Finite Group Databasebeta

← D3×#4781 #11863708

Subgroups — D3×#4781 #11863708

Order 1152.

1705 conjugacy classes of subgroups.

The subgroup lattice has 1057 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#237C211yesmaximal, characteristic, complemented
2C2×D3×#213C211yesmaximal, characteristic, complemented
3C2×D3×#204C211yesmaximal, characteristic, complemented
4D3×#895C211yesmaximal, characteristic, complemented
5#10592480C211yesmaximal, characteristic, complemented
6C3×#4781C211yesmaximal, characteristic, complemented
7C3×D3×#102C211yesmaximal, characteristic, complemented
8#10591457C211yesmaximal, characteristic, complemented
9#10591452C211yesmaximal, characteristic, complemented
10#10590968C211yesmaximal, characteristic, complemented
11#10590964C211yesmaximal, characteristic, complemented
12D3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
13#10590617C211yesmaximal, characteristic, complemented
14#10590613C211yesmaximal, characteristic, complemented
15D3×#810C211yesmaximal, characteristic, complemented
16D3×#449—31nomaximal
17C2×#4781—31nomaximal
18C2×#3830C2211yescharacteristic, complemented
19C2×C3×#237C2211yescharacteristic, complemented
20C2×C3×D3×D4C2211yescharacteristic
21C2×D3×#67—21no—
22C2×#3805—21no—
23C2×#3804—21no—
24C22×D3×Dic3—21no—
25D3×#237—24no—
26D3×#237—24no—
27C2×D3×D12—21no—
28C2×D3×D12C2211yescharacteristic
29C2×C4×D32C2211yescharacteristic
30C2×#3796C2211yescharacteristic, complemented
31C2×#3795C2211yescharacteristic, complemented
32C2×D3×Dic6C2211yescharacteristic
33C2×#3753C2211yescharacteristic, complemented
34C2×#3744C2211yescharacteristic, complemented
35#64104C2211yescharacteristic, complemented
36C2×C3×#213C2211yescharacteristic, complemented
37C2×C3×#204C2211yescharacteristic, complemented
38C2×C3×D3×C8C2211yescharacteristic
39C3×#895C2211yescharacteristic, complemented
40C3×D3×C4⋊C4C2211yescharacteristic
41D3×#213—24no—
42D3×(C2×D3)⋊C4—21no—
43#63916C2211yescharacteristic, complemented
44#63910—21no—
45#63909C2211yescharacteristic, complemented
46#63886—21no—
47C2×#3717C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic
52D3×#204—24no—
53C32×#102C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55#63637C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63565C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#237—31no—
67C22×#213—31no—
68C2×D3×SD16—31no—
69C2×D3×D8—31no—
70C22×#204—31no—
71D3×#121—31no—
72C2×#895—31no—
73C3×#449—31no—
74C2×C3×#102—31no—
75#5238—31no—
76#5172—31no—
77#5158—31no—
78C2×(C2×D3)⋊C8—31no—
79#5037—31no—
80C2×#810—31no—
81#4810—31no—
82D3×#103—31no—
83#4781—31no—
84#4781—31no—
85#4781—31no—
86#4781—31no—
87#4781—31no—
88#4781—31no—
89#4781—31no—
90#4781—31no—
91#4781—61no—
92#4781D311yescharacteristic, direct product factor
93D3×#102D311yescharacteristic, complemented
94#4734—31no—
95D3×C22⋊C8—31no—
96C23×C3×D3—21no—
97C22×D32—21no—
98C22×D32D411yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C2×#638—21no—
101C22×C3⋊Dic3—21no—
102#3830—22no—
103#3830—22no—
104C2×C4⋊(C3⋊D3)—21no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3C2311yescharacteristic
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C22×C3×Dic3—21no—
111C3×#237—22no—
112C3×#237—22no—
113C3×D3×D4—22no—
114C3×D3×D4D414yescomplemented
115C2×C3×D12—21no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122D3×#67—28no—
123C2×#627—21no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#626—21no—
127C2×#626—21no—
128C2×#625—21no—
129C2×#624D411yescharacteristic
130#3805—28no—
131#3804—28no—
132C2×D3×Dic3—28no—
133C2×D3×Dic3—21no—
134C2×D3×Dic3—21no—
135C2×D3×Dic3—21no—
136C2×D3×Dic3D411yescharacteristic
137C2×D3×Dic3D411yescharacteristic
138D3×D12—22no—
139D3×D12—22no—
140D3×D12—44no—
141C4×D32—22no—
142C4×D32—22no—
143#3796—22no—
144#3796—22no—
145#3795—22no—
146#3795—22no—
147D3×Dic6—22no—
148D3×Dic6D414yescomplemented
149C2×C32×C8C2311yescharacteristic
150C32×C4⋊C4C2311yescharacteristic
151#3753—22no—
152#3752—21no—
153C2×C3⋊(C3⋊C8)C2311yescharacteristic
154#3744—22no—
155C3×#213—22no—
156C3×(C2×D3)⋊C4—21no—
157C3×C4⋊Dic3C2311yescharacteristic
158C3×Dic3⋊C4—21no—
159C2×C3×C3⋊C8C2311yescharacteristic
160C2×C3×C3⋊C8C2311yescharacteristic
161C3×#204—22no—
162C3×D3×C8—22no—
163#3722—21no—
164(C2×D3)⋊Dic3—21no—
165#3717—22no—
166#3716—22no—
167#3714—22no—
168#3713—22no—
169D3×C3⋊C8—22no—
170C2×#449—91noSylow
171C2×C3×#41—31no—
172C22×C3×D4—31no—
173C22×#67—61no—
174C23×Dic3—61no—
175D3×#41—64no—
176D3×#41—64no—
177C2×#239—31no—
178C2×D3×Q8—31no—
179C2×#237—31no—
180C2×#237—31no—
181C2×#237—31no—
182C2×#237—31no—
183C2×#237—61no—
184C2×#237—64no—
185C2×#237—61no—
186C2×#237—61no—
187C2×#237—64no—
188C2×#237—61no—
189C2×#237C2×D311yescharacteristic, complemented
190C2×D3×D4—31no—
191C2×D3×D4—61no—
192C2×D3×D4—61no—
193C2×D3×D4C2×D311yescharacteristic
194C2×#235—31no—
195C2×#235—61no—
196C22×D12—31no—
197C22×D12—61no—
198C22×C4×D3—31no—
199C22×C4×D3—31no—
200C22×C4×D3—61no—
201C22×Dic6—31no—
202C2×C3×SD16—31no—
203C2×C3×D8—31no—
204C22×C3×C8—31no—
205C3×#121—31no—
206C2×C3×C4⋊C4—31no—
207C2×#215—31no—
208#939—61no—
209#938—31no—
210C2×#214—31no—
211C2×#213—31no—
212C2×#213—31no—
213C2×#213—31no—
214C2×#213—31no—
215C2×#213—31no—
216C2×#213—61no—
217C2×#213—64no—
218C2×#213C2×D311yescharacteristic, complemented
219#930—31no—
220C2×(C2×D3)⋊C4—61no—
221C22×C3⋊C8—31no—
222D3×SD16—64no—
223D3×D8—64no—
224C2×D24—31no—
225C2×#204—31no—
226C2×#204—31no—
227C2×#204—31no—
228C2×#204—31no—
229C2×#204—61no—
230C2×#204—64no—
231C2×#204C2×D311yescharacteristic, complemented
232C2×D3×C8—31no—
233C2×D3×C8C2×D311yescharacteristic
234#895—31no—
235#895—31no—
236#895—31no—
237#895—31no—
238#895—61no—
239#895—61no—
240#895—61no—
241#895C2×D311yescharacteristic, complemented
242D3×C4⋊C4C2×D311yescharacteristic
243#884—61no—
244D3×C22⋊C4—61no—
245C3×#103—31no—
246C3×#102—21no—
247C3×#102—31no—
248C3×#102—31no—
249C3×#102—31no—
250C3×#102C2×D311yescharacteristic, complemented
251C3×#102C2×D311yescharacteristic, complemented
252C3×C22⋊C8—31no—
253#835—31no—
254#832C2×D311yescharacteristic, complemented
255#830—31no—
256#821C2×D311yescharacteristic, complemented
257(C2×D3)⋊C8—31no—
258(C2×D3)⋊C8—31no—
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—61no—
263(C2×D3)⋊C8C2×D311yescharacteristic, complemented
264#816—31no—
265#810—31no—
266#810—31no—
267#810—31no—
268#810—31no—
269#810—61no—
270#810C2×D311yescharacteristic, complemented
271#809C2×D311yescharacteristic, complemented
272C23×C32—21no—
273C22×C3⋊D3—21no—
274C22×C3⋊D3C2×D411yescharacteristic
275C22×C3×D3—21no—
276C22×C3×D3—24no—
277C22×C3×D3—21no—
278C22×C3×D3—42no—
279C22×C3×D3—42no—
280C22×C3×D3C2×D411yescharacteristic
281C22×C3×D3C2×D411yescharacteristic
282C2×D32—22no—
283C2×D32—22no—
284C2×D32—22no—
285C2×D32—42no—
286C2×D32—42no—
287C2×D32—42no—
288C32×D4—21no—
289C32×D4C2×D412yescomplemented
290C2×C32×C4—21no—
291C2×C32×C4C2411yescharacteristic
292#638—24no—
293C2×C3⋊Dic3—24no—
294C2×C3⋊Dic3—21no—
295C2×C3⋊Dic3C2×D411yescharacteristic
296C4⋊(C3⋊D3)—21no—
297C4⋊(C3⋊D3)—21no—
298C4⋊(C3⋊D3)—42no—
299C4×C3⋊D3—21no—
300C4×C3⋊D3—21no—
301#634—21no—
302#634C2×D412yescomplemented
303C3×#67—24no—
304C3×#67—24no—
305C2×C3×Dic3—24no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3C2×D411yescharacteristic
309C2×C3×Dic3C2×D411yescharacteristic
310C3×D12—21no—
311C3×D12—21no—
312C3×D12—21no—
313C3×D12—42no—
314C3×D12C2×D412yescomplemented
315C3×C4×D3—21no—
316C3×C4×D3—21no—
317C3×C4×D3—42no—
318C3×C4×D3C2×D412yes—
319C3×C4×D3C2×D412yes—
320C3×Dic6—21no—
321C3×Dic6C2×D412yescomplemented
322#627—24no—
323#626—24no—
324#626—42no—
325#626—42no—
326#626—42no—
327#625—24no—
328#624—22no—
329D3×Dic3—24no—
330D3×Dic3—24no—
331D3×Dic3—24no—
332D3×Dic3—22no—
333D3×Dic3—22no—
334C32×C8—21no—
335C3⋊(C3⋊C8)—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C22×#41—91no—
339C22×SD16—91no—
340C22×D8—91no—
341C2×#121—91no—
342#449—31no—
343#449—91no—
344#449—91no—
345#449—91no—
346#449—91no—
347#449—91no—
348#449—91no—
349#449—91no—
350C2×#103—91no—
351C2×#102—31no—
352C2×C22⋊C8—91no—
353C24×C3—61no—
354C23×D3—21no—
355C23×D3—31no—
356C23×D3—31no—
357C23×D3—61no—
358C23×D3—61no—
359C3×#41—62no—
360C3×#41—62no—
361C2×C3×Q8—31no—
362C2×C3×D4—21no—
363C2×C3×D4—34no—
364C2×C3×D4—31no—
365C2×C3×D4—31no—
366C2×C3×D4—61no—
367C2×C3×D4—62no—
368C2×C3×D4—61no—
369C2×C3×D4—61no—
370C2×C3×D4C22×D311yescharacteristic
371C2×C3×D4C22×D311yescharacteristic
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—61no—
375C22×C3×C4—61no—
376C2×#67—21no—
377C2×#67—21no—
378C2×#67—61no—
379C2×#67—61no—
380C2×#67—61no—
381C2×#67—68no—
382C2×#67—61no—
383C2×#67—61no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67—61no—
387C2×#67—121no—
388C22×Dic3—21no—
389C22×Dic3—31no—
390C22×Dic3—31no—
391C22×Dic3—61no—
392C22×Dic3—61no—
393C22×Dic3—68no—
394C22×Dic3—61no—
395C22×Dic3—61no—
396C22×Dic3—61no—
397C22×Dic3—121no—
398#239—62no—
399#239—62no—
400D3×Q8—34no—
401D3×Q8—62no—
402#237—22no—
403#237—22no—
404#237—62no—
405#237—62no—
406#237—62no—
407#237—62no—
408#237—62no—
409#237—68no—
410#237—68no—
411#237—68no—
412#237—62no—
413#237—62no—
414#237—62no—
415#237—122no—
416#237—122no—
417D3×D4—22no—
418D3×D4—68no—
419D3×D4—62no—
420D3×D4—62no—
421D3×D4—124no—
422D3×D4D1214yescomplemented
423#235—62no—
424#235—68no—
425#235—62no—
426C2×D12—21no—
427C2×D12—31no—
428C2×D12—31no—
429C2×D12—61no—
430C2×D12—62no—
431C2×D12—62no—
432C2×D12—61no—
433C2×D12—61no—
434C2×D12—61no—
435C2×D12—61no—
436C2×D12—61no—
437C2×D12—61no—
438C2×D12—121no—
439C2×D12—124no—
440C2×D12C22×D311yescharacteristic
441C2×D12C22×D311yescharacteristic
442C2×C4×D3—21no—
443C2×C4×D3—31no—
444C2×C4×D3—31no—
445C2×C4×D3—31no—
446C2×C4×D3—31no—
447C2×C4×D3—31no—
448C2×C4×D3—31no—
449C2×C4×D3—61no—
450C2×C4×D3—62no—
451C2×C4×D3—62no—
452C2×C4×D3—61no—
453C2×C4×D3—61no—
454C2×C4×D3—68no—
455C2×C4×D3—61no—
456C2×C4×D3—62no—
457C2×C4×D3—62no—
458C2×C4×D3C22×D311yescharacteristic
459C2×C4×D3C22×D311yescharacteristic
460C2×Dic6—31no—
461C2×Dic6—31no—
462C2×Dic6—34no—
463C2×Dic6—61no—
464C2×Dic6—62no—
465C2×Dic6—61no—
466C2×Dic6—61no—
467C2×Dic6C22×D311yescharacteristic
468C3×SD16—62no—
469C3×D8—62no—
470C2×C3×C8—21no—
471C2×C3×C8—31no—
472C2×C3×C8—31no—
473C2×C3×C8—62no—
474C2×C3×C8C22×D311yescharacteristic
475C2×C3×C8C22×D311yescharacteristic
476C3×C4⋊C4—21no—
477C3×C4⋊C4—31no—
478C3×C4⋊C4—61no—
479C3×C4⋊C4C22×D311yescharacteristic
480C3×C4⋊C4C22×D311yescharacteristic
481C3×C22⋊C4—61no—
482#217—61no—
483#215—62no—
484#214—62no—
485#213—22no—
486#213—62no—
487#213—62no—
488#213—62no—
489#213—62no—
490#213—62no—
491#213—122no—
492(C2×D3)⋊C4—21no—
493(C2×D3)⋊C4—61no—
494(C2×D3)⋊C4—61no—
495(C2×D3)⋊C4—61no—
496(C2×D3)⋊C4—61no—
497(C2×D3)⋊C4—61no—
498(C2×D3)⋊C4—121no—
499C4⋊Dic3C22×D311yescharacteristic
500Dic3⋊C4—21no—
501C2×C3⋊C8—31no—
502C2×C3⋊C8—31no—
503C2×C3⋊C8—61no—
504C2×C3⋊C8—62no—
505C2×C3⋊C8C22×D311yescharacteristic
506C2×C3⋊C8C22×D311yescharacteristic
507D24—62no—
508#204—22no—
509#204—62no—
510#204—62no—
511#204—62no—
512#204—62no—
513#204—122no—
514D3×C8—22no—
515D3×C8—62no—
516C22×C32—22no—
517C22×C32—41no—
518C22×C32—41no—
519C22×C32C22×D411yescharacteristic
520C2×C3⋊D3—21no—
521C2×C3⋊D3—21no—
522C2×C3⋊D3—21no—
523C2×C3⋊D3—41no—
524C2×C3⋊D3—41no—
525C2×C3⋊D3—41no—
526C2×C3×D3—22no—
527C2×C3×D3—21no—
528C2×C3×D3—21no—
529C2×C3×D3—21no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532C2×C3×D3—48no—
533C2×C3×D3—41no—
534C2×C3×D3—41no—
535C2×C3×D3—41no—
536C2×C3×D3#12012yes—
537C2×C3×D3#13512yes—
538C2×C3×D3AGL(1,ℤ/8)12yes—
539D32—44no—
540D32—84no—
541C32×C4—41no—
542C32×C4C22×D411yescharacteristic
543C32×C4C22×D411yescharacteristic
544C3⋊Dic3—21no—
545C3⋊Dic3—22no—
546C3×Dic3—21no—
547C3×Dic3—22no—
548C3×Dic3—41no—
549C3×Dic3#12012yes—
550C2×#41—31no—
551C2×#41—91no—
552C2×#41—91no—
553C2×#41—91no—
554C2×#41—181no—
555C2×#41—181no—
556C2×#41—184no—
557C2×#41—184no—
558C22×Q8—91no—
559C22×D4—31no—
560C22×D4—91no—
561C22×D4—181no—
562C22×D4—181no—
563C23×C4—91no—
564C23×C4—181no—
565C2×SD16—31no—
566C2×SD16—91no—
567C2×SD16—91no—
568C2×SD16—91no—
569C2×SD16—184no—
570C2×D8—31no—
571C2×D8—91no—
572C2×D8—91no—
573C2×D8—91no—
574C2×D8—184no—
575C22×C8—31no—
576C22×C8—91no—
577#121—31no—
578#121—91no—
579#121—91no—
580#121—91no—
581#121—181no—
582#121—181no—
583C2×C4⋊C4—31no—
584C2×C22⋊C4—181no—
585#103—31no—
586#103—91no—
587#103—91no—
588#103—91no—
589#102—31no—
590#102—31no—
591#102—31no—
592#102D3211yescharacteristic, complemented
593C22⋊C8—31no—
594C22⋊C8—91no—
595C22⋊C8—91no—
596C22⋊C8—91no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—31no—
600C23×C3—31no—
601C23×C3—41no—
602C23×C3—64no—
603C23×C3—61no—
604C23×C3—61no—
605C23×C3—122no—
606C23×C3—122no—
607C22×D3—21no—
608C22×D3—24no—
609C22×D3—21no—
610C22×D3—31no—
611C22×D3—31no—
612C22×D3—42no—
613C22×D3—42no—
614C22×D3—61no—
615C22×D3—62no—
616C22×D3—62no—
617C22×D3—62no—
618C22×D3—62no—
619C22×D3—62no—
620C22×D3—62no—
621C22×D3—61no—
622C22×D3—61no—
623C22×D3—121no—
624C22×D3—122no—
625C22×D3—122no—
626C22×D3—122no—
627C22×D3—122no—
628C22×D3—122no—
629C22×D3—122no—
630C22×D3D3×D411yescharacteristic
631C22×D3D3×D411yescharacteristic
632C3×Q8—32no—
633C3×Q8—61no—
634C3×D4—21no—
635C3×D4—21no—
636C3×D4—22no—
637C3×D4—32no—
638C3×D4—41no—
639C3×D4—64no—
640C3×D4—64no—
641C3×D4—61no—
642C3×D4—61no—
643C3×D4—61no—
644C3×D4—122no—
645C3×D4C2×D1212yescomplemented
646C3×D4D3×D412yescomplemented
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—31no—
651C2×C3×C4—32no—
652C2×C3×C4—32no—
653C2×C3×C4—31no—
654C2×C3×C4—41no—
655C2×C3×C4—64no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4—122no—
661C2×C3×C4C23×D311yescharacteristic
662C2×C3×C4C23×D311yescharacteristic
663#67—24no—
664#67—24no—
665#67—64no—
666#67—64no—
667#67—64no—
668#67—64no—
669#67—64no—
670#67—124no—
671#67—122no—
672#67—122no—
673#67—122no—
674C2×Dic3—24no—
675C2×Dic3—21no—
676C2×Dic3—21no—
677C2×Dic3—31no—
678C2×Dic3—31no—
679C2×Dic3—61no—
680C2×Dic3—64no—
681C2×Dic3—62no—
682C2×Dic3—64no—
683C2×Dic3—64no—
684C2×Dic3—64no—
685C2×Dic3—64no—
686C2×Dic3—61no—
687C2×Dic3—61no—
688C2×Dic3—62no—
689C2×Dic3—121no—
690C2×Dic3—124no—
691C2×Dic3D3×D411yescharacteristic
692C2×Dic3D3×D411yescharacteristic
693D12—21no—
694D12—21no—
695D12—21no—
696D12—42no—
697D12—64no—
698D12—61no—
699D12—61no—
700D12—61no—
701D12—61no—
702D12—121no—
703D12—121no—
704D12—122no—
705D12—122no—
706D12—122no—
707D12—122no—
708D12—122no—
709D12—242no—
710D12C2×D1212yescomplemented
711C4×D3—21no—
712C4×D3—21no—
713C4×D3—42no—
714C4×D3—62no—
715C4×D3—62no—
716C4×D3—64no—
717C4×D3—64no—
718C4×D3—62no—
719C4×D3—64no—
720C4×D3—61no—
721C4×D3—61no—
722C4×D3—61no—
723C4×D3—61no—
724C4×D3—62no—
725C4×D3—121no—
726C4×D3—121no—
727C4×D3C2×D1212yes—
728C4×D3D3×D412yes—
729Dic6—21no—
730Dic6—32no—
731Dic6—32no—
732Dic6—62no—
733Dic6—64no—
734Dic6—61no—
735Dic6—61no—
736Dic6—64no—
737Dic6—121no—
738Dic6D3×D412yescomplemented
739C3×C8—21no—
740C3×C8—21no—
741C3×C8—41no—
742C3×C8—61no—
743C3×C8—61no—
744C3⋊C8—21no—
745C3⋊C8—21no—
746C3⋊C8—61no—
747C3⋊C8—61no—
748C3⋊C8—121no—
749C2×C32—42no—
750C2×C32C2×#12011yescharacteristic
751C2×C32C2×#13511yescharacteristic
752C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
753C3⋊D3—41no—
754C3⋊D3—81no—
755C3×D3—41no—
756C3×D3—42no—
757C3×D3—81no—
758C3×D3#44914yescomplemented
759C24—61no—
760C24—91no—
761C24—181no—
762#41—62no—
763#41—62no—
764#41—182no—
765#41—182no—
766#41—188no—
767#41—182no—
768#41—182no—
769#41—188no—
770#41—182no—
771#41—182no—
772C2×Q8—31no—
773C2×Q8—94no—
774C2×Q8—91no—
775C2×Q8—181no—
776C2×Q8—182no—
777C2×D4—34no—
778C2×D4—31no—
779C2×D4—31no—
780C2×D4—61no—
781C2×D4—62no—
782C2×D4—61no—
783C2×D4—61no—
784C2×D4—91no—
785C2×D4—181no—
786C2×D4—182no—
787C2×D4—182no—
788C2×D4—181no—
789C2×D4—181no—
790C2×D4—181no—
791C2×D4—181no—
792C2×D4—188no—
793C2×D4—181no—
794C2×D4—181no—
795C2×D4—364no—
796C2×D4C2×D3211yescharacteristic
797C22×C4—31no—
798C22×C4—31no—
799C22×C4—61no—
800C22×C4—61no—
801C22×C4—91no—
802C22×C4—91no—
803C22×C4—91no—
804C22×C4—91no—
805C22×C4—182no—
806C22×C4—182no—
807C22×C4—181no—
808C22×C4—181no—
809C22×C4—181no—
810C22×C4—188no—
811C22×C4—181no—
812SD16—62no—
813SD16—182no—
814SD16—182no—
815SD16—182no—
816D8—62no—
817D8—182no—
818D8—182no—
819D8—182no—
820C2×C8—31no—
821C2×C8—31no—
822C2×C8—62no—
823C2×C8—91no—
824C2×C8—182no—
825C2×C8C2×D3211yescharacteristic
826C4⋊C4—31no—
827C4⋊C4—61no—
828C4⋊C4C2×D3211yescharacteristic
829C22⋊C4—61no—
830C22⋊C4—181no—
831C22⋊C4—181no—
832C22⋊C4—181no—
833C22×C3—22no—
834C22×C3—22no—
835C22×C3—21no—
836C22×C3—32no—
837C22×C3—32no—
838C22×C3—32no—
839C22×C3—42no—
840C22×C3—41no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—61no—
845C22×C3—61no—
846C22×C3—61no—
847C22×C3—62no—
848C22×C3—81no—
849C22×C3—81no—
850C22×C3—128no—
851C22×C3—121no—
852C22×C3—121no—
853C22×C3—121no—
854C22×C3—121no—
855C22×C3—121no—
856C22×C3C2×D3×D411yescharacteristic
857C22×C3C2×D3×D411yescharacteristic
858C2×D3—22no—
859C2×D3—21no—
860C2×D3—21no—
861C2×D3—21no—
862C2×D3—41no—
863C2×D3—41no—
864C2×D3—48no—
865C2×D3—41no—
866C2×D3—41no—
867C2×D3—41no—
868C2×D3—61no—
869C2×D3—61no—
870C2×D3—61no—
871C2×D3—61no—
872C2×D3—61no—
873C2×D3—61no—
874C2×D3—121no—
875C2×D3—121no—
876C2×D3—121no—
877C2×D3—124no—
878C2×D3—124no—
879C2×D3—121no—
880C2×D3—121no—
881C2×D3—121no—
882C2×D3—121no—
883C2×D3—121no—
884C2×D3—121no—
885C2×D3—241no—
886C2×D3—241no—
887C2×D3—241no—
888C2×D3—244no—
889C2×D3—244no—
890C2×D3#88212yes—
891C2×D3#91112yes—
892C2×D3#91612yes—
893C3×C4—21no—
894C3×C4—21no—
895C3×C4—32no—
896C3×C4—41no—
897C3×C4—41no—
898C3×C4—62no—
899C3×C4—61no—
900C3×C4—81no—
901C3×C4—121no—
902C3×C4C22×D1211yescharacteristic
903C3×C4C2×D3×D411yescharacteristic
904C3×C4C2×D3×D411yescharacteristic
905C3×C4C2×D3×D411yescharacteristic
906Dic3—22no—
907Dic3—21no—
908Dic3—41no—
909Dic3—62no—
910Dic3—61no—
911Dic3—62no—
912Dic3—61no—
913Dic3—122no—
914Dic3—121no—
915Dic3#88212yes—
916C32C2×#44911yescharacteristic, complemented, Sylow
917C23—21no—
918C23—31no—
919C23—31no—
920C23—64no—
921C23—61no—
922C23—61no—
923C23—91no—
924C23—122no—
925C23—122no—
926C23—182no—
927C23—182no—
928C23—182no—
929C23—181no—
930C23—362no—
931C23—362no—
932C23—362no—
933Q8—32no—
934Q8—61no—
935Q8—92no—
936Q8—184no—
937Q8—181no—
938D4—21no—
939D4—32no—
940D4—64no—
941D4—64no—
942D4—61no—
943D4—61no—
944D4—61no—
945D4—122no—
946D4—184no—
947D4—184no—
948D4—184no—
949D4—181no—
950D4—181no—
951D4—362no—
952D4—362no—
953D4—362no—
954D4—362no—
955D4D3×D1212yescomplemented
956C2×C4—21no—
957C2×C4—31no—
958C2×C4—32no—
959C2×C4—32no—
960C2×C4—31no—
961C2×C4—64no—
962C2×C4—61no—
963C2×C4—61no—
964C2×C4—61no—
965C2×C4—61no—
966C2×C4—91no—
967C2×C4—122no—
968C2×C4—182no—
969C2×C4—182no—
970C2×C4—182no—
971C2×C4—184no—
972C2×C4—184no—
973C2×C4—184no—
974C2×C4—184no—
975C2×C4—181no—
976C2×C4—181no—
977C2×C4—181no—
978C2×C4C22×D3211yescharacteristic
979C8—21no—
980C8—61no—
981C8—61no—
982C8—181no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—34no—
987C2×C3—42no—
988C2×C3—42no—
989C2×C3—82no—
990C2×C3—121no—
991C2×C3—122no—
992C2×C3—241no—
993C2×C3C2×#88211yescharacteristic
994C2×C3D3×#12011yescharacteristic
995C2×C3C2×#91111yescharacteristic
996C2×C3C2×#91611yescharacteristic
997C2×C3D3×#13511yescharacteristic
998C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
999D3—42no—
1000D3—41no—
1001D3—81no—
1002D3—121no—
1003D3—121no—
1004D3—241no—
1005D3—241no—
1006D3—241no—
1007D3—481no—
1008D3#478114yesdirect product factor
1009C22—22no—
1010C22—32no—
1011C22—32no—
1012C22—32no—
1013C22—41no—
1014C22—41no—
1015C22—61no—
1016C22—61no—
1017C22—61no—
1018C22—62no—
1019C22—128no—
1020C22—121no—
1021C22—121no—
1022C22—121no—
1023C22—121no—
1024C22—121no—
1025C22—181no—
1026C22—181no—
1027C22—181no—
1028C22—364no—
1029C22—361no—
1030C22—361no—
1031C22—361no—
1032C22—724no—
1033C22D32×D411yescharacteristic
1034C4—32no—
1035C4—41no—
1036C4—61no—
1037C4—62no—
1038C4—121no—
1039C4—181no—
1040C4—182no—
1041C4C2×D3×D1211yescharacteristic
1042C4D32×D411yescharacteristic
1043C3—21no—
1044C3C2×#478111yescharacteristic, complemented
1045C3D3×#44911yescharacteristic, complemented
1046C2—34no—
1047C2—42no—
1048C2—121no—
1049C2—122no—
1050C2—241no—
1051C2—361no—
1052C2—721no—
1053C2D3×#88211yescharacteristic
1054C2D3×#91111yescharacteristic
1055C2D3×#91611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32C2×#449
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. C2×D3×#237C2semidirect
2. C2×D3×#213C2semidirect
3. C2×D3×#204C2semidirect
4. D3×#895C2semidirect
5. #10592480C2semidirect
6. C3×#4781C2semidirect
7. C3×D3×#102C2semidirect
8. #10591457C2semidirect
9. #10591452C2semidirect
10. #10590968C2semidirect
11. #10590964C2semidirect
12. D3×(C2×D3)⋊C8C2semidirect
13. #10590617C2semidirect
14. #10590613C2semidirect
15. D3×#810C2semidirect
18. C2×#3830C22semidirect
19. C2×C3×#237C22semidirect
30. C2×#3796C22semidirect
31. C2×#3795C22semidirect
33. C2×#3753C22semidirect
34. C2×#3744C22semidirect
35. #64104C22semidirect
36. C2×C3×#213C22semidirect
37. C2×C3×#204C22semidirect
39. C3×#895C22semidirect
43. #63916C22semidirect
45. #63909C22semidirect
47. C2×#3717C22semidirect
48. C2×#3716C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
53. C32×#102C22semidirect
54. #63647C22semidirect
55. #63637C22semidirect
56. C3×#832C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#810C22semidirect
60. C3×#809C22semidirect
61. #63567C22semidirect
62. #63565C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
92. #4781D3direct (N × H)
93. D3×#102D3semidirect
114. C3×D3×D4D4semidirect
148. D3×Dic6D4semidirect
189. C2×#237C2×D3semidirect
218. C2×#213C2×D3semidirect
231. C2×#204C2×D3semidirect
241. #895C2×D3semidirect
250. C3×#102C2×D3semidirect
251. C3×#102C2×D3semidirect
254. #832C2×D3semidirect
256. #821C2×D3semidirect
263. (C2×D3)⋊C8C2×D3semidirect
270. #810C2×D3semidirect
271. #809C2×D3semidirect
289. C32×D4C2×D4semidirect
302. #634C2×D4semidirect
314. C3×D12C2×D4semidirect
321. C3×Dic6C2×D4semidirect
422. D3×D4D12semidirect
592. #102D32semidirect
645. C3×D4C2×D12semidirect
646. C3×D4D3×D4semidirect
710. D12C2×D12semidirect
738. Dic6D3×D4semidirect
758. C3×D3#449semidirect
916. C32C2×#449semidirect
955. D4D3×D12semidirect
1008. D3#4781direct (N × H)
1044. C3C2×#4781semidirect
1045. C3D3×#449semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2372
C2×D3×#2132
C2×D3×#2042
D3×#8952
#105924802
C3×#47812
C3×D3×#1022
#105914572
#105914522
#105909682
#105909642
D3×(C2×D3)⋊C82
#105906172
#105906132
D3×#8102
D3×#4493
C2×#47813