Finite Group Databasebeta

← C3×#29262 #10647869

Subgroups — C3×#29262 #10647869

Order 768.

800 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
2C3×C4×#124C211yesmaximal, characteristic
3C3×#2096C211yesmaximal, characteristic, complemented
4C3×#2093C211yesmaximal, characteristic
5C3×#2024C211yesmaximal, characteristic, complemented
6C3×#2023C211yesmaximal, characteristic
7C3×#1983C212yesmaximal
8C3×#1949C212yesmaximal, complemented
9C3×#1864C212yesmaximal
10C3×#1863C212yesmaximal, complemented
11C3×#1831C211yesmaximal, characteristic, complemented
12#29262C311yesmaximal, characteristic, direct product factor, Sylow
13C2×C3×C4⋊Q8C2211yescharacteristic
14C2×C3×#124C2211yescharacteristic
15C2×C3×C4×Q8—21no—
16C2×C3×C4×Q8C2211yescharacteristic
17C2×C3×C4×D4C2211yescharacteristic
18C2×C3×#107C2212yes—
19C2×C3×#106C2212yes—
20C2×C3×C4⋊C8C2212yes—
21C2×C3×#103C2212yes—
22C2×C3×#103C2212yes—
23C2×C3×#102C2212yes—
24C2×C3×#102C2212yes—
25C3×#391—21no—
26C3×#391C2211yescharacteristic
27C3×#390C2211yescharacteristic
28C3×#389—21no—
29C3×#389C2212yes—
30C3×#388—21no—
31C3×#388—21no—
32C3×#384C2211yescharacteristic
33C3×#382C2211yescharacteristic
34C3×C4×C4⋊C4—21no—
35C3×C4×C4⋊C4C2212yes—
36C3×C4×C22⋊C4—21no—
37C3×C4×C22⋊C4—21no—
38C3×C43C2211yescharacteristic
39C3×#340C2212yes—
40C3×#340C2212yes—
41C3×#336C2211yescharacteristic
42C3×#336C2211yescharacteristic
43C3×#336C2212yes—
44C4×C4⋊Q8C2×C311yescharacteristic, complemented
45C4×#124C2×C311yescharacteristic
46#2096C2×C311yescharacteristic, complemented
47#2093C2×C311yescharacteristic
48#2024C2×C311yescharacteristic, complemented
49#2023C2×C311yescharacteristic
50#1983C2×C312yes—
51#1949C2×C312yescomplemented
52#1864C2×C312yes—
53#1863C2×C312yescomplemented
54#1831C2×C311yescharacteristic, complemented
55C22×C3×Q8—21no—
56C22×C3×Q8C2311yescharacteristic
57C22×C3×D4C2311yescharacteristic
58C23×C3×C4—21no—
59C22×C3×C8C2312yes—
60C22×C3×C8C2312yes—
61C3×C4⋊Q8—24no—
62C3×#124—22no—
63C3×#124Q814yescomplemented
64C3×C4×Q8—42no—
65C3×C4×Q8—44no—
66C3×C4×D4—42no—
67C2×C3×C4⋊C4—21no—
68C2×C3×C4⋊C4—21no—
69C2×C3×C4⋊C4—21no—
70C2×C3×C4⋊C4—21no—
71C2×C3×C4⋊C4—22no—
72C2×C3×C4⋊C4C2312yes—
73C2×C3×C4⋊C4C2311yescharacteristic
74C2×C3×C4⋊C4C2311yescharacteristic
75C2×C3×C4⋊C4C2312yes—
76C2×C3×C22⋊C4—21no—
77C2×C3×C22⋊C4—21no—
78C2×C3×C22⋊C4—21no—
79C2×C3×C22⋊C4—21no—
80C2×C3×C22⋊C4—21no—
81C2×C3×C42—21no—
82C2×C3×C42—22no—
83C2×C3×C42D411yescharacteristic
84C2×C3×C42D411yescharacteristic
85C2×C3×C42D411yescharacteristic
86C2×C3×C42D411yescharacteristic
87C2×C3×C42C2311yescharacteristic
88C2×C3×C42C2311yescharacteristic
89C2×C3×C42C2311yescharacteristic
90C3×#107—42no—
91C3×#106—42no—
92C3×C4⋊C8—24no—
93C3×#103—24no—
94C3×#103—42no—
95C3×#102—24no—
96C3×#102—42no—
97C3×#95—21no—
98C3×#95—21no—
99C3×#95—21no—
100C3×#95—21no—
101C3×#95—22no—
102C3×#95—22no—
103C2×C4⋊Q8C22×C311yescharacteristic
104C2×#124C22×C311yescharacteristic
105C2×C4×Q8—21no—
106C2×C4×Q8C22×C311yescharacteristic
107C2×C4×D4C22×C311yescharacteristic
108C2×#107C22×C312yes—
109C2×#106C22×C312yes—
110C2×C4⋊C8C22×C312yes—
111C2×#103C22×C312yes—
112C2×#103C22×C312yes—
113C2×#102C22×C312yes—
114C2×#102C22×C312yes—
115#391—21no—
116#391C22×C311yescharacteristic
117#390C22×C311yescharacteristic
118#389—21no—
119#389C22×C312yes—
120#388—21no—
121#388—21no—
122#384C22×C311yescharacteristic
123#382C22×C311yescharacteristic
124C4×C4⋊C4—21no—
125C4×C4⋊C4C22×C312yes—
126C4×C22⋊C4—21no—
127C4×C22⋊C4—21no—
128C43C22×C311yescharacteristic
129#340C22×C312yes—
130#340C22×C312yes—
131#336C22×C311yescharacteristic
132#336C22×C311yescharacteristic
133#336C22×C312yes—
134C24×C3—21no—
135C2×C3×Q8—24no—
136C2×C3×Q8—21no—
137C2×C3×Q8—22no—
138C2×C3×Q8—22no—
139C2×C3×Q8—42no—
140C2×C3×Q8—42no—
141C2×C3×Q8C2×Q812yes—
142C2×C3×D4—22no—
143C2×C3×D4—21no—
144C2×C3×D4—22no—
145C2×C3×D4C2×Q812yes—
146C22×C3×C4—21no—
147C22×C3×C4—22no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—22no—
151C22×C3×C4—42no—
152C22×C3×C4—42no—
153C22×C3×C4—42no—
154C22×C3×C4C2×D411yescharacteristic
155C22×C3×C4C2×D411yescharacteristic
156C22×C3×C4C2×D411yescharacteristic
157C22×C3×C4C2×D411yescharacteristic
158C22×C3×C4C2×D411yescharacteristic
159C22×C3×C4C2×D411yescharacteristic
160C22×C3×C4C2411yescharacteristic
161C2×C3×C8—22no—
162C2×C3×C8—22no—
163C2×C3×C8—22no—
164C2×C3×C8—22no—
165C2×C3×C8—22no—
166C2×C3×C8—22no—
167C3×C4⋊C4—24no—
168C3×C4⋊C4—22no—
169C3×C4⋊C4—22no—
170C3×C4⋊C4—22no—
171C3×C4⋊C4—22no—
172C3×C4⋊C4—22no—
173C3×C4⋊C4—42no—
174C3×C4⋊C4—44no—
175C3×C4⋊C4—42no—
176C3×C4⋊C4—42no—
177C3×C4⋊C4#4114yes—
178C3×C22⋊C4—24no—
179C3×C22⋊C4—24no—
180C3×C22⋊C4—42no—
181C3×C22⋊C4—42no—
182C3×C22⋊C4—42no—
183C3×C42—22no—
184C3×C42—22no—
185C3×C42—22no—
186C3×C42—22no—
187C3×C42—22no—
188C3×C42—41no—
189C3×C42—42no—
190C3×C42—44no—
191C3×C42C2×Q812yes—
192C3×C42#4112yes—
193C22×Q8—21no—
194C22×Q8C23×C311yescharacteristic
195C22×D4C23×C311yescharacteristic
196C23×C4—21no—
197C22×C8C23×C312yes—
198C22×C8C23×C312yes—
199C4⋊Q8—24no—
200#124—22no—
201#124C3×Q814yescomplemented
202C4×Q8—42no—
203C4×Q8—44no—
204C4×D4—42no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4C23×C311yescharacteristic
211C2×C4⋊C4C23×C311yescharacteristic
212C2×C4⋊C4C23×C312yes—
213C2×C4⋊C4C23×C312yes—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C42—22no—
220C2×C42—21no—
221C2×C42C3×D411yescharacteristic
222C2×C42C3×D411yescharacteristic
223C2×C42C3×D411yescharacteristic
224C2×C42C3×D411yescharacteristic
225C2×C42C23×C311yescharacteristic
226C2×C42C23×C311yescharacteristic
227C2×C42C23×C311yescharacteristic
228#107—42no—
229#106—42no—
230C4⋊C8—24no—
231#103—24no—
232#103—42no—
233#102—24no—
234#102—42no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95—22no—
240#95—22no—
241C23×C3—22no—
242C23×C3—41no—
243C23×C3—41no—
244C23×C3—41no—
245C23×C3—41no—
246C23×C3—41no—
247C23×C3—41no—
248C23×C3C22×D411yescharacteristic
249C3×Q8—24no—
250C3×Q8—48no—
251C3×Q8—42no—
252C3×D4—24no—
253C3×D4—42no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—22no—
265C2×C3×C4—24no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—41no—
270C2×C3×C4—41no—
271C2×C3×C4—42no—
272C2×C3×C4—42no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—42no—
276C2×C3×C4—41no—
277C2×C3×C4—42no—
278C2×C3×C4—42no—
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—84no—
283C2×C3×C4C22⋊Q812yes—
284C2×C3×C4C22⋊Q812yes—
285C2×C3×C4#13512yes—
286C2×C3×C4AGL(1,ℤ/8)12yes—
287C2×C3×C4#13712yes—
288C2×C3×C4C22×Q811yescharacteristic
289C2×C3×C4C2×#4112yes—
290C2×C3×C4C2×#4111yescharacteristic
291C2×C3×C4H(5,𝔽2)12yes—
292C3×C8—42no—
293C3×C8—42no—
294C24—21no—
295C2×Q8—24no—
296C2×Q8—21no—
297C2×Q8—22no—
298C2×Q8—22no—
299C2×Q8—42no—
300C2×Q8—42no—
301C2×Q8C2×C3×Q812yes—
302C2×D4—22no—
303C2×D4—21no—
304C2×D4—22no—
305C2×D4C2×C3×Q812yes—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4C2×C3×D411yescharacteristic
315C22×C4C2×C3×D411yescharacteristic
316C22×C4C2×C3×D411yescharacteristic
317C22×C4C2×C3×D411yescharacteristic
318C22×C4C2×C3×D411yescharacteristic
319C22×C4C2×C3×D411yescharacteristic
320C22×C4C24×C311yescharacteristic
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—22no—
327C4⋊C4—24no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—44no—
334C4⋊C4—42no—
335C4⋊C4—42no—
336C4⋊C4—42no—
337C4⋊C4C3×#4114yes—
338C22⋊C4—24no—
339C22⋊C4—24no—
340C22⋊C4—42no—
341C22⋊C4—42no—
342C22⋊C4—42no—
343C42—22no—
344C42—22no—
345C42—22no—
346C42—22no—
347C42—22no—
348C42—41no—
349C42—44no—
350C42—42no—
351C42C2×C3×Q812yes—
352C42C3×#4112yes—
353C22×C3—42no—
354C22×C3—42no—
355C22×C3—42no—
356C22×C3—81no—
357C22×C3—81no—
358C22×C3—81no—
359C22×C3—81no—
360C22×C3C2×C22⋊Q811yescharacteristic
361C22×C3#52511yescharacteristic
362C22×C3#53511yescharacteristic
363C22×C3C2×#13511yescharacteristic
364C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
365C22×C3C2×#13711yescharacteristic
366C22×C3#57511yescharacteristic
367C3×C4—22no—
368C3×C4—22no—
369C3×C4—22no—
370C3×C4—22no—
371C3×C4—22no—
372C3×C4—42no—
373C3×C4—44no—
374C3×C4—41no—
375C3×C4—81no—
376C3×C4—82no—
377C3×C4—81no—
378C3×C4#55412yes—
379C3×C4#55912yes—
380C23—22no—
381C23—41no—
382C23—41no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23C22×C3×D411yescharacteristic
388Q8—24no—
389Q8—48no—
390Q8—42no—
391D4—24no—
392D4—42no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—22no—
406C2×C4—24no—
407C2×C4—21no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—42no—
421C2×C4—84no—
422C2×C4C3×C22⋊Q812yes—
423C2×C4C3×C22⋊Q812yes—
424C2×C4C3×#13512yes—
425C2×C4C3×AGL(1,ℤ/8)12yes—
426C2×C4C3×#13712yes—
427C2×C4C22×C3×Q811yescharacteristic
428C2×C4C2×C3×#4111yescharacteristic
429C2×C4C2×C3×#4112yes—
430C2×C4C3×H(5,𝔽2)12yes—
431C8—42no—
432C8—42no—
433C2×C3—82no—
434C2×C3#258011yescharacteristic
435C2×C3#307611yescharacteristic
436C2×C3#307911yescharacteristic
437C2×C3#310811yescharacteristic
438C2×C3#311411yescharacteristic
439C2×C3#320711yescharacteristic
440C2×C3#321511yescharacteristic
441C22—42no—
442C22—42no—
443C22—42no—
444C22—81no—
445C22—81no—
446C22—81no—
447C22—81no—
448C22C2×C3×C22⋊Q811yescharacteristic
449C22C3×#52511yescharacteristic
450C22C3×#53511yescharacteristic
451C22C2×C3×#13511yescharacteristic
452C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
453C22C2×C3×#13711yescharacteristic
454C22C3×#57511yescharacteristic
455C4—22no—
456C4—22no—
457C4—22no—
458C4—22no—
459C4—22no—
460C4—41no—
461C4—42no—
462C4—44no—
463C4—81no—
464C4—82no—
465C4—81no—
466C4C3×#55412yes—
467C4C3×#55912yes—
468C3#2926211yescharacteristic, direct product factor, Sylow
469C2—82no—
470C2C3×#258011yescharacteristic
471C2C3×#307611yescharacteristic
472C2C3×#307911yescharacteristic
473C2C3×#310811yescharacteristic
474C2C3×#311411yescharacteristic
475C2C3×#320711yescharacteristic
476C2C3×#321511yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×C4×C4⋊Q8C2semidirect
3. C3×#2096C2semidirect
5. C3×#2024C2semidirect
8. C3×#1949C2semidirect
10. C3×#1863C2semidirect
11. C3×#1831C2semidirect
12. #29262C3direct (N × H)
44. C4×C4⋊Q8C2×C3semidirect
46. #2096C2×C3semidirect
48. #2024C2×C3semidirect
51. #1949C2×C3semidirect
53. #1863C2×C3semidirect
54. #1831C2×C3semidirect
63. C3×#124Q8semidirect
201. #124C3×Q8semidirect
468. C3#29262direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C4×C4⋊Q82
C3×C4×#1242
C3×#20962
C3×#20932
C3×#20242
C3×#20232
C3×#19832
C3×#19492
C3×#18642
C3×#18632
C3×#18312
#292623