Finite Group Databasebeta

← C3×#80156 #11883907

Subgroups — C3×#80156 #11883907

Order 1152.

1186 conjugacy classes of subgroups.

The subgroup lattice has 943 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×#67C211yesmaximal, characteristic, complemented
2C2×C3×#932C211yesmaximal, characteristic, complemented
3C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
4C3×#5633C211yesmaximal, characteristic, complemented
5C32×#450C211yesmaximal, characteristic, complemented
6C3×#5176C211yesmaximal, characteristic, complemented
7C3×#5170C211yesmaximal, characteristic, complemented
8C3×#5165C211yesmaximal, characteristic, complemented
9C3×#5049C211yesmaximal, characteristic, complemented
10C3×#4775C211yesmaximal, characteristic, complemented
11C3×#4773C211yesmaximal, characteristic, complemented
12C3×#4762C211yesmaximal, characteristic, complemented
13C3×#4757C211yesmaximal, characteristic, complemented
14C3×#4734C211yesmaximal, characteristic, complemented
15C3×#4728C211yesmaximal, characteristic, complemented
16C3×#3265—31nomaximal
17#80156C311yesmaximal, characteristic, direct product factor
18C22×C32×D4C2211yescharacteristic
19C22×C3×#67—21no—
20C2×C3×D3×Q8C2211yescharacteristic, complemented
21C2×C3×D3×D4C2211yescharacteristic
22C2×C3×#235C2211yescharacteristic, complemented
23C2×C32×SD16C2211yescharacteristic
24C2×C32×SD16C2211yescharacteristic, complemented
25C32×C22⋊Q8C2211yescharacteristic, complemented
26C3×#953—21no—
27C3×#947C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic, complemented
29C3×#940C2211yescharacteristic
30C3×#939—21no—
31C3×#938C2211yescharacteristic
32C3×#937—21no—
33C3×D4×Dic3C2211yescharacteristic
34C2×C3×#214C2211yescharacteristic
35C2×C3×#214C2211yescharacteristic, complemented
36C3×#932—24no—
37C2×C3×#213C2211yescharacteristic
38C2×C3×#213C2211yescharacteristic, complemented
39C3×#930C2211yescharacteristic
40C3×C4×#67C2211yescharacteristic
41C2×C3×#208C2211yescharacteristic, complemented
42C3×D3×SD16—24no—
43C2×C3×D24C2211yescharacteristic, complemented
44C2×C3×#204C2211yescharacteristic, complemented
45C2×C3×D3×C8C2211yescharacteristic, complemented
46C3×#896—21no—
47C3×#895C2211yescharacteristic, complemented
48C3×#893—21no—
49C3×#887C2211yescharacteristic, complemented
50C3×#885—21no—
51C3×#884—21no—
52C32×#102C2211yescharacteristic
53C32×#102C2211yescharacteristic, complemented
54C32×C22⋊C8C2211yescharacteristic, complemented
55C3×#835C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, 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—
67D4×#67C2×C311yescharacteristic, complemented
68C2×#932C2×C311yescharacteristic, complemented
69C2×D3×SD16C2×C311yescharacteristic, complemented
70#5633C2×C311yescharacteristic, complemented
71C3×#496—31no—
72C3×#468—31no—
73C3×#466—31no—
74C3×#463—31no—
75C3×#460—31no—
76C3×#450—21no—
77C3×#450D311yescharacteristic, complemented
78C3×#450C2×C311yescharacteristic, complemented
79C3×#449—31no—
80C3×#448—31no—
81C3×#447—31no—
82C3×#440—31no—
83C3×#435—31no—
84#5176C2×C311yescharacteristic, complemented
85#5170C2×C311yescharacteristic, complemented
86#5165C2×C311yescharacteristic, complemented
87#5049C2×C311yescharacteristic, complemented
88#4775C2×C311yescharacteristic, complemented
89#4773C2×C311yescharacteristic, complemented
90#4762C2×C311yescharacteristic, complemented
91#4757C2×C311yescharacteristic, complemented
92#4734C2×C311yescharacteristic, complemented
93#4728C2×C311yescharacteristic, complemented
94C24×C32—21no—
95C23×C3×D3—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4—22no—
98C2×C32×D4—21no—
99C2×C32×D4—41no—
100C2×C32×D4C2311yescharacteristic
101C2×C32×D4C2311yescharacteristic
102C22×C32×C4C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×#67—44no—
110C2×C3×#67D411yescharacteristic
111C22×C3×Dic3—21no—
112C3×D3×Q8—22no—
113C3×D3×Q8—41no—
114C3×D3×D4—22no—
115C3×D3×D4—41no—
116C3×#235—22no—
117C3×#235—41no—
118C2×C3×D12—21no—
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×SD16—41no—
128C2×C32×C8C2311yescharacteristic
129C2×C32×C8C2311yescharacteristic
130C32×C4⋊C4—21no—
131C32×C4⋊C4C2311yescharacteristic
132C32×C22⋊C4—21no—
133C3×#217—21no—
134C3×#217—21no—
135C3×#217D411yescharacteristic
136C3×#215—22no—
137C3×#214—22no—
138C3×#214D414yescomplemented
139C3×#213—22no—
140C3×#213—22no—
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×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×D24—41no—
155C3×#204—22no—
156C3×D3×C8—22no—
157#3265—31noSylow
158C2×C3×#41—31no—
159C22×C3×Q8—31no—
160C22×C3×D4—21no—
161C22×C3×D4—31no—
162C22×C3×D4—61no—
163C22×C3×D4C2×D311yescharacteristic
164C22×C3×D4C22×C311yescharacteristic
165C22×#67—21no—
166C2×D3×Q8C22×C311yescharacteristic, complemented
167C2×D3×D4C22×C311yescharacteristic
168C2×#235C22×C311yescharacteristic, complemented
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
178C2×C3×SD16C2×D311yescharacteristic, complemented
179C2×C3×SD16C22×C311yescharacteristic
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—21no—
190C3×C22⋊Q8—61no—
191C3×C22⋊Q8C2×D311yescharacteristic, complemented
192C3×C22⋊Q8C22×C311yescharacteristic, complemented
193C3×#121—31no—
194C3×#121—31no—
195C3×#121—31no—
196C3×#121—61no—
197C3×#121—61no—
198C3×#120—61no—
199C3×#120—61no—
200C3×C4×Q8—31no—
201C3×C4×D4—31no—
202C3×C4×D4—31no—
203C3×C4×D4—61no—
204#953—21no—
205#947C22×C311yescharacteristic, complemented
206C2×#215C22×C311yescharacteristic, complemented
207#940C22×C311yescharacteristic
208#939—21no—
209#938C22×C311yescharacteristic
210#937—21no—
211D4×Dic3C22×C311yescharacteristic
212C2×#214C22×C311yescharacteristic
213C2×#214C22×C311yescharacteristic, complemented
214#932—24no—
215C2×#213C22×C311yescharacteristic
216C2×#213C22×C311yescharacteristic, complemented
217#930C22×C311yescharacteristic
218C4×#67C22×C311yescharacteristic
219C2×#208C22×C311yescharacteristic, complemented
220D3×SD16—24no—
221C2×D24C22×C311yescharacteristic, complemented
222C2×#204C22×C311yescharacteristic, complemented
223C2×D3×C8C22×C311yescharacteristic, complemented
224#896—21no—
225#895C22×C311yescharacteristic, complemented
226#893—21no—
227#887C22×C311yescharacteristic, complemented
228#885—21no—
229#884—21no—
230C3×#107—31no—
231C3×C4⋊C8—31no—
232C3×#103—31no—
233C3×#103—31no—
234C3×#102—21no—
235C3×#102—21no—
236C3×#102—31no—
237C3×#102—31no—
238C3×#102C2×D311yescharacteristic
239C3×#102C2×D311yescharacteristic, complemented
240C3×#102C22×C311yescharacteristic
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#835C22×C311yescharacteristic, complemented
248#821C22×C311yescharacteristic, complemented
249(C2×D3)⋊C8C22×C311yescharacteristic, complemented
250#816C22×C311yescharacteristic, complemented
251#815C22×C311yescharacteristic, complemented
252Dic3⋊C8C22×C311yescharacteristic, complemented
253#809C22×C311yescharacteristic, complemented
254#807C22×C311yescharacteristic, complemented
255C23×C32—21no—
256C23×C32—21no—
257C23×C32—42no—
258C23×C32—42no—
259C23×C32—81no—
260C23×C32C2×D411yescharacteristic
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—42no—
264C22×C3×D3—42no—
265C22×C3×D3—81no—
266C22×C3×D3C2×D411yescharacteristic
267C32×Q8—21no—
268C32×Q8—21no—
269C32×D4—21no—
270C32×D4—21no—
271C32×D4—21no—
272C32×D4—42no—
273C32×D4C2×D412yes—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4C2×D411yescharacteristic
279C2×C32×C4C2411yescharacteristic
280C3×#67—22no—
281C3×#67—42no—
282C3×#67—42no—
283C3×#67—42no—
284C3×#67—42no—
285C3×#67—42no—
286C3×#67—81no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—42no—
290C2×C3×Dic3C2×D411yescharacteristic
291C2×C3×Dic3C2×D411yescharacteristic
292C2×C3×Dic3C2×D411yescharacteristic
293C3×D12—21no—
294C3×D12—21no—
295C3×D12—21no—
296C3×D12—21no—
297C3×D12—42no—
298C3×C4×D3—21no—
299C3×C4×D3—21no—
300C3×C4×D3—42no—
301C3×C4×D3—42no—
302C3×Dic6—21no—
303C3×Dic6—42no—
304C3×Dic6C2×D412yescomplemented
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#450C3×D311yescharacteristic, complemented
319#449—31no—
320#448—31no—
321#447—31no—
322#440—31no—
323#435—31no—
324C24×C3—21no—
325C24×C3—21no—
326C24×C3—41no—
327C24×C3—61no—
328C23×D3—21no—
329C3×#41—62no—
330C3×#41—121no—
331C2×C3×Q8—21no—
332C2×C3×Q8—31no—
333C2×C3×Q8—61no—
334C2×C3×Q8—62no—
335C2×C3×Q8—121no—
336C2×C3×Q8C22×D311yescharacteristic
337C2×C3×Q8C23×C311yescharacteristic
338C2×C3×D4—22no—
339C2×C3×D4—22no—
340C2×C3×D4—21no—
341C2×C3×D4—21no—
342C2×C3×D4—21no—
343C2×C3×D4—21no—
344C2×C3×D4—31no—
345C2×C3×D4—31no—
346C2×C3×D4—31no—
347C2×C3×D4—41no—
348C2×C3×D4—42no—
349C2×C3×D4—41no—
350C2×C3×D4—41no—
351C2×C3×D4—42no—
352C2×C3×D4—61no—
353C2×C3×D4—61no—
354C2×C3×D4—61no—
355C2×C3×D4—61no—
356C2×C3×D4—62no—
357C2×C3×D4—61no—
358C2×C3×D4—61no—
359C2×C3×D4—61no—
360C2×C3×D4—121no—
361C2×C3×D4—124no—
362C2×C3×D4C22×D311yescharacteristic
363C2×C3×D4C22×D311yescharacteristic
364C2×C3×D4C23×C311yescharacteristic
365C2×C3×D4C23×C311yescharacteristic
366C22×C3×C4—21no—
367C22×C3×C4—31no—
368C22×C3×C4—61no—
369C22×C3×C4—61no—
370C22×C3×C4—61no—
371C22×C3×C4C22×D311yescharacteristic
372C22×C3×C4C23×C311yescharacteristic
373C2×#67—21no—
374C2×#67—21no—
375C2×#67—21no—
376C2×#67—21no—
377C2×#67—21no—
378C2×#67—21no—
379C2×#67—44no—
380C2×#67C3×D411yescharacteristic
381C22×Dic3—21no—
382D3×Q8—22no—
383D3×Q8—41no—
384D3×D4—22no—
385D3×D4—41no—
386#235—22no—
387#235—41no—
388C2×D12—21no—
389C2×D12C23×C311yescharacteristic
390C2×D12C23×C311yescharacteristic
391C2×C4×D3—21no—
392C2×C4×D3—21no—
393C2×C4×D3C23×C311yescharacteristic
394C2×Dic6—21no—
395C2×Dic6C23×C311yescharacteristic
396C3×SD16—22no—
397C3×SD16—22no—
398C3×SD16—34no—
399C3×SD16—42no—
400C3×SD16—41no—
401C3×SD16—41no—
402C3×SD16—42no—
403C3×SD16—62no—
404C3×SD16—62no—
405C3×SD16—62no—
406C3×D8—62no—
407C3×D8—62no—
408C3×D8—121no—
409C3×M16—62no—
410C2×C3×C8—21no—
411C2×C3×C8—21no—
412C2×C3×C8—31no—
413C2×C3×C8—31no—
414C2×C3×C8—62no—
415C2×C3×C8C22×D311yescharacteristic
416C2×C3×C8C22×D311yescharacteristic
417C2×C3×C8C23×C311yescharacteristic
418C2×C3×C8C23×C311yescharacteristic
419C3×C4⋊C4—21no—
420C3×C4⋊C4—21no—
421C3×C4⋊C4—21no—
422C3×C4⋊C4—31no—
423C3×C4⋊C4—31no—
424C3×C4⋊C4—41no—
425C3×C4⋊C4—61no—
426C3×C4⋊C4C22×D311yescharacteristic
427C3×C4⋊C4C23×C311yescharacteristic
428C3×C22⋊C4—21no—
429C3×C22⋊C4—21no—
430C3×C22⋊C4—31no—
431C3×C22⋊C4—31no—
432C3×C22⋊C4—41no—
433C3×C22⋊C4—61no—
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#217—21no—
442#217—21no—
443#217C3×D411yescharacteristic
444#215—22no—
445#214—22no—
446#214C3×D414yescomplemented
447#213—22no—
448#213—22no—
449(C2×D3)⋊C4—21no—
450(C2×D3)⋊C4—21no—
451(C2×D3)⋊C4—21no—
452(C2×D3)⋊C4—21no—
453(C2×D3)⋊C4C3×D411yescharacteristic
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
462D24—41no—
463#204—22no—
464D3×C8—22no—
465C22×C32—21no—
466C22×C32—21no—
467C22×C32—22no—
468C22×C32—21no—
469C22×C32—41no—
470C22×C32—41no—
471C22×C32—41no—
472C22×C32—41no—
473C22×C32—41no—
474C22×C32—84no—
475C22×C32C22×D411yescharacteristic
476C2×C3×D3—21no—
477C2×C3×D3—21no—
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×D3AGL(1,ℤ/8)12yescomplemented
486C32×C4—21no—
487C32×C4—41no—
488C32×C4—41no—
489C32×C4C22×D411yescharacteristic
490C32×C4H(5,𝔽2)11yescharacteristic
491C3×Dic3—22no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—21no—
495C3×Dic3—41no—
496C2×#41—31no—
497C22×Q8—31no—
498C22×D4—31no—
499C22×D4—61no—
500C22×D4C2×C3×D311yescharacteristic
501AGL(1,ℤ/8)—64no—
502C2×SD16—31no—
503C2×SD16—31no—
504C2×SD16—31no—
505C2×SD16—31no—
506C2×SD16—64no—
507C2×SD16C2×C3×D311yescharacteristic
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—61no—
518C22⋊Q8C2×C3×D311yescharacteristic, complemented
519#121—31no—
520#121—31no—
521#121—31no—
522#121—61no—
523#121—61no—
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#103—31no—
534#102—31no—
535#102—31no—
536#102C2×C3×D311yescharacteristic
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—42no—
550C23×C3—42no—
551C23×C3—42no—
552C23×C3—42no—
553C23×C3—44no—
554C23×C3—61no—
555C23×C3—61no—
556C23×C3—82no—
557C23×C3—81no—
558C23×C3—81no—
559C23×C3—82no—
560C23×C3—122no—
561C23×C3—122no—
562C23×C3—241no—
563C23×C3D3×D411yescharacteristic
564C23×C3C2×C3×D411yescharacteristic
565C22×D3—21no—
566C22×D3—21no—
567C22×D3—42no—
568C22×D3—42no—
569C22×D3—81no—
570C22×D3C2×C3×D411yescharacteristic
571C3×Q8—21no—
572C3×Q8—21no—
573C3×Q8—21no—
574C3×Q8—21no—
575C3×Q8—32no—
576C3×Q8—41no—
577C3×Q8—41no—
578C3×Q8—61no—
579C3×Q8—122no—
580C3×D4—22no—
581C3×D4—21no—
582C3×D4—21no—
583C3×D4—21no—
584C3×D4—21no—
585C3×D4—21no—
586C3×D4—21no—
587C3×D4—22no—
588C3×D4—41no—
589C3×D4—41no—
590C3×D4—42no—
591C3×D4—42no—
592C3×D4—44no—
593C3×D4—62no—
594C3×D4—61no—
595C3×D4—61no—
596C3×D4—61no—
597C3×D4—61no—
598C3×D4—122no—
599C3×D4—122no—
600C3×D4—122no—
601C3×D4—122no—
602C3×D4—122no—
603C3×D4—122no—
604C3×D4—241no—
605C3×D4D3×D412yes—
606C3×D4C2×C3×D412yes—
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—61no—
625C2×C3×C4—61no—
626C2×C3×C4—61no—
627C2×C3×C4—61no—
628C2×C3×C4—122no—
629C2×C3×C4—122no—
630C2×C3×C4—122no—
631C2×C3×C4D3×D411yescharacteristic
632C2×C3×C4C2×C3×D411yescharacteristic
633C2×C3×C4C23×D311yescharacteristic
634C2×C3×C4C24×C311yescharacteristic
635#67—22no—
636#67—42no—
637#67—42no—
638#67—42no—
639#67—42no—
640#67—42no—
641#67—81no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—42no—
645C2×Dic3C2×C3×D411yescharacteristic
646C2×Dic3C2×C3×D411yescharacteristic
647C2×Dic3C2×C3×D411yescharacteristic
648D12—21no—
649D12—21no—
650D12—21no—
651D12—21no—
652D12—42no—
653C4×D3—21no—
654C4×D3—21no—
655C4×D3—42no—
656C4×D3—42no—
657Dic6—21no—
658Dic6—42no—
659Dic6C2×C3×D412yescomplemented
660C3×C8—21no—
661C3×C8—21no—
662C3×C8—21no—
663C3×C8—21no—
664C3×C8—32no—
665C3×C8—41no—
666C3×C8—41no—
667C3×C8—61no—
668C3⋊C8—21no—
669C3⋊C8C2×C3×D412yescomplemented
670C2×C32—41no—
671C2×C32—42no—
672C2×C32—81no—
673C2×C32D4211yescharacteristic
674C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
675C2×C32#57711yescharacteristic
676C3×D3—22no—
677C3×D3—81no—
678C3×D3—81no—
679C24—21no—
680C24—61no—
681#41—62no—
682#41—121no—
683C2×Q8—31no—
684C2×Q8—61no—
685C2×Q8—62no—
686C2×Q8—121no—
687C2×Q8C22×C3×D311yescharacteristic
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—31no—
691C2×D4—31no—
692C2×D4—31no—
693C2×D4—41no—
694C2×D4—61no—
695C2×D4—61no—
696C2×D4—61no—
697C2×D4—61no—
698C2×D4—62no—
699C2×D4—61no—
700C2×D4—61no—
701C2×D4—61no—
702C2×D4—121no—
703C2×D4—124no—
704C2×D4C22×C3×D311yescharacteristic
705C2×D4C22×C3×D311yescharacteristic
706C22×C4—31no—
707C22×C4—61no—
708C22×C4—61no—
709C22×C4—61no—
710C22×C4C22×C3×D311yescharacteristic
711SD16—22no—
712SD16—34no—
713SD16—41no—
714SD16—62no—
715SD16—62no—
716SD16—62no—
717D8—62no—
718D8—62no—
719D8—121no—
720M16—62no—
721C2×C8—31no—
722C2×C8—31no—
723C2×C8—62no—
724C2×C8C22×C3×D311yescharacteristic
725C2×C8C22×C3×D311yescharacteristic
726C4⋊C4—21no—
727C4⋊C4—31no—
728C4⋊C4—31no—
729C4⋊C4—61no—
730C4⋊C4C22×C3×D311yescharacteristic
731C22⋊C4—21no—
732C22⋊C4—31no—
733C22⋊C4—31no—
734C22⋊C4—61no—
735C22⋊C4—61no—
736C22⋊C4—61no—
737C22⋊C4—61no—
738C22⋊C4—61no—
739C22⋊C4—61no—
740C42—31no—
741C42—61no—
742C22×C3—22no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—22no—
749C22×C3—21no—
750C22×C3—22no—
751C22×C3—21no—
752C22×C3—32no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—42no—
756C22×C3—42no—
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—41no—
766C22×C3—41no—
767C22×C3—61no—
768C22×C3—61no—
769C22×C3—81no—
770C22×C3—81no—
771C22×C3—81no—
772C22×C3—81no—
773C22×C3—84no—
774C22×C3—84no—
775C22×C3—88no—
776C22×C3—121no—
777C22×C3—121no—
778C22×C3—121no—
779C22×C3—121no—
780C22×C3—121no—
781C22×C3—121no—
782C22×C3—244no—
783C22×C3C2×D3×D411yescharacteristic
784C22×C3C22×C3×D411yescharacteristic
785C2×D3—21no—
786C2×D3—21no—
787C2×D3—41no—
788C2×D3—41no—
789C2×D3—41no—
790C2×D3—41no—
791C2×D3—41no—
792C2×D3—41no—
793C2×D3—84no—
794C2×D3C3×AGL(1,ℤ/8)12yescomplemented
795C3×C4—21no—
796C3×C4—21no—
797C3×C4—21no—
798C3×C4—21no—
799C3×C4—41no—
800C3×C4—41no—
801C3×C4—41no—
802C3×C4—41no—
803C3×C4—41no—
804C3×C4—61no—
805C3×C4—61no—
806C3×C4—61no—
807C3×C4—62no—
808C3×C4—81no—
809C3×C4—81no—
810C3×C4—121no—
811C3×C4C2×D3×D411yescharacteristic
812C3×C4#100411yescharacteristic
813C3×C4C22×C3×D411yescharacteristic
814C3×C4C3×H(5,𝔽2)11yescharacteristic
815Dic3—21no—
816Dic3—21no—
817Dic3—22no—
818Dic3—21no—
819Dic3—41no—
820C32#326511yescharacteristic, complemented, Sylow
821C23—21no—
822C23—21no—
823C23—31no—
824C23—42no—
825C23—42no—
826C23—61no—
827C23—61no—
828C23—81no—
829C23—122no—
830C23—122no—
831C23—241no—
832C23C3×D3×D411yescharacteristic
833Q8—21no—
834Q8—21no—
835Q8—32no—
836Q8—61no—
837Q8—122no—
838D4—21no—
839D4—21no—
840D4—21no—
841D4—42no—
842D4—62no—
843D4—61no—
844D4—61no—
845D4—61no—
846D4—61no—
847D4—122no—
848D4—122no—
849D4—122no—
850D4—122no—
851D4—122no—
852D4—122no—
853D4—241no—
854D4C3×D3×D412yes—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—31no—
860C2×C4—31no—
861C2×C4—31no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—122no—
867C2×C4—122no—
868C2×C4—122no—
869C2×C4C3×D3×D411yescharacteristic
870C2×C4C23×C3×D311yescharacteristic
871C8—21no—
872C8—21no—
873C8—32no—
874C8—61no—
875C2×C3—21no—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—42no—
879C2×C3—41no—
880C2×C3—42no—
881C2×C3—42no—
882C2×C3—41no—
883C2×C3—62no—
884C2×C3—82no—
885C2×C3—82no—
886C2×C3—81no—
887C2×C3—81no—
888C2×C3—241no—
889C2×C3—241no—
890C2×C3#559011yescharacteristic
891C2×C3#576211yescharacteristic
892C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
893C2×C3C3×D4211yescharacteristic
894C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
895C2×C3C3×#57711yescharacteristic
896D3—22no—
897D3—81no—
898D3—81no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—22no—
903C22—32no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—61no—
910C22—61no—
911C22—84no—
912C22—121no—
913C22—121no—
914C22—121no—
915C22—121no—
916C22—121no—
917C22—121no—
918C22—244no—
919C22C2×C3×D3×D411yescharacteristic
920C4—21no—
921C4—41no—
922C4—41no—
923C4—61no—
924C4—61no—
925C4—61no—
926C4—62no—
927C4—121no—
928C4C2×C3×D3×D411yescharacteristic
929C4C3×#100411yescharacteristic
930C3—21no—
931C3#8015611yescharacteristic, direct product factor
932C3C3×#326511yescharacteristic, complemented
933C2—41no—
934C2—42no—
935C2—62no—
936C2—81no—
937C2—241no—
938C2—241no—
939C2C3×#559011yescharacteristic
940C2C3×#576211yescharacteristic
941C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#450C2
socleC22×C32C22×D4
hypercenterC3×#450D3
hypocenterC3C3×#3265
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#450

Complements

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

NH ≅ G/Ntype
1. C3×D4×#67C2semidirect
2. C2×C3×#932C2semidirect
3. C2×C3×D3×SD16C2semidirect
4. C3×#5633C2semidirect
5. C32×#450C2semidirect
6. C3×#5176C2semidirect
7. C3×#5170C2semidirect
8. C3×#5165C2semidirect
9. C3×#5049C2semidirect
10. C3×#4775C2semidirect
11. C3×#4773C2semidirect
12. C3×#4762C2semidirect
13. C3×#4757C2semidirect
14. C3×#4734C2semidirect
15. C3×#4728C2semidirect
17. #80156C3direct (N × H)
20. C2×C3×D3×Q8C22semidirect
22. C2×C3×#235C22semidirect
24. C2×C32×SD16C22semidirect
25. C32×C22⋊Q8C22semidirect
27. C3×#947C22semidirect
28. C2×C3×#215C22semidirect
35. C2×C3×#214C22semidirect
38. C2×C3×#213C22semidirect
41. C2×C3×#208C22semidirect
43. C2×C3×D24C22semidirect
44. C2×C3×#204C22semidirect
45. C2×C3×D3×C8C22semidirect
47. C3×#895C22semidirect
49. C3×#887C22semidirect
53. C32×#102C22semidirect
54. C32×C22⋊C8C22semidirect
55. C3×#835C22semidirect
56. C3×#821C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#816C22semidirect
59. C3×#815C22semidirect
60. C3×Dic3⋊C8C22semidirect
61. C3×#809C22semidirect
62. C3×#807C22semidirect
67. D4×#67C2×C3semidirect
68. C2×#932C2×C3semidirect
69. C2×D3×SD16C2×C3semidirect
70. #5633C2×C3semidirect
77. C3×#450D3semidirect
78. C3×#450C2×C3semidirect
84. #5176C2×C3semidirect
85. #5170C2×C3semidirect
86. #5165C2×C3semidirect
87. #5049C2×C3semidirect
88. #4775C2×C3semidirect
89. #4773C2×C3semidirect
90. #4762C2×C3semidirect
91. #4757C2×C3semidirect
92. #4734C2×C3semidirect
93. #4728C2×C3semidirect
138. C3×#214D4semidirect
166. C2×D3×Q8C22×C3semidirect
168. C2×#235C22×C3semidirect
178. C2×C3×SD16C2×D3semidirect
180. C2×C3×SD16C22×C3semidirect
191. C3×C22⋊Q8C2×D3semidirect
192. C3×C22⋊Q8C22×C3semidirect
205. #947C22×C3semidirect
206. C2×#215C22×C3semidirect
213. C2×#214C22×C3semidirect
216. C2×#213C22×C3semidirect
219. C2×#208C22×C3semidirect
221. C2×D24C22×C3semidirect
222. C2×#204C22×C3semidirect
223. C2×D3×C8C22×C3semidirect
225. #895C22×C3semidirect
227. #887C22×C3semidirect
239. C3×#102C2×D3semidirect
241. C3×#102C22×C3semidirect
244. C3×C22⋊C8C2×D3semidirect
245. C3×C22⋊C8C22×C3semidirect
247. #835C22×C3semidirect
248. #821C22×C3semidirect
249. (C2×D3)⋊C8C22×C3semidirect
250. #816C22×C3semidirect
251. #815C22×C3semidirect
252. Dic3⋊C8C22×C3semidirect
253. #809C22×C3semidirect
254. #807C22×C3semidirect
304. C3×Dic6C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
318. #450C3×D3semidirect
446. #214C3×D4semidirect
485. C2×C3×D3AGL(1,ℤ/8)semidirect
508. C2×SD16C2×C3×D3semidirect
518. C22⋊Q8C2×C3×D3semidirect
537. #102C2×C3×D3semidirect
539. C22⋊C8C2×C3×D3semidirect
659. Dic6C2×C3×D4semidirect
669. C3⋊C8C2×C3×D4semidirect
794. C2×D3C3×AGL(1,ℤ/8)semidirect
820. C32#3265semidirect
931. C3#80156direct (N × H)
932. C3C3×#3265semidirect

Maximal subgroups

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

subgroupindex
C3×D4×#672
C2×C3×#9322
C2×C3×D3×SD162
C3×#56332
C32×#4502
C3×#51762
C3×#51702
C3×#51652
C3×#50492
C3×#47752
C3×#47732
C3×#47622
C3×#47572
C3×#47342
C3×#47282
C3×#32653
#801563