Finite Group Databasebeta

← D3×#4966 #11857907

Subgroups — D3×#4966 #11857907

Order 1152.

1713 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic
2C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×D3×#208C211yesmaximal, characteristic, complemented
4#10592665C211yesmaximal, characteristic, complemented
5C3×#4966C211yesmaximal, characteristic, complemented
6#10591106C211yesmaximal, characteristic, complemented
7#10591087C211yesmaximal, characteristic, complemented
8#10590609C212yesmaximal, complemented
9#10590607C212yesmaximal, complemented
10D3×#810C212yesmaximal, complemented
11D3×#809C212yesmaximal, complemented
12C2×#4966—31nomaximal
13D3×#417—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C22×C3×C4×D3—21no—
17C22×C3×C4×D3C2211yescharacteristic
18C2×D3×#67—21no—
19C2×#3804—21no—
20D3×#235—24no—
21D3×#235C418yescomplemented
22C2×D3×D12C2211yescharacteristic
23C2×C4×D32—21no—
24C2×#3799C2211yescharacteristic
25C2×#3798—21no—
26C2×#3795C2211yescharacteristic
27C2×D3×Dic6C2211yescharacteristic
28C2×C32×C4⋊C4C2211yescharacteristic, complemented
29C2×#3748C2211yescharacteristic, complemented
30C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
31C2×C3×Dic3⋊C4—21no—
32C2×C3×#208C2211yescharacteristic, complemented
33C3×D3×C4⋊C4—21no—
34C3×D3×C4⋊C4—21no—
35C3×D3×C4⋊C4C2212yes—
36C3×D3×C4⋊C4C2212yescomplemented
37C2×#3711C2212yescomplemented
38D3×#208—24no—
39C2×D3×C3⋊C8C2212yes—
40#63637C2212yescomplemented
41#63636C2212yescomplemented
42C3×#810C2212yescomplemented
43C3×#809C2212yescomplemented
44#63567C2212yescomplemented
45#63565C2212yescomplemented
46#63564C2212yescomplemented
47#63562C2212yescomplemented
48C2×D3×#41—31no—
49C22×#235—31no—
50C22×C3×C4⋊C4—31no—
51C22×#208—31no—
52C2×D3×M16—31no—
53C2×D3×C4⋊C4D311yescharacteristic, complemented
54C3×#417—31no—
55#5232—31no—
56#5133—31no—
57C2×#810—32no—
58#4966—31no—
59#4966—31no—
60#4966—31no—
61#4966—31no—
62#4966—32no—
63#4966—32no—
64#4966—61no—
65#4966D311yescharacteristic, direct product factor
66C2×#809—32no—
67#4803—32no—
68D3×#103—32no—
69#4771—32no—
70D3×#102—32no—
71C23×C3×D3D411yescharacteristic
72C22×D32—21no—
73C22×C32×C4—21no—
74C22×C32×C4C2311yescharacteristic
75C2×#638—21no—
76#3828—22no—
77#3828C2×C414yescomplemented
78C2×C4⋊(C3⋊D3)C2311yescharacteristic
79C2×C4×C3⋊D3—21no—
80C2×#634C2311yescharacteristic
81C2×C3×#67—21no—
82C22×C3×Dic3—21no—
83C22×C3×Dic3D411yescharacteristic
84C3×#235—22no—
85C3×#235C2×C414yescomplemented
86C2×C3×D12C2311yescharacteristic
87C2×C3×C4×D3—21no—
88C2×C3×C4×D3—22no—
89C2×C3×C4×D3—22no—
90C2×C3×C4×D3—44no—
91C2×C3×C4×D3C2×C414yes—
92C2×C3×C4×D3D411yescharacteristic
93C2×C3×C4×D3D411yescharacteristic
94C2×C3×C4×D3D414yes—
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×C4×D3C2311yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98D3×#67—28no—
99C2×#627—21no—
100C2×#626—21no—
101C2×#626—21no—
102C2×#625—21no—
103C2×#624—21no—
104#3804—28no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107D3×D12—22no—
108D3×D12C2×C414yescomplemented
109C4×D32—28no—
110#3799—22no—
111#3799C2×C414yescomplemented
112#3798—28no—
113#3795—22no—
114#3795C2×C414yescomplemented
115D3×Dic6—22no—
116D3×Dic6C2×C414yescomplemented
117C32×C4⋊C4—21no—
118C32×C4⋊C4C2312yes—
119#3748—22no—
120C2×C3⋊(C3⋊C8)C2312yes—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2312yes—
123C3×Dic3⋊C4—22no—
124C3×Dic3⋊C4—22no—
125C3×#208—22no—
126C2×C3×C3⋊C8C2312yes—
127#3711—24no—
128D3×C3⋊C8—24no—
129C2×#417—91noSylow
130C2×C3×#41—31no—
131C23×C3×C4—31no—
132C23×C3×C4—61no—
133C22×#67—61no—
134D3×#41—38no—
135D3×#41—64no—
136C2×#239—31no—
137C2×D3×Q8—31no—
138C2×#237—31no—
139C2×#237—61no—
140C2×D3×D4—31no—
141C2×D3×D4—61no—
142C2×#235—31no—
143C2×#235—31no—
144C2×#235—38no—
145C2×#235—31no—
146C2×#235—31no—
147C2×#235—61no—
148C2×#235—61no—
149C2×#235—64no—
150C2×#235—61no—
151C2×#235—61no—
152C2×#235C2×D311yescharacteristic
153C22×D12—31no—
154C22×C4×D3—21no—
155C22×C4×D3—61no—
156C22×C4×D3—61no—
157C22×C4×D3C2×D311yescharacteristic
158C22×Dic6—31no—
159C2×C3×M16—31no—
160C2×C3×C4⋊C4—21no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C4⋊C4—32no—
163C2×C3×C4⋊C4—32no—
164C2×C3×C4⋊C4—61no—
165C2×C3×C4⋊C4—61no—
166C2×C3×C4⋊C4—61no—
167C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
168C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
169C2×C4⋊Dic3C2×D311yescharacteristic, complemented
170C2×Dic3⋊C4—21no—
171C2×#208—31no—
172C2×#208—31no—
173C2×#208—32no—
174C2×#208—61no—
175C2×#208—64no—
176C2×#208C2×D311yescharacteristic, complemented
177C22×C3⋊C8—32no—
178D3×M16—64no—
179C2×ΓL(1,𝔽25)—32no—
180C2×D3×C8—32no—
181D3×C4⋊C4—21no—
182D3×C4⋊C4—21no—
183D3×C4⋊C4C2×D312yes—
184D3×C4⋊C4C2×D312yescomplemented
185C3×#103—32no—
186C3×#102—32no—
187#835—32no—
188#832—32no—
189#821—32no—
190#816—32no—
191#810—32no—
192#810—32no—
193#810—32no—
194#810—32no—
195#810—62no—
196#810C2×D312yescomplemented
197#809—32no—
198#809—32no—
199#809—32no—
200#809—32no—
201#809—62no—
202#809C2×D312yescomplemented
203C23×C32C2×D411yescharacteristic
204C22×C3⋊D3—21no—
205C22×C3×D3—22no—
206C22×C3×D3—22no—
207C22×C3×D3—21no—
208C22×C3×D3C22⋊C414yes—
209C22×C3×D3C2×D411yescharacteristic
210C22×C3×D3C2×D411yescharacteristic
211C2×D32—24no—
212C2×D32—42no—
213C2×D32—42no—
214C2×C32×C4—22no—
215C2×C32×C4—42no—
216C2×C32×C4C22×C412yes—
217C2×C32×C4C2×D412yes—
218C2×C32×C4C2×D411yescharacteristic
219C2×C32×C4C2411yescharacteristic
220#638—24no—
221C2×C3⋊Dic3—21no—
222C4⋊(C3⋊D3)—21no—
223C4⋊(C3⋊D3)C22×C412yescomplemented
224C4×C3⋊D3—24no—
225#634—21no—
226#634C22×C412yescomplemented
227C3×#67—24no—
228C2×C3×Dic3—21no—
229C2×C3×Dic3—22no—
230C2×C3×Dic3—42no—
231C2×C3×Dic3C22⋊C414yes—
232C2×C3×Dic3C2×D411yescharacteristic
233C2×C3×Dic3C2×D411yescharacteristic
234C3×D12—21no—
235C3×D12C22×C412yescomplemented
236C3×C4×D3—24no—
237C3×C4×D3—44no—
238C3×C4×D3—44no—
239C3×C4×D3C22⋊C414yes—
240C3×C4×D3C22⋊C414yes—
241C3×C4×D3C22×C412yes—
242C3×C4×D3C22×C412yes—
243C3×C4×D3C2×D412yes—
244C3×C4×D3C2×D412yes—
245C3×Dic6—21no—
246C3×Dic6C22×C412yescomplemented
247#627—24no—
248#626—24no—
249#626—24no—
250#625—24no—
251#624—24no—
252D3×Dic3—24no—
253D3×Dic3—24no—
254C3⋊(C3⋊C8)—22no—
255C3×C3⋊C8—22no—
256C22×#41—91no—
257C22×M16—91no—
258C22×C4⋊C4—31no—
259#417—31no—
260#417—92no—
261#417—92no—
262#417—91no—
263#417—91no—
264#417—91no—
265C2×#103—92no—
266C2×#102—92no—
267C24×C3—31no—
268C23×D3—61no—
269C23×D3—61no—
270C23×D3#6711yescharacteristic
271C3×#41—34no—
272C3×#41—62no—
273C2×C3×Q8—31no—
274C2×C3×D4—31no—
275C2×C3×D4—61no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—31no—
280C22×C3×C4—34no—
281C22×C3×C4—34no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—41no—
287C22×C3×C4—62no—
288C22×C3×C4—62no—
289C22×C3×C4—61no—
290C22×C3×C4—61no—
291C22×C3×C4—124no—
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C22×D311yescharacteristic
294C2×#67—21no—
295C2×#67—61no—
296C2×#67—68no—
297C2×#67—61no—
298C2×#67—61no—
299C2×#67—61no—
300C2×#67—61no—
301C2×#67—61no—
302C2×#67—121no—
303C22×Dic3—21no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306C22×Dic3#6711yescharacteristic
307#239—34no—
308#239—62no—
309D3×Q8—34no—
310D3×Q8—62no—
311#237—34no—
312#237—68no—
313#237—62no—
314D3×D4—34no—
315D3×D4—68no—
316D3×D4—62no—
317#235—22no—
318#235—34no—
319#235—34no—
320#235—34no—
321#235—34no—
322#235—64no—
323#235—62no—
324#235—68no—
325#235—62no—
326#235—68no—
327#235—62no—
328#235—62no—
329#235—68no—
330#235—122no—
331#235C4×D314yescomplemented
332C2×D12—31no—
333C2×D12—31no—
334C2×D12—34no—
335C2×D12—61no—
336C2×D12—62no—
337C2×D12—61no—
338C2×D12—61no—
339C2×D12C22×D311yescharacteristic
340C2×C4×D3—21no—
341C2×C4×D3—22no—
342C2×C4×D3—22no—
343C2×C4×D3—44no—
344C2×C4×D3—68no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—61no—
350C2×C4×D3—61no—
351C2×C4×D3—68no—
352C2×C4×D3—121no—
353C2×C4×D3C4×D314yes—
354C2×C4×D3D1214yes—
355C2×C4×D3#6711yescharacteristic
356C2×C4×D3#6711yescharacteristic
357C2×C4×D3C22×D311yescharacteristic
358C2×C4×D3C22×D311yescharacteristic
359C2×Dic6—31no—
360C2×Dic6—31no—
361C2×Dic6—34no—
362C2×Dic6—61no—
363C2×Dic6—62no—
364C2×Dic6—61no—
365C2×Dic6—61no—
366C2×Dic6C22×D311yescharacteristic
367C3×M16—62no—
368C2×C3×C8—32no—
369C3×C4⋊C4—21no—
370C3×C4⋊C4—21no—
371C3×C4⋊C4—22no—
372C3×C4⋊C4—32no—
373C3×C4⋊C4—41no—
374C3×C4⋊C4—62no—
375C3×C4⋊C4—62no—
376C3×C4⋊C4—61no—
377C3×C4⋊C4C22×D312yes—
378C3×C4⋊C4C22×D312yes—
379C4⋊Dic3—21no—
380C4⋊Dic3C22×D312yes—
381Dic3⋊C4—22no—
382Dic3⋊C4—22no—
383#208—22no—
384#208—64no—
385#208—62no—
386#208—62no—
387#208—122no—
388C2×C3⋊C8—32no—
389C2×C3⋊C8—32no—
390C2×C3⋊C8—62no—
391C2×C3⋊C8—64no—
392C2×C3⋊C8C22×D312yes—
393ΓL(1,𝔽25)—64no—
394D3×C8—64no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32C2×C22⋊C412yes—
398C22×C32C22×D411yescharacteristic
399C2×C3⋊D3—22no—
400C2×C3⋊D3—41no—
401C2×C3⋊D3—41no—
402C2×C3×D3—21no—
403C2×C3×D3—21no—
404C2×C3×D3—28no—
405C2×C3×D3—22no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C2×C3×D3C2×C22⋊C412yes—
409C2×C3×D3C2×C22⋊C412yes—
410C2×C3×D3AGL(1,ℤ/8)12yes—
411C2×C3×D3#13712yes—
412D32—48no—
413C32×C4—42no—
414C32×C4C2×C22⋊C412yes—
415C32×C4C23×C411yescharacteristic
416C32×C4C22×D411yescharacteristic
417C3⋊Dic3—22no—
418C3×Dic3—22no—
419C3×Dic3—42no—
420C3×Dic3C2×C22⋊C412yes—
421C3×Dic3C2×C22⋊C412yes—
422C2×#41—31no—
423C2×#41—91no—
424C2×#41—91no—
425C2×#41—98no—
426C2×#41—91no—
427C2×#41—181no—
428C2×#41—181no—
429C2×#41—184no—
430C22×Q8—91no—
431C22×D4—91no—
432C22×D4—181no—
433C23×C4—31no—
434C23×C4—61no—
435C23×C4—181no—
436C2×M16—31no—
437C2×M16—92no—
438C2×M16—91no—
439C2×M16—184no—
440C22×C8—92no—
441C2×C4⋊C4—31no—
442C2×C4⋊C4—32no—
443C2×C4⋊C4—32no—
444C2×C4⋊C4—61no—
445C2×C4⋊C4—61no—
446C2×C4⋊C4—61no—
447C2×C4⋊C4D3211yescharacteristic, complemented
448#103—32no—
449#103—92no—
450#103—92no—
451#103—92no—
452#102—32no—
453#102—92no—
454#102—92no—
455#102—92no—
456C23×C3—21no—
457C23×C3—31no—
458C23×C3—34no—
459C23×C3—31no—
460C23×C3—62no—
461C23×C3—62no—
462C23×C3—61no—
463C23×C3D3×D411yescharacteristic
464C23×C3C2×#6711yescharacteristic
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—21no—
468C22×D3—64no—
469C22×D3—61no—
470C22×D3—61no—
471C22×D3—64no—
472C22×D3—121no—
473C22×D3—122no—
474C22×D3—122no—
475C22×D3—122no—
476C22×D3—122no—
477C22×D3(C2×D3)⋊C414yes—
478C22×D3C2×#6711yescharacteristic
479C22×D3C2×#6711yescharacteristic
480C3×Q8—32no—
481C3×Q8—61no—
482C3×D4—32no—
483C3×D4—64no—
484C3×D4—61no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—21no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—21no—
491C2×C3×C4—34no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—34no—
495C2×C3×C4—34no—
496C2×C3×C4—32no—
497C2×C3×C4—32no—
498C2×C3×C4—32no—
499C2×C3×C4—32no—
500C2×C3×C4—42no—
501C2×C3×C4—42no—
502C2×C3×C4—42no—
503C2×C3×C4—61no—
504C2×C3×C4—64no—
505C2×C3×C4—62no—
506C2×C3×C4—82no—
507C2×C3×C4—124no—
508C2×C3×C4—124no—
509C2×C3×C4—122no—
510C2×C3×C4C2×C4×D312yes—
511C2×C3×C4C2×C4×D312yes—
512C2×C3×C4C2×D1212yes—
513C2×C3×C4D3×D412yes—
514C2×C3×C4D3×D411yescharacteristic
515C2×C3×C4C2×#6711yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518#67—24no—
519#67—64no—
520#67—64no—
521#67—64no—
522#67—64no—
523#67—64no—
524#67—64no—
525#67—124no—
526C2×Dic3—21no—
527C2×Dic3—22no—
528C2×Dic3—42no—
529C2×Dic3—64no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—64no—
533C2×Dic3—121no—
534C2×Dic3(C2×D3)⋊C414yes—
535C2×Dic3C2×#6711yescharacteristic
536C2×Dic3C2×#6711yescharacteristic
537D12—21no—
538D12—32no—
539D12—32no—
540D12—62no—
541D12—64no—
542D12—64no—
543D12—61no—
544D12—61no—
545D12—121no—
546D12C2×C4×D312yescomplemented
547C4×D3—24no—
548C4×D3—44no—
549C4×D3—44no—
550C4×D3—64no—
551C4×D3—64no—
552C4×D3—64no—
553C4×D3—64no—
554C4×D3—64no—
555C4×D3—64no—
556C4×D3—124no—
557C4×D3(C2×D3)⋊C414yes—
558C4×D3(C2×D3)⋊C414yes—
559C4×D3C2×C4×D312yes—
560C4×D3C2×C4×D312yes—
561C4×D3C2×D1212yes—
562C4×D3C2×D1212yes—
563Dic6—21no—
564Dic6—32no—
565Dic6—32no—
566Dic6—62no—
567Dic6—64no—
568Dic6—61no—
569Dic6—61no—
570Dic6—64no—
571Dic6—121no—
572Dic6C2×C4×D312yescomplemented
573C3×C8—62no—
574C3⋊C8—22no—
575C3⋊C8—62no—
576C3⋊C8—62no—
577C3⋊C8—122no—
578C2×C32—22no—
579C2×C32C22×C22⋊C411yescharacteristic
580C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
581C2×C32C2×#13711yescharacteristic
582C3⋊D3—42no—
583C3×D3—22no—
584C3×D3—42no—
585C3×D3#41714yescomplemented
586C24—31no—
587C24—181no—
588#41—34no—
589#41—62no—
590#41—94no—
591#41—94no—
592#41—94no—
593#41—188no—
594#41—188no—
595#41—182no—
596#41—182no—
597#41—182no—
598C2×Q8—31no—
599C2×Q8—94no—
600C2×Q8—91no—
601C2×Q8—181no—
602C2×Q8—182no—
603C2×D4—31no—
604C2×D4—61no—
605C2×D4—94no—
606C2×D4—91no—
607C2×D4—182no—
608C2×D4—181no—
609C2×D4—181no—
610C2×D4—188no—
611C2×D4—181no—
612C2×D4—181no—
613C22×C4—21no—
614C22×C4—31no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—34no—
618C22×C4—34no—
619C22×C4—31no—
620C22×C4—31no—
621C22×C4—62no—
622C22×C4—62no—
623C22×C4—61no—
624C22×C4—61no—
625C22×C4—124no—
626C22×C4—181no—
627C22×C4—188no—
628C22×C4—181no—
629C22×C4—181no—
630C22×C4—181no—
631C22×C4C2×D3211yescharacteristic
632M16—62no—
633M16—184no—
634M16—182no—
635C2×C8—32no—
636C2×C8—92no—
637C2×C8—184no—
638C4⋊C4—21no—
639C4⋊C4—32no—
640C4⋊C4—62no—
641C4⋊C4—62no—
642C4⋊C4—61no—
643C4⋊C4C2×D3212yes—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—22no—
650C22×C3—32no—
651C22×C3—32no—
652C22×C3—32no—
653C22×C3—32no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—68no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—62no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3D3×C22⋊C412yes—
663C22×C3C2×(C2×D3)⋊C412yes—
664C22×C3C2×D3×D411yescharacteristic
665C22×C3C22×#6711yescharacteristic
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—28no—
669C2×D3—22no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—62no—
673C2×D3—62no—
674C2×D3—122no—
675C2×D3—128no—
676C2×D3—121no—
677C2×D3—121no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3—128no—
681C2×D3—241no—
682C2×D3—241no—
683C2×D3C2×(C2×D3)⋊C412yes—
684C2×D3C2×(C2×D3)⋊C412yes—
685C2×D3#93212yes—
686C2×D3#94212yes—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—22no—
690C3×C4—32no—
691C3×C4—32no—
692C3×C4—42no—
693C3×C4—42no—
694C3×C4—62no—
695C3×C4—82no—
696C3×C4—122no—
697C3×C4D3×C22⋊C412yes—
698C3×C4C2×(C2×D3)⋊C412yes—
699C3×C4C22×C4×D311yescharacteristic
700C3×C4C22×C4×D311yescharacteristic
701C3×C4C22×D1211yescharacteristic
702C3×C4C2×D3×D411yescharacteristic
703Dic3—22no—
704Dic3—42no—
705Dic3—62no—
706Dic3—62no—
707Dic3—122no—
708Dic3C2×(C2×D3)⋊C412yes—
709Dic3C2×(C2×D3)⋊C412yes—
710C32C2×#41711yescharacteristic, complemented, Sylow
711C23—31no—
712C23—31no—
713C23—34no—
714C23—62no—
715C23—62no—
716C23—61no—
717C23—184no—
718C23—181no—
719C23—362no—
720C23—362no—
721C23D3×#6711yescharacteristic
722Q8—32no—
723Q8—61no—
724Q8—92no—
725Q8—184no—
726Q8—181no—
727D4—32no—
728D4—64no—
729D4—61no—
730D4—92no—
731D4—184no—
732D4—184no—
733D4—184no—
734D4—184no—
735D4—181no—
736C2×C4—22no—
737C2×C4—31no—
738C2×C4—31no—
739C2×C4—34no—
740C2×C4—32no—
741C2×C4—32no—
742C2×C4—32no—
743C2×C4—32no—
744C2×C4—34no—
745C2×C4—34no—
746C2×C4—42no—
747C2×C4—61no—
748C2×C4—64no—
749C2×C4—62no—
750C2×C4—124no—
751C2×C4—124no—
752C2×C4—122no—
753C2×C4—184no—
754C2×C4—184no—
755C2×C4—184no—
756C2×C4—181no—
757C2×C4—184no—
758C2×C4C4×D3212yes—
759C2×C4D3×D1212yes—
760C2×C4D3×#6711yescharacteristic
761C2×C4C22×D3211yescharacteristic
762C8—62no—
763C8—182no—
764C2×C3—22no—
765C2×C3—22no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—34no—
770C2×C3—42no—
771C2×C3—62no—
772C2×C3—122no—
773C2×C3C2×D3×C22⋊C411yescharacteristic
774C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
775C2×C3D3×#13711yescharacteristic
776C2×C3C22×(C2×D3)⋊C411yescharacteristic
777C2×C3C2×#93211yescharacteristic
778C2×C3C2×#94211yescharacteristic
779D3—22no—
780D3—42no—
781D3—122no—
782D3—122no—
783D3—242no—
784D3#496614yesdirect product factor
785C22—21no—
786C22—21no—
787C22—32no—
788C22—32no—
789C22—32no—
790C22—32no—
791C22—68no—
792C22—61no—
793C22—61no—
794C22—62no—
795C22—121no—
796C22—121no—
797C22—182no—
798C22—368no—
799C22—361no—
800C22—361no—
801C22D3×(C2×D3)⋊C412yes—
802C22C2×D3×#6711yescharacteristic
803C4—32no—
804C4—32no—
805C4—42no—
806C4—62no—
807C4—122no—
808C4—182no—
809C4D3×(C2×D3)⋊C412yes—
810C4C2×C4×D3211yescharacteristic
811C4C2×D3×D1211yescharacteristic
812C3—21no—
813C3D3×#41711yescharacteristic, complemented
814C3C2×#496611yescharacteristic, complemented
815C2—22no—
816C2—34no—
817C2—62no—
818C2—122no—
819C2—362no—
820C2C2×D3×(C2×D3)⋊C411yescharacteristic
821C2D3×#93211yescharacteristic
822C2D3×#94211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC2×D3×#235C2
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#417
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×C4⋊C4C2semidirect
3. C2×D3×#208C2semidirect
4. #10592665C2semidirect
5. C3×#4966C2semidirect
6. #10591106C2semidirect
7. #10591087C2semidirect
8. #10590609C2semidirect
9. #10590607C2semidirect
10. D3×#810C2semidirect
11. D3×#809C2semidirect
21. D3×#235C4semidirect
28. C2×C32×C4⋊C4C22semidirect
29. C2×#3748C22semidirect
30. C2×C3×C4⋊Dic3C22semidirect
32. C2×C3×#208C22semidirect
36. C3×D3×C4⋊C4C22semidirect
37. C2×#3711C22semidirect
40. #63637C22semidirect
41. #63636C22semidirect
42. C3×#810C22semidirect
43. C3×#809C22semidirect
44. #63567C22semidirect
45. #63565C22semidirect
46. #63564C22semidirect
47. #63562C22semidirect
53. C2×D3×C4⋊C4D3semidirect
65. #4966D3direct (N × H)
77. #3828C2×C4semidirect
85. C3×#235C2×C4semidirect
108. D3×D12C2×C4semidirect
111. #3799C2×C4semidirect
114. #3795C2×C4semidirect
116. D3×Dic6C2×C4semidirect
167. C2×C3×C4⋊C4C2×D3semidirect
168. C2×C3×C4⋊C4C2×D3semidirect
169. C2×C4⋊Dic3C2×D3semidirect
176. C2×#208C2×D3semidirect
184. D3×C4⋊C4C2×D3semidirect
196. #810C2×D3semidirect
202. #809C2×D3semidirect
223. C4⋊(C3⋊D3)C22×C4semidirect
226. #634C22×C4semidirect
235. C3×D12C22×C4semidirect
246. C3×Dic6C22×C4semidirect
331. #235C4×D3semidirect
447. C2×C4⋊C4D32semidirect
546. D12C2×C4×D3semidirect
572. Dic6C2×C4×D3semidirect
585. C3×D3#417semidirect
710. C32C2×#417semidirect
784. D3#4966direct (N × H)
813. C3D3×#417semidirect
814. C3C2×#4966semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
C2×C3×D3×C4⋊C42
C2×D3×#2082
#105926652
C3×#49662
#105911062
#105910872
#105906092
#105906072
D3×#8102
D3×#8092
C2×#49663
D3×#4173