Finite Group Databasebeta

← C3×#10979 #10629586

Subgroups — C3×#10979 #10629586

Order 768.

1382 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#532C211yesmaximal, characteristic
2C2×C3×#421C212yesmaximal, complemented
3C2×C3×#410C211yesmaximal, characteristic, complemented
4C3×#2879C211yesmaximal, characteristic, complemented
5C2×C3×#339C212yesmaximal, complemented
6#10979C311yesmaximal, characteristic, direct product factor, Sylow
7C22×C3×#41C2211yescharacteristic
8C22×C3×#41C2211yescharacteristic
9C22×C3×M16C2212yes—
10C3×#532—24no—
11C3×#532—24no—
12C2×C3×C4⋊Q8C411yescharacteristic, complemented
13C2×C3×#127C411yescharacteristic, complemented
14C2×C3×#124C411yescharacteristic, complemented
15C2×C3×#124C411yescharacteristic, complemented
16C2×C3×#121—22no—
17C2×C3×C4×D4—22no—
18C2×C3×#117C2212yes—
19C22×C3×C42C2211yescharacteristic
20C3×#421—24no—
21C3×#421—24no—
22C2×C3×#104—24no—
23C3×#410—24no—
24C2×C3×#99—22no—
25C3×#408—24no—
26C3×#407—22no—
27C3×#339—24no—
28C2×#532C2×C311yescharacteristic
29C2×#421C2×C312yescomplemented
30C2×#410C2×C311yescharacteristic, complemented
31#2879C2×C311yescharacteristic, complemented
32C2×#339C2×C312yescomplemented
33C2×C3×#41—22no—
34C2×C3×#41—22no—
35C2×C3×#41—22no—
36C2×C3×#41—22no—
37C2×C3×#41—22no—
38C2×C3×#41—22no—
39C2×C3×#41—22no—
40C2×C3×#41—22no—
41C2×C3×#41—22no—
42C2×C3×#41—22no—
43C2×C3×#41—22no—
44C2×C3×#41D414yes—
45C22×C3×Q8C2×C411yescharacteristic
46C22×C3×Q8C2×C411yescharacteristic
47C22×C3×D4—22no—
48C22×C3×D4—21no—
49C22×C3×D4C2×C411yescharacteristic
50C22×C3×D4C2×C411yescharacteristic
51C22×C3×D4D412yes—
52C23×C3×C4—21no—
53C23×C3×C4—21no—
54C23×C3×C4D412yes—
55C23×C3×C4C2311yescharacteristic
56C2×C3×M16—22no—
57C2×C3×M16—22no—
58C2×C3×M16—22no—
59C2×C3×M16—22no—
60C2×C3×M16—22no—
61C2×C3×M16D414yescomplemented
62C22×C3×C8—22no—
63C3×C4⋊Q8—22no—
64C3×C4⋊Q8—22no—
65C3×#127—22no—
66C3×#127—22no—
67C3×#124—22no—
68C3×#124—22no—
69C3×#124—22no—
70C3×#124—22no—
71C3×#121—216no—
72C3×C4×D4—216no—
73C3×#117—22no—
74C3×#117—22no—
75C3×#117—22no—
76C3×#117D414yescomplemented
77C2×C3×C4⋊C4—22no—
78C2×C3×C4⋊C4—22no—
79C2×C3×C22⋊C4—22no—
80C2×C3×C22⋊C4—22no—
81C2×C3×C22⋊C4—22no—
82C2×C3×C42—21no—
83C2×C3×C42—22no—
84C2×C3×C42—22no—
85C2×C3×C42C2×C411yescharacteristic
86C2×C3×C42C2×C411yescharacteristic
87C2×C3×C42D414yes—
88C3×#104—216no—
89C3×#99—28no—
90C3×C22⋊C8—28no—
91C22×#41C22×C311yescharacteristic
92C22×#41C22×C311yescharacteristic
93C22×M16C22×C312yes—
94#532—24no—
95#532—24no—
96C2×C4⋊Q8C3×C411yescharacteristic, complemented
97C2×#127C3×C411yescharacteristic, complemented
98C2×#124C3×C411yescharacteristic, complemented
99C2×#124C3×C411yescharacteristic, complemented
100C2×#121—22no—
101C2×C4×D4—22no—
102C2×#117C22×C312yes—
103C22×C42C22×C311yescharacteristic
104#421—24no—
105#421—24no—
106C2×#104—24no—
107#410—24no—
108C2×#99—22no—
109#408—24no—
110#407—22no—
111#339—24no—
112C24×C3—21no—
113C24×C3C22⋊C412yes—
114C24×C3C2×D411yescharacteristic
115C3×#41—24no—
116C3×#41—24no—
117C3×#41—24no—
118C3×#41—24no—
119C3×#41—42no—
120C3×#41—42no—
121C3×#41—42no—
122C3×#41—42no—
123C3×#41—42no—
124C3×#41—42no—
125C3×#41—42no—
126C3×#41—42no—
127C3×#41—42no—
128C3×#41—42no—
129C3×#41—42no—
130C3×#41—42no—
131C2×C3×Q8—21no—
132C2×C3×Q8—21no—
133C2×C3×Q8—21no—
134C2×C3×Q8—22no—
135C2×C3×Q8—22no—
136C2×C3×Q8—22no—
137C2×C3×Q8—22no—
138C2×C3×Q8C22⋊C412yes—
139C2×C3×D4—28no—
140C2×C3×D4—22no—
141C2×C3×D4—24no—
142C2×C3×D4—24no—
143C2×C3×D4—24no—
144C2×C3×D4—22no—
145C2×C3×D4—21no—
146C2×C3×D4—21no—
147C2×C3×D4—21no—
148C2×C3×D4—22no—
149C2×C3×D4—22no—
150C2×C3×D4—22no—
151C2×C3×D4—22no—
152C2×C3×D4—48no—
153C2×C3×D4—41no—
154C2×C3×D4—42no—
155C2×C3×D4—41no—
156C2×C3×D4C22⋊C412yes—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—24no—
161C22×C3×C4—24no—
162C22×C3×C4—24no—
163C22×C3×C4—22no—
164C22×C3×C4—24no—
165C22×C3×C4—22no—
166C22×C3×C4—44no—
167C22×C3×C4—41no—
168C22×C3×C4—42no—
169C22×C3×C4—41no—
170C22×C3×C4—42no—
171C22×C3×C4C22⋊C412yes—
172C22×C3×C4C22×C411yescharacteristic
173C22×C3×C4C2×D412yes—
174C22×C3×C4C2×D412yes—
175C22×C3×C4C2×D412yes—
176C22×C3×C4C2×D412yes—
177C22×C3×C4C2×D411yescharacteristic
178C22×C3×C4#4112yes—
179C22×C3×C4#4112yes—
180C3×M16—24no—
181C3×M16—24no—
182C3×M16—42no—
183C3×M16—42no—
184C2×C3×C8—24no—
185C2×C3×C8—42no—
186C2×C3×C8—42no—
187C3×C4⋊C4—28no—
188C3×C4⋊C4—24no—
189C3×C4⋊C4—42no—
190C3×C22⋊C4—28no—
191C3×C22⋊C4—28no—
192C3×C22⋊C4—24no—
193C3×C22⋊C4—42no—
194C3×C42—21no—
195C3×C42—21no—
196C3×C42—24no—
197C3×C42—24no—
198C3×C42—42no—
199C3×C42C22⋊C412yes—
200C3×C42C22⋊C412yes—
201C2×#41—22no—
202C2×#41—22no—
203C2×#41—22no—
204C2×#41—22no—
205C2×#41—22no—
206C2×#41—22no—
207C2×#41—22no—
208C2×#41—22no—
209C2×#41—22no—
210C2×#41—22no—
211C2×#41—22no—
212C2×#41C3×D414yes—
213C22×Q8C2×C3×C411yescharacteristic
214C22×Q8C2×C3×C411yescharacteristic
215C22×D4—22no—
216C22×D4—21no—
217C22×D4C2×C3×C411yescharacteristic
218C22×D4C2×C3×C411yescharacteristic
219C22×D4C3×D412yes—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4C3×D412yes—
223C23×C4C23×C311yescharacteristic
224C2×M16—22no—
225C2×M16—22no—
226C2×M16—22no—
227C2×M16—22no—
228C2×M16—22no—
229C2×M16C3×D414yescomplemented
230C22×C8—22no—
231C4⋊Q8—22no—
232C4⋊Q8—22no—
233#127—22no—
234#127—22no—
235#124—22no—
236#124—22no—
237#124—22no—
238#124—22no—
239#121—216no—
240C4×D4—216no—
241#117—22no—
242#117—22no—
243#117—22no—
244#117C3×D414yescomplemented
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C22⋊C4—22no—
248C2×C22⋊C4—22no—
249C2×C22⋊C4—22no—
250C2×C42—21no—
251C2×C42—22no—
252C2×C42—22no—
253C2×C42C2×C3×C411yescharacteristic
254C2×C42C2×C3×C411yescharacteristic
255C2×C42C3×D414yes—
256#104—216no—
257#99—28no—
258C22⋊C8—28no—
259C23×C3—22no—
260C23×C3—22no—
261C23×C3—22no—
262C23×C3—22no—
263C23×C3—42no—
264C23×C3—44no—
265C23×C3—44no—
266C23×C3—41no—
267C23×C3—41no—
268C23×C3C2×C22⋊C411yescharacteristic
269C23×C3#12012yes—
270C23×C3#12011yescharacteristic
271C23×C3#12112yes—
272C23×C3#12311yescharacteristic
273C3×Q8—24no—
274C3×Q8—42no—
275C3×Q8—42no—
276C3×Q8—42no—
277C3×D4—24no—
278C3×D4—416no—
279C3×D4—44no—
280C3×D4—44no—
281C3×D4—44no—
282C3×D4—44no—
283C3×D4—42no—
284C3×D4—42no—
285C3×D4—42no—
286C2×C3×C4—24no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—48no—
294C2×C3×C4—42no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—44no—
298C2×C3×C4—44no—
299C2×C3×C4—44no—
300C2×C3×C4—44no—
301C2×C3×C4—44no—
302C2×C3×C4—84no—
303C2×C3×C4C2×C22⋊C411yescharacteristic
304C2×C3×C4C2×C22⋊C411yescharacteristic
305C2×C3×C4C4×D412yes—
306C2×C3×C4C4×D412yes—
307C2×C3×C4#12012yes—
308C2×C3×C4#12012yes—
309C2×C3×C4#12011yescharacteristic
310C2×C3×C4#12112yes—
311C2×C3×C4#12112yes—
312C2×C3×C4#12112yes—
313C2×C3×C4#12112yes—
314C2×C3×C4#12112yes—
315C2×C3×C4#12312yes—
316C2×C3×C4#12311yescharacteristic
317C2×C3×C4#12412yes—
318C2×C3×C4#12712yes—
319C3×C8—44no—
320C24—21no—
321C24C3×C22⋊C412yes—
322C24C2×C3×D411yescharacteristic
323#41—24no—
324#41—24no—
325#41—24no—
326#41—24no—
327#41—42no—
328#41—42no—
329#41—42no—
330#41—42no—
331#41—42no—
332#41—42no—
333#41—42no—
334#41—42no—
335#41—42no—
336#41—42no—
337#41—42no—
338#41—42no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8C3×C22⋊C412yes—
347C2×D4—28no—
348C2×D4—22no—
349C2×D4—24no—
350C2×D4—24no—
351C2×D4—24no—
352C2×D4—22no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—22no—
360C2×D4—48no—
361C2×D4—41no—
362C2×D4—42no—
363C2×D4—41no—
364C2×D4C3×C22⋊C412yes—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—24no—
369C22×C4—22no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—22no—
374C22×C4—44no—
375C22×C4—41no—
376C22×C4—42no—
377C22×C4—41no—
378C22×C4—42no—
379C22×C4C3×C22⋊C412yes—
380C22×C4C22×C3×C411yescharacteristic
381C22×C4C2×C3×D412yes—
382C22×C4C2×C3×D412yes—
383C22×C4C2×C3×D412yes—
384C22×C4C2×C3×D412yes—
385C22×C4C2×C3×D411yescharacteristic
386C22×C4C3×#4112yes—
387C22×C4C3×#4112yes—
388M16—24no—
389M16—24no—
390M16—42no—
391M16—42no—
392C2×C8—24no—
393C2×C8—42no—
394C2×C8—42no—
395C4⋊C4—28no—
396C4⋊C4—24no—
397C4⋊C4—42no—
398C22⋊C4—28no—
399C22⋊C4—28no—
400C22⋊C4—24no—
401C22⋊C4—42no—
402C42—21no—
403C42—21no—
404C42—24no—
405C42—24no—
406C42—42no—
407C42C3×C22⋊C412yes—
408C42C3×C22⋊C412yes—
409C22×C3—22no—
410C22×C3—24no—
411C22×C3—42no—
412C22×C3—41no—
413C22×C3—41no—
414C22×C3—44no—
415C22×C3—44no—
416C22×C3—44no—
417C22×C3—42no—
418C22×C3—42no—
419C22×C3—82no—
420C22×C3—82no—
421C22×C3—82no—
422C22×C3#37911yescharacteristic
423C22×C3#38611yescharacteristic
424C22×C3#38611yescharacteristic
425C22×C3#39212yes—
426C22×C3#39412yes—
427C3×C4—24no—
428C3×C4—42no—
429C3×C4—42no—
430C3×C4—42no—
431C3×C4—84no—
432C3×C4#38612yes—
433C3×C4#39012yes—
434C3×C4#39212yes—
435C3×C4#39412yes—
436C23—22no—
437C23—22no—
438C23—22no—
439C23—22no—
440C23—42no—
441C23—44no—
442C23—44no—
443C23—41no—
444C23—41no—
445C23C2×C3×C22⋊C411yescharacteristic
446C23C3×#12012yes—
447C23C3×#12011yescharacteristic
448C23C3×#12112yes—
449C23C3×#12311yescharacteristic
450Q8—24no—
451Q8—42no—
452Q8—42no—
453Q8—42no—
454D4—24no—
455D4—416no—
456D4—44no—
457D4—44no—
458D4—44no—
459D4—44no—
460D4—42no—
461D4—42no—
462D4—42no—
463C2×C4—24no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—48no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—44no—
475C2×C4—44no—
476C2×C4—44no—
477C2×C4—44no—
478C2×C4—44no—
479C2×C4—84no—
480C2×C4C2×C3×C22⋊C411yescharacteristic
481C2×C4C2×C3×C22⋊C411yescharacteristic
482C2×C4C3×C4×D412yes—
483C2×C4C3×C4×D412yes—
484C2×C4C3×#12012yes—
485C2×C4C3×#12011yescharacteristic
486C2×C4C3×#12012yes—
487C2×C4C3×#12112yes—
488C2×C4C3×#12112yes—
489C2×C4C3×#12112yes—
490C2×C4C3×#12112yes—
491C2×C4C3×#12112yes—
492C2×C4C3×#12312yes—
493C2×C4C3×#12311yescharacteristic
494C2×C4C3×#12412yes—
495C2×C4C3×#12712yes—
496C8—44no—
497C2×C3—21no—
498C2×C3—22no—
499C2×C3—21no—
500C2×C3—22no—
501C2×C3—82no—
502C2×C3—82no—
503C2×C3#143811yescharacteristic
504C2×C3#188412yes—
505C22—22no—
506C22—24no—
507C22—42no—
508C22—41no—
509C22—41no—
510C22—44no—
511C22—44no—
512C22—44no—
513C22—42no—
514C22—42no—
515C22—82no—
516C22—82no—
517C22—82no—
518C22C3×#37911yescharacteristic
519C22C3×#38611yescharacteristic
520C22C3×#38611yescharacteristic
521C22C3×#39212yes—
522C22C3×#39412yes—
523C4—24no—
524C4—42no—
525C4—42no—
526C4—42no—
527C4—84no—
528C4C3×#38612yes—
529C4C3×#39012yes—
530C4C3×#39212yes—
531C4C3×#39412yes—
532C3#1097911yescharacteristic, direct product factor, Sylow
533C2—21no—
534C2—22no—
535C2—21no—
536C2—22no—
537C2—82no—
538C2—82no—
539C2C3×#143811yescharacteristic
540C2C3×#188412yes—
subgroupG/H
centerC2×C3×C4#120
commutatorC22×C4C22×C3×C4
Frattini, cosocleC23×C4C23×C3
socleC22×C3#386
prime radicalC2×C3×#532C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C3×C4 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#421C2semidirect
3. C2×C3×#410C2semidirect
4. C3×#2879C2semidirect
5. C2×C3×#339C2semidirect
6. #10979C3direct (N × H)
12. C2×C3×C4⋊Q8C4semidirect
13. C2×C3×#127C4semidirect
14. C2×C3×#124C4semidirect
15. C2×C3×#124C4semidirect
29. C2×#421C2×C3semidirect
30. C2×#410C2×C3semidirect
31. #2879C2×C3semidirect
32. C2×#339C2×C3semidirect
61. C2×C3×M16D4semidirect
76. C3×#117D4semidirect
96. C2×C4⋊Q8C3×C4semidirect
97. C2×#127C3×C4semidirect
98. C2×#124C3×C4semidirect
99. C2×#124C3×C4semidirect
229. C2×M16C3×D4semidirect
244. #117C3×D4semidirect
532. C3#10979direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5322
C2×C3×#4212
C2×C3×#4102
C3×#28792
C2×C3×#3392
#109793