Finite Group Databasebeta

← C3×#14670 #10633277

Subgroups — C3×#14670 #10633277

Order 768.

1038 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#389C211yesmaximal, characteristic
2C3×#1445C212yesmaximal
3C3×#1445C212yesmaximal
4C3×#1443C212yesmaximal
5C3×#1442C212yesmaximal
6C3×#1441C212yesmaximal
7C3×#1441C212yesmaximal
8C3×#1434C211yesmaximal, characteristic
9C3×#1434C211yesmaximal, characteristic
10#14670C311yesmaximal, characteristic, direct product factor, Sylow
11C22×C3×C4⋊C4C2211yescharacteristic
12C22×C3×C4⋊C4C2212yes—
13C22×C3×C4⋊C4C2211yescharacteristic
14C22×C3×C4⋊C4C2212yes—
15C22×C3×C42C2211yescharacteristic
16C3×#389C418yescomplemented
17C2×C3×#95C2212yes—
18C2×C3×#95C2212yes—
19C2×C3×#95C2211yescharacteristic
20C2×C3×#95C2212yes—
21C2×C3×#95C2211yescharacteristic
22C2×C3×#95C2212yes—
23C2×C3×#95C2211yescharacteristic
24C2×C3×#95C2211yescharacteristic
25C2×C3×#95C2212yes—
26C2×C3×#95C2212yes—
27C2×C3×#95C2212yes—
28C2×C3×#95C2212yes—
29C2×C3×#95C2212yes—
30C2×C3×#95C2212yes—
31C2×C3×#95C2212yes—
32C2×C3×#95C2212yes—
33C2×#389C2×C311yescharacteristic
34#1445C2×C312yes—
35#1445C2×C312yes—
36#1443C2×C312yes—
37#1442C2×C312yes—
38#1441C2×C312yes—
39#1441C2×C312yes—
40#1434C2×C311yescharacteristic
41#1434C2×C311yescharacteristic
42C23×C3×C4C2312yes—
43C23×C3×C4C2312yes—
44C23×C3×C4C2312yes—
45C23×C3×C4C2312yes—
46C23×C3×C4C2311yescharacteristic
47C23×C3×C4C2312yes—
48C23×C3×C4C2311yescharacteristic
49C23×C3×C4C2312yes—
50C23×C3×C4C2311yescharacteristic
51C2×C3×C4⋊C4—24no—
52C2×C3×C4⋊C4—42no—
53C2×C3×C4⋊C4—42no—
54C2×C3×C4⋊C4—42no—
55C2×C3×C4⋊C4—42no—
56C2×C3×C4⋊C4—42no—
57C2×C3×C4⋊C4—42no—
58C2×C3×C4⋊C4C2×C414yes—
59C2×C3×C4⋊C4C2×C418yes—
60C2×C3×C4⋊C4C2×C414yes—
61C2×C3×C42—42no—
62C2×C3×C42C2×C414yes—
63C3×#95—24no—
64C3×#95—24no—
65C3×#95—41no—
66C3×#95—41no—
67C3×#95—41no—
68C3×#95—42no—
69C3×#95—42no—
70C3×#95—41no—
71C3×#95—42no—
72C3×#95—42no—
73C3×#95—42no—
74C3×#95—42no—
75C3×#95—42no—
76C3×#95—42no—
77C3×#95—42no—
78C3×#95C2×C418yes—
79C22×C4⋊C4C22×C311yescharacteristic
80C22×C4⋊C4C22×C312yes—
81C22×C4⋊C4C22×C311yescharacteristic
82C22×C4⋊C4C22×C312yes—
83C22×C42C22×C311yescharacteristic
84#389C3×C418yescomplemented
85C2×#95C22×C312yes—
86C2×#95C22×C312yes—
87C2×#95C22×C311yescharacteristic
88C2×#95C22×C312yes—
89C2×#95C22×C311yescharacteristic
90C2×#95C22×C312yes—
91C2×#95C22×C311yescharacteristic
92C2×#95C22×C311yescharacteristic
93C2×#95C22×C312yes—
94C2×#95C22×C312yes—
95C2×#95C22×C312yes—
96C2×#95C22×C312yes—
97C2×#95C22×C312yes—
98C2×#95C22×C312yes—
99C2×#95C22×C312yes—
100C2×#95C22×C312yes—
101C24×C3C2411yescharacteristic
102C22×C3×C4—22no—
103C22×C3×C4—21no—
104C22×C3×C4—21no—
105C22×C3×C4—22no—
106C22×C3×C4—22no—
107C22×C3×C4—22no—
108C22×C3×C4—21no—
109C22×C3×C4—21no—
110C22×C3×C4—22no—
111C22×C3×C4—22no—
112C22×C3×C4—22no—
113C22×C3×C4—22no—
114C22×C3×C4—22no—
115C22×C3×C4—22no—
116C22×C3×C4—22no—
117C22×C3×C4—22no—
118C22×C3×C4—22no—
119C22×C3×C4—22no—
120C22×C3×C4—22no—
121C22×C3×C4—22no—
122C22×C3×C4—21no—
123C22×C3×C4—22no—
124C22×C3×C4—21no—
125C22×C3×C4—22no—
126C22×C3×C4—22no—
127C22×C3×C4—22no—
128C22×C3×C4—22no—
129C22×C3×C4—22no—
130C22×C3×C4—22no—
131C22×C3×C4—22no—
132C22×C3×C4—22no—
133C22×C3×C4—22no—
134C22×C3×C4—22no—
135C22×C3×C4—22no—
136C22×C3×C4—22no—
137C22×C3×C4—22no—
138C22×C3×C4—22no—
139C22×C3×C4—22no—
140C22×C3×C4—22no—
141C22×C3×C4—22no—
142C22×C3×C4—22no—
143C22×C3×C4—22no—
144C22×C3×C4—22no—
145C22×C3×C4—22no—
146C22×C3×C4—22no—
147C22×C3×C4—22no—
148C22×C3×C4—22no—
149C22×C3×C4—22no—
150C22×C3×C4—22no—
151C22×C3×C4—22no—
152C22×C3×C4—22no—
153C22×C3×C4C22×C412yes—
154C22×C3×C4C22×C414yes—
155C22×C3×C4C22×C414yes—
156C22×C3×C4C22×C412yes—
157C22×C3×C4C22×C412yes—
158C22×C3×C4#4114yes—
159C3×C4⋊C4—28no—
160C3×C4⋊C4—44no—
161C3×C4⋊C4—48no—
162C3×C4⋊C4—48no—
163C3×C42—44no—
164C23×C4C23×C312yes—
165C23×C4C23×C312yes—
166C23×C4C23×C312yes—
167C23×C4C23×C312yes—
168C23×C4C23×C312yes—
169C23×C4C23×C312yes—
170C23×C4C23×C311yescharacteristic
171C23×C4C23×C311yescharacteristic
172C23×C4C23×C311yescharacteristic
173C2×C4⋊C4—24no—
174C2×C4⋊C4—42no—
175C2×C4⋊C4—42no—
176C2×C4⋊C4—42no—
177C2×C4⋊C4—42no—
178C2×C4⋊C4—42no—
179C2×C4⋊C4—42no—
180C2×C4⋊C4C2×C3×C414yes—
181C2×C4⋊C4C2×C3×C418yes—
182C2×C4⋊C4C2×C3×C414yes—
183C2×C42—42no—
184C2×C42C2×C3×C414yes—
185#95—24no—
186#95—24no—
187#95—41no—
188#95—41no—
189#95—41no—
190#95—42no—
191#95—42no—
192#95—41no—
193#95—42no—
194#95—42no—
195#95—42no—
196#95—42no—
197#95—42no—
198#95—42no—
199#95—42no—
200#95C2×C3×C418yes—
201C23×C3C23×C411yescharacteristic
202C23×C3C2×#4112yes—
203C23×C3H(5,𝔽2)12yes—
204C23×C3H(5,𝔽2)12yes—
205C23×C3H(5,𝔽2)11yescharacteristic
206C23×C3H(5,𝔽2)11yescharacteristic
207C23×C32−1+411yescharacteristic
208C23×C32−1+411yescharacteristic
209C23×C32−1+412yes—
210C23×C32−1+411yescharacteristic
211C23×C32−1+411yescharacteristic
212C2×C3×C4—22no—
213C2×C3×C4—22no—
214C2×C3×C4—24no—
215C2×C3×C4—24no—
216C2×C3×C4—24no—
217C2×C3×C4—22no—
218C2×C3×C4—22no—
219C2×C3×C4—22no—
220C2×C3×C4—24no—
221C2×C3×C4—24no—
222C2×C3×C4—24no—
223C2×C3×C4—22no—
224C2×C3×C4—24no—
225C2×C3×C4—22no—
226C2×C3×C4—24no—
227C2×C3×C4—22no—
228C2×C3×C4—42no—
229C2×C3×C4—42no—
230C2×C3×C4—42no—
231C2×C3×C4—42no—
232C2×C3×C4—42no—
233C2×C3×C4—42no—
234C2×C3×C4—42no—
235C2×C3×C4—42no—
236C2×C3×C4—42no—
237C2×C3×C4—42no—
238C2×C3×C4—42no—
239C2×C3×C4—42no—
240C2×C3×C4—42no—
241C2×C3×C4—42no—
242C2×C3×C4—42no—
243C2×C3×C4—42no—
244C2×C3×C4—42no—
245C2×C3×C4—42no—
246C2×C3×C4—42no—
247C2×C3×C4—42no—
248C2×C3×C4—42no—
249C2×C3×C4—42no—
250C2×C3×C4—42no—
251C2×C3×C4—42no—
252C2×C3×C4—42no—
253C2×C3×C4—42no—
254C2×C3×C4—42no—
255C2×C3×C4—42no—
256C2×C3×C4—42no—
257C2×C3×C4—42no—
258C2×C3×C4—42no—
259C2×C3×C4—42no—
260C2×C3×C4—42no—
261C2×C3×C4—42no—
262C2×C3×C4—42no—
263C2×C3×C4—42no—
264C2×C3×C4—42no—
265C2×C3×C4—42no—
266C2×C3×C4—42no—
267C2×C3×C4—42no—
268C2×C3×C4#11714yes—
269C24C24×C311yescharacteristic
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4C22×C3×C412yes—
322C22×C4C22×C3×C414yes—
323C22×C4C22×C3×C414yes—
324C22×C4C22×C3×C412yes—
325C22×C4C22×C3×C412yes—
326C22×C4C3×#4114yes—
327C4⋊C4—28no—
328C4⋊C4—44no—
329C4⋊C4—48no—
330C4⋊C4—48no—
331C42—44no—
332C22×C3C2×#11711yescharacteristic
333C22×C3#51811yescharacteristic
334C22×C3#51811yescharacteristic
335C22×C3#51911yescharacteristic
336C22×C3#51911yescharacteristic
337C22×C3#52011yescharacteristic
338C22×C3#52011yescharacteristic
339C22×C3#53912yes—
340C22×C3#53912yes—
341C22×C3#54012yes—
342C22×C3#54112yes—
343C22×C3#54212yes—
344C22×C3#54212yes—
345C22×C3#56012yes—
346C22×C3#56212yes—
347C22×C3#56212yes—
348C22×C3#56211yescharacteristic
349C22×C3#56311yescharacteristic
350C22×C3#56312yes—
351C22×C3#56312yes—
352C22×C3#56311yescharacteristic
353C22×C3#56312yes—
354C22×C3#56411yescharacteristic
355C3×C4—24no—
356C3×C4—44no—
357C3×C4—42no—
358C3×C4—44no—
359C3×C4—42no—
360C3×C4—82no—
361C3×C4—82no—
362C3×C4—82no—
363C3×C4—82no—
364C23C23×C3×C411yescharacteristic
365C23C2×C3×#4112yes—
366C23C3×H(5,𝔽2)11yescharacteristic
367C23C3×H(5,𝔽2)12yes—
368C23C3×H(5,𝔽2)12yes—
369C23C3×H(5,𝔽2)11yescharacteristic
370C23C3×2−1+411yescharacteristic
371C23C3×2−1+412yes—
372C23C3×2−1+411yescharacteristic
373C23C3×2−1+411yescharacteristic
374C23C3×2−1+411yescharacteristic
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—24no—
378C2×C4—24no—
379C2×C4—24no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—24no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—24no—
389C2×C4—22no—
390C2×C4—24no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4C3×#11714yes—
432C2×C3#231311yescharacteristic
433C2×C3#231911yescharacteristic
434C2×C3#232011yescharacteristic
435C2×C3#237711yescharacteristic
436C2×C3#237811yescharacteristic
437C2×C3#238111yescharacteristic
438C2×C3#238211yescharacteristic
439C2×C3#283612yes—
440C2×C3#283712yes—
441C2×C3#283812yes—
442C2×C3#283912yes—
443C22C2×C3×#11711yescharacteristic
444C22C3×#51811yescharacteristic
445C22C3×#51811yescharacteristic
446C22C3×#51911yescharacteristic
447C22C3×#51911yescharacteristic
448C22C3×#52011yescharacteristic
449C22C3×#52011yescharacteristic
450C22C3×#53912yes—
451C22C3×#53912yes—
452C22C3×#54012yes—
453C22C3×#54112yes—
454C22C3×#54212yes—
455C22C3×#54212yes—
456C22C3×#56012yes—
457C22C3×#56212yes—
458C22C3×#56212yes—
459C22C3×#56211yescharacteristic
460C22C3×#56312yes—
461C22C3×#56312yes—
462C22C3×#56312yes—
463C22C3×#56311yescharacteristic
464C22C3×#56311yescharacteristic
465C22C3×#56411yescharacteristic
466C4—24no—
467C4—42no—
468C4—44no—
469C4—42no—
470C4—44no—
471C4—82no—
472C4—82no—
473C4—82no—
474C4—82no—
475C3#1467011yescharacteristic, direct product factor, Sylow
476C2C3×#231311yescharacteristic
477C2C3×#231911yescharacteristic
478C2C3×#232011yescharacteristic
479C2C3×#237711yescharacteristic
480C2C3×#237811yescharacteristic
481C2C3×#238111yescharacteristic
482C2C3×#238211yescharacteristic
483C2C3×#283612yes—
484C2C3×#283712yes—
485C2C3×#283812yes—
486C2C3×#283912yes—
subgroupG/H
center, socle, prime radicalC24×C3C24
commutatorC23C23×C3×C4
Frattini, cosocleC24C24×C3
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
10. #14670C3direct (N × H)
16. C3×#389C4semidirect
84. #389C3×C4semidirect
475. C3#14670direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3892
C3×#14452
C3×#14432
C3×#14422
C3×#14412
C3×#14342
#146703