Finite Group Databasebeta

← C3×#83212 #11868780

Subgroups — C3×#83212 #11868780

Order 1152.

977 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4⋊Q8C211yesmaximal, characteristic, complemented
2C3×C4×#235C211yesmaximal, characteristic
3C3×#5094C212yesmaximal, complemented
4C3×#5091C212yesmaximal, complemented
5C3×#5087C212yesmaximal, complemented
6C3×#5084C212yesmaximal, complemented
7C3×#4966C212yesmaximal
8C3×#4964C212yesmaximal, complemented
9C3×#4924C211yesmaximal, characteristic, complemented
10C3×#3079—31nomaximal
11#83212C311yesmaximal, characteristic, direct product factor
12C22×C32×Q8—21no—
13C2×C3×#235C2211yescharacteristic
14C32×C4⋊Q8—21no—
15C32×C4⋊Q8—21no—
16C32×C4⋊Q8C2212yes—
17C32×C4⋊Q8C2212yes—
18C2×C32×C4⋊C4—21no—
19C2×C32×C4⋊C4C2212yes—
20C2×C32×C42C2211yescharacteristic
21C3×C4×#67—21no—
22C3×C4×#67—21no—
23C3×#926C2211yescharacteristic
24C2×C3×#208C2212yes—
25C3×C4×D12C2211yescharacteristic
26C3×C4×D12C2211yescharacteristic
27C3×#872—21no—
28C3×C42×D3—21no—
29C3×C4×Dic6C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C3×#810C2214yes—
32C3×#809C2214yes—
33C3×#808C2214yes—
34C3×#807C2214yes—
35C3×C4⋊(C3⋊C8)C2212yes—
36C3×C4⋊(C3⋊C8)C2212yes—
37C2×C3×C4⋊Q8—21no—
38C2×C3×C4⋊Q8D311yescharacteristic, complemented
39C2×C3×C4⋊Q8C2×C311yescharacteristic, complemented
40C3×C4×#41—31no—
41C4×#235C2×C311yescharacteristic
42C3×#477—32no—
43C3×#476—32no—
44C3×#475—32no—
45C3×#474—32no—
46C3×#428—32no—
47C3×#423—31no—
48C3×#417—32no—
49#5094C2×C312yescomplemented
50#5091C2×C312yescomplemented
51#5087C2×C312yescomplemented
52#5084C2×C312yescomplemented
53#4966C2×C312yes—
54#4964C2×C312yescomplemented
55#4924C2×C311yescharacteristic, complemented
56C2×C32×Q8—22no—
57C2×C32×Q8—22no—
58C2×C32×Q8—44no—
59C22×C32×C4—22no—
60C22×C32×C4D411yescharacteristic
61C22×C32×C4D411yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C2×C3×#67—21no—
64C3×#235—22no—
65C3×#235Q814yescomplemented
66C2×C3×D12C2311yescharacteristic
67C2×C3×C4×D3—21no—
68C2×C3×C4×D3—21no—
69C2×C3×C4×D3—21no—
70C2×C3×Dic6C2311yescharacteristic
71C32×C4⋊C4—22no—
72C32×C4⋊C4—22no—
73C32×C4⋊C4—22no—
74C32×C4⋊C4C2314yes—
75C32×C42D411yescharacteristic
76C32×C42D411yescharacteristic
77C32×C42C2311yescharacteristic
78C32×C42C2311yescharacteristic
79C3×#217—21no—
80C3×(C2×D3)⋊C4—21no—
81C3×(C2×D3)⋊C4—21no—
82C3×C4⋊Dic3C2311yescharacteristic
83C3×C4⋊Dic3C2311yescharacteristic
84C3×Dic3⋊C4—21no—
85C3×Dic3⋊C4—21no—
86C3×C4×Dic3—21no—
87C3×C4×Dic3—21no—
88C3×C4×Dic3—21no—
89C3×#208—24no—
90C2×C3×C3⋊C8C2314yes—
91#3079—31noSylow
92C2×C3×#41—31no—
93C22×C3×Q8—22no—
94C22×C3×Q8—21no—
95C22×C3×Q8—21no—
96C2×#235C22×C311yescharacteristic
97C2×C3×M16—32no—
98C3×C4⋊Q8—22no—
99C3×C4⋊Q8—22no—
100C3×C4⋊Q8—21no—
101C3×C4⋊Q8—21no—
102C3×C4⋊Q8—21no—
103C3×C4⋊Q8—21no—
104C3×C4⋊Q8—22no—
105C3×C4⋊Q8—22no—
106C3×C4⋊Q8C2×D312yes—
107C3×C4⋊Q8C2×D312yes—
108C3×C4⋊Q8C22×C312yes—
109C3×C4⋊Q8C22×C312yes—
110C3×C4×Q8—31no—
111C3×C4×Q8—31no—
112C3×C4×D4—31no—
113C3×C4×D4—31no—
114C3×C4×D4—61no—
115C3×C4×D4—61no—
116C3×#117—31no—
117C3×#117—61no—
118C2×C3×C4⋊C4—22no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—22no—
122C2×C3×C4⋊C4C2×D312yes—
123C2×C3×C4⋊C4C22×C312yes—
124C2×C3×C42—21no—
125C2×C3×C42—61no—
126C2×C3×C42C2×D311yescharacteristic
127C2×C3×C42C22×C311yescharacteristic
128C4×#67—21no—
129C4×#67—21no—
130#926C22×C311yescharacteristic
131C2×#208C22×C312yes—
132C4×D12C22×C311yescharacteristic
133C4×D12C22×C311yescharacteristic
134#872—21no—
135C42×D3—21no—
136C4×Dic6C22×C311yescharacteristic
137C4×Dic6C22×C311yescharacteristic
138C3×#107—34no—
139C3×#106—34no—
140C3×C4⋊C8—32no—
141C3×C4⋊C8—32no—
142C3×#103—34no—
143C3×#102—34no—
144#810C22×C314yes—
145#809C22×C314yes—
146#808C22×C314yes—
147#807C22×C314yes—
148C4⋊(C3⋊C8)C22×C312yes—
149C4⋊(C3⋊C8)C22×C312yes—
150C23×C32C2×D411yescharacteristic
151C22×C3×D3—21no—
152C32×Q8—44no—
153C32×Q8—44no—
154C2×C32×C4—22no—
155C2×C32×C4—22no—
156C2×C32×C4—24no—
157C2×C32×C4—44no—
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×Q812yes—
164C2×C32×C4#4112yes—
165C2×C32×C4C2411yescharacteristic
166C3×#67—24no—
167C2×C3×Dic3—21no—
168C2×C3×Dic3—21no—
169C2×C3×Dic3—21no—
170C3×D12—21no—
171C3×D12C2×Q812yescomplemented
172C3×C4×D3—24no—
173C3×C4×D3—42no—
174C3×C4×D3—42no—
175C3×Dic6—21no—
176C3×Dic6C2×Q812yescomplemented
177C3×C3⋊C8—24no—
178C2×C4⋊Q8C3×D311yescharacteristic, complemented
179C4×#41—31no—
180#477—32no—
181#476—32no—
182#475—32no—
183#474—32no—
184#428—32no—
185#423—31no—
186#417—32no—
187C3×#41—34no—
188C3×#41—62no—
189C2×C3×Q8—24no—
190C2×C3×Q8—24no—
191C2×C3×Q8—22no—
192C2×C3×Q8—22no—
193C2×C3×Q8—22no—
194C2×C3×Q8—22no—
195C2×C3×Q8—31no—
196C2×C3×Q8—48no—
197C2×C3×Q8—44no—
198C2×C3×Q8—44no—
199C2×C3×D4—31no—
200C2×C3×D4—61no—
201C22×C3×C4—24no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—61no—
208C22×C3×C4—61no—
209C22×C3×C4—61no—
210C22×C3×C4#6711yescharacteristic
211C22×C3×C4#6711yescharacteristic
212C22×C3×C4C3×D411yescharacteristic
213C22×C3×C4C3×D411yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C23×C311yescharacteristic
216C2×#67—21no—
217#235—22no—
218#235C3×Q814yescomplemented
219C2×D12C23×C311yescharacteristic
220C2×C4×D3—21no—
221C2×C4×D3—21no—
222C2×C4×D3—21no—
223C2×Dic6C23×C311yescharacteristic
224C3×M16—64no—
225C2×C3×C8—34no—
226C3×C4⋊C4—24no—
227C3×C4⋊C4—24no—
228C3×C4⋊C4—24no—
229C3×C4⋊C4—22no—
230C3×C4⋊C4—22no—
231C3×C4⋊C4—22no—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—22no—
235C3×C4⋊C4—24no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4C22×D314yes—
241C3×C4⋊C4C23×C314yes—
242C3×C22⋊C4—61no—
243C3×C22⋊C4—61no—
244C3×C22⋊C4—61no—
245C3×C42—21no—
246C3×C42—21no—
247C3×C42—21no—
248C3×C42—21no—
249C3×C42—61no—
250C3×C42—61no—
251C3×C42—61no—
252C3×C42#6711yescharacteristic
253C3×C42#6711yescharacteristic
254C3×C42C3×D411yescharacteristic
255C3×C42C3×D411yescharacteristic
256C3×C42C22×D311yescharacteristic
257C3×C42C22×D311yescharacteristic
258C3×C42C23×C311yescharacteristic
259C3×C42C23×C311yescharacteristic
260#217—21no—
261(C2×D3)⋊C4—21no—
262(C2×D3)⋊C4—21no—
263C4⋊Dic3C23×C311yescharacteristic
264C4⋊Dic3C23×C311yescharacteristic
265Dic3⋊C4—21no—
266Dic3⋊C4—21no—
267C4×Dic3—21no—
268C4×Dic3—21no—
269C4×Dic3—21no—
270#208—24no—
271C2×C3⋊C8C23×C314yes—
272C22×C32—21no—
273C22×C32—21no—
274C22×C32C22⋊Q812yes—
275C22×C32C22×D411yescharacteristic
276C2×C3×D3—22no—
277C2×C3×D3—41no—
278C2×C3×D3—41no—
279C32×C4—21no—
280C32×C4—21no—
281C32×C4—44no—
282C32×C4C22⋊Q812yes—
283C32×C4AGL(1,ℤ/8)12yes—
284C32×C4#13712yes—
285C32×C4C22×Q811yescharacteristic
286C32×C4C2×#4111yescharacteristic
287C3×Dic3—22no—
288C3×Dic3—41no—
289C3×Dic3—41no—
290C2×#41—31no—
291C22×Q8—21no—
292C2×M16—32no—
293C4⋊Q8—21no—
294C4⋊Q8—21no—
295C4⋊Q8C2×C3×D312yes—
296C4⋊Q8C2×C3×D312yes—
297C4×Q8—31no—
298C4×Q8—31no—
299C4×D4—31no—
300C4×D4—31no—
301C4×D4—61no—
302C4×D4—61no—
303#117—31no—
304#117—61no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4C2×C3×D312yes—
307C2×C42—61no—
308C2×C42C2×C3×D311yescharacteristic
309#107—34no—
310#106—34no—
311C4⋊C8—32no—
312C4⋊C8—32no—
313#103—34no—
314#102—34no—
315C23×C3—21no—
316C23×C3—61no—
317C23×C3C2×#6711yescharacteristic
318C23×C3C2×C3×D411yescharacteristic
319C22×D3—21no—
320C3×Q8—32no—
321C3×Q8—48no—
322C3×Q8—44no—
323C3×Q8—44no—
324C3×Q8—48no—
325C3×Q8—44no—
326C3×Q8—44no—
327C3×Q8—61no—
328C3×D4—32no—
329C3×D4—64no—
330C3×D4—61no—
331C2×C3×C4—24no—
332C2×C3×C4—24no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—28no—
338C2×C3×C4—24no—
339C2×C3×C4—24no—
340C2×C3×C4—21no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—48no—
349C2×C3×C4—44no—
350C2×C3×C4—44no—
351C2×C3×C4—61no—
352C2×C3×C4—64no—
353C2×C3×C4—61no—
354C2×C3×C4—61no—
355C2×C3×C4—122no—
356C2×C3×C4—122no—
357C2×C3×C4D3×Q812yes—
358C2×C3×C4#23912yes—
359C2×C3×C4C2×#6711yescharacteristic
360C2×C3×C4C2×#6711yescharacteristic
361C2×C3×C4C2×#6711yescharacteristic
362C2×C3×C4C2×#6711yescharacteristic
363C2×C3×C4C2×#6711yescharacteristic
364C2×C3×C4C2×C3×D411yescharacteristic
365C2×C3×C4C2×C3×D411yescharacteristic
366C2×C3×C4C2×C3×D411yescharacteristic
367C2×C3×C4C2×C3×D411yescharacteristic
368C2×C3×C4C2×C3×D411yescharacteristic
369C2×C3×C4C2×C3×Q812yes—
370C2×C3×C4C3×#4112yes—
371C2×C3×C4C23×D311yescharacteristic
372C2×C3×C4C24×C311yescharacteristic
373#67—24no—
374C2×Dic3—21no—
375C2×Dic3—21no—
376C2×Dic3—21no—
377D12—21no—
378D12C2×C3×Q812yescomplemented
379C4×D3—24no—
380C4×D3—42no—
381C4×D3—42no—
382Dic6—21no—
383Dic6C2×C3×Q812yescomplemented
384C3×C8—64no—
385C3⋊C8—24no—
386C2×C32—22no—
387C2×C32C2×C22⋊Q811yescharacteristic
388C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
389C2×C32C2×#13711yescharacteristic
390C3×D3—42no—
391#41—34no—
392#41—62no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—31no—
396C2×Q8—44no—
397C2×D4—31no—
398C2×D4—61no—
399C22×C4—22no—
400C22×C4—61no—
401C22×C4—61no—
402C22×C4—61no—
403C22×C4C3×#6711yescharacteristic
404C22×C4C3×#6711yescharacteristic
405C22×C4C22×C3×D311yescharacteristic
406M16—64no—
407C2×C8—34no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—31no—
412C4⋊C4—31no—
413C4⋊C4—61no—
414C4⋊C4—61no—
415C4⋊C4C22×C3×D314yes—
416C22⋊C4—61no—
417C22⋊C4—61no—
418C22⋊C4—61no—
419C42—61no—
420C42—61no—
421C42—61no—
422C42C3×#6711yescharacteristic
423C42C3×#6711yescharacteristic
424C42C22×C3×D311yescharacteristic
425C42C22×C3×D311yescharacteristic
426C22×C3—22no—
427C22×C3—22no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—22no—
433C22×C3—21no—
434C22×C3—62no—
435C22×C3—121no—
436C22×C3—121no—
437C22×C3#94612yes—
438C22×C3C3×C22⋊Q812yes—
439C22×C3C22×#6711yescharacteristic
440C22×C3C22×C3×D411yescharacteristic
441C2×D3—22no—
442C2×D3—41no—
443C2×D3—41no—
444C3×C4—22no—
445C3×C4—22no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—22no—
451C3×C4—22no—
452C3×C4—22no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—48no—
456C3×C4—44no—
457C3×C4—44no—
458C3×C4—62no—
459C3×C4—121no—
460C3×C4—121no—
461C3×C4#93212yes—
462C3×C4#94212yes—
463C3×C4#94612yes—
464C3×C4C3×C22⋊Q812yes—
465C3×C4C3×AGL(1,ℤ/8)12yes—
466C3×C4C3×#13712yes—
467C3×C4C2×D3×Q811yescharacteristic
468C3×C4C2×#23911yescharacteristic
469C3×C4C22×C3×Q811yescharacteristic
470C3×C4C2×C3×#4111yescharacteristic
471Dic3—22no—
472Dic3—41no—
473Dic3—41no—
474C32#307911yescharacteristic, complemented, Sylow
475C23—61no—
476C23C2×C3×#6711yescharacteristic
477Q8—32no—
478Q8—44no—
479Q8—44no—
480Q8—61no—
481D4—32no—
482D4—64no—
483D4—61no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—44no—
488C2×C4—61no—
489C2×C4—64no—
490C2×C4—61no—
491C2×C4—61no—
492C2×C4—122no—
493C2×C4—122no—
494C2×C4C3×D3×Q812yes—
495C2×C4C3×#23912yes—
496C2×C4C2×C3×#6711yescharacteristic
497C2×C4C2×C3×#6711yescharacteristic
498C2×C4C2×C3×#6711yescharacteristic
499C2×C4C2×C3×#6711yescharacteristic
500C2×C4C2×C3×#6711yescharacteristic
501C2×C4C23×C3×D311yescharacteristic
502C8—64no—
503C2×C3—24no—
504C2×C3—22no—
505C2×C3—22no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—122no—
510C2×C3C2×#93211yescharacteristic
511C2×C3C2×#94211yescharacteristic
512C2×C3C2×#94611yescharacteristic
513C2×C3C2×C3×C22⋊Q811yescharacteristic
514C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
515C2×C3C2×C3×#13711yescharacteristic
516D3—42no—
517C22—21no—
518C22—21no—
519C22—62no—
520C22—121no—
521C22—121no—
522C22C3×#94612yes—
523C22C22×C3×#6711yescharacteristic
524C4—21no—
525C4—21no—
526C4—44no—
527C4—62no—
528C4—121no—
529C4—121no—
530C4C3×#93212yes—
531C4C3×#94212yes—
532C4C3×#94612yes—
533C4C2×C3×D3×Q811yescharacteristic
534C4C2×C3×#23911yescharacteristic
535C3—21no—
536C3#8321211yescharacteristic, direct product factor
537C3C3×#307911yescharacteristic, complemented
538C2—22no—
539C2—122no—
540C2C2×C3×#93211yescharacteristic
541C2C2×C3×#94211yescharacteristic
542C2C2×C3×#94611yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×C4⋊Q8C2
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
hypercenterC2×C3×C4⋊Q8D3
hypocenterC3C3×#3079
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C2×C3×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4⋊Q8C2semidirect
3. C3×#5094C2semidirect
4. C3×#5091C2semidirect
5. C3×#5087C2semidirect
6. C3×#5084C2semidirect
8. C3×#4964C2semidirect
9. C3×#4924C2semidirect
11. #83212C3direct (N × H)
38. C2×C3×C4⋊Q8D3semidirect
39. C2×C3×C4⋊Q8C2×C3semidirect
49. #5094C2×C3semidirect
50. #5091C2×C3semidirect
51. #5087C2×C3semidirect
52. #5084C2×C3semidirect
54. #4964C2×C3semidirect
55. #4924C2×C3semidirect
65. C3×#235Q8semidirect
171. C3×D12C2×Q8semidirect
176. C3×Dic6C2×Q8semidirect
178. C2×C4⋊Q8C3×D3semidirect
218. #235C3×Q8semidirect
378. D12C2×C3×Q8semidirect
383. Dic6C2×C3×Q8semidirect
474. C32#3079semidirect
536. C3#83212direct (N × H)
537. C3C3×#3079semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4⋊Q82
C3×C4×#2352
C3×#50942
C3×#50912
C3×#50872
C3×#50842
C3×#49662
C3×#49642
C3×#49242
C3×#30793
#832123