Finite Group Databasebeta

← C3×#68250 #11780241

Subgroups — C3×#68250 #11780241

Order 1152.

435 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5584C211yesmaximal, characteristic
2C3×#5020C211yesmaximal, characteristic, complemented
3C3×#4841C211yesmaximal, characteristic
4C3×#4682C211yesmaximal, characteristic, complemented
5C32×Q8⋊C8C211yesmaximal, characteristic, complemented
6C3×#4482C211yesmaximal, characteristic, complemented
7C3×#4459C211yesmaximal, characteristic
8C3×#1650—31nomaximal
9#68250C311yesmaximal, characteristic, direct product factor
10C32×C4×Q8C2211yescharacteristic
11C3×#946—21no—
12C2×C3×#204—21no—
13C3×#898—22no—
14C3×#892—21no—
15C3×#875—21no—
16C3×C4×D12C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6—21no—
20C32×C4⋊C8C2211yescharacteristic
21C32×C4×C8C2211yescharacteristic
22C3×#835—21no—
23C3×#818—22no—
24C3×#816—21no—
25C3×#808—21no—
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27C3×#556—31no—
28#5584C2×C311yescharacteristic
29C3×#500—31no—
30C3×#475—31no—
31C3×#461—31no—
32#5020C2×C311yescharacteristic, complemented
33#4841C2×C311yescharacteristic
34#4682C2×C311yescharacteristic, complemented
35C3×#332—31no—
36C3×Q8⋊C8—21no—
37C3×Q8⋊C8D311yescharacteristic, complemented
38C3×Q8⋊C8C2×C311yescharacteristic, complemented
39C3×D4⋊C8—31no—
40#4482C2×C311yescharacteristic, complemented
41#4459C2×C311yescharacteristic
42C2×C32×Q8D411yescharacteristic
43C2×C3×D12D411yescharacteristic
44C2×C3×C4×D3—21no—
45C2×C3×Dic6—21no—
46C2×C3×Dic6—21no—
47C2×C32×C8—21no—
48C2×C32×C8—21no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4D411yescharacteristic
51C32×C42—21no—
52C32×C42C2311yescharacteristic
53C3×(C2×D3)⋊C4—22no—
54C3×(C2×D3)⋊C4—22no—
55C3×(C2×D3)⋊C4—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D412yes—
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—22no—
62C3×C4×Dic3—22no—
63C2×C3×C3⋊C8—21no—
64C3×#204—42no—
65#1650—31noSylow
66C2×C3×SD16—61no—
67C3×C4⋊Q8—31no—
68C3×C4⋊Q8—31no—
69C3×#126—62no—
70C3×#124—61no—
71C3×C22⋊Q8—61no—
72C3×C4×Q8—21no—
73C3×C4×Q8—61no—
74C3×C4×Q8C2×D311yescharacteristic
75C3×C4×Q8C22×C311yescharacteristic
76C3×C4×D4—31no—
77C3×#117—61no—
78#946—21no—
79C2×#204—21no—
80#898—22no—
81#892—21no—
82#875—21no—
83C4×D12C22×C311yescharacteristic
84#869C22×C311yescharacteristic
85#869C22×C311yescharacteristic
86C4×Dic6—21no—
87C3×#107—62no—
88C3×#106—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—22no—
100#816—21no—
101#808—21no—
102C4⋊(C3⋊C8)C22×C311yescharacteristic
103C22×C3×D3—21no—
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—22no—
113C2×C3×Dic3—41no—
114C3×D12—21no—
115C3×D12—21no—
116C3×C4×D3—41no—
117C3×C4×D3—41no—
118C3×Dic6—41no—
119C3×Dic6—41no—
120C3×Dic6—41no—
121C3×Dic6—41no—
122C32×C8—22no—
123C32×C8—41no—
124C3×C3⋊C8—41no—
125#556—31no—
126#500—31no—
127#475—31no—
128#461—31no—
129#332—31no—
130Q8⋊C8C3×D311yescharacteristic, complemented
131D4⋊C8—31no—
132C2×C3×Q8—21no—
133C2×C3×Q8—61no—
134C2×C3×Q8—61no—
135C2×C3×Q8D1211yescharacteristic
136C2×C3×Q8C3×D411yescharacteristic
137C2×C3×D4—31no—
138C22×C3×C4—61no—
139C2×D12C3×D411yescharacteristic
140C2×C4×D3—21no—
141C2×Dic6—21no—
142C2×Dic6—21no—
143C3×SD16—122no—
144C2×C3×C8—21no—
145C2×C3×C8—21no—
146C2×C3×C8—21no—
147C2×C3×C8—21no—
148C2×C3×C8—41no—
149C2×C3×C8—41no—
150C2×C3×C8—61no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—21no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—31no—
155C3×C4⋊C4—32no—
156C3×C4⋊C4—41no—
157C3×C4⋊C4—62no—
158C3×C4⋊C4—61no—
159C3×C4⋊C4—61no—
160C3×C4⋊C4—61no—
161C3×C4⋊C4D1211yescharacteristic
162C3×C4⋊C4C3×D411yescharacteristic
163C3×C22⋊C4—62no—
164C3×C22⋊C4—62no—
165C3×C22⋊C4—61no—
166C3×C42—21no—
167C3×C42—21no—
168C3×C42—21no—
169C3×C42—41no—
170C3×C42—62no—
171C3×C42C22×D311yescharacteristic
172C3×C42C23×C311yescharacteristic
173(C2×D3)⋊C4—22no—
174(C2×D3)⋊C4—22no—
175(C2×D3)⋊C4—21no—
176C4⋊Dic3—21no—
177C4⋊Dic3—21no—
178C4⋊Dic3—21no—
179C4⋊Dic3C3×D411yescharacteristic
180C4⋊Dic3C3×D412yes—
181Dic3⋊C4—22no—
182C4×Dic3—22no—
183C2×C3⋊C8—21no—
184#204—42no—
185C22×C32#12011yescharacteristic
186C2×C3×D3—41no—
187C2×C3×D3—41no—
188C2×C3×D3—41no—
189C32×C4—21no—
190C32×C4—41no—
191C32×C4—41no—
192C32×C4#13511yescharacteristic
193C32×C4#13511yescharacteristic
194C32×C4AGL(1,ℤ/8)11yescharacteristic
195C32×C4#13711yescharacteristic
196C3×Dic3—42no—
197C3×Dic3—41no—
198C3×Dic3—81no—
199C2×SD16—61no—
200C4⋊Q8—31no—
201C4⋊Q8—31no—
202#126—62no—
203#124—61no—
204C22⋊Q8—61no—
205C4×Q8—61no—
206C4×Q8C2×C3×D311yescharacteristic
207C4×D4—31no—
208#117—61no—
209#107—62no—
210#106—61no—
211C4⋊C8—31no—
212C4⋊C8C2×C3×D311yescharacteristic
213#103—61no—
214#103—61no—
215C4×C8C2×C3×D311yescharacteristic
216C23×C3—61no—
217C22×D3—21no—
218C3×Q8—22no—
219C3×Q8—21no—
220C3×Q8—21no—
221C3×Q8—21no—
222C3×Q8—21no—
223C3×Q8—41no—
224C3×Q8—121no—
225C3×Q8—121no—
226C3×Q8—121no—
227C3×Q8—121no—
228C3×D4—61no—
229C3×D4—61no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4—61no—
240C2×C3×C4—62no—
241C2×C3×C4—121no—
242C2×C3×C4—121no—
243C2×C3×C4—121no—
244C2×C3×C4C2×D1211yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4D3×D411yescharacteristic
247C2×C3×C4C2×C3×D411yescharacteristic
248C2×C3×C4C2×C3×D411yescharacteristic
249C2×C3×C4C2×C3×D411yescharacteristic
250C2×Dic3—21no—
251C2×Dic3—22no—
252C2×Dic3—41no—
253D12—21no—
254D12—21no—
255C4×D3—41no—
256C4×D3—41no—
257Dic6—41no—
258Dic6—41no—
259Dic6—41no—
260Dic6—41no—
261C3×C8—22no—
262C3×C8—22no—
263C3×C8—42no—
264C3×C8—41no—
265C3×C8—41no—
266C3×C8—81no—
267C3×C8—121no—
268C3⋊C8—41no—
269C2×C32#44911yescharacteristic
270C2×C32#45211yescharacteristic
271C2×C32#45611yescharacteristic
272C3×D3—81no—
273C2×Q8—61no—
274C2×Q8—61no—
275C2×Q8C3×D1211yescharacteristic
276C2×D4—31no—
277C22×C4—61no—
278SD16—122no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—61no—
282C4⋊C4—21no—
283C4⋊C4—31no—
284C4⋊C4—32no—
285C4⋊C4—62no—
286C4⋊C4—61no—
287C4⋊C4—61no—
288C4⋊C4—61no—
289C4⋊C4C3×D1211yescharacteristic
290C22⋊C4—62no—
291C22⋊C4—62no—
292C22⋊C4—61no—
293C42—21no—
294C42—62no—
295C42C22×C3×D311yescharacteristic
296C22×C3—21no—
297C22×C3—121no—
298C22×C3—121no—
299C22×C3—121no—
300C22×C3#88211yescharacteristic
301C22×C3C3×#12011yescharacteristic
302C2×D3—41no—
303C2×D3—41no—
304C2×D3—41no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—41no—
312C3×C4—42no—
313C3×C4—41no—
314C3×C4—41no—
315C3×C4—41no—
316C3×C4—41no—
317C3×C4—81no—
318C3×C4—121no—
319C3×C4—122no—
320C3×C4—241no—
321C3×C4#90411yescharacteristic
322C3×C4#90911yescharacteristic
323C3×C4#91411yescharacteristic
324C3×C4#91911yescharacteristic
325C3×C4C3×#13511yescharacteristic
326C3×C4C3×#13511yescharacteristic
327C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
328C3×C4C3×#13711yescharacteristic
329Dic3—42no—
330Dic3—41no—
331Dic3—81no—
332C32#165011yescharacteristic, complemented, Sylow
333C23—61no—
334Q8—21no—
335Q8—21no—
336Q8—121no—
337Q8—121no—
338Q8—121no—
339Q8—121no—
340D4—61no—
341D4—61no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—61no—
345C2×C4—62no—
346C2×C4—121no—
347C2×C4—121no—
348C2×C4—121no—
349C2×C4C2×C3×D1211yescharacteristic
350C2×C4C3×D3×D411yescharacteristic
351C2×C4C3×D3×D411yescharacteristic
352C8—22no—
353C8—41no—
354C8—121no—
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—241no—
359C2×C3#473311yescharacteristic
360C2×C3#481011yescharacteristic
361C2×C3#482611yescharacteristic
362C2×C3C3×#44911yescharacteristic
363C2×C3C3×#45211yescharacteristic
364C2×C3C3×#45611yescharacteristic
365D3—81no—
366C22—121no—
367C22—121no—
368C22—121no—
369C22C3×#88211yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—121no—
374C4—122no—
375C4—241no—
376C4C3×#90411yescharacteristic
377C4C3×#90911yescharacteristic
378C4C3×#91411yescharacteristic
379C4C3×#91911yescharacteristic
380C3—21no—
381C3#6825011yescharacteristic, direct product factor
382C3C3×#165011yescharacteristic, complemented
383C2—241no—
384C2C3×#473311yescharacteristic
385C2C3×#481011yescharacteristic
386C2C3×#482611yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×Q8⋊C8C2
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC3×Q8⋊C8D3
hypocenterC3C3×#1650
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×#5020C2semidirect
4. C3×#4682C2semidirect
5. C32×Q8⋊C8C2semidirect
6. C3×#4482C2semidirect
9. #68250C3direct (N × H)
32. #5020C2×C3semidirect
34. #4682C2×C3semidirect
37. C3×Q8⋊C8D3semidirect
38. C3×Q8⋊C8C2×C3semidirect
40. #4482C2×C3semidirect
130. Q8⋊C8C3×D3semidirect
332. C32#1650semidirect
381. C3#68250direct (N × H)
382. C3C3×#1650semidirect

Maximal subgroups

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

subgroupindex
C3×#55842
C3×#50202
C3×#48412
C3×#46822
C32×Q8⋊C82
C3×#44822
C3×#44592
C3×#16503
#682503