Finite Group Databasebeta

← C3×#68302 #11775102

Subgroups — C3×#68302 #11775102

Order 1152.

713 conjugacy classes of subgroups.

The subgroup lattice has 567 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5606C211yesmaximal, characteristic
2C3×#4726C211yesmaximal, characteristic, complemented
3C3×D3×#95C211yesmaximal, characteristic, complemented
4C32×#327C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic, complemented
6C3×#4467C211yesmaximal, characteristic, complemented
7C3×#4452C211yesmaximal, characteristic, complemented
8C3×#1504—31nomaximal
9#68302C311yesmaximal, characteristic, direct product factor
10C2×C3×#237C411yescharacteristic, complemented
11C22×C3×C4×D3—21no—
12C22×C3×C4×D3C2211yescharacteristic
13C32×#121C2211yescharacteristic
14C3×#938C411yescharacteristic, complemented
15C3×#937—21no—
16C3×D4×Dic3—21no—
17C3×#924C2211yescharacteristic
18C2×C3×ΓL(1,𝔽25)—21no—
19C3×#897C411yescharacteristic, complemented
20C3×#892C411yescharacteristic, complemented
21C3×#883—21no—
22C3×#67⋊C4—21no—
23C32×C22⋊C8C2211yescharacteristic
24C32×#95C2211yescharacteristic
25C3×C3⋊#95—21no—
26C3×C3⋊#95C2211yescharacteristic
27C3×#830C2211yescharacteristic
28C3×(C2×D3)⋊C8—21no—
29C3×#525—31no—
30#5606C2×C311yescharacteristic
31C3×#407—31no—
32C2×C3×#95—31no—
33#4726C2×C311yescharacteristic, complemented
34D3×#95C2×C311yescharacteristic, complemented
35C3×#328—31no—
36C3×#328—31no—
37C3×#327—21no—
38C3×#327—31no—
39C3×#327D311yescharacteristic, complemented
40C3×#327C2×C311yescharacteristic, complemented
41#4537C2×C311yescharacteristic, complemented
42#4467C2×C311yescharacteristic, complemented
43#4452C2×C311yescharacteristic, complemented
44C23×C3×D3D411yescharacteristic
45C2×C32×D4—21no—
46C2×C32×D4C2×C411yescharacteristic, complemented
47C22×C32×C4—21no—
48C22×C32×C4C2311yescharacteristic
49C2×C3×#67—21no—
50C2×C3×#67—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C3×#237—42no—
55C2×C3×C4×D3—24no—
56C2×C3×C4×D3—42no—
57C2×C3×C4×D3—42no—
58C2×C3×C4×D3—42no—
59C2×C3×C4×D3C2×C411yescharacteristic
60C2×C3×C4×D3C2×C411yescharacteristic
61C2×C3×C4×D3D411yescharacteristic
62C2×C3×C4×D3D411yescharacteristic
63C2×C3×Dic6C2×C411yescharacteristic, complemented
64C2×C32×C8—21no—
65C32×C4⋊C4C2×C411yescharacteristic, complemented
66C32×C22⋊C4—21no—
67C3×#217—21no—
68C3×#217—21no—
69C3×(C2×D3)⋊C4—21no—
70C3×(C2×D3)⋊C4—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3C2×C411yescharacteristic, complemented
73C3×Dic3⋊C4—21no—
74C3×C4×Dic3—21no—
75C2×C3×C3⋊C8—21no—
76C3×ΓL(1,𝔽25)—42no—
77#1504—31noSylow
78C2×C3×#41—31no—
79C23×C3×C4—31no—
80C23×C3×C4—61no—
81C2×#237C3×C411yescharacteristic, complemented
82C22×C4×D3—21no—
83C22×C4×D3C22×C311yescharacteristic
84C2×C3×M16—61no—
85C3×#123—61no—
86C3×C22⋊Q8—31no—
87C3×C22⋊Q8—31no—
88C3×#121—21no—
89C3×#121—31no—
90C3×#121C2×D311yescharacteristic
91C3×#121C22×C311yescharacteristic
92C3×#120—61no—
93C3×C4×D4—61no—
94C3×C4×D4—61no—
95C3×#117—31no—
96#938C3×C411yescharacteristic, complemented
97#937—21no—
98D4×Dic3—21no—
99#924C22×C311yescharacteristic
100C2×ΓL(1,𝔽25)—21no—
101#897C3×C411yescharacteristic, complemented
102#892C3×C411yescharacteristic, complemented
103#883—21no—
104#67⋊C4—21no—
105C3×C22⋊C8—21no—
106C3×C22⋊C8—31no—
107C3×C22⋊C8—61no—
108C3×C22⋊C8C2×D311yescharacteristic
109C3×C22⋊C8C22×C311yescharacteristic
110C3×#95—21no—
111C3×#95—31no—
112C3×#95—61no—
113C3×#95C2×D311yescharacteristic
114C3×#95C22×C311yescharacteristic
115C3⋊#95—21no—
116C3⋊#95C22×C311yescharacteristic
117#830C22×C311yescharacteristic
118(C2×D3)⋊C8—21no—
119C23×C32—21no—
120C23×C32C2×D411yescharacteristic
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—22no—
124C22×C3×D3—22no—
125C22×C3×D3C22⋊C411yescharacteristic
126C22×C3×D3C22⋊C411yescharacteristic
127C32×D4—41no—
128C32×D4—41no—
129C32×D4—41no—
130C2×C32×C4—22no—
131C2×C32×C4—21no—
132C2×C32×C4—41no—
133C2×C32×C4—41no—
134C2×C32×C4—41no—
135C2×C32×C4C22×C411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C3×#67—42no—
138C3×#67—42no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—42no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3C22⋊C411yescharacteristic
147C2×C3×Dic3C22⋊C411yescharacteristic
148C3×C4×D3—22no—
149C3×C4×D3—22no—
150C3×C4×D3—41no—
151C3×C4×D3—41no—
152C3×C4×D3—48no—
153C3×Dic6—41no—
154C32×C8—41no—
155C3×C3⋊C8—41no—
156#525—31no—
157#407—31no—
158C2×#95—31no—
159#328—31no—
160#328—31no—
161#327—31no—
162#327C3×D311yescharacteristic, complemented
163C24×C3—31no—
164C23×D3C3×D411yescharacteristic
165C3×#41—122no—
166C2×C3×Q8—31no—
167C2×C3×D4—21no—
168C2×C3×D4—21no—
169C2×C3×D4—21no—
170C2×C3×D4—41no—
171C2×C3×D4—61no—
172C2×C3×D4—61no—
173C2×C3×D4C4×D311yescharacteristic, complemented
174C2×C3×D4C2×C3×C411yescharacteristic, complemented
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—31no—
179C22×C3×C4—31no—
180C22×C3×C4—31no—
181C22×C3×C4—31no—
182C22×C3×C4—31no—
183C22×C3×C4—41no—
184C22×C3×C4—64no—
185C22×C3×C4—61no—
186C22×C3×C4—61no—
187C22×C3×C4—122no—
188C22×C3×C4—122no—
189C22×C3×C4—122no—
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C23×C311yescharacteristic
192C2×#67—21no—
193C2×#67—21no—
194C22×Dic3—21no—
195C22×Dic3—21no—
196C22×Dic3C3×D411yescharacteristic
197#237—42no—
198C2×C4×D3—24no—
199C2×C4×D3—42no—
200C2×C4×D3—42no—
201C2×C4×D3—42no—
202C2×C4×D3C2×C3×C411yescharacteristic
203C2×C4×D3C2×C3×C411yescharacteristic
204C2×C4×D3C3×D411yescharacteristic
205C2×C4×D3C3×D411yescharacteristic
206C2×Dic6C2×C3×C411yescharacteristic, complemented
207C3×M16—122no—
208C2×C3×C8—21no—
209C2×C3×C8—21no—
210C2×C3×C8—41no—
211C2×C3×C8—61no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—31no—
214C3×C4⋊C4—61no—
215C3×C4⋊C4—61no—
216C3×C4⋊C4C4×D311yescharacteristic, complemented
217C3×C4⋊C4C2×C3×C411yescharacteristic, complemented
218C3×C22⋊C4—21no—
219C3×C22⋊C4—21no—
220C3×C22⋊C4—41no—
221C3×C22⋊C4—61no—
222C3×C22⋊C4—61no—
223C3×C22⋊C4—61no—
224C3×C22⋊C4—61no—
225C3×C42—61no—
226#217—21no—
227#217—21no—
228(C2×D3)⋊C4—21no—
229(C2×D3)⋊C4—21no—
230C4⋊Dic3—21no—
231C4⋊Dic3C2×C3×C411yescharacteristic, complemented
232Dic3⋊C4—21no—
233C4×Dic3—21no—
234C2×C3⋊C8—21no—
235ΓL(1,𝔽25)—42no—
236C22×C32—21no—
237C22×C32—21no—
238C22×C32—41no—
239C22×C32—41no—
240C22×C32—41no—
241C22×C32C2×C22⋊C411yescharacteristic
242C22×C32AGL(1,ℤ/8)11yescharacteristic
243C22×C32#13711yescharacteristic
244C2×C3×D3—24no—
245C2×C3×D3—24no—
246C2×C3×D3—21no—
247C2×C3×D3—21no—
248C2×C3×D3—21no—
249C2×C3×D3—21no—
250C2×C3×D3#9912yes—
251C2×C3×D3#10412yes—
252C32×C4—21no—
253C32×C4—21no—
254C32×C4—42no—
255C32×C4—41no—
256C3×Dic3—21no—
257C3×Dic3—21no—
258C3×Dic3—42no—
259C3×Dic3—41no—
260C3×Dic3—41no—
261C2×#41—31no—
262C23×C4—31no—
263C23×C4—61no—
264C2×M16—61no—
265#123—61no—
266C22⋊Q8—31no—
267C22⋊Q8—31no—
268#121—31no—
269#121C2×C3×D311yescharacteristic
270#120—61no—
271C4×D4—61no—
272C4×D4—61no—
273#117—31no—
274C22⋊C8—31no—
275C22⋊C8—61no—
276C22⋊C8C2×C3×D311yescharacteristic
277#95—31no—
278#95—61no—
279#95C2×C3×D311yescharacteristic
280C23×C3—21no—
281C23×C3—21no—
282C23×C3—21no—
283C23×C3—31no—
284C23×C3—31no—
285C23×C3—41no—
286C23×C3—62no—
287C23×C3—62no—
288C23×C3—61no—
289C23×C3—61no—
290C23×C3D3×D411yescharacteristic
291C23×C3C2×C3×D411yescharacteristic
292C22×D3—21no—
293C22×D3—21no—
294C22×D3—22no—
295C22×D3—22no—
296C22×D3C3×C22⋊C411yescharacteristic
297C22×D3C3×C22⋊C411yescharacteristic
298C3×Q8—121no—
299C3×D4—41no—
300C3×D4—41no—
301C3×D4—41no—
302C3×D4—41no—
303C3×D4—41no—
304C3×D4—41no—
305C3×D4—81no—
306C3×D4—81no—
307C3×D4—81no—
308C3×D4—122no—
309C3×D4—122no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—31no—
317C2×C3×C4—31no—
318C2×C3×C4—41no—
319C2×C3×C4—42no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4—61no—
330C2×C3×C4—61no—
331C2×C3×C4—81no—
332C2×C3×C4—81no—
333C2×C3×C4—81no—
334C2×C3×C4—121no—
335C2×C3×C4—121no—
336C2×C3×C4—128no—
337C2×C3×C4—121no—
338C2×C3×C4—122no—
339C2×C3×C4—121no—
340C2×C3×C4—121no—
341C2×C3×C4C2×C4×D311yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4C22×C3×C411yescharacteristic
344C2×C3×C4C2×C3×D411yescharacteristic
345#67—42no—
346#67—42no—
347C2×Dic3—22no—
348C2×Dic3—21no—
349C2×Dic3—21no—
350C2×Dic3—41no—
351C2×Dic3—42no—
352C2×Dic3—41no—
353C2×Dic3—41no—
354C2×Dic3C3×C22⋊C411yescharacteristic
355C2×Dic3C3×C22⋊C411yescharacteristic
356C4×D3—22no—
357C4×D3—22no—
358C4×D3—41no—
359C4×D3—41no—
360C4×D3—48no—
361Dic6—41no—
362C3×C8—41no—
363C3×C8—41no—
364C3×C8—81no—
365C3×C8—121no—
366C3⋊C8—41no—
367C2×C32—21no—
368C2×C32—21no—
369C2×C32—81no—
370C2×C32C2×#9911yescharacteristic
371C2×C32#41711yescharacteristic
372C2×C32C2×#10411yescharacteristic
373C3×D3—22no—
374C3×D3—22no—
375C24—31no—
376#41—122no—
377C2×Q8—31no—
378C2×D4—21no—
379C2×D4—61no—
380C2×D4—61no—
381C2×D4C3×C4×D311yescharacteristic, complemented
382C22×C4—21no—
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—31no—
386C22×C4—31no—
387C22×C4—31no—
388C22×C4—64no—
389C22×C4—61no—
390C22×C4—61no—
391C22×C4—122no—
392C22×C4—122no—
393C22×C4—122no—
394C22×C4C22×C3×D311yescharacteristic
395M16—122no—
396C2×C8—21no—
397C2×C8—61no—
398C4⋊C4—31no—
399C4⋊C4—61no—
400C4⋊C4—61no—
401C4⋊C4C3×C4×D311yescharacteristic, complemented
402C22⋊C4—21no—
403C22⋊C4—61no—
404C22⋊C4—61no—
405C22⋊C4—61no—
406C22⋊C4—61no—
407C42—61no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—32no—
416C22×C3—32no—
417C22×C3—41no—
418C22×C3—41no—
419C22×C3—41no—
420C22×C3—41no—
421C22×C3—41no—
422C22×C3—41no—
423C22×C3—41no—
424C22×C3—41no—
425C22×C3—64no—
426C22×C3—64no—
427C22×C3—61no—
428C22×C3—61no—
429C22×C3—61no—
430C22×C3—61no—
431C22×C3—81no—
432C22×C3—81no—
433C22×C3—81no—
434C22×C3D3×C22⋊C411yescharacteristic
435C22×C3#91111yescharacteristic
436C22×C3#91511yescharacteristic
437C22×C3C2×C3×C22⋊C411yescharacteristic
438C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
439C22×C3C3×#13711yescharacteristic
440C2×D3—24no—
441C2×D3—24no—
442C2×D3—21no—
443C2×D3—21no—
444C2×D3—21no—
445C2×D3—21no—
446C2×D3C3×#9912yes—
447C2×D3C3×#10412yes—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—41no—
453C3×C4—41no—
454C3×C4—42no—
455C3×C4—42no—
456C3×C4—41no—
457C3×C4—41no—
458C3×C4—61no—
459C3×C4—61no—
460C3×C4—81no—
461C3×C4—82no—
462C3×C4—122no—
463C3×C4—121no—
464C3×C4—121no—
465Dic3—21no—
466Dic3—21no—
467Dic3—42no—
468Dic3—41no—
469Dic3—41no—
470C32#150411yescharacteristic, complemented, Sylow
471C23—21no—
472C23—31no—
473C23—31no—
474C23—62no—
475C23—62no—
476C23—61no—
477C23—61no—
478C23C3×D3×D411yescharacteristic
479Q8—121no—
480D4—41no—
481D4—41no—
482D4—41no—
483D4—122no—
484D4—122no—
485C2×C4—22no—
486C2×C4—21no—
487C2×C4—31no—
488C2×C4—31no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—62no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—121no—
498C2×C4—121no—
499C2×C4—128no—
500C2×C4—121no—
501C2×C4—122no—
502C2×C4—121no—
503C2×C4—121no—
504C2×C4C2×C3×C4×D311yescharacteristic
505C2×C4C3×D3×D411yescharacteristic
506C8—41no—
507C8—121no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—41no—
516C2×C3—41no—
517C2×C3—62no—
518C2×C3—62no—
519C2×C3—81no—
520C2×C3—81no—
521C2×C3—161no—
522C2×C3D3×#9911yescharacteristic
523C2×C3#477111yescharacteristic
524C2×C3D3×#10411yescharacteristic
525C2×C3C2×C3×#9911yescharacteristic
526C2×C3C3×#41711yescharacteristic
527C2×C3C2×C3×#10411yescharacteristic
528D3—22no—
529D3—22no—
530C22—21no—
531C22—21no—
532C22—32no—
533C22—32no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—64no—
538C22—64no—
539C22—61no—
540C22—61no—
541C22—61no—
542C22—61no—
543C22C3×D3×C22⋊C411yescharacteristic
544C22C3×#91111yescharacteristic
545C22C3×#91511yescharacteristic
546C4—21no—
547C4—21no—
548C4—42no—
549C4—41no—
550C4—61no—
551C4—61no—
552C4—122no—
553C4—121no—
554C4—121no—
555C3—21no—
556C3#6830211yescharacteristic, direct product factor
557C3C3×#150411yescharacteristic, complemented
558C2—21no—
559C2—21no—
560C2—62no—
561C2—62no—
562C2—81no—
563C2C3×D3×#9911yescharacteristic
564C2C3×#477111yescharacteristic
565C2C3×D3×#10411yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#327C2
socleC22×C32C2×C22⋊C4
prime radicalC3×#5606C2
cosocleC22×C3×C4C23×C3
hypercenterC3×#327D3
hypocenterC3C3×#1504
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#327

Complements

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

NH ≅ G/Ntype
2. C3×#4726C2semidirect
3. C3×D3×#95C2semidirect
4. C32×#327C2semidirect
5. C3×#4537C2semidirect
6. C3×#4467C2semidirect
7. C3×#4452C2semidirect
9. #68302C3direct (N × H)
10. C2×C3×#237C4semidirect
14. C3×#938C4semidirect
19. C3×#897C4semidirect
20. C3×#892C4semidirect
33. #4726C2×C3semidirect
34. D3×#95C2×C3semidirect
39. C3×#327D3semidirect
40. C3×#327C2×C3semidirect
41. #4537C2×C3semidirect
42. #4467C2×C3semidirect
43. #4452C2×C3semidirect
46. C2×C32×D4C2×C4semidirect
63. C2×C3×Dic6C2×C4semidirect
65. C32×C4⋊C4C2×C4semidirect
72. C3×C4⋊Dic3C2×C4semidirect
81. C2×#237C3×C4semidirect
96. #938C3×C4semidirect
101. #897C3×C4semidirect
102. #892C3×C4semidirect
162. #327C3×D3semidirect
173. C2×C3×D4C4×D3semidirect
174. C2×C3×D4C2×C3×C4semidirect
206. C2×Dic6C2×C3×C4semidirect
216. C3×C4⋊C4C4×D3semidirect
217. C3×C4⋊C4C2×C3×C4semidirect
231. C4⋊Dic3C2×C3×C4semidirect
381. C2×D4C3×C4×D3semidirect
401. C4⋊C4C3×C4×D3semidirect
470. C32#1504semidirect
556. C3#68302direct (N × H)
557. C3C3×#1504semidirect

Maximal subgroups

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

subgroupindex
C3×#56062
C3×#47262
C3×D3×#952
C32×#3272
C3×#45372
C3×#44672
C3×#44522
C3×#15043
#683023