Finite Group Databasebeta

← C3×#69649 #11791126

Subgroups — C3×#69649 #11791126

Order 1152.

809 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#214C211yesmaximal, characteristic
2C32×#390C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4C2×C3×#810C211yesmaximal, characteristic, complemented
5C2×C3×#807C211yesmaximal, characteristic, complemented
6C3×#4929C211yesmaximal, characteristic, complemented
7C2×C3×#803C211yesmaximal, characteristic, complemented
8C3×#1973—31nomaximal
9#69649C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C32×C22⋊C4—22no—
14C2×C32×C42C2211yescharacteristic
15C2×C3×#214—22no—
16C2×C3×#214—22no—
17C2×C3×#214C414yescomplemented
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#832—22no—
22C3×C3⋊#95—22no—
23C3×#810—22no—
24C3×#807—22no—
25C3×#803—22no—
26C22×C3×SD16—31no—
27C22×#214C2×C311yescharacteristic
28C2×C3×#107—31no—
29C2×C3×#103—31no—
30C2×C3×#102—31no—
31C2×C3×#97—31no—
32C3×#391—31no—
33C3×#390—21no—
34C3×#390D311yescharacteristic
35C3×#390C2×C311yescharacteristic
36C2×#832C2×C311yescharacteristic
37C2×#810C2×C311yescharacteristic, complemented
38C2×#807C2×C311yescharacteristic, complemented
39#4929C2×C311yescharacteristic, complemented
40C2×#803C2×C311yescharacteristic, complemented
41C24×C32—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4C2×C412yes—
48C22×C32×C4—21no—
49C22×C32×C4D412yes—
50C22×C32×C4C2311yescharacteristic
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6C2×C412yes—
59C32×C4⋊C4—21no—
60C32×C4⋊C4—21no—
61C32×C22⋊C4—44no—
62C32×C42—21no—
63C32×C42—21no—
64C3×#214—28no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8C2×C412yes—
70C2×C3×C3⋊C8D412yes—
71C2×C3×C3⋊C8D412yes—
72C2×C3×C3⋊C8D412yes—
73#1973—31noSylow
74C22×C3×Q8—31no—
75C22×C3×D4—21no—
76C22×C3×D4C2×D311yescharacteristic
77C22×C3×D4C22×C311yescharacteristic
78C22×Dic6C22×C311yescharacteristic
79C2×C3×SD16—34no—
80C2×C3×SD16—62no—
81C2×C3×SD16—62no—
82C22×C3×C8—31no—
83C22×C3×C8—31no—
84C2×C3×C4⋊C4—21no—
85C2×C3×C4⋊C4—31no—
86C2×C3×C4⋊C4C2×D311yescharacteristic
87C2×C3×C4⋊C4C22×C311yescharacteristic
88C2×C3×C22⋊C4—24no—
89C2×C3×C22⋊C4—22no—
90C2×C3×C22⋊C4—22no—
91C2×C3×C42—21no—
92C2×C3×C42C2×D311yescharacteristic
93C2×C3×C42C22×C311yescharacteristic
94C2×#214—22no—
95C2×#214—22no—
96C2×#214C3×C414yescomplemented
97C2×C4⋊Dic3C22×C311yescharacteristic
98C22×C3⋊C8C22×C311yescharacteristic
99C22×C3⋊C8C22×C311yescharacteristic
100C3×#107—62no—
101C3×#103—62no—
102C3×#102—62no—
103C3×#97—62no—
104C3×#95—62no—
105#832—22no—
106C3⋊#95—22no—
107#810—22no—
108#807—22no—
109#803—22no—
110C23×C32—22no—
111C23×C32—41no—
112C23×C32—41no—
113C23×C32—42no—
114C23×C32—42no—
115C23×C32C2×D411yescharacteristic
116C32×D4—22no—
117C32×D4—22no—
118C32×D4—41no—
119C32×D4—41no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4—22no—
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—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—42no—
136C3×Dic6—22no—
137C3×Dic6—22no—
138C3×Dic6—41no—
139C3×Dic6—41no—
140C3×C3⋊C8—22no—
141C3×C3⋊C8C22⋊C414yescomplemented
142C22×SD16—31no—
143C2×#107—31no—
144C2×#103—31no—
145C2×#102—31no—
146C2×#97—31no—
147#391—31no—
148#390C3×D311yescharacteristic
149C24×C3—22no—
150C24×C3—21no—
151C24×C3—21no—
152C2×C3×Q8—32no—
153C2×C3×Q8—61no—
154C2×C3×Q8—61no—
155C2×C3×Q8—61no—
156C2×C3×Q8—61no—
157C2×C3×Q8—61no—
158C2×C3×D4—22no—
159C2×C3×D4—21no—
160C2×C3×D4—21no—
161C2×C3×D4—21no—
162C2×C3×D4—21no—
163C2×C3×D4—21no—
164C2×C3×D4—21no—
165C2×C3×D4—21no—
166C2×C3×D4—21no—
167C2×C3×D4—21no—
168C2×C3×D4—21no—
169C2×C3×D4—22no—
170C2×C3×D4—41no—
171C2×C3×D4—41no—
172C2×C3×D4—41no—
173C2×C3×D4—41no—
174C2×C3×D4C4×D312yes—
175C2×C3×D4C2×C3×C412yes—
176C22×C3×C4—22no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—22no—
180C22×C3×C4—21no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4#6712yes—
184C22×C3×C4C3×D412yes—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C23×C311yescharacteristic
187C22×Dic3—21no—
188C22×Dic3—21no—
189C2×Dic6—21no—
190C2×Dic6—21no—
191C2×Dic6—21no—
192C2×Dic6—21no—
193C2×Dic6—21no—
194C2×Dic6C2×C3×C412yes—
195C3×SD16—68no—
196C2×C3×C8—32no—
197C2×C3×C8—32no—
198C2×C3×C8—32no—
199C2×C3×C8—32no—
200C2×C3×C8—61no—
201C2×C3×C8—61no—
202C3×C4⋊C4—21no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—21no—
206C3×C4⋊C4—41no—
207C3×C4⋊C4—41no—
208C3×C4⋊C4—61no—
209C3×C4⋊C4—61no—
210C3×C22⋊C4—48no—
211C3×C22⋊C4—44no—
212C3×C22⋊C4—44no—
213C3×C42—21no—
214C3×C42—21no—
215C3×C42—21no—
216C3×C42—21no—
217C3×C42—41no—
218C3×C42—41no—
219#214—28no—
220C4⋊Dic3—21no—
221C4⋊Dic3—21no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8C2×C3×C412yes—
225C2×C3⋊C8C3×D412yes—
226C2×C3⋊C8C3×D412yes—
227C2×C3⋊C8C3×D412yes—
228C22×C32—42no—
229C22×C32—44no—
230C22×C32—82no—
231C22×C32—81no—
232C22×C32—81no—
233C22×C32C4×D411yescharacteristic
234C22×C32#12111yescharacteristic
235C22×C32#12711yescharacteristic
236C22×C32AGL(1,ℤ/8)12yes—
237C22×C32#13712yes—
238C32×C4—42no—
239C32×C4—81no—
240C32×C4C2×C22⋊C411yescharacteristic
241C32×C4C4×D411yescharacteristic
242C32×C4#12111yescharacteristic
243C32×C4#12411yescharacteristic
244C3×Dic3—42no—
245C3×Dic3—81no—
246C22×Q8—31no—
247C22×D4C2×C3×D311yescharacteristic
248C2×SD16—34no—
249C2×SD16—62no—
250C2×SD16—62no—
251C22×C8—31no—
252C22×C8—31no—
253C2×C4⋊C4—31no—
254C2×C4⋊C4C2×C3×D311yescharacteristic
255C2×C22⋊C4—22no—
256C2×C42C2×C3×D311yescharacteristic
257#107—62no—
258#103—62no—
259#102—62no—
260#97—62no—
261#95—62no—
262C23×C3—24no—
263C23×C3—22no—
264C23×C3—22no—
265C23×C3—21no—
266C23×C3—44no—
267C23×C3—42no—
268C23×C3—42no—
269C23×C3—44no—
270C23×C3—42no—
271C23×C3—41no—
272C23×C3—41no—
273C23×C3—42no—
274C23×C3—41no—
275C23×C3—41no—
276C23×C3—42no—
277C23×C3—42no—
278C23×C3C2×#6711yescharacteristic
279C23×C3C2×C3×D411yescharacteristic
280C3×Q8—62no—
281C3×Q8—62no—
282C3×Q8—121no—
283C3×Q8—121no—
284C3×D4—22no—
285C3×D4—22no—
286C3×D4—22no—
287C3×D4—22no—
288C3×D4—42no—
289C3×D4—42no—
290C3×D4—42no—
291C3×D4—42no—
292C3×D4—41no—
293C3×D4—41no—
294C3×D4—41no—
295C3×D4—41no—
296C2×C3×C4—24no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—42no—
310C2×C3×C4—42no—
311C2×C3×C4—44no—
312C2×C3×C4—42no—
313C2×C3×C4—42no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—42no—
317C2×C3×C4—62no—
318C2×C3×C4—121no—
319C2×C3×C4—121no—
320C2×C3×C4—122no—
321C2×C3×C4—121no—
322C2×C3×C4C2×C4×D311yescharacteristic
323C2×C3×C4#23511yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4D3×D411yescharacteristic
327C2×C3×C4#23711yescharacteristic
328C2×C3×C4C22×C3×C411yescharacteristic
329C2×C3×C4C2×C3×D411yescharacteristic
330C2×C3×C4C2×C3×D411yescharacteristic
331C2×C3×C4C2×C3×D411yescharacteristic
332C2×C3×C4C3×#4111yescharacteristic
333C2×C3×C4C3×#4111yescharacteristic
334C2×Dic3—22no—
335C2×Dic3—41no—
336C2×Dic3—41no—
337C2×Dic3—41no—
338C2×Dic3—42no—
339Dic6—22no—
340Dic6—22no—
341Dic6—41no—
342Dic6—41no—
343C3×C8—34no—
344C3×C8—62no—
345C3⋊C8—22no—
346C3⋊C8C3×C22⋊C414yescomplemented
347C2×C32—82no—
348C2×C32#39011yescharacteristic
349C2×C32#44012yes—
350C2×C32#46812yes—
351C2×C32#49611yescharacteristic
352C2×C32#49711yescharacteristic
353C24—21no—
354C2×Q8—32no—
355C2×Q8—61no—
356C2×Q8—61no—
357C2×Q8—61no—
358C2×Q8—61no—
359C2×Q8—61no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4C3×C4×D312yes—
366C22×C4—21no—
367C22×C4—61no—
368C22×C4—61no—
369C22×C4C3×#6712yes—
370C22×C4C22×C3×D311yescharacteristic
371SD16—68no—
372C2×C8—32no—
373C2×C8—32no—
374C2×C8—32no—
375C2×C8—32no—
376C2×C8—61no—
377C2×C8—61no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—61no—
381C4⋊C4—61no—
382C22⋊C4—44no—
383C42—21no—
384C42—21no—
385C22×C3—21no—
386C22×C3—22no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—22no—
390C22×C3—44no—
391C22×C3—48no—
392C22×C3—42no—
393C22×C3—42no—
394C22×C3—44no—
395C22×C3—44no—
396C22×C3—84no—
397C22×C3—82no—
398C22×C3—82no—
399C22×C3—82no—
400C22×C3—81no—
401C22×C3—81no—
402C22×C3—82no—
403C22×C3—81no—
404C22×C3—81no—
405C22×C3C4×#6711yescharacteristic
406C22×C3#93212yes—
407C22×C3#93911yescharacteristic
408C22×C3#94011yescharacteristic
409C22×C3#95112yes—
410C22×C3C3×C4×D411yescharacteristic
411C22×C3C3×#12111yescharacteristic
412C22×C3C3×#12711yescharacteristic
413C22×C3C3×AGL(1,ℤ/8)12yes—
414C22×C3C3×#13712yes—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—44no—
420C3×C4—42no—
421C3×C4—42no—
422C3×C4—82no—
423C3×C4—81no—
424C3×C4—81no—
425C3×C4—122no—
426C3×C4—241no—
427C3×C4D3×C22⋊C411yescharacteristic
428C3×C4#67⋊C411yescharacteristic
429C3×C4#88411yescharacteristic
430C3×C4#88511yescharacteristic
431C3×C4C2×C3×C22⋊C411yescharacteristic
432C3×C4C3×C4×D411yescharacteristic
433C3×C4C3×#12111yescharacteristic
434C3×C4C3×#12411yescharacteristic
435Dic3—42no—
436Dic3—81no—
437C32#197311yescharacteristic, complemented, Sylow
438C23—22no—
439C23—42no—
440C23—41no—
441C23—41no—
442C23—42no—
443C23C2×C3×#6711yescharacteristic
444Q8—62no—
445Q8—62no—
446Q8—121no—
447Q8—121no—
448D4—22no—
449D4—22no—
450D4—41no—
451D4—41no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—62no—
458C2×C4—121no—
459C2×C4—121no—
460C2×C4—122no—
461C2×C4—121no—
462C2×C4C2×C3×C4×D311yescharacteristic
463C2×C4C3×#23511yescharacteristic
464C2×C4C3×D3×D411yescharacteristic
465C2×C4C3×D3×D411yescharacteristic
466C2×C4C3×D3×D411yescharacteristic
467C2×C4C3×#23711yescharacteristic
468C8—34no—
469C8—62no—
470C2×C3—21no—
471C2×C3—22no—
472C2×C3—22no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—84no—
476C2×C3—82no—
477C2×C3—82no—
478C2×C3#495711yescharacteristic
479C2×C3#501812yes—
480C2×C3#504212yes—
481C2×C3#506011yescharacteristic
482C2×C3#507411yescharacteristic
483C2×C3C3×#39011yescharacteristic
484C2×C3C3×#44012yes—
485C2×C3C3×#46812yes—
486C2×C3C3×#49611yescharacteristic
487C2×C3C3×#49711yescharacteristic
488C22—42no—
489C22—44no—
490C22—82no—
491C22—81no—
492C22—81no—
493C22C3×C4×#6711yescharacteristic
494C22C3×#93212yes—
495C22C3×#93911yescharacteristic
496C22C3×#94011yescharacteristic
497C22C3×#95112yes—
498C4—42no—
499C4—81no—
500C4—122no—
501C4—241no—
502C4C3×D3×C22⋊C411yescharacteristic
503C4C3×#67⋊C411yescharacteristic
504C4C3×#88411yescharacteristic
505C4C3×#88511yescharacteristic
506C3—21no—
507C3#6964911yescharacteristic, direct product factor
508C3C3×#197311yescharacteristic, complemented
509C2—82no—
510C2C3×#495711yescharacteristic
511C2C3×#501812yes—
512C2C3×#504212yes—
513C2C3×#506011yescharacteristic
514C2C3×#507411yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#390C2
socleC23×C32C2×D4
prime radicalC22×C32×D4C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#390D3
hypocenterC3C3×#1973
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C3×#390

Complements

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

NH ≅ G/Ntype
4. C2×C3×#810C2semidirect
5. C2×C3×#807C2semidirect
6. C3×#4929C2semidirect
7. C2×C3×#803C2semidirect
9. #69649C3direct (N × H)
17. C2×C3×#214C4semidirect
37. C2×#810C2×C3semidirect
38. C2×#807C2×C3semidirect
39. #4929C2×C3semidirect
40. C2×#803C2×C3semidirect
96. C2×#214C3×C4semidirect
141. C3×C3⋊C8C22⋊C4semidirect
346. C3⋊C8C3×C22⋊C4semidirect
437. C32#1973semidirect
507. C3#69649direct (N × H)
508. C3C3×#1973semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2142
C32×#3902
C2×C3×#8322
C2×C3×#8102
C2×C3×#8072
C3×#49292
C2×C3×#8032
C3×#19733
#696493