Finite Group Databasebeta

← C3×#85804 #11909871

Subgroups — C3×#85804 #11909871

Order 1152.

2133 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×Q8C211yesmaximal, characteristic, complemented
2C3×Q8×#67C212yesmaximal, complemented
3C3×#5584C213yesmaximal, complemented
4C3×#5583C216yesmaximal, complemented
5C3×Q8×D12C211yesmaximal, characteristic, complemented
6C3×#5572C212yesmaximal, complemented
7C3×#5570C211yesmaximal, characteristic, complemented
8C3×#5567C213yesmaximal, complemented
9C3×#5513C216yesmaximal, complemented
10C3×#5479C213yesmaximal
11C3×#5470C213yesmaximal, complemented
12C3×#3523—31nomaximal
13#85804C311yesmaximal, characteristic, direct product factor
14C22×C32×Q8C2211yescharacteristic
15C2×C3×D3×Q8C2212yes—
16C32×C4×Q8C2213yes—
17C32×C4×Q8C2211yescharacteristic
18C32×C4×Q8C2211yescharacteristic
19C32×C4×Q8C2213yes—
20C2×C32×C4⋊C4C2213yes—
21C2×C32×C42C2213yes—
22C3×#946C2216yes—
23C3×Q8×Dic3C2212yes—
24C3×#944C2216yes—
25C3×#930C2211yescharacteristic
26C3×#929C2216yes—
27C3×C4×#67C2216yes—
28C3×#926C2216yes—
29C3×#924C2216yes—
30C3×#924C2213yes—
31C3×#898C22112yes—
32C3×#897C2216yes—
33C3×#892C2216yes—
34C3×#890C2216yes—
35C3×#889C22112yes—
36C3×#887C2216yes—
37C3×#876C2216yes—
38C3×#875C2213yes—
39C3×C4×D12C2213yes—
40C3×#872C2216yes—
41C3×#870C2213yes—
42C3×#870C2216yes—
43C3×#869C2213yes—
44C3×#869C2213yes—
45C3×C4×Dic6C2213yes—
46C3×C4×Dic6C2216yes—
47C3×C4×Dic6C2216yes—
48C3×#557—33no—
49C3×#557—31no—
50C3×#556—33no—
51C3×#552—36no—
52C3×D4×Q8—32no—
53C3×D4×Q8—31no—
54C3×#541—36no—
55C3×#533—33no—
56C3×#529—33no—
57C3×#519—32no—
58C2×C3×C4×Q8—21no—
59C2×C3×C4×Q8D311yescharacteristic, complemented
60C2×C3×C4×Q8C2×C311yescharacteristic, complemented
61Q8×#67C2×C312yescomplemented
62#5584C2×C313yescomplemented
63#5583C2×C316yescomplemented
64Q8×D12C2×C311yescharacteristic, complemented
65#5572C2×C312yescomplemented
66#5570C2×C311yescharacteristic, complemented
67#5567C2×C313yescomplemented
68#5513C2×C316yescomplemented
69#5479C2×C313yes—
70#5470C2×C313yescomplemented
71C2×C32×Q8—24no—
72C2×C32×Q8C2313yes—
73C2×C32×Q8C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C22×C32×C4C2313yes—
76C22×C32×C4C2313yes—
77C2×C3×#67C2312yes—
78C3×D3×Q8—28no—
79C2×C3×D12C2311yescharacteristic
80C2×C3×C4×D3C2316yes—
81C2×C3×Dic6C2316yes—
82C2×C3×Dic6C2313yes—
83C32×C4⋊C4C2313yes—
84C32×C4⋊C4C2316yes—
85C32×C4⋊C4C2313yes—
86C32×C42C2313yes—
87C32×C42C2313yes—
88C32×C42C2313yes—
89C32×C42C2313yes—
90C3×#217C2316yes—
91C3×(C2×D3)⋊C4C2316yes—
92C3×(C2×D3)⋊C4C2316yes—
93C3×(C2×D3)⋊C4C2316yes—
94C3×(C2×D3)⋊C4C2312yes—
95C3×C4⋊Dic3C2316yes—
96C3×C4⋊Dic3C2316yes—
97C3×C4⋊Dic3C2316yes—
98C3×C4⋊Dic3C2313yes—
99C3×C4⋊Dic3C2311yescharacteristic
100C3×Dic3⋊C4C2316yes—
101C3×Dic3⋊C4C2316yes—
102C3×Dic3⋊C4C2316yes—
103C3×Dic3⋊C4C23112yes—
104C3×Dic3⋊C4C2316yes—
105C3×C4×Dic3C23112yes—
106C3×C4×Dic3C2316yes—
107#3523—31noSylow
108C22×C3×Q8—21no—
109C22×C3×Q8—32no—
110C22×C3×Q8C2×D311yescharacteristic
111C22×C3×Q8C22×C311yescharacteristic
112C2×D3×Q8C22×C312yes—
113C3×C4⋊Q8—36no—
114C3×C4⋊Q8—33no—
115C3×C4⋊Q8—33no—
116C3×#126—312no—
117C3×#126—36no—
118C3×#125—312no—
119C3×#125—36no—
120C3×#125—33no—
121C3×#125—36no—
122C3×#124—33no—
123C3×#123—36no—
124C3×C22⋊Q8—36no—
125C3×C22⋊Q8—33no—
126C3×C22⋊Q8—36no—
127C3×C22⋊Q8—36no—
128C3×#121—31no—
129C3×C4×Q8—21no—
130C3×C4×Q8—23no—
131C3×C4×Q8—21no—
132C3×C4×Q8—23no—
133C3×C4×Q8—32no—
134C3×C4×Q8—36no—
135C3×C4×Q8—36no—
136C3×C4×Q8—33no—
137C3×C4×Q8—36no—
138C3×C4×Q8C2×D311yescharacteristic
139C3×C4×Q8C2×D313yes—
140C3×C4×Q8C2×D311yescharacteristic
141C3×C4×Q8C2×D313yes—
142C3×C4×Q8C22×C313yes—
143C3×C4×Q8C22×C311yescharacteristic
144C3×C4×Q8C22×C311yescharacteristic
145C3×C4×Q8C22×C313yes—
146C3×C4×D4—36no—
147C3×C4×D4—33no—
148C3×#117—36no—
149C3×#117—36no—
150C3×#117—36no—
151C2×C3×C4⋊C4—23no—
152C2×C3×C4⋊C4C2×D313yes—
153C2×C3×C4⋊C4C22×C313yes—
154C2×C3×C42—23no—
155C2×C3×C42C2×D313yes—
156C2×C3×C42C22×C313yes—
157#946C22×C316yes—
158Q8×Dic3C22×C312yes—
159#944C22×C316yes—
160#930C22×C311yescharacteristic
161#929C22×C316yes—
162C4×#67C22×C316yes—
163#926C22×C316yes—
164#924C22×C313yes—
165#924C22×C316yes—
166#898C22×C3112yes—
167#897C22×C316yes—
168#892C22×C316yes—
169#890C22×C316yes—
170#889C22×C3112yes—
171#887C22×C316yes—
172#876C22×C316yes—
173#875C22×C313yes—
174C4×D12C22×C313yes—
175#872C22×C316yes—
176#870C22×C316yes—
177#870C22×C313yes—
178#869C22×C313yes—
179#869C22×C313yes—
180C4×Dic6C22×C316yes—
181C4×Dic6C22×C316yes—
182C4×Dic6C22×C313yes—
183C23×C32C2411yescharacteristic
184C22×C3×D3C2412yes—
185C32×Q8—26no—
186C32×Q8#4114yes—
187C2×C32×C4—26no—
188C2×C32×C4—22no—
189C2×C32×C4—26no—
190C2×C32×C4C2413yes—
191C2×C32×C4C2411yescharacteristic
192C2×C32×C4C2413yes—
193C2×C32×C4C2413yes—
194C2×C32×C4C2413yes—
195C2×C32×C4C2411yescharacteristic
196C3×#67—24no—
197C2×C3×Dic3C2412yes—
198C2×C3×Dic3C2416yes—
199C2×C3×Dic3C2416yes—
200C3×D12—22no—
201C3×C4×D3—212no—
202C3×Dic6—212no—
203C3×Dic6—26no—
204#557—33no—
205#557—31no—
206#556—33no—
207#552—36no—
208D4×Q8—32no—
209D4×Q8—31no—
210#541—36no—
211#533—33no—
212#529—33no—
213#519—32no—
214C2×C4×Q8C3×D311yescharacteristic, complemented
215C2×C3×Q8—28no—
216C2×C3×Q8—24no—
217C2×C3×Q8—24no—
218C2×C3×Q8—23no—
219C2×C3×Q8—21no—
220C2×C3×Q8—33no—
221C2×C3×Q8—36no—
222C2×C3×Q8—68no—
223C2×C3×Q8C22×D313yes—
224C2×C3×Q8C22×D311yescharacteristic
225C2×C3×Q8C23×C313yes—
226C2×C3×Q8C23×C311yescharacteristic
227C2×C3×D4—32no—
228C2×C3×D4—31no—
229C22×C3×C4—21no—
230C22×C3×C4—23no—
231C22×C3×C4—23no—
232C22×C3×C4—36no—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D313yes—
235C22×C3×C4C22×D313yes—
236C22×C3×C4C23×C311yescharacteristic
237C22×C3×C4C23×C313yes—
238C22×C3×C4C23×C313yes—
239C2×#67C23×C312yes—
240D3×Q8—28no—
241C2×D12C23×C311yescharacteristic
242C2×C4×D3C23×C316yes—
243C2×Dic6C23×C313yes—
244C2×Dic6C23×C316yes—
245C3×C4⋊C4—23no—
246C3×C4⋊C4—23no—
247C3×C4⋊C4—26no—
248C3×C4⋊C4—36no—
249C3×C4⋊C4—36no—
250C3×C4⋊C4—36no—
251C3×C4⋊C4—312no—
252C3×C4⋊C4—36no—
253C3×C4⋊C4—36no—
254C3×C4⋊C4—36no—
255C3×C4⋊C4—36no—
256C3×C4⋊C4—33no—
257C3×C4⋊C4—31no—
258C3×C4⋊C4C22×D313yes—
259C3×C4⋊C4C22×D313yes—
260C3×C4⋊C4C22×D316yes—
261C3×C4⋊C4C23×C313yes—
262C3×C4⋊C4C23×C316yes—
263C3×C4⋊C4C23×C313yes—
264C3×C22⋊C4—36no—
265C3×C22⋊C4—32no—
266C3×C22⋊C4—36no—
267C3×C22⋊C4—36no—
268C3×C22⋊C4—36no—
269C3×C42—23no—
270C3×C42—23no—
271C3×C42—23no—
272C3×C42—23no—
273C3×C42—312no—
274C3×C42—36no—
275C3×C42C22×D313yes—
276C3×C42C22×D313yes—
277C3×C42C22×D313yes—
278C3×C42C22×D313yes—
279C3×C42C23×C313yes—
280C3×C42C23×C313yes—
281C3×C42C23×C313yes—
282C3×C42C23×C313yes—
283#217C23×C316yes—
284(C2×D3)⋊C4C23×C312yes—
285(C2×D3)⋊C4C23×C316yes—
286(C2×D3)⋊C4C23×C316yes—
287(C2×D3)⋊C4C23×C316yes—
288C4⋊Dic3C23×C311yescharacteristic
289C4⋊Dic3C23×C313yes—
290C4⋊Dic3C23×C316yes—
291C4⋊Dic3C23×C316yes—
292C4⋊Dic3C23×C316yes—
293Dic3⋊C4C23×C316yes—
294Dic3⋊C4C23×C3112yes—
295Dic3⋊C4C23×C316yes—
296Dic3⋊C4C23×C316yes—
297Dic3⋊C4C23×C316yes—
298C4×Dic3C23×C3112yes—
299C4×Dic3C23×C316yes—
300C22×C32—21no—
301C22×C32—21no—
302C22×C322−1+412yes—
303C22×C32C2511yescharacteristic
304C2×C3×D3—22no—
305C2×C3×D3—22no—
306C2×C3×D3—22no—
307C32×C4—23no—
308C32×C4—21no—
309C32×C4—23no—
310C32×C4—23no—
311C32×C4C2×#4116yes—
312C32×C42−1+412yes—
313C3×Dic3—26no—
314C3×Dic3—26no—
315C3×Dic3—22no—
316C22×Q8—32no—
317C22×Q8C2×C3×D311yescharacteristic
318C4⋊Q8—36no—
319C4⋊Q8—33no—
320C4⋊Q8—33no—
321#126—312no—
322#126—36no—
323#125—312no—
324#125—36no—
325#125—33no—
326#125—36no—
327#124—33no—
328#123—36no—
329C22⋊Q8—36no—
330C22⋊Q8—33no—
331C22⋊Q8—36no—
332C22⋊Q8—36no—
333#121—31no—
334C4×Q8—32no—
335C4×Q8—36no—
336C4×Q8—36no—
337C4×Q8—33no—
338C4×Q8—36no—
339C4×Q8C2×C3×D311yescharacteristic
340C4×Q8C2×C3×D313yes—
341C4×Q8C2×C3×D311yescharacteristic
342C4×Q8C2×C3×D313yes—
343C4×D4—36no—
344C4×D4—33no—
345#117—36no—
346#117—36no—
347#117—36no—
348C2×C4⋊C4C2×C3×D313yes—
349C2×C42C2×C3×D313yes—
350C23×C3—21no—
351C23×C3—32no—
352C23×C3C23×D311yescharacteristic
353C23×C3C24×C311yescharacteristic
354C22×D3C24×C312yes—
355C3×Q8—212no—
356C3×Q8—26no—
357C3×Q8—26no—
358C3×Q8—24no—
359C3×Q8—612no—
360C3×Q8—66no—
361C3×Q8#23514yes—
362C3×Q8C3×#4114yes—
363C3×D4—64no—
364C3×D4—62no—
365C2×C3×C4—24no—
366C2×C3×C4—212no—
367C2×C3×C4—26no—
368C2×C3×C4—26no—
369C2×C3×C4—26no—
370C2×C3×C4—22no—
371C2×C3×C4—26no—
372C2×C3×C4—22no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—23no—
376C2×C3×C4—23no—
377C2×C3×C4—23no—
378C2×C3×C4—23no—
379C2×C3×C4—36no—
380C2×C3×C4—32no—
381C2×C3×C4—36no—
382C2×C3×C4—46no—
383C2×C3×C4—612no—
384C2×C3×C4C23×D313yes—
385C2×C3×C4C23×D311yescharacteristic
386C2×C3×C4C23×D313yes—
387C2×C3×C4C23×D313yes—
388C2×C3×C4C23×D313yes—
389C2×C3×C4C23×D311yescharacteristic
390C2×C3×C4C24×C313yes—
391C2×C3×C4C24×C311yescharacteristic
392C2×C3×C4C24×C313yes—
393C2×C3×C4C24×C313yes—
394C2×C3×C4C24×C313yes—
395C2×C3×C4C24×C311yescharacteristic
396#67—24no—
397C2×Dic3C24×C312yes—
398C2×Dic3C24×C316yes—
399C2×Dic3C24×C316yes—
400D12—22no—
401C4×D3—212no—
402Dic6—212no—
403Dic6—26no—
404C2×C32—22no—
405C2×C32C22×#4111yescharacteristic
406C2×C32C2×2−1+411yescharacteristic
407C2×C32C2×2−1+411yescharacteristic
408C3×D3—42no—
409C2×Q8—24no—
410C2×Q8—33no—
411C2×Q8—36no—
412C2×Q8—68no—
413C2×Q8C22×C3×D313yes—
414C2×Q8C22×C3×D311yescharacteristic
415C2×D4—32no—
416C2×D4—31no—
417C22×C4—36no—
418C22×C4C22×C3×D311yescharacteristic
419C22×C4C22×C3×D313yes—
420C22×C4C22×C3×D313yes—
421C4⋊C4—36no—
422C4⋊C4—36no—
423C4⋊C4—36no—
424C4⋊C4—36no—
425C4⋊C4—36no—
426C4⋊C4—33no—
427C4⋊C4—36no—
428C4⋊C4—31no—
429C4⋊C4—312no—
430C4⋊C4—36no—
431C4⋊C4C22×C3×D313yes—
432C4⋊C4C22×C3×D313yes—
433C4⋊C4C22×C3×D316yes—
434C22⋊C4—36no—
435C22⋊C4—32no—
436C22⋊C4—36no—
437C22⋊C4—36no—
438C22⋊C4—36no—
439C42—312no—
440C42—36no—
441C42C22×C3×D313yes—
442C42C22×C3×D313yes—
443C42C22×C3×D313yes—
444C42C22×C3×D313yes—
445C22×C3—22no—
446C22×C3—22no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—22no—
452C22×C3—21no—
453C22×C3—62no—
454C22×C3—62no—
455C22×C3—62no—
456C22×C3#101012yes—
457C22×C3C3×2−1+412yes—
458C22×C3C24×D311yescharacteristic
459C22×C3C25×C311yescharacteristic
460C2×D3—22no—
461C2×D3—22no—
462C2×D3—22no—
463C3×C4—26no—
464C3×C4—22no—
465C3×C4—23no—
466C3×C4—21no—
467C3×C4—23no—
468C3×C4—23no—
469C3×C4—23no—
470C3×C4—21no—
471C3×C4—23no—
472C3×C4—23no—
473C3×C4—26no—
474C3×C4—22no—
475C3×C4—43no—
476C3×C4—43no—
477C3×C4—66no—
478C3×C4—66no—
479C3×C4—62no—
480C3×C4C2×#23516yes—
481C3×C4#100712yes—
482C3×C4C2×C3×#4116yes—
483C3×C4C3×2−1+412yes—
484Dic3—26no—
485Dic3—26no—
486Dic3—22no—
487C32#352311yescharacteristic, complemented, Sylow
488C23—32no—
489C23C23×C3×D311yescharacteristic
490Q8—26no—
491Q8—612no—
492Q8—66no—
493Q8C3×#23514yes—
494D4—64no—
495D4—62no—
496C2×C4—26no—
497C2×C4—26no—
498C2×C4—22no—
499C2×C4—36no—
500C2×C4—32no—
501C2×C4—36no—
502C2×C4—612no—
503C2×C4C23×C3×D313yes—
504C2×C4C23×C3×D311yescharacteristic
505C2×C4C23×C3×D313yes—
506C2×C4C23×C3×D313yes—
507C2×C4C23×C3×D313yes—
508C2×C4C23×C3×D311yescharacteristic
509C2×C3—24no—
510C2×C3—22no—
511C2×C3—22no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—122no—
516C2×C3C22×#23511yescharacteristic
517C2×C3C2×#100711yescharacteristic
518C2×C3C2×#101011yescharacteristic
519C2×C3C22×C3×#4111yescharacteristic
520C2×C3C2×C3×2−1+411yescharacteristic
521C2×C3C2×C3×2−1+411yescharacteristic
522D3—42no—
523C22—21no—
524C22—21no—
525C22—62no—
526C22—62no—
527C22—62no—
528C22C3×#101012yes—
529C22C24×C3×D311yescharacteristic
530C4—23no—
531C4—21no—
532C4—23no—
533C4—23no—
534C4—66no—
535C4—66no—
536C4—62no—
537C4C2×C3×#23516yes—
538C4C3×#100712yes—
539C3—21no—
540C3#8580411yescharacteristic, direct product factor
541C3C3×#352311yescharacteristic, complemented
542C2—22no—
543C2—122no—
544C2C22×C3×#23511yescharacteristic
545C2C2×C3×#100711yescharacteristic
546C2C2×C3×#101011yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×C4×Q8C2
socleC22×C32C25
prime radicalC3×#930C22
hypercenterC2×C3×C4×Q8D3
hypocenterC3C3×#3523
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×Q8C2semidirect
2. C3×Q8×#67C2semidirect
3. C3×#5584C2semidirect
4. C3×#5583C2semidirect
5. C3×Q8×D12C2semidirect
6. C3×#5572C2semidirect
7. C3×#5570C2semidirect
8. C3×#5567C2semidirect
9. C3×#5513C2semidirect
11. C3×#5470C2semidirect
13. #85804C3direct (N × H)
59. C2×C3×C4×Q8D3semidirect
60. C2×C3×C4×Q8C2×C3semidirect
61. Q8×#67C2×C3semidirect
62. #5584C2×C3semidirect
63. #5583C2×C3semidirect
64. Q8×D12C2×C3semidirect
65. #5572C2×C3semidirect
66. #5570C2×C3semidirect
67. #5567C2×C3semidirect
68. #5513C2×C3semidirect
70. #5470C2×C3semidirect
214. C2×C4×Q8C3×D3semidirect
487. C32#3523semidirect
540. C3#85804direct (N × H)
541. C3C3×#3523semidirect

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×Q8×#672
C3×#55842
C3×#55832
C3×Q8×D122
C3×#55722
C3×#55702
C3×#55672
C3×#55132
C3×#54792
C3×#54702
C3×#35233
#858043