Finite Group Databasebeta

← C3×#70260 #11791120

Subgroups — C3×#70260 #11791120

Order 1152.

761 conjugacy classes of subgroups.

The subgroup lattice has 505 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#215C211yesmaximal, characteristic
2C2×C32×#103C211yesmaximal, characteristic, complemented
3C3×#5229C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic
5C2×C3×#815C211yesmaximal, characteristic, complemented
6C3×#4988C211yesmaximal, characteristic
7C2×C3×#807C211yesmaximal, characteristic, complemented
8C3×#1973—31nomaximal
9#70260C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C3×#215—22no—
15C2×C3×#215—22no—
16C2×C3×#215C414yescomplemented
17C2×C3×(C2×D3)⋊C4—22no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C32×#103—22no—
22C3×C3⋊#95—22no—
23C3×#821—22no—
24C3×#815—22no—
25C3×#807—22no—
26C22×C3×SD16—31no—
27C22×#215C2×C311yescharacteristic
28C2×C3×#107—31no—
29C2×C3×#103—21no—
30C2×C3×#103D311yescharacteristic, complemented
31C2×C3×#103C2×C311yescharacteristic, complemented
32C2×C3×#102—31no—
33C2×C3×#97—31no—
34C3×#391—31no—
35C3×#390—31no—
36#5229C2×C311yescharacteristic, complemented
37C2×#821C2×C311yescharacteristic
38C2×#815C2×C311yescharacteristic, complemented
39#4988C2×C311yescharacteristic
40C2×#807C2×C311yescharacteristic, complemented
41C23×C3×D3—21no—
42C2×C32×Q8—21no—
43C2×C32×Q8—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8C2×C412yes—
48C22×C32×C4—21no—
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3×Dic3—21no—
52C22×C3×Dic3D412yes—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12C2×C412yes—
59C2×C32×C8—21no—
60C2×C32×C8—21no—
61C2×C32×C8D412yes—
62C32×C4⋊C4—21no—
63C32×C4⋊C4—21no—
64C3×#215—28no—
65C3×(C2×D3)⋊C4—44no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4×Dic3—21no—
69C3×C4×Dic3—21no—
70C2×C3×C3⋊C8C2×C412yes—
71C2×C3×C3⋊C8D412yes—
72C2×C3×C3⋊C8D412yes—
73#1973—31noSylow
74C22×C3×Q8—21no—
75C22×C3×Q8C2×D311yescharacteristic
76C22×C3×Q8C22×C311yescharacteristic
77C22×C3×D4—31no—
78C22×D12C22×C311yescharacteristic
79C2×C3×SD16—34no—
80C2×C3×SD16—62no—
81C2×C3×SD16—62no—
82C22×C3×C8—21no—
83C22×C3×C8—31no—
84C22×C3×C8C2×D311yescharacteristic
85C22×C3×C8C22×C311yescharacteristic
86C2×C3×C4⋊C4—21no—
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4C2×D311yescharacteristic
89C2×C3×C4⋊C4C22×C311yescharacteristic
90C2×C3×C22⋊C4—62no—
91C2×C3×C42—31no—
92C2×#215—22no—
93C2×#215—22no—
94C2×#215C3×C414yescomplemented
95C2×(C2×D3)⋊C4—22no—
96C2×C4⋊Dic3C22×C311yescharacteristic
97C2×C4×Dic3C22×C311yescharacteristic
98C22×C3⋊C8C22×C311yescharacteristic
99C3×#107—62no—
100C3×#103—24no—
101C3×#103—22no—
102C3×#103—22no—
103C3×#102—62no—
104C3×#97—62no—
105C3×#95—62no—
106C3⋊#95—22no—
107#821—22no—
108#815—22no—
109#807—22no—
110C23×C32C2×D411yescharacteristic
111C22×C3×D3—22no—
112C22×C3×D3—41no—
113C22×C3×D3—41no—
114C22×C3×D3—42no—
115C22×C3×D3—42no—
116C32×Q8—22no—
117C32×Q8—22no—
118C32×Q8—41no—
119C32×Q8—41no—
120C2×C32×C4—22no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4—41no—
124C2×C32×C4—42no—
125C2×C32×C4C22×C411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C3×Dic3—22no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—42no—
136C3×D12—22no—
137C3×D12—22no—
138C3×D12—41no—
139C3×D12—41no—
140C32×C8—22no—
141C3×C3⋊C8C22⋊C414yescomplemented
142C22×SD16—31no—
143C2×#107—31no—
144C2×#103C3×D311yescharacteristic, complemented
145C2×#102—31no—
146C2×#97—31no—
147#391—31no—
148#390—31no—
149C24×C3—61no—
150C23×D3—21no—
151C2×C3×Q8—21no—
152C2×C3×Q8—21no—
153C2×C3×Q8—22no—
154C2×C3×Q8—22no—
155C2×C3×Q8—21no—
156C2×C3×Q8—21no—
157C2×C3×Q8—21no—
158C2×C3×Q8—21no—
159C2×C3×Q8—21no—
160C2×C3×Q8—21no—
161C2×C3×Q8—21no—
162C2×C3×Q8—21no—
163C2×C3×Q8—22no—
164C2×C3×Q8—41no—
165C2×C3×Q8—41no—
166C2×C3×Q8—41no—
167C2×C3×Q8C4×D312yes—
168C2×C3×Q8C2×C3×C412yes—
169C2×C3×D4—32no—
170C2×C3×D4—61no—
171C2×C3×D4—61no—
172C2×C3×D4—61no—
173C2×C3×D4—61no—
174C2×C3×D4—61no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—32no—
181C22×C3×C4—41no—
182C22×C3×C4—41no—
183C22×C3×C4—61no—
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C23×C311yescharacteristic
186C22×Dic3—21no—
187C22×Dic3C3×D412yes—
188C2×D12—21no—
189C2×D12—21no—
190C2×D12—21no—
191C2×D12—21no—
192C2×D12—21no—
193C2×D12C2×C3×C412yes—
194C3×SD16—68no—
195C2×C3×C8—21no—
196C2×C3×C8—21no—
197C2×C3×C8—21no—
198C2×C3×C8—21no—
199C2×C3×C8—22no—
200C2×C3×C8—32no—
201C2×C3×C8—32no—
202C2×C3×C8—32no—
203C2×C3×C8—41no—
204C2×C3×C8—41no—
205C2×C3×C8#6712yes—
206C2×C3×C8C3×D412yes—
207C3×C4⋊C4—22no—
208C3×C4⋊C4—21no—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—41no—
213C3×C4⋊C4—61no—
214C3×C4⋊C4—61no—
215C3×C22⋊C4—124no—
216C3×C42—61no—
217C3×C42—61no—
218#215—28no—
219(C2×D3)⋊C4—44no—
220C4⋊Dic3—21no—
221C4⋊Dic3—21no—
222C4×Dic3—21no—
223C4×Dic3—21no—
224C2×C3⋊C8C2×C3×C412yes—
225C2×C3⋊C8C3×D412yes—
226C2×C3⋊C8C3×D412yes—
227C22×C32C4×D411yescharacteristic
228C22×C32#12111yescharacteristic
229C22×C32#12711yescharacteristic
230C22×C32AGL(1,ℤ/8)12yes—
231C22×C32#13712yes—
232C2×C3×D3—42no—
233C2×C3×D3—44no—
234C2×C3×D3—82no—
235C2×C3×D3—81no—
236C2×C3×D3—81no—
237C32×C4—42no—
238C32×C4—81no—
239C32×C4C2×C22⋊C411yescharacteristic
240C32×C4C4×D411yescharacteristic
241C32×C4#12111yescharacteristic
242C32×C4#12411yescharacteristic
243C3×Dic3—42no—
244C3×Dic3—81no—
245C22×Q8C2×C3×D311yescharacteristic
246C22×D4—31no—
247C2×SD16—34no—
248C2×SD16—62no—
249C2×SD16—62no—
250C22×C8—31no—
251C22×C8C2×C3×D311yescharacteristic
252C2×C4⋊C4—31no—
253C2×C4⋊C4C2×C3×D311yescharacteristic
254C2×C22⋊C4—62no—
255C2×C42—31no—
256#107—62no—
257#103—22no—
258#102—62no—
259#97—62no—
260#95—62no—
261C23×C3—21no—
262C23×C3—62no—
263C23×C3—121no—
264C23×C3—122no—
265C23×C3—122no—
266C23×C3—121no—
267C23×C3D3×D411yescharacteristic
268C23×C3C2×C3×D411yescharacteristic
269C22×D3—22no—
270C22×D3—41no—
271C22×D3—41no—
272C22×D3—42no—
273C22×D3—42no—
274C3×Q8—24no—
275C3×Q8—22no—
276C3×Q8—22no—
277C3×Q8—22no—
278C3×Q8—22no—
279C3×Q8—42no—
280C3×Q8—42no—
281C3×Q8—42no—
282C3×Q8—41no—
283C3×Q8—41no—
284C3×Q8—41no—
285C3×Q8—41no—
286C3×D4—62no—
287C3×D4—62no—
288C3×D4—121no—
289C3×D4—121no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—42no—
299C2×C3×C4—42no—
300C2×C3×C4—42no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—42no—
306C2×C3×C4—42no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—42no—
310C2×C3×C4—62no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4—82no—
314C2×C3×C4—122no—
315C2×C3×C4—121no—
316C2×C3×C4C2×C4×D311yescharacteristic
317C2×C3×C4#23511yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4#23711yescharacteristic
321C2×C3×C4C2×#6711yescharacteristic
322C2×C3×C4C22×C3×C411yescharacteristic
323C2×C3×C4C2×C3×D411yescharacteristic
324C2×C3×C4C2×C3×D411yescharacteristic
325C2×C3×C4C2×C3×D411yescharacteristic
326C2×C3×C4C3×#4111yescharacteristic
327C2×C3×C4C3×#4111yescharacteristic
328C2×Dic3—22no—
329C2×Dic3—22no—
330C2×Dic3—22no—
331C2×Dic3—41no—
332C2×Dic3—42no—
333D12—22no—
334D12—22no—
335D12—41no—
336D12—41no—
337C3×C8—22no—
338C3×C8—22no—
339C3×C8—34no—
340C3×C8—42no—
341C3⋊C8C3×C22⋊C414yescomplemented
342C2×C32#39011yescharacteristic
343C2×C32#44012yes—
344C2×C32#46812yes—
345C2×C32#49611yescharacteristic
346C2×C32#49711yescharacteristic
347C3×D3—82no—
348C24—61no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8C3×C4×D312yes—
355C2×D4—32no—
356C2×D4—61no—
357C2×D4—61no—
358C2×D4—61no—
359C2×D4—61no—
360C2×D4—61no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—32no—
364C22×C4—61no—
365C22×C4C22×C3×D311yescharacteristic
366SD16—68no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—32no—
370C2×C8—32no—
371C2×C8—32no—
372C2×C8C3×#6712yes—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—61no—
376C4⋊C4—61no—
377C22⋊C4—124no—
378C42—61no—
379C42—61no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—21no—
385C22×C3—122no—
386C22×C3—124no—
387C22×C3—241no—
388C22×C3—241no—
389C22×C3—242no—
390C22×C3#67⋊C411yescharacteristic
391C22×C3#88411yescharacteristic
392C22×C3#91412yes—
393C22×C3#91812yes—
394C22×C3#94011yescharacteristic
395C22×C3C3×C4×D411yescharacteristic
396C22×C3C3×#12111yescharacteristic
397C22×C3C3×#12711yescharacteristic
398C22×C3C3×AGL(1,ℤ/8)12yes—
399C22×C3C3×#13712yes—
400C2×D3—42no—
401C2×D3—44no—
402C2×D3—82no—
403C2×D3—81no—
404C2×D3—81no—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—44no—
410C3×C4—42no—
411C3×C4—42no—
412C3×C4—82no—
413C3×C4—81no—
414C3×C4—81no—
415C3×C4—122no—
416C3×C4—241no—
417C3×C4D3×C22⋊C411yescharacteristic
418C3×C4#88511yescharacteristic
419C3×C4C4×#6711yescharacteristic
420C3×C4#93911yescharacteristic
421C3×C4C2×C3×C22⋊C411yescharacteristic
422C3×C4C3×C4×D411yescharacteristic
423C3×C4C3×#12111yescharacteristic
424C3×C4C3×#12411yescharacteristic
425Dic3—42no—
426Dic3—81no—
427C32#197311yescharacteristic, complemented, Sylow
428C23—62no—
429C23—121no—
430C23—122no—
431C23—122no—
432C23—121no—
433C23C3×D3×D411yescharacteristic
434Q8—22no—
435Q8—22no—
436Q8—41no—
437Q8—41no—
438D4—62no—
439D4—62no—
440D4—121no—
441D4—121no—
442C2×C4—22no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—62no—
448C2×C4—62no—
449C2×C4—62no—
450C2×C4—122no—
451C2×C4—121no—
452C2×C4C2×C3×C4×D311yescharacteristic
453C2×C4C3×#23511yescharacteristic
454C2×C4C3×D3×D411yescharacteristic
455C2×C4C3×D3×D411yescharacteristic
456C2×C4C3×#23711yescharacteristic
457C2×C4C2×C3×#6711yescharacteristic
458C8—22no—
459C8—34no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—22no—
464C2×C3—22no—
465C2×C3—242no—
466C2×C3#481212yes—
467C2×C3#481712yes—
468C2×C3#495711yescharacteristic
469C2×C3#517611yescharacteristic
470C2×C3#519011yescharacteristic
471C2×C3C3×#39011yescharacteristic
472C2×C3C3×#44012yes—
473C2×C3C3×#46812yes—
474C2×C3C3×#49611yescharacteristic
475C2×C3C3×#49711yescharacteristic
476D3—82no—
477C22—122no—
478C22—124no—
479C22—241no—
480C22—241no—
481C22—242no—
482C22C3×#67⋊C411yescharacteristic
483C22C3×#88411yescharacteristic
484C22C3×#91412yes—
485C22C3×#91812yes—
486C22C3×#94011yescharacteristic
487C4—42no—
488C4—81no—
489C4—122no—
490C4—241no—
491C4C3×D3×C22⋊C411yescharacteristic
492C4C3×#88511yescharacteristic
493C4C3×C4×#6711yescharacteristic
494C4C3×#93911yescharacteristic
495C3—21no—
496C3#7026011yescharacteristic, direct product factor
497C3C3×#197311yescharacteristic, complemented
498C2—242no—
499C2C3×#481212yes—
500C2C3×#481712yes—
501C2C3×#495711yescharacteristic
502C2C3×#517611yescharacteristic
503C2C3×#519011yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#103C2
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#103D3
hypocenterC3C3×#1973
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#103

Complements

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

NH ≅ G/Ntype
2. C2×C32×#103C2semidirect
3. C3×#5229C2semidirect
5. C2×C3×#815C2semidirect
7. C2×C3×#807C2semidirect
9. #70260C3direct (N × H)
16. C2×C3×#215C4semidirect
30. C2×C3×#103D3semidirect
31. C2×C3×#103C2×C3semidirect
36. #5229C2×C3semidirect
38. C2×#815C2×C3semidirect
40. C2×#807C2×C3semidirect
94. C2×#215C3×C4semidirect
141. C3×C3⋊C8C22⋊C4semidirect
144. C2×#103C3×D3semidirect
341. C3⋊C8C3×C22⋊C4semidirect
427. C32#1973semidirect
496. C3#70260direct (N × H)
497. C3C3×#1973semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2152
C2×C32×#1032
C3×#52292
C2×C3×#8212
C2×C3×#8152
C3×#49882
C2×C3×#8072
C3×#19733
#702603