Finite Group Databasebeta

← C3×#14139 #10632746

Subgroups — C3×#14139 #10632746

Order 768.

2526 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic
2C23×C3×C4⋊C4C211yesmaximal, characteristic
3C2×C3×#391C212yesmaximal, complemented
4C2×C3×C4×C22⋊C4C211yesmaximal, characteristic
5C3×#1441C214yesmaximal, complemented
6C3×C4⋊#95C212yesmaximal, complemented
7C3×C22⋊#95C214yesmaximal
8#14139C311yesmaximal, characteristic, direct product factor, Sylow
9C23×C3×Q8C2211yescharacteristic
10C24×C3×C4C2212yes—
11C24×C3×C4C2211yescharacteristic
12C2×C3×C22⋊Q8—24no—
13C2×C3×C22⋊Q8—24no—
14C2×C3×C22⋊Q8C418yescomplemented
15C22×C3×C4⋊C4—24no—
16C22×C3×C4⋊C4—28no—
17C22×C3×C4⋊C4C2212yes—
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2212yes—
20C22×C3×C4⋊C4C2212yes—
21C22×C3×C22⋊C4C2212yes—
22C22×C3×C22⋊C4C2212yes—
23C22×C3×C42C2212yes—
24C3×#391—28no—
25C3×C4×C22⋊C4—24no—
26C2×C3×#95C2212yes—
27C2×C3×#95C2218yes—
28C2×C3×#95C2218yes—
29C22×C22⋊Q8C2×C311yescharacteristic
30C23×C4⋊C4C2×C311yescharacteristic
31C2×#391C2×C312yescomplemented
32C2×C4×C22⋊C4C2×C311yescharacteristic
33#1441C2×C314yescomplemented
34C4⋊#95C2×C312yescomplemented
35C22⋊#95C2×C314yes—
36C25×C3C2311yescharacteristic
37C22×C3×Q8—24no—
38C22×C3×Q8—22no—
39C22×C3×Q8—22no—
40C22×C3×Q8—24no—
41C22×C3×Q8C2×C414yescomplemented
42C23×C3×C4—24no—
43C23×C3×C4—24no—
44C23×C3×C4—24no—
45C23×C3×C4—28no—
46C23×C3×C4—28no—
47C23×C3×C4—44no—
48C23×C3×C4C2×C414yes—
49C23×C3×C4D414yes—
50C23×C3×C4D414yes—
51C23×C3×C4C2312yes—
52C23×C3×C4C2312yes—
53C23×C3×C4C2314yes—
54C23×C3×C4C2314yes—
55C23×C3×C4C2311yescharacteristic
56C23×C3×C4C2311yescharacteristic
57C3×C22⋊Q8—232no—
58C2×C3×C4⋊C4—232no—
59C2×C3×C4⋊C4—28no—
60C2×C3×C4⋊C4—24no—
61C2×C3×C4⋊C4—24no—
62C2×C3×C4⋊C4—24no—
63C2×C3×C4⋊C4—22no—
64C2×C3×C4⋊C4—22no—
65C2×C3×C4⋊C4—24no—
66C2×C3×C4⋊C4—24no—
67C2×C3×C4⋊C4C2×C414yescomplemented
68C2×C3×C4⋊C4C2×C418yescomplemented
69C2×C3×C4⋊C4D418yes—
70C2×C3×C22⋊C4—24no—
71C2×C3×C22⋊C4—24no—
72C2×C3×C22⋊C4—24no—
73C2×C3×C22⋊C4—24no—
74C2×C3×C22⋊C4C2×C418yes—
75C2×C3×C22⋊C4Q818yescomplemented
76C2×C3×C42—24no—
77C2×C3×C42—24no—
78C2×C3×C42—24no—
79C3×#95—24no—
80C3×#95—216no—
81C3×#95—48no—
82C23×Q8C22×C311yescharacteristic
83C24×C4C22×C312yes—
84C24×C4C22×C311yescharacteristic
85C2×C22⋊Q8—24no—
86C2×C22⋊Q8—24no—
87C2×C22⋊Q8C3×C418yescomplemented
88C22×C4⋊C4—24no—
89C22×C4⋊C4—28no—
90C22×C4⋊C4C22×C312yes—
91C22×C4⋊C4C22×C311yescharacteristic
92C22×C4⋊C4C22×C312yes—
93C22×C4⋊C4C22×C312yes—
94C22×C22⋊C4C22×C312yes—
95C22×C22⋊C4C22×C312yes—
96C22×C42C22×C312yes—
97#391—28no—
98C4×C22⋊C4—24no—
99C2×#95C22×C318yes—
100C2×#95C22×C312yes—
101C2×#95C22×C318yes—
102C24×C3—22no—
103C24×C3—22no—
104C24×C3—22no—
105C24×C3—22no—
106C24×C3C22×C412yes—
107C24×C3C2×D412yes—
108C24×C3C2×D412yes—
109C24×C3C2×Q814yes—
110C24×C3#4114yes—
111C24×C3C2411yescharacteristic
112C2×C3×Q8—28no—
113C2×C3×Q8—216no—
114C2×C3×Q8—44no—
115C2×C3×Q8—48no—
116C2×C3×Q8—44no—
117C22×C3×C4—22no—
118C22×C3×C4—22no—
119C22×C3×C4—216no—
120C22×C3×C4—28no—
121C22×C3×C4—216no—
122C22×C3×C4—28no—
123C22×C3×C4—216no—
124C22×C3×C4—24no—
125C22×C3×C4—24no—
126C22×C3×C4—24no—
127C22×C3×C4—22no—
128C22×C3×C4—22no—
129C22×C3×C4—22no—
130C22×C3×C4—22no—
131C22×C3×C4—24no—
132C22×C3×C4—24no—
133C22×C3×C4—24no—
134C22×C3×C4—24no—
135C22×C3×C4—28no—
136C22×C3×C4—24no—
137C22×C3×C4—24no—
138C22×C3×C4—24no—
139C22×C3×C4—28no—
140C22×C3×C4—24no—
141C22×C3×C4—24no—
142C22×C3×C4—432no—
143C22×C3×C4—48no—
144C22×C3×C4—48no—
145C22×C3×C4C22⋊C4116yes—
146C22×C3×C4C22×C414yes—
147C22×C3×C4C22×C414yes—
148C22×C3×C4C22×C412yes—
149C22×C3×C4C22×C412yes—
150C22×C3×C4C2×D418yes—
151C22×C3×C4C2×D412yes—
152C22×C3×C4C2×D412yes—
153C22×C3×C4C2×D412yes—
154C22×C3×C4C2×D412yes—
155C22×C3×C4C2×D414yes—
156C22×C3×C4C2×Q818yes—
157C22×C3×C4#4114yes—
158C3×C4⋊C4—216no—
159C3×C4⋊C4—28no—
160C3×C4⋊C4—216no—
161C3×C4⋊C4—216no—
162C3×C22⋊C4—216no—
163C3×C22⋊C4—216no—
164C3×C42—48no—
165C25C23×C311yescharacteristic
166C22×Q8—22no—
167C22×Q8—22no—
168C22×Q8—24no—
169C22×Q8—24no—
170C22×Q8C2×C3×C414yescomplemented
171C23×C4—24no—
172C23×C4—24no—
173C23×C4—24no—
174C23×C4—28no—
175C23×C4—28no—
176C23×C4—44no—
177C23×C4C2×C3×C414yes—
178C23×C4C3×D414yes—
179C23×C4C3×D414yes—
180C23×C4C23×C312yes—
181C23×C4C23×C312yes—
182C23×C4C23×C314yes—
183C23×C4C23×C314yes—
184C23×C4C23×C311yescharacteristic
185C23×C4C23×C311yescharacteristic
186C22⋊Q8—232no—
187C2×C4⋊C4—232no—
188C2×C4⋊C4—28no—
189C2×C4⋊C4—24no—
190C2×C4⋊C4—24no—
191C2×C4⋊C4—24no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—24no—
195C2×C4⋊C4—24no—
196C2×C4⋊C4C2×C3×C414yescomplemented
197C2×C4⋊C4C2×C3×C418yescomplemented
198C2×C4⋊C4C3×D418yes—
199C2×C22⋊C4—24no—
200C2×C22⋊C4—24no—
201C2×C22⋊C4—24no—
202C2×C22⋊C4—24no—
203C2×C22⋊C4C2×C3×C418yes—
204C2×C22⋊C4C3×Q818yescomplemented
205C2×C42—24no—
206C2×C42—24no—
207C2×C42—24no—
208#95—24no—
209#95—216no—
210#95—48no—
211C23×C3—24no—
212C23×C3—24no—
213C23×C3—22no—
214C23×C3—24no—
215C23×C3—22no—
216C23×C3—22no—
217C23×C3—22no—
218C23×C3—24no—
219C23×C3—28no—
220C23×C3—28no—
221C23×C3—28no—
222C23×C3—28no—
223C23×C3C2×C22⋊C414yes—
224C23×C3C4×Q818yes—
225C23×C3C22⋊Q818yes—
226C23×C3#12414yes—
227C23×C3C4⋊Q814yes—
228C23×C3C23×C411yescharacteristic
229C23×C3C22×D411yescharacteristic
230C23×C3C22×D411yescharacteristic
231C23×C3C22×D412yes—
232C23×C3C22×Q812yes—
233C23×C3C2×#4112yes—
234C23×C3C2×#4112yes—
235C23×C3H(5,𝔽2)12yes—
236C23×C32−1+412yes—
237C3×Q8—416no—
238C2×C3×C4—24no—
239C2×C3×C4—22no—
240C2×C3×C4—24no—
241C2×C3×C4—22no—
242C2×C3×C4—232no—
243C2×C3×C4—24no—
244C2×C3×C4—24no—
245C2×C3×C4—28no—
246C2×C3×C4—28no—
247C2×C3×C4—28no—
248C2×C3×C4—28no—
249C2×C3×C4—216no—
250C2×C3×C4—28no—
251C2×C3×C4—28no—
252C2×C3×C4—432no—
253C2×C3×C4—42no—
254C2×C3×C4—44no—
255C2×C3×C4—44no—
256C2×C3×C4—42no—
257C2×C3×C4—44no—
258C2×C3×C4—42no—
259C2×C3×C4—44no—
260C2×C3×C4—42no—
261C2×C3×C4—44no—
262C2×C3×C4—44no—
263C2×C3×C4—44no—
264C2×C3×C4—48no—
265C2×C3×C4—44no—
266C2×C3×C4C2×C22⋊C414yes—
267C2×C3×C4C2×C22⋊C414yes—
268C2×C3×C4C4×D418yes—
269C2×C3×C4#12014yes—
270C2×C3×C4#12118yes—
271C2×C3×C4#12314yes—
272C24—22no—
273C24—22no—
274C24—22no—
275C24—22no—
276C24C22×C3×C412yes—
277C24C2×C3×D412yes—
278C24C2×C3×D412yes—
279C24C2×C3×Q814yes—
280C24C3×#4114yes—
281C24C24×C311yescharacteristic
282C2×Q8—28no—
283C2×Q8—216no—
284C2×Q8—44no—
285C2×Q8—48no—
286C2×Q8—44no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—216no—
290C22×C4—28no—
291C22×C4—216no—
292C22×C4—28no—
293C22×C4—216no—
294C22×C4—24no—
295C22×C4—24no—
296C22×C4—24no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—24no—
302C22×C4—24no—
303C22×C4—24no—
304C22×C4—24no—
305C22×C4—28no—
306C22×C4—24no—
307C22×C4—24no—
308C22×C4—24no—
309C22×C4—28no—
310C22×C4—24no—
311C22×C4—24no—
312C22×C4—432no—
313C22×C4—48no—
314C22×C4—48no—
315C22×C4C3×C22⋊C4116yes—
316C22×C4C22×C3×C414yes—
317C22×C4C22×C3×C414yes—
318C22×C4C22×C3×C412yes—
319C22×C4C22×C3×C412yes—
320C22×C4C2×C3×D418yes—
321C22×C4C2×C3×D412yes—
322C22×C4C2×C3×D412yes—
323C22×C4C2×C3×D412yes—
324C22×C4C2×C3×D412yes—
325C22×C4C2×C3×D414yes—
326C22×C4C2×C3×Q818yes—
327C22×C4C3×#4114yes—
328C4⋊C4—216no—
329C4⋊C4—28no—
330C4⋊C4—216no—
331C4⋊C4—216no—
332C22⋊C4—216no—
333C22⋊C4—216no—
334C42—48no—
335C22×C3—24no—
336C22×C3—216no—
337C22×C3—216no—
338C22×C3—24no—
339C22×C3—24no—
340C22×C3—24no—
341C22×C3—24no—
342C22×C3—24no—
343C22×C3#39118yescomplemented
344C22×C3C22×C22⋊C411yescharacteristic
345C22×C3C2×C4×D412yes—
346C22×C3C2×C4×Q812yes—
347C22×C3#52012yes—
348C22×C3C2×#12011yescharacteristic
349C22×C3C2×#12112yes—
350C22×C3C2×C22⋊Q812yes—
351C22×C3C2×#12311yescharacteristic
352C22×C3C2×#12411yescharacteristic
353C22×C3C2×C4⋊Q811yescharacteristic
354C22×C3#53511yescharacteristic
355C22×C3#53611yescharacteristic
356C22×C3#53712yes—
357C22×C3#54614yes—
358C22×C3D4×Q814yes—
359C22×C3#55214yes—
360C22×C3#55414yes—
361C3×C4—24no—
362C3×C4—44no—
363C3×C4—48no—
364C3×C4—48no—
365C3×C4—44no—
366C3×C4#38618yes—
367C23—24no—
368C23—24no—
369C23—22no—
370C23—24no—
371C23—22no—
372C23—22no—
373C23—22no—
374C23—24no—
375C23—28no—
376C23—28no—
377C23—28no—
378C23—28no—
379C23C2×C3×C22⋊C414yes—
380C23C3×C4×Q818yes—
381C23C3×C22⋊Q818yes—
382C23C3×#12414yes—
383C23C3×C4⋊Q814yes—
384C23C23×C3×C411yescharacteristic
385C23C22×C3×D411yescharacteristic
386C23C22×C3×D411yescharacteristic
387C23C22×C3×D412yes—
388C23C22×C3×Q812yes—
389C23C2×C3×#4112yes—
390C23C2×C3×#4112yes—
391C23C3×H(5,𝔽2)12yes—
392C23C3×2−1+412yes—
393Q8—416no—
394C2×C4—24no—
395C2×C4—22no—
396C2×C4—24no—
397C2×C4—22no—
398C2×C4—232no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—28no—
402C2×C4—28no—
403C2×C4—28no—
404C2×C4—28no—
405C2×C4—216no—
406C2×C4—28no—
407C2×C4—28no—
408C2×C4—432no—
409C2×C4—42no—
410C2×C4—44no—
411C2×C4—44no—
412C2×C4—42no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—44no—
418C2×C4—44no—
419C2×C4—48no—
420C2×C4—44no—
421C2×C4—44no—
422C2×C4C2×C3×C22⋊C414yes—
423C2×C4C2×C3×C22⋊C414yes—
424C2×C4C3×C4×D418yes—
425C2×C4C3×#12014yes—
426C2×C4C3×#12118yes—
427C2×C4C3×#12314yes—
428C2×C3—28no—
429C2×C3C2×#38611yescharacteristic
430C2×C3C2×#39111yescharacteristic
431C2×C3#231111yescharacteristic
432C2×C3#236014yes—
433C2×C3#241714yes—
434C2×C3#243411yescharacteristic
435C2×C3#243511yescharacteristic
436C2×C3#250211yescharacteristic
437C2×C3#250311yescharacteristic
438C22—216no—
439C22—216no—
440C22—24no—
441C22—24no—
442C22—24no—
443C22—24no—
444C22—24no—
445C22—24no—
446C22C3×#39118yescomplemented
447C22C22×C3×C22⋊C411yescharacteristic
448C22C2×C3×C4×D412yes—
449C22C2×C3×C4×Q812yes—
450C22C3×#52012yes—
451C22C2×C3×#12011yescharacteristic
452C22C2×C3×#12112yes—
453C22C2×C3×C22⋊Q812yes—
454C22C2×C3×#12311yescharacteristic
455C22C2×C3×#12411yescharacteristic
456C22C2×C3×C4⋊Q811yescharacteristic
457C22C3×#53511yescharacteristic
458C22C3×#53611yescharacteristic
459C22C3×#53712yes—
460C22C3×#54614yes—
461C22C3×D4×Q814yes—
462C22C3×#55214yes—
463C22C3×#55414yes—
464C4—24no—
465C4—48no—
466C4—48no—
467C4—44no—
468C4—44no—
469C4C3×#38618yes—
470C3#1413911yescharacteristic, direct product factor, Sylow
471C2—28no—
472C2C2×C3×#38611yescharacteristic
473C2C2×C3×#39111yescharacteristic
474C2C3×#231111yescharacteristic
475C2C3×#236014yes—
476C2C3×#241714yes—
477C2C3×#243411yescharacteristic
478C2C3×#243511yescharacteristic
479C2C3×#250211yescharacteristic
480C2C3×#250311yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutatorC23C23×C3×C4
Frattini, cosocleC24C24×C3
prime radicalC25×C3C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C3×#391C2semidirect
5. C3×#1441C2semidirect
6. C3×C4⋊#95C2semidirect
8. #14139C3direct (N × H)
14. C2×C3×C22⋊Q8C4semidirect
31. C2×#391C2×C3semidirect
33. #1441C2×C3semidirect
34. C4⋊#95C2×C3semidirect
41. C22×C3×Q8C2×C4semidirect
67. C2×C3×C4⋊C4C2×C4semidirect
68. C2×C3×C4⋊C4C2×C4semidirect
75. C2×C3×C22⋊C4Q8semidirect
87. C2×C22⋊Q8C3×C4semidirect
170. C22×Q8C2×C3×C4semidirect
196. C2×C4⋊C4C2×C3×C4semidirect
197. C2×C4⋊C4C2×C3×C4semidirect
204. C2×C22⋊C4C3×Q8semidirect
343. C22×C3#391semidirect
446. C22C3×#391semidirect
470. C3#14139direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊Q82
C23×C3×C4⋊C42
C2×C3×#3912
C2×C3×C4×C22⋊C42
C3×#14412
C3×C4⋊#952
C3×C22⋊#952
#141393