Finite Group Databasebeta

← #11864140

Subgroups — #11864140

Order 1152.

1761 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic, complemented
2C2×#64141C211yesmaximal, characteristic, complemented
3C2×C3×#938C211yesmaximal, characteristic, complemented
4C2×C3×#932C211yesmaximal, characteristic, complemented
5#10591521C212yesmaximal, complemented
6#10591519C212yesmaximal, complemented
7#10591517C212yesmaximal, complemented
8#10591515C212yesmaximal, complemented
9#10591106C211yesmaximal, characteristic, complemented
10#10591087C211yesmaximal, characteristic, complemented
11#10591069C211yesmaximal, characteristic, complemented
12#83946—31nomaximal
13#82624—31nomaximal
14C22×C32×D4C2211yescharacteristic, complemented
15C2×#3828C2211yescharacteristic
16C22×C3×#67—21no—
17C2×C3×#235C2211yescharacteristic
18C22×C3×C4×D3C2211yescharacteristic
19C2×D3×#67—21no—
20C2×#3804—21no—
21D3×#235—24no—
22D3×#235—24no—
23C2×D3×D12C2211yescharacteristic, complemented
24C2×C4×D32—21no—
25C2×#3799C2211yescharacteristic, complemented
26C2×#3798—21no—
27C2×#3795C2211yescharacteristic, complemented
28C2×D3×Dic6C2211yescharacteristic, complemented
29C2×#3754C2212yescomplemented
30#64141—24no—
31C2×#3753C2212yescomplemented
32C2×#3748C2211yescharacteristic, complemented
33C2×C3×#217—21no—
34C3×#938—21no—
35C3×#938—21no—
36C3×#938C2212yes—
37C3×#938C2212yescomplemented
38C2×C3×#214C2212yescomplemented
39C3×#932—24no—
40C2×C3×#213C2212yescomplemented
41C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
42C2×C3×#208C2211yescharacteristic, complemented
43#63567C2212yescomplemented
44#63565C2212yescomplemented
45#63564C2212yescomplemented
46#63562C2212yescomplemented
47(C2×D3)⋊(C3⋊C8)C2212yescomplemented
48(C2×D3)⋊(C3⋊C8)C2212yescomplemented
49C2×D3×#41—31no—
50C22×#235—31no—
51C2×C3×AGL(1,ℤ/8)—31no—
52C2×C3×#121—31no—
53C2×#938D311yescharacteristic, complemented
54C2×#932—31no—
55C2×#932—31no—
56C2×#932—61no—
57C2×#932D311yescharacteristic, complemented
58#5232—31no—
59#5207—31no—
60#5172—32no—
61#5170—32no—
62#5158—32no—
63#5156—32no—
64#5133—31no—
65#5126—31no—
66#5040—32no—
67#5037—32no—
68#5037—32no—
69#5036—32no—
70#4966—31no—
71#4966—31no—
72C24×C32—21no—
73C23×C3×D3D411yescharacteristic
74C22×D32—21no—
75C2×C32×D4—22no—
76C2×C32×D4—22no—
77C2×C32×D4—21no—
78C2×C32×D4C2312yes—
79C22×C32×C4C2311yescharacteristic
80C2×#638—21no—
81#3828—22no—
82#3828D414yescomplemented
83C2×C4⋊(C3⋊D3)C2311yescharacteristic
84C2×C4×C3⋊D3—21no—
85C2×#634C2311yescharacteristic
86C2×C3×#67—21no—
87C2×C3×#67—22no—
88C2×C3×#67—22no—
89C2×C3×#67—44no—
90C22×C3×Dic3—21no—
91C22×C3×Dic3D411yescharacteristic
92C3×#235—22no—
93C3×#235D414yescomplemented
94C2×C3×D12C2311yescharacteristic
95C2×C3×C4×D3—21no—
96C2×C3×C4×D3—22no—
97C2×C3×C4×D3—22no—
98C2×C3×C4×D3D411yescharacteristic
99C2×C3×C4×D3D411yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103D3×#67—28no—
104C2×#627—21no—
105C2×#626—21no—
106C2×#626—21no—
107C2×#625—21no—
108C2×#624—21no—
109#3804—28no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112D3×D12—22no—
113D3×D12—22no—
114C4×D32—28no—
115#3799—22no—
116#3799—22no—
117#3798—28no—
118#3795—22no—
119#3795—22no—
120D3×Dic6—22no—
121D3×Dic6—22no—
122#3754—24no—
123#3753—24no—
124#3748—22no—
125C2×C3⋊(C3⋊C8)C2312yes—
126C3×#217—22no—
127C3×#217—22no—
128C3×#214—24no—
129C3×#213—24no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3C2312yes—
132C3×#208—22no—
133C2×C3×C3⋊C8C2312yes—
134#3006—91noSylow
135C2×C3×#41—31no—
136C22×C3×D4—21no—
137C22×C3×D4—61no—
138C22×C3×D4C2×D311yescharacteristic, complemented
139C22×C3×D4C2×D311yescharacteristic, complemented
140C23×C3×C4—31no—
141C22×#67—21no—
142C22×#67—61no—
143D3×#41—64no—
144D3×#41—64no—
145C2×#239—31no—
146C2×D3×Q8—31no—
147C2×#237—31no—
148C2×#237—61no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C2×#235—31no—
152C2×#235—31no—
153C2×#235—31no—
154C2×#235—31no—
155C2×#235—61no—
156C2×#235—61no—
157C2×#235—64no—
158C2×#235—61no—
159C2×#235—64no—
160C2×#235—61no—
161C2×#235C2×D311yescharacteristic
162C22×D12—31no—
163C22×C4×D3—61no—
164C22×C4×D3—61no—
165C22×C4×D3C2×D311yescharacteristic
166C22×Dic6—31no—
167C3×AGL(1,ℤ/8)—64no—
168C2×C3×SD16—32no—
169C2×C3×D8—32no—
170C2×C3×M16—31no—
171C3×#121—32no—
172C3×#121—32no—
173C3×#121—61no—
174C3×#121—61no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C22⋊C4—61no—
177C2×#217—21no—
178#938—21no—
179#938—21no—
180#938C2×D312yes—
181#938C2×D312yescomplemented
182C2×#214—32no—
183C2×#214—32no—
184C2×#214—62no—
185C2×#214C2×D312yescomplemented
186#932—24no—
187#932—64no—
188#932—64no—
189#932—68no—
190C2×#213—32no—
191C2×#213—32no—
192C2×#213—62no—
193C2×#213C2×D312yescomplemented
194C2×C4⋊Dic3C2×D311yescharacteristic, complemented
195C2×#208—31no—
196C2×#208—31no—
197C2×#208—61no—
198C2×#208C2×D311yescharacteristic, complemented
199#835—32no—
200#832—32no—
201#830—32no—
202#830—32no—
203#821—32no—
204(C2×D3)⋊C8—32no—
205(C2×D3)⋊C8—32no—
206#816—32no—
207#810—32no—
208#810—32no—
209#809—32no—
210#809—32no—
211C23×C32—22no—
212C23×C32—42no—
213C23×C32—42no—
214C23×C32—42no—
215C23×C32C2×D411yescharacteristic
216C22×C3⋊D3—21no—
217C22×C3×D3—22no—
218C22×C3×D3—21no—
219C22×C3×D3—22no—
220C22×C3×D3—41no—
221C22×C3×D3C2×D411yescharacteristic
222C22×C3×D3C2×D411yescharacteristic
223C2×D32—24no—
224C2×D32—42no—
225C2×D32—42no—
226C32×D4—22no—
227C32×D4—22no—
228C32×D4—42no—
229C2×C32×C4C2×D412yes—
230C2×C32×C4C2×D411yescharacteristic
231C2×C32×C4C2×D412yes—
232C2×C32×C4C2411yescharacteristic
233#638—24no—
234C2×C3⋊Dic3—21no—
235C4⋊(C3⋊D3)—21no—
236C4⋊(C3⋊D3)C2×D412yescomplemented
237C4×C3⋊D3—24no—
238#634—21no—
239#634C2×D412yescomplemented
240C3×#67—24no—
241C3×#67—44no—
242C3×#67—44no—
243C2×C3×Dic3—22no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—22no—
246C2×C3×Dic3—42no—
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C3×D12—21no—
250C3×D12C2×D412yescomplemented
251C3×C4×D3—22no—
252C3×C4×D3—24no—
253C3×C4×D3—22no—
254C3×C4×D3—21no—
255C3×C4×D3—21no—
256C3×C4×D3—21no—
257C3×C4×D3—21no—
258C3×Dic6—21no—
259C3×Dic6C2×D412yescomplemented
260#627—24no—
261#626—24no—
262#626—24no—
263#625—24no—
264#624—24no—
265D3×Dic3—24no—
266D3×Dic3—24no—
267C3⋊(C3⋊C8)—22no—
268C3×C3⋊C8—22no—
269C22×#41—91no—
270C2×AGL(1,ℤ/8)—31no—
271C2×AGL(1,ℤ/8)—91no—
272C2×#121—31no—
273#449—92no—
274#449—92no—
275#448—92no—
276#447—92no—
277#417—91no—
278#417—91no—
279#407—91no—
280C24×C3—21no—
281C24×C3—21no—
282C24×C3—31no—
283C24×C3—41no—
284C23×D3—61no—
285C23×D3—61no—
286C23×D3#6711yescharacteristic
287C3×#41—34no—
288C3×#41—62no—
289C2×C3×Q8—31no—
290C2×C3×D4—24no—
291C2×C3×D4—22no—
292C2×C3×D4—22no—
293C2×C3×D4—22no—
294C2×C3×D4—21no—
295C2×C3×D4—22no—
296C2×C3×D4—21no—
297C2×C3×D4—22no—
298C2×C3×D4—31no—
299C2×C3×D4—42no—
300C2×C3×D4—41no—
301C2×C3×D4—61no—
302C2×C3×D4—62no—
303C2×C3×D4—62no—
304C2×C3×D4—124no—
305C2×C3×D4C22×D312yes—
306C2×C3×D4C22×D312yes—
307C22×C3×C4—21no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—62no—
314C22×C3×C4—61no—
315C22×C3×C4—62no—
316C22×C3×C4—61no—
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C2×#67—21no—
320C2×#67—22no—
321C2×#67—22no—
322C2×#67—44no—
323C2×#67—61no—
324C2×#67—68no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—121no—
331C22×Dic3—21no—
332C22×Dic3—61no—
333C22×Dic3—61no—
334C22×Dic3#6711yescharacteristic
335#239—62no—
336#239—62no—
337D3×Q8—62no—
338D3×Q8—62no—
339#237—62no—
340#237—62no—
341#237—68no—
342D3×D4—62no—
343D3×D4—62no—
344D3×D4—68no—
345#235—22no—
346#235—34no—
347#235—34no—
348#235—64no—
349#235—62no—
350#235—62no—
351#235—68no—
352#235—68no—
353#235—68no—
354#235—62no—
355#235—62no—
356#235—62no—
357#235—62no—
358#235—122no—
359#235#6714yescomplemented
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—61no—
363C2×D12—62no—
364C2×D12—61no—
365C2×D12—61no—
366C2×D12—62no—
367C2×D12C22×D311yescharacteristic
368C2×C4×D3—21no—
369C2×C4×D3—22no—
370C2×C4×D3—22no—
371C2×C4×D3—68no—
372C2×C4×D3—68no—
373C2×C4×D3—61no—
374C2×C4×D3—61no—
375C2×C4×D3—61no—
376C2×C4×D3—61no—
377C2×C4×D3—61no—
378C2×C4×D3—61no—
379C2×C4×D3—121no—
380C2×C4×D3#6711yescharacteristic
381C2×C4×D3#6711yescharacteristic
382C2×C4×D3C22×D311yescharacteristic
383C2×C4×D3C22×D311yescharacteristic
384C2×Dic6—31no—
385C2×Dic6—31no—
386C2×Dic6—61no—
387C2×Dic6—62no—
388C2×Dic6—61no—
389C2×Dic6—61no—
390C2×Dic6—62no—
391C2×Dic6C22×D311yescharacteristic
392C3×SD16—64no—
393C3×D8—64no—
394C3×M16—62no—
395C2×C3×C8—32no—
396C3×C4⋊C4—32no—
397C3×C4⋊C4—61no—
398C3×C22⋊C4—62no—
399C3×C22⋊C4—62no—
400#217—22no—
401#217—22no—
402#214—24no—
403#214—64no—
404#214—64no—
405#214—68no—
406#213—24no—
407#213—64no—
408#213—64no—
409#213—68no—
410C4⋊Dic3—21no—
411C4⋊Dic3C22×D312yes—
412#208—22no—
413#208—64no—
414#208—62no—
415#208—62no—
416C2×C3⋊C8—32no—
417C2×C3⋊C8—32no—
418C2×C3⋊C8—62no—
419C2×C3⋊C8C22×D312yes—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32—42no—
423C22×C32—42no—
424C22×C32—42no—
425C22×C32—84no—
426C22×C32#12012yes—
427C22×C32C22×D411yescharacteristic
428C2×C3⋊D3—22no—
429C2×C3⋊D3—41no—
430C2×C3⋊D3—41no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—22no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—21no—
437C2×C3×D3—44no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C2×C3×D3AGL(1,ℤ/8)12yescomplemented
441D32—48no—
442C32×C4#12012yes—
443C32×C4C22×D411yescharacteristic
444C32×C4C22×D411yescharacteristic
445C3⋊Dic3—22no—
446C3×Dic3—21no—
447C3×Dic3—22no—
448C3×Dic3—21no—
449C3×Dic3—42no—
450C2×#41—31no—
451C2×#41—91no—
452C2×#41—91no—
453C2×#41—91no—
454C2×#41—181no—
455C2×#41—181no—
456C2×#41—184no—
457C2×#41—184no—
458C22×Q8—91no—
459C22×D4—61no—
460C22×D4—91no—
461C22×D4—181no—
462C22×D4D3211yescharacteristic, complemented
463C23×C4—31no—
464C23×C4—181no—
465AGL(1,ℤ/8)—64no—
466AGL(1,ℤ/8)—184no—
467C2×SD16—32no—
468C2×SD16—92no—
469C2×D8—32no—
470C2×D8—92no—
471C2×M16—31no—
472C2×M16—91no—
473#121—32no—
474#121—32no—
475#121—61no—
476#121—61no—
477C2×C4⋊C4—31no—
478C2×C22⋊C4—61no—
479#103—92no—
480#103—92no—
481#102—92no—
482#102—92no—
483C22⋊C8—92no—
484C22⋊C8—92no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—21no—
488C23×C3—31no—
489C23×C3—31no—
490C23×C3—42no—
491C23×C3—42no—
492C23×C3—44no—
493C23×C3—42no—
494C23×C3—42no—
495C23×C3—42no—
496C23×C3—42no—
497C23×C3—42no—
498C23×C3—62no—
499C23×C3—62no—
500C23×C3—61no—
501C23×C3—82no—
502C23×C3—82no—
503C23×C3—121no—
504C23×C3D3×D411yescharacteristic
505C23×C3C2×#6711yescharacteristic
506C22×D3—22no—
507C22×D3—21no—
508C22×D3—22no—
509C22×D3—41no—
510C22×D3—64no—
511C22×D3—64no—
512C22×D3—61no—
513C22×D3—61no—
514C22×D3—121no—
515C22×D3—122no—
516C22×D3—122no—
517C22×D3—122no—
518C22×D3—122no—
519C22×D3C2×#6711yescharacteristic
520C22×D3C2×#6711yescharacteristic
521C3×Q8—32no—
522C3×Q8—61no—
523C3×D4—24no—
524C3×D4—22no—
525C3×D4—22no—
526C3×D4—22no—
527C3×D4—22no—
528C3×D4—32no—
529C3×D4—42no—
530C3×D4—44no—
531C3×D4—42no—
532C3×D4—42no—
533C3×D4—64no—
534C3×D4—61no—
535C3×D4—124no—
536C3×D4—124no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—31no—
542C2×C3×C4—31no—
543C2×C3×C4—62no—
544C2×C3×C4—61no—
545C2×C3×C4—62no—
546C2×C3×C4—64no—
547C2×C3×C4—62no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—62no—
553C2×C3×C4—122no—
554C2×C3×C4D3×D411yescharacteristic
555C2×C3×C4D3×D412yes—
556C2×C3×C4D3×D412yes—
557C2×C3×C4D3×D412yes—
558C2×C3×C4C2×#6711yescharacteristic
559C2×C3×C4C2×#6712yes—
560C2×C3×C4C23×D311yescharacteristic
561C2×C3×C4C23×D311yescharacteristic
562#67—24no—
563#67—44no—
564#67—44no—
565#67—64no—
566#67—64no—
567#67—64no—
568#67—64no—
569#67—64no—
570#67—64no—
571#67—124no—
572C2×Dic3—22no—
573C2×Dic3—21no—
574C2×Dic3—22no—
575C2×Dic3—42no—
576C2×Dic3—64no—
577C2×Dic3—64no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—121no—
581C2×Dic3C2×#6711yescharacteristic
582C2×Dic3C2×#6711yescharacteristic
583D12—21no—
584D12—32no—
585D12—32no—
586D12—62no—
587D12—64no—
588D12—64no—
589D12—61no—
590D12—61no—
591D12—121no—
592D12C2×#6712yescomplemented
593C4×D3—22no—
594C4×D3—22no—
595C4×D3—24no—
596C4×D3—21no—
597C4×D3—21no—
598C4×D3—21no—
599C4×D3—21no—
600C4×D3—64no—
601C4×D3—64no—
602C4×D3—64no—
603C4×D3—64no—
604C4×D3—64no—
605C4×D3—64no—
606C4×D3—124no—
607Dic6—21no—
608Dic6—32no—
609Dic6—32no—
610Dic6—62no—
611Dic6—64no—
612Dic6—64no—
613Dic6—61no—
614Dic6—61no—
615Dic6—121no—
616Dic6C2×#6712yescomplemented
617C3×C8—62no—
618C3⋊C8—22no—
619C3⋊C8—64no—
620C3⋊C8—62no—
621C3⋊C8—62no—
622C2×C32—22no—
623C2×C32—82no—
624C2×C32C2×#12011yescharacteristic
625C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
626C2×C32#57511yescharacteristic
627C3⋊D3—42no—
628C3×D3—22no—
629C3×D3—42no—
630C3×D3—41no—
631C24—21no—
632C24—31no—
633C24—181no—
634#41—34no—
635#41—62no—
636#41—94no—
637#41—188no—
638#41—182no—
639#41—182no—
640#41—188no—
641#41—182no—
642#41—182no—
643#41—182no—
644C2×Q8—31no—
645C2×Q8—91no—
646C2×Q8—181no—
647C2×Q8—182no—
648C2×Q8—182no—
649C2×D4—22no—
650C2×D4—21no—
651C2×D4—22no—
652C2×D4—31no—
653C2×D4—61no—
654C2×D4—62no—
655C2×D4—62no—
656C2×D4—91no—
657C2×D4—124no—
658C2×D4—181no—
659C2×D4—182no—
660C2×D4—182no—
661C2×D4—181no—
662C2×D4—188no—
663C2×D4—181no—
664C2×D4—181no—
665C2×D4C2×D3212yes—
666C22×C4—31no—
667C22×C4—31no—
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—62no—
672C22×C4—61no—
673C22×C4—62no—
674C22×C4—61no—
675C22×C4—181no—
676C22×C4—181no—
677C22×C4—188no—
678C22×C4—181no—
679C22×C4—181no—
680C22×C4C2×D3211yescharacteristic
681SD16—64no—
682SD16—184no—
683D8—64no—
684D8—184no—
685M16—62no—
686M16—182no—
687C2×C8—32no—
688C2×C8—92no—
689C4⋊C4—32no—
690C4⋊C4—61no—
691C22⋊C4—62no—
692C22⋊C4—62no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—22no—
699C22×C3—32no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—44no—
703C22×C3—42no—
704C22×C3—42no—
705C22×C3—42no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—42no—
709C22×C3—61no—
710C22×C3—61no—
711C22×C3—61no—
712C22×C3—61no—
713C22×C3—62no—
714C22×C3—61no—
715C22×C3—82no—
716C22×C3—82no—
717C22×C3—84no—
718C22×C3—84no—
719C22×C3—88no—
720C22×C3—124no—
721C22×C3—121no—
722C22×C3—121no—
723C22×C3#93712yes—
724C22×C3#93712yes—
725C22×C3C2×D3×D411yescharacteristic
726C22×C3C22×#6711yescharacteristic
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—21no—
731C2×D3—22no—
732C2×D3—21no—
733C2×D3—44no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—62no—
737C2×D3—62no—
738C2×D3—122no—
739C2×D3—128no—
740C2×D3—128no—
741C2×D3—121no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—241no—
746C2×D3—241no—
747C2×D3#93212yescomplemented
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—22no—
751C3×C4—61no—
752C3×C4—62no—
753C3×C4—61no—
754C3×C4—122no—
755C3×C4#93712yes—
756C3×C4#93712yes—
757C3×C4C2×D3×D411yescharacteristic
758C3×C4C2×D3×D411yescharacteristic
759C3×C4C2×D3×D411yescharacteristic
760C3×C4C22×#6711yescharacteristic
761Dic3—22no—
762Dic3—21no—
763Dic3—21no—
764Dic3—42no—
765Dic3—62no—
766Dic3—62no—
767Dic3—122no—
768C32#300611yescharacteristic, complemented, Sylow
769C23—22no—
770C23—31no—
771C23—31no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—62no—
776C23—61no—
777C23—62no—
778C23—121no—
779C23—184no—
780C23—181no—
781C23—362no—
782C23—362no—
783C23D3×#6711yescharacteristic
784Q8—32no—
785Q8—61no—
786Q8—92no—
787Q8—184no—
788Q8—181no—
789D4—22no—
790D4—22no—
791D4—32no—
792D4—42no—
793D4—64no—
794D4—61no—
795D4—92no—
796D4—124no—
797D4—124no—
798D4—184no—
799D4—184no—
800D4—184no—
801D4—184no—
802D4—181no—
803C2×C4—31no—
804C2×C4—31no—
805C2×C4—61no—
806C2×C4—62no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—62no—
812C2×C4—62no—
813C2×C4—64no—
814C2×C4—62no—
815C2×C4—122no—
816C2×C4—184no—
817C2×C4—184no—
818C2×C4—184no—
819C2×C4—181no—
820C2×C4—184no—
821C2×C4D3×#6712yes—
822C2×C4D3×#6711yescharacteristic
823C2×C4#381112yes—
824C2×C4C22×D3211yescharacteristic
825C8—62no—
826C8—182no—
827C2×C3—22no—
828C2×C3—22no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—42no—
833C2×C3—62no—
834C2×C3—84no—
835C2×C3—82no—
836C2×C3—82no—
837C2×C3—122no—
838C2×C3—121no—
839C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
840C2×C3#577311yescharacteristic
841C2×C3C2×#93211yescharacteristic
842C2×C3C2×#93711yescharacteristic
843C2×C3C2×#93711yescharacteristic
844C2×C3#582211yescharacteristic
845D3—22no—
846D3—41no—
847D3—42no—
848D3—122no—
849D3—122no—
850D3—242no—
851C22—21no—
852C22—21no—
853C22—32no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—61no—
858C22—61no—
859C22—61no—
860C22—61no—
861C22—61no—
862C22—62no—
863C22—84no—
864C22—124no—
865C22—121no—
866C22—121no—
867C22—182no—
868C22—368no—
869C22—361no—
870C22—361no—
871C22#6398312yes—
872C22C2×D3×#6711yescharacteristic
873C4—61no—
874C4—61no—
875C4—62no—
876C4—122no—
877C4—182no—
878C4#6398312yes—
879C4C2×D3×#6711yescharacteristic
880C4C2×#381111yescharacteristic
881C3—21no—
882C3#8262411yescharacteristic, complemented
883C3#8394611yescharacteristic, complemented
884C2—22no—
885C2—62no—
886C2—82no—
887C2—121no—
888C2—122no—
889C2—362no—
890C2D3×#93211yescharacteristic
891C2#1059509511yescharacteristic
892C2C2×#6398311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3006
LCSG ▷ C2×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×D3×#235C2semidirect
2. C2×#64141C2semidirect
3. C2×C3×#938C2semidirect
4. C2×C3×#932C2semidirect
5. #10591521C2semidirect
6. #10591519C2semidirect
7. #10591517C2semidirect
8. #10591515C2semidirect
9. #10591106C2semidirect
10. #10591087C2semidirect
11. #10591069C2semidirect
14. C22×C32×D4C22semidirect
23. C2×D3×D12C22semidirect
25. C2×#3799C22semidirect
27. C2×#3795C22semidirect
28. C2×D3×Dic6C22semidirect
29. C2×#3754C22semidirect
31. C2×#3753C22semidirect
32. C2×#3748C22semidirect
37. C3×#938C22semidirect
38. C2×C3×#214C22semidirect
40. C2×C3×#213C22semidirect
41. C2×C3×C4⋊Dic3C22semidirect
42. C2×C3×#208C22semidirect
43. #63567C22semidirect
44. #63565C22semidirect
45. #63564C22semidirect
46. #63562C22semidirect
47. (C2×D3)⋊(C3⋊C8)C22semidirect
48. (C2×D3)⋊(C3⋊C8)C22semidirect
53. C2×#938D3semidirect
57. C2×#932D3semidirect
82. #3828D4semidirect
93. C3×#235D4semidirect
138. C22×C3×D4C2×D3semidirect
139. C22×C3×D4C2×D3semidirect
181. #938C2×D3semidirect
185. C2×#214C2×D3semidirect
193. C2×#213C2×D3semidirect
194. C2×C4⋊Dic3C2×D3semidirect
198. C2×#208C2×D3semidirect
236. C4⋊(C3⋊D3)C2×D4semidirect
239. #634C2×D4semidirect
250. C3×D12C2×D4semidirect
259. C3×Dic6C2×D4semidirect
359. #235#67semidirect
440. C2×C3×D3AGL(1,ℤ/8)semidirect
462. C22×D4D32semidirect
592. D12C2×#67semidirect
616. Dic6C2×#67semidirect
747. C2×D3#932semidirect
768. C32#3006semidirect
882. C3#82624semidirect
883. C3#83946semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
C2×#641412
C2×C3×#9382
C2×C3×#9322
#105915212
#105915192
#105915172
#105915152
#105911062
#105910872
#105910692
#839463
#826243