Finite Group Databasebeta

← #11864144

Subgroups — #11864144

Order 1152.

1693 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic, complemented
3C2×#63908C211yesmaximal, characteristic, complemented
4C2×#63823C211yesmaximal, characteristic, complemented
5#10592931C211yesmaximal, characteristic, complemented
6#10591586C212yesmaximal, complemented
7#10591583C212yesmaximal, complemented
8#10591450C212yesmaximal, complemented
9#10591447C212yesmaximal, complemented
10#10591088C211yesmaximal, characteristic, complemented
11#10591069C211yesmaximal, characteristic, complemented
12#84082—31nomaximal
13#83946—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C3×D3×#41—24no—
16C3×D3×#41—24no—
17C2×C3×#239C2211yescharacteristic, complemented
18C2×C3×D3×Q8C2211yescharacteristic, complemented
19C2×C3×#237—21no—
20C2×C3×#237C2211yescharacteristic, complemented
21C2×C3×D3×D4—21no—
22C2×C3×D3×D4C2211yescharacteristic, complemented
23C2×C3×#235—21no—
24C2×C3×#235C2211yescharacteristic
25C22×C3×D12C2211yescharacteristic, complemented
26C22×C3×C4×D3—21no—
27C22×C3×C4×D3C2211yescharacteristic
28C22×#625—21no—
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
30C2×#3748C2211yescharacteristic, complemented
31C3×#949—24no—
32C2×C3×#215C2212yescomplemented
33C2×C3×#213C2212yescomplemented
34C2×C3×#208C2211yescharacteristic, complemented
35C2×(C2×D3)⋊Dic3—21no—
36#63908—21no—
37#63908—21no—
38#63908C2212yes—
39#63908C2212yescomplemented
40C2×#3715C2212yescomplemented
41#63823—24no—
42C2×#3713C2212yescomplemented
43#63662C2212yescomplemented
44#63659C2212yescomplemented
45#63566C2212yescomplemented
46#63563C2212yescomplemented
47(C2×D3)⋊(C3⋊C8)C2212yescomplemented
48(C2×D3)⋊(C3⋊C8)C2212yescomplemented
49C22×C3×#41—31no—
50C2×D3×#41D311yescharacteristic, complemented
51C2×C3×AGL(1,ℤ/8)—31no—
52C2×#949—31no—
53C2×#949D311yescharacteristic, complemented
54C2×#938—31no—
55C2×#932—31no—
56C2×#930—31no—
57#5238—32no—
58#5238—32no—
59#5232—31no—
60#5232—31no—
61#5232—31no—
62#5232—61no—
63#5227—32no—
64#5217—32no—
65#5207—31no—
66#5172—32no—
67#5170—32no—
68#5158—32no—
69#5156—32no—
70#5133—31no—
71#5126—31no—
72C23×C3×D3—21no—
73C23×C3×D3—21no—
74C23×C3×D3D411yescharacteristic
75C32×#41—22no—
76C32×#41D414yescomplemented
77C2×C32×Q8C2311yescharacteristic
78C2×C32×D4—21no—
79C2×C32×D4C2311yescharacteristic
80C22×C32×C4—21no—
81C22×C32×C4C2311yescharacteristic
82C22×C3⋊Dic3—21no—
83C2×C3×#67—21no—
84C2×C3×#67—21no—
85C2×C3×#67—21no—
86C22×C3×Dic3—21no—
87C22×C3×Dic3D411yescharacteristic
88C3×#239—22no—
89C3×#239—22no—
90C3×D3×Q8—22no—
91C3×D3×Q8—22no—
92C3×#237—28no—
93C3×#237—22no—
94C3×#237—22no—
95C3×D3×D4—28no—
96C3×D3×D4—22no—
97C3×D3×D4—22no—
98C3×#235—28no—
99C3×#235—22no—
100C3×#235D414yescomplemented
101C2×C3×D12—21no—
102C2×C3×D12—22no—
103C2×C3×D12—22no—
104C2×C3×D12—21no—
105C2×C3×D12C2312yes—
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—28no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—22no—
111C2×C3×C4×D3—22no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3D411yescharacteristic
114C2×C3×C4×D3D411yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×Dic6—21no—
118C2×C3×Dic6C2311yescharacteristic
119C2×#625—22no—
120C2×#625—22no—
121C2×#625—44no—
122C4⋊(C3⋊Dic3)—21no—
123C4⋊(C3⋊Dic3)C2312yes—
124#3748—22no—
125C2×C3⋊(C3⋊C8)C2312yes—
126C3×#215—24no—
127C3×#213—24no—
128C3×#208—22no—
129C2×C3×C3⋊C8C2312yes—
130(C2×D3)⋊Dic3—22no—
131(C2×D3)⋊Dic3—22no—
132#3715—24no—
133#3713—24no—
134#3006—91noSylow
135C2×C3×#41—21no—
136C2×C3×#41—31no—
137C2×C3×#41—31no—
138C2×C3×#41—31no—
139C2×C3×#41—61no—
140C2×C3×#41—61no—
141C2×C3×#41—64no—
142C2×C3×#41—64no—
143C2×C3×#41C2×D311yescharacteristic
144C2×C3×#41C2×D311yescharacteristic
145C22×C3×Q8—31no—
146C22×C3×D4—31no—
147C22×C3×D4—31no—
148C22×C3×D4—61no—
149C23×C3×C4—31no—
150C23×C3×C4—61no—
151C22×#67—61no—
152C22×#67—61no—
153D3×#41—24no—
154D3×#41—24no—
155C2×#239C2×D311yescharacteristic, complemented
156C2×D3×Q8C2×D311yescharacteristic, complemented
157C2×#237—21no—
158C2×#237C2×D311yescharacteristic, complemented
159C2×D3×D4—21no—
160C2×D3×D4C2×D311yescharacteristic, complemented
161C2×#235—21no—
162C2×#235C2×D311yescharacteristic
163C22×D12C2×D311yescharacteristic, complemented
164C22×C4×D3—21no—
165C22×C4×D3C2×D311yescharacteristic
166C3×AGL(1,ℤ/8)—64no—
167C2×C3×SD16—32no—
168C2×C3×D8—32no—
169C2×C3×M16—31no—
170C2×#217—61no—
171#949—24no—
172#949—64no—
173C2×#215—32no—
174C2×#215C2×D312yescomplemented
175#938—32no—
176#938—32no—
177#938—61no—
178#938—61no—
179C2×#214—32no—
180#932—64no—
181C2×#213—32no—
182C2×#213—32no—
183C2×#213C2×D312yescomplemented
184#930—32no—
185#930—32no—
186#930—61no—
187#930—61no—
188C2×(C2×D3)⋊C4—61no—
189C2×C4⋊Dic3—31no—
190C2×C4⋊Dic3—31no—
191C2×C4⋊Dic3—61no—
192C2×#208—31no—
193C2×#208—31no—
194C2×#208—61no—
195C2×#208C2×D311yescharacteristic, complemented
196#835—32no—
197#835—32no—
198#835—32no—
199#835—62no—
200#832—32no—
201#832—32no—
202#832—32no—
203#832—62no—
204#830—32no—
205#830—32no—
206#821—32no—
207(C2×D3)⋊C8—32no—
208(C2×D3)⋊C8—32no—
209#816—32no—
210C23×C32—21no—
211C23×C32C2×D411yescharacteristic
212C22×C3×D3—24no—
213C22×C3×D3—22no—
214C22×C3×D3—21no—
215C22×C3×D3—22no—
216C22×C3×D3—22no—
217C22×C3×D3—41no—
218C22×C3×D3—42no—
219C22×C3×D3—42no—
220C22×C3×D3—42no—
221C22×C3×D3—42no—
222C22×C3×D3—42no—
223C22×C3×D3C2×D411yescharacteristic
224C22×C3×D3C2×D411yescharacteristic
225C32×Q8—21no—
226C32×Q8C2×D412yescomplemented
227C32×D4—24no—
228C32×D4—21no—
229C32×D4C2×D412yescomplemented
230C2×C32×C4—21no—
231C2×C32×C4—24no—
232C2×C32×C4C2×D411yescharacteristic
233C2×C32×C4C2×D412yes—
234C2×C32×C4C2×D412yes—
235C2×C32×C4C2411yescharacteristic
236C2×C3⋊Dic3—22no—
237C2×C3⋊Dic3—42no—
238C3×#67—24no—
239C3×#67—24no—
240C3×#67—24no—
241C2×C3×Dic3—24no—
242C2×C3×Dic3—22no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3C2×D411yescharacteristic
245C2×C3×Dic3C2×D411yescharacteristic
246C3×D12—24no—
247C3×D12—21no—
248C3×D12—22no—
249C3×D12—22no—
250C3×D12—42no—
251C3×D12C2×D412yescomplemented
252C3×C4×D3—24no—
253C3×C4×D3—24no—
254C3×C4×D3—22no—
255C3×C4×D3—24no—
256C3×C4×D3—22no—
257C3×C4×D3—21no—
258C3×C4×D3—21no—
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×Dic6—24no—
262C3×Dic6—21no—
263C3×Dic6C2×D412yescomplemented
264#625—44no—
265#625—44no—
266C3⋊(C3⋊C8)—22no—
267C3×C3⋊C8—22no—
268C22×#41—31no—
269C2×AGL(1,ℤ/8)—31no—
270C2×AGL(1,ℤ/8)—91no—
271C2×#121—91no—
272#449—92no—
273#449—92no—
274#448—92no—
275#447—92no—
276#417—91no—
277#417—91no—
278#407—91no—
279C24×C3—31no—
280C24×C3—61no—
281C24×C3—61no—
282C23×D3—21no—
283C23×D3—21no—
284C23×D3#6711yescharacteristic
285C3×#41—22no—
286C3×#41—22no—
287C3×#41—24no—
288C3×#41—34no—
289C3×#41—42no—
290C3×#41—68no—
291C3×#41—62no—
292C3×#41—68no—
293C3×#41—62no—
294C3×#41—62no—
295C3×#41—62no—
296C3×#41—62no—
297C3×#41#6714yescomplemented
298C3×#41#6714yescomplemented
299C2×C3×Q8—21no—
300C2×C3×Q8—31no—
301C2×C3×Q8—61no—
302C2×C3×Q8—62no—
303C2×C3×Q8—62no—
304C2×C3×Q8C22×D311yescharacteristic
305C2×C3×Q8C22×D311yescharacteristic
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—31no—
310C2×C3×D4—32no—
311C2×C3×D4—41no—
312C2×C3×D4—61no—
313C2×C3×D4—61no—
314C2×C3×D4—62no—
315C2×C3×D4—68no—
316C2×C3×D4—61no—
317C2×C3×D4—61no—
318C2×C3×D4—62no—
319C2×C3×D4—62no—
320C2×C3×D4—62no—
321C2×C3×D4—61no—
322C2×C3×D4C22×D311yescharacteristic
323C2×C3×D4C22×D311yescharacteristic
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—41no—
333C22×C3×C4—61no—
334C22×C3×C4—61no—
335C22×C3×C4—68no—
336C22×C3×C4—61no—
337C22×C3×C4—62no—
338C22×C3×C4—61no—
339C22×C3×C4—62no—
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C2×#67—21no—
343C2×#67—21no—
344C2×#67—21no—
345C2×#67—62no—
346C2×#67—62no—
347C2×#67—62no—
348C2×#67—62no—
349C2×#67—124no—
350C2×#67—124no—
351C22×Dic3—21no—
352C22×Dic3—61no—
353C22×Dic3—61no—
354C22×Dic3—121no—
355C22×Dic3#6711yescharacteristic
356#239—22no—
357#239—22no—
358D3×Q8—22no—
359D3×Q8—22no—
360#237—28no—
361#237—22no—
362#237—22no—
363D3×D4—28no—
364D3×D4—22no—
365D3×D4—22no—
366#235—28no—
367#235—22no—
368#235#6714yescomplemented
369C2×D12—21no—
370C2×D12—22no—
371C2×D12—22no—
372C2×D12—21no—
373C2×D12C22×D312yes—
374C2×D12C22×D311yescharacteristic
375C2×C4×D3—28no—
376C2×C4×D3—21no—
377C2×C4×D3—21no—
378C2×C4×D3—22no—
379C2×C4×D3—22no—
380C2×C4×D3—21no—
381C2×C4×D3#6711yescharacteristic
382C2×C4×D3#6711yescharacteristic
383C2×C4×D3C22×D311yescharacteristic
384C2×C4×D3C22×D311yescharacteristic
385C2×Dic6—21no—
386C2×Dic6C22×D311yescharacteristic
387C3×SD16—64no—
388C3×D8—64no—
389C3×M16—62no—
390C2×C3×C8—32no—
391#217—62no—
392#217—62no—
393#215—24no—
394#215—64no—
395#214—64no—
396#213—24no—
397#213—64no—
398#213—64no—
399(C2×D3)⋊C4—62no—
400(C2×D3)⋊C4—62no—
401C4⋊Dic3—32no—
402C4⋊Dic3—32no—
403C4⋊Dic3—62no—
404C4⋊Dic3—61no—
405C4⋊Dic3—61no—
406C4⋊Dic3—121no—
407#208—22no—
408#208—62no—
409#208—62no—
410#208—122no—
411C2×C3⋊C8—32no—
412C2×C3⋊C8—32no—
413C2×C3⋊C8—62no—
414C2×C3⋊C8C22×D312yes—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—22no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32#12012yes—
421C22×C32C22×D411yescharacteristic
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—22no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—44no—
429C2×C3×D3—48no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—42no—
433C2×C3×D3—42no—
434C2×C3×D3—42no—
435C2×C3×D3—84no—
436C2×C3×D3AGL(1,ℤ/8)12yescomplemented
437C32×C4—22no—
438C32×C4#12012yes—
439C32×C4C22×D411yescharacteristic
440C32×C4C22×D411yescharacteristic
441C3⋊Dic3—42no—
442C3×Dic3—21no—
443C3×Dic3—22no—
444C3×Dic3—21no—
445C2×#41—31no—
446C2×#41—31no—
447C2×#41—31no—
448C2×#41—61no—
449C2×#41—61no—
450C2×#41—64no—
451C2×#41—64no—
452C2×#41D3211yescharacteristic
453C22×Q8—31no—
454C22×D4—31no—
455C22×D4—31no—
456C22×D4—61no—
457C22×D4—181no—
458C23×C4—31no—
459C23×C4—61no—
460AGL(1,ℤ/8)—64no—
461AGL(1,ℤ/8)—184no—
462C2×SD16—32no—
463C2×SD16—92no—
464C2×D8—32no—
465C2×D8—92no—
466C2×M16—31no—
467C2×M16—91no—
468#121—92no—
469#121—92no—
470#121—181no—
471#121—181no—
472C2×C4⋊C4—91no—
473C2×C22⋊C4—181no—
474#103—92no—
475#103—92no—
476#102—92no—
477#102—92no—
478C22⋊C8—92no—
479C22⋊C8—92no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3—31no—
485C23×C3—41no—
486C23×C3—62no—
487C23×C3—64no—
488C23×C3—62no—
489C23×C3—61no—
490C23×C3—62no—
491C23×C3—121no—
492C23×C3—122no—
493C23×C3—122no—
494C23×C3—122no—
495C23×C3—122no—
496C23×C3—122no—
497C23×C3D3×D411yescharacteristic
498C23×C3C2×#6711yescharacteristic
499C22×D3—24no—
500C22×D3—22no—
501C22×D3—21no—
502C22×D3—22no—
503C22×D3—22no—
504C22×D3—41no—
505C22×D3—42no—
506C22×D3—42no—
507C22×D3—42no—
508C22×D3—42no—
509C22×D3—42no—
510C22×D3C2×#6711yescharacteristic
511C22×D3C2×#6711yescharacteristic
512C3×Q8—21no—
513C3×Q8—21no—
514C3×Q8—22no—
515C3×Q8—32no—
516C3×Q8—41no—
517C3×Q8—64no—
518C3×Q8—61no—
519C3×Q8C2×#6712yescomplemented
520C3×Q8C2×#6712yescomplemented
521C3×D4—24no—
522C3×D4—24no—
523C3×D4—21no—
524C3×D4—21no—
525C3×D4—22no—
526C3×D4—32no—
527C3×D4—41no—
528C3×D4—44no—
529C3×D4—64no—
530C3×D4—64no—
531C3×D4—64no—
532C3×D4—64no—
533C3×D4—61no—
534C3×D4—62no—
535C3×D4—62no—
536C3×D4—122no—
537C3×D4C2×#6712yescomplemented
538C3×D4C2×#6712yescomplemented
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—24no—
542C2×C3×C4—24no—
543C2×C3×C4—21no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—21no—
547C2×C3×C4—31no—
548C2×C3×C4—31no—
549C2×C3×C4—44no—
550C2×C3×C4—41no—
551C2×C3×C4—64no—
552C2×C3×C4—64no—
553C2×C3×C4—64no—
554C2×C3×C4—62no—
555C2×C3×C4—61no—
556C2×C3×C4—62no—
557C2×C3×C4—62no—
558C2×C3×C4—64no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4D3×D411yescharacteristic
564C2×C3×C4D3×D412yes—
565C2×C3×C4C2×#6712yes—
566C2×C3×C4C2×#6712yes—
567C2×C3×C4C2×#6711yescharacteristic
568C2×C3×C4C2×#6712yes—
569C2×C3×C4C23×D311yescharacteristic
570C2×C3×C4C23×D311yescharacteristic
571#67—24no—
572#67—24no—
573#67—24no—
574#67—124no—
575#67—124no—
576#67—124no—
577#67—124no—
578C2×Dic3—24no—
579C2×Dic3—22no—
580C2×Dic3—21no—
581C2×Dic3—62no—
582C2×Dic3—62no—
583C2×Dic3—122no—
584C2×Dic3—122no—
585C2×Dic3—122no—
586C2×Dic3—242no—
587C2×Dic3C2×#6711yescharacteristic
588C2×Dic3C2×#6711yescharacteristic
589D12—24no—
590D12—22no—
591D12—21no—
592D12—22no—
593D12—42no—
594D12C2×#6712yescomplemented
595C4×D3—24no—
596C4×D3—24no—
597C4×D3—22no—
598C4×D3—24no—
599C4×D3—22no—
600C4×D3—21no—
601C4×D3—21no—
602C4×D3—21no—
603C4×D3—21no—
604Dic6—24no—
605Dic6—21no—
606Dic6C2×#6712yescomplemented
607C3×C8—62no—
608C3⋊C8—22no—
609C3⋊C8—62no—
610C3⋊C8—62no—
611C3⋊C8—122no—
612C2×C32—22no—
613C2×C32—42no—
614C2×C32C2×#12011yescharacteristic
615C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
616C2×C32#57511yescharacteristic
617C3×D3—22no—
618C3×D3—41no—
619C3×D3—42no—
620C3×D3—82no—
621C24—31no—
622C24—61no—
623C24—61no—
624#41—22no—
625#41—34no—
626#41—68no—
627#41—62no—
628#41—68no—
629#41—62no—
630#41—62no—
631#41—62no—
632#41—62no—
633#41#62514yescomplemented
634C2×Q8—31no—
635C2×Q8—61no—
636C2×Q8—62no—
637C2×Q8—62no—
638C2×Q8C2×D3211yescharacteristic
639C2×D4—21no—
640C2×D4—31no—
641C2×D4—32no—
642C2×D4—61no—
643C2×D4—61no—
644C2×D4—62no—
645C2×D4—68no—
646C2×D4—61no—
647C2×D4—61no—
648C2×D4—62no—
649C2×D4—62no—
650C2×D4—62no—
651C2×D4—61no—
652C2×D4—182no—
653C2×D4—182no—
654C2×D4—364no—
655C2×D4C2×D3211yescharacteristic
656C22×C4—21no—
657C22×C4—31no—
658C22×C4—31no—
659C22×C4—31no—
660C22×C4—31no—
661C22×C4—31no—
662C22×C4—61no—
663C22×C4—61no—
664C22×C4—68no—
665C22×C4—61no—
666C22×C4—62no—
667C22×C4—62no—
668C22×C4—61no—
669C22×C4—181no—
670C22×C4C2×D3211yescharacteristic
671SD16—64no—
672SD16—184no—
673D8—64no—
674D8—184no—
675M16—62no—
676M16—182no—
677C2×C8—32no—
678C2×C8—92no—
679C4⋊C4—92no—
680C4⋊C4—181no—
681C22⋊C4—182no—
682C22⋊C4—182no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—21no—
690C22×C3—22no—
691C22×C3—32no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—42no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—61no—
700C22×C3—61no—
701C22×C3—61no—
702C22×C3—61no—
703C22×C3—62no—
704C22×C3—61no—
705C22×C3—81no—
706C22×C3—81no—
707C22×C3—124no—
708C22×C3—128no—
709C22×C3—121no—
710C22×C3—121no—
711C22×C3—122no—
712C22×C3—122no—
713C22×C3—122no—
714C22×C3—244no—
715C22×C3#93712yes—
716C22×C3#95312yes—
717C22×C3C2×D3×D411yescharacteristic
718C22×C3C22×#6711yescharacteristic
719C2×D3—21no—
720C2×D3—21no—
721C2×D3—21no—
722C2×D3—21no—
723C2×D3—21no—
724C2×D3—22no—
725C2×D3—44no—
726C2×D3—48no—
727C2×D3—41no—
728C2×D3—41no—
729C2×D3—42no—
730C2×D3—42no—
731C2×D3—42no—
732C2×D3—84no—
733C2×D3#94912yescomplemented
734C3×C4—22no—
735C3×C4—22no—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—22no—
739C3×C4—42no—
740C3×C4—61no—
741C3×C4—61no—
742C3×C4—62no—
743C3×C4#93712yes—
744C3×C4#95312yes—
745C3×C4C2×D3×D411yescharacteristic
746C3×C4C22×#6711yescharacteristic
747C3×C4C22×#6711yescharacteristic
748C3×C4C22×#6711yescharacteristic
749Dic3—21no—
750Dic3—22no—
751Dic3—21no—
752Dic3—122no—
753Dic3—122no—
754Dic3—242no—
755C32#300611yescharacteristic, complemented, Sylow
756C23—21no—
757C23—31no—
758C23—31no—
759C23—62no—
760C23—64no—
761C23—61no—
762C23—62no—
763C23—62no—
764C23—121no—
765C23—122no—
766C23—122no—
767C23—122no—
768C23—122no—
769C23—122no—
770C23D3×#6711yescharacteristic
771Q8—21no—
772Q8—32no—
773Q8—64no—
774Q8—61no—
775Q8C2×#62512yescomplemented
776D4—24no—
777D4—21no—
778D4—32no—
779D4—64no—
780D4—64no—
781D4—64no—
782D4—64no—
783D4—61no—
784D4—62no—
785D4—62no—
786D4—122no—
787D4—364no—
788D4—364no—
789D4C2×#62512yescomplemented
790C2×C4—21no—
791C2×C4—24no—
792C2×C4—31no—
793C2×C4—31no—
794C2×C4—64no—
795C2×C4—64no—
796C2×C4—64no—
797C2×C4—61no—
798C2×C4—62no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—62no—
804C2×C4—62no—
805C2×C4—64no—
806C2×C4—182no—
807C2×C4—362no—
808C2×C4C2×#62512yes—
809C2×C4D3×#6712yes—
810C2×C4D3×#6711yescharacteristic
811C2×C4C22×D3211yescharacteristic
812C8—62no—
813C8—182no—
814C2×C3—22no—
815C2×C3—22no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—42no—
820C2×C3—42no—
821C2×C3—42no—
822C2×C3—62no—
823C2×C3—82no—
824C2×C3—121no—
825C2×C3—122no—
826C2×C3—242no—
827C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
828C2×C3#577311yescharacteristic
829C2×C3C2×#93711yescharacteristic
830C2×C3C2×#94911yescharacteristic
831C2×C3#582211yescharacteristic
832C2×C3C2×#95311yescharacteristic
833D3—22no—
834D3—41no—
835D3—42no—
836D3—82no—
837C22—21no—
838C22—21no—
839C22—22no—
840C22—32no—
841C22—41no—
842C22—41no—
843C22—61no—
844C22—61no—
845C22—61no—
846C22—61no—
847C22—62no—
848C22—61no—
849C22—124no—
850C22—128no—
851C22—121no—
852C22—121no—
853C22—122no—
854C22—122no—
855C22—122no—
856C22—244no—
857C22#6397612yes—
858C22C2×D3×#6711yescharacteristic
859C4—22no—
860C4—61no—
861C4—61no—
862C4—62no—
863C4—362no—
864C4#6397612yes—
865C4C22×#62511yescharacteristic
866C4C2×D3×#6711yescharacteristic
867C3—21no—
868C3#8394611yescharacteristic, complemented
869C3#8408211yescharacteristic, complemented
870C2—22no—
871C2—42no—
872C2—62no—
873C2—121no—
874C2—122no—
875C2—242no—
876C2D3×#94911yescharacteristic
877C2#1059546911yescharacteristic
878C2C2×#6397611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3006
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×#41C2semidirect
2. C2×C3×#949C2semidirect
3. C2×#63908C2semidirect
4. C2×#63823C2semidirect
5. #10592931C2semidirect
6. #10591586C2semidirect
7. #10591583C2semidirect
8. #10591450C2semidirect
9. #10591447C2semidirect
10. #10591088C2semidirect
11. #10591069C2semidirect
17. C2×C3×#239C22semidirect
18. C2×C3×D3×Q8C22semidirect
20. C2×C3×#237C22semidirect
22. C2×C3×D3×D4C22semidirect
25. C22×C3×D12C22semidirect
29. C2×C4⋊(C3⋊Dic3)C22semidirect
30. C2×#3748C22semidirect
32. C2×C3×#215C22semidirect
33. C2×C3×#213C22semidirect
34. C2×C3×#208C22semidirect
39. #63908C22semidirect
40. C2×#3715C22semidirect
42. C2×#3713C22semidirect
43. #63662C22semidirect
44. #63659C22semidirect
45. #63566C22semidirect
46. #63563C22semidirect
47. (C2×D3)⋊(C3⋊C8)C22semidirect
48. (C2×D3)⋊(C3⋊C8)C22semidirect
50. C2×D3×#41D3semidirect
53. C2×#949D3semidirect
76. C32×#41D4semidirect
100. C3×#235D4semidirect
155. C2×#239C2×D3semidirect
156. C2×D3×Q8C2×D3semidirect
158. C2×#237C2×D3semidirect
160. C2×D3×D4C2×D3semidirect
163. C22×D12C2×D3semidirect
174. C2×#215C2×D3semidirect
183. C2×#213C2×D3semidirect
195. C2×#208C2×D3semidirect
226. C32×Q8C2×D4semidirect
229. C32×D4C2×D4semidirect
251. C3×D12C2×D4semidirect
263. C3×Dic6C2×D4semidirect
297. C3×#41#67semidirect
298. C3×#41#67semidirect
368. #235#67semidirect
436. C2×C3×D3AGL(1,ℤ/8)semidirect
519. C3×Q8C2×#67semidirect
520. C3×Q8C2×#67semidirect
537. C3×D4C2×#67semidirect
538. C3×D4C2×#67semidirect
594. D12C2×#67semidirect
606. Dic6C2×#67semidirect
633. #41#625semidirect
733. C2×D3#949semidirect
755. C32#3006semidirect
775. Q8C2×#625semidirect
789. D4C2×#625semidirect
868. C3#83946semidirect
869. C3#84082semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
C2×C3×#9492
C2×#639082
C2×#638232
#105929312
#105915862
#105915832
#105914502
#105914472
#105910882
#105910692
#840823
#839463