Finite Group Databasebeta

← C3×#71167 #11778543

Subgroups — C3×#71167 #11778543

Order 1152.

565 conjugacy classes of subgroups.

The subgroup lattice has 511 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5597C211yesmaximal, characteristic
2C32×#480C211yesmaximal, characteristic, complemented
3C3×#4983C211yesmaximal, characteristic, complemented
4C3×#4967C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic, complemented
6C3×#4470C211yesmaximal, characteristic, complemented
7C3×#4469C211yesmaximal, characteristic, complemented
8C3×#1610—31nomaximal
9#71167C311yesmaximal, characteristic, direct product factor
10C2×C3×#237—21no—
11C32×#121C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C3×#939—21no—
14C3×#939—21no—
15C3×#930C2211yescharacteristic
16C2×C3×Dic3⋊C4—21no—
17C2×C3×Dic3⋊C4C2211yescharacteristic
18C3×#896—21no—
19C3×#884—21no—
20C3×#878—21no—
21C32×#107—21no—
22C32×#102—21no—
23C32×C22⋊C8C2211yescharacteristic
24C3×C3⋊#95—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×#809—21no—
28C3×#807—21no—
29C3×#537—31no—
30#5597C2×C311yescharacteristic
31C3×#480—21no—
32C3×#480—31no—
33C3×#480D311yescharacteristic, complemented
34C3×#480C2×C311yescharacteristic, complemented
35C3×#398—31no—
36#4983C2×C311yescharacteristic, complemented
37#4967C2×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×D4—21no—
45C2×C32×D4D411yescharacteristic
46C22×C32×C4—21no—
47C22×C32×C4C2311yescharacteristic
48C2×C3×#67—21no—
49C2×C3×#67—21no—
50C2×C3×#67—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C22×C3×Dic3D411yescharacteristic
55C3×#237—42no—
56C3×#237—42no—
57C2×C3×D12D411yescharacteristic
58C2×C3×C4×D3—21no—
59C2×C3×Dic6—21no—
60C2×C32×C8—21no—
61C32×C4⋊C4—21no—
62C32×C4⋊C4—21no—
63C32×C4⋊C4D411yescharacteristic
64C32×C22⋊C4—21no—
65C3×#217—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×(C2×D3)⋊C4—21no—
68C3×C4⋊Dic3D411yescharacteristic
69C3×Dic3⋊C4—21no—
70C3×Dic3⋊C4—21no—
71C3×Dic3⋊C4—21no—
72C3×Dic3⋊C4—42no—
73C2×C3×C3⋊C8—21no—
74#1610—31noSylow
75C2×C3×#41—61no—
76C2×#237—21no—
77C3×C22⋊Q8—61no—
78C3×C22⋊Q8—61no—
79C3×#121—21no—
80C3×#121—31no—
81C3×#121—61no—
82C3×#121—61no—
83C3×#121—61no—
84C3×#121C2×D311yescharacteristic
85C3×#121C22×C311yescharacteristic
86C2×C3×C4⋊C4—21no—
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—61no—
89C2×C3×C4⋊C4C2×D311yescharacteristic
90C2×C3×C4⋊C4C22×C311yescharacteristic
91#939—21no—
92#939—21no—
93#930C22×C311yescharacteristic
94C2×Dic3⋊C4—21no—
95C2×Dic3⋊C4C22×C311yescharacteristic
96#896—21no—
97#884—21no—
98#878—21no—
99C3×#107—22no—
100C3×#107—21no—
101C3×#107—21no—
102C3×#107—61no—
103C3×#102—22no—
104C3×#102—21no—
105C3×#102—21no—
106C3×#102—61no—
107C3×C22⋊C8—21no—
108C3×C22⋊C8—31no—
109C3×C22⋊C8C2×D311yescharacteristic
110C3×C22⋊C8C22×C311yescharacteristic
111C3×#95—31no—
112C3×#95—61no—
113C3⋊#95—21no—
114C3⋊#95C22×C311yescharacteristic
115#830C22×C311yescharacteristic
116#809—21no—
117#807—21no—
118C23×C32—21no—
119C23×C32C2×D411yescharacteristic
120C22×C3×D3—21no—
121C32×D4—41no—
122C32×D4—41no—
123C32×D4—41no—
124C2×C32×C4—21no—
125C2×C32×C4—41no—
126C2×C32×C4—41no—
127C2×C32×C4—41no—
128C2×C32×C4—41no—
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C3×#67—42no—
132C3×#67—41no—
133C3×#67—41no—
134C3×#67—81no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—42no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3D812yes—
145C3×D12—41no—
146C3×C4×D3—42no—
147C3×Dic6—42no—
148C32×C8—41no—
149C3×C3⋊C8—41no—
150#537—31no—
151#480—31no—
152#480C3×D311yescharacteristic, complemented
153#398—31no—
154#327—31no—
155#327—31no—
156#324—31no—
157C3×#41—122no—
158C3×#41—122no—
159C2×C3×Q8—61no—
160C2×C3×D4—21no—
161C2×C3×D4—21no—
162C2×C3×D4—21no—
163C2×C3×D4—31no—
164C2×C3×D4—41no—
165C2×C3×D4—61no—
166C2×C3×D4—61no—
167C2×C3×D4—61no—
168C2×C3×D4#6711yescharacteristic
169C2×C3×D4C3×D411yescharacteristic
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
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×C4C22×D311yescharacteristic
180C22×C3×C4C23×C311yescharacteristic
181C2×#67—21no—
182C2×#67—21no—
183C2×#67—21no—
184C22×Dic3—21no—
185C22×Dic3—21no—
186C22×Dic3C3×D411yescharacteristic
187C22×Dic3C3×D411yescharacteristic
188#237—42no—
189#237—42no—
190C2×D12C3×D411yescharacteristic
191C2×C4×D3—21no—
192C2×Dic6—21no—
193C2×C3×C8—22no—
194C2×C3×C8—21no—
195C2×C3×C8—21no—
196C2×C3×C8—61no—
197C3×C4⋊C4—22no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—21no—
203C3×C4⋊C4—31no—
204C3×C4⋊C4—41no—
205C3×C4⋊C4—61no—
206C3×C4⋊C4—61no—
207C3×C4⋊C4—61no—
208C3×C4⋊C4—122no—
209C3×C4⋊C4#6711yescharacteristic
210C3×C4⋊C4C3×D411yescharacteristic
211C3×C22⋊C4—21no—
212C3×C22⋊C4—21no—
213C3×C22⋊C4—41no—
214C3×C22⋊C4—61no—
215C3×C22⋊C4—61no—
216C3×C22⋊C4—61no—
217#217—21no—
218(C2×D3)⋊C4—21no—
219(C2×D3)⋊C4—21no—
220C4⋊Dic3C3×D411yescharacteristic
221Dic3⋊C4—21no—
222Dic3⋊C4—21no—
223Dic3⋊C4—21no—
224Dic3⋊C4—42no—
225C2×C3⋊C8—21no—
226C22×C32—21no—
227C22×C32—21no—
228C22×C32—41no—
229C22×C32—41no—
230C22×C32—41no—
231C22×C32#12011yescharacteristic
232C22×C32C2×D811yescharacteristic
233C22×C32AGL(1,ℤ/8)11yescharacteristic
234C2×C3×D3—41no—
235C2×C3×D3—41no—
236C2×C3×D3—41no—
237C32×C4—21no—
238C32×C4—21no—
239C32×C4—41no—
240C32×C4—81no—
241C3×Dic3—22no—
242C3×Dic3—42no—
243C3×Dic3—41no—
244C3×Dic3—41no—
245C2×#41—61no—
246C22⋊Q8—61no—
247C22⋊Q8—61no—
248#121—31no—
249#121—61no—
250#121—61no—
251#121—61no—
252#121C2×C3×D311yescharacteristic
253C2×C4⋊C4—31no—
254C2×C4⋊C4—61no—
255C2×C4⋊C4C2×C3×D311yescharacteristic
256#107—21no—
257#107—61no—
258#102—21no—
259#102—61no—
260C22⋊C8—31no—
261C22⋊C8C2×C3×D311yescharacteristic
262#95—31no—
263#95—61no—
264C23×C3—21no—
265C23×C3—21no—
266C23×C3—21no—
267C23×C3—41no—
268C23×C3—61no—
269C23×C3D3×D411yescharacteristic
270C23×C3C2×C3×D411yescharacteristic
271C22×D3—21no—
272C3×Q8—122no—
273C3×D4—41no—
274C3×D4—41no—
275C3×D4—42no—
276C3×D4—41no—
277C3×D4—41no—
278C3×D4—41no—
279C3×D4—41no—
280C3×D4—81no—
281C3×D4—81no—
282C3×D4—121no—
283C3×D4—122no—
284C3×D4—121no—
285C3×D4—121no—
286C3×D4—241no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—32no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—42no—
296C2×C3×C4—42no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—61no—
304C2×C3×C4—61no—
305C2×C3×C4—62no—
306C2×C3×C4—61no—
307C2×C3×C4—61no—
308C2×C3×C4—81no—
309C2×C3×C4—81no—
310C2×C3×C4—122no—
311C2×C3×C4—122no—
312C2×C3×C4—121no—
313C2×C3×C4—121no—
314C2×C3×C4—121no—
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4C2×#6711yescharacteristic
317C2×C3×C4C2×C3×D411yescharacteristic
318C2×C3×C4C2×C3×D411yescharacteristic
319#67—42no—
320#67—41no—
321#67—41no—
322#67—81no—
323C2×Dic3—21no—
324C2×Dic3—21no—
325C2×Dic3—22no—
326C2×Dic3—21no—
327C2×Dic3—21no—
328C2×Dic3—42no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—41no—
332C2×Dic3C3×D812yes—
333D12—41no—
334C4×D3—42no—
335Dic6—42no—
336C3×C8—42no—
337C3×C8—41no—
338C3×C8—41no—
339C3×C8—121no—
340C3⋊C8—41no—
341C2×C32—21no—
342C2×C32—21no—
343C2×C32—81no—
344C2×C32#44711yescharacteristic
345C2×C32#45611yescharacteristic
346C2×C32#45811yescharacteristic
347C3×D3—81no—
348#41—122no—
349#41—122no—
350C2×Q8—61no—
351C2×D4—21no—
352C2×D4—31no—
353C2×D4—61no—
354C2×D4—61no—
355C2×D4—61no—
356C2×D4C3×#6711yescharacteristic
357C22×C4—21no—
358C22×C4—31no—
359C22×C4—31no—
360C22×C4—61no—
361C22×C4—61no—
362C22×C4—61no—
363C22×C4C22×C3×D311yescharacteristic
364C2×C8—21no—
365C2×C8—61no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—31no—
369C4⋊C4—61no—
370C4⋊C4—61no—
371C4⋊C4—61no—
372C4⋊C4—122no—
373C4⋊C4C3×#6711yescharacteristic
374C22⋊C4—21no—
375C22⋊C4—61no—
376C22⋊C4—61no—
377C22⋊C4—61no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—41no—
386C22×C3—41no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3—81no—
394C22×C3—81no—
395C22×C3—81no—
396C22×C3—121no—
397C22×C3—121no—
398C22×C3—121no—
399C22×C3D3×D811yescharacteristic
400C22×C3#91111yescharacteristic
401C22×C3#93711yescharacteristic
402C22×C3C3×#12011yescharacteristic
403C22×C3C2×C3×D811yescharacteristic
404C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
405C2×D3—41no—
406C2×D3—41no—
407C2×D3—41no—
408C3×C4—22no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—41no—
414C3×C4—41no—
415C3×C4—41no—
416C3×C4—62no—
417C3×C4—81no—
418C3×C4—82no—
419C3×C4—81no—
420C3×C4—81no—
421C3×C4—122no—
422C3×C4—121no—
423C3×C4—121no—
424Dic3—22no—
425Dic3—42no—
426Dic3—41no—
427Dic3—41no—
428C32#161011yescharacteristic, complemented, Sylow
429C23—21no—
430C23—61no—
431C23C3×D3×D411yescharacteristic
432Q8—122no—
433D4—41no—
434D4—41no—
435D4—41no—
436D4—121no—
437D4—122no—
438D4—121no—
439D4—121no—
440D4—241no—
441C2×C4—21no—
442C2×C4—32no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—61no—
448C2×C4—61no—
449C2×C4—62no—
450C2×C4—61no—
451C2×C4—61no—
452C2×C4—122no—
453C2×C4—122no—
454C2×C4—121no—
455C2×C4—121no—
456C2×C4—121no—
457C2×C4C3×D3×D411yescharacteristic
458C2×C4C2×C3×#6711yescharacteristic
459C8—41no—
460C8—121no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—41no—
469C2×C3—41no—
470C2×C3—81no—
471C2×C3—81no—
472C2×C3—161no—
473C2×C3—241no—
474C2×C3#505311yescharacteristic
475C2×C3#515611yescharacteristic
476C2×C3#520511yescharacteristic
477C2×C3C3×#44711yescharacteristic
478C2×C3C3×#45611yescharacteristic
479C2×C3C3×#45811yescharacteristic
480D3—81no—
481C22—21no—
482C22—21no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—121no—
487C22—121no—
488C22—121no—
489C22C3×D3×D811yescharacteristic
490C22C3×#91111yescharacteristic
491C22C3×#93711yescharacteristic
492C4—21no—
493C4—21no—
494C4—41no—
495C4—62no—
496C4—81no—
497C4—122no—
498C4—121no—
499C4—121no—
500C3—21no—
501C3#7116711yescharacteristic, direct product factor
502C3C3×#161011yescharacteristic, complemented
503C2—21no—
504C2—21no—
505C2—81no—
506C2—241no—
507C2C3×#505311yescharacteristic
508C2C3×#515611yescharacteristic
509C2C3×#520511yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#480C2
socleC22×C32#120
prime radicalC3×#5597C2
hypercenterC3×#480D3
hypocenterC3C3×#1610
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#480

Complements

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

NH ≅ G/Ntype
2. C32×#480C2semidirect
3. C3×#4983C2semidirect
4. C3×#4967C2semidirect
5. C3×#4537C2semidirect
6. C3×#4470C2semidirect
7. C3×#4469C2semidirect
9. #71167C3direct (N × H)
33. C3×#480D3semidirect
34. C3×#480C2×C3semidirect
36. #4983C2×C3semidirect
37. #4967C2×C3semidirect
41. #4537C2×C3semidirect
42. #4470C2×C3semidirect
43. #4469C2×C3semidirect
152. #480C3×D3semidirect
428. C32#1610semidirect
501. C3#71167direct (N × H)
502. C3C3×#1610semidirect

Maximal subgroups

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

subgroupindex
C3×#55972
C32×#4802
C3×#49832
C3×#49672
C3×#45372
C3×#44702
C3×#44692
C3×#16103
#711673