Finite Group Databasebeta

← C3×#70629 #11791123

Subgroups — C3×#70629 #11791123

Order 1152.

745 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic
2C2×C32×#107C211yesmaximal, characteristic, complemented
3C2×C3×#815C211yesmaximal, characteristic, complemented
4C3×#4988C211yesmaximal, characteristic
5C3×#4973C211yesmaximal, characteristic, complemented
6C2×C3×#810C211yesmaximal, characteristic, complemented
7C2×C3×#809C211yesmaximal, characteristic
8C3×#1973—31nomaximal
9#70629C311yesmaximal, characteristic, direct product factor
10C22×C3×D12C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4—22no—
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×C3×#204—22no—
19C2×C3×#204—22no—
20C2×C3×#204C414yescomplemented
21C32×#107—22no—
22C3×C3⋊#95—22no—
23C3×#815—22no—
24C3×#810—22no—
25C3×#809—22no—
26C22×C3×SD16—31no—
27C22×#204C2×C311yescharacteristic
28C2×C3×#107—21no—
29C2×C3×#107D311yescharacteristic, complemented
30C2×C3×#107C2×C311yescharacteristic, complemented
31C2×C3×#103—31no—
32C2×C3×#102—31no—
33C2×C3×#97—31no—
34C3×#391—31no—
35C3×#390—31no—
36C2×#815C2×C311yescharacteristic, complemented
37#4988C2×C311yescharacteristic
38#4973C2×C311yescharacteristic, complemented
39C2×#810C2×C311yescharacteristic, complemented
40C2×#809C2×C311yescharacteristic
41C23×C3×D3—21no—
42C22×C32×C4—21no—
43C22×C32×C4—21no—
44C22×C32×C4C2311yescharacteristic
45C22×C3×Dic3—21no—
46C22×C3×Dic3D412yes—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12C2×C412yes—
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×C8C2×C412yes—
60C2×C32×C8D412yes—
61C2×C32×C8D412yes—
62C32×C4⋊C4—21no—
63C32×C4⋊C4—21no—
64C32×C4⋊C4—21no—
65C32×C4⋊C4—21no—
66C3×(C2×D3)⋊C4—44no—
67C3×C4×Dic3—21no—
68C3×C4×Dic3—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8D412yes—
72C3×#204—28no—
73#1973—31noSylow
74C22×C3×Q8—31no—
75C22×C3×D4—31no—
76C22×D12C22×C311yescharacteristic
77C22×Dic6C22×C311yescharacteristic
78C2×C3×SD16—34no—
79C2×C3×SD16—62no—
80C2×C3×SD16—62no—
81C22×C3×C8—21no—
82C22×C3×C8—31no—
83C22×C3×C8C2×D311yescharacteristic
84C22×C3×C8C22×C311yescharacteristic
85C2×C3×C4⋊C4—21no—
86C2×C3×C4⋊C4—21no—
87C2×C3×C4⋊C4C2×D311yescharacteristic
88C2×C3×C4⋊C4C2×D311yescharacteristic
89C2×C3×C4⋊C4C22×C311yescharacteristic
90C2×C3×C4⋊C4C22×C311yescharacteristic
91C2×C3×C22⋊C4—62no—
92C2×C3×C42—31no—
93C2×(C2×D3)⋊C4—22no—
94C2×C4×Dic3C22×C311yescharacteristic
95C22×C3⋊C8C22×C311yescharacteristic
96C2×#204—22no—
97C2×#204—22no—
98C2×#204C3×C414yescomplemented
99C3×#107—24no—
100C3×#107—22no—
101C3×#107—22no—
102C3×#103—62no—
103C3×#102—62no—
104C3×#97—62no—
105C3×#95—62no—
106C3⋊#95—22no—
107#815—22no—
108#810—22no—
109#809—22no—
110C23×C32C2×D411yescharacteristic
111C22×C3×D3—22no—
112C22×C3×D3—41no—
113C22×C3×D3—41no—
114C22×C3×D3—42no—
115C22×C3×D3—42no—
116C2×C32×C4—41no—
117C2×C32×C4—41no—
118C2×C32×C4—42no—
119C2×C32×C4—42no—
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4#4111yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C3×Dic3—22no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C3×D12—22no—
133C3×D12—22no—
134C3×D12—41no—
135C3×D12—41no—
136C3×Dic6—22no—
137C3×Dic6—22no—
138C3×Dic6—41no—
139C3×Dic6—41no—
140C32×C8C22⋊C414yescomplemented
141C3×C3⋊C8—22no—
142C22×SD16—31no—
143C2×#107C3×D311yescharacteristic, complemented
144C2×#103—31no—
145C2×#102—31no—
146C2×#97—31no—
147#391—31no—
148#390—31no—
149C24×C3—61no—
150C23×D3—21no—
151C2×C3×Q8—32no—
152C2×C3×Q8—61no—
153C2×C3×Q8—61no—
154C2×C3×Q8—61no—
155C2×C3×Q8—61no—
156C2×C3×Q8—61no—
157C2×C3×D4—32no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—21no—
168C22×C3×C4—32no—
169C22×C3×C4—41no—
170C22×C3×C4—41no—
171C22×C3×C4—61no—
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C23×C311yescharacteristic
174C22×Dic3—21no—
175C22×Dic3C3×D412yes—
176C2×D12—21no—
177C2×D12—21no—
178C2×D12—21no—
179C2×D12—21no—
180C2×D12—21no—
181C2×D12C2×C3×C412yes—
182C2×Dic6—21no—
183C2×Dic6—21no—
184C2×Dic6—21no—
185C2×Dic6—21no—
186C2×Dic6—21no—
187C2×Dic6C2×C3×C412yes—
188C3×SD16—68no—
189C2×C3×C8—22no—
190C2×C3×C8—22no—
191C2×C3×C8—22no—
192C2×C3×C8—32no—
193C2×C3×C8—61no—
194C2×C3×C8—61no—
195C2×C3×C8C4×D312yes—
196C2×C3×C8D1212yes—
197C2×C3×C8#6712yes—
198C2×C3×C8C2×C3×C412yes—
199C2×C3×C8C3×D412yes—
200C2×C3×C8C3×D412yes—
201C3×C4⋊C4—22no—
202C3×C4⋊C4—22no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—21no—
206C3×C4⋊C4—21no—
207C3×C4⋊C4—21no—
208C3×C4⋊C4—21no—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—41no—
212C3×C4⋊C4—41no—
213C3×C22⋊C4—124no—
214C3×C42—61no—
215C3×C42—61no—
216(C2×D3)⋊C4—44no—
217C4×Dic3—21no—
218C4×Dic3—21no—
219C2×C3⋊C8—21no—
220C2×C3⋊C8—21no—
221C2×C3⋊C8C3×D412yes—
222#204—28no—
223C22×C32C4×D411yescharacteristic
224C22×C32#12111yescharacteristic
225C22×C32#12711yescharacteristic
226C22×C32AGL(1,ℤ/8)12yes—
227C22×C32#13712yes—
228C2×C3×D3—42no—
229C2×C3×D3—44no—
230C2×C3×D3—82no—
231C2×C3×D3—81no—
232C2×C3×D3—81no—
233C32×C4—81no—
234C32×C4—81no—
235C32×C4C2×C22⋊C411yescharacteristic
236C32×C4C4×D411yescharacteristic
237C32×C4#12111yescharacteristic
238C32×C4#12411yescharacteristic
239C3×Dic3—42no—
240C3×Dic3—42no—
241C22×Q8—31no—
242C22×D4—31no—
243C2×SD16—34no—
244C2×SD16—62no—
245C2×SD16—62no—
246C22×C8—31no—
247C22×C8C2×C3×D311yescharacteristic
248C2×C4⋊C4C2×C3×D311yescharacteristic
249C2×C4⋊C4C2×C3×D311yescharacteristic
250C2×C22⋊C4—62no—
251C2×C42—31no—
252#107—22no—
253#103—62no—
254#102—62no—
255#97—62no—
256#95—62no—
257C23×C3—21no—
258C23×C3—62no—
259C23×C3—121no—
260C23×C3—122no—
261C23×C3—122no—
262C23×C3—121no—
263C23×C3D3×D411yescharacteristic
264C23×C3C2×C3×D411yescharacteristic
265C22×D3—22no—
266C22×D3—41no—
267C22×D3—41no—
268C22×D3—42no—
269C22×D3—42no—
270C3×Q8—62no—
271C3×Q8—62no—
272C3×Q8—121no—
273C3×Q8—121no—
274C3×D4—62no—
275C3×D4—62no—
276C3×D4—121no—
277C3×D4—121no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—42no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—42no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—42no—
293C2×C3×C4—42no—
294C2×C3×C4—62no—
295C2×C3×C4—62no—
296C2×C3×C4—62no—
297C2×C3×C4—62no—
298C2×C3×C4—82no—
299C2×C3×C4—82no—
300C2×C3×C4—121no—
301C2×C3×C4—121no—
302C2×C3×C4C2×C4×D311yescharacteristic
303C2×C3×C4C2×D1211yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4#23911yescharacteristic
306C2×C3×C4#23911yescharacteristic
307C2×C3×C4C2×#6711yescharacteristic
308C2×C3×C4C22×C3×C411yescharacteristic
309C2×C3×C4C2×C3×D411yescharacteristic
310C2×C3×C4C2×C3×D411yescharacteristic
311C2×C3×C4C2×C3×D411yescharacteristic
312C2×C3×C4C3×#4111yescharacteristic
313C2×C3×C4C3×#4111yescharacteristic
314C2×Dic3—22no—
315C2×Dic3—22no—
316C2×Dic3—22no—
317C2×Dic3—22no—
318C2×Dic3—41no—
319C2×Dic3—41no—
320D12—22no—
321D12—22no—
322D12—41no—
323D12—41no—
324Dic6—22no—
325Dic6—22no—
326Dic6—41no—
327Dic6—41no—
328C3×C8—24no—
329C3×C8—62no—
330C3×C8(C2×D3)⋊C414yescomplemented
331C3×C8C3×C22⋊C414yescomplemented
332C3⋊C8—22no—
333C2×C32#39011yescharacteristic
334C2×C32#44012yes—
335C2×C32#46812yes—
336C2×C32#49611yescharacteristic
337C2×C32#49711yescharacteristic
338C3×D3—82no—
339C24—61no—
340C2×Q8—32no—
341C2×Q8—61no—
342C2×Q8—61no—
343C2×Q8—61no—
344C2×Q8—61no—
345C2×Q8—61no—
346C2×D4—32no—
347C2×D4—61no—
348C2×D4—61no—
349C2×D4—61no—
350C2×D4—61no—
351C2×D4—61no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—32no—
355C22×C4—61no—
356C22×C4C22×C3×D311yescharacteristic
357SD16—68no—
358C2×C8—32no—
359C2×C8—61no—
360C2×C8—61no—
361C2×C8C3×C4×D312yes—
362C2×C8C3×D1212yes—
363C2×C8C3×#6712yes—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C22⋊C4—124no—
369C42—61no—
370C42—61no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—22no—
374C22×C3—22no—
375C22×C3—21no—
376C22×C3—124no—
377C22×C3—122no—
378C22×C3—242no—
379C22×C3—241no—
380C22×C3—241no—
381C22×C3#89311yescharacteristic
382C22×C3#89511yescharacteristic
383C22×C3#91112yes—
384C22×C3#91812yes—
385C22×C3#94011yescharacteristic
386C22×C3C3×C4×D411yescharacteristic
387C22×C3C3×#12111yescharacteristic
388C22×C3C3×#12711yescharacteristic
389C22×C3C3×AGL(1,ℤ/8)12yes—
390C22×C3C3×#13712yes—
391C2×D3—42no—
392C2×D3—44no—
393C2×D3—82no—
394C2×D3—81no—
395C2×D3—81no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—82no—
401C3×C4—82no—
402C3×C4—81no—
403C3×C4—81no—
404C3×C4—81no—
405C3×C4—81no—
406C3×C4—122no—
407C3×C4—122no—
408C3×C4#89311yescharacteristic
409C3×C4#89511yescharacteristic
410C3×C4C2×(C2×D3)⋊C411yescharacteristic
411C3×C4#94711yescharacteristic
412C3×C4C2×C3×C22⋊C411yescharacteristic
413C3×C4C3×C4×D411yescharacteristic
414C3×C4C3×#12111yescharacteristic
415C3×C4C3×#12411yescharacteristic
416Dic3—42no—
417Dic3—42no—
418C32#197311yescharacteristic, complemented, Sylow
419C23—62no—
420C23—121no—
421C23—122no—
422C23—122no—
423C23—121no—
424C23C3×D3×D411yescharacteristic
425Q8—62no—
426Q8—62no—
427Q8—121no—
428Q8—121no—
429D4—62no—
430D4—62no—
431D4—121no—
432D4—121no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—62no—
440C2×C4—62no—
441C2×C4—121no—
442C2×C4—121no—
443C2×C4C2×C3×C4×D311yescharacteristic
444C2×C4C2×C3×D1211yescharacteristic
445C2×C4C3×D3×D411yescharacteristic
446C2×C4C3×#23911yescharacteristic
447C2×C4C3×#23911yescharacteristic
448C2×C4C2×C3×#6711yescharacteristic
449C8—62no—
450C8C3×(C2×D3)⋊C414yescomplemented
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—22no—
454C2×C3—22no—
455C2×C3—21no—
456C2×C3—242no—
457C2×C3#488612yes—
458C2×C3#488912yes—
459C2×C3#498811yescharacteristic
460C2×C3#515411yescharacteristic
461C2×C3#519011yescharacteristic
462C2×C3C3×#39011yescharacteristic
463C2×C3C3×#44012yes—
464C2×C3C3×#46812yes—
465C2×C3C3×#49611yescharacteristic
466C2×C3C3×#49711yescharacteristic
467D3—82no—
468C22—122no—
469C22—124no—
470C22—241no—
471C22—242no—
472C22—241no—
473C22C3×#89311yescharacteristic
474C22C3×#89511yescharacteristic
475C22C3×#91112yes—
476C22C3×#91812yes—
477C22C3×#94011yescharacteristic
478C4—81no—
479C4—81no—
480C4—122no—
481C4—122no—
482C4C3×#89311yescharacteristic
483C4C3×#89511yescharacteristic
484C4C2×C3×(C2×D3)⋊C411yescharacteristic
485C4C3×#94711yescharacteristic
486C3—21no—
487C3#7062911yescharacteristic, direct product factor
488C3C3×#197311yescharacteristic, complemented
489C2—242no—
490C2C3×#488612yes—
491C2C3×#488912yes—
492C2C3×#498811yescharacteristic
493C2C3×#515411yescharacteristic
494C2C3×#519011yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#107C2
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#107D3
hypocenterC3C3×#1973
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#107

Complements

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

NH ≅ G/Ntype
2. C2×C32×#107C2semidirect
3. C2×C3×#815C2semidirect
5. C3×#4973C2semidirect
6. C2×C3×#810C2semidirect
9. #70629C3direct (N × H)
20. C2×C3×#204C4semidirect
29. C2×C3×#107D3semidirect
30. C2×C3×#107C2×C3semidirect
36. C2×#815C2×C3semidirect
38. #4973C2×C3semidirect
39. C2×#810C2×C3semidirect
98. C2×#204C3×C4semidirect
140. C32×C8C22⋊C4semidirect
143. C2×#107C3×D3semidirect
330. C3×C8(C2×D3)⋊C4semidirect
331. C3×C8C3×C22⋊C4semidirect
418. C32#1973semidirect
450. C8C3×(C2×D3)⋊C4semidirect
487. C3#70629direct (N × H)
488. C3C3×#1973semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2042
C2×C32×#1072
C2×C3×#8152
C3×#49882
C3×#49732
C2×C3×#8102
C2×C3×#8092
C3×#19733
#706293