Finite Group Databasebeta

← C3×#68537 #11781017

Subgroups — C3×#68537 #11781017

Order 1152.

359 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#4842C211yesmaximal, characteristic
2C3×#4841C211yesmaximal, characteristic
3C3×C8×D12C211yesmaximal, characteristic
4C3×#4680C211yesmaximal, characteristic, complemented
5C32×#334C211yesmaximal, characteristic, complemented
6C3×#4482C211yesmaximal, characteristic, complemented
7C3×#4481C211yesmaximal, characteristic, complemented
8C3×#1671—31nomaximal
9#68537C311yesmaximal, 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×#817—21no—
21C3×#817—21no—
22C3×#817—21no—
23C3×#816—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×#498—31no—
26C3×#476—31no—
27C3×#461—31no—
28C3×C8×D4—31no—
29#4842C2×C311yescharacteristic
30#4841C2×C311yescharacteristic
31C8×D12C2×C311yescharacteristic
32#4680C2×C311yescharacteristic, complemented
33C3×#334—21no—
34C3×#334D311yescharacteristic, complemented
35C3×#334C2×C311yescharacteristic, complemented
36C3×#333—31no—
37C3×#332—31no—
38#4482C2×C311yescharacteristic, complemented
39#4481C2×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#1671—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×#106—61no—
70C3×#106—61no—
71C3×#106—61no—
72C3×C4⋊C8—21no—
73C3×C4⋊C8—21no—
74C3×C4⋊C8—31no—
75C3×C4⋊C8C2×D311yescharacteristic
76C3×C4⋊C8C2×D311yescharacteristic
77C3×C4⋊C8C22×C311yescharacteristic
78C3×C4⋊C8C22×C311yescharacteristic
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#817—21no—
88#817—21no—
89#817—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—81no—
106C32×C8—21no—
107C32×C8—41no—
108C32×C8—41no—
109C32×C8SD1612yescomplemented
110C3×C3⋊C8—41no—
111#498—31no—
112#476—31no—
113#461—31no—
114C8×D4—31no—
115#334C3×D311yescharacteristic, complemented
116#333—31no—
117#332—31no—
118C2×C3×Q8—61no—
119C2×C3×Q8—61no—
120C2×C3×D4—31no—
121C22×C3×C4—61no—
122C2×D12C3×D411yescharacteristic
123C2×C4×D3—21no—
124C2×Dic6—21no—
125C2×Dic6—21no—
126C3×SD16—122no—
127C2×C3×C8—21no—
128C2×C3×C8—21no—
129C2×C3×C8—21no—
130C2×C3×C8—21no—
131C2×C3×C8—21no—
132C2×C3×C8—21no—
133C2×C3×C8—41no—
134C2×C3×C8—41no—
135C2×C3×C8—61no—
136C2×C3×C8—122no—
137C2×C3×C8D1211yescharacteristic
138C2×C3×C8D1211yescharacteristic
139C2×C3×C8C3×D411yescharacteristic
140C2×C3×C8C3×D411yescharacteristic
141C3×C4⋊C4—31no—
142C3×C4⋊C4—61no—
143C3×C4⋊C4—61no—
144C3×C4⋊C4—61no—
145C3×C4⋊C4—61no—
146C3×C22⋊C4—61no—
147C3×C42—21no—
148C3×C42C22×D311yescharacteristic
149C3×C42C23×C311yescharacteristic
150(C2×D3)⋊C4—21no—
151C4⋊Dic3—21no—
152C4⋊Dic3—21no—
153C4⋊Dic3—21no—
154C4⋊Dic3—21no—
155C4⋊Dic3C3×D411yescharacteristic
156C2×C3⋊C8—21no—
157#204—42no—
158D3×C8—42no—
159C22×C32#12111yescharacteristic
160C2×C3×D3—22no—
161C2×C3×D3—41no—
162C2×C3×D3—41no—
163C32×C4—21no—
164C32×C4C2×SD1611yescharacteristic
165C32×C4C2×SD1611yescharacteristic
166C32×C4#13511yescharacteristic
167C32×C4#13711yescharacteristic
168C3×Dic3—41no—
169C3×Dic3—81no—
170C3×Dic3—81no—
171C2×SD16—61no—
172C22×C8—61no—
173C4⋊Q8—31no—
174C4⋊Q8—31no—
175C4×D4—31no—
176#106—61no—
177#106—61no—
178#106—61no—
179C4⋊C8—31no—
180C4⋊C8C2×C3×D311yescharacteristic
181C4⋊C8C2×C3×D311yescharacteristic
182#103—61no—
183#102—61no—
184C22⋊C8—61no—
185C4×C8C2×C3×D311yescharacteristic
186C23×C3—61no—
187C22×D3—21no—
188C3×Q8—121no—
189C3×Q8—121no—
190C3×Q8—241no—
191C3×D4—32no—
192C3×D4—61no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—61no—
197C2×C3×C4—121no—
198C2×C3×C4—121no—
199C2×C3×C4—121no—
200C2×C3×C4—121no—
201C2×C3×C4C2×D1211yescharacteristic
202C2×C3×C4D3×D411yescharacteristic
203C2×C3×C4#23911yescharacteristic
204C2×C3×C4C2×C3×D411yescharacteristic
205C2×C3×C4C2×C3×D411yescharacteristic
206C2×C3×C4C3×#4111yescharacteristic
207C2×Dic3—21no—
208C2×Dic3—41no—
209C2×Dic3—41no—
210D12—21no—
211D12C3×SD1612yes—
212C4×D3—41no—
213C4×D3—41no—
214Dic6—41no—
215Dic6—41no—
216Dic6—81no—
217C3×C8—21no—
218C3×C8—21no—
219C3×C8—22no—
220C3×C8—41no—
221C3×C8—41no—
222C3×C8—41no—
223C3×C8—41no—
224C3×C8—41no—
225C3×C8—81no—
226C3×C8—81no—
227C3×C8—121no—
228C3×C8#20412yescomplemented
229C3×C8C3×SD1612yescomplemented
230C3⋊C8—41no—
231C2×C32#46111yescharacteristic
232C2×C32#46511yescharacteristic
233C2×C32#47111yescharacteristic
234C3×D3—42no—
235C2×Q8—61no—
236C2×Q8—61no—
237C2×D4—31no—
238C22×C4—61no—
239SD16—122no—
240C2×C8—21no—
241C2×C8—21no—
242C2×C8—61no—
243C2×C8—122no—
244C2×C8C3×D1211yescharacteristic
245C2×C8C3×D1211yescharacteristic
246C4⋊C4—31no—
247C4⋊C4—61no—
248C4⋊C4—61no—
249C4⋊C4—61no—
250C4⋊C4—61no—
251C22⋊C4—61no—
252C42C22×C3×D311yescharacteristic
253C22×C3—21no—
254C22×C3—62no—
255C22×C3—121no—
256C22×C3—121no—
257C22×C3#89511yescharacteristic
258C22×C3C3×#12111yescharacteristic
259C2×D3—22no—
260C2×D3—41no—
261C2×D3—41no—
262C3×C4—21no—
263C3×C4—21no—
264C3×C4—21no—
265C3×C4—21no—
266C3×C4—21no—
267C3×C4—21no—
268C3×C4—41no—
269C3×C4—121no—
270C3×C4—241no—
271C3×C4—241no—
272C3×C4C2×#20411yescharacteristic
273C3×C4#90911yescharacteristic
274C3×C4D3×SD1611yescharacteristic
275C3×C4#91611yescharacteristic
276C3×C4C2×C3×SD1611yescharacteristic
277C3×C4C2×C3×SD1611yescharacteristic
278C3×C4C3×#13511yescharacteristic
279C3×C4C3×#13711yescharacteristic
280Dic3—41no—
281Dic3—81no—
282Dic3—81no—
283C32#167111yescharacteristic, complemented, Sylow
284C23—61no—
285Q8—121no—
286Q8—121no—
287Q8—241no—
288D4—32no—
289D4—61no—
290C2×C4—61no—
291C2×C4—121no—
292C2×C4—121no—
293C2×C4—121no—
294C2×C4—121no—
295C2×C4C2×C3×D1211yescharacteristic
296C2×C4C3×D3×D411yescharacteristic
297C2×C4C3×#23911yescharacteristic
298C8—21no—
299C8—41no—
300C8—41no—
301C8—121no—
302C8C3×#20412yescomplemented
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—122no—
307C2×C3#484111yescharacteristic
308C2×C3#486411yescharacteristic
309C2×C3#489811yescharacteristic
310C2×C3C3×#46111yescharacteristic
311C2×C3C3×#46511yescharacteristic
312C2×C3C3×#47111yescharacteristic
313D3—42no—
314C22—62no—
315C22—121no—
316C22—121no—
317C22C3×#89511yescharacteristic
318C4—21no—
319C4—121no—
320C4—241no—
321C4—241no—
322C4C2×C3×#20411yescharacteristic
323C4C3×#90911yescharacteristic
324C4C3×D3×SD1611yescharacteristic
325C4C3×#91611yescharacteristic
326C3—21no—
327C3#6853711yescharacteristic, direct product factor
328C3C3×#167111yescharacteristic, complemented
329C2—122no—
330C2C3×#484111yescharacteristic
331C2C3×#486411yescharacteristic
332C2C3×#489811yescharacteristic
subgroupG/H
centerC22×C3#895
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#334C2
socleC22×C32#121
prime radicalC2×C3×D12D4
hypercenterC3×#334D3
hypocenterC3C3×#1671
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×#4680C2semidirect
5. C32×#334C2semidirect
6. C3×#4482C2semidirect
7. C3×#4481C2semidirect
9. #68537C3direct (N × H)
32. #4680C2×C3semidirect
34. C3×#334D3semidirect
35. C3×#334C2×C3semidirect
38. #4482C2×C3semidirect
39. #4481C2×C3semidirect
109. C32×C8SD16semidirect
115. #334C3×D3semidirect
228. C3×C8#204semidirect
229. C3×C8C3×SD16semidirect
283. C32#1671semidirect
302. C8C3×#204semidirect
327. C3#68537direct (N × H)
328. C3C3×#1671semidirect

Maximal subgroups

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

subgroupindex
C3×#48422
C3×#48412
C3×C8×D122
C3×#46802
C32×#3342
C3×#44822
C3×#44812
C3×#16713
#685373