Finite Group Databasebeta

← C3×#68768 #11792197

Subgroups — C3×#68768 #11792197

Order 1152.

779 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#909C211yesmaximal, characteristic
2C3×#5526C211yesmaximal, characteristic
3C2×C3×#869C211yesmaximal, characteristic, complemented
4C2×C3×#824C211yesmaximal, characteristic, complemented
5C3×#5004C211yesmaximal, characteristic, complemented
6C2×C3×#805C211yesmaximal, characteristic
7C32×#339C211yesmaximal, characteristic, complemented
8C3×#2005—31nomaximal
9#68768C311yesmaximal, characteristic, direct product factor
10C2×C3×#235C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C32×#117C2211yescharacteristic
15C2×C32×C42C2211yescharacteristic
16C2×C3×C4⋊Dic3—22no—
17C2×C3×#208C2211yescharacteristic
18C3×#909—22no—
19C3×#909—22no—
20C2×C3×Dic12—21no—
21C2×C3×#204—21no—
22C3×#897—22no—
23C3×#886—22no—
24C3×#875—21no—
25C3×#869—21no—
26C3×#869—22no—
27C3×#869—22no—
28C3×#824—22no—
29C3×#810—22no—
30C3×#805—22no—
31C2×C3×#137—31no—
32C3×#536—31no—
33C2×C3×C4⋊Q8—31no—
34C2×#909C2×C311yescharacteristic
35#5526C2×C311yescharacteristic
36C2×#869C2×C311yescharacteristic, complemented
37C2×C3×#104—31no—
38C3×#419—31no—
39C2×C3×#101—31no—
40C2×#824C2×C311yescharacteristic, complemented
41#5004C2×C311yescharacteristic, complemented
42C2×#805C2×C311yescharacteristic
43C3×#339—21no—
44C3×#339D311yescharacteristic, complemented
45C3×#339C2×C311yescharacteristic, complemented
46C22×C32×C4—21no—
47C22×C32×C4C2311yescharacteristic
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D412yes—
51C3×#235—21no—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235—21no—
55C2×C3×D12D411yescharacteristic
56C2×C3×C4×D3—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6D411yescharacteristic
69C2×C3×Dic6D412yes—
70C32×M16—21no—
71C32×M16D412yes—
72C2×C32×C8—21no—
73C32×C4⋊C4D412yes—
74C32×C22⋊C4—21no—
75C32×C42—21no—
76C32×C42—21no—
77C32×C42D412yes—
78C3×(C2×D3)⋊C4—24no—
79C3×C4⋊Dic3—24no—
80C3×C4⋊Dic3—28no—
81C3×#208—21no—
82C3×#208—21no—
83C2×C3×C3⋊C8—21no—
84C3×Dic12—24no—
85C3×#204—24no—
86#2005—31noSylow
87C2×C3×#41—31no—
88C22×C3×Q8—31no—
89C22×C3×Q8—31no—
90C2×#235C22×C311yescharacteristic
91C22×Dic6C22×C311yescharacteristic
92C22×Dic6C22×C311yescharacteristic
93C3×#137—62no—
94C3×#137—62no—
95C2×C3×Q16—61no—
96C2×C3×SD16—61no—
97C2×C3×M16—21no—
98C2×C3×M16—31no—
99C2×C3×M16C2×D311yescharacteristic
100C2×C3×M16C22×C311yescharacteristic
101C3×C4⋊Q8—62no—
102C3×C4⋊Q8—61no—
103C3×C4⋊Q8—62no—
104C3×#124—61no—
105C3×#123—62no—
106C3×C22⋊Q8—62no—
107C3×#117—21no—
108C3×#117C2×D311yescharacteristic
109C3×#117C22×C311yescharacteristic
110C2×C3×C4⋊C4—62no—
111C2×C3×C42—21no—
112C2×C3×C42C2×D311yescharacteristic
113C2×C3×C42C22×C311yescharacteristic
114C2×C4⋊Dic3—22no—
115C2×#208C22×C311yescharacteristic
116#909—22no—
117#909—22no—
118C2×Dic12—21no—
119C2×#204—21no—
120#897—22no—
121#886—22no—
122#875—21no—
123#869—22no—
124#869—21no—
125#869—22no—
126C3×#104—62no—
127C3×#103—62no—
128C3×#101—62no—
129#824—22no—
130#810—22no—
131#805—22no—
132C23×C32C2×D411yescharacteristic
133C22×C3×D3—21no—
134C2×C32×C4—24no—
135C2×C32×C4—22no—
136C2×C32×C4—22no—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C3×#67—41no—
144C3×#67—41no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C3×D12—21no—
153C3×D12—21no—
154C3×C4×D3—41no—
155C3×C4×D3—41no—
156C3×Dic6—22no—
157C3×Dic6—21no—
158C3×Dic6—22no—
159C3×Dic6—21no—
160C3×Dic6—41no—
161C3×Dic6—41no—
162C3×Dic6—41no—
163C3×Dic6—41no—
164C3×Dic6—41no—
165C3×Dic6—41no—
166C32×C8—22no—
167C3×C3⋊C8—41no—
168C2×#137—31no—
169#536—31no—
170C2×C4⋊Q8—31no—
171C2×#104—31no—
172#419—31no—
173C2×#101—31no—
174#339C3×D311yescharacteristic, complemented
175C3×#41—61no—
176C3×#41—61no—
177C3×#41—61no—
178C3×#41—61no—
179C2×C3×Q8—31no—
180C2×C3×Q8—32no—
181C2×C3×Q8—61no—
182C2×C3×Q8—61no—
183C2×C3×Q8—61no—
184C2×C3×Q8—61no—
185C2×C3×Q8—61no—
186C2×C3×Q8—61no—
187C2×C3×Q8—61no—
188C2×C3×Q8—61no—
189C2×C3×Q8—61no—
190C2×C3×Q8—61no—
191C2×C3×Q8—61no—
192C2×C3×D4—31no—
193C2×C3×D4—61no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—32no—
198C22×C3×C4—41no—
199C22×C3×C4—61no—
200C22×C3×C4—61no—
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C23×C311yescharacteristic
203C2×#67—21no—
204C22×Dic3—21no—
205C22×Dic3C3×D412yes—
206#235—21no—
207#235—21no—
208#235—21no—
209#235—21no—
210C2×D12C3×D411yescharacteristic
211C2×C4×D3—21no—
212C2×Dic6—21no—
213C2×Dic6—21no—
214C2×Dic6—21no—
215C2×Dic6—21no—
216C2×Dic6—21no—
217C2×Dic6—21no—
218C2×Dic6—21no—
219C2×Dic6—21no—
220C2×Dic6—21no—
221C2×Dic6—21no—
222C2×Dic6—21no—
223C2×Dic6C3×D411yescharacteristic
224C2×Dic6C3×D412yes—
225C3×Q16—64no—
226C3×SD16—64no—
227C3×M16—21no—
228C3×M16—21no—
229C3×M16—22no—
230C3×M16—41no—
231C3×M16—61no—
232C3×M16—61no—
233C3×M16D1212yes—
234C3×M16C3×D412yes—
235C2×C3×C8—21no—
236C2×C3×C8—21no—
237C2×C3×C8—41no—
238C2×C3×C8—61no—
239C3×C4⋊C4—22no—
240C3×C4⋊C4—68no—
241C3×C4⋊C4—64no—
242C3×C4⋊C4D1212yes—
243C3×C4⋊C4C3×D412yes—
244C3×C22⋊C4—21no—
245C3×C22⋊C4—21no—
246C3×C22⋊C4—41no—
247C3×C22⋊C4—64no—
248C3×C42—21no—
249C3×C42—21no—
250C3×C42—21no—
251C3×C42—21no—
252C3×C42—22no—
253C3×C42—41no—
254C3×C42—41no—
255C3×C42D1212yes—
256C3×C42C3×D412yes—
257(C2×D3)⋊C4—24no—
258C4⋊Dic3—28no—
259C4⋊Dic3—24no—
260#208—21no—
261#208—21no—
262C2×C3⋊C8—21no—
263Dic12—24no—
264#204—24no—
265C22×C32—22no—
266C22×C32#12011yescharacteristic
267C22×C32#12011yescharacteristic
268C22×C32#12111yescharacteristic
269C2×C3×D3—41no—
270C2×C3×D3—42no—
271C32×C4—24no—
272C32×C4—42no—
273C32×C4#12011yescharacteristic
274C32×C4#12111yescharacteristic
275C32×C4#12111yescharacteristic
276C32×C4#12711yescharacteristic
277C3×Dic3—42no—
278C3×Dic3—41no—
279C3×Dic3—42no—
280C2×#41—31no—
281C22×Q8—31no—
282C22×Q8—31no—
283#137—62no—
284#137—62no—
285C2×Q16—61no—
286C2×SD16—61no—
287C2×M16—31no—
288C2×M16C2×C3×D311yescharacteristic
289C4⋊Q8—62no—
290C4⋊Q8—61no—
291C4⋊Q8—62no—
292#124—61no—
293#123—62no—
294C22⋊Q8—62no—
295#117C2×C3×D311yescharacteristic
296C2×C4⋊C4—62no—
297C2×C42C2×C3×D311yescharacteristic
298#104—62no—
299#103—62no—
300#101—62no—
301C23×C3—21no—
302C23×C3—61no—
303C23×C3D3×D411yescharacteristic
304C23×C3C2×C3×D411yescharacteristic
305C22×D3—21no—
306C3×Q8—62no—
307C3×Q8—61no—
308C3×Q8—62no—
309C3×Q8—61no—
310C3×Q8—121no—
311C3×Q8—121no—
312C3×Q8—121no—
313C3×Q8—121no—
314C3×Q8—121no—
315C3×Q8—121no—
316C3×D4—61no—
317C3×D4—61no—
318C3×D4—121no—
319C3×D4—121no—
320C2×C3×C4—24no—
321C2×C3×C4—24no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—42no—
333C2×C3×C4—44no—
334C2×C3×C4—42no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—61no—
339C2×C3×C4—62no—
340C2×C3×C4—121no—
341C2×C3×C4—121no—
342C2×C3×C4—121no—
343C2×C3×C4—121no—
344C2×C3×C4C2×D1211yescharacteristic
345C2×C3×C4C2×D1211yescharacteristic
346C2×C3×C4C2×D1211yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4#23911yescharacteristic
350C2×C3×C4C2×C3×D411yescharacteristic
351C2×C3×C4C2×C3×D411yescharacteristic
352C2×C3×C4C2×C3×D411yescharacteristic
353C2×C3×C4C2×C3×D411yescharacteristic
354C2×C3×C4C2×C3×D411yescharacteristic
355C2×C3×C4C3×#4111yescharacteristic
356#67—41no—
357#67—41no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—21no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—41no—
364C2×Dic3—41no—
365D12—21no—
366D12—21no—
367C4×D3—41no—
368C4×D3—41no—
369Dic6—22no—
370Dic6—21no—
371Dic6—22no—
372Dic6—21no—
373Dic6—41no—
374Dic6—41no—
375Dic6—41no—
376Dic6—41no—
377Dic6—41no—
378Dic6—41no—
379C3×C8—22no—
380C3×C8—22no—
381C3×C8—42no—
382C3×C8—121no—
383C3⋊C8—41no—
384C2×C32—21no—
385C2×C32—21no—
386C2×C32#39211yescharacteristic
387C2×C32#45612yes—
388C3×D3—81no—
389#41—61no—
390#41—61no—
391#41—61no—
392#41—61no—
393C2×Q8—31no—
394C2×Q8—32no—
395C2×Q8—61no—
396C2×Q8—61no—
397C2×Q8—61no—
398C2×Q8—61no—
399C2×Q8—61no—
400C2×Q8—61no—
401C2×Q8—61no—
402C2×Q8—61no—
403C2×Q8—61no—
404C2×Q8—61no—
405C2×Q8—61no—
406C2×D4—31no—
407C2×D4—61no—
408C22×C4—21no—
409C22×C4—32no—
410C22×C4—61no—
411C22×C4—61no—
412C22×C4C22×C3×D311yescharacteristic
413Q16—64no—
414SD16—64no—
415M16—21no—
416M16—61no—
417M16—61no—
418M16C3×D1212yes—
419C2×C8—21no—
420C2×C8—61no—
421C4⋊C4—68no—
422C4⋊C4—64no—
423C4⋊C4C3×D1212yes—
424C22⋊C4—21no—
425C22⋊C4—64no—
426C42—21no—
427C42—21no—
428C42C3×D1212yes—
429C22×C3—22no—
430C22×C3—22no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—42no—
435C22×C3—121no—
436C22×C3—122no—
437C22×C3#88211yescharacteristic
438C22×C3#88211yescharacteristic
439C22×C3#89511yescharacteristic
440C22×C3C3×#12011yescharacteristic
441C22×C3C3×#12011yescharacteristic
442C22×C3C3×#12111yescharacteristic
443C2×D3—41no—
444C2×D3—42no—
445C3×C4—24no—
446C3×C4—24no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—44no—
452C3×C4—42no—
453C3×C4—42no—
454C3×C4—82no—
455C3×C4—122no—
456C3×C4—121no—
457C3×C4—122no—
458C3×C4#87411yescharacteristic
459C3×C4#88211yescharacteristic
460C3×C4#89511yescharacteristic
461C3×C4#89511yescharacteristic
462C3×C4C3×#12011yescharacteristic
463C3×C4C3×#12111yescharacteristic
464C3×C4C3×#12111yescharacteristic
465C3×C4C3×#12711yescharacteristic
466Dic3—42no—
467Dic3—41no—
468Dic3—42no—
469C32#200511yescharacteristic, complemented, Sylow
470C23—61no—
471C23C3×D3×D411yescharacteristic
472Q8—62no—
473Q8—61no—
474Q8—62no—
475Q8—61no—
476Q8—121no—
477Q8—121no—
478Q8—121no—
479Q8—121no—
480Q8—121no—
481Q8—121no—
482D4—61no—
483D4—61no—
484D4—121no—
485D4—121no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—61no—
492C2×C4—62no—
493C2×C4—62no—
494C2×C4—121no—
495C2×C4—121no—
496C2×C4—121no—
497C2×C4—121no—
498C2×C4C2×C3×D1211yescharacteristic
499C2×C4C2×C3×D1211yescharacteristic
500C2×C4C2×C3×D1211yescharacteristic
501C2×C4C3×D3×D411yescharacteristic
502C2×C4C3×D3×D411yescharacteristic
503C2×C4C3×#23911yescharacteristic
504C8—22no—
505C8—121no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—22no—
512C2×C3—41no—
513C2×C3—41no—
514C2×C3—241no—
515C2×C3#467111yescharacteristic
516C2×C3#482612yes—
517C2×C3C3×#39211yescharacteristic
518C2×C3C3×#45612yes—
519D3—81no—
520C22—22no—
521C22—121no—
522C22—122no—
523C22C3×#88211yescharacteristic
524C22C3×#88211yescharacteristic
525C22C3×#89511yescharacteristic
526C4—24no—
527C4—42no—
528C4—122no—
529C4—121no—
530C4—122no—
531C4C3×#87411yescharacteristic
532C4C3×#88211yescharacteristic
533C4C3×#89511yescharacteristic
534C4C3×#89511yescharacteristic
535C3—21no—
536C3#6876811yescharacteristic, direct product factor
537C3C3×#200511yescharacteristic, complemented
538C2—21no—
539C2—21no—
540C2—241no—
541C2C3×#467111yescharacteristic
542C2C3×#482612yes—
subgroupG/H
centerC22×C3#882
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#339C2
socleC22×C32#120
prime radicalC2×C3×#235C22
hypercenterC3×#339D3
hypocenterC3C3×#2005
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#339

Complements

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

NH ≅ G/Ntype
3. C2×C3×#869C2semidirect
4. C2×C3×#824C2semidirect
5. C3×#5004C2semidirect
7. C32×#339C2semidirect
9. #68768C3direct (N × H)
36. C2×#869C2×C3semidirect
40. C2×#824C2×C3semidirect
41. #5004C2×C3semidirect
44. C3×#339D3semidirect
45. C3×#339C2×C3semidirect
174. #339C3×D3semidirect
469. C32#2005semidirect
536. C3#68768direct (N × H)
537. C3C3×#2005semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9092
C3×#55262
C2×C3×#8692
C2×C3×#8242
C3×#50042
C2×C3×#8052
C32×#3392
C3×#20053
#687683