Finite Group Databasebeta

← C3×#80121 #11883922

Subgroups — C3×#80121 #11883922

Order 1152.

1173 conjugacy classes of subgroups.

The subgroup lattice has 941 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5831C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic, complemented
3C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
4C3×#5609C211yesmaximal, characteristic, complemented
5C32×#449C211yesmaximal, characteristic, complemented
6C3×#5163C211yesmaximal, characteristic, complemented
7C3×#5156C211yesmaximal, characteristic, complemented
8C3×#5154C211yesmaximal, characteristic, complemented
9C3×#5042C211yesmaximal, characteristic, complemented
10C3×#4817C211yesmaximal, characteristic, complemented
11C3×#4806C211yesmaximal, characteristic, complemented
12C3×#4787C211yesmaximal, characteristic, complemented
13C3×#4775C211yesmaximal, characteristic, complemented
14C3×#4731C211yesmaximal, characteristic, complemented
15C3×#4728C211yesmaximal, characteristic, complemented
16C3×#3265—31nomaximal
17#80121C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic, complemented
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C2×C3×D3×D4—21no—
21C2×C3×D3×D4C2211yescharacteristic
22C22×C3×D12C2211yescharacteristic
23C2×C32×SD16C2211yescharacteristic, complemented
24C2×C32×D8C2211yescharacteristic, complemented
25C32×#121C2211yescharacteristic
26C3×#949—24no—
27C3×Q8×Dic3C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic
29C2×C3×#215C2211yescharacteristic, complemented
30C3×#940C2211yescharacteristic
31C3×#938—21no—
32C3×#938C2211yescharacteristic, complemented
33C3×#937—21no—
34C3×#936—21no—
35C3×#936C2211yescharacteristic, complemented
36C2×C3×#214C2211yescharacteristic, complemented
37C2×C3×#213C2211yescharacteristic
38C2×C3×#213C2211yescharacteristic, complemented
39C3×C4×#67—21no—
40C3×C4×#67C2211yescharacteristic
41C3×#924—21no—
42C3×#924C2211yescharacteristic, complemented
43C2×C3×#208C2211yescharacteristic, complemented
44C3×D3×SD16—24no—
45C2×C3×#204C2211yescharacteristic
46C2×C3×#204C2211yescharacteristic, complemented
47C2×C3×D3×C8C2211yescharacteristic, complemented
48C3×#895C2211yescharacteristic
49C3×#893C2211yescharacteristic
50C3×#884—21no—
51C3×#882—21no—
52C32×#103C2211yescharacteristic, complemented
53C32×#102C2211yescharacteristic, complemented
54C32×C22⋊C8C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#815C2211yescharacteristic, complemented
60C3×Dic3⋊C8C2211yescharacteristic, complemented
61C3×#810C2211yescharacteristic, complemented
62C3×#807C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C22×C3×SD16—31no—
65C3×#548—31no—
66C3×D42—31no—
67#5831C2×C311yescharacteristic, complemented
68C2×#949C2×C311yescharacteristic, complemented
69C2×D3×SD16C2×C311yescharacteristic, complemented
70#5609C2×C311yescharacteristic, complemented
71C3×#496—31no—
72C3×#468—31no—
73C3×#466—31no—
74C3×#463—31no—
75C3×#460—31no—
76C3×#450—31no—
77C3×#449—21no—
78C3×#449D311yescharacteristic, complemented
79C3×#449C2×C311yescharacteristic, complemented
80C3×#448—31no—
81C3×#447—31no—
82C3×#440—31no—
83C3×#435—31no—
84#5163C2×C311yescharacteristic, complemented
85#5156C2×C311yescharacteristic, complemented
86#5154C2×C311yescharacteristic, complemented
87#5042C2×C311yescharacteristic, complemented
88#4817C2×C311yescharacteristic, complemented
89#4806C2×C311yescharacteristic, complemented
90#4787C2×C311yescharacteristic, complemented
91#4775C2×C311yescharacteristic, complemented
92#4731C2×C311yescharacteristic, complemented
93#4728C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C23×C3×D3—21no—
96C32×#41—22no—
97C32×#41—41no—
98C2×C32×Q8C2311yescharacteristic
99C2×C32×D4—21no—
100C2×C32×D4—21no—
101C2×C32×D4C2311yescharacteristic
102C2×C32×D4C2311yescharacteristic
103C22×C32×C4—21no—
104C22×C32×C4C2311yescharacteristic
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×#67D411yescharacteristic
110C3×D3×Q8—22no—
111C3×D3×Q8—41no—
112C3×D3×D4—22no—
113C3×D3×D4—41no—
114C3×D3×D4—44no—
115C2×C3×D12—22no—
116C2×C3×D12—21no—
117C2×C3×D12—21no—
118C2×C3×D12—41no—
119C2×C3×D12C2311yescharacteristic
120C2×C3×D12C2311yescharacteristic
121C2×C3×C4×D3—21no—
122C2×C3×C4×D3—21no—
123C2×C3×C4×D3C2311yescharacteristic
124C2×C3×Dic6—21no—
125C2×C3×Dic6C2311yescharacteristic
126C32×SD16—22no—
127C32×D8—41no—
128C2×C32×C8C2311yescharacteristic
129C2×C32×C8C2311yescharacteristic
130C32×C4⋊C4C2311yescharacteristic
131C32×C22⋊C4—21no—
132C3×#217—21no—
133C3×#217—21no—
134C3×#217—21no—
135C3×#217—21no—
136C3×#217D411yescharacteristic
137C3×#215—22no—
138C3×#215D414yescomplemented
139C3×#214—22no—
140C3×#213—22no—
141C3×#213—22no—
142C3×(C2×D3)⋊C4—21no—
143C3×(C2×D3)⋊C4—21no—
144C3×(C2×D3)⋊C4D411yescharacteristic
145C3×C4⋊Dic3—21no—
146C3×C4⋊Dic3C2311yescharacteristic
147C3×Dic3⋊C4—21no—
148C3×Dic3⋊C4D411yescharacteristic
149C3×C4×Dic3—21no—
150C3×C4×Dic3C2311yescharacteristic
151C3×#208—22no—
152C2×C3×C3⋊C8C2311yescharacteristic
153C2×C3×C3⋊C8C2311yescharacteristic
154C3×#204—22no—
155C3×#204—41no—
156C3×D3×C8—22no—
157#3265—31noSylow
158C2×C3×#41—21no—
159C2×C3×#41C2×D311yescharacteristic, complemented
160C2×C3×#41C22×C311yescharacteristic, complemented
161C22×C3×Q8—31no—
162C22×C3×D4—31no—
163C22×C3×D4—31no—
164C22×C3×D4—61no—
165C2×D3×Q8C22×C311yescharacteristic, complemented
166C2×D3×D4—21no—
167C2×D3×D4C22×C311yescharacteristic
168C22×D12C22×C311yescharacteristic
169C3×AGL(1,ℤ/8)—64no—
170C2×C3×SD16—21no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×SD16—31no—
174C2×C3×SD16—31no—
175C2×C3×SD16—31no—
176C2×C3×SD16—64no—
177C2×C3×SD16C2×D311yescharacteristic, complemented
178C2×C3×SD16C22×C311yescharacteristic, complemented
179C2×C3×D8—21no—
180C2×C3×D8—31no—
181C2×C3×D8—31no—
182C2×C3×D8C2×D311yescharacteristic, complemented
183C2×C3×D8C22×C311yescharacteristic, complemented
184C2×C3×M16—31no—
185C22×C3×C8—31no—
186C3×#127—31no—
187C3×#124—31no—
188C3×#124—61no—
189C3×C22⋊Q8—31no—
190C3×C22⋊Q8—61no—
191C3×#121—21no—
192C3×#121—31no—
193C3×#121—31no—
194C3×#121—61no—
195C3×#121—61no—
196C3×#121C2×D311yescharacteristic
197C3×#121C22×C311yescharacteristic
198C3×#120—61no—
199C3×#120—61no—
200C3×C4×Q8—31no—
201C3×C4×D4—31no—
202C3×C4×D4—31no—
203C3×C4×D4—61no—
204#949—24no—
205Q8×Dic3C22×C311yescharacteristic, complemented
206C2×#215C22×C311yescharacteristic
207C2×#215C22×C311yescharacteristic, complemented
208#940C22×C311yescharacteristic
209#938—21no—
210#938C22×C311yescharacteristic, complemented
211#937—21no—
212#936—21no—
213#936C22×C311yescharacteristic, complemented
214C2×#214C22×C311yescharacteristic, complemented
215C2×#213C22×C311yescharacteristic
216C2×#213C22×C311yescharacteristic, complemented
217C4×#67—21no—
218C4×#67C22×C311yescharacteristic
219#924—21no—
220#924C22×C311yescharacteristic, complemented
221C2×#208C22×C311yescharacteristic, complemented
222D3×SD16—24no—
223C2×#204C22×C311yescharacteristic
224C2×#204C22×C311yescharacteristic, complemented
225C2×D3×C8C22×C311yescharacteristic, complemented
226#895C22×C311yescharacteristic
227#893C22×C311yescharacteristic
228#884—21no—
229#882—21no—
230C3×#107—31no—
231C3×C4⋊C8—31no—
232C3×#103—21no—
233C3×#103—31no—
234C3×#103C2×D311yescharacteristic, complemented
235C3×#103C22×C311yescharacteristic, complemented
236C3×#102—21no—
237C3×#102—31no—
238C3×#102—31no—
239C3×#102—31no—
240C3×#102C2×D311yescharacteristic, complemented
241C3×#102C22×C311yescharacteristic, complemented
242C3×C22⋊C8—21no—
243C3×C22⋊C8—31no—
244C3×C22⋊C8C2×D311yescharacteristic, complemented
245C3×C22⋊C8C22×C311yescharacteristic, complemented
246C3×#97—31no—
247#832C22×C311yescharacteristic, complemented
248#821C22×C311yescharacteristic
249#821C22×C311yescharacteristic, complemented
250(C2×D3)⋊C8C22×C311yescharacteristic, complemented
251#815C22×C311yescharacteristic, complemented
252Dic3⋊C8C22×C311yescharacteristic, complemented
253#810C22×C311yescharacteristic, complemented
254#807C22×C311yescharacteristic, complemented
255C23×C32—21no—
256C23×C32—21no—
257C23×C32C2×D411yescharacteristic
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—42no—
263C22×C3×D3—42no—
264C22×C3×D3—81no—
265C22×C3×D3—81no—
266C22×C3×D3C2×D411yescharacteristic
267C32×Q8—21no—
268C32×Q8C2×D412yescomplemented
269C32×D4—21no—
270C32×D4—21no—
271C32×D4—21no—
272C32×D4—21no—
273C32×D4—42no—
274C32×D4—42no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4—21no—
279C2×C32×C4—42no—
280C2×C32×C4C2×D411yescharacteristic
281C2×C32×C4C2411yescharacteristic
282C3×#67—22no—
283C3×#67—42no—
284C3×#67—42no—
285C3×#67—42no—
286C3×#67—81no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D411yescharacteristic
291C2×C3×Dic3C2×D411yescharacteristic
292C3×D12—21no—
293C3×D12—21no—
294C3×D12—21no—
295C3×D12—42no—
296C3×D12—42no—
297C3×D12C2×D412yes—
298C3×C4×D3—21no—
299C3×C4×D3—21no—
300C3×C4×D3—42no—
301C3×C4×D3—42no—
302C3×Dic6—21no—
303C3×Dic6—21no—
304C3×Dic6—42no—
305C32×C8—21no—
306C32×C8—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8C2×D412yescomplemented
309C2×AGL(1,ℤ/8)—31no—
310C22×SD16—31no—
311#548—31no—
312D42—31no—
313#496—31no—
314#468—31no—
315#466—31no—
316#463—31no—
317#460—31no—
318#450—31no—
319#449C3×D311yescharacteristic, complemented
320#448—31no—
321#447—31no—
322#440—31no—
323#435—31no—
324C24×C3—61no—
325C24×C3—61no—
326C23×D3—21no—
327C23×D3—21no—
328C3×#41—22no—
329C3×#41—22no—
330C3×#41—42no—
331C3×#41—41no—
332C3×#41—41no—
333C3×#41—42no—
334C2×C3×Q8—21no—
335C2×C3×Q8—31no—
336C2×C3×Q8—61no—
337C2×C3×Q8—62no—
338C2×C3×Q8—121no—
339C2×C3×Q8C22×D311yescharacteristic
340C2×C3×Q8C23×C311yescharacteristic
341C2×C3×D4—21no—
342C2×C3×D4—21no—
343C2×C3×D4—21no—
344C2×C3×D4—21no—
345C2×C3×D4—21no—
346C2×C3×D4—21no—
347C2×C3×D4—31no—
348C2×C3×D4—31no—
349C2×C3×D4—31no—
350C2×C3×D4—41no—
351C2×C3×D4—41no—
352C2×C3×D4—62no—
353C2×C3×D4—61no—
354C2×C3×D4—61no—
355C2×C3×D4—61no—
356C2×C3×D4—61no—
357C2×C3×D4—62no—
358C2×C3×D4—61no—
359C2×C3×D4—61no—
360C2×C3×D4—121no—
361C2×C3×D4—121no—
362C2×C3×D4—124no—
363C2×C3×D4C22×D311yescharacteristic
364C2×C3×D4C22×D311yescharacteristic
365C2×C3×D4C23×C311yescharacteristic
366C2×C3×D4C23×C311yescharacteristic
367C22×C3×C4—21no—
368C22×C3×C4—21no—
369C22×C3×C4—21no—
370C22×C3×C4—31no—
371C22×C3×C4—41no—
372C22×C3×C4—61no—
373C22×C3×C4—61no—
374C22×C3×C4C22×D311yescharacteristic
375C22×C3×C4C23×C311yescharacteristic
376C2×#67—21no—
377C2×#67—21no—
378C2×#67—21no—
379C2×#67—21no—
380C2×#67C3×D411yescharacteristic
381D3×Q8—22no—
382D3×Q8—41no—
383D3×D4—22no—
384D3×D4—41no—
385D3×D4—44no—
386C2×D12—22no—
387C2×D12—21no—
388C2×D12—21no—
389C2×D12—41no—
390C2×D12C23×C311yescharacteristic
391C2×D12C23×C311yescharacteristic
392C2×C4×D3—21no—
393C2×C4×D3—21no—
394C2×C4×D3C23×C311yescharacteristic
395C2×Dic6—21no—
396C2×Dic6C23×C311yescharacteristic
397C3×SD16—22no—
398C3×SD16—22no—
399C3×SD16—34no—
400C3×SD16—42no—
401C3×SD16—62no—
402C3×SD16—62no—
403C3×SD16—62no—
404C3×SD16—121no—
405C3×D8—41no—
406C3×D8—41no—
407C3×D8—42no—
408C3×D8—62no—
409C3×D8—62no—
410C3×M16—62no—
411C2×C3×C8—21no—
412C2×C3×C8—21no—
413C2×C3×C8—31no—
414C2×C3×C8—31no—
415C2×C3×C8—62no—
416C2×C3×C8C22×D311yescharacteristic
417C2×C3×C8C22×D311yescharacteristic
418C2×C3×C8C23×C311yescharacteristic
419C2×C3×C8C23×C311yescharacteristic
420C3×C4⋊C4—21no—
421C3×C4⋊C4—31no—
422C3×C4⋊C4—31no—
423C3×C4⋊C4—61no—
424C3×C4⋊C4—61no—
425C3×C4⋊C4C22×D311yescharacteristic
426C3×C4⋊C4C23×C311yescharacteristic
427C3×C22⋊C4—21no—
428C3×C22⋊C4—21no—
429C3×C22⋊C4—31no—
430C3×C22⋊C4—31no—
431C3×C22⋊C4—41no—
432C3×C22⋊C4—61no—
433C3×C22⋊C4—61no—
434C3×C22⋊C4—61no—
435C3×C22⋊C4—61no—
436C3×C22⋊C4—61no—
437C3×C22⋊C4—61no—
438C3×C42—31no—
439C3×C42—61no—
440#217—21no—
441#217—21no—
442#217—21no—
443#217—21no—
444#217C3×D411yescharacteristic
445#215—22no—
446#215C3×D414yescomplemented
447#214—22no—
448#213—22no—
449#213—22no—
450(C2×D3)⋊C4—21no—
451(C2×D3)⋊C4—21no—
452(C2×D3)⋊C4C3×D411yescharacteristic
453C4⋊Dic3—21no—
454C4⋊Dic3C23×C311yescharacteristic
455Dic3⋊C4—21no—
456Dic3⋊C4C3×D411yescharacteristic
457C4×Dic3—21no—
458C4×Dic3C23×C311yescharacteristic
459#208—22no—
460C2×C3⋊C8C23×C311yescharacteristic
461C2×C3⋊C8C23×C311yescharacteristic
462#204—22no—
463#204—41no—
464D3×C8—22no—
465C22×C32—21no—
466C22×C32—21no—
467C22×C32—21no—
468C22×C32—41no—
469C22×C32—41no—
470C22×C32—41no—
471C22×C32—41no—
472C22×C32—41no—
473C22×C32—41no—
474C22×C32C22×D411yescharacteristic
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—22no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—84no—
484C2×C3×D3—84no—
485C2×C3×D3AGL(1,ℤ/8)12yescomplemented
486C32×C4—22no—
487C32×C4—21no—
488C32×C4—41no—
489C32×C4C22×D411yescharacteristic
490C32×C4H(5,𝔽2)11yescharacteristic
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—41no—
495C3×Dic3—41no—
496C2×#41C2×C3×D311yescharacteristic, complemented
497C22×Q8—31no—
498C22×D4—31no—
499C22×D4—31no—
500C22×D4—61no—
501AGL(1,ℤ/8)—64no—
502C2×SD16—31no—
503C2×SD16—31no—
504C2×SD16—31no—
505C2×SD16—31no—
506C2×SD16—31no—
507C2×SD16—64no—
508C2×SD16C2×C3×D311yescharacteristic, complemented
509C2×D8—31no—
510C2×D8—31no—
511C2×D8C2×C3×D311yescharacteristic, complemented
512C2×M16—31no—
513C22×C8—31no—
514#127—31no—
515#124—31no—
516#124—61no—
517C22⋊Q8—31no—
518C22⋊Q8—61no—
519#121—31no—
520#121—31no—
521#121—61no—
522#121—61no—
523#121C2×C3×D311yescharacteristic
524#120—61no—
525#120—61no—
526C4×Q8—31no—
527C4×D4—31no—
528C4×D4—31no—
529C4×D4—61no—
530#107—31no—
531C4⋊C8—31no—
532#103—31no—
533#103C2×C3×D311yescharacteristic, complemented
534#102—31no—
535#102—31no—
536#102—31no—
537#102C2×C3×D311yescharacteristic, complemented
538C22⋊C8—31no—
539C22⋊C8C2×C3×D311yescharacteristic, complemented
540#97—31no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—31no—
547C23×C3—41no—
548C23×C3—41no—
549C23×C3—61no—
550C23×C3—61no—
551C23×C3—122no—
552C23×C3—122no—
553C23×C3—122no—
554C23×C3—122no—
555C23×C3—241no—
556C23×C3—241no—
557C23×C3D3×D411yescharacteristic
558C23×C3C2×C3×D411yescharacteristic
559C22×D3—21no—
560C22×D3—21no—
561C22×D3—42no—
562C22×D3—42no—
563C22×D3—42no—
564C22×D3—42no—
565C22×D3—81no—
566C22×D3—81no—
567C22×D3C2×C3×D411yescharacteristic
568C3×Q8—21no—
569C3×Q8—21no—
570C3×Q8—22no—
571C3×Q8—41no—
572C3×Q8—61no—
573C3×Q8—61no—
574C3×Q8—122no—
575C3×Q8D3×D412yescomplemented
576C3×Q8C2×C3×D412yescomplemented
577C3×D4—22no—
578C3×D4—21no—
579C3×D4—21no—
580C3×D4—21no—
581C3×D4—21no—
582C3×D4—21no—
583C3×D4—21no—
584C3×D4—21no—
585C3×D4—21no—
586C3×D4—32no—
587C3×D4—41no—
588C3×D4—41no—
589C3×D4—41no—
590C3×D4—42no—
591C3×D4—42no—
592C3×D4—42no—
593C3×D4—42no—
594C3×D4—44no—
595C3×D4—62no—
596C3×D4—61no—
597C3×D4—61no—
598C3×D4—61no—
599C3×D4—82no—
600C3×D4—122no—
601C3×D4—122no—
602C3×D4—122no—
603C3×D4—122no—
604C3×D4—122no—
605C3×D4—241no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—31no—
617C2×C3×C4—31no—
618C2×C3×C4—31no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—42no—
624C2×C3×C4—42no—
625C2×C3×C4—44no—
626C2×C3×C4—61no—
627C2×C3×C4—61no—
628C2×C3×C4—61no—
629C2×C3×C4—61no—
630C2×C3×C4—122no—
631C2×C3×C4—122no—
632C2×C3×C4D3×D411yescharacteristic
633C2×C3×C4C2×C3×D411yescharacteristic
634C2×C3×C4C23×D311yescharacteristic
635C2×C3×C4C24×C311yescharacteristic
636#67—22no—
637#67—42no—
638#67—42no—
639#67—42no—
640#67—81no—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3C2×C3×D411yescharacteristic
644C2×Dic3C2×C3×D411yescharacteristic
645C2×Dic3C2×C3×D411yescharacteristic
646D12—21no—
647D12—21no—
648D12—21no—
649D12—42no—
650D12—42no—
651D12C2×C3×D412yes—
652C4×D3—21no—
653C4×D3—21no—
654C4×D3—42no—
655C4×D3—42no—
656Dic6—21no—
657Dic6—21no—
658Dic6—42no—
659C3×C8—21no—
660C3×C8—21no—
661C3×C8—21no—
662C3×C8—21no—
663C3×C8—32no—
664C3×C8—41no—
665C3×C8—41no—
666C3×C8—61no—
667C3⋊C8—21no—
668C3⋊C8C2×C3×D412yescomplemented
669C2×C32—41no—
670C2×C32—81no—
671C2×C32—81no—
672C2×C32D4211yescharacteristic
673C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
674C2×C32#57711yescharacteristic
675C3×D3—22no—
676C3×D3—42no—
677C3×D3—81no—
678C24—61no—
679C24—61no—
680#41—22no—
681#41—41no—
682C2×Q8—31no—
683C2×Q8—61no—
684C2×Q8—62no—
685C2×Q8—121no—
686C2×Q8C22×C3×D311yescharacteristic
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—31no—
690C2×D4—31no—
691C2×D4—31no—
692C2×D4—62no—
693C2×D4—61no—
694C2×D4—61no—
695C2×D4—61no—
696C2×D4—61no—
697C2×D4—62no—
698C2×D4—61no—
699C2×D4—61no—
700C2×D4—121no—
701C2×D4—121no—
702C2×D4—124no—
703C2×D4C22×C3×D311yescharacteristic
704C2×D4C22×C3×D311yescharacteristic
705C22×C4—21no—
706C22×C4—31no—
707C22×C4—61no—
708C22×C4—61no—
709C22×C4C22×C3×D311yescharacteristic
710SD16—22no—
711SD16—34no—
712SD16—62no—
713SD16—62no—
714SD16—62no—
715SD16—121no—
716D8—41no—
717D8—62no—
718D8—62no—
719M16—62no—
720C2×C8—31no—
721C2×C8—31no—
722C2×C8—62no—
723C2×C8C22×C3×D311yescharacteristic
724C2×C8C22×C3×D311yescharacteristic
725C4⋊C4—31no—
726C4⋊C4—31no—
727C4⋊C4—61no—
728C4⋊C4—61no—
729C4⋊C4C22×C3×D311yescharacteristic
730C22⋊C4—21no—
731C22⋊C4—31no—
732C22⋊C4—31no—
733C22⋊C4—61no—
734C22⋊C4—61no—
735C22⋊C4—61no—
736C22⋊C4—61no—
737C22⋊C4—61no—
738C22⋊C4—61no—
739C42—31no—
740C42—61no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—32no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—42no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—41no—
760C22×C3—41no—
761C22×C3—41no—
762C22×C3—41no—
763C22×C3—41no—
764C22×C3—41no—
765C22×C3—61no—
766C22×C3—61no—
767C22×C3—62no—
768C22×C3—81no—
769C22×C3—81no—
770C22×C3—81no—
771C22×C3—81no—
772C22×C3—81no—
773C22×C3—121no—
774C22×C3—121no—
775C22×C3—121no—
776C22×C3—121no—
777C22×C3—121no—
778C22×C3—244no—
779C22×C3—244no—
780C22×C3C2×D3×D411yescharacteristic
781C22×C3C22×C3×D411yescharacteristic
782C2×D3—21no—
783C2×D3—21no—
784C2×D3—22no—
785C2×D3—41no—
786C2×D3—41no—
787C2×D3—41no—
788C2×D3—41no—
789C2×D3—41no—
790C2×D3—84no—
791C2×D3—84no—
792C2×D3C3×AGL(1,ℤ/8)12yescomplemented
793C3×C4—21no—
794C3×C4—22no—
795C3×C4—22no—
796C3×C4—21no—
797C3×C4—21no—
798C3×C4—21no—
799C3×C4—41no—
800C3×C4—42no—
801C3×C4—41no—
802C3×C4—41no—
803C3×C4—61no—
804C3×C4—61no—
805C3×C4—61no—
806C3×C4—81no—
807C3×C4—121no—
808C3×C4—121no—
809C3×C4C2×D3×D411yescharacteristic
810C3×C4#100411yescharacteristic
811C3×C4C22×C3×D411yescharacteristic
812C3×C4C3×H(5,𝔽2)11yescharacteristic
813Dic3—21no—
814Dic3—21no—
815Dic3—21no—
816Dic3—41no—
817Dic3—41no—
818C32#326511yescharacteristic, complemented, Sylow
819C23—21no—
820C23—21no—
821C23—31no—
822C23—61no—
823C23—61no—
824C23—122no—
825C23—122no—
826C23—122no—
827C23—122no—
828C23—241no—
829C23—241no—
830C23C3×D3×D411yescharacteristic
831Q8—21no—
832Q8—61no—
833Q8—61no—
834Q8—122no—
835Q8C3×D3×D412yescomplemented
836D4—21no—
837D4—21no—
838D4—21no—
839D4—21no—
840D4—32no—
841D4—42no—
842D4—42no—
843D4—62no—
844D4—61no—
845D4—61no—
846D4—61no—
847D4—122no—
848D4—122no—
849D4—122no—
850D4—122no—
851D4—122no—
852D4—241no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—31no—
858C2×C4—31no—
859C2×C4—31no—
860C2×C4—42no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—122no—
866C2×C4—122no—
867C2×C4C3×D3×D411yescharacteristic
868C2×C4C23×C3×D311yescharacteristic
869C8—21no—
870C8—21no—
871C8—32no—
872C8—61no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—41no—
877C2×C3—41no—
878C2×C3—62no—
879C2×C3—81no—
880C2×C3—82no—
881C2×C3—81no—
882C2×C3—81no—
883C2×C3—81no—
884C2×C3—81no—
885C2×C3—122no—
886C2×C3—161no—
887C2×C3—241no—
888C2×C3#559011yescharacteristic
889C2×C3#577011yescharacteristic
890C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
891C2×C3C3×D4211yescharacteristic
892C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
893C2×C3C3×#57711yescharacteristic
894D3—22no—
895D3—42no—
896D3—81no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—32no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—61no—
908C22—61no—
909C22—62no—
910C22—121no—
911C22—121no—
912C22—121no—
913C22—121no—
914C22—121no—
915C22—244no—
916C22—244no—
917C22C2×C3×D3×D411yescharacteristic
918C4—21no—
919C4—22no—
920C4—41no—
921C4—61no—
922C4—61no—
923C4—61no—
924C4—121no—
925C4—121no—
926C4C2×C3×D3×D411yescharacteristic
927C4C3×#100411yescharacteristic
928C3—21no—
929C3#8012111yescharacteristic, direct product factor
930C3C3×#326511yescharacteristic, complemented
931C2—41no—
932C2—62no—
933C2—81no—
934C2—81no—
935C2—122no—
936C2—241no—
937C2C3×#559011yescharacteristic
938C2C3×#577011yescharacteristic
939C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#449C2
socleC22×C32C22×D4
hypercenterC3×#449D3
hypocenterC3C3×#3265
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#449

Complements

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

NH ≅ G/Ntype
1. C3×#5831C2semidirect
2. C2×C3×#949C2semidirect
3. C2×C3×D3×SD16C2semidirect
4. C3×#5609C2semidirect
5. C32×#449C2semidirect
6. C3×#5163C2semidirect
7. C3×#5156C2semidirect
8. C3×#5154C2semidirect
9. C3×#5042C2semidirect
10. C3×#4817C2semidirect
11. C3×#4806C2semidirect
12. C3×#4787C2semidirect
13. C3×#4775C2semidirect
14. C3×#4731C2semidirect
15. C3×#4728C2semidirect
17. #80121C3direct (N × H)
18. C2×C32×#41C22semidirect
19. C2×C3×D3×Q8C22semidirect
23. C2×C32×SD16C22semidirect
24. C2×C32×D8C22semidirect
27. C3×Q8×Dic3C22semidirect
29. C2×C3×#215C22semidirect
32. C3×#938C22semidirect
35. C3×#936C22semidirect
36. C2×C3×#214C22semidirect
38. C2×C3×#213C22semidirect
42. C3×#924C22semidirect
43. C2×C3×#208C22semidirect
46. C2×C3×#204C22semidirect
47. C2×C3×D3×C8C22semidirect
52. C32×#103C22semidirect
53. C32×#102C22semidirect
54. C32×C22⋊C8C22semidirect
55. C3×#832C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#815C22semidirect
60. C3×Dic3⋊C8C22semidirect
61. C3×#810C22semidirect
62. C3×#807C22semidirect
67. #5831C2×C3semidirect
68. C2×#949C2×C3semidirect
69. C2×D3×SD16C2×C3semidirect
70. #5609C2×C3semidirect
78. C3×#449D3semidirect
79. C3×#449C2×C3semidirect
84. #5163C2×C3semidirect
85. #5156C2×C3semidirect
86. #5154C2×C3semidirect
87. #5042C2×C3semidirect
88. #4817C2×C3semidirect
89. #4806C2×C3semidirect
90. #4787C2×C3semidirect
91. #4775C2×C3semidirect
92. #4731C2×C3semidirect
93. #4728C2×C3semidirect
138. C3×#215D4semidirect
159. C2×C3×#41C2×D3semidirect
160. C2×C3×#41C22×C3semidirect
165. C2×D3×Q8C22×C3semidirect
177. C2×C3×SD16C2×D3semidirect
178. C2×C3×SD16C22×C3semidirect
182. C2×C3×D8C2×D3semidirect
183. C2×C3×D8C22×C3semidirect
205. Q8×Dic3C22×C3semidirect
207. C2×#215C22×C3semidirect
210. #938C22×C3semidirect
213. #936C22×C3semidirect
214. C2×#214C22×C3semidirect
216. C2×#213C22×C3semidirect
220. #924C22×C3semidirect
221. C2×#208C22×C3semidirect
224. C2×#204C22×C3semidirect
225. C2×D3×C8C22×C3semidirect
234. C3×#103C2×D3semidirect
235. C3×#103C22×C3semidirect
240. C3×#102C2×D3semidirect
241. C3×#102C22×C3semidirect
244. C3×C22⋊C8C2×D3semidirect
245. C3×C22⋊C8C22×C3semidirect
247. #832C22×C3semidirect
249. #821C22×C3semidirect
250. (C2×D3)⋊C8C22×C3semidirect
251. #815C22×C3semidirect
252. Dic3⋊C8C22×C3semidirect
253. #810C22×C3semidirect
254. #807C22×C3semidirect
268. C32×Q8C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
319. #449C3×D3semidirect
446. #215C3×D4semidirect
485. C2×C3×D3AGL(1,ℤ/8)semidirect
496. C2×#41C2×C3×D3semidirect
508. C2×SD16C2×C3×D3semidirect
511. C2×D8C2×C3×D3semidirect
533. #103C2×C3×D3semidirect
537. #102C2×C3×D3semidirect
539. C22⋊C8C2×C3×D3semidirect
575. C3×Q8D3×D4semidirect
576. C3×Q8C2×C3×D4semidirect
668. C3⋊C8C2×C3×D4semidirect
792. C2×D3C3×AGL(1,ℤ/8)semidirect
818. C32#3265semidirect
835. Q8C3×D3×D4semidirect
929. C3#80121direct (N × H)
930. C3C3×#3265semidirect

Maximal subgroups

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

subgroupindex
C3×#58312
C2×C3×#9492
C2×C3×D3×SD162
C3×#56092
C32×#4492
C3×#51632
C3×#51562
C3×#51542
C3×#50422
C3×#48172
C3×#48062
C3×#47872
C3×#47752
C3×#47312
C3×#47282
C3×#32653
#801213