Finite Group Databasebeta

← C3×#29803 #10648410

Subgroups — C3×#29803 #10648410

Order 768.

954 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#464C211yesmaximal, characteristic, complemented
2C2×C3×#460C211yesmaximal, characteristic, complemented
3C3×#2657C211yesmaximal, characteristic
4C3×#2320C211yesmaximal, characteristic, complemented
5C3×#2042C212yesmaximal, complemented
6C3×#2041C212yesmaximal, complemented
7C3×#2015C212yesmaximal, complemented
8C3×#2014C212yesmaximal, complemented
9C3×#1983C211yesmaximal, characteristic, complemented
10C3×#1982C211yesmaximal, characteristic, complemented
11C3×#1832C211yesmaximal, characteristic, complemented
12#29803C311yesmaximal, characteristic, direct product factor, Sylow
13C22×C3×Q16C2211yescharacteristic
14C22×C3×SD16C2211yescharacteristic
15C22×C3×SD16C2212yes—
16C2×C3×#127C2211yescharacteristic
17C2×C3×#127C2212yes—
18C2×C3×#124C2211yescharacteristic
19C2×C3×#124C2212yes—
20C2×C3×C4×Q8C2211yescharacteristic
21C3×#464—24no—
22C3×#460—24no—
23C2×C3×C4⋊C8C2211yescharacteristic
24C2×C3×C4⋊C8C2211yescharacteristic
25C2×C3×#103C2211yescharacteristic
26C2×C3×#103C2212yes—
27C2×C3×#102C2211yescharacteristic
28C2×C3×#102C2212yes—
29C2×C3×#102C2212yes—
30C2×C3×#102C2212yes—
31C2×C3×#102C2212yes—
32C3×#392—21no—
33C3×#392—21no—
34C3×#392—22no—
35C3×#391C2212yes—
36C3×#389C2212yes—
37C3×#387—22no—
38C3×#383—21no—
39C3×#382—21no—
40C3×C4×C4⋊C4C2211yescharacteristic
41C3×#376C2211yescharacteristic
42C3×#336C2212yes—
43C3×#336C2212yes—
44C2×#464C2×C311yescharacteristic, complemented
45C2×#460C2×C311yescharacteristic, complemented
46#2657C2×C311yescharacteristic
47#2320C2×C311yescharacteristic, complemented
48#2042C2×C312yescomplemented
49#2041C2×C312yescomplemented
50#2015C2×C312yescomplemented
51#2014C2×C312yescomplemented
52#1983C2×C311yescharacteristic, complemented
53#1982C2×C311yescharacteristic, complemented
54#1832C2×C311yescharacteristic, complemented
55C22×C3×Q8C2311yescharacteristic
56C22×C3×Q8C2311yescharacteristic
57C22×C3×D4—22no—
58C22×C3×D4—22no—
59C22×C3×D4—21no—
60C22×C3×D4—21no—
61C22×C3×D4C2311yescharacteristic
62C22×C3×D4C2312yes—
63C2×C3×Q16—22no—
64C2×C3×Q16—42no—
65C2×C3×SD16—24no—
66C2×C3×SD16—22no—
67C2×C3×SD16—42no—
68C2×C3×SD16—42no—
69C2×C3×SD16—42no—
70C22×C3×C8C2312yes—
71C22×C3×C8C2311yescharacteristic
72C22×C3×C8C2311yescharacteristic
73C3×#127—22no—
74C3×#127—22no—
75C3×#127—42no—
76C3×#127—42no—
77C3×#124—22no—
78C3×#124—22no—
79C3×#124—42no—
80C3×#124—42no—
81C3×C4×Q8—22no—
82C3×C4×Q8D414yescomplemented
83C2×C3×C4⋊C4—21no—
84C2×C3×C4⋊C4—22no—
85C2×C3×C4⋊C4C2312yes—
86C2×C3×C4⋊C4C2311yescharacteristic
87C2×C3×C22⋊C4—22no—
88C2×C3×C22⋊C4—22no—
89C2×C3×C22⋊C4—21no—
90C2×C3×C22⋊C4—21no—
91C2×C3×C42—21no—
92C2×C3×C42—21no—
93C2×C3×C42C2312yes—
94C2×C3×C42C2311yescharacteristic
95C3×C4⋊C8—22no—
96C3×C4⋊C8—22no—
97C3×#103—22no—
98C3×#103—42no—
99C3×#102—24no—
100C3×#102—22no—
101C3×#102—42no—
102C3×#102—42no—
103C3×#102—42no—
104C3×#95—21no—
105C3×#95—22no—
106C3×#95—22no—
107C3×#95—22no—
108C3×#95D411yescharacteristic
109C3×#95D411yescharacteristic
110C3×#95D412yes—
111C22×Q16C22×C311yescharacteristic
112C22×SD16C22×C312yes—
113C22×SD16C22×C311yescharacteristic
114C2×#127C22×C311yescharacteristic
115C2×#127C22×C312yes—
116C2×#124C22×C311yescharacteristic
117C2×#124C22×C312yes—
118C2×C4×Q8C22×C311yescharacteristic
119#464—24no—
120#460—24no—
121C2×C4⋊C8C22×C311yescharacteristic
122C2×C4⋊C8C22×C311yescharacteristic
123C2×#103C22×C311yescharacteristic
124C2×#103C22×C312yes—
125C2×#102C22×C312yes—
126C2×#102C22×C311yescharacteristic
127C2×#102C22×C312yes—
128C2×#102C22×C312yes—
129C2×#102C22×C312yes—
130#392—21no—
131#392—21no—
132#392—22no—
133#391C22×C312yes—
134#389C22×C312yes—
135#387—22no—
136#383—21no—
137#382—21no—
138C4×C4⋊C4C22×C311yescharacteristic
139#376C22×C311yescharacteristic
140#336C22×C312yes—
141#336C22×C312yes—
142C24×C3—21no—
143C24×C3—22no—
144C2×C3×Q8—21no—
145C2×C3×Q8—21no—
146C2×C3×Q8—21no—
147C2×C3×Q8—22no—
148C2×C3×Q8—22no—
149C2×C3×Q8—22no—
150C2×C3×Q8—22no—
151C2×C3×Q8C2×D412yes—
152C2×C3×D4—21no—
153C2×C3×D4—22no—
154C2×C3×D4—21no—
155C2×C3×D4—22no—
156C2×C3×D4—22no—
157C2×C3×D4—22no—
158C2×C3×D4—22no—
159C2×C3×D4—22no—
160C2×C3×D4—22no—
161C2×C3×D4—22no—
162C2×C3×D4—44no—
163C2×C3×D4—44no—
164C2×C3×D4—42no—
165C2×C3×D4—42no—
166C2×C3×D4—81no—
167C2×C3×D4—82no—
168C2×C3×D4—81no—
169C2×C3×D4—82no—
170C2×C3×D4—82no—
171C2×C3×D4—82no—
172C2×C3×D4—82no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—22no—
176C22×C3×C4—21no—
177C22×C3×C4C2×D412yes—
178C22×C3×C4C2×D412yes—
179C22×C3×C4C2×D411yescharacteristic
180C22×C3×C4C2×D411yescharacteristic
181C22×C3×C4C2411yescharacteristic
182C3×Q16—44no—
183C3×SD16—48no—
184C3×SD16—44no—
185C2×C3×C8—22no—
186C2×C3×C8—21no—
187C2×C3×C8—21no—
188C2×C3×C8—22no—
189C2×C3×C8—22no—
190C2×C3×C8—22no—
191C2×C3×C8—22no—
192C3×C4⋊C4—24no—
193C3×C4⋊C4—21no—
194C3×C4⋊C4—22no—
195C3×C4⋊C4—22no—
196C3×C4⋊C4—82no—
197C3×C4⋊C4C2×D412yes—
198C3×C22⋊C4—44no—
199C3×C22⋊C4—44no—
200C3×C22⋊C4—42no—
201C3×C22⋊C4—42no—
202C3×C42—24no—
203C3×C42—22no—
204C3×C42—22no—
205C3×C42—81no—
206C3×C42C2×D412yes—
207C3×C42#4112yes—
208C22×Q8C23×C311yescharacteristic
209C22×Q8C23×C311yescharacteristic
210C22×D4—22no—
211C22×D4—22no—
212C22×D4—21no—
213C22×D4—21no—
214C22×D4C23×C311yescharacteristic
215C22×D4C23×C312yes—
216C2×Q16—22no—
217C2×Q16—42no—
218C2×SD16—24no—
219C2×SD16—22no—
220C2×SD16—42no—
221C2×SD16—42no—
222C2×SD16—42no—
223C22×C8C23×C312yes—
224C22×C8C23×C311yescharacteristic
225C22×C8C23×C311yescharacteristic
226#127—22no—
227#127—22no—
228#127—42no—
229#127—42no—
230#124—22no—
231#124—22no—
232#124—42no—
233#124—42no—
234C4×Q8—22no—
235C4×Q8C3×D414yescomplemented
236C2×C4⋊C4—21no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4C23×C312yes—
239C2×C4⋊C4C23×C311yescharacteristic
240C2×C22⋊C4—22no—
241C2×C22⋊C4—22no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C42—21no—
245C2×C42—21no—
246C2×C42C23×C312yes—
247C2×C42C23×C311yescharacteristic
248C4⋊C8—22no—
249C4⋊C8—22no—
250#103—22no—
251#103—42no—
252#102—24no—
253#102—22no—
254#102—42no—
255#102—42no—
256#102—42no—
257#95—21no—
258#95—22no—
259#95—22no—
260#95—22no—
261#95C3×D411yescharacteristic
262#95C3×D411yescharacteristic
263#95C3×D412yes—
264C23×C3—41no—
265C23×C3—42no—
266C23×C3—42no—
267C23×C3—42no—
268C23×C3—42no—
269C23×C3—41no—
270C23×C3—42no—
271C23×C3—41no—
272C23×C3—42no—
273C23×C3—42no—
274C23×C3—42no—
275C23×C3—42no—
276C23×C3C22×D411yescharacteristic
277C3×Q8—22no—
278C3×Q8—22no—
279C3×Q8—42no—
280C3×Q8—41no—
281C3×Q8—41no—
282C3×Q8—42no—
283C3×D4—41no—
284C3×D4—42no—
285C3×D4—41no—
286C3×D4—42no—
287C3×D4—42no—
288C3×D4—42no—
289C3×D4—42no—
290C3×D4—84no—
291C3×D4—84no—
292C3×D4—88no—
293C3×D4—88no—
294C2×C3×C4—21no—
295C2×C3×C4—22no—
296C2×C3×C4—21no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—42no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—42no—
310C2×C3×C4—42no—
311C2×C3×C4—42no—
312C2×C3×C4—42no—
313C2×C3×C4#12112yes—
314C2×C3×C4#12112yes—
315C2×C3×C4C22×D411yescharacteristic
316C2×C3×C4C2×#4111yescharacteristic
317C2×C3×C4H(5,𝔽2)12yes—
318C2×C3×C4H(5,𝔽2)12yes—
319C3×C8—42no—
320C3×C8—41no—
321C3×C8—41no—
322C24—21no—
323C24—22no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—22no—
328C2×Q8—22no—
329C2×Q8—22no—
330C2×Q8—22no—
331C2×Q8C2×C3×D412yes—
332C2×D4—21no—
333C2×D4—22no—
334C2×D4—21no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—22no—
340C2×D4—22no—
341C2×D4—22no—
342C2×D4—44no—
343C2×D4—44no—
344C2×D4—42no—
345C2×D4—42no—
346C2×D4—81no—
347C2×D4—82no—
348C2×D4—81no—
349C2×D4—82no—
350C2×D4—82no—
351C2×D4—82no—
352C2×D4—82no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—21no—
357C22×C4C2×C3×D412yes—
358C22×C4C2×C3×D412yes—
359C22×C4C2×C3×D411yescharacteristic
360C22×C4C2×C3×D411yescharacteristic
361C22×C4C24×C311yescharacteristic
362Q16—44no—
363SD16—48no—
364SD16—44no—
365C2×C8—22no—
366C2×C8—21no—
367C2×C8—21no—
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—22no—
371C2×C8—22no—
372C4⋊C4—24no—
373C4⋊C4—21no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—82no—
377C4⋊C4C2×C3×D412yes—
378C22⋊C4—44no—
379C22⋊C4—44no—
380C22⋊C4—42no—
381C22⋊C4—42no—
382C42—24no—
383C42—22no—
384C42—22no—
385C42—81no—
386C42C2×C3×D412yes—
387C42C3×#4112yes—
388C22×C3—81no—
389C22×C3—82no—
390C22×C3—82no—
391C22×C3—82no—
392C22×C3—82no—
393C22×C3—82no—
394C22×C3—82no—
395C22×C3—82no—
396C22×C3—82no—
397C22×C3—81no—
398C22×C3—82no—
399C22×C3—81no—
400C22×C3C2×#12111yescharacteristic
401C22×C3#53512yes—
402C22×C3#57611yescharacteristic
403C22×C3#57711yescharacteristic
404C22×C3#57712yes—
405C3×C4—22no—
406C3×C4—22no—
407C3×C4—42no—
408C3×C4—42no—
409C3×C4—42no—
410C3×C4—42no—
411C3×C4—81no—
412C3×C4—82no—
413C3×C4#53511yescharacteristic
414C3×C4#53511yescharacteristic
415C3×C4#54012yes—
416C23—41no—
417C23—42no—
418C23—41no—
419C23—42no—
420C23—42no—
421C23—42no—
422C23—42no—
423C23—41no—
424C23—42no—
425C23—42no—
426C23—42no—
427C23—42no—
428C23C22×C3×D411yescharacteristic
429Q8—22no—
430Q8—22no—
431Q8—42no—
432Q8—41no—
433Q8—41no—
434Q8—42no—
435D4—41no—
436D4—42no—
437D4—41no—
438D4—42no—
439D4—42no—
440D4—42no—
441D4—42no—
442D4—84no—
443D4—84no—
444D4—88no—
445D4—88no—
446C2×C4—21no—
447C2×C4—22no—
448C2×C4—21no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—41no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4C3×#12112yes—
466C2×C4C3×#12112yes—
467C2×C4C22×C3×D411yescharacteristic
468C2×C4C2×C3×#4111yescharacteristic
469C2×C4C3×H(5,𝔽2)12yes—
470C2×C4C3×H(5,𝔽2)12yes—
471C8—42no—
472C8—41no—
473C8—41no—
474C2×C3—161no—
475C2×C3—162no—
476C2×C3#261911yescharacteristic
477C2×C3#304311yescharacteristic
478C2×C3#304511yescharacteristic
479C2×C3#322212yes—
480C2×C3#322412yes—
481C22—81no—
482C22—82no—
483C22—82no—
484C22—82no—
485C22—82no—
486C22—82no—
487C22—82no—
488C22—82no—
489C22—82no—
490C22—81no—
491C22—82no—
492C22—81no—
493C22C2×C3×#12111yescharacteristic
494C22C3×#53512yes—
495C22C3×#57611yescharacteristic
496C22C3×#57711yescharacteristic
497C22C3×#57712yes—
498C4—22no—
499C4—22no—
500C4—42no—
501C4—42no—
502C4—42no—
503C4—42no—
504C4—81no—
505C4—82no—
506C4C3×#53511yescharacteristic
507C4C3×#53511yescharacteristic
508C4C3×#54012yes—
509C3#2980311yescharacteristic, direct product factor, Sylow
510C2—161no—
511C2—162no—
512C2C3×#261911yescharacteristic
513C2C3×#304311yescharacteristic
514C2C3×#304511yescharacteristic
515C2C3×#322212yes—
516C2C3×#322412yes—
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2657C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×#376 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#464C2semidirect
2. C2×C3×#460C2semidirect
4. C3×#2320C2semidirect
5. C3×#2042C2semidirect
6. C3×#2041C2semidirect
7. C3×#2015C2semidirect
8. C3×#2014C2semidirect
9. C3×#1983C2semidirect
10. C3×#1982C2semidirect
11. C3×#1832C2semidirect
12. #29803C3direct (N × H)
44. C2×#464C2×C3semidirect
45. C2×#460C2×C3semidirect
47. #2320C2×C3semidirect
48. #2042C2×C3semidirect
49. #2041C2×C3semidirect
50. #2015C2×C3semidirect
51. #2014C2×C3semidirect
52. #1983C2×C3semidirect
53. #1982C2×C3semidirect
54. #1832C2×C3semidirect
82. C3×C4×Q8D4semidirect
235. C4×Q8C3×D4semidirect
509. C3#29803direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4642
C2×C3×#4602
C3×#26572
C3×#23202
C3×#20422
C3×#20412
C3×#20152
C3×#20142
C3×#19832
C3×#19822
C3×#18322
#298033