Finite Group Databasebeta

← C3×#19093 #10637700

Subgroups — C3×#19093 #10637700

Order 768.

782 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3563C211yesmaximal, characteristic
2C3×#3240C211yesmaximal, characteristic
3C3×#3237C211yesmaximal, characteristic, complemented
4C3×#3236C211yesmaximal, characteristic, complemented
5C3×#1664C212yesmaximal, complemented
6C3×#1664C212yesmaximal, complemented
7C3×#1663C212yesmaximal, complemented
8C3×#1663C212yesmaximal, complemented
9C3×#1537C211yesmaximal, characteristic, complemented
10C3×#1535C211yesmaximal, characteristic
11C3×#1534C211yesmaximal, characteristic, complemented
12#19093C311yesmaximal, characteristic, direct product factor, Sylow
13C3×#564C2212yes—
14C3×#563C2212yes—
15C3×#557—21no—
16C3×#554—21no—
17C3×#552—21no—
18C3×#552—22no—
19C3×#552—21no—
20C3×#544—21no—
21C3×#544—21no—
22C3×#541—21no—
23C3×#541—22no—
24C3×#539—21no—
25C3×#533C2211yescharacteristic
26C3×#533C2211yescharacteristic
27C3×#529C2211yescharacteristic
28C2×C3×#125C2211yescharacteristic
29C3×#501C2212yes—
30C3×#501C2212yes—
31C3×#501C2211yescharacteristic
32C3×#501C2211yescharacteristic
33C3×#491C2212yes—
34C3×#491C2212yes—
35C3×#489C2211yescharacteristic
36C3×#489C2211yescharacteristic
37C3×#485—21no—
38C3×#485—22no—
39C3×#484—21no—
40C3×#483—21no—
41C3×#482—21no—
42C3×#479—22no—
43C3×#479—21no—
44C3×#478—21no—
45C3×#477—21no—
46C3×#475—21no—
47C3×#432C2211yescharacteristic
48C3×#432C2211yescharacteristic
49C3×#432C2211yescharacteristic
50C3×#330C2212yes—
51C3×#330C2212yes—
52C3×#330C2212yes—
53C3×#330C2212yes—
54C3×#330C2212yes—
55C3×#329C2212yes—
56#3563C2×C311yescharacteristic
57#3240C2×C311yescharacteristic
58#3237C2×C311yescharacteristic, complemented
59#3236C2×C311yescharacteristic, complemented
60#1664C2×C312yescomplemented
61#1664C2×C312yescomplemented
62#1663C2×C312yescomplemented
63#1663C2×C312yescomplemented
64#1537C2×C311yescharacteristic, complemented
65#1535C2×C311yescharacteristic
66#1534C2×C311yescharacteristic, complemented
67C3×C4⋊Q8—22no—
68C3×C4⋊Q8—21no—
69C3×C4⋊Q8—22no—
70C3×C4⋊Q8D411yescharacteristic
71C3×C4⋊Q8D411yescharacteristic
72C3×C4⋊Q8C2311yescharacteristic
73C3×C4⋊Q8C2311yescharacteristic
74C3×#126—22no—
75C3×#126—22no—
76C3×#126—22no—
77C3×#126—22no—
78C3×#126—21no—
79C3×#125—22no—
80C3×#125—22no—
81C3×#125—21no—
82C3×#125—22no—
83C3×#125—22no—
84C3×#125—22no—
85C3×#125—22no—
86C3×#125—22no—
87C3×#125—22no—
88C3×#125—21no—
89C3×#125—21no—
90C3×#125—21no—
91C3×#125D412yes—
92C3×#125C2312yes—
93C3×#125C2312yes—
94C3×#125C2311yescharacteristic
95C3×#124C2311yescharacteristic
96C3×#123—22no—
97C3×#123—22no—
98C3×#123—21no—
99C3×C22⋊Q8—22no—
100C3×C22⋊Q8—21no—
101C3×C22⋊Q8—21no—
102C3×C22⋊Q8—22no—
103C3×C22⋊Q8—21no—
104C3×C22⋊Q8—21no—
105C3×C22⋊Q8—22no—
106C3×C22⋊Q8—22no—
107C3×C22⋊Q8—21no—
108C3×C22⋊Q8—21no—
109C3×C22⋊Q8D411yescharacteristic
110C3×#121D411yescharacteristic
111C3×C4×Q8—21no—
112C3×C4×Q8—22no—
113C3×C4×Q8—21no—
114C3×C4×Q8—21no—
115C3×C4×Q8—21no—
116C3×C4×Q8—21no—
117C3×C4×Q8—21no—
118C3×C4×Q8D411yescharacteristic
119C3×C4×D4—22no—
120C3×C4×D4—21no—
121C3×C4×D4D411yescharacteristic
122C3×#117—22no—
123C3×#117—21no—
124C3×#117—22no—
125C3×#117—21no—
126C3×#117—21no—
127C3×#117D412yes—
128C2×C3×C4⋊C4—21no—
129C2×C3×C4⋊C4—21no—
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4D411yescharacteristic
132C2×C3×C4⋊C4D411yescharacteristic
133C2×C3×C42C2311yescharacteristic
134C3×#107—22no—
135C3×#107—21no—
136C3×#107—21no—
137C3×#107—22no—
138C3×#106—22no—
139C3×#106—21no—
140C3×#106—21no—
141C3×#106—22no—
142C3×C4⋊C8—21no—
143C3×C4⋊C8—21no—
144C3×C4⋊C8—21no—
145C3×#103—21no—
146C3×#103—21no—
147C3×#103—22no—
148C3×#103—22no—
149C3×#103—22no—
150C3×#103—22no—
151C3×#102—21no—
152C3×#102—21no—
153C3×C22⋊C8—21no—
154C3×C22⋊C8—21no—
155C3×C22⋊C8—21no—
156C3×#97C2312yes—
157C3×#97C2312yes—
158C3×#97C2311yescharacteristic
159C3×#97C2311yescharacteristic
160#564C22×C312yes—
161#563C22×C312yes—
162#557—21no—
163#554—21no—
164#552—21no—
165#552—22no—
166#552—21no—
167#544—21no—
168#544—21no—
169#541—21no—
170#541—22no—
171#539—21no—
172#533C22×C311yescharacteristic
173#533C22×C311yescharacteristic
174#529C22×C311yescharacteristic
175C2×#125C22×C311yescharacteristic
176#501C22×C311yescharacteristic
177#501C22×C311yescharacteristic
178#501C22×C312yes—
179#501C22×C312yes—
180#491C22×C312yes—
181#491C22×C312yes—
182#489C22×C311yescharacteristic
183#489C22×C311yescharacteristic
184#485—21no—
185#485—22no—
186#484—21no—
187#483—21no—
188#482—21no—
189#479—22no—
190#479—21no—
191#478—21no—
192#477—21no—
193#475—21no—
194#432C22×C311yescharacteristic
195#432C22×C311yescharacteristic
196#432C22×C311yescharacteristic
197#330C22×C312yes—
198#330C22×C312yes—
199#330C22×C312yes—
200#330C22×C312yes—
201#330C22×C312yes—
202#329C22×C312yes—
203C2×C3×Q8—22no—
204C2×C3×Q8—21no—
205C2×C3×Q8—21no—
206C2×C3×Q8—21no—
207C2×C3×Q8—21no—
208C2×C3×Q8C2×D411yescharacteristic
209C2×C3×D4—21no—
210C2×C3×D4C2×D411yescharacteristic
211C22×C3×C4—21no—
212C22×C3×C4—22no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4C2×D411yescharacteristic
216C22×C3×C4C2×D411yescharacteristic
217C22×C3×C4C2×D411yescharacteristic
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C2×C3×C8—22no—
221C2×C3×C8—22no—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—22no—
225C3×C4⋊C4—22no—
226C3×C4⋊C4—22no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4—22no—
229C3×C4⋊C4—22no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—22no—
239C3×C4⋊C4—22no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—21no—
242C3×C4⋊C4—22no—
243C3×C4⋊C4—22no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—41no—
249C3×C4⋊C4—41no—
250C3×C4⋊C4C2×D412yes—
251C3×C4⋊C4C2×D412yes—
252C3×C4⋊C4C2×D412yes—
253C3×C4⋊C4C2×D412yes—
254C3×C4⋊C4C2×D411yescharacteristic
255C3×C4⋊C4C2×D411yescharacteristic
256C3×C22⋊C4—22no—
257C3×C22⋊C4—22no—
258C3×C22⋊C4—22no—
259C3×C22⋊C4—21no—
260C3×C22⋊C4—22no—
261C3×C22⋊C4—21no—
262C3×C22⋊C4—21no—
263C3×C22⋊C4—21no—
264C3×C22⋊C4—21no—
265C3×C22⋊C4—41no—
266C3×C42—22no—
267C3×C42—22no—
268C3×C42—22no—
269C3×C42—22no—
270C3×C42—21no—
271C3×C42—41no—
272C3×C42C2×D411yescharacteristic
273C3×C42C2×D411yescharacteristic
274C3×C42C2×D411yescharacteristic
275C3×C42C2411yescharacteristic
276C4⋊Q8—22no—
277C4⋊Q8—21no—
278C4⋊Q8—22no—
279C4⋊Q8C3×D411yescharacteristic
280C4⋊Q8C3×D411yescharacteristic
281C4⋊Q8C23×C311yescharacteristic
282C4⋊Q8C23×C311yescharacteristic
283#126—22no—
284#126—22no—
285#126—22no—
286#126—22no—
287#126—21no—
288#125—22no—
289#125—22no—
290#125—21no—
291#125—22no—
292#125—22no—
293#125—22no—
294#125—22no—
295#125—22no—
296#125—22no—
297#125—21no—
298#125—21no—
299#125—21no—
300#125C3×D412yes—
301#125C23×C312yes—
302#125C23×C311yescharacteristic
303#125C23×C312yes—
304#124C23×C311yescharacteristic
305#123—22no—
306#123—22no—
307#123—21no—
308C22⋊Q8—22no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311C22⋊Q8—22no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C22⋊Q8—22no—
315C22⋊Q8—22no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8C3×D411yescharacteristic
319#121C3×D411yescharacteristic
320C4×Q8—21no—
321C4×Q8—22no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×Q8—21no—
327C4×Q8C3×D411yescharacteristic
328C4×D4—22no—
329C4×D4—21no—
330C4×D4C3×D411yescharacteristic
331#117—22no—
332#117—21no—
333#117—22no—
334#117—21no—
335#117—21no—
336#117C3×D412yes—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4C3×D411yescharacteristic
341C2×C4⋊C4C3×D411yescharacteristic
342C2×C42C23×C311yescharacteristic
343#107—22no—
344#107—21no—
345#107—21no—
346#107—22no—
347#106—22no—
348#106—21no—
349#106—21no—
350#106—22no—
351C4⋊C8—21no—
352C4⋊C8—21no—
353C4⋊C8—21no—
354#103—21no—
355#103—21no—
356#103—22no—
357#103—22no—
358#103—22no—
359#103—22no—
360#102—21no—
361#102—21no—
362C22⋊C8—21no—
363C22⋊C8—21no—
364C22⋊C8—21no—
365#97C23×C312yes—
366#97C23×C312yes—
367#97C23×C311yescharacteristic
368#97C23×C311yescharacteristic
369C23×C3—21no—
370C23×C3#12011yescharacteristic
371C3×Q8—41no—
372C3×Q8—42no—
373C3×Q8—42no—
374C3×Q8—42no—
375C3×Q8—81no—
376C3×Q8—82no—
377C3×D4—41no—
378C3×D4—42no—
379C2×C3×C4—22no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—42no—
390C2×C3×C4—42no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—81no—
394C2×C3×C4—82no—
395C2×C3×C4#12011yescharacteristic
396C2×C3×C4#12011yescharacteristic
397C2×C3×C4#12011yescharacteristic
398C2×C3×C4C22×D411yescharacteristic
399C2×C3×C4C22×D411yescharacteristic
400C2×C3×C4C22×D411yescharacteristic
401C3×C8—42no—
402C3×C8—42no—
403C3×C8—41no—
404C3×C8—41no—
405C2×Q8—22no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8C2×C3×D411yescharacteristic
411C2×D4—21no—
412C2×D4C2×C3×D411yescharacteristic
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4C2×C3×D411yescharacteristic
418C22×C4C2×C3×D411yescharacteristic
419C22×C4C2×C3×D411yescharacteristic
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—22no—
423C2×C8—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—41no—
451C4⋊C4—41no—
452C4⋊C4C2×C3×D412yes—
453C4⋊C4C2×C3×D412yes—
454C4⋊C4C2×C3×D412yes—
455C4⋊C4C2×C3×D412yes—
456C4⋊C4C2×C3×D411yescharacteristic
457C4⋊C4C2×C3×D411yescharacteristic
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—21no—
462C22⋊C4—22no—
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—41no—
468C42—22no—
469C42—22no—
470C42—22no—
471C42—22no—
472C42—21no—
473C42—41no—
474C42C2×C3×D411yescharacteristic
475C42C2×C3×D411yescharacteristic
476C42C2×C3×D411yescharacteristic
477C42C24×C311yescharacteristic
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—41no—
482C22×C3—41no—
483C22×C3—41no—
484C22×C3C2×#12011yescharacteristic
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—21no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—21no—
491C3×C4—41no—
492C3×C4—42no—
493C3×C4—41no—
494C3×C4—42no—
495C3×C4—42no—
496C3×C4—42no—
497C3×C4—41no—
498C3×C4—81no—
499C3×C4—81no—
500C23—21no—
501C23C3×#12011yescharacteristic
502Q8—41no—
503Q8—42no—
504Q8—42no—
505Q8—42no—
506Q8—81no—
507Q8—82no—
508D4—41no—
509D4—42no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—81no—
525C2×C4—82no—
526C2×C4C3×#12011yescharacteristic
527C2×C4C3×#12011yescharacteristic
528C2×C4C3×#12011yescharacteristic
529C2×C4C22×C3×D411yescharacteristic
530C2×C4C22×C3×D411yescharacteristic
531C2×C4C22×C3×D411yescharacteristic
532C8—42no—
533C8—42no—
534C8—41no—
535C8—41no—
536C2×C3—41no—
537C2×C3—81no—
538C2×C3#302011yescharacteristic
539C2×C3#302011yescharacteristic
540C2×C3#302211yescharacteristic
541C22—21no—
542C22—21no—
543C22—21no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22C2×C3×#12011yescharacteristic
548C4—21no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—21no—
554C4—41no—
555C4—42no—
556C4—41no—
557C4—42no—
558C4—42no—
559C4—42no—
560C4—41no—
561C4—81no—
562C4—81no—
563C3#1909311yescharacteristic, direct product factor, Sylow
564C2—41no—
565C2—81no—
566C2C3×#302011yescharacteristic
567C2C3×#302011yescharacteristic
568C2C3×#302211yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC42C24×C3
prime radicalC3×#121D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
3. C3×#3237C2semidirect
4. C3×#3236C2semidirect
5. C3×#1664C2semidirect
6. C3×#1664C2semidirect
7. C3×#1663C2semidirect
8. C3×#1663C2semidirect
9. C3×#1537C2semidirect
11. C3×#1534C2semidirect
12. #19093C3direct (N × H)
58. #3237C2×C3semidirect
59. #3236C2×C3semidirect
60. #1664C2×C3semidirect
61. #1664C2×C3semidirect
62. #1663C2×C3semidirect
63. #1663C2×C3semidirect
64. #1537C2×C3semidirect
66. #1534C2×C3semidirect
563. C3#19093direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35632
C3×#32402
C3×#32372
C3×#32362
C3×#16642
C3×#16632
C3×#15372
C3×#15352
C3×#15342
#190933