Finite Group Databasebeta

← C3×C4×#916 #11859968

Subgroups — C3×C4×#916 #11859968

Order 1152.

1061 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#916C211yesmaximal, characteristic
2C3×C4×#239C211yesmaximal, characteristic, complemented
3C3×C4×#237C211yesmaximal, characteristic, complemented
4C32×C4×SD16C211yesmaximal, characteristic, complemented
5C3×Dic3×SD16C211yesmaximal, characteristic, complemented
6C3×C4×#216C211yesmaximal, characteristic, complemented
7C3×C4×#213C211yesmaximal, characteristic, complemented
8C3×#4860C211yesmaximal, characteristic, complemented
9C3×#4852C211yesmaximal, characteristic, complemented
10C3×#4804C211yesmaximal, characteristic, complemented
11C3×#4790C211yesmaximal, characteristic, complemented
12C3×#4772C211yesmaximal, characteristic, complemented
13C3×#4756C211yesmaximal, characteristic, complemented
14C3×C4×#204C211yesmaximal, characteristic, complemented
15C3×C4×D3×C8C211yesmaximal, characteristic, complemented
16C3×C4×#135—31nomaximal
17C4×#916C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27C3×C4×#67—21no—
28C2×C3×C4×Dic3—21no—
29C3×#916C418yesdirect product factor
30C2×C3×#204C2211yescharacteristic
31C2×C3×D3×C8C2211yescharacteristic
32C2×C3×D3×C8C2211yescharacteristic
33C3×#893—21no—
34C3×#893C2211yescharacteristic
35C3×#892—21no—
36C3×#892C2211yescharacteristic
37C3×#892C2211yescharacteristic
38C3×#887C2211yescharacteristic
39C3×#67⋊C4—21no—
40C3×#877—21no—
41C3×C4×D12—21no—
42C3×C4×D12C2211yescharacteristic
43C3×C42×D3—21no—
44C3×C42×D3C2211yescharacteristic
45C3×C4×Dic6C2211yescharacteristic
46C32×#106C2211yescharacteristic
47C32×#103C2211yescharacteristic
48C32×#102C2211yescharacteristic
49C32×C4×C8C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#832C2211yescharacteristic
52C3×#821C2211yescharacteristic
53C3×#817C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×C8×Dic3C2211yescharacteristic
56C3×C8×Dic3C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×C4×C3⋊C8C2211yescharacteristic
62C2×C3×#135—31no—
63C3×C4×#41—31no—
64C3×C4×#41—31no—
65C2×#916C2×C311yescharacteristic
66C4×#239C2×C311yescharacteristic, complemented
67C4×#237C2×C311yescharacteristic, complemented
68C3×C4×Q16—31no—
69C3×C4×Q16—31no—
70C3×C4×SD16—21no—
71C3×C4×SD16—31no—
72C3×C4×SD16—31no—
73C3×C4×SD16—31no—
74C3×C4×SD16D311yescharacteristic, complemented
75C3×C4×SD16C2×C311yescharacteristic, complemented
76C3×C4×D8—31no—
77C3×C4×D8—31no—
78C3×#427—31no—
79C3×#416—31no—
80C3×#416—31no—
81C2×C3×C4×C8—31no—
82Dic3×SD16C2×C311yescharacteristic, complemented
83C4×#216C2×C311yescharacteristic, complemented
84C4×#213C2×C311yescharacteristic, complemented
85#4860C2×C311yescharacteristic, complemented
86#4852C2×C311yescharacteristic, complemented
87#4804C2×C311yescharacteristic, complemented
88#4790C2×C311yescharacteristic, complemented
89#4772C2×C311yescharacteristic, complemented
90#4756C2×C311yescharacteristic, complemented
91C4×#204C2×C311yescharacteristic, complemented
92C4×D3×C8C2×C311yescharacteristic, complemented
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4—21no—
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—21no—
99C3×#239—22no—
100C3×#239C2×C414yescomplemented
101C3×#237—22no—
102C3×#237C2×C414yescomplemented
103C2×C3×D12—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3D411yescharacteristic
109C2×C3×C4×D3D411yescharacteristic
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C32×SD16C2×C414yescomplemented
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4—21no—
116C32×C4⋊C4C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C22⋊C4—21no—
119C32×C42—21no—
120C32×C42C2311yescharacteristic
121C3×#217—21no—
122C3×#216C2×C414yescomplemented
123C3×#213C2×C414yescomplemented
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3—21no—
138C3×C4×Dic3D411yescharacteristic
139C3×C4×Dic3D411yescharacteristic
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×#204C2×C414yescomplemented
144C3×D3×C8—22no—
145C3×D3×C8C2×C414yescomplemented
146C4×#135—31noSylow
147C2×C3×#41—31no—
148C2×C3×#41—31no—
149C2×#239C22×C311yescharacteristic
150C2×#237C22×C311yescharacteristic
151C3×#135—38no—
152C2×C3×Q16—31no—
153C2×C3×SD16—21no—
154C2×C3×SD16—31no—
155C2×C3×SD16C2×D311yescharacteristic
156C2×C3×SD16C22×C311yescharacteristic
157C2×C3×D8—31no—
158C22×C3×C8—31no—
159C22×C3×C8—31no—
160C3×C4×Q8—21no—
161C3×C4×Q8—31no—
162C3×C4×Q8—31no—
163C3×C4×Q8—31no—
164C3×C4×Q8C2×D311yescharacteristic
165C3×C4×Q8C22×C311yescharacteristic
166C3×C4×D4—21no—
167C3×C4×D4—31no—
168C3×C4×D4—31no—
169C3×C4×D4—31no—
170C3×C4×D4—61no—
171C3×C4×D4—61no—
172C3×C4×D4—61no—
173C3×C4×D4—61no—
174C3×C4×D4C2×D311yescharacteristic
175C3×C4×D4C22×C311yescharacteristic
176C3×#117—31no—
177C3×#117—31no—
178C3×#117—61no—
179C3×#117—61no—
180C2×C3×C42—31no—
181C2×C3×C42—61no—
182C2×C3×C42—61no—
183Q8×Dic3C22×C311yescharacteristic
184C2×#216C22×C311yescharacteristic
185D4×Dic3C22×C311yescharacteristic
186C2×#213C22×C311yescharacteristic
187C4×#67—21no—
188C2×C4×Dic3—21no—
189#916C3×C418yesdirect product factor
190C2×#204C22×C311yescharacteristic
191C2×D3×C8C22×C311yescharacteristic
192C2×D3×C8C22×C311yescharacteristic
193#893—21no—
194#893C22×C311yescharacteristic
195#892—21no—
196#892C22×C311yescharacteristic
197#892C22×C311yescharacteristic
198#887C22×C311yescharacteristic
199#67⋊C4—21no—
200#877—21no—
201C4×D12—21no—
202C4×D12C22×C311yescharacteristic
203C42×D3—21no—
204C42×D3C22×C311yescharacteristic
205C4×Dic6C22×C311yescharacteristic
206C3×#107—31no—
207C3×#107—31no—
208C3×#106—21no—
209C3×#106—31no—
210C3×#106C2×D311yescharacteristic
211C3×#106C22×C311yescharacteristic
212C3×#103—21no—
213C3×#103—31no—
214C3×#103—31no—
215C3×#103—31no—
216C3×#103C2×D311yescharacteristic
217C3×#103C22×C311yescharacteristic
218C3×#102—21no—
219C3×#102—31no—
220C3×#102—31no—
221C3×#102—31no—
222C3×#102C2×D311yescharacteristic
223C3×#102C22×C311yescharacteristic
224C3×C4×C8—21no—
225C3×C4×C8—31no—
226C3×C4×C8—31no—
227C3×C4×C8—31no—
228C3×C4×C8C2×D311yescharacteristic
229C3×C4×C8C22×C311yescharacteristic
230#835C22×C311yescharacteristic
231#832C22×C311yescharacteristic
232#821C22×C311yescharacteristic
233#817C22×C311yescharacteristic
234#816C22×C311yescharacteristic
235C8×Dic3C22×C311yescharacteristic
236C8×Dic3C22×C311yescharacteristic
237#810C22×C311yescharacteristic
238#809C22×C311yescharacteristic
239#807C22×C311yescharacteristic
240#807C22×C311yescharacteristic
241C4×C3⋊C8C22×C311yescharacteristic
242C23×C32—21no—
243C22×C3×D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8C22×C412yes—
247C32×D4—21no—
248C32×D4C22×C412yes—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—42no—
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256C3×#67—24no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—24no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—42no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—24no—
266C3×D12—21no—
267C3×D12C22×C412yes—
268C3×C4×D3—22no—
269C3×C4×D3—24no—
270C3×C4×D3—22no—
271C3×C4×D3—42no—
272C3×C4×D3—42no—
273C3×C4×D3C22×C412yes—
274C3×C4×D3#4112yes—
275C3×Dic6—21no—
276C3×Dic6C22×C412yes—
277C32×C8—21no—
278C32×C8C22×C412yes—
279C3×C3⋊C8—21no—
280C3×C3⋊C8C22×C412yes—
281C2×#135—31no—
282C4×#41—31no—
283C4×#41—31no—
284C4×Q16—31no—
285C4×Q16—31no—
286C4×SD16—31no—
287C4×SD16—31no—
288C4×SD16—31no—
289C4×SD16C3×D311yescharacteristic, complemented
290C4×D8—31no—
291C4×D8—31no—
292#427—31no—
293#416—31no—
294#416—31no—
295C2×C4×C8—31no—
296C3×#41—34no—
297C3×#41—34no—
298C3×#41—62no—
299C3×#41—62no—
300C2×C3×Q8—21no—
301C2×C3×Q8—31no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C23×C311yescharacteristic
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4—61no—
307C2×C3×D4—61no—
308C2×C3×D4C22×D311yescharacteristic
309C2×C3×D4C23×C311yescharacteristic
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—41no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×C3×C4—61no—
321C2×#67—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324#239—22no—
325#239C2×C3×C414yescomplemented
326#237—22no—
327#237C2×C3×C414yescomplemented
328C2×D12—21no—
329C2×D12C23×C311yescharacteristic
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×C4×D3—21no—
333C2×C4×D3C3×D411yescharacteristic
334C2×C4×D3C3×D411yescharacteristic
335C2×C4×D3C23×C311yescharacteristic
336C2×Dic6C23×C311yescharacteristic
337C3×Q16—34no—
338C3×SD16—24no—
339C3×SD16—34no—
340C3×SD16C4×D314yescomplemented
341C3×SD16C2×C3×C414yescomplemented
342C3×D8—34no—
343C2×C3×C8—21no—
344C2×C3×C8—21no—
345C2×C3×C8—31no—
346C2×C3×C8—34no—
347C2×C3×C8—31no—
348C2×C3×C8—62no—
349C2×C3×C8C22×D311yescharacteristic
350C2×C3×C8C22×D311yescharacteristic
351C2×C3×C8C23×C311yescharacteristic
352C2×C3×C8C23×C311yescharacteristic
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—41no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C4⋊C4C23×C311yescharacteristic
366C3×C4⋊C4C23×C311yescharacteristic
367C3×C22⋊C4—21no—
368C3×C22⋊C4—21no—
369C3×C22⋊C4—41no—
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—21no—
377C3×C42—21no—
378C3×C42—31no—
379C3×C42—31no—
380C3×C42—31no—
381C3×C42—41no—
382C3×C42—61no—
383C3×C42—61no—
384C3×C42—61no—
385C3×C42—61no—
386C3×C42—61no—
387C3×C42C22×D311yescharacteristic
388C3×C42C23×C311yescharacteristic
389#217—21no—
390#216C2×C3×C414yescomplemented
391#213C2×C3×C414yescomplemented
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—21no—
396C4⋊Dic3—21no—
397C4⋊Dic3C23×C311yescharacteristic
398C4⋊Dic3C23×C311yescharacteristic
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401C4×Dic3—21no—
402C4×Dic3—21no—
403C4×Dic3—21no—
404C4×Dic3—21no—
405C4×Dic3—21no—
406C4×Dic3C3×D411yescharacteristic
407C4×Dic3C3×D411yescharacteristic
408C4×Dic3C23×C311yescharacteristic
409C2×C3⋊C8C23×C311yescharacteristic
410C2×C3⋊C8C23×C311yescharacteristic
411#204C2×C3×C414yescomplemented
412D3×C8—22no—
413D3×C8C2×C3×C414yescomplemented
414C22×C32—22no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32C22×D411yescharacteristic
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3C4×D412yes—
424C32×C4—22no—
425C32×C4—21no—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4#13512yescomplemented
429C32×C4C23×C411yescharacteristic
430C32×C4C2×#4111yescharacteristic
431C3×Dic3—22no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3C4×D412yes—
436C3×Dic3#13512yescomplemented
437C2×#41—31no—
438C2×#41—31no—
439#135—38no—
440C2×Q16—31no—
441C2×SD16—31no—
442C2×SD16C2×C3×D311yescharacteristic
443C2×D8—31no—
444C22×C8—31no—
445C22×C8—31no—
446C4×Q8—31no—
447C4×Q8—31no—
448C4×Q8—31no—
449C4×Q8C2×C3×D311yescharacteristic
450C4×D4—31no—
451C4×D4—31no—
452C4×D4—31no—
453C4×D4—61no—
454C4×D4—61no—
455C4×D4—61no—
456C4×D4—61no—
457C4×D4C2×C3×D311yescharacteristic
458#117—31no—
459#117—31no—
460#117—61no—
461#117—61no—
462C2×C42—31no—
463C2×C42—61no—
464C2×C42—61no—
465#107—31no—
466#107—31no—
467#106—31no—
468#106C2×C3×D311yescharacteristic
469#103—31no—
470#103—31no—
471#103—31no—
472#103C2×C3×D311yescharacteristic
473#102—31no—
474#102—31no—
475#102—31no—
476#102C2×C3×D311yescharacteristic
477C4×C8—31no—
478C4×C8—31no—
479C4×C8—31no—
480C4×C8C2×C3×D311yescharacteristic
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3—41no—
485C23×C3—61no—
486C22×D3—21no—
487C22×D3C2×C3×D411yescharacteristic
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—22no—
491C3×Q8—32no—
492C3×Q8—41no—
493C3×Q8—61no—
494C3×Q8C2×C4×D312yes—
495C3×Q8C22×C3×C412yes—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—22no—
499C3×D4—32no—
500C3×D4—41no—
501C3×D4—64no—
502C3×D4—64no—
503C3×D4—61no—
504C3×D4C2×C4×D312yes—
505C3×D4C22×C3×C412yes—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—32no—
518C2×C3×C4—32no—
519C2×C3×C4—31no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—42no—
524C2×C3×C4—42no—
525C2×C3×C4—62no—
526C2×C3×C4—64no—
527C2×C3×C4—64no—
528C2×C3×C4—61no—
529C2×C3×C4—62no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—82no—
533C2×C3×C4—122no—
534C2×C3×C4—122no—
535C2×C3×C4—122no—
536C2×C3×C4D3×D411yescharacteristic
537C2×C3×C4D3×D411yescharacteristic
538C2×C3×C4C2×C3×D411yescharacteristic
539C2×C3×C4C2×C3×D411yescharacteristic
540C2×C3×C4C23×D311yescharacteristic
541C2×C3×C4C24×C311yescharacteristic
542#67—24no—
543C2×Dic3—21no—
544C2×Dic3—24no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—42no—
548C2×Dic3C2×C3×D411yescharacteristic
549C2×Dic3C2×C3×D411yescharacteristic
550C2×Dic3C2×C3×D411yescharacteristic
551D12—24no—
552D12—21no—
553D12C22×C3×C412yes—
554C4×D3—22no—
555C4×D3—24no—
556C4×D3—22no—
557C4×D3—42no—
558C4×D3—42no—
559C4×D3C22×C3×C412yes—
560C4×D3C3×#4112yes—
561Dic6—21no—
562Dic6C22×C3×C412yes—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—22no—
566C3×C8—32no—
567C3×C8—41no—
568C3×C8—61no—
569C3×C8C2×C4×D312yes—
570C3×C8C22×C3×C412yes—
571C3⋊C8—21no—
572C3⋊C8C22×C3×C412yes—
573C2×C32—42no—
574C2×C32C2×C4×D411yescharacteristic
575C2×C32C2×#13511yescharacteristic
576C2×C32C2×#13511yescharacteristic
577C3×D3—22no—
578C3×D3—42no—
579#41—34no—
580#41—34no—
581#41—62no—
582#41—62no—
583C2×Q8—31no—
584C2×Q8C22×C3×D311yescharacteristic
585C2×D4—31no—
586C2×D4—61no—
587C2×D4—61no—
588C2×D4C22×C3×D311yescharacteristic
589C22×C4—21no—
590C22×C4—31no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—61no—
598Q16—34no—
599SD16—34no—
600SD16C3×C4×D314yescomplemented
601D8—34no—
602C2×C8—31no—
603C2×C8—34no—
604C2×C8—31no—
605C2×C8—62no—
606C2×C8C22×C3×D311yescharacteristic
607C2×C8C22×C3×D311yescharacteristic
608C4⋊C4—21no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4C22×C3×D311yescharacteristic
615C4⋊C4C22×C3×D311yescharacteristic
616C22⋊C4—21no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C42—21no—
623C42—31no—
624C42—31no—
625C42—31no—
626C42—61no—
627C42—61no—
628C42—61no—
629C42—61no—
630C42—61no—
631C42C22×C3×D311yescharacteristic
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—21no—
635C22×C3—32no—
636C22×C3—42no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—62no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3C2×D3×D411yescharacteristic
649C22×C3C22×C3×D411yescharacteristic
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—22no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3C3×C4×D412yes—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—22no—
659C3×C4—22no—
660C3×C4—22no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—32no—
664C3×C4—32no—
665C3×C4—41no—
666C3×C4—42no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—61no—
672C3×C4—62no—
673C3×C4—81no—
674C3×C4—81no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4#91612yesdirect product factor
678C3×C4C3×#13512yescomplemented
679C3×C4C22×C4×D311yescharacteristic
680C3×C4D3×#4111yescharacteristic
681C3×C4C23×C3×C411yescharacteristic
682C3×C4C2×C3×#4111yescharacteristic
683Dic3—21no—
684Dic3—22no—
685Dic3—41no—
686Dic3—41no—
687Dic3C3×C4×D412yes—
688Dic3C3×#13512yescomplemented
689C32C4×#13511yescharacteristic, complemented, Sylow
690C23—21no—
691C23—31no—
692C23—61no—
693Q8—21no—
694Q8—32no—
695Q8—61no—
696Q8C2×C3×C4×D312yes—
697D4—21no—
698D4—32no—
699D4—64no—
700D4—64no—
701D4—61no—
702D4C2×C3×C4×D312yes—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—31no—
707C2×C4—31no—
708C2×C4—32no—
709C2×C4—32no—
710C2×C4—31no—
711C2×C4—42no—
712C2×C4—62no—
713C2×C4—64no—
714C2×C4—64no—
715C2×C4—61no—
716C2×C4—62no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—122no—
720C2×C4—122no—
721C2×C4—122no—
722C2×C4C3×D3×D411yescharacteristic
723C2×C4C3×D3×D411yescharacteristic
724C2×C4C23×C3×D311yescharacteristic
725C8—21no—
726C8—32no—
727C8—61no—
728C8C2×C3×C4×D312yes—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—42no—
733C2×C3—42no—
734C2×C3—62no—
735C2×C3—82no—
736C2×C3—122no—
737C2×C3C4×D3×D411yescharacteristic
738C2×C3C2×#91611yescharacteristic
739C2×C3D3×#13511yescharacteristic
740C2×C3C2×C3×C4×D411yescharacteristic
741C2×C3C2×C3×#13511yescharacteristic
742C2×C3C2×C3×#13511yescharacteristic
743D3—22no—
744D3—42no—
745C22—22no—
746C22—32no—
747C22—41no—
748C22—41no—
749C22—61no—
750C22—61no—
751C22—62no—
752C22—121no—
753C22—121no—
754C22C2×C3×D3×D411yescharacteristic
755C4—21no—
756C4—22no—
757C4—32no—
758C4—32no—
759C4—41no—
760C4—41no—
761C4—61no—
762C4—62no—
763C4—121no—
764C4—121no—
765C4C3×#91612yesdirect product factor
766C4C22×C3×C4×D311yescharacteristic
767C4C3×D3×#4111yescharacteristic
768C3—21no—
769C3C4×#91611yescharacteristic, direct product factor
770C3C3×C4×#13511yescharacteristic, complemented
771C2—42no—
772C2—62no—
773C2—122no—
774C2C3×C4×D3×D411yescharacteristic
775C2C2×C3×#91611yescharacteristic
776C2C3×D3×#13511yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×C4×SD16C2
socleC22×C32C22×D4
prime radicalC2×C3×#916C2
cosocleC2×C3×C4C24×C3
hypercenterC3×C4×SD16D3
hypocenterC3C3×C4×#135
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C3×C4×#239C2semidirect
3. C3×C4×#237C2semidirect
4. C32×C4×SD16C2semidirect
5. C3×Dic3×SD16C2semidirect
6. C3×C4×#216C2semidirect
7. C3×C4×#213C2semidirect
8. C3×#4860C2semidirect
9. C3×#4852C2semidirect
10. C3×#4804C2semidirect
11. C3×#4790C2semidirect
12. C3×#4772C2semidirect
13. C3×#4756C2semidirect
14. C3×C4×#204C2semidirect
15. C3×C4×D3×C8C2semidirect
17. C4×#916C3direct (N × H)
29. C3×#916C4direct (N × H)
66. C4×#239C2×C3semidirect
67. C4×#237C2×C3semidirect
74. C3×C4×SD16D3semidirect
75. C3×C4×SD16C2×C3semidirect
82. Dic3×SD16C2×C3semidirect
83. C4×#216C2×C3semidirect
84. C4×#213C2×C3semidirect
85. #4860C2×C3semidirect
86. #4852C2×C3semidirect
87. #4804C2×C3semidirect
88. #4790C2×C3semidirect
89. #4772C2×C3semidirect
90. #4756C2×C3semidirect
91. C4×#204C2×C3semidirect
92. C4×D3×C8C2×C3semidirect
100. C3×#239C2×C4semidirect
102. C3×#237C2×C4semidirect
112. C32×SD16C2×C4semidirect
122. C3×#216C2×C4semidirect
123. C3×#213C2×C4semidirect
143. C3×#204C2×C4semidirect
145. C3×D3×C8C2×C4semidirect
189. #916C3×C4direct (N × H)
289. C4×SD16C3×D3semidirect
325. #239C2×C3×C4semidirect
327. #237C2×C3×C4semidirect
340. C3×SD16C4×D3semidirect
341. C3×SD16C2×C3×C4semidirect
390. #216C2×C3×C4semidirect
391. #213C2×C3×C4semidirect
411. #204C2×C3×C4semidirect
413. D3×C8C2×C3×C4semidirect
428. C32×C4#135semidirect
436. C3×Dic3#135semidirect
600. SD16C3×C4×D3semidirect
677. C3×C4#916direct (N × H)
678. C3×C4C3×#135semidirect
688. Dic3C3×#135semidirect
689. C32C4×#135semidirect
765. C4C3×#916direct (N × H)
769. C3C4×#916direct (N × H)
770. C3C3×C4×#135semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9162
C3×C4×#2392
C3×C4×#2372
C32×C4×SD162
C3×Dic3×SD162
C3×C4×#2162
C3×C4×#2132
C3×#48602
C3×#48522
C3×#48042
C3×#47902
C3×#47722
C3×#47562
C3×C4×#2042
C3×C4×D3×C82
C3×C4×#1353
C4×#9163