Finite Group Databasebeta

← C3×#68335 #11775222

Subgroups — C3×#68335 #11775222

Order 1152.

628 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×C22⋊Q8C211yesmaximal, characteristic
2C3×#4726C211yesmaximal, characteristic
3C3×#4666C211yesmaximal, characteristic
4C32×#328C211yesmaximal, characteristic, complemented
5C3×#4538C211yesmaximal, characteristic, complemented
6C3×#4467C211yesmaximal, characteristic, complemented
7C3×#4452C211yesmaximal, characteristic, complemented
8C3×#1508—31nomaximal
9#68335C311yesmaximal, characteristic, direct product factor
10C2×C3×D3×Q8C411yescharacteristic, complemented
11C22×C3×C4×D3C2211yescharacteristic
12C32×C22⋊Q8C2211yescharacteristic
13C3×#946C411yescharacteristic, complemented
14C2×C3×(C2×D3)⋊C4—21no—
15C3×#924C2211yescharacteristic
16C2×C3×C4×Dic3—21no—
17C2×C3×ΓL(1,𝔽25)—21no—
18C3×#897C411yescharacteristic, complemented
19C3×#896—21no—
20C3×D3×C4⋊C4—21no—
21C3×D3×C4⋊C4C411yescharacteristic, complemented
22C3×D3×C22⋊C4—21no—
23C3×#878—21no—
24C32×C22⋊C8C2211yescharacteristic
25C32×#95C2211yescharacteristic
26C3×C3⋊#95C2211yescharacteristic
27C3×#830C2211yescharacteristic
28C3×(C2×D3)⋊C8—21no—
29C2×C3×C22⋊Q8—31no—
30D3×C22⋊Q8C2×C311yescharacteristic
31C3×#407—31no—
32C3×C4×C22⋊C4—31no—
33#4726C2×C311yescharacteristic
34#4666C2×C311yescharacteristic
35C3×#328—21no—
36C3×#328—31no—
37C3×#328—31no—
38C3×#328—31no—
39C3×#328D311yescharacteristic, complemented
40C3×#328C2×C311yescharacteristic, complemented
41#4538C2×C311yescharacteristic, complemented
42#4467C2×C311yescharacteristic, complemented
43#4452C2×C311yescharacteristic, complemented
44C23×C3×D3D411yescharacteristic
45C2×C32×Q8C2×C411yescharacteristic
46C22×C32×C4—21no—
47C22×C32×C4C2311yescharacteristic
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C3×D3×Q8—42no—
51C2×C3×C4×D3—21no—
52C2×C3×C4×D3—21no—
53C2×C3×C4×D3—42no—
54C2×C3×C4×D3C2×C411yescharacteristic
55C2×C3×C4×D3C2×C411yescharacteristic
56C2×C3×C4×D3D411yescharacteristic
57C2×C3×C4×D3D411yescharacteristic
58C2×C3×Dic6—21no—
59C2×C3×Dic6C2×C411yescharacteristic
60C2×C32×C8—21no—
61C32×C4⋊C4—21no—
62C32×C4⋊C4C2×C411yescharacteristic
63C32×C22⋊C4—21no—
64C3×#217—21no—
65C3×(C2×D3)⋊C4—24no—
66C3×(C2×D3)⋊C4—21no—
67C3×(C2×D3)⋊C4—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3C2×C411yescharacteristic
70C3×Dic3⋊C4—21no—
71C3×Dic3⋊C4—21no—
72C3×Dic3⋊C4—21no—
73C3×C4×Dic3—42no—
74C2×C3×C3⋊C8—21no—
75C3×ΓL(1,𝔽25)—42no—
76#1508—31noSylow
77C22×C3×Q8—31no—
78C23×C3×C4—31no—
79C2×D3×Q8C3×C411yescharacteristic, complemented
80C22×C4×D3C22×C311yescharacteristic
81C2×C3×M16—61no—
82C3×C22⋊Q8—21no—
83C3×C22⋊Q8—31no—
84C3×C22⋊Q8—31no—
85C3×C22⋊Q8—31no—
86C3×C22⋊Q8—61no—
87C3×C22⋊Q8—61no—
88C3×C22⋊Q8C2×D311yescharacteristic
89C3×C22⋊Q8C22×C311yescharacteristic
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4—61no—
92C2×C3×C22⋊C4—61no—
93C2×C3×C22⋊C4—61no—
94C2×C3×C42—61no—
95#946C3×C411yescharacteristic, complemented
96C2×(C2×D3)⋊C4—21no—
97#924C22×C311yescharacteristic
98C2×C4×Dic3—21no—
99C2×ΓL(1,𝔽25)—21no—
100#897C3×C411yescharacteristic, complemented
101#896—21no—
102D3×C4⋊C4—21no—
103D3×C4⋊C4C3×C411yescharacteristic, complemented
104D3×C22⋊C4—21no—
105#878—21no—
106C3×C22⋊C8—21no—
107C3×C22⋊C8—31no—
108C3×C22⋊C8—61no—
109C3×C22⋊C8C2×D311yescharacteristic
110C3×C22⋊C8C22×C311yescharacteristic
111C3×#95—21no—
112C3×#95—31no—
113C3×#95C2×D311yescharacteristic
114C3×#95C22×C311yescharacteristic
115C3⋊#95C22×C311yescharacteristic
116#830C22×C311yescharacteristic
117(C2×D3)⋊C8—21no—
118C23×C32C2×D411yescharacteristic
119C22×C3×D3—21no—
120C22×C3×D3—21no—
121C22×C3×D3—22no—
122C22×C3×D3—41no—
123C22×C3×D3C22⋊C411yescharacteristic
124C22×C3×D3C22⋊C411yescharacteristic
125C32×Q8—41no—
126C2×C32×C4—22no—
127C2×C32×C4—21no—
128C2×C32×C4—21no—
129C2×C32×C4—41no—
130C2×C32×C4—41no—
131C2×C32×C4—41no—
132C2×C32×C4C22×C411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C3×Dic3—22no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3C22⋊C411yescharacteristic
141C2×C3×Dic3C22⋊C411yescharacteristic
142C3×C4×D3—22no—
143C3×C4×D3—22no—
144C3×C4×D3—41no—
145C3×C4×D3—41no—
146C3×C4×D3—42no—
147C3×C4×D3—42no—
148C3×Dic6—42no—
149C3×Dic6—41no—
150C32×C8—41no—
151C3×C3⋊C8—41no—
152C2×C22⋊Q8—31no—
153#407—31no—
154C4×C22⋊C4—31no—
155#328—31no—
156#328—31no—
157#328—31no—
158#328C3×D311yescharacteristic, complemented
159C24×C3—31no—
160C23×D3C3×D411yescharacteristic
161C2×C3×Q8—21no—
162C2×C3×Q8—31no—
163C2×C3×Q8—61no—
164C2×C3×Q8—122no—
165C2×C3×Q8C4×D311yescharacteristic
166C2×C3×Q8C2×C3×C411yescharacteristic
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—31no—
171C22×C3×C4—31no—
172C22×C3×C4—31no—
173C22×C3×C4—31no—
174C22×C3×C4—31no—
175C22×C3×C4—41no—
176C22×C3×C4—61no—
177C22×C3×C4—61no—
178C22×C3×C4—61no—
179C22×C3×C4—122no—
180C22×C3×C4C22×D311yescharacteristic
181C22×C3×C4C23×C311yescharacteristic
182C22×Dic3—21no—
183C22×Dic3C3×D411yescharacteristic
184D3×Q8—42no—
185C2×C4×D3—21no—
186C2×C4×D3—21no—
187C2×C4×D3—42no—
188C2×C4×D3C2×C3×C411yescharacteristic
189C2×C4×D3C2×C3×C411yescharacteristic
190C2×C4×D3C3×D411yescharacteristic
191C2×C4×D3C3×D411yescharacteristic
192C2×Dic6—21no—
193C2×Dic6C2×C3×C411yescharacteristic
194C3×M16—122no—
195C2×C3×C8—21no—
196C2×C3×C8—21no—
197C2×C3×C8—41no—
198C2×C3×C8—61no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—31no—
203C3×C4⋊C4—41no—
204C3×C4⋊C4—61no—
205C3×C4⋊C4—61no—
206C3×C4⋊C4—61no—
207C3×C4⋊C4—61no—
208C3×C4⋊C4C4×D311yescharacteristic
209C3×C4⋊C4C2×C3×C411yescharacteristic
210C3×C22⋊C4—21no—
211C3×C22⋊C4—21no—
212C3×C22⋊C4—41no—
213C3×C22⋊C4—61no—
214C3×C22⋊C4—61no—
215C3×C22⋊C4—64no—
216C3×C22⋊C4—61no—
217C3×C42—122no—
218#217—21no—
219(C2×D3)⋊C4—24no—
220(C2×D3)⋊C4—21no—
221(C2×D3)⋊C4—21no—
222C4⋊Dic3—21no—
223C4⋊Dic3C2×C3×C411yescharacteristic
224Dic3⋊C4—21no—
225Dic3⋊C4—21no—
226Dic3⋊C4—21no—
227C4×Dic3—42no—
228C2×C3⋊C8—21no—
229ΓL(1,𝔽25)—42no—
230C22×C32—21no—
231C22×C32—21no—
232C22×C32C2×C22⋊C411yescharacteristic
233C22×C32#13711yescharacteristic
234C22×C32#13711yescharacteristic
235C2×C3×D3—21no—
236C2×C3×D3—21no—
237C2×C3×D3—21no—
238C2×C3×D3—21no—
239C2×C3×D3—21no—
240C2×C3×D3—42no—
241C2×C3×D3—42no—
242C2×C3×D3#10412yes—
243C32×C4—21no—
244C32×C4—21no—
245C32×C4—42no—
246C32×C4—41no—
247C32×C4—41no—
248C3×Dic3—21no—
249C3×Dic3—42no—
250C3×Dic3—41no—
251C3×Dic3—41no—
252C3×Dic3#9912yes—
253C22×Q8—31no—
254C23×C4—31no—
255C2×M16—61no—
256C22⋊Q8—31no—
257C22⋊Q8—31no—
258C22⋊Q8—31no—
259C22⋊Q8—61no—
260C22⋊Q8—61no—
261C22⋊Q8C2×C3×D311yescharacteristic
262C2×C4⋊C4—31no—
263C2×C4⋊C4—61no—
264C2×C22⋊C4—61no—
265C2×C22⋊C4—61no—
266C2×C42—61no—
267C22⋊C8—31no—
268C22⋊C8—61no—
269C22⋊C8C2×C3×D311yescharacteristic
270#95—31no—
271#95C2×C3×D311yescharacteristic
272C23×C3—21no—
273C23×C3—31no—
274C23×C3—31no—
275C23×C3—62no—
276C23×C3—61no—
277C23×C3—61no—
278C23×C3—121no—
279C23×C3D3×D411yescharacteristic
280C23×C3C2×C3×D411yescharacteristic
281C22×D3—21no—
282C22×D3—21no—
283C22×D3—22no—
284C22×D3—41no—
285C22×D3C3×C22⋊C411yescharacteristic
286C22×D3C3×C22⋊C411yescharacteristic
287C3×Q8—41no—
288C3×Q8—41no—
289C3×Q8—81no—
290C3×Q8—121no—
291C3×Q8—122no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—31no—
301C2×C3×C4—31no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—42no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—41no—
310C2×C3×C4—41no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—61no—
316C2×C3×C4—61no—
317C2×C3×C4—81no—
318C2×C3×C4—81no—
319C2×C3×C4—81no—
320C2×C3×C4—121no—
321C2×C3×C4—121no—
322C2×C3×C4—122no—
323C2×C3×C4—122no—
324C2×C3×C4—121no—
325C2×C3×C4—121no—
326C2×C3×C4C2×C4×D311yescharacteristic
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4C22×C3×C411yescharacteristic
329C2×C3×C4C2×C3×D411yescharacteristic
330C2×Dic3—22no—
331C2×Dic3—22no—
332C2×Dic3—21no—
333C2×Dic3—21no—
334C2×Dic3—41no—
335C2×Dic3—41no—
336C2×Dic3C3×C22⋊C411yescharacteristic
337C2×Dic3C3×C22⋊C411yescharacteristic
338C4×D3—22no—
339C4×D3—22no—
340C4×D3—41no—
341C4×D3—41no—
342C4×D3—42no—
343C4×D3—42no—
344Dic6—42no—
345Dic6—41no—
346C3×C8—41no—
347C3×C8—41no—
348C3×C8—81no—
349C3×C8—121no—
350C3⋊C8—41no—
351C2×C32—21no—
352C2×C32—21no—
353C2×C32C2×#9911yescharacteristic
354C2×C32#41911yescharacteristic
355C2×C32C2×#10411yescharacteristic
356C3×D3—22no—
357C3×D3—41no—
358C24—31no—
359C2×Q8—31no—
360C2×Q8—61no—
361C2×Q8—122no—
362C2×Q8C3×C4×D311yescharacteristic
363C22×C4—21no—
364C22×C4—31no—
365C22×C4—31no—
366C22×C4—31no—
367C22×C4—31no—
368C22×C4—31no—
369C22×C4—61no—
370C22×C4—61no—
371C22×C4—61no—
372C22×C4—122no—
373C22×C4C22×C3×D311yescharacteristic
374M16—122no—
375C2×C8—21no—
376C2×C8—61no—
377C4⋊C4—21no—
378C4⋊C4—31no—
379C4⋊C4—61no—
380C4⋊C4—61no—
381C4⋊C4—61no—
382C4⋊C4—61no—
383C4⋊C4C3×C4×D311yescharacteristic
384C22⋊C4—21no—
385C22⋊C4—61no—
386C22⋊C4—61no—
387C22⋊C4—64no—
388C22⋊C4—61no—
389C42—122no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—32no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—61no—
401C22×C3—61no—
402C22×C3—61no—
403C22×C3—61no—
404C22×C3—61no—
405C22×C3—122no—
406C22×C3—122no—
407C22×C3D3×C22⋊C411yescharacteristic
408C22×C3#91511yescharacteristic
409C22×C3#91811yescharacteristic
410C22×C3C2×C3×C22⋊C411yescharacteristic
411C22×C3C3×#13711yescharacteristic
412C22×C3C3×#13711yescharacteristic
413C2×D3—21no—
414C2×D3—21no—
415C2×D3—21no—
416C2×D3—21no—
417C2×D3—21no—
418C2×D3—42no—
419C2×D3—42no—
420C2×D3C3×#10412yes—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—32no—
426C3×C4—41no—
427C3×C4—41no—
428C3×C4—42no—
429C3×C4—42no—
430C3×C4—41no—
431C3×C4—41no—
432C3×C4—41no—
433C3×C4—41no—
434C3×C4—61no—
435C3×C4—81no—
436C3×C4—81no—
437C3×C4—82no—
438C3×C4—122no—
439C3×C4—121no—
440C3×C4—121no—
441Dic3—21no—
442Dic3—42no—
443Dic3—41no—
444Dic3—41no—
445Dic3C3×#9912yes—
446C32#150811yescharacteristic, complemented, Sylow
447C23—31no—
448C23—31no—
449C23—62no—
450C23—61no—
451C23—61no—
452C23—121no—
453C23C3×D3×D411yescharacteristic
454Q8—41no—
455Q8—121no—
456Q8—122no—
457C2×C4—22no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—31no—
461C2×C4—31no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—121no—
472C2×C4—121no—
473C2×C4—122no—
474C2×C4—122no—
475C2×C4—121no—
476C2×C4—121no—
477C2×C4C2×C3×C4×D311yescharacteristic
478C2×C4C3×D3×D411yescharacteristic
479C8—41no—
480C8—121no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—41no—
489C2×C3—41no—
490C2×C3—62no—
491C2×C3—121no—
492C2×C3D3×#9911yescharacteristic
493C2×C3#480211yescharacteristic
494C2×C3D3×#10411yescharacteristic
495C2×C3C2×C3×#9911yescharacteristic
496C2×C3C3×#41911yescharacteristic
497C2×C3C2×C3×#10411yescharacteristic
498D3—22no—
499D3—41no—
500C22—21no—
501C22—21no—
502C22—32no—
503C22—61no—
504C22—61no—
505C22—61no—
506C22—61no—
507C22—61no—
508C22—122no—
509C22—122no—
510C22C3×D3×C22⋊C411yescharacteristic
511C22C3×#91511yescharacteristic
512C22C3×#91811yescharacteristic
513C4—21no—
514C4—21no—
515C4—32no—
516C4—42no—
517C4—41no—
518C4—41no—
519C4—61no—
520C4—122no—
521C4—121no—
522C4—121no—
523C3—21no—
524C3#6833511yescharacteristic, direct product factor
525C3C3×#150811yescharacteristic, complemented
526C2—21no—
527C2—21no—
528C2—62no—
529C2—121no—
530C2C3×D3×#9911yescharacteristic
531C2C3×#480211yescharacteristic
532C2C3×D3×#10411yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#328C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C3×D3D4
cosocleC22×C3×C4C23×C3
hypercenterC3×#328D3
hypocenterC3C3×#1508
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#328

Complements

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

NH ≅ G/Ntype
4. C32×#328C2semidirect
5. C3×#4538C2semidirect
6. C3×#4467C2semidirect
7. C3×#4452C2semidirect
9. #68335C3direct (N × H)
10. C2×C3×D3×Q8C4semidirect
13. C3×#946C4semidirect
18. C3×#897C4semidirect
21. C3×D3×C4⋊C4C4semidirect
39. C3×#328D3semidirect
40. C3×#328C2×C3semidirect
41. #4538C2×C3semidirect
42. #4467C2×C3semidirect
43. #4452C2×C3semidirect
79. C2×D3×Q8C3×C4semidirect
95. #946C3×C4semidirect
100. #897C3×C4semidirect
103. D3×C4⋊C4C3×C4semidirect
158. #328C3×D3semidirect
446. C32#1508semidirect
524. C3#68335direct (N × H)
525. C3C3×#1508semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C22⋊Q82
C3×#47262
C3×#46662
C32×#3282
C3×#45382
C3×#44672
C3×#44522
C3×#15083
#683353