Finite Group Databasebeta

← C3×#83931 #11865836

Subgroups — C3×#83931 #11865836

Order 1152.

1245 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C3×#5832C211yesmaximal, characteristic, complemented
3C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
4C2×C3×#932C211yesmaximal, characteristic, complemented
5C3×#5232C211yesmaximal, characteristic, complemented
6C3×#5165C212yesmaximal, complemented
7C3×#5162C212yesmaximal, complemented
8C3×#5153C212yesmaximal, complemented
9C3×#5150C212yesmaximal, complemented
10C3×#5133C211yesmaximal, characteristic, complemented
11C3×#5118C211yesmaximal, characteristic, complemented
12C3×#3036—31nomaximal
13#83931C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C22×C32×D4C2211yescharacteristic
16C23×C3×Dic3—21no—
17C2×C3×#235C2211yescharacteristic
18C32×AGL(1,ℤ/8)—24no—
19C2×C32×SD16C2212yes—
20C2×C32×D8C2212yes—
21C2×C32×M16C2211yescharacteristic
22C2×C3×#217—21no—
23C3×#947C2211yescharacteristic, complemented
24C3×#944C2211yescharacteristic, complemented
25C3×#940C2211yescharacteristic, complemented
26C3×#939—21no—
27C3×#939—21no—
28C3×#936C2211yescharacteristic, complemented
29C3×D4×Dic3—21no—
30C3×D4×Dic3—21no—
31C3×D4×Dic3C2212yes—
32C3×D4×Dic3C2212yes—
33C2×C3×#214C2212yes—
34C3×#932—24no—
35C2×C3×#213C2212yes—
36C3×C4×#67—21no—
37C3×C4×#67—21no—
38C2×C3×C4⋊Dic3C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40C2×C3×#208C2211yescharacteristic
41C3×#835C2212yescomplemented
42C3×#832C2212yescomplemented
43C3×#821C2212yescomplemented
44C3×#816C2212yescomplemented
45C3×Dic3⋊C8C2212yescomplemented
46C3×Dic3⋊C8C2212yescomplemented
47C2×C3×AGL(1,ℤ/8)—21no—
48C2×C3×AGL(1,ℤ/8)—31no—
49C2×C3×AGL(1,ℤ/8)D311yescharacteristic, complemented
50C2×C3×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
51C3×#532—31no—
52C2×C3×C4×D4—31no—
53#5832C2×C311yescharacteristic, complemented
54C2×D4×Dic3C2×C311yescharacteristic, complemented
55C2×#932C2×C311yescharacteristic, complemented
56C3×#463—32no—
57C3×#463—32no—
58C3×#461—32no—
59C3×#459—32no—
60C3×#423—31no—
61C3×#417—31no—
62C3×#417—31no—
63#5232C2×C311yescharacteristic, complemented
64#5165C2×C312yescomplemented
65#5162C2×C312yescomplemented
66#5153C2×C312yescomplemented
67#5150C2×C312yescomplemented
68#5133C2×C311yescharacteristic, complemented
69#5118C2×C311yescharacteristic, complemented
70C24×C32—21no—
71C32×#41—22no—
72C32×#41—22no—
73C2×C32×Q8C2311yescharacteristic
74C2×C32×D4—21no—
75C2×C32×D4—21no—
76C2×C32×D4—22no—
77C2×C32×D4D414yescomplemented
78C2×C32×D4C2311yescharacteristic
79C2×C32×D4C2312yes—
80C22×C32×C4—21no—
81C22×C32×C4C2311yescharacteristic
82C2×C3×#67—21no—
83C2×C3×#67—21no—
84C2×C3×#67—21no—
85C22×C3×Dic3—21no—
86C22×C3×Dic3—22no—
87C22×C3×Dic3—22no—
88C22×C3×Dic3—44no—
89C22×C3×Dic3D411yescharacteristic
90C22×C3×Dic3D411yescharacteristic
91C3×#235—22no—
92C3×#235—22no—
93C2×C3×D12C2311yescharacteristic
94C2×C3×C4×D3—21no—
95C2×C3×Dic6C2311yescharacteristic
96C32×SD16—24no—
97C32×D8—24no—
98C32×M16—22no—
99C2×C32×C8C2312yes—
100C3×#217—21no—
101C3×#217—21no—
102C3×#217—22no—
103C3×#217—22no—
104C3×#214—24no—
105C3×#213—24no—
106C3×(C2×D3)⋊C4—21no—
107C3×(C2×D3)⋊C4—21no—
108C3×C4⋊Dic3—21no—
109C3×C4⋊Dic3C2312yes—
110C3×Dic3⋊C4—21no—
111C3×Dic3⋊C4—21no—
112C3×C4×Dic3D411yescharacteristic
113C3×C4×Dic3D411yescharacteristic
114C3×C4×Dic3C2311yescharacteristic
115C3×C4×Dic3C2311yescharacteristic
116C3×#208—22no—
117C2×C3×C3⋊C8C2312yes—
118#3036—31noSylow
119C2×C3×#41—21no—
120C2×C3×#41—31no—
121C2×C3×#41C2×D311yescharacteristic
122C2×C3×#41C22×C311yescharacteristic
123C22×C3×D4—21no—
124C22×C3×D4C2×D311yescharacteristic
125C22×C3×D4C22×C311yescharacteristic
126C23×C3×C4—61no—
127C23×Dic3—21no—
128C2×#235C22×C311yescharacteristic
129C3×AGL(1,ℤ/8)—28no—
130C3×AGL(1,ℤ/8)—24no—
131C3×AGL(1,ℤ/8)—24no—
132C3×AGL(1,ℤ/8)—64no—
133C2×C3×SD16—22no—
134C2×C3×SD16—32no—
135C2×C3×SD16C2×D312yes—
136C2×C3×SD16C22×C312yes—
137C2×C3×D8—22no—
138C2×C3×D8—32no—
139C2×C3×D8C2×D312yes—
140C2×C3×D8C22×C312yes—
141C2×C3×M16—21no—
142C2×C3×M16—31no—
143C2×C3×M16C2×D311yescharacteristic
144C2×C3×M16C22×C311yescharacteristic
145C3×C4⋊Q8—31no—
146C3×#127—31no—
147C3×#124—31no—
148C3×#124—31no—
149C3×#121—61no—
150C3×#121—61no—
151C3×C4×D4—32no—
152C3×C4×D4—32no—
153C3×C4×D4—61no—
154C3×C4×D4—61no—
155C3×C4×D4—61no—
156C3×C4×D4—61no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C22⋊C4—61no—
159C2×C3×C42—31no—
160C2×#217—21no—
161#947C22×C311yescharacteristic, complemented
162#944C22×C311yescharacteristic, complemented
163#940C22×C311yescharacteristic, complemented
164#939—21no—
165#939—21no—
166#936C22×C311yescharacteristic, complemented
167D4×Dic3—21no—
168D4×Dic3—21no—
169D4×Dic3C22×C312yes—
170D4×Dic3C22×C312yes—
171C2×#214C22×C312yes—
172#932—24no—
173C2×#213C22×C312yes—
174C4×#67—21no—
175C4×#67—21no—
176C2×C4⋊Dic3C22×C311yescharacteristic
177C2×C4×Dic3C22×C311yescharacteristic
178C2×#208C22×C311yescharacteristic
179C3×C4⋊C8—32no—
180C3×C4⋊C8—32no—
181C3×#103—32no—
182C3×#103—32no—
183C3×#102—32no—
184C3×#102—32no—
185#835C22×C312yescomplemented
186#832C22×C312yescomplemented
187#821C22×C312yescomplemented
188#816C22×C312yescomplemented
189Dic3⋊C8C22×C312yescomplemented
190Dic3⋊C8C22×C312yescomplemented
191C23×C32—24no—
192C23×C32—22no—
193C23×C32—21no—
194C23×C32—42no—
195C23×C32—42no—
196C23×C32C2×D411yescharacteristic
197C22×C3×D3—21no—
198C32×Q8—21no—
199C32×Q8—21no—
200C32×D4—21no—
201C32×D4—24no—
202C32×D4—22no—
203C32×D4—21no—
204C32×D4—42no—
205C32×D4C2×D414yes—
206C2×C32×C4—21no—
207C2×C32×C4—42no—
208C2×C32×C4C2×D411yescharacteristic
209C2×C32×C4C2×D412yes—
210C2×C32×C4#4112yes—
211C2×C32×C4C2411yescharacteristic
212C3×#67—42no—
213C3×#67—42no—
214C3×#67—42no—
215C2×C3×Dic3—22no—
216C2×C3×Dic3—21no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—41no—
219C2×C3×Dic3—44no—
220C2×C3×Dic3—42no—
221C2×C3×Dic3—44no—
222C2×C3×Dic3C2×D411yescharacteristic
223C2×C3×Dic3C2×D411yescharacteristic
224C2×C3×Dic3C2×D411yescharacteristic
225C2×C3×Dic3C2×D411yescharacteristic
226C3×D12—21no—
227C3×D12—21no—
228C3×C4×D3—42no—
229C3×Dic6—21no—
230C3×Dic6—21no—
231C32×C8—22no—
232C3×C3⋊C8—22no—
233C2×AGL(1,ℤ/8)—31no—
234C2×AGL(1,ℤ/8)C3×D311yescharacteristic, complemented
235#532—31no—
236C2×C4×D4—31no—
237#463—32no—
238#463—32no—
239#461—32no—
240#459—32no—
241#423—31no—
242#417—31no—
243#417—31no—
244C24×C3—21no—
245C24×C3—21no—
246C24×C3—41no—
247C3×#41—24no—
248C3×#41—22no—
249C3×#41—22no—
250C3×#41—22no—
251C3×#41—22no—
252C3×#41—42no—
253C3×#41—62no—
254C3×#41—62no—
255C2×C3×Q8—21no—
256C2×C3×Q8—31no—
257C2×C3×Q8C22×D311yescharacteristic
258C2×C3×Q8C23×C311yescharacteristic
259C2×C3×D4—21no—
260C2×C3×D4—21no—
261C2×C3×D4—21no—
262C2×C3×D4—22no—
263C2×C3×D4—21no—
264C2×C3×D4—22no—
265C2×C3×D4—24no—
266C2×C3×D4—21no—
267C2×C3×D4—22no—
268C2×C3×D4—31no—
269C2×C3×D4—41no—
270C2×C3×D4—42no—
271C2×C3×D4—41no—
272C2×C3×D4—61no—
273C2×C3×D4—61no—
274C2×C3×D4—61no—
275C2×C3×D4#6714yescomplemented
276C2×C3×D4C3×D414yescomplemented
277C2×C3×D4C22×D311yescharacteristic
278C2×C3×D4C22×D312yes—
279C2×C3×D4C23×C311yescharacteristic
280C2×C3×D4C23×C312yes—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
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×C4C23×C311yescharacteristic
294C2×#67—21no—
295C2×#67—21no—
296C2×#67—21no—
297C22×Dic3—21no—
298C22×Dic3—22no—
299C22×Dic3—22no—
300C22×Dic3—44no—
301C22×Dic3C3×D411yescharacteristic
302C22×Dic3C3×D411yescharacteristic
303#235—22no—
304#235—22no—
305C2×D12C23×C311yescharacteristic
306C2×C4×D3—21no—
307C2×Dic6C23×C311yescharacteristic
308C3×SD16—28no—
309C3×SD16—24no—
310C3×SD16—24no—
311C3×SD16—64no—
312C3×D8—28no—
313C3×D8—24no—
314C3×D8—24no—
315C3×D8—64no—
316C3×M16—24no—
317C3×M16—22no—
318C3×M16—22no—
319C3×M16—62no—
320C2×C3×C8—22no—
321C2×C3×C8—32no—
322C2×C3×C8C22×D312yes—
323C2×C3×C8C23×C312yes—
324C3×C4⋊C4—32no—
325C3×C4⋊C4—61no—
326C3×C4⋊C4—61no—
327C3×C4⋊C4—61no—
328C3×C22⋊C4—61no—
329C3×C22⋊C4—61no—
330C3×C22⋊C4—62no—
331C3×C22⋊C4—62no—
332C3×C22⋊C4—61no—
333C3×C22⋊C4—61no—
334C3×C42—31no—
335C3×C42—31no—
336C3×C42—31no—
337C3×C42—31no—
338#217—21no—
339#217—21no—
340#217—22no—
341#217—22no—
342#214—24no—
343#213—24no—
344(C2×D3)⋊C4—21no—
345(C2×D3)⋊C4—21no—
346C4⋊Dic3—21no—
347C4⋊Dic3C23×C312yes—
348Dic3⋊C4—21no—
349Dic3⋊C4—21no—
350C4×Dic3C3×D411yescharacteristic
351C4×Dic3C3×D411yescharacteristic
352C4×Dic3C23×C311yescharacteristic
353C4×Dic3C23×C311yescharacteristic
354#208—22no—
355C2×C3⋊C8C23×C312yes—
356C22×C32—21no—
357C22×C32—21no—
358C22×C32—24no—
359C22×C32—41no—
360C22×C32—48no—
361C22×C32—42no—
362C22×C32—42no—
363C22×C32—41no—
364C22×C32—41no—
365C22×C32#12112yes—
366C22×C32C22×D411yescharacteristic
367C2×C3×D3—41no—
368C2×C3×D3—41no—
369C2×C3×D3—41no—
370C32×C4—41no—
371C32×C4#12112yes—
372C32×C4C22×D411yescharacteristic
373C32×C4C2×#4111yescharacteristic
374C3×Dic3—21no—
375C3×Dic3—21no—
376C3×Dic3—21no—
377C3×Dic3—41no—
378C3×Dic3—42no—
379C3×Dic3AGL(1,ℤ/8)12yescomplemented
380C2×#41—31no—
381C2×#41C2×C3×D311yescharacteristic
382C22×D4C2×C3×D311yescharacteristic
383C23×C4—61no—
384AGL(1,ℤ/8)—24no—
385AGL(1,ℤ/8)—64no—
386C2×SD16—32no—
387C2×SD16C2×C3×D312yes—
388C2×D8—32no—
389C2×D8C2×C3×D312yes—
390C2×M16—31no—
391C2×M16C2×C3×D311yescharacteristic
392C4⋊Q8—31no—
393#127—31no—
394#124—31no—
395#124—31no—
396#121—61no—
397#121—61no—
398C4×D4—32no—
399C4×D4—32no—
400C4×D4—61no—
401C4×D4—61no—
402C4×D4—61no—
403C4×D4—61no—
404C2×C4⋊C4—31no—
405C2×C22⋊C4—61no—
406C2×C42—31no—
407C4⋊C8—32no—
408C4⋊C8—32no—
409#103—32no—
410#103—32no—
411#102—32no—
412#102—32no—
413C23×C3—24no—
414C23×C3—24no—
415C23×C3—22no—
416C23×C3—22no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—41no—
421C23×C3—44no—
422C23×C3—42no—
423C23×C3—42no—
424C23×C3—42no—
425C23×C3—42no—
426C23×C3—42no—
427C23×C3—61no—
428C23×C3—82no—
429C23×C3—82no—
430C23×C3D3×D411yescharacteristic
431C23×C3C2×C3×D411yescharacteristic
432C22×D3—21no—
433C3×Q8—22no—
434C3×Q8—21no—
435C3×Q8—21no—
436C3×Q8—21no—
437C3×Q8—21no—
438C3×Q8—41no—
439C3×Q8—61no—
440C3×Q8—61no—
441C3×D4—22no—
442C3×D4—24no—
443C3×D4—24no—
444C3×D4—22no—
445C3×D4—21no—
446C3×D4—21no—
447C3×D4—21no—
448C3×D4—22no—
449C3×D4—21no—
450C3×D4—24no—
451C3×D4—44no—
452C3×D4—42no—
453C3×D4—41no—
454C3×D4—44no—
455C3×D4—42no—
456C3×D4—42no—
457C3×D4—61no—
458C3×D4—61no—
459C3×D4—122no—
460C3×D4—122no—
461C3×D4—122no—
462C3×D4C2×#6714yes—
463C3×D4C2×C3×D414yes—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—31no—
471C2×C3×C4—31no—
472C2×C3×C4—31no—
473C2×C3×C4—31no—
474C2×C3×C4—41no—
475C2×C3×C4—44no—
476C2×C3×C4—42no—
477C2×C3×C4—42no—
478C2×C3×C4—62no—
479C2×C3×C4—62no—
480C2×C3×C4—61no—
481C2×C3×C4—124no—
482C2×C3×C4—121no—
483C2×C3×C4—124no—
484C2×C3×C4—122no—
485C2×C3×C4—122no—
486C2×C3×C4D3×D411yescharacteristic
487C2×C3×C4#23712yes—
488C2×C3×C4C2×#6712yes—
489C2×C3×C4C2×C3×D411yescharacteristic
490C2×C3×C4C2×C3×D412yes—
491C2×C3×C4C3×#4112yes—
492C2×C3×C4C23×D311yescharacteristic
493C2×C3×C4C24×C311yescharacteristic
494#67—42no—
495#67—42no—
496#67—42no—
497C2×Dic3—22no—
498C2×Dic3—21no—
499C2×Dic3—22no—
500C2×Dic3—41no—
501C2×Dic3—44no—
502C2×Dic3—42no—
503C2×Dic3—44no—
504C2×Dic3C2×C3×D411yescharacteristic
505C2×Dic3C2×C3×D411yescharacteristic
506C2×Dic3C2×C3×D411yescharacteristic
507C2×Dic3C2×C3×D411yescharacteristic
508D12—21no—
509D12—21no—
510C4×D3—42no—
511Dic6—21no—
512Dic6—21no—
513C3×C8—24no—
514C3×C8—22no—
515C3×C8—22no—
516C3×C8—62no—
517C3⋊C8—22no—
518C2×C32—22no—
519C2×C32—44no—
520C2×C32—81no—
521C2×C32C2×#12111yescharacteristic
522C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
523C2×C32#57511yescharacteristic
524C3×D3—81no—
525C24—21no—
526#41—22no—
527#41—22no—
528#41—62no—
529#41—62no—
530C2×Q8—31no—
531C2×Q8C22×C3×D311yescharacteristic
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—22no—
535C2×D4—31no—
536C2×D4—61no—
537C2×D4—61no—
538C2×D4—61no—
539C2×D4C3×#6714yescomplemented
540C2×D4C22×C3×D311yescharacteristic
541C2×D4C22×C3×D312yes—
542C22×C4—21no—
543C22×C4—31no—
544C22×C4—31no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—124no—
550C22×C4C22×C3×D311yescharacteristic
551SD16—24no—
552SD16—64no—
553D8—24no—
554D8—64no—
555M16—22no—
556M16—62no—
557C2×C8—32no—
558C2×C8C22×C3×D312yes—
559C4⋊C4—32no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C22⋊C4—61no—
564C22⋊C4—61no—
565C22⋊C4—62no—
566C22⋊C4—62no—
567C22⋊C4—61no—
568C22⋊C4—61no—
569C42—31no—
570C42—31no—
571C42—31no—
572C42—31no—
573C22×C3—21no—
574C22×C3—21no—
575C22×C3—21no—
576C22×C3—21no—
577C22×C3—24no—
578C22×C3—24no—
579C22×C3—22no—
580C22×C3—21no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—44no—
584C22×C3—48no—
585C22×C3—48no—
586C22×C3—42no—
587C22×C3—42no—
588C22×C3—42no—
589C22×C3—42no—
590C22×C3—42no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3—41no—
597C22×C3—82no—
598C22×C3—82no—
599C22×C3—81no—
600C22×C3—81no—
601C22×C3—88no—
602C22×C3—121no—
603C22×C3—121no—
604C22×C3—121no—
605C22×C3#93912yes—
606C22×C3C3×#12112yes—
607C22×C3C2×D3×D411yescharacteristic
608C22×C3C22×C3×D411yescharacteristic
609C2×D3—41no—
610C2×D3—41no—
611C2×D3—41no—
612C3×C4—22no—
613C3×C4—21no—
614C3×C4—21no—
615C3×C4—32no—
616C3×C4—42no—
617C3×C4—41no—
618C3×C4—41no—
619C3×C4—61no—
620C3×C4—61no—
621C3×C4—61no—
622C3×C4—122no—
623C3×C4—121no—
624C3×C4#93912yes—
625C3×C4C3×#12112yes—
626C3×C4C2×#23711yescharacteristic
627C3×C4C22×#6711yescharacteristic
628C3×C4C22×C3×D411yescharacteristic
629C3×C4C2×C3×#4111yescharacteristic
630Dic3—21no—
631Dic3—21no—
632Dic3—21no—
633Dic3—42no—
634Dic3—41no—
635Dic3C3×AGL(1,ℤ/8)12yescomplemented
636C32#303611yescharacteristic, complemented, Sylow
637C23—24no—
638C23—22no—
639C23—21no—
640C23—42no—
641C23—42no—
642C23—61no—
643C23C3×D3×D411yescharacteristic
644Q8—21no—
645Q8—21no—
646Q8—61no—
647Q8—61no—
648D4—24no—
649D4—22no—
650D4—21no—
651D4—21no—
652D4—42no—
653D4—61no—
654D4—61no—
655D4—122no—
656D4—122no—
657D4—122no—
658D4C2×C3×#6714yes—
659C2×C4—21no—
660C2×C4—31no—
661C2×C4—31no—
662C2×C4—31no—
663C2×C4—31no—
664C2×C4—42no—
665C2×C4—62no—
666C2×C4—62no—
667C2×C4—61no—
668C2×C4—124no—
669C2×C4—121no—
670C2×C4—124no—
671C2×C4—122no—
672C2×C4—122no—
673C2×C4C3×D3×D411yescharacteristic
674C2×C4C3×#23712yes—
675C2×C4C2×C3×#6712yes—
676C2×C4C23×C3×D311yescharacteristic
677C8—22no—
678C8—62no—
679C2×C3—22no—
680C2×C3—22no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—42no—
685C2×C3—44no—
686C2×C3—44no—
687C2×C3—84no—
688C2×C3—82no—
689C2×C3—81no—
690C2×C3—81no—
691C2×C3—241no—
692C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
693C2×C3#577311yescharacteristic
694C2×C3C2×#93911yescharacteristic
695C2×C3C2×C3×#12111yescharacteristic
696C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
697C2×C3C3×#57511yescharacteristic
698D3—81no—
699C22—21no—
700C22—21no—
701C22—24no—
702C22—48no—
703C22—42no—
704C22—42no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—121no—
709C22—121no—
710C22—121no—
711C22C3×#93912yes—
712C22C2×C3×D3×D411yescharacteristic
713C4—32no—
714C4—41no—
715C4—61no—
716C4—61no—
717C4—61no—
718C4—122no—
719C4—121no—
720C4C3×#93912yes—
721C4C2×C3×#23711yescharacteristic
722C4C22×C3×#6711yescharacteristic
723C3—21no—
724C3#8393111yescharacteristic, direct product factor
725C3C3×#303611yescharacteristic, complemented
726C2—22no—
727C2—44no—
728C2—81no—
729C2—241no—
730C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
731C2C3×#577311yescharacteristic
732C2C2×C3×#93911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×AGL(1,ℤ/8)C2
socleC22×C32C22×D4
hypercenterC2×C3×AGL(1,ℤ/8)D3
hypocenterC3C3×#3036
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×C32×AGL(1,ℤ/8)C2semidirect
2. C3×#5832C2semidirect
3. C2×C3×D4×Dic3C2semidirect
4. C2×C3×#932C2semidirect
5. C3×#5232C2semidirect
6. C3×#5165C2semidirect
7. C3×#5162C2semidirect
8. C3×#5153C2semidirect
9. C3×#5150C2semidirect
10. C3×#5133C2semidirect
11. C3×#5118C2semidirect
13. #83931C3direct (N × H)
23. C3×#947C22semidirect
24. C3×#944C22semidirect
25. C3×#940C22semidirect
28. C3×#936C22semidirect
41. C3×#835C22semidirect
42. C3×#832C22semidirect
43. C3×#821C22semidirect
44. C3×#816C22semidirect
45. C3×Dic3⋊C8C22semidirect
46. C3×Dic3⋊C8C22semidirect
49. C2×C3×AGL(1,ℤ/8)D3semidirect
50. C2×C3×AGL(1,ℤ/8)C2×C3semidirect
53. #5832C2×C3semidirect
54. C2×D4×Dic3C2×C3semidirect
55. C2×#932C2×C3semidirect
63. #5232C2×C3semidirect
64. #5165C2×C3semidirect
65. #5162C2×C3semidirect
66. #5153C2×C3semidirect
67. #5150C2×C3semidirect
68. #5133C2×C3semidirect
69. #5118C2×C3semidirect
77. C2×C32×D4D4semidirect
161. #947C22×C3semidirect
162. #944C22×C3semidirect
163. #940C22×C3semidirect
166. #936C22×C3semidirect
185. #835C22×C3semidirect
186. #832C22×C3semidirect
187. #821C22×C3semidirect
188. #816C22×C3semidirect
189. Dic3⋊C8C22×C3semidirect
190. Dic3⋊C8C22×C3semidirect
234. C2×AGL(1,ℤ/8)C3×D3semidirect
275. C2×C3×D4#67semidirect
276. C2×C3×D4C3×D4semidirect
379. C3×Dic3AGL(1,ℤ/8)semidirect
539. C2×D4C3×#67semidirect
635. Dic3C3×AGL(1,ℤ/8)semidirect
636. C32#3036semidirect
724. C3#83931direct (N × H)
725. C3C3×#3036semidirect

Maximal subgroups

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

subgroupindex
C2×C32×AGL(1,ℤ/8)2
C3×#58322
C2×C3×D4×Dic32
C2×C3×#9322
C3×#52322
C3×#51652
C3×#51622
C3×#51532
C3×#51502
C3×#51332
C3×#51182
C3×#30363
#839313