Finite Group Databasebeta

← C3×#80834 #11883934

Subgroups — C3×#80834 #11883934

Order 1152.

1152 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
2C2×C3×#908C211yesmaximal, characteristic, complemented
3C3×#5633C211yesmaximal, characteristic, complemented
4C3×#5609C211yesmaximal, characteristic, complemented
5C32×#468C211yesmaximal, characteristic, complemented
6C3×#5176C211yesmaximal, characteristic, complemented
7C3×#5127C211yesmaximal, characteristic, complemented
8C3×#5046C211yesmaximal, characteristic, complemented
9C3×#5037C211yesmaximal, characteristic, complemented
10C3×#4889C211yesmaximal, characteristic, complemented
11C3×#4883C211yesmaximal, characteristic, complemented
12C3×#4819C211yesmaximal, characteristic, complemented
13C3×#4806C211yesmaximal, characteristic, complemented
14C3×#4773C211yesmaximal, characteristic, complemented
15C3×#4762C211yesmaximal, characteristic, complemented
16C3×#3265—31nomaximal
17#80834C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic, complemented
19C2×C3×D3×D4—21no—
20C2×C3×D3×D4C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic, complemented
22C22×C3×D12C2211yescharacteristic
23C2×C32×SD16C2211yescharacteristic, complemented
24C2×C32×M16C2211yescharacteristic, complemented
25C32×C22⋊Q8C2211yescharacteristic, complemented
26C32×#121C2211yescharacteristic
27C3×#947C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic
29C2×C3×#215C2211yescharacteristic, complemented
30C3×#940C2211yescharacteristic
31C3×#937—21no—
32C2×C3×#214C2211yescharacteristic, complemented
33C2×C3×#213C2211yescharacteristic, complemented
34C3×C4×#67C2211yescharacteristic
35C3×D3×SD16—24no—
36C3×#908—24no—
37C2×C3×D24C2211yescharacteristic
38C2×C3×D24C2211yescharacteristic, complemented
39C2×C3×#204C2211yescharacteristic
40C2×C3×#204C2211yescharacteristic, complemented
41C2×C3×D3×C8C2211yescharacteristic, complemented
42C3×#896—21no—
43C3×#895C2211yescharacteristic
44C3×#895C2211yescharacteristic, complemented
45C3×#893—21no—
46C3×#893C2211yescharacteristic
47C3×#887C2211yescharacteristic, complemented
48C3×#885—21no—
49C3×#884—21no—
50C3×#884—21no—
51C3×#882—21no—
52C32×#107C2211yescharacteristic, complemented
53C32×#103C2211yescharacteristic, complemented
54C32×#102C2211yescharacteristic, complemented
55C3×#830C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×#815C2211yescharacteristic, complemented
58C3×Dic3⋊C8C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic
61C3×#809C2211yescharacteristic, complemented
62C3×#809C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C22×C3×SD16—31no—
65C3×#548—31no—
66C3×D42—31no—
67C2×D3×SD16C2×C311yescharacteristic, complemented
68C2×#908C2×C311yescharacteristic, complemented
69#5633C2×C311yescharacteristic, complemented
70#5609C2×C311yescharacteristic, complemented
71C3×#496—31no—
72C3×#468—21no—
73C3×#468D311yescharacteristic, complemented
74C3×#468C2×C311yescharacteristic, complemented
75C3×#466—31no—
76C3×#463—31no—
77C3×#460—31no—
78C3×#450—31no—
79C3×#449—31no—
80C3×#448—31no—
81C3×#447—31no—
82C3×#440—31no—
83C3×#435—31no—
84#5176C2×C311yescharacteristic, complemented
85#5127C2×C311yescharacteristic, complemented
86#5046C2×C311yescharacteristic, complemented
87#5037C2×C311yescharacteristic, complemented
88#4889C2×C311yescharacteristic, complemented
89#4883C2×C311yescharacteristic, complemented
90#4819C2×C311yescharacteristic, complemented
91#4806C2×C311yescharacteristic, complemented
92#4773C2×C311yescharacteristic, complemented
93#4762C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C23×C3×D3—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4—21no—
98C2×C32×D4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67D411yescharacteristic
105C3×D3×Q8—22no—
106C3×D3×Q8—41no—
107C3×D3×D4—22no—
108C3×D3×D4—41no—
109C3×D3×D4—44no—
110C3×#235—22no—
111C3×#235—41no—
112C2×C3×D12—22no—
113C2×C3×D12—21no—
114C2×C3×D12—21no—
115C2×C3×D12—21no—
116C2×C3×D12—41no—
117C2×C3×D12C2311yescharacteristic
118C2×C3×D12C2311yescharacteristic
119C2×C3×D12C2311yescharacteristic
120C2×C3×C4×D3—21no—
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×M16—22no—
128C2×C32×C8C2311yescharacteristic
129C2×C32×C8C2311yescharacteristic
130C32×C4⋊C4—21no—
131C32×C4⋊C4C2311yescharacteristic
132C32×C4⋊C4C2311yescharacteristic
133C32×C22⋊C4—21no—
134C32×C22⋊C4—21no—
135C3×#217D411yescharacteristic
136C3×#215—22no—
137C3×#215—41no—
138C3×#214—22no—
139C3×#213—41no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4—21no—
142C3×(C2×D3)⋊C4—21no—
143C3×(C2×D3)⋊C4—21no—
144C3×(C2×D3)⋊C4—21no—
145C3×(C2×D3)⋊C4D411yescharacteristic
146C3×Dic3⋊C4—21no—
147C3×Dic3⋊C4D411yescharacteristic
148C3×C4×Dic3—21no—
149C3×C4×Dic3C2311yescharacteristic
150C2×C3×C3⋊C8C2311yescharacteristic
151C2×C3×C3⋊C8C2311yescharacteristic
152C3×D24—22no—
153C3×D24—22no—
154C3×#204—22no—
155C3×#204D414yescomplemented
156C3×D3×C8—22no—
157#3265—31noSylow
158C2×C3×#41—31no—
159C22×C3×Q8—31no—
160C22×C3×D4—31no—
161C22×C3×D4—31no—
162C22×C3×D4—61no—
163C2×D3×Q8C22×C311yescharacteristic, complemented
164C2×D3×D4—21no—
165C2×D3×D4C22×C311yescharacteristic
166C2×#235C22×C311yescharacteristic, complemented
167C22×D12C22×C311yescharacteristic
168C3×AGL(1,ℤ/8)—64no—
169C2×C3×SD16—21no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×SD16—31no—
174C2×C3×SD16—31no—
175C2×C3×SD16—64no—
176C2×C3×SD16C2×D311yescharacteristic, complemented
177C2×C3×SD16C22×C311yescharacteristic, complemented
178C2×C3×D8—31no—
179C2×C3×D8—31no—
180C2×C3×D8—31no—
181C2×C3×M16—21no—
182C2×C3×M16C2×D311yescharacteristic, complemented
183C2×C3×M16C22×C311yescharacteristic, complemented
184C22×C3×C8—31no—
185C3×#127—31no—
186C3×#124—31no—
187C3×#124—61no—
188C3×C22⋊Q8—21no—
189C3×C22⋊Q8—61no—
190C3×C22⋊Q8C2×D311yescharacteristic, complemented
191C3×C22⋊Q8C22×C311yescharacteristic, complemented
192C3×#121—21no—
193C3×#121—31no—
194C3×#121—31no—
195C3×#121—61no—
196C3×#121—61no—
197C3×#121C2×D311yescharacteristic
198C3×#121C22×C311yescharacteristic
199C3×#120—61no—
200C3×#120—61no—
201C3×C4×Q8—31no—
202C3×C4×D4—31no—
203C3×C4×D4—31no—
204C3×C4×D4—61no—
205#947C22×C311yescharacteristic, complemented
206C2×#215C22×C311yescharacteristic
207C2×#215C22×C311yescharacteristic, complemented
208#940C22×C311yescharacteristic
209#937—21no—
210C2×#214C22×C311yescharacteristic, complemented
211C2×#213C22×C311yescharacteristic, complemented
212C4×#67C22×C311yescharacteristic
213D3×SD16—24no—
214#908—24no—
215C2×D24C22×C311yescharacteristic
216C2×D24C22×C311yescharacteristic, complemented
217C2×#204C22×C311yescharacteristic
218C2×#204C22×C311yescharacteristic, complemented
219C2×D3×C8C22×C311yescharacteristic, complemented
220#896—21no—
221#895C22×C311yescharacteristic
222#895C22×C311yescharacteristic, complemented
223#893—21no—
224#893C22×C311yescharacteristic
225#887C22×C311yescharacteristic, complemented
226#885—21no—
227#884—21no—
228#884—21no—
229#882—21no—
230C3×#107—21no—
231C3×#107C2×D311yescharacteristic, complemented
232C3×#107C22×C311yescharacteristic, complemented
233C3×C4⋊C8—31no—
234C3×#103—21no—
235C3×#103—31no—
236C3×#103C2×D311yescharacteristic, complemented
237C3×#103C22×C311yescharacteristic, complemented
238C3×#102—21no—
239C3×#102—31no—
240C3×#102—31no—
241C3×#102—31no—
242C3×#102C2×D311yescharacteristic, complemented
243C3×#102C22×C311yescharacteristic, complemented
244C3×C22⋊C8—31no—
245C3×C22⋊C8—31no—
246C3×#97—31no—
247#830C22×C311yescharacteristic, complemented
248(C2×D3)⋊C8C22×C311yescharacteristic, complemented
249#815C22×C311yescharacteristic, complemented
250Dic3⋊C8C22×C311yescharacteristic, complemented
251#810C22×C311yescharacteristic, complemented
252#809C22×C311yescharacteristic
253#809C22×C311yescharacteristic, complemented
254#809C22×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×D4—21no—
270C32×D4—21no—
271C32×D4—42no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4C2×D411yescharacteristic
278C2×C32×C4C2411yescharacteristic
279C3×#67—22no—
280C3×#67—42no—
281C3×#67—42no—
282C3×#67—42no—
283C3×#67—81no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—21no—
291C3×D12—21no—
292C3×D12—21no—
293C3×D12—42no—
294C3×D12—42no—
295C3×D12—42no—
296C3×D12C2×D412yes—
297C3×C4×D3—21no—
298C3×C4×D3—21no—
299C3×C4×D3—42no—
300C3×C4×D3—42no—
301C3×C4×D3—42no—
302C3×Dic6—21no—
303C3×Dic6—42no—
304C3×Dic6C2×D412yescomplemented
305C32×C8—21no—
306C32×C8C2×D412yescomplemented
307C3×C3⋊C8—21no—
308C3×C3⋊C8—21no—
309C2×AGL(1,ℤ/8)—31no—
310C22×SD16—31no—
311#548—31no—
312D42—31no—
313#496—31no—
314#468C3×D311yescharacteristic, complemented
315#466—31no—
316#463—31no—
317#460—31no—
318#450—31no—
319#449—31no—
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—62no—
329C3×#41—121no—
330C2×C3×Q8—21no—
331C2×C3×Q8—31no—
332C2×C3×Q8—61no—
333C2×C3×Q8—62no—
334C2×C3×Q8—121no—
335C2×C3×Q8C22×D311yescharacteristic
336C2×C3×Q8C23×C311yescharacteristic
337C2×C3×D4—21no—
338C2×C3×D4—21no—
339C2×C3×D4—21no—
340C2×C3×D4—31no—
341C2×C3×D4—31no—
342C2×C3×D4—31no—
343C2×C3×D4—31no—
344C2×C3×D4—41no—
345C2×C3×D4—62no—
346C2×C3×D4—61no—
347C2×C3×D4—61no—
348C2×C3×D4—61no—
349C2×C3×D4—61no—
350C2×C3×D4—61no—
351C2×C3×D4—62no—
352C2×C3×D4—61no—
353C2×C3×D4—61no—
354C2×C3×D4—121no—
355C2×C3×D4—121no—
356C2×C3×D4—124no—
357C2×C3×D4C22×D311yescharacteristic
358C2×C3×D4C23×C311yescharacteristic
359C22×C3×C4—21no—
360C22×C3×C4—31no—
361C22×C3×C4—61no—
362C22×C3×C4—61no—
363C22×C3×C4—61no—
364C22×C3×C4C22×D311yescharacteristic
365C22×C3×C4C23×C311yescharacteristic
366C2×#67—21no—
367C2×#67—21no—
368C2×#67—21no—
369C2×#67—21no—
370C2×#67C3×D411yescharacteristic
371D3×Q8—22no—
372D3×Q8—41no—
373D3×D4—22no—
374D3×D4—41no—
375D3×D4—44no—
376#235—22no—
377#235—41no—
378C2×D12—22no—
379C2×D12—21no—
380C2×D12—21no—
381C2×D12—21no—
382C2×D12—41no—
383C2×D12C23×C311yescharacteristic
384C2×D12C23×C311yescharacteristic
385C2×D12C23×C311yescharacteristic
386C2×C4×D3—21no—
387C2×C4×D3—21no—
388C2×C4×D3—21no—
389C2×C4×D3C23×C311yescharacteristic
390C2×Dic6—21no—
391C2×Dic6C23×C311yescharacteristic
392C3×SD16—22no—
393C3×SD16—22no—
394C3×SD16—34no—
395C3×SD16—42no—
396C3×SD16—62no—
397C3×SD16—62no—
398C3×SD16—62no—
399C3×SD16—121no—
400C3×D8—62no—
401C3×D8—62no—
402C3×D8—121no—
403C3×M16—22no—
404C3×M16—22no—
405C3×M16—42no—
406C2×C3×C8—21no—
407C2×C3×C8—21no—
408C2×C3×C8—31no—
409C2×C3×C8—31no—
410C2×C3×C8—62no—
411C2×C3×C8C22×D311yescharacteristic
412C2×C3×C8C22×D311yescharacteristic
413C2×C3×C8C23×C311yescharacteristic
414C2×C3×C8C23×C311yescharacteristic
415C3×C4⋊C4—21no—
416C3×C4⋊C4—21no—
417C3×C4⋊C4—21no—
418C3×C4⋊C4—21no—
419C3×C4⋊C4—31no—
420C3×C4⋊C4—41no—
421C3×C4⋊C4—61no—
422C3×C4⋊C4C22×D311yescharacteristic
423C3×C4⋊C4C22×D311yescharacteristic
424C3×C4⋊C4C23×C311yescharacteristic
425C3×C4⋊C4C23×C311yescharacteristic
426C3×C22⋊C4—21no—
427C3×C22⋊C4—21no—
428C3×C22⋊C4—21no—
429C3×C22⋊C4—21no—
430C3×C22⋊C4—31no—
431C3×C22⋊C4—31no—
432C3×C22⋊C4—41no—
433C3×C22⋊C4—41no—
434C3×C22⋊C4—61no—
435C3×C22⋊C4—61no—
436C3×C22⋊C4—61no—
437C3×C22⋊C4—61no—
438C3×C22⋊C4—61no—
439C3×C42—31no—
440C3×C42—61no—
441#217C3×D411yescharacteristic
442#215—22no—
443#215—41no—
444#214—22no—
445#213—41no—
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)⋊C4C3×D411yescharacteristic
452Dic3⋊C4—21no—
453Dic3⋊C4C3×D411yescharacteristic
454C4×Dic3—21no—
455C4×Dic3C23×C311yescharacteristic
456C2×C3⋊C8C23×C311yescharacteristic
457C2×C3⋊C8C23×C311yescharacteristic
458D24—22no—
459D24—22no—
460#204—22no—
461#204C3×D414yescomplemented
462D3×C8—22no—
463C22×C32—21no—
464C22×C32—21no—
465C22×C32—21no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32C22×D411yescharacteristic
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—22no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—84no—
482C2×C3×D3—84no—
483C2×C3×D3AGL(1,ℤ/8)12yescomplemented
484C32×C4—21no—
485C32×C4—41no—
486C32×C4—41no—
487C32×C4—41no—
488C32×C4C22×D411yescharacteristic
489C32×C4H(5,𝔽2)11yescharacteristic
490C3×Dic3—22no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C2×#41—31no—
495C22×Q8—31no—
496C22×D4—31no—
497C22×D4—31no—
498C22×D4—61no—
499AGL(1,ℤ/8)—64no—
500C2×SD16—31no—
501C2×SD16—31no—
502C2×SD16—31no—
503C2×SD16—31no—
504C2×SD16—31no—
505C2×SD16—64no—
506C2×SD16C2×C3×D311yescharacteristic, complemented
507C2×D8—31no—
508C2×D8—31no—
509C2×D8—31no—
510C2×M16C2×C3×D311yescharacteristic, complemented
511C22×C8—31no—
512#127—31no—
513#124—31no—
514#124—61no—
515C22⋊Q8—61no—
516C22⋊Q8C2×C3×D311yescharacteristic, complemented
517#121—31no—
518#121—31no—
519#121—61no—
520#121—61no—
521#121C2×C3×D311yescharacteristic
522#120—61no—
523#120—61no—
524C4×Q8—31no—
525C4×D4—31no—
526C4×D4—31no—
527C4×D4—61no—
528#107C2×C3×D311yescharacteristic, complemented
529C4⋊C8—31no—
530#103—31no—
531#103C2×C3×D311yescharacteristic, complemented
532#102—31no—
533#102—31no—
534#102—31no—
535#102C2×C3×D311yescharacteristic, complemented
536C22⋊C8—31no—
537C22⋊C8—31no—
538#97—31no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—21no—
542C23×C3—31no—
543C23×C3—41no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—61no—
547C23×C3—122no—
548C23×C3—122no—
549C23×C3—122no—
550C23×C3—122no—
551C23×C3—241no—
552C23×C3—241no—
553C23×C3D3×D411yescharacteristic
554C23×C3C2×C3×D411yescharacteristic
555C22×D3—21no—
556C22×D3—21no—
557C22×D3—21no—
558C22×D3—42no—
559C22×D3—42no—
560C22×D3—42no—
561C22×D3—42no—
562C22×D3—81no—
563C22×D3—81no—
564C22×D3C2×C3×D411yescharacteristic
565C3×Q8—21no—
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—21no—
569C3×Q8—32no—
570C3×Q8—41no—
571C3×Q8—41no—
572C3×Q8—61no—
573C3×Q8—122no—
574C3×D4—21no—
575C3×D4—21no—
576C3×D4—21no—
577C3×D4—21no—
578C3×D4—32no—
579C3×D4—41no—
580C3×D4—41no—
581C3×D4—42no—
582C3×D4—42no—
583C3×D4—62no—
584C3×D4—61no—
585C3×D4—61no—
586C3×D4—61no—
587C3×D4—61no—
588C3×D4—61no—
589C3×D4—82no—
590C3×D4—122no—
591C3×D4—122no—
592C3×D4—122no—
593C3×D4—122no—
594C3×D4—122no—
595C3×D4—122no—
596C3×D4—241no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—31no—
610C2×C3×C4—31no—
611C2×C3×C4—31no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—61no—
620C2×C3×C4—122no—
621C2×C3×C4—122no—
622C2×C3×C4—122no—
623C2×C3×C4D3×D411yescharacteristic
624C2×C3×C4C2×C3×D411yescharacteristic
625C2×C3×C4C23×D311yescharacteristic
626C2×C3×C4C24×C311yescharacteristic
627#67—22no—
628#67—42no—
629#67—42no—
630#67—42no—
631#67—81no—
632C2×Dic3—21no—
633C2×Dic3C2×C3×D411yescharacteristic
634C2×Dic3C2×C3×D411yescharacteristic
635C2×Dic3C2×C3×D411yescharacteristic
636D12—21no—
637D12—21no—
638D12—21no—
639D12—21no—
640D12—21no—
641D12—42no—
642D12—42no—
643D12—42no—
644D12C2×C3×D412yes—
645C4×D3—21no—
646C4×D3—21no—
647C4×D3—42no—
648C4×D3—42no—
649C4×D3—42no—
650Dic6—21no—
651Dic6—42no—
652Dic6C2×C3×D412yescomplemented
653C3×C8—21no—
654C3×C8—21no—
655C3×C8—22no—
656C3×C8—41no—
657C3×C8—61no—
658C3×C8—61no—
659C3×C8D3×D412yescomplemented
660C3×C8C2×C3×D412yescomplemented
661C3⋊C8—21no—
662C3⋊C8—21no—
663C2×C32—41no—
664C2×C32—81no—
665C2×C32D4211yescharacteristic
666C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
667C2×C32#57711yescharacteristic
668C3×D3—22no—
669C3×D3—42no—
670C3×D3—81no—
671C3×D3—81no—
672C24—61no—
673C24—61no—
674#41—62no—
675#41—121no—
676C2×Q8—31no—
677C2×Q8—61no—
678C2×Q8—62no—
679C2×Q8—121no—
680C2×Q8C22×C3×D311yescharacteristic
681C2×D4—21no—
682C2×D4—31no—
683C2×D4—31no—
684C2×D4—31no—
685C2×D4—31no—
686C2×D4—62no—
687C2×D4—61no—
688C2×D4—61no—
689C2×D4—61no—
690C2×D4—61no—
691C2×D4—61no—
692C2×D4—62no—
693C2×D4—61no—
694C2×D4—61no—
695C2×D4—121no—
696C2×D4—121no—
697C2×D4—124no—
698C2×D4C22×C3×D311yescharacteristic
699C22×C4—31no—
700C22×C4—61no—
701C22×C4—61no—
702C22×C4—61no—
703C22×C4C22×C3×D311yescharacteristic
704SD16—22no—
705SD16—34no—
706SD16—62no—
707SD16—62no—
708SD16—62no—
709SD16—121no—
710D8—62no—
711D8—62no—
712D8—121no—
713M16—22no—
714C2×C8—31no—
715C2×C8—31no—
716C2×C8—62no—
717C2×C8C22×C3×D311yescharacteristic
718C2×C8C22×C3×D311yescharacteristic
719C4⋊C4—21no—
720C4⋊C4—31no—
721C4⋊C4—61no—
722C4⋊C4C22×C3×D311yescharacteristic
723C4⋊C4C22×C3×D311yescharacteristic
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—31no—
727C22⋊C4—31no—
728C22⋊C4—61no—
729C22⋊C4—61no—
730C22⋊C4—61no—
731C22⋊C4—61no—
732C22⋊C4—61no—
733C42—31no—
734C42—61no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—32no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—61no—
753C22×C3—61no—
754C22×C3—62no—
755C22×C3—81no—
756C22×C3—81no—
757C22×C3—81no—
758C22×C3—121no—
759C22×C3—121no—
760C22×C3—121no—
761C22×C3—121no—
762C22×C3—121no—
763C22×C3—121no—
764C22×C3—121no—
765C22×C3—121no—
766C22×C3—244no—
767C22×C3—244no—
768C22×C3C2×D3×D411yescharacteristic
769C22×C3C22×C3×D411yescharacteristic
770C2×D3—21no—
771C2×D3—21no—
772C2×D3—22no—
773C2×D3—41no—
774C2×D3—41no—
775C2×D3—41no—
776C2×D3—41no—
777C2×D3—41no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3—41no—
781C2×D3—84no—
782C2×D3—84no—
783C2×D3C3×AGL(1,ℤ/8)12yescomplemented
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—21no—
787C3×C4—21no—
788C3×C4—41no—
789C3×C4—41no—
790C3×C4—41no—
791C3×C4—41no—
792C3×C4—41no—
793C3×C4—41no—
794C3×C4—41no—
795C3×C4—61no—
796C3×C4—61no—
797C3×C4—61no—
798C3×C4—62no—
799C3×C4—81no—
800C3×C4—81no—
801C3×C4—81no—
802C3×C4C2×D3×D411yescharacteristic
803C3×C4#100911yescharacteristic
804C3×C4C22×C3×D411yescharacteristic
805C3×C4C3×H(5,𝔽2)11yescharacteristic
806Dic3—21no—
807Dic3—21no—
808Dic3—22no—
809Dic3—21no—
810C32#326511yescharacteristic, complemented, Sylow
811C23—21no—
812C23—31no—
813C23—61no—
814C23—61no—
815C23—61no—
816C23—122no—
817C23—122no—
818C23—122no—
819C23—122no—
820C23—241no—
821C23—241no—
822C23C3×D3×D411yescharacteristic
823Q8—21no—
824Q8—21no—
825Q8—32no—
826Q8—61no—
827Q8—122no—
828D4—21no—
829D4—21no—
830D4—32no—
831D4—42no—
832D4—62no—
833D4—61no—
834D4—61no—
835D4—61no—
836D4—61no—
837D4—61no—
838D4—122no—
839D4—122no—
840D4—122no—
841D4—122no—
842D4—122no—
843D4—122no—
844D4—241no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—31no—
851C2×C4—31no—
852C2×C4—31no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—122no—
857C2×C4—122no—
858C2×C4—122no—
859C2×C4C3×D3×D411yescharacteristic
860C2×C4C23×C3×D311yescharacteristic
861C8—21no—
862C8—61no—
863C8—61no—
864C8C3×D3×D412yescomplemented
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—41no—
869C2×C3—41no—
870C2×C3—62no—
871C2×C3—81no—
872C2×C3—81no—
873C2×C3—81no—
874C2×C3—122no—
875C2×C3—161no—
876C2×C3—241no—
877C2×C3—241no—
878C2×C3#560911yescharacteristic
879C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
880C2×C3#577811yescharacteristic
881C2×C3C3×D4211yescharacteristic
882C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
883C2×C3C3×#57711yescharacteristic
884D3—22no—
885D3—42no—
886D3—81no—
887D3—81no—
888C22—21no—
889C22—21no—
890C22—21no—
891C22—32no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—61no—
896C22—61no—
897C22—62no—
898C22—121no—
899C22—121no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—121no—
904C22—121no—
905C22—121no—
906C22—244no—
907C22—244no—
908C22C2×C3×D3×D411yescharacteristic
909C4—21no—
910C4—41no—
911C4—41no—
912C4—41no—
913C4—61no—
914C4—61no—
915C4—61no—
916C4—62no—
917C4C2×C3×D3×D411yescharacteristic
918C4C3×#100911yescharacteristic
919C3—21no—
920C3#8083411yescharacteristic, direct product factor
921C3C3×#326511yescharacteristic, complemented
922C2—41no—
923C2—62no—
924C2—81no—
925C2—122no—
926C2—241no—
927C2—241no—
928C2C3×#560911yescharacteristic
929C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
930C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#468C2
socleC22×C32C22×D4
hypercenterC3×#468D3
hypocenterC3C3×#3265
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#468

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×SD16C2semidirect
2. C2×C3×#908C2semidirect
3. C3×#5633C2semidirect
4. C3×#5609C2semidirect
5. C32×#468C2semidirect
6. C3×#5176C2semidirect
7. C3×#5127C2semidirect
8. C3×#5046C2semidirect
9. C3×#5037C2semidirect
10. C3×#4889C2semidirect
11. C3×#4883C2semidirect
12. C3×#4819C2semidirect
13. C3×#4806C2semidirect
14. C3×#4773C2semidirect
15. C3×#4762C2semidirect
17. #80834C3direct (N × H)
18. C2×C3×D3×Q8C22semidirect
21. C2×C3×#235C22semidirect
23. C2×C32×SD16C22semidirect
24. C2×C32×M16C22semidirect
25. C32×C22⋊Q8C22semidirect
27. C3×#947C22semidirect
29. C2×C3×#215C22semidirect
32. C2×C3×#214C22semidirect
33. C2×C3×#213C22semidirect
38. C2×C3×D24C22semidirect
40. C2×C3×#204C22semidirect
41. C2×C3×D3×C8C22semidirect
44. C3×#895C22semidirect
47. C3×#887C22semidirect
52. C32×#107C22semidirect
53. C32×#103C22semidirect
54. C32×#102C22semidirect
55. C3×#830C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×#815C22semidirect
58. C3×Dic3⋊C8C22semidirect
59. C3×#810C22semidirect
61. C3×#809C22semidirect
62. C3×#809C22semidirect
67. C2×D3×SD16C2×C3semidirect
68. C2×#908C2×C3semidirect
69. #5633C2×C3semidirect
70. #5609C2×C3semidirect
73. C3×#468D3semidirect
74. C3×#468C2×C3semidirect
84. #5176C2×C3semidirect
85. #5127C2×C3semidirect
86. #5046C2×C3semidirect
87. #5037C2×C3semidirect
88. #4889C2×C3semidirect
89. #4883C2×C3semidirect
90. #4819C2×C3semidirect
91. #4806C2×C3semidirect
92. #4773C2×C3semidirect
93. #4762C2×C3semidirect
155. C3×#204D4semidirect
163. C2×D3×Q8C22×C3semidirect
166. C2×#235C22×C3semidirect
176. C2×C3×SD16C2×D3semidirect
177. C2×C3×SD16C22×C3semidirect
182. C2×C3×M16C2×D3semidirect
183. C2×C3×M16C22×C3semidirect
190. C3×C22⋊Q8C2×D3semidirect
191. C3×C22⋊Q8C22×C3semidirect
205. #947C22×C3semidirect
207. C2×#215C22×C3semidirect
210. C2×#214C22×C3semidirect
211. C2×#213C22×C3semidirect
216. C2×D24C22×C3semidirect
218. C2×#204C22×C3semidirect
219. C2×D3×C8C22×C3semidirect
222. #895C22×C3semidirect
225. #887C22×C3semidirect
231. C3×#107C2×D3semidirect
232. C3×#107C22×C3semidirect
236. C3×#103C2×D3semidirect
237. C3×#103C22×C3semidirect
242. C3×#102C2×D3semidirect
243. C3×#102C22×C3semidirect
247. #830C22×C3semidirect
248. (C2×D3)⋊C8C22×C3semidirect
249. #815C22×C3semidirect
250. Dic3⋊C8C22×C3semidirect
251. #810C22×C3semidirect
253. #809C22×C3semidirect
254. #809C22×C3semidirect
304. C3×Dic6C2×D4semidirect
306. C32×C8C2×D4semidirect
314. #468C3×D3semidirect
461. #204C3×D4semidirect
483. C2×C3×D3AGL(1,ℤ/8)semidirect
506. C2×SD16C2×C3×D3semidirect
510. C2×M16C2×C3×D3semidirect
516. C22⋊Q8C2×C3×D3semidirect
528. #107C2×C3×D3semidirect
531. #103C2×C3×D3semidirect
535. #102C2×C3×D3semidirect
652. Dic6C2×C3×D4semidirect
659. C3×C8D3×D4semidirect
660. C3×C8C2×C3×D4semidirect
783. C2×D3C3×AGL(1,ℤ/8)semidirect
810. C32#3265semidirect
864. C8C3×D3×D4semidirect
920. C3#80834direct (N × H)
921. C3C3×#3265semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×SD162
C2×C3×#9082
C3×#56332
C3×#56092
C32×#4682
C3×#51762
C3×#51272
C3×#50462
C3×#50372
C3×#48892
C3×#48832
C3×#48192
C3×#48062
C3×#47732
C3×#47622
C3×#32653
#808343