Finite Group Databasebeta

← C3×#19832 #10638439

Subgroups — C3×#19832 #10638439

Order 768.

580 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3364C211yesmaximal, characteristic, complemented
2C3×#3359C211yesmaximal, characteristic, complemented
3C3×#3340C211yesmaximal, characteristic
4C3×#3329C211yesmaximal, characteristic
5C3×#1718C211yesmaximal, characteristic, complemented
6C3×#1699C211yesmaximal, characteristic, complemented
7C3×#1684C211yesmaximal, characteristic, complemented
8C3×#1679C211yesmaximal, characteristic, complemented
9C3×#1672C211yesmaximal, characteristic, complemented
10C3×#1650C211yesmaximal, characteristic, complemented
11C3×#1649C211yesmaximal, characteristic, complemented
12C3×#1646C211yesmaximal, characteristic
13C3×#1636C211yesmaximal, characteristic, complemented
14C3×#1583C211yesmaximal, characteristic, complemented
15C3×SD16⋊C8C211yesmaximal, characteristic, complemented
16#19832C311yesmaximal, characteristic, direct product factor, Sylow
17C3×#557C2211yescharacteristic
18C3×#556C2211yescharacteristic
19C3×#555C2211yescharacteristic
20C3×D4×Q8C2211yescharacteristic
21C3×#500C2211yescharacteristic
22C3×#498C2211yescharacteristic
23C3×#488—21no—
24C3×#487—21no—
25C3×#487C2211yescharacteristic
26C3×#487C2211yescharacteristic
27C3×#487C2211yescharacteristic
28C3×#487C2211yescharacteristic
29C3×#485—21no—
30C3×#485—21no—
31C3×#482—21no—
32C3×#479—21no—
33C3×#477C2211yescharacteristic
34C3×#477C2211yescharacteristic
35C3×#475—21no—
36C3×#475C2211yescharacteristic
37C3×#474C2211yescharacteristic
38C3×#474C2211yescharacteristic
39C3×#468—21no—
40C3×#465—21no—
41C3×#464—21no—
42C3×#462C2211yescharacteristic
43C3×#461—21no—
44C3×#461C2211yescharacteristic
45C3×#461C2211yescharacteristic
46C3×#448—21no—
47C3×C8×Q8C2211yescharacteristic
48C3×C8×Q8C2211yescharacteristic
49C3×C4×Q16—21no—
50C3×C4×SD16—21no—
51C3×C4×SD16C2211yescharacteristic
52C3×C4×SD16C2211yescharacteristic
53C3×#436C2211yescharacteristic
54C3×C8×D4C2211yescharacteristic
55C3×#427—21no—
56C3×#419—21no—
57C3×#335C2211yescharacteristic
58C3×#334C2211yescharacteristic
59C3×#333C2211yescharacteristic
60C3×#332C2211yescharacteristic
61C3×#332C2211yescharacteristic
62C3×#332C2211yescharacteristic
63C3×Q8⋊C8C2211yescharacteristic
64C3×Q8⋊C8C2211yescharacteristic
65C3×D4⋊C8C2211yescharacteristic
66C3×D4⋊C8C2211yescharacteristic
67C3×#322C2211yescharacteristic
68#3364C2×C311yescharacteristic, complemented
69#3359C2×C311yescharacteristic, complemented
70#3340C2×C311yescharacteristic
71#3329C2×C311yescharacteristic
72#1718C2×C311yescharacteristic, complemented
73#1699C2×C311yescharacteristic, complemented
74#1684C2×C311yescharacteristic, complemented
75#1679C2×C311yescharacteristic, complemented
76#1672C2×C311yescharacteristic, complemented
77#1650C2×C311yescharacteristic, complemented
78#1649C2×C311yescharacteristic, complemented
79#1646C2×C311yescharacteristic
80#1636C2×C311yescharacteristic, complemented
81#1583C2×C311yescharacteristic, complemented
82SD16⋊C8C2×C311yescharacteristic, complemented
83C22×C3×Q8—21no—
84C2×C3×Q16—21no—
85C2×C3×SD16—21no—
86C2×C3×SD16—21no—
87C2×C3×SD16D411yescharacteristic
88C2×C3×SD16D411yescharacteristic
89C2×C3×M16—21no—
90C22×C3×C8—21no—
91C3×C4⋊Q8—21no—
92C3×C4⋊Q8—21no—
93C3×C4⋊Q8C2311yescharacteristic
94C3×C4⋊Q8C2311yescharacteristic
95C3×C4⋊Q8C2311yescharacteristic
96C3×C4⋊Q8C2311yescharacteristic
97C3×#126—41no—
98C3×#125—21no—
99C3×#125—41no—
100C3×#124—21no—
101C3×#124—41no—
102C3×C22⋊Q8—21no—
103C3×C22⋊Q8—21no—
104C3×C22⋊Q8—41no—
105C3×#121—21no—
106C3×#121—21no—
107C3×C4×Q8—21no—
108C3×C4×Q8—21no—
109C3×C4×Q8—21no—
110C3×C4×Q8C2311yescharacteristic
111C3×C4×Q8C2311yescharacteristic
112C3×C4×D4—21no—
113C3×C4×D4C2311yescharacteristic
114C3×C4×D4C2311yescharacteristic
115C3×#117—21no—
116C3×#117—21no—
117C3×#117—21no—
118C3×#107—21no—
119C3×#107—21no—
120C3×#107—21no—
121C3×#107—21no—
122C3×#107—41no—
123C3×#106—21no—
124C3×#106—21no—
125C3×#106—21no—
126C3×#106D411yescharacteristic
127C3×#106D411yescharacteristic
128C3×C4⋊C8—21no—
129C3×C4⋊C8—21no—
130C3×C4⋊C8C2311yescharacteristic
131C3×C4⋊C8C2311yescharacteristic
132C3×C4⋊C8C2311yescharacteristic
133C3×C4⋊C8C2311yescharacteristic
134C3×#103—21no—
135C3×#103—21no—
136C3×#103—21no—
137C3×#103—21no—
138C3×#103—21no—
139C3×#103—21no—
140C3×#103—21no—
141C3×#103—21no—
142C3×#103—21no—
143C3×#103—21no—
144C3×#103—21no—
145C3×#103—21no—
146C3×#103—41no—
147C3×#103D411yescharacteristic
148C3×#103D411yescharacteristic
149C3×#102—21no—
150C3×#102—21no—
151C3×#102D411yescharacteristic
152C3×#102D411yescharacteristic
153C3×C22⋊C8—21no—
154C3×C22⋊C8—21no—
155C3×C4×C8—21no—
156C3×C4×C8—21no—
157C3×C4×C8C2311yescharacteristic
158C3×C4×C8C2311yescharacteristic
159C3×C4×C8C2311yescharacteristic
160#557C22×C311yescharacteristic
161#556C22×C311yescharacteristic
162#555C22×C311yescharacteristic
163D4×Q8C22×C311yescharacteristic
164#500C22×C311yescharacteristic
165#498C22×C311yescharacteristic
166#488—21no—
167#487—21no—
168#487C22×C311yescharacteristic
169#487C22×C311yescharacteristic
170#487C22×C311yescharacteristic
171#487C22×C311yescharacteristic
172#485—21no—
173#485—21no—
174#482—21no—
175#479—21no—
176#477C22×C311yescharacteristic
177#477C22×C311yescharacteristic
178#475—21no—
179#475C22×C311yescharacteristic
180#474C22×C311yescharacteristic
181#474C22×C311yescharacteristic
182#468—21no—
183#465—21no—
184#464—21no—
185#462C22×C311yescharacteristic
186#461—21no—
187#461C22×C311yescharacteristic
188#461C22×C311yescharacteristic
189#448—21no—
190C8×Q8C22×C311yescharacteristic
191C8×Q8C22×C311yescharacteristic
192C4×Q16—21no—
193C4×SD16—21no—
194C4×SD16C22×C311yescharacteristic
195C4×SD16C22×C311yescharacteristic
196#436C22×C311yescharacteristic
197C8×D4C22×C311yescharacteristic
198#427—21no—
199#419—21no—
200#335C22×C311yescharacteristic
201#334C22×C311yescharacteristic
202#333C22×C311yescharacteristic
203#332C22×C311yescharacteristic
204#332C22×C311yescharacteristic
205#332C22×C311yescharacteristic
206Q8⋊C8C22×C311yescharacteristic
207Q8⋊C8C22×C311yescharacteristic
208D4⋊C8C22×C311yescharacteristic
209D4⋊C8C22×C311yescharacteristic
210#322C22×C311yescharacteristic
211C2×C3×Q8—21no—
212C2×C3×Q8—21no—
213C2×C3×Q8—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—41no—
216C2×C3×Q8—42no—
217C2×C3×Q8—81no—
218C2×C3×Q8C2×D411yescharacteristic
219C2×C3×Q8C2×D411yescharacteristic
220C2×C3×D4—41no—
221C2×C3×D4C2×D411yescharacteristic
222C2×C3×D4C2×D411yescharacteristic
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—41no—
226C3×Q16—42no—
227C3×SD16—22no—
228C3×SD16—41no—
229C3×SD16—42no—
230C3×SD16—81no—
231C3×M16—81no—
232C2×C3×C8—21no—
233C2×C3×C8—21no—
234C2×C3×C8—21no—
235C2×C3×C8—21no—
236C2×C3×C8—21no—
237C2×C3×C8—42no—
238C2×C3×C8C2×D411yescharacteristic
239C2×C3×C8C2×D411yescharacteristic
240C2×C3×C8C2×D411yescharacteristic
241C2×C3×C8C2×D411yescharacteristic
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—41no—
253C3×C4⋊C4—41no—
254C3×C4⋊C4—41no—
255C3×C4⋊C4—41no—
256C3×C4⋊C4—41no—
257C3×C4⋊C4C2×D411yescharacteristic
258C3×C4⋊C4C2×D411yescharacteristic
259C3×C4⋊C4C2×D411yescharacteristic
260C3×C4⋊C4C2×D411yescharacteristic
261C3×C22⋊C4—21no—
262C3×C22⋊C4—21no—
263C3×C22⋊C4—41no—
264C3×C22⋊C4—41no—
265C3×C22⋊C4—41no—
266C3×C22⋊C4—41no—
267C3×C22⋊C4—41no—
268C3×C42—21no—
269C3×C42—21no—
270C3×C42—41no—
271C3×C42—41no—
272C3×C42—41no—
273C3×C42C2411yescharacteristic
274C22×Q8—21no—
275C2×Q16—21no—
276C2×SD16—21no—
277C2×SD16—21no—
278C2×SD16C3×D411yescharacteristic
279C2×SD16C3×D411yescharacteristic
280C2×M16—21no—
281C22×C8—21no—
282C4⋊Q8—21no—
283C4⋊Q8—21no—
284C4⋊Q8C23×C311yescharacteristic
285C4⋊Q8C23×C311yescharacteristic
286C4⋊Q8C23×C311yescharacteristic
287C4⋊Q8C23×C311yescharacteristic
288#126—41no—
289#125—21no—
290#125—41no—
291#124—21no—
292#124—41no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C22⋊Q8—41no—
296#121—21no—
297#121—21no—
298C4×Q8—21no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×Q8C23×C311yescharacteristic
302C4×Q8C23×C311yescharacteristic
303C4×D4—21no—
304C4×D4C23×C311yescharacteristic
305C4×D4C23×C311yescharacteristic
306#117—21no—
307#117—21no—
308#117—21no—
309#107—21no—
310#107—21no—
311#107—21no—
312#107—21no—
313#107—41no—
314#106—21no—
315#106—21no—
316#106—21no—
317#106C3×D411yescharacteristic
318#106C3×D411yescharacteristic
319C4⋊C8—21no—
320C4⋊C8—21no—
321C4⋊C8C23×C311yescharacteristic
322C4⋊C8C23×C311yescharacteristic
323C4⋊C8C23×C311yescharacteristic
324C4⋊C8C23×C311yescharacteristic
325#103—21no—
326#103—21no—
327#103—21no—
328#103—21no—
329#103—21no—
330#103—21no—
331#103—21no—
332#103—21no—
333#103—21no—
334#103—21no—
335#103—21no—
336#103—21no—
337#103—41no—
338#103C3×D411yescharacteristic
339#103C3×D411yescharacteristic
340#102—21no—
341#102—21no—
342#102C3×D411yescharacteristic
343#102C3×D411yescharacteristic
344C22⋊C8—21no—
345C22⋊C8—21no—
346C4×C8—21no—
347C4×C8—21no—
348C4×C8C23×C311yescharacteristic
349C4×C8C23×C311yescharacteristic
350C4×C8C23×C311yescharacteristic
351C23×C3—21no—
352C23×C3—21no—
353C3×Q8—21no—
354C3×Q8—21no—
355C3×Q8—21no—
356C3×Q8—41no—
357C3×Q8—41no—
358C3×Q8—41no—
359C3×Q8—41no—
360C3×Q8—41no—
361C3×Q8—41no—
362C3×Q8—82no—
363C3×Q8—81no—
364C3×Q8#13512yes—
365C3×D4—21no—
366C3×D4—21no—
367C3×D4—21no—
368C3×D4—21no—
369C3×D4—161no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—41no—
377C2×C3×C4—41no—
378C2×C3×C4—41no—
379C2×C3×C4—41no—
380C2×C3×C4—41no—
381C2×C3×C4—41no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—82no—
385C2×C3×C4C22×D411yescharacteristic
386C2×C3×C4C22×D411yescharacteristic
387C2×C3×C4H(5,𝔽2)11yescharacteristic
388C3×C8—21no—
389C3×C8—21no—
390C3×C8—21no—
391C3×C8—21no—
392C3×C8—41no—
393C3×C8—41no—
394C3×C8—41no—
395C3×C8—41no—
396C3×C8—41no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—41no—
402C2×Q8—42no—
403C2×Q8—81no—
404C2×Q8C2×C3×D411yescharacteristic
405C2×Q8C2×C3×D411yescharacteristic
406C2×D4—41no—
407C2×D4C2×C3×D411yescharacteristic
408C2×D4C2×C3×D411yescharacteristic
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—41no—
412Q16—42no—
413SD16—22no—
414SD16—41no—
415SD16—42no—
416SD16—81no—
417M16—81no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8—42no—
424C2×C8C2×C3×D411yescharacteristic
425C2×C8C2×C3×D411yescharacteristic
426C2×C8C2×C3×D411yescharacteristic
427C2×C8C2×C3×D411yescharacteristic
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—41no—
439C4⋊C4—41no—
440C4⋊C4—41no—
441C4⋊C4—41no—
442C4⋊C4—41no—
443C4⋊C4C2×C3×D411yescharacteristic
444C4⋊C4C2×C3×D411yescharacteristic
445C4⋊C4C2×C3×D411yescharacteristic
446C4⋊C4C2×C3×D411yescharacteristic
447C22⋊C4—21no—
448C22⋊C4—21no—
449C22⋊C4—41no—
450C22⋊C4—41no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C22⋊C4—41no—
454C42—21no—
455C42—21no—
456C42—41no—
457C42—41no—
458C42—41no—
459C42C24×C311yescharacteristic
460C22×C3—41no—
461C22×C3—41no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3—41no—
465C22×C3—41no—
466C22×C3D4211yescharacteristic
467C3×C4—22no—
468C3×C4—21no—
469C3×C4—41no—
470C3×C4—41no—
471C3×C4—41no—
472C3×C4—41no—
473C3×C4—41no—
474C3×C4—81no—
475C3×C4—81no—
476C3×C4—81no—
477C3×C4—81no—
478C3×C4C2×#13511yescharacteristic
479C3×C4#57511yescharacteristic
480C3×C4#57711yescharacteristic
481C3×C4#57811yescharacteristic
482C23—21no—
483C23—21no—
484Q8—21no—
485Q8—21no—
486Q8—21no—
487Q8—41no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—82no—
494Q8—81no—
495Q8C3×#13512yes—
496D4—21no—
497D4—21no—
498D4—21no—
499D4—21no—
500D4—161no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—82no—
516C2×C4C22×C3×D411yescharacteristic
517C2×C4C22×C3×D411yescharacteristic
518C2×C4C3×H(5,𝔽2)11yescharacteristic
519C8—21no—
520C8—21no—
521C8—21no—
522C8—21no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8—41no—
528C2×C3—81no—
529C2×C3—81no—
530C2×C3#326911yescharacteristic
531C2×C3#328211yescharacteristic
532C2×C3#328911yescharacteristic
533C22—41no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22C3×D4211yescharacteristic
540C4—22no—
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4C2×C3×#13511yescharacteristic
552C4C3×#57511yescharacteristic
553C4C3×#57711yescharacteristic
554C4C3×#57811yescharacteristic
555C3#1983211yescharacteristic, direct product factor, Sylow
556C2—81no—
557C2—81no—
558C2C3×#326911yescharacteristic
559C2C3×#328211yescharacteristic
560C2C3×#328911yescharacteristic
subgroupG/H
center, socleC22×C3D42
commutator, Frattini, cosocleC42C24×C3
prime radicalC3×#555C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#3364C2semidirect
2. C3×#3359C2semidirect
5. C3×#1718C2semidirect
6. C3×#1699C2semidirect
7. C3×#1684C2semidirect
8. C3×#1679C2semidirect
9. C3×#1672C2semidirect
10. C3×#1650C2semidirect
11. C3×#1649C2semidirect
13. C3×#1636C2semidirect
14. C3×#1583C2semidirect
15. C3×SD16⋊C8C2semidirect
16. #19832C3direct (N × H)
68. #3364C2×C3semidirect
69. #3359C2×C3semidirect
72. #1718C2×C3semidirect
73. #1699C2×C3semidirect
74. #1684C2×C3semidirect
75. #1679C2×C3semidirect
76. #1672C2×C3semidirect
77. #1650C2×C3semidirect
78. #1649C2×C3semidirect
80. #1636C2×C3semidirect
81. #1583C2×C3semidirect
82. SD16⋊C8C2×C3semidirect
555. C3#19832direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#33642
C3×#33592
C3×#33402
C3×#33292
C3×#17182
C3×#16992
C3×#16842
C3×#16792
C3×#16722
C3×#16502
C3×#16492
C3×#16462
C3×#16362
C3×#15832
C3×SD16⋊C82
#198323