Finite Group Databasebeta

← D3×#2857 #11001117

Subgroups — D3×#2857 #11001117

Order 768.

3790 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×D3×C22⋊Q8C212yesmaximal
3C22×C42×D3C211yesmaximal, characteristic
4C3×#2857C211yesmaximal, characteristic, complemented
5#83269C211yesmaximal, characteristic, complemented
6#82811C212yesmaximal, complemented
7#82076C211yesmaximal, characteristic, complemented
8#76664C212yesmaximal, complemented
9D3×#391C212yesmaximal, complemented
10#76288C214yesmaximal, complemented
11D3×#389C214yesmaximal, complemented
12#74376C211yesmaximal, characteristic, complemented
13D3×#384C211yesmaximal, characteristic, complemented
14D3×#380C214yesmaximal
15#74001C214yesmaximal, complemented
16C2×#2857—31nomaximal, Sylow
17C22×D3×Q8C2212yes—
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2212yes—
20C2×C3×C4⋊Q8C2211yescharacteristic, complemented
21C2×C3×C22⋊Q8C2212yes—
22C22×C3×C42C2211yescharacteristic
23C2×#946C2212yes—
24C2×#944C2212yescomplemented
25C2×#924C2212yes—
26C22×C4×Dic3C2212yes—
27C22×C4×Dic3C2211yescharacteristic
28D3×C4⋊Q8—28no—
29D3×C22⋊Q8—216no—
30C2×#897C2212yes—
31C2×#896C2214yes—
32C2×D3×C4⋊C4C2214yes—
33C2×D3×C4⋊C4C2214yes—
34C2×D3×C4⋊C4C2212yes—
35C2×D3×C4⋊C4C2214yes—
36C2×#888C2214yescomplemented
37C2×D3×C22⋊C4C2214yes—
38C2×#878C2214yes—
39C2×C42×D3—28no—
40C2×C42×D3C2212yes—
41C2×C42×D3C2211yescharacteristic
42C2×C42×D3C2211yescharacteristic
43C2×C42×D3C2211yescharacteristic
44C2×C42×D3C2212yes—
45C2×C42×D3C2211yescharacteristic
46C2×#869C2211yescharacteristic, complemented
47C3×#391C2212yescomplemented
48C3×#389C2214yescomplemented
49C3×#384C2211yescharacteristic, complemented
50C3×#380C2214yes—
51#5229C2212yescomplemented
52#5212C2214yes—
53#4987C2214yes—
54#4987C2214yes—
55#4984C2214yescomplemented
56#4976C2218yescomplemented
57#4975C2214yescomplemented
58#4975C2212yescomplemented
59#4973C2212yescomplemented
60#4972C2214yescomplemented
61#4942C2218yes—
62#4935C2211yescharacteristic, complemented
63#4929C2212yescomplemented
64#4928C2214yescomplemented
65#4667C2218yes—
66D3×#95C2218yes—
67#4647C2218yescomplemented
68#4646C2218yescomplemented
69C22×C4⋊Q8—31no—
70C22×C22⋊Q8—32no—
71C23×C42—31no—
72#2857—31no—
73#2857—32no—
74#2857—34no—
75#2857—31no—
76#2857—34no—
77#2857—31no—
78#2857—32no—
79#2857D311yescharacteristic, direct product factor
80C2×#391—32no—
81C2×#389—34no—
82C2×#384—31no—
83C2×#380—34no—
84C24×D3C2311yescharacteristic
85C22×C3×Q8C2312yes—
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2312yes—
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2312yes—
90C2×D3×Q8—28no—
91C2×D3×Q8—28no—
92C2×D3×Q8—28no—
93C22×C4×D3—24no—
94C22×C4×D3—28no—
95C22×C4×D3—24no—
96C22×C4×D3—28no—
97C22×C4×D3D418yes—
98C22×C4×D3Q8116yescomplemented
99C22×C4×D3C2314yes—
100C22×C4×D3C2314yes—
101C22×C4×D3C2311yescharacteristic
102C22×C4×D3C2311yescharacteristic
103C22×C4×D3C2311yescharacteristic
104C22×C4×D3C2312yes—
105C22×C4×D3C2312yes—
106C22×C4×D3C2312yes—
107C22×C4×D3C2311yescharacteristic
108C22×C4×D3C2312yes—
109C22×Dic6C2314yes—
110C22×Dic6C2312yes—
111C3×C4⋊Q8—24no—
112C3×C22⋊Q8—28no—
113C2×C3×C4⋊C4C2314yes—
114C2×C3×C4⋊C4C2312yes—
115C2×C3×C4⋊C4C2314yes—
116C2×C3×C4⋊C4C2314yes—
117C2×C3×C22⋊C4C2314yes—
118C2×C3×C42—24no—
119C2×C3×C42C2312yes—
120C2×C3×C42C2311yescharacteristic
121C2×C3×C42C2311yescharacteristic
122C2×#217C2314yes—
123#946—28no—
124#944—28no—
125C2×(C2×D3)⋊C4C2314yes—
126C2×(C2×D3)⋊C4C2314yes—
127C2×C4⋊Dic3C2314yes—
128C2×C4⋊Dic3C2314yes—
129C2×C4⋊Dic3C2314yes—
130C2×C4⋊Dic3C2312yes—
131#924—28no—
132C2×Dic3⋊C4C2314yes—
133C2×Dic3⋊C4C2314yes—
134C2×Dic3⋊C4C2318yes—
135C2×Dic3⋊C4C2318yes—
136C2×Dic3⋊C4C2314yes—
137C2×C4×Dic3—28no—
138C2×C4×Dic3—24no—
139C2×C4×Dic3C2312yes—
140C2×C4×Dic3C2312yes—
141C2×C4×Dic3C2312yes—
142C2×C4×Dic3C2311yescharacteristic
143C2×C4×Dic3C2312yes—
144C2×C4×Dic3C2312yes—
145C2×C4×Dic3C2311yescharacteristic
146#897—28no—
147#896—216no—
148D3×C4⋊C4—216no—
149D3×C4⋊C4—216no—
150D3×C4⋊C4—28no—
151D3×C4⋊C4—216no—
152#888—216no—
153D3×C22⋊C4—216no—
154#878—216no—
155C42×D3—24no—
156C42×D3—28no—
157C42×D3—24no—
158C42×D3—28no—
159C42×D3—24no—
160C42×D3D418yes—
161#869—24no—
162C3×#95C2318yes—
163C3⋊#95C2318yes—
164C3⋊#95C2318yes—
165C3⋊#95C2318yes—
166C23×Q8—32no—
167C24×C4—31no—
168C24×C4—32no—
169C2×C4⋊Q8—32no—
170C2×C4⋊Q8—34no—
171C2×C4⋊Q8—31no—
172C2×C4⋊Q8—68no—
173C2×C4⋊Q8C2×D311yescharacteristic, complemented
174C2×C22⋊Q8—32no—
175C2×C22⋊Q8—32no—
176C2×C22⋊Q8—34no—
177C2×C22⋊Q8—32no—
178C2×C22⋊Q8—34no—
179C2×C22⋊Q8—616no—
180C2×C22⋊Q8C2×D312yes—
181C22×C4⋊C4—32no—
182C22×C4⋊C4—34no—
183C22×C4⋊C4—34no—
184C22×C4⋊C4—34no—
185C22×C22⋊C4—34no—
186C22×C42—31no—
187C22×C42—32no—
188C22×C42—31no—
189C22×C42—31no—
190C22×C42—32no—
191C22×C42—31no—
192C22×C42—32no—
193C22×C42—31no—
194C22×C42—68no—
195C22×C42C2×D311yescharacteristic
196#391—32no—
197#391—32no—
198#391—32no—
199#391—38no—
200#391C2×D312yescomplemented
201#389—34no—
202#389—38no—
203#389—34no—
204#389—34no—
205#389—38no—
206#389C2×D314yescomplemented
207#384—34no—
208#384—32no—
209#384—31no—
210#384C2×D311yescharacteristic, complemented
211#380—34no—
212#380—34no—
213#380—34no—
214#380—38no—
215#380—38no—
216#380C2×D314yes—
217C2×#95—38no—
218C24×C3C2411yescharacteristic
219C23×D3—22no—
220C23×D3—22no—
221C23×D3—24no—
222C23×D3C2×D414yes—
223C23×D3C2×Q818yes—
224C23×D3C2411yescharacteristic
225C23×D3C2411yescharacteristic
226C2×C3×Q8—24no—
227C2×C3×Q8—24no—
228C2×C3×Q8—24no—
229C22×C3×C4—22no—
230C22×C3×C4—24no—
231C22×C3×C4—22no—
232C22×C3×C4—24no—
233C22×C3×C4C2×D414yes—
234C22×C3×C4C2×Q818yescomplemented
235C22×C3×C4C2414yes—
236C22×C3×C4C2414yes—
237C22×C3×C4C2411yescharacteristic
238C22×C3×C4C2412yes—
239C22×C3×C4C2411yescharacteristic
240C22×C3×C4C2412yes—
241C22×Dic3—22no—
242C22×Dic3—24no—
243C22×Dic3—22no—
244C22×Dic3—24no—
245C22×Dic3C2×D414yes—
246C22×Dic3C2×Q818yescomplemented
247C22×Dic3C2414yes—
248C22×Dic3C2414yes—
249C22×Dic3C2411yescharacteristic
250C22×Dic3C2412yes—
251C22×Dic3C2411yescharacteristic
252C22×Dic3C2412yes—
253D3×Q8—432no—
254C2×C4×D3—22no—
255C2×C4×D3—24no—
256C2×C4×D3—22no—
257C2×C4×D3—24no—
258C2×C4×D3—22no—
259C2×C4×D3—24no—
260C2×C4×D3—22no—
261C2×C4×D3—24no—
262C2×C4×D3—22no—
263C2×C4×D3—24no—
264C2×C4×D3—22no—
265C2×C4×D3—24no—
266C2×C4×D3—232no—
267C2×C4×D3—264no—
268C2×C4×D3—28no—
269C2×C4×D3—28no—
270C2×C4×D3—28no—
271C2×C4×D3—216no—
272C2×C4×D3—28no—
273C2×C4×D3C2×D414yes—
274C2×C4×D3C2×D414yes—
275C2×C4×D3C2×D414yes—
276C2×C4×D3C2×D414yes—
277C2×C4×D3C2×D414yes—
278C2×C4×D3C2×D418yes—
279C2×C4×D3C2×Q818yes—
280C2×C4×D3C2×Q818yes—
281C2×C4×D3C2×Q818yescomplemented
282C2×C4×D3C2×Q818yescomplemented
283C2×C4×D3#4114yes—
284C2×C4×D3#4118yes—
285C2×Dic6—24no—
286C2×Dic6—24no—
287C2×Dic6—24no—
288C2×Dic6—28no—
289C2×Dic6—28no—
290C2×Dic6—28no—
291C3×C4⋊C4—28no—
292C3×C4⋊C4—28no—
293C3×C4⋊C4—24no—
294C3×C4⋊C4—28no—
295C3×C22⋊C4—28no—
296C3×C42—22no—
297C3×C42—24no—
298C3×C42C2×D414yes—
299#217—28no—
300(C2×D3)⋊C4—28no—
301(C2×D3)⋊C4—28no—
302C4⋊Dic3—28no—
303C4⋊Dic3—24no—
304C4⋊Dic3—28no—
305C4⋊Dic3—28no—
306Dic3⋊C4—28no—
307Dic3⋊C4—28no—
308Dic3⋊C4—28no—
309Dic3⋊C4—216no—
310Dic3⋊C4—216no—
311C4×Dic3—22no—
312C4×Dic3—24no—
313C4×Dic3—24no—
314C4×Dic3—24no—
315C4×Dic3—24no—
316C4×Dic3C2×D418yes—
317C4×Dic3C2×D414yes—
318C25—31no—
319C22×Q8—34no—
320C22×Q8—32no—
321C22×Q8—68no—
322C22×Q8—68no—
323C22×Q8—68no—
324C22×Q8C22×D312yes—
325C23×C4—32no—
326C23×C4—31no—
327C23×C4—31no—
328C23×C4—32no—
329C23×C4—38no—
330C23×C4—316no—
331C23×C4—31no—
332C23×C4—31no—
333C23×C4—31no—
334C23×C4—32no—
335C23×C4—32no—
336C23×C4—32no—
337C23×C4—34no—
338C23×C4—34no—
339C23×C4—68no—
340C23×C4—64no—
341C23×C4—68no—
342C23×C4—64no—
343C23×C4C22×D311yescharacteristic
344C23×C4C22×D312yes—
345C4⋊Q8—24no—
346C4⋊Q8—616no—
347C4⋊Q8—68no—
348C4⋊Q8—64no—
349C22⋊Q8—28no—
350C22⋊Q8—616no—
351C22⋊Q8—616no—
352C22⋊Q8—68no—
353C22⋊Q8—68no—
354C22⋊Q8—68no—
355C2×C4⋊C4—34no—
356C2×C4⋊C4—32no—
357C2×C4⋊C4—34no—
358C2×C4⋊C4—34no—
359C2×C4⋊C4—34no—
360C2×C4⋊C4—38no—
361C2×C4⋊C4—34no—
362C2×C4⋊C4—38no—
363C2×C4⋊C4—34no—
364C2×C4⋊C4—68no—
365C2×C4⋊C4—616no—
366C2×C4⋊C4—616no—
367C2×C4⋊C4—616no—
368C2×C4⋊C4C22×D312yes—
369C2×C4⋊C4C22×D314yes—
370C2×C4⋊C4C22×D314yes—
371C2×C4⋊C4C22×D314yes—
372C2×C22⋊C4—34no—
373C2×C22⋊C4—34no—
374C2×C22⋊C4—34no—
375C2×C22⋊C4—616no—
376C2×C22⋊C4C22×D314yes—
377C2×C42—24no—
378C2×C42—31no—
379C2×C42—32no—
380C2×C42—38no—
381C2×C42—32no—
382C2×C42—32no—
383C2×C42—32no—
384C2×C42—32no—
385C2×C42—31no—
386C2×C42—64no—
387C2×C42—68no—
388C2×C42—68no—
389C2×C42—64no—
390C2×C42—64no—
391C2×C42—68no—
392C2×C42—64no—
393C2×C42C22×D312yes—
394C2×C42C22×D311yescharacteristic
395C2×C42C22×D311yescharacteristic
396#95—38no—
397#95—38no—
398#95—38no—
399#95C22×D318yes—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—22no—
403C23×C3C22×D412yes—
404C23×C3C22×Q814yes—
405C23×C3C2511yescharacteristic
406C22×D3—21no—
407C22×D3—21no—
408C22×D3—22no—
409C22×D3—28no—
410C22×D3—216no—
411C22×D3—28no—
412C22×D3—216no—
413C22×D3C4⋊Q8116yescomplemented
414C22×D3C22×D412yes—
415C22×D3C22×D412yes—
416C22×D3C22×D412yes—
417C22×D3C22×Q814yes—
418C22×D3C22×Q814yes—
419C22×D3C2×#4112yes—
420C22×D3C2×#4114yes—
421C3×Q8—48no—
422C2×C3×C4—21no—
423C2×C3×C4—22no—
424C2×C3×C4—21no—
425C2×C3×C4—22no—
426C2×C3×C4—28no—
427C2×C3×C4—216no—
428C2×C3×C4—24no—
429C2×C3×C4—24no—
430C2×C3×C4—24no—
431C2×C3×C4—28no—
432C2×C3×C4—24no—
433C2×C3×C4C22×D412yes—
434C2×C3×C4C22×D412yes—
435C2×C3×C4C22×D412yes—
436C2×C3×C4C22×D414yes—
437C2×C3×C4C22×Q814yes—
438C2×C3×C4C22×Q814yes—
439C2×C3×C4C2×#4112yes—
440C2×C3×C4C2×#4114yes—
441C2×Dic3—21no—
442C2×Dic3—22no—
443C2×Dic3—21no—
444C2×Dic3—22no—
445C2×Dic3—28no—
446C2×Dic3—216no—
447C2×Dic3—24no—
448C2×Dic3—24no—
449C2×Dic3—24no—
450C2×Dic3—28no—
451C2×Dic3—24no—
452C2×Dic3C22×D412yes—
453C2×Dic3C22×D412yes—
454C2×Dic3C22×D412yes—
455C2×Dic3C22×D414yes—
456C2×Dic3C22×Q814yes—
457C2×Dic3C22×Q814yes—
458C2×Dic3C2×#4112yes—
459C2×Dic3C2×#4114yes—
460C4×D3—28no—
461C4×D3—216no—
462C4×D3—28no—
463C4×D3—216no—
464C4×D3—28no—
465C4×D3—216no—
466C4×D3—416no—
467C4×D3—416no—
468C4×D3#121116yes—
469C4×D3C22⋊Q8132yescomplemented
470Dic6—48no—
471Dic6—416no—
472C24—31no—
473C24—34no—
474C24—38no—
475C24—31no—
476C24—62no—
477C24—62no—
478C24—64no—
479C24C23×D311yescharacteristic
480C2×Q8—24no—
481C2×Q8—24no—
482C2×Q8—24no—
483C2×Q8—68no—
484C2×Q8—68no—
485C2×Q8—68no—
486C2×Q8—64no—
487C2×Q8—64no—
488C2×Q8—64no—
489C2×Q8—1232no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—32no—
495C22×C4—31no—
496C22×C4—38no—
497C22×C4—34no—
498C22×C4—34no—
499C22×C4—38no—
500C22×C4—38no—
501C22×C4—34no—
502C22×C4—34no—
503C22×C4—38no—
504C22×C4—32no—
505C22×C4—31no—
506C22×C4—34no—
507C22×C4—34no—
508C22×C4—34no—
509C22×C4—38no—
510C22×C4—38no—
511C22×C4—38no—
512C22×C4—34no—
513C22×C4—34no—
514C22×C4—64no—
515C22×C4—62no—
516C22×C4—64no—
517C22×C4—62no—
518C22×C4—632no—
519C22×C4—664no—
520C22×C4—62no—
521C22×C4—64no—
522C22×C4—62no—
523C22×C4—64no—
524C22×C4—68no—
525C22×C4—68no—
526C22×C4—68no—
527C22×C4—616no—
528C22×C4—68no—
529C22×C4—64no—
530C22×C4—62no—
531C22×C4—64no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4—64no—
535C22×C4—62no—
536C22×C4—64no—
537C22×C4D3×D414yes—
538C22×C4D3×Q818yescomplemented
539C22×C4C23×D314yes—
540C22×C4C23×D314yes—
541C22×C4C23×D311yescharacteristic
542C22×C4C23×D312yes—
543C22×C4C23×D311yescharacteristic
544C22×C4C23×D312yes—
545C4⋊C4—24no—
546C4⋊C4—28no—
547C4⋊C4—28no—
548C4⋊C4—28no—
549C4⋊C4—68no—
550C4⋊C4—68no—
551C4⋊C4—68no—
552C4⋊C4—616no—
553C4⋊C4—616no—
554C4⋊C4—68no—
555C4⋊C4—64no—
556C4⋊C4—68no—
557C4⋊C4—68no—
558C22⋊C4—28no—
559C22⋊C4—68no—
560C22⋊C4—68no—
561C22⋊C4—68no—
562C42—22no—
563C42—24no—
564C42—34no—
565C42—38no—
566C42—64no—
567C42—64no—
568C42—64no—
569C42—62no—
570C42—64no—
571C42D3×D414yes—
572C22×C3—22no—
573C22×C3—24no—
574C22×C3—22no—
575C22×C3—24no—
576C22×C3C2×C4⋊Q814yescomplemented
577C22×C3C23×D411yescharacteristic
578C22×C3C23×D411yescharacteristic
579C22×C3C23×Q812yes—
580C22×C3C22×#4111yescharacteristic
581C22×C3C22×#4112yes—
582C2×D3—22no—
583C2×D3—24no—
584C2×D3—22no—
585C2×D3—24no—
586C2×D3—232no—
587C2×D3C2×#12114yes—
588C2×D3C2×C22⋊Q818yes—
589C2×D3C2×C4⋊Q814yes—
590C2×D3C2×C4⋊Q814yescomplemented
591C2×D3#53214yes—
592C2×D3#53318yes—
593C3×C4—22no—
594C3×C4—24no—
595C3×C4—44no—
596C3×C4—44no—
597C3×C4C2×#12114yes—
598C3×C4C2×C22⋊Q818yescomplemented
599Dic3—22no—
600Dic3—24no—
601Dic3—44no—
602Dic3—44no—
603Dic3C2×#12114yes—
604Dic3C2×C22⋊Q818yescomplemented
605C23—21no—
606C23—21no—
607C23—22no—
608C23—32no—
609C23—32no—
610C23—34no—
611C23—32no—
612C23—34no—
613C23—32no—
614C23—34no—
615C23—316no—
616C23—68no—
617C23—616no—
618C23—616no—
619C23—68no—
620C23—61no—
621C23—61no—
622C23—62no—
623C23C2×D3×D412yes—
624C23C2×D3×Q814yes—
625C23C24×D311yescharacteristic
626Q8—48no—
627Q8—1216no—
628Q8—128no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—28no—
634C2×C4—216no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—28no—
639C2×C4—24no—
640C2×C4—34no—
641C2×C4—32no—
642C2×C4—32no—
643C2×C4—34no—
644C2×C4—34no—
645C2×C4—32no—
646C2×C4—316no—
647C2×C4—332no—
648C2×C4—32no—
649C2×C4—34no—
650C2×C4—68no—
651C2×C4—616no—
652C2×C4—68no—
653C2×C4—616no—
654C2×C4—68no—
655C2×C4—616no—
656C2×C4—61no—
657C2×C4—62no—
658C2×C4—61no—
659C2×C4—62no—
660C2×C4—68no—
661C2×C4—616no—
662C2×C4—64no—
663C2×C4—64no—
664C2×C4—64no—
665C2×C4—68no—
666C2×C4—64no—
667C2×C4—1216no—
668C2×C4—1216no—
669C2×C4C2×D3×D412yes—
670C2×C4C2×D3×D412yes—
671C2×C4C2×D3×D412yes—
672C2×C4C2×D3×D414yes—
673C2×C4C2×D3×Q814yes—
674C2×C4C2×D3×Q814yes—
675C2×C4D3×#4112yes—
676C2×C4D3×#4114yes—
677C2×C3—24no—
678C2×C3C22×#12111yescharacteristic
679C2×C3C22×C22⋊Q812yes—
680C2×C3C22×C4⋊Q811yescharacteristic
681C2×C3C2×#53211yescharacteristic
682C2×C3C2×#53312yes—
683D3—24no—
684D3#285718yesdirect product factor
685C22—24no—
686C22—22no—
687C22—24no—
688C22—22no—
689C22—38no—
690C22—34no—
691C22—34no—
692C22—38no—
693C22—34no—
694C22—34no—
695C22—632no—
696C22—64no—
697C22—62no—
698C22—64no—
699C22—62no—
700C22D3×C4⋊Q814yescomplemented
701C22C22×D3×D411yescharacteristic
702C22C22×D3×D411yescharacteristic
703C22C22×D3×Q812yes—
704C22C2×D3×#4111yescharacteristic
705C22C2×D3×#4112yes—
706C4—22no—
707C4—24no—
708C4—34no—
709C4—38no—
710C4—44no—
711C4—44no—
712C4—62no—
713C4—64no—
714C4—124no—
715C4—124no—
716C4D3×#12114yes—
717C4D3×C22⋊Q818yescomplemented
718C3C2×#285711yescharacteristic, complemented, Sylow
719C2—24no—
720C2—38no—
721C2—64no—
722C2C2×D3×#12111yescharacteristic
723C2C2×D3×C22⋊Q812yes—
724C2C2×D3×C4⋊Q811yescharacteristic
725C2D3×#53211yescharacteristic
726C2D3×#53312yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2857C2
prime radicalC24×D3C23
hypercenter#2857D3
hypocenterC3C2×#2857
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2857

Complements

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

NH ≅ G/Ntype
1. C2×D3×C4⋊Q8C2semidirect
4. C3×#2857C2semidirect
5. #83269C2semidirect
6. #82811C2semidirect
7. #82076C2semidirect
8. #76664C2semidirect
9. D3×#391C2semidirect
10. #76288C2semidirect
11. D3×#389C2semidirect
12. #74376C2semidirect
13. D3×#384C2semidirect
15. #74001C2semidirect
20. C2×C3×C4⋊Q8C22semidirect
24. C2×#944C22semidirect
36. C2×#888C22semidirect
46. C2×#869C22semidirect
47. C3×#391C22semidirect
48. C3×#389C22semidirect
49. C3×#384C22semidirect
51. #5229C22semidirect
55. #4984C22semidirect
56. #4976C22semidirect
57. #4975C22semidirect
58. #4975C22semidirect
59. #4973C22semidirect
60. #4972C22semidirect
62. #4935C22semidirect
63. #4929C22semidirect
64. #4928C22semidirect
67. #4647C22semidirect
68. #4646C22semidirect
79. #2857D3direct (N × H)
98. C22×C4×D3Q8semidirect
173. C2×C4⋊Q8C2×D3semidirect
200. #391C2×D3semidirect
206. #389C2×D3semidirect
210. #384C2×D3semidirect
234. C22×C3×C4C2×Q8semidirect
246. C22×Dic3C2×Q8semidirect
281. C2×C4×D3C2×Q8semidirect
282. C2×C4×D3C2×Q8semidirect
413. C22×D3C4⋊Q8semidirect
469. C4×D3C22⋊Q8semidirect
538. C22×C4D3×Q8semidirect
576. C22×C3C2×C4⋊Q8semidirect
590. C2×D3C2×C4⋊Q8semidirect
598. C3×C4C2×C22⋊Q8semidirect
604. Dic3C2×C22⋊Q8semidirect
684. D3#2857direct (N × H)
700. C22D3×C4⋊Q8semidirect
717. C4D3×C22⋊Q8semidirect
718. C3C2×#2857semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊Q82
C2×D3×C22⋊Q82
C22×C42×D32
C3×#28572
#832692
#828112
#820762
#766642
D3×#3912
#762882
D3×#3892
#743762
D3×#3842
D3×#3802
#740012
C2×#28573