Finite Group Databasebeta

← C3×#13408 #10632015

Subgroups — C3×#13408 #10632015

Order 768.

482 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#495C211yesmaximal, characteristic
2C2×C3×#358C211yesmaximal, characteristic, complemented
3C2×C3×#358C211yesmaximal, characteristic, complemented
4C2×C3×#357C211yesmaximal, characteristic
5C2×C3×#357C211yesmaximal, characteristic
6C3×#1942C211yesmaximal, characteristic, complemented
7C3×#1374C211yesmaximal, characteristic, complemented
8#13408C311yesmaximal, characteristic, direct product factor, Sylow
9C22×C3×Q16C2211yescharacteristic
10C22×C3×SD16—21no—
11C22×C3×D8C2211yescharacteristic
12C2×C3×#124—21no—
13C22×C3×C16C2211yescharacteristic
14C22×C3×C16C2211yescharacteristic
15C3×#495—22no—
16C3×#495—22no—
17C2×C3×#107C2211yescharacteristic
18C2×C3×#107C2211yescharacteristic
19C2×C3×C4×C8C2211yescharacteristic
20C3×#389—21no—
21C3×#358—22no—
22C3×#358—22no—
23C3×#357—22no—
24C3×#357—22no—
25C3×#340—21no—
26C2×#495C2×C311yescharacteristic
27C2×#358C2×C311yescharacteristic, complemented
28C2×#358C2×C311yescharacteristic, complemented
29C2×#357C2×C311yescharacteristic
30C2×#357C2×C311yescharacteristic
31#1942C2×C311yescharacteristic, complemented
32#1374C2×C311yescharacteristic, complemented
33C22×C3×Q8—21no—
34C22×C3×D4—21no—
35C2×C3×Q16—21no—
36C2×C3×Q16—21no—
37C2×C3×Q16—21no—
38C2×C3×Q16—21no—
39C2×C3×Q16—21no—
40C2×C3×Q16D412yes—
41C2×C3×SD16—24no—
42C2×C3×SD16—42no—
43C2×C3×SD16—42no—
44C2×C3×D8—21no—
45C2×C3×D8—21no—
46C2×C3×D8—21no—
47C2×C3×D8—21no—
48C2×C3×D8—21no—
49C2×C3×D8D412yes—
50C22×C3×C8D411yescharacteristic
51C22×C3×C8C2311yescharacteristic
52C3×#124—24no—
53C3×#124—42no—
54C2×C3×C4⋊C4—21no—
55C2×C3×C4⋊C4—21no—
56C2×C3×C4⋊C4—41no—
57C2×C3×C22⋊C4—41no—
58C2×C3×C22⋊C4—41no—
59C2×C3×C42D411yescharacteristic
60C2×C3×C16—21no—
61C2×C3×C16—21no—
62C2×C3×C16—21no—
63C2×C3×C16—21no—
64C2×C3×C16—21no—
65C2×C3×C16—21no—
66C3×#107—21no—
67C3×#107—21no—
68C3×#107—21no—
69C3×#107D412yes—
70C3×C4×C8—21no—
71C3×C4×C8—21no—
72C3×#95—41no—
73C22×Q16C22×C311yescharacteristic
74C22×SD16—21no—
75C22×D8C22×C311yescharacteristic
76C2×#124—21no—
77C22×C16C22×C311yescharacteristic
78C22×C16C22×C311yescharacteristic
79#495—22no—
80#495—22no—
81C2×#107C22×C311yescharacteristic
82C2×#107C22×C311yescharacteristic
83C2×C4×C8C22×C311yescharacteristic
84#389—21no—
85#358—22no—
86#358—22no—
87#357—22no—
88#357—22no—
89#340—21no—
90C24×C3—41no—
91C2×C3×Q8—22no—
92C2×C3×Q8—41no—
93C2×C3×Q8—41no—
94C2×C3×Q8—41no—
95C2×C3×Q8—41no—
96C2×C3×Q8—41no—
97C2×C3×D4—22no—
98C2×C3×D4—41no—
99C2×C3×D4—41no—
100C2×C3×D4—41no—
101C2×C3×D4—41no—
102C2×C3×D4—41no—
103C22×C3×C4—41no—
104C22×C3×C4—41no—
105C22×C3×C4—41no—
106C22×C3×C4D811yescharacteristic
107C22×C3×C4D811yescharacteristic
108C22×C3×C4C2×D411yescharacteristic
109C3×Q16—22no—
110C3×Q16—22no—
111C3×Q16—41no—
112C3×Q16—41no—
113C3×SD16—48no—
114C3×D8—22no—
115C3×D8—22no—
116C3×D8—41no—
117C3×D8—41no—
118C2×C3×C8—21no—
119C2×C3×C8—21no—
120C2×C3×C8SD1612yes—
121C2×C3×C8C2×D411yescharacteristic
122C2×C3×C8C2×D411yescharacteristic
123C2×C3×C8C2×D411yescharacteristic
124C2×C3×C8#4111yescharacteristic
125C2×C3×C8#4111yescharacteristic
126C2×C3×C8#4111yescharacteristic
127C3×C4⋊C4—22no—
128C3×C4⋊C4—41no—
129C3×C4⋊C4—41no—
130C3×C4⋊C4—41no—
131C3×C4⋊C4—82no—
132C3×C22⋊C4—44no—
133C3×C22⋊C4—44no—
134C3×C42—21no—
135C3×C42—21no—
136C3×C16—41no—
137C3×C16—41no—
138C22×Q8—21no—
139C22×D4—21no—
140C2×Q16—21no—
141C2×Q16—21no—
142C2×Q16—21no—
143C2×Q16—21no—
144C2×Q16—21no—
145C2×Q16C3×D412yes—
146C2×SD16—24no—
147C2×SD16—42no—
148C2×SD16—42no—
149C2×D8—21no—
150C2×D8—21no—
151C2×D8—21no—
152C2×D8—21no—
153C2×D8—21no—
154C2×D8C3×D412yes—
155C22×C8C3×D411yescharacteristic
156C22×C8C23×C311yescharacteristic
157#124—24no—
158#124—42no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—41no—
162C2×C22⋊C4—41no—
163C2×C22⋊C4—41no—
164C2×C42C3×D411yescharacteristic
165C2×C16—21no—
166C2×C16—21no—
167C2×C16—21no—
168C2×C16—21no—
169C2×C16—21no—
170C2×C16—21no—
171#107—21no—
172#107—21no—
173#107—21no—
174#107C3×D412yes—
175C4×C8—21no—
176C4×C8—21no—
177#95—41no—
178C23×C3—42no—
179C23×C3—81no—
180C23×C3—81no—
181C23×C3—81no—
182C23×C3—81no—
183C23×C3—81no—
184C23×C3—81no—
185C23×C3C2×D811yescharacteristic
186C3×Q8—42no—
187C3×Q8—42no—
188C3×Q8—81no—
189C3×Q8—81no—
190C3×D4—42no—
191C3×D4—42no—
192C3×D4—81no—
193C3×D4—81no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—42no—
201C2×C3×C4—42no—
202C2×C3×C4—81no—
203C2×C3×C4—81no—
204C2×C3×C4—81no—
205C2×C3×C4—81no—
206C2×C3×C4—81no—
207C2×C3×C4—81no—
208C2×C3×C4—81no—
209C2×C3×C4#12011yescharacteristic
210C2×C3×C4#12111yescharacteristic
211C2×C3×C4#12411yescharacteristic
212C2×C3×C4C2×SD1611yescharacteristic
213C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
214C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
215C3×C8—22no—
216C3×C8#12111yescharacteristic
217C3×C8#12111yescharacteristic
218C3×C8#12311yescharacteristic
219C3×C8#12311yescharacteristic
220C24—41no—
221C2×Q8—22no—
222C2×Q8—41no—
223C2×Q8—41no—
224C2×Q8—41no—
225C2×Q8—41no—
226C2×Q8—41no—
227C2×D4—22no—
228C2×D4—41no—
229C2×D4—41no—
230C2×D4—41no—
231C2×D4—41no—
232C2×D4—41no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4C3×D811yescharacteristic
237C22×C4C3×D811yescharacteristic
238C22×C4C2×C3×D411yescharacteristic
239Q16—22no—
240Q16—22no—
241Q16—41no—
242Q16—41no—
243SD16—48no—
244D8—22no—
245D8—22no—
246D8—41no—
247D8—41no—
248C2×C8—21no—
249C2×C8—21no—
250C2×C8C3×SD1612yes—
251C2×C8C2×C3×D411yescharacteristic
252C2×C8C2×C3×D411yescharacteristic
253C2×C8C2×C3×D411yescharacteristic
254C2×C8C3×#4111yescharacteristic
255C2×C8C3×#4111yescharacteristic
256C2×C8C3×#4111yescharacteristic
257C4⋊C4—22no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—82no—
262C22⋊C4—44no—
263C22⋊C4—44no—
264C42—21no—
265C42—21no—
266C16—41no—
267C16—41no—
268C22×C3—82no—
269C22×C3—82no—
270C22×C3—82no—
271C22×C3—161no—
272C22×C3—161no—
273C22×C3—161no—
274C22×C3—161no—
275C22×C3#44711yescharacteristic
276C22×C3#45911yescharacteristic
277C22×C3#48611yescharacteristic
278C22×C3#50811yescharacteristic
279C22×C3#50811yescharacteristic
280C22×C3#50911yescharacteristic
281C22×C3#51011yescharacteristic
282C3×C4—41no—
283C3×C4—41no—
284C3×C4—82no—
285C3×C4—82no—
286C3×C4—161no—
287C3×C4#39411yescharacteristic
288C3×C4#45011yescharacteristic
289C3×C4#46011yescharacteristic
290C3×C4#49011yescharacteristic
291C23—42no—
292C23—81no—
293C23—81no—
294C23—81no—
295C23—81no—
296C23—81no—
297C23—81no—
298C23C2×C3×D811yescharacteristic
299Q8—42no—
300Q8—42no—
301Q8—81no—
302Q8—81no—
303D4—42no—
304D4—42no—
305D4—81no—
306D4—81no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4C3×#12011yescharacteristic
323C2×C4C3×#12111yescharacteristic
324C2×C4C3×#12411yescharacteristic
325C2×C4C2×C3×SD1611yescharacteristic
326C2×C4C3×AGL(1,ℤ/8)11yescharacteristic
327C2×C4C3×AGL(1,ℤ/8)11yescharacteristic
328C8—22no—
329C8C3×#12111yescharacteristic
330C8C3×#12111yescharacteristic
331C8C3×#12311yescharacteristic
332C8C3×#12311yescharacteristic
333C2×C3—162no—
334C2×C3#204111yescharacteristic
335C2×C3#218611yescharacteristic
336C2×C3#218911yescharacteristic
337C2×C3#221011yescharacteristic
338C2×C3#221111yescharacteristic
339C2×C3#224211yescharacteristic
340C2×C3#224311yescharacteristic
341C22—82no—
342C22—82no—
343C22—82no—
344C22—161no—
345C22—161no—
346C22—161no—
347C22—161no—
348C22C3×#44711yescharacteristic
349C22C3×#45911yescharacteristic
350C22C3×#48611yescharacteristic
351C22C3×#50811yescharacteristic
352C22C3×#50811yescharacteristic
353C22C3×#50911yescharacteristic
354C22C3×#51011yescharacteristic
355C4—41no—
356C4—41no—
357C4—82no—
358C4—82no—
359C4—161no—
360C4C3×#39411yescharacteristic
361C4C3×#45011yescharacteristic
362C4C3×#46011yescharacteristic
363C4C3×#49011yescharacteristic
364C3#1340811yescharacteristic, direct product factor, Sylow
365C2—162no—
366C2C3×#204111yescharacteristic
367C2C3×#218611yescharacteristic
368C2C3×#218911yescharacteristic
369C2C3×#221011yescharacteristic
370C2C3×#221111yescharacteristic
371C2C3×#224211yescharacteristic
372C2C3×#224311yescharacteristic
subgroupG/H
center, socleC23×C3C2×D8
commutator, Frattini, cosocleC22×C8C23×C3
prime radicalC22×C3×D8C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C2×C3×C4×C8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#358C2semidirect
3. C2×C3×#358C2semidirect
6. C3×#1942C2semidirect
7. C3×#1374C2semidirect
8. #13408C3direct (N × H)
27. C2×#358C2×C3semidirect
28. C2×#358C2×C3semidirect
31. #1942C2×C3semidirect
32. #1374C2×C3semidirect
364. C3#13408direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4952
C2×C3×#3582
C2×C3×#3572
C3×#19422
C3×#13742
#134083