Finite Group Databasebeta

← C3×#14474 #10633081

Subgroups — C3×#14474 #10633081

Order 768.

1398 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#125C211yesmaximal, characteristic
2C2×C3×#387C212yesmaximal
3C3×#1445C212yesmaximal
4C3×#1445C212yesmaximal
5C3×#1441C212yesmaximal
6C3×#1436C212yesmaximal
7C3×C4⋊#95C212yesmaximal
8C3×#1434C211yesmaximal, characteristic
9C3×#1434C211yesmaximal, characteristic
10#14474C311yesmaximal, characteristic, direct product factor, Sylow
11C2×C3×#125—28no—
12C2×C3×#125C418yescomplemented
13C22×C3×C4⋊C4C2212yes—
14C22×C3×C4⋊C4C2212yes—
15C22×C3×C4⋊C4C2212yes—
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C42C2212yes—
19C22×C3×C42C2211yescharacteristic
20C3×#387—28no—
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×#95C2211yescharacteristic
32C2×C3×#95C2211yescharacteristic
33C2×C3×#95C2212yes—
34C2×C3×#95C2212yes—
35C22×#125C2×C311yescharacteristic
36C2×#387C2×C312yes—
37#1445C2×C312yes—
38#1445C2×C312yes—
39#1441C2×C312yes—
40#1436C2×C312yes—
41C4⋊#95C2×C312yes—
42#1434C2×C311yescharacteristic
43#1434C2×C311yescharacteristic
44C23×C3×C4C2312yes—
45C23×C3×C4C2312yes—
46C23×C3×C4C2311yescharacteristic
47C23×C3×C4C2311yescharacteristic
48C23×C3×C4C2312yes—
49C23×C3×C4C2312yes—
50C23×C3×C4C2312yes—
51C23×C3×C4C2311yescharacteristic
52C23×C3×C4C2312yes—
53C3×#125—232no—
54C2×C3×C4⋊C4—24no—
55C2×C3×C4⋊C4—24no—
56C2×C3×C4⋊C4—24no—
57C2×C3×C4⋊C4—24no—
58C2×C3×C4⋊C4—24no—
59C2×C3×C4⋊C4—24no—
60C2×C3×C4⋊C4—24no—
61C2×C3×C4⋊C4—42no—
62C2×C3×C4⋊C4C2×C418yes—
63C2×C3×C4⋊C4C2×C418yes—
64C2×C3×C4⋊C4C2×C414yes—
65C2×C3×C4⋊C4C2×C414yes—
66C2×C3×C4⋊C4D418yes—
67C2×C3×C42—24no—
68C2×C3×C42—24no—
69C2×C3×C42—24no—
70C2×C3×C42—42no—
71C2×C3×C42C2×C414yes—
72C3×#95—24no—
73C3×#95—24no—
74C3×#95—24no—
75C3×#95—24no—
76C3×#95—24no—
77C3×#95—24no—
78C3×#95—24no—
79C3×#95—24no—
80C3×#95—41no—
81C3×#95—42no—
82C3×#95—41no—
83C3×#95—41no—
84C3×#95—42no—
85C3×#95—41no—
86C2×#125—28no—
87C2×#125C3×C418yescomplemented
88C22×C4⋊C4C22×C312yes—
89C22×C4⋊C4C22×C312yes—
90C22×C4⋊C4C22×C312yes—
91C22×C4⋊C4C22×C311yescharacteristic
92C22×C4⋊C4C22×C311yescharacteristic
93C22×C42C22×C312yes—
94C22×C42C22×C311yescharacteristic
95#387—28no—
96C2×#95C22×C312yes—
97C2×#95C22×C312yes—
98C2×#95C22×C312yes—
99C2×#95C22×C312yes—
100C2×#95C22×C312yes—
101C2×#95C22×C312yes—
102C2×#95C22×C312yes—
103C2×#95C22×C312yes—
104C2×#95C22×C311yescharacteristic
105C2×#95C22×C311yescharacteristic
106C2×#95C22×C311yescharacteristic
107C2×#95C22×C311yescharacteristic
108C2×#95C22×C312yes—
109C2×#95C22×C312yes—
110C24×C3C2411yescharacteristic
111C22×C3×C4—22no—
112C22×C3×C4—22no—
113C22×C3×C4—22no—
114C22×C3×C4—22no—
115C22×C3×C4—21no—
116C22×C3×C4—21no—
117C22×C3×C4—22no—
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—22no—
125C22×C3×C4—22no—
126C22×C3×C4—22no—
127C22×C3×C4—22no—
128C22×C3×C4—22no—
129C22×C3×C4—22no—
130C22×C3×C4—21no—
131C22×C3×C4—21no—
132C22×C3×C4—22no—
133C22×C3×C4—22no—
134C22×C3×C4—22no—
135C22×C3×C4—22no—
136C22×C3×C4—21no—
137C22×C3×C4—21no—
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×C4—22no—
154C22×C3×C4—22no—
155C22×C3×C4—22no—
156C22×C3×C4—22no—
157C22×C3×C4—22no—
158C22×C3×C4C22×C412yes—
159C22×C3×C4C22×C412yes—
160C22×C3×C4C22×C414yes—
161C22×C3×C4C22×C412yes—
162C22×C3×C4C22×C414yes—
163C22×C3×C4C2×D414yes—
164C22×C3×C4C2×D414yes—
165C22×C3×C4C2×D414yes—
166C22×C3×C4#4114yes—
167C22×C3×C4#4114yes—
168C3×C4⋊C4—216no—
169C3×C4⋊C4—216no—
170C3×C4⋊C4—28no—
171C3×C4⋊C4—48no—
172C3×C4⋊C4C22⋊C4116yes—
173C3×C42—28no—
174C3×C42—48no—
175C23×C4C23×C312yes—
176C23×C4C23×C312yes—
177C23×C4C23×C312yes—
178C23×C4C23×C311yescharacteristic
179C23×C4C23×C311yescharacteristic
180C23×C4C23×C312yes—
181C23×C4C23×C312yes—
182C23×C4C23×C312yes—
183C23×C4C23×C311yescharacteristic
184#125—232no—
185C2×C4⋊C4—24no—
186C2×C4⋊C4—24no—
187C2×C4⋊C4—24no—
188C2×C4⋊C4—24no—
189C2×C4⋊C4—24no—
190C2×C4⋊C4—24no—
191C2×C4⋊C4—24no—
192C2×C4⋊C4—42no—
193C2×C4⋊C4C2×C3×C418yes—
194C2×C4⋊C4C2×C3×C418yes—
195C2×C4⋊C4C2×C3×C414yes—
196C2×C4⋊C4C2×C3×C414yes—
197C2×C4⋊C4C3×D418yes—
198C2×C42—24no—
199C2×C42—24no—
200C2×C42—24no—
201C2×C42—42no—
202C2×C42C2×C3×C414yes—
203#95—24no—
204#95—24no—
205#95—24no—
206#95—24no—
207#95—24no—
208#95—24no—
209#95—24no—
210#95—24no—
211#95—41no—
212#95—42no—
213#95—41no—
214#95—41no—
215#95—42no—
216#95—41no—
217C23×C3C23×C411yescharacteristic
218C23×C3C22×D412yes—
219C23×C3C2×#4112yes—
220C23×C3C2×#4112yes—
221C23×C3H(5,𝔽2)11yescharacteristic
222C23×C3H(5,𝔽2)11yescharacteristic
223C23×C32−1+412yes—
224C23×C32−1+411yescharacteristic
225C23×C32−1+411yescharacteristic
226C23×C32−1+411yescharacteristic
227C23×C32−1+411yescharacteristic
228C2×C3×C4—24no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×C3×C4—24no—
232C2×C3×C4—24no—
233C2×C3×C4—24no—
234C2×C3×C4—24no—
235C2×C3×C4—24no—
236C2×C3×C4—24no—
237C2×C3×C4—24no—
238C2×C3×C4—22no—
239C2×C3×C4—22no—
240C2×C3×C4—24no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4—24no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—24no—
247C2×C3×C4—24no—
248C2×C3×C4—24no—
249C2×C3×C4—24no—
250C2×C3×C4—24no—
251C2×C3×C4—24no—
252C2×C3×C4—24no—
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—42no—
269C2×C3×C4—42no—
270C2×C3×C4—42no—
271C2×C3×C4—42no—
272C2×C3×C4—42no—
273C2×C3×C4—42no—
274C2×C3×C4—42no—
275C2×C3×C4—42no—
276C2×C3×C4—42no—
277C2×C3×C4—42no—
278C2×C3×C4—42no—
279C2×C3×C4—42no—
280C2×C3×C4—42no—
281C2×C3×C4—42no—
282C2×C3×C4—42no—
283C2×C3×C4C2×C22⋊C414yes—
284C2×C3×C4C2×C22⋊C418yes—
285C24C24×C311yescharacteristic
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—22no—
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—21no—
306C22×C4—22no—
307C22×C4—21no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—21no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4C22×C3×C412yes—
334C22×C4C22×C3×C412yes—
335C22×C4C22×C3×C414yes—
336C22×C4C22×C3×C412yes—
337C22×C4C22×C3×C414yes—
338C22×C4C2×C3×D414yes—
339C22×C4C2×C3×D414yes—
340C22×C4C2×C3×D414yes—
341C22×C4C3×#4114yes—
342C22×C4C3×#4114yes—
343C4⋊C4—216no—
344C4⋊C4—216no—
345C4⋊C4—28no—
346C4⋊C4—48no—
347C4⋊C4C3×C22⋊C4116yes—
348C42—28no—
349C42—48no—
350C22×C3C22×C22⋊C411yescharacteristic
351C22×C3C4×#4111yescharacteristic
352C22×C3C4×#4111yescharacteristic
353C22×C3#51911yescharacteristic
354C22×C3#51911yescharacteristic
355C22×C3#52011yescharacteristic
356C22×C3#52011yescharacteristic
357C22×C3#53612yes—
358C22×C3#53612yes—
359C22×C3#53912yes—
360C22×C3#53912yes—
361C22×C3#54112yes—
362C22×C3#54112yes—
363C22×C3#54612yes—
364C22×C3#54712yes—
365C22×C3#54812yes—
366C22×C3#55012yes—
367C22×C3#55212yes—
368C22×C3#55212yes—
369C22×C3#56211yescharacteristic
370C22×C3#56311yescharacteristic
371C22×C3#56311yescharacteristic
372C22×C3#56411yescharacteristic
373C3×C4—24no—
374C3×C4—28no—
375C3×C4—42no—
376C3×C4—42no—
377C3×C4—44no—
378C3×C4—44no—
379C3×C4—44no—
380C3×C4—82no—
381C3×C4—82no—
382C23C23×C3×C411yescharacteristic
383C23C22×C3×D412yes—
384C23C2×C3×#4112yes—
385C23C2×C3×#4112yes—
386C23C3×H(5,𝔽2)11yescharacteristic
387C23C3×H(5,𝔽2)11yescharacteristic
388C23C3×2−1+411yescharacteristic
389C23C3×2−1+411yescharacteristic
390C23C3×2−1+411yescharacteristic
391C23C3×2−1+411yescharacteristic
392C23C3×2−1+412yes—
393C2×C4—24no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—24no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—24no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—24no—
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×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4C2×C3×C22⋊C414yes—
449C2×C4C2×C3×C22⋊C418yes—
450C2×C3#231011yescharacteristic
451C2×C3#233611yescharacteristic
452C2×C3#233611yescharacteristic
453C2×C3#233911yescharacteristic
454C2×C3#234111yescharacteristic
455C2×C3#237111yescharacteristic
456C2×C3#238211yescharacteristic
457C2×C3#269012yes—
458C2×C3#269412yes—
459C2×C3#271912yes—
460C2×C3#272112yes—
461C22C22×C3×C22⋊C411yescharacteristic
462C22C3×C4×#4111yescharacteristic
463C22C3×C4×#4111yescharacteristic
464C22C3×#51911yescharacteristic
465C22C3×#51911yescharacteristic
466C22C3×#52011yescharacteristic
467C22C3×#52011yescharacteristic
468C22C3×#53612yes—
469C22C3×#53612yes—
470C22C3×#53912yes—
471C22C3×#53912yes—
472C22C3×#54112yes—
473C22C3×#54112yes—
474C22C3×#54612yes—
475C22C3×#54712yes—
476C22C3×#54812yes—
477C22C3×#55012yes—
478C22C3×#55212yes—
479C22C3×#55212yes—
480C22C3×#56211yescharacteristic
481C22C3×#56311yescharacteristic
482C22C3×#56311yescharacteristic
483C22C3×#56411yescharacteristic
484C4—24no—
485C4—28no—
486C4—44no—
487C4—44no—
488C4—42no—
489C4—42no—
490C4—44no—
491C4—82no—
492C4—82no—
493C3#1447411yescharacteristic, direct product factor, Sylow
494C2C3×#231011yescharacteristic
495C2C3×#233611yescharacteristic
496C2C3×#233611yescharacteristic
497C2C3×#233911yescharacteristic
498C2C3×#234111yescharacteristic
499C2C3×#237111yescharacteristic
500C2C3×#238211yescharacteristic
501C2C3×#269012yes—
502C2C3×#269412yes—
503C2C3×#271912yes—
504C2C3×#272112yes—
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. #14474C3direct (N × H)
12. C2×C3×#125C4semidirect
87. C2×#125C3×C4semidirect
493. C3#14474direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1252
C2×C3×#3872
C3×#14452
C3×#14412
C3×#14362
C3×C4⋊#952
C3×#14342
#144743