Finite Group Databasebeta

← C3×#79774 #11860377

Subgroups — C3×#79774 #11860377

Order 1152.

1028 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#915C211yesmaximal, characteristic
2C3×C4×D3×Q8C211yesmaximal, characteristic, complemented
3C3×C4×#237C211yesmaximal, characteristic
4C32×#440C211yesmaximal, characteristic, complemented
5C3×Dic3×SD16C211yesmaximal, characteristic, complemented
6C3×#5030C211yesmaximal, characteristic, complemented
7C3×#5018C211yesmaximal, characteristic, complemented
8C3×#4881C211yesmaximal, characteristic, complemented
9C3×#4873C211yesmaximal, characteristic, complemented
10C3×#4802C211yesmaximal, characteristic, complemented
11C3×#4790C211yesmaximal, characteristic, complemented
12C3×#4771C211yesmaximal, characteristic
13C3×#4758C211yesmaximal, characteristic, complemented
14C3×#4716C211yesmaximal, characteristic, complemented
15C3×#4707C211yesmaximal, characteristic, complemented
16C3×C4×#137—31nomaximal
17#79774C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27C3×C4×#67—21no—
28C2×C3×C4×Dic3—21no—
29C3×#915C418yescomplemented
30C2×C3×Dic12C2211yescharacteristic
31C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
32C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
33C3×#892C2211yescharacteristic
34C3×D3×C4⋊C4—21no—
35C3×D3×C4⋊C4C2211yescharacteristic
36C3×#887—21no—
37C3×#887C2211yescharacteristic
38C3×#887C2211yescharacteristic
39C3×#67⋊C4—21no—
40C3×#877—21no—
41C3×C42×D3—21no—
42C3×C42×D3C2211yescharacteristic
43C3×C4×Dic6—21no—
44C3×C4×Dic6C2211yescharacteristic
45C3×C4×Dic6C2211yescharacteristic
46C32×#107C2211yescharacteristic
47C32×#103C2211yescharacteristic
48C32×#102C2211yescharacteristic
49C32×#97C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#832C2211yescharacteristic
52C3×#817C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×C8×Dic3C2211yescharacteristic
56C3×C8×Dic3C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#810C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#803C2211yescharacteristic
62C2×C3×#137—31no—
63C3×C4×#41—31no—
64C2×C3×C4×Q8—31no—
65C2×#915C2×C311yescharacteristic
66C4×D3×Q8C2×C311yescharacteristic, complemented
67C4×#237C2×C311yescharacteristic
68C3×#441—31no—
69C3×#441—31no—
70C3×#440—21no—
71C3×#440—31no—
72C3×#440D311yescharacteristic, complemented
73C3×#440C2×C311yescharacteristic, complemented
74C3×C4×Q16—31no—
75C3×C4×Q16—31no—
76C3×C4×SD16—31no—
77C3×C4×SD16—31no—
78C3×#428—31no—
79C3×#419—31no—
80C3×#417—31no—
81C3×C4×M16—31no—
82Dic3×SD16C2×C311yescharacteristic, complemented
83#5030C2×C311yescharacteristic, complemented
84#5018C2×C311yescharacteristic, complemented
85#4881C2×C311yescharacteristic, complemented
86#4873C2×C311yescharacteristic, complemented
87#4802C2×C311yescharacteristic, complemented
88#4790C2×C311yescharacteristic, complemented
89#4771C2×C311yescharacteristic
90#4758C2×C311yescharacteristic, complemented
91#4716C2×C311yescharacteristic, complemented
92#4707C2×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×D3×Q8—22no—
100C3×D3×Q8C2×C414yescomplemented
101C3×#237—22no—
102C3×#237C2×C414yes—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3D411yescharacteristic
106C2×C3×C4×D3D411yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6—21no—
109C2×C3×Dic6C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C32×SD16C2×C414yescomplemented
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4—21no—
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C22⋊C4—21no—
118C32×C42—21no—
119C32×C42C2311yescharacteristic
120C3×#217—21no—
121C3×#216C2×C414yescomplemented
122C3×#214C2×C414yescomplemented
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×C4×Dic3—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×Dic12C2×C414yescomplemented
144C3×ΓL(1,𝔽25)—22no—
145C3×ΓL(1,𝔽25)C2×C414yescomplemented
146C4×#137—31noSylow
147C2×C3×#41—31no—
148C22×C3×Q8—31no—
149C2×D3×Q8C22×C311yescharacteristic
150C2×#237C22×C311yescharacteristic
151C3×#137—38no—
152C2×C3×Q16—31no—
153C2×C3×Q16—31no—
154C2×C3×SD16—21no—
155C2×C3×SD16—31no—
156C2×C3×SD16C2×D311yescharacteristic
157C2×C3×SD16C22×C311yescharacteristic
158C2×C3×M16—31no—
159C2×C3×M16—31no—
160C3×C4×Q8—21no—
161C3×C4×Q8—31no—
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×Q8C22×C311yescharacteristic
170C3×C4×D4—21no—
171C3×C4×D4—31no—
172C3×C4×D4—61no—
173C3×C4×D4—61no—
174C3×C4×D4C2×D311yescharacteristic
175C3×C4×D4C22×C311yescharacteristic
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
184C2×#216C22×C311yescharacteristic
185D4×Dic3C22×C311yescharacteristic
186C2×#214C22×C311yescharacteristic
187C4×#67—21no—
188C2×C4×Dic3—21no—
189#915C3×C418yescomplemented
190C2×Dic12C22×C311yescharacteristic
191C2×ΓL(1,𝔽25)C22×C311yescharacteristic
192C2×ΓL(1,𝔽25)C22×C311yescharacteristic
193#892C22×C311yescharacteristic
194D3×C4⋊C4—21no—
195D3×C4⋊C4C22×C311yescharacteristic
196#887—21no—
197#887C22×C311yescharacteristic
198#887C22×C311yescharacteristic
199#67⋊C4—21no—
200#877—21no—
201C42×D3—21no—
202C42×D3C22×C311yescharacteristic
203C4×Dic6—21no—
204C4×Dic6C22×C311yescharacteristic
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—31no—
214C3×#103—31no—
215C3×#103—31no—
216C3×#103—31no—
217C3×#103—31no—
218C3×#103C2×D311yescharacteristic
219C3×#103C22×C311yescharacteristic
220C3×#102—21no—
221C3×#102—31no—
222C3×#102C2×D311yescharacteristic
223C3×#102C22×C311yescharacteristic
224C3×#97—21no—
225C3×#97—31no—
226C3×#97C2×D311yescharacteristic
227C3×#97C22×C311yescharacteristic
228C3×C4×C8—31no—
229C3×C4×C8—31no—
230#835C22×C311yescharacteristic
231#832C22×C311yescharacteristic
232#817C22×C311yescharacteristic
233#816C22×C311yescharacteristic
234#816C22×C311yescharacteristic
235C8×Dic3C22×C311yescharacteristic
236C8×Dic3C22×C311yescharacteristic
237#810C22×C311yescharacteristic
238#810C22×C311yescharacteristic
239#808C22×C311yescharacteristic
240#807C22×C311yescharacteristic
241#803C22×C311yescharacteristic
242C23×C32—21no—
243C22×C3×D3C2×D411yescharacteristic
244C32×Q8—21no—
245C32×Q8C22×C412yes—
246C32×D4—21no—
247C32×D4C22×C412yes—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—42no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2411yescharacteristic
255C3×#67—24no—
256C2×C3×Dic3—21no—
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×C4×D3—24no—
266C3×C4×D3—22no—
267C3×C4×D3—41no—
268C3×C4×D3—42no—
269C3×C4×D3C22×C412yes—
270C3×C4×D3#4112yes—
271C3×Dic6—21no—
272C3×Dic6—21no—
273C3×Dic6—24no—
274C3×Dic6C22×C412yes—
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#440C3×D311yescharacteristic, complemented
287C4×Q16—31no—
288C4×Q16—31no—
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—34no—
299C2×C3×Q8—31no—
300C2×C3×Q8—31no—
301C2×C3×Q8—61no—
302C2×C3×Q8—62no—
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×Q8C23×C311yescharacteristic
305C2×C3×D4—21no—
306C2×C3×D4—61no—
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C23×C311yescharacteristic
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—41no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4—61no—
319C2×#67—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322D3×Q8—22no—
323D3×Q8C2×C3×C414yescomplemented
324#237—22no—
325#237C2×C3×C414yes—
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
333C2×Dic6C23×C311yescharacteristic
334C3×Q16—34no—
335C3×Q16—34no—
336C3×SD16—24no—
337C3×SD16—34no—
338C3×SD16C4×D314yescomplemented
339C3×SD16C2×C3×C414yescomplemented
340C3×M16—34no—
341C3×M16—62no—
342C2×C3×C8—21no—
343C2×C3×C8—21no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C23×C311yescharacteristic
349C2×C3×C8C23×C311yescharacteristic
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—41no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
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×C42—21no—
373C3×C42—21no—
374C3×C42—21no—
375C3×C42—31no—
376C3×C42—31no—
377C3×C42—31no—
378C3×C42—41no—
379C3×C42—61no—
380C3×C42—61no—
381C3×C42—61no—
382C3×C42—61no—
383C3×C42—61no—
384C3×C42—61no—
385C3×C42C22×D311yescharacteristic
386C3×C42C23×C311yescharacteristic
387#217—21no—
388#216C2×C3×C414yescomplemented
389#214C2×C3×C414yescomplemented
390(C2×D3)⋊C4—21no—
391C4⋊Dic3—21no—
392C4⋊Dic3C23×C311yescharacteristic
393C4⋊Dic3C23×C311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399C4×Dic3—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
410Dic12C2×C3×C414yescomplemented
411ΓL(1,𝔽25)—22no—
412ΓL(1,𝔽25)C2×C3×C414yescomplemented
413C22×C32—22no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32C22×D411yescharacteristic
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3C4×D412yes—
420C32×C4—22no—
421C32×C4—21no—
422C32×C4—21no—
423C32×C4—41no—
424C32×C4—41no—
425C32×C4C23×C411yescharacteristic
426C32×C4C2×#4111yescharacteristic
427C3×Dic3—22no—
428C3×Dic3—22no—
429C3×Dic3—21no—
430C3×Dic3—41no—
431C3×Dic3—41no—
432C3×Dic3C4×D412yes—
433C3×Dic3#13712yescomplemented
434C2×#41—31no—
435C22×Q8—31no—
436#137—38no—
437C2×Q16—31no—
438C2×Q16—31no—
439C2×SD16—31no—
440C2×SD16C2×C3×D311yescharacteristic
441C2×M16—31no—
442C2×M16—31no—
443C4×Q8—31no—
444C4×Q8—31no—
445C4×Q8—31no—
446C4×Q8—31no—
447C4×Q8—31no—
448C4×Q8—61no—
449C4×Q8—61no—
450C4×Q8C2×C3×D311yescharacteristic
451C4×D4—31no—
452C4×D4—61no—
453C4×D4—61no—
454C4×D4C2×C3×D311yescharacteristic
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#103—31no—
471#103C2×C3×D311yescharacteristic
472#102—31no—
473#102C2×C3×D311yescharacteristic
474#97—31no—
475#97C2×C3×D311yescharacteristic
476C4×C8—31no—
477C4×C8—31no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—31no—
481C23×C3—41no—
482C22×D3C2×C3×D411yescharacteristic
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—22no—
486C3×Q8—32no—
487C3×Q8—32no—
488C3×Q8—41no—
489C3×Q8—64no—
490C3×Q8—61no—
491C3×Q8—61no—
492C3×Q8C2×C4×D312yes—
493C3×Q8C22×C3×C412yes—
494C3×D4—21no—
495C3×D4—21no—
496C3×D4—22no—
497C3×D4—41no—
498C3×D4—64no—
499C3×D4C2×C4×D312yes—
500C3×D4C22×C3×C412yes—
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—31no—
511C2×C3×C4—31no—
512C2×C3×C4—32no—
513C2×C3×C4—32no—
514C2×C3×C4—31no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—42no—
519C2×C3×C4—42no—
520C2×C3×C4—62no—
521C2×C3×C4—64no—
522C2×C3×C4—64no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—82no—
528C2×C3×C4—121no—
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—24no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—42no—
544C2×Dic3C2×C3×D411yescharacteristic
545C2×Dic3C2×C3×D411yescharacteristic
546C2×Dic3C2×C3×D411yescharacteristic
547C4×D3—24no—
548C4×D3—22no—
549C4×D3—41no—
550C4×D3—42no—
551C4×D3C22×C3×C412yes—
552C4×D3C3×#4112yes—
553Dic6—21no—
554Dic6—21no—
555Dic6—24no—
556Dic6C22×C3×C412yes—
557Dic6C22×C3×C412yes—
558C3×C8—21no—
559C3×C8—21no—
560C3×C8—22no—
561C3×C8—32no—
562C3×C8—41no—
563C3×C8—61no—
564C3×C8C2×C4×D312yes—
565C3×C8C22×C3×C412yes—
566C3⋊C8—21no—
567C3⋊C8C22×C3×C412yes—
568C2×C32—42no—
569C2×C32C2×C4×D411yescharacteristic
570C2×C32C2×#13711yescharacteristic
571C2×C32#57511yescharacteristic
572C3×D3—22no—
573#41—34no—
574#41—62no—
575C2×Q8—34no—
576C2×Q8—31no—
577C2×Q8—31no—
578C2×Q8—61no—
579C2×Q8—62no—
580C2×Q8C22×C3×D311yescharacteristic
581C2×D4—61no—
582C2×D4C22×C3×D311yescharacteristic
583C22×C4—21no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—31no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—61no—
590C22×C4—61no—
591Q16—34no—
592Q16—34no—
593SD16—34no—
594SD16C3×C4×D314yescomplemented
595M16—34no—
596M16—62no—
597C2×C8—31no—
598C2×C8—31no—
599C2×C8C22×C3×D311yescharacteristic
600C2×C8C22×C3×D311yescharacteristic
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⋊C4—61no—
610C4⋊C4C22×C3×D311yescharacteristic
611C4⋊C4C22×C3×D311yescharacteristic
612C22⋊C4—21no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C42—21no—
616C42—31no—
617C42—31no—
618C42—31no—
619C42—61no—
620C42—61no—
621C42—61no—
622C42—61no—
623C42—61no—
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—81no—
638C22×C3—81no—
639C22×C3C2×D3×D411yescharacteristic
640C22×C3C22×C3×D411yescharacteristic
641C2×D3—21no—
642C2×D3—21no—
643C2×D3C3×C4×D412yes—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—22no—
649C3×C4—22no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—32no—
653C3×C4—32no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—42no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—61no—
662C3×C4—62no—
663C3×C4—62no—
664C3×C4—81no—
665C3×C4—81no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4C22×C4×D311yescharacteristic
669C3×C4D3×#4111yescharacteristic
670C3×C4C23×C3×C411yescharacteristic
671C3×C4C2×C3×#4111yescharacteristic
672Dic3—21no—
673Dic3—22no—
674Dic3—22no—
675Dic3—41no—
676Dic3—41no—
677Dic3C3×C4×D412yes—
678Dic3C3×#13712yescomplemented
679C32C4×#13711yescharacteristic, complemented, Sylow
680C23—21no—
681C23—31no—
682Q8—21no—
683Q8—32no—
684Q8—32no—
685Q8—64no—
686Q8—61no—
687Q8—61no—
688Q8C2×C3×C4×D312yes—
689D4—21no—
690D4—64no—
691D4C2×C3×C4×D312yes—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—32no—
698C2×C4—32no—
699C2×C4—31no—
700C2×C4—42no—
701C2×C4—62no—
702C2×C4—64no—
703C2×C4—64no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—121no—
709C2×C4—122no—
710C2×C4—122no—
711C2×C4C3×D3×D411yescharacteristic
712C2×C4C3×D3×D411yescharacteristic
713C2×C4C23×C3×D311yescharacteristic
714C8—21no—
715C8—32no—
716C8—61no—
717C8C2×C3×C4×D312yes—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—42no—
722C2×C3—42no—
723C2×C3—62no—
724C2×C3—82no—
725C2×C3C4×D3×D411yescharacteristic
726C2×C3#577311yescharacteristic
727C2×C3D3×#13711yescharacteristic
728C2×C3C2×C3×C4×D411yescharacteristic
729C2×C3C2×C3×#13711yescharacteristic
730C2×C3C3×#57511yescharacteristic
731D3—22no—
732C22—22no—
733C22—32no—
734C22—41no—
735C22—41no—
736C22—61no—
737C22—61no—
738C22C2×C3×D3×D411yescharacteristic
739C4—21no—
740C4—21no—
741C4—22no—
742C4—32no—
743C4—32no—
744C4—41no—
745C4—41no—
746C4—61no—
747C4—62no—
748C4—62no—
749C4—121no—
750C4—121no—
751C4C22×C3×C4×D311yescharacteristic
752C4C3×D3×#4111yescharacteristic
753C3—21no—
754C3#7977411yescharacteristic, direct product factor
755C3C3×C4×#13711yescharacteristic, complemented
756C2—42no—
757C2—62no—
758C2C3×C4×D3×D411yescharacteristic
759C2C3×#577311yescharacteristic
760C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×#440C2
socleC22×C32C22×D4
prime radicalC2×C3×#237C22
cosocleC2×C3×C4C24×C3
hypercenterC3×#440D3
hypocenterC3C3×C4×#137
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#440

Complements

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

NH ≅ G/Ntype
2. C3×C4×D3×Q8C2semidirect
4. C32×#440C2semidirect
5. C3×Dic3×SD16C2semidirect
6. C3×#5030C2semidirect
7. C3×#5018C2semidirect
8. C3×#4881C2semidirect
9. C3×#4873C2semidirect
10. C3×#4802C2semidirect
11. C3×#4790C2semidirect
13. C3×#4758C2semidirect
14. C3×#4716C2semidirect
15. C3×#4707C2semidirect
17. #79774C3direct (N × H)
29. C3×#915C4semidirect
66. C4×D3×Q8C2×C3semidirect
72. C3×#440D3semidirect
73. C3×#440C2×C3semidirect
82. Dic3×SD16C2×C3semidirect
83. #5030C2×C3semidirect
84. #5018C2×C3semidirect
85. #4881C2×C3semidirect
86. #4873C2×C3semidirect
87. #4802C2×C3semidirect
88. #4790C2×C3semidirect
90. #4758C2×C3semidirect
91. #4716C2×C3semidirect
92. #4707C2×C3semidirect
100. C3×D3×Q8C2×C4semidirect
111. C32×SD16C2×C4semidirect
121. C3×#216C2×C4semidirect
122. C3×#214C2×C4semidirect
143. C3×Dic12C2×C4semidirect
145. C3×ΓL(1,𝔽25)C2×C4semidirect
189. #915C3×C4semidirect
286. #440C3×D3semidirect
323. D3×Q8C2×C3×C4semidirect
338. C3×SD16C4×D3semidirect
339. C3×SD16C2×C3×C4semidirect
388. #216C2×C3×C4semidirect
389. #214C2×C3×C4semidirect
410. Dic12C2×C3×C4semidirect
412. ΓL(1,𝔽25)C2×C3×C4semidirect
433. C3×Dic3#137semidirect
594. SD16C3×C4×D3semidirect
678. Dic3C3×#137semidirect
679. C32C4×#137semidirect
754. C3#79774direct (N × H)
755. 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×#9152
C3×C4×D3×Q82
C3×C4×#2372
C32×#4402
C3×Dic3×SD162
C3×#50302
C3×#50182
C3×#48812
C3×#48732
C3×#48022
C3×#47902
C3×#47712
C3×#47582
C3×#47162
C3×#47072
C3×C4×#1373
#797743