Finite Group Databasebeta

← C3×#68396 #11781236

Subgroups — C3×#68396 #11781236

Order 1152.

394 conjugacy classes of subgroups.

The subgroup lattice has 367 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5072C211yesmaximal, characteristic
2C3×#5070C211yesmaximal, characteristic, complemented
3C3×#4842C211yesmaximal, characteristic, complemented
4C3×#4834C211yesmaximal, characteristic, complemented
5C32×#331C211yesmaximal, characteristic, complemented
6C3×#4481C211yesmaximal, characteristic, complemented
7C3×#4480C211yesmaximal, characteristic, complemented
8C3×#1677—31nomaximal
9#68396C311yesmaximal, characteristic, direct product factor
10C32×#127C2211yescharacteristic
11C2×C3×#213—21no—
12C2×C3×D3×C8—21no—
13C3×C4×D12C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C32×C4⋊C8C2211yescharacteristic
16C32×C4⋊C8C2211yescharacteristic
17C3×#832—21no—
18C3×#832—21no—
19C3×#832—21no—
20C3×#821—21no—
21C3×(C2×D3)⋊C8—21no—
22C3×#817—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#486—31no—
26C3×#476—31no—
27C3×#459—31no—
28C3×C8×D4—31no—
29#5072C2×C311yescharacteristic
30#5070C2×C311yescharacteristic, complemented
31#4842C2×C311yescharacteristic, complemented
32#4834C2×C311yescharacteristic, complemented
33C3×#334—31no—
34C3×#333—31no—
35C3×#331—21no—
36C3×#331D311yescharacteristic, complemented
37C3×#331C2×C311yescharacteristic, complemented
38#4481C2×C311yescharacteristic, complemented
39#4480C2×C311yescharacteristic, complemented
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C3×D12D411yescharacteristic
44C2×C3×C4×D3—21no—
45C2×C3×Dic6—21no—
46C2×C32×C8—21no—
47C2×C32×C8—21no—
48C32×C42C2311yescharacteristic
49C3×#213—42no—
50C3×(C2×D3)⋊C4—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3D411yescharacteristic
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57C3×D3×C8—42no—
58#1677—31noSylow
59C2×C3×D8—61no—
60C22×C3×C8—61no—
61C3×C4⋊Q8—31no—
62C3×#127—21no—
63C3×#127C2×D311yescharacteristic
64C3×#127C22×C311yescharacteristic
65C3×C4×D4—31no—
66C2×#213—21no—
67C2×D3×C8—21no—
68C4×D12C22×C311yescharacteristic
69#869C22×C311yescharacteristic
70C3×#106—61no—
71C3×C4⋊C8—21no—
72C3×C4⋊C8—21no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8C2×D311yescharacteristic
75C3×C4⋊C8C2×D311yescharacteristic
76C3×C4⋊C8C22×C311yescharacteristic
77C3×C4⋊C8C22×C311yescharacteristic
78C3×#102—61no—
79C3×#102—61no—
80C3×#102—61no—
81C3×#102—61no—
82C3×C22⋊C8—61no—
83C3×C4×C8—31no—
84#832—21no—
85#832—21no—
86#832—21no—
87#821—21no—
88(C2×D3)⋊C8—21no—
89#817—21no—
90C4⋊(C3⋊C8)C22×C311yescharacteristic
91C4×C3⋊C8C22×C311yescharacteristic
92C23×C32—41no—
93C22×C3×D3—21no—
94C32×D4—41no—
95C32×D4—41no—
96C32×D4—41no—
97C32×D4—41no—
98C32×D4—81no—
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C3×Dic3—21no—
103C2×C3×Dic3—41no—
104C3×D12—21no—
105C3×D12SD1612yes—
106C3×C4×D3—41no—
107C3×C4×D3—41no—
108C3×Dic6—81no—
109C32×C8—41no—
110C32×C8—41no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—21no—
113C3×C3⋊C8—41no—
114#486—31no—
115#476—31no—
116#459—31no—
117C8×D4—31no—
118#334—31no—
119#333—31no—
120#331C3×D311yescharacteristic, complemented
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—31no—
130C2×C3×D4—41no—
131C2×C3×D4—41no—
132C22×C3×C4—61no—
133C2×D12C3×D411yescharacteristic
134C2×C4×D3—21no—
135C2×Dic6—21no—
136C3×D8—122no—
137C2×C3×C8—21no—
138C2×C3×C8—21no—
139C2×C3×C8—21no—
140C2×C3×C8—21no—
141C2×C3×C8—31no—
142C2×C3×C8—31no—
143C2×C3×C8—41no—
144C2×C3×C8—41no—
145C2×C3×C8—61no—
146C2×C3×C8—122no—
147C3×C4⋊C4—31no—
148C3×C4⋊C4—61no—
149C3×C4⋊C4—61no—
150C3×C22⋊C4—61no—
151C3×C42—21no—
152C3×C42C22×D311yescharacteristic
153C3×C42C23×C311yescharacteristic
154#213—42no—
155(C2×D3)⋊C4—21no—
156C4⋊Dic3—21no—
157C4⋊Dic3—21no—
158C4⋊Dic3C3×D411yescharacteristic
159C2×C3⋊C8—21no—
160C2×C3⋊C8C3×D411yescharacteristic
161C2×C3⋊C8C3×D411yescharacteristic
162D3×C8—42no—
163C22×C32—81no—
164C22×C32—81no—
165C22×C32—81no—
166C22×C32#12111yescharacteristic
167C2×C3×D3—22no—
168C2×C3×D3—41no—
169C2×C3×D3—41no—
170C32×C4—21no—
171C32×C4C2×SD1611yescharacteristic
172C32×C4#13511yescharacteristic
173C32×C4#13511yescharacteristic
174C32×C4AGL(1,ℤ/8)11yescharacteristic
175C3×Dic3—41no—
176C3×Dic3—81no—
177C2×D8—61no—
178C22×C8—61no—
179C4⋊Q8—31no—
180#127C2×C3×D311yescharacteristic
181C4×D4—31no—
182#106—61no—
183C4⋊C8—31no—
184C4⋊C8C2×C3×D311yescharacteristic
185C4⋊C8C2×C3×D311yescharacteristic
186#102—61no—
187#102—61no—
188#102—61no—
189#102—61no—
190C22⋊C8—61no—
191C4×C8—31no—
192C23×C3—42no—
193C23×C3—41no—
194C23×C3—41no—
195C23×C3—61no—
196C22×D3—21no—
197C3×Q8—241no—
198C3×D4—32no—
199C3×D4—41no—
200C3×D4—41no—
201C3×D4—41no—
202C3×D4—41no—
203C3×D4—41no—
204C3×D4—41no—
205C3×D4—41no—
206C3×D4—41no—
207C3×D4—61no—
208C3×D4—81no—
209C3×D4—81no—
210C3×D4—81no—
211C3×D4—81no—
212C3×D4—81no—
213C3×D4—81no—
214C3×D4—82no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—61no—
219C2×C3×C4—121no—
220C2×C3×C4—121no—
221C2×C3×C4—121no—
222C2×C3×C4#23511yescharacteristic
223C2×C3×C4D3×D411yescharacteristic
224C2×C3×C4D3×D411yescharacteristic
225C2×C3×C4C2×C3×D411yescharacteristic
226C2×C3×C4C2×C3×D411yescharacteristic
227C2×C3×C4C3×#4111yescharacteristic
228C2×Dic3—21no—
229C2×Dic3—41no—
230D12—21no—
231D12C3×SD1612yes—
232C4×D3—41no—
233C4×D3—41no—
234Dic6—81no—
235C3×C8—41no—
236C3×C8—41no—
237C3×C8—41no—
238C3×C8—41no—
239C3×C8—61no—
240C3×C8—61no—
241C3×C8—81no—
242C3×C8—81no—
243C3×C8—121no—
244C3⋊C8—21no—
245C3⋊C8—21no—
246C3⋊C8—41no—
247C2×C32—161no—
248C2×C32#46311yescharacteristic
249C2×C32#46511yescharacteristic
250C2×C32#47211yescharacteristic
251C3×D3—42no—
252C2×Q8—61no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—31no—
257C22×C4—61no—
258D8—122no—
259C2×C8—21no—
260C2×C8—21no—
261C2×C8—31no—
262C2×C8—31no—
263C2×C8—61no—
264C2×C8—122no—
265C4⋊C4—31no—
266C4⋊C4—61no—
267C4⋊C4—61no—
268C22⋊C4—61no—
269C42C22×C3×D311yescharacteristic
270C22×C3—21no—
271C22×C3—62no—
272C22×C3—82no—
273C22×C3—82no—
274C22×C3—82no—
275C22×C3—81no—
276C22×C3—81no—
277C22×C3—81no—
278C22×C3—81no—
279C22×C3—81no—
280C22×C3—81no—
281C22×C3—121no—
282C22×C3—121no—
283C22×C3#88411yescharacteristic
284C22×C3C3×#12111yescharacteristic
285C2×D3—22no—
286C2×D3—41no—
287C2×D3—41no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—41no—
295C3×C4—121no—
296C3×C4—241no—
297C3×C4#91111yescharacteristic
298C3×C4#91211yescharacteristic
299C3×C4D3×SD1611yescharacteristic
300C3×C4#91611yescharacteristic
301C3×C4C2×C3×SD1611yescharacteristic
302C3×C4C3×#13511yescharacteristic
303C3×C4C3×#13511yescharacteristic
304C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
305Dic3—41no—
306Dic3—81no—
307C32#167711yescharacteristic, complemented, Sylow
308C23—41no—
309C23—61no—
310Q8—241no—
311D4—32no—
312D4—41no—
313D4—41no—
314D4—41no—
315D4—41no—
316D4—61no—
317D4—81no—
318C2×C4—61no—
319C2×C4—121no—
320C2×C4—121no—
321C2×C4—121no—
322C2×C4C3×#23511yescharacteristic
323C2×C4C3×D3×D411yescharacteristic
324C2×C4C3×D3×D411yescharacteristic
325C8—41no—
326C8—41no—
327C8—61no—
328C8—61no—
329C8—121no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—122no—
334C2×C3—162no—
335C2×C3—161no—
336C2×C3—161no—
337C2×C3#474911yescharacteristic
338C2×C3#477811yescharacteristic
339C2×C3#478711yescharacteristic
340C2×C3C3×#46311yescharacteristic
341C2×C3C3×#46511yescharacteristic
342C2×C3C3×#47211yescharacteristic
343D3—42no—
344C22—62no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22—121no—
349C22—121no—
350C22C3×#88411yescharacteristic
351C4—21no—
352C4—121no—
353C4—241no—
354C4C3×#91111yescharacteristic
355C4C3×#91211yescharacteristic
356C4C3×D3×SD1611yescharacteristic
357C4C3×#91611yescharacteristic
358C3—21no—
359C3#6839611yescharacteristic, direct product factor
360C3C3×#167711yescharacteristic, complemented
361C2—122no—
362C2—161no—
363C2C3×#474911yescharacteristic
364C2C3×#477811yescharacteristic
365C2C3×#478711yescharacteristic
subgroupG/H
centerC22×C3#884
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#331C2
socleC22×C32#121
prime radicalC3×#5072C2
hypercenterC3×#331D3
hypocenterC3C3×#1677
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
2. C3×#5070C2semidirect
3. C3×#4842C2semidirect
4. C3×#4834C2semidirect
5. C32×#331C2semidirect
6. C3×#4481C2semidirect
7. C3×#4480C2semidirect
9. #68396C3direct (N × H)
30. #5070C2×C3semidirect
31. #4842C2×C3semidirect
32. #4834C2×C3semidirect
36. C3×#331D3semidirect
37. C3×#331C2×C3semidirect
38. #4481C2×C3semidirect
39. #4480C2×C3semidirect
120. #331C3×D3semidirect
307. C32#1677semidirect
359. C3#68396direct (N × H)
360. C3C3×#1677semidirect

Maximal subgroups

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

subgroupindex
C3×#50722
C3×#50702
C3×#48422
C3×#48342
C32×#3312
C3×#44812
C3×#44802
C3×#16773
#683963