Finite Group Databasebeta

← C3×#79240 #11868792

Subgroups — C3×#79240 #11868792

Order 1152.

891 conjugacy classes of subgroups.

The subgroup lattice has 597 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5522C211yesmaximal, characteristic
2C2×C3×#888C211yesmaximal, characteristic, complemented
3C32×#428C211yesmaximal, characteristic, complemented
4C3×#5133C211yesmaximal, characteristic
5C3×#5118C211yesmaximal, characteristic, complemented
6C3×#4995C211yesmaximal, characteristic, complemented
7C3×#4966C211yesmaximal, characteristic
8C3×#4890C212yesmaximal, complemented
9C3×#4875C212yesmaximal, complemented
10C3×#4870C212yesmaximal, complemented
11C3×#4854C212yesmaximal, complemented
12C3×#3079—31nomaximal
13#79240C311yesmaximal, characteristic, direct product factor
14C2×C3×#235C2211yescharacteristic
15C22×C3×Dic6—21no—
16C2×C32×M16C2211yescharacteristic
17C32×#117C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×Dic3⋊C4—21no—
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C3×#893C2211yescharacteristic
24C3×#893C2211yescharacteristic
25C3×#888—21no—
26C3×#888—21no—
27C3×#888C2212yes—
28C3×#888C2212yes—
29C3×#887C2211yescharacteristic
30C3×#887C2211yescharacteristic
31C3×#67⋊C4—21no—
32C3×#67⋊C4—21no—
33C3×#872—21no—
34C3×C42×D3—21no—
35C32×#107C2212yes—
36C32×#106C2212yes—
37C3×#821C2212yes—
38C3×#816C2212yes—
39C3×Dic3⋊C8C2212yes—
40C3×Dic3⋊C8C2212yes—
41C3×#810C2212yes—
42C3×#809C2212yes—
43C3×#808C2212yes—
44C3×#807C2212yes—
45C2×C3×C4⋊Q8—31no—
46C3×C4×#41—31no—
47#5522C2×C311yescharacteristic
48C2×#888C2×C311yescharacteristic, complemented
49C3×#477—32no—
50C3×#476—32no—
51C3×#475—32no—
52C3×#474—32no—
53C3×#428—21no—
54C3×#428—31no—
55C3×#428D311yescharacteristic, complemented
56C3×#428C2×C311yescharacteristic, complemented
57C3×#423—31no—
58C3×#417—31no—
59C3×#417—31no—
60#5133C2×C311yescharacteristic
61#5118C2×C311yescharacteristic, complemented
62#4995C2×C311yescharacteristic, complemented
63#4966C2×C311yescharacteristic
64#4890C2×C312yescomplemented
65#4875C2×C312yescomplemented
66#4870C2×C312yescomplemented
67#4854C2×C312yescomplemented
68C22×C32×C4—21no—
69C22×C32×C4C2311yescharacteristic
70C2×C3×#67—21no—
71C22×C3×Dic3—21no—
72C22×C3×Dic3D411yescharacteristic
73C22×C3×Dic3D411yescharacteristic
74C3×#235—22no—
75C3×#235Q814yescomplemented
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3—21no—
80C2×C3×Dic6—22no—
81C2×C3×Dic6—22no—
82C2×C3×Dic6—44no—
83C2×C3×Dic6C2311yescharacteristic
84C32×M16—22no—
85C2×C32×C8C2312yes—
86C32×C4⋊C4—21no—
87C32×C4⋊C4C2311yescharacteristic
88C32×C4⋊C4C2311yescharacteristic
89C32×C4⋊C4C2312yes—
90C32×C22⋊C4—21no—
91C32×C42—21no—
92C3×(C2×D3)⋊C4—21no—
93C3×(C2×D3)⋊C4—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3C2312yes—
96C3×Dic3⋊C4—21no—
97C3×Dic3⋊C4—21no—
98C3×Dic3⋊C4—22no—
99C3×Dic3⋊C4—22no—
100C3×C4×Dic3—21no—
101C3×C4×Dic3—21no—
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3D411yescharacteristic
104C3×C4×Dic3C2311yescharacteristic
105C3×C4×Dic3C2311yescharacteristic
106C3×#208—22no—
107C2×C3×C3⋊C8C2312yes—
108#3079—31noSylow
109C2×C3×#41—31no—
110C22×C3×Q8—61no—
111C2×#235C22×C311yescharacteristic
112C22×Dic6—21no—
113C2×C3×M16—21no—
114C2×C3×M16—31no—
115C2×C3×M16C2×D311yescharacteristic
116C2×C3×M16C22×C311yescharacteristic
117C3×C4⋊Q8—32no—
118C3×C4⋊Q8—32no—
119C3×C4⋊Q8—61no—
120C3×C4⋊Q8—61no—
121C3×C4×Q8—31no—
122C3×C4×Q8—31no—
123C3×C4×D4—31no—
124C3×C4×D4—31no—
125C3×C4×D4—61no—
126C3×C4×D4—61no—
127C3×#117—21no—
128C3×#117—61no—
129C3×#117C2×D311yescharacteristic
130C3×#117C22×C311yescharacteristic
131C2×C3×C4⋊C4—21no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C4⋊C4—61no—
134C2×C3×C4⋊C4C2×D311yescharacteristic
135C2×C3×C4⋊C4C22×C311yescharacteristic
136C2×C3×C42—31no—
137C2×C3×C42—61no—
138C2×C4⋊Dic3C22×C311yescharacteristic
139C2×Dic3⋊C4—21no—
140C2×C4×Dic3C22×C311yescharacteristic
141C2×#208C22×C311yescharacteristic
142#893C22×C311yescharacteristic
143#893C22×C311yescharacteristic
144#888—21no—
145#888—21no—
146#888C22×C312yes—
147#888C22×C312yes—
148#887C22×C311yescharacteristic
149#887C22×C311yescharacteristic
150#67⋊C4—21no—
151#67⋊C4—21no—
152#872—21no—
153C42×D3—21no—
154C3×#107—22no—
155C3×#107—32no—
156C3×#107C2×D312yes—
157C3×#107C22×C312yes—
158C3×#106—22no—
159C3×#106—32no—
160C3×#106C2×D312yes—
161C3×#106C22×C312yes—
162C3×C4⋊C8—32no—
163C3×C4⋊C8—32no—
164C3×#103—32no—
165C3×#103—32no—
166C3×#102—32no—
167C3×#102—32no—
168#821C22×C312yes—
169#816C22×C312yes—
170Dic3⋊C8C22×C312yes—
171Dic3⋊C8C22×C312yes—
172#810C22×C312yes—
173#809C22×C312yes—
174#808C22×C312yes—
175#807C22×C312yes—
176C23×C32C2×D411yescharacteristic
177C22×C3×D3—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—22no—
181C2×C32×C4—42no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2×Q812yes—
184C2×C32×C4#4112yes—
185C2×C32×C4C2411yescharacteristic
186C3×#67—24no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—42no—
192C2×C3×Dic3C2×D411yescharacteristic
193C2×C3×Dic3C2×D411yescharacteristic
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C3×D12—21no—
197C3×D12C2×Q812yescomplemented
198C3×C4×D3—24no—
199C3×C4×D3—42no—
200C3×C4×D3—42no—
201C3×Dic6—21no—
202C3×Dic6—44no—
203C3×Dic6—44no—
204C3×Dic6C2×Q812yescomplemented
205C32×C8—22no—
206C3×C3⋊C8—22no—
207C2×C4⋊Q8—31no—
208C4×#41—31no—
209#477—32no—
210#476—32no—
211#475—32no—
212#474—32no—
213#428—31no—
214#428C3×D311yescharacteristic, complemented
215#423—31no—
216#417—31no—
217#417—31no—
218C3×#41—34no—
219C3×#41—62no—
220C2×C3×Q8—31no—
221C2×C3×Q8—62no—
222C2×C3×Q8—62no—
223C2×C3×Q8—124no—
224C2×C3×D4—31no—
225C2×C3×D4—61no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—31no—
230C22×C3×C4—31no—
231C22×C3×C4—41no—
232C22×C3×C4—61no—
233C22×C3×C4—61no—
234C22×C3×C4—61no—
235C22×C3×C4—61no—
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C23×C311yescharacteristic
238C2×#67—21no—
239C22×Dic3—21no—
240C22×Dic3C3×D411yescharacteristic
241C22×Dic3C3×D411yescharacteristic
242#235—22no—
243#235C3×Q814yescomplemented
244C2×D12C23×C311yescharacteristic
245C2×C4×D3—21no—
246C2×C4×D3—21no—
247C2×C4×D3—21no—
248C2×Dic6—22no—
249C2×Dic6—22no—
250C2×Dic6—44no—
251C2×Dic6C23×C311yescharacteristic
252C3×M16—24no—
253C3×M16—22no—
254C3×M16—22no—
255C3×M16—62no—
256C2×C3×C8—22no—
257C2×C3×C8—32no—
258C2×C3×C8C22×D312yes—
259C2×C3×C8C23×C312yes—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—22no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—32no—
266C3×C4⋊C4—41no—
267C3×C4⋊C4—62no—
268C3×C4⋊C4—62no—
269C3×C4⋊C4—61no—
270C3×C4⋊C4—61no—
271C3×C4⋊C4—61no—
272C3×C4⋊C4C22×D312yes—
273C3×C4⋊C4C22×D311yescharacteristic
274C3×C4⋊C4C22×D311yescharacteristic
275C3×C4⋊C4C23×C311yescharacteristic
276C3×C4⋊C4C23×C311yescharacteristic
277C3×C4⋊C4C23×C312yes—
278C3×C22⋊C4—21no—
279C3×C22⋊C4—21no—
280C3×C22⋊C4—41no—
281C3×C22⋊C4—61no—
282C3×C22⋊C4—61no—
283C3×C42—21no—
284C3×C42—21no—
285C3×C42—31no—
286C3×C42—31no—
287C3×C42—31no—
288C3×C42—31no—
289C3×C42—41no—
290C3×C42—61no—
291C3×C42—61no—
292(C2×D3)⋊C4—21no—
293(C2×D3)⋊C4—21no—
294C4⋊Dic3—21no—
295C4⋊Dic3C23×C312yes—
296Dic3⋊C4—21no—
297Dic3⋊C4—21no—
298Dic3⋊C4—22no—
299Dic3⋊C4—22no—
300C4×Dic3—21no—
301C4×Dic3—21no—
302C4×Dic3C3×D411yescharacteristic
303C4×Dic3C3×D411yescharacteristic
304C4×Dic3C23×C311yescharacteristic
305C4×Dic3C23×C311yescharacteristic
306#208—22no—
307C2×C3⋊C8C23×C312yes—
308C22×C32—21no—
309C22×C32—21no—
310C22×C32C22⋊Q812yes—
311C22×C32C22×D411yescharacteristic
312C2×C3×D3—22no—
313C2×C3×D3—41no—
314C2×C3×D3—41no—
315C32×C4—42no—
316C32×C4—41no—
317C32×C4—41no—
318C32×C4C22⋊Q812yes—
319C32×C4C22×Q811yescharacteristic
320C32×C4C2×#4111yescharacteristic
321C3×Dic3—22no—
322C3×Dic3—21no—
323C3×Dic3—21no—
324C3×Dic3—42no—
325C3×Dic3AGL(1,ℤ/8)12yes—
326C3×Dic3#13712yes—
327C2×#41—31no—
328C22×Q8—61no—
329C2×M16—31no—
330C2×M16C2×C3×D311yescharacteristic
331C4⋊Q8—32no—
332C4⋊Q8—32no—
333C4⋊Q8—61no—
334C4⋊Q8—61no—
335C4×Q8—31no—
336C4×Q8—31no—
337C4×D4—31no—
338C4×D4—31no—
339C4×D4—61no—
340C4×D4—61no—
341#117—61no—
342#117C2×C3×D311yescharacteristic
343C2×C4⋊C4—31no—
344C2×C4⋊C4—61no—
345C2×C4⋊C4C2×C3×D311yescharacteristic
346C2×C42—31no—
347C2×C42—61no—
348#107—32no—
349#107C2×C3×D312yes—
350#106—32no—
351#106C2×C3×D312yes—
352C4⋊C8—32no—
353C4⋊C8—32no—
354#103—32no—
355#103—32no—
356#102—32no—
357#102—32no—
358C23×C3—21no—
359C23×C3—61no—
360C23×C3D3×D411yescharacteristic
361C23×C3C2×C3×D411yescharacteristic
362C22×D3—21no—
363C3×Q8—32no—
364C3×Q8—61no—
365C3×Q8—124no—
366C3×Q8—124no—
367C3×D4—32no—
368C3×D4—64no—
369C3×D4—61no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—22no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—22no—
376C2×C3×C4—21no—
377C2×C3×C4—22no—
378C2×C3×C4—21no—
379C2×C3×C4—22no—
380C2×C3×C4—31no—
381C2×C3×C4—31no—
382C2×C3×C4—31no—
383C2×C3×C4—31no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—42no—
387C2×C3×C4—42no—
388C2×C3×C4—42no—
389C2×C3×C4—62no—
390C2×C3×C4—62no—
391C2×C3×C4—61no—
392C2×C3×C4—64no—
393C2×C3×C4—62no—
394C2×C3×C4—82no—
395C2×C3×C4—122no—
396C2×C3×C4—122no—
397C2×C3×C4—122no—
398C2×C3×C4#23512yes—
399C2×C3×C4D3×D411yescharacteristic
400C2×C3×C4D3×Q812yes—
401C2×C3×C4C2×C3×D411yescharacteristic
402C2×C3×C4C2×C3×Q812yes—
403C2×C3×C4C3×#4112yes—
404C2×C3×C4C23×D311yescharacteristic
405C2×C3×C4C24×C311yescharacteristic
406#67—24no—
407C2×Dic3—21no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—42no—
412C2×Dic3C2×C3×D411yescharacteristic
413C2×Dic3C2×C3×D411yescharacteristic
414C2×Dic3C2×C3×D411yescharacteristic
415C2×Dic3C2×C3×D411yescharacteristic
416D12—21no—
417D12C2×C3×Q812yescomplemented
418C4×D3—24no—
419C4×D3—42no—
420C4×D3—42no—
421Dic6—21no—
422Dic6—44no—
423Dic6—44no—
424Dic6C2×C3×Q812yescomplemented
425C3×C8—24no—
426C3×C8—22no—
427C3×C8—22no—
428C3×C8—62no—
429C3⋊C8—22no—
430C2×C32—22no—
431C2×C32C2×C22⋊Q811yescharacteristic
432C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
433C2×C32C2×#13711yescharacteristic
434C3×D3—42no—
435#41—34no—
436#41—62no—
437C2×Q8—31no—
438C2×Q8—62no—
439C2×Q8—62no—
440C2×Q8—124no—
441C2×D4—31no—
442C2×D4—61no—
443C22×C4—21no—
444C22×C4—31no—
445C22×C4—31no—
446C22×C4—61no—
447C22×C4—61no—
448C22×C4—61no—
449C22×C4—61no—
450C22×C4C22×C3×D311yescharacteristic
451M16—22no—
452M16—62no—
453C2×C8—32no—
454C2×C8C22×C3×D312yes—
455C4⋊C4—21no—
456C4⋊C4—32no—
457C4⋊C4—62no—
458C4⋊C4—62no—
459C4⋊C4—61no—
460C4⋊C4—61no—
461C4⋊C4—61no—
462C4⋊C4C22×C3×D312yes—
463C4⋊C4C22×C3×D311yescharacteristic
464C4⋊C4C22×C3×D311yescharacteristic
465C22⋊C4—21no—
466C22⋊C4—61no—
467C22⋊C4—61no—
468C42—21no—
469C42—31no—
470C42—31no—
471C42—31no—
472C42—31no—
473C42—61no—
474C42—61no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—22no—
480C22×C3—21no—
481C22×C3—41no—
482C22×C3—41no—
483C22×C3—62no—
484C22×C3—121no—
485C22×C3—121no—
486C22×C3#89612yes—
487C22×C3C3×C22⋊Q812yes—
488C22×C3C2×D3×D411yescharacteristic
489C22×C3C22×C3×D411yescharacteristic
490C2×D3—22no—
491C2×D3—41no—
492C2×D3—41no—
493C3×C4—22no—
494C3×C4—21no—
495C3×C4—21no—
496C3×C4—32no—
497C3×C4—32no—
498C3×C4—42no—
499C3×C4—41no—
500C3×C4—41no—
501C3×C4—42no—
502C3×C4—41no—
503C3×C4—41no—
504C3×C4—62no—
505C3×C4—61no—
506C3×C4—61no—
507C3×C4—82no—
508C3×C4—81no—
509C3×C4—81no—
510C3×C4—122no—
511C3×C4#89612yes—
512C3×C4C3×C22⋊Q812yes—
513C3×C4C2×#23511yescharacteristic
514C3×C4C2×D3×Q811yescharacteristic
515C3×C4C22×C3×Q811yescharacteristic
516C3×C4C2×C3×#4111yescharacteristic
517Dic3—21no—
518Dic3—21no—
519Dic3—22no—
520Dic3—42no—
521Dic3C3×AGL(1,ℤ/8)12yes—
522Dic3C3×#13712yes—
523C32#307911yescharacteristic, complemented, Sylow
524C23—61no—
525C23C3×D3×D411yescharacteristic
526Q8—32no—
527Q8—61no—
528Q8—124no—
529Q8—124no—
530D4—32no—
531D4—64no—
532D4—61no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—31no—
537C2×C4—31no—
538C2×C4—31no—
539C2×C4—31no—
540C2×C4—42no—
541C2×C4—62no—
542C2×C4—62no—
543C2×C4—61no—
544C2×C4—64no—
545C2×C4—62no—
546C2×C4—122no—
547C2×C4—122no—
548C2×C4—122no—
549C2×C4C3×#23512yes—
550C2×C4C3×D3×D411yescharacteristic
551C2×C4C3×D3×Q812yes—
552C2×C4C23×C3×D311yescharacteristic
553C8—22no—
554C8—62no—
555C2×C3—22no—
556C2×C3—22no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—42no—
561C2×C3—122no—
562C2×C3C2×#89611yescharacteristic
563C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
564C2×C3D3×#13711yescharacteristic
565C2×C3C2×C3×C22⋊Q811yescharacteristic
566C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
567C2×C3C2×C3×#13711yescharacteristic
568D3—42no—
569C22—21no—
570C22—21no—
571C22—62no—
572C22—121no—
573C22—121no—
574C22C3×#89612yes—
575C22C2×C3×D3×D411yescharacteristic
576C4—32no—
577C4—32no—
578C4—42no—
579C4—41no—
580C4—41no—
581C4—62no—
582C4—61no—
583C4—61no—
584C4—122no—
585C4C3×#89612yes—
586C4C2×C3×#23511yescharacteristic
587C4C2×C3×D3×Q811yescharacteristic
588C3—21no—
589C3#7924011yescharacteristic, direct product factor
590C3C3×#307911yescharacteristic, complemented
591C2—22no—
592C2—122no—
593C2C2×C3×#89611yescharacteristic
594C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
595C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#428C2
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
hypercenterC3×#428D3
hypocenterC3C3×#3079
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#428

Complements

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

NH ≅ G/Ntype
2. C2×C3×#888C2semidirect
3. C32×#428C2semidirect
5. C3×#5118C2semidirect
6. C3×#4995C2semidirect
8. C3×#4890C2semidirect
9. C3×#4875C2semidirect
10. C3×#4870C2semidirect
11. C3×#4854C2semidirect
13. #79240C3direct (N × H)
48. C2×#888C2×C3semidirect
55. C3×#428D3semidirect
56. C3×#428C2×C3semidirect
61. #5118C2×C3semidirect
62. #4995C2×C3semidirect
64. #4890C2×C3semidirect
65. #4875C2×C3semidirect
66. #4870C2×C3semidirect
67. #4854C2×C3semidirect
75. C3×#235Q8semidirect
197. C3×D12C2×Q8semidirect
204. C3×Dic6C2×Q8semidirect
214. #428C3×D3semidirect
243. #235C3×Q8semidirect
417. D12C2×C3×Q8semidirect
424. Dic6C2×C3×Q8semidirect
523. C32#3079semidirect
589. C3#79240direct (N × H)
590. C3C3×#3079semidirect

Maximal subgroups

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

subgroupindex
C3×#55222
C2×C3×#8882
C32×#4282
C3×#51332
C3×#51182
C3×#49952
C3×#49662
C3×#48902
C3×#48752
C3×#48702
C3×#48542
C3×#30793
#792403