Finite Group Databasebeta

← C3×#71024 #11781651

Subgroups — C3×#71024 #11781651

Order 1152.

400 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#460C211yesmaximal, characteristic
2C3×#5076C211yesmaximal, characteristic
3C3×#5024C211yesmaximal, characteristic, complemented
4C3×#5020C211yesmaximal, characteristic, complemented
5C3×#4544C211yesmaximal, characteristic
6C3×#4486C211yesmaximal, characteristic, complemented
7C3×#4479C211yesmaximal, characteristic, complemented
8C3×#1686—31nomaximal
9#71024C311yesmaximal, characteristic, direct product factor
10C2×C32×SD16—21no—
11C32×#127C2211yescharacteristic
12C32×C4×Q8C2211yescharacteristic
13C2×C3×#214—21no—
14C2×C3×#214—21no—
15C3×#869C2211yescharacteristic
16C32×C4⋊C8C2211yescharacteristic
17C32×#102—21no—
18C3×#835—21no—
19C3×#808—21no—
20C3×C4⋊(C3⋊C8)—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×#803—21no—
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#492—31no—
26C3×#475—31no—
27C3×#460—21no—
28C3×#460D311yescharacteristic
29C3×#460C2×C311yescharacteristic
30C3×#446—31no—
31#5076C2×C311yescharacteristic
32#5024C2×C311yescharacteristic, complemented
33#5020C2×C311yescharacteristic, complemented
34C3×#335—31no—
35C3×#332—31no—
36C3×#331—31no—
37#4544C2×C311yescharacteristic
38#4486C2×C311yescharacteristic, complemented
39#4479C2×C311yescharacteristic, complemented
40C2×C32×Q8D411yescharacteristic
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C3×Dic6—21no—
45C32×SD16—42no—
46C2×C32×C8—21no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4D411yescharacteristic
49C32×C42—21no—
50C32×C42C2311yescharacteristic
51C3×#214—42no—
52C3×#214—42no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8D411yescharacteristic
58C2×C3×C3⋊C8D411yescharacteristic
59#1686—31noSylow
60C2×C3×SD16—22no—
61C2×C3×SD16—21no—
62C2×C3×SD16—21no—
63C2×C3×SD16—61no—
64C2×C3×SD16—61no—
65C3×C4⋊Q8—31no—
66C3×#127—21no—
67C3×#127C2×D311yescharacteristic
68C3×#127C22×C311yescharacteristic
69C3×C4×Q8—21no—
70C3×C4×Q8C2×D311yescharacteristic
71C3×C4×Q8C22×C311yescharacteristic
72C2×#214—21no—
73C2×#214—21no—
74#869C22×C311yescharacteristic
75C3×#106—61no—
76C3×C4⋊C8—21no—
77C3×C4⋊C8—31no—
78C3×C4⋊C8—31no—
79C3×C4⋊C8—61no—
80C3×C4⋊C8C2×D311yescharacteristic
81C3×C4⋊C8C22×C311yescharacteristic
82C3×#103—61no—
83C3×#102—22no—
84C3×#102—21no—
85C3×#102—21no—
86C3×#97—61no—
87C3×C4×C8—31no—
88#835—21no—
89#808—21no—
90C4⋊(C3⋊C8)—21no—
91C4⋊(C3⋊C8)C22×C311yescharacteristic
92C4⋊(C3⋊C8)C22×C311yescharacteristic
93#803—21no—
94C4×C3⋊C8C22×C311yescharacteristic
95C23×C32—41no—
96C32×Q8—21no—
97C32×Q8—21no—
98C32×D4—41no—
99C32×D4—41no—
100C32×D4—41no—
101C32×D4—41no—
102C32×D4—81no—
103C2×C32×C4—21no—
104C2×C32×C4—21no—
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C2×C3×Dic3—41no—
109C3×Dic6—41no—
110C3×Dic6—41no—
111C32×C8—41no—
112C3×C3⋊C8—21no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8—41no—
115C3×C3⋊C8SD1612yescomplemented
116#492—31no—
117#475—31no—
118#460C3×D311yescharacteristic
119#446—31no—
120#335—31no—
121#332—31no—
122#331—31no—
123C2×C3×Q8—21no—
124C2×C3×Q8—61no—
125C2×C3×Q8#6711yescharacteristic
126C2×C3×Q8C3×D411yescharacteristic
127C2×C3×D4—22no—
128C2×C3×D4—21no—
129C2×C3×D4—21no—
130C2×C3×D4—21no—
131C2×C3×D4—21no—
132C2×C3×D4—21no—
133C2×C3×D4—21no—
134C2×C3×D4—41no—
135C2×C3×D4—41no—
136C2×Dic6—21no—
137C3×SD16—44no—
138C3×SD16—42no—
139C3×SD16—42no—
140C3×SD16—122no—
141C3×SD16—122no—
142C2×C3×C8—22no—
143C2×C3×C8—21no—
144C2×C3×C8—21no—
145C2×C3×C8—31no—
146C2×C3×C8—31no—
147C2×C3×C8—61no—
148C2×C3×C8—61no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—41no—
153C3×C4⋊C4—61no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4#6711yescharacteristic
156C3×C4⋊C4C3×D411yescharacteristic
157C3×C42—21no—
158C3×C42—21no—
159C3×C42—21no—
160C3×C42—41no—
161C3×C42C22×D311yescharacteristic
162C3×C42C23×C311yescharacteristic
163#214—42no—
164#214—42no—
165C4⋊Dic3—21no—
166C4⋊Dic3—21no—
167C2×C3⋊C8—21no—
168C2×C3⋊C8—21no—
169C2×C3⋊C8C3×D411yescharacteristic
170C2×C3⋊C8C3×D411yescharacteristic
171C22×C32—81no—
172C22×C32—81no—
173C22×C32—81no—
174C22×C32#12111yescharacteristic
175C32×C4—21no—
176C32×C4—41no—
177C32×C4—41no—
178C32×C4C2×SD1611yescharacteristic
179C32×C4AGL(1,ℤ/8)11yescharacteristic
180C32×C4AGL(1,ℤ/8)11yescharacteristic
181C32×C4#13711yescharacteristic
182C3×Dic3—81no—
183C2×SD16—21no—
184C2×SD16—61no—
185C2×SD16—61no—
186C4⋊Q8—31no—
187#127C2×C3×D311yescharacteristic
188C4×Q8C2×C3×D311yescharacteristic
189#106—61no—
190C4⋊C8—31no—
191C4⋊C8—31no—
192C4⋊C8—61no—
193C4⋊C8C2×C3×D311yescharacteristic
194#103—61no—
195#102—21no—
196#97—61no—
197C4×C8—31no—
198C23×C3—42no—
199C23×C3—41no—
200C23×C3—41no—
201C3×Q8—22no—
202C3×Q8—21no—
203C3×Q8—21no—
204C3×Q8—21no—
205C3×Q8—21no—
206C3×Q8—41no—
207C3×Q8—121no—
208C3×Q8—121no—
209C3×D4—42no—
210C3×D4—42no—
211C3×D4—41no—
212C3×D4—41no—
213C3×D4—41no—
214C3×D4—41no—
215C3×D4—41no—
216C3×D4—41no—
217C3×D4—41no—
218C3×D4—41no—
219C3×D4—81no—
220C3×D4—81no—
221C3×D4—81no—
222C3×D4—81no—
223C3×D4—82no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—41no—
232C2×C3×C4—41no—
233C2×C3×C4—121no—
234C2×C3×C4D3×D411yescharacteristic
235C2×C3×C4#23711yescharacteristic
236C2×C3×C4C2×#6711yescharacteristic
237C2×C3×C4C2×C3×D411yescharacteristic
238C2×C3×C4C2×C3×D411yescharacteristic
239C2×C3×C4C3×#4111yescharacteristic
240C2×Dic3—41no—
241Dic6—41no—
242Dic6—41no—
243C3×C8—32no—
244C3×C8—42no—
245C3×C8—41no—
246C3×C8—41no—
247C3×C8—61no—
248C3×C8—121no—
249C3×C8—121no—
250C3⋊C8—21no—
251C3⋊C8—41no—
252C3⋊C8—41no—
253C3⋊C8C3×SD1612yescomplemented
254C2×C32—161no—
255C2×C32#46011yescharacteristic
256C2×C32#46811yescharacteristic
257C2×C32#47111yescharacteristic
258C2×Q8—61no—
259C2×Q8C3×#6711yescharacteristic
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263SD16—42no—
264SD16—122no—
265SD16—122no—
266C2×C8—21no—
267C2×C8—31no—
268C2×C8—31no—
269C2×C8—61no—
270C2×C8—61no—
271C4⋊C4—21no—
272C4⋊C4—61no—
273C4⋊C4—61no—
274C4⋊C4C3×#6711yescharacteristic
275C42—21no—
276C42C22×C3×D311yescharacteristic
277C22×C3—21no—
278C22×C3—82no—
279C22×C3—82no—
280C22×C3—82no—
281C22×C3—81no—
282C22×C3—81no—
283C22×C3—81no—
284C22×C3—81no—
285C22×C3—81no—
286C22×C3—81no—
287C22×C3#93911yescharacteristic
288C22×C3C3×#12111yescharacteristic
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—41no—
296C3×C4—42no—
297C3×C4—41no—
298C3×C4—41no—
299C3×C4—41no—
300C3×C4—41no—
301C3×C4—81no—
302C3×C4—241no—
303C3×C4D3×SD1611yescharacteristic
304C3×C4#91411yescharacteristic
305C3×C4#93211yescharacteristic
306C3×C4#95111yescharacteristic
307C3×C4C2×C3×SD1611yescharacteristic
308C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
309C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
310C3×C4C3×#13711yescharacteristic
311Dic3—81no—
312C32#168611yescharacteristic, complemented, Sylow
313C23—41no—
314Q8—21no—
315Q8—21no—
316Q8—121no—
317Q8—121no—
318D4—41no—
319D4—41no—
320D4—41no—
321D4—41no—
322D4—81no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—121no—
326C2×C4C3×D3×D411yescharacteristic
327C2×C4C3×#23711yescharacteristic
328C2×C4C2×C3×#6711yescharacteristic
329C8—32no—
330C8—41no—
331C8—61no—
332C8—121no—
333C8—121no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—162no—
338C2×C3—161no—
339C2×C3—161no—
340C2×C3#504211yescharacteristic
341C2×C3#516311yescharacteristic
342C2×C3#520011yescharacteristic
343C2×C3C3×#46011yescharacteristic
344C2×C3C3×#46811yescharacteristic
345C2×C3C3×#47111yescharacteristic
346C22—81no—
347C22—81no—
348C22—81no—
349C22C3×#93911yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—241no—
354C4C3×D3×SD1611yescharacteristic
355C4C3×#91411yescharacteristic
356C4C3×#93211yescharacteristic
357C4C3×#95111yescharacteristic
358C3—21no—
359C3#7102411yescharacteristic, direct product factor
360C3C3×#168611yescharacteristic, complemented
361C2—161no—
362C2C3×#504211yescharacteristic
363C2C3×#516311yescharacteristic
364C2C3×#520011yescharacteristic
subgroupG/H
centerC22×C3#939
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#460C2
socleC22×C32#121
prime radicalC32×#127C22
hypercenterC3×#460D3
hypocenterC3C3×#1686
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#460

Complements

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

NH ≅ G/Ntype
3. C3×#5024C2semidirect
4. C3×#5020C2semidirect
6. C3×#4486C2semidirect
7. C3×#4479C2semidirect
9. #71024C3direct (N × H)
32. #5024C2×C3semidirect
33. #5020C2×C3semidirect
38. #4486C2×C3semidirect
39. #4479C2×C3semidirect
115. C3×C3⋊C8SD16semidirect
253. C3⋊C8C3×SD16semidirect
312. C32#1686semidirect
359. C3#71024direct (N × H)
360. C3C3×#1686semidirect

Maximal subgroups

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

subgroupindex
C32×#4602
C3×#50762
C3×#50242
C3×#50202
C3×#45442
C3×#44862
C3×#44792
C3×#16863
#710243