Finite Group Databasebeta

← C3×#84087 #11802711

Subgroups — C3×#84087 #11802711

Order 1152.

2205 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×#41C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic, complemented
3C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#5229C212yesmaximal, complemented
5C3×#5221C212yesmaximal, complemented
6C3×#5220C214yesmaximal, complemented
7C3×#5212C214yesmaximal, complemented
8C3×#2311—31nomaximal
9#84087C311yesmaximal, characteristic, direct product factor
10C2×C32×#41—24no—
11C2×C32×#41—24no—
12C2×C32×#41C418yescomplemented
13C22×C32×Q8C2211yescharacteristic
14C22×C32×D4C2212yes—
15C22×C32×D4C2211yescharacteristic
16C23×C32×C4C2212yes—
17C23×C32×C4C2211yescharacteristic
18C23×C3×Dic3C2212yes—
19C2×C3×#217C2212yes—
20C2×C3×#217C2218yes—
21C3×#926—24no—
22C2×C3×C4⋊Dic3—24no—
23C2×C3×C4⋊Dic3C2212yes—
24C2×C3×C4⋊Dic3C2212yes—
25C2×C3×C4⋊Dic3C2212yes—
26C2×C3×C4×Dic3C2212yes—
27C3×C3⋊#95C2218yes—
28C22×C3×#41—21no—
29C22×C3×#41D311yescharacteristic
30C22×C3×#41C2×C311yescharacteristic
31C2×C3×#117—31no—
32C22×C3×C4⋊C4—31no—
33C2×#926C2×C311yescharacteristic, complemented
34C22×C4⋊Dic3C2×C311yescharacteristic, complemented
35C3×#391—32no—
36C3×#390—32no—
37C3×#386—34no—
38C3×#380—34no—
39#5229C2×C312yescomplemented
40#5221C2×C312yescomplemented
41#5220C2×C314yescomplemented
42#5212C2×C314yescomplemented
43C24×C32C2312yes—
44C24×C32C2311yescharacteristic
45C32×#41—232no—
46C2×C32×Q8—22no—
47C2×C32×Q8—22no—
48C2×C32×Q8C2×C414yescomplemented
49C2×C32×D4—24no—
50C2×C32×D4—24no—
51C2×C32×D4—22no—
52C2×C32×D4—22no—
53C2×C32×D4C2×C418yes—
54C2×C32×D4C2×C414yescomplemented
55C22×C32×C4—24no—
56C22×C32×C4—24no—
57C22×C32×C4C2×C414yes—
58C22×C32×C4C2×C418yescomplemented
59C22×C32×C4D414yes—
60C22×C32×C4D414yes—
61C22×C32×C4C2312yes—
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C3×Dic3—24no—
65C22×C3×Dic3—44no—
66C22×C3×Dic3C2314yes—
67C22×C3×Dic3C2314yes—
68C3×#217—24no—
69C3×#217—48no—
70C3×C4⋊Dic3—24no—
71C3×C4⋊Dic3—24no—
72C3×C4⋊Dic3—24no—
73C3×C4×Dic3—24no—
74#2311—31noSylow
75C2×C3×#41—28no—
76C2×C3×#41—28no—
77C2×C3×#41—24no—
78C2×C3×#41—24no—
79C2×C3×#41—24no—
80C2×C3×#41—24no—
81C2×C3×#41—28no—
82C2×C3×#41Dic318yescomplemented
83C2×C3×#41C3×C418yescomplemented
84C22×C3×Q8—21no—
85C22×C3×Q8C2×D311yescharacteristic
86C22×C3×Q8C22×C311yescharacteristic
87C22×C3×D4—22no—
88C22×C3×D4—21no—
89C22×C3×D4C2×D312yes—
90C22×C3×D4C2×D311yescharacteristic
91C22×C3×D4C22×C312yes—
92C22×C3×D4C22×C311yescharacteristic
93C23×C3×C4—22no—
94C23×C3×C4—21no—
95C23×C3×C4—32no—
96C23×C3×C4C2×D312yes—
97C23×C3×C4C2×D311yescharacteristic
98C23×C3×C4C22×C312yes—
99C23×C3×C4C22×C311yescharacteristic
100C23×Dic3C22×C312yes—
101C3×#117—64no—
102C2×C3×C4⋊C4—32no—
103C2×C3×C4⋊C4—32no—
104C2×C3×C4⋊C4—32no—
105C2×C3×C4⋊C4—64no—
106C2×C3×C22⋊C4—32no—
107C2×C3×C22⋊C4—38no—
108C2×C3×C42—32no—
109C2×#217C22×C312yes—
110C2×#217C22×C318yes—
111#926—24no—
112C2×C4⋊Dic3—24no—
113C2×C4⋊Dic3C22×C312yes—
114C2×C4⋊Dic3C22×C312yes—
115C2×C4⋊Dic3C22×C312yes—
116C2×C4×Dic3C22×C312yes—
117C3×#95—38no—
118C3⋊#95C22×C318yes—
119C23×C32—22no—
120C23×C32—22no—
121C23×C32—22no—
122C23×C32—22no—
123C23×C32—24no—
124C23×C32—24no—
125C23×C32C22×C414yes—
126C23×C32C22×C412yes—
127C23×C32C2×D412yes—
128C23×C32C2×D412yes—
129C23×C32C2411yescharacteristic
130C32×Q8—28no—
131C32×D4—216no—
132C32×D4—28no—
133C2×C32×C4—22no—
134C2×C32×C4—22no—
135C2×C32×C4—216no—
136C2×C32×C4C22⋊C4116yescomplemented
137C2×C32×C4C22×C414yes—
138C2×C32×C4C22×C412yes—
139C2×C32×C4C22×C412yes—
140C2×C32×C4C2×D412yes—
141C2×C32×C4C2×D412yes—
142C2×C32×C4C2×D412yes—
143C2×C32×C4C2×D412yes—
144C2×C3×Dic3—24no—
145C2×C3×Dic3—24no—
146C2×C3×Dic3—24no—
147C2×C3×Dic3—28no—
148C2×C3×Dic3—24no—
149C2×C3×Dic3—48no—
150C22×#41C3×D311yescharacteristic
151C2×#117—31no—
152C22×C4⋊C4—31no—
153#391—32no—
154#390—32no—
155#386—34no—
156#380—34no—
157C24×C3—22no—
158C24×C3—21no—
159C24×C3C22×D312yes—
160C24×C3C22×D311yescharacteristic
161C24×C3C23×C312yes—
162C24×C3C23×C311yescharacteristic
163C3×#41—264no—
164C3×#41—232no—
165C3×#41—232no—
166C2×C3×Q8—24no—
167C2×C3×Q8—24no—
168C2×C3×Q8—22no—
169C2×C3×Q8—22no—
170C2×C3×Q8—22no—
171C2×C3×Q8—22no—
172C2×C3×Q8—24no—
173C2×C3×Q8C2×Dic314yescomplemented
174C2×C3×Q8C2×C3×C414yescomplemented
175C2×C3×D4—28no—
176C2×C3×D4—28no—
177C2×C3×D4—24no—
178C2×C3×D4—24no—
179C2×C3×D4—24no—
180C2×C3×D4—24no—
181C2×C3×D4—24no—
182C2×C3×D4—24no—
183C2×C3×D4—22no—
184C2×C3×D4—22no—
185C2×C3×D4—22no—
186C2×C3×D4—22no—
187C2×C3×D4—28no—
188C2×C3×D4—24no—
189C2×C3×D4C2×Dic318yes—
190C2×C3×D4C2×Dic314yescomplemented
191C2×C3×D4C2×C3×C418yes—
192C2×C3×D4C2×C3×C414yescomplemented
193C22×C3×C4—28no—
194C22×C3×C4—28no—
195C22×C3×C4—24no—
196C22×C3×C4—24no—
197C22×C3×C4—24no—
198C22×C3×C4—24no—
199C22×C3×C4—24no—
200C22×C3×C4—28no—
201C22×C3×C4—24no—
202C22×C3×C4—24no—
203C22×C3×C4—21no—
204C22×C3×C4—22no—
205C22×C3×C4—21no—
206C22×C3×C4—34no—
207C22×C3×C4—34no—
208C22×C3×C4—64no—
209C22×C3×C4—124no—
210C22×C3×C4C2×Dic314yes—
211C22×C3×C4C2×Dic318yescomplemented
212C22×C3×C4#6714yes—
213C22×C3×C4#6714yes—
214C22×C3×C4C2×C3×C414yes—
215C22×C3×C4C2×C3×C418yescomplemented
216C22×C3×C4C3×D414yes—
217C22×C3×C4C3×D414yes—
218C22×C3×C4C22×D312yes—
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C23×C312yes—
222C22×C3×C4C23×C311yescharacteristic
223C22×C3×C4C23×C311yescharacteristic
224C22×Dic3—24no—
225C22×Dic3—44no—
226C22×Dic3C23×C314yes—
227C22×Dic3C23×C314yes—
228C3×C4⋊C4—64no—
229C3×C4⋊C4—64no—
230C3×C4⋊C4—64no—
231C3×C22⋊C4—64no—
232C3×C22⋊C4—128no—
233C3×C42—64no—
234#217—24no—
235#217—48no—
236C4⋊Dic3—24no—
237C4⋊Dic3—24no—
238C4⋊Dic3—24no—
239C4×Dic3—24no—
240C22×C32—24no—
241C22×C32—24no—
242C22×C32—22no—
243C22×C32—22no—
244C22×C32—24no—
245C22×C32—28no—
246C22×C32—42no—
247C22×C32—42no—
248C22×C32—44no—
249C22×C32C2×C22⋊C414yes—
250C22×C32C23×C411yescharacteristic
251C22×C32C22×D411yescharacteristic
252C22×C32C22×D411yescharacteristic
253C22×C32H(5,𝔽2)12yes—
254C22×C322−1+412yes—
255C32×C4—24no—
256C32×C4C2×C22⋊C414yes—
257C32×C4C2×C22⋊C414yes—
258C3×Dic3—44no—
259C3×Dic3—44no—
260C2×#41—24no—
261C2×#41—24no—
262C2×#41C3×Dic318yescomplemented
263C22×Q8C2×C3×D311yescharacteristic
264C22×D4C2×C3×D312yes—
265C22×D4C2×C3×D311yescharacteristic
266C23×C4—32no—
267C23×C4C2×C3×D312yes—
268C23×C4C2×C3×D311yescharacteristic
269#117—64no—
270C2×C4⋊C4—32no—
271C2×C4⋊C4—32no—
272C2×C4⋊C4—32no—
273C2×C4⋊C4—64no—
274C2×C22⋊C4—32no—
275C2×C22⋊C4—38no—
276C2×C42—32no—
277#95—38no—
278C23×C3—22no—
279C23×C3—22no—
280C23×C3—22no—
281C23×C3—22no—
282C23×C3—24no—
283C23×C3—24no—
284C23×C3—24no—
285C23×C3—24no—
286C23×C3—22no—
287C23×C3—22no—
288C23×C3—22no—
289C23×C3—22no—
290C23×C3—24no—
291C23×C3—24no—
292C23×C3—21no—
293C23×C3—24no—
294C23×C3—22no—
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—42no—
298C23×C3—42no—
299C23×C3—44no—
300C23×C3—44no—
301C23×C3C22×Dic314yes—
302C23×C3C22×Dic312yes—
303C23×C3C2×#6712yes—
304C23×C3C2×#6712yes—
305C23×C3C22×C3×C414yes—
306C23×C3C22×C3×C412yes—
307C23×C3C2×C3×D412yes—
308C23×C3C2×C3×D412yes—
309C23×C3C23×D311yescharacteristic
310C23×C3C24×C311yescharacteristic
311C3×Q8—216no—
312C3×Q8—28no—
313C3×Q8—28no—
314C3×D4—232no—
315C3×D4—216no—
316C3×D4—216no—
317C3×D4—216no—
318C3×D4—28no—
319C3×D4—28no—
320C2×C3×C4—24no—
321C2×C3×C4—24no—
322C2×C3×C4—232no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—216no—
328C2×C3×C4—216no—
329C2×C3×C4—216no—
330C2×C3×C4—22no—
331C2×C3×C4—24no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—64no—
338C2×C3×C4—68no—
339C2×C3×C4—64no—
340C2×C3×C4—64no—
341C2×C3×C4—64no—
342C2×C3×C4—128no—
343C2×C3×C4#217116yescomplemented
344C2×C3×C4C3×C22⋊C4116yescomplemented
345C2×C3×C4C22×Dic314yes—
346C2×C3×C4C22×Dic312yes—
347C2×C3×C4C22×Dic312yes—
348C2×C3×C4C2×#6712yes—
349C2×C3×C4C2×#6712yes—
350C2×C3×C4C2×#6712yes—
351C2×C3×C4C2×#6712yes—
352C2×C3×C4C22×C3×C414yes—
353C2×C3×C4C22×C3×C412yes—
354C2×C3×C4C22×C3×C412yes—
355C2×C3×C4C2×C3×D412yes—
356C2×C3×C4C2×C3×D412yes—
357C2×C3×C4C2×C3×D412yes—
358C2×C3×C4C2×C3×D412yes—
359C2×Dic3—24no—
360C2×Dic3—24no—
361C2×Dic3—24no—
362C2×Dic3—28no—
363C2×Dic3—24no—
364C2×Dic3—48no—
365C2×C32—24no—
366C2×C32—44no—
367C2×C32C22×C22⋊C411yescharacteristic
368C2×C32#52012yes—
369C2×C32#53511yescharacteristic
370C2×C32#53611yescharacteristic
371C2×C32#53712yes—
372C24C22×C3×D312yes—
373C24C22×C3×D311yescharacteristic
374#41—232no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8C2×C3×Dic314yescomplemented
378C2×D4—24no—
379C2×D4—24no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4C2×C3×Dic318yes—
383C2×D4C2×C3×Dic314yescomplemented
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—34no—
387C22×C4—34no—
388C22×C4—64no—
389C22×C4—124no—
390C22×C4C2×C3×Dic314yes—
391C22×C4C2×C3×Dic318yescomplemented
392C22×C4C3×#6714yes—
393C22×C4C3×#6714yes—
394C22×C4C22×C3×D312yes—
395C22×C4C22×C3×D311yescharacteristic
396C22×C4C22×C3×D311yescharacteristic
397C4⋊C4—64no—
398C4⋊C4—64no—
399C4⋊C4—64no—
400C22⋊C4—64no—
401C22⋊C4—128no—
402C42—64no—
403C22×C3—22no—
404C22×C3—24no—
405C22×C3—22no—
406C22×C3—24no—
407C22×C3—24no—
408C22×C3—22no—
409C22×C3—22no—
410C22×C3—24no—
411C22×C3—28no—
412C22×C3—28no—
413C22×C3—24no—
414C22×C3—24no—
415C22×C3—28no—
416C22×C3—24no—
417C22×C3—22no—
418C22×C3—22no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—42no—
423C22×C3—44no—
424C22×C3—42no—
425C22×C3—44no—
426C22×C3—48no—
427C22×C3—44no—
428C22×C3—44no—
429C22×C3—48no—
430C22×C3—42no—
431C22×C3—42no—
432C22×C3—44no—
433C22×C3—42no—
434C22×C3—42no—
435C22×C3—44no—
436C22×C3C2×#21714yes—
437C22×C3C2×C3×C22⋊C414yes—
438C22×C3#100912yes—
439C22×C3#101012yes—
440C22×C3C23×Dic311yescharacteristic
441C22×C3C22×#6711yescharacteristic
442C22×C3C22×#6711yescharacteristic
443C22×C3C23×C3×C411yescharacteristic
444C22×C3C22×C3×D411yescharacteristic
445C22×C3C22×C3×D411yescharacteristic
446C22×C3C3×H(5,𝔽2)12yes—
447C22×C3C3×2−1+412yes—
448C3×C4—28no—
449C3×C4—24no—
450C3×C4—24no—
451C3×C4—24no—
452C3×C4—24no—
453C3×C4—124no—
454C3×C4—124no—
455C3×C4C2×#21714yes—
456C3×C4C2×#21714yes—
457C3×C4C2×C3×C22⋊C414yes—
458C3×C4C2×C3×C22⋊C414yes—
459Dic3—44no—
460Dic3—44no—
461C32#231111yescharacteristic, complemented, Sylow
462C23—22no—
463C23—22no—
464C23—24no—
465C23—24no—
466C23—22no—
467C23—22no—
468C23C22×C3×Dic314yes—
469C23C22×C3×Dic312yes—
470C23C2×C3×#6712yes—
471C23C2×C3×#6712yes—
472C23C23×C3×D311yescharacteristic
473Q8—28no—
474D4—216no—
475D4—28no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—216no—
479C2×C4—64no—
480C2×C4—68no—
481C2×C4—64no—
482C2×C4—64no—
483C2×C4—64no—
484C2×C4—128no—
485C2×C4C3×#217116yescomplemented
486C2×C4C22×C3×Dic314yes—
487C2×C4C22×C3×Dic312yes—
488C2×C4C22×C3×Dic312yes—
489C2×C4C2×C3×#6712yes—
490C2×C4C2×C3×#6712yes—
491C2×C4C2×C3×#6712yes—
492C2×C4C2×C3×#6712yes—
493C2×C3—24no—
494C2×C3—24no—
495C2×C3—21no—
496C2×C3—22no—
497C2×C3—21no—
498C2×C3—22no—
499C2×C3—21no—
500C2×C3—44no—
501C2×C3—48no—
502C2×C3—44no—
503C2×C3—44no—
504C2×C3#582511yescharacteristic
505C2×C3#582712yes—
506C2×C3#583011yescharacteristic
507C2×C3#583312yes—
508C2×C3C22×#21711yescharacteristic
509C2×C3C22×C3×C22⋊C411yescharacteristic
510C2×C3C3×#52012yes—
511C2×C3C3×#53511yescharacteristic
512C2×C3C3×#53611yescharacteristic
513C2×C3C3×#53712yes—
514C22—22no—
515C22—24no—
516C22—22no—
517C22—24no—
518C22—28no—
519C22—24no—
520C22—42no—
521C22—42no—
522C22—44no—
523C22C2×C3×#21714yes—
524C22C3×#100912yes—
525C22C3×#101012yes—
526C22C23×C3×Dic311yescharacteristic
527C22C22×C3×#6711yescharacteristic
528C22C22×C3×#6711yescharacteristic
529C4—24no—
530C4—124no—
531C4—124no—
532C4C2×C3×#21714yes—
533C4C2×C3×#21714yes—
534C3—21no—
535C3#8408711yescharacteristic, direct product factor
536C3C3×#231111yescharacteristic, complemented
537C2—24no—
538C2—44no—
539C2C3×#582511yescharacteristic
540C2C3×#582712yes—
541C2C3×#583011yescharacteristic
542C2C3×#583312yes—
543C2C22×C3×#21711yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
Fitting, prime radicalC22×C32×#41C2
socleC23×C32C24
cosocleC23×C3C24×C3
hypercenterC22×C3×#41D3
hypocenterC3C3×#2311
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×#41

Complements

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

NH ≅ G/Ntype
2. C2×C3×#926C2semidirect
3. C22×C3×C4⋊Dic3C2semidirect
4. C3×#5229C2semidirect
5. C3×#5221C2semidirect
6. C3×#5220C2semidirect
7. C3×#5212C2semidirect
9. #84087C3direct (N × H)
12. C2×C32×#41C4semidirect
33. C2×#926C2×C3semidirect
34. C22×C4⋊Dic3C2×C3semidirect
39. #5229C2×C3semidirect
40. #5221C2×C3semidirect
41. #5220C2×C3semidirect
42. #5212C2×C3semidirect
48. C2×C32×Q8C2×C4semidirect
54. C2×C32×D4C2×C4semidirect
58. C22×C32×C4C2×C4semidirect
82. C2×C3×#41Dic3semidirect
83. C2×C3×#41C3×C4semidirect
136. C2×C32×C4C22⋊C4semidirect
173. C2×C3×Q8C2×Dic3semidirect
174. C2×C3×Q8C2×C3×C4semidirect
190. C2×C3×D4C2×Dic3semidirect
192. C2×C3×D4C2×C3×C4semidirect
211. C22×C3×C4C2×Dic3semidirect
215. C22×C3×C4C2×C3×C4semidirect
262. C2×#41C3×Dic3semidirect
343. C2×C3×C4#217semidirect
344. C2×C3×C4C3×C22⋊C4semidirect
377. C2×Q8C2×C3×Dic3semidirect
383. C2×D4C2×C3×Dic3semidirect
391. C22×C4C2×C3×Dic3semidirect
461. C32#2311semidirect
485. C2×C4C3×#217semidirect
535. C3#84087direct (N × H)
536. C3C3×#2311semidirect

Maximal subgroups

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

subgroupindex
C22×C32×#412
C2×C3×#9262
C22×C3×C4⋊Dic32
C3×#52292
C3×#52212
C3×#52202
C3×#52122
C3×#23113
#840873