Finite Group Databasebeta

← C3×#70714 #11793892

Subgroups — C3×#70714 #11793892

Order 1152.

617 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#908C211yesmaximal, characteristic
2C2×C32×#108C211yesmaximal, characteristic, complemented
3C3×#5133C211yesmaximal, characteristic, complemented
4C2×C3×#823C211yesmaximal, characteristic, complemented
5C2×C3×#821C211yesmaximal, characteristic, complemented
6C3×#5110C211yesmaximal, characteristic, complemented
7C3×#4554C211yesmaximal, characteristic, complemented
8C3×#2051—31nomaximal
9#70714C311yesmaximal, characteristic, direct product factor
10C2×C3×#235C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#908—22no—
18C3×#908—22no—
19C2×C3×D24—21no—
20C2×C3×#204—21no—
21C32×#108—22no—
22C3×#823—22no—
23C3×#821—21no—
24C3×#821—22no—
25C3×(C2×D3)⋊C8—22no—
26C3×#816—21no—
27C2×C3×AGL(1,ℤ/8)—31no—
28C2×#908C2×C311yescharacteristic
29C2×C3×#108—21no—
30C2×C3×#108D311yescharacteristic, complemented
31C2×C3×#108C2×C311yescharacteristic, complemented
32C3×#417—31no—
33C2×C3×#102—31no—
34C2×C3×#100—31no—
35C3×#408—31no—
36#5133C2×C311yescharacteristic, complemented
37C2×#823C2×C311yescharacteristic, complemented
38C2×#821C2×C311yescharacteristic, complemented
39#5110C2×C311yescharacteristic, complemented
40C3×#343—31no—
41#4554C2×C311yescharacteristic, complemented
42C23×C3×D3—21no—
43C22×C32×C4C2311yescharacteristic
44C2×C3×#67—21no—
45C22×C3×Dic3—21no—
46C3×#235—21no—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12D411yescharacteristic
56C2×C3×D12D412yes—
57C2×C3×C4×D3—21no—
58C2×C3×Dic6D411yescharacteristic
59C32×M16—21no—
60C32×M16—21no—
61C32×M16—21no—
62C32×M16D412yes—
63C2×C32×C8—21no—
64C2×C32×C8—21no—
65C2×C32×C8—21no—
66C2×C32×C8—21no—
67C2×C32×C8D412yes—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×#208—21no—
71C3×#208—21no—
72C2×C3×C3⋊C8—21no—
73C3×D24—24no—
74C3×#204—24no—
75#2051—31noSylow
76C2×C3×#41—31no—
77C22×C3×D4—31no—
78C2×#235C22×C311yescharacteristic
79C22×D12C22×C311yescharacteristic
80C3×AGL(1,ℤ/8)—62no—
81C3×AGL(1,ℤ/8)—62no—
82C2×C3×SD16—61no—
83C2×C3×D8—61no—
84C2×C3×M16—21no—
85C2×C3×M16—21no—
86C2×C3×M16—31no—
87C2×C3×M16C2×D311yescharacteristic
88C2×C3×M16C2×D311yescharacteristic
89C2×C3×M16C22×C311yescharacteristic
90C2×C3×M16C22×C311yescharacteristic
91C22×C3×C8—21no—
92C22×C3×C8C2×D311yescharacteristic
93C22×C3×C8C22×C311yescharacteristic
94C2×C3×C4⋊C4—31no—
95C2×C4⋊Dic3C22×C311yescharacteristic
96C2×#208C22×C311yescharacteristic
97#908—22no—
98#908—22no—
99C2×D24—21no—
100C2×#204—21no—
101C3×#108—24no—
102C3×#108—22no—
103C3×#108—22no—
104C3×#103—61no—
105C3×#102—61no—
106C3×#102—62no—
107C3×#100—62no—
108C3×C22⋊C8—62no—
109#823—22no—
110#821—21no—
111#821—22no—
112(C2×D3)⋊C8—22no—
113#816—21no—
114C23×C32#4111yescharacteristic
115C22×C3×D3—21no—
116C22×C3×D3—22no—
117C22×C3×D3—41no—
118C22×C3×D3—41no—
119C22×C3×D3—81no—
120C22×C3×D3—81no—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C3×#67—41no—
128C3×#67—41no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—81no—
132C3×D12—22no—
133C3×D12—21no—
134C3×D12—22no—
135C3×D12—21no—
136C3×D12—41no—
137C3×D12—41no—
138C3×C4×D3—41no—
139C3×C4×D3—41no—
140C3×Dic6—21no—
141C3×Dic6—21no—
142C32×C8—22no—
143C32×C8—22no—
144C32×C8—41no—
145C3×C3⋊C8—41no—
146C2×AGL(1,ℤ/8)—31no—
147C2×#108C3×D311yescharacteristic, complemented
148#417—31no—
149C2×#102—31no—
150C2×#100—31no—
151#408—31no—
152#343—31no—
153C24×C3—61no—
154C23×D3—21no—
155C3×#41—61no—
156C3×#41—61no—
157C3×#41—61no—
158C3×#41—61no—
159C2×C3×Q8—31no—
160C2×C3×D4—32no—
161C2×C3×D4—31no—
162C2×C3×D4—61no—
163C2×C3×D4—61no—
164C2×C3×D4—61no—
165C2×C3×D4—61no—
166C2×C3×D4—61no—
167C2×C3×D4—61no—
168C22×C3×C4—21no—
169C22×C3×C4—61no—
170C22×C3×C4—61no—
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C23×C311yescharacteristic
173C2×#67—21no—
174C22×Dic3—21no—
175#235—21no—
176#235—21no—
177#235—21no—
178#235—21no—
179C2×D12—21no—
180C2×D12—21no—
181C2×D12—21no—
182C2×D12—21no—
183C2×D12—21no—
184C2×D12C3×D411yescharacteristic
185C2×D12C3×D412yes—
186C2×C4×D3—21no—
187C2×Dic6C3×D411yescharacteristic
188C3×SD16—64no—
189C3×D8—64no—
190C3×M16—21no—
191C3×M16—21no—
192C3×M16—22no—
193C3×M16—21no—
194C3×M16—21no—
195C3×M16—21no—
196C3×M16—21no—
197C3×M16—22no—
198C3×M16—41no—
199C3×M16—41no—
200C3×M16—61no—
201C3×M16—61no—
202C3×M16#6712yes—
203C3×M16C3×D412yes—
204C2×C3×C8—22no—
205C2×C3×C8—22no—
206C2×C3×C8—21no—
207C2×C3×C8—21no—
208C2×C3×C8—21no—
209C2×C3×C8—21no—
210C2×C3×C8—21no—
211C2×C3×C8—21no—
212C2×C3×C8—21no—
213C2×C3×C8—21no—
214C2×C3×C8—22no—
215C2×C3×C8—41no—
216C2×C3×C8—41no—
217C2×C3×C8—61no—
218C2×C3×C8D1212yes—
219C2×C3×C8C3×D412yes—
220C3×C4⋊C4—61no—
221C3×C4⋊C4—61no—
222C4⋊Dic3—21no—
223C4⋊Dic3—21no—
224#208—21no—
225#208—21no—
226C2×C3⋊C8—21no—
227D24—24no—
228#204—24no—
229C22×C32—21no—
230C22×C32—21no—
231C22×C32#12111yescharacteristic
232C22×C32#12311yescharacteristic
233C22×C32#12411yescharacteristic
234C2×C3×D3—41no—
235C2×C3×D3—42no—
236C2×C3×D3—41no—
237C2×C3×D3—41no—
238C2×C3×D3—82no—
239C2×C3×D3—81no—
240C2×C3×D3—81no—
241C2×C3×D3—82no—
242C32×C4#12011yescharacteristic
243C32×C4#12111yescharacteristic
244C32×C4#12111yescharacteristic
245C32×C4#12311yescharacteristic
246C3×Dic3—41no—
247C3×Dic3—81no—
248C2×#41—31no—
249C22×D4—31no—
250AGL(1,ℤ/8)—62no—
251AGL(1,ℤ/8)—62no—
252C2×SD16—61no—
253C2×D8—61no—
254C2×M16—31no—
255C2×M16C2×C3×D311yescharacteristic
256C2×M16C2×C3×D311yescharacteristic
257C22×C8C2×C3×D311yescharacteristic
258C2×C4⋊C4—31no—
259#108—22no—
260#103—61no—
261#102—61no—
262#102—62no—
263#100—62no—
264C22⋊C8—62no—
265C23×C3—21no—
266C23×C3—61no—
267C23×C3—62no—
268C23×C3—121no—
269C23×C3—121no—
270C23×C3—241no—
271C23×C3—241no—
272C23×C3#23911yescharacteristic
273C23×C3C3×#4111yescharacteristic
274C22×D3—21no—
275C22×D3—22no—
276C22×D3—41no—
277C22×D3—41no—
278C22×D3—81no—
279C22×D3—81no—
280C3×Q8—61no—
281C3×Q8—61no—
282C3×D4—61no—
283C3×D4—62no—
284C3×D4—61no—
285C3×D4—62no—
286C3×D4—121no—
287C3×D4—121no—
288C3×D4—121no—
289C3×D4—121no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—61no—
297C2×C3×C4—121no—
298C2×C3×C4—121no—
299C2×C3×C4—121no—
300C2×C3×C4—241no—
301C2×C3×C4C2×D1211yescharacteristic
302C2×C3×C4#23511yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4#23911yescharacteristic
306C2×C3×C4C2×#6711yescharacteristic
307C2×C3×C4C2×C3×D411yescharacteristic
308C2×C3×C4C2×C3×D411yescharacteristic
309C2×C3×C4C2×C3×D411yescharacteristic
310C2×C3×C4C2×C3×D411yescharacteristic
311C2×C3×C4C3×#4111yescharacteristic
312C2×C3×C4C3×#4111yescharacteristic
313#67—41no—
314#67—41no—
315C2×Dic3—21no—
316C2×Dic3—41no—
317C2×Dic3—81no—
318D12—22no—
319D12—21no—
320D12—22no—
321D12—21no—
322D12—41no—
323D12—41no—
324C4×D3—41no—
325C4×D3—41no—
326Dic6—21no—
327Dic6—21no—
328C3×C8—24no—
329C3×C8—22no—
330C3×C8—22no—
331C3×C8—22no—
332C3×C8—22no—
333C3×C8—42no—
334C3×C8—42no—
335C3×C8—41no—
336C3×C8—41no—
337C3×C8—121no—
338C3⋊C8—41no—
339C2×C32—21no—
340C2×C32—21no—
341C2×C32#39411yescharacteristic
342C2×C32#47111yescharacteristic
343C2×C32#47211yescharacteristic
344C3×D3—81no—
345C3×D3—82no—
346C24—61no—
347#41—61no—
348#41—61no—
349#41—61no—
350#41—61no—
351C2×Q8—31no—
352C2×D4—32no—
353C2×D4—31no—
354C2×D4—61no—
355C2×D4—61no—
356C2×D4—61no—
357C2×D4—61no—
358C2×D4—61no—
359C2×D4—61no—
360C22×C4—61no—
361C22×C4—61no—
362C22×C4C22×C3×D311yescharacteristic
363SD16—64no—
364D8—64no—
365M16—21no—
366M16—21no—
367M16—21no—
368M16—61no—
369M16—61no—
370M16C3×#6712yes—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—61no—
376C2×C8C3×D1212yes—
377C4⋊C4—61no—
378C4⋊C4—61no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—41no—
387C22×C3—41no—
388C22×C3—121no—
389C22×C3—121no—
390C22×C3—121no—
391C22×C3—122no—
392C22×C3—242no—
393C22×C3—242no—
394C22×C3—241no—
395C22×C3—241no—
396C22×C3#89411yescharacteristic
397C22×C3#89511yescharacteristic
398C22×C3#94711yescharacteristic
399C22×C3C3×#12111yescharacteristic
400C22×C3C3×#12311yescharacteristic
401C22×C3C3×#12411yescharacteristic
402C2×D3—41no—
403C2×D3—42no—
404C2×D3—41no—
405C2×D3—41no—
406C2×D3—82no—
407C2×D3—81no—
408C2×D3—81no—
409C2×D3—82no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—121no—
415C3×C4—241no—
416C3×C4#89411yescharacteristic
417C3×C4#89511yescharacteristic
418C3×C4#93011yescharacteristic
419C3×C4#93711yescharacteristic
420C3×C4C3×#12011yescharacteristic
421C3×C4C3×#12111yescharacteristic
422C3×C4C3×#12111yescharacteristic
423C3×C4C3×#12311yescharacteristic
424Dic3—41no—
425Dic3—81no—
426C32#205111yescharacteristic, complemented, Sylow
427C23—61no—
428C23—62no—
429C23—121no—
430C23—121no—
431C23—241no—
432C23—241no—
433C23C3×#23911yescharacteristic
434Q8—61no—
435Q8—61no—
436D4—61no—
437D4—62no—
438D4—61no—
439D4—62no—
440D4—121no—
441D4—121no—
442D4—121no—
443D4—121no—
444C2×C4—61no—
445C2×C4—121no—
446C2×C4—121no—
447C2×C4—121no—
448C2×C4—241no—
449C2×C4C2×C3×D1211yescharacteristic
450C2×C4C3×#23511yescharacteristic
451C2×C4C3×D3×D411yescharacteristic
452C2×C4C3×D3×D411yescharacteristic
453C2×C4C3×#23911yescharacteristic
454C2×C4C2×C3×#6711yescharacteristic
455C8—22no—
456C8—22no—
457C8—41no—
458C8—121no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—41no—
467C2×C3—41no—
468C2×C3—241no—
469C2×C3—242no—
470C2×C3#489711yescharacteristic
471C2×C3#489811yescharacteristic
472C2×C3#499111yescharacteristic
473C2×C3C3×#39411yescharacteristic
474C2×C3C3×#47111yescharacteristic
475C2×C3C3×#47211yescharacteristic
476D3—81no—
477D3—82no—
478C22—21no—
479C22—21no—
480C22—121no—
481C22—122no—
482C22—121no—
483C22—121no—
484C22—242no—
485C22—242no—
486C22—241no—
487C22—241no—
488C22C3×#89411yescharacteristic
489C22C3×#89511yescharacteristic
490C22C3×#94711yescharacteristic
491C4—121no—
492C4—241no—
493C4C3×#89411yescharacteristic
494C4C3×#89511yescharacteristic
495C4C3×#93011yescharacteristic
496C4C3×#93711yescharacteristic
497C3—21no—
498C3#7071411yescharacteristic, direct product factor
499C3C3×#205111yescharacteristic, complemented
500C2—21no—
501C2—21no—
502C2—241no—
503C2—242no—
504C2C3×#489711yescharacteristic
505C2C3×#489811yescharacteristic
506C2C3×#499111yescharacteristic
subgroupG/H
centerC22×C3#895
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#108C2
socleC22×C32#121
prime radicalC2×C3×#908C2
hypercenterC2×C3×#108D3
hypocenterC3C3×#2051
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#108

Complements

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

NH ≅ G/Ntype
2. C2×C32×#108C2semidirect
3. C3×#5133C2semidirect
4. C2×C3×#823C2semidirect
5. C2×C3×#821C2semidirect
6. C3×#5110C2semidirect
7. C3×#4554C2semidirect
9. #70714C3direct (N × H)
30. C2×C3×#108D3semidirect
31. C2×C3×#108C2×C3semidirect
36. #5133C2×C3semidirect
37. C2×#823C2×C3semidirect
38. C2×#821C2×C3semidirect
39. #5110C2×C3semidirect
41. #4554C2×C3semidirect
147. C2×#108C3×D3semidirect
426. C32#2051semidirect
498. C3#70714direct (N × H)
499. C3C3×#2051semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9082
C2×C32×#1082
C3×#51332
C2×C3×#8232
C2×C3×#8212
C3×#51102
C3×#45542
C3×#20513
#707143