Finite Group Databasebeta

← C3×#70141 #11785001

Subgroups — C3×#70141 #11785001

Order 1152.

1147 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic
2C32×#413C211yesmaximal, characteristic, complemented
3C3×#5240C211yesmaximal, characteristic, complemented
4C3×#5139C212yesmaximal, complemented
5C3×#5120C212yesmaximal, complemented
6C3×#1796—31nomaximal
7#70141C311yesmaximal, characteristic, direct product factor
8C2×C32×#41C2211yescharacteristic
9C3×#1010—24no—
10C3×#1010—24no—
11C2×C3×D3×Q8—21no—
12C2×C3×#237—22no—
13C2×C3×#237—21no—
14C2×C3×#235C412yescomplemented
15C2×C3×#235C2211yescharacteristic
16C22×C3×Dic6C412yescomplemented
17C22×C3×Dic6C2211yescharacteristic
18C2×C32×M16C2212yes—
19C3×#926C2212yes—
20C32×#101—21no—
21C32×#100—21no—
22C3×#834—22no—
23C3×#825—24no—
24C3×#816—24no—
25C2×C3×2−1+4—31no—
26C2×#1010C2×C311yescharacteristic
27C3×#421—32no—
28C3×#419—32no—
29C3×#413—21no—
30C3×#413D311yescharacteristic, complemented
31C3×#413C2×C311yescharacteristic, complemented
32C3×#410—31no—
33#5240C2×C311yescharacteristic, complemented
34#5139C2×C312yescomplemented
35#5120C2×C312yescomplemented
36C32×#41—22no—
37C32×#41—22no—
38C2×C32×Q8D411yescharacteristic
39C2×C32×D4D412yes—
40C2×C32×D4D411yescharacteristic
41C22×C32×C4C2×C412yes—
42C22×C32×C4C2311yescharacteristic
43C2×C3×#67—22no—
44C2×C3×#67—21no—
45C22×C3×Dic3—22no—
46C22×C3×Dic3—21no—
47C3×D3×Q8—28no—
48C3×#237—216no—
49C3×#237—28no—
50C3×#235—22no—
51C3×#235—24no—
52C3×#235—24no—
53C3×#235D414yes—
54C2×C3×D12C2×C411yescharacteristic
55C2×C3×C4×D3—22no—
56C2×C3×C4×D3—21no—
57C2×C3×Dic6—22no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—22no—
60C2×C3×Dic6—24no—
61C2×C3×Dic6—24no—
62C2×C3×Dic6C2×C411yescharacteristic
63C2×C3×Dic6C2×C412yes—
64C2×C3×Dic6D414yes—
65C32×M16—22no—
66C32×M16—22no—
67C2×C32×C8—22no—
68C3×#217—22no—
69C3×C4⋊Dic3—22no—
70C3×C4×Dic3—22no—
71#1796—31noSylow
72C3×2−1+4—64no—
73C3×2−1+4—64no—
74C2×C3×#41—21no—
75C2×C3×#41—32no—
76C2×C3×#41—31no—
77C2×C3×#41—62no—
78C2×C3×#41—61no—
79C2×C3×#41C2×D311yescharacteristic
80C2×C3×#41C22×C311yescharacteristic
81C22×C3×Q8—32no—
82C22×C3×Q8—31no—
83C22×C3×Q8—61no—
84#1010—24no—
85#1010—24no—
86C2×D3×Q8—21no—
87C2×#237—22no—
88C2×#237—21no—
89C2×#235C3×C412yescomplemented
90C2×#235C22×C311yescharacteristic
91C22×Dic6C3×C412yescomplemented
92C22×Dic6C22×C311yescharacteristic
93C2×C3×M16—22no—
94C2×C3×M16C2×D312yes—
95C2×C3×M16C22×C312yes—
96C3×#117—32no—
97#926C22×C312yes—
98C3×#104—64no—
99C3×#103—64no—
100C3×#101—22no—
101C3×#101—21no—
102C3×#101—21no—
103C3×#100—22no—
104C3×#100—21no—
105C3×#100—21no—
106C3×#99—62no—
107#834—22no—
108#825—24no—
109#816—24no—
110C23×C32C22⋊C412yes—
111C23×C32C2×D411yescharacteristic
112C22×C3×D3—21no—
113C32×Q8—22no—
114C32×D4—24no—
115C32×D4—22no—
116C2×C32×C4—22no—
117C2×C32×C4—22no—
118C2×C32×C4C22⋊C412yes—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D412yes—
121C2×C32×C4C2×D412yes—
122C2×C32×C4C2×D411yescharacteristic
123C3×#67—28no—
124C3×#67—24no—
125C2×C3×Dic3—28no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—24no—
129C2×C3×Dic3—42no—
130C3×D12—21no—
131C3×D12C22⋊C412yes—
132C3×C4×D3—28no—
133C3×C4×D3—24no—
134C3×Dic6—28no—
135C3×Dic6—22no—
136C3×Dic6—21no—
137C3×Dic6—24no—
138C3×Dic6C22⋊C412yes—
139C3×Dic6C22⋊C414yes—
140C32×C8—42no—
141C2×2−1+4—31no—
142#421—32no—
143#419—32no—
144#413C3×D311yescharacteristic, complemented
145#410—31no—
146C3×#41—22no—
147C3×#41—22no—
148C3×#41—22no—
149C3×#41—22no—
150C3×#41—34no—
151C3×#41—42no—
152C3×#41—42no—
153C3×#41—64no—
154C3×#41—64no—
155C3×#41—616no—
156C3×#41—68no—
157C3×#41—62no—
158C2×C3×Q8—21no—
159C2×C3×Q8—32no—
160C2×C3×Q8—31no—
161C2×C3×Q8—34no—
162C2×C3×Q8—64no—
163C2×C3×Q8—64no—
164C2×C3×Q8—68no—
165C2×C3×Q8—62no—
166C2×C3×Q8—62no—
167C2×C3×Q8—61no—
168C2×C3×Q8#6711yescharacteristic
169C2×C3×Q8C3×D411yescharacteristic
170C2×C3×D4—22no—
171C2×C3×D4—21no—
172C2×C3×D4—31no—
173C2×C3×D4—62no—
174C2×C3×D4—61no—
175C2×C3×D4D1212yes—
176C2×C3×D4#6711yescharacteristic
177C2×C3×D4C3×D412yes—
178C2×C3×D4C3×D411yescharacteristic
179C22×C3×C4—22no—
180C22×C3×C4—21no—
181C22×C3×C4—62no—
182C22×C3×C4—61no—
183C22×C3×C4—62no—
184C22×C3×C4—61no—
185C22×C3×C4C4×D312yes—
186C22×C3×C4C2×C3×C412yes—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C23×C311yescharacteristic
189C2×#67—22no—
190C2×#67—21no—
191C22×Dic3—22no—
192C22×Dic3—21no—
193D3×Q8—28no—
194#237—216no—
195#237—28no—
196#235—22no—
197#235—24no—
198#235—24no—
199#235C3×D414yes—
200C2×D12C2×C3×C411yescharacteristic
201C2×C4×D3—22no—
202C2×C4×D3—21no—
203C2×Dic6—22no—
204C2×Dic6—21no—
205C2×Dic6—22no—
206C2×Dic6—24no—
207C2×Dic6—24no—
208C2×Dic6C2×C3×C411yescharacteristic
209C2×Dic6C2×C3×C412yes—
210C2×Dic6C3×D414yes—
211C3×M16—24no—
212C3×M16—22no—
213C3×M16—22no—
214C3×M16—22no—
215C3×M16—22no—
216C3×M16—42no—
217C2×C3×C8—22no—
218C2×C3×C8—22no—
219C2×C3×C8—42no—
220C3×C4⋊C4—62no—
221C3×C22⋊C4—62no—
222C3×C42—62no—
223#217—22no—
224C4⋊Dic3—22no—
225C4×Dic3—22no—
226C22×C32—22no—
227C22×C32—41no—
228C22×C32—42no—
229C22×C32C2×C22⋊C411yescharacteristic
230C22×C32#12012yes—
231C2×C3×D3—22no—
232C2×C3×D3—42no—
233C32×C4—22no—
234C32×C4C2×C22⋊C411yescharacteristic
235C32×C4C2×C22⋊C411yescharacteristic
236C32×C4#12012yes—
237C3×Dic3—22no—
238C3×Dic3—24no—
239C3×Dic3—82no—
2402−1+4—64no—
2412−1+4—64no—
242C2×#41—32no—
243C2×#41—31no—
244C2×#41—62no—
245C2×#41—61no—
246C2×#41C2×C3×D311yescharacteristic
247C22×Q8—32no—
248C22×Q8—31no—
249C22×Q8—61no—
250C2×M16C2×C3×D312yes—
251#117—32no—
252#104—64no—
253#103—64no—
254#101—21no—
255#100—21no—
256#99—62no—
257C23×C3—22no—
258C23×C3—21no—
259C23×C3—61no—
260C23×C3(C2×D3)⋊C412yes—
261C23×C3C3×C22⋊C412yes—
262C23×C3C2×D1211yescharacteristic
263C23×C3C2×C3×D411yescharacteristic
264C22×D3—21no—
265C3×Q8—22no—
266C3×Q8—22no—
267C3×Q8—34no—
268C3×Q8—32no—
269C3×Q8—42no—
270C3×Q8—68no—
271C3×Q8—62no—
272C3×Q8—61no—
273C3×Q8—64no—
274C3×D4—24no—
275C3×D4—24no—
276C3×D4—22no—
277C3×D4—22no—
278C3×D4—32no—
279C3×D4—42no—
280C3×D4—44no—
281C3×D4—68no—
282C3×D4—64no—
283C3×D4—61no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—21no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—21no—
293C2×C3×C4—42no—
294C2×C3×C4—42no—
295C2×C3×C4—68no—
296C2×C3×C4—68no—
297C2×C3×C4—64no—
298C2×C3×C4—61no—
299C2×C3×C4—62no—
300C2×C3×C4—64no—
301C2×C3×C4—122no—
302C2×C3×C4(C2×D3)⋊C412yes—
303C2×C3×C4C3×C22⋊C412yes—
304C2×C3×C4C2×C4×D311yescharacteristic
305C2×C3×C4D3×D412yes—
306C2×C3×C4D3×D412yes—
307C2×C3×C4C2×#6711yescharacteristic
308C2×C3×C4C22×C3×C411yescharacteristic
309C2×C3×C4C2×C3×D412yes—
310C2×C3×C4C2×C3×D412yes—
311C2×C3×C4C2×C3×D411yescharacteristic
312#67—28no—
313#67—24no—
314C2×Dic3—28no—
315C2×Dic3—21no—
316C2×Dic3—22no—
317C2×Dic3—24no—
318C2×Dic3—42no—
319D12—21no—
320D12C3×C22⋊C412yes—
321C4×D3—28no—
322C4×D3—24no—
323Dic6—28no—
324Dic6—22no—
325Dic6—21no—
326Dic6—24no—
327Dic6C3×C22⋊C412yes—
328Dic6C3×C22⋊C414yes—
329C3×C8—44no—
330C3×C8—42no—
331C3×C8—42no—
332C2×C32—22no—
333C2×C32—21no—
334C2×C32—42no—
335C2×C32#37911yescharacteristic
336C3×D3—42no—
337#41—22no—
338#41—22no—
339#41—34no—
340#41—64no—
341#41—64no—
342#41—616no—
343#41—68no—
344#41—62no—
345C2×Q8—32no—
346C2×Q8—31no—
347C2×Q8—34no—
348C2×Q8—64no—
349C2×Q8—64no—
350C2×Q8—68no—
351C2×Q8—62no—
352C2×Q8—62no—
353C2×Q8—61no—
354C2×Q8C3×#6711yescharacteristic
355C2×D4—31no—
356C2×D4—62no—
357C2×D4—61no—
358C2×D4C3×D1212yes—
359C2×D4C3×#6711yescharacteristic
360C22×C4—62no—
361C22×C4—61no—
362C22×C4—62no—
363C22×C4—61no—
364C22×C4C3×C4×D312yes—
365C22×C4C22×C3×D311yescharacteristic
366M16—22no—
367M16—22no—
368C2×C8—22no—
369C4⋊C4—62no—
370C22⋊C4—62no—
371C42—62no—
372C22×C3—22no—
373C22×C3—22no—
374C22×C3—22no—
375C22×C3—21no—
376C22×C3—42no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—42no—
380C22×C3—42no—
381C22×C3—62no—
382C22×C3—81no—
383C22×C3—82no—
384C22×C3—122no—
385C22×C3#88212yes—
386C22×C3C2×(C2×D3)⋊C411yescharacteristic
387C22×C3C2×C3×C22⋊C411yescharacteristic
388C22×C3C3×#12012yes—
389C2×D3—22no—
390C2×D3—42no—
391C3×C4—22no—
392C3×C4—22no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—22no—
396C3×C4—42no—
397C3×C4—64no—
398C3×C4—62no—
399C3×C4—242no—
400C3×C4D3×C22⋊C411yescharacteristic
401C3×C4D3×C22⋊C411yescharacteristic
402C3×C4#93712yes—
403C3×C4C2×C3×C22⋊C411yescharacteristic
404C3×C4C2×C3×C22⋊C411yescharacteristic
405C3×C4C3×#12012yes—
406Dic3—22no—
407Dic3—24no—
408Dic3—82no—
409C32#179611yescharacteristic, complemented, Sylow
410C23—61no—
411C23C3×(C2×D3)⋊C412yes—
412C23C2×C3×D1211yescharacteristic
413Q8—22no—
414Q8—34no—
415Q8—32no—
416Q8—68no—
417Q8—62no—
418Q8—61no—
419Q8—64no—
420D4—24no—
421D4—22no—
422D4—32no—
423D4—68no—
424D4—64no—
425D4—61no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—68no—
429C2×C4—68no—
430C2×C4—64no—
431C2×C4—61no—
432C2×C4—62no—
433C2×C4—64no—
434C2×C4—122no—
435C2×C4C3×(C2×D3)⋊C412yes—
436C2×C4C2×C3×C4×D311yescharacteristic
437C2×C4C3×D3×D412yes—
438C2×C4C3×D3×D412yes—
439C2×C4C2×C3×#6711yescharacteristic
440C8—42no—
441C2×C3—22no—
442C2×C3—21no—
443C2×C3—22no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—41no—
447C2×C3—42no—
448C2×C3—42no—
449C2×C3—42no—
450C2×C3—82no—
451C2×C3—122no—
452C2×C3#495511yescharacteristic
453C2×C3C3×#37911yescharacteristic
454D3—42no—
455C22—22no—
456C22—41no—
457C22—42no—
458C22—62no—
459C22—122no—
460C22C3×#88212yes—
461C22C2×C3×(C2×D3)⋊C411yescharacteristic
462C4—22no—
463C4—64no—
464C4—62no—
465C4—242no—
466C4C3×D3×C22⋊C411yescharacteristic
467C4C3×D3×C22⋊C411yescharacteristic
468C4C3×#93712yes—
469C3—21no—
470C3#7014111yescharacteristic, direct product factor
471C3C3×#179611yescharacteristic, complemented
472C2—22no—
473C2—21no—
474C2—42no—
475C2—122no—
476C2C3×#495511yescharacteristic
subgroupG/H
centerC2×C3#4955
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#413C2
socleC2×C32#379
prime radicalC2×C3×#1010C2
cosocleC22×C3×C4C23×C3
hypercenterC3×#413D3
hypocenterC3C3×#1796
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#413

Complements

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

NH ≅ G/Ntype
2. C32×#413C2semidirect
3. C3×#5240C2semidirect
4. C3×#5139C2semidirect
5. C3×#5120C2semidirect
7. #70141C3direct (N × H)
14. C2×C3×#235C4semidirect
16. C22×C3×Dic6C4semidirect
30. C3×#413D3semidirect
31. C3×#413C2×C3semidirect
33. #5240C2×C3semidirect
34. #5139C2×C3semidirect
35. #5120C2×C3semidirect
89. C2×#235C3×C4semidirect
91. C22×Dic6C3×C4semidirect
144. #413C3×D3semidirect
409. C32#1796semidirect
470. C3#70141direct (N × H)
471. C3C3×#1796semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C32×#4132
C3×#52402
C3×#51392
C3×#51202
C3×#17963
#701413