Finite Group Databasebeta

← C3×C4×#949 #11860259

Subgroups — C3×C4×#949 #11860259

Order 1152.

1251 conjugacy classes of subgroups.

The subgroup lattice has 695 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×#41C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic
3C2×C3×C4×D12C211yesmaximal, characteristic, complemented
4C3×#5232C211yesmaximal, characteristic, complemented
5C3×#5026C212yesmaximal, complemented
6C3×C4×#215C212yesmaximal, complemented
7C3×#5014C212yesmaximal, complemented
8C3×C4×#213C212yesmaximal, complemented
9C3×#5001C211yesmaximal, characteristic, complemented
10C3×#4995C211yesmaximal, characteristic, complemented
11C3×C4×#208C211yesmaximal, characteristic, complemented
12C3×C4×AGL(1,ℤ/8)—31nomaximal
13C4×#949C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×C3×C4×D3—21no—
17C32×C4×Q8C2211yescharacteristic, complemented
18C32×C4×Q8C2211yescharacteristic, complemented
19C32×C4×D4—21no—
20C32×C4×D4—21no—
21C32×C4×D4C2211yescharacteristic, complemented
22C32×C4×D4C2211yescharacteristic, complemented
23C32×#117—21no—
24C32×#117C2211yescharacteristic
25C2×C32×C42—21no—
26C2×C32×C42C2211yescharacteristic
27C3×#949C418yesdirect product factor
28C2×C3×#215C2212yes—
29C2×C3×#213C2212yes—
30C2×C3×(C2×D3)⋊C4—21no—
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×#208C2211yescharacteristic
33C2×C3×#208C2211yescharacteristic
34C3×C4×D12—21no—
35C3×C4×D12—21no—
36C3×C4×D12C2212yes—
37C3×C4×D12C2212yes—
38C3×#835C2212yescomplemented
39C3×#832C2212yescomplemented
40C3×#809C2212yes—
41C3×#809C2212yes—
42C3×#808C2212yescomplemented
43C3×#807C2212yescomplemented
44C3×#803C2212yescomplemented
45C3×C4×C3⋊C8C2212yescomplemented
46C2×C3×AGL(1,ℤ/8)—31no—
47C3×C4×#41—21no—
48C3×C4×#41D311yescharacteristic, complemented
49C3×C4×#41C2×C311yescharacteristic, complemented
50C2×C3×C4×D4—31no—
51C2×#949C2×C311yescharacteristic
52C2×C4×D12C2×C311yescharacteristic, complemented
53C3×#442—32no—
54C3×#440—32no—
55C3×C4×SD16—32no—
56C3×C4×D8—32no—
57C3×#428—31no—
58C3×#418—31no—
59C3×#417—31no—
60C3×C4×M16—31no—
61#5232C2×C311yescharacteristic, complemented
62#5026C2×C312yescomplemented
63C4×#215C2×C312yescomplemented
64#5014C2×C312yescomplemented
65C4×#213C2×C312yescomplemented
66#5001C2×C311yescharacteristic, complemented
67#4995C2×C311yescharacteristic, complemented
68C4×#208C2×C311yescharacteristic, complemented
69C23×C3×D3—21no—
70C32×#41—22no—
71C32×#41C2×C414yescomplemented
72C2×C32×Q8C2311yescharacteristic
73C2×C32×D4—21no—
74C2×C32×D4C2311yescharacteristic
75C22×C32×C4—21no—
76C22×C32×C4—21no—
77C22×C32×C4—21no—
78C22×C32×C4D411yescharacteristic
79C22×C32×C4D411yescharacteristic
80C22×C32×C4C2311yescharacteristic
81C22×C3×Dic3—21no—
82C2×C3×D12—21no—
83C2×C3×D12—22no—
84C2×C3×D12C2×C414yescomplemented
85C2×C3×D12C2312yes—
86C2×C3×C4×D3—22no—
87C2×C3×C4×D3—22no—
88C2×C3×C4×D3—44no—
89C32×C4⋊C4—21no—
90C32×C4⋊C4—21no—
91C32×C4⋊C4C2311yescharacteristic
92C32×C4⋊C4C2311yescharacteristic
93C32×C22⋊C4—21no—
94C32×C22⋊C4—21no—
95C32×C22⋊C4—21no—
96C32×C42—21no—
97C32×C42—21no—
98C32×C42—21no—
99C32×C42D411yescharacteristic
100C32×C42D411yescharacteristic
101C32×C42C2311yescharacteristic
102C32×C42C2311yescharacteristic
103C3×#215C2×C418yescomplemented
104C3×#213C2×C418yescomplemented
105C3×(C2×D3)⋊C4—22no—
106C3×(C2×D3)⋊C4—22no—
107C3×C4⋊Dic3—21no—
108C3×C4⋊Dic3C2312yes—
109C3×#208—22no—
110C3×#208C2×C414yescomplemented
111C2×C3×C3⋊C8C2312yes—
112C2×C3×C3⋊C8C2312yes—
113C4×AGL(1,ℤ/8)—31noSylow
114C2×C3×#41—21no—
115C2×C3×#41C2×D311yescharacteristic
116C2×C3×#41C22×C311yescharacteristic
117C22×C3×D4—31no—
118C23×C3×C4—61no—
119C22×D12C22×C311yescharacteristic
120C22×C4×D3—21no—
121C3×AGL(1,ℤ/8)—38no—
122C2×C3×SD16—32no—
123C2×C3×D8—32no—
124C2×C3×M16—31no—
125C2×C3×M16—31no—
126C3×C4×Q8—21no—
127C3×C4×Q8—21no—
128C3×C4×Q8C2×D311yescharacteristic, complemented
129C3×C4×Q8C2×D311yescharacteristic, complemented
130C3×C4×Q8C22×C311yescharacteristic, complemented
131C3×C4×Q8C22×C311yescharacteristic, complemented
132C3×C4×D4—22no—
133C3×C4×D4—22no—
134C3×C4×D4—21no—
135C3×C4×D4—21no—
136C3×C4×D4—21no—
137C3×C4×D4—21no—
138C3×C4×D4—21no—
139C3×C4×D4—21no—
140C3×C4×D4—32no—
141C3×C4×D4—32no—
142C3×C4×D4—61no—
143C3×C4×D4—61no—
144C3×C4×D4C2×D311yescharacteristic, complemented
145C3×C4×D4C2×D311yescharacteristic, complemented
146C3×C4×D4C22×C311yescharacteristic, complemented
147C3×C4×D4C22×C311yescharacteristic, complemented
148C3×#117—22no—
149C3×#117—21no—
150C3×#117—21no—
151C3×#117—21no—
152C3×#117C2×D311yescharacteristic
153C3×#117C22×C311yescharacteristic
154C2×C3×C4⋊C4—31no—
155C2×C3×C22⋊C4—61no—
156C2×C3×C42—22no—
157C2×C3×C42—21no—
158C2×C3×C42—21no—
159C2×C3×C42—21no—
160C2×C3×C42C2×D311yescharacteristic
161C2×C3×C42C22×C311yescharacteristic
162#949C3×C418yesdirect product factor
163C2×#215C22×C312yes—
164C2×#213C22×C312yes—
165C2×(C2×D3)⋊C4—21no—
166C2×C4⋊Dic3C22×C311yescharacteristic
167C2×#208C22×C311yescharacteristic
168C2×#208C22×C311yescharacteristic
169C4×D12—21no—
170C4×D12—21no—
171C4×D12C22×C312yes—
172C4×D12C22×C312yes—
173C3×#107—32no—
174C3×#106—32no—
175C3×#103—32no—
176C3×#102—32no—
177C3×#102—32no—
178C3×#102—32no—
179C3×#97—32no—
180C3×C4×C8—32no—
181#835C22×C312yescomplemented
182#832C22×C312yescomplemented
183#809C22×C312yes—
184#809C22×C312yes—
185#808C22×C312yescomplemented
186#807C22×C312yescomplemented
187#803C22×C312yescomplemented
188C4×C3⋊C8C22×C312yescomplemented
189C23×C32—21no—
190C23×C32C2×D411yescharacteristic
191C22×C3×D3—24no—
192C22×C3×D3—22no—
193C22×C3×D3—42no—
194C22×C3×D3—42no—
195C32×Q8—21no—
196C32×Q8C22×C412yescomplemented
197C32×D4—24no—
198C32×D4—21no—
199C32×D4C22×C412yescomplemented
200C2×C32×C4—21no—
201C2×C32×C4—24no—
202C2×C32×C4—21no—
203C2×C32×C4—21no—
204C2×C32×C4—22no—
205C2×C32×C4—41no—
206C2×C32×C4—42no—
207C2×C32×C4—42no—
208C2×C32×C4C22×C412yes—
209C2×C32×C4C2×D411yescharacteristic
210C2×C32×C4C2×D411yescharacteristic
211C2×C32×C4C2×D411yescharacteristic
212C2×C32×C4C2×D411yescharacteristic
213C2×C32×C4C2×D411yescharacteristic
214C2×C32×C4#4112yes—
215C2×C32×C4C2411yescharacteristic
216C2×C3×Dic3—22no—
217C2×C3×Dic3—42no—
218C3×D12—24no—
219C3×D12—22no—
220C3×D12C22×C414yes—
221C3×C4×D3—44no—
222C3×C4×D3—44no—
223C3×C3⋊C8—22no—
224C3×C3⋊C8C22×C414yescomplemented
225C2×AGL(1,ℤ/8)—31no—
226C4×#41C3×D311yescharacteristic, complemented
227C2×C4×D4—31no—
228#442—32no—
229#440—32no—
230C4×SD16—32no—
231C4×D8—32no—
232#428—31no—
233#418—31no—
234#417—31no—
235C4×M16—31no—
236C24×C3—61no—
237C23×D3—21no—
238C3×#41—24no—
239C3×#41—22no—
240C3×#41—22no—
241C3×#41—24no—
242C3×#41C4×D314yescomplemented
243C3×#41C2×C3×C414yescomplemented
244C2×C3×Q8—21no—
245C2×C3×Q8C22×D311yescharacteristic
246C2×C3×Q8C23×C311yescharacteristic
247C2×C3×D4—22no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—34no—
252C2×C3×D4—32no—
253C2×C3×D4—62no—
254C2×C3×D4—61no—
255C2×C3×D4C22×D311yescharacteristic
256C2×C3×D4C23×C311yescharacteristic
257C22×C3×C4—22no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—61no—
270C22×C3×C4—62no—
271C22×C3×C4—62no—
272C22×C3×C4—124no—
273C22×C3×C4#6711yescharacteristic
274C22×C3×C4#6711yescharacteristic
275C22×C3×C4C3×D411yescharacteristic
276C22×C3×C4C3×D411yescharacteristic
277C22×C3×C4C22×D311yescharacteristic
278C22×C3×C4C23×C311yescharacteristic
279C22×Dic3—21no—
280C2×D12—21no—
281C2×D12—22no—
282C2×D12C2×C3×C414yescomplemented
283C2×D12C23×C312yes—
284C2×C4×D3—22no—
285C2×C4×D3—22no—
286C2×C4×D3—44no—
287C3×SD16—38no—
288C3×D8—38no—
289C3×M16—34no—
290C3×M16—62no—
291C2×C3×C8—32no—
292C2×C3×C8—32no—
293C3×C4⋊C4—22no—
294C3×C4⋊C4—22no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—32no—
302C3×C4⋊C4—61no—
303C3×C4⋊C4C22×D311yescharacteristic
304C3×C4⋊C4C22×D311yescharacteristic
305C3×C4⋊C4C23×C311yescharacteristic
306C3×C4⋊C4C23×C311yescharacteristic
307C3×C22⋊C4—22no—
308C3×C22⋊C4—22no—
309C3×C22⋊C4—22no—
310C3×C22⋊C4—21no—
311C3×C22⋊C4—21no—
312C3×C22⋊C4—21no—
313C3×C22⋊C4—21no—
314C3×C22⋊C4—21no—
315C3×C22⋊C4—21no—
316C3×C22⋊C4—62no—
317C3×C22⋊C4—62no—
318C3×C42—22no—
319C3×C42—22no—
320C3×C42—22no—
321C3×C42—21no—
322C3×C42—21no—
323C3×C42—21no—
324C3×C42—21no—
325C3×C42—21no—
326C3×C42—21no—
327C3×C42—21no—
328C3×C42—21no—
329C3×C42—21no—
330C3×C42—21no—
331C3×C42#6711yescharacteristic
332C3×C42#6711yescharacteristic
333C3×C42C3×D411yescharacteristic
334C3×C42C3×D411yescharacteristic
335C3×C42C22×D311yescharacteristic
336C3×C42C22×D311yescharacteristic
337C3×C42C23×C311yescharacteristic
338C3×C42C23×C311yescharacteristic
339#215C2×C3×C418yescomplemented
340#213C2×C3×C418yescomplemented
341(C2×D3)⋊C4—22no—
342(C2×D3)⋊C4—22no—
343C4⋊Dic3—21no—
344C4⋊Dic3C23×C312yes—
345#208—22no—
346#208C2×C3×C414yescomplemented
347C2×C3⋊C8C23×C312yes—
348C2×C3⋊C8C23×C312yes—
349C22×C32—22no—
350C22×C32—21no—
351C22×C32—21no—
352C22×C32—41no—
353C22×C32—41no—
354C22×C32C4×D412yes—
355C22×C32C22×D411yescharacteristic
356C2×C3×D3—24no—
357C2×C3×D3—48no—
358C2×C3×D3—42no—
359C2×C3×D3—42no—
360C32×C4—22no—
361C32×C4—21no—
362C32×C4—21no—
363C32×C4—21no—
364C32×C4—41no—
365C32×C4—41no—
366C32×C4C4×D412yes—
367C32×C4AGL(1,ℤ/8)12yescomplemented
368C32×C4C23×C411yescharacteristic
369C32×C4C2×#4111yescharacteristic
370C3×Dic3—42no—
371C2×#41C2×C3×D311yescharacteristic
372C22×D4—31no—
373C23×C4—61no—
374AGL(1,ℤ/8)—38no—
375C2×SD16—32no—
376C2×D8—32no—
377C2×M16—31no—
378C2×M16—31no—
379C4×Q8C2×C3×D311yescharacteristic, complemented
380C4×Q8C2×C3×D311yescharacteristic, complemented
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—32no—
384C4×D4—32no—
385C4×D4—61no—
386C4×D4—61no—
387C4×D4C2×C3×D311yescharacteristic, complemented
388C4×D4C2×C3×D311yescharacteristic, complemented
389#117—21no—
390#117C2×C3×D311yescharacteristic
391C2×C4⋊C4—31no—
392C2×C22⋊C4—61no—
393C2×C42—21no—
394C2×C42C2×C3×D311yescharacteristic
395#107—32no—
396#106—32no—
397#103—32no—
398#102—32no—
399#102—32no—
400#102—32no—
401#97—32no—
402C4×C8—32no—
403C23×C3—22no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—64no—
408C23×C3—62no—
409C23×C3—122no—
410C23×C3—122no—
411C23×C3C2×#6711yescharacteristic
412C23×C3C2×C3×D411yescharacteristic
413C22×D3—24no—
414C22×D3—22no—
415C22×D3—42no—
416C22×D3—42no—
417C3×Q8—22no—
418C3×Q8—21no—
419C3×Q8—21no—
420C3×Q8—22no—
421C3×Q8C2×C4×D312yescomplemented
422C3×Q8C22×C3×C412yescomplemented
423C3×D4—28no—
424C3×D4—22no—
425C3×D4—24no—
426C3×D4—24no—
427C3×D4—21no—
428C3×D4—21no—
429C3×D4—22no—
430C3×D4—34no—
431C3×D4—64no—
432C3×D4—62no—
433C3×D4C2×C4×D312yescomplemented
434C3×D4C22×C3×C412yescomplemented
435C2×C3×C4—22no—
436C2×C3×C4—28no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—24no—
440C2×C3×C4—22no—
441C2×C3×C4—24no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—42no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—42no—
461C2×C3×C4—44no—
462C2×C3×C4—42no—
463C2×C3×C4—42no—
464C2×C3×C4—44no—
465C2×C3×C4—42no—
466C2×C3×C4—42no—
467C2×C3×C4—62no—
468C2×C3×C4—124no—
469C2×C3×C4—122no—
470C2×C3×C4—124no—
471C2×C3×C4C2×C4×D312yes—
472C2×C3×C4#23512yes—
473C2×C3×C4C2×#6711yescharacteristic
474C2×C3×C4C2×#6711yescharacteristic
475C2×C3×C4C2×#6711yescharacteristic
476C2×C3×C4C2×#6711yescharacteristic
477C2×C3×C4C2×#6711yescharacteristic
478C2×C3×C4C22×C3×C412yes—
479C2×C3×C4C2×C3×D411yescharacteristic
480C2×C3×C4C2×C3×D411yescharacteristic
481C2×C3×C4C2×C3×D411yescharacteristic
482C2×C3×C4C2×C3×D411yescharacteristic
483C2×C3×C4C2×C3×D411yescharacteristic
484C2×C3×C4C3×#4112yes—
485C2×C3×C4C23×D311yescharacteristic
486C2×C3×C4C24×C311yescharacteristic
487C2×Dic3—22no—
488C2×Dic3—42no—
489D12—24no—
490D12—22no—
491D12C22×C3×C414yes—
492C4×D3—44no—
493C4×D3—44no—
494C3×C8—34no—
495C3×C8—62no—
496C3⋊C8—22no—
497C3⋊C8C22×C3×C414yescomplemented
498C2×C32—22no—
499C2×C32—42no—
500C2×C32C2×C4×D411yescharacteristic
501C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
502C2×C32#57511yescharacteristic
503C3×D3—44no—
504C24—61no—
505#41—22no—
506#41C3×C4×D314yescomplemented
507C2×Q8C22×C3×D311yescharacteristic
508C2×D4—21no—
509C2×D4—32no—
510C2×D4—34no—
511C2×D4—62no—
512C2×D4—61no—
513C2×D4C22×C3×D311yescharacteristic
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—61no—
518C22×C4—62no—
519C22×C4—62no—
520C22×C4—124no—
521C22×C4C3×#6711yescharacteristic
522C22×C4C3×#6711yescharacteristic
523C22×C4C22×C3×D311yescharacteristic
524SD16—38no—
525D8—38no—
526M16—34no—
527M16—62no—
528C2×C8—32no—
529C2×C8—32no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—32no—
533C4⋊C4—61no—
534C4⋊C4C22×C3×D311yescharacteristic
535C4⋊C4C22×C3×D311yescharacteristic
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—62no—
540C22⋊C4—62no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42C3×#6711yescharacteristic
545C42C3×#6711yescharacteristic
546C42C22×C3×D311yescharacteristic
547C42C22×C3×D311yescharacteristic
548C22×C3—21no—
549C22×C3—21no—
550C22×C3—21no—
551C22×C3—21no—
552C22×C3—24no—
553C22×C3—22no—
554C22×C3—22no—
555C22×C3—22no—
556C22×C3—21no—
557C22×C3—41no—
558C22×C3—41no—
559C22×C3—42no—
560C22×C3—42no—
561C22×C3—41no—
562C22×C3—41no—
563C22×C3—41no—
564C22×C3—41no—
565C22×C3—64no—
566C22×C3—128no—
567C22×C3—122no—
568C22×C3—122no—
569C22×C3C4×#6712yes—
570C22×C3C3×C4×D412yes—
571C22×C3C22×#6711yescharacteristic
572C22×C3C22×C3×D411yescharacteristic
573C2×D3—24no—
574C2×D3—48no—
575C2×D3—42no—
576C2×D3—42no—
577C3×C4—24no—
578C3×C4—22no—
579C3×C4—21no—
580C3×C4—21no—
581C3×C4—21no—
582C3×C4—22no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—22no—
587C3×C4—22no—
588C3×C4—22no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—42no—
594C3×C4—42no—
595C3×C4—41no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—41no—
599C3×C4—122no—
600C3×C4C4×#6712yes—
601C3×C4#94912yesdirect product factor
602C3×C4C3×C4×D412yes—
603C3×C4C3×AGL(1,ℤ/8)12yescomplemented
604C3×C4C22×C4×D311yescharacteristic
605C3×C4C2×#23511yescharacteristic
606C3×C4C23×C3×C411yescharacteristic
607C3×C4C2×C3×#4111yescharacteristic
608Dic3—42no—
609C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
610C23—21no—
611C23—64no—
612C23—62no—
613C23—122no—
614C23—122no—
615C23C2×C3×#6711yescharacteristic
616Q8—21no—
617Q8C2×C3×C4×D312yescomplemented
618D4—24no—
619D4—21no—
620D4—34no—
621D4—64no—
622D4—62no—
623D4C2×C3×C4×D312yescomplemented
624C2×C4—21no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—41no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—62no—
633C2×C4—124no—
634C2×C4—122no—
635C2×C4—124no—
636C2×C4C2×C3×C4×D312yes—
637C2×C4C3×#23512yes—
638C2×C4C2×C3×#6711yescharacteristic
639C2×C4C2×C3×#6711yescharacteristic
640C2×C4C2×C3×#6711yescharacteristic
641C2×C4C2×C3×#6711yescharacteristic
642C2×C4C2×C3×#6711yescharacteristic
643C2×C4C23×C3×D311yescharacteristic
644C8—34no—
645C8—62no—
646C2×C3—22no—
647C2×C3—22no—
648C2×C3—21no—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—42no—
652C2×C3—44no—
653C2×C3—42no—
654C2×C3—42no—
655C2×C3—124no—
656C2×C3C2×C4×#6711yescharacteristic
657C2×C3C2×#94911yescharacteristic
658C2×C3#582211yescharacteristic
659C2×C3C2×C3×C4×D411yescharacteristic
660C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
661C2×C3C3×#57511yescharacteristic
662D3—44no—
663C22—21no—
664C22—21no—
665C22—22no—
666C22—41no—
667C22—41no—
668C22—64no—
669C22—128no—
670C22—122no—
671C22—122no—
672C22C3×C4×#6712yes—
673C22C22×C3×#6711yescharacteristic
674C4—22no—
675C4—21no—
676C4—21no—
677C4—21no—
678C4—41no—
679C4—41no—
680C4—122no—
681C4C3×C4×#6712yes—
682C4C3×#94912yesdirect product factor
683C4C22×C3×C4×D311yescharacteristic
684C4C2×C3×#23511yescharacteristic
685C3—21no—
686C3C4×#94911yescharacteristic, direct product factor
687C3C3×C4×AGL(1,ℤ/8)11yescharacteristic, complemented
688C2—22no—
689C2—42no—
690C2—124no—
691C2C2×C3×C4×#6711yescharacteristic
692C2C2×C3×#94911yescharacteristic
693C2C3×#582211yescharacteristic
subgroupG/H
centerC2×C3×C4C2×#67
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×C4×#41C2
socleC22×C32C22×D4
prime radicalC2×C3×#949C2
cosocleC2×C3×C4C24×C3
hypercenterC3×C4×#41D3
hypocenterC3C3×C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×C4×#41

Complements

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

NH ≅ G/Ntype
1. C32×C4×#41C2semidirect
3. C2×C3×C4×D12C2semidirect
4. C3×#5232C2semidirect
5. C3×#5026C2semidirect
6. C3×C4×#215C2semidirect
7. C3×#5014C2semidirect
8. C3×C4×#213C2semidirect
9. C3×#5001C2semidirect
10. C3×#4995C2semidirect
11. C3×C4×#208C2semidirect
13. C4×#949C3direct (N × H)
17. C32×C4×Q8C22semidirect
18. C32×C4×Q8C22semidirect
21. C32×C4×D4C22semidirect
22. C32×C4×D4C22semidirect
27. C3×#949C4direct (N × H)
38. C3×#835C22semidirect
39. C3×#832C22semidirect
42. C3×#808C22semidirect
43. C3×#807C22semidirect
44. C3×#803C22semidirect
45. C3×C4×C3⋊C8C22semidirect
48. C3×C4×#41D3semidirect
49. C3×C4×#41C2×C3semidirect
52. C2×C4×D12C2×C3semidirect
61. #5232C2×C3semidirect
62. #5026C2×C3semidirect
63. C4×#215C2×C3semidirect
64. #5014C2×C3semidirect
65. C4×#213C2×C3semidirect
66. #5001C2×C3semidirect
67. #4995C2×C3semidirect
68. C4×#208C2×C3semidirect
71. C32×#41C2×C4semidirect
84. C2×C3×D12C2×C4semidirect
103. C3×#215C2×C4semidirect
104. C3×#213C2×C4semidirect
110. C3×#208C2×C4semidirect
128. C3×C4×Q8C2×D3semidirect
129. C3×C4×Q8C2×D3semidirect
130. C3×C4×Q8C22×C3semidirect
131. C3×C4×Q8C22×C3semidirect
144. C3×C4×D4C2×D3semidirect
145. C3×C4×D4C2×D3semidirect
146. C3×C4×D4C22×C3semidirect
147. C3×C4×D4C22×C3semidirect
162. #949C3×C4direct (N × H)
181. #835C22×C3semidirect
182. #832C22×C3semidirect
185. #808C22×C3semidirect
186. #807C22×C3semidirect
187. #803C22×C3semidirect
188. C4×C3⋊C8C22×C3semidirect
196. C32×Q8C22×C4semidirect
199. C32×D4C22×C4semidirect
224. C3×C3⋊C8C22×C4semidirect
226. C4×#41C3×D3semidirect
242. C3×#41C4×D3semidirect
243. C3×#41C2×C3×C4semidirect
282. C2×D12C2×C3×C4semidirect
339. #215C2×C3×C4semidirect
340. #213C2×C3×C4semidirect
346. #208C2×C3×C4semidirect
367. C32×C4AGL(1,ℤ/8)semidirect
379. C4×Q8C2×C3×D3semidirect
380. C4×Q8C2×C3×D3semidirect
387. C4×D4C2×C3×D3semidirect
388. C4×D4C2×C3×D3semidirect
421. C3×Q8C2×C4×D3semidirect
422. C3×Q8C22×C3×C4semidirect
433. C3×D4C2×C4×D3semidirect
434. C3×D4C22×C3×C4semidirect
497. C3⋊C8C22×C3×C4semidirect
506. #41C3×C4×D3semidirect
601. C3×C4#949direct (N × H)
603. C3×C4C3×AGL(1,ℤ/8)semidirect
609. C32C4×AGL(1,ℤ/8)semidirect
617. Q8C2×C3×C4×D3semidirect
623. D4C2×C3×C4×D3semidirect
682. C4C3×#949direct (N × H)
686. C3C4×#949direct (N × H)
687. C3C3×C4×AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
C32×C4×#412
C2×C3×#9492
C2×C3×C4×D122
C3×#52322
C3×#50262
C3×C4×#2152
C3×#50142
C3×C4×#2132
C3×#50012
C3×#49952
C3×C4×#2082
C3×C4×AGL(1,ℤ/8)3
C4×#9493