Finite Group Databasebeta

← C3×#71054 #11781386

Subgroups — C3×#71054 #11781386

Order 1152.

354 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#462C211yesmaximal, characteristic
2C3×#5093C211yesmaximal, characteristic
3C3×Q8×C3⋊C8C211yesmaximal, characteristic
4C3×#5020C211yesmaximal, characteristic
5C3×#4547C211yesmaximal, characteristic
6C3×#4486C211yesmaximal, characteristic
7C3×#4480C211yesmaximal, characteristic
8C3×#1680—31nomaximal
9#71054C311yesmaximal, characteristic, direct product factor
10C2×C32×Q16—21no—
11C32×C4⋊Q8C2211yescharacteristic
12C32×C4×Q8C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C32×C4⋊C8C2211yescharacteristic
15C32×#103—21no—
16C3×#835—21no—
17C3×#810—21no—
18C3×#810—21no—
19C3×#808—21no—
20C3×C4⋊(C3⋊C8)—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8—21no—
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#487—31no—
26C3×#475—31no—
27C3×#462—21no—
28C3×#462D311yescharacteristic
29C3×#462C2×C311yescharacteristic
30C3×C8×Q8—31no—
31#5093C2×C311yescharacteristic
32Q8×C3⋊C8C2×C311yescharacteristic
33#5020C2×C311yescharacteristic
34C3×#334—31no—
35C3×#332—31no—
36C3×#332—31no—
37#4547C2×C311yescharacteristic
38#4486C2×C311yescharacteristic
39#4480C2×C311yescharacteristic
40C2×C32×Q8—21no—
41C2×C32×Q8D411yescharacteristic
42C2×C3×Dic6—21no—
43C32×Q16—42no—
44C2×C32×C8—21no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4D411yescharacteristic
49C32×C42—21no—
50C32×C42C2311yescharacteristic
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#1680—31noSylow
58C2×C3×Q16—22no—
59C2×C3×Q16—21no—
60C2×C3×Q16—21no—
61C3×C4⋊Q8—21no—
62C3×C4⋊Q8—31no—
63C3×C4⋊Q8C2×D311yescharacteristic
64C3×C4⋊Q8C22×C311yescharacteristic
65C3×C4×Q8—21no—
66C3×C4×Q8C2×D311yescharacteristic
67C3×C4×Q8C22×C311yescharacteristic
68#869C22×C311yescharacteristic
69C3×#106—61no—
70C3×C4⋊C8—21no—
71C3×C4⋊C8—31no—
72C3×C4⋊C8—31no—
73C3×C4⋊C8—61no—
74C3×C4⋊C8C2×D311yescharacteristic
75C3×C4⋊C8C22×C311yescharacteristic
76C3×#103—22no—
77C3×#103—21no—
78C3×#103—21no—
79C3×#103—61no—
80C3×#103—61no—
81C3×#103—61no—
82C3×C4×C8—31no—
83C3×C4×C8—61no—
84#835—21no—
85#810—21no—
86#810—21no—
87#808—21no—
88C4⋊(C3⋊C8)—21no—
89C4⋊(C3⋊C8)C22×C311yescharacteristic
90C4⋊(C3⋊C8)C22×C311yescharacteristic
91C4×C3⋊C8—21no—
92C4×C3⋊C8C22×C311yescharacteristic
93C32×Q8—21no—
94C32×Q8—41no—
95C32×Q8—41no—
96C32×Q8SD1612yes—
97C2×C32×C4—21no—
98C2×C32×C4—21no—
99C2×C32×C4—41no—
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C3×Dic3—41no—
104C3×Dic6—41no—
105C3×Dic6—41no—
106C32×C8—41no—
107C3×C3⋊C8—21no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—41no—
110C3×C3⋊C8—41no—
111#487—31no—
112#475—31no—
113#462C3×D311yescharacteristic
114C8×Q8—31no—
115#334—31no—
116#332—31no—
117#332—31no—
118C2×C3×Q8—22no—
119C2×C3×Q8—21no—
120C2×C3×Q8—21no—
121C2×C3×Q8—21no—
122C2×C3×Q8—61no—
123C2×C3×Q8#6711yescharacteristic
124C2×C3×Q8C3×D411yescharacteristic
125C2×Dic6—21no—
126C3×Q16—44no—
127C3×Q16—42no—
128C3×Q16—42no—
129C2×C3×C8—22no—
130C2×C3×C8—21no—
131C2×C3×C8—21no—
132C2×C3×C8—31no—
133C2×C3×C8—31no—
134C2×C3×C8—61no—
135C2×C3×C8—61no—
136C3×C4⋊C4—21no—
137C3×C4⋊C4—21no—
138C3×C4⋊C4—21no—
139C3×C4⋊C4—21no—
140C3×C4⋊C4—21no—
141C3×C4⋊C4—21no—
142C3×C4⋊C4—21no—
143C3×C4⋊C4—41no—
144C3×C4⋊C4—41no—
145C3×C4⋊C4—41no—
146C3×C4⋊C4—61no—
147C3×C4⋊C4—61no—
148C3×C4⋊C4#6711yescharacteristic
149C3×C4⋊C4C3×D411yescharacteristic
150C3×C42—21no—
151C3×C42—21no—
152C3×C42—21no—
153C3×C42—41no—
154C3×C42C22×D311yescharacteristic
155C3×C42C23×C311yescharacteristic
156C4⋊Dic3—21no—
157C4⋊Dic3—21no—
158C2×C3⋊C8—21no—
159C2×C3⋊C8—21no—
160C2×C3⋊C8C3×D411yescharacteristic
161C2×C3⋊C8C3×D411yescharacteristic
162C22×C32#12111yescharacteristic
163C32×C4—22no—
164C32×C4—21no—
165C32×C4—41no—
166C32×C4—81no—
167C32×C4C2×SD1611yescharacteristic
168C32×C4#13511yescharacteristic
169C32×C4#13511yescharacteristic
170C32×C4#13711yescharacteristic
171C3×Dic3—81no—
172C2×Q16—21no—
173C4⋊Q8—31no—
174C4⋊Q8C2×C3×D311yescharacteristic
175C4×Q8C2×C3×D311yescharacteristic
176#106—61no—
177C4⋊C8—31no—
178C4⋊C8—31no—
179C4⋊C8—61no—
180C4⋊C8C2×C3×D311yescharacteristic
181#103—21no—
182#103—61no—
183#103—61no—
184#103—61no—
185C4×C8—31no—
186C4×C8—61no—
187C3×Q8—21no—
188C3×Q8—21no—
189C3×Q8—22no—
190C3×Q8—41no—
191C3×Q8—42no—
192C3×Q8—42no—
193C3×Q8—41no—
194C3×Q8—41no—
195C3×Q8—41no—
196C3×Q8—41no—
197C3×Q8—121no—
198C3×Q8—121no—
199C3×Q8#21412yes—
200C3×Q8C3×SD1612yes—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—41no—
209C2×C3×C4—41no—
210C2×C3×C4—42no—
211C2×C3×C4—41no—
212C2×C3×C4—41no—
213C2×C3×C4—121no—
214C2×C3×C4D3×D411yescharacteristic
215C2×C3×C4#23711yescharacteristic
216C2×C3×C4C2×#6711yescharacteristic
217C2×C3×C4C2×C3×D411yescharacteristic
218C2×C3×C4C2×C3×D411yescharacteristic
219C2×C3×C4C3×#4111yescharacteristic
220C2×Dic3—41no—
221Dic6—41no—
222Dic6—41no—
223C3×C8—42no—
224C3×C8—41no—
225C3×C8—41no—
226C3×C8—61no—
227C3×C8—61no—
228C3×C8—121no—
229C3×C8—121no—
230C3⋊C8—21no—
231C3⋊C8—21no—
232C3⋊C8—41no—
233C3⋊C8—41no—
234C2×C32#46411yescharacteristic
235C2×C32#46511yescharacteristic
236C2×C32#47311yescharacteristic
237C2×Q8—21no—
238C2×Q8—61no—
239C2×Q8C3×#6711yescharacteristic
240Q16—42no—
241C2×C8—21no—
242C2×C8—31no—
243C2×C8—31no—
244C2×C8—61no—
245C2×C8—61no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—61no—
250C4⋊C4—61no—
251C4⋊C4C3×#6711yescharacteristic
252C42—21no—
253C42C22×C3×D311yescharacteristic
254C22×C3—21no—
255C22×C3#93911yescharacteristic
256C22×C3C3×#12111yescharacteristic
257C3×C4—21no—
258C3×C4—22no—
259C3×C4—22no—
260C3×C4—21no—
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—21no—
264C3×C4—21no—
265C3×C4—41no—
266C3×C4—42no—
267C3×C4—41no—
268C3×C4—41no—
269C3×C4—81no—
270C3×C4—82no—
271C3×C4—81no—
272C3×C4—81no—
273C3×C4—241no—
274C3×C4#91811yescharacteristic
275C3×C4#91911yescharacteristic
276C3×C4C2×#21411yescharacteristic
277C3×C4#95011yescharacteristic
278C3×C4C2×C3×SD1611yescharacteristic
279C3×C4C3×#13511yescharacteristic
280C3×C4C3×#13511yescharacteristic
281C3×C4C3×#13711yescharacteristic
282Dic3—81no—
283C32#168011yescharacteristic, complemented, Sylow
284Q8—21no—
285Q8—41no—
286Q8—41no—
287Q8—121no—
288Q8—121no—
289Q8C3×#21412yes—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—121no—
294C2×C4C3×D3×D411yescharacteristic
295C2×C4C3×#23711yescharacteristic
296C2×C4C2×C3×#6711yescharacteristic
297C8—41no—
298C8—61no—
299C8—61no—
300C8—121no—
301C8—121no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3#504111yescharacteristic
306C2×C3#518511yescharacteristic
307C2×C3#520411yescharacteristic
308C2×C3C3×#46411yescharacteristic
309C2×C3C3×#46511yescharacteristic
310C2×C3C3×#47311yescharacteristic
311C22C3×#93911yescharacteristic
312C4—21no—
313C4—22no—
314C4—41no—
315C4—81no—
316C4—241no—
317C4C3×#91811yescharacteristic
318C4C3×#91911yescharacteristic
319C4C2×C3×#21411yescharacteristic
320C4C3×#95011yescharacteristic
321C3—21no—
322C3#7105411yescharacteristic, direct product factor
323C3C3×#168011yescharacteristic, complemented
324C2C3×#504111yescharacteristic
325C2C3×#518511yescharacteristic
326C2C3×#520411yescharacteristic
subgroupG/H
centerC22×C3#939
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#462C2
socle, prime radicalC22×C32#121
hypercenterC3×#462D3
hypocenterC3C3×#1680
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#462

Complements

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

NH ≅ G/Ntype
9. #71054C3direct (N × H)
283. C32#1680semidirect
322. C3#71054direct (N × H)
323. C3C3×#1680semidirect

Maximal subgroups

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

subgroupindex
C32×#4622
C3×#50932
C3×Q8×C3⋊C82
C3×#50202
C3×#45472
C3×#44862
C3×#44802
C3×#16803
#710543