Finite Group Databasebeta

← C3×#68539 #11781336

Subgroups — C3×#68539 #11781336

Order 1152.

359 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#4846C211yesmaximal, characteristic
2C3×#4841C211yesmaximal, characteristic
3C3×C8×D12C211yesmaximal, characteristic
4C3×#4681C211yesmaximal, characteristic, complemented
5C32×#334C211yesmaximal, characteristic, complemented
6C3×#4486C211yesmaximal, characteristic, complemented
7C3×#4482C211yesmaximal, characteristic, complemented
8C3×#1679—31nomaximal
9#68539C311yesmaximal, characteristic, direct product factor
10C2×C3×#204—21no—
11C2×C3×D3×C8—21no—
12C3×C4×D12C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C32×C4⋊C8C2211yescharacteristic
16C32×C4⋊C8C2211yescharacteristic
17C32×C4×C8C2211yescharacteristic
18C3×#821—21no—
19C3×(C2×D3)⋊C8—21no—
20C3×#818—21no—
21C3×#816—21no—
22C3×#816—21no—
23C3×#816—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×#487—31no—
26C3×#474—31no—
27C3×#461—31no—
28C3×C8×D4—31no—
29#4846C2×C311yescharacteristic
30#4841C2×C311yescharacteristic
31C8×D12C2×C311yescharacteristic
32#4681C2×C311yescharacteristic, complemented
33C3×#334—21no—
34C3×#334D311yescharacteristic, complemented
35C3×#334C2×C311yescharacteristic, complemented
36C3×#332—31no—
37C3×#332—31no—
38#4486C2×C311yescharacteristic, complemented
39#4482C2×C311yescharacteristic, complemented
40C2×C3×D12D411yescharacteristic
41C2×C3×C4×D3—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—21no—
44C2×C32×C8—21no—
45C2×C32×C8—21no—
46C2×C32×C8D411yescharacteristic
47C2×C32×C8D411yescharacteristic
48C32×C42C2311yescharacteristic
49C3×(C2×D3)⋊C4—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3D411yescharacteristic
55C2×C3×C3⋊C8—21no—
56C3×#204—42no—
57C3×D3×C8—42no—
58#1679—31noSylow
59C2×C3×SD16—61no—
60C22×C3×C8—61no—
61C3×C4⋊Q8—31no—
62C3×C4⋊Q8—31no—
63C3×C4×D4—31no—
64C2×#204—21no—
65C2×D3×C8—21no—
66C4×D12C22×C311yescharacteristic
67#869C22×C311yescharacteristic
68#869C22×C311yescharacteristic
69C3×#107—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×#103—61no—
78C3×#103—61no—
79C3×#103—61no—
80C3×#102—61no—
81C3×C22⋊C8—61no—
82C3×C4×C8—21no—
83C3×C4×C8C2×D311yescharacteristic
84C3×C4×C8C22×C311yescharacteristic
85#821—21no—
86(C2×D3)⋊C8—21no—
87#818—21no—
88#816—21no—
89#816—21no—
90#816—21no—
91C4⋊(C3⋊C8)C22×C311yescharacteristic
92C22×C3×D3—21no—
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4#4111yescharacteristic
96C2×C3×Dic3—21no—
97C2×C3×Dic3—41no—
98C2×C3×Dic3—41no—
99C3×D12—21no—
100C3×D12SD1612yes—
101C3×C4×D3—41no—
102C3×C4×D3—41no—
103C3×Dic6—41no—
104C3×Dic6—41no—
105C3×Dic6—41no—
106C3×Dic6—41no—
107C32×C8—21no—
108C32×C8—21no—
109C32×C8—41no—
110C32×C8—41no—
111C3×C3⋊C8—41no—
112#487—31no—
113#474—31no—
114#461—31no—
115C8×D4—31no—
116#334C3×D311yescharacteristic, complemented
117#332—31no—
118#332—31no—
119C2×C3×Q8—61no—
120C2×C3×Q8—61no—
121C2×C3×D4—31no—
122C22×C3×C4—61no—
123C2×D12C3×D411yescharacteristic
124C2×C4×D3—21no—
125C2×Dic6—21no—
126C2×Dic6—21no—
127C3×SD16—122no—
128C2×C3×C8—21no—
129C2×C3×C8—21no—
130C2×C3×C8—21no—
131C2×C3×C8—21no—
132C2×C3×C8—21no—
133C2×C3×C8—21no—
134C2×C3×C8—41no—
135C2×C3×C8—41no—
136C2×C3×C8—61no—
137C2×C3×C8—122no—
138C2×C3×C8D1211yescharacteristic
139C2×C3×C8D1211yescharacteristic
140C2×C3×C8C3×D411yescharacteristic
141C2×C3×C8C3×D411yescharacteristic
142C3×C4⋊C4—31no—
143C3×C4⋊C4—61no—
144C3×C4⋊C4—61no—
145C3×C4⋊C4—61no—
146C3×C4⋊C4—61no—
147C3×C22⋊C4—61no—
148C3×C42—21no—
149C3×C42C22×D311yescharacteristic
150C3×C42C23×C311yescharacteristic
151(C2×D3)⋊C4—21no—
152C4⋊Dic3—21no—
153C4⋊Dic3—21no—
154C4⋊Dic3—21no—
155C4⋊Dic3—21no—
156C4⋊Dic3C3×D411yescharacteristic
157C2×C3⋊C8—21no—
158#204—42no—
159D3×C8—42no—
160C22×C32#12111yescharacteristic
161C2×C3×D3—22no—
162C2×C3×D3—41no—
163C2×C3×D3—41no—
164C32×C4—21no—
165C32×C4C2×SD1611yescharacteristic
166C32×C4#13511yescharacteristic
167C32×C4#13511yescharacteristic
168C32×C4AGL(1,ℤ/8)11yescharacteristic
169C3×Dic3—41no—
170C3×Dic3—81no—
171C3×Dic3—81no—
172C2×SD16—61no—
173C22×C8—61no—
174C4⋊Q8—31no—
175C4⋊Q8—31no—
176C4×D4—31no—
177#107—61no—
178C4⋊C8—31no—
179C4⋊C8C2×C3×D311yescharacteristic
180C4⋊C8C2×C3×D311yescharacteristic
181#103—61no—
182#103—61no—
183#103—61no—
184#102—61no—
185C22⋊C8—61no—
186C4×C8C2×C3×D311yescharacteristic
187C23×C3—61no—
188C22×D3—21no—
189C3×Q8—121no—
190C3×Q8—121no—
191C3×Q8—121no—
192C3×Q8—121no—
193C3×D4—32no—
194C3×D4—61no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—61no—
199C2×C3×C4—121no—
200C2×C3×C4—121no—
201C2×C3×C4—121no—
202C2×C3×C4—121no—
203C2×C3×C4C2×D1211yescharacteristic
204C2×C3×C4D3×D411yescharacteristic
205C2×C3×C4#23911yescharacteristic
206C2×C3×C4C2×C3×D411yescharacteristic
207C2×C3×C4C2×C3×D411yescharacteristic
208C2×C3×C4C3×#4111yescharacteristic
209C2×Dic3—21no—
210C2×Dic3—41no—
211C2×Dic3—41no—
212D12—21no—
213D12C3×SD1612yes—
214C4×D3—41no—
215C4×D3—41no—
216Dic6—41no—
217Dic6—41no—
218Dic6—41no—
219Dic6—41no—
220C3×C8—22no—
221C3×C8—21no—
222C3×C8—21no—
223C3×C8—21no—
224C3×C8—21no—
225C3×C8—41no—
226C3×C8—41no—
227C3×C8—41no—
228C3×C8—41no—
229C3×C8—41no—
230C3×C8—81no—
231C3×C8—81no—
232C3×C8—121no—
233C3⋊C8—41no—
234C2×C32#46311yescharacteristic
235C2×C32#46511yescharacteristic
236C2×C32#47311yescharacteristic
237C3×D3—42no—
238C2×Q8—61no—
239C2×Q8—61no—
240C2×D4—31no—
241C22×C4—61no—
242SD16—122no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—61no—
246C2×C8—122no—
247C2×C8C3×D1211yescharacteristic
248C2×C8C3×D1211yescharacteristic
249C4⋊C4—31no—
250C4⋊C4—61no—
251C4⋊C4—61no—
252C4⋊C4—61no—
253C4⋊C4—61no—
254C22⋊C4—61no—
255C42C22×C3×D311yescharacteristic
256C22×C3—21no—
257C22×C3—62no—
258C22×C3—121no—
259C22×C3—121no—
260C22×C3#89511yescharacteristic
261C22×C3C3×#12111yescharacteristic
262C2×D3—22no—
263C2×D3—41no—
264C2×D3—41no—
265C3×C4—21no—
266C3×C4—21no—
267C3×C4—21no—
268C3×C4—21no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—41no—
272C3×C4—121no—
273C3×C4—241no—
274C3×C4—241no—
275C3×C4#90411yescharacteristic
276C3×C4#90811yescharacteristic
277C3×C4D3×SD1611yescharacteristic
278C3×C4#91611yescharacteristic
279C3×C4C2×C3×SD1611yescharacteristic
280C3×C4C3×#13511yescharacteristic
281C3×C4C3×#13511yescharacteristic
282C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
283Dic3—41no—
284Dic3—81no—
285Dic3—81no—
286C32#167911yescharacteristic, complemented, Sylow
287C23—61no—
288Q8—121no—
289Q8—121no—
290Q8—121no—
291Q8—121no—
292D4—32no—
293D4—61no—
294C2×C4—61no—
295C2×C4—121no—
296C2×C4—121no—
297C2×C4—121no—
298C2×C4—121no—
299C2×C4C2×C3×D1211yescharacteristic
300C2×C4C3×D3×D411yescharacteristic
301C2×C4C3×#23911yescharacteristic
302C8—21no—
303C8—21no—
304C8—41no—
305C8—41no—
306C8—121no—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—122no—
311C2×C3#484411yescharacteristic
312C2×C3#486411yescharacteristic
313C2×C3#489611yescharacteristic
314C2×C3C3×#46311yescharacteristic
315C2×C3C3×#46511yescharacteristic
316C2×C3C3×#47311yescharacteristic
317D3—42no—
318C22—62no—
319C22—121no—
320C22—121no—
321C22C3×#89511yescharacteristic
322C4—21no—
323C4—121no—
324C4—241no—
325C4—241no—
326C4C3×#90411yescharacteristic
327C4C3×#90811yescharacteristic
328C4C3×D3×SD1611yescharacteristic
329C4C3×#91611yescharacteristic
330C3—21no—
331C3#6853911yescharacteristic, direct product factor
332C3C3×#167911yescharacteristic, complemented
333C2—122no—
334C2C3×#484411yescharacteristic
335C2C3×#486411yescharacteristic
336C2C3×#489611yescharacteristic
subgroupG/H
centerC22×C3#895
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#334C2
socleC22×C32#121
prime radicalC2×C3×D12D4
hypercenterC3×#334D3
hypocenterC3C3×#1679
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
4. C3×#4681C2semidirect
5. C32×#334C2semidirect
6. C3×#4486C2semidirect
7. C3×#4482C2semidirect
9. #68539C3direct (N × H)
32. #4681C2×C3semidirect
34. C3×#334D3semidirect
35. C3×#334C2×C3semidirect
38. #4486C2×C3semidirect
39. #4482C2×C3semidirect
116. #334C3×D3semidirect
286. C32#1679semidirect
331. C3#68539direct (N × H)
332. C3C3×#1679semidirect

Maximal subgroups

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

subgroupindex
C3×#48462
C3×#48412
C3×C8×D122
C3×#46812
C32×#3342
C3×#44862
C3×#44822
C3×#16793
#685393