Finite Group Databasebeta

← C3×#68260 #11779336

Subgroups — C3×#68260 #11779336

Order 1152.

471 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5585C211yesmaximal, characteristic
2C3×#5021C211yesmaximal, characteristic, complemented
3C3×#4850C211yesmaximal, characteristic, complemented
4C3×#4693C211yesmaximal, characteristic
5C32×Q8⋊C8C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic
7C3×#4456C211yesmaximal, characteristic, complemented
8C3×#1630—31nomaximal
9#68260C311yesmaximal, characteristic, direct product factor
10C32×C4×Q8C2211yescharacteristic
11C3×#947—21no—
12C2×C3×#204—22no—
13C3×#894—22no—
14C3×#893—21no—
15C3×#875—21no—
16C3×#874C2211yescharacteristic
17C3×C4×D12—21no—
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic
21C32×C4×C8C2211yescharacteristic
22C3×#835—21no—
23C3×#818—21no—
24C3×#816—21no—
25C3×#807—21no—
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27C3×#559—31no—
28#5585C2×C311yescharacteristic
29C3×#492—31no—
30C3×#477—31no—
31C3×#477—31no—
32#5021C2×C311yescharacteristic, complemented
33#4850C2×C311yescharacteristic, complemented
34#4693C2×C311yescharacteristic
35C3×#331—31no—
36C3×Q8⋊C8—21no—
37C3×Q8⋊C8—31no—
38C3×Q8⋊C8D311yescharacteristic, complemented
39C3×Q8⋊C8C2×C311yescharacteristic, complemented
40#4485C2×C311yescharacteristic
41#4456C2×C311yescharacteristic, complemented
42C2×C32×Q8D411yescharacteristic
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12D412yes—
46C2×C3×C4×D3—22no—
47C2×C3×Dic6—21no—
48C2×C3×Dic6D411yescharacteristic
49C2×C32×C8—21no—
50C2×C32×C8—21no—
51C32×C4⋊C4—21no—
52C32×C4⋊C4D411yescharacteristic
53C32×C42—21no—
54C32×C42C2311yescharacteristic
55C3×(C2×D3)⋊C4—22no—
56C3×(C2×D3)⋊C4—22no—
57C3×(C2×D3)⋊C4—22no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—21no—
62C3×C4×Dic3—21no—
63C2×C3×C3⋊C8—21no—
64C3×#204—44no—
65#1630—31noSylow
66C2×C3×SD16—62no—
67C3×C4⋊Q8—31no—
68C3×#127—31no—
69C3×#124—61no—
70C3×#124—61no—
71C3×#123—62no—
72C3×C4×Q8—21no—
73C3×C4×Q8—31no—
74C3×C4×Q8C2×D311yescharacteristic
75C3×C4×Q8C22×C311yescharacteristic
76C3×C4×D4—61no—
77C3×C4×D4—61no—
78#947—21no—
79C2×#204—22no—
80#894—22no—
81#893—21no—
82#875—21no—
83#874C22×C311yescharacteristic
84C4×D12—21no—
85#869C22×C311yescharacteristic
86C4×Dic6C22×C311yescharacteristic
87C3×#107—61no—
88C3×#107—61no—
89C3×C4⋊C8—21no—
90C3×C4⋊C8—31no—
91C3×C4⋊C8C2×D311yescharacteristic
92C3×C4⋊C8C22×C311yescharacteristic
93C3×#103—61no—
94C3×#103—61no—
95C3×C4×C8—21no—
96C3×C4×C8C2×D311yescharacteristic
97C3×C4×C8C22×C311yescharacteristic
98#835—21no—
99#818—21no—
100#816—21no—
101#807—21no—
102C4⋊(C3⋊C8)C22×C311yescharacteristic
103C22×C3×D3—22no—
104C32×Q8—21no—
105C32×Q8—21no—
106C2×C32×C4—21no—
107C2×C32×C4—21no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C3×Dic3—21no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—41no—
114C3×D12—42no—
115C3×D12—41no—
116C3×D12—41no—
117C3×D12—41no—
118C3×D12—41no—
119C3×C4×D3—82no—
120C3×Dic6—21no—
121C3×Dic6—21no—
122C3×Dic6—42no—
123C32×C8—22no—
124C32×C8—41no—
125C3×C3⋊C8—41no—
126#559—31no—
127#492—31no—
128#477—31no—
129#477—31no—
130#331—31no—
131Q8⋊C8—31no—
132Q8⋊C8C3×D311yescharacteristic, complemented
133C2×C3×Q8—21no—
134C2×C3×Q8—31no—
135C2×C3×Q8—61no—
136C2×C3×Q8D1211yescharacteristic
137C2×C3×Q8C3×D411yescharacteristic
138C2×C3×D4—32no—
139C2×C3×D4—61no—
140C2×C3×D4—61no—
141C22×C3×C4—62no—
142C2×D12—21no—
143C2×D12—21no—
144C2×D12C3×D412yes—
145C2×C4×D3—22no—
146C2×Dic6—21no—
147C2×Dic6C3×D411yescharacteristic
148C3×SD16—124no—
149C2×C3×C8—21no—
150C2×C3×C8—21no—
151C2×C3×C8—21no—
152C2×C3×C8—21no—
153C2×C3×C8—41no—
154C2×C3×C8—41no—
155C2×C3×C8—61no—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4—21no—
159C3×C4⋊C4—31no—
160C3×C4⋊C4—41no—
161C3×C4⋊C4—61no—
162C3×C4⋊C4—61no—
163C3×C4⋊C4—61no—
164C3×C4⋊C4D1211yescharacteristic
165C3×C4⋊C4C3×D411yescharacteristic
166C3×C22⋊C4—62no—
167C3×C22⋊C4—62no—
168C3×C22⋊C4—62no—
169C3×C42—21no—
170C3×C42—21no—
171C3×C42—21no—
172C3×C42—41no—
173C3×C42—61no—
174C3×C42C22×D311yescharacteristic
175C3×C42C23×C311yescharacteristic
176(C2×D3)⋊C4—22no—
177(C2×D3)⋊C4—22no—
178(C2×D3)⋊C4—22no—
179C4⋊Dic3—21no—
180C4⋊Dic3—21no—
181C4⋊Dic3C3×D411yescharacteristic
182Dic3⋊C4—21no—
183C4×Dic3—21no—
184C2×C3⋊C8—21no—
185#204—44no—
186C22×C32#12011yescharacteristic
187C2×C3×D3—42no—
188C2×C3×D3—42no—
189C2×C3×D3—42no—
190C32×C4—21no—
191C32×C4—41no—
192C32×C4—41no—
193C32×C4#13511yescharacteristic
194C32×C4#13511yescharacteristic
195C32×C4#13711yescharacteristic
196C32×C4#13711yescharacteristic
197C3×Dic3—41no—
198C3×Dic3—41no—
199C3×Dic3—81no—
200C2×SD16—62no—
201C4⋊Q8—31no—
202#127—31no—
203#124—61no—
204#124—61no—
205#123—62no—
206C4×Q8—31no—
207C4×Q8C2×C3×D311yescharacteristic
208C4×D4—61no—
209C4×D4—61no—
210#107—61no—
211#107—61no—
212C4⋊C8—31no—
213C4⋊C8C2×C3×D311yescharacteristic
214#103—61no—
215#103—61no—
216C4×C8C2×C3×D311yescharacteristic
217C23×C3—62no—
218C22×D3—22no—
219C3×Q8—22no—
220C3×Q8—21no—
221C3×Q8—21no—
222C3×Q8—21no—
223C3×Q8—21no—
224C3×Q8—41no—
225C3×Q8—61no—
226C3×Q8—61no—
227C3×Q8—122no—
228C3×D4—122no—
229C3×D4—121no—
230C3×D4—121no—
231C3×D4—121no—
232C3×D4—121no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—41no—
241C2×C3×C4—41no—
242C2×C3×C4—61no—
243C2×C3×C4—61no—
244C2×C3×C4—121no—
245C2×C3×C4—242no—
246C2×C3×C4C2×D1211yescharacteristic
247C2×C3×C4D3×D411yescharacteristic
248C2×C3×C4D3×D411yescharacteristic
249C2×C3×C4C2×C3×D411yescharacteristic
250C2×C3×C4C2×C3×D411yescharacteristic
251C2×C3×C4C2×C3×D411yescharacteristic
252C2×Dic3—21no—
253C2×Dic3—21no—
254C2×Dic3—41no—
255D12—42no—
256D12—41no—
257D12—41no—
258D12—41no—
259D12—41no—
260C4×D3—82no—
261Dic6—21no—
262Dic6—21no—
263Dic6—42no—
264C3×C8—22no—
265C3×C8—22no—
266C3×C8—42no—
267C3×C8—41no—
268C3×C8—41no—
269C3×C8—81no—
270C3×C8—121no—
271C3⋊C8—41no—
272C2×C32#45211yescharacteristic
273C2×C32#45211yescharacteristic
274C2×C32#45311yescharacteristic
275C3×D3—82no—
276C2×Q8—31no—
277C2×Q8—61no—
278C2×Q8C3×D1211yescharacteristic
279C2×D4—32no—
280C2×D4—61no—
281C2×D4—61no—
282C22×C4—62no—
283SD16—124no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—61no—
287C4⋊C4—21no—
288C4⋊C4—31no—
289C4⋊C4—61no—
290C4⋊C4—61no—
291C4⋊C4—61no—
292C4⋊C4C3×D1211yescharacteristic
293C22⋊C4—62no—
294C22⋊C4—62no—
295C22⋊C4—62no—
296C42—21no—
297C42—61no—
298C42C22×C3×D311yescharacteristic
299C22×C3—21no—
300C22×C3—122no—
301C22×C3—122no—
302C22×C3—122no—
303C22×C3#88211yescharacteristic
304C22×C3C3×#12011yescharacteristic
305C2×D3—42no—
306C2×D3—42no—
307C2×D3—42no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—41no—
315C3×C4—42no—
316C3×C4—41no—
317C3×C4—41no—
318C3×C4—41no—
319C3×C4—41no—
320C3×C4—81no—
321C3×C4—121no—
322C3×C4—121no—
323C3×C4—241no—
324C3×C4#90411yescharacteristic
325C3×C4#90911yescharacteristic
326C3×C4#91611yescharacteristic
327C3×C4#91811yescharacteristic
328C3×C4C3×#13511yescharacteristic
329C3×C4C3×#13511yescharacteristic
330C3×C4C3×#13711yescharacteristic
331C3×C4C3×#13711yescharacteristic
332Dic3—41no—
333Dic3—41no—
334Dic3—81no—
335C32#163011yescharacteristic, complemented, Sylow
336C23—62no—
337Q8—21no—
338Q8—21no—
339Q8—61no—
340Q8—61no—
341Q8—122no—
342D4—122no—
343D4—121no—
344D4—121no—
345D4—121no—
346D4—121no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—61no—
350C2×C4—61no—
351C2×C4—121no—
352C2×C4—242no—
353C2×C4C2×C3×D1211yescharacteristic
354C2×C4C3×D3×D411yescharacteristic
355C2×C4C3×D3×D411yescharacteristic
356C8—22no—
357C8—41no—
358C8—121no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—242no—
363C2×C3#473311yescharacteristic
364C2×C3#480811yescharacteristic
365C2×C3#482211yescharacteristic
366C2×C3C3×#45211yescharacteristic
367C2×C3C3×#45211yescharacteristic
368C2×C3C3×#45311yescharacteristic
369D3—82no—
370C22—122no—
371C22—122no—
372C22—122no—
373C22C3×#88211yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—121no—
378C4—121no—
379C4—241no—
380C4C3×#90411yescharacteristic
381C4C3×#90911yescharacteristic
382C4C3×#91611yescharacteristic
383C4C3×#91811yescharacteristic
384C3—21no—
385C3#6826011yescharacteristic, direct product factor
386C3C3×#163011yescharacteristic, complemented
387C2—242no—
388C2C3×#473311yescharacteristic
389C2C3×#480811yescharacteristic
390C2C3×#482211yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×Q8⋊C8C2
socleC22×C32#120
prime radicalC3×#874C22
hypercenterC3×Q8⋊C8D3
hypocenterC3C3×#1630
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#5021C2semidirect
3. C3×#4850C2semidirect
5. C32×Q8⋊C8C2semidirect
7. C3×#4456C2semidirect
9. #68260C3direct (N × H)
32. #5021C2×C3semidirect
33. #4850C2×C3semidirect
38. C3×Q8⋊C8D3semidirect
39. C3×Q8⋊C8C2×C3semidirect
41. #4456C2×C3semidirect
132. Q8⋊C8C3×D3semidirect
335. C32#1630semidirect
385. C3#68260direct (N × H)
386. C3C3×#1630semidirect

Maximal subgroups

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

subgroupindex
C3×#55852
C3×#50212
C3×#48502
C3×#46932
C32×Q8⋊C82
C3×#44852
C3×#44562
C3×#16303
#682603