesmaximal, complemented
8#10591110C211yesmaximal, characteristic, complemented
9C2×#63558C211yesmaximal, characteristic, complemented
10#84104—31nomaximal
11#84005—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C3×#1009—22no—
14C3×#1009—22no—
15C3×#1009—22no—
16C3×#1009C2214yes—
17C2×C3×#239—21no—
18C2×C3×D3×D4—21no—
19C2×C3×D3×D4—22no—
20C2×C3×#235—21no—
21C2×C3×#235C2211yescharacteristic
22C2×C3×#235C2211yescharacteristic, complemented
23C22×C3×D12—21no—
24C22×C3×D12C2211yescharacteristic
25#64135C2211yescharacteristic, complemented
26C2×#3748C2211yescharacteristic, complemented
27C3×#951C2212yescomplemented
28C3×#950—22no—
29C3×#949C2212yescomplemented
30C3×#942—21no—
31C3×#932—21no—
32C2×C3×#208C2211yescharacteristic, complemented
33#63976—22no—
34#63914C2212yescomplemented
35#63908—22no—
36#63863C2212yescomplemented
37#63827—21no—
38#63827C2212yescomplemented
39#63823—21no—
40#63823C2212yescomplemented
41#63822—22no—
42#63664C2214yescomplemented
43#63568C2214yescomplemented
44#63558C2214yescomplemented
45C2×C3×H(5,𝔽2)—31no—
46C2×#1009D311yescharacteristic, complemented
47C3×#575—31no—
48#5830—31no—
49#5822—31no—
50#5822—31no—
51#5822D311yescharacteristic, complemented
52#5805—31no—
53#5242—34no—
54#5241—34no—
55#5236—31no—
56#5236—31no—
57#5236—31no—
58#5236—61no—
59C2×#833—31no—
60#5202—34no—
61#5198—34no—
62#5139—31no—
63C2×#823—31no—
64C23×C3×D3—22no—
65C23×C3×D3D412yes—
66C32×#41—21no—
67C32×#41—21no—
68C32×#41D412yescomplemented
69C32×#41C2312yes—
70C2×C32×Q8D411yescharacteristic, complemented
71C2×C32×D4—21no—
72C2×C32×D4D411yescharacteristic, complemented
73C22×C32×C4—21no—
74C22×C32×C4C2311yescharacteristic
75C2×C3×#67—22no—
76C2×C3×#67—21no—
77C2×C3×#67—21no—
78C3×#239—24no—
79C3×#239—24no—
80C3×D3×D4—28no—
81C3×D3×D4—24no—
82C3×D3×D4—28no—
83C3×D3×D4—24no—
84C3×#235—24no—
85C3×#235—21no—
86C3×#235—21no—
87C3×#235—21no—
88C3×#235—21no—
89C3×#235—21no—
90C3×#235—21no—
91C3×#235—24no—
92C3×#235D412yescomplemented
93C3×#235C2312yes—
94C2×C3×D12—22no—
95C2×C3×D12—24no—
96C2×C3×D12—21no—
97C2×C3×D12—21no—
98C2×C3×D12—21no—
99C2×C3×D12—21no—
100C2×C3×D12—24no—
101C2×C3×D12D412yes—
102C2×C3×D12D411yescharacteristic, complemented
103C2×C3×D12C2312yes—
104C2×C3×D12C2311yescharacteristic, complemented
105C2×C3×C4×D3—22no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×Dic6D411yescharacteristic, complemented
109C2×C3×Dic6C2311yescharacteristic, complemented
110C2×#625—24no—
111#3757—21no—
112C4⋊(C3⋊Dic3)—21no—
113C4×C3⋊Dic3C2312yescomplemented
114#3748—21no—
115#3748C2312yescomplemented
116C2×C3⋊(C3⋊C8)—21no—
117C3×#216—22no—
118C3×#215—22no—
119C3×#214—22no—
120C3×#213—22no—
121C3×#208—21no—
122C3×#208C2312yescomplemented
123C2×C3×C3⋊C8—21no—
124(C2×D3)⋊Dic3—24no—
125#3718—22no—
126#3715—22no—
127#3715—22no—
128#3713—22no—
129#3019—91noSylow
130C3×H(5,𝔽2)—34no—
131C3×H(5,𝔽2)—62no—
132C3×H(5,𝔽2)—62no—
133C3×H(5,𝔽2)—62no—
134C2×C3×#41—21no—
135C2×C3×#41—31no—
136C2×C3×#41—31no—
137C2×C3×#41—61no—
138C2×C3×#41—61no—
139C2×C3×#41C2×D311yescharacteristic
140C2×C3×#41C2×D311yescharacteristic
141C22×C3×D4—31no—
142C22×C3×D4—61no—
143C22×C3×D4—62no—
144C22×C3×D4—61no—
145#1009—22no—
146#1009—22no—
147#1009—22no—
148#1009C2×D314yes—
149C2×#239—21no—
150C2×D3×D4—22no—
151C2×D3×D4—21no—
152C2×#235—21no—
153C2×#235C2×D311yescharacteristic
154C2×#235C2×D311yescharacteristic, complemented
155C22×D12—21no—
156C22×D12C2×D311yescharacteristic
157C3×#137—32no—
158C3×#137—61no—
159C3×AGL(1,ℤ/8)—32no—
160C3×AGL(1,ℤ/8)—61no—
161C3×#135—62no—
162C2×C3×M16—31no—
163#953—62no—
164#951—32no—
165#951—61no—
166#951C2×D312yescomplemented
167#950—22no—
168#950—62no—
169#950—62no—
170#949—32no—
171#949—61no—
172#949C2×D312yescomplemented
173#947—32no—
174#942—21no—
175#942—32no—
176#942—61no—
177#940—32no—
178#940—32no—
179#938—62no—
180#937—62no—
181#936—32no—
182#932—21no—
183#932—32no—
184#932—61no—
185#930—62no—
186#926—31no—
187#926—31no—
188#926—61no—
189C2×#208—31no—
190C2×#208—31no—
191C2×#208—61no—
192C2×#208C2×D311yescharacteristic, complemented
193#837—34no—
194#837—34no—
195#837—34no—
196#837—64no—
197#833—34no—
198#825—34no—
199#823—34no—
200C23×C32—21no—
201C23×C32C2×D411yescharacteristic
202C22×C3×D3—21no—
203C22×C3×D3—22no—
204C22×C3×D3—28no—
205C22×C3×D3—22no—
206C22×C3×D3—21no—
207C22×C3×D3—82no—
208C22×C3×D3—84no—
209C22×C3×D3C2×D414yes—
210C32×Q8—21no—
211C32×Q8C2×D412yes—
212C32×D4—22no—
213C32×D4—22no—
214C32×D4—21no—
215C32×D4C2×D412yes—
216C2×C32×C4—21no—
217C2×C32×C4—22no—
218C2×C32×C4—22no—
219C2×C32×C4C2×D411yescharacteristic
220C2×C32×C4C2×D411yescharacteristic
221C2×C32×C4C2×D411yescharacteristic
222C2×C32×C4C2×D411yescharacteristic
223C2×C32×C4C2×D411yescharacteristic
224C2×C32×C4C2411yescharacteristic
225C2×C3⋊Dic3—22no—
226C3×#67—28no—
227C3×#67—22no—
228C3×#67—22no—
229C3×#67—41no—
230C3×#67—41no—
231C2×C3×Dic3—21no—
232C2×C3×Dic3—21no—
233C3×D12—28no—
234C3×D12—22no—
235C3×D12—21no—
236C3×D12—22no—
237C3×D12—22no—
238C3×D12—22no—
239C3×D12—21no—
240C3×D12—21no—
241C3×D12C2×D412yes—
242C3×C4×D3—28no—
243C3×C4×D3—22no—
244C3×C4×D3—22no—
245C3×C4×D3—41no—
246C3×C4×D3—41no—
247C3×Dic6—21no—
248C3×Dic6—21no—
249C3×Dic6—21no—
250C3×Dic6C2×D412yes—
251#625—84no—
252C3⋊(C3⋊C8)—22no—
253C3×C3⋊C8—22no—
254C2×H(5,𝔽2)—31no—
255#575—31no—
256#575—91no—
257#535—91no—
258#455—94no—
259#453—94no—
260#421—91no—
261#421—91no—
262C2×#100—91no—
263C24×C3—32no—
264C24×C3—62no—
265C23×D3—22no—
266C23×D3#6712yes—
267C3×#41—21no—
268C3×#41—21no—
269C3×#41—21no—
270C3×#41—21no—
271C3×#41—22no—
272C3×#41—22no—
273C3×#41—32no—
274C3×#41—32no—
275C3×#41—41no—
276C3×#41—41no—
277C3×#41—64no—
278C3×#41—64no—
279C3×#41—64no—
280C3×#41—64no—
281C3×#41—61no—
282C3×#41—61no—
283C3×#41—61no—
284C3×#41—61no—
285C3×#41—61no—
286C3×#41—61no—
287C3×#41#6712yescomplemented
288C3×#41#6712yescomplemented
289C3×#41C22×D312yes—
290C3×#41C22×D312yes—
291C2×C3×Q8—21no—
292C2×C3×Q8—31no—
293C2×C3×Q8—31no—
294C2×C3×Q8#6711yescharacteristic, complemented
295C2×C3×Q8#6711yescharacteristic, complemented
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—21no—
299C2×C3×D4—31no—
300C2×C3×D4—32no—
301C2×C3×D4—32no—
302C2×C3×D4—31no—
303C2×C3×D4—41no—
304C2×C3×D4—64no—
305C2×C3×D4—62no—
306C2×C3×D4—64no—
307C2×C3×D4—68no—
308C2×C3×D4—68no—
309C2×C3×D4—64no—
310C2×C3×D4—62no—
311C2×C3×D4—61no—
312C2×C3×D4—64no—
313C2×C3×D4—61no—
314C2×C3×D4—61no—
315C2×C3×D4—61no—
316C2×C3×D4—61no—
317C2×C3×D4—61no—
318C2×C3×D4#6711yescharacteristic, complemented
319C2×C3×D4#6711yescharacteristic, complemented
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—41no—
324C22×C3×C4—62no—
325C22×C3×C4—61no—
326C22×C3×C4—61no—
327C22×C3×C4C22×D311yescharacteristic
328C22×C3×C4C22×D311yescharacteristic
329C2×#67—22no—
330C2×#67—21no—
331C2×#67—21no—
332C2×#67—64no—
333C2×#67—64no—
334#239—24no—
335#239—24no—
336D3×D4—28no—
337D3×D4—24no—
338D3×D4—28no—
339D3×D4—24no—
340#235—24no—
341#235—21no—
342#235—21no—
343#235—21no—
344#235—21no—
345#235—21no—
346#235—21no—
347#235—24no—
348#235#6712yescomplemented
349#235C22×D312yes—
350C2×D12—22no—
351C2×D12—24no—
352C2×D12—21no—
353C2×D12—21no—
354C2×D12—21no—
355C2×D12—21no—
356C2×D12—24no—
357C2×D12#6712yes—
358C2×D12#6711yescharacteristic, complemented
359C2×D12C22×D312yes—
360C2×D12C22×D311yescharacteristic, complemented
361C2×C4×D3—22no—
362C2×C4×D3—21no—
363C2×C4×D3—21no—
364C2×Dic6#6711yescharacteristic, complemented
365C2×Dic6C22×D311yescharacteristic, complemented
366C3×Q16—62no—
367C3×SD16—62no—
368C3×SD16—62no—
369C3×D8—62no—
370C3×M16—32no—
371C3×M16—61no—
372C2×C3×C8—61no—
373#217—64no—
374#217—61no—
375#217—61no—
376#217—121no—
377#216—22no—
378#216—62no—
379#216—62no—
380#215—22no—
381#215—62no—
382#215—62no—
383#214—22no—
384#214—62no—
385#214—62no—
386#213—22no—
387#213—62no—
388#213—62no—
389(C2×D3)⋊C4—64no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—121no—
393C4×Dic3—32no—
394C4×Dic3—32no—
395C4×Dic3—62no—
396#208—21no—
397#208—32no—
398#208—32no—
399#208—62no—
400#208—61no—
401#208—61no—
402#208—121no—
403#208C22×D312yescomplemented
404C2×C3⋊C8—21no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—121no—
408C22×C32—22no—
409C22×C32—41no—
410C22×C32—42no—
411C22×C32#12011yescharacteristic
412C22×C32#12011yescharacteristic
413C22×C32C22×D411yescharacteristic
414C2×C3×D3—24no—
415C2×C3×D3—22no—
416C2×C3×D3—44no—
417C2×C3×D3—42no—
418C2×C3×D3—44no—
419C2×C3×D3—42no—
420C2×C3×D3—41no—
421C2×C3×D3—82no—
422C2×C3×D3—88no—
423C32×C4—22no—
424C32×C4#12011yescharacteristic
425C32×C4#12011yescharacteristic
426C32×C4C22×D411yescharacteristic
427C32×C4C22×D411yescharacteristic
428C3⋊Dic3—42no—
429C3×Dic3—22no—
430C3×Dic3—41no—
431H(5,𝔽2)—34no—
432H(5,𝔽2)—62no—
433H(5,𝔽2)—62no—
434H(5,𝔽2)—62no—
435C2×#41—31no—
436C2×#41—31no—
437C2×#41—61no—
438C2×#41—61no—
439C2×#41D3211yescharacteristic
440C22×D4—31no—
441C22×D4—61no—
442C22×D4—62no—
443C22×D4—61no—
444#137—32no—
445#137—61no—
446#137—92no—
447#137—181no—
448AGL(1,ℤ/8)—32no—
449AGL(1,ℤ/8)—61no—
450AGL(1,ℤ/8)—92no—
451AGL(1,ℤ/8)—181no—
452#135—62no—
453#135—182no—
454C2×M16—31no—
455C2×M16—91no—
456#127—92no—
457#124—92no—
458#121—182no—
459#120—182no—
460#117—91no—
461#104—94no—
462#104—94no—
463#100—94no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—34no—
468C23×C3—41no—
469C23×C3—68no—
470C23×C3—61no—
471C23×C3—62no—
472C23×C3—62no—
473C23×C3—61no—
474C23×C3—242no—
475C23×C3—244no—
476C23×C3D3×D411yescharacteristic
477C23×C3C2×#6711yescharacteristic
478C22×D3—22no—
479C22×D3—21no—
480C22×D3—28no—
481C22×D3—22no—
482C22×D3—21no—
483C22×D3—82no—
484C22×D3—84no—
485C22×D3C2×#6714yes—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—22no—
489C3×Q8—32no—
490C3×Q8—41no—
491C3×Q8—61no—
492C3×Q8—61no—
493C3×Q8—61no—
494C3×Q8C2×#6712yes—
495C3×Q8C2×#6712yes—
496C3×D4—22no—
497C3×D4—22no—
498C3×D4—22no—
499C3×D4—22no—
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—22no—
503C3×D4—32no—
504C3×D4—41no—
505C3×D4—42no—
506C3×D4—42no—
507C3×D4—68no—
508C3×D4—68no—
509C3×D4—62no—
510C3×D4—62no—
511C3×D4—61no—
512C3×D4—62no—
513C3×D4—62no—
514C3×D4—62no—
515C3×D4—62no—
516C3×D4—61no—
517C3×D4—61no—
518C3×D4—121no—
519C3×D4—121no—
520C3×D4C2×#6712yes—
521C3×D4C2×#6712yes—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—42no—
535C2×C3×C4—42no—
536C2×C3×C4—41no—
537C2×C3×C4—68no—
538C2×C3×C4—61no—
539C2×C3×C4—62no—
540C2×C3×C4—62no—
541C2×C3×C4—61no—
542C2×C3×C4—121no—
543C2×C3×C4—121no—
544C2×C3×C4D3×D411yescharacteristic
545C2×C3×C4D3×D411yescharacteristic
546C2×C3×C4D3×D411yescharacteristic
547C2×C3×C4C2×#6711yescharacteristic
548C2×C3×C4C2×#6711yescharacteristic
549C2×C3×C4C2×#6711yescharacteristic
550C2×C3×C4C2×#6711yescharacteristic
551C2×C3×C4C2×#6711yescharacteristic
552C2×C3×C4C2×#6711yescharacteristic
553C2×C3×C4C2×#6711yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555C2×C3×C4C23×D311yescharacteristic
556#67—28no—
557#67—22no—
558#67—22no—
559#67—41no—
560#67—41no—
561#67—244no—
562#67—244no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—62no—
566C2×Dic3—62no—
567C2×Dic3—122no—
568D12—28no—
569D12—22no—
570D12—21no—
571D12—22no—
572D12—21no—
573D12—22no—
574D12—22no—
575D12—21no—
576D12C2×#6712yes—
577C4×D3—28no—
578C4×D3—22no—
579C4×D3—22no—
580C4×D3—41no—
581C4×D3—41no—
582Dic6—21no—
583Dic6—21no—
584Dic6—21no—
585Dic6C2×#6712yes—
586C3×C8—62no—
587C3⋊C8—22no—
588C3⋊C8—62no—
589C3⋊C8—62no—
590C3⋊C8—122no—
591C2×C32—21no—
592C2×C32—21no—
593C2×C32—21no—
594C2×C32—42no—
595C2×C32C2×#12011yescharacteristic
596C3×D3—44no—
597C3×D3—42no—
598C3×D3—81no—
599C24—32no—
600C24—62no—
601#41—21no—
602#41—21no—
603#41—32no—
604#41—32no—
605#41—64no—
606#41—64no—
607#41—64no—
608#41—64no—
609#41—61no—
610#41—61no—
611#41—61no—
612#41—61no—
613#41—61no—
614#41—61no—
615#41#62512yescomplemented
616#41C2×D3212yes—
617C2×Q8—31no—
618C2×Q8—31no—
619C2×Q8#62511yescharacteristic, complemented
620C2×D4—21no—
621C2×D4—32no—
622C2×D4—31no—
623C2×D4—31no—
624C2×D4—32no—
625C2×D4—64no—
626C2×D4—62no—
627C2×D4—64no—
628C2×D4—68no—
629C2×D4—68no—
630C2×D4—64no—
631C2×D4—62no—
632C2×D4—61no—
633C2×D4—64no—
634C2×D4—61no—
635C2×D4—61no—
636C2×D4—61no—
637C2×D4—61no—
638C2×D4—61no—
639C2×D4—184no—
640C2×D4#62511yescharacteristic, complemented
641C22×C4—21no—
642C22×C4—62no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4C2×D3211yescharacteristic
646Q16—62no—
647Q16—182no—
648SD16—62no—
649SD16—62no—
650SD16—182no—
651SD16—182no—
652D8—62no—
653D8—182no—
654M16—32no—
655M16—61no—
656M16—92no—
657M16—181no—
658C2×C8—61no—
659C2×C8—181no—
660C4⋊C4—181no—
661C22⋊C4—184no—
662C22⋊C4—181no—
663C42—92no—
664C22×C3—22no—
665C22×C3—22no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—42no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—42no—
673C22×C3—42no—
674C22×C3—62no—
675C22×C3—64no—
676C22×C3—81no—
677C22×C3—82no—
678C22×C3—124no—
679C22×C3—124no—
680C22×C3—122no—
681C22×C3—122no—
682C22×C3—121no—
683C22×C3—242no—
684C22×C3—248no—
685C22×C3#93711yescharacteristic
686C22×C3#93711yescharacteristic
687C22×C3#95311yescharacteristic
688C22×C3#95311yescharacteristic
689C22×C3C2×D3×D411yescharacteristic
690C22×C3C22×#6711yescharacteristic
691C2×D3—24no—
692C2×D3—22no—
693C2×D3—44no—
694C2×D3—42no—
695C2×D3—44no—
696C2×D3—42no—
697C2×D3—41no—
698C2×D3—82no—
699C2×D3—88no—
700C3×C4—22no—
701C3×C4—22no—
702C3×C4—21no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—42no—
707C3×C4—62no—
708C3×C4—121no—
709C3×C4#93711yescharacteristic
710C3×C4#93711yescharacteristic
711C3×C4#95311yescharacteristic
712C3×C4#95311yescharacteristic
713C3×C4C2×D3×D411yescharacteristic
714C3×C4C22×#6711yescharacteristic
715C3×C4C22×#6711yescharacteristic
716C3×C4C22×#6711yescharacteristic
717Dic3—22no—
718Dic3—41no—
719Dic3—122no—
720Dic3—122no—
721Dic3—242no—
722C32#301911yescharacteristic, complemented, Sylow
723C23—21no—
724C23—34no—
725C23—68no—
726C23—61no—
727C23—62no—
728C23—62no—
729C23—61no—
730C23—242no—
731C23—244no—
732C23D3×#6711yescharacteristic
733Q8—21no—
734Q8—32no—
735Q8—61no—
736Q8—61no—
737Q8—61no—
738Q8C2×#62512yes—
739D4—22no—
740D4—22no—
741D4—21no—
742D4—32no—
743D4—68no—
744D4—68no—
745D4—62no—
746D4—62no—
747D4—62no—
748D4—61no—
749D4—62no—
750D4—61no—
751D4—61no—
752D4—62no—
753D4—62no—
754D4—121no—
755D4—121no—
756D4—724no—
757D4C2×#62512yes—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—68no—
762C2×C4—61no—
763C2×C4—62no—
764C2×C4—62no—
765C2×C4—61no—
766C2×C4—121no—
767C2×C4—121no—
768C2×C4—182no—
769C2×C4C2×#62511yescharacteristic
770C2×C4C2×#62511yescharacteristic
771C2×C4D3×#6711yescharacteristic
772C2×C4D3×#6711yescharacteristic
773C2×C4D3×#6711yescharacteristic
774C2×C4C22×D3211yescharacteristic
775C8—62no—
776C8—182no—
777C2×C3—21no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—41no—
785C2×C3—41no—
786C2×C3—41no—
787C2×C3—42no—
788C2×C3—42no—
789C2×C3—82no—
790C2×C3—124no—
791C2×C3—122no—
792C2×C3—241no—
793C2×C3C2×#93711yescharacteristic
794C2×C3C2×#95311yescharacteristic
795D3—44no—
796D3—42no—
797D3—81no—
798C22—22no—
799C22—41no—
800C22—42no—
801C22—62no—
802C22—64no—
803C22—124no—
804C22—124no—
805C22—122no—
806C22—122no—
807C22—121no—
808C22—242no—
809C22—248no—
810C22#6397611yescharacteristic
811C22#6397611yescharacteristic
812C22C2×D3×#6711yescharacteristic
813C4—22no—
814C4—62no—
815C4—121no—
816C4—362no—
817C4#6397611yescharacteristic
818C4#6397611yescharacteristic
819C4C22×#62511yescharacteristic
820C4C2×D3×#6711yescharacteristic
821C3—21no—
822C3#8400511yescharacteristic, complemented
823C3#8410411yescharacteristic, complemented
824C2—21no—
825C2—21no—
826C2—21no—
827C2—42no—
828C2—124no—
829C2—122no—
830C2—241no—
831C2C2×#6397611yescharacteristic
subgroupG/H
centerC2C2×#63976
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×#120
hypercenterC2×#41D32
hypocenterC32#3019
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1009C2semidirect
2. C3×#5822C2semidirect
3. #10595040C2semidirect
4. #10594786C2semidirect
5. #10592935C2semidirect
6. #10591665C2semidirect
7. #10591664C2semidirect
8. #10591110C2semidirect
9. C2×#63558C2semidirect
22. C2×C3×#235C22semidirect
25. #64135C22semidirect
26. C2×#3748C22semidirect
27. C3×#951C22semidirect
29. C3×#949C22semidirect
32. C2×C3×#208C22semidirect
34. #63914C22semidirect
36. #63863C22semidirect
38. #63827C22semidirect
40. #63823C22semidirect
42. #63664C22semidirect
43. #63568C22semidirect
44. #63558C22semidirect
46. C2×#1009D3semidirect
51. #5822D3semidirect
68. C32×#41D4semidirect
70. C2×C32×Q8D4semidirect
72. C2×C32×D4D4semidirect
92. C3×#235D4semidirect
102. C2×C3×D12D4semidirect
104. C2×C3×D12C23semidirect
108. C2×C3×Dic6D4semidirect
109. C2×C3×Dic6C23semidirect
113. C4×C3⋊Dic3C23semidirect
115. #3748C23semidirect
122. C3×#208C23semidirect
154. C2×#235C2×D3semidirect
166. #951C2×D3semidirect
172. #949C2×D3semidirect
192. C2×#208C2×D3semidirect
287. C3×#41#67semidirect
288. C3×#41#67semidirect
294. C2×C3×Q8#67semidirect
295. C2×C3×Q8#67semidirect
318. C2×C3×D4#67semidirect
319. C2×C3×D4#67semidirect
348. #235#67semidirect
358. C2×D12#67semidirect
360. C2×D12C22×D3semidirect
364. C2×Dic6#67semidirect
365. C2×Dic6C22×D3semidirect
403. #208C22×D3semidirect
615. #41#625semidirect
619. C2×Q8#625semidirect
640. C2×D4#625semidirect
722. C32#3019semidirect
822. C3#84005semidirect
823. C3#84104semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10092
C3×#58222
#105950402
#105947862
#105929352
#105916652
#105916642
#105911102
C2×#635582
#841043
#840053