Finite Group Databasebeta

← C3×#70975 #11778317

Subgroups — C3×#70975 #11778317

Order 1152.

643 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5597C211yesmaximal, characteristic
2C32×#448C211yesmaximal, characteristic, complemented
3C3×#5230C211yesmaximal, characteristic, complemented
4C3×#5227C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic, complemented
6C3×#4470C211yesmaximal, characteristic, complemented
7C3×#4469C211yesmaximal, characteristic, complemented
8C3×#1604—31nomaximal
9#70975C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C2×C3×#237—21no—
12C2×C32×SD16—21no—
13C32×#121C2211yescharacteristic
14C2×C3×#215—21no—
15C3×#939—21no—
16C3×#939—21no—
17C3×#930C2211yescharacteristic
18C2×C3×Dic3⋊C4—21no—
19C2×C3×Dic3⋊C4C2211yescharacteristic
20C3×#896—21no—
21C3×#884—21no—
22C3×#878—21no—
23C32×#103—21no—
24C32×C22⋊C8C2211yescharacteristic
25C3×#835—21no—
26C3×C3⋊#95—21no—
27C3×C3⋊#95C2211yescharacteristic
28C3×#830C2211yescharacteristic
29C3×#537—31no—
30#5597C2×C311yescharacteristic
31C3×#448—21no—
32C3×#448—31no—
33C3×#448D311yescharacteristic, complemented
34C3×#448C2×C311yescharacteristic, complemented
35C3×#395—31no—
36#5230C2×C311yescharacteristic, complemented
37#5227C2×C311yescharacteristic, complemented
38C3×#327—31no—
39C3×#327—31no—
40C3×#324—31no—
41#4537C2×C311yescharacteristic, complemented
42#4470C2×C311yescharacteristic, complemented
43#4469C2×C311yescharacteristic, complemented
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—42no—
47C2×C32×D4—21no—
48C2×C32×D4D411yescharacteristic
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C2×C3×#67—21no—
52C2×C3×#67—21no—
53C2×C3×#67—21no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3D411yescharacteristic
57C22×C3×Dic3D411yescharacteristic
58C3×#237—42no—
59C3×#237—42no—
60C2×C3×D12D411yescharacteristic
61C2×C3×C4×D3—21no—
62C2×C3×Dic6—21no—
63C32×SD16—42no—
64C2×C32×C8—21no—
65C32×C4⋊C4D411yescharacteristic
66C32×C22⋊C4—21no—
67C3×#217—21no—
68C3×#215—42no—
69C3×(C2×D3)⋊C4—21no—
70C3×(C2×D3)⋊C4—21no—
71C3×C4⋊Dic3D411yescharacteristic
72C3×Dic3⋊C4—21no—
73C3×Dic3⋊C4—21no—
74C3×Dic3⋊C4—21no—
75C3×Dic3⋊C4—42no—
76C2×C3×C3⋊C8—21no—
77#1604—31noSylow
78C2×C3×#41—61no—
79C22×C3×Q8—21no—
80C22×C3×Q8C2×D311yescharacteristic
81C22×C3×Q8C22×C311yescharacteristic
82C2×#237—21no—
83C2×C3×SD16—22no—
84C2×C3×SD16—21no—
85C2×C3×SD16—21no—
86C2×C3×SD16—61no—
87C3×C22⋊Q8—61no—
88C3×C22⋊Q8—61no—
89C3×#121—21no—
90C3×#121—31no—
91C3×#121—61no—
92C3×#121—61no—
93C3×#121—61no—
94C3×#121C2×D311yescharacteristic
95C3×#121C22×C311yescharacteristic
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—61no—
98C2×#215—21no—
99#939—21no—
100#939—21no—
101#930C22×C311yescharacteristic
102C2×Dic3⋊C4—21no—
103C2×Dic3⋊C4C22×C311yescharacteristic
104#896—21no—
105#884—21no—
106#878—21no—
107C3×#103—22no—
108C3×#103—21no—
109C3×#103—21no—
110C3×#103—61no—
111C3×C22⋊C8—21no—
112C3×C22⋊C8—31no—
113C3×C22⋊C8C2×D311yescharacteristic
114C3×C22⋊C8C22×C311yescharacteristic
115C3×#95—31no—
116C3×#95—61no—
117#835—21no—
118C3⋊#95—21no—
119C3⋊#95C22×C311yescharacteristic
120#830C22×C311yescharacteristic
121C23×C32—21no—
122C23×C32C2×D411yescharacteristic
123C22×C3×D3—21no—
124C32×Q8—22no—
125C32×Q8—22no—
126C32×Q8—41no—
127C32×Q8—41no—
128C32×D4—41no—
129C32×D4—41no—
130C32×D4—41no—
131C2×C32×C4—22no—
132C2×C32×C4—21no—
133C2×C32×C4—41no—
134C2×C32×C4—41no—
135C2×C32×C4—41no—
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C3×#67—42no—
139C3×#67—41no—
140C3×#67—41no—
141C3×#67—81no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—42no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3SD1612yescomplemented
152C3×D12—41no—
153C3×C4×D3—42no—
154C3×Dic6—42no—
155C32×C8—41no—
156C3×C3⋊C8—41no—
157#537—31no—
158#448—31no—
159#448C3×D311yescharacteristic, complemented
160#395—31no—
161#327—31no—
162#327—31no—
163#324—31no—
164C3×#41—122no—
165C3×#41—122no—
166C2×C3×Q8—22no—
167C2×C3×Q8—21no—
168C2×C3×Q8—21no—
169C2×C3×Q8—21no—
170C2×C3×Q8—21no—
171C2×C3×Q8—41no—
172C2×C3×Q8—42no—
173C2×C3×Q8—42no—
174C2×C3×Q8—44no—
175C2×C3×Q8—61no—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×C3×D4—21no—
179C2×C3×D4—31no—
180C2×C3×D4—41no—
181C2×C3×D4—61no—
182C2×C3×D4—61no—
183C2×C3×D4—61no—
184C2×C3×D4#6711yescharacteristic
185C2×C3×D4C3×D411yescharacteristic
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—31no—
190C22×C3×C4—31no—
191C22×C3×C4—41no—
192C22×C3×C4—61no—
193C22×C3×C4—61no—
194C22×C3×C4—61no—
195C22×C3×C4C22×D311yescharacteristic
196C22×C3×C4C23×C311yescharacteristic
197C2×#67—21no—
198C2×#67—21no—
199C2×#67—21no—
200C22×Dic3—21no—
201C22×Dic3—21no—
202C22×Dic3C3×D411yescharacteristic
203C22×Dic3C3×D411yescharacteristic
204#237—42no—
205#237—42no—
206C2×D12C3×D411yescharacteristic
207C2×C4×D3—21no—
208C2×Dic6—21no—
209C3×SD16—42no—
210C3×SD16—42no—
211C3×SD16—44no—
212C3×SD16—122no—
213C2×C3×C8—22no—
214C2×C3×C8—21no—
215C2×C3×C8—21no—
216C2×C3×C8—61no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—31no—
219C3×C4⋊C4—61no—
220C3×C4⋊C4—61no—
221C3×C4⋊C4—61no—
222C3×C4⋊C4—122no—
223C3×C4⋊C4#6711yescharacteristic
224C3×C4⋊C4C3×D411yescharacteristic
225C3×C22⋊C4—21no—
226C3×C22⋊C4—21no—
227C3×C22⋊C4—41no—
228C3×C22⋊C4—61no—
229C3×C22⋊C4—61no—
230C3×C22⋊C4—61no—
231#217—21no—
232#215—42no—
233(C2×D3)⋊C4—21no—
234(C2×D3)⋊C4—21no—
235C4⋊Dic3C3×D411yescharacteristic
236Dic3⋊C4—21no—
237Dic3⋊C4—21no—
238Dic3⋊C4—21no—
239Dic3⋊C4—42no—
240C2×C3⋊C8—21no—
241C22×C32—21no—
242C22×C32—21no—
243C22×C32—41no—
244C22×C32—41no—
245C22×C32—41no—
246C22×C32#12011yescharacteristic
247C22×C32C2×SD1611yescharacteristic
248C22×C32AGL(1,ℤ/8)11yescharacteristic
249C2×C3×D3—41no—
250C2×C3×D3—41no—
251C2×C3×D3—41no—
252C32×C4—21no—
253C32×C4—21no—
254C32×C4—42no—
255C32×C4—41no—
256C3×Dic3—22no—
257C3×Dic3—42no—
258C3×Dic3—41no—
259C3×Dic3—41no—
260C2×#41—61no—
261C22×Q8C2×C3×D311yescharacteristic
262C2×SD16—21no—
263C2×SD16—61no—
264C22⋊Q8—61no—
265C22⋊Q8—61no—
266#121—31no—
267#121—61no—
268#121—61no—
269#121—61no—
270#121C2×C3×D311yescharacteristic
271C2×C4⋊C4—31no—
272C2×C4⋊C4—61no—
273#103—21no—
274#103—61no—
275C22⋊C8—31no—
276C22⋊C8C2×C3×D311yescharacteristic
277#95—31no—
278#95—61no—
279C23×C3—21no—
280C23×C3—21no—
281C23×C3—21no—
282C23×C3—41no—
283C23×C3—61no—
284C23×C3D3×D411yescharacteristic
285C23×C3C2×C3×D411yescharacteristic
286C22×D3—21no—
287C3×Q8—22no—
288C3×Q8—24no—
289C3×Q8—22no—
290C3×Q8—22no—
291C3×Q8—22no—
292C3×Q8—42no—
293C3×Q8—42no—
294C3×Q8—41no—
295C3×Q8—41no—
296C3×Q8—41no—
297C3×Q8—41no—
298C3×Q8—42no—
299C3×Q8—122no—
300C3×D4—41no—
301C3×D4—41no—
302C3×D4—42no—
303C3×D4—41no—
304C3×D4—41no—
305C3×D4—41no—
306C3×D4—41no—
307C3×D4—81no—
308C3×D4—81no—
309C3×D4—121no—
310C3×D4—122no—
311C3×D4—121no—
312C3×D4—121no—
313C3×D4—241no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—32no—
321C2×C3×C4—42no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4—42no—
326C2×C3×C4—41no—
327C2×C3×C4—41no—
328C2×C3×C4—42no—
329C2×C3×C4—42no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4—61no—
333C2×C3×C4—61no—
334C2×C3×C4—62no—
335C2×C3×C4—61no—
336C2×C3×C4—61no—
337C2×C3×C4—122no—
338C2×C3×C4—122no—
339C2×C3×C4—121no—
340C2×C3×C4—121no—
341C2×C3×C4—121no—
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4C2×#6711yescharacteristic
344C2×C3×C4C2×C3×D411yescharacteristic
345C2×C3×C4C2×C3×D411yescharacteristic
346#67—42no—
347#67—41no—
348#67—41no—
349#67—81no—
350C2×Dic3—21no—
351C2×Dic3—21no—
352C2×Dic3—22no—
353C2×Dic3—21no—
354C2×Dic3—21no—
355C2×Dic3—42no—
356C2×Dic3—41no—
357C2×Dic3—41no—
358C2×Dic3—41no—
359C2×Dic3C3×SD1612yescomplemented
360D12—41no—
361C4×D3—42no—
362Dic6—42no—
363C3×C8—42no—
364C3×C8—41no—
365C3×C8—41no—
366C3×C8—121no—
367C3⋊C8—41no—
368C2×C32—21no—
369C2×C32—21no—
370C2×C32—81no—
371C2×C32#45011yescharacteristic
372C2×C32#45611yescharacteristic
373C2×C32B(4,𝔽2)11yescharacteristic
374C3×D3—81no—
375#41—122no—
376#41—122no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—42no—
380C2×Q8—61no—
381C2×D4—21no—
382C2×D4—31no—
383C2×D4—61no—
384C2×D4—61no—
385C2×D4—61no—
386C2×D4C3×#6711yescharacteristic
387C22×C4—21no—
388C22×C4—31no—
389C22×C4—31no—
390C22×C4—61no—
391C22×C4—61no—
392C22×C4—61no—
393C22×C4C22×C3×D311yescharacteristic
394SD16—42no—
395SD16—122no—
396C2×C8—21no—
397C2×C8—61no—
398C4⋊C4—31no—
399C4⋊C4—61no—
400C4⋊C4—61no—
401C4⋊C4—61no—
402C4⋊C4—122no—
403C4⋊C4C3×#6711yescharacteristic
404C22⋊C4—21no—
405C22⋊C4—61no—
406C22⋊C4—61no—
407C22⋊C4—61no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—41no—
418C22×C3—41no—
419C22×C3—41no—
420C22×C3—41no—
421C22×C3—41no—
422C22×C3—41no—
423C22×C3—81no—
424C22×C3—81no—
425C22×C3—81no—
426C22×C3—121no—
427C22×C3—121no—
428C22×C3—121no—
429C22×C3D3×SD1611yescharacteristic
430C22×C3#91411yescharacteristic
431C22×C3#93711yescharacteristic
432C22×C3C3×#12011yescharacteristic
433C22×C3C2×C3×SD1611yescharacteristic
434C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
435C2×D3—41no—
436C2×D3—41no—
437C2×D3—41no—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—41no—
444C3×C4—44no—
445C3×C4—41no—
446C3×C4—42no—
447C3×C4—41no—
448C3×C4—42no—
449C3×C4—62no—
450C3×C4—81no—
451C3×C4—122no—
452C3×C4—121no—
453C3×C4—121no—
454Dic3—22no—
455Dic3—42no—
456Dic3—41no—
457Dic3—41no—
458C32#160411yescharacteristic, complemented, Sylow
459C23—21no—
460C23—61no—
461C23C3×D3×D411yescharacteristic
462Q8—22no—
463Q8—22no—
464Q8—41no—
465Q8—41no—
466Q8—122no—
467D4—41no—
468D4—41no—
469D4—41no—
470D4—121no—
471D4—122no—
472D4—121no—
473D4—121no—
474D4—241no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—32no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—61no—
482C2×C4—61no—
483C2×C4—62no—
484C2×C4—61no—
485C2×C4—61no—
486C2×C4—122no—
487C2×C4—122no—
488C2×C4—121no—
489C2×C4—121no—
490C2×C4—121no—
491C2×C4C3×D3×D411yescharacteristic
492C2×C4C2×C3×#6711yescharacteristic
493C8—41no—
494C8—121no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—41no—
503C2×C3—41no—
504C2×C3—81no—
505C2×C3—81no—
506C2×C3—161no—
507C2×C3—241no—
508C2×C3#503211yescharacteristic
509C2×C3#516911yescharacteristic
510C2×C3#520511yescharacteristic
511C2×C3C3×#45011yescharacteristic
512C2×C3C3×#45611yescharacteristic
513C2×C3C3×B(4,𝔽2)11yescharacteristic
514D3—81no—
515C22—21no—
516C22—21no—
517C22—41no—
518C22—41no—
519C22—41no—
520C22—121no—
521C22—121no—
522C22—121no—
523C22C3×D3×SD1611yescharacteristic
524C22C3×#91411yescharacteristic
525C22C3×#93711yescharacteristic
526C4—21no—
527C4—21no—
528C4—41no—
529C4—42no—
530C4—62no—
531C4—122no—
532C4—121no—
533C4—121no—
534C3—21no—
535C3#7097511yescharacteristic, direct product factor
536C3C3×#160411yescharacteristic, complemented
537C2—21no—
538C2—21no—
539C2—81no—
540C2—241no—
541C2C3×#503211yescharacteristic
542C2C3×#516911yescharacteristic
543C2C3×#520511yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#448C2
socleC22×C32#120
prime radicalC3×#5597C2
hypercenterC3×#448D3
hypocenterC3C3×#1604
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#448

Complements

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

NH ≅ G/Ntype
2. C32×#448C2semidirect
3. C3×#5230C2semidirect
4. C3×#5227C2semidirect
5. C3×#4537C2semidirect
6. C3×#4470C2semidirect
7. C3×#4469C2semidirect
9. #70975C3direct (N × H)
33. C3×#448D3semidirect
34. C3×#448C2×C3semidirect
36. #5230C2×C3semidirect
37. #5227C2×C3semidirect
41. #4537C2×C3semidirect
42. #4470C2×C3semidirect
43. #4469C2×C3semidirect
151. C2×C3×Dic3SD16semidirect
159. #448C3×D3semidirect
359. C2×Dic3C3×SD16semidirect
458. C32#1604semidirect
535. C3#70975direct (N × H)
536. C3C3×#1604semidirect

Maximal subgroups

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

subgroupindex
C3×#55972
C32×#4482
C3×#52302
C3×#52272
C3×#45372
C3×#44702
C3×#44692
C3×#16043
#709753