Finite Group Databasebeta

← C3×#41×Dic6 #11903743

Subgroups — C3×#41×Dic6 #11903743

Order 1152.

2291 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×#41C211yesmaximal, characteristic
2C3×Dic3×#41C212yesmaximal
3C3×#5570C211yesmaximal, characteristic, complemented
4C3×#5569C212yesmaximal, complemented
5C3×Q8×Dic6C211yesmaximal, characteristic, complemented
6C3×#5543C213yesmaximal, complemented
7C3×#5539C216yesmaximal, complemented
8C3×D4×Dic6C213yesmaximal, complemented
9C3×#5517C216yesmaximal, complemented
10C3×#5470C213yesmaximal, complemented
11C2×C3×C4×Dic6C213yesmaximal, complemented
12C3×Q8×#41—31nomaximal
13#41×Dic6C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C22×C3×Dic6C2213yes—
16C32×C4×Q8C2211yescharacteristic
17C32×C4×Q8C2211yescharacteristic
18C32×C4×D4C2213yes—
19C32×C4×D4C2213yes—
20C32×#117C2213yes—
21C2×C32×C42C2213yes—
22C3×Q8×Dic3C2212yes—
23C3×Q8×Dic3C2212yes—
24C3×D4×Dic3C2216yes—
25C3×D4×Dic3C2216yes—
26C3×#926C2216yes—
27C2×C3×C4⋊Dic3C2213yes—
28C3×#924C2216yes—
29C3×#924C2216yes—
30C2×C3×Dic3⋊C4C2216yes—
31C2×C3×C4×Dic3C2216yes—
32C3×#890C2216yes—
33C3×#890C2216yes—
34C3×#888C2216yes—
35C3×#888C2216yes—
36C3×#878C22112yes—
37C3×#878C22112yes—
38C3×#870C2216yes—
39C3×#869C2213yes—
40C3×#869C2213yes—
41C3×C4×Dic6C2216yes—
42C3×C4×Dic6C2216yes—
43C3×C4×Dic6C2213yes—
44C3×C4×Dic6C2216yes—
45C3×C4×Dic6C2213yes—
46C3×C4×Dic6C2211yescharacteristic
47C3×C4×Dic6C2213yes—
48C3×Q82—31no—
49C3×#557—32no—
50C3×#557—31no—
51C3×#554—36no—
52C3×#554—33no—
53C3×D4×Q8—33no—
54C3×#533—36no—
55C3×#533—33no—
56C3×C4×#41—21no—
57C3×C4×#41—32no—
58C3×C4×#41D311yescharacteristic
59C3×C4×#41C2×C311yescharacteristic
60C2×C3×C4×Q8—33no—
61Dic3×#41C2×C312yes—
62#5570C2×C311yescharacteristic, complemented
63#5569C2×C312yescomplemented
64Q8×Dic6C2×C311yescharacteristic, complemented
65#5543C2×C313yescomplemented
66#5539C2×C316yescomplemented
67D4×Dic6C2×C313yescomplemented
68#5517C2×C316yescomplemented
69#5470C2×C313yescomplemented
70C2×C4×Dic6C2×C313yescomplemented
71C32×#41Q818yescomplemented
72C2×C32×Q8C2311yescharacteristic
73C2×C32×D4C2313yes—
74C22×C32×C4C2313yes—
75C22×C32×C4C2313yes—
76C22×C32×C4C2313yes—
77C22×C3×Dic3C2316yes—
78C22×C3×Dic3C2316yes—
79C2×C3×Dic6—212no—
80C2×C3×Dic6C2316yes—
81C2×C3×Dic6C2313yes—
82C2×C3×Dic6C2316yes—
83C2×C3×Dic6C2311yescharacteristic
84C32×C4⋊C4C2313yes—
85C32×C4⋊C4C2313yes—
86C32×C22⋊C4C2316yes—
87C32×C42C2311yescharacteristic
88C32×C42C2313yes—
89C32×C42C2313yes—
90C32×C42C2313yes—
91C3×#217C23112yes—
92C3×C4⋊Dic3C2316yes—
93C3×C4⋊Dic3C2316yes—
94C3×C4⋊Dic3C2316yes—
95C3×C4⋊Dic3C2316yes—
96C3×C4⋊Dic3C2313yes—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×Dic3⋊C4C2316yes—
99C3×Dic3⋊C4C23112yes—
100C3×Dic3⋊C4C2316yes—
101C3×Dic3⋊C4C2312yes—
102C3×Dic3⋊C4C2316yes—
103C3×C4×Dic3C2316yes—
104C3×C4×Dic3C2316yes—
105C3×C4×Dic3C2312yes—
106C3×C4×Dic3C2316yes—
107Q8×#41—31noSylow
108C2×C3×#41—21no—
109C2×C3×#41C2×D311yescharacteristic
110C2×C3×#41C22×C311yescharacteristic
111C22×C3×Q8—33no—
112C22×Dic6C22×C313yes—
113C3×C4⋊Q8—36no—
114C3×C4⋊Q8—36no—
115C3×C4⋊Q8—33no—
116C3×C4⋊Q8—33no—
117C3×#125—36no—
118C3×#125—36no—
119C3×#125—36no—
120C3×C22⋊Q8—36no—
121C3×C22⋊Q8—36no—
122C3×C22⋊Q8—312no—
123C3×C22⋊Q8—312no—
124C3×C4×Q8—21no—
125C3×C4×Q8—21no—
126C3×C4×Q8—32no—
127C3×C4×Q8—32no—
128C3×C4×Q8—33no—
129C3×C4×Q8—31no—
130C3×C4×Q8—36no—
131C3×C4×Q8—33no—
132C3×C4×Q8—33no—
133C3×C4×Q8—36no—
134C3×C4×Q8—36no—
135C3×C4×Q8C2×D311yescharacteristic
136C3×C4×Q8C2×D311yescharacteristic
137C3×C4×Q8C22×C311yescharacteristic
138C3×C4×Q8C22×C311yescharacteristic
139C3×C4×D4—23no—
140C3×C4×D4—23no—
141C3×C4×D4—36no—
142C3×C4×D4—36no—
143C3×C4×D4C2×D313yes—
144C3×C4×D4C2×D313yes—
145C3×C4×D4C22×C313yes—
146C3×C4×D4C22×C313yes—
147C3×#117—23no—
148C3×#117—36no—
149C3×#117C2×D313yes—
150C3×#117C22×C313yes—
151C2×C3×C4⋊C4—36no—
152C2×C3×C4⋊C4—33no—
153C2×C3×C42—23no—
154C2×C3×C42—36no—
155C2×C3×C42C2×D313yes—
156C2×C3×C42C22×C313yes—
157Q8×Dic3C22×C312yes—
158Q8×Dic3C22×C312yes—
159D4×Dic3C22×C316yes—
160D4×Dic3C22×C316yes—
161#926C22×C316yes—
162C2×C4⋊Dic3C22×C313yes—
163#924C22×C316yes—
164#924C22×C316yes—
165C2×Dic3⋊C4C22×C316yes—
166C2×C4×Dic3C22×C316yes—
167#890C22×C316yes—
168#890C22×C316yes—
169#888C22×C316yes—
170#888C22×C316yes—
171#878C22×C3112yes—
172#878C22×C3112yes—
173#870C22×C316yes—
174#869C22×C313yes—
175#869C22×C313yes—
176C4×Dic6C22×C311yescharacteristic
177C4×Dic6C22×C313yes—
178C4×Dic6C22×C316yes—
179C4×Dic6C22×C313yes—
180C4×Dic6C22×C316yes—
181C4×Dic6C22×C313yes—
182C4×Dic6C22×C316yes—
183C23×C32C2413yes—
184C32×Q8C2×Q814yescomplemented
185C32×D4C2×Q8112yescomplemented
186C2×C32×C4—26no—
187C2×C32×C4—43no—
188C2×C32×C4C2×Q8112yescomplemented
189C2×C32×C4C2411yescharacteristic
190C2×C32×C4C2413yes—
191C2×C32×C4C2413yes—
192C2×C32×C4C2413yes—
193C2×C32×C4C2411yescharacteristic
194C2×C32×C4C2411yescharacteristic
195C2×C3×Dic3—212no—
196C2×C3×Dic3—46no—
197C2×C3×Dic3C2412yes—
198C2×C3×Dic3C2416yes—
199C2×C3×Dic3C2416yes—
200C2×C3×Dic3C2412yes—
201C3×Dic6—26no—
202C3×Dic6—212no—
203C3×Dic6—46no—
204C3×Dic6#4114yesdirect product factor
205Q82—31no—
206#557—32no—
207#557—31no—
208#554—36no—
209#554—33no—
210D4×Q8—33no—
211#533—36no—
212#533—33no—
213C4×#41—32no—
214C4×#41C3×D311yescharacteristic
215C2×C4×Q8—33no—
216C3×#41—28no—
217C3×#41Dic618yesdirect product factor
218C3×#41C3×Q818yescomplemented
219C2×C3×Q8—21no—
220C2×C3×Q8—31no—
221C2×C3×Q8—36no—
222C2×C3×Q8—33no—
223C2×C3×Q8—36no—
224C2×C3×Q8—612no—
225C2×C3×Q8C22×D311yescharacteristic
226C2×C3×Q8C23×C311yescharacteristic
227C2×C3×D4—23no—
228C2×C3×D4C22×D313yes—
229C2×C3×D4C23×C313yes—
230C22×C3×C4—23no—
231C22×C3×C4—23no—
232C22×C3×C4—23no—
233C22×C3×C4—36no—
234C22×C3×C4—36no—
235C22×C3×C4C22×D313yes—
236C22×C3×C4C22×D313yes—
237C22×C3×C4C22×D313yes—
238C22×C3×C4C23×C313yes—
239C22×C3×C4C23×C313yes—
240C22×C3×C4C23×C313yes—
241C22×Dic3C23×C316yes—
242C22×Dic3C23×C316yes—
243C2×Dic6—212no—
244C2×Dic6C23×C313yes—
245C2×Dic6C23×C316yes—
246C2×Dic6C23×C316yes—
247C2×Dic6C23×C311yescharacteristic
248C3×C4⋊C4—23no—
249C3×C4⋊C4—23no—
250C3×C4⋊C4—32no—
251C3×C4⋊C4—36no—
252C3×C4⋊C4—36no—
253C3×C4⋊C4—36no—
254C3×C4⋊C4—312no—
255C3×C4⋊C4—31no—
256C3×C4⋊C4—36no—
257C3×C4⋊C4—33no—
258C3×C4⋊C4—36no—
259C3×C4⋊C4—36no—
260C3×C4⋊C4—36no—
261C3×C4⋊C4C22×D313yes—
262C3×C4⋊C4C22×D313yes—
263C3×C4⋊C4C23×C313yes—
264C3×C4⋊C4C23×C313yes—
265C3×C22⋊C4—26no—
266C3×C22⋊C4—312no—
267C3×C22⋊C4C22×D316yes—
268C3×C22⋊C4C23×C316yes—
269C3×C42—21no—
270C3×C42—23no—
271C3×C42—23no—
272C3×C42—23no—
273C3×C42—36no—
274C3×C42—36no—
275C3×C42—32no—
276C3×C42—36no—
277C3×C42C22×D313yes—
278C3×C42C22×D313yes—
279C3×C42C22×D311yescharacteristic
280C3×C42C22×D313yes—
281C3×C42C23×C311yescharacteristic
282C3×C42C23×C313yes—
283C3×C42C23×C313yes—
284C3×C42C23×C313yes—
285#217C23×C3112yes—
286C4⋊Dic3C23×C311yescharacteristic
287C4⋊Dic3C23×C313yes—
288C4⋊Dic3C23×C316yes—
289C4⋊Dic3C23×C316yes—
290C4⋊Dic3C23×C316yes—
291C4⋊Dic3C23×C316yes—
292Dic3⋊C4C23×C312yes—
293Dic3⋊C4C23×C316yes—
294Dic3⋊C4C23×C316yes—
295Dic3⋊C4C23×C316yes—
296Dic3⋊C4C23×C3112yes—
297C4×Dic3C23×C312yes—
298C4×Dic3C23×C316yes—
299C4×Dic3C23×C316yes—
300C4×Dic3C23×C316yes—
301C22×C32—23no—
302C22×C32—23no—
303C22×C32C22×Q816yes—
304C22×C32C2511yescharacteristic
305C32×C4—21no—
306C32×C4—23no—
307C32×C4—23no—
308C32×C4C22×Q812yes—
309C32×C4C22×Q816yes—
310C32×C4C2×#4112yes—
311C3×Dic3—26no—
312C3×Dic3—26no—
313C3×Dic3—22no—
314C3×Dic3C2×#4114yes—
315C2×#41C2×C3×D311yescharacteristic
316C22×Q8—33no—
317C4⋊Q8—36no—
318C4⋊Q8—36no—
319C4⋊Q8—33no—
320C4⋊Q8—33no—
321#125—36no—
322#125—36no—
323#125—36no—
324C22⋊Q8—36no—
325C22⋊Q8—36no—
326C22⋊Q8—312no—
327C22⋊Q8—312no—
328C4×Q8—32no—
329C4×Q8—32no—
330C4×Q8—31no—
331C4×Q8—36no—
332C4×Q8—33no—
333C4×Q8—33no—
334C4×Q8—33no—
335C4×Q8—36no—
336C4×Q8—36no—
337C4×Q8C2×C3×D311yescharacteristic
338C4×Q8C2×C3×D311yescharacteristic
339C4×D4—36no—
340C4×D4—36no—
341C4×D4C2×C3×D313yes—
342C4×D4C2×C3×D313yes—
343#117—36no—
344#117C2×C3×D313yes—
345C2×C4⋊C4—36no—
346C2×C4⋊C4—33no—
347C2×C42—36no—
348C2×C42C2×C3×D313yes—
349C23×C3—23no—
350C23×C3C23×D313yes—
351C23×C3C24×C313yes—
352C3×Q8—24no—
353C3×Q8—34no—
354C3×Q8—612no—
355C3×Q8—66no—
356C3×Q8—126no—
357C3×Q8C2×Dic614yescomplemented
358C3×Q8C2×C3×Q814yescomplemented
359C3×D4—212no—
360C3×D4C2×Dic6112yescomplemented
361C3×D4C2×C3×Q8112yescomplemented
362C2×C3×C4—26no—
363C2×C3×C4—26no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—23no—
368C2×C3×C4—23no—
369C2×C3×C4—23no—
370C2×C3×C4—212no—
371C2×C3×C4—32no—
372C2×C3×C4—32no—
373C2×C3×C4—36no—
374C2×C3×C4—36no—
375C2×C3×C4—46no—
376C2×C3×C4—43no—
377C2×C3×C4—43no—
378C2×C3×C4—46no—
379C2×C3×C4—612no—
380C2×C3×C4—126no—
381C2×C3×C4C2×Dic6112yescomplemented
382C2×C3×C4C2×C3×Q8112yescomplemented
383C2×C3×C4C23×D311yescharacteristic
384C2×C3×C4C23×D313yes—
385C2×C3×C4C23×D313yes—
386C2×C3×C4C23×D313yes—
387C2×C3×C4C23×D311yescharacteristic
388C2×C3×C4C23×D311yescharacteristic
389C2×C3×C4C24×C311yescharacteristic
390C2×C3×C4C24×C313yes—
391C2×C3×C4C24×C313yes—
392C2×C3×C4C24×C311yescharacteristic
393C2×C3×C4C24×C313yes—
394C2×C3×C4C24×C311yescharacteristic
395C2×Dic3—212no—
396C2×Dic3—46no—
397C2×Dic3C24×C312yes—
398C2×Dic3C24×C316yes—
399C2×Dic3C24×C316yes—
400C2×Dic3C24×C312yes—
401Dic6—26no—
402Dic6—212no—
403Dic6—46no—
404Dic6C3×#4114yesdirect product factor
405C2×C32—26no—
406C2×C32C23×Q811yescharacteristic
407C2×C32C22×#4111yescharacteristic
408C2×C32#58511yescharacteristic
409#41C3×Dic618yesdirect product factor
410C2×Q8—31no—
411C2×Q8—36no—
412C2×Q8—33no—
413C2×Q8—36no—
414C2×Q8—612no—
415C2×Q8C22×C3×D311yescharacteristic
416C2×D4C22×C3×D313yes—
417C22×C4—36no—
418C22×C4—36no—
419C22×C4C22×C3×D313yes—
420C22×C4C22×C3×D313yes—
421C22×C4C22×C3×D313yes—
422C4⋊C4—32no—
423C4⋊C4—31no—
424C4⋊C4—36no—
425C4⋊C4—36no—
426C4⋊C4—36no—
427C4⋊C4—36no—
428C4⋊C4—33no—
429C4⋊C4—36no—
430C4⋊C4—36no—
431C4⋊C4—312no—
432C4⋊C4—36no—
433C4⋊C4C22×C3×D313yes—
434C4⋊C4C22×C3×D313yes—
435C22⋊C4—312no—
436C22⋊C4C22×C3×D316yes—
437C42—32no—
438C42—36no—
439C42—36no—
440C42—36no—
441C42C22×C3×D311yescharacteristic
442C42C22×C3×D313yes—
443C42C22×C3×D313yes—
444C42C22×C3×D313yes—
445C22×C3—23no—
446C22×C3—23no—
447C22×C3—23no—
448C22×C3—23no—
449C22×C3—26no—
450C22×C3—21no—
451C22×C3—43no—
452C22×C3—43no—
453C22×C3C22×Dic616yes—
454C22×C3C22×C3×Q816yes—
455C22×C3C24×D311yescharacteristic
456C22×C3C25×C311yescharacteristic
457C3×C4—22no—
458C3×C4—23no—
459C3×C4—21no—
460C3×C4—23no—
461C3×C4—23no—
462C3×C4—23no—
463C3×C4—21no—
464C3×C4—22no—
465C3×C4—26no—
466C3×C4—22no—
467C3×C4—34no—
468C3×C4—43no—
469C3×C4—43no—
470C3×C4—66no—
471C3×C4—62no—
472C3×C4—66no—
473C3×C4C22×Dic612yes—
474C3×C4C22×Dic616yes—
475C3×C4D3×#4112yes—
476C3×C4C22×C3×Q812yes—
477C3×C4C22×C3×Q816yes—
478C3×C4C2×C3×#4112yes—
479Dic3—26no—
480Dic3—26no—
481Dic3—22no—
482Dic3C2×C3×#4114yes—
483C32Q8×#4111yescharacteristic, complemented, Sylow
484C23C23×C3×D313yes—
485Q8—34no—
486Q8—612no—
487Q8—66no—
488Q8—126no—
489Q8C2×C3×Dic614yescomplemented
490D4C2×C3×Dic6112yescomplemented
491C2×C4—26no—
492C2×C4—32no—
493C2×C4—32no—
494C2×C4—36no—
495C2×C4—36no—
496C2×C4—43no—
497C2×C4—612no—
498C2×C4—126no—
499C2×C4C2×C3×Dic6112yescomplemented
500C2×C4C23×C3×D311yescharacteristic
501C2×C4C23×C3×D313yes—
502C2×C4C23×C3×D313yes—
503C2×C4C23×C3×D311yescharacteristic
504C2×C4C23×C3×D313yes—
505C2×C4C23×C3×D311yescharacteristic
506C2×C3—26no—
507C2×C3—26no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—46no—
512C2×C3C23×Dic611yescharacteristic
513C2×C3C2×D3×#4111yescharacteristic
514C2×C3#596411yescharacteristic
515C2×C3C23×C3×Q811yescharacteristic
516C2×C3C22×C3×#4111yescharacteristic
517C2×C3C3×#58511yescharacteristic
518C22—23no—
519C22—23no—
520C22C22×C3×Dic616yes—
521C22C24×C3×D311yescharacteristic
522C4—23no—
523C4—21no—
524C4—23no—
525C4—34no—
526C4—66no—
527C4—62no—
528C4—66no—
529C4C22×C3×Dic612yes—
530C4C22×C3×Dic616yes—
531C4C3×D3×#4112yes—
532C3—21no—
533C3#41×Dic611yescharacteristic, direct product factor
534C3C3×Q8×#4111yescharacteristic, complemented
535C2—26no—
536C2C23×C3×Dic611yescharacteristic
537C2C2×C3×D3×#4111yescharacteristic
538C2C3×#596411yescharacteristic
subgroupG/H
centerC2×C3×C4C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×C4×#41C2
socleC22×C32C25
prime radicalC2×C32×#41C22
hypercenterC3×C4×#41D3
hypocenterC3C3×Q8×#41
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×#41

Complements

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

NH ≅ G/Ntype
3. C3×#5570C2semidirect
4. C3×#5569C2semidirect
5. C3×Q8×Dic6C2semidirect
6. C3×#5543C2semidirect
7. C3×#5539C2semidirect
8. C3×D4×Dic6C2semidirect
9. C3×#5517C2semidirect
10. C3×#5470C2semidirect
11. C2×C3×C4×Dic6C2semidirect
13. #41×Dic6C3direct (N × H)
62. #5570C2×C3semidirect
63. #5569C2×C3semidirect
64. Q8×Dic6C2×C3semidirect
65. #5543C2×C3semidirect
66. #5539C2×C3semidirect
67. D4×Dic6C2×C3semidirect
68. #5517C2×C3semidirect
69. #5470C2×C3semidirect
70. C2×C4×Dic6C2×C3semidirect
71. C32×#41Q8semidirect
184. C32×Q8C2×Q8semidirect
185. C32×D4C2×Q8semidirect
188. C2×C32×C4C2×Q8semidirect
204. C3×Dic6#41direct (N × H)
217. C3×#41Dic6direct (N × H)
218. C3×#41C3×Q8semidirect
357. C3×Q8C2×Dic6semidirect
358. C3×Q8C2×C3×Q8semidirect
360. C3×D4C2×Dic6semidirect
361. C3×D4C2×C3×Q8semidirect
381. C2×C3×C4C2×Dic6semidirect
382. C2×C3×C4C2×C3×Q8semidirect
404. Dic6C3×#41direct (N × H)
409. #41C3×Dic6direct (N × H)
483. C32Q8×#41semidirect
489. Q8C2×C3×Dic6semidirect
490. D4C2×C3×Dic6semidirect
499. C2×C4C2×C3×Dic6semidirect
533. C3#41×Dic6direct (N × H)
534. C3C3×Q8×#41semidirect

Maximal subgroups

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

subgroupindex
C32×C4×#412
C3×Dic3×#412
C3×#55702
C3×#55692
C3×Q8×Dic62
C3×#55432
C3×#55392
C3×D4×Dic62
C3×#55172
C3×#54702
C2×C3×C4×Dic62
C3×Q8×#413
#41×Dic63