Finite Group Databasebeta

← C3×#33746 #10652353

Subgroups — C3×#33746 #10652353

Order 768.

556 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3169C211yesmaximal, characteristic, complemented
2C3×#3168C211yesmaximal, characteristic, complemented
3C3×#2255C211yesmaximal, characteristic, complemented
4C3×#2250C211yesmaximal, characteristic, complemented
5C3×#2244C211yesmaximal, characteristic, complemented
6C3×#2243C211yesmaximal, characteristic, complemented
7C3×#2217C212yesmaximal, complemented
8C3×#2215C212yesmaximal, complemented
9C3×#2177C212yesmaximal, complemented
10C3×#2175C212yesmaximal, complemented
11C2×C3×#346C211yesmaximal, characteristic, complemented
12#33746C311yesmaximal, characteristic, direct product factor, Sylow
13C3×#532—21no—
14C3×#529—21no—
15C2×C3×SD32C2212yes—
16C2×C3×D16C2212yes—
17C22×C3×C16C2212yes—
18C3×#500C2211yescharacteristic
19C3×#499C2211yescharacteristic
20C3×#495C2211yescharacteristic
21C3×#493C2211yescharacteristic
22C3×#488—21no—
23C3×#486—21no—
24C3×#467C2211yescharacteristic
25C3×#466—21no—
26C3×#466C2211yescharacteristic
27C3×#466C2212yes—
28C3×#465—21no—
29C3×C4×Q16C2211yescharacteristic
30C3×C4×SD16—21no—
31C3×C4×D8—21no—
32C3×C4×D8C2211yescharacteristic
33C3×C4×D8C2212yes—
34C2×C3×C4×C8C2211yescharacteristic
35C3×#367C2212yes—
36C3×#366C2212yes—
37C3×#358C2212yes—
38C3×#357C2212yes—
39C3×#357C2212yes—
40C3×#357C2212yes—
41C3×#346C2211yescharacteristic
42C3×#346C2212yes—
43C3×#346C2211yescharacteristic
44#3169C2×C311yescharacteristic, complemented
45#3168C2×C311yescharacteristic, complemented
46#2255C2×C311yescharacteristic, complemented
47#2250C2×C311yescharacteristic, complemented
48#2244C2×C311yescharacteristic, complemented
49#2243C2×C311yescharacteristic, complemented
50#2217C2×C312yescomplemented
51#2215C2×C312yescomplemented
52#2177C2×C312yescomplemented
53#2175C2×C312yescomplemented
54C2×#346C2×C311yescharacteristic, complemented
55C2×C3×#41—41no—
56C2×C3×Q16C2311yescharacteristic
57C2×C3×SD16—21no—
58C2×C3×D8—21no—
59C2×C3×D8C2311yescharacteristic
60C2×C3×D8C2312yes—
61C22×C3×C8D411yescharacteristic
62C22×C3×C8C2311yescharacteristic
63C3×C4⋊Q8—21no—
64C3×#127—21no—
65C3×#126—41no—
66C3×#125—21no—
67C3×#124—21no—
68C3×#124—41no—
69C3×#123—41no—
70C3×C22⋊Q8—21no—
71C3×#121—21no—
72C3×#121—22no—
73C3×#121—41no—
74C3×C4×Q8—21no—
75C3×C4×D4—22no—
76C3×C4×D4—21no—
77C3×C4×D4—41no—
78C3×C4×D4—41no—
79C3×#117—41no—
80C2×C3×C42D411yescharacteristic
81C3×SD32—24no—
82C3×D16—24no—
83C2×C3×C16—24no—
84C2×C3×C16C2312yes—
85C2×C3×C16C2312yes—
86C3×#107—21no—
87C3×#107C2311yescharacteristic
88C3×#107C2312yes—
89C3×#107C2311yescharacteristic
90C3×#106—21no—
91C3×#103—21no—
92C3×#103—21no—
93C3×#102—22no—
94C3×#102—21no—
95C3×#102—22no—
96C3×#102—21no—
97C3×C4×C8D411yescharacteristic
98C3×C4×C8D411yescharacteristic
99C3×C4×C8C2311yescharacteristic
100C3×C4×C8C2311yescharacteristic
101#532—21no—
102#529—21no—
103C2×SD32C22×C312yes—
104C2×D16C22×C312yes—
105C22×C16C22×C312yes—
106#500C22×C311yescharacteristic
107#499C22×C311yescharacteristic
108#495C22×C311yescharacteristic
109#493C22×C311yescharacteristic
110#488—21no—
111#486—21no—
112#467C22×C311yescharacteristic
113#466—21no—
114#466C22×C311yescharacteristic
115#466C22×C312yes—
116#465—21no—
117C4×Q16C22×C311yescharacteristic
118C4×SD16—21no—
119C4×D8—21no—
120C4×D8C22×C311yescharacteristic
121C4×D8C22×C312yes—
122C2×C4×C8C22×C311yescharacteristic
123#367C22×C312yes—
124#366C22×C312yes—
125#358C22×C312yes—
126#357C22×C312yes—
127#357C22×C312yes—
128#357C22×C312yes—
129#346C22×C312yes—
130#346C22×C311yescharacteristic
131#346C22×C311yescharacteristic
132C3×#41—84no—
133C2×C3×Q8—21no—
134C2×C3×Q8—41no—
135C2×C3×D4—21no—
136C2×C3×D4—22no—
137C2×C3×D4—41no—
138C2×C3×D4—42no—
139C2×C3×D4—41no—
140C2×C3×D4—41no—
141C22×C3×C4—41no—
142C22×C3×C4—42no—
143C22×C3×C4D811yescharacteristic
144C22×C3×C4D811yescharacteristic
145C22×C3×C4C2×D411yescharacteristic
146C3×Q16—22no—
147C3×SD16—42no—
148C3×D8—22no—
149C3×D8—22no—
150C3×D8—22no—
151C3×D8—42no—
152C2×C3×C8—22no—
153C2×C3×C8—22no—
154C2×C3×C8C2×D411yescharacteristic
155C2×C3×C8C2×D411yescharacteristic
156C2×C3×C8C2×D411yescharacteristic
157C2×C3×C8C2411yescharacteristic
158C3×C4⋊C4—22no—
159C3×C4⋊C4—21no—
160C3×C4⋊C4—21no—
161C3×C4⋊C4—41no—
162C3×C4⋊C4—41no—
163C3×C4⋊C4—41no—
164C3×C4⋊C4—41no—
165C3×C4⋊C4—41no—
166C3×C22⋊C4—41no—
167C3×C22⋊C4—41no—
168C3×C22⋊C4—41no—
169C3×C22⋊C4—42no—
170C3×C22⋊C4—41no—
171C3×C22⋊C4—42no—
172C3×C22⋊C4—41no—
173C3×C42—41no—
174C3×C42D811yescharacteristic
175C3×C42D811yescharacteristic
176C3×C42C2×D411yescharacteristic
177C3×C42C2×D411yescharacteristic
178C3×C16—22no—
179C3×C16#4114yescomplemented
180C2×#41—41no—
181C2×Q16C23×C311yescharacteristic
182C2×SD16—21no—
183C2×D8—21no—
184C2×D8C23×C312yes—
185C2×D8C23×C311yescharacteristic
186C22×C8C3×D411yescharacteristic
187C22×C8C23×C311yescharacteristic
188C4⋊Q8—21no—
189#127—21no—
190#126—41no—
191#125—21no—
192#124—21no—
193#124—41no—
194#123—41no—
195C22⋊Q8—21no—
196#121—21no—
197#121—22no—
198#121—41no—
199C4×Q8—21no—
200C4×D4—21no—
201C4×D4—22no—
202C4×D4—41no—
203C4×D4—41no—
204#117—41no—
205C2×C42C3×D411yescharacteristic
206SD32—24no—
207D16—24no—
208C2×C16—24no—
209C2×C16C23×C312yes—
210C2×C16C23×C312yes—
211#107—21no—
212#107C23×C311yescharacteristic
213#107C23×C311yescharacteristic
214#107C23×C312yes—
215#106—21no—
216#103—21no—
217#103—21no—
218#102—22no—
219#102—21no—
220#102—22no—
221#102—21no—
222C4×C8C3×D411yescharacteristic
223C4×C8C3×D411yescharacteristic
224C4×C8C23×C311yescharacteristic
225C4×C8C23×C311yescharacteristic
226C23×C3—41no—
227C23×C3—42no—
228C23×C3C2×D811yescharacteristic
229C3×Q8—41no—
230C3×Q8—41no—
231C3×Q8—82no—
232C3×D4—41no—
233C3×D4—42no—
234C3×D4—42no—
235C3×D4—41no—
236C3×D4—82no—
237C3×D4—82no—
238C3×D4—82no—
239C3×D4—84no—
240C2×C3×C4—22no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—42no—
248C2×C3×C4—82no—
249C2×C3×C4—84no—
250C2×C3×C4C2×D811yescharacteristic
251C2×C3×C4C2×D811yescharacteristic
252C2×C3×C4C2×D811yescharacteristic
253C2×C3×C4C2×D811yescharacteristic
254C2×C3×C4C2×D811yescharacteristic
255C2×C3×C4C22×D411yescharacteristic
256C3×C8—21no—
257C3×C8—21no—
258C3×C8#13512yes—
259C3×C8C2×#4112yes—
260#41—84no—
261C2×Q8—21no—
262C2×Q8—41no—
263C2×D4—21no—
264C2×D4—22no—
265C2×D4—41no—
266C2×D4—42no—
267C2×D4—41no—
268C2×D4—41no—
269C22×C4—41no—
270C22×C4—42no—
271C22×C4C3×D811yescharacteristic
272C22×C4C3×D811yescharacteristic
273C22×C4C2×C3×D411yescharacteristic
274Q16—22no—
275SD16—42no—
276D8—22no—
277D8—22no—
278D8—22no—
279D8—42no—
280C2×C8—22no—
281C2×C8—22no—
282C2×C8C2×C3×D411yescharacteristic
283C2×C8C2×C3×D411yescharacteristic
284C2×C8C2×C3×D411yescharacteristic
285C2×C8C24×C311yescharacteristic
286C4⋊C4—22no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—42no—
298C22⋊C4—41no—
299C22⋊C4—42no—
300C22⋊C4—41no—
301C42—41no—
302C42C3×D811yescharacteristic
303C42C3×D811yescharacteristic
304C42C2×C3×D411yescharacteristic
305C42C2×C3×D411yescharacteristic
306C16—22no—
307C16C3×#4114yescomplemented
308C22×C3—21no—
309C22×C3—21no—
310C22×C3—82no—
311C22×C3—81no—
312C22×C3—81no—
313C22×C3—82no—
314C22×C3—82no—
315C22×C3—81no—
316C22×C3#50912yes—
317C22×C3C22×D811yescharacteristic
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—82no—
324C3×C4—81no—
325C3×C4—81no—
326C3×C4—81no—
327C3×C4#53211yescharacteristic
328C3×C4C2×#13511yescharacteristic
329C23—41no—
330C23—42no—
331C23C2×C3×D811yescharacteristic
332Q8—41no—
333Q8—41no—
334Q8—82no—
335D4—42no—
336D4—41no—
337D4—41no—
338D4—42no—
339D4—82no—
340D4—82no—
341D4—84no—
342D4—82no—
343C2×C4—22no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—84no—
352C2×C4—82no—
353C2×C4C2×C3×D811yescharacteristic
354C2×C4C2×C3×D811yescharacteristic
355C2×C4C2×C3×D811yescharacteristic
356C2×C4C2×C3×D811yescharacteristic
357C2×C4C2×C3×D811yescharacteristic
358C2×C4C22×C3×D411yescharacteristic
359C8—21no—
360C8—21no—
361C8C3×#13512yes—
362C8C2×C3×#4112yes—
363C2×C3—22no—
364C2×C3—162no—
365C2×C3—161no—
366C2×C3#316911yescharacteristic
367C2×C3C2×#50911yescharacteristic
368C2×C3#341411yescharacteristic
369C22—21no—
370C22—21no—
371C22—82no—
372C22—81no—
373C22—81no—
374C22—82no—
375C22—82no—
376C22—81no—
377C22C3×#50912yes—
378C22C22×C3×D811yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—82no—
385C4—81no—
386C4—81no—
387C4—81no—
388C4C3×#53211yescharacteristic
389C4C2×C3×#13511yescharacteristic
390C3#3374611yescharacteristic, direct product factor, Sylow
391C2—22no—
392C2—162no—
393C2—161no—
394C2C3×#316911yescharacteristic
395C2C2×C3×#50911yescharacteristic
396C2C3×#341411yescharacteristic
subgroupG/H
center, socleC22×C3C22×D8
commutator, Frattini, cosocleC2×C8C24×C3
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C2×C3×C4×C8 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#3169C2semidirect
2. C3×#3168C2semidirect
3. C3×#2255C2semidirect
4. C3×#2250C2semidirect
5. C3×#2244C2semidirect
6. C3×#2243C2semidirect
7. C3×#2217C2semidirect
8. C3×#2215C2semidirect
9. C3×#2177C2semidirect
10. C3×#2175C2semidirect
11. C2×C3×#346C2semidirect
12. #33746C3direct (N × H)
44. #3169C2×C3semidirect
45. #3168C2×C3semidirect
46. #2255C2×C3semidirect
47. #2250C2×C3semidirect
48. #2244C2×C3semidirect
49. #2243C2×C3semidirect
50. #2217C2×C3semidirect
51. #2215C2×C3semidirect
52. #2177C2×C3semidirect
53. #2175C2×C3semidirect
54. C2×#346C2×C3semidirect
179. C3×C16#41semidirect
307. C16C3×#41semidirect
390. C3#33746direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#31692
C3×#31682
C3×#22552
C3×#22502
C3×#22442
C3×#22432
C3×#22172
C3×#22152
C3×#21772
C3×#21752
C2×C3×#3462
#337463