Finite Group Databasebeta

← C3×#15052 #10633659

Subgroups — C3×#15052 #10633659

Order 768.

1066 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#1443C212yesmaximal
2C3×#1442C212yesmaximal
3C3×#1442C212yesmaximal
4C3×#1441C212yesmaximal
5C3×#1436C212yesmaximal
6C3×C4⋊#95C211yesmaximal, characteristic
7C3×#1434C212yesmaximal
8C3×#1434C211yesmaximal, characteristic
9C3×C4×#95C211yesmaximal, characteristic
10#15052C311yesmaximal, characteristic, direct product factor, Sylow
11C22×C3×C4⋊C4C2212yes—
12C22×C3×C4⋊C4C2212yes—
13C22×C3×C42C2212yes—
14C22×C3×C42C2211yescharacteristic
15C2×C3×#95C2211yescharacteristic
16C2×C3×#95C2211yescharacteristic
17C2×C3×#95C2212yes—
18C2×C3×#95C2211yescharacteristic
19C2×C3×#95C2212yes—
20C2×C3×#95C2211yescharacteristic
21C2×C3×#95C2212yes—
22C2×C3×#95C2212yes—
23C2×C3×#95C2212yes—
24C2×C3×#95C2212yes—
25C2×C3×#95C2212yes—
26C2×C3×#95C2212yes—
27C2×C3×#95C2212yes—
28C2×C3×#95C2212yes—
29C2×C3×#95C2211yescharacteristic
30C2×C3×#95C2211yescharacteristic
31C2×C3×#95C2212yes—
32#1443C2×C312yes—
33#1442C2×C312yes—
34#1442C2×C312yes—
35#1441C2×C312yes—
36#1436C2×C312yes—
37C4⋊#95C2×C311yescharacteristic
38#1434C2×C312yes—
39#1434C2×C311yescharacteristic
40C4×#95C2×C311yescharacteristic
41C23×C3×C4C2312yes—
42C23×C3×C4C2312yes—
43C23×C3×C4C2312yes—
44C23×C3×C4C2311yescharacteristic
45C23×C3×C4C2312yes—
46C23×C3×C4C2312yes—
47C23×C3×C4C2312yes—
48C23×C3×C4C2311yescharacteristic
49C23×C3×C4C2311yescharacteristic
50C2×C3×C4⋊C4—24no—
51C2×C3×C4⋊C4—24no—
52C2×C3×C4⋊C4—24no—
53C2×C3×C4⋊C4—42no—
54C2×C3×C4⋊C4—42no—
55C2×C3×C4⋊C4—42no—
56C2×C3×C42—24no—
57C2×C3×C42—24no—
58C2×C3×C42—42no—
59C2×C3×C42—42no—
60C2×C3×C42Q814yes—
61C3×#95—24no—
62C3×#95—22no—
63C3×#95—22no—
64C3×#95—24no—
65C3×#95—24no—
66C3×#95—24no—
67C3×#95—24no—
68C3×#95—24no—
69C3×#95—24no—
70C3×#95—22no—
71C3×#95—24no—
72C3×#95—22no—
73C3×#95—41no—
74C3×#95—41no—
75C3×#95—42no—
76C3×#95—42no—
77C3×#95—42no—
78C22×C4⋊C4C22×C312yes—
79C22×C4⋊C4C22×C312yes—
80C22×C42C22×C312yes—
81C22×C42C22×C311yescharacteristic
82C2×#95C22×C311yescharacteristic
83C2×#95C22×C311yescharacteristic
84C2×#95C22×C312yes—
85C2×#95C22×C311yescharacteristic
86C2×#95C22×C312yes—
87C2×#95C22×C311yescharacteristic
88C2×#95C22×C312yes—
89C2×#95C22×C312yes—
90C2×#95C22×C312yes—
91C2×#95C22×C312yes—
92C2×#95C22×C312yes—
93C2×#95C22×C312yes—
94C2×#95C22×C312yes—
95C2×#95C22×C312yes—
96C2×#95C22×C311yescharacteristic
97C2×#95C22×C311yescharacteristic
98C2×#95C22×C312yes—
99C24×C3C2411yescharacteristic
100C22×C3×C4—22no—
101C22×C3×C4—22no—
102C22×C3×C4—22no—
103C22×C3×C4—22no—
104C22×C3×C4—22no—
105C22×C3×C4—22no—
106C22×C3×C4—22no—
107C22×C3×C4—22no—
108C22×C3×C4—22no—
109C22×C3×C4—22no—
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—21no—
118C22×C3×C4—22no—
119C22×C3×C4—22no—
120C22×C3×C4—22no—
121C22×C3×C4—22no—
122C22×C3×C4—22no—
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×C4C2×Q812yes—
148C22×C3×C4C2×Q812yes—
149C22×C3×C4C2×Q812yes—
150C22×C3×C4#4114yes—
151C22×C3×C4#4114yes—
152C22×C3×C4#4114yes—
153C22×C3×C4#4112yes—
154C22×C3×C4#4112yes—
155C22×C3×C4#4112yes—
156C22×C3×C4#4112yes—
157C3×C4⋊C4—48no—
158C3×C4⋊C4—48no—
159C3×C42—44no—
160C3×C42—48no—
161C23×C4C23×C312yes—
162C23×C4C23×C312yes—
163C23×C4C23×C312yes—
164C23×C4C23×C311yescharacteristic
165C23×C4C23×C312yes—
166C23×C4C23×C312yes—
167C23×C4C23×C312yes—
168C23×C4C23×C311yescharacteristic
169C23×C4C23×C311yescharacteristic
170C2×C4⋊C4—24no—
171C2×C4⋊C4—24no—
172C2×C4⋊C4—24no—
173C2×C4⋊C4—42no—
174C2×C4⋊C4—42no—
175C2×C4⋊C4—42no—
176C2×C42—24no—
177C2×C42—24no—
178C2×C42—42no—
179C2×C42—42no—
180C2×C42C3×Q814yes—
181#95—24no—
182#95—22no—
183#95—22no—
184#95—24no—
185#95—24no—
186#95—24no—
187#95—24no—
188#95—24no—
189#95—24no—
190#95—22no—
191#95—24no—
192#95—22no—
193#95—41no—
194#95—41no—
195#95—42no—
196#95—42no—
197#95—42no—
198C23×C3C22×Q811yescharacteristic
199C23×C3C2×#4111yescharacteristic
200C23×C3C2×#4111yescharacteristic
201C23×C3C2×#4111yescharacteristic
202C23×C3C2×#4111yescharacteristic
203C23×C3C2×#4112yes—
204C23×C3C2×#4112yes—
205C23×C3C2×#4112yes—
206C23×C3H(5,𝔽2)11yescharacteristic
207C23×C3H(5,𝔽2)12yes—
208C23×C32−1+411yescharacteristic
209C2×C3×C4—22no—
210C2×C3×C4—22no—
211C2×C3×C4—22no—
212C2×C3×C4—22no—
213C2×C3×C4—24no—
214C2×C3×C4—24no—
215C2×C3×C4—24no—
216C2×C3×C4—24no—
217C2×C3×C4—24no—
218C2×C3×C4—24no—
219C2×C3×C4—24no—
220C2×C3×C4—24no—
221C2×C3×C4—22no—
222C2×C3×C4—24no—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—24no—
226C2×C3×C4—24no—
227C2×C3×C4—24no—
228C2×C3×C4—24no—
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#12514yes—
265C2×C3×C4#12514yes—
266C24C24×C311yescharacteristic
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—21no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—22no—
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×C4C2×C3×Q812yes—
315C22×C4C2×C3×Q812yes—
316C22×C4C2×C3×Q812yes—
317C22×C4C3×#4114yes—
318C22×C4C3×#4114yes—
319C22×C4C3×#4114yes—
320C22×C4C3×#4112yes—
321C22×C4C3×#4112yes—
322C22×C4C3×#4112yes—
323C22×C4C3×#4112yes—
324C4⋊C4—48no—
325C4⋊C4—48no—
326C42—44no—
327C42—48no—
328C22×C3C2×#12511yescharacteristic
329C22×C3C2×#12511yescharacteristic
330C22×C3#52912yes—
331C22×C3#52912yes—
332C22×C3#52912yes—
333C22×C3#52912yes—
334C22×C3#53311yescharacteristic
335C22×C3#53311yescharacteristic
336C22×C3#53311yescharacteristic
337C22×C3#53812yes—
338C22×C3#54212yes—
339C22×C3#54311yescharacteristic
340C22×C3#54411yescharacteristic
341C22×C3#55112yes—
342C22×C3#55112yes—
343C22×C3#55212yes—
344C22×C3#55312yes—
345C22×C3#55312yes—
346C22×C3#55312yes—
347C22×C3#55511yescharacteristic
348C22×C3#55611yescharacteristic
349C22×C3#55611yescharacteristic
350C22×C3#55911yescharacteristic
351C3×C4—24no—
352C3×C4—24no—
353C3×C4—44no—
354C3×C4—42no—
355C3×C4—44no—
356C3×C4—44no—
357C3×C4—82no—
358C3×C4—82no—
359C3×C4—82no—
360C23C22×C3×Q811yescharacteristic
361C23C2×C3×#4111yescharacteristic
362C23C2×C3×#4111yescharacteristic
363C23C2×C3×#4111yescharacteristic
364C23C2×C3×#4111yescharacteristic
365C23C2×C3×#4112yes—
366C23C2×C3×#4112yes—
367C23C2×C3×#4112yes—
368C23C3×H(5,𝔽2)11yescharacteristic
369C23C3×H(5,𝔽2)12yes—
370C23C3×2−1+411yescharacteristic
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—24no—
376C2×C4—24no—
377C2×C4—24no—
378C2×C4—24no—
379C2×C4—24no—
380C2×C4—24no—
381C2×C4—24no—
382C2×C4—24no—
383C2×C4—22no—
384C2×C4—24no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—24no—
388C2×C4—24no—
389C2×C4—24no—
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×C4C3×#12514yes—
427C2×C4C3×#12514yes—
428C2×C3#240211yescharacteristic
429C2×C3#251812yes—
430C2×C3#252512yes—
431C2×C3#252712yes—
432C2×C3#256911yescharacteristic
433C2×C3#256911yescharacteristic
434C2×C3#257111yescharacteristic
435C2×C3#259512yes—
436C2×C3#260611yescharacteristic
437C2×C3#266511yescharacteristic
438C2×C3#286411yescharacteristic
439C22C2×C3×#12511yescharacteristic
440C22C2×C3×#12511yescharacteristic
441C22C3×#52912yes—
442C22C3×#52912yes—
443C22C3×#52912yes—
444C22C3×#52912yes—
445C22C3×#53311yescharacteristic
446C22C3×#53311yescharacteristic
447C22C3×#53311yescharacteristic
448C22C3×#53812yes—
449C22C3×#54212yes—
450C22C3×#54311yescharacteristic
451C22C3×#54411yescharacteristic
452C22C3×#55112yes—
453C22C3×#55112yes—
454C22C3×#55212yes—
455C22C3×#55312yes—
456C22C3×#55312yes—
457C22C3×#55312yes—
458C22C3×#55511yescharacteristic
459C22C3×#55611yescharacteristic
460C22C3×#55611yescharacteristic
461C22C3×#55911yescharacteristic
462C4—24no—
463C4—24no—
464C4—42no—
465C4—44no—
466C4—44no—
467C4—44no—
468C4—82no—
469C4—82no—
470C4—82no—
471C3#1505211yescharacteristic, direct product factor, Sylow
472C2C3×#240211yescharacteristic
473C2C3×#251812yes—
474C2C3×#252512yes—
475C2C3×#252712yes—
476C2C3×#256911yescharacteristic
477C2C3×#256911yescharacteristic
478C2C3×#257111yescharacteristic
479C2C3×#259512yes—
480C2C3×#260611yescharacteristic
481C2C3×#266511yescharacteristic
482C2C3×#286411yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C3C24
commutator, Frattini, cosocleC24C24×C3
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
10. #15052C3direct (N × H)
471. C3#15052direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#14432
C3×#14422
C3×#14412
C3×#14362
C3×C4⋊#952
C3×#14342
C3×C4×#952
#150523