Finite Group Databasebeta

← C3×#68406 #11779762

Subgroups — C3×#68406 #11779762

Order 1152.

466 conjugacy classes of subgroups.

The subgroup lattice has 399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5713C211yesmaximal, characteristic
2C3×#5070C211yesmaximal, characteristic
3C3×#4851C211yesmaximal, characteristic, complemented
4C3×#4849C211yesmaximal, characteristic, complemented
5C32×#331C211yesmaximal, characteristic
6C3×#4484C211yesmaximal, characteristic, complemented
7C3×#4484C211yesmaximal, characteristic, complemented
8C3×#1640—31nomaximal
9#68406C311yesmaximal, characteristic, direct product factor
10C32×#127C2211yescharacteristic
11C3×#936—21no—
12C3×#936—21no—
13C3×#935—22no—
14C3×D4×Dic3—21no—
15C3×D4×Dic3—21no—
16C2×C3×Dic12—21no—
17C3×#869C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic
21C32×C4⋊C8C2211yescharacteristic
22C3×#832—22no—
23C3×#817—21no—
24C3×#816—21no—
25C3×#816—21no—
26C3×C4×C3⋊C8C2211yescharacteristic
27C3×#559—31no—
28#5713C2×C311yescharacteristic
29C3×#486—31no—
30C3×#475—31no—
31C3×#462—31no—
32#5070C2×C311yescharacteristic
33#4851C2×C311yescharacteristic, complemented
34#4849C2×C311yescharacteristic, complemented
35C3×#331—21no—
36C3×#331D311yescharacteristic
37C3×#331C2×C311yescharacteristic
38C3×Q8⋊C8—31no—
39C3×Q8⋊C8—31no—
40#4484C2×C311yescharacteristic, complemented
41#4484C2×C311yescharacteristic, complemented
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4D412yes—
45C22×C3×Dic3—22no—
46C2×C3×Dic6—21no—
47C2×C3×Dic6D411yescharacteristic
48C2×C3×Dic6D411yescharacteristic
49C2×C32×C8—21no—
50C2×C32×C8—21no—
51C32×C42C2311yescharacteristic
52C3×#217—22no—
53C3×#217—22no—
54C3×#217—22no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3D411yescharacteristic
58C3×C4⋊Dic3D411yescharacteristic
59C3×Dic3⋊C4—21no—
60C3×Dic3⋊C4—21no—
61C3×C4×Dic3—21no—
62C3×C4×Dic3—21no—
63C2×C3×C3⋊C8—21no—
64C3×Dic12—42no—
65#1640—31noSylow
66C2×C3×Q16—61no—
67C3×C4⋊Q8—31no—
68C3×#127—21no—
69C3×#127C2×D311yescharacteristic
70C3×#127C22×C311yescharacteristic
71C3×#124—61no—
72C3×#124—61no—
73C3×#123—62no—
74C3×C4×Q8—31no—
75C3×C4×Q8—31no—
76C3×C4×D4—61no—
77C3×C4×D4—61no—
78#936—21no—
79#936—21no—
80#935—22no—
81D4×Dic3—21no—
82D4×Dic3—21no—
83C2×Dic12—21no—
84#869C22×C311yescharacteristic
85C4×Dic6C22×C311yescharacteristic
86C4×Dic6C22×C311yescharacteristic
87C3×#106—61no—
88C3×C4⋊C8—21no—
89C3×C4⋊C8—21no—
90C3×C4⋊C8C2×D311yescharacteristic
91C3×C4⋊C8C2×D311yescharacteristic
92C3×C4⋊C8C22×C311yescharacteristic
93C3×C4⋊C8C22×C311yescharacteristic
94C3×#103—61no—
95C3×#103—61no—
96C3×#102—62no—
97C3×C4×C8—31no—
98#832—22no—
99#817—21no—
100#816—21no—
101#816—21no—
102C4×C3⋊C8C22×C311yescharacteristic
103C23×C32—22no—
104C32×D4—42no—
105C32×D4—41no—
106C32×D4—41no—
107C32×D4—41no—
108C32×D4—41no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C3×Dic3—21no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—41no—
117C2×C3×Dic3—82no—
118C3×Dic6—21no—
119C3×Dic6—21no—
120C3×Dic6—21no—
121C3×Dic6—21no—
122C3×Dic6—41no—
123C3×Dic6—41no—
124C32×C8—41no—
125C32×C8—41no—
126C3×C3⋊C8—41no—
127#559—31no—
128#486—31no—
129#475—31no—
130#462—31no—
131#331C3×D311yescharacteristic
132Q8⋊C8—31no—
133Q8⋊C8—31no—
134C2×C3×Q8—31no—
135C2×C3×Q8—31no—
136C2×C3×Q8—61no—
137C2×C3×D4—21no—
138C2×C3×D4—21no—
139C2×C3×D4—21no—
140C2×C3×D4—21no—
141C2×C3×D4—22no—
142C2×C3×D4—41no—
143C2×C3×D4—41no—
144C2×C3×D4D1212yes—
145C2×C3×D4C3×D412yes—
146C22×C3×C4—62no—
147C22×Dic3—22no—
148C2×Dic6—21no—
149C2×Dic6C3×D411yescharacteristic
150C2×Dic6C3×D411yescharacteristic
151C3×Q16—122no—
152C2×C3×C8—21no—
153C2×C3×C8—21no—
154C2×C3×C8—21no—
155C2×C3×C8—21no—
156C2×C3×C8—41no—
157C2×C3×C8—41no—
158C2×C3×C8—61no—
159C3×C4⋊C4—31no—
160C3×C4⋊C4—31no—
161C3×C4⋊C4—61no—
162C3×C4⋊C4—61no—
163C3×C4⋊C4—61no—
164C3×C4⋊C4—61no—
165C3×C22⋊C4—62no—
166C3×C22⋊C4—62no—
167C3×C22⋊C4—62no—
168C3×C42—21no—
169C3×C42—61no—
170C3×C42—61no—
171C3×C42C22×D311yescharacteristic
172C3×C42C23×C311yescharacteristic
173#217—22no—
174#217—22no—
175#217—22no—
176C4⋊Dic3—21no—
177C4⋊Dic3—21no—
178C4⋊Dic3C3×D411yescharacteristic
179C4⋊Dic3C3×D411yescharacteristic
180Dic3⋊C4—21no—
181Dic3⋊C4—21no—
182C4×Dic3—21no—
183C4×Dic3—21no—
184C2×C3⋊C8—21no—
185Dic12—42no—
186C22×C32—42no—
187C22×C32—42no—
188C22×C32—42no—
189C22×C32#12011yescharacteristic
190C32×C4—21no—
191C32×C4#13511yescharacteristic
192C32×C4#13511yescharacteristic
193C32×C4AGL(1,ℤ/8)11yescharacteristic
194C32×C4#13711yescharacteristic
195C3×Dic3—41no—
196C3×Dic3—41no—
197C3×Dic3—41no—
198C3×Dic3—41no—
199C3×Dic3—81no—
200C2×Q16—61no—
201C4⋊Q8—31no—
202#127C2×C3×D311yescharacteristic
203#124—61no—
204#124—61no—
205#123—62no—
206C4×Q8—31no—
207C4×Q8—31no—
208C4×D4—61no—
209C4×D4—61no—
210#106—61no—
211C4⋊C8C2×C3×D311yescharacteristic
212C4⋊C8C2×C3×D311yescharacteristic
213#103—61no—
214#103—61no—
215#102—62no—
216C4×C8—31no—
217C23×C3—22no—
218C23×C3—22no—
219C23×C3—42no—
220C3×Q8—61no—
221C3×Q8—61no—
222C3×Q8—61no—
223C3×Q8—61no—
224C3×Q8—121no—
225C3×Q8—121no—
226C3×D4—42no—
227C3×D4—42no—
228C3×D4—41no—
229C3×D4—41no—
230C3×D4—41no—
231C3×D4—41no—
232C3×D4—41no—
233C3×D4—41no—
234C3×D4—41no—
235C3×D4—41no—
236C3×D4—81no—
237C3×D4—81no—
238C3×D4—81no—
239C3×D4—81no—
240C3×D4—82no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—61no—
245C2×C3×C4—61no—
246C2×C3×C4—61no—
247C2×C3×C4—61no—
248C2×C3×C4—121no—
249C2×C3×C4—242no—
250C2×C3×C4C2×D1211yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4C2×C3×D411yescharacteristic
254C2×C3×C4C2×C3×D411yescharacteristic
255C2×C3×C4C2×C3×D411yescharacteristic
256C2×Dic3—21no—
257C2×Dic3—21no—
258C2×Dic3—21no—
259C2×Dic3—21no—
260C2×Dic3—41no—
261C2×Dic3—82no—
262Dic6—21no—
263Dic6—21no—
264Dic6—21no—
265Dic6—21no—
266Dic6—41no—
267Dic6—41no—
268C3×C8—41no—
269C3×C8—41no—
270C3×C8—41no—
271C3×C8—41no—
272C3×C8—81no—
273C3×C8—81no—
274C3×C8—121no—
275C3⋊C8—41no—
276C2×C32—82no—
277C2×C32#44911yescharacteristic
278C2×C32#45211yescharacteristic
279C2×C32#45511yescharacteristic
280C2×Q8—31no—
281C2×Q8—31no—
282C2×Q8—61no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4C3×D1212yes—
286C22×C4—62no—
287Q16—122no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—61no—
291C4⋊C4—31no—
292C4⋊C4—31no—
293C4⋊C4—61no—
294C4⋊C4—61no—
295C4⋊C4—61no—
296C4⋊C4—61no—
297C22⋊C4—62no—
298C22⋊C4—62no—
299C22⋊C4—62no—
300C42—61no—
301C42—61no—
302C42C22×C3×D311yescharacteristic
303C22×C3—21no—
304C22×C3—42no—
305C22×C3—42no—
306C22×C3—42no—
307C22×C3—42no—
308C22×C3—42no—
309C22×C3—42no—
310C22×C3—82no—
311C22×C3—82no—
312C22×C3—82no—
313C22×C3#88211yescharacteristic
314C22×C3C3×#12011yescharacteristic
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—41no—
322C3×C4—121no—
323C3×C4—121no—
324C3×C4—121no—
325C3×C4—121no—
326C3×C4—241no—
327C3×C4#91111yescharacteristic
328C3×C4#91211yescharacteristic
329C3×C4#91511yescharacteristic
330C3×C4#91611yescharacteristic
331C3×C4C3×#13511yescharacteristic
332C3×C4C3×#13511yescharacteristic
333C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
334C3×C4C3×#13711yescharacteristic
335Dic3—41no—
336Dic3—41no—
337Dic3—41no—
338Dic3—41no—
339Dic3—81no—
340C32#164011yescharacteristic, complemented, Sylow
341C23—22no—
342Q8—61no—
343Q8—61no—
344Q8—61no—
345Q8—61no—
346Q8—121no—
347Q8—121no—
348D4—42no—
349D4—41no—
350D4—41no—
351D4—41no—
352D4—41no—
353C2×C4—61no—
354C2×C4—61no—
355C2×C4—61no—
356C2×C4—61no—
357C2×C4—121no—
358C2×C4—242no—
359C2×C4C2×C3×D1211yescharacteristic
360C2×C4C3×D3×D411yescharacteristic
361C2×C4C3×D3×D411yescharacteristic
362C8—41no—
363C8—41no—
364C8—121no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—82no—
369C2×C3—82no—
370C2×C3—162no—
371C2×C3#474611yescharacteristic
372C2×C3#478111yescharacteristic
373C2×C3#478311yescharacteristic
374C2×C3C3×#44911yescharacteristic
375C2×C3C3×#45211yescharacteristic
376C2×C3C3×#45511yescharacteristic
377C22—42no—
378C22—42no—
379C22—42no—
380C22C3×#88211yescharacteristic
381C4—21no—
382C4—121no—
383C4—121no—
384C4—121no—
385C4—121no—
386C4—241no—
387C4C3×#91111yescharacteristic
388C4C3×#91211yescharacteristic
389C4C3×#91511yescharacteristic
390C4C3×#91611yescharacteristic
391C3—21no—
392C3#6840611yescharacteristic, direct product factor
393C3C3×#164011yescharacteristic, complemented
394C2—82no—
395C2C3×#474611yescharacteristic
396C2C3×#478111yescharacteristic
397C2C3×#478311yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#331C2
socleC22×C32#120
prime radicalC32×#127C22
hypercenterC3×#331D3
hypocenterC3C3×#1640
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×#4851C2semidirect
4. C3×#4849C2semidirect
6. C3×#4484C2semidirect
7. C3×#4484C2semidirect
9. #68406C3direct (N × H)
33. #4851C2×C3semidirect
34. #4849C2×C3semidirect
40. #4484C2×C3semidirect
41. #4484C2×C3semidirect
340. C32#1640semidirect
392. C3#68406direct (N × H)
393. C3C3×#1640semidirect

Maximal subgroups

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

subgroupindex
C3×#57132
C3×#50702
C3×#48512
C3×#48492
C32×#3312
C3×#44842
C3×#16403
#684063