Finite Group Databasebeta

← C3×#72003 #11788336

Subgroups — C3×#72003 #11788336

Order 1152.

825 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×M16C211yesmaximal, characteristic
2C2×C3×#924C211yesmaximal, characteristic
3C3×#5207C211yesmaximal, characteristic
4C2×C3×#824C212yesmaximal, complemented
5C3×#4554C212yesmaximal, complemented
6C3×#1901—31nomaximal
7#72003C311yesmaximal, characteristic, direct product factor
8C23×C32×C4C2211yescharacteristic
9C22×C3×Dic6C2211yescharacteristic
10C2×C32×M16—21no—
11C2×C32×M16—24no—
12C2×C32×M16C2212yes—
13C22×C32×C8—21no—
14C2×C3×#217C412yes—
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C3×#924—21no—
17C3×#924—21no—
18C3×#924—21no—
19C3×#924—21no—
20C2×C3×Dic3⋊C4C412yes—
21C2×C3×#208C2212yes—
22C3×#830—21no—
23C3×#830—21no—
24C3×#824—24no—
25C22×C3×M16—21no—
26C22×C3×M16D311yescharacteristic
27C22×C3×M16C2×C311yescharacteristic
28C2×C3×C22⋊Q8—31no—
29C2×#924C2×C311yescharacteristic
30C2×C3×#101—32no—
31C3×#407—31no—
32#5207C2×C311yescharacteristic
33C2×#824C2×C312yescomplemented
34C3×#343—32no—
35#4554C2×C312yescomplemented
36C24×C32C2×C411yescharacteristic
37C22×C32×C4—22no—
38C22×C32×C4—22no—
39C22×C32×C4C2×C411yescharacteristic
40C22×C32×C4D411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C22×C32×C4D411yescharacteristic
43C22×C32×C4D411yescharacteristic
44C22×C32×C4C2311yescharacteristic
45C22×C3×Dic3C2×C412yes—
46C22×C3×Dic3C2×C412yes—
47C2×C3×Dic6—21no—
48C2×C3×Dic6—21no—
49C2×C3×Dic6—22no—
50C2×C3×Dic6—22no—
51C32×M16—24no—
52C32×M16—22no—
53C32×M16D414yes—
54C2×C32×C8—24no—
55C2×C32×C8—22no—
56C3×#217—22no—
57C3×#217—22no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×Dic3⋊C4—22no—
61C3×Dic3⋊C4—22no—
62C3×#208—22no—
63C3×#208—22no—
64C2×C3×C3⋊C8—22no—
65#1901—31noSylow
66C22×C3×Q8—31no—
67C23×C3×C4—21no—
68C23×C3×C4C2×D311yescharacteristic
69C23×C3×C4C22×C311yescharacteristic
70C22×Dic6C22×C311yescharacteristic
71C2×C3×M16—22no—
72C2×C3×M16—28no—
73C2×C3×M16—21no—
74C2×C3×M16—21no—
75C2×C3×M16—24no—
76C2×C3×M16—24no—
77C2×C3×M16—22no—
78C2×C3×M16—32no—
79C2×C3×M16C2×D312yes—
80C2×C3×M16C22×C312yes—
81C22×C3×C8—22no—
82C22×C3×C8—21no—
83C22×C3×C8—21no—
84C3×C22⋊Q8—61no—
85C3×C22⋊Q8—61no—
86C3×C22⋊Q8—61no—
87C3×C22⋊Q8—61no—
88C2×C3×C4⋊C4—32no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C22⋊C4—32no—
91C2×#217C3×C412yes—
92C2×C4⋊Dic3C22×C311yescharacteristic
93#924—21no—
94#924—21no—
95#924—21no—
96#924—21no—
97C2×Dic3⋊C4C3×C412yes—
98C2×#208C22×C312yes—
99C3×#101—64no—
100C3×C22⋊C8—61no—
101C3×C22⋊C8—61no—
102#830—21no—
103#830—21no—
104#824—24no—
105C23×C32—22no—
106C23×C32—22no—
107C23×C32—41no—
108C23×C32C22⋊C411yescharacteristic
109C23×C32C22⋊C411yescharacteristic
110C23×C32C22×C411yescharacteristic
111C2×C32×C4—22no—
112C2×C32×C4—21no—
113C2×C32×C4—21no—
114C2×C32×C4—22no—
115C2×C32×C4—22no—
116C2×C32×C4—21no—
117C2×C32×C4—21no—
118C2×C32×C4C22⋊C411yescharacteristic
119C2×C32×C4C22⋊C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D412yes—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4#4112yes—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—24no—
127C2×C3×Dic3—42no—
128C3×Dic6—41no—
129C3×Dic6—42no—
130C3×Dic6—41no—
131C32×C8—24no—
132C3×C3⋊C8—42no—
133C22×M16C3×D311yescharacteristic
134C2×C22⋊Q8—31no—
135C2×#101—32no—
136#407—31no—
137#343—32no—
138C24×C3—21no—
139C24×C3C4×D311yescharacteristic
140C24×C3C2×C3×C411yescharacteristic
141C2×C3×Q8—61no—
142C2×C3×Q8—62no—
143C2×C3×Q8—62no—
144C2×C3×Q8—61no—
145C22×C3×C4—24no—
146C22×C3×C4—24no—
147C22×C3×C4—22no—
148C22×C3×C4—22no—
149C22×C3×C4—22no—
150C22×C3×C4—22no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—32no—
158C22×C3×C4—32no—
159C22×C3×C4C4×D311yescharacteristic
160C22×C3×C4D1211yescharacteristic
161C22×C3×C4D1211yescharacteristic
162C22×C3×C4#6711yescharacteristic
163C22×C3×C4#6711yescharacteristic
164C22×C3×C4C2×C3×C411yescharacteristic
165C22×C3×C4C3×D411yescharacteristic
166C22×C3×C4C3×D411yescharacteristic
167C22×C3×C4C3×D411yescharacteristic
168C22×C3×C4C3×D411yescharacteristic
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C23×C311yescharacteristic
171C22×Dic3C2×C3×C412yes—
172C22×Dic3C2×C3×C412yes—
173C2×Dic6—22no—
174C2×Dic6—21no—
175C2×Dic6—21no—
176C2×Dic6—22no—
177C3×M16—28no—
178C3×M16—24no—
179C3×M16—24no—
180C3×M16—24no—
181C3×M16—22no—
182C3×M16—22no—
183C3×M16—24no—
184C3×M16—62no—
185C3×M16—62no—
186C3×M16#6714yes—
187C3×M16C3×D414yes—
188C2×C3×C8—28no—
189C2×C3×C8—24no—
190C2×C3×C8—24no—
191C2×C3×C8—24no—
192C2×C3×C8—22no—
193C2×C3×C8—22no—
194C2×C3×C8—62no—
195C3×C4⋊C4—62no—
196C3×C4⋊C4—62no—
197C3×C4⋊C4—61no—
198C3×C4⋊C4—61no—
199C3×C22⋊C4—62no—
200C3×C22⋊C4—62no—
201#217—22no—
202#217—22no—
203C4⋊Dic3—21no—
204C4⋊Dic3—21no—
205Dic3⋊C4—22no—
206Dic3⋊C4—22no—
207#208—22no—
208#208—22no—
209C2×C3⋊C8—22no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32—21no—
213C22×C32—21no—
214C22×C32—21no—
215C22×C32—21no—
216C22×C32—21no—
217C22×C32—44no—
218C22×C32#10112yescomplemented
219C22×C32C2×C22⋊C411yescharacteristic
220C22×C32C4×D412yes—
221C32×C4—21no—
222C32×C4—21no—
223C32×C4#12011yescharacteristic
224C32×C4#12112yes—
225C32×C4#12311yescharacteristic
226C3×Dic3—42no—
227C3×Dic3—42no—
228C22×Q8—31no—
229C23×C4C2×C3×D311yescharacteristic
230C2×M16—21no—
231C2×M16—24no—
232C2×M16—32no—
233C2×M16C2×C3×D312yes—
234C22×C8—21no—
235C22⋊Q8—61no—
236C22⋊Q8—61no—
237C22⋊Q8—61no—
238C22⋊Q8—61no—
239C2×C4⋊C4—32no—
240C2×C4⋊C4—31no—
241C2×C22⋊C4—32no—
242#101—64no—
243C22⋊C8—61no—
244C22⋊C8—61no—
245C23×C3—24no—
246C23×C3—22no—
247C23×C3—22no—
248C23×C3—22no—
249C23×C3—22no—
250C23×C3—21no—
251C23×C3—21no—
252C23×C3—21no—
253C23×C3—42no—
254C23×C3—41no—
255C23×C3—41no—
256C23×C3—42no—
257C23×C3(C2×D3)⋊C411yescharacteristic
258C23×C3(C2×D3)⋊C411yescharacteristic
259C23×C3C3×C22⋊C411yescharacteristic
260C23×C3C3×C22⋊C411yescharacteristic
261C23×C3C2×C4×D311yescharacteristic
262C23×C3C22×C3×C411yescharacteristic
263C3×Q8—121no—
264C3×Q8—122no—
265C3×Q8—121no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—24no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—24no—
272C2×C3×C4—24no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—22no—
291C2×C3×C4—21no—
292C2×C3×C4—22no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—64no—
296C2×C3×C4—122no—
297C2×C3×C4(C2×D3)⋊C411yescharacteristic
298C2×C3×C4(C2×D3)⋊C411yescharacteristic
299C2×C3×C4C3×C22⋊C411yescharacteristic
300C2×C3×C4C3×C22⋊C411yescharacteristic
301C2×C3×C4C2×D1211yescharacteristic
302C2×C3×C4#23512yes—
303C2×C3×C4C2×#6711yescharacteristic
304C2×C3×C4C2×#6712yes—
305C2×C3×C4C2×C3×D411yescharacteristic
306C2×C3×C4C2×C3×D412yes—
307C2×C3×C4C2×C3×D411yescharacteristic
308C2×C3×C4C3×#4112yes—
309C2×Dic3—22no—
310C2×Dic3—22no—
311C2×Dic3—24no—
312C2×Dic3—42no—
313Dic6—41no—
314Dic6—42no—
315Dic6—41no—
316C3×C8—28no—
317C3×C8—24no—
318C3×C8—24no—
319C3×C8—122no—
320C3⋊C8—42no—
321C2×C32—22no—
322C2×C32—22no—
323C2×C32—41no—
324C2×C32#38611yescharacteristic
325C2×C32C2×#10111yescharacteristic
326C2×C32#41311yescharacteristic
327C24C3×C4×D311yescharacteristic
328C2×Q8—61no—
329C2×Q8—62no—
330C2×Q8—62no—
331C2×Q8—61no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—32no—
335C22×C4—32no—
336C22×C4C3×C4×D311yescharacteristic
337C22×C4C3×D1211yescharacteristic
338C22×C4C3×D1211yescharacteristic
339C22×C4C3×#6711yescharacteristic
340C22×C4C3×#6711yescharacteristic
341C22×C4C22×C3×D311yescharacteristic
342M16—24no—
343M16—22no—
344M16—62no—
345M16—62no—
346M16C3×#6714yes—
347C2×C8—24no—
348C2×C8—22no—
349C2×C8—62no—
350C4⋊C4—62no—
351C4⋊C4—62no—
352C4⋊C4—61no—
353C4⋊C4—61no—
354C22⋊C4—62no—
355C22⋊C4—62no—
356C22×C3—22no—
357C22×C3—22no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—22no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—22no—
375C22×C3—22no—
376C22×C3—41no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—41no—
380C22×C3—44no—
381C22×C3—44no—
382C22×C3—48no—
383C22×C3#82412yescomplemented
384C22×C3C3×#10112yescomplemented
385C22×C3C2×(C2×D3)⋊C411yescharacteristic
386C22×C3C4×#6712yes—
387C22×C3C2×C3×C22⋊C411yescharacteristic
388C22×C3C3×C4×D412yes—
389C3×C4—22no—
390C3×C4—22no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—22no—
397C3×C4—21no—
398C3×C4—122no—
399C3×C4—122no—
400C3×C4#92911yescharacteristic
401C3×C4#93012yes—
402C3×C4#95311yescharacteristic
403C3×C4C3×#12011yescharacteristic
404C3×C4C3×#12112yes—
405C3×C4C3×#12311yescharacteristic
406Dic3—42no—
407Dic3—42no—
408C32#190111yescharacteristic, complemented, Sylow
409C23—22no—
410C23—22no—
411C23—41no—
412C23C3×(C2×D3)⋊C411yescharacteristic
413C23C3×(C2×D3)⋊C411yescharacteristic
414C23C2×C3×C4×D311yescharacteristic
415Q8—121no—
416Q8—122no—
417Q8—121no—
418C2×C4—22no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—64no—
428C2×C4—122no—
429C2×C4C3×(C2×D3)⋊C411yescharacteristic
430C2×C4C3×(C2×D3)⋊C411yescharacteristic
431C2×C4C2×C3×D1211yescharacteristic
432C2×C4C3×#23512yes—
433C2×C4C2×C3×#6711yescharacteristic
434C2×C4C2×C3×#6712yes—
435C8—24no—
436C8—122no—
437C2×C3—24no—
438C2×C3—22no—
439C2×C3—22no—
440C2×C3—22no—
441C2×C3—22no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—42no—
446C2×C3—42no—
447C2×C3—41no—
448C2×C3—41no—
449C2×C3#513211yescharacteristic
450C2×C3C2×#82411yescharacteristic
451C2×C3#521311yescharacteristic
452C2×C3C3×#38611yescharacteristic
453C2×C3C2×C3×#10111yescharacteristic
454C2×C3C3×#41311yescharacteristic
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—44no—
463C22C3×#82412yescomplemented
464C22C2×C3×(C2×D3)⋊C411yescharacteristic
465C22C3×C4×#6712yes—
466C4—21no—
467C4—21no—
468C4—122no—
469C4—122no—
470C4C3×#92911yescharacteristic
471C4C3×#93012yes—
472C4C3×#95311yescharacteristic
473C3—21no—
474C3#7200311yescharacteristic, direct product factor
475C3C3×#190111yescharacteristic, complemented
476C2—22no—
477C2—22no—
478C2—41no—
479C2C3×#513211yescharacteristic
480C2C2×C3×#82411yescharacteristic
481C2C3×#521311yescharacteristic
subgroupG/H
centerC22×C3C2×(C2×D3)⋊C4
commutatorC23×C3C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC22×C32×M16C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C3×C4C23×C3
hypercenterC22×C3×M16D3
hypocenterC3C3×#1901
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C22×C3×M16

Complements

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

NH ≅ G/Ntype
4. C2×C3×#824C2semidirect
5. C3×#4554C2semidirect
7. #72003C3direct (N × H)
33. C2×#824C2×C3semidirect
35. #4554C2×C3semidirect
218. C22×C32#101semidirect
383. C22×C3#824semidirect
384. C22×C3C3×#101semidirect
408. C32#1901semidirect
463. C22C3×#824semidirect
474. C3#72003direct (N × H)
475. C3C3×#1901semidirect

Maximal subgroups

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

subgroupindex
C22×C32×M162
C2×C3×#9242
C3×#52072
C2×C3×#8242
C3×#45542
C3×#19013
#720033