Finite Group Databasebeta

← C3×#72102 #11788377

Subgroups — C3×#72102 #11788377

Order 1152.

737 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#137C211yesmaximal, characteristic
2C3×#5819C211yesmaximal, characteristic
3C3×#5236C211yesmaximal, characteristic
4C2×C3×#836C211yesmaximal, characteristic, complemented
5C3×#5225C211yesmaximal, characteristic, complemented
6C3×C3⋊#338C211yesmaximal, characteristic, complemented
7C3×#4556C211yesmaximal, characteristic, complemented
8C3×#1902—31nomaximal
9#72102C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C22×C32×Q8C2211yescharacteristic
12C32×#137—22no—
13C32×#137—22no—
14C2×C32×Q16C412yescomplemented
15C2×C32×SD16C412yescomplemented
16C2×C32×M16C2211yescharacteristic
17C3×#948—22no—
18C3×#948—22no—
19C3×#926C2211yescharacteristic
20C2×C3×#208—22no—
21C2×C3×#208C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C3×#837—22no—
25C3×#836—22no—
26C3×#835—22no—
27C2×C3×#137—21no—
28C2×C3×#137D311yescharacteristic
29C2×C3×#137C2×C311yescharacteristic
30C3×#568—31no—
31#5819C2×C311yescharacteristic
32C3×#421—31no—
33C3×#419—31no—
34C2×C3×#101—31no—
35#5236C2×C311yescharacteristic
36C2×#836C2×C311yescharacteristic, complemented
37#5225C2×C311yescharacteristic, complemented
38C3×#344—31no—
39C3×#338—31no—
40C3⋊#338C2×C311yescharacteristic, complemented
41#4556C2×C311yescharacteristic, complemented
42C32×#41—21no—
43C32×#41—21no—
44C32×#41D412yes—
45C32×#41D412yes—
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8—21no—
51C2×C32×Q8C2×C412yes—
52C2×C32×Q8C2×C411yescharacteristic
53C2×C32×D4—21no—
54C2×C32×D4C2×C411yescharacteristic
55C22×C32×C4—21no—
56C22×C32×C4—21no—
57C22×C32×C4C2311yescharacteristic
58C32×Q16—24no—
59C32×SD16—24no—
60C32×M16—21no—
61C32×M16—21no—
62C2×C32×C8C2×C412yes—
63C3×#217—21no—
64C3×C4⋊Dic3—21no—
65C3×C4×Dic3—21no—
66C3×#208—24no—
67C3×#208—21no—
68C3×#208—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208D412yes—
73C2×C3×C3⋊C8—24no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8D412yes—
77#1902—31noSylow
78C2×C3×#41—21no—
79C2×C3×#41C2×D311yescharacteristic
80C2×C3×#41C22×C311yescharacteristic
81C22×C3×Q8—21no—
82C22×C3×Q8C2×D311yescharacteristic
83C22×C3×Q8C22×C311yescharacteristic
84C3×#137—24no—
85C3×#137—24no—
86C3×#137—22no—
87C3×#137—22no—
88C3×#137—22no—
89C3×#137—22no—
90C2×C3×Q16—22no—
91C2×C3×Q16Dic312yescomplemented
92C2×C3×Q16C3×C412yescomplemented
93C2×C3×SD16—22no—
94C2×C3×SD16Dic312yescomplemented
95C2×C3×SD16C3×C412yescomplemented
96C3×#131—62no—
97C3×#131—62no—
98C2×C3×M16—21no—
99C2×C3×M16—31no—
100C2×C3×M16—31no—
101C2×C3×M16—31no—
102C2×C3×M16—62no—
103C2×C3×M16C2×D311yescharacteristic
104C2×C3×M16C22×C311yescharacteristic
105C3×#117—31no—
106#948—22no—
107#948—22no—
108#926C22×C311yescharacteristic
109C2×#208—22no—
110C2×#208C22×C311yescharacteristic
111C2×#208C22×C311yescharacteristic
112C2×#208C22×C311yescharacteristic
113C3×#104—62no—
114C3×#103—62no—
115C3×#101—62no—
116#837—22no—
117#836—22no—
118#835—22no—
119C23×C32—21no—
120C23×C32#4111yescharacteristic
121C32×Q8—22no—
122C32×Q8—21no—
123C32×Q8—22no—
124C32×Q8—41no—
125C32×Q8—41no—
126C32×Q8C22⋊C412yes—
127C32×D4—22no—
128C32×D4—22no—
129C32×D4—21no—
130C32×D4C22⋊C412yes—
131C2×C32×C4—21no—
132C2×C32×C4—22no—
133C2×C32×C4—22no—
134C2×C32×C4—22no—
135C2×C32×C4—41no—
136C2×C32×C4—41no—
137C2×C32×C4C22×C411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C3×Dic3—41no—
144C32×C8—22no—
145C3×C3⋊C8—22no—
146C3×C3⋊C8—22no—
147C3×C3⋊C8—41no—
148C2×#137C3×D311yescharacteristic
149#568—31no—
150#421—31no—
151#419—31no—
152C2×#101—31no—
153#344—31no—
154#338—31no—
155C3×#41—21no—
156C3×#41—21no—
157C3×#41—21no—
158C3×#41—21no—
159C3×#41—22no—
160C3×#41—22no—
161C3×#41—41no—
162C3×#41—41no—
163C3×#41#6712yes—
164C3×#41#6712yes—
165C3×#41C3×D412yes—
166C3×#41C3×D412yes—
167C2×C3×Q8—21no—
168C2×C3×Q8—21no—
169C2×C3×Q8—22no—
170C2×C3×Q8—22no—
171C2×C3×Q8—21no—
172C2×C3×Q8—21no—
173C2×C3×Q8—21no—
174C2×C3×Q8—21no—
175C2×C3×Q8—21no—
176C2×C3×Q8—21no—
177C2×C3×Q8—21no—
178C2×C3×Q8—21no—
179C2×C3×Q8—22no—
180C2×C3×Q8—21no—
181C2×C3×Q8—41no—
182C2×C3×Q8—41no—
183C2×C3×Q8—41no—
184C2×C3×Q8C2×Dic312yes—
185C2×C3×Q8C2×Dic311yescharacteristic
186C2×C3×Q8C2×C3×C412yes—
187C2×C3×Q8C2×C3×C411yescharacteristic
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—41no—
192C2×C3×D4C2×Dic311yescharacteristic
193C2×C3×D4C2×C3×C411yescharacteristic
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—41no—
200C22×C3×C4—41no—
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C23×C311yescharacteristic
203C3×Q16—28no—
204C3×Q16—24no—
205C3×Q16—24no—
206C3×SD16—28no—
207C3×SD16—24no—
208C3×SD16—24no—
209C3×M16—22no—
210C3×M16—22no—
211C3×M16—21no—
212C3×M16—21no—
213C3×M16—21no—
214C3×M16—21no—
215C3×M16—32no—
216C3×M16—64no—
217C3×M16—61no—
218C3×M16—61no—
219C3×M16—61no—
220C3×M16—61no—
221C3×M16—61no—
222C2×C3×C8—22no—
223C2×C3×C8—32no—
224C2×C3×C8—64no—
225C2×C3×C8—61no—
226C2×C3×C8—61no—
227C2×C3×C8C2×Dic312yes—
228C2×C3×C8C2×C3×C412yes—
229C3×C4⋊C4—61no—
230C3×C22⋊C4—61no—
231C3×C42—61no—
232#217—21no—
233C4⋊Dic3—21no—
234C4×Dic3—21no—
235#208—24no—
236#208—21no—
237#208—21no—
238#208—21no—
239#208—21no—
240#208—21no—
241#208C3×D412yes—
242C2×C3⋊C8—24no—
243C2×C3⋊C8—21no—
244C2×C3⋊C8—21no—
245C2×C3⋊C8C3×D412yes—
246C22×C32—22no—
247C22×C32—41no—
248C22×C32—81no—
249C22×C32C4×D411yescharacteristic
250C22×C32#12111yescharacteristic
251C22×C32#12311yescharacteristic
252C32×C4—22no—
253C32×C4—42no—
254C32×C4C2×C22⋊C411yescharacteristic
255C32×C4C4×D411yescharacteristic
256C32×C4#12011yescharacteristic
257C32×C4#12111yescharacteristic
258C3×Dic3—81no—
259C2×#41C2×C3×D311yescharacteristic
260C22×Q8C2×C3×D311yescharacteristic
261#137—22no—
262#137—22no—
263C2×Q16C3×Dic312yescomplemented
264C2×SD16C3×Dic312yescomplemented
265#131—62no—
266#131—62no—
267C2×M16—31no—
268C2×M16—31no—
269C2×M16—31no—
270C2×M16—62no—
271C2×M16C2×C3×D311yescharacteristic
272#117—31no—
273#104—62no—
274#103—62no—
275#101—62no—
276C23×C3—21no—
277C23×C3—21no—
278C23×C3—21no—
279C23×C3—41no—
280C23×C3#23711yescharacteristic
281C23×C3C3×#4111yescharacteristic
282C3×Q8—21no—
283C3×Q8—21no—
284C3×Q8—24no—
285C3×Q8—22no—
286C3×Q8—22no—
287C3×Q8—22no—
288C3×Q8—22no—
289C3×Q8—22no—
290C3×Q8—42no—
291C3×Q8—41no—
292C3×Q8—42no—
293C3×Q8—42no—
294C3×Q8—41no—
295C3×Q8—41no—
296C3×Q8—41no—
297C3×Q8—41no—
298C3×Q8#21712yes—
299C3×Q8C3×C22⋊C412yes—
300C3×D4—22no—
301C3×D4—22no—
302C3×D4—22no—
303C3×D4—22no—
304C3×D4—21no—
305C3×D4—21no—
306C3×D4—22no—
307C3×D4—41no—
308C3×D4—42no—
309C3×D4—42no—
310C3×D4#21712yes—
311C3×D4C3×C22⋊C412yes—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—42no—
327C2×C3×C4—42no—
328C2×C3×C4—41no—
329C2×C3×C4—42no—
330C2×C3×C4—42no—
331C2×C3×C4—42no—
332C2×C3×C4—41no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4—41no—
336C2×C3×C4—121no—
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4#23711yescharacteristic
340C2×C3×C4C22×Dic311yescharacteristic
341C2×C3×C4C2×#6711yescharacteristic
342C2×C3×C4C2×#6711yescharacteristic
343C2×C3×C4C22×C3×C411yescharacteristic
344C2×C3×C4C2×C3×D411yescharacteristic
345C2×C3×C4C2×C3×D411yescharacteristic
346C2×C3×C4C2×C3×D411yescharacteristic
347C2×C3×C4C2×C3×D411yescharacteristic
348C2×C3×C4C3×#4111yescharacteristic
349C2×Dic3—41no—
350C3×C8—24no—
351C3×C8—22no—
352C3×C8—22no—
353C3×C8—62no—
354C3×C8—62no—
355C3×C8—121no—
356C3⋊C8—22no—
357C3⋊C8—22no—
358C3⋊C8—41no—
359C2×C32—21no—
360C2×C32—21no—
361C2×C32—21no—
362C2×C32—42no—
363C2×C32#38611yescharacteristic
364#41—21no—
365#41—21no—
366#41C3×#6712yes—
367#41C3×#6712yes—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8C2×C3×Dic312yes—
374C2×Q8C2×C3×Dic311yescharacteristic
375C2×D4—21no—
376C2×D4C2×C3×Dic311yescharacteristic
377C22×C4—21no—
378C22×C4—21no—
379C22×C4C22×C3×D311yescharacteristic
380Q16—24no—
381SD16—24no—
382M16—21no—
383M16—21no—
384M16—32no—
385M16—64no—
386M16—61no—
387M16—61no—
388M16—61no—
389M16—61no—
390M16—61no—
391C2×C8—32no—
392C2×C8—64no—
393C2×C8—61no—
394C2×C8—61no—
395C2×C8C2×C3×Dic312yes—
396C4⋊C4—61no—
397C22⋊C4—61no—
398C42—61no—
399C22×C3—22no—
400C22×C3—22no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—42no—
405C22×C3—41no—
406C22×C3—41no—
407C22×C3—42no—
408C22×C3—81no—
409C22×C3—81no—
410C22×C3—82no—
411C22×C3D4×Dic311yescharacteristic
412C22×C3#93511yescharacteristic
413C22×C3#93911yescharacteristic
414C22×C3C3×C4×D411yescharacteristic
415C22×C3C3×#12111yescharacteristic
416C22×C3C3×#12311yescharacteristic
417C3×C4—22no—
418C3×C4—22no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—42no—
424C3×C4—44no—
425C3×C4—42no—
426C3×C4—42no—
427C3×C4—241no—
428C3×C4D4×Dic311yescharacteristic
429C3×C4#93711yescharacteristic
430C3×C4#93911yescharacteristic
431C3×C4C2×#21711yescharacteristic
432C3×C4C2×C3×C22⋊C411yescharacteristic
433C3×C4C3×C4×D411yescharacteristic
434C3×C4C3×#12011yescharacteristic
435C3×C4C3×#12111yescharacteristic
436Dic3—81no—
437C32#190211yescharacteristic, complemented, Sylow
438C23—21no—
439C23C3×#23711yescharacteristic
440Q8—21no—
441Q8—22no—
442Q8—22no—
443Q8—41no—
444Q8—41no—
445Q8C3×#21712yes—
446D4—22no—
447D4—22no—
448D4—21no—
449D4C3×#21712yes—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—121no—
457C2×C4C3×D3×D411yescharacteristic
458C2×C4C3×D3×D411yescharacteristic
459C2×C4C3×#23711yescharacteristic
460C2×C4C22×C3×Dic311yescharacteristic
461C2×C4C2×C3×#6711yescharacteristic
462C2×C4C2×C3×#6711yescharacteristic
463C8—22no—
464C8—62no—
465C8—62no—
466C8—121no—
467C2×C3—22no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—41no—
476C2×C3—41no—
477C2×C3—42no—
478C2×C3—42no—
479C2×C3—82no—
480C2×C3#522011yescharacteristic
481C2×C3C3×#38611yescharacteristic
482C22—22no—
483C22—41no—
484C22—81no—
485C22C3×D4×Dic311yescharacteristic
486C22C3×#93511yescharacteristic
487C22C3×#93911yescharacteristic
488C4—22no—
489C4—42no—
490C4—241no—
491C4C3×D4×Dic311yescharacteristic
492C4C3×#93711yescharacteristic
493C4C3×#93911yescharacteristic
494C4C2×C3×#21711yescharacteristic
495C3—21no—
496C3#7210211yescharacteristic, direct product factor
497C3C3×#190211yescharacteristic, complemented
498C2—21no—
499C2—21no—
500C2—21no—
501C2—42no—
502C2C3×#522011yescharacteristic
subgroupG/H
centerC2×C3#5220
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#137C2
socleC2×C32#386
prime radicalC2×C32×#41C22
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#137D3
hypocenterC3C3×#1902
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C2×C3×#137

Complements

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

NH ≅ G/Ntype
4. C2×C3×#836C2semidirect
5. C3×#5225C2semidirect
6. C3×C3⋊#338C2semidirect
7. C3×#4556C2semidirect
9. #72102C3direct (N × H)
14. C2×C32×Q16C4semidirect
15. C2×C32×SD16C4semidirect
36. C2×#836C2×C3semidirect
37. #5225C2×C3semidirect
40. C3⋊#338C2×C3semidirect
41. #4556C2×C3semidirect
91. C2×C3×Q16Dic3semidirect
92. C2×C3×Q16C3×C4semidirect
94. C2×C3×SD16Dic3semidirect
95. C2×C3×SD16C3×C4semidirect
263. C2×Q16C3×Dic3semidirect
264. C2×SD16C3×Dic3semidirect
437. C32#1902semidirect
496. C3#72102direct (N × H)
497. C3C3×#1902semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1372
C3×#58192
C3×#52362
C2×C3×#8362
C3×#52252
C3×C3⋊#3382
C3×#45562
C3×#19023
#721023