Finite Group Databasebeta

← C3×C4×#918 #11860371

Subgroups — C3×C4×#918 #11860371

Order 1152.

1023 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#918C211yesmaximal, characteristic
2C3×C4×#239C211yesmaximal, characteristic
3C3×C4×D3×Q8C211yesmaximal, characteristic, complemented
4C32×C4×Q16C211yesmaximal, characteristic, complemented
5C3×#5184C211yesmaximal, characteristic, complemented
6C3×C4×#216C211yesmaximal, characteristic, complemented
7C3×C4×#215C211yesmaximal, characteristic, complemented
8C3×#4889C211yesmaximal, characteristic, complemented
9C3×#4881C211yesmaximal, characteristic, complemented
10C3×#4817C211yesmaximal, characteristic, complemented
11C3×#4803C211yesmaximal, characteristic
12C3×#4802C211yesmaximal, characteristic, complemented
13C3×#4789C211yesmaximal, characteristic, complemented
14C3×C4×#204C211yesmaximal, characteristic, complemented
15C3×C4×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
16C3×C4×#137—31nomaximal
17C4×#918C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic
22C32×C4×Q8C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic
27C3×#918C418yesdirect product factor
28C2×C3×#204C2211yescharacteristic
29C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
30C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
31C3×#893—21no—
32C3×#893C2211yescharacteristic
33C3×#892—21no—
34C3×#892C2211yescharacteristic
35C3×D3×C4⋊C4—21no—
36C3×D3×C4⋊C4C2211yescharacteristic
37C3×#887—21no—
38C3×#887C2211yescharacteristic
39C3×C4×D12—21no—
40C3×C4×D12C2211yescharacteristic
41C3×C42×D3—21no—
42C3×C42×D3—21no—
43C3×C42×D3C2211yescharacteristic
44C3×C4×Dic6—21no—
45C3×C4×Dic6C2211yescharacteristic
46C32×#107C2211yescharacteristic
47C32×#103C2211yescharacteristic
48C32×#103C2211yescharacteristic
49C32×C4×C8C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#835C2211yescharacteristic
52C3×#821C2211yescharacteristic
53C3×#817C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×#815C2211yescharacteristic
56C3×#815C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×C4×C3⋊C8C2211yescharacteristic
62C2×C3×#137—31no—
63C3×C4×#41—31no—
64C2×C3×C4×Q8—31no—
65C2×#918C2×C311yescharacteristic
66C4×#239C2×C311yescharacteristic
67C4×D3×Q8C2×C311yescharacteristic, complemented
68C3×#441—31no—
69C3×#441—31no—
70C3×#440—31no—
71C3×#440—31no—
72C3×C4×Q16—21no—
73C3×C4×Q16—31no—
74C3×C4×Q16D311yescharacteristic, complemented
75C3×C4×Q16C2×C311yescharacteristic, complemented
76C3×C4×SD16—31no—
77C3×C4×SD16—31no—
78C3×#428—31no—
79C3×#419—31no—
80C3×#417—31no—
81C3×C4×M16—31no—
82#5184C2×C311yescharacteristic, complemented
83C4×#216C2×C311yescharacteristic, complemented
84C4×#215C2×C311yescharacteristic, complemented
85#4889C2×C311yescharacteristic, complemented
86#4881C2×C311yescharacteristic, complemented
87#4817C2×C311yescharacteristic, complemented
88#4803C2×C311yescharacteristic
89#4802C2×C311yescharacteristic, complemented
90#4789C2×C311yescharacteristic, complemented
91C4×#204C2×C311yescharacteristic, complemented
92C4×ΓL(1,𝔽25)C2×C311yescharacteristic, complemented
93C2×C32×Q8C2311yescharacteristic
94C2×C32×Q8C2311yescharacteristic
95C3×#239—22no—
96C3×#239C2×C414yes—
97C3×D3×Q8—22no—
98C3×D3×Q8C2×C414yescomplemented
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3D411yescharacteristic
107C2×C3×C4×D3D411yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6—21no—
110C2×C3×Dic6C2311yescharacteristic
111C32×Q16C2×C414yescomplemented
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4—21no—
115C32×C4⋊C4—21no—
116C32×C4⋊C4C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C42—21no—
119C32×C42—21no—
120C32×C42C2311yescharacteristic
121C3×#216C2×C414yescomplemented
122C3×#215C2×C414yescomplemented
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
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×ΓL(1,𝔽25)—22no—
145C3×ΓL(1,𝔽25)C2×C414yescomplemented
146C4×#137—31noSylow
147C2×C3×#41—31no—
148C22×C3×Q8—31no—
149C2×#239C22×C311yescharacteristic
150C2×D3×Q8C22×C311yescharacteristic
151C3×#137—38no—
152C2×C3×Q16—21no—
153C2×C3×Q16—31no—
154C2×C3×Q16C2×D311yescharacteristic
155C2×C3×Q16C22×C311yescharacteristic
156C2×C3×SD16—31no—
157C2×C3×SD16—31no—
158C2×C3×M16—31no—
159C2×C3×M16—31no—
160C3×C4×Q8—21no—
161C3×C4×Q8—21no—
162C3×C4×Q8—31no—
163C3×C4×Q8—31no—
164C3×C4×Q8—31no—
165C3×C4×Q8—31no—
166C3×C4×Q8—61no—
167C3×C4×Q8—61no—
168C3×C4×Q8C2×D311yescharacteristic
169C3×C4×Q8C2×D311yescharacteristic
170C3×C4×Q8C22×C311yescharacteristic
171C3×C4×Q8C22×C311yescharacteristic
172C3×C4×D4—31no—
173C3×C4×D4—31no—
174C3×C4×D4—61no—
175C3×C4×D4—61no—
176C3×#117—31no—
177C3×#117—61no—
178C2×C3×C4⋊C4—31no—
179C2×C3×C4⋊C4—61no—
180C2×C3×C42—31no—
181C2×C3×C42—61no—
182C2×C3×C42—61no—
183Q8×Dic3C22×C311yescharacteristic
184Q8×Dic3C22×C311yescharacteristic
185C2×#216C22×C311yescharacteristic
186C2×#215C22×C311yescharacteristic
187#918C3×C418yesdirect product factor
188C2×#204C22×C311yescharacteristic
189C2×ΓL(1,𝔽25)C22×C311yescharacteristic
190C2×ΓL(1,𝔽25)C22×C311yescharacteristic
191#893—21no—
192#893C22×C311yescharacteristic
193#892—21no—
194#892C22×C311yescharacteristic
195D3×C4⋊C4—21no—
196D3×C4⋊C4C22×C311yescharacteristic
197#887—21no—
198#887C22×C311yescharacteristic
199C4×D12—21no—
200C4×D12C22×C311yescharacteristic
201C42×D3—21no—
202C42×D3—21no—
203C42×D3C22×C311yescharacteristic
204C4×Dic6—21no—
205C4×Dic6C22×C311yescharacteristic
206C3×#107—21no—
207C3×#107—31no—
208C3×#107C2×D311yescharacteristic
209C3×#107C22×C311yescharacteristic
210C3×#106—31no—
211C3×#106—31no—
212C3×#103—21no—
213C3×#103—21no—
214C3×#103—31no—
215C3×#103—31no—
216C3×#103—31no—
217C3×#103—31no—
218C3×#103C2×D311yescharacteristic
219C3×#103C2×D311yescharacteristic
220C3×#103C22×C311yescharacteristic
221C3×#103C22×C311yescharacteristic
222C3×#102—31no—
223C3×#102—31no—
224C3×#97—31no—
225C3×#97—31no—
226C3×C4×C8—21no—
227C3×C4×C8—31no—
228C3×C4×C8C2×D311yescharacteristic
229C3×C4×C8C22×C311yescharacteristic
230#835C22×C311yescharacteristic
231#835C22×C311yescharacteristic
232#821C22×C311yescharacteristic
233#817C22×C311yescharacteristic
234#816C22×C311yescharacteristic
235#815C22×C311yescharacteristic
236#815C22×C311yescharacteristic
237#810C22×C311yescharacteristic
238#809C22×C311yescharacteristic
239#808C22×C311yescharacteristic
240#807C22×C311yescharacteristic
241C4×C3⋊C8C22×C311yescharacteristic
242C22×C3×D3—21no—
243C22×C3×D3C2×D411yescharacteristic
244C32×Q8—21no—
245C32×Q8—21no—
246C32×Q8C22×C412yes—
247C32×Q8C22×C412yes—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2411yescharacteristic
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—24no—
262C3×D12—21no—
263C3×D12C22×C412yes—
264C3×C4×D3—24no—
265C3×C4×D3—22no—
266C3×C4×D3—24no—
267C3×C4×D3—41no—
268C3×C4×D3—42no—
269C3×C4×D3—42no—
270C3×C4×D3—42no—
271C3×C4×D3C22×C412yes—
272C3×C4×D3#4112yes—
273C3×Dic6—21no—
274C3×Dic6—24no—
275C3×Dic6C22×C412yes—
276C32×C8—21no—
277C32×C8C22×C412yes—
278C3×C3⋊C8—21no—
279C3×C3⋊C8C22×C412yes—
280C2×#137—31no—
281C4×#41—31no—
282C2×C4×Q8—31no—
283#441—31no—
284#441—31no—
285#440—31no—
286#440—31no—
287C4×Q16—31no—
288C4×Q16C3×D311yescharacteristic, complemented
289C4×SD16—31no—
290C4×SD16—31no—
291#428—31no—
292#419—31no—
293#417—31no—
294C4×M16—31no—
295C3×#41—34no—
296C3×#41—62no—
297C2×C3×Q8—21no—
298C2×C3×Q8—21no—
299C2×C3×Q8—34no—
300C2×C3×Q8—31no—
301C2×C3×Q8—61no—
302C2×C3×Q8—62no—
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×Q8C22×D311yescharacteristic
305C2×C3×Q8C23×C311yescharacteristic
306C2×C3×Q8C23×C311yescharacteristic
307C2×C3×D4—31no—
308C2×C3×D4—61no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317#239—22no—
318#239C2×C3×C414yes—
319D3×Q8—22no—
320D3×Q8C2×C3×C414yescomplemented
321C2×D12—21no—
322C2×D12C23×C311yescharacteristic
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×C4×D3—21no—
327C2×C4×D3—21no—
328C2×C4×D3C3×D411yescharacteristic
329C2×C4×D3C3×D411yescharacteristic
330C2×C4×D3C23×C311yescharacteristic
331C2×Dic6—21no—
332C2×Dic6C23×C311yescharacteristic
333C3×Q16—24no—
334C3×Q16—34no—
335C3×Q16C4×D314yescomplemented
336C3×Q16C2×C3×C414yescomplemented
337C3×SD16—34no—
338C3×SD16—34no—
339C3×M16—34no—
340C3×M16—62no—
341C2×C3×C8—21no—
342C2×C3×C8—21no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C23×C311yescharacteristic
348C2×C3×C8C23×C311yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—41no—
358C3×C4⋊C4—41no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C4⋊C4C23×C311yescharacteristic
367C3×C4⋊C4C23×C311yescharacteristic
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C42—21no—
372C3×C42—21no—
373C3×C42—21no—
374C3×C42—21no—
375C3×C42—21no—
376C3×C42—31no—
377C3×C42—31no—
378C3×C42—31no—
379C3×C42—41no—
380C3×C42—41no—
381C3×C42—61no—
382C3×C42—61no—
383C3×C42—61no—
384C3×C42—61no—
385C3×C42—61no—
386C3×C42C22×D311yescharacteristic
387C3×C42C23×C311yescharacteristic
388#216C2×C3×C414yescomplemented
389#215C2×C3×C414yescomplemented
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4—21no—
393C4⋊Dic3—21no—
394C4⋊Dic3—21no—
395C4⋊Dic3C23×C311yescharacteristic
396C4⋊Dic3C23×C311yescharacteristic
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400C4×Dic3—21no—
401C4×Dic3—21no—
402C4×Dic3—21no—
403C4×Dic3—21no—
404C4×Dic3—21no—
405C4×Dic3C3×D411yescharacteristic
406C4×Dic3C3×D411yescharacteristic
407C4×Dic3C23×C311yescharacteristic
408C2×C3⋊C8C23×C311yescharacteristic
409C2×C3⋊C8C23×C311yescharacteristic
410#204C2×C3×C414yescomplemented
411ΓL(1,𝔽25)—22no—
412ΓL(1,𝔽25)C2×C3×C414yescomplemented
413C22×C32C22×D411yescharacteristic
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—22no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3C4×D412yes—
420C32×C4—22no—
421C32×C4—22no—
422C32×C4—21no—
423C32×C4—41no—
424C32×C4—41no—
425C32×C4#13712yescomplemented
426C32×C4C23×C411yescharacteristic
427C32×C4C2×#4111yescharacteristic
428C3×Dic3—22no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C3×Dic3C4×D412yes—
434C2×#41—31no—
435C22×Q8—31no—
436#137—38no—
437C2×Q16—31no—
438C2×Q16C2×C3×D311yescharacteristic
439C2×SD16—31no—
440C2×SD16—31no—
441C2×M16—31no—
442C2×M16—31no—
443C4×Q8—31no—
444C4×Q8—31no—
445C4×Q8—31no—
446C4×Q8—31no—
447C4×Q8—61no—
448C4×Q8—61no—
449C4×Q8C2×C3×D311yescharacteristic
450C4×Q8C2×C3×D311yescharacteristic
451C4×D4—31no—
452C4×D4—31no—
453C4×D4—61no—
454C4×D4—61no—
455#117—31no—
456#117—61no—
457C2×C4⋊C4—31no—
458C2×C4⋊C4—61no—
459C2×C42—31no—
460C2×C42—61no—
461C2×C42—61no—
462#107—31no—
463#107C2×C3×D311yescharacteristic
464#106—31no—
465#106—31no—
466#103—31no—
467#103—31no—
468#103—31no—
469#103—31no—
470#103C2×C3×D311yescharacteristic
471#103C2×C3×D311yescharacteristic
472#102—31no—
473#102—31no—
474#97—31no—
475#97—31no—
476C4×C8—31no—
477C4×C8C2×C3×D311yescharacteristic
478C23×C3—31no—
479C23×C3—61no—
480C22×D3—21no—
481C22×D3C2×C3×D411yescharacteristic
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—22no—
487C3×Q8—22no—
488C3×Q8—32no—
489C3×Q8—41no—
490C3×Q8—41no—
491C3×Q8—64no—
492C3×Q8—61no—
493C3×Q8C2×C4×D312yes—
494C3×Q8C2×C4×D312yes—
495C3×Q8C22×C3×C412yes—
496C3×Q8C22×C3×C412yes—
497C3×D4—32no—
498C3×D4—64no—
499C3×D4—61no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
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—32no—
513C2×C3×C4—32no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—64no—
521C2×C3×C4—64no—
522C2×C3×C4—61no—
523C2×C3×C4—62no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—121no—
527C2×C3×C4—122no—
528C2×C3×C4—122no—
529C2×C3×C4—122no—
530C2×C3×C4D3×D411yescharacteristic
531C2×C3×C4D3×D411yescharacteristic
532C2×C3×C4C2×C3×D411yescharacteristic
533C2×C3×C4C2×C3×D411yescharacteristic
534C2×C3×C4C23×D311yescharacteristic
535C2×C3×C4C24×C311yescharacteristic
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3C2×C3×D411yescharacteristic
540C2×Dic3C2×C3×D411yescharacteristic
541C2×Dic3C2×C3×D411yescharacteristic
542D12—24no—
543D12—21no—
544D12C22×C3×C412yes—
545C4×D3—24no—
546C4×D3—22no—
547C4×D3—24no—
548C4×D3—41no—
549C4×D3—42no—
550C4×D3—42no—
551C4×D3—42no—
552C4×D3C22×C3×C412yes—
553C4×D3C3×#4112yes—
554Dic6—21no—
555Dic6—24no—
556Dic6C22×C3×C412yes—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—22no—
560C3×C8—32no—
561C3×C8—41no—
562C3×C8—61no—
563C3×C8C2×C4×D312yes—
564C3×C8C22×C3×C412yes—
565C3⋊C8—21no—
566C3⋊C8C22×C3×C412yes—
567C2×C32C2×C4×D411yescharacteristic
568C2×C32C2×#13711yescharacteristic
569C2×C32#57511yescharacteristic
570C3×D3—22no—
571C3×D3—42no—
572#41—34no—
573#41—62no—
574C2×Q8—34no—
575C2×Q8—31no—
576C2×Q8—61no—
577C2×Q8—62no—
578C2×Q8C22×C3×D311yescharacteristic
579C2×Q8C22×C3×D311yescharacteristic
580C2×D4—31no—
581C2×D4—61no—
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—61no—
590Q16—34no—
591Q16C3×C4×D314yescomplemented
592SD16—34no—
593SD16—34no—
594M16—34no—
595M16—62no—
596C2×C8—31no—
597C2×C8—31no—
598C2×C8C22×C3×D311yescharacteristic
599C2×C8C22×C3×D311yescharacteristic
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—31no—
603C4⋊C4—31no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4C22×C3×D311yescharacteristic
610C4⋊C4C22×C3×D311yescharacteristic
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C42—21no—
615C42—21no—
616C42—31no—
617C42—31no—
618C42—31no—
619C42—61no—
620C42—61no—
621C42—61no—
622C42—61no—
623C42—61no—
624C42C22×C3×D311yescharacteristic
625C22×C3—21no—
626C22×C3—32no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3—62no—
630C22×C3—121no—
631C22×C3—121no—
632C22×C3C2×D3×D411yescharacteristic
633C22×C3C22×C3×D411yescharacteristic
634C2×D3—21no—
635C2×D3—21no—
636C2×D3—22no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3C3×C4×D412yes—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—22no—
645C3×C4—22no—
646C3×C4—22no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—32no—
650C3×C4—41no—
651C3×C4—42no—
652C3×C4—42no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—61no—
658C3×C4—61no—
659C3×C4—62no—
660C3×C4—81no—
661C3×C4—81no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4#91812yesdirect product factor
665C3×C4C3×#13712yescomplemented
666C3×C4C22×C4×D311yescharacteristic
667C3×C4D3×#4111yescharacteristic
668C3×C4C23×C3×C411yescharacteristic
669C3×C4C2×C3×#4111yescharacteristic
670Dic3—21no—
671Dic3—21no—
672Dic3—22no—
673Dic3—41no—
674Dic3—41no—
675Dic3C3×C4×D412yes—
676C32C4×#13711yescharacteristic, complemented, Sylow
677C23—31no—
678C23—61no—
679Q8—21no—
680Q8—21no—
681Q8—32no—
682Q8—64no—
683Q8—61no—
684Q8C2×C3×C4×D312yes—
685Q8C2×C3×C4×D312yes—
686D4—32no—
687D4—64no—
688D4—61no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—31no—
694C2×C4—32no—
695C2×C4—32no—
696C2×C4—31no—
697C2×C4—31no—
698C2×C4—64no—
699C2×C4—64no—
700C2×C4—61no—
701C2×C4—62no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—121no—
705C2×C4—122no—
706C2×C4—122no—
707C2×C4—122no—
708C2×C4C3×D3×D411yescharacteristic
709C2×C4C3×D3×D411yescharacteristic
710C2×C4C23×C3×D311yescharacteristic
711C8—21no—
712C8—32no—
713C8—61no—
714C8C2×C3×C4×D312yes—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—62no—
719C2×C3—122no—
720C2×C3C4×D3×D411yescharacteristic
721C2×C3C2×#91811yescharacteristic
722C2×C3#576811yescharacteristic
723C2×C3C2×C3×C4×D411yescharacteristic
724C2×C3C2×C3×#13711yescharacteristic
725C2×C3C3×#57511yescharacteristic
726D3—22no—
727D3—42no—
728C22—32no—
729C22—61no—
730C22—61no—
731C22—62no—
732C22—121no—
733C22—121no—
734C22C2×C3×D3×D411yescharacteristic
735C4—21no—
736C4—22no—
737C4—22no—
738C4—32no—
739C4—41no—
740C4—41no—
741C4—61no—
742C4—61no—
743C4—62no—
744C4—121no—
745C4—121no—
746C4C3×#91812yesdirect product factor
747C4C22×C3×C4×D311yescharacteristic
748C4C3×D3×#4111yescharacteristic
749C3—21no—
750C3C4×#91811yescharacteristic, direct product factor
751C3C3×C4×#13711yescharacteristic, complemented
752C2—62no—
753C2—122no—
754C2C3×C4×D3×D411yescharacteristic
755C2C2×C3×#91811yescharacteristic
756C2C3×#576811yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×C4×Q16C2
socleC22×C32C22×D4
prime radicalC2×C3×#239C22
cosocleC2×C3×C4C24×C3
hypercenterC3×C4×Q16D3
hypocenterC3C3×C4×#137
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×C4×Q16

Complements

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

NH ≅ G/Ntype
3. C3×C4×D3×Q8C2semidirect
4. C32×C4×Q16C2semidirect
5. C3×#5184C2semidirect
6. C3×C4×#216C2semidirect
7. C3×C4×#215C2semidirect
8. C3×#4889C2semidirect
9. C3×#4881C2semidirect
10. C3×#4817C2semidirect
12. C3×#4802C2semidirect
13. C3×#4789C2semidirect
14. C3×C4×#204C2semidirect
15. C3×C4×ΓL(1,𝔽25)C2semidirect
17. C4×#918C3direct (N × H)
27. C3×#918C4direct (N × H)
67. C4×D3×Q8C2×C3semidirect
74. C3×C4×Q16D3semidirect
75. C3×C4×Q16C2×C3semidirect
82. #5184C2×C3semidirect
83. C4×#216C2×C3semidirect
84. C4×#215C2×C3semidirect
85. #4889C2×C3semidirect
86. #4881C2×C3semidirect
87. #4817C2×C3semidirect
89. #4802C2×C3semidirect
90. #4789C2×C3semidirect
91. C4×#204C2×C3semidirect
92. C4×ΓL(1,𝔽25)C2×C3semidirect
98. C3×D3×Q8C2×C4semidirect
111. C32×Q16C2×C4semidirect
121. C3×#216C2×C4semidirect
122. C3×#215C2×C4semidirect
143. C3×#204C2×C4semidirect
145. C3×ΓL(1,𝔽25)C2×C4semidirect
187. #918C3×C4direct (N × H)
288. C4×Q16C3×D3semidirect
320. D3×Q8C2×C3×C4semidirect
335. C3×Q16C4×D3semidirect
336. C3×Q16C2×C3×C4semidirect
388. #216C2×C3×C4semidirect
389. #215C2×C3×C4semidirect
410. #204C2×C3×C4semidirect
412. ΓL(1,𝔽25)C2×C3×C4semidirect
425. C32×C4#137semidirect
591. Q16C3×C4×D3semidirect
664. C3×C4#918direct (N × H)
665. C3×C4C3×#137semidirect
676. C32C4×#137semidirect
746. C4C3×#918direct (N × H)
750. C3C4×#918direct (N × H)
751. C3C3×C4×#137semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9182
C3×C4×#2392
C3×C4×D3×Q82
C32×C4×Q162
C3×#51842
C3×C4×#2162
C3×C4×#2152
C3×#48892
C3×#48812
C3×#48172
C3×#48032
C3×#48022
C3×#47892
C3×C4×#2042
C3×C4×ΓL(1,𝔽25)2
C3×C4×#1373
C4×#9183