Finite Group Databasebeta

← C3×#70192 #11791132

Subgroups — C3×#70192 #11791132

Order 1152.

781 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#214C211yesmaximal, characteristic
2C2×C32×#102C211yesmaximal, characteristic
3C3×#5221C211yesmaximal, characteristic
4C2×C3×#816C211yesmaximal, characteristic, complemented
5C2×C3×#815C211yesmaximal, characteristic, complemented
6C3×#4973C211yesmaximal, characteristic, complemented
7C2×C3×#807C211yesmaximal, characteristic, complemented
8C3×#1973—31nomaximal
9#70192C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C3×#217—22no—
15C2×C3×#214—22no—
16C2×C3×#214—22no—
17C2×C3×#214C414yescomplemented
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C32×#102—22no—
22C3×C3⋊#95—22no—
23C3×#816—22no—
24C3×#815—22no—
25C3×#807—22no—
26C22×C3×SD16—31no—
27C22×#214C2×C311yescharacteristic
28C2×C3×#107—31no—
29C2×C3×#103—31no—
30C2×C3×#102—21no—
31C2×C3×#102D311yescharacteristic
32C2×C3×#102C2×C311yescharacteristic
33C2×C3×#97—31no—
34C3×#391—31no—
35C3×#390—31no—
36#5221C2×C311yescharacteristic
37C2×#816C2×C311yescharacteristic, complemented
38C2×#815C2×C311yescharacteristic, complemented
39#4973C2×C311yescharacteristic, complemented
40C2×#807C2×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×C4C2311yescharacteristic
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3D412yes—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6C2×C412yes—
59C2×C32×C8—21no—
60C2×C32×C8—21no—
61C2×C32×C8D412yes—
62C32×C4⋊C4—21no—
63C32×C4⋊C4—21no—
64C3×#217—44no—
65C3×#214—28no—
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—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—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×#217—22no—
93C2×#214—22no—
94C2×#214—22no—
95C2×#214C3×C414yescomplemented
96C2×C4⋊Dic3C22×C311yescharacteristic
97C2×C4×Dic3C22×C311yescharacteristic
98C22×C3⋊C8C22×C311yescharacteristic
99C3×#107—62no—
100C3×#103—62no—
101C3×#102—24no—
102C3×#102—22no—
103C3×#102—22no—
104C3×#97—62no—
105C3×#95—62no—
106C3⋊#95—22no—
107#816—22no—
108#815—22no—
109#807—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—41no—
121C2×C32×C4—42no—
122C2×C32×C4C22×C411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C3×Dic3—22no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—22no—
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—
140C32×C8—22no—
141C3×C3⋊C8C22⋊C414yescomplemented
142C22×SD16—31no—
143C2×#107—31no—
144C2×#103—31no—
145C2×#102C3×D311yescharacteristic
146C2×#97—31no—
147#391—31no—
148#390—31no—
149C24×C3—21no—
150C24×C3—21no—
151C24×C3—41no—
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—22no—
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—21no—
170C2×C3×D4—22no—
171C2×C3×D4—41no—
172C2×C3×D4—41no—
173C2×C3×D4—41no—
174C2×C3×D4C4×D312yes—
175C2×C3×D4C2×C3×C412yes—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—32no—
180C22×C3×C4—41no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C23×C311yescharacteristic
185C22×Dic3—21no—
186C22×Dic3—21no—
187C22×Dic3C3×D412yes—
188C2×Dic6—21no—
189C2×Dic6—21no—
190C2×Dic6—21no—
191C2×Dic6—21no—
192C2×Dic6—21no—
193C2×Dic6C2×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#217—44no—
219#214—28no—
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×C32—42no—
228C22×C32—44no—
229C22×C32—82no—
230C22×C32—81no—
231C22×C32—81no—
232C22×C32C4×D411yescharacteristic
233C22×C32#12111yescharacteristic
234C22×C32#12711yescharacteristic
235C22×C32AGL(1,ℤ/8)12yes—
236C22×C32#13712yes—
237C32×C4—81no—
238C32×C4C2×C22⋊C411yescharacteristic
239C32×C4C4×D411yescharacteristic
240C32×C4#12111yescharacteristic
241C32×C4#12411yescharacteristic
242C3×Dic3—42no—
243C3×Dic3—42no—
244C3×Dic3—81no—
245C22×Q8—31no—
246C22×D4C2×C3×D311yescharacteristic
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—62no—
258#102—22no—
259#97—62no—
260#95—62no—
261C23×C3—22no—
262C23×C3—22no—
263C23×C3—21no—
264C23×C3—42no—
265C23×C3—42no—
266C23×C3—42no—
267C23×C3—41no—
268C23×C3—42no—
269C23×C3—42no—
270C23×C3—41no—
271C23×C3—41no—
272C23×C3—41no—
273C23×C3—42no—
274C23×C3—42no—
275C23×C3—82no—
276C23×C3—82no—
277C23×C3D3×D411yescharacteristic
278C23×C3C2×C3×D411yescharacteristic
279C3×Q8—62no—
280C3×Q8—62no—
281C3×Q8—121no—
282C3×Q8—121no—
283C3×D4—24no—
284C3×D4—22no—
285C3×D4—22no—
286C3×D4—22no—
287C3×D4—22no—
288C3×D4—42no—
289C3×D4—42no—
290C3×D4—42no—
291C3×D4—41no—
292C3×D4—41no—
293C3×D4—41no—
294C3×D4—41no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—42no—
302C2×C3×C4—42no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—42no—
306C2×C3×C4—62no—
307C2×C3×C4—62no—
308C2×C3×C4—62no—
309C2×C3×C4—62no—
310C2×C3×C4—82no—
311C2×C3×C4—121no—
312C2×C3×C4—121no—
313C2×C3×C4—122no—
314C2×C3×C4—121no—
315C2×C3×C4C2×C4×D311yescharacteristic
316C2×C3×C4#23511yescharacteristic
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4#23711yescharacteristic
320C2×C3×C4C2×#6711yescharacteristic
321C2×C3×C4C22×C3×C411yescharacteristic
322C2×C3×C4C2×C3×D411yescharacteristic
323C2×C3×C4C2×C3×D411yescharacteristic
324C2×C3×C4C2×C3×D411yescharacteristic
325C2×C3×C4C3×#4111yescharacteristic
326C2×C3×C4C3×#4111yescharacteristic
327C2×Dic3—22no—
328C2×Dic3—22no—
329C2×Dic3—22no—
330C2×Dic3—22no—
331C2×Dic3—41no—
332C2×Dic3—41no—
333C2×Dic3—41no—
334C2×Dic3—42no—
335Dic6—22no—
336Dic6—22no—
337Dic6—41no—
338Dic6—41no—
339C3×C8—22no—
340C3×C8—22no—
341C3×C8—34no—
342C3×C8—42no—
343C3⋊C8C3×C22⋊C414yescomplemented
344C2×C32—82no—
345C2×C32#39011yescharacteristic
346C2×C32#44012yes—
347C2×C32#46812yes—
348C2×C32#49611yescharacteristic
349C2×C32#49711yescharacteristic
350C24—21no—
351C2×Q8—32no—
352C2×Q8—61no—
353C2×Q8—61no—
354C2×Q8—61no—
355C2×Q8—61no—
356C2×Q8—61no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4C3×C4×D312yes—
363C22×C4—21no—
364C22×C4—32no—
365C22×C4—61no—
366C22×C4—61no—
367C22×C4C22×C3×D311yescharacteristic
368SD16—68no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—32no—
372C2×C8—32no—
373C2×C8—32no—
374C2×C8C3×#6712yes—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—61no—
378C4⋊C4—61no—
379C22⋊C4—124no—
380C42—61no—
381C42—61no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—22no—
385C22×C3—22no—
386C22×C3—21no—
387C22×C3—44no—
388C22×C3—42no—
389C22×C3—42no—
390C22×C3—44no—
391C22×C3—44no—
392C22×C3—84no—
393C22×C3—82no—
394C22×C3—84no—
395C22×C3—82no—
396C22×C3—81no—
397C22×C3—81no—
398C22×C3—82no—
399C22×C3—82no—
400C22×C3—81no—
401C22×C3—81no—
402C22×C3#67⋊C411yescharacteristic
403C22×C3#88411yescharacteristic
404C22×C3#91112yes—
405C22×C3#91512yes—
406C22×C3#94011yescharacteristic
407C22×C3C3×C4×D411yescharacteristic
408C22×C3C3×#12111yescharacteristic
409C22×C3C3×#12711yescharacteristic
410C22×C3C3×AGL(1,ℤ/8)12yes—
411C22×C3C3×#13712yes—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—82no—
417C3×C4—81no—
418C3×C4—81no—
419C3×C4—122no—
420C3×C4—122no—
421C3×C4—241no—
422C3×C4D3×C22⋊C411yescharacteristic
423C3×C4#88511yescharacteristic
424C3×C4C4×#6711yescharacteristic
425C3×C4#93911yescharacteristic
426C3×C4C2×C3×C22⋊C411yescharacteristic
427C3×C4C3×C4×D411yescharacteristic
428C3×C4C3×#12111yescharacteristic
429C3×C4C3×#12411yescharacteristic
430Dic3—42no—
431Dic3—42no—
432Dic3—81no—
433C32#197311yescharacteristic, complemented, Sylow
434C23—22no—
435C23—41no—
436C23—42no—
437C23—42no—
438C23—41no—
439C23C3×D3×D411yescharacteristic
440Q8—62no—
441Q8—62no—
442Q8—121no—
443Q8—121no—
444D4—22no—
445D4—22no—
446D4—41no—
447D4—41no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—62no—
451C2×C4—62no—
452C2×C4—62no—
453C2×C4—62no—
454C2×C4—121no—
455C2×C4—121no—
456C2×C4—122no—
457C2×C4—121no—
458C2×C4C2×C3×C4×D311yescharacteristic
459C2×C4C3×#23511yescharacteristic
460C2×C4C3×D3×D411yescharacteristic
461C2×C4C3×D3×D411yescharacteristic
462C2×C4C3×#23711yescharacteristic
463C2×C4C2×C3×#6711yescharacteristic
464C8—22no—
465C8—34no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—22no—
469C2×C3—22no—
470C2×C3—21no—
471C2×C3—84no—
472C2×C3—82no—
473C2×C3—82no—
474C2×C3#475712yes—
475C2×C3#478012yes—
476C2×C3#495711yescharacteristic
477C2×C3#515411yescharacteristic
478C2×C3#516711yescharacteristic
479C2×C3C3×#39011yescharacteristic
480C2×C3C3×#44012yes—
481C2×C3C3×#46812yes—
482C2×C3C3×#49611yescharacteristic
483C2×C3C3×#49711yescharacteristic
484C22—42no—
485C22—44no—
486C22—81no—
487C22—82no—
488C22—81no—
489C22C3×#67⋊C411yescharacteristic
490C22C3×#88411yescharacteristic
491C22C3×#91112yes—
492C22C3×#91512yes—
493C22C3×#94011yescharacteristic
494C4—81no—
495C4—122no—
496C4—122no—
497C4—241no—
498C4C3×D3×C22⋊C411yescharacteristic
499C4C3×#88511yescharacteristic
500C4C3×C4×#6711yescharacteristic
501C4C3×#93911yescharacteristic
502C3—21no—
503C3#7019211yescharacteristic, direct product factor
504C3C3×#197311yescharacteristic, complemented
505C2—82no—
506C2C3×#475712yes—
507C2C3×#478012yes—
508C2C3×#495711yescharacteristic
509C2C3×#515411yescharacteristic
510C2C3×#516711yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC22×C32×D4C22
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#102D3
hypocenterC3C3×#1973
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#102

Complements

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

NH ≅ G/Ntype
4. C2×C3×#816C2semidirect
5. C2×C3×#815C2semidirect
6. C3×#4973C2semidirect
7. C2×C3×#807C2semidirect
9. #70192C3direct (N × H)
17. C2×C3×#214C4semidirect
37. C2×#816C2×C3semidirect
38. C2×#815C2×C3semidirect
39. #4973C2×C3semidirect
40. C2×#807C2×C3semidirect
95. C2×#214C3×C4semidirect
141. C3×C3⋊C8C22⋊C4semidirect
343. C3⋊C8C3×C22⋊C4semidirect
433. C32#1973semidirect
503. C3#70192direct (N × H)
504. 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
C2×C32×#1022
C3×#52212
C2×C3×#8162
C2×C3×#8152
C3×#49732
C2×C3×#8072
C3×#19733
#701923