Finite Group Databasebeta

← C3×#71160 #11779358

Subgroups — C3×#71160 #11779358

Order 1152.

560 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5577C211yesmaximal, characteristic
2C32×#477C211yesmaximal, characteristic, complemented
3C3×#5085C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic, complemented
5C3×#4535C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic, complemented
7C3×#4483C211yesmaximal, characteristic, complemented
8C3×#1631—31nomaximal
9#71160C311yesmaximal, characteristic, direct product factor
10C2×C3×#239—21no—
11C32×C4⋊Q8C2211yescharacteristic
12C32×C4×Q8C2211yescharacteristic
13C2×C3×#215—22no—
14C3×#895—22no—
15C3×#895—21no—
16C3×#874—21no—
17C3×#874C2211yescharacteristic
18C3×C4×D12—21no—
19C3×C4×D12C2211yescharacteristic
20C32×#107—21no—
21C32×C4⋊C8C2211yescharacteristic
22C32×#103—21no—
23C3×#809—21no—
24C3×#808—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27C3×#550—31no—
28#5577C2×C311yescharacteristic
29C3×#492—31no—
30C3×#477—21no—
31C3×#477D311yescharacteristic, complemented
32C3×#477C2×C311yescharacteristic, complemented
33C3×#476—31no—
34#5085C2×C311yescharacteristic, complemented
35#5084C2×C311yescharacteristic, complemented
36C3×#331—31no—
37C3×Q8⋊C8—31no—
38C3×D4⋊C8—31no—
39#4535C2×C311yescharacteristic, complemented
40#4485C2×C311yescharacteristic, complemented
41#4483C2×C311yescharacteristic, complemented
42C2×C32×Q8—21no—
43C2×C32×Q8D411yescharacteristic
44C3×#239—42no—
45C3×#239—42no—
46C2×C3×D12—22no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12—22no—
50C2×C3×D12D411yescharacteristic
51C2×C3×D12D412yes—
52C2×C3×C4×D3—22no—
53C2×C3×C4×D3—21no—
54C2×C32×C8—21no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4—21no—
57C32×C4⋊C4—21no—
58C32×C4⋊C4D411yescharacteristic
59C32×C42—21no—
60C32×C42C2311yescharacteristic
61C3×#215—44no—
62C3×(C2×D3)⋊C4—22no—
63C3×(C2×D3)⋊C4—21no—
64C3×C4⋊Dic3D411yescharacteristic
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#1631—31noSylow
68C2×C3×#41—61no—
69C2×#239—21no—
70C2×C3×SD16—62no—
71C3×C4⋊Q8—21no—
72C3×C4⋊Q8C2×D311yescharacteristic
73C3×C4⋊Q8C22×C311yescharacteristic
74C3×#127—31no—
75C3×#127—61no—
76C3×#121—62no—
77C3×#121—61no—
78C3×C4×Q8—21no—
79C3×C4×Q8C2×D311yescharacteristic
80C3×C4×Q8C22×C311yescharacteristic
81C3×C4×D4—31no—
82C3×C4×D4—61no—
83C2×#215—22no—
84#895—22no—
85#895—21no—
86#874—21no—
87#874C22×C311yescharacteristic
88C4×D12—21no—
89C4×D12C22×C311yescharacteristic
90C3×#107—22no—
91C3×#107—21no—
92C3×#107—21no—
93C3×#106—61no—
94C3×C4⋊C8—21no—
95C3×C4⋊C8—31no—
96C3×C4⋊C8C2×D311yescharacteristic
97C3×C4⋊C8C22×C311yescharacteristic
98C3×#103—22no—
99C3×#103—21no—
100C3×#103—21no—
101C3×#102—61no—
102C3×C4×C8—31no—
103#809—21no—
104#808—21no—
105C4⋊(C3⋊C8)C22×C311yescharacteristic
106C4×C3⋊C8C22×C311yescharacteristic
107C22×C3×D3—21no—
108C22×C3×D3—22no—
109C32×Q8—21no—
110C32×Q8—42no—
111C32×Q8SD1612yescomplemented
112C2×C32×C4—21no—
113C2×C32×C4—21no—
114C2×C32×C4—41no—
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C3×Dic3—21no—
119C3×D12—21no—
120C3×D12—21no—
121C3×D12—42no—
122C3×D12—44no—
123C3×D12—41no—
124C3×D12—41no—
125C3×D12—41no—
126C3×D12—41no—
127C3×D12—82no—
128C3×C4×D3—44no—
129C3×C4×D3—41no—
130C3×C4×D3—41no—
131C32×C8—41no—
132C3×C3⋊C8—22no—
133C3×C3⋊C8—41no—
134#550—31no—
135#492—31no—
136#477C3×D311yescharacteristic, complemented
137#476—31no—
138#331—31no—
139Q8⋊C8—31no—
140D4⋊C8—31no—
141C3×#41—122no—
142C3×#41—122no—
143C2×C3×Q8—21no—
144C2×C3×Q8—21no—
145C2×C3×Q8—21no—
146C2×C3×Q8—41no—
147C2×C3×Q8#6711yescharacteristic
148C2×C3×Q8C3×D411yescharacteristic
149C2×C3×D4—31no—
150C2×C3×D4—32no—
151C2×C3×D4—62no—
152C2×C3×D4—62no—
153C2×C3×D4—61no—
154C2×C3×D4—61no—
155C22×C3×C4—62no—
156C22×C3×C4—61no—
157#239—42no—
158#239—42no—
159C2×D12—22no—
160C2×D12—21no—
161C2×D12—21no—
162C2×D12—22no—
163C2×D12C3×D411yescharacteristic
164C2×D12C3×D412yes—
165C2×C4×D3—22no—
166C2×C4×D3—21no—
167C3×SD16—124no—
168C2×C3×C8—22no—
169C2×C3×C8—21no—
170C2×C3×C8—21no—
171C2×C3×C8—61no—
172C2×C3×C8—61no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—22no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—31no—
182C3×C4⋊C4—41no—
183C3×C4⋊C4—41no—
184C3×C4⋊C4#6711yescharacteristic
185C3×C4⋊C4C3×D411yescharacteristic
186C3×C22⋊C4—62no—
187C3×C22⋊C4—61no—
188C3×C42—21no—
189C3×C42—21no—
190C3×C42—21no—
191C3×C42—41no—
192C3×C42C22×D311yescharacteristic
193C3×C42C23×C311yescharacteristic
194#215—44no—
195(C2×D3)⋊C4—22no—
196(C2×D3)⋊C4—21no—
197C4⋊Dic3C3×D411yescharacteristic
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C22×C32#12011yescharacteristic
201C2×C3×D3—42no—
202C2×C3×D3—41no—
203C2×C3×D3—41no—
204C2×C3×D3—42no—
205C2×C3×D3—42no—
206C2×C3×D3—41no—
207C32×C4—22no—
208C32×C4—21no—
209C32×C4—41no—
210C32×C4—81no—
211C32×C4C2×SD1611yescharacteristic
212C32×C4#13511yescharacteristic
213C32×C4AGL(1,ℤ/8)11yescharacteristic
214C32×C4#13711yescharacteristic
215C3×Dic3—41no—
216C2×#41—61no—
217C2×SD16—62no—
218C4⋊Q8C2×C3×D311yescharacteristic
219#127—31no—
220#127—61no—
221#121—62no—
222#121—61no—
223C4×Q8C2×C3×D311yescharacteristic
224C4×D4—31no—
225C4×D4—61no—
226#107—21no—
227#106—61no—
228C4⋊C8—31no—
229C4⋊C8C2×C3×D311yescharacteristic
230#103—21no—
231#102—61no—
232C4×C8—31no—
233C23×C3—61no—
234C23×C3—62no—
235C22×D3—21no—
236C22×D3—22no—
237C3×Q8—21no—
238C3×Q8—21no—
239C3×Q8—22no—
240C3×Q8—41no—
241C3×Q8—42no—
242C3×Q8—42no—
243C3×Q8—82no—
244C3×Q8#21512yescomplemented
245C3×Q8C3×SD1612yescomplemented
246C3×D4—61no—
247C3×D4—61no—
248C3×D4—122no—
249C3×D4—124no—
250C3×D4—121no—
251C3×D4—121no—
252C3×D4—121no—
253C3×D4—121no—
254C3×D4—242no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—42no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—61no—
268C2×C3×C4—124no—
269C2×C3×C4—121no—
270C2×C3×C4—121no—
271C2×C3×C4D3×D411yescharacteristic
272C2×C3×C4D3×D411yescharacteristic
273C2×C3×C4C2×#6711yescharacteristic
274C2×C3×C4C2×C3×D411yescharacteristic
275C2×C3×C4C2×C3×D411yescharacteristic
276C2×C3×C4C2×C3×D411yescharacteristic
277C2×Dic3—21no—
278D12—21no—
279D12—21no—
280D12—42no—
281D12—44no—
282D12—41no—
283D12—41no—
284D12—41no—
285D12—41no—
286D12—82no—
287C4×D3—44no—
288C4×D3—41no—
289C4×D3—41no—
290C3×C8—42no—
291C3×C8—41no—
292C3×C8—41no—
293C3×C8—62no—
294C3×C8—121no—
295C3⋊C8—22no—
296C3⋊C8—41no—
297C2×C32#45011yescharacteristic
298C2×C32#45211yescharacteristic
299C2×C32#45311yescharacteristic
300C3×D3—81no—
301C3×D3—82no—
302#41—122no—
303#41—122no—
304C2×Q8—21no—
305C2×Q8C3×#6711yescharacteristic
306C2×D4—31no—
307C2×D4—32no—
308C2×D4—62no—
309C2×D4—62no—
310C2×D4—61no—
311C2×D4—61no—
312C22×C4—62no—
313C22×C4—61no—
314SD16—124no—
315C2×C8—21no—
316C2×C8—61no—
317C2×C8—61no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—31no—
322C4⋊C4C3×#6711yescharacteristic
323C22⋊C4—62no—
324C22⋊C4—61no—
325C42—21no—
326C42C22×C3×D311yescharacteristic
327C22×C3—21no—
328C22×C3—121no—
329C22×C3—122no—
330C22×C3—122no—
331C22×C3—121no—
332C22×C3—122no—
333C22×C3—121no—
334C22×C3#93711yescharacteristic
335C22×C3C3×#12011yescharacteristic
336C2×D3—42no—
337C2×D3—41no—
338C2×D3—41no—
339C2×D3—42no—
340C2×D3—42no—
341C2×D3—41no—
342C3×C4—21no—
343C3×C4—22no—
344C3×C4—22no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—41no—
351C3×C4—42no—
352C3×C4—41no—
353C3×C4—41no—
354C3×C4—81no—
355C3×C4—82no—
356C3×C4—81no—
357C3×C4—81no—
358C3×C4—121no—
359C3×C4#91811yescharacteristic
360C3×C4#91911yescharacteristic
361C3×C4C2×#21511yescharacteristic
362C3×C4#94911yescharacteristic
363C3×C4C2×C3×SD1611yescharacteristic
364C3×C4C3×#13511yescharacteristic
365C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
366C3×C4C3×#13711yescharacteristic
367Dic3—41no—
368C32#163111yescharacteristic, complemented, Sylow
369C23—61no—
370C23—62no—
371Q8—21no—
372Q8—42no—
373Q8C3×#21512yescomplemented
374D4—61no—
375D4—61no—
376D4—122no—
377D4—124no—
378D4—121no—
379D4—121no—
380D4—121no—
381D4—121no—
382D4—242no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—41no—
386C2×C4—61no—
387C2×C4—124no—
388C2×C4—121no—
389C2×C4—121no—
390C2×C4C3×D3×D411yescharacteristic
391C2×C4C3×D3×D411yescharacteristic
392C2×C4C2×C3×#6711yescharacteristic
393C8—41no—
394C8—62no—
395C8—121no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—241no—
400C2×C3—242no—
401C2×C3#504611yescharacteristic
402C2×C3#518711yescharacteristic
403C2×C3#519811yescharacteristic
404C2×C3C3×#45011yescharacteristic
405C2×C3C3×#45211yescharacteristic
406C2×C3C3×#45311yescharacteristic
407D3—81no—
408D3—82no—
409C22—121no—
410C22—122no—
411C22—122no—
412C22—121no—
413C22—122no—
414C22—121no—
415C22C3×#93711yescharacteristic
416C4—21no—
417C4—22no—
418C4—41no—
419C4—81no—
420C4—121no—
421C4C3×#91811yescharacteristic
422C4C3×#91911yescharacteristic
423C4C2×C3×#21511yescharacteristic
424C4C3×#94911yescharacteristic
425C3—21no—
426C3#7116011yescharacteristic, direct product factor
427C3C3×#163111yescharacteristic, complemented
428C2—241no—
429C2—242no—
430C2C3×#504611yescharacteristic
431C2C3×#518711yescharacteristic
432C2C3×#519811yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#477C2
socleC22×C32#120
prime radicalC3×#5577C2
hypercenterC3×#477D3
hypocenterC3C3×#1631
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#477

Complements

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

NH ≅ G/Ntype
2. C32×#477C2semidirect
3. C3×#5085C2semidirect
4. C3×#5084C2semidirect
5. C3×#4535C2semidirect
6. C3×#4485C2semidirect
7. C3×#4483C2semidirect
9. #71160C3direct (N × H)
31. C3×#477D3semidirect
32. C3×#477C2×C3semidirect
34. #5085C2×C3semidirect
35. #5084C2×C3semidirect
39. #4535C2×C3semidirect
40. #4485C2×C3semidirect
41. #4483C2×C3semidirect
111. C32×Q8SD16semidirect
136. #477C3×D3semidirect
244. C3×Q8#215semidirect
245. C3×Q8C3×SD16semidirect
368. C32#1631semidirect
373. Q8C3×#215semidirect
426. C3#71160direct (N × H)
427. C3C3×#1631semidirect

Maximal subgroups

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

subgroupindex
C3×#55772
C32×#4772
C3×#50852
C3×#50842
C3×#45352
C3×#44852
C3×#44832
C3×#16313
#711603