Finite Group Databasebeta

← C3×#68536 #11780792

Subgroups — C3×#68536 #11780792

Order 1152.

403 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#4846C211yesmaximal, characteristic, complemented
2C3×#4843C211yesmaximal, characteristic
3C3×#4693C211yesmaximal, characteristic, complemented
4C3×C8×D12C211yesmaximal, characteristic, complemented
5C32×#334C211yesmaximal, characteristic, complemented
6C3×#4486C211yesmaximal, characteristic, complemented
7C3×#4485C211yesmaximal, characteristic, complemented
8C3×#1665—31nomaximal
9#68536C311yesmaximal, characteristic, direct product factor
10C2×C3×D24—21no—
11C2×C3×#204—21no—
12C2×C3×#204—21no—
13C2×C3×D3×C8—21no—
14C3×#874C2211yescharacteristic
15C3×C4×D12C2211yescharacteristic
16C3×#869C2211yescharacteristic
17C32×C4⋊C8C2211yescharacteristic
18C32×C4⋊C8C2211yescharacteristic
19C32×C4×C8C2211yescharacteristic
20C3×#821—21no—
21C3×#821—21no—
22C3×(C2×D3)⋊C8—21no—
23C3×#818—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×#492—31no—
26C3×#474—31no—
27C3×#459—31no—
28C3×C8×D4—31no—
29#4846C2×C311yescharacteristic, complemented
30#4843C2×C311yescharacteristic
31#4693C2×C311yescharacteristic, complemented
32C8×D12C2×C311yescharacteristic, complemented
33C3×#334—21no—
34C3×#334D311yescharacteristic, complemented
35C3×#334C2×C311yescharacteristic, complemented
36C3×#332—31no—
37C3×#331—31no—
38#4486C2×C311yescharacteristic, complemented
39#4485C2×C311yescharacteristic, complemented
40C2×C3×D12—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12D411yescharacteristic
44C2×C3×C4×D3—21no—
45C2×C3×Dic6—21no—
46C2×C32×C8—21no—
47C2×C32×C8—21no—
48C2×C32×C8D411yescharacteristic
49C2×C32×C8D411yescharacteristic
50C32×C42C2311yescharacteristic
51C3×(C2×D3)⋊C4—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3D411yescharacteristic
55C2×C3×C3⋊C8—21no—
56C3×D24—42no—
57C3×#204—42no—
58C3×#204—42no—
59C3×D3×C8—42no—
60#1665—31noSylow
61C2×C3×SD16—61no—
62C2×C3×SD16—61no—
63C2×C3×D8—61no—
64C22×C3×C8—61no—
65C3×C4⋊Q8—31no—
66C3×#127—31no—
67C3×C4×D4—31no—
68C2×D24—21no—
69C2×#204—21no—
70C2×#204—21no—
71C2×D3×C8—21no—
72#874C22×C311yescharacteristic
73C4×D12C22×C311yescharacteristic
74#869C22×C311yescharacteristic
75C3×#107—61no—
76C3×C4⋊C8—21no—
77C3×C4⋊C8—21no—
78C3×C4⋊C8—31no—
79C3×C4⋊C8C2×D311yescharacteristic
80C3×C4⋊C8C2×D311yescharacteristic
81C3×C4⋊C8C22×C311yescharacteristic
82C3×C4⋊C8C22×C311yescharacteristic
83C3×#102—61no—
84C3×#102—61no—
85C3×C22⋊C8—61no—
86C3×C4×C8—21no—
87C3×C4×C8C2×D311yescharacteristic
88C3×C4×C8C22×C311yescharacteristic
89#821—21no—
90#821—21no—
91(C2×D3)⋊C8—21no—
92#818—21no—
93C4⋊(C3⋊C8)C22×C311yescharacteristic
94C22×C3×D3—21no—
95C22×C3×D3—41no—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C2×C3×Dic3—21no—
100C2×C3×Dic3—41no—
101C3×D12—21no—
102C3×D12—41no—
103C3×D12—41no—
104C3×D12—41no—
105C3×D12—41no—
106C3×D12—81no—
107C3×D12SD1612yescomplemented
108C3×C4×D3—41no—
109C3×C4×D3—41no—
110C3×Dic6—41no—
111C3×Dic6—41no—
112C32×C8—21no—
113C32×C8—41no—
114C32×C8—41no—
115C32×C8D812yescomplemented
116C3×C3⋊C8—41no—
117#492—31no—
118#474—31no—
119#459—31no—
120C8×D4—31no—
121#334C3×D311yescharacteristic, complemented
122#332—31no—
123#331—31no—
124C2×C3×Q8—61no—
125C2×C3×D4—31no—
126C2×C3×D4—61no—
127C2×C3×D4—61no—
128C2×C3×D4—61no—
129C22×C3×C4—61no—
130C2×D12—21no—
131C2×D12—21no—
132C2×D12—21no—
133C2×D12C3×D411yescharacteristic
134C2×C4×D3—21no—
135C2×Dic6—21no—
136C3×SD16—122no—
137C3×SD16—122no—
138C3×D8—122no—
139C2×C3×C8—21no—
140C2×C3×C8—21no—
141C2×C3×C8—21no—
142C2×C3×C8—21no—
143C2×C3×C8—21no—
144C2×C3×C8—21no—
145C2×C3×C8—41no—
146C2×C3×C8—41no—
147C2×C3×C8—61no—
148C2×C3×C8—122no—
149C2×C3×C8D1211yescharacteristic
150C2×C3×C8D1211yescharacteristic
151C2×C3×C8C3×D411yescharacteristic
152C2×C3×C8C3×D411yescharacteristic
153C3×C4⋊C4—31no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4—61no—
156C3×C22⋊C4—61no—
157C3×C42—21no—
158C3×C42C22×D311yescharacteristic
159C3×C42C23×C311yescharacteristic
160(C2×D3)⋊C4—21no—
161C4⋊Dic3—21no—
162C4⋊Dic3—21no—
163C4⋊Dic3C3×D411yescharacteristic
164C2×C3⋊C8—21no—
165D24—42no—
166#204—42no—
167#204—42no—
168D3×C8—42no—
169C22×C32#12111yescharacteristic
170C2×C3×D3—22no—
171C2×C3×D3—41no—
172C2×C3×D3—41no—
173C2×C3×D3—81no—
174C2×C3×D3—81no—
175C2×C3×D3—81no—
176C32×C4—21no—
177C32×C4C2×D811yescharacteristic
178C32×C4C2×SD1611yescharacteristic
179C32×C4#13511yescharacteristic
180C32×C4AGL(1,ℤ/8)11yescharacteristic
181C3×Dic3—41no—
182C3×Dic3—81no—
183C2×SD16—61no—
184C2×SD16—61no—
185C2×D8—61no—
186C22×C8—61no—
187C4⋊Q8—31no—
188#127—31no—
189C4×D4—31no—
190#107—61no—
191C4⋊C8—31no—
192C4⋊C8C2×C3×D311yescharacteristic
193C4⋊C8C2×C3×D311yescharacteristic
194#102—61no—
195#102—61no—
196C22⋊C8—61no—
197C4×C8C2×C3×D311yescharacteristic
198C23×C3—61no—
199C23×C3—121no—
200C22×D3—21no—
201C22×D3—41no—
202C3×Q8—121no—
203C3×Q8—121no—
204C3×D4—32no—
205C3×D4—61no—
206C3×D4—121no—
207C3×D4—121no—
208C3×D4—121no—
209C3×D4—121no—
210C3×D4—241no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—61no—
215C2×C3×C4—121no—
216C2×C3×C4—121no—
217C2×C3×C4—121no—
218C2×C3×C4C2×D1211yescharacteristic
219C2×C3×C4D3×D411yescharacteristic
220C2×C3×C4#23911yescharacteristic
221C2×C3×C4C2×C3×D411yescharacteristic
222C2×C3×C4C2×C3×D411yescharacteristic
223C2×C3×C4C3×#4111yescharacteristic
224C2×Dic3—21no—
225C2×Dic3—41no—
226D12—21no—
227D12—41no—
228D12—41no—
229D12—41no—
230D12—41no—
231D12—81no—
232D12C3×SD1612yescomplemented
233C4×D3—41no—
234C4×D3—41no—
235Dic6—41no—
236Dic6—41no—
237C3×C8—21no—
238C3×C8—21no—
239C3×C8—22no—
240C3×C8—41no—
241C3×C8—41no—
242C3×C8—41no—
243C3×C8—41no—
244C3×C8—41no—
245C3×C8—81no—
246C3×C8—81no—
247C3×C8—121no—
248C3×C8D2412yescomplemented
249C3×C8C3×D812yescomplemented
250C3⋊C8—41no—
251C2×C32#45911yescharacteristic
252C2×C32#46511yescharacteristic
253C2×C32#47111yescharacteristic
254C3×D3—42no—
255C3×D3—161no—
256C2×Q8—61no—
257C2×D4—31no—
258C2×D4—61no—
259C2×D4—61no—
260C2×D4—61no—
261C22×C4—61no—
262SD16—122no—
263SD16—122no—
264D8—122no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—61no—
268C2×C8—122no—
269C2×C8C3×D1211yescharacteristic
270C2×C8C3×D1211yescharacteristic
271C4⋊C4—31no—
272C4⋊C4—61no—
273C4⋊C4—61no—
274C22⋊C4—61no—
275C42C22×C3×D311yescharacteristic
276C22×C3—21no—
277C22×C3—62no—
278C22×C3—121no—
279C22×C3—121no—
280C22×C3—241no—
281C22×C3—241no—
282C22×C3—241no—
283C22×C3#89511yescharacteristic
284C22×C3C3×#12111yescharacteristic
285C2×D3—22no—
286C2×D3—41no—
287C2×D3—41no—
288C2×D3—81no—
289C2×D3—81no—
290C2×D3—81no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—41no—
298C3×C4—121no—
299C3×C4—241no—
300C3×C4C2×D2411yescharacteristic
301C3×C4#90811yescharacteristic
302C3×C4D3×SD1611yescharacteristic
303C3×C4#91611yescharacteristic
304C3×C4C2×C3×D811yescharacteristic
305C3×C4C2×C3×SD1611yescharacteristic
306C3×C4C3×#13511yescharacteristic
307C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
308Dic3—41no—
309Dic3—81no—
310C32#166511yescharacteristic, complemented, Sylow
311C23—61no—
312C23—121no—
313Q8—121no—
314Q8—121no—
315D4—32no—
316D4—61no—
317D4—121no—
318D4—121no—
319D4—121no—
320D4—121no—
321D4—241no—
322C2×C4—61no—
323C2×C4—121no—
324C2×C4—121no—
325C2×C4—121no—
326C2×C4C2×C3×D1211yescharacteristic
327C2×C4C3×D3×D411yescharacteristic
328C2×C4C3×#23911yescharacteristic
329C8—21no—
330C8—41no—
331C8—41no—
332C8—121no—
333C8C3×D2412yescomplemented
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—122no—
338C2×C3—481no—
339C2×C3#484311yescharacteristic
340C2×C3#486411yescharacteristic
341C2×C3#489811yescharacteristic
342C2×C3C3×#45911yescharacteristic
343C2×C3C3×#46511yescharacteristic
344C2×C3C3×#47111yescharacteristic
345D3—42no—
346D3—161no—
347C22—62no—
348C22—121no—
349C22—121no—
350C22—241no—
351C22—241no—
352C22—241no—
353C22C3×#89511yescharacteristic
354C4—21no—
355C4—121no—
356C4—241no—
357C4C2×C3×D2411yescharacteristic
358C4C3×#90811yescharacteristic
359C4C3×D3×SD1611yescharacteristic
360C4C3×#91611yescharacteristic
361C3—21no—
362C3#6853611yescharacteristic, direct product factor
363C3C3×#166511yescharacteristic, complemented
364C2—122no—
365C2—481no—
366C2C3×#484311yescharacteristic
367C2C3×#486411yescharacteristic
368C2C3×#489811yescharacteristic
subgroupG/H
centerC22×C3#895
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#334C2
socleC22×C32#121
prime radicalC3×#4843C2
hypercenterC3×#334D3
hypocenterC3C3×#1665
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#334

Complements

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

NH ≅ G/Ntype
1. C3×#4846C2semidirect
3. C3×#4693C2semidirect
4. C3×C8×D12C2semidirect
5. C32×#334C2semidirect
6. C3×#4486C2semidirect
7. C3×#4485C2semidirect
9. #68536C3direct (N × H)
29. #4846C2×C3semidirect
31. #4693C2×C3semidirect
32. C8×D12C2×C3semidirect
34. C3×#334D3semidirect
35. C3×#334C2×C3semidirect
38. #4486C2×C3semidirect
39. #4485C2×C3semidirect
107. C3×D12SD16semidirect
115. C32×C8D8semidirect
121. #334C3×D3semidirect
232. D12C3×SD16semidirect
248. C3×C8D24semidirect
249. C3×C8C3×D8semidirect
310. C32#1665semidirect
333. C8C3×D24semidirect
362. C3#68536direct (N × H)
363. C3C3×#1665semidirect

Maximal subgroups

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

subgroupindex
C3×#48462
C3×#48432
C3×#46932
C3×C8×D122
C32×#3342
C3×#44862
C3×#44852
C3×#16653
#685363