Finite Group Databasebeta

← C3×#68409 #11780913

Subgroups — C3×#68409 #11780913

Order 1152.

418 conjugacy classes of subgroups.

The subgroup lattice has 383 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5075C211yesmaximal, characteristic, complemented
2C3×#5073C211yesmaximal, characteristic
3C3×#4848C211yesmaximal, characteristic, complemented
4C3×#4830C211yesmaximal, characteristic, complemented
5C32×#331C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic, complemented
7C3×#4479C211yesmaximal, characteristic, complemented
8C3×#1668—31nomaximal
9#68409C311yesmaximal, characteristic, direct product factor
10C32×#127C2211yescharacteristic
11C2×C3×#214—21no—
12C2×C3×#213—21no—
13C2×C3×#213—21no—
14C2×C3×#204—21no—
15C3×#874C2211yescharacteristic
16C3×C4×Dic6C2211yescharacteristic
17C32×C4⋊C8C2211yescharacteristic
18C32×C4⋊C8C2211yescharacteristic
19C3×#832—21no—
20C3×#821—21no—
21C3×Dic3⋊C8—21no—
22C3×C8×Dic3—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#493—31no—
26C3×#460—31no—
27C3×#460—31no—
28C3×C8×Q8—31no—
29#5075C2×C311yescharacteristic, complemented
30#5073C2×C311yescharacteristic
31#4848C2×C311yescharacteristic, complemented
32#4830C2×C311yescharacteristic, complemented
33C3×#335—31no—
34C3×#331—21no—
35C3×#331—31no—
36C3×#331D311yescharacteristic, complemented
37C3×#331C2×C311yescharacteristic, complemented
38#4485C2×C311yescharacteristic, complemented
39#4479C2×C311yescharacteristic, complemented
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×Dic6D411yescharacteristic
47C2×C32×C8—21no—
48C2×C32×C8—21no—
49C32×C42C2311yescharacteristic
50C3×#214—42no—
51C3×#213—42no—
52C3×#213—42no—
53C3×C4⋊Dic3D411yescharacteristic
54C3×Dic3⋊C4—21no—
55C3×C4×Dic3—21no—
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8D411yescharacteristic
58C2×C3×C3⋊C8D411yescharacteristic
59C3×#204—42no—
60#1668—31noSylow
61C2×C3×SD16—61no—
62C2×C3×SD16—61no—
63C2×C3×D8—61no—
64C2×C3×D8—61no—
65C3×#127—21no—
66C3×#127—31no—
67C3×#127C2×D311yescharacteristic
68C3×#127C22×C311yescharacteristic
69C3×C4×Q8—31no—
70C2×#214—21no—
71C2×#213—21no—
72C2×#213—21no—
73C2×#204—21no—
74#874C22×C311yescharacteristic
75C4×Dic6C22×C311yescharacteristic
76C3×C4⋊C8—21no—
77C3×C4⋊C8—21no—
78C3×C4⋊C8—31no—
79C3×C4⋊C8—61no—
80C3×C4⋊C8C2×D311yescharacteristic
81C3×C4⋊C8C2×D311yescharacteristic
82C3×C4⋊C8C22×C311yescharacteristic
83C3×C4⋊C8C22×C311yescharacteristic
84C3×#102—61no—
85C3×#102—61no—
86C3×C4×C8—31no—
87C3×C4×C8—61no—
88#832—21no—
89#821—21no—
90Dic3⋊C8—21no—
91C8×Dic3—21no—
92C4⋊(C3⋊C8)C22×C311yescharacteristic
93C4×C3⋊C8C22×C311yescharacteristic
94C23×C32—41no—
95C22×C3×D3—41no—
96C32×D4—41no—
97C32×D4—41no—
98C32×D4—41no—
99C32×D4—41no—
100C32×D4—81no—
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C3×Dic3—21no—
105C2×C3×Dic3—21no—
106C3×D12—41no—
107C3×D12—41no—
108C3×D12—41no—
109C3×D12—41no—
110C3×D12—81no—
111C3×Dic6—21no—
112C3×Dic6D812yescomplemented
113C32×C8—41no—
114C32×C8—41no—
115C3×C3⋊C8—21no—
116C3×C3⋊C8—41no—
117C3×C3⋊C8SD1612yescomplemented
118#493—31no—
119#460—31no—
120#460—31no—
121C8×Q8—31no—
122#335—31no—
123#331—31no—
124#331C3×D311yescharacteristic, complemented
125C2×C3×Q8—31no—
126C2×C3×D4—22no—
127C2×C3×D4—21no—
128C2×C3×D4—21no—
129C2×C3×D4—21no—
130C2×C3×D4—21no—
131C2×C3×D4—21no—
132C2×C3×D4—21no—
133C2×C3×D4—41no—
134C2×C3×D4—41no—
135C2×C3×D4—61no—
136C2×C3×D4—61no—
137C2×C3×D4—61no—
138C2×D12—21no—
139C2×D12—21no—
140C2×D12—21no—
141C2×Dic6C3×D411yescharacteristic
142C3×SD16—122no—
143C3×SD16—122no—
144C3×D8—122no—
145C3×D8—122no—
146C2×C3×C8—21no—
147C2×C3×C8—21no—
148C2×C3×C8—21no—
149C2×C3×C8—21no—
150C2×C3×C8—31no—
151C2×C3×C8—31no—
152C2×C3×C8—41no—
153C2×C3×C8—41no—
154C2×C3×C8—61no—
155C3×C4⋊C4—31no—
156C3×C4⋊C4—61no—
157C3×C42—21no—
158C3×C42—61no—
159C3×C42C22×D311yescharacteristic
160C3×C42C23×C311yescharacteristic
161#214—42no—
162#213—42no—
163#213—42no—
164C4⋊Dic3C3×D411yescharacteristic
165Dic3⋊C4—21no—
166C4×Dic3—21no—
167C2×C3⋊C8—21no—
168C2×C3⋊C8C3×D411yescharacteristic
169C2×C3⋊C8C3×D411yescharacteristic
170#204—42no—
171C22×C32—81no—
172C22×C32—81no—
173C22×C32—81no—
174C22×C32#12111yescharacteristic
175C2×C3×D3—81no—
176C2×C3×D3—81no—
177C2×C3×D3—81no—
178C32×C4—21no—
179C32×C4C2×D811yescharacteristic
180C32×C4C2×SD1611yescharacteristic
181C32×C4#13511yescharacteristic
182C32×C4AGL(1,ℤ/8)11yescharacteristic
183C3×Dic3—22no—
184C3×Dic3—41no—
185C2×SD16—61no—
186C2×SD16—61no—
187C2×D8—61no—
188C2×D8—61no—
189#127—31no—
190#127C2×C3×D311yescharacteristic
191C4×Q8—31no—
192C4⋊C8—31no—
193C4⋊C8—61no—
194C4⋊C8C2×C3×D311yescharacteristic
195C4⋊C8C2×C3×D311yescharacteristic
196#102—61no—
197#102—61no—
198C4×C8—31no—
199C4×C8—61no—
200C23×C3—42no—
201C23×C3—41no—
202C23×C3—41no—
203C23×C3—121no—
204C22×D3—41no—
205C3×Q8—32no—
206C3×Q8—61no—
207C3×D4—41no—
208C3×D4—41no—
209C3×D4—41no—
210C3×D4—41no—
211C3×D4—41no—
212C3×D4—41no—
213C3×D4—41no—
214C3×D4—41no—
215C3×D4—81no—
216C3×D4—81no—
217C3×D4—81no—
218C3×D4—81no—
219C3×D4—81no—
220C3×D4—81no—
221C3×D4—82no—
222C3×D4—121no—
223C3×D4—121no—
224C3×D4—121no—
225C3×D4—121no—
226C3×D4—241no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—61no—
231C2×C3×C4—61no—
232C2×C3×C4#23511yescharacteristic
233C2×C3×C4D3×D411yescharacteristic
234C2×C3×C4D3×D411yescharacteristic
235C2×C3×C4C2×C3×D411yescharacteristic
236C2×C3×C4C2×C3×D411yescharacteristic
237C2×C3×C4C3×#4111yescharacteristic
238C2×Dic3—21no—
239C2×Dic3—21no—
240D12—41no—
241D12—41no—
242D12—41no—
243D12—41no—
244D12—81no—
245Dic6—21no—
246Dic6C3×D812yescomplemented
247C3×C8—32no—
248C3×C8—41no—
249C3×C8—41no—
250C3×C8—41no—
251C3×C8—41no—
252C3×C8—61no—
253C3×C8—81no—
254C3×C8—81no—
255C3×C8—121no—
256C3⋊C8—21no—
257C3⋊C8—41no—
258C3⋊C8C3×SD1612yescomplemented
259C2×C32—161no—
260C2×C32#46011yescharacteristic
261C2×C32#46611yescharacteristic
262C2×C32#47211yescharacteristic
263C3×D3—161no—
264C2×Q8—31no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—61no—
269C2×D4—61no—
270C2×D4—61no—
271SD16—122no—
272SD16—122no—
273D8—122no—
274D8—122no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—31no—
278C2×C8—31no—
279C2×C8—61no—
280C4⋊C4—31no—
281C4⋊C4—61no—
282C42—61no—
283C42C22×C3×D311yescharacteristic
284C22×C3—21no—
285C22×C3—82no—
286C22×C3—82no—
287C22×C3—82no—
288C22×C3—81no—
289C22×C3—81no—
290C22×C3—81no—
291C22×C3—81no—
292C22×C3—81no—
293C22×C3—81no—
294C22×C3—241no—
295C22×C3—241no—
296C22×C3—241no—
297C22×C3#88411yescharacteristic
298C22×C3C3×#12111yescharacteristic
299C2×D3—81no—
300C2×D3—81no—
301C2×D3—81no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—41no—
309C3×C4—62no—
310C3×C4—121no—
311C3×C4D3×D811yescharacteristic
312C3×C4#91111yescharacteristic
313C3×C4D3×SD1611yescharacteristic
314C3×C4#91611yescharacteristic
315C3×C4C2×C3×D811yescharacteristic
316C3×C4C2×C3×SD1611yescharacteristic
317C3×C4C3×#13511yescharacteristic
318C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
319Dic3—22no—
320Dic3—41no—
321C32#166811yescharacteristic, complemented, Sylow
322C23—41no—
323C23—121no—
324Q8—32no—
325Q8—61no—
326D4—41no—
327D4—41no—
328D4—41no—
329D4—41no—
330D4—81no—
331D4—121no—
332D4—121no—
333D4—121no—
334D4—121no—
335D4—241no—
336C2×C4—61no—
337C2×C4—61no—
338C2×C4C3×#23511yescharacteristic
339C2×C4C3×D3×D411yescharacteristic
340C2×C4C3×D3×D411yescharacteristic
341C8—32no—
342C8—41no—
343C8—41no—
344C8—61no—
345C8—121no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—162no—
350C2×C3—161no—
351C2×C3—161no—
352C2×C3—481no—
353C2×C3#474911yescharacteristic
354C2×C3#476211yescharacteristic
355C2×C3#477511yescharacteristic
356C2×C3C3×#46011yescharacteristic
357C2×C3C3×#46611yescharacteristic
358C2×C3C3×#47211yescharacteristic
359D3—161no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—241no—
364C22—241no—
365C22—241no—
366C22C3×#88411yescharacteristic
367C4—21no—
368C4—62no—
369C4—121no—
370C4C3×D3×D811yescharacteristic
371C4C3×#91111yescharacteristic
372C4C3×D3×SD1611yescharacteristic
373C4C3×#91611yescharacteristic
374C3—21no—
375C3#6840911yescharacteristic, direct product factor
376C3C3×#166811yescharacteristic, complemented
377C2—161no—
378C2—481no—
379C2C3×#474911yescharacteristic
380C2C3×#476211yescharacteristic
381C2C3×#477511yescharacteristic
subgroupG/H
centerC22×C3#884
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#331C2
socleC22×C32#121
prime radicalC3×#5073C2
hypercenterC3×#331D3
hypocenterC3C3×#1668
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#331

Complements

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

NH ≅ G/Ntype
1. C3×#5075C2semidirect
3. C3×#4848C2semidirect
4. C3×#4830C2semidirect
5. C32×#331C2semidirect
6. C3×#4485C2semidirect
7. C3×#4479C2semidirect
9. #68409C3direct (N × H)
29. #5075C2×C3semidirect
31. #4848C2×C3semidirect
32. #4830C2×C3semidirect
36. C3×#331D3semidirect
37. C3×#331C2×C3semidirect
38. #4485C2×C3semidirect
39. #4479C2×C3semidirect
112. C3×Dic6D8semidirect
117. C3×C3⋊C8SD16semidirect
124. #331C3×D3semidirect
246. Dic6C3×D8semidirect
258. C3⋊C8C3×SD16semidirect
321. C32#1668semidirect
375. C3#68409direct (N × H)
376. C3C3×#1668semidirect

Maximal subgroups

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

subgroupindex
C3×#50752
C3×#50732
C3×#48482
C3×#48302
C32×#3312
C3×#44852
C3×#44792
C3×#16683
#684093