Finite Group Databasebeta

← C3×#68446 #11781436

Subgroups — C3×#68446 #11781436

Order 1152.

396 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5088C211yesmaximal, characteristic, complemented
2C3×#5083C211yesmaximal, characteristic, complemented
3C3×#4843C211yesmaximal, characteristic
4C3×#4834C211yesmaximal, characteristic, complemented
5C32×#332C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic, complemented
7C3×#4479C211yesmaximal, characteristic, complemented
8C3×#1681—31nomaximal
9#68446C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C2×C3×#215—21no—
12C2×C3×D24—21no—
13C2×C3×D3×C8—21no—
14C3×#874C2211yescharacteristic
15C3×C4×D12C2211yescharacteristic
16C32×C4⋊C8C2211yescharacteristic
17C32×C4⋊C8C2211yescharacteristic
18C3×#835—21no—
19C3×#821—21no—
20C3×(C2×D3)⋊C8—21no—
21C3×#809—21no—
22C3×#809—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#486—31no—
26C3×#461—31no—
27C3×#459—31no—
28C3×C8×D4—31no—
29#5088C2×C311yescharacteristic, complemented
30#5083C2×C311yescharacteristic, complemented
31#4843C2×C311yescharacteristic
32#4834C2×C311yescharacteristic, complemented
33C3×#335—31no—
34C3×#332—21no—
35C3×#332D311yescharacteristic, complemented
36C3×#332C2×C311yescharacteristic, complemented
37C3×#331—31no—
38#4485C2×C311yescharacteristic, complemented
39#4479C2×C311yescharacteristic, complemented
40C2×C32×Q8—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C32×C8—21no—
47C2×C32×C8—21no—
48C32×C4⋊C4—21no—
49C32×C4⋊C4—21no—
50C32×C42C2311yescharacteristic
51C3×#215—42no—
52C3×(C2×D3)⋊C4—21no—
53C3×C4⋊Dic3D411yescharacteristic
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57C3×D24—42no—
58C3×D3×C8—42no—
59#1681—31noSylow
60C2×C3×SD16—61no—
61C2×C3×D8—61no—
62C22×C3×C8—61no—
63C3×C4⋊Q8—21no—
64C3×C4⋊Q8C2×D311yescharacteristic
65C3×C4⋊Q8C22×C311yescharacteristic
66C3×#127—31no—
67C3×C4×D4—31no—
68C2×#215—21no—
69C2×D24—21no—
70C2×D3×C8—21no—
71#874C22×C311yescharacteristic
72C4×D12C22×C311yescharacteristic
73C3×C4⋊C8—21no—
74C3×C4⋊C8—21no—
75C3×C4⋊C8—31no—
76C3×C4⋊C8C2×D311yescharacteristic
77C3×C4⋊C8C2×D311yescharacteristic
78C3×C4⋊C8C22×C311yescharacteristic
79C3×C4⋊C8C22×C311yescharacteristic
80C3×#103—61no—
81C3×#102—61no—
82C3×#102—61no—
83C3×#102—61no—
84C3×C22⋊C8—61no—
85C3×C4×C8—31no—
86#835—21no—
87#821—21no—
88(C2×D3)⋊C8—21no—
89#809—21no—
90#809—21no—
91C4⋊(C3⋊C8)C22×C311yescharacteristic
92C4×C3⋊C8C22×C311yescharacteristic
93C22×C3×D3—21no—
94C22×C3×D3—41no—
95C32×Q8—41no—
96C32×Q8—41no—
97C2×C32×C4—41no—
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C3×Dic3—21no—
102C3×D12—21no—
103C3×D12—41no—
104C3×D12—41no—
105C3×D12—41no—
106C3×D12—41no—
107C3×D12—81no—
108C3×D12D812yes—
109C3×C4×D3—41no—
110C3×C4×D3—41no—
111C32×C8—41no—
112C32×C8—41no—
113C3×C3⋊C8—21no—
114C3×C3⋊C8—21no—
115C3×C3⋊C8—41no—
116#486—31no—
117#461—31no—
118#459—31no—
119C8×D4—31no—
120#335—31no—
121#332C3×D311yescharacteristic, complemented
122#331—31no—
123C2×C3×Q8—21no—
124C2×C3×Q8—21no—
125C2×C3×Q8—41no—
126C2×C3×D4—31no—
127C2×C3×D4—61no—
128C2×C3×D4—61no—
129C2×C3×D4—61no—
130C22×C3×C4—61no—
131C2×D12—21no—
132C2×D12—21no—
133C2×D12—21no—
134C2×D12C3×D411yescharacteristic
135C2×C4×D3—21no—
136C3×SD16—122no—
137C3×D8—122no—
138C2×C3×C8—21no—
139C2×C3×C8—21no—
140C2×C3×C8—21no—
141C2×C3×C8—21no—
142C2×C3×C8—31no—
143C2×C3×C8—31no—
144C2×C3×C8—41no—
145C2×C3×C8—41no—
146C2×C3×C8—61no—
147C2×C3×C8—122no—
148C3×C4⋊C4—22no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—21no—
153C3×C4⋊C4—31no—
154C3×C4⋊C4—41no—
155C3×C22⋊C4—61no—
156C3×C42—21no—
157C3×C42C22×D311yescharacteristic
158C3×C42C23×C311yescharacteristic
159#215—42no—
160(C2×D3)⋊C4—21no—
161C4⋊Dic3C3×D411yescharacteristic
162C2×C3⋊C8—21no—
163C2×C3⋊C8C3×D411yescharacteristic
164C2×C3⋊C8C3×D411yescharacteristic
165D24—42no—
166D3×C8—42no—
167C22×C32#12111yescharacteristic
168C2×C3×D3—22no—
169C2×C3×D3—41no—
170C2×C3×D3—41no—
171C2×C3×D3—81no—
172C2×C3×D3—81no—
173C2×C3×D3—81no—
174C32×C4—21no—
175C32×C4—81no—
176C32×C4C2×D811yescharacteristic
177C32×C4#13511yescharacteristic
178C32×C4#13511yescharacteristic
179C32×C4AGL(1,ℤ/8)11yescharacteristic
180C3×Dic3—41no—
181C2×SD16—61no—
182C2×D8—61no—
183C22×C8—61no—
184C4⋊Q8C2×C3×D311yescharacteristic
185#127—31no—
186C4×D4—31no—
187C4⋊C8—31no—
188C4⋊C8C2×C3×D311yescharacteristic
189C4⋊C8C2×C3×D311yescharacteristic
190#103—61no—
191#102—61no—
192#102—61no—
193#102—61no—
194C22⋊C8—61no—
195C4×C8—31no—
196C23×C3—61no—
197C23×C3—121no—
198C22×D3—21no—
199C22×D3—41no—
200C3×Q8—41no—
201C3×Q8—41no—
202C3×Q8—41no—
203C3×Q8—41no—
204C3×Q8—81no—
205C3×Q8—81no—
206C3×D4—32no—
207C3×D4—61no—
208C3×D4—121no—
209C3×D4—121no—
210C3×D4—121no—
211C3×D4—121no—
212C3×D4—241no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—42no—
217C2×C3×C4—41no—
218C2×C3×C4—41no—
219C2×C3×C4—61no—
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—
229D12—21no—
230D12—41no—
231D12—41no—
232D12—41no—
233D12—41no—
234D12—81no—
235D12C3×D812yes—
236C4×D3—41no—
237C4×D3—41no—
238C3×C8—41no—
239C3×C8—41no—
240C3×C8—41no—
241C3×C8—41no—
242C3×C8—61no—
243C3×C8—61no—
244C3×C8—81no—
245C3×C8—81no—
246C3×C8—121no—
247C3⋊C8—21no—
248C3⋊C8—21no—
249C3⋊C8—41no—
250C2×C32#46311yescharacteristic
251C2×C32#46611yescharacteristic
252C2×C32#47111yescharacteristic
253C3×D3—42no—
254C3×D3—161no—
255C2×Q8—21no—
256C2×D4—31no—
257C2×D4—61no—
258C2×D4—61no—
259C2×D4—61no—
260C22×C4—61no—
261SD16—122no—
262D8—122no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—31no—
266C2×C8—31no—
267C2×C8—61no—
268C2×C8—122no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—31no—
272C22⋊C4—61no—
273C42C22×C3×D311yescharacteristic
274C22×C3—21no—
275C22×C3—62no—
276C22×C3—121no—
277C22×C3—121no—
278C22×C3—241no—
279C22×C3—241no—
280C22×C3—241no—
281C22×C3#88411yescharacteristic
282C22×C3C3×#12111yescharacteristic
283C2×D3—22no—
284C2×D3—41no—
285C2×D3—41no—
286C2×D3—81no—
287C2×D3—81no—
288C2×D3—81no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—41no—
296C3×C4—82no—
297C3×C4—81no—
298C3×C4—81no—
299C3×C4—121no—
300C3×C4D3×D811yescharacteristic
301C3×C4#91411yescharacteristic
302C3×C4#91611yescharacteristic
303C3×C4#91911yescharacteristic
304C3×C4C2×C3×D811yescharacteristic
305C3×C4C3×#13511yescharacteristic
306C3×C4C3×#13511yescharacteristic
307C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
308Dic3—41no—
309C32#168111yescharacteristic, complemented, Sylow
310C23—61no—
311C23—121no—
312Q8—41no—
313Q8—41no—
314D4—32no—
315D4—61no—
316D4—121no—
317D4—121no—
318D4—121no—
319D4—121no—
320D4—241no—
321C2×C4—41no—
322C2×C4—61no—
323C2×C4—121no—
324C2×C4—121no—
325C2×C4C3×#23511yescharacteristic
326C2×C4C3×D3×D411yescharacteristic
327C2×C4C3×D3×D411yescharacteristic
328C8—41no—
329C8—41no—
330C8—61no—
331C8—61no—
332C8—121no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—122no—
337C2×C3—481no—
338C2×C3#475411yescharacteristic
339C2×C3#477511yescharacteristic
340C2×C3#481911yescharacteristic
341C2×C3C3×#46311yescharacteristic
342C2×C3C3×#46611yescharacteristic
343C2×C3C3×#47111yescharacteristic
344D3—42no—
345D3—161no—
346C22—62no—
347C22—121no—
348C22—121no—
349C22—241no—
350C22—241no—
351C22—241no—
352C22C3×#88411yescharacteristic
353C4—21no—
354C4—81no—
355C4—121no—
356C4C3×D3×D811yescharacteristic
357C4C3×#91411yescharacteristic
358C4C3×#91611yescharacteristic
359C4C3×#91911yescharacteristic
360C3—21no—
361C3#6844611yescharacteristic, direct product factor
362C3C3×#168111yescharacteristic, complemented
363C2—122no—
364C2—481no—
365C2C3×#475411yescharacteristic
366C2C3×#477511yescharacteristic
367C2C3×#481911yescharacteristic
subgroupG/H
centerC22×C3#884
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#332C2
socleC22×C32#121
prime radicalC3×#4843C2
hypercenterC3×#332D3
hypocenterC3C3×#1681
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#332

Complements

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

NH ≅ G/Ntype
1. C3×#5088C2semidirect
2. C3×#5083C2semidirect
4. C3×#4834C2semidirect
5. C32×#332C2semidirect
6. C3×#4485C2semidirect
7. C3×#4479C2semidirect
9. #68446C3direct (N × H)
29. #5088C2×C3semidirect
30. #5083C2×C3semidirect
32. #4834C2×C3semidirect
35. C3×#332D3semidirect
36. C3×#332C2×C3semidirect
38. #4485C2×C3semidirect
39. #4479C2×C3semidirect
121. #332C3×D3semidirect
309. C32#1681semidirect
361. C3#68446direct (N × H)
362. C3C3×#1681semidirect

Maximal subgroups

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

subgroupindex
C3×#50882
C3×#50832
C3×#48432
C3×#48342
C32×#3322
C3×#44852
C3×#44792
C3×#16813
#684463