Finite Group Databasebeta

← C3×#81141 #11870865

Subgroups — C3×#81141 #11870865

Order 1152.

959 conjugacy classes of subgroups.

The subgroup lattice has 787 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5691C211yesmaximal, characteristic, complemented
2C3×C4×D3×D4C211yesmaximal, characteristic, complemented
3C32×#478C211yesmaximal, characteristic, complemented
4C3×#5066C211yesmaximal, characteristic, complemented
5C3×#5016C211yesmaximal, characteristic, complemented
6C3×#4884C211yesmaximal, characteristic, complemented
7C3×#4872C211yesmaximal, characteristic, complemented
8C3×#4863C211yesmaximal, characteristic, complemented
9C3×#4852C211yesmaximal, characteristic, complemented
10C3×#4844C211yesmaximal, characteristic, complemented
11C3×#4833C211yesmaximal, characteristic, complemented
12C3×#4776C211yesmaximal, characteristic, complemented
13C3×#4773C211yesmaximal, characteristic
14C3×#4758C211yesmaximal, characteristic, complemented
15C3×#4756C211yesmaximal, characteristic, complemented
16C3×#3105—31nomaximal
17#81141C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×D4C2211yescharacteristic
19C22×C3×C4×D3—21no—
20C32×#125C2211yescharacteristic, complemented
21C32×C4×D4C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C2×C3×#214C2211yescharacteristic
24C2×C3×#213C2211yescharacteristic
25C3×C4×#67—21no—
26C2×C3×D24C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic
28C3×#898—21no—
29C3×#897C2211yescharacteristic
30C3×#895C2211yescharacteristic
31C3×#894—21no—
32C3×#893—21no—
33C3×#893C2211yescharacteristic
34C3×#893C2211yescharacteristic, complemented
35C3×#892—21no—
36C3×D3×C4⋊C4C2211yescharacteristic
37C3×#887C2211yescharacteristic, complemented
38C3×#67⋊C4—21no—
39C3×D3×C22⋊C4—21no—
40C3×#875C2211yescharacteristic, complemented
41C3×C4×D12C2211yescharacteristic
42C3×C42×D3C2211yescharacteristic
43C32×#107C2211yescharacteristic, complemented
44C32×#106C2211yescharacteristic, complemented
45C32×C4⋊C8C2211yescharacteristic, complemented
46C32×#102C2211yescharacteristic
47C32×#102C2211yescharacteristic
48C3×#821C2211yescharacteristic, complemented
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic, complemented
52C3×C8×Dic3C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54C3×#810C2211yescharacteristic, complemented
55C3×#809C2211yescharacteristic
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic, complemented
58C3×#808C2211yescharacteristic, complemented
59C3×#807C2211yescharacteristic, complemented
60C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#529—31no—
62C2×C3×C4×D4—31no—
63#5691C2×C311yescharacteristic, complemented
64C4×D3×D4C2×C311yescharacteristic, complemented
65C3×#484—31no—
66C3×#481—31no—
67C3×#478—21no—
68C3×#478—31no—
69C3×#478D311yescharacteristic, complemented
70C3×#478C2×C311yescharacteristic, complemented
71C3×#463—31no—
72C3×#463—31no—
73C3×#450—31no—
74C3×#447—31no—
75C3×C4×SD16—31no—
76C3×C4×SD16—31no—
77C3×C4×D8—31no—
78C3×C4×D8—31no—
79C3×#431—31no—
80#5066C2×C311yescharacteristic, complemented
81#5016C2×C311yescharacteristic, complemented
82#4884C2×C311yescharacteristic, complemented
83#4872C2×C311yescharacteristic, complemented
84#4863C2×C311yescharacteristic, complemented
85#4852C2×C311yescharacteristic, complemented
86#4844C2×C311yescharacteristic, complemented
87#4833C2×C311yescharacteristic, complemented
88#4776C2×C311yescharacteristic, complemented
89#4773C2×C311yescharacteristic
90#4758C2×C311yescharacteristic, complemented
91#4756C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C3×#67—21no—
96C22×C3×Dic3—21no—
97C3×D3×D4—22no—
98C3×D3×D4—22no—
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—44no—
107C2×C3×C4×D3D411yescharacteristic
108C2×C3×C4×D3D411yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4—21no—
114C32×C4⋊C4—21no—
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C22⋊C4—21no—
119C32×C42C2311yescharacteristic
120C3×#217—21no—
121C3×#214—22no—
122C3×#213—22no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3D411yescharacteristic
136C3×C4×Dic3D411yescharacteristic
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×D24—22no—
141C3×#204—22no—
142#3105—31noSylow
143C22×C3×D4—31no—
144C23×C3×C4—61no—
145C2×D3×D4C22×C311yescharacteristic
146C22×C4×D3—21no—
147C2×C3×SD16—31no—
148C2×C3×SD16—31no—
149C2×C3×D8—31no—
150C2×C3×D8—31no—
151C3×#126—61no—
152C3×#125—21no—
153C3×#125C2×D311yescharacteristic, complemented
154C3×#125C22×C311yescharacteristic, complemented
155C3×#124—31no—
156C3×#123—61no—
157C3×C22⋊Q8—31no—
158C3×#121—31no—
159C3×C4×Q8—31no—
160C3×C4×D4—21no—
161C3×C4×D4—31no—
162C3×C4×D4—31no—
163C3×C4×D4—31no—
164C3×C4×D4—31no—
165C3×C4×D4—61no—
166C3×C4×D4—61no—
167C3×C4×D4—61no—
168C3×C4×D4C2×D311yescharacteristic
169C3×C4×D4C22×C311yescharacteristic
170C3×#117—61no—
171C2×C3×C4⋊C4—31no—
172C2×C3×C22⋊C4—61no—
173C2×C3×C42—31no—
174D4×Dic3C22×C311yescharacteristic
175C2×#214C22×C311yescharacteristic
176C2×#213C22×C311yescharacteristic
177C4×#67—21no—
178C2×D24C22×C311yescharacteristic
179C2×#204C22×C311yescharacteristic
180#898—21no—
181#897C22×C311yescharacteristic
182#895C22×C311yescharacteristic
183#894—21no—
184#893—21no—
185#893C22×C311yescharacteristic
186#893C22×C311yescharacteristic, complemented
187#892—21no—
188D3×C4⋊C4C22×C311yescharacteristic
189#887C22×C311yescharacteristic, complemented
190#67⋊C4—21no—
191D3×C22⋊C4—21no—
192#875C22×C311yescharacteristic, complemented
193C4×D12C22×C311yescharacteristic
194C42×D3C22×C311yescharacteristic
195C3×#107—21no—
196C3×#107—31no—
197C3×#107C2×D311yescharacteristic, complemented
198C3×#107C22×C311yescharacteristic, complemented
199C3×#106—21no—
200C3×#106—31no—
201C3×#106C2×D311yescharacteristic, complemented
202C3×#106C22×C311yescharacteristic, complemented
203C3×C4⋊C8—21no—
204C3×C4⋊C8—31no—
205C3×C4⋊C8C2×D311yescharacteristic, complemented
206C3×C4⋊C8C22×C311yescharacteristic, complemented
207C3×#103—31no—
208C3×#103—31no—
209C3×#102—21no—
210C3×#102—21no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102C2×D311yescharacteristic
216C3×#102C2×D311yescharacteristic
217C3×#102C22×C311yescharacteristic
218C3×#102C22×C311yescharacteristic
219C3×C22⋊C8—31no—
220C3×C22⋊C8—31no—
221C3×C4×C8—31no—
222C3×C4×C8—31no—
223#821C22×C311yescharacteristic, complemented
224(C2×D3)⋊C8C22×C311yescharacteristic
225(C2×D3)⋊C8C22×C311yescharacteristic
226#816C22×C311yescharacteristic, complemented
227C8×Dic3C22×C311yescharacteristic, complemented
228C8×Dic3C22×C311yescharacteristic, complemented
229#810C22×C311yescharacteristic, complemented
230#809C22×C311yescharacteristic
231#809C22×C311yescharacteristic
232#809C22×C311yescharacteristic, complemented
233#808C22×C311yescharacteristic, complemented
234#807C22×C311yescharacteristic, complemented
235C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
236C23×C32—21no—
237C22×C3×D3—24no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—42no—
241C22×C3×D3—42no—
242C22×C3×D3C2×D411yescharacteristic
243C32×D4—21no—
244C32×D4#4112yes—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—42no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C3×#67—24no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—42no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—21no—
262C3×D12—42no—
263C3×D12#4112yes—
264C3×C4×D3—22no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—22no—
268C3×C4×D3—42no—
269C3×C4×D3—42no—
270C3×C4×D3—42no—
271C3×C4×D3—42no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C32×C8—21no—
275C32×C8—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278#529—31no—
279C2×C4×D4—31no—
280#484—31no—
281#481—31no—
282#478—31no—
283#478C3×D311yescharacteristic, complemented
284#463—31no—
285#463—31no—
286#450—31no—
287#447—31no—
288C4×SD16—31no—
289C4×SD16—31no—
290C4×D8—31no—
291C4×D8—31no—
292#431—31no—
293C24×C3—61no—
294C23×D3—21no—
295C2×C3×Q8—31no—
296C2×C3×D4—21no—
297C2×C3×D4—31no—
298C2×C3×D4—31no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×C3×D4—62no—
302C2×C3×D4—62no—
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C23×C311yescharacteristic
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—41no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4—124no—
317C2×#67—21no—
318C22×Dic3—21no—
319D3×D4—22no—
320D3×D4—22no—
321C2×D12—21no—
322C2×D12C23×C311yescharacteristic
323C2×D12C23×C311yescharacteristic
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×C4×D3—21no—
327C2×C4×D3—21no—
328C2×C4×D3—44no—
329C2×C4×D3C3×D411yescharacteristic
330C2×C4×D3C3×D411yescharacteristic
331C2×C4×D3C23×C311yescharacteristic
332C2×Dic6C23×C311yescharacteristic
333C3×SD16—62no—
334C3×SD16—62no—
335C3×D8—62no—
336C3×D8—62no—
337C2×C3×C8—21no—
338C2×C3×C8—21no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C23×C311yescharacteristic
344C2×C3×C8C23×C311yescharacteristic
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—41no—
354C3×C4⋊C4—41no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C23×C311yescharacteristic
362C3×C4⋊C4C23×C311yescharacteristic
363C3×C4⋊C4C23×C311yescharacteristic
364C3×C22⋊C4—21no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—41no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C42—21no—
376C3×C42—31no—
377C3×C42—31no—
378C3×C42—31no—
379C3×C42—61no—
380C3×C42C22×D311yescharacteristic
381C3×C42C23×C311yescharacteristic
382#217—21no—
383#214—22no—
384#213—22no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—21no—
392C4⋊Dic3—21no—
393C4⋊Dic3C23×C311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396C4×Dic3—21no—
397C4×Dic3C3×D411yescharacteristic
398C4×Dic3C3×D411yescharacteristic
399C4×Dic3C23×C311yescharacteristic
400C2×C3⋊C8C23×C311yescharacteristic
401C2×C3⋊C8C23×C311yescharacteristic
402D24—22no—
403#204—22no—
404C22×C32—22no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32C22×D411yescharacteristic
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—22no—
411C2×C3×D3—48no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C2×C3×D3#13512yes—
418C32×C4—21no—
419C32×C4—21no—
420C32×C4—41no—
421C32×C4—41no—
422C32×C4—41no—
423C32×C4C2×#4111yescharacteristic
424C32×C4C2×#4111yescharacteristic
425C3×Dic3—21no—
426C3×Dic3—21no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3AGL(1,ℤ/8)12yes—
430C22×D4—31no—
431C23×C4—61no—
432C2×SD16—31no—
433C2×SD16—31no—
434C2×D8—31no—
435C2×D8—31no—
436#126—61no—
437#125C2×C3×D311yescharacteristic, complemented
438#124—31no—
439#123—61no—
440C22⋊Q8—31no—
441#121—31no—
442C4×Q8—31no—
443C4×D4—31no—
444C4×D4—31no—
445C4×D4—31no—
446C4×D4—31no—
447C4×D4—61no—
448C4×D4—61no—
449C4×D4—61no—
450C4×D4C2×C3×D311yescharacteristic
451#117—61no—
452C2×C4⋊C4—31no—
453C2×C22⋊C4—61no—
454C2×C42—31no—
455#107—31no—
456#107C2×C3×D311yescharacteristic, complemented
457#106—31no—
458#106C2×C3×D311yescharacteristic, complemented
459C4⋊C8—31no—
460C4⋊C8C2×C3×D311yescharacteristic, complemented
461#103—31no—
462#103—31no—
463#102—31no—
464#102—31no—
465#102—31no—
466#102—31no—
467#102C2×C3×D311yescharacteristic
468#102C2×C3×D311yescharacteristic
469C22⋊C8—31no—
470C22⋊C8—31no—
471C4×C8—31no—
472C4×C8—31no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—31no—
476C23×C3—41no—
477C23×C3—64no—
478C23×C3—61no—
479C23×C3—61no—
480C23×C3—122no—
481C23×C3—122no—
482C22×D3—24no—
483C22×D3—21no—
484C22×D3—21no—
485C22×D3—42no—
486C22×D3—42no—
487C22×D3C2×C3×D411yescharacteristic
488C3×Q8—61no—
489C3×Q8—61no—
490C3×D4—21no—
491C3×D4—21no—
492C3×D4—22no—
493C3×D4—32no—
494C3×D4—41no—
495C3×D4—64no—
496C3×D4—61no—
497C3×D4—61no—
498C3×D4—61no—
499C3×D4—122no—
500C3×D4#23912yes—
501C3×D4C3×#4112yes—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—42no—
518C2×C3×C4—42no—
519C2×C3×C4—62no—
520C2×C3×C4—62no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—82no—
526C2×C3×C4—122no—
527C2×C3×C4—122no—
528C2×C3×C4—122no—
529C2×C3×C4—122no—
530C2×C3×C4—122no—
531C2×C3×C4D3×D411yescharacteristic
532C2×C3×C4D3×D411yescharacteristic
533C2×C3×C4C2×C3×D411yescharacteristic
534C2×C3×C4C2×C3×D411yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536C2×C3×C4C24×C311yescharacteristic
537#67—24no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—42no—
541C2×Dic3C2×C3×D411yescharacteristic
542C2×Dic3C2×C3×D411yescharacteristic
543C2×Dic3C2×C3×D411yescharacteristic
544D12—21no—
545D12—21no—
546D12—21no—
547D12—42no—
548D12C3×#4112yes—
549C4×D3—22no—
550C4×D3—21no—
551C4×D3—21no—
552C4×D3—22no—
553C4×D3—42no—
554C4×D3—42no—
555C4×D3—42no—
556C4×D3—42no—
557Dic6—21no—
558Dic6—21no—
559C3×C8—21no—
560C3×C8—21no—
561C3×C8—21no—
562C3×C8—21no—
563C3×C8—41no—
564C3×C8—41no—
565C3×C8—61no—
566C3×C8—61no—
567C3⋊C8—21no—
568C3⋊C8—21no—
569C2×C32—42no—
570C2×C32#52511yescharacteristic
571C2×C32C2×#13511yescharacteristic
572C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
573C3×D3—22no—
574C3×D3—42no—
575C3×D3—81no—
576C24—61no—
577C2×Q8—31no—
578C2×D4—31no—
579C2×D4—31no—
580C2×D4—61no—
581C2×D4—61no—
582C2×D4—62no—
583C2×D4—62no—
584C2×D4C22×C3×D311yescharacteristic
585C22×C4—21no—
586C22×C4—31no—
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—124no—
595SD16—62no—
596SD16—62no—
597D8—62no—
598D8—62no—
599C2×C8—31no—
600C2×C8—31no—
601C2×C8C22×C3×D311yescharacteristic
602C2×C8C22×C3×D311yescharacteristic
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—31no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4C22×C3×D311yescharacteristic
610C4⋊C4C22×C3×D311yescharacteristic
611C4⋊C4C22×C3×D311yescharacteristic
612C22⋊C4—21no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C42—31no—
622C42—31no—
623C42—31no—
624C42—61no—
625C42C22×C3×D311yescharacteristic
626C22×C3—22no—
627C22×C3—22no—
628C22×C3—21no—
629C22×C3—32no—
630C22×C3—42no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—62no—
638C22×C3—81no—
639C22×C3—81no—
640C22×C3—128no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3C2×D3×D411yescharacteristic
647C22×C3C22×C3×D411yescharacteristic
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—22no—
651C2×D3—48no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3C3×#13512yes—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—32no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—81no—
676C3×C4—81no—
677C3×C4—81no—
678C3×C4—121no—
679C3×C4—121no—
680C3×C4C2×#23911yescharacteristic
681C3×C4D3×#4111yescharacteristic
682C3×C4C2×C3×#4111yescharacteristic
683C3×C4C2×C3×#4111yescharacteristic
684Dic3—21no—
685Dic3—21no—
686Dic3—41no—
687Dic3—41no—
688Dic3C3×AGL(1,ℤ/8)12yes—
689C32#310511yescharacteristic, complemented, Sylow
690C23—21no—
691C23—31no—
692C23—64no—
693C23—61no—
694C23—61no—
695C23—122no—
696C23—122no—
697Q8—61no—
698Q8—61no—
699D4—21no—
700D4—32no—
701D4—64no—
702D4—61no—
703D4—61no—
704D4—61no—
705D4—122no—
706D4C3×#23912yes—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—31no—
711C2×C4—31no—
712C2×C4—31no—
713C2×C4—42no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—122no—
721C2×C4—122no—
722C2×C4—122no—
723C2×C4—122no—
724C2×C4—122no—
725C2×C4C3×D3×D411yescharacteristic
726C2×C4C3×D3×D411yescharacteristic
727C2×C4C23×C3×D311yescharacteristic
728C8—21no—
729C8—21no—
730C8—61no—
731C8—61no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—42no—
736C2×C3—42no—
737C2×C3—62no—
738C2×C3—82no—
739C2×C3—122no—
740C2×C3—241no—
741C2×C3#562711yescharacteristic
742C2×C3D3×#13511yescharacteristic
743C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
744C2×C3C3×#52511yescharacteristic
745C2×C3C2×C3×#13511yescharacteristic
746C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
747D3—22no—
748D3—42no—
749D3—81no—
750C22—22no—
751C22—32no—
752C22—41no—
753C22—41no—
754C22—61no—
755C22—61no—
756C22—62no—
757C22—128no—
758C22—121no—
759C22—121no—
760C22—121no—
761C22—121no—
762C22—121no—
763C22C2×C3×D3×D411yescharacteristic
764C4—21no—
765C4—21no—
766C4—32no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—61no—
771C4—61no—
772C4—121no—
773C4—121no—
774C4C2×C3×#23911yescharacteristic
775C4C3×D3×#4111yescharacteristic
776C3—21no—
777C3#8114111yescharacteristic, direct product factor
778C3C3×#310511yescharacteristic, complemented
779C2—42no—
780C2—62no—
781C2—122no—
782C2—241no—
783C2C3×#562711yescharacteristic
784C2C3×D3×#13511yescharacteristic
785C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#478C2
socleC22×C32C22×D4
prime radicalC3×#4773C2
hypercenterC3×#478D3
hypocenterC3C3×#3105
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#478

Complements

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

NH ≅ G/Ntype
1. C3×#5691C2semidirect
2. C3×C4×D3×D4C2semidirect
3. C32×#478C2semidirect
4. C3×#5066C2semidirect
5. C3×#5016C2semidirect
6. C3×#4884C2semidirect
7. C3×#4872C2semidirect
8. C3×#4863C2semidirect
9. C3×#4852C2semidirect
10. C3×#4844C2semidirect
11. C3×#4833C2semidirect
12. C3×#4776C2semidirect
14. C3×#4758C2semidirect
15. C3×#4756C2semidirect
17. #81141C3direct (N × H)
20. C32×#125C22semidirect
34. C3×#893C22semidirect
37. C3×#887C22semidirect
40. C3×#875C22semidirect
43. C32×#107C22semidirect
44. C32×#106C22semidirect
45. C32×C4⋊C8C22semidirect
48. C3×#821C22semidirect
51. C3×#816C22semidirect
52. C3×C8×Dic3C22semidirect
53. C3×C8×Dic3C22semidirect
54. C3×#810C22semidirect
57. C3×#809C22semidirect
58. C3×#808C22semidirect
59. C3×#807C22semidirect
60. C3×C4⋊(C3⋊C8)C22semidirect
63. #5691C2×C3semidirect
64. C4×D3×D4C2×C3semidirect
69. C3×#478D3semidirect
70. C3×#478C2×C3semidirect
80. #5066C2×C3semidirect
81. #5016C2×C3semidirect
82. #4884C2×C3semidirect
83. #4872C2×C3semidirect
84. #4863C2×C3semidirect
85. #4852C2×C3semidirect
86. #4844C2×C3semidirect
87. #4833C2×C3semidirect
88. #4776C2×C3semidirect
90. #4758C2×C3semidirect
91. #4756C2×C3semidirect
153. C3×#125C2×D3semidirect
154. C3×#125C22×C3semidirect
186. #893C22×C3semidirect
189. #887C22×C3semidirect
192. #875C22×C3semidirect
197. C3×#107C2×D3semidirect
198. C3×#107C22×C3semidirect
201. C3×#106C2×D3semidirect
202. C3×#106C22×C3semidirect
205. C3×C4⋊C8C2×D3semidirect
206. C3×C4⋊C8C22×C3semidirect
223. #821C22×C3semidirect
226. #816C22×C3semidirect
227. C8×Dic3C22×C3semidirect
228. C8×Dic3C22×C3semidirect
229. #810C22×C3semidirect
232. #809C22×C3semidirect
233. #808C22×C3semidirect
234. #807C22×C3semidirect
235. C4⋊(C3⋊C8)C22×C3semidirect
283. #478C3×D3semidirect
437. #125C2×C3×D3semidirect
456. #107C2×C3×D3semidirect
458. #106C2×C3×D3semidirect
460. C4⋊C8C2×C3×D3semidirect
689. C32#3105semidirect
777. C3#81141direct (N × H)
778. C3C3×#3105semidirect

Maximal subgroups

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

subgroupindex
C3×#56912
C3×C4×D3×D42
C32×#4782
C3×#50662
C3×#50162
C3×#48842
C3×#48722
C3×#48632
C3×#48522
C3×#48442
C3×#48332
C3×#47762
C3×#47732
C3×#47582
C3×#47562
C3×#31053
#811413