Finite Group Databasebeta

← C3×#71273 #11781648

Subgroups — C3×#71273 #11781648

Order 1152.

407 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×#492C211yesmaximal, characteristic
2C3×#5094C211yesmaximal, characteristic, complemented
3C3×#5075C211yesmaximal, characteristic
4C3×#4679C211yesmaximal, characteristic, complemented
5C3×#4547C211yesmaximal, characteristic, complemented
6C3×#4544C211yesmaximal, characteristic
7C3×#4458C211yesmaximal, characteristic, complemented
8C3×#1686—31nomaximal
9#71273C311yesmaximal, characteristic, direct product factor
10C2×C32×SD16—21no—
11C2×C32×SD16—21no—
12C32×C4⋊Q8C2211yescharacteristic
13C32×#127C2211yescharacteristic
14C2×C3×#214—21no—
15C3×C4×Dic6C2211yescharacteristic
16C32×C4×C8C2211yescharacteristic
17C3×#832—21no—
18C3×#815—21no—
19C3×Dic3⋊C8—21no—
20C3×#810—21no—
21C3×#808—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×#492—21no—
26C3×#492D311yescharacteristic
27C3×#492C2×C311yescharacteristic
28C3×#475—31no—
29C3×#460—31no—
30C3×#446—31no—
31#5094C2×C311yescharacteristic, complemented
32#5075C2×C311yescharacteristic
33#4679C2×C311yescharacteristic, complemented
34C3×#335—31no—
35C3×#332—31no—
36C3×#331—31no—
37#4547C2×C311yescharacteristic, complemented
38#4544C2×C311yescharacteristic
39#4458C2×C311yescharacteristic, complemented
40C2×C32×Q8—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C3×Dic6D411yescharacteristic
45C32×SD16—42no—
46C32×SD16—42no—
47C2×C32×C8D411yescharacteristic
48C2×C32×C8D411yescharacteristic
49C32×C4⋊C4—21no—
50C32×C4⋊C4—21no—
51C32×C42C2311yescharacteristic
52C3×#214—42no—
53C3×C4⋊Dic3D411yescharacteristic
54C3×Dic3⋊C4—21no—
55C3×C4×Dic3—21no—
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8—21no—
58C2×C3×C3⋊C8—21no—
59#1686—31noSylow
60C2×C3×SD16—22no—
61C2×C3×SD16—22no—
62C2×C3×SD16—21no—
63C2×C3×SD16—21no—
64C2×C3×SD16—21no—
65C2×C3×SD16—21no—
66C2×C3×SD16—61no—
67C3×C4⋊Q8—21no—
68C3×C4⋊Q8C2×D311yescharacteristic
69C3×C4⋊Q8C22×C311yescharacteristic
70C3×#127—21no—
71C3×#127C2×D311yescharacteristic
72C3×#127C22×C311yescharacteristic
73C3×C4×Q8—31no—
74C2×#214—21no—
75C4×Dic6C22×C311yescharacteristic
76C3×#106—61no—
77C3×C4⋊C8—31no—
78C3×C4⋊C8—31no—
79C3×C4⋊C8—31no—
80C3×C4⋊C8—61no—
81C3×#103—61no—
82C3×#102—61no—
83C3×#97—61no—
84C3×C4×C8—21no—
85C3×C4×C8C2×D311yescharacteristic
86C3×C4×C8C22×C311yescharacteristic
87#832—21no—
88#815—21no—
89Dic3⋊C8—21no—
90#810—21no—
91#808—21no—
92C4⋊(C3⋊C8)C22×C311yescharacteristic
93C4⋊(C3⋊C8)C22×C311yescharacteristic
94C4⋊(C3⋊C8)C22×C311yescharacteristic
95C23×C32—41no—
96C32×Q8—41no—
97C32×Q8—41no—
98C32×D4—41no—
99C32×D4—41no—
100C32×D4—41no—
101C32×D4—41no—
102C32×D4—81no—
103C2×C32×C4—41no—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4#4111yescharacteristic
107C2×C3×Dic3—21no—
108C2×C3×Dic3—21no—
109C3×Dic6—21no—
110C3×Dic6—21no—
111C32×C8—21no—
112C32×C8SD1612yescomplemented
113C3×C3⋊C8—41no—
114C3×C3⋊C8—41no—
115C3×C3⋊C8—41no—
116#492C3×D311yescharacteristic
117#475—31no—
118#460—31no—
119#446—31no—
120#335—31no—
121#332—31no—
122#331—31no—
123C2×C3×Q8—22no—
124C2×C3×Q8—21no—
125C2×C3×Q8—21no—
126C2×C3×Q8—31no—
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×Dic6C3×D411yescharacteristic
137C3×SD16—44no—
138C3×SD16—42no—
139C3×SD16—42no—
140C3×SD16—44no—
141C3×SD16—42no—
142C3×SD16—42no—
143C3×SD16—122no—
144C2×C3×C8—21no—
145C2×C3×C8—21no—
146C2×C3×C8—61no—
147C2×C3×C8—61no—
148C2×C3×C8—61no—
149C2×C3×C8#6711yescharacteristic
150C2×C3×C8#6711yescharacteristic
151C2×C3×C8C3×D411yescharacteristic
152C2×C3×C8C3×D411yescharacteristic
153C3×C4⋊C4—21no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—31no—
158C3×C4⋊C4—41no—
159C3×C4⋊C4—41no—
160C3×C4⋊C4—61no—
161C3×C42—21no—
162C3×C42—61no—
163C3×C42C22×D311yescharacteristic
164C3×C42C23×C311yescharacteristic
165#214—42no—
166C4⋊Dic3C3×D411yescharacteristic
167Dic3⋊C4—21no—
168C4×Dic3—21no—
169C2×C3⋊C8—21no—
170C2×C3⋊C8—21no—
171C2×C3⋊C8—21no—
172C22×C32—81no—
173C22×C32—81no—
174C22×C32—81no—
175C22×C32#12111yescharacteristic
176C32×C4—21no—
177C32×C4—81no—
178C32×C4C2×SD1611yescharacteristic
179C32×C4AGL(1,ℤ/8)11yescharacteristic
180C32×C4AGL(1,ℤ/8)11yescharacteristic
181C32×C4#13711yescharacteristic
182C3×Dic3—41no—
183C3×Dic3—41no—
184C2×SD16—21no—
185C2×SD16—21no—
186C2×SD16—61no—
187C4⋊Q8C2×C3×D311yescharacteristic
188#127C2×C3×D311yescharacteristic
189C4×Q8—31no—
190#106—61no—
191C4⋊C8—31no—
192C4⋊C8—31no—
193C4⋊C8—31no—
194C4⋊C8—61no—
195#103—61no—
196#102—61no—
197#97—61no—
198C4×C8C2×C3×D311yescharacteristic
199C23×C3—42no—
200C23×C3—41no—
201C23×C3—41no—
202C3×Q8—42no—
203C3×Q8—42no—
204C3×Q8—41no—
205C3×Q8—41no—
206C3×Q8—41no—
207C3×Q8—41no—
208C3×Q8—61no—
209C3×Q8—61no—
210C3×D4—42no—
211C3×D4—42no—
212C3×D4—41no—
213C3×D4—41no—
214C3×D4—41no—
215C3×D4—41no—
216C3×D4—41no—
217C3×D4—41no—
218C3×D4—41no—
219C3×D4—41no—
220C3×D4—81no—
221C3×D4—81no—
222C3×D4—81no—
223C3×D4—81no—
224C3×D4—82no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—42no—
229C2×C3×C4—41no—
230C2×C3×C4—41no—
231C2×C3×C4—61no—
232C2×C3×C4—61no—
233C2×C3×C4D3×D411yescharacteristic
234C2×C3×C4#23711yescharacteristic
235C2×C3×C4C2×#6711yescharacteristic
236C2×C3×C4C2×C3×D411yescharacteristic
237C2×C3×C4C2×C3×D411yescharacteristic
238C2×C3×C4C3×#4111yescharacteristic
239C2×Dic3—21no—
240C2×Dic3—21no—
241Dic6—21no—
242Dic6—21no—
243C3×C8—22no—
244C3×C8—21no—
245C3×C8—21no—
246C3×C8—22no—
247C3×C8—121no—
248C3×C8—121no—
249C3×C8—121no—
250C3×C8#21412yescomplemented
251C3×C8C3×SD1612yescomplemented
252C3⋊C8—41no—
253C3⋊C8—41no—
254C3⋊C8—41no—
255C2×C32—161no—
256C2×C32#46011yescharacteristic
257C2×C32#46811yescharacteristic
258C2×C32#47111yescharacteristic
259C2×Q8—21no—
260C2×Q8—31no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264SD16—42no—
265SD16—42no—
266SD16—122no—
267C2×C8—61no—
268C2×C8—61no—
269C2×C8—61no—
270C2×C8C3×#6711yescharacteristic
271C2×C8C3×#6711yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—31no—
275C4⋊C4—61no—
276C42—61no—
277C42C22×C3×D311yescharacteristic
278C22×C3—21no—
279C22×C3—82no—
280C22×C3—82no—
281C22×C3—82no—
282C22×C3—81no—
283C22×C3—81no—
284C22×C3—81no—
285C22×C3—81no—
286C22×C3—81no—
287C22×C3—81no—
288C22×C3#93811yescharacteristic
289C22×C3C3×#12111yescharacteristic
290C3×C4—22no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—82no—
298C3×C4—81no—
299C3×C4—81no—
300C3×C4—121no—
301C3×C4—121no—
302C3×C4#91411yescharacteristic
303C3×C4#91511yescharacteristic
304C3×C4#93211yescharacteristic
305C3×C4C2×#21411yescharacteristic
306C3×C4C2×C3×SD1611yescharacteristic
307C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
308C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
309C3×C4C3×#13711yescharacteristic
310Dic3—41no—
311Dic3—41no—
312C32#168611yescharacteristic, complemented, Sylow
313C23—41no—
314Q8—41no—
315Q8—41no—
316Q8—61no—
317Q8—61no—
318D4—41no—
319D4—41no—
320D4—41no—
321D4—41no—
322D4—81no—
323C2×C4—41no—
324C2×C4—61no—
325C2×C4—61no—
326C2×C4C3×D3×D411yescharacteristic
327C2×C4C3×#23711yescharacteristic
328C2×C4C2×C3×#6711yescharacteristic
329C8—21no—
330C8—121no—
331C8—121no—
332C8—121no—
333C8C3×#21412yescomplemented
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—162no—
338C2×C3—161no—
339C2×C3—161no—
340C2×C3#507511yescharacteristic
341C2×C3#517411yescharacteristic
342C2×C3#517711yescharacteristic
343C2×C3C3×#46011yescharacteristic
344C2×C3C3×#46811yescharacteristic
345C2×C3C3×#47111yescharacteristic
346C22—81no—
347C22—81no—
348C22—81no—
349C22C3×#93811yescharacteristic
350C4—21no—
351C4—81no—
352C4—121no—
353C4—121no—
354C4C3×#91411yescharacteristic
355C4C3×#91511yescharacteristic
356C4C3×#93211yescharacteristic
357C4C2×C3×#21411yescharacteristic
358C3—21no—
359C3#7127311yescharacteristic, direct product factor
360C3C3×#168611yescharacteristic, complemented
361C2—161no—
362C2C3×#507511yescharacteristic
363C2C3×#517411yescharacteristic
364C2C3×#517711yescharacteristic
subgroupG/H
centerC22×C3#938
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#492C2
socleC22×C32#121
prime radicalC32×#127C22
hypercenterC3×#492D3
hypocenterC3C3×#1686
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#492

Complements

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

NH ≅ G/Ntype
2. C3×#5094C2semidirect
4. C3×#4679C2semidirect
5. C3×#4547C2semidirect
7. C3×#4458C2semidirect
9. #71273C3direct (N × H)
31. #5094C2×C3semidirect
33. #4679C2×C3semidirect
37. #4547C2×C3semidirect
39. #4458C2×C3semidirect
112. C32×C8SD16semidirect
250. C3×C8#214semidirect
251. C3×C8C3×SD16semidirect
312. C32#1686semidirect
333. C8C3×#214semidirect
359. C3#71273direct (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×#4922
C3×#50942
C3×#50752
C3×#46792
C3×#45472
C3×#45442
C3×#44582
C3×#16863
#712733