Finite Group Databasebeta

← C3×#71164 #11778430

Subgroups — C3×#71164 #11778430

Order 1152.

617 conjugacy classes of subgroups.

The subgroup lattice has 551 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5605C211yesmaximal, characteristic
2C32×#480C211yesmaximal, characteristic, complemented
3C3×#4992C211yesmaximal, characteristic, complemented
4C3×#4967C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic, complemented
6C3×#4470C211yesmaximal, characteristic, complemented
7C3×#4468C211yesmaximal, characteristic, complemented
8C3×#1607—31nomaximal
9#71164C311yesmaximal, characteristic, direct product factor
10C2×C3×D3×D4—21no—
11C32×#121C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic, complemented
13C3×#939—21no—
14C3×#937—21no—
15C3×#930C2211yescharacteristic
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×(C2×D3)⋊C4C2211yescharacteristic
18C3×#894—21no—
19C3×#883—21no—
20C3×#882—21no—
21C32×#107—21no—
22C32×#102—21no—
23C32×C22⋊C8C2211yescharacteristic, complemented
24C3×C3⋊#95—21no—
25C3×C3⋊#95C2211yescharacteristic, complemented
26C3×#830C2211yescharacteristic, complemented
27C3×#809—21no—
28C3×#807—21no—
29C3×#534—31no—
30#5605C2×C311yescharacteristic
31C3×#480—21no—
32C3×#480—31no—
33C3×#480D311yescharacteristic, complemented
34C3×#480C2×C311yescharacteristic, complemented
35C3×#397—31no—
36#4992C2×C311yescharacteristic, complemented
37#4967C2×C311yescharacteristic, complemented
38C3×#327—31no—
39C3×#327—31no—
40C3×#323—31no—
41#4537C2×C311yescharacteristic, complemented
42#4470C2×C311yescharacteristic, complemented
43#4468C2×C311yescharacteristic, complemented
44C23×C3×D3—21no—
45C23×C3×D3D411yescharacteristic
46C2×C32×D4—21no—
47C2×C32×D4D411yescharacteristic
48C22×C32×C4—21no—
49C22×C32×C4C2311yescharacteristic
50C2×C3×#67—21no—
51C2×C3×#67—21no—
52C2×C3×#67—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C3×D3×D4—42no—
56C3×D3×D4—42no—
57C2×C3×D12—21no—
58C2×C3×D12D411yescharacteristic
59C2×C3×C4×D3—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×(C2×D3)⋊C4—21no—
69C3×(C2×D3)⋊C4—21no—
70C3×(C2×D3)⋊C4—42no—
71C3×C4⋊Dic3D411yescharacteristic
72C3×Dic3⋊C4—21no—
73C2×C3×C3⋊C8—21no—
74#1607—31noSylow
75C22×C3×D4—61no—
76C2×D3×D4—21no—
77C3×#123—61no—
78C3×#123—61no—
79C3×#121—21no—
80C3×#121—31no—
81C3×#121—61no—
82C3×#121C2×D311yescharacteristic
83C3×#121C22×C311yescharacteristic
84C3×#120—61no—
85C3×#120—61no—
86C2×C3×C4⋊C4—21no—
87C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
88C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
89C2×C3×C22⋊C4—31no—
90C2×C3×C22⋊C4—61no—
91#939—21no—
92#937—21no—
93#930C22×C311yescharacteristic
94C2×(C2×D3)⋊C4—21no—
95C2×(C2×D3)⋊C4C22×C311yescharacteristic
96#894—21no—
97#883—21no—
98#882—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, complemented
110C3×C22⋊C8C22×C311yescharacteristic, complemented
111C3×#95—31no—
112C3×#95—61no—
113C3⋊#95—21no—
114C3⋊#95C22×C311yescharacteristic, complemented
115#830C22×C311yescharacteristic, complemented
116#809—21no—
117#807—21no—
118C23×C32—21no—
119C23×C32C2×D411yescharacteristic
120C22×C3×D3—21no—
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—42no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3—81no—
127C22×C3×D3—81no—
128C22×C3×D3D812yes—
129C32×D4—41no—
130C32×D4—41no—
131C32×D4—41no—
132C2×C32×C4—21no—
133C2×C32×C4—41no—
134C2×C32×C4—41no—
135C2×C32×C4—41no—
136C2×C32×C4—41no—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C3×#67—42no—
140C3×#67—41no—
141C3×#67—41no—
142C3×#67—81no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C3×D12—41no—
150C3×D12—42no—
151C3×C4×D3—42no—
152C32×C8—41no—
153C3×C3⋊C8—41no—
154#534—31no—
155#480—31no—
156#480C3×D311yescharacteristic, complemented
157#397—31no—
158#327—31no—
159#327—31no—
160#323—31no—
161C24×C3—31no—
162C24×C3—61no—
163C23×D3—21no—
164C23×D3C3×D411yescharacteristic
165C2×C3×D4—21no—
166C2×C3×D4—21no—
167C2×C3×D4—21no—
168C2×C3×D4—31no—
169C2×C3×D4—41no—
170C2×C3×D4—61no—
171C2×C3×D4—61no—
172C2×C3×D4—61no—
173C2×C3×D4—61no—
174C2×C3×D4—122no—
175C2×C3×D4—122no—
176C2×C3×D4#6711yescharacteristic
177C2×C3×D4C3×D411yescharacteristic
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—31no—
182C22×C3×C4—41no—
183C22×C3×C4—61no—
184C22×C3×C4—61no—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C23×C311yescharacteristic
187C2×#67—21no—
188C2×#67—21no—
189C2×#67—21no—
190C22×Dic3—21no—
191C22×Dic3C3×D411yescharacteristic
192D3×D4—42no—
193D3×D4—42no—
194C2×D12—21no—
195C2×D12C3×D411yescharacteristic
196C2×C4×D3—21no—
197C2×C3×C8—22no—
198C2×C3×C8—21no—
199C2×C3×C8—21no—
200C2×C3×C8—61no—
201C3×C4⋊C4—22no—
202C3×C4⋊C4—21no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—21no—
206C3×C4⋊C4—21no—
207C3×C4⋊C4—31no—
208C3×C4⋊C4—41no—
209C3×C4⋊C4—61no—
210C3×C4⋊C4#6711yescharacteristic
211C3×C4⋊C4C3×D411yescharacteristic
212C3×C22⋊C4—21no—
213C3×C22⋊C4—21no—
214C3×C22⋊C4—41no—
215C3×C22⋊C4—61no—
216C3×C22⋊C4—61no—
217C3×C22⋊C4—61no—
218C3×C22⋊C4—61no—
219C3×C22⋊C4—61no—
220C3×C22⋊C4—122no—
221#217—21no—
222(C2×D3)⋊C4—21no—
223(C2×D3)⋊C4—21no—
224(C2×D3)⋊C4—21no—
225(C2×D3)⋊C4—21no—
226(C2×D3)⋊C4—42no—
227C4⋊Dic3C3×D411yescharacteristic
228Dic3⋊C4—21no—
229C2×C3⋊C8—21no—
230C22×C32—21no—
231C22×C32—21no—
232C22×C32—41no—
233C22×C32—41no—
234C22×C32—41no—
235C22×C32#12011yescharacteristic
236C22×C32C2×D811yescharacteristic
237C22×C32AGL(1,ℤ/8)11yescharacteristic
238C2×C3×D3—22no—
239C2×C3×D3—41no—
240C2×C3×D3—41no—
241C2×C3×D3—42no—
242C2×C3×D3—41no—
243C2×C3×D3—41no—
244C2×C3×D3—41no—
245C2×C3×D3—81no—
246C2×C3×D3—84no—
247C32×C4—21no—
248C32×C4—21no—
249C32×C4—41no—
250C32×C4—81no—
251C3×Dic3—41no—
252C3×Dic3—41no—
253C3×Dic3—81no—
254C22×D4—61no—
255#123—61no—
256#123—61no—
257#121—31no—
258#121—61no—
259#121C2×C3×D311yescharacteristic
260#120—61no—
261#120—61no—
262C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
263C2×C22⋊C4—31no—
264C2×C22⋊C4—61no—
265#107—21no—
266#107—61no—
267#102—21no—
268#102—61no—
269C22⋊C8—31no—
270C22⋊C8C2×C3×D311yescharacteristic, complemented
271#95—31no—
272#95—61no—
273C23×C3—21no—
274C23×C3—21no—
275C23×C3—21no—
276C23×C3—32no—
277C23×C3—41no—
278C23×C3—61no—
279C23×C3—61no—
280C23×C3—61no—
281C23×C3—121no—
282C23×C3—121no—
283C23×C3—122no—
284C23×C3—241no—
285C23×C3—241no—
286C23×C3D3×D411yescharacteristic
287C23×C3C2×C3×D411yescharacteristic
288C22×D3—21no—
289C22×D3—21no—
290C22×D3—21no—
291C22×D3—42no—
292C22×D3—41no—
293C22×D3—41no—
294C22×D3—81no—
295C22×D3—81no—
296C22×D3C3×D812yes—
297C3×D4—41no—
298C3×D4—41no—
299C3×D4—42no—
300C3×D4—41no—
301C3×D4—41no—
302C3×D4—41no—
303C3×D4—41no—
304C3×D4—81no—
305C3×D4—81no—
306C3×D4—121no—
307C3×D4—122no—
308C3×D4—122no—
309C3×D4—121no—
310C3×D4—121no—
311C3×D4—241no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—41no—
317C2×C3×C4—41no—
318C2×C3×C4—41no—
319C2×C3×C4—42no—
320C2×C3×C4—42no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4—41no—
327C2×C3×C4—61no—
328C2×C3×C4—61no—
329C2×C3×C4—81no—
330C2×C3×C4—81no—
331C2×C3×C4—122no—
332C2×C3×C4—121no—
333C2×C3×C4—121no—
334C2×C3×C4—121no—
335C2×C3×C4—121no—
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4C2×#6711yescharacteristic
338C2×C3×C4C2×C3×D411yescharacteristic
339C2×C3×C4C2×C3×D411yescharacteristic
340#67—42no—
341#67—41no—
342#67—41no—
343#67—81no—
344C2×Dic3—21no—
345C2×Dic3—21no—
346C2×Dic3—41no—
347C2×Dic3—41no—
348C2×Dic3—41no—
349C2×Dic3—41no—
350D12—41no—
351D12—42no—
352C4×D3—42no—
353C3×C8—42no—
354C3×C8—41no—
355C3×C8—41no—
356C3×C8—121no—
357C3⋊C8—41no—
358C2×C32—21no—
359C2×C32—21no—
360C2×C32—81no—
361C2×C32#44711yescharacteristic
362C2×C32#45511yescharacteristic
363C2×C32#45811yescharacteristic
364C3×D3—42no—
365C3×D3—81no—
366C24—31no—
367C24—61no—
368C2×D4—21no—
369C2×D4—31no—
370C2×D4—61no—
371C2×D4—61no—
372C2×D4—61no—
373C2×D4—61no—
374C2×D4—122no—
375C2×D4—122no—
376C2×D4C3×#6711yescharacteristic
377C22×C4—21no—
378C22×C4—31no—
379C22×C4—61no—
380C22×C4—61no—
381C22×C4C22×C3×D311yescharacteristic
382C2×C8—21no—
383C2×C8—61no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—31no—
387C4⋊C4—61no—
388C4⋊C4C3×#6711yescharacteristic
389C22⋊C4—21no—
390C22⋊C4—61no—
391C22⋊C4—61no—
392C22⋊C4—61no—
393C22⋊C4—61no—
394C22⋊C4—61no—
395C22⋊C4—122no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—41no—
404C22×C3—41no—
405C22×C3—41no—
406C22×C3—41no—
407C22×C3—41no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3—62no—
412C22×C3—81no—
413C22×C3—81no—
414C22×C3—81no—
415C22×C3—122no—
416C22×C3—121no—
417C22×C3—121no—
418C22×C3—121no—
419C22×C3—121no—
420C22×C3—121no—
421C22×C3—241no—
422C22×C3—244no—
423C22×C3D3×D811yescharacteristic
424C22×C3#91111yescharacteristic
425C22×C3#93711yescharacteristic
426C22×C3C3×#12011yescharacteristic
427C22×C3C2×C3×D811yescharacteristic
428C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
429C2×D3—22no—
430C2×D3—41no—
431C2×D3—41no—
432C2×D3—42no—
433C2×D3—41no—
434C2×D3—41no—
435C2×D3—41no—
436C2×D3—81no—
437C2×D3—84no—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—41no—
444C3×C4—41no—
445C3×C4—41no—
446C3×C4—81no—
447C3×C4—82no—
448C3×C4—81no—
449C3×C4—81no—
450C3×C4—121no—
451C3×C4—121no—
452C3×C4—241no—
453Dic3—41no—
454Dic3—41no—
455Dic3—81no—
456C32#160711yescharacteristic, complemented, Sylow
457C23—21no—
458C23—32no—
459C23—61no—
460C23—61no—
461C23—61no—
462C23—121no—
463C23—121no—
464C23—122no—
465C23—241no—
466C23—241no—
467C23C3×D3×D411yescharacteristic
468D4—41no—
469D4—41no—
470D4—41no—
471D4—121no—
472D4—122no—
473D4—122no—
474D4—121no—
475D4—121no—
476D4—241no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—61no—
483C2×C4—61no—
484C2×C4—122no—
485C2×C4—121no—
486C2×C4—121no—
487C2×C4—121no—
488C2×C4—121no—
489C2×C4C3×D3×D411yescharacteristic
490C2×C4C2×C3×#6711yescharacteristic
491C8—41no—
492C8—121no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—41no—
501C2×C3—41no—
502C2×C3—81no—
503C2×C3—81no—
504C2×C3—122no—
505C2×C3—161no—
506C2×C3—241no—
507C2×C3#505311yescharacteristic
508C2×C3#515611yescharacteristic
509C2×C3#520211yescharacteristic
510C2×C3C3×#44711yescharacteristic
511C2×C3C3×#45511yescharacteristic
512C2×C3C3×#45811yescharacteristic
513D3—42no—
514D3—81no—
515C22—21no—
516C22—21no—
517C22—41no—
518C22—41no—
519C22—41no—
520C22—62no—
521C22—122no—
522C22—121no—
523C22—121no—
524C22—121no—
525C22—121no—
526C22—121no—
527C22—241no—
528C22—244no—
529C22C3×D3×D811yescharacteristic
530C22C3×#91111yescharacteristic
531C22C3×#93711yescharacteristic
532C4—21no—
533C4—21no—
534C4—41no—
535C4—81no—
536C4—121no—
537C4—121no—
538C4—241no—
539C3—21no—
540C3#7116411yescharacteristic, direct product factor
541C3C3×#160711yescharacteristic, complemented
542C2—21no—
543C2—21no—
544C2—81no—
545C2—122no—
546C2—241no—
547C2C3×#505311yescharacteristic
548C2C3×#515611yescharacteristic
549C2C3×#520211yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#480C2
socleC22×C32#120
prime radicalC3×#5605C2
hypercenterC3×#480D3
hypocenterC3C3×#1607
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×#4992C2semidirect
4. C3×#4967C2semidirect
5. C3×#4537C2semidirect
6. C3×#4470C2semidirect
7. C3×#4468C2semidirect
9. #71164C3direct (N × H)
12. C2×C32×C4⋊C4C22semidirect
23. C32×C22⋊C8C22semidirect
25. C3×C3⋊#95C22semidirect
26. C3×#830C22semidirect
33. C3×#480D3semidirect
34. C3×#480C2×C3semidirect
36. #4992C2×C3semidirect
37. #4967C2×C3semidirect
41. #4537C2×C3semidirect
42. #4470C2×C3semidirect
43. #4468C2×C3semidirect
87. C2×C3×C4⋊C4C2×D3semidirect
88. C2×C3×C4⋊C4C22×C3semidirect
109. C3×C22⋊C8C2×D3semidirect
110. C3×C22⋊C8C22×C3semidirect
114. C3⋊#95C22×C3semidirect
115. #830C22×C3semidirect
156. #480C3×D3semidirect
262. C2×C4⋊C4C2×C3×D3semidirect
270. C22⋊C8C2×C3×D3semidirect
456. C32#1607semidirect
540. C3#71164direct (N × H)
541. C3C3×#1607semidirect

Maximal subgroups

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

subgroupindex
C3×#56052
C32×#4802
C3×#49922
C3×#49672
C3×#45372
C3×#44702
C3×#44682
C3×#16073
#711643