Finite Group Databasebeta

← C3×#83950 #11867108

Subgroups — C3×#83950 #11867108

Order 1152.

1245 conjugacy classes of subgroups.

The subgroup lattice has 758 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×#5828C211yesmaximal, characteristic, complemented
3C2×C3×#938C211yesmaximal, characteristic, complemented
4C2×C3×D3×M16C211yesmaximal, characteristic, complemented
5C3×#5232C211yesmaximal, characteristic, complemented
6C3×#5215C211yesmaximal, characteristic, complemented
7C3×#5174C212yesmaximal, complemented
8C3×#5171C212yesmaximal, complemented
9C3×#5159C212yesmaximal, complemented
10C3×#5157C212yesmaximal, complemented
11C3×#5121C211yesmaximal, characteristic, complemented
12C3×#3055—31nomaximal
13#83950C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C22×C32×D4C2211yescharacteristic
16C22×C3×#67—21no—
17C22×C3×C4×D3C2211yescharacteristic
18C32×AGL(1,ℤ/8)—24no—
19C2×C32×SD16C2212yescomplemented
20C2×C32×D8C2212yescomplemented
21C2×C32×M16C2211yescharacteristic
22C2×C3×#217—21no—
23C3×#946C2211yescharacteristic, complemented
24C3×#946C2211yescharacteristic, complemented
25C3×#938—21no—
26C3×#938—21no—
27C3×#938C2212yes—
28C3×#938C2212yes—
29C3×#938C2211yescharacteristic, complemented
30C3×#938C2211yescharacteristic, complemented
31C3×#937—21no—
32C3×#935—21no—
33C3×C4×#67—21no—
34C3×C4×#67—21no—
35C3×#926C2211yescharacteristic
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C2×C3×#208C2211yescharacteristic
38C3×D3×M16—24no—
39C2×C3×ΓL(1,𝔽25)C2212yescomplemented
40C2×C3×D3×C8C2212yescomplemented
41C3×#835C2212yescomplemented
42C3×#832C2212yescomplemented
43C3×#832C2212yescomplemented
44C3×#832C2212yescomplemented
45C3×#818C2212yescomplemented
46C3×#817C2212yescomplemented
47C2×C3×AGL(1,ℤ/8)—21no—
48C2×C3×AGL(1,ℤ/8)D311yescharacteristic, complemented
49C2×C3×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
50C22×C3×M16—31no—
51C3×#525—31no—
52C2×C3×#121—31no—
53#5828C2×C311yescharacteristic, complemented
54C2×#938C2×C311yescharacteristic, complemented
55C2×D3×M16C2×C311yescharacteristic, complemented
56C3×#469—32no—
57C3×#468—32no—
58C3×#466—32no—
59C3×#465—32no—
60C3×#428—31no—
61C3×#418—31no—
62C3×#417—31no—
63#5232C2×C311yescharacteristic, complemented
64#5215C2×C311yescharacteristic, complemented
65#5174C2×C312yescomplemented
66#5171C2×C312yescomplemented
67#5159C2×C312yescomplemented
68#5157C2×C312yescomplemented
69#5121C2×C311yescharacteristic, complemented
70C24×C32—21no—
71C23×C3×D3D411yescharacteristic
72C32×#41—22no—
73C32×#41—22no—
74C2×C32×Q8C2311yescharacteristic
75C2×C32×D4—21no—
76C2×C32×D4—22no—
77C2×C32×D4—21no—
78C2×C32×D4—22no—
79C2×C32×D4C2312yes—
80C2×C32×D4C2311yescharacteristic
81C22×C32×C4—21no—
82C22×C32×C4C2311yescharacteristic
83C2×C3×#67—21no—
84C2×C3×#67—21no—
85C2×C3×#67—22no—
86C2×C3×#67—22no—
87C2×C3×#67—44no—
88C22×C3×Dic3—21no—
89C22×C3×Dic3D411yescharacteristic
90C2×C3×C4×D3—22no—
91C2×C3×C4×D3—22no—
92C2×C3×C4×D3D411yescharacteristic
93C2×C3×C4×D3D411yescharacteristic
94C2×C3×C4×D3C2311yescharacteristic
95C2×C3×C4×D3C2311yescharacteristic
96C32×SD16—24no—
97C32×D8—24no—
98C32×M16D414yescomplemented
99C2×C32×C8C2312yes—
100C3×#217—21no—
101C3×#217—21no—
102C3×#217—21no—
103C3×#217—22no—
104C3×#217—22no—
105C3×(C2×D3)⋊C4—21no—
106C3×(C2×D3)⋊C4—21no—
107C3×C4⋊Dic3—21no—
108C3×C4⋊Dic3C2312yes—
109C3×C4⋊Dic3C2311yescharacteristic
110C3×C4⋊Dic3C2311yescharacteristic
111C3×Dic3⋊C4—21no—
112C3×Dic3⋊C4—21no—
113C3×C4×Dic3—21no—
114C3×#208—22no—
115C2×C3×C3⋊C8C2312yes—
116C3×ΓL(1,𝔽25)—24no—
117C3×D3×C8—24no—
118#3055—31noSylow
119C2×C3×#41—21no—
120C2×C3×#41C2×D311yescharacteristic
121C2×C3×#41C22×C311yescharacteristic
122C22×C3×D4—21no—
123C22×C3×D4—61no—
124C22×C3×D4C2×D311yescharacteristic
125C22×C3×D4C22×C311yescharacteristic
126C23×C3×C4—31no—
127C22×#67—21no—
128C22×C4×D3C22×C311yescharacteristic
129C3×AGL(1,ℤ/8)—28no—
130C3×AGL(1,ℤ/8)—24no—
131C3×AGL(1,ℤ/8)—24no—
132C2×C3×SD16—22no—
133C2×C3×SD16C2×D312yescomplemented
134C2×C3×SD16C22×C312yescomplemented
135C2×C3×D8—22no—
136C2×C3×D8C2×D312yescomplemented
137C2×C3×D8C22×C312yescomplemented
138C2×C3×M16—21no—
139C2×C3×M16—31no—
140C2×C3×M16—32no—
141C2×C3×M16—64no—
142C2×C3×M16C2×D311yescharacteristic
143C2×C3×M16C22×C311yescharacteristic
144C22×C3×C8—32no—
145C3×#123—61no—
146C3×C22⋊Q8—31no—
147C3×C22⋊Q8—31no—
148C3×#121—32no—
149C3×#121—32no—
150C3×#121—31no—
151C3×#121—31no—
152C3×#121—61no—
153C3×#121—61no—
154C3×#120—61no—
155C3×C4×D4—61no—
156C3×C4×D4—61no—
157C3×#117—31no—
158C2×C3×C4⋊C4—31no—
159C2×C3×C22⋊C4—61no—
160C2×#217—21no—
161#946C22×C311yescharacteristic, complemented
162#946C22×C311yescharacteristic, complemented
163#938—21no—
164#938—21no—
165#938C22×C312yes—
166#938C22×C312yes—
167#938C22×C311yescharacteristic, complemented
168#938C22×C311yescharacteristic, complemented
169#937—21no—
170#935—21no—
171C4×#67—21no—
172C4×#67—21no—
173#926C22×C311yescharacteristic
174C2×C4⋊Dic3C22×C311yescharacteristic
175C2×#208C22×C311yescharacteristic
176D3×M16—24no—
177C2×ΓL(1,𝔽25)C22×C312yescomplemented
178C2×D3×C8C22×C312yescomplemented
179C3×#107—32no—
180C3×#106—32no—
181C3×#103—32no—
182C3×#102—32no—
183C3×#102—32no—
184C3×#102—32no—
185#835C22×C312yescomplemented
186#832C22×C312yescomplemented
187#832C22×C312yescomplemented
188#832C22×C312yescomplemented
189#818C22×C312yescomplemented
190#817C22×C312yescomplemented
191C23×C32—22no—
192C23×C32—21no—
193C23×C32—42no—
194C23×C32—42no—
195C23×C32—42no—
196C23×C32C2×D411yescharacteristic
197C22×C3×D3—22no—
198C22×C3×D3—22no—
199C22×C3×D3—41no—
200C22×C3×D3C2×D411yescharacteristic
201C22×C3×D3C2×D411yescharacteristic
202C32×Q8—21no—
203C32×Q8—21no—
204C32×D4—21no—
205C32×D4—22no—
206C32×D4—22no—
207C32×D4—21no—
208C32×D4—42no—
209C32×D4—42no—
210C2×C32×C4—21no—
211C2×C32×C4—42no—
212C2×C32×C4C2×D411yescharacteristic
213C2×C32×C4C2×D412yes—
214C2×C32×C4#4112yes—
215C2×C32×C4C2411yescharacteristic
216C3×#67—42no—
217C3×#67—44no—
218C3×#67—42no—
219C3×#67—44no—
220C2×C3×Dic3—22no—
221C2×C3×Dic3—21no—
222C2×C3×Dic3—21no—
223C2×C3×Dic3—22no—
224C2×C3×Dic3—42no—
225C2×C3×Dic3C2×D411yescharacteristic
226C2×C3×Dic3C2×D411yescharacteristic
227C3×C4×D3—22no—
228C3×C4×D3—22no—
229C3×C4×D3—21no—
230C3×C4×D3—21no—
231C3×C4×D3—21no—
232C3×C4×D3—21no—
233C32×C8C2×D414yescomplemented
234C3×C3⋊C8—22no—
235C2×AGL(1,ℤ/8)C3×D311yescharacteristic, complemented
236C22×M16—31no—
237#525—31no—
238C2×#121—31no—
239#469—32no—
240#468—32no—
241#466—32no—
242#465—32no—
243#428—31no—
244#418—31no—
245#417—31no—
246C24×C3—21no—
247C24×C3—21no—
248C24×C3—31no—
249C24×C3—41no—
250C23×D3C3×D411yescharacteristic
251C3×#41—24no—
252C3×#41—22no—
253C3×#41—22no—
254C3×#41—22no—
255C3×#41—22no—
256C3×#41—42no—
257C2×C3×Q8—21no—
258C2×C3×Q8C22×D311yescharacteristic
259C2×C3×Q8C23×C311yescharacteristic
260C2×C3×D4—24no—
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4—22no—
265C2×C3×D4—22no—
266C2×C3×D4—22no—
267C2×C3×D4—21no—
268C2×C3×D4—22no—
269C2×C3×D4—21no—
270C2×C3×D4—22no—
271C2×C3×D4—41no—
272C2×C3×D4—42no—
273C2×C3×D4—41no—
274C2×C3×D4—61no—
275C2×C3×D4—61no—
276C2×C3×D4—62no—
277C2×C3×D4—62no—
278C2×C3×D4—124no—
279C2×C3×D4C22×D311yescharacteristic
280C2×C3×D4C22×D312yes—
281C2×C3×D4C23×C312yes—
282C2×C3×D4C23×C311yescharacteristic
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—41no—
292C22×C3×C4—62no—
293C22×C3×C4—62no—
294C22×C3×C4—61no—
295C22×C3×C4C22×D311yescharacteristic
296C22×C3×C4C23×C311yescharacteristic
297C2×#67—21no—
298C2×#67—21no—
299C2×#67—22no—
300C2×#67—22no—
301C2×#67—44no—
302C22×Dic3—21no—
303C22×Dic3C3×D411yescharacteristic
304C2×C4×D3—22no—
305C2×C4×D3—22no—
306C2×C4×D3C3×D411yescharacteristic
307C2×C4×D3C3×D411yescharacteristic
308C2×C4×D3C23×C311yescharacteristic
309C2×C4×D3C23×C311yescharacteristic
310C3×SD16—28no—
311C3×SD16—24no—
312C3×SD16—24no—
313C3×D8—28no—
314C3×D8—24no—
315C3×D8—24no—
316C3×M16—24no—
317C3×M16—62no—
318C3×M16—64no—
319C3×M16#6714yescomplemented
320C3×M16C3×D414yescomplemented
321C2×C3×C8—22no—
322C2×C3×C8—32no—
323C2×C3×C8—64no—
324C2×C3×C8C22×D312yes—
325C2×C3×C8C23×C312yes—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—32no—
329C3×C4⋊C4—61no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—61no—
332C3×C22⋊C4—61no—
333C3×C22⋊C4—61no—
334C3×C22⋊C4—62no—
335C3×C22⋊C4—62no—
336C3×C22⋊C4—61no—
337C3×C22⋊C4—61no—
338C3×C22⋊C4—61no—
339C3×C42—61no—
340#217—21no—
341#217—21no—
342#217—21no—
343#217—22no—
344#217—22no—
345(C2×D3)⋊C4—21no—
346(C2×D3)⋊C4—21no—
347C4⋊Dic3—21no—
348C4⋊Dic3C23×C311yescharacteristic
349C4⋊Dic3C23×C312yes—
350C4⋊Dic3C23×C311yescharacteristic
351Dic3⋊C4—21no—
352Dic3⋊C4—21no—
353C4×Dic3—21no—
354#208—22no—
355C2×C3⋊C8C23×C312yes—
356ΓL(1,𝔽25)—24no—
357D3×C8—24no—
358C22×C32—21no—
359C22×C32—21no—
360C22×C32—41no—
361C22×C32—42no—
362C22×C32—42no—
363C22×C32—41no—
364C22×C32—41no—
365C22×C32—42no—
366C22×C32—84no—
367C22×C32#12112yes—
368C22×C32C22×D411yescharacteristic
369C2×C3×D3—21no—
370C2×C3×D3—21no—
371C2×C3×D3—21no—
372C2×C3×D3—21no—
373C2×C3×D3—21no—
374C2×C3×D3—44no—
375C2×C3×D3AGL(1,ℤ/8)12yescomplemented
376C32×C4—41no—
377C32×C4#12112yes—
378C32×C4C22×D411yescharacteristic
379C32×C4C2×#4111yescharacteristic
380C3×Dic3—21no—
381C3×Dic3—21no—
382C3×Dic3—42no—
383C3×Dic3—41no—
384C3×Dic3—41no—
385C2×#41C2×C3×D311yescharacteristic
386C22×D4—61no—
387C22×D4C2×C3×D311yescharacteristic
388C23×C4—31no—
389AGL(1,ℤ/8)—24no—
390C2×SD16C2×C3×D312yescomplemented
391C2×D8C2×C3×D312yescomplemented
392C2×M16—31no—
393C2×M16—32no—
394C2×M16—64no—
395C2×M16C2×C3×D311yescharacteristic
396C22×C8—32no—
397#123—61no—
398C22⋊Q8—31no—
399C22⋊Q8—31no—
400#121—32no—
401#121—32no—
402#121—31no—
403#121—31no—
404#121—61no—
405#121—61no—
406#120—61no—
407C4×D4—61no—
408C4×D4—61no—
409#117—31no—
410C2×C4⋊C4—31no—
411C2×C22⋊C4—61no—
412#107—32no—
413#106—32no—
414#103—32no—
415#102—32no—
416#102—32no—
417#102—32no—
418C23×C3—21no—
419C23×C3—22no—
420C23×C3—21no—
421C23×C3—22no—
422C23×C3—21no—
423C23×C3—31no—
424C23×C3—31no—
425C23×C3—41no—
426C23×C3—42no—
427C23×C3—42no—
428C23×C3—44no—
429C23×C3—42no—
430C23×C3—42no—
431C23×C3—42no—
432C23×C3—42no—
433C23×C3—42no—
434C23×C3—62no—
435C23×C3—62no—
436C23×C3—82no—
437C23×C3—82no—
438C23×C3—121no—
439C23×C3D3×D411yescharacteristic
440C23×C3C2×C3×D411yescharacteristic
441C22×D3—22no—
442C22×D3—22no—
443C22×D3—41no—
444C22×D3C2×C3×D411yescharacteristic
445C22×D3C2×C3×D411yescharacteristic
446C3×Q8—22no—
447C3×Q8—21no—
448C3×Q8—21no—
449C3×Q8—21no—
450C3×Q8—21no—
451C3×Q8—41no—
452C3×D4—22no—
453C3×D4—24no—
454C3×D4—22no—
455C3×D4—21no—
456C3×D4—21no—
457C3×D4—22no—
458C3×D4—21no—
459C3×D4—22no—
460C3×D4—22no—
461C3×D4—21no—
462C3×D4—42no—
463C3×D4—41no—
464C3×D4—44no—
465C3×D4—44no—
466C3×D4—42no—
467C3×D4—42no—
468C3×D4—42no—
469C3×D4—42no—
470C3×D4—122no—
471C3×D4—124no—
472C3×D4—122no—
473C3×D4—124no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—31no—
481C2×C3×C4—31no—
482C2×C3×C4—41no—
483C2×C3×C4—44no—
484C2×C3×C4—42no—
485C2×C3×C4—42no—
486C2×C3×C4—62no—
487C2×C3×C4—62no—
488C2×C3×C4—62no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—62no—
496C2×C3×C4—122no—
497C2×C3×C4D3×D411yescharacteristic
498C2×C3×C4#23712yes—
499C2×C3×C4C2×#6712yes—
500C2×C3×C4C2×C3×D411yescharacteristic
501C2×C3×C4C2×C3×D412yes—
502C2×C3×C4C3×#4112yes—
503C2×C3×C4C23×D311yescharacteristic
504C2×C3×C4C24×C311yescharacteristic
505#67—42no—
506#67—44no—
507#67—42no—
508#67—44no—
509C2×Dic3—22no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—22no—
513C2×Dic3—42no—
514C2×Dic3C2×C3×D411yescharacteristic
515C2×Dic3C2×C3×D411yescharacteristic
516C4×D3—22no—
517C4×D3—22no—
518C4×D3—21no—
519C4×D3—21no—
520C4×D3—21no—
521C4×D3—21no—
522C3×C8—24no—
523C3×C8—62no—
524C3×C8C2×#6714yescomplemented
525C3×C8C2×C3×D414yescomplemented
526C3⋊C8—22no—
527C2×C32—22no—
528C2×C32—81no—
529C2×C32—82no—
530C2×C32C2×#12111yescharacteristic
531C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
532C2×C32#57511yescharacteristic
533C3×D3—22no—
534C3×D3—41no—
535C24—21no—
536C24—31no—
537#41—22no—
538#41—22no—
539C2×Q8C22×C3×D311yescharacteristic
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—61no—
545C2×D4—61no—
546C2×D4—62no—
547C2×D4—62no—
548C2×D4—124no—
549C2×D4C22×C3×D311yescharacteristic
550C2×D4C22×C3×D312yes—
551C22×C4—21no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—31no—
556C22×C4—31no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4—61no—
560C22×C4C22×C3×D311yescharacteristic
561SD16—24no—
562D8—24no—
563M16—62no—
564M16—64no—
565M16C3×#6714yescomplemented
566C2×C8—32no—
567C2×C8—64no—
568C2×C8C22×C3×D312yes—
569C4⋊C4—31no—
570C4⋊C4—31no—
571C4⋊C4—32no—
572C4⋊C4—61no—
573C4⋊C4—61no—
574C4⋊C4—61no—
575C22⋊C4—61no—
576C22⋊C4—61no—
577C22⋊C4—62no—
578C22⋊C4—62no—
579C22⋊C4—61no—
580C22⋊C4—61no—
581C22⋊C4—61no—
582C42—61no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—22no—
588C22×C3—21no—
589C22×C3—32no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—42no—
593C22×C3—44no—
594C22×C3—42no—
595C22×C3—41no—
596C22×C3—41no—
597C22×C3—42no—
598C22×C3—42no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—42no—
602C22×C3—41no—
603C22×C3—42no—
604C22×C3—41no—
605C22×C3—42no—
606C22×C3—61no—
607C22×C3—61no—
608C22×C3—61no—
609C22×C3—61no—
610C22×C3—61no—
611C22×C3—82no—
612C22×C3—82no—
613C22×C3—81no—
614C22×C3—81no—
615C22×C3—84no—
616C22×C3—84no—
617C22×C3—88no—
618C22×C3—124no—
619C22×C3#93812yes—
620C22×C3C3×#12112yes—
621C22×C3C2×D3×D411yescharacteristic
622C22×C3C22×C3×D411yescharacteristic
623C2×D3—21no—
624C2×D3—21no—
625C2×D3—21no—
626C2×D3—21no—
627C2×D3—21no—
628C2×D3—44no—
629C2×D3C3×AGL(1,ℤ/8)12yescomplemented
630C3×C4—22no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—42no—
634C3×C4—41no—
635C3×C4—41no—
636C3×C4—61no—
637C3×C4—61no—
638C3×C4—122no—
639C3×C4—121no—
640C3×C4—121no—
641C3×C4#93812yes—
642C3×C4C3×#12112yes—
643C3×C4C2×#23711yescharacteristic
644C3×C4C22×#6711yescharacteristic
645C3×C4C22×C3×D411yescharacteristic
646C3×C4C2×C3×#4111yescharacteristic
647Dic3—21no—
648Dic3—21no—
649Dic3—42no—
650Dic3—41no—
651Dic3—41no—
652C32#305511yescharacteristic, complemented, Sylow
653C23—21no—
654C23—22no—
655C23—31no—
656C23—31no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—62no—
661C23—62no—
662C23—121no—
663C23C3×D3×D411yescharacteristic
664Q8—21no—
665Q8—21no—
666D4—22no—
667D4—21no—
668D4—21no—
669D4—22no—
670D4—42no—
671D4—42no—
672D4—124no—
673D4—122no—
674D4—124no—
675D4—122no—
676C2×C4—21no—
677C2×C4—31no—
678C2×C4—31no—
679C2×C4—42no—
680C2×C4—62no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—62no—
690C2×C4—122no—
691C2×C4C3×D3×D411yescharacteristic
692C2×C4C3×#23712yes—
693C2×C4C2×C3×#6712yes—
694C2×C4C23×C3×D311yescharacteristic
695C8—62no—
696C8C2×C3×#6714yescomplemented
697C2×C3—22no—
698C2×C3—22no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—42no—
703C2×C3—62no—
704C2×C3—84no—
705C2×C3—82no—
706C2×C3—82no—
707C2×C3—81no—
708C2×C3—82no—
709C2×C3—81no—
710C2×C3—121no—
711C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
712C2×C3#577311yescharacteristic
713C2×C3C2×#93811yescharacteristic
714C2×C3C2×C3×#12111yescharacteristic
715C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
716C2×C3C3×#57511yescharacteristic
717D3—22no—
718D3—41no—
719C22—21no—
720C22—21no—
721C22—32no—
722C22—42no—
723C22—41no—
724C22—41no—
725C22—42no—
726C22—41no—
727C22—42no—
728C22—61no—
729C22—61no—
730C22—61no—
731C22—61no—
732C22—61no—
733C22—84no—
734C22—124no—
735C22C3×#93812yes—
736C22C2×C3×D3×D411yescharacteristic
737C4—41no—
738C4—61no—
739C4—61no—
740C4—122no—
741C4—121no—
742C4—121no—
743C4C3×#93812yes—
744C4C2×C3×#23711yescharacteristic
745C4C22×C3×#6711yescharacteristic
746C3—21no—
747C3#8395011yescharacteristic, direct product factor
748C3C3×#305511yescharacteristic, complemented
749C2—22no—
750C2—62no—
751C2—82no—
752C2—81no—
753C2—121no—
754C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
755C2C3×#577311yescharacteristic
756C2C2×C3×#93811yescharacteristic
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×#3055
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×#5828C2semidirect
3. C2×C3×#938C2semidirect
4. C2×C3×D3×M16C2semidirect
5. C3×#5232C2semidirect
6. C3×#5215C2semidirect
7. C3×#5174C2semidirect
8. C3×#5171C2semidirect
9. C3×#5159C2semidirect
10. C3×#5157C2semidirect
11. C3×#5121C2semidirect
13. #83950C3direct (N × H)
19. C2×C32×SD16C22semidirect
20. C2×C32×D8C22semidirect
23. C3×#946C22semidirect
24. C3×#946C22semidirect
29. C3×#938C22semidirect
30. C3×#938C22semidirect
39. C2×C3×ΓL(1,𝔽25)C22semidirect
40. C2×C3×D3×C8C22semidirect
41. C3×#835C22semidirect
42. C3×#832C22semidirect
43. C3×#832C22semidirect
44. C3×#832C22semidirect
45. C3×#818C22semidirect
46. C3×#817C22semidirect
48. C2×C3×AGL(1,ℤ/8)D3semidirect
49. C2×C3×AGL(1,ℤ/8)C2×C3semidirect
53. #5828C2×C3semidirect
54. C2×#938C2×C3semidirect
55. C2×D3×M16C2×C3semidirect
63. #5232C2×C3semidirect
64. #5215C2×C3semidirect
65. #5174C2×C3semidirect
66. #5171C2×C3semidirect
67. #5159C2×C3semidirect
68. #5157C2×C3semidirect
69. #5121C2×C3semidirect
98. C32×M16D4semidirect
133. C2×C3×SD16C2×D3semidirect
134. C2×C3×SD16C22×C3semidirect
136. C2×C3×D8C2×D3semidirect
137. C2×C3×D8C22×C3semidirect
161. #946C22×C3semidirect
162. #946C22×C3semidirect
167. #938C22×C3semidirect
168. #938C22×C3semidirect
177. C2×ΓL(1,𝔽25)C22×C3semidirect
178. C2×D3×C8C22×C3semidirect
185. #835C22×C3semidirect
186. #832C22×C3semidirect
187. #832C22×C3semidirect
188. #832C22×C3semidirect
189. #818C22×C3semidirect
190. #817C22×C3semidirect
233. C32×C8C2×D4semidirect
235. C2×AGL(1,ℤ/8)C3×D3semidirect
319. C3×M16#67semidirect
320. C3×M16C3×D4semidirect
375. C2×C3×D3AGL(1,ℤ/8)semidirect
390. C2×SD16C2×C3×D3semidirect
391. C2×D8C2×C3×D3semidirect
524. C3×C8C2×#67semidirect
525. C3×C8C2×C3×D4semidirect
565. M16C3×#67semidirect
629. C2×D3C3×AGL(1,ℤ/8)semidirect
652. C32#3055semidirect
696. C8C2×C3×#67semidirect
747. C3#83950direct (N × H)
748. C3C3×#3055semidirect

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×#58282
C2×C3×#9382
C2×C3×D3×M162
C3×#52322
C3×#52152
C3×#51742
C3×#51712
C3×#51592
C3×#51572
C3×#51212
C3×#30553
#839503