Finite Group Databasebeta

← D3×#5222 #11808148

Subgroups — D3×#5222 #11808148

Order 1152.

2623 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×D4C211yesmaximal, characteristic
2C2×D3×#217C212yesmaximal, complemented
3C2×D3×#217C212yesmaximal, complemented
4C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
5#10592921C211yesmaximal, characteristic, complemented
6C3×#5222C211yesmaximal, characteristic, complemented
7#10591709C212yesmaximal, complemented
8#10591708C212yesmaximal, complemented
9D3×C3⋊#95C211yesmaximal, characteristic, complemented
10#10591302C211yesmaximal, characteristic, complemented
11#10591300C211yesmaximal, characteristic, complemented
12C2×#5222—31nomaximal
13D3×#394—31nomaximal
14C24×C3×D3C2212yes—
15C22×C32×D4C2211yescharacteristic
16C22×C3×#67C2212yes—
17C2×C3×D3×D4—24no—
18C2×C3×D3×D4—28no—
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C22×D3×Dic3C2212yes—
23C22×D3×Dic3C2211yescharacteristic
24C2×#3757C2212yescomplemented
25C2×#3757C2212yescomplemented
26C2×#3750C2211yescharacteristic, complemented
27C2×C3×#217C2212yescomplemented
28C2×C3×#217C2212yescomplemented
29C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
30D3×#217—28no—
31D3×#217—28no—
32C2×#3724C2211yescharacteristic, complemented
33C2×Dic3⋊Dic3C2211yescharacteristic, complemented
34C2×(C2×D3)⋊Dic3C2212yescomplemented
35C2×(C2×D3)⋊Dic3C2212yescomplemented
36C2×(C2×D3)⋊Dic3C2212yescomplemented
37C2×(C2×D3)⋊Dic3C2212yescomplemented
38D3×Dic3⋊C4—24no—
39#63658C2211yescharacteristic, complemented
40C3×C3⋊#95C2211yescharacteristic, complemented
41#63579C2212yescomplemented
42C23×C3×D4—31no—
43C22×D3×D4D311yescharacteristic
44C22×#217—32no—
45C22×#217—32no—
46C22×Dic3⋊C4—31no—
47C2×D3×C4⋊C4—31no—
48C2×D3×C22⋊C4—32no—
49C2×D3×C22⋊C4—32no—
50C3×#394—31no—
51#5222—31no—
52#5222—31no—
53#5222—32no—
54#5222—32no—
55#5222—31no—
56#5222—31no—
57#5222—61no—
58#5222D311yescharacteristic, direct product factor
59C2×C3⋊#95—31no—
60#4991—31no—
61#4961—32no—
62#4959—32no—
63#4672—31no—
64D3×#95—31no—
65C24×C32C2312yes—
66C23×C3×D3—24no—
67C23×C3×D3—24no—
68C23×C3×D3—24no—
69C23×C3×D3—24no—
70C23×C3×D3—24no—
71C23×C3×D3—24no—
72C23×C3×D3D418yes—
73C23×C3×D3C2312yes—
74C23×C3×D3C2311yescharacteristic
75C2×C32×D4—24no—
76C2×C32×D4—22no—
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3C2312yes—
79C22×C3⋊Dic3C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81C2×C3×#67—24no—
82C2×C3×#67—24no—
83C2×C3×#67—24no—
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2311yescharacteristic
88C3×D3×D4—232no—
89C2×C3×D12—24no—
90C2×C3×D12—22no—
91C2×C3×C4×D3—24no—
92C2×C3×C4×D3D414yes—
93C2×D3×Dic3—22no—
94C2×D3×Dic3—22no—
95C2×D3×Dic3—22no—
96C2×D3×Dic3—24no—
97C2×D3×Dic3—24no—
98C2×D3×Dic3—24no—
99C2×D3×Dic3—24no—
100C2×D3×Dic3D414yescomplemented
101#3757—24no—
102#3757—24no—
103#3750—22no—
104C3×#217—24no—
105C3×#217—24no—
106C3×Dic3⋊C4—22no—
107#3724—22no—
108Dic3⋊Dic3—22no—
109(C2×D3)⋊Dic3—24no—
110(C2×D3)⋊Dic3—24no—
111(C2×D3)⋊Dic3—24no—
112(C2×D3)⋊Dic3—24no—
113C2×#394—91noSylow
114C25×C3—32no—
115C24×D3C2×D312yes—
116C22×C3×D4—21no—
117C22×C3×D4—32no—
118C22×C3×D4—31no—
119C22×C3×D4—64no—
120C22×C3×D4—68no—
121C22×C3×D4C2×D311yescharacteristic
122C22×C3×D4C2×D311yescharacteristic
123C23×C3×C4—31no—
124C22×#67C2×D312yes—
125C23×Dic3—31no—
126C23×Dic3—32no—
127C23×Dic3—31no—
128C2×D3×D4—28no—
129C2×D3×D4—24no—
130C22×D12C2×D311yescharacteristic
131C22×C4×D3—31no—
132C22×C4×D3—32no—
133C22×C4×D3—31no—
134C22×C4×D3C2×D311yescharacteristic
135C2×C3×C4⋊C4—31no—
136C2×C3×C22⋊C4—32no—
137C2×C3×C22⋊C4—32no—
138C2×#217—32no—
139C2×#217—32no—
140C2×#217—32no—
141C2×#217—32no—
142C2×#217—32no—
143C2×#217—32no—
144C2×#217—32no—
145C2×#217—32no—
146C2×#217—62no—
147C2×#217—62no—
148C2×#217—68no—
149C2×#217—68no—
150C2×#217C2×D312yescomplemented
151C2×#217C2×D312yescomplemented
152C2×(C2×D3)⋊C4—32no—
153C2×(C2×D3)⋊C4—32no—
154C2×(C2×D3)⋊C4—32no—
155C2×(C2×D3)⋊C4—32no—
156C2×C4⋊Dic3—31no—
157C2×Dic3⋊C4—31no—
158C2×Dic3⋊C4—31no—
159C2×Dic3⋊C4—31no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—61no—
163C2×Dic3⋊C4—64no—
164C2×Dic3⋊C4C2×D311yescharacteristic, complemented
165D3×C4⋊C4—64no—
166D3×C22⋊C4—68no—
167D3×C22⋊C4—68no—
168C3×#95—31no—
169C3⋊#95—31no—
170C3⋊#95—31no—
171C3⋊#95—32no—
172C3⋊#95—32no—
173C3⋊#95—61no—
174C3⋊#95C2×D311yescharacteristic, complemented
175C23×C32—22no—
176C23×C32—22no—
177C23×C32—22no—
178C23×C32—22no—
179C23×C32—22no—
180C23×C32—22no—
181C23×C32C2×D414yes—
182C23×C32C2411yescharacteristic
183C22×C3×D3—22no—
184C22×C3×D3—22no—
185C22×C3×D3—22no—
186C22×C3×D3—22no—
187C22×C3×D3—22no—
188C22×C3×D3—22no—
189C22×C3×D3—216no—
190C22×C3×D3—216no—
191C22×C3×D3—216no—
192C22×C3×D3—48no—
193C22×C3×D3—48no—
194C22×C3×D3—48no—
195C22×C3×D3—48no—
196C22×C3×D3C2×D412yes—
197C22×C3×D3C2×D414yes—
198C22×C3×D3C2×D414yes—
199C22×C3×D3C2×D412yes—
200C22×C3×D3#4112yes—
201C22×C3×D3#4114yes—
202C32×D4—28no—
203C2×C32×C4—22no—
204C2×C32×C4C2×D412yes—
205C2×C3⋊Dic3—21no—
206C2×C3⋊Dic3—21no—
207C2×C3⋊Dic3—22no—
208C2×C3⋊Dic3—22no—
209C2×C3⋊Dic3—22no—
210C2×C3⋊Dic3—21no—
211C2×C3⋊Dic3—22no—
212C2×C3⋊Dic3C2×D412yescomplemented
213C3×#67—216no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3—22no—
216C2×C3×Dic3—21no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—22no—
219C2×C3×Dic3—22no—
220C2×C3×Dic3—21no—
221C2×C3×Dic3—22no—
222C2×C3×Dic3C2×D412yes—
223C2×C3×Dic3C2×D412yescomplemented
224C3×D12—28no—
225C3×C4×D3—28no—
226D3×Dic3—28no—
227D3×Dic3—44no—
228D3×Dic3—48no—
229C23×D4—31no—
230C22×C4⋊C4—91no—
231C22×C22⋊C4—92no—
232C22×C22⋊C4—92no—
233#394—31no—
234#394—91no—
235#394—92no—
236#394—92no—
237#394—91no—
238#394—91no—
239C2×#95—91no—
240C24×C3—22no—
241C24×C3—31no—
242C24×C3—38no—
243C24×C3—32no—
244C24×C3—64no—
245C24×C3—64no—
246C24×C3—64no—
247C24×C3—64no—
248C24×C3—64no—
249C24×C3—64no—
250C24×C3C22×D312yes—
251C24×C3C22×D312yes—
252C23×D3—24no—
253C23×D3—24no—
254C23×D3—24no—
255C23×D3—24no—
256C23×D3—24no—
257C23×D3—24no—
258C23×D3#6718yes—
259C23×D3C22×D312yes—
260C23×D3C22×D311yescharacteristic
261C2×C3×D4—24no—
262C2×C3×D4—24no—
263C2×C3×D4—22no—
264C2×C3×D4—22no—
265C2×C3×D4—42no—
266C2×C3×D4—44no—
267C2×C3×D4—64no—
268C2×C3×D4—64no—
269C2×C3×D4—632no—
270C2×C3×D4—64no—
271C2×C3×D4—64no—
272C2×C3×D4—62no—
273C22×C3×C4—21no—
274C22×C3×C4—31no—
275C22×C3×C4—31no—
276C22×C3×C4—34no—
277C22×C3×C4—32no—
278C22×C3×C4—31no—
279C22×C3×C4—64no—
280C22×C3×C4C22×D311yescharacteristic
281C22×C3×C4C22×D311yescharacteristic
282C2×#67—24no—
283C2×#67—24no—
284C2×#67—24no—
285C22×Dic3—31no—
286C22×Dic3—31no—
287C22×Dic3—34no—
288C22×Dic3—32no—
289C22×Dic3—32no—
290C22×Dic3—31no—
291C22×Dic3—31no—
292C22×Dic3—61no—
293C22×Dic3—62no—
294C22×Dic3—61no—
295C22×Dic3—62no—
296C22×Dic3—62no—
297C22×Dic3—62no—
298C22×Dic3—64no—
299C22×Dic3—64no—
300C22×Dic3—64no—
301C22×Dic3—64no—
302C22×Dic3C22×D312yes—
303C22×Dic3C22×D311yescharacteristic
304C22×Dic3C22×D311yescharacteristic
305C22×Dic3C22×D311yescharacteristic
306D3×D4—232no—
307C2×D12—24no—
308C2×D12—22no—
309C2×C4×D3—24no—
310C2×C4×D3—34no—
311C2×C4×D3—62no—
312C2×C4×D3—62no—
313C2×C4×D3—64no—
314C2×C4×D3—64no—
315C2×C4×D3—64no—
316C2×C4×D3—64no—
317C2×C4×D3—62no—
318C2×C4×D3#6714yes—
319C3×C4⋊C4—62no—
320C3×C22⋊C4—64no—
321C3×C22⋊C4—64no—
322#217—24no—
323#217—24no—
324#217—64no—
325#217—64no—
326#217—64no—
327#217—64no—
328#217—64no—
329#217—64no—
330#217—64no—
331#217—64no—
332#217—124no—
333#217—124no—
334(C2×D3)⋊C4—64no—
335(C2×D3)⋊C4—64no—
336(C2×D3)⋊C4—64no—
337(C2×D3)⋊C4—64no—
338C4⋊Dic3—62no—
339Dic3⋊C4—22no—
340Dic3⋊C4—62no—
341Dic3⋊C4—62no—
342Dic3⋊C4—62no—
343Dic3⋊C4—62no—
344Dic3⋊C4—62no—
345Dic3⋊C4—122no—
346C22×C32—24no—
347C22×C32—24no—
348C22×C32—24no—
349C22×C32—42no—
350C22×C32—42no—
351C22×C32—42no—
352C22×C32—42no—
353C22×C32C22×D411yescharacteristic
354C22×C32C22×D412yes—
355C22×C32C22×D411yescharacteristic
356C22×C32C2×#4111yescharacteristic
357C22×C32C2×#4112yes—
358C2×C3×D3—24no—
359C2×C3×D3—24no—
360C2×C3×D3—24no—
361C2×C3×D3—42no—
362C2×C3×D3—42no—
363C2×C3×D3—42no—
364C2×C3×D3—42no—
365C2×C3×D3—432no—
366C2×C3×D3#12014yes—
367C2×C3×D3#12114yes—
368C2×C3×D3#12118yes—
369C2×C3×D3#12318yes—
370C2×C3×D3#12414yes—
371C32×C4—22no—
372C3⋊Dic3—22no—
373C3⋊Dic3—41no—
374C3⋊Dic3—42no—
375C3×Dic3—22no—
376C3×Dic3—22no—
377C3×Dic3—41no—
378C3×Dic3—42no—
379C25—32no—
380C22×D4—32no—
381C22×D4—31no—
382C22×D4—64no—
383C22×D4—68no—
384C22×D4D3211yescharacteristic
385C23×C4—31no—
386C23×C4—91no—
387C23×C4—91no—
388C23×C4—92no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—91no—
391C2×C4⋊C4—91no—
392C2×C4⋊C4—91no—
393C2×C4⋊C4—184no—
394C2×C22⋊C4—32no—
395C2×C22⋊C4—32no—
396C2×C22⋊C4—92no—
397C2×C22⋊C4—92no—
398C2×C22⋊C4—92no—
399C2×C22⋊C4—92no—
400C2×C22⋊C4—92no—
401C2×C22⋊C4—92no—
402C2×C22⋊C4—188no—
403C2×C22⋊C4—188no—
404#95—31no—
405#95—92no—
406#95—91no—
407C23×C3—22no—
408C23×C3—22no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—22no—
416C23×C3—22no—
417C23×C3—22no—
418C23×C3—22no—
419C23×C3—21no—
420C23×C3—24no—
421C23×C3—32no—
422C23×C3—32no—
423C23×C3—34no—
424C23×C3—32no—
425C23×C3—34no—
426C23×C3—34no—
427C23×C3—42no—
428C23×C3—42no—
429C23×C3—42no—
430C23×C3—42no—
431C23×C3—42no—
432C23×C3—42no—
433C23×C3—616no—
434C23×C3—616no—
435C23×C3—616no—
436C23×C3—62no—
437C23×C3—62no—
438C23×C3—62no—
439C23×C3—62no—
440C23×C3—62no—
441C23×C3—62no—
442C23×C3—128no—
443C23×C3—128no—
444C23×C3—128no—
445C23×C3—128no—
446C23×C3D3×D414yes—
447C23×C3C2×#6714yes—
448C23×C3C23×D311yescharacteristic
449C23×C3C23×D311yescharacteristic
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—216no—
457C22×D3—216no—
458C22×D3—216no—
459C22×D3—48no—
460C22×D3—48no—
461C22×D3—48no—
462C22×D3—48no—
463C22×D3D3×D412yes—
464C22×D3#23712yes—
465C22×D3#23714yes—
466C22×D3C2×#6714yes—
467C22×D3C2×#6714yes—
468C22×D3C2×#6712yes—
469C3×D4—28no—
470C3×D4—28no—
471C3×D4—48no—
472C3×D4—68no—
473C3×D4—616no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—32no—
478C2×C3×C4—32no—
479C2×C3×C4—42no—
480C2×C3×C4—68no—
481C2×C3×C4—62no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—62no—
485C2×C3×C4—62no—
486C2×C3×C4—61no—
487C2×C3×C4—62no—
488C2×C3×C4—62no—
489C2×C3×C4D3×D412yes—
490C2×C3×C4C2×#6712yes—
491#67—216no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—22no—
495C2×Dic3—21no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—32no—
501C2×Dic3—32no—
502C2×Dic3—62no—
503C2×Dic3—68no—
504C2×Dic3—61no—
505C2×Dic3—61no—
506C2×Dic3—61no—
507C2×Dic3—61no—
508C2×Dic3—61no—
509C2×Dic3—62no—
510C2×Dic3—62no—
511C2×Dic3—62no—
512C2×Dic3—62no—
513C2×Dic3—62no—
514C2×Dic3—62no—
515C2×Dic3—61no—
516C2×Dic3—62no—
517C2×Dic3—62no—
518C2×Dic3—121no—
519C2×Dic3—121no—
520C2×Dic3—121no—
521C2×Dic3—122no—
522C2×Dic3—122no—
523C2×Dic3—122no—
524C2×Dic3—122no—
525C2×Dic3—124no—
526C2×Dic3—128no—
527C2×Dic3D3×D412yescomplemented
528C2×Dic3C2×#6712yes—
529D12—28no—
530C4×D3—28no—
531C4×D3—68no—
532C4×D3—128no—
533C4×D3—124no—
534C2×C32—44no—
535C2×C32C2×#12011yescharacteristic
536C2×C32C2×#12111yescharacteristic
537C2×C32C2×#12112yes—
538C2×C32C2×#12312yes—
539C2×C32C2×#12411yescharacteristic
540C3×D3—44no—
541C3×D3#39418yescomplemented
542C24—31no—
543C24—32no—
544C24—38no—
545C24—64no—
546C24—64no—
547C24—64no—
548C24—64no—
549C24—64no—
550C24—64no—
551C24C2×D3212yes—
552C2×D4—24no—
553C2×D4—22no—
554C2×D4—64no—
555C2×D4—64no—
556C2×D4—632no—
557C2×D4—64no—
558C2×D4—64no—
559C2×D4—62no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—34no—
563C22×C4—32no—
564C22×C4—31no—
565C22×C4—64no—
566C22×C4—94no—
567C22×C4—91no—
568C22×C4—92no—
569C22×C4—91no—
570C22×C4—182no—
571C22×C4—182no—
572C22×C4—184no—
573C22×C4—184no—
574C22×C4—184no—
575C22×C4—182no—
576C22×C4—184no—
577C22×C4C2×D3211yescharacteristic
578C4⋊C4—62no—
579C4⋊C4—182no—
580C4⋊C4—182no—
581C4⋊C4—182no—
582C22⋊C4—64no—
583C22⋊C4—64no—
584C22⋊C4—184no—
585C22⋊C4—184no—
586C22⋊C4—184no—
587C22⋊C4—184no—
588C22⋊C4—184no—
589C22⋊C4—184no—
590C22×C3—24no—
591C22×C3—24no—
592C22×C3—24no—
593C22×C3—24no—
594C22×C3—24no—
595C22×C3—24no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—22no—
599C22×C3—21no—
600C22×C3—22no—
601C22×C3—38no—
602C22×C3—34no—
603C22×C3—34no—
604C22×C3—34no—
605C22×C3—38no—
606C22×C3—44no—
607C22×C3—44no—
608C22×C3—44no—
609C22×C3—42no—
610C22×C3—42no—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3—42no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—64no—
618C22×C3—64no—
619C22×C3—64no—
620C22×C3—82no—
621C22×C3—82no—
622C22×C3—82no—
623C22×C3—82no—
624C22×C3—1232no—
625C22×C3—122no—
626C22×C3—122no—
627C22×C3—122no—
628C22×C3—122no—
629C22×C3C2×D3×D411yescharacteristic
630C22×C3C2×D3×D411yescharacteristic
631C22×C3C2×D3×D412yes—
632C22×C3C2×D3×D411yescharacteristic
633C22×C3C2×#23711yescharacteristic
634C22×C3C2×#23712yes—
635C22×C3D3×#4111yescharacteristic
636C22×C3D3×#4112yes—
637C22×C3C22×#6712yes—
638C22×C3C22×#6711yescharacteristic
639C2×D3—24no—
640C2×D3—24no—
641C2×D3—24no—
642C2×D3—42no—
643C2×D3—42no—
644C2×D3—42no—
645C2×D3—42no—
646C2×D3—432no—
647C2×D3#93518yes—
648C2×D3#93614yes—
649C2×D3#93814yes—
650C2×D3#93918yes—
651C2×D3#95314yes—
652C3×C4—22no—
653C3×C4—22no—
654C3×C4—42no—
655C3×C4—62no—
656C3×C4—62no—
657C3×C4—122no—
658C3×C4—121no—
659Dic3—22no—
660Dic3—22no—
661Dic3—41no—
662Dic3—42no—
663Dic3—62no—
664Dic3—62no—
665Dic3—122no—
666Dic3—122no—
667Dic3—121no—
668Dic3—121no—
669Dic3—122no—
670Dic3—241no—
671Dic3—242no—
672C32C2×#39411yescharacteristic, complemented, Sylow
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—32no—
680C23—32no—
681C23—34no—
682C23—32no—
683C23—34no—
684C23—34no—
685C23—616no—
686C23—616no—
687C23—616no—
688C23—62no—
689C23—62no—
690C23—62no—
691C23—62no—
692C23—62no—
693C23—62no—
694C23—128no—
695C23—128no—
696C23—128no—
697C23—128no—
698C23D3×#6714yes—
699C23C22×D3211yescharacteristic
700D4—28no—
701D4—68no—
702D4—616no—
703C2×C4—22no—
704C2×C4—32no—
705C2×C4—32no—
706C2×C4—68no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—62no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—61no—
715C2×C4—92no—
716C2×C4—188no—
717C2×C4—181no—
718C2×C4—181no—
719C2×C4—182no—
720C2×C4—182no—
721C2×C4—182no—
722C2×C4—182no—
723C2×C4—181no—
724C2×C4—364no—
725C2×C4—368no—
726C2×C4D3×#6712yes—
727C2×C3—22no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—22no—
732C2×C3—38no—
733C2×C3—44no—
734C2×C3—44no—
735C2×C3—84no—
736C2×C3—124no—
737C2×C3D3×#12011yescharacteristic
738C2×C3D3×#12111yescharacteristic
739C2×C3D3×#12112yes—
740C2×C3D3×#12312yes—
741C2×C3D3×#12411yescharacteristic
742C2×C3C2×#93512yes—
743C2×C3C2×#93611yescharacteristic
744C2×C3C2×#93811yescharacteristic
745C2×C3C2×#93912yes—
746C2×C3C2×#95311yescharacteristic
747D3—44no—
748D3#522218yesdirect product factor
749C22—24no—
750C22—24no—
751C22—24no—
752C22—38no—
753C22—34no—
754C22—34no—
755C22—34no—
756C22—38no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—64no—
762C22—64no—
763C22—64no—
764C22—1232no—
765C22—122no—
766C22—122no—
767C22—122no—
768C22—122no—
769C22D32×D411yescharacteristic
770C22D3×#23711yescharacteristic
771C22D3×#23712yes—
772C22C2×D3×#6712yes—
773C22C2×D3×#6711yescharacteristic
774C4—22no—
775C4—62no—
776C4—62no—
777C4—121no—
778C4—122no—
779C4—182no—
780C4—361no—
781C4—362no—
782C3—21no—
783C3D3×#39411yescharacteristic, complemented
784C3C2×#522211yescharacteristic, complemented
785C2—38no—
786C2—44no—
787C2—124no—
788C2D3×#93512yes—
789C2D3×#93611yescharacteristic
790C2D3×#93811yescharacteristic
791C2D3×#93912yes—
792C2D3×#95311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
prime radicalC22×C3×D3×D4C2
hypercenterC22×D4D32
hypocenterC32C2×#394
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×D3×#217C2semidirect
3. C2×D3×#217C2semidirect
4. C2×D3×Dic3⋊C4C2semidirect
5. #10592921C2semidirect
6. C3×#5222C2semidirect
7. #10591709C2semidirect
8. #10591708C2semidirect
9. D3×C3⋊#95C2semidirect
10. #10591302C2semidirect
11. #10591300C2semidirect
24. C2×#3757C22semidirect
25. C2×#3757C22semidirect
26. C2×#3750C22semidirect
27. C2×C3×#217C22semidirect
28. C2×C3×#217C22semidirect
29. C2×C3×Dic3⋊C4C22semidirect
32. C2×#3724C22semidirect
33. C2×Dic3⋊Dic3C22semidirect
34. C2×(C2×D3)⋊Dic3C22semidirect
35. C2×(C2×D3)⋊Dic3C22semidirect
36. C2×(C2×D3)⋊Dic3C22semidirect
37. C2×(C2×D3)⋊Dic3C22semidirect
39. #63658C22semidirect
40. C3×C3⋊#95C22semidirect
41. #63579C22semidirect
58. #5222D3direct (N × H)
100. C2×D3×Dic3D4semidirect
150. C2×#217C2×D3semidirect
151. C2×#217C2×D3semidirect
164. C2×Dic3⋊C4C2×D3semidirect
174. C3⋊#95C2×D3semidirect
212. C2×C3⋊Dic3C2×D4semidirect
223. C2×C3×Dic3C2×D4semidirect
527. C2×Dic3D3×D4semidirect
541. C3×D3#394semidirect
672. C32C2×#394semidirect
748. D3#5222direct (N × H)
783. C3D3×#394semidirect
784. C3C2×#5222semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×D42
C2×D3×#2172
C2×D3×Dic3⋊C42
#105929212
C3×#52222
#105917092
#105917082
D3×C3⋊#952
#105913022
#105913002
C2×#52223
D3×#3943