Finite Group Databasebeta

← C3×#30433 #10649040

Subgroups — C3×#30433 #10649040

Order 768.

886 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3061C212yesmaximal, complemented
2C3×#3013C212yesmaximal, complemented
3C3×#2095C211yesmaximal, characteristic, complemented
4C3×#2078C212yesmaximal, complemented
5C3×#2039C212yesmaximal, complemented
6C3×#2007C211yesmaximal, characteristic, complemented
7C3×#1908C212yesmaximal, complemented
8C3×#1876C212yesmaximal, complemented
9C3×#1793C211yesmaximal, characteristic, complemented
10#30433C311yesmaximal, characteristic, direct product factor, Sylow
11C2×C3×2−1+4C2211yescharacteristic
12C2×C3×#137C2212yes—
13C2×C3×#135C2212yes—
14C2×C3×#131C2212yes—
15C3×#537C2211yescharacteristic
16C3×#537C2212yes—
17C3×#468—22no—
18C3×#468—22no—
19C3×#467—22no—
20C3×#466—22no—
21C3×#452—22no—
22C3×#451—22no—
23C3×#449—22no—
24C3×#448—22no—
25C2×C3×#107C2212yes—
26C2×C3×#104C2212yes—
27C2×C3×#104C2212yes—
28C3×#417C2212yes—
29C3×#417C2212yes—
30C3×#417C2212yes—
31C2×C3×#103C2212yes—
32C2×C3×#101C2211yescharacteristic
33C3×#408C2212yes—
34C3×#391C2211yescharacteristic
35C3×#384C2211yescharacteristic
36C3×#343C2211yescharacteristic
37C3×#343C2212yes—
38C3×#341C2212yes—
39C3×#336C2211yescharacteristic
40#3061C2×C312yescomplemented
41#3013C2×C312yescomplemented
42#2095C2×C311yescharacteristic, complemented
43#2078C2×C312yescomplemented
44#2039C2×C312yescomplemented
45#2007C2×C311yescharacteristic, complemented
46#1908C2×C312yescomplemented
47#1876C2×C312yescomplemented
48#1793C2×C311yescharacteristic, complemented
49C3×2−1+4—22no—
50C3×2−1+4—41no—
51C3×2−1+4—42no—
52C2×C3×#41—22no—
53C2×C3×#41—41no—
54C2×C3×#41C2312yes—
55C2×C3×#41C2312yes—
56C22×C3×Q8—22no—
57C22×C3×Q8C2311yescharacteristic
58C3×#137—24no—
59C3×#137—42no—
60C3×#135—42no—
61C3×#135—42no—
62C2×C3×Q16—22no—
63C2×C3×Q16D412yes—
64C2×C3×SD16—22no—
65C2×C3×SD16D412yes—
66C2×C3×SD16D412yes—
67C2×C3×D8D412yes—
68C3×#131—42no—
69C3×#131—42no—
70C2×C3×M16—22no—
71C2×C3×M16C2312yes—
72C2×C3×M16C2312yes—
73C22×C3×C8—22no—
74C22×C3×C8C2312yes—
75C3×C22⋊Q8—22no—
76C3×C22⋊Q8—22no—
77C3×C22⋊Q8—22no—
78C3×#121—22no—
79C3×#121—22no—
80C3×#121—22no—
81C3×#121—41no—
82C3×#121—42no—
83C2×C3×C4⋊C4—41no—
84C2×C3×C4⋊C4C2312yes—
85C2×C3×C4⋊C4C2311yescharacteristic
86C2×C3×C42C2311yescharacteristic
87C3×#107—22no—
88C3×#107—22no—
89C3×#104—42no—
90C3×#104—42no—
91C3×#103—22no—
92C3×#103—22no—
93C3×#103—22no—
94C3×#103—22no—
95C3×#103—22no—
96C3×#102—22no—
97C3×#102—22no—
98C3×#102—22no—
99C3×#101—41no—
100C3×C22⋊C8—22no—
101C3×C22⋊C8—22no—
102C3×#95—41no—
103C2×2−1+4C22×C311yescharacteristic
104C2×#137C22×C312yes—
105C2×#135C22×C312yes—
106C2×#131C22×C312yes—
107#537C22×C312yes—
108#537C22×C311yescharacteristic
109#468—22no—
110#468—22no—
111#467—22no—
112#466—22no—
113#452—22no—
114#451—22no—
115#449—22no—
116#448—22no—
117C2×#107C22×C312yes—
118C2×#104C22×C312yes—
119C2×#104C22×C312yes—
120#417C22×C312yes—
121#417C22×C312yes—
122#417C22×C312yes—
123C2×#103C22×C312yes—
124C2×#101C22×C311yescharacteristic
125#408C22×C312yes—
126#391C22×C311yescharacteristic
127#384C22×C311yescharacteristic
128#343C22×C311yescharacteristic
129#343C22×C312yes—
130#341C22×C312yes—
131#336C22×C311yescharacteristic
132C3×#41—22no—
133C3×#41—22no—
134C3×#41—22no—
135C3×#41—22no—
136C3×#41—22no—
137C3×#41—22no—
138C3×#41—22no—
139C3×#41—22no—
140C3×#41—44no—
141C3×#41—44no—
142C3×#41—44no—
143C3×#41—44no—
144C2×C3×Q8—21no—
145C2×C3×Q8—22no—
146C2×C3×Q8—22no—
147C2×C3×Q8—41no—
148C2×C3×Q8—44no—
149C2×C3×Q8—44no—
150C2×C3×Q8C2×D412yes—
151C2×C3×Q8C2×D412yes—
152C2×C3×Q8#4112yes—
153C2×C3×D4—22no—
154C2×C3×D4—22no—
155C2×C3×D4—41no—
156C2×C3×D4—41no—
157C2×C3×D4—42no—
158C2×C3×D4C2×D412yes—
159C2×C3×D4C2×D412yes—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—22no—
163C22×C3×C4—22no—
164C22×C3×C4—21no—
165C22×C3×C4—22no—
166C22×C3×C4—42no—
167C22×C3×C4C2411yescharacteristic
168C3×Q16—42no—
169C3×Q16—44no—
170C3×SD16—42no—
171C3×SD16—42no—
172C3×SD16—44no—
173C3×D8—42no—
174C3×M16—22no—
175C3×M16—22no—
176C3×M16—22no—
177C3×M16—22no—
178C3×M16—44no—
179C2×C3×C8—22no—
180C2×C3×C8—22no—
181C2×C3×C8—22no—
182C2×C3×C8—22no—
183C2×C3×C8—44no—
184C2×C3×C8C2×D412yes—
185C2×C3×C8C2×D412yes—
186C3×C4⋊C4—22no—
187C3×C4⋊C4—22no—
188C3×C4⋊C4—22no—
189C3×C4⋊C4—41no—
190C3×C4⋊C4—42no—
191C3×C4⋊C4—82no—
192C3×C22⋊C4—42no—
193C3×C22⋊C4—42no—
194C3×C22⋊C4—42no—
195C3×C42—22no—
1962−1+4—22no—
1972−1+4—41no—
1982−1+4—42no—
199C2×#41—22no—
200C2×#41—41no—
201C2×#41C23×C312yes—
202C2×#41C23×C312yes—
203C22×Q8—22no—
204C22×Q8C23×C311yescharacteristic
205#137—24no—
206#137—42no—
207#135—42no—
208#135—42no—
209C2×Q16—22no—
210C2×Q16C3×D412yes—
211C2×SD16—22no—
212C2×SD16C3×D412yes—
213C2×SD16C3×D412yes—
214C2×D8C3×D412yes—
215#131—42no—
216#131—42no—
217C2×M16—22no—
218C2×M16C23×C312yes—
219C2×M16C23×C312yes—
220C22×C8—22no—
221C22×C8C23×C312yes—
222C22⋊Q8—22no—
223C22⋊Q8—22no—
224C22⋊Q8—22no—
225#121—22no—
226#121—22no—
227#121—22no—
228#121—41no—
229#121—42no—
230C2×C4⋊C4—41no—
231C2×C4⋊C4C23×C312yes—
232C2×C4⋊C4C23×C311yescharacteristic
233C2×C42C23×C311yescharacteristic
234#107—22no—
235#107—22no—
236#104—42no—
237#104—42no—
238#103—22no—
239#103—22no—
240#103—22no—
241#103—22no—
242#103—22no—
243#102—22no—
244#102—22no—
245#102—22no—
246#101—41no—
247C22⋊C8—22no—
248C22⋊C8—22no—
249#95—41no—
250C23×C3—22no—
251C23×C3—22no—
252C23×C3H(5,𝔽2)11yescharacteristic
253C3×Q8—22no—
254C3×Q8—22no—
255C3×Q8—24no—
256C3×Q8—22no—
257C3×Q8—22no—
258C3×Q8—44no—
259C3×Q8—42no—
260C3×D4—22no—
261C3×D4—22no—
262C3×D4—22no—
263C3×D4—22no—
264C3×D4—44no—
265C3×D4—42no—
266C3×D4—42no—
267C3×D4—42no—
268C3×D4—42no—
269C3×D4—161no—
270C3×D4—162no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—41no—
276C2×C3×C4—48no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—42no—
281C2×C3×C4—42no—
282C2×C3×C4—42no—
283C2×C3×C4—42no—
284C2×C3×C4—42no—
285C2×C3×C4—41no—
286C2×C3×C4—82no—
287C2×C3×C4—81no—
288C2×C3×C4C22×D412yes—
289C2×C3×C4C2×#4111yescharacteristic
290C2×C3×C4H(5,𝔽2)11yescharacteristic
291C2×C3×C4H(5,𝔽2)12yes—
292C3×C8—22no—
293C3×C8—22no—
294C3×C8—42no—
295C3×C8—42no—
296#41—22no—
297#41—22no—
298#41—22no—
299#41—22no—
300#41—22no—
301#41—22no—
302#41—22no—
303#41—22no—
304#41—44no—
305#41—44no—
306#41—44no—
307#41—44no—
308C2×Q8—21no—
309C2×Q8—22no—
310C2×Q8—22no—
311C2×Q8—41no—
312C2×Q8—44no—
313C2×Q8—44no—
314C2×Q8C2×C3×D412yes—
315C2×Q8C2×C3×D412yes—
316C2×Q8C3×#4112yes—
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—42no—
322C2×D4C2×C3×D412yes—
323C2×D4C2×C3×D412yes—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—21no—
329C22×C4—22no—
330C22×C4—42no—
331C22×C4C24×C311yescharacteristic
332Q16—42no—
333Q16—44no—
334SD16—42no—
335SD16—42no—
336SD16—44no—
337D8—42no—
338M16—22no—
339M16—22no—
340M16—22no—
341M16—22no—
342M16—44no—
343C2×C8—22no—
344C2×C8—22no—
345C2×C8—22no—
346C2×C8—22no—
347C2×C8—44no—
348C2×C8C2×C3×D412yes—
349C2×C8C2×C3×D412yes—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—41no—
354C4⋊C4—42no—
355C4⋊C4—82no—
356C22⋊C4—42no—
357C22⋊C4—42no—
358C22⋊C4—42no—
359C42—22no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—42no—
363C22×C3—42no—
364C22×C3—42no—
365C22×C3—42no—
366C22×C3—42no—
367C22×C3—42no—
368C22×C3#53811yescharacteristic
369C22×C3D4211yescharacteristic
370C22×C3#56011yescharacteristic
371C3×C4—42no—
372C3×C4—42no—
373C3×C4—42no—
374C3×C4—42no—
375C3×C4—82no—
376C3×C4—81no—
377C3×C4#53412yes—
378C3×C4#54612yes—
379C23—22no—
380C23—22no—
381C23C3×H(5,𝔽2)11yescharacteristic
382Q8—22no—
383Q8—22no—
384Q8—24no—
385Q8—22no—
386Q8—22no—
387Q8—44no—
388Q8—42no—
389D4—22no—
390D4—22no—
391D4—22no—
392D4—22no—
393D4—44no—
394D4—42no—
395D4—42no—
396D4—42no—
397D4—42no—
398D4—161no—
399D4—162no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—41no—
405C2×C4—48no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—82no—
416C2×C4—81no—
417C2×C4C22×C3×D412yes—
418C2×C4C2×C3×#4111yescharacteristic
419C2×C4C3×H(5,𝔽2)11yescharacteristic
420C2×C4C3×H(5,𝔽2)12yes—
421C8—22no—
422C8—22no—
423C8—42no—
424C8—42no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—82no—
428C2×C3—82no—
429C2×C3#266811yescharacteristic
430C2×C3#328811yescharacteristic
431C2×C3#329311yescharacteristic
432C22—21no—
433C22—21no—
434C22—42no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22—42no—
439C22—42no—
440C22C3×#53811yescharacteristic
441C22C3×D4211yescharacteristic
442C22C3×#56011yescharacteristic
443C4—42no—
444C4—42no—
445C4—42no—
446C4—42no—
447C4—82no—
448C4—81no—
449C4C3×#53412yes—
450C4C3×#54612yes—
451C3#3043311yescharacteristic, direct product factor, Sylow
452C2—21no—
453C2—21no—
454C2—82no—
455C2—82no—
456C2C3×#266811yescharacteristic
457C2C3×#328811yescharacteristic
458C2C3×#329311yescharacteristic
subgroupG/H
center, socleC22×C3D42
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#3061C2semidirect
2. C3×#3013C2semidirect
3. C3×#2095C2semidirect
4. C3×#2078C2semidirect
5. C3×#2039C2semidirect
6. C3×#2007C2semidirect
7. C3×#1908C2semidirect
8. C3×#1876C2semidirect
9. C3×#1793C2semidirect
10. #30433C3direct (N × H)
40. #3061C2×C3semidirect
41. #3013C2×C3semidirect
42. #2095C2×C3semidirect
43. #2078C2×C3semidirect
44. #2039C2×C3semidirect
45. #2007C2×C3semidirect
46. #1908C2×C3semidirect
47. #1876C2×C3semidirect
48. #1793C2×C3semidirect
451. C3#30433direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#30612
C3×#30132
C3×#20952
C3×#20782
C3×#20392
C3×#20072
C3×#19082
C3×#18762
C3×#17932
#304333