Finite Group Databasebeta

← C3×#80060 #11883892

Subgroups — C3×#80060 #11883892

Order 1152.

1171 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5817C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic, complemented
3C2×C3×#914C211yesmaximal, characteristic, complemented
4C3×#5609C211yesmaximal, characteristic, complemented
5C32×#448C211yesmaximal, characteristic, complemented
6C3×#5176C211yesmaximal, characteristic, complemented
7C3×#5169C211yesmaximal, characteristic, complemented
8C3×#5163C211yesmaximal, characteristic, complemented
9C3×#5038C211yesmaximal, characteristic, complemented
10C3×#4819C211yesmaximal, characteristic, complemented
11C3×#4817C211yesmaximal, characteristic, complemented
12C3×#4812C211yesmaximal, characteristic, complemented
13C3×#4810C211yesmaximal, characteristic, complemented
14C3×#4732C211yesmaximal, characteristic, complemented
15C3×#4730C211yesmaximal, characteristic, complemented
16C3×#3265—31nomaximal
17#80060C311yesmaximal, characteristic, direct product factor
18C22×C32×Q8C2211yescharacteristic, complemented
19C2×C3×#239C2211yescharacteristic, complemented
20C2×C3×D3×D4—21no—
21C2×C3×D3×D4C2211yescharacteristic
22C22×C3×D12C2211yescharacteristic
23C2×C32×SD16C2211yescharacteristic, complemented
24C2×C32×SD16C2211yescharacteristic, complemented
25C32×#121C2211yescharacteristic
26C3×#947—21no—
27C3×#947C2211yescharacteristic, complemented
28C3×#946—21no—
29C3×#946C2211yescharacteristic, complemented
30C3×Q8×Dic3C2211yescharacteristic, complemented
31C2×C3×#215—24no—
32C2×C3×#215C2211yescharacteristic
33C2×C3×#215C2211yescharacteristic
34C2×C3×#215C2211yescharacteristic, complemented
35C2×C3×#215C2211yescharacteristic, complemented
36C3×#940C2211yescharacteristic
37C3×#937—21no—
38C2×C3×#213C2211yescharacteristic, complemented
39C3×#930—21no—
40C3×#930C2211yescharacteristic, complemented
41C3×C4×#67—21no—
42C3×C4×#67C2211yescharacteristic
43C22×C3×C3⋊C8C2211yescharacteristic, complemented
44C3×#914—24no—
45C2×C3×D24C2211yescharacteristic
46C2×C3×D24C2211yescharacteristic, complemented
47C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
48C3×#895C2211yescharacteristic
49C3×#893C2211yescharacteristic
50C3×#884—21no—
51C3×#882—21no—
52C32×#103C2211yescharacteristic, complemented
53C32×#103C2211yescharacteristic, 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×#809C2211yescharacteristic, complemented
62C3×#807C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C22×C3×SD16—31no—
65C3×#548—31no—
66C3×D42—31no—
67#5817C2×C311yescharacteristic, complemented
68C22×#215C2×C311yescharacteristic, complemented
69C2×#914C2×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—31no—
78C3×#448—21no—
79C3×#448D311yescharacteristic, complemented
80C3×#448C2×C311yescharacteristic, complemented
81C3×#447—31no—
82C3×#440—31no—
83C3×#435—31no—
84#5176C2×C311yescharacteristic, complemented
85#5169C2×C311yescharacteristic, complemented
86#5163C2×C311yescharacteristic, complemented
87#5038C2×C311yescharacteristic, complemented
88#4819C2×C311yescharacteristic, complemented
89#4817C2×C311yescharacteristic, complemented
90#4812C2×C311yescharacteristic, complemented
91#4810C2×C311yescharacteristic, complemented
92#4732C2×C311yescharacteristic, complemented
93#4730C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C23×C3×D3—21no—
96C2×C32×Q8—21no—
97C2×C32×Q8—22no—
98C2×C32×Q8—41no—
99C2×C32×Q8C2311yescharacteristic
100C2×C32×Q8C2311yescharacteristic
101C2×C32×D4—21no—
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×#239—22no—
111C3×#239—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—21no—
119C2×C3×D12—41no—
120C2×C3×D12C2311yescharacteristic
121C2×C3×D12C2311yescharacteristic
122C2×C3×D12C2311yescharacteristic
123C2×C3×C4×D3—21no—
124C2×C3×C4×D3—21no—
125C2×C3×C4×D3C2311yescharacteristic
126C32×SD16—22no—
127C32×SD16—41no—
128C2×C32×C8C2311yescharacteristic
129C2×C32×C8C2311yescharacteristic
130C32×C4⋊C4C2311yescharacteristic
131C32×C22⋊C4—21no—
132C3×#217D411yescharacteristic
133C3×#215—22no—
134C3×#215—22no—
135C3×#215—22no—
136C3×#215D414yescomplemented
137C3×#213—22no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4—21no—
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
151C2×C3×C3⋊C8—22no—
152C2×C3×C3⋊C8C2311yescharacteristic
153C2×C3×C3⋊C8C2311yescharacteristic
154C3×D24—22no—
155C3×D24—41no—
156C3×ΓL(1,𝔽25)—22no—
157#3265—31noSylow
158C2×C3×#41—31no—
159C22×C3×Q8—21no—
160C22×C3×Q8C2×D311yescharacteristic, complemented
161C22×C3×Q8C22×C311yescharacteristic, complemented
162C22×C3×D4—31no—
163C22×C3×D4—31no—
164C22×C3×D4—61no—
165C2×#239C22×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—21no—
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×SD16C2×D311yescharacteristic, complemented
179C2×C3×SD16C22×C311yescharacteristic, complemented
180C2×C3×SD16C22×C311yescharacteristic, complemented
181C2×C3×D8—31no—
182C2×C3×D8—31no—
183C2×C3×D8—31no—
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#947—21no—
205#947C22×C311yescharacteristic, complemented
206#946—21no—
207#946C22×C311yescharacteristic, complemented
208Q8×Dic3C22×C311yescharacteristic, complemented
209C2×#215—24no—
210C2×#215C22×C311yescharacteristic
211C2×#215C22×C311yescharacteristic
212C2×#215C22×C311yescharacteristic, complemented
213C2×#215C22×C311yescharacteristic, complemented
214#940C22×C311yescharacteristic
215#937—21no—
216C2×#213C22×C311yescharacteristic, complemented
217#930—21no—
218#930C22×C311yescharacteristic, complemented
219C4×#67—21no—
220C4×#67C22×C311yescharacteristic
221C22×C3⋊C8C22×C311yescharacteristic, complemented
222#914—24no—
223C2×D24C22×C311yescharacteristic
224C2×D24C22×C311yescharacteristic, complemented
225C2×ΓL(1,𝔽25)C22×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—21no—
234C3×#103C2×D311yescharacteristic, complemented
235C3×#103C2×D311yescharacteristic, complemented
236C3×#103C22×C311yescharacteristic, complemented
237C3×#103C22×C311yescharacteristic, complemented
238C3×#102—31no—
239C3×#102—31no—
240C3×#102—31no—
241C3×#102—31no—
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#809C22×C311yescharacteristic, complemented
254#807C22×C311yescharacteristic, complemented
255C23×C32—21no—
256C23×C32C2×D411yescharacteristic
257C22×C3×D3—21no—
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×Q8—21no—
269C32×Q8—21no—
270C32×Q8—42no—
271C32×Q8C2×D412yescomplemented
272C32×D4—21no—
273C32×D4—21no—
274C32×D4—42no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4—21no—
279C2×C32×C4—21no—
280C2×C32×C4—42no—
281C2×C32×C4C2×D411yescharacteristic
282C2×C32×C4C2411yescharacteristic
283C3×#67—22no—
284C3×#67—42no—
285C3×#67—42no—
286C3×#67—42no—
287C3×#67—81no—
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—21no—
296C3×D12—21no—
297C3×D12—42no—
298C3×D12—42no—
299C3×D12—42no—
300C3×D12C2×D412yes—
301C3×C4×D3—21no—
302C3×C4×D3—21no—
303C3×C4×D3—42no—
304C3×C4×D3—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#449—31no—
320#448C3×D311yescharacteristic, complemented
321#447—31no—
322#440—31no—
323#435—31no—
324C24×C3—61no—
325C24×C3—61no—
326C23×D3—21no—
327C23×D3—21no—
328C3×#41—62no—
329C3×#41—121no—
330C2×C3×Q8—21no—
331C2×C3×Q8—21no—
332C2×C3×Q8—22no—
333C2×C3×Q8—22no—
334C2×C3×Q8—21no—
335C2×C3×Q8—21no—
336C2×C3×Q8—41no—
337C2×C3×Q8—42no—
338C2×C3×Q8—41no—
339C2×C3×Q8—41no—
340C2×C3×Q8—42no—
341C2×C3×Q8C22×D311yescharacteristic
342C2×C3×Q8C22×D311yescharacteristic
343C2×C3×Q8C23×C311yescharacteristic
344C2×C3×Q8C23×C311yescharacteristic
345C2×C3×D4—21no—
346C2×C3×D4—21no—
347C2×C3×D4—21no—
348C2×C3×D4—31no—
349C2×C3×D4—31no—
350C2×C3×D4—31no—
351C2×C3×D4—31no—
352C2×C3×D4—41no—
353C2×C3×D4—62no—
354C2×C3×D4—61no—
355C2×C3×D4—61no—
356C2×C3×D4—61no—
357C2×C3×D4—61no—
358C2×C3×D4—61no—
359C2×C3×D4—62no—
360C2×C3×D4—61no—
361C2×C3×D4—61no—
362C2×C3×D4—121no—
363C2×C3×D4—121no—
364C2×C3×D4—124no—
365C2×C3×D4C22×D311yescharacteristic
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
381#239—22no—
382#239—41no—
383D3×D4—22no—
384D3×D4—41no—
385D3×D4—44no—
386C2×D12—22no—
387C2×D12—21no—
388C2×D12—21no—
389C2×D12—21no—
390C2×D12—41no—
391C2×D12C23×C311yescharacteristic
392C2×D12C23×C311yescharacteristic
393C2×D12C23×C311yescharacteristic
394C2×C4×D3—21no—
395C2×C4×D3—21no—
396C2×C4×D3C23×C311yescharacteristic
397C3×SD16—22no—
398C3×SD16—22no—
399C3×SD16—34no—
400C3×SD16—42no—
401C3×SD16—41no—
402C3×SD16—41no—
403C3×SD16—42no—
404C3×SD16—62no—
405C3×SD16—62no—
406C3×SD16—62no—
407C3×D8—62no—
408C3×D8—62no—
409C3×D8—121no—
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#217C3×D411yescharacteristic
441#215—22no—
442#215—22no—
443#215—22no—
444#215C3×D414yescomplemented
445#213—22no—
446(C2×D3)⋊C4—21no—
447(C2×D3)⋊C4—21no—
448(C2×D3)⋊C4—21no—
449(C2×D3)⋊C4—21no—
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
459C2×C3⋊C8—22no—
460C2×C3⋊C8C23×C311yescharacteristic
461C2×C3⋊C8C23×C311yescharacteristic
462D24—22no—
463D24—41no—
464ΓL(1,𝔽25)—22no—
465C22×C32—21no—
466C22×C32—21no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32—41no—
470C22×C32AGL(1,ℤ/8)12yescomplemented
471C22×C32C22×D411yescharacteristic
472C2×C3×D3—21no—
473C2×C3×D3—22no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3—84no—
485C2×C3×D3—84no—
486C32×C4—22no—
487C32×C4—21no—
488C32×C4—41no—
489C32×C4—41no—
490C32×C4C22×D411yescharacteristic
491C32×C4H(5,𝔽2)11yescharacteristic
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—21no—
495C3×Dic3—41no—
496C2×#41—31no—
497C22×Q8C2×C3×D311yescharacteristic, complemented
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—64no—
507C2×SD16C2×C3×D311yescharacteristic, complemented
508C2×SD16C2×C3×D311yescharacteristic, complemented
509C2×D8—31no—
510C2×D8—31no—
511C2×D8—31no—
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#103C2×C3×D311yescharacteristic, complemented
533#103C2×C3×D311yescharacteristic, complemented
534#102—31no—
535#102—31no—
536#102—31no—
537#102—31no—
538C22⋊C8—31no—
539C22⋊C8C2×C3×D311yescharacteristic, complemented
540#97—31no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—31no—
545C23×C3—41no—
546C23×C3—61no—
547C23×C3—61no—
548C23×C3—61no—
549C23×C3—122no—
550C23×C3—122no—
551C23×C3—122no—
552C23×C3—122no—
553C23×C3—241no—
554C23×C3—241no—
555C23×C3D3×D411yescharacteristic
556C23×C3C2×C3×D411yescharacteristic
557C22×D3—21no—
558C22×D3—21no—
559C22×D3—21no—
560C22×D3—42no—
561C22×D3—42no—
562C22×D3—42no—
563C22×D3—42no—
564C22×D3—81no—
565C22×D3—81no—
566C22×D3C2×C3×D411yescharacteristic
567C3×Q8—21no—
568C3×Q8—21no—
569C3×Q8—22no—
570C3×Q8—21no—
571C3×Q8—21no—
572C3×Q8—21no—
573C3×Q8—21no—
574C3×Q8—22no—
575C3×Q8—41no—
576C3×Q8—41no—
577C3×Q8—42no—
578C3×Q8—42no—
579C3×Q8—44no—
580C3×Q8D3×D412yescomplemented
581C3×Q8C2×C3×D412yescomplemented
582C3×D4—21no—
583C3×D4—21no—
584C3×D4—21no—
585C3×D4—21no—
586C3×D4—32no—
587C3×D4—41no—
588C3×D4—41no—
589C3×D4—42no—
590C3×D4—42no—
591C3×D4—62no—
592C3×D4—61no—
593C3×D4—61no—
594C3×D4—61no—
595C3×D4—61no—
596C3×D4—61no—
597C3×D4—82no—
598C3×D4—122no—
599C3×D4—122no—
600C3×D4—122no—
601C3×D4—122no—
602C3×D4—122no—
603C3×D4—122no—
604C3×D4—241no—
605C2×C3×C4—21no—
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—21no—
617C2×C3×C4—31no—
618C2×C3×C4—31no—
619C2×C3×C4—31no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—42no—
626C2×C3×C4—42no—
627C2×C3×C4—44no—
628C2×C3×C4—61no—
629C2×C3×C4—61no—
630C2×C3×C4—61no—
631C2×C3×C4—122no—
632C2×C3×C4—122no—
633C2×C3×C4D3×D411yescharacteristic
634C2×C3×C4C2×C3×D411yescharacteristic
635C2×C3×C4C23×D311yescharacteristic
636C2×C3×C4C24×C311yescharacteristic
637#67—22no—
638#67—42no—
639#67—42no—
640#67—42no—
641#67—81no—
642C2×Dic3—21no—
643C2×Dic3C2×C3×D411yescharacteristic
644C2×Dic3C2×C3×D411yescharacteristic
645C2×Dic3C2×C3×D411yescharacteristic
646D12—21no—
647D12—21no—
648D12—21no—
649D12—21no—
650D12—21no—
651D12—42no—
652D12—42no—
653D12—42no—
654D12C2×C3×D412yes—
655C4×D3—21no—
656C4×D3—21no—
657C4×D3—42no—
658C4×D3—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—22no—
670C2×C32—81no—
671C2×C32D4211yescharacteristic
672C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
673C2×C32#57711yescharacteristic
674C3×D3—41no—
675C3×D3—42no—
676C3×D3—81no—
677C3×D3—81no—
678C24—61no—
679C24—61no—
680#41—62no—
681#41—121no—
682C2×Q8—21no—
683C2×Q8—22no—
684C2×Q8—41no—
685C2×Q8C22×C3×D311yescharacteristic
686C2×Q8C22×C3×D311yescharacteristic
687C2×D4—21no—
688C2×D4—31no—
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—61no—
698C2×D4—62no—
699C2×D4—61no—
700C2×D4—61no—
701C2×D4—121no—
702C2×D4—121no—
703C2×D4—124no—
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—41no—
713SD16—62no—
714SD16—62no—
715SD16—62no—
716D8—62no—
717D8—62no—
718D8—121no—
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—22no—
746C22×C3—21no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—61no—
756C22×C3—61no—
757C22×C3—61no—
758C22×C3—62no—
759C22×C3—81no—
760C22×C3—81no—
761C22×C3—81no—
762C22×C3—121no—
763C22×C3—121no—
764C22×C3—121no—
765C22×C3—121no—
766C22×C3—121no—
767C22×C3—121no—
768C22×C3—121no—
769C22×C3—121no—
770C22×C3—244no—
771C22×C3—244no—
772C22×C3#91412yescomplemented
773C22×C3C3×AGL(1,ℤ/8)12yescomplemented
774C22×C3C2×D3×D411yescharacteristic
775C22×C3C22×C3×D411yescharacteristic
776C2×D3—21no—
777C2×D3—21no—
778C2×D3—21no—
779C2×D3—22no—
780C2×D3—41no—
781C2×D3—41no—
782C2×D3—41no—
783C2×D3—41no—
784C2×D3—41no—
785C2×D3—41no—
786C2×D3—41no—
787C2×D3—41no—
788C2×D3—84no—
789C2×D3—84no—
790C3×C4—21no—
791C3×C4—22no—
792C3×C4—22no—
793C3×C4—21no—
794C3×C4—21no—
795C3×C4—21no—
796C3×C4—41no—
797C3×C4—42no—
798C3×C4—42no—
799C3×C4—41no—
800C3×C4—41no—
801C3×C4—41no—
802C3×C4—41no—
803C3×C4—61no—
804C3×C4—61no—
805C3×C4—61no—
806C3×C4—81no—
807C3×C4—121no—
808C3×C4C2×D3×D411yescharacteristic
809C3×C4#100411yescharacteristic
810C3×C4C22×C3×D411yescharacteristic
811C3×C4C3×H(5,𝔽2)11yescharacteristic
812Dic3—21no—
813Dic3—21no—
814Dic3—21no—
815Dic3—41no—
816C32#326511yescharacteristic, complemented, Sylow
817C23—21no—
818C23—31no—
819C23—61no—
820C23—61no—
821C23—61no—
822C23—122no—
823C23—122no—
824C23—122no—
825C23—122no—
826C23—241no—
827C23—241no—
828C23C3×D3×D411yescharacteristic
829Q8—21no—
830Q8—21no—
831Q8—21no—
832Q8—42no—
833Q8C3×D3×D412yescomplemented
834D4—21no—
835D4—21no—
836D4—32no—
837D4—42no—
838D4—62no—
839D4—61no—
840D4—61no—
841D4—61no—
842D4—61no—
843D4—61no—
844D4—122no—
845D4—122no—
846D4—122no—
847D4—122no—
848D4—122no—
849D4—122no—
850D4—241no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—31no—
857C2×C4—31no—
858C2×C4—31no—
859C2×C4—42no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—122no—
864C2×C4—122no—
865C2×C4C3×D3×D411yescharacteristic
866C2×C4C23×C3×D311yescharacteristic
867C8—21no—
868C8—21no—
869C8—32no—
870C8—61no—
871C2×C3—22no—
872C2×C3—22no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—42no—
877C2×C3—81no—
878C2×C3—81no—
879C2×C3—121no—
880C2×C3—122no—
881C2×C3—161no—
882C2×C3—241no—
883C2×C3—241no—
884C2×C3#559011yescharacteristic
885C2×C3C2×#91411yescharacteristic
886C2×C3#577811yescharacteristic
887C2×C3C3×D4211yescharacteristic
888C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
889C2×C3C3×#57711yescharacteristic
890D3—41no—
891D3—42no—
892D3—81no—
893D3—81no—
894C22—21no—
895C22—21no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—61no—
900C22—61no—
901C22—61no—
902C22—62no—
903C22—121no—
904C22—121no—
905C22—121no—
906C22—121no—
907C22—121no—
908C22—121no—
909C22—121no—
910C22—121no—
911C22—244no—
912C22—244no—
913C22C3×#91412yescomplemented
914C22C2×C3×D3×D411yescharacteristic
915C4—21no—
916C4—22no—
917C4—41no—
918C4—41no—
919C4—61no—
920C4—61no—
921C4—61no—
922C4—121no—
923C4C2×C3×D3×D411yescharacteristic
924C4C3×#100411yescharacteristic
925C3—21no—
926C3#8006011yescharacteristic, direct product factor
927C3C3×#326511yescharacteristic, complemented
928C2—22no—
929C2—81no—
930C2—121no—
931C2—122no—
932C2—241no—
933C2—241no—
934C2C3×#559011yescharacteristic
935C2C2×C3×#91411yescharacteristic
936C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#448C2
socleC22×C32C22×D4
hypercenterC3×#448D3
hypocenterC3C3×#3265
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#448

Complements

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

NH ≅ G/Ntype
1. C3×#5817C2semidirect
2. C22×C3×#215C2semidirect
3. C2×C3×#914C2semidirect
4. C3×#5609C2semidirect
5. C32×#448C2semidirect
6. C3×#5176C2semidirect
7. C3×#5169C2semidirect
8. C3×#5163C2semidirect
9. C3×#5038C2semidirect
10. C3×#4819C2semidirect
11. C3×#4817C2semidirect
12. C3×#4812C2semidirect
13. C3×#4810C2semidirect
14. C3×#4732C2semidirect
15. C3×#4730C2semidirect
17. #80060C3direct (N × H)
18. C22×C32×Q8C22semidirect
19. C2×C3×#239C22semidirect
23. C2×C32×SD16C22semidirect
24. C2×C32×SD16C22semidirect
27. C3×#947C22semidirect
29. C3×#946C22semidirect
30. C3×Q8×Dic3C22semidirect
34. C2×C3×#215C22semidirect
35. C2×C3×#215C22semidirect
38. C2×C3×#213C22semidirect
40. C3×#930C22semidirect
43. C22×C3×C3⋊C8C22semidirect
46. C2×C3×D24C22semidirect
47. C2×C3×ΓL(1,𝔽25)C22semidirect
52. C32×#103C22semidirect
53. C32×#103C22semidirect
54. C32×C22⋊C8C22semidirect
55. C3×#832C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#815C22semidirect
60. C3×Dic3⋊C8C22semidirect
61. C3×#809C22semidirect
62. C3×#807C22semidirect
67. #5817C2×C3semidirect
68. C22×#215C2×C3semidirect
69. C2×#914C2×C3semidirect
70. #5609C2×C3semidirect
79. C3×#448D3semidirect
80. C3×#448C2×C3semidirect
84. #5176C2×C3semidirect
85. #5169C2×C3semidirect
86. #5163C2×C3semidirect
87. #5038C2×C3semidirect
88. #4819C2×C3semidirect
89. #4817C2×C3semidirect
90. #4812C2×C3semidirect
91. #4810C2×C3semidirect
92. #4732C2×C3semidirect
93. #4730C2×C3semidirect
136. C3×#215D4semidirect
160. C22×C3×Q8C2×D3semidirect
161. C22×C3×Q8C22×C3semidirect
165. C2×#239C22×C3semidirect
177. C2×C3×SD16C2×D3semidirect
178. C2×C3×SD16C2×D3semidirect
179. C2×C3×SD16C22×C3semidirect
180. C2×C3×SD16C22×C3semidirect
205. #947C22×C3semidirect
207. #946C22×C3semidirect
208. Q8×Dic3C22×C3semidirect
212. C2×#215C22×C3semidirect
213. C2×#215C22×C3semidirect
216. C2×#213C22×C3semidirect
218. #930C22×C3semidirect
221. C22×C3⋊C8C22×C3semidirect
224. C2×D24C22×C3semidirect
225. C2×ΓL(1,𝔽25)C22×C3semidirect
234. C3×#103C2×D3semidirect
235. C3×#103C2×D3semidirect
236. C3×#103C22×C3semidirect
237. C3×#103C22×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. #809C22×C3semidirect
254. #807C22×C3semidirect
271. C32×Q8C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
320. #448C3×D3semidirect
444. #215C3×D4semidirect
470. C22×C32AGL(1,ℤ/8)semidirect
497. C22×Q8C2×C3×D3semidirect
507. C2×SD16C2×C3×D3semidirect
508. C2×SD16C2×C3×D3semidirect
532. #103C2×C3×D3semidirect
533. #103C2×C3×D3semidirect
539. C22⋊C8C2×C3×D3semidirect
580. C3×Q8D3×D4semidirect
581. C3×Q8C2×C3×D4semidirect
668. C3⋊C8C2×C3×D4semidirect
772. C22×C3#914semidirect
773. C22×C3C3×AGL(1,ℤ/8)semidirect
816. C32#3265semidirect
833. Q8C3×D3×D4semidirect
913. C22C3×#914semidirect
926. C3#80060direct (N × H)
927. C3C3×#3265semidirect

Maximal subgroups

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

subgroupindex
C3×#58172
C22×C3×#2152
C2×C3×#9142
C3×#56092
C32×#4482
C3×#51762
C3×#51692
C3×#51632
C3×#50382
C3×#48192
C3×#48172
C3×#48122
C3×#48102
C3×#47322
C3×#47302
C3×#32653
#800603