Finite Group Databasebeta

← C2×D3×#807 #11858402

Subgroups — C2×D3×#807 #11858402

Order 1152.

1265 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C4⋊C4C211yesmaximal, characteristic
2C2×D3×C4⋊Dic3C211yesmaximal, characteristic
3C22×D3×C3⋊C8C211yesmaximal, characteristic
4C2×#63634C211yesmaximal, characteristic, complemented
5C2×C3×#807C211yesmaximal, characteristic, complemented
6C2×#63576C211yesmaximal, characteristic, complemented
7C2×#63575C211yesmaximal, characteristic, complemented
8D3×#807C218yesmaximal, direct product factor
9C22×#807—31nomaximal
10C2×D3×#107—31nomaximal
11C22×C3×C4×D3—21no—
12C22×C3×C4×D3C2211yescharacteristic
13C22×D3×Dic3—21no—
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×Dic3⋊C4—21no—
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×D3×C4⋊C4—22no—
22C3×D3×C4⋊C4C2214yes—
23C2×Dic3⋊Dic3—21no—
24D3×C4⋊Dic3—22no—
25D3×C4⋊Dic3C2214yes—
26C2×D3×C3⋊C8C418yescomplemented
27C2×D3×C3⋊C8C2214yes—
28#63634C2214yescomplemented
29C3×#807C2214yescomplemented
30#63576C2214yescomplemented
31#63575C2214yescomplemented
32C22×C3×C4⋊C4—31no—
33C22×C4⋊Dic3—31no—
34C23×C3⋊C8—31no—
35C22×D3×C8—31no—
36C2×D3×C4⋊C4—31no—
37C2×D3×C4⋊C4D311yescharacteristic
38C2×C3×#107—31no—
39C2×#818—31no—
40C2×#807—31no—
41C2×#807—31no—
42C2×#807—31no—
43C2×#807—31no—
44C2×#807—31no—
45C2×#807—38no—
46C2×#807—61no—
47C2×#807D311yescharacteristic, direct product factor
48D3×#107—38no—
49C23×C3×D3D411yescharacteristic
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3D411yescharacteristic
56C2×C3×C4×D3—24no—
57C2×C3×C4×D3—44no—
58C2×C3×C4×D3C2×C414yes—
59C2×C3×C4×D3D412yes—
60C2×C3×C4×D3Q814yes—
61C2×C3×C4×D3C2312yes—
62C2×D3×Dic3—24no—
63C2×D3×Dic3—44no—
64C32×C4⋊C4—21no—
65C32×C4⋊C4C2312yes—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)C2312yes—
68C2×C3⋊(C3⋊C8)C2×C414yescomplemented
69C2×C3⋊(C3⋊C8)C2312yes—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3C2312yes—
73C3×C4⋊Dic3C2312yes—
74C3×Dic3⋊C4—24no—
75C2×C3×C3⋊C8C2×C414yescomplemented
76C2×C3×C3⋊C8C2312yes—
77Dic3⋊Dic3—24no—
78D3×C3⋊C8C2×C4116yescomplemented
79C22×#107—91noSylow
80C23×C3×C4—31no—
81C23×C3×C4—61no—
82C23×Dic3—61no—
83C22×C4×D3—21no—
84C22×C4×D3—61no—
85C22×C4×D3C2×D311yescharacteristic
86C22×C3×C8—31no—
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4—31no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4—34no—
91C2×C3×C4⋊C4—62no—
92C2×C3×C4⋊C4—61no—
93C2×C3×C4⋊C4C2×D311yescharacteristic
94C2×C3×C4⋊C4C2×D311yescharacteristic
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—34no—
98C2×C4⋊Dic3—61no—
99C2×C4⋊Dic3—62no—
100C2×C4⋊Dic3—61no—
101C2×C4⋊Dic3C2×D311yescharacteristic
102C2×C4⋊Dic3C2×D311yescharacteristic
103C2×Dic3⋊C4—21no—
104C2×Dic3⋊C4—61no—
105C22×C3⋊C8—31no—
106C22×C3⋊C8—31no—
107C22×C3⋊C8—38no—
108C22×C3⋊C8—34no—
109C22×C3⋊C8—61no—
110C22×C3⋊C8C2×D311yescharacteristic
111C2×D3×C8—38no—
112C2×D3×C8—34no—
113D3×C4⋊C4—22no—
114D3×C4⋊C4—34no—
115D3×C4⋊C4—62no—
116D3×C4⋊C4C2×D314yes—
117C3×#107—34no—
118#818—34no—
119#807—34no—
120#807—34no—
121#807—34no—
122#807—34no—
123#807—34no—
124#807—64no—
125#807C2×D314yesdirect product factor
126C23×C32C2×D411yescharacteristic
127C22×C3×D3C4⋊C414yes—
128C22×C3×D3D814yes—
129C22×C3×D3Q1614yes—
130C22×C3×D3C2×D412yes—
131C2×C32×C4—22no—
132C2×C32×C4—42no—
133C2×C32×C4C22×C412yes—
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×Q812yes—
136C2×C32×C4C2411yescharacteristic
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—42no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—42no—
142C2×C3×Dic3—42no—
143C2×C3×Dic3C4⋊C414yes—
144C2×C3×Dic3C2×D412yes—
145C3×C4×D3—48no—
146C3×C4×D3C4⋊C418yes—
147C3×C4×D3C22×C414yes—
148C3×C4×D3C2×Q814yes—
149D3×Dic3—48no—
150C3⋊(C3⋊C8)C22×C414yescomplemented
151C3×C3⋊C8C22×C414yescomplemented
152C23×C8—91no—
153C22×C4⋊C4—31no—
154C22×C4⋊C4—91no—
155C2×#107—31no—
156C2×#107—98no—
157C2×#107—91no—
158C2×#107—91no—
159C2×#107—91no—
160C24×C3—31no—
161C23×D3#6711yescharacteristic
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—31no—
166C22×C3×C4—34no—
167C22×C3×C4—32no—
168C22×C3×C4—34no—
169C22×C3×C4—32no—
170C22×C3×C4—41no—
171C22×C3×C4—64no—
172C22×C3×C4—61no—
173C22×C3×C4—61no—
174C22×C3×C4—124no—
175C22×C3×C4C22×D311yescharacteristic
176C22×C3×C4C22×D311yescharacteristic
177C22×Dic3—21no—
178C22×Dic3—21no—
179C22×Dic3—64no—
180C22×Dic3—61no—
181C22×Dic3—61no—
182C22×Dic3—121no—
183C22×Dic3—124no—
184C22×Dic3#6711yescharacteristic
185C2×C4×D3—24no—
186C2×C4×D3—44no—
187C2×C4×D3—64no—
188C2×C4×D3—124no—
189C2×C4×D3Dic614yes—
190C2×C4×D3C4×D314yes—
191C2×C4×D3#6712yes—
192C2×C4×D3C22×D312yes—
193C2×C3×C8—34no—
194C2×C3×C8—32no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—22no—
198C3×C4⋊C4—32no—
199C3×C4⋊C4—32no—
200C3×C4⋊C4—41no—
201C3×C4⋊C4—64no—
202C3×C4⋊C4—61no—
203C3×C4⋊C4—61no—
204C3×C4⋊C4C22×D312yes—
205C3×C4⋊C4C22×D312yes—
206C4⋊Dic3—21no—
207C4⋊Dic3—21no—
208C4⋊Dic3—32no—
209C4⋊Dic3—32no—
210C4⋊Dic3—62no—
211C4⋊Dic3—64no—
212C4⋊Dic3—61no—
213C4⋊Dic3—61no—
214C4⋊Dic3—121no—
215C4⋊Dic3C22×D312yes—
216C4⋊Dic3C22×D312yes—
217Dic3⋊C4—24no—
218Dic3⋊C4—64no—
219C2×C3⋊C8—34no—
220C2×C3⋊C8—34no—
221C2×C3⋊C8—32no—
222C2×C3⋊C8—32no—
223C2×C3⋊C8—316no—
224C2×C3⋊C8—62no—
225C2×C3⋊C8—64no—
226C2×C3⋊C8C4×D314yescomplemented
227C2×C3⋊C8C22×D312yes—
228D3×C8—316no—
229C22×C32C2×C4⋊C412yes—
230C22×C32C2×D812yes—
231C22×C32C2×Q1612yes—
232C22×C32C22×D411yescharacteristic
233C2×C3×D3#107116yescomplemented
234C2×C3×D3C2×C4⋊C414yes—
235C2×C3×D3C2×D814yes—
236C2×C3×D3C2×Q1614yes—
237C32×C4—42no—
238C32×C4C2×C4⋊C412yes—
239C32×C4C23×C411yescharacteristic
240C32×C4C22×Q811yescharacteristic
241C3⋊Dic3—42no—
242C3×Dic3—42no—
243C3×Dic3—42no—
244C3×Dic3C2×C4⋊C414yes—
245C23×C4—31no—
246C23×C4—61no—
247C23×C4—181no—
248C22×C8—31no—
249C22×C8—98no—
250C22×C8—94no—
251C22×C8—91no—
252C2×C4⋊C4—31no—
253C2×C4⋊C4—31no—
254C2×C4⋊C4—34no—
255C2×C4⋊C4—62no—
256C2×C4⋊C4—61no—
257C2×C4⋊C4—94no—
258C2×C4⋊C4—91no—
259C2×C4⋊C4—182no—
260C2×C4⋊C4—181no—
261C2×C4⋊C4D3211yescharacteristic
262#107—34no—
263#107—94no—
264#107—94no—
265#107—94no—
266C23×C3—21no—
267C23×C3—34no—
268C23×C3—34no—
269C23×C3—34no—
270C23×C3—32no—
271C23×C3D3×D411yescharacteristic
272C23×C3C2×#6711yescharacteristic
273C22×D3Dic3⋊C414yes—
274C22×D3#21314yes—
275C22×D3#21614yes—
276C22×D3C2×#6712yes—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—21no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—21no—
283C2×C3×C4—34no—
284C2×C3×C4—32no—
285C2×C3×C4—38no—
286C2×C3×C4—34no—
287C2×C3×C4—34no—
288C2×C3×C4—42no—
289C2×C3×C4—42no—
290C2×C3×C4—42no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—82no—
294C2×C3×C4—128no—
295C2×C3×C4—122no—
296C2×C3×C4—122no—
297C2×C3×C4C2×Dic612yes—
298C2×C3×C4C2×C4×D312yes—
299C2×C3×C4C2×C4×D312yes—
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4D3×Q812yes—
302C2×C3×C4C2×#6711yescharacteristic
303C2×C3×C4C23×D311yescharacteristic
304C2×C3×C4C23×D311yescharacteristic
305C2×Dic3—22no—
306C2×Dic3—22no—
307C2×Dic3—42no—
308C2×Dic3—42no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—122no—
312C2×Dic3—128no—
313C2×Dic3—122no—
314C2×Dic3—122no—
315C2×Dic3—242no—
316C2×Dic3Dic3⋊C414yes—
317C2×Dic3C2×#6712yes—
318C4×D3—48no—
319C4×D3—128no—
320C4×D3Dic3⋊C418yes—
321C4×D3C2×Dic614yes—
322C4×D3C2×C4×D314yes—
323C3×C8—34no—
324C3⋊C8—34no—
325C3⋊C8—34no—
326C3⋊C8—64no—
327C3⋊C8C2×C4×D314yescomplemented
328C2×C32C2×#10714yescomplemented
329C2×C32C22×C4⋊C411yescharacteristic
330C2×C32C22×D811yescharacteristic
331C2×C32C22×Q1611yescharacteristic
332C3×D3C2×#10718yescomplemented
333C24—31no—
334C22×C4—21no—
335C22×C4—31no—
336C22×C4—32no—
337C22×C4—34no—
338C22×C4—34no—
339C22×C4—32no—
340C22×C4—64no—
341C22×C4—61no—
342C22×C4—61no—
343C22×C4—124no—
344C22×C4—184no—
345C22×C4—181no—
346C22×C4—364no—
347C22×C4C2×D3211yescharacteristic
348C2×C8—32no—
349C2×C8—34no—
350C2×C8—916no—
351C2×C8—92no—
352C2×C8—94no—
353C4⋊C4—21no—
354C4⋊C4—32no—
355C4⋊C4—32no—
356C4⋊C4—64no—
357C4⋊C4—61no—
358C4⋊C4—61no—
359C4⋊C4—92no—
360C4⋊C4—184no—
361C4⋊C4—181no—
362C4⋊C4C2×D3212yes—
363C22×C3—21no—
364C22×C3—22no—
365C22×C3—22no—
366C22×C3—22no—
367C22×C3—316no—
368C22×C3—34no—
369C22×C3—34no—
370C22×C3—34no—
371C22×C3D3×C4⋊C412yes—
372C22×C3D3×D812yes—
373C22×C3D3×Q1612yes—
374C22×C3C2×Dic3⋊C412yes—
375C22×C3C2×#21312yes—
376C22×C3C2×#21612yes—
377C22×C3C2×D3×D411yescharacteristic
378C22×C3C22×#6711yescharacteristic
379C2×D3#807116yesdirect product factor
380C2×D3C2×Dic3⋊C414yes—
381C2×D3C2×#21314yes—
382C2×D3C2×#21614yes—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—22no—
386C3×C4—34no—
387C3×C4—42no—
388C3×C4—42no—
389C3×C4—82no—
390C3×C4—122no—
391C3×C4—122no—
392C3×C4D3×C4⋊C412yes—
393C3×C4C2×Dic3⋊C412yes—
394C3×C4C22×Dic611yescharacteristic
395C3×C4C22×C4×D311yescharacteristic
396C3×C4C22×C4×D311yescharacteristic
397C3×C4C2×D3×Q811yescharacteristic
398Dic3—42no—
399Dic3—42no—
400Dic3—122no—
401Dic3—122no—
402Dic3—242no—
403Dic3C2×Dic3⋊C414yes—
404C32C22×#10711yescharacteristic, complemented, Sylow
405C23—32no—
406C23—34no—
407C23—34no—
408C23—34no—
409C23D3×#6711yescharacteristic
410C2×C4—22no—
411C2×C4—32no—
412C2×C4—34no—
413C2×C4—34no—
414C2×C4—34no—
415C2×C4—38no—
416C2×C4—42no—
417C2×C4—62no—
418C2×C4—62no—
419C2×C4—128no—
420C2×C4—122no—
421C2×C4—122no—
422C2×C4—182no—
423C2×C4—368no—
424C2×C4—362no—
425C2×C4D3×Dic612yes—
426C2×C4C4×D3212yes—
427C2×C4D3×#6711yescharacteristic
428C2×C4C22×D3211yescharacteristic
429C8—34no—
430C8—94no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—24no—
434C2×C3—21no—
435C2×C3—38no—
436C2×C3D3×#10714yescomplemented
437C2×C3C2×#80714yescomplemented
438C2×C3C2×D3×C4⋊C411yescharacteristic
439C2×C3C2×D3×D811yescharacteristic
440C2×C3C2×D3×Q1611yescharacteristic
441C2×C3C22×Dic3⋊C411yescharacteristic
442C2×C3C22×#21311yescharacteristic
443C2×C3C22×#21611yescharacteristic
444D3C2×#80718yesdirect product factor
445C22—34no—
446C22—34no—
447C22—316no—
448C22—34no—
449C22D3×Dic3⋊C412yes—
450C22D3×#21312yes—
451C22D3×#21612yes—
452C22C2×D3×#6711yescharacteristic
453C4—34no—
454C4—42no—
455C4—122no—
456C4—122no—
457C4—362no—
458C4D3×Dic3⋊C412yes—
459C4C2×D3×Dic611yescharacteristic
460C4C2×C4×D3211yescharacteristic
461C3—21no—
462C3C2×D3×#10711yescharacteristic, complemented
463C3C22×#80711yescharacteristic, complemented
464C2—38no—
465C2D3×#80714yesdirect product factor
466C2C2×D3×Dic3⋊C411yescharacteristic
467C2C2×D3×#21311yescharacteristic
468C2C2×D3×#21611yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32C22×#107
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#63634C2semidirect
5. C2×C3×#807C2semidirect
6. C2×#63576C2semidirect
7. C2×#63575C2semidirect
8. D3×#807C2direct (N × H)
26. C2×D3×C3⋊C8C4semidirect
28. #63634C22semidirect
29. C3×#807C22semidirect
30. #63576C22semidirect
31. #63575C22semidirect
47. C2×#807D3direct (N × H)
68. C2×C3⋊(C3⋊C8)C2×C4semidirect
75. C2×C3×C3⋊C8C2×C4semidirect
78. D3×C3⋊C8C2×C4semidirect
125. #807C2×D3direct (N × H)
150. C3⋊(C3⋊C8)C22×C4semidirect
151. C3×C3⋊C8C22×C4semidirect
226. C2×C3⋊C8C4×D3semidirect
233. C2×C3×D3#107semidirect
327. C3⋊C8C2×C4×D3semidirect
328. C2×C32C2×#107semidirect
332. C3×D3C2×#107semidirect
379. C2×D3#807direct (N × H)
404. C32C22×#107semidirect
436. C2×C3D3×#107semidirect
437. C2×C3C2×#807semidirect
444. D3C2×#807direct (N × H)
462. C3C2×D3×#107semidirect
463. C3C22×#807semidirect
465. C2D3×#807direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D3×C4⋊C42
C2×D3×C4⋊Dic32
C22×D3×C3⋊C82
C2×#636342
C2×C3×#8072
C2×#635762
C2×#635752
D3×#8072
C22×#8073
C2×D3×#1073