Finite Group Databasebeta

← C3×#82270 #11802699

Subgroups — C3×#82270 #11802699

Order 1152.

1925 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic
2C2×C32×#117C211yesmaximal, characteristic, complemented
3C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#4987C214yesmaximal, complemented
5C3×#4958C214yesmaximal, complemented
6C3×#4939C212yesmaximal, complemented
7C3×#4929C212yesmaximal, complemented
8C3×#2311—31nomaximal
9#82270C311yesmaximal, characteristic, direct product factor
10C23×C32×C4C2211yescharacteristic
11C22×C3×#67C2212yes—
12C23×C3×Dic3C2212yes—
13C2×C3×#235—24no—
14C2×C3×#235—24no—
15C2×C3×#235C418yescomplemented
16C22×C3×D12C2211yescharacteristic
17C22×C3×C4×D3C2212yes—
18C22×C3×Dic6C2211yescharacteristic
19C32×#117—24no—
20C2×C32×C4⋊C4C2212yes—
21C2×C32×C22⋊C4C2212yes—
22C2×C32×C42C2212yes—
23C2×C3×(C2×D3)⋊C4C2218yes—
24C2×C3×C4⋊Dic3—24no—
25C2×C3×C4⋊Dic3C2212yes—
26C2×C3×C4⋊Dic3C2212yes—
27C3×C3⋊#95C2218yes—
28C22×C3×#41—31no—
29C22×#235C2×C311yescharacteristic
30C2×C3×#117—21no—
31C2×C3×#117D311yescharacteristic, complemented
32C2×C3×#117C2×C311yescharacteristic, complemented
33C22×C3×C4⋊C4—31no—
34C22×C4⋊Dic3C2×C311yescharacteristic, complemented
35C3×#391—32no—
36C3×#390—32no—
37C3×#386—34no—
38C3×#380—34no—
39#4987C2×C314yescomplemented
40#4958C2×C314yescomplemented
41#4939C2×C312yescomplemented
42#4929C2×C312yescomplemented
43C24×C32C2311yescharacteristic
44C23×C3×D3C2312yes—
45C22×C32×C4C2×C414yes—
46C22×C32×C4D414yes—
47C22×C32×C4D414yes—
48C22×C32×C4C2314yes—
49C22×C32×C4C2311yescharacteristic
50C22×C32×C4C2311yescharacteristic
51C2×C3×#67—24no—
52C2×C3×#67—24no—
53C2×C3×#67C2×C418yes—
54C22×C3×Dic3—24no—
55C22×C3×Dic3—44no—
56C22×C3×Dic3C2314yes—
57C22×C3×Dic3C2312yes—
58C3×#235—232no—
59C2×C3×D12—22no—
60C2×C3×D12—22no—
61C2×C3×D12C2×C414yescomplemented
62C2×C3×C4×D3—24no—
63C2×C3×C4×D3—24no—
64C2×C3×C4×D3C2×C418yescomplemented
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6C2×C414yescomplemented
68C32×C4⋊C4—24no—
69C32×C22⋊C4—24no—
70C32×C42—24no—
71C3×(C2×D3)⋊C4—48no—
72C3×C4⋊Dic3—24no—
73C3×C4⋊Dic3—24no—
74#2311—31noSylow
75C2×C3×#41—38no—
76C2×C3×#41—64no—
77C2×C3×#41—64no—
78C22×C3×Q8—31no—
79C22×C3×D4—32no—
80C22×C3×D4—31no—
81C23×C3×C4—21no—
82C23×C3×C4—32no—
83C23×C3×C4—32no—
84C23×C3×C4C2×D311yescharacteristic
85C23×C3×C4C22×C311yescharacteristic
86C22×#67C22×C312yes—
87C23×Dic3C22×C312yes—
88C2×#235—24no—
89C2×#235—24no—
90C2×#235C3×C418yescomplemented
91C22×D12C22×C311yescharacteristic
92C22×C4×D3C22×C312yes—
93C22×Dic6C22×C311yescharacteristic
94C3×#117—28no—
95C3×#117—24no—
96C3×#117—24no—
97C2×C3×C4⋊C4—22no—
98C2×C3×C4⋊C4—32no—
99C2×C3×C4⋊C4—32no—
100C2×C3×C4⋊C4—64no—
101C2×C3×C4⋊C4C2×D312yes—
102C2×C3×C4⋊C4C22×C312yes—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—38no—
105C2×C3×C22⋊C4C2×D312yes—
106C2×C3×C22⋊C4C22×C312yes—
107C2×C3×C42—22no—
108C2×C3×C42C2×D312yes—
109C2×C3×C42C22×C312yes—
110C2×(C2×D3)⋊C4C22×C318yes—
111C2×C4⋊Dic3—24no—
112C2×C4⋊Dic3C22×C312yes—
113C2×C4⋊Dic3C22×C312yes—
114C3×#95—38no—
115C3⋊#95C22×C318yes—
116C23×C32—22no—
117C23×C32—22no—
118C23×C32C22×C412yes—
119C23×C32C2×D412yes—
120C23×C32C2×D412yes—
121C23×C32C2411yescharacteristic
122C22×C3×D3—22no—
123C22×C3×D3—22no—
124C22×C3×D3—24no—
125C22×C3×D3—24no—
126C22×C3×D3C22×C414yes—
127C2×C32×C4—24no—
128C2×C32×C4—24no—
129C2×C32×C4—24no—
130C2×C32×C4C22⋊C4116yescomplemented
131C2×C32×C4C22×C412yes—
132C2×C32×C4C22×C412yes—
133C2×C32×C4C2×D412yes—
134C2×C32×C4C2×D412yes—
135C2×C32×C4C2×D412yes—
136C2×C32×C4C2×D412yes—
137C3×#67—216no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—24no—
141C2×C3×Dic3—28no—
142C2×C3×Dic3—48no—
143C2×C3×Dic3C22×C414yes—
144C3×D12—28no—
145C3×C4×D3—216no—
146C3×Dic6—28no—
147C22×#41—31no—
148C2×#117C3×D311yescharacteristic, complemented
149C22×C4⋊C4—31no—
150#391—32no—
151#390—32no—
152#386—34no—
153#380—34no—
154C24×C3—21no—
155C24×C3—32no—
156C24×C3C22×D311yescharacteristic
157C24×C3C23×C311yescharacteristic
158C23×D3C23×C312yes—
159C3×#41—632no—
160C2×C3×Q8—34no—
161C2×C3×Q8—62no—
162C2×C3×Q8—62no—
163C2×C3×D4—38no—
164C2×C3×D4—34no—
165C2×C3×D4—64no—
166C2×C3×D4—64no—
167C2×C3×D4—62no—
168C2×C3×D4—62no—
169C22×C3×C4—24no—
170C22×C3×C4—24no—
171C22×C3×C4—24no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—24no—
175C22×C3×C4—32no—
176C22×C3×C4—38no—
177C22×C3×C4—34no—
178C22×C3×C4—64no—
179C22×C3×C4—64no—
180C22×C3×C4—64no—
181C22×C3×C4—124no—
182C22×C3×C4C4×D314yes—
183C22×C3×C4D1214yes—
184C22×C3×C4#6714yes—
185C22×C3×C4C2×C3×C414yes—
186C22×C3×C4C3×D414yes—
187C22×C3×C4C3×D414yes—
188C22×C3×C4C22×D314yes—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C23×C314yes—
192C22×C3×C4C23×C311yescharacteristic
193C22×C3×C4C23×C311yescharacteristic
194C2×#67—24no—
195C2×#67—24no—
196C2×#67C2×C3×C418yes—
197C22×Dic3—24no—
198C22×Dic3—44no—
199C22×Dic3C23×C314yes—
200C22×Dic3C23×C312yes—
201#235—232no—
202C2×D12—22no—
203C2×D12—22no—
204C2×D12C2×C3×C414yescomplemented
205C2×C4×D3—24no—
206C2×C4×D3—24no—
207C2×C4×D3C2×C3×C418yescomplemented
208C2×Dic6—22no—
209C2×Dic6—22no—
210C2×Dic6C2×C3×C414yescomplemented
211C3×C4⋊C4—28no—
212C3×C4⋊C4—24no—
213C3×C4⋊C4—24no—
214C3×C4⋊C4—64no—
215C3×C4⋊C4—64no—
216C3×C22⋊C4—28no—
217C3×C22⋊C4—24no—
218C3×C22⋊C4—24no—
219C3×C22⋊C4—128no—
220C3×C42—28no—
221C3×C42—24no—
222C3×C42—24no—
223(C2×D3)⋊C4—48no—
224C4⋊Dic3—24no—
225C4⋊Dic3—24no—
226C22×C32—24no—
227C22×C32—22no—
228C22×C32—22no—
229C22×C32—24no—
230C22×C32C2×C22⋊C414yes—
231C22×C32C23×C411yescharacteristic
232C22×C32C22×D411yescharacteristic
233C22×C32C22×D411yescharacteristic
234C22×C32H(5,𝔽2)12yes—
235C22×C322−1+412yes—
236C2×C3×D3—24no—
237C2×C3×D3—28no—
238C2×C3×D3—42no—
239C2×C3×D3—42no—
240C2×C3×D3—44no—
241C32×C4—44no—
242C32×C4C2×C22⋊C414yes—
243C32×C4C2×C22⋊C414yes—
244C3×Dic3—24no—
245C3×Dic3—44no—
246C2×#41—38no—
247C2×#41—64no—
248C2×#41—64no—
249C22×Q8—31no—
250C22×D4—32no—
251C22×D4—31no—
252C23×C4—32no—
253C23×C4—32no—
254C23×C4C2×C3×D311yescharacteristic
255#117—24no—
256C2×C4⋊C4—32no—
257C2×C4⋊C4—32no—
258C2×C4⋊C4—64no—
259C2×C4⋊C4C2×C3×D312yes—
260C2×C22⋊C4—38no—
261C2×C22⋊C4C2×C3×D312yes—
262C2×C42C2×C3×D312yes—
263#95—38no—
264C23×C3—22no—
265C23×C3—22no—
266C23×C3—22no—
267C23×C3—22no—
268C23×C3—21no—
269C23×C3—22no—
270C23×C3—22no—
271C23×C3—22no—
272C23×C3—34no—
273C23×C3—42no—
274C23×C3—42no—
275C23×C3—62no—
276C23×C3—64no—
277C23×C3—64no—
278C23×C3—62no—
279C23×C3C2×C4×D312yes—
280C23×C3C2×D1212yes—
281C23×C3C2×#6712yes—
282C23×C3C22×C3×C412yes—
283C23×C3C2×C3×D412yes—
284C23×C3C2×C3×D412yes—
285C23×C3C23×D311yescharacteristic
286C23×C3C24×C311yescharacteristic
287C22×D3—22no—
288C22×D3—22no—
289C22×D3—24no—
290C22×D3—24no—
291C22×D3C22×C3×C414yes—
292C3×Q8—68no—
293C3×D4—616no—
294C3×D4—68no—
295C2×C3×C4—28no—
296C2×C3×C4—24no—
297C2×C3×C4—24no—
298C2×C3×C4—24no—
299C2×C3×C4—24no—
300C2×C3×C4—24no—
301C2×C3×C4—24no—
302C2×C3×C4—216no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—34no—
310C2×C3×C4—44no—
311C2×C3×C4—44no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4—616no—
315C2×C3×C4—64no—
316C2×C3×C4—68no—
317C2×C3×C4—128no—
318C2×C3×C4(C2×D3)⋊C4116yescomplemented
319C2×C3×C4C3×C22⋊C4116yescomplemented
320C2×C3×C4C2×C4×D312yes—
321C2×C3×C4C2×C4×D312yes—
322C2×C3×C4C2×D1212yes—
323C2×C3×C4C2×D1212yes—
324C2×C3×C4C2×#6712yes—
325C2×C3×C4C2×#6712yes—
326C2×C3×C4C22×C3×C412yes—
327C2×C3×C4C22×C3×C412yes—
328C2×C3×C4C2×C3×D412yes—
329C2×C3×C4C2×C3×D412yes—
330C2×C3×C4C2×C3×D412yes—
331C2×C3×C4C2×C3×D412yes—
332#67—216no—
333C2×Dic3—22no—
334C2×Dic3—22no—
335C2×Dic3—24no—
336C2×Dic3—28no—
337C2×Dic3—48no—
338C2×Dic3C22×C3×C414yes—
339D12—28no—
340C4×D3—216no—
341Dic6—28no—
342C2×C32—24no—
343C2×C32C22×C22⋊C411yescharacteristic
344C2×C32#52012yes—
345C2×C32#53511yescharacteristic
346C2×C32#53611yescharacteristic
347C2×C32#53712yes—
348C3×D3—44no—
349C24—32no—
350C24C22×C3×D311yescharacteristic
351#41—632no—
352C2×Q8—34no—
353C2×Q8—62no—
354C2×Q8—62no—
355C2×D4—38no—
356C2×D4—34no—
357C2×D4—64no—
358C2×D4—64no—
359C2×D4—62no—
360C2×D4—62no—
361C22×C4—32no—
362C22×C4—38no—
363C22×C4—34no—
364C22×C4—64no—
365C22×C4—64no—
366C22×C4—64no—
367C22×C4—124no—
368C22×C4C3×C4×D314yes—
369C22×C4C3×D1214yes—
370C22×C4C3×#6714yes—
371C22×C4C22×C3×D314yes—
372C22×C4C22×C3×D311yescharacteristic
373C22×C4C22×C3×D311yescharacteristic
374C4⋊C4—24no—
375C4⋊C4—64no—
376C4⋊C4—64no—
377C22⋊C4—24no—
378C22⋊C4—128no—
379C42—24no—
380C22×C3—24no—
381C22×C3—22no—
382C22×C3—22no—
383C22×C3—24no—
384C22×C3—24no—
385C22×C3—22no—
386C22×C3—22no—
387C22×C3—24no—
388C22×C3—24no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—22no—
392C22×C3—22no—
393C22×C3—21no—
394C22×C3—44no—
395C22×C3—42no—
396C22×C3—42no—
397C22×C3—44no—
398C22×C3—68no—
399C22×C3—64no—
400C22×C3—122no—
401C22×C3—122no—
402C22×C3—124no—
403C22×C3C2×(C2×D3)⋊C414yes—
404C22×C3C2×C3×C22⋊C414yes—
405C22×C3C22×C4×D311yescharacteristic
406C22×C3C22×D1211yescharacteristic
407C22×C3#100912yes—
408C22×C3#101012yes—
409C22×C3C22×#6711yescharacteristic
410C22×C3C23×C3×C411yescharacteristic
411C22×C3C22×C3×D411yescharacteristic
412C22×C3C22×C3×D411yescharacteristic
413C22×C3C3×H(5,𝔽2)12yes—
414C22×C3C3×2−1+412yes—
415C2×D3—24no—
416C2×D3—28no—
417C2×D3—42no—
418C2×D3—42no—
419C2×D3—44no—
420C3×C4—24no—
421C3×C4—24no—
422C3×C4—48no—
423C3×C4—44no—
424C3×C4—44no—
425C3×C4—64no—
426C3×C4—124no—
427C3×C4C2×(C2×D3)⋊C414yes—
428C3×C4C2×(C2×D3)⋊C414yes—
429C3×C4C2×C3×C22⋊C414yes—
430C3×C4C2×C3×C22⋊C414yes—
431Dic3—24no—
432Dic3—44no—
433C32#231111yescharacteristic, complemented, Sylow
434C23—22no—
435C23—22no—
436C23—34no—
437C23—62no—
438C23—64no—
439C23—64no—
440C23—62no—
441C23C2×C3×C4×D312yes—
442C23C2×C3×D1212yes—
443C23C2×C3×#6712yes—
444C23C23×C3×D311yescharacteristic
445Q8—68no—
446D4—616no—
447D4—68no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—34no—
452C2×C4—62no—
453C2×C4—62no—
454C2×C4—616no—
455C2×C4—64no—
456C2×C4—68no—
457C2×C4—128no—
458C2×C4C3×(C2×D3)⋊C4116yescomplemented
459C2×C4C2×C3×C4×D312yes—
460C2×C4C2×C3×C4×D312yes—
461C2×C4C2×C3×D1212yes—
462C2×C4C2×C3×D1212yes—
463C2×C4C2×C3×#6712yes—
464C2×C4C2×C3×#6712yes—
465C2×C3—24no—
466C2×C3—24no—
467C2×C3—22no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—22no—
472C2×C3—44no—
473C2×C3—124no—
474C2×C3#552312yes—
475C2×C3#552511yescharacteristic
476C2×C3#552611yescharacteristic
477C2×C3C22×(C2×D3)⋊C411yescharacteristic
478C2×C3#583312yes—
479C2×C3C22×C3×C22⋊C411yescharacteristic
480C2×C3C3×#52012yes—
481C2×C3C3×#53511yescharacteristic
482C2×C3C3×#53611yescharacteristic
483C2×C3C3×#53712yes—
484D3—44no—
485C22—24no—
486C22—22no—
487C22—22no—
488C22—24no—
489C22—68no—
490C22—64no—
491C22—122no—
492C22—122no—
493C22—124no—
494C22C2×C3×(C2×D3)⋊C414yes—
495C22C22×C3×C4×D311yescharacteristic
496C22C22×C3×D1211yescharacteristic
497C22C3×#100912yes—
498C22C3×#101012yes—
499C22C22×C3×#6711yescharacteristic
500C4—44no—
501C4—64no—
502C4—124no—
503C4C2×C3×(C2×D3)⋊C414yes—
504C4C2×C3×(C2×D3)⋊C414yes—
505C3—21no—
506C3#8227011yescharacteristic, direct product factor
507C3C3×#231111yescharacteristic, complemented
508C2—24no—
509C2—124no—
510C2C3×#552312yes—
511C2C3×#552511yescharacteristic
512C2C3×#552611yescharacteristic
513C2C22×C3×(C2×D3)⋊C411yescharacteristic
514C2C3×#583312yes—
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC2×C32×#117C2
socleC23×C32C24
prime radicalC22×C3×#235C2
cosocleC23×C3C24×C3
hypercenterC2×C3×#117D3
hypocenterC3C3×#2311
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#117

Complements

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

NH ≅ G/Ntype
2. C2×C32×#117C2semidirect
3. C22×C3×C4⋊Dic3C2semidirect
4. C3×#4987C2semidirect
5. C3×#4958C2semidirect
6. C3×#4939C2semidirect
7. C3×#4929C2semidirect
9. #82270C3direct (N × H)
15. C2×C3×#235C4semidirect
31. C2×C3×#117D3semidirect
32. C2×C3×#117C2×C3semidirect
34. C22×C4⋊Dic3C2×C3semidirect
39. #4987C2×C3semidirect
40. #4958C2×C3semidirect
41. #4939C2×C3semidirect
42. #4929C2×C3semidirect
61. C2×C3×D12C2×C4semidirect
64. C2×C3×C4×D3C2×C4semidirect
67. C2×C3×Dic6C2×C4semidirect
90. C2×#235C3×C4semidirect
130. C2×C32×C4C22⋊C4semidirect
148. C2×#117C3×D3semidirect
204. C2×D12C2×C3×C4semidirect
207. C2×C4×D3C2×C3×C4semidirect
210. C2×Dic6C2×C3×C4semidirect
318. C2×C3×C4(C2×D3)⋊C4semidirect
319. C2×C3×C4C3×C22⋊C4semidirect
433. C32#2311semidirect
458. C2×C4C3×(C2×D3)⋊C4semidirect
506. C3#82270direct (N × H)
507. C3C3×#2311semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C2×C32×#1172
C22×C3×C4⋊Dic32
C3×#49872
C3×#49582
C3×#49392
C3×#49292
C3×#23113
#822703