Finite Group Databasebeta

← C3×#68411 #11781470

Subgroups — C3×#68411 #11781470

Order 1152.

374 conjugacy classes of subgroups.

The subgroup lattice has 351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5075C211yesmaximal, characteristic
2C3×#5070C211yesmaximal, characteristic
3C3×#4849C211yesmaximal, characteristic, complemented
4C3×#4830C211yesmaximal, characteristic, complemented
5C32×#331C211yesmaximal, characteristic
6C3×#4486C211yesmaximal, characteristic, complemented
7C3×#4479C211yesmaximal, characteristic, complemented
8C3×#1682—31nomaximal
9#68411C311yesmaximal, characteristic, direct product factor
10C32×#127C2211yescharacteristic
11C2×C3×#214—21no—
12C2×C3×Dic12—21no—
13C3×#869C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15C32×C4⋊C8C2211yescharacteristic
16C32×C4⋊C8C2211yescharacteristic
17C3×#832—21no—
18C3×#832—21no—
19C3×#832—21no—
20C3×#816—21no—
21C3×Dic3⋊C8—21no—
22C3×C8×Dic3—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#486—31no—
26C3×#462—31no—
27C3×#460—31no—
28C3×C8×Q8—31no—
29#5075C2×C311yescharacteristic
30#5070C2×C311yescharacteristic
31#4849C2×C311yescharacteristic, complemented
32#4830C2×C311yescharacteristic, complemented
33C3×#335—31no—
34C3×#332—31no—
35C3×#331—21no—
36C3×#331D311yescharacteristic
37C3×#331C2×C311yescharacteristic
38#4486C2×C311yescharacteristic, complemented
39#4479C2×C311yescharacteristic, complemented
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C3×Dic6—21no—
44C2×C3×Dic6D411yescharacteristic
45C2×C32×C8—21no—
46C2×C32×C8—21no—
47C32×C42C2311yescharacteristic
48C3×#214—42no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3D411yescharacteristic
52C3×Dic3⋊C4—21no—
53C3×C4×Dic3—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57C3×Dic12—42no—
58#1682—31noSylow
59C2×C3×Q16—61no—
60C2×C3×SD16—61no—
61C3×C4⋊Q8—31no—
62C3×#127—21no—
63C3×#127C2×D311yescharacteristic
64C3×#127C22×C311yescharacteristic
65C3×C4×Q8—31no—
66C2×#214—21no—
67C2×Dic12—21no—
68#869C22×C311yescharacteristic
69C4×Dic6C22×C311yescharacteristic
70C3×C4⋊C8—21no—
71C3×C4⋊C8—21no—
72C3×C4⋊C8—31no—
73C3×C4⋊C8—61no—
74C3×C4⋊C8C2×D311yescharacteristic
75C3×C4⋊C8C2×D311yescharacteristic
76C3×C4⋊C8C22×C311yescharacteristic
77C3×C4⋊C8C22×C311yescharacteristic
78C3×#103—61no—
79C3×#102—61no—
80C3×#102—61no—
81C3×#102—61no—
82C3×C4×C8—31no—
83C3×C4×C8—61no—
84#832—21no—
85#832—21no—
86#832—21no—
87#816—21no—
88Dic3⋊C8—21no—
89C8×Dic3—21no—
90C4⋊(C3⋊C8)C22×C311yescharacteristic
91C4×C3⋊C8C22×C311yescharacteristic
92C23×C32—41no—
93C32×D4—41no—
94C32×D4—41no—
95C32×D4—41no—
96C32×D4—41no—
97C32×D4—81no—
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C3×Dic3—21no—
102C2×C3×Dic3—21no—
103C2×C3×Dic3—41no—
104C3×Dic6—21no—
105C3×Dic6—41no—
106C3×Dic6—41no—
107C3×Dic6D812yes—
108C32×C8—41no—
109C32×C8—41no—
110C3×C3⋊C8—21no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—41no—
113#486—31no—
114#462—31no—
115#460—31no—
116C8×Q8—31no—
117#335—31no—
118#332—31no—
119#331C3×D311yescharacteristic
120C2×C3×Q8—31no—
121C2×C3×Q8—61no—
122C2×C3×D4—22no—
123C2×C3×D4—21no—
124C2×C3×D4—21no—
125C2×C3×D4—21no—
126C2×C3×D4—21no—
127C2×C3×D4—21no—
128C2×C3×D4—21no—
129C2×C3×D4—41no—
130C2×C3×D4—41no—
131C2×Dic6—21no—
132C2×Dic6C3×D411yescharacteristic
133C3×Q16—122no—
134C3×SD16—122no—
135C2×C3×C8—21no—
136C2×C3×C8—21no—
137C2×C3×C8—21no—
138C2×C3×C8—21no—
139C2×C3×C8—31no—
140C2×C3×C8—31no—
141C2×C3×C8—41no—
142C2×C3×C8—41no—
143C2×C3×C8—61no—
144C3×C4⋊C4—31no—
145C3×C4⋊C4—61no—
146C3×C4⋊C4—61no—
147C3×C4⋊C4—61no—
148C3×C42—21no—
149C3×C42—61no—
150C3×C42C22×D311yescharacteristic
151C3×C42C23×C311yescharacteristic
152#214—42no—
153C4⋊Dic3—21no—
154C4⋊Dic3—21no—
155C4⋊Dic3C3×D411yescharacteristic
156Dic3⋊C4—21no—
157C4×Dic3—21no—
158C2×C3⋊C8—21no—
159C2×C3⋊C8C3×D411yescharacteristic
160C2×C3⋊C8C3×D411yescharacteristic
161Dic12—42no—
162C22×C32—81no—
163C22×C32—81no—
164C22×C32—81no—
165C22×C32#12111yescharacteristic
166C32×C4—21no—
167C32×C4C2×D811yescharacteristic
168C32×C4#13511yescharacteristic
169C32×C4#13511yescharacteristic
170C32×C4#13711yescharacteristic
171C3×Dic3—22no—
172C3×Dic3—41no—
173C3×Dic3—81no—
174C2×Q16—61no—
175C2×SD16—61no—
176C4⋊Q8—31no—
177#127C2×C3×D311yescharacteristic
178C4×Q8—31no—
179C4⋊C8—31no—
180C4⋊C8—61no—
181C4⋊C8C2×C3×D311yescharacteristic
182C4⋊C8C2×C3×D311yescharacteristic
183#103—61no—
184#102—61no—
185#102—61no—
186#102—61no—
187C4×C8—31no—
188C4×C8—61no—
189C23×C3—42no—
190C23×C3—41no—
191C23×C3—41no—
192C3×Q8—32no—
193C3×Q8—61no—
194C3×Q8—121no—
195C3×Q8—121no—
196C3×D4—41no—
197C3×D4—41no—
198C3×D4—41no—
199C3×D4—41no—
200C3×D4—41no—
201C3×D4—41no—
202C3×D4—41no—
203C3×D4—41no—
204C3×D4—81no—
205C3×D4—81no—
206C3×D4—81no—
207C3×D4—81no—
208C3×D4—81no—
209C3×D4—81no—
210C3×D4—82no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—61no—
215C2×C3×C4—61no—
216C2×C3×C4—121no—
217C2×C3×C4#23511yescharacteristic
218C2×C3×C4D3×D411yescharacteristic
219C2×C3×C4D3×D411yescharacteristic
220C2×C3×C4C2×C3×D411yescharacteristic
221C2×C3×C4C2×C3×D411yescharacteristic
222C2×C3×C4C3×#4111yescharacteristic
223C2×Dic3—21no—
224C2×Dic3—21no—
225C2×Dic3—41no—
226Dic6—21no—
227Dic6—41no—
228Dic6—41no—
229Dic6C3×D812yes—
230C3×C8—41no—
231C3×C8—41no—
232C3×C8—41no—
233C3×C8—41no—
234C3×C8—61no—
235C3×C8—61no—
236C3×C8—81no—
237C3×C8—81no—
238C3×C8—121no—
239C3⋊C8—21no—
240C3⋊C8—21no—
241C3⋊C8—41no—
242C2×C32—161no—
243C2×C32#46411yescharacteristic
244C2×C32#46611yescharacteristic
245C2×C32#47111yescharacteristic
246C2×Q8—31no—
247C2×Q8—61no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—21no—
251Q16—122no—
252SD16—122no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—31no—
256C2×C8—31no—
257C2×C8—61no—
258C4⋊C4—31no—
259C4⋊C4—61no—
260C4⋊C4—61no—
261C4⋊C4—61no—
262C42—61no—
263C42C22×C3×D311yescharacteristic
264C22×C3—21no—
265C22×C3—82no—
266C22×C3—82no—
267C22×C3—82no—
268C22×C3—81no—
269C22×C3—81no—
270C22×C3—81no—
271C22×C3—81no—
272C22×C3—81no—
273C22×C3—81no—
274C22×C3#88411yescharacteristic
275C22×C3C3×#12111yescharacteristic
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—41no—
283C3×C4—62no—
284C3×C4—121no—
285C3×C4—241no—
286C3×C4D3×D811yescharacteristic
287C3×C4#91211yescharacteristic
288C3×C4#91511yescharacteristic
289C3×C4#91611yescharacteristic
290C3×C4C2×C3×D811yescharacteristic
291C3×C4C3×#13511yescharacteristic
292C3×C4C3×#13511yescharacteristic
293C3×C4C3×#13711yescharacteristic
294Dic3—22no—
295Dic3—41no—
296Dic3—81no—
297C32#168211yescharacteristic, complemented, Sylow
298C23—41no—
299Q8—32no—
300Q8—61no—
301Q8—121no—
302Q8—121no—
303D4—41no—
304D4—41no—
305D4—41no—
306D4—41no—
307D4—81no—
308C2×C4—61no—
309C2×C4—61no—
310C2×C4—121no—
311C2×C4C3×#23511yescharacteristic
312C2×C4C3×D3×D411yescharacteristic
313C2×C4C3×D3×D411yescharacteristic
314C8—41no—
315C8—41no—
316C8—61no—
317C8—61no—
318C8—121no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—162no—
323C2×C3—161no—
324C2×C3—161no—
325C2×C3#474811yescharacteristic
326C2×C3#476711yescharacteristic
327C2×C3#477511yescharacteristic
328C2×C3C3×#46411yescharacteristic
329C2×C3C3×#46611yescharacteristic
330C2×C3C3×#47111yescharacteristic
331C22—81no—
332C22—81no—
333C22—81no—
334C22C3×#88411yescharacteristic
335C4—21no—
336C4—62no—
337C4—121no—
338C4—241no—
339C4C3×D3×D811yescharacteristic
340C4C3×#91211yescharacteristic
341C4C3×#91511yescharacteristic
342C4C3×#91611yescharacteristic
343C3—21no—
344C3#6841111yescharacteristic, direct product factor
345C3C3×#168211yescharacteristic, complemented
346C2—161no—
347C2C3×#474811yescharacteristic
348C2C3×#476711yescharacteristic
349C2C3×#477511yescharacteristic
subgroupG/H
centerC22×C3#884
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#331C2
socleC22×C32#121
prime radicalC32×#127C22
hypercenterC3×#331D3
hypocenterC3C3×#1682
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
3. C3×#4849C2semidirect
4. C3×#4830C2semidirect
6. C3×#4486C2semidirect
7. C3×#4479C2semidirect
9. #68411C3direct (N × H)
31. #4849C2×C3semidirect
32. #4830C2×C3semidirect
38. #4486C2×C3semidirect
39. #4479C2×C3semidirect
297. C32#1682semidirect
344. C3#68411direct (N × H)
345. C3C3×#1682semidirect

Maximal subgroups

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

subgroupindex
C3×#50752
C3×#50702
C3×#48492
C3×#48302
C32×#3312
C3×#44862
C3×#44792
C3×#16823
#684113