Finite Group Databasebeta

← C3×#68410 #11781283

Subgroups — C3×#68410 #11781283

Order 1152.

362 conjugacy classes of subgroups.

The subgroup lattice has 343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5075C211yesmaximal, characteristic
2C3×#5070C211yesmaximal, characteristic
3C3×#4850C211yesmaximal, characteristic, complemented
4C3×#4830C211yesmaximal, characteristic, complemented
5C32×#331C211yesmaximal, characteristic
6C3×#4481C211yesmaximal, characteristic, complemented
7C3×#4480C211yesmaximal, characteristic, complemented
8C3×#1678—31nomaximal
9#68410C311yesmaximal, characteristic, direct product factor
10C32×#127C2211yescharacteristic
11C2×C3×#214—21no—
12C3×#869C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14C32×C4⋊C8C2211yescharacteristic
15C32×C4⋊C8C2211yescharacteristic
16C3×#832—21no—
17C3×#832—21no—
18C3×#832—21no—
19C3×#818—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×#477—31no—
27C3×#460—31no—
28C3×C8×Q8—31no—
29#5075C2×C311yescharacteristic
30#5070C2×C311yescharacteristic
31#4850C2×C311yescharacteristic, complemented
32#4830C2×C311yescharacteristic, complemented
33C3×#334—31no—
34C3×#333—31no—
35C3×#331—21no—
36C3×#331D311yescharacteristic
37C3×#331C2×C311yescharacteristic
38#4481C2×C311yescharacteristic, complemented
39#4480C2×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
57#1678—31noSylow
58C2×C3×SD16—61no—
59C3×C4⋊Q8—31no—
60C3×#127—21no—
61C3×#127C2×D311yescharacteristic
62C3×#127C22×C311yescharacteristic
63C3×C4×Q8—31no—
64C2×#214—21no—
65#869C22×C311yescharacteristic
66C4×Dic6C22×C311yescharacteristic
67C3×#107—61no—
68C3×C4⋊C8—21no—
69C3×C4⋊C8—21no—
70C3×C4⋊C8—31no—
71C3×C4⋊C8—61no—
72C3×C4⋊C8C2×D311yescharacteristic
73C3×C4⋊C8C2×D311yescharacteristic
74C3×C4⋊C8C22×C311yescharacteristic
75C3×C4⋊C8C22×C311yescharacteristic
76C3×#103—61no—
77C3×#102—61no—
78C3×#102—61no—
79C3×#102—61no—
80C3×C4×C8—31no—
81C3×C4×C8—61no—
82#832—21no—
83#832—21no—
84#832—21no—
85#818—21no—
86#816—21no—
87Dic3⋊C8—21no—
88C8×Dic3—21no—
89C4⋊(C3⋊C8)C22×C311yescharacteristic
90C4×C3⋊C8C22×C311yescharacteristic
91C23×C32—41no—
92C32×D4—41no—
93C32×D4—41no—
94C32×D4—41no—
95C32×D4—41no—
96C32×D4—81no—
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4#4111yescharacteristic
100C2×C3×Dic3—21no—
101C2×C3×Dic3—21no—
102C2×C3×Dic3—41no—
103C3×Dic6—21no—
104C3×Dic6—81no—
105C3×Dic6SD1612yes—
106C32×C8—41no—
107C32×C8—41no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—41no—
111#486—31no—
112#477—31no—
113#460—31no—
114C8×Q8—31no—
115#334—31no—
116#333—31no—
117#331C3×D311yescharacteristic
118C2×C3×Q8—31no—
119C2×C3×Q8—61no—
120C2×C3×D4—22no—
121C2×C3×D4—21no—
122C2×C3×D4—21no—
123C2×C3×D4—21no—
124C2×C3×D4—21no—
125C2×C3×D4—21no—
126C2×C3×D4—21no—
127C2×C3×D4—41no—
128C2×C3×D4—41no—
129C2×Dic6—21no—
130C2×Dic6C3×D411yescharacteristic
131C3×SD16—122no—
132C2×C3×C8—21no—
133C2×C3×C8—21no—
134C2×C3×C8—21no—
135C2×C3×C8—21no—
136C2×C3×C8—31no—
137C2×C3×C8—31no—
138C2×C3×C8—41no—
139C2×C3×C8—41no—
140C2×C3×C8—61no—
141C3×C4⋊C4—31no—
142C3×C4⋊C4—61no—
143C3×C4⋊C4—61no—
144C3×C4⋊C4—61no—
145C3×C42—21no—
146C3×C42—61no—
147C3×C42C22×D311yescharacteristic
148C3×C42C23×C311yescharacteristic
149#214—42no—
150C4⋊Dic3—21no—
151C4⋊Dic3—21no—
152C4⋊Dic3C3×D411yescharacteristic
153Dic3⋊C4—21no—
154C4×Dic3—21no—
155C2×C3⋊C8—21no—
156C2×C3⋊C8C3×D411yescharacteristic
157C2×C3⋊C8C3×D411yescharacteristic
158C22×C32—81no—
159C22×C32—81no—
160C22×C32—81no—
161C22×C32#12111yescharacteristic
162C32×C4—21no—
163C32×C4C2×SD1611yescharacteristic
164C32×C4#13511yescharacteristic
165C32×C4#13511yescharacteristic
166C32×C4#13711yescharacteristic
167C3×Dic3—22no—
168C3×Dic3—41no—
169C3×Dic3—81no—
170C2×SD16—61no—
171C4⋊Q8—31no—
172#127C2×C3×D311yescharacteristic
173C4×Q8—31no—
174#107—61no—
175C4⋊C8—31no—
176C4⋊C8—61no—
177C4⋊C8C2×C3×D311yescharacteristic
178C4⋊C8C2×C3×D311yescharacteristic
179#103—61no—
180#102—61no—
181#102—61no—
182#102—61no—
183C4×C8—31no—
184C4×C8—61no—
185C23×C3—42no—
186C23×C3—41no—
187C23×C3—41no—
188C3×Q8—32no—
189C3×Q8—61no—
190C3×Q8—241no—
191C3×D4—41no—
192C3×D4—41no—
193C3×D4—41no—
194C3×D4—41no—
195C3×D4—41no—
196C3×D4—41no—
197C3×D4—41no—
198C3×D4—41no—
199C3×D4—81no—
200C3×D4—81no—
201C3×D4—81no—
202C3×D4—81no—
203C3×D4—81no—
204C3×D4—81no—
205C3×D4—82no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—61no—
210C2×C3×C4—61no—
211C2×C3×C4—121no—
212C2×C3×C4#23511yescharacteristic
213C2×C3×C4D3×D411yescharacteristic
214C2×C3×C4D3×D411yescharacteristic
215C2×C3×C4C2×C3×D411yescharacteristic
216C2×C3×C4C2×C3×D411yescharacteristic
217C2×C3×C4C3×#4111yescharacteristic
218C2×Dic3—21no—
219C2×Dic3—21no—
220C2×Dic3—41no—
221Dic6—21no—
222Dic6—81no—
223Dic6C3×SD1612yes—
224C3×C8—41no—
225C3×C8—41no—
226C3×C8—41no—
227C3×C8—41no—
228C3×C8—61no—
229C3×C8—61no—
230C3×C8—81no—
231C3×C8—81no—
232C3×C8—121no—
233C3⋊C8—21no—
234C3⋊C8—21no—
235C3⋊C8—41no—
236C2×C32—161no—
237C2×C32#46411yescharacteristic
238C2×C32#46511yescharacteristic
239C2×C32#47211yescharacteristic
240C2×Q8—31no—
241C2×Q8—61no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—21no—
245SD16—122no—
246C2×C8—21no—
247C2×C8—21no—
248C2×C8—31no—
249C2×C8—31no—
250C2×C8—61no—
251C4⋊C4—31no—
252C4⋊C4—61no—
253C4⋊C4—61no—
254C4⋊C4—61no—
255C42—61no—
256C42C22×C3×D311yescharacteristic
257C22×C3—21no—
258C22×C3—82no—
259C22×C3—82no—
260C22×C3—82no—
261C22×C3—81no—
262C22×C3—81no—
263C22×C3—81no—
264C22×C3—81no—
265C22×C3—81no—
266C22×C3—81no—
267C22×C3#88411yescharacteristic
268C22×C3C3×#12111yescharacteristic
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—41no—
276C3×C4—62no—
277C3×C4—121no—
278C3×C4—241no—
279C3×C4#91211yescharacteristic
280C3×C4#91211yescharacteristic
281C3×C4D3×SD1611yescharacteristic
282C3×C4#91511yescharacteristic
283C3×C4C2×C3×SD1611yescharacteristic
284C3×C4C3×#13511yescharacteristic
285C3×C4C3×#13511yescharacteristic
286C3×C4C3×#13711yescharacteristic
287Dic3—22no—
288Dic3—41no—
289Dic3—81no—
290C32#167811yescharacteristic, complemented, Sylow
291C23—41no—
292Q8—32no—
293Q8—61no—
294Q8—241no—
295D4—41no—
296D4—41no—
297D4—41no—
298D4—41no—
299D4—81no—
300C2×C4—61no—
301C2×C4—61no—
302C2×C4—121no—
303C2×C4C3×#23511yescharacteristic
304C2×C4C3×D3×D411yescharacteristic
305C2×C4C3×D3×D411yescharacteristic
306C8—41no—
307C8—41no—
308C8—61no—
309C8—61no—
310C8—121no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—162no—
315C2×C3—161no—
316C2×C3—161no—
317C2×C3#474911yescharacteristic
318C2×C3#476711yescharacteristic
319C2×C3#477811yescharacteristic
320C2×C3C3×#46411yescharacteristic
321C2×C3C3×#46511yescharacteristic
322C2×C3C3×#47211yescharacteristic
323C22—81no—
324C22—81no—
325C22—81no—
326C22C3×#88411yescharacteristic
327C4—21no—
328C4—62no—
329C4—121no—
330C4—241no—
331C4C3×#91211yescharacteristic
332C4C3×#91211yescharacteristic
333C4C3×D3×SD1611yescharacteristic
334C4C3×#91511yescharacteristic
335C3—21no—
336C3#6841011yescharacteristic, direct product factor
337C3C3×#167811yescharacteristic, complemented
338C2—161no—
339C2C3×#474911yescharacteristic
340C2C3×#476711yescharacteristic
341C2C3×#477811yescharacteristic
subgroupG/H
centerC22×C3#884
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#331C2
socleC22×C32#121
prime radicalC32×#127C22
hypercenterC3×#331D3
hypocenterC3C3×#1678
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×#4850C2semidirect
4. C3×#4830C2semidirect
6. C3×#4481C2semidirect
7. C3×#4480C2semidirect
9. #68410C3direct (N × H)
31. #4850C2×C3semidirect
32. #4830C2×C3semidirect
38. #4481C2×C3semidirect
39. #4480C2×C3semidirect
290. C32#1678semidirect
336. C3#68410direct (N × H)
337. C3C3×#1678semidirect

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×#48502
C3×#48302
C32×#3312
C3×#44812
C3×#44802
C3×#16783
#684103