Finite Group Databasebeta

← C3×#72019 #11788662

Subgroups — C3×#72019 #11788662

Order 1152.

757 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#131C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic
3C3×#5232C211yesmaximal, characteristic
4C2×C3×#824C211yesmaximal, characteristic, complemented
5C2×C3×#816C211yesmaximal, characteristic, complemented
6C3×#4554C211yesmaximal, characteristic, complemented
7C3×#4552C211yesmaximal, characteristic, complemented
8C3×#1908—31nomaximal
9#72019C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C32×#131—22no—
13C32×#131—22no—
14C2×C32×M16—21no—
15C2×C32×M16C2211yescharacteristic
16C22×C32×C8—21no—
17C22×C32×C8C2211yescharacteristic
18C3×#951—22no—
19C3×#951C414yescomplemented
20C2×C3×#216—21no—
21C2×C3×#214—21no—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C3×#835—21no—
26C3×#832—21no—
27C3×#824—22no—
28C3×#816—21no—
29C3×#816—21no—
30C2×C3×#137—31no—
31C2×C3×#131—21no—
32C2×C3×#131D311yescharacteristic
33C2×C3×#131C2×C311yescharacteristic
34C2×#951C2×C311yescharacteristic
35C3×#417—31no—
36C2×C3×#103—31no—
37C2×C3×#101—31no—
38#5232C2×C311yescharacteristic
39C2×#824C2×C311yescharacteristic, complemented
40C2×#816C2×C311yescharacteristic, complemented
41C3×#343—31no—
42C3×#341—31no—
43#4554C2×C311yescharacteristic, complemented
44#4552C2×C311yescharacteristic, complemented
45C32×#41—21no—
46C32×#41—21no—
47C32×#41C2×C412yes—
48C32×#41D412yes—
49C2×C32×Q8D411yescharacteristic
50C2×C32×D4—21no—
51C2×C32×D4D411yescharacteristic
52C22×C32×C4—21no—
53C22×C32×C4C2311yescharacteristic
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6C2×C412yes—
62C32×M16—24no—
63C32×M16—21no—
64C32×M16D412yes—
65C2×C32×C8—24no—
66C2×C32×C8—21no—
67C2×C32×C8—21no—
68C2×C32×C8—21no—
69C2×C32×C8D411yescharacteristic
70C2×C32×C8D411yescharacteristic
71C3×#216—24no—
72C3×#214—24no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×#208—21no—
76C3×#208—21no—
77C3×#208—21no—
78C3×#208C2×C412yes—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8—21no—
81#1908—31noSylow
82C2×C3×#41—21no—
83C2×C3×#41C2×D311yescharacteristic
84C2×C3×#41C22×C311yescharacteristic
85C22×C3×Q8—31no—
86C22×Dic6C22×C311yescharacteristic
87C3×#137—34no—
88C3×#137—62no—
89C2×C3×Q16—61no—
90C2×C3×SD16—61no—
91C3×#131—24no—
92C3×#131—24no—
93C3×#131—22no—
94C3×#131—22no—
95C3×#131—22no—
96C3×#131—22no—
97C2×C3×M16—22no—
98C2×C3×M16—21no—
99C2×C3×M16—21no—
100C2×C3×M16—21no—
101C2×C3×M16—31no—
102C2×C3×M16—31no—
103C2×C3×M16C2×D311yescharacteristic
104C2×C3×M16C22×C311yescharacteristic
105C22×C3×C8—22no—
106C22×C3×C8—21no—
107C22×C3×C8—21no—
108C22×C3×C8—21no—
109C22×C3×C8C2×D311yescharacteristic
110C22×C3×C8C22×C311yescharacteristic
111C2×C3×C4⋊C4—31no—
112#951—22no—
113#951C3×C414yescomplemented
114C2×#216—21no—
115C2×#214—21no—
116C2×C4⋊Dic3C22×C311yescharacteristic
117C2×#208C22×C311yescharacteristic
118C2×#208C22×C311yescharacteristic
119C3×#103—61no—
120C3×#103—61no—
121C3×#103—61no—
122C3×#102—61no—
123C3×#101—62no—
124#835—21no—
125#832—21no—
126#824—22no—
127#816—21no—
128#816—21no—
129C23×C32—21no—
130C23×C32#4111yescharacteristic
131C32×Q8—21no—
132C32×Q8C22⋊C412yes—
133C32×D4—22no—
134C32×D4—22no—
135C32×D4—21no—
136C32×D4C22⋊C412yes—
137C2×C32×C4—21no—
138C2×C32×C4—22no—
139C2×C32×C4—22no—
140C2×C32×C4C22×C411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4#4111yescharacteristic
146C2×C3×Dic3—22no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—81no—
151C3×Dic6—22no—
152C3×Dic6—22no—
153C3×Dic6—41no—
154C3×Dic6—41no—
155C32×C8—21no—
156C32×C8—22no—
157C32×C8—21no—
158C3×C3⋊C8—22no—
159C3×C3⋊C8—41no—
160C2×#137—31no—
161C2×#131C3×D311yescharacteristic
162#417—31no—
163C2×#103—31no—
164C2×#101—31no—
165#343—31no—
166#341—31no—
167C3×#41—22no—
168C3×#41—22no—
169C3×#41—21no—
170C3×#41—21no—
171C3×#41—21no—
172C3×#41—21no—
173C3×#41—22no—
174C3×#41—22no—
175C3×#41C4×D312yes—
176C3×#41#6712yes—
177C3×#41C2×C3×C412yes—
178C3×#41C3×D412yes—
179C2×C3×Q8—21no—
180C2×C3×Q8—32no—
181C2×C3×Q8—61no—
182C2×C3×Q8—61no—
183C2×C3×Q8—61no—
184C2×C3×Q8—61no—
185C2×C3×Q8—61no—
186C2×C3×Q8D1211yescharacteristic
187C2×C3×Q8C3×D411yescharacteristic
188C2×C3×D4—22no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4D1211yescharacteristic
193C2×C3×D4C3×D411yescharacteristic
194C22×C3×C4—22no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—61no—
199C22×C3×C4—61no—
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C23×C311yescharacteristic
202C22×Dic3—21no—
203C22×Dic3—21no—
204C2×Dic6—21no—
205C2×Dic6—21no—
206C2×Dic6—21no—
207C2×Dic6—21no—
208C2×Dic6—21no—
209C2×Dic6C2×C3×C412yes—
210C3×Q16—64no—
211C3×SD16—64no—
212C3×M16—28no—
213C3×M16—24no—
214C3×M16—24no—
215C3×M16—22no—
216C3×M16—21no—
217C3×M16—21no—
218C3×M16—22no—
219C3×M16—32no—
220C3×M16—61no—
221C3×M16—61no—
222C3×M16—61no—
223C3×M16#6712yes—
224C3×M16C3×D412yes—
225C2×C3×C8—22no—
226C2×C3×C8—28no—
227C2×C3×C8—24no—
228C2×C3×C8—24no—
229C2×C3×C8—22no—
230C2×C3×C8—22no—
231C2×C3×C8—21no—
232C2×C3×C8—21no—
233C2×C3×C8—21no—
234C2×C3×C8—21no—
235C2×C3×C8—21no—
236C2×C3×C8—21no—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—61no—
240C2×C3×C8—61no—
241C2×C3×C8#6711yescharacteristic
242C2×C3×C8#6711yescharacteristic
243C2×C3×C8C3×D411yescharacteristic
244C2×C3×C8C3×D411yescharacteristic
245C3×C4⋊C4—61no—
246C3×C4⋊C4—61no—
247#216—24no—
248#214—24no—
249C4⋊Dic3—21no—
250C4⋊Dic3—21no—
251#208—21no—
252#208—21no—
253#208—21no—
254#208C2×C3×C412yes—
255C2×C3⋊C8—21no—
256C2×C3⋊C8—21no—
257C22×C32—22no—
258C22×C32—21no—
259C22×C32—21no—
260C22×C32—41no—
261C22×C32—41no—
262C22×C32C4×D411yescharacteristic
263C22×C32#12111yescharacteristic
264C22×C32#12311yescharacteristic
265C32×C4—22no—
266C32×C4C2×C22⋊C411yescharacteristic
267C32×C4C4×D411yescharacteristic
268C32×C4#12011yescharacteristic
269C32×C4#12111yescharacteristic
270C3×Dic3—42no—
271C3×Dic3—81no—
272C2×#41C2×C3×D311yescharacteristic
273C22×Q8—31no—
274#137—34no—
275#137—62no—
276C2×Q16—61no—
277C2×SD16—61no—
278#131—22no—
279#131—22no—
280C2×M16—21no—
281C2×M16—31no—
282C2×M16—31no—
283C2×M16C2×C3×D311yescharacteristic
284C22×C8—21no—
285C22×C8C2×C3×D311yescharacteristic
286C2×C4⋊C4—31no—
287#103—61no—
288#103—61no—
289#103—61no—
290#102—61no—
291#101—62no—
292C23×C3—22no—
293C23×C3—21no—
294C23×C3—21no—
295C23×C3—21no—
296C23×C3#23511yescharacteristic
297C23×C3C3×#4111yescharacteristic
298C3×Q8—22no—
299C3×Q8—21no—
300C3×Q8—21no—
301C3×Q8—22no—
302C3×Q8—62no—
303C3×Q8—62no—
304C3×Q8—121no—
305C3×Q8—121no—
306C3×Q8(C2×D3)⋊C412yes—
307C3×Q8C3×C22⋊C412yes—
308C3×D4—24no—
309C3×D4—24no—
310C3×D4—22no—
311C3×D4—22no—
312C3×D4—22no—
313C3×D4—22no—
314C3×D4—22no—
315C3×D4—21no—
316C3×D4—21no—
317C3×D4—22no—
318C3×D4(C2×D3)⋊C412yes—
319C3×D4C3×C22⋊C412yes—
320C2×C3×C4—24no—
321C2×C3×C4—22no—
322C2×C3×C4—24no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—62no—
336C2×C3×C4—121no—
337C2×C3×C4—121no—
338C2×C3×C4—121no—
339C2×C3×C4—241no—
340C2×C3×C4C2×C4×D311yescharacteristic
341C2×C3×C4C2×D1211yescharacteristic
342C2×C3×C4#23511yescharacteristic
343C2×C3×C4C2×#6711yescharacteristic
344C2×C3×C4C2×#6711yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C22×C3×C411yescharacteristic
347C2×C3×C4C2×C3×D411yescharacteristic
348C2×C3×C4C2×C3×D411yescharacteristic
349C2×C3×C4C2×C3×D411yescharacteristic
350C2×C3×C4C2×C3×D411yescharacteristic
351C2×C3×C4C3×#4111yescharacteristic
352C2×Dic3—22no—
353C2×Dic3—41no—
354C2×Dic3—41no—
355C2×Dic3—41no—
356C2×Dic3—81no—
357Dic6—22no—
358Dic6—22no—
359Dic6—41no—
360Dic6—41no—
361C3×C8—22no—
362C3×C8—24no—
363C3×C8—22no—
364C3×C8—21no—
365C3×C8—22no—
366C3×C8—21no—
367C3×C8—21no—
368C3×C8—22no—
369C3×C8—21no—
370C3×C8—62no—
371C3×C8—121no—
372C3⋊C8—22no—
373C3⋊C8—41no—
374C2×C32—21no—
375C2×C32—21no—
376C2×C32—42no—
377C2×C32#38611yescharacteristic
378C2×C32#47111yescharacteristic
379C2×C32#47311yescharacteristic
380#41—21no—
381#41—21no—
382#41C3×C4×D312yes—
383#41C3×#6712yes—
384C2×Q8—32no—
385C2×Q8—61no—
386C2×Q8—61no—
387C2×Q8—61no—
388C2×Q8—61no—
389C2×Q8—61no—
390C2×Q8C3×D1211yescharacteristic
391C2×D4—21no—
392C2×D4C3×D1211yescharacteristic
393C22×C4—21no—
394C22×C4—61no—
395C22×C4—61no—
396C22×C4C22×C3×D311yescharacteristic
397Q16—64no—
398SD16—64no—
399M16—24no—
400M16—21no—
401M16—32no—
402M16—61no—
403M16—61no—
404M16—61no—
405M16C3×#6712yes—
406C2×C8—24no—
407C2×C8—21no—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—61no—
411C2×C8—61no—
412C2×C8C3×#6711yescharacteristic
413C2×C8C3×#6711yescharacteristic
414C4⋊C4—61no—
415C4⋊C4—61no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—24no—
421C22×C3—22no—
422C22×C3—22no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—41no—
427C22×C3—41no—
428C22×C3—42no—
429C22×C3—42no—
430C22×C3—41no—
431C22×C3—41no—
432C22×C3—41no—
433C22×C3—41no—
434C22×C3C4×#6711yescharacteristic
435C22×C3#92911yescharacteristic
436C22×C3#93011yescharacteristic
437C22×C3C3×C4×D411yescharacteristic
438C22×C3C3×#12111yescharacteristic
439C22×C3C3×#12311yescharacteristic
440C3×C4—24no—
441C3×C4—22no—
442C3×C4—22no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—122no—
448C3×C4—241no—
449C3×C4C2×(C2×D3)⋊C411yescharacteristic
450C3×C4C4×#6711yescharacteristic
451C3×C4#93011yescharacteristic
452C3×C4#95311yescharacteristic
453C3×C4C2×C3×C22⋊C411yescharacteristic
454C3×C4C3×C4×D411yescharacteristic
455C3×C4C3×#12011yescharacteristic
456C3×C4C3×#12111yescharacteristic
457Dic3—42no—
458Dic3—81no—
459C32#190811yescharacteristic, complemented, Sylow
460C23—21no—
461C23C3×#23511yescharacteristic
462Q8—21no—
463Q8—62no—
464Q8—62no—
465Q8—121no—
466Q8—121no—
467Q8C3×(C2×D3)⋊C412yes—
468D4—22no—
469D4—22no—
470D4—21no—
471D4C3×(C2×D3)⋊C412yes—
472C2×C4—21no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—62no—
476C2×C4—121no—
477C2×C4—121no—
478C2×C4—121no—
479C2×C4—241no—
480C2×C4C2×C3×C4×D311yescharacteristic
481C2×C4C2×C3×D1211yescharacteristic
482C2×C4C3×#23511yescharacteristic
483C2×C4C2×C3×#6711yescharacteristic
484C2×C4C2×C3×#6711yescharacteristic
485C2×C4C2×C3×#6711yescharacteristic
486C8—21no—
487C8—22no—
488C8—21no—
489C8—62no—
490C8—121no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—41no—
499C2×C3—41no—
500C2×C3—44no—
501C2×C3—42no—
502C2×C3—42no—
503C2×C3#514111yescharacteristic
504C2×C3#514311yescharacteristic
505C2×C3#521311yescharacteristic
506C2×C3C3×#38611yescharacteristic
507C2×C3C3×#47111yescharacteristic
508C2×C3C3×#47311yescharacteristic
509C22—21no—
510C22—21no—
511C22—22no—
512C22—41no—
513C22—41no—
514C22C3×C4×#6711yescharacteristic
515C22C3×#92911yescharacteristic
516C22C3×#93011yescharacteristic
517C4—22no—
518C4—122no—
519C4—241no—
520C4C2×C3×(C2×D3)⋊C411yescharacteristic
521C4C3×C4×#6711yescharacteristic
522C4C3×#93011yescharacteristic
523C4C3×#95311yescharacteristic
524C3—21no—
525C3#7201911yescharacteristic, direct product factor
526C3C3×#190811yescharacteristic, complemented
527C2—21no—
528C2—21no—
529C2—42no—
530C2C3×#514111yescharacteristic
531C2C3×#514311yescharacteristic
532C2C3×#521311yescharacteristic
subgroupG/H
centerC22×C3#930
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#131C2
socleC22×C32#121
prime radicalC2×C32×#41C22
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#131D3
hypocenterC3C3×#1908
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#131

Complements

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

NH ≅ G/Ntype
4. C2×C3×#824C2semidirect
5. C2×C3×#816C2semidirect
6. C3×#4554C2semidirect
7. C3×#4552C2semidirect
9. #72019C3direct (N × H)
19. C3×#951C4semidirect
39. C2×#824C2×C3semidirect
40. C2×#816C2×C3semidirect
43. #4554C2×C3semidirect
44. #4552C2×C3semidirect
113. #951C3×C4semidirect
459. C32#1908semidirect
525. C3#72019direct (N × H)
526. C3C3×#1908semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1312
C2×C3×#9512
C3×#52322
C2×C3×#8242
C2×C3×#8162
C3×#45542
C3×#45522
C3×#19083
#720193