Finite Group Databasebeta

← C3×#33747 #10652354

Subgroups — C3×#33747 #10652354

Order 768.

512 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3170C211yesmaximal, characteristic, complemented
2C3×#3168C211yesmaximal, characteristic
3C3×#2255C211yesmaximal, characteristic, complemented
4C3×#2251C211yesmaximal, characteristic, complemented
5C3×#2245C211yesmaximal, characteristic, complemented
6C3×#2243C211yesmaximal, characteristic, complemented
7C3×#2217C212yesmaximal
8C3×#2216C212yesmaximal, complemented
9C3×#2176C212yesmaximal, complemented
10C3×#2175C212yesmaximal, complemented
11C2×C3×#346C211yesmaximal, characteristic, complemented
12#33747C311yesmaximal, characteristic, direct product factor, Sylow
13C3×#533—21no—
14C3×#529—21no—
15C2×C3×Q32C2212yes—
16C2×C3×SD32C2212yes—
17C22×C3×C16C2212yes—
18C3×#500C2211yescharacteristic
19C3×#499C2211yescharacteristic
20C3×#495C2211yescharacteristic
21C3×#494C2211yescharacteristic
22C3×#488—21no—
23C3×#487—21no—
24C3×#467—21no—
25C3×#467C2211yescharacteristic
26C3×#467C2212yes—
27C3×#466C2211yescharacteristic
28C3×#465—21no—
29C3×C4×Q16—21no—
30C3×C4×Q16C2211yescharacteristic
31C3×C4×Q16C2212yes—
32C3×C4×SD16—21no—
33C3×C4×D8C2211yescharacteristic
34C2×C3×C4×C8C2211yescharacteristic
35C3×#367C2212yes—
36C3×#366C2212yes—
37C3×#358C2212yes—
38C3×#358C2212yes—
39C3×#358C2212yes—
40C3×#357C2212yes—
41C3×#346C2211yescharacteristic
42C3×#346C2211yescharacteristic
43C3×#346C2212yes—
44#3170C2×C311yescharacteristic, complemented
45#3168C2×C311yescharacteristic
46#2255C2×C311yescharacteristic, complemented
47#2251C2×C311yescharacteristic, complemented
48#2245C2×C311yescharacteristic, complemented
49#2243C2×C311yescharacteristic, complemented
50#2217C2×C312yes—
51#2216C2×C312yescomplemented
52#2176C2×C312yescomplemented
53#2175C2×C312yescomplemented
54C2×#346C2×C311yescharacteristic, complemented
55C2×C3×Q16—21no—
56C2×C3×Q16C2312yes—
57C2×C3×Q16C2311yescharacteristic
58C2×C3×SD16—21no—
59C2×C3×D8C2311yescharacteristic
60C22×C3×C8D411yescharacteristic
61C22×C3×C8C2311yescharacteristic
62C3×C4⋊Q8—21no—
63C3×C4⋊Q8—21no—
64C3×#126—41no—
65C3×#125—21no—
66C3×#125—41no—
67C3×#124—21no—
68C3×#123—41no—
69C3×C22⋊Q8—21no—
70C3×C22⋊Q8—22no—
71C3×C22⋊Q8—41no—
72C3×#121—21no—
73C3×C4×Q8—21no—
74C3×C4×Q8—22no—
75C3×C4×Q8—41no—
76C3×C4×D4—21no—
77C3×C4×D4—41no—
78C3×#117—41no—
79C3×#117—41no—
80C2×C3×C42D411yescharacteristic
81C3×Q32—24no—
82C3×SD32—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—22no—
93C3×#103—21no—
94C3×#103—22no—
95C3×#102—21no—
96C3×#102—21no—
97C3×C4×C8D411yescharacteristic
98C3×C4×C8D411yescharacteristic
99C3×C4×C8C2311yescharacteristic
100C3×C4×C8C2311yescharacteristic
101#533—21no—
102#529—21no—
103C2×Q32C22×C312yes—
104C2×SD32C22×C312yes—
105C22×C16C22×C312yes—
106#500C22×C311yescharacteristic
107#499C22×C311yescharacteristic
108#495C22×C311yescharacteristic
109#494C22×C311yescharacteristic
110#488—21no—
111#487—21no—
112#467—21no—
113#467C22×C311yescharacteristic
114#467C22×C312yes—
115#466C22×C311yescharacteristic
116#465—21no—
117C4×Q16—21no—
118C4×Q16C22×C311yescharacteristic
119C4×Q16C22×C312yes—
120C4×SD16—21no—
121C4×D8C22×C311yescharacteristic
122C2×C4×C8C22×C311yescharacteristic
123#367C22×C312yes—
124#366C22×C312yes—
125#358C22×C312yes—
126#358C22×C312yes—
127#358C22×C312yes—
128#357C22×C312yes—
129#346C22×C312yes—
130#346C22×C311yescharacteristic
131#346C22×C311yescharacteristic
132C2×C3×Q8—21no—
133C2×C3×Q8—22no—
134C2×C3×Q8—41no—
135C2×C3×D4—21no—
136C2×C3×D4—41no—
137C22×C3×C4—41no—
138C22×C3×C4D811yescharacteristic
139C22×C3×C4D811yescharacteristic
140C22×C3×C4C2×D411yescharacteristic
141C3×Q16—22no—
142C3×Q16—22no—
143C3×Q16—22no—
144C3×Q16—42no—
145C3×SD16—42no—
146C3×D8—22no—
147C2×C3×C8—22no—
148C2×C3×C8—22no—
149C2×C3×C8C2×D411yescharacteristic
150C2×C3×C8C2×D411yescharacteristic
151C2×C3×C8C2×D411yescharacteristic
152C2×C3×C8C2411yescharacteristic
153C3×C4⋊C4—21no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—22no—
156C3×C4⋊C4—41no—
157C3×C4⋊C4—41no—
158C3×C4⋊C4—41no—
159C3×C4⋊C4—41no—
160C3×C4⋊C4—41no—
161C3×C4⋊C4—42no—
162C3×C4⋊C4—41no—
163C3×C4⋊C4—42no—
164C3×C4⋊C4—41no—
165C3×C22⋊C4—42no—
166C3×C22⋊C4—41no—
167C3×C22⋊C4—41no—
168C3×C22⋊C4—41no—
169C3×C22⋊C4—41no—
170C3×C22⋊C4—41no—
171C3×C42—41no—
172C3×C42—42no—
173C3×C42D811yescharacteristic
174C3×C42D811yescharacteristic
175C3×C42C2×D411yescharacteristic
176C3×C42C2×D411yescharacteristic
177C3×C16—22no—
178C3×C16#4114yes—
179C2×Q16—21no—
180C2×Q16C23×C312yes—
181C2×Q16C23×C311yescharacteristic
182C2×SD16—21no—
183C2×D8C23×C311yescharacteristic
184C22×C8C3×D411yescharacteristic
185C22×C8C23×C311yescharacteristic
186C4⋊Q8—21no—
187C4⋊Q8—21no—
188#126—41no—
189#125—21no—
190#125—41no—
191#124—21no—
192#123—41no—
193C22⋊Q8—21no—
194C22⋊Q8—22no—
195C22⋊Q8—41no—
196#121—21no—
197C4×Q8—21no—
198C4×Q8—22no—
199C4×Q8—41no—
200C4×D4—21no—
201C4×D4—41no—
202#117—41no—
203#117—41no—
204C2×C42C3×D411yescharacteristic
205Q32—24no—
206SD32—24no—
207C2×C16—24no—
208C2×C16C23×C312yes—
209C2×C16C23×C312yes—
210#107—21no—
211#107C23×C312yes—
212#107C23×C311yescharacteristic
213#107C23×C311yescharacteristic
214#106—21no—
215#103—21no—
216#103—22no—
217#103—21no—
218#103—22no—
219#102—21no—
220#102—21no—
221C4×C8C3×D411yescharacteristic
222C4×C8C3×D411yescharacteristic
223C4×C8C23×C311yescharacteristic
224C4×C8C23×C311yescharacteristic
225C23×C3—41no—
226C23×C3C2×D811yescharacteristic
227C3×Q8—42no—
228C3×Q8—41no—
229C3×Q8—41no—
230C3×Q8—42no—
231C3×Q8—82no—
232C3×D4—41no—
233C3×D4—41no—
234C3×D4—82no—
235C2×C3×C4—22no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—42no—
242C2×C3×C4—42no—
243C2×C3×C4—41no—
244C2×C3×C4—82no—
245C2×C3×C4C2×D811yescharacteristic
246C2×C3×C4C2×D811yescharacteristic
247C2×C3×C4C2×D811yescharacteristic
248C2×C3×C4C2×D811yescharacteristic
249C2×C3×C4C2×D811yescharacteristic
250C2×C3×C4C22×D411yescharacteristic
251C3×C8—21no—
252C3×C8—21no—
253C3×C8#13512yes—
254C3×C8C2×#4112yes—
255C2×Q8—21no—
256C2×Q8—22no—
257C2×Q8—41no—
258C2×D4—21no—
259C2×D4—41no—
260C22×C4—41no—
261C22×C4C3×D811yescharacteristic
262C22×C4C3×D811yescharacteristic
263C22×C4C2×C3×D411yescharacteristic
264Q16—22no—
265Q16—22no—
266Q16—22no—
267Q16—42no—
268SD16—42no—
269D8—22no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8C2×C3×D411yescharacteristic
273C2×C8C2×C3×D411yescharacteristic
274C2×C8C2×C3×D411yescharacteristic
275C2×C8C24×C311yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—22no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—42no—
285C4⋊C4—41no—
286C4⋊C4—42no—
287C4⋊C4—41no—
288C22⋊C4—42no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C42—41no—
295C42—42no—
296C42C3×D811yescharacteristic
297C42C3×D811yescharacteristic
298C42C2×C3×D411yescharacteristic
299C42C2×C3×D411yescharacteristic
300C16—22no—
301C16C3×#4114yes—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—81no—
305C22×C3—81no—
306C22×C3—81no—
307C22×C3#51012yes—
308C22×C3C22×D811yescharacteristic
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—81no—
315C3×C4—81no—
316C3×C4—82no—
317C3×C4—81no—
318C3×C4—82no—
319C3×C4#53211yescharacteristic
320C3×C4C2×#13511yescharacteristic
321C23—41no—
322C23C2×C3×D811yescharacteristic
323Q8—41no—
324Q8—42no—
325Q8—42no—
326Q8—41no—
327Q8—82no—
328D4—41no—
329D4—41no—
330D4—82no—
331C2×C4—22no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—82no—
341C2×C4C2×C3×D811yescharacteristic
342C2×C4C2×C3×D811yescharacteristic
343C2×C4C2×C3×D811yescharacteristic
344C2×C4C2×C3×D811yescharacteristic
345C2×C4C2×C3×D811yescharacteristic
346C2×C4C22×C3×D411yescharacteristic
347C8—21no—
348C8—21no—
349C8C3×#13512yes—
350C8C2×C3×#4112yes—
351C2×C3—22no—
352C2×C3—161no—
353C2×C3#316911yescharacteristic
354C2×C3C2×#51011yescharacteristic
355C2×C3#341411yescharacteristic
356C22—21no—
357C22—21no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22C3×#51012yes—
362C22C22×C3×D811yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—81no—
369C4—81no—
370C4—82no—
371C4—81no—
372C4—82no—
373C4C3×#53211yescharacteristic
374C4C2×C3×#13511yescharacteristic
375C3#3374711yescharacteristic, direct product factor, Sylow
376C2—22no—
377C2—161no—
378C2C3×#316911yescharacteristic
379C2C2×C3×#51011yescharacteristic
380C2C3×#341411yescharacteristic
subgroupG/H
center, socleC22×C3C22×D8
commutator, Frattini, cosocleC2×C8C24×C3
prime radicalC3×#466C22
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×#3170C2semidirect
3. C3×#2255C2semidirect
4. C3×#2251C2semidirect
5. C3×#2245C2semidirect
6. C3×#2243C2semidirect
8. C3×#2216C2semidirect
9. C3×#2176C2semidirect
10. C3×#2175C2semidirect
11. C2×C3×#346C2semidirect
12. #33747C3direct (N × H)
44. #3170C2×C3semidirect
46. #2255C2×C3semidirect
47. #2251C2×C3semidirect
48. #2245C2×C3semidirect
49. #2243C2×C3semidirect
51. #2216C2×C3semidirect
52. #2176C2×C3semidirect
53. #2175C2×C3semidirect
54. C2×#346C2×C3semidirect
375. C3#33747direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#31702
C3×#31682
C3×#22552
C3×#22512
C3×#22452
C3×#22432
C3×#22172
C3×#22162
C3×#21762
C3×#21752
C2×C3×#3462
#337473