Finite Group Databasebeta

← C3×#68538 #11781242

Subgroups — C3×#68538 #11781242

Order 1152.

379 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#4843C211yesmaximal, characteristic
2C3×#4842C211yesmaximal, characteristic, complemented
3C3×#4694C211yesmaximal, characteristic, complemented
4C3×C8×D12C211yesmaximal, characteristic, complemented
5C32×#334C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic, complemented
7C3×#4481C211yesmaximal, characteristic, complemented
8C3×#1677—31nomaximal
9#68538C311yesmaximal, characteristic, direct product factor
10C2×C3×D24—21no—
11C2×C3×D3×C8—21no—
12C3×#874C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C32×C4⋊C8C2211yescharacteristic
16C32×C4⋊C8C2211yescharacteristic
17C32×C4×C8C2211yescharacteristic
18C3×#821—21no—
19C3×#821—21no—
20C3×#821—21no—
21C3×#821—21no—
22C3×(C2×D3)⋊C8—21no—
23C3×#817—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×#486—31no—
26C3×#476—31no—
27C3×#459—31no—
28C3×C8×D4—31no—
29#4843C2×C311yescharacteristic
30#4842C2×C311yescharacteristic, complemented
31#4694C2×C311yescharacteristic, complemented
32C8×D12C2×C311yescharacteristic, complemented
33C3×#334—21no—
34C3×#334D311yescharacteristic, complemented
35C3×#334C2×C311yescharacteristic, complemented
36C3×#333—31no—
37C3×#331—31no—
38#4485C2×C311yescharacteristic, complemented
39#4481C2×C311yescharacteristic, complemented
40C2×C3×D12—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12D411yescharacteristic
44C2×C3×C4×D3—21no—
45C2×C3×Dic6—21no—
46C2×C32×C8—21no—
47C2×C32×C8—21no—
48C2×C32×C8D411yescharacteristic
49C2×C32×C8D411yescharacteristic
50C32×C42C2311yescharacteristic
51C3×(C2×D3)⋊C4—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3D411yescharacteristic
55C2×C3×C3⋊C8—21no—
56C3×D24—42no—
57C3×D3×C8—42no—
58#1677—31noSylow
59C2×C3×D8—61no—
60C22×C3×C8—61no—
61C3×C4⋊Q8—31no—
62C3×#127—31no—
63C3×C4×D4—31no—
64C2×D24—21no—
65C2×D3×C8—21no—
66#874C22×C311yescharacteristic
67C4×D12C22×C311yescharacteristic
68#869C22×C311yescharacteristic
69C3×#106—61no—
70C3×C4⋊C8—21no—
71C3×C4⋊C8—21no—
72C3×C4⋊C8—31no—
73C3×C4⋊C8C2×D311yescharacteristic
74C3×C4⋊C8C2×D311yescharacteristic
75C3×C4⋊C8C22×C311yescharacteristic
76C3×C4⋊C8C22×C311yescharacteristic
77C3×#102—61no—
78C3×#102—61no—
79C3×#102—61no—
80C3×#102—61no—
81C3×C22⋊C8—61no—
82C3×C4×C8—21no—
83C3×C4×C8C2×D311yescharacteristic
84C3×C4×C8C22×C311yescharacteristic
85#821—21no—
86#821—21no—
87#821—21no—
88#821—21no—
89(C2×D3)⋊C8—21no—
90#817—21no—
91C4⋊(C3⋊C8)C22×C311yescharacteristic
92C22×C3×D3—21no—
93C22×C3×D3—41no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3×Dic3—21no—
98C2×C3×Dic3—41no—
99C3×D12—21no—
100C3×D12—41no—
101C3×D12—41no—
102C3×D12—41no—
103C3×D12—41no—
104C3×D12—81no—
105C3×D12SD1612yes—
106C3×C4×D3—41no—
107C3×C4×D3—41no—
108C3×Dic6—81no—
109C32×C8—21no—
110C32×C8—21no—
111C32×C8—41no—
112C32×C8—41no—
113C3×C3⋊C8—41no—
114#486—31no—
115#476—31no—
116#459—31no—
117C8×D4—31no—
118#334C3×D311yescharacteristic, complemented
119#333—31no—
120#331—31no—
121C2×C3×Q8—61no—
122C2×C3×D4—31no—
123C2×C3×D4—61no—
124C2×C3×D4—61no—
125C2×C3×D4—61no—
126C22×C3×C4—61no—
127C2×D12—21no—
128C2×D12—21no—
129C2×D12—21no—
130C2×D12C3×D411yescharacteristic
131C2×C4×D3—21no—
132C2×Dic6—21no—
133C3×D8—122no—
134C2×C3×C8—21no—
135C2×C3×C8—21no—
136C2×C3×C8—21no—
137C2×C3×C8—21no—
138C2×C3×C8—21no—
139C2×C3×C8—21no—
140C2×C3×C8—41no—
141C2×C3×C8—41no—
142C2×C3×C8—61no—
143C2×C3×C8—122no—
144C2×C3×C8D1211yescharacteristic
145C2×C3×C8D1211yescharacteristic
146C2×C3×C8C3×D411yescharacteristic
147C2×C3×C8C3×D411yescharacteristic
148C3×C4⋊C4—31no—
149C3×C4⋊C4—61no—
150C3×C4⋊C4—61no—
151C3×C22⋊C4—61no—
152C3×C42—21no—
153C3×C42C22×D311yescharacteristic
154C3×C42C23×C311yescharacteristic
155(C2×D3)⋊C4—21no—
156C4⋊Dic3—21no—
157C4⋊Dic3—21no—
158C4⋊Dic3C3×D411yescharacteristic
159C2×C3⋊C8—21no—
160D24—42no—
161D3×C8—42no—
162C22×C32#12111yescharacteristic
163C2×C3×D3—22no—
164C2×C3×D3—41no—
165C2×C3×D3—41no—
166C2×C3×D3—81no—
167C2×C3×D3—81no—
168C2×C3×D3—81no—
169C32×C4—21no—
170C32×C4C2×SD1611yescharacteristic
171C32×C4#13511yescharacteristic
172C32×C4#13511yescharacteristic
173C32×C4AGL(1,ℤ/8)11yescharacteristic
174C3×Dic3—41no—
175C3×Dic3—81no—
176C2×D8—61no—
177C22×C8—61no—
178C4⋊Q8—31no—
179#127—31no—
180C4×D4—31no—
181#106—61no—
182C4⋊C8—31no—
183C4⋊C8C2×C3×D311yescharacteristic
184C4⋊C8C2×C3×D311yescharacteristic
185#102—61no—
186#102—61no—
187#102—61no—
188#102—61no—
189C22⋊C8—61no—
190C4×C8C2×C3×D311yescharacteristic
191C23×C3—61no—
192C23×C3—121no—
193C22×D3—21no—
194C22×D3—41no—
195C3×Q8—241no—
196C3×D4—32no—
197C3×D4—61no—
198C3×D4—121no—
199C3×D4—121no—
200C3×D4—121no—
201C3×D4—121no—
202C3×D4—241no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—61no—
207C2×C3×C4—121no—
208C2×C3×C4—121no—
209C2×C3×C4—121no—
210C2×C3×C4C2×D1211yescharacteristic
211C2×C3×C4D3×D411yescharacteristic
212C2×C3×C4#23911yescharacteristic
213C2×C3×C4C2×C3×D411yescharacteristic
214C2×C3×C4C2×C3×D411yescharacteristic
215C2×C3×C4C3×#4111yescharacteristic
216C2×Dic3—21no—
217C2×Dic3—41no—
218D12—21no—
219D12—41no—
220D12—41no—
221D12—41no—
222D12—41no—
223D12—81no—
224D12C3×SD1612yes—
225C4×D3—41no—
226C4×D3—41no—
227Dic6—81no—
228C3×C8—22no—
229C3×C8—21no—
230C3×C8—21no—
231C3×C8—21no—
232C3×C8—21no—
233C3×C8—41no—
234C3×C8—41no—
235C3×C8—41no—
236C3×C8—41no—
237C3×C8—41no—
238C3×C8—81no—
239C3×C8—81no—
240C3×C8—121no—
241C3⋊C8—41no—
242C2×C32#46311yescharacteristic
243C2×C32#46511yescharacteristic
244C2×C32#47211yescharacteristic
245C3×D3—42no—
246C3×D3—161no—
247C2×Q8—61no—
248C2×D4—31no—
249C2×D4—61no—
250C2×D4—61no—
251C2×D4—61no—
252C22×C4—61no—
253D8—122no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—61no—
257C2×C8—122no—
258C2×C8C3×D1211yescharacteristic
259C2×C8C3×D1211yescharacteristic
260C4⋊C4—31no—
261C4⋊C4—61no—
262C4⋊C4—61no—
263C22⋊C4—61no—
264C42C22×C3×D311yescharacteristic
265C22×C3—21no—
266C22×C3—62no—
267C22×C3—121no—
268C22×C3—121no—
269C22×C3—241no—
270C22×C3—241no—
271C22×C3—241no—
272C22×C3#89511yescharacteristic
273C22×C3C3×#12111yescharacteristic
274C2×D3—22no—
275C2×D3—41no—
276C2×D3—41no—
277C2×D3—81no—
278C2×D3—81no—
279C2×D3—81no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—41no—
287C3×C4—121no—
288C3×C4—241no—
289C3×C4#90411yescharacteristic
290C3×C4#90811yescharacteristic
291C3×C4D3×SD1611yescharacteristic
292C3×C4#91611yescharacteristic
293C3×C4C2×C3×SD1611yescharacteristic
294C3×C4C3×#13511yescharacteristic
295C3×C4C3×#13511yescharacteristic
296C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
297Dic3—41no—
298Dic3—81no—
299C32#167711yescharacteristic, complemented, Sylow
300C23—61no—
301C23—121no—
302Q8—241no—
303D4—32no—
304D4—61no—
305D4—121no—
306D4—121no—
307D4—121no—
308D4—121no—
309D4—241no—
310C2×C4—61no—
311C2×C4—121no—
312C2×C4—121no—
313C2×C4—121no—
314C2×C4C2×C3×D1211yescharacteristic
315C2×C4C3×D3×D411yescharacteristic
316C2×C4C3×#23911yescharacteristic
317C8—21no—
318C8—21no—
319C8—41no—
320C8—41no—
321C8—121no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3—122no—
326C2×C3—481no—
327C2×C3#484411yescharacteristic
328C2×C3#486411yescharacteristic
329C2×C3#489711yescharacteristic
330C2×C3C3×#46311yescharacteristic
331C2×C3C3×#46511yescharacteristic
332C2×C3C3×#47211yescharacteristic
333D3—42no—
334D3—161no—
335C22—62no—
336C22—121no—
337C22—121no—
338C22—241no—
339C22—241no—
340C22—241no—
341C22C3×#89511yescharacteristic
342C4—21no—
343C4—121no—
344C4—241no—
345C4C3×#90411yescharacteristic
346C4C3×#90811yescharacteristic
347C4C3×D3×SD1611yescharacteristic
348C4C3×#91611yescharacteristic
349C3—21no—
350C3#6853811yescharacteristic, direct product factor
351C3C3×#167711yescharacteristic, complemented
352C2—122no—
353C2—481no—
354C2C3×#484411yescharacteristic
355C2C3×#486411yescharacteristic
356C2C3×#489711yescharacteristic
subgroupG/H
centerC22×C3#895
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#334C2
socleC22×C32#121
prime radicalC3×#4843C2
hypercenterC3×#334D3
hypocenterC3C3×#1677
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#334

Complements

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

NH ≅ G/Ntype
2. C3×#4842C2semidirect
3. C3×#4694C2semidirect
4. C3×C8×D12C2semidirect
5. C32×#334C2semidirect
6. C3×#4485C2semidirect
7. C3×#4481C2semidirect
9. #68538C3direct (N × H)
30. #4842C2×C3semidirect
31. #4694C2×C3semidirect
32. C8×D12C2×C3semidirect
34. C3×#334D3semidirect
35. C3×#334C2×C3semidirect
38. #4485C2×C3semidirect
39. #4481C2×C3semidirect
118. #334C3×D3semidirect
299. C32#1677semidirect
350. C3#68538direct (N × H)
351. C3C3×#1677semidirect

Maximal subgroups

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

subgroupindex
C3×#48432
C3×#48422
C3×#46942
C3×C8×D122
C32×#3342
C3×#44852
C3×#44812
C3×#16773
#685383