Finite Group Databasebeta

← C3×#71237 #11779607

Subgroups — C3×#71237 #11779607

Order 1152.

505 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5727C211yesmaximal, characteristic
2C32×#487C211yesmaximal, characteristic, complemented
3C3×#5091C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic
5C3×#4547C211yesmaximal, characteristic, complemented
6C3×#4459C211yesmaximal, characteristic
7C3×#4456C211yesmaximal, characteristic, complemented
8C3×#1637—31nomaximal
9#71237C311yesmaximal, characteristic, direct product factor
10C2×C3×D3×Q8—21no—
11C32×C4⋊Q8C2211yescharacteristic
12C32×C4⋊Q8C2211yescharacteristic
13C3×#946—21no—
14C3×#896—22no—
15C3×#893—21no—
16C3×#888—21no—
17C3×C4×D12C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19C32×#103—22no—
20C32×C4×C8C2211yescharacteristic
21C3×#810—21no—
22C3×#809—21no—
23C3×#808—21no—
24C3×#807—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27C3×D4×Q8—31no—
28#5727C2×C311yescharacteristic
29C3×#487—21no—
30C3×#487D311yescharacteristic, complemented
31C3×#487C2×C311yescharacteristic, complemented
32C3×#477—31no—
33C3×#476—31no—
34#5091C2×C311yescharacteristic, complemented
35#5084C2×C311yescharacteristic
36C3×#332—31no—
37C3×Q8⋊C8—31no—
38C3×D4⋊C8—31no—
39#4547C2×C311yescharacteristic, complemented
40#4459C2×C311yescharacteristic
41#4456C2×C311yescharacteristic, complemented
42C2×C32×Q8—21no—
43C2×C32×Q8—21no—
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×Dic6D411yescharacteristic
51C2×C32×C8—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4D412yes—
56C32×C42C2311yescharacteristic
57C3×(C2×D3)⋊C4—22no—
58C3×(C2×D3)⋊C4—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—22no—
62C3×Dic3⋊C4—21no—
63C3×C4×Dic3—21no—
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—21no—
71C3×C4⋊Q8—61no—
72C3×C4⋊Q8C2×D311yescharacteristic
73C3×C4⋊Q8C2×D311yescharacteristic
74C3×C4⋊Q8C22×C311yescharacteristic
75C3×C4⋊Q8C22×C311yescharacteristic
76C3×C22⋊Q8—61no—
77C3×C22⋊Q8—62no—
78C3×C4×Q8—31no—
79C3×C4×D4—31no—
80C3×C4×D4—61no—
81#946—21no—
82#896—22no—
83#893—21no—
84#888—21no—
85C4×D12C22×C311yescharacteristic
86C4×Dic6C22×C311yescharacteristic
87C3×#107—61no—
88C3×#106—61no—
89C3×C4⋊C8—31no—
90C3×C4⋊C8—31no—
91C3×#103—24no—
92C3×#103—22no—
93C3×#103—22no—
94C3×#103—61no—
95C3×#102—61no—
96C3×C4×C8—21no—
97C3×C4×C8C2×D311yescharacteristic
98C3×C4×C8C22×C311yescharacteristic
99#810—21no—
100#809—21no—
101#808—21no—
102#807—21no—
103C4⋊(C3⋊C8)C22×C311yescharacteristic
104C4⋊(C3⋊C8)C22×C311yescharacteristic
105C22×C3×D3—21no—
106C32×Q8—42no—
107C32×Q8—41no—
108C32×Q8—41no—
109C2×C32×C4—22no—
110C2×C32×C4—41no—
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C3×Dic3—21no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—21no—
117C3×D12—21no—
118C3×D12Q1612yes—
119C3×C4×D3—44no—
120C3×C4×D3—41no—
121C3×C4×D3—41no—
122C3×Dic6—21no—
123C3×Dic6—44no—
124C3×Dic6SD1612yes—
125C32×C8—41no—
126C3×C3⋊C8—41no—
127C3×C3⋊C8—41no—
128D4×Q8—31no—
129#487C3×D311yescharacteristic, complemented
130#477—31no—
131#476—31no—
132#332—31no—
133Q8⋊C8—31no—
134D4⋊C8—31no—
135C2×C3×Q8—21no—
136C2×C3×Q8—21no—
137C2×C3×Q8—22no—
138C2×C3×Q8—21no—
139C2×C3×Q8—21no—
140C2×C3×Q8—31no—
141C2×C3×Q8—41no—
142C2×C3×Q8—62no—
143C2×C3×Q8—122no—
144C2×C3×Q8—122no—
145C2×C3×D4—31no—
146C22×C3×C4—62no—
147C22×C3×C4—61no—
148D3×Q8—42no—
149D3×Q8—42no—
150C2×D12C3×D411yescharacteristic
151C2×C4×D3—22no—
152C2×C4×D3—21no—
153C2×Dic6—22no—
154C2×Dic6C3×D411yescharacteristic
155C2×C3×C8—22no—
156C2×C3×C8—21no—
157C2×C3×C8—21no—
158C2×C3×C8—61no—
159C2×C3×C8—61no—
160C3×C4⋊C4—21no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—22no—
167C3×C4⋊C4—31no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—41no—
170C3×C4⋊C4—41no—
171C3×C4⋊C4—41no—
172C3×C4⋊C4—62no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4#6712yes—
175C3×C4⋊C4C3×D412yes—
176C3×C22⋊C4—62no—
177C3×C22⋊C4—61no—
178C3×C42—21no—
179C3×C42—61no—
180C3×C42C22×D311yescharacteristic
181C3×C42C23×C311yescharacteristic
182(C2×D3)⋊C4—22no—
183(C2×D3)⋊C4—21no—
184C4⋊Dic3C3×D411yescharacteristic
185C4⋊Dic3C3×D411yescharacteristic
186Dic3⋊C4—22no—
187Dic3⋊C4—21no—
188C4×Dic3—21no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—21no—
191C22×C32#12011yescharacteristic
192C2×C3×D3—22no—
193C2×C3×D3—41no—
194C2×C3×D3—41no—
195C32×C4—21no—
196C32×C4—42no—
197C32×C4—81no—
198C32×C4C2×SD1611yescharacteristic
199C32×C4C2×Q1611yescharacteristic
200C32×C4AGL(1,ℤ/8)11yescharacteristic
201C32×C4#13711yescharacteristic
202C3×Dic3—22no—
203C3×Dic3—41no—
204C3×Dic3—41no—
205C22×Q8—61no—
206C4⋊Q8—61no—
207C4⋊Q8C2×C3×D311yescharacteristic
208C4⋊Q8C2×C3×D311yescharacteristic
209C22⋊Q8—61no—
210C22⋊Q8—62no—
211C4×Q8—31no—
212C4×D4—31no—
213C4×D4—61no—
214#107—61no—
215#106—61no—
216C4⋊C8—31no—
217C4⋊C8—31no—
218#103—22no—
219#103—61no—
220#102—61no—
221C4×C8C2×C3×D311yescharacteristic
222C23×C3—61no—
223C22×D3—21no—
224C3×Q8—32no—
225C3×Q8—44no—
226C3×Q8—42no—
227C3×Q8—42no—
228C3×Q8—41no—
229C3×Q8—41no—
230C3×Q8—41no—
231C3×Q8—41no—
232C3×Q8—61no—
233C3×Q8—81no—
234C3×Q8—81no—
235C3×Q8—124no—
236C3×D4—32no—
237C3×D4—61no—
238C2×C3×C4—22no—
239C2×C3×C4—22no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—42no—
244C2×C3×C4—42no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—61no—
248C2×C3×C4—61no—
249C2×C3×C4—61no—
250C2×C3×C4—124no—
251C2×C3×C4—121no—
252C2×C3×C4—121no—
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4C2×#6711yescharacteristic
256C2×C3×C4C2×C3×D411yescharacteristic
257C2×C3×C4C2×C3×D411yescharacteristic
258C2×C3×C4C2×C3×D411yescharacteristic
259C2×Dic3—21no—
260C2×Dic3—21no—
261C2×Dic3—21no—
262D12—21no—
263D12C3×Q1612yes—
264C4×D3—44no—
265C4×D3—41no—
266C4×D3—41no—
267Dic6—21no—
268Dic6—44no—
269Dic6C3×SD1612yes—
270C3×C8—42no—
271C3×C8—41no—
272C3×C8—41no—
273C3×C8—121no—
274C3×C8—121no—
275C3⋊C8—41no—
276C3⋊C8—41no—
277C2×C32#45011yescharacteristic
278C2×C32#45111yescharacteristic
279C2×C32#45411yescharacteristic
280C3×D3—42no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—31no—
284C2×Q8—62no—
285C2×Q8—122no—
286C2×Q8—122no—
287C2×D4—31no—
288C22×C4—62no—
289C22×C4—61no—
290C2×C8—21no—
291C2×C8—61no—
292C2×C8—61no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—31no—
297C4⋊C4—31no—
298C4⋊C4—62no—
299C4⋊C4—61no—
300C4⋊C4C3×#6712yes—
301C22⋊C4—62no—
302C22⋊C4—61no—
303C42—61no—
304C42C22×C3×D311yescharacteristic
305C22×C3—21no—
306C22×C3—62no—
307C22×C3—121no—
308C22×C3—121no—
309C22×C3#93711yescharacteristic
310C22×C3C3×#12011yescharacteristic
311C2×D3—22no—
312C2×D3—41no—
313C2×D3—41no—
314C3×C4—22no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—42no—
322C3×C4—42no—
323C3×C4—62no—
324C3×C4—82no—
325C3×C4—82no—
326C3×C4—81no—
327C3×C4—81no—
328C3×C4—121no—
329C3×C4—121no—
330C3×C4D3×SD1611yescharacteristic
331C3×C4#91411yescharacteristic
332C3×C4D3×Q1611yescharacteristic
333C3×C4#91811yescharacteristic
334C3×C4C2×C3×SD1611yescharacteristic
335C3×C4C2×C3×Q1611yescharacteristic
336C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
337C3×C4C3×#13711yescharacteristic
338Dic3—22no—
339Dic3—41no—
340Dic3—41no—
341C32#163711yescharacteristic, complemented, Sylow
342C23—61no—
343Q8—32no—
344Q8—42no—
345Q8—41no—
346Q8—41no—
347Q8—61no—
348Q8—124no—
349D4—32no—
350D4—61no—
351C2×C4—22no—
352C2×C4—41no—
353C2×C4—61no—
354C2×C4—61no—
355C2×C4—61no—
356C2×C4—124no—
357C2×C4—121no—
358C2×C4—121no—
359C2×C4C3×D3×D411yescharacteristic
360C2×C4C3×D3×D411yescharacteristic
361C2×C4C2×C3×#6711yescharacteristic
362C8—41no—
363C8—121no—
364C8—121no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—122no—
369C2×C3#506211yescharacteristic
370C2×C3#516911yescharacteristic
371C2×C3#518611yescharacteristic
372C2×C3C3×#45011yescharacteristic
373C2×C3C3×#45111yescharacteristic
374C2×C3C3×#45411yescharacteristic
375D3—42no—
376C22—62no—
377C22—121no—
378C22—121no—
379C22C3×#93711yescharacteristic
380C4—21no—
381C4—42no—
382C4—62no—
383C4—81no—
384C4—121no—
385C4—121no—
386C4C3×D3×SD1611yescharacteristic
387C4C3×#91411yescharacteristic
388C4C3×D3×Q1611yescharacteristic
389C4C3×#91811yescharacteristic
390C3—21no—
391C3#7123711yescharacteristic, direct product factor
392C3C3×#163711yescharacteristic, complemented
393C2—122no—
394C2C3×#506211yescharacteristic
395C2C3×#516911yescharacteristic
396C2C3×#518611yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#487C2
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC3×#487D3
hypocenterC3C3×#1637
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#487

Complements

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

NH ≅ G/Ntype
2. C32×#487C2semidirect
3. C3×#5091C2semidirect
5. C3×#4547C2semidirect
7. C3×#4456C2semidirect
9. #71237C3direct (N × H)
30. C3×#487D3semidirect
31. C3×#487C2×C3semidirect
34. #5091C2×C3semidirect
39. #4547C2×C3semidirect
41. #4456C2×C3semidirect
129. #487C3×D3semidirect
341. C32#1637semidirect
391. C3#71237direct (N × H)
392. C3C3×#1637semidirect

Maximal subgroups

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

subgroupindex
C3×#57272
C32×#4872
C3×#50912
C3×#50842
C3×#45472
C3×#44592
C3×#44562
C3×#16373
#712373