Finite Group Databasebeta

← C3×#71163 #11779610

Subgroups — C3×#71163 #11779610

Order 1152.

504 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×D12C211yesmaximal, characteristic
2C32×#477C211yesmaximal, characteristic, complemented
3C3×#5084C211yesmaximal, characteristic
4C3×#5079C211yesmaximal, characteristic, complemented
5C3×#4535C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic
7C3×#4482C211yesmaximal, characteristic, complemented
8C3×#1637—31nomaximal
9#71163C311yesmaximal, characteristic, direct product factor
10C2×C3×D3×Q8—21no—
11C32×C4⋊Q8C2211yescharacteristic
12C32×C4×Q8C2211yescharacteristic
13C3×#897—21no—
14C3×#897—22no—
15C3×C4×D12—21no—
16C3×C4×D12C2211yescharacteristic
17C3×#869—21no—
18C3×#869C2211yescharacteristic
19C32×#107—21no—
20C32×C4⋊C8C2211yescharacteristic
21C32×#103—21no—
22C3×#835—22no—
23C3×#809—21no—
24C3×#808—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27C3×D4×Q8—31no—
28Q8×D12C2×C311yescharacteristic
29C3×#487—31no—
30C3×#477—21no—
31C3×#477D311yescharacteristic, complemented
32C3×#477C2×C311yescharacteristic, complemented
33C3×#476—31no—
34#5084C2×C311yescharacteristic
35#5079C2×C311yescharacteristic, complemented
36C3×#332—31no—
37C3×Q8⋊C8—31no—
38C3×D4⋊C8—31no—
39#4535C2×C311yescharacteristic, complemented
40#4483C2×C311yescharacteristic
41#4482C2×C311yescharacteristic, complemented
42C2×C32×Q8—21no—
43C2×C32×Q8D411yescharacteristic
44C3×D3×Q8—42no—
45C3×D3×Q8—42no—
46C2×C3×D12D411yescharacteristic
47C2×C3×C4×D3—22no—
48C2×C3×C4×D3—21no—
49C2×C3×Dic6—22no—
50C2×C3×Dic6—21no—
51C2×C32×C8—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4D411yescharacteristic
56C32×C42—21no—
57C32×C42C2311yescharacteristic
58C3×(C2×D3)⋊C4—22no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3—22no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3D412yes—
63C3×C4⋊Dic3D411yescharacteristic
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66#1637—31noSylow
67C22×C3×Q8—61no—
68C2×D3×Q8—21no—
69C3×C4⋊Q8—21no—
70C3×C4⋊Q8—31no—
71C3×C4⋊Q8—61no—
72C3×C4⋊Q8C2×D311yescharacteristic
73C3×C4⋊Q8C22×C311yescharacteristic
74C3×C22⋊Q8—62no—
75C3×C22⋊Q8—61no—
76C3×C4×Q8—21no—
77C3×C4×Q8C2×D311yescharacteristic
78C3×C4×Q8C22×C311yescharacteristic
79C3×C4×D4—31no—
80C3×C4×D4—61no—
81#897—21no—
82#897—22no—
83C4×D12—21no—
84C4×D12C22×C311yescharacteristic
85#869—21no—
86#869C22×C311yescharacteristic
87C3×#107—22no—
88C3×#107—21no—
89C3×#107—21no—
90C3×#106—61no—
91C3×C4⋊C8—21no—
92C3×C4⋊C8—31no—
93C3×C4⋊C8C2×D311yescharacteristic
94C3×C4⋊C8C22×C311yescharacteristic
95C3×#103—22no—
96C3×#103—21no—
97C3×#103—21no—
98C3×#103—62no—
99C3×#102—61no—
100C3×C4×C8—31no—
101#835—22no—
102#809—21no—
103#808—21no—
104C4⋊(C3⋊C8)C22×C311yescharacteristic
105C4×C3⋊C8C22×C311yescharacteristic
106C22×C3×D3—21no—
107C32×Q8—21no—
108C32×Q8—42no—
109C32×Q8SD1612yes—
110C2×C32×C4—21no—
111C2×C32×C4—21no—
112C2×C32×C4—41no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C3×Dic3—21no—
117C2×C3×Dic3—22no—
118C3×D12—21no—
119C3×D12Q1612yes—
120C3×C4×D3—44no—
121C3×C4×D3—41no—
122C3×C4×D3—41no—
123C3×Dic6—44no—
124C3×Dic6—41no—
125C3×Dic6—41no—
126C32×C8—41no—
127C3×C3⋊C8—41no—
128C3×C3⋊C8—41no—
129D4×Q8—31no—
130#487—31no—
131#477C3×D311yescharacteristic, complemented
132#476—31no—
133#332—31no—
134Q8⋊C8—31no—
135D4⋊C8—31no—
136C2×C3×Q8—21no—
137C2×C3×Q8—21no—
138C2×C3×Q8—21no—
139C2×C3×Q8—41no—
140C2×C3×Q8—62no—
141C2×C3×Q8—61no—
142C2×C3×Q8—122no—
143C2×C3×Q8—122no—
144C2×C3×Q8#6711yescharacteristic
145C2×C3×Q8C3×D411yescharacteristic
146C2×C3×D4—31no—
147C22×C3×C4—62no—
148C22×C3×C4—61no—
149D3×Q8—42no—
150D3×Q8—42no—
151C2×D12C3×D411yescharacteristic
152C2×C4×D3—22no—
153C2×C4×D3—21no—
154C2×Dic6—22no—
155C2×Dic6—21no—
156C2×C3×C8—22no—
157C2×C3×C8—21no—
158C2×C3×C8—21no—
159C2×C3×C8—61no—
160C2×C3×C8—61no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—22no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—32no—
170C3×C4⋊C4—31no—
171C3×C4⋊C4—41no—
172C3×C4⋊C4—41no—
173C3×C4⋊C4—62no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4#6711yescharacteristic
176C3×C4⋊C4C3×D411yescharacteristic
177C3×C22⋊C4—62no—
178C3×C22⋊C4—61no—
179C3×C42—21no—
180C3×C42—21no—
181C3×C42—21no—
182C3×C42—41no—
183C3×C42C22×D311yescharacteristic
184C3×C42C23×C311yescharacteristic
185(C2×D3)⋊C4—22no—
186(C2×D3)⋊C4—21no—
187C4⋊Dic3—22no—
188C4⋊Dic3—21no—
189C4⋊Dic3C3×D411yescharacteristic
190C4⋊Dic3C3×D412yes—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—21no—
193C22×C32#12011yescharacteristic
194C2×C3×D3—22no—
195C2×C3×D3—41no—
196C2×C3×D3—41no—
197C32×C4—22no—
198C32×C4—21no—
199C32×C4—41no—
200C32×C4—81no—
201C32×C4C2×SD1611yescharacteristic
202C32×C4C2×Q1611yescharacteristic
203C32×C4AGL(1,ℤ/8)11yescharacteristic
204C32×C4#13711yescharacteristic
205C3×Dic3—41no—
206C3×Dic3—42no—
207C22×Q8—61no—
208C4⋊Q8—31no—
209C4⋊Q8—61no—
210C4⋊Q8C2×C3×D311yescharacteristic
211C22⋊Q8—62no—
212C22⋊Q8—61no—
213C4×Q8C2×C3×D311yescharacteristic
214C4×D4—31no—
215C4×D4—61no—
216#107—21no—
217#106—61no—
218C4⋊C8—31no—
219C4⋊C8C2×C3×D311yescharacteristic
220#103—21no—
221#103—62no—
222#102—61no—
223C4×C8—31no—
224C23×C3—61no—
225C22×D3—21no—
226C3×Q8—21no—
227C3×Q8—21no—
228C3×Q8—22no—
229C3×Q8—41no—
230C3×Q8—42no—
231C3×Q8—42no—
232C3×Q8—82no—
233C3×Q8—124no—
234C3×Q8—121no—
235C3×Q8—121no—
236C3×Q8#21512yes—
237C3×Q8C3×SD1612yes—
238C3×D4—32no—
239C3×D4—61no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—42no—
250C2×C3×C4—41no—
251C2×C3×C4—41no—
252C2×C3×C4—62no—
253C2×C3×C4—61no—
254C2×C3×C4—124no—
255C2×C3×C4—121no—
256C2×C3×C4—121no—
257C2×C3×C4D3×D411yescharacteristic
258C2×C3×C4D3×D411yescharacteristic
259C2×C3×C4C2×#6711yescharacteristic
260C2×C3×C4C2×C3×D411yescharacteristic
261C2×C3×C4C2×C3×D411yescharacteristic
262C2×C3×C4C2×C3×D411yescharacteristic
263C2×Dic3—21no—
264C2×Dic3—22no—
265D12—21no—
266D12C3×Q1612yes—
267C4×D3—44no—
268C4×D3—41no—
269C4×D3—41no—
270Dic6—44no—
271Dic6—41no—
272Dic6—41no—
273C3×C8—42no—
274C3×C8—41no—
275C3×C8—41no—
276C3×C8—121no—
277C3×C8—121no—
278C3⋊C8—41no—
279C3⋊C8—41no—
280C2×C32#45011yescharacteristic
281C2×C32#45111yescharacteristic
282C2×C32#45411yescharacteristic
283C3×D3—42no—
284C2×Q8—21no—
285C2×Q8—62no—
286C2×Q8—61no—
287C2×Q8—122no—
288C2×Q8—122no—
289C2×Q8C3×#6711yescharacteristic
290C2×D4—31no—
291C22×C4—62no—
292C22×C4—61no—
293C2×C8—21no—
294C2×C8—61no—
295C2×C8—61no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—32no—
300C4⋊C4—31no—
301C4⋊C4—62no—
302C4⋊C4—61no—
303C4⋊C4C3×#6711yescharacteristic
304C22⋊C4—62no—
305C22⋊C4—61no—
306C42—21no—
307C42C22×C3×D311yescharacteristic
308C22×C3—21no—
309C22×C3—62no—
310C22×C3—121no—
311C22×C3—121no—
312C22×C3#93711yescharacteristic
313C22×C3C3×#12011yescharacteristic
314C2×D3—22no—
315C2×D3—41no—
316C2×D3—41no—
317C3×C4—21no—
318C3×C4—22no—
319C3×C4—22no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—41no—
326C3×C4—42no—
327C3×C4—41no—
328C3×C4—41no—
329C3×C4—81no—
330C3×C4—82no—
331C3×C4—81no—
332C3×C4—81no—
333C3×C4—122no—
334C3×C4—121no—
335C3×C4D3×Q1611yescharacteristic
336C3×C4#91811yescharacteristic
337C3×C4C2×#21511yescharacteristic
338C3×C4#94911yescharacteristic
339C3×C4C2×C3×SD1611yescharacteristic
340C3×C4C2×C3×Q1611yescharacteristic
341C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
342C3×C4C3×#13711yescharacteristic
343Dic3—41no—
344Dic3—42no—
345C32#163711yescharacteristic, complemented, Sylow
346C23—61no—
347Q8—21no—
348Q8—42no—
349Q8—124no—
350Q8—121no—
351Q8—121no—
352Q8C3×#21512yes—
353D4—32no—
354D4—61no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—41no—
358C2×C4—62no—
359C2×C4—61no—
360C2×C4—124no—
361C2×C4—121no—
362C2×C4—121no—
363C2×C4C3×D3×D411yescharacteristic
364C2×C4C3×D3×D411yescharacteristic
365C2×C4C2×C3×#6711yescharacteristic
366C8—41no—
367C8—121no—
368C8—121no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—122no—
373C2×C3#504611yescharacteristic
374C2×C3#518611yescharacteristic
375C2×C3#520111yescharacteristic
376C2×C3C3×#45011yescharacteristic
377C2×C3C3×#45111yescharacteristic
378C2×C3C3×#45411yescharacteristic
379D3—42no—
380C22—62no—
381C22—121no—
382C22—121no—
383C22C3×#93711yescharacteristic
384C4—21no—
385C4—22no—
386C4—41no—
387C4—81no—
388C4—122no—
389C4—121no—
390C4C3×D3×Q1611yescharacteristic
391C4C3×#91811yescharacteristic
392C4C2×C3×#21511yescharacteristic
393C4C3×#94911yescharacteristic
394C3—21no—
395C3#7116311yescharacteristic, direct product factor
396C3C3×#163711yescharacteristic, complemented
397C2—122no—
398C2C3×#504611yescharacteristic
399C2C3×#518611yescharacteristic
400C2C3×#520111yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#477C2
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC3×#477D3
hypocenterC3C3×#1637
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
4. C3×#5079C2semidirect
5. C3×#4535C2semidirect
7. C3×#4482C2semidirect
9. #71163C3direct (N × H)
31. C3×#477D3semidirect
32. C3×#477C2×C3semidirect
35. #5079C2×C3semidirect
39. #4535C2×C3semidirect
41. #4482C2×C3semidirect
131. #477C3×D3semidirect
345. C32#1637semidirect
395. C3#71163direct (N × H)
396. C3C3×#1637semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×D122
C32×#4772
C3×#50842
C3×#50792
C3×#45352
C3×#44832
C3×#44822
C3×#16373
#711633