Finite Group Databasebeta

← C2×#10590747 #11860075

Subgroups — C2×#10590747 #11860075

Order 1152.

1169 conjugacy classes of subgroups.

The subgroup lattice has 487 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic3×D12C211yesmaximal, characteristic
2C2×#63844C211yesmaximal, characteristic, complemented
3C22×#3716C211yesmaximal, characteristic
4C2×#63643C211yesmaximal, characteristic, complemented
5C2×C3×#821C211yesmaximal, characteristic
6C2×C3×#815C211yesmaximal, characteristic, complemented
7C2×#63575C211yesmaximal, characteristic, complemented
8#10590747C218yesmaximal, direct product factor
9C2×#4757—31nomaximal
10C2×#4710—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×D3×Dic3—21no—
14C22×C32×C8C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4×Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×#3724—21no—
20C2×(C2×D3)⋊Dic3—21no—
21C2×Dic32—21no—
22Dic3×D12—22no—
23Dic3×D12C2214yes—
24#63844—22no—
25#63844C2214yescomplemented
26C2×#3716C418yescomplemented
27C2×#3716C2214yes—
28#63643C2214yescomplemented
29C3×#821C2214yes—
30C3×#815C2214yescomplemented
31#63575C2214yescomplemented
32C2×D4×Dic3—31no—
33C22×#214—31no—
34C22×#204—31no—
35C2×#887—31no—
36C2×C4×D12—31no—
37C2×C4×Dic6—31no—
38C2×C3×#102—31no—
39C2×C3×#97—31no—
40C2×#821D311yescharacteristic
41C2×#818—31no—
42C2×#816—31no—
43C2×#816—31no—
44C2×#816—61no—
45C2×#815D311yescharacteristic, complemented
46C2×#807—31no—
47#4757—38no—
48#4710—38no—
49C23×C3×D3—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C22×C3⋊Dic3—21no—
53C2×#634—21no—
54C2×#634—22no—
55C2×#634C2×C414yescomplemented
56C2×#634C2312yes—
57C22×C3×Dic3—21no—
58C22×C3×Dic3D411yescharacteristic
59C22×C3×Dic3D411yescharacteristic
60C2×C3×D12—21no—
61C2×C3×D12—22no—
62C2×C3×D12C2×C414yes—
63C2×C3×D12C2312yes—
64C2×D3×Dic3—24no—
65C2×D3×Dic3—44no—
66C2×C32×C8—22no—
67C2×C32×C8C2312yes—
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)C2312yes—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3C2312yes—
72C3×C4×Dic3D412yes—
73C3×C4×Dic3C2312yes—
74C2×C3×C3⋊C8C2×C414yescomplemented
75C2×C3×C3⋊C8C2312yes—
76#3724—24no—
77(C2×D3)⋊Dic3—24no—
78Dic32—24no—
79#3716C2×C4116yescomplemented
80C2×#440—91noSylow
81C22×C3×D4—31no—
82C23×Dic3—61no—
83C22×D12C2×D311yescharacteristic
84C22×C4×D3—61no—
85C22×Dic6—31no—
86C22×Dic6—31no—
87C22×Dic6—61no—
88C22×C3×C8—21no—
89C22×C3×C8—31no—
90C22×C3×C8C2×D311yescharacteristic
91C22×C3×C8C2×D311yescharacteristic
92C2×C3×C4⋊C4—31no—
93C2×C3×C42—31no—
94C2×#217—61no—
95D4×Dic3—34no—
96D4×Dic3—62no—
97C2×#214—38no—
98C2×#214—34no—
99C2×(C2×D3)⋊C4—61no—
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—31no—
102C2×C4⋊Dic3—61no—
103C2×C4⋊Dic3C2×D311yescharacteristic
104C2×Dic3⋊C4—61no—
105C2×Dic3⋊C4—61no—
106C2×C4×Dic3—61no—
107C2×C4×Dic3—61no—
108C2×C4×Dic3C2×D311yescharacteristic
109C22×C3⋊C8C2×D311yescharacteristic
110C2×#204—38no—
111C2×#204—34no—
112#887—34no—
113#887—62no—
114C4×D12—34no—
115C4×D12—62no—
116C4×Dic6—34no—
117C4×Dic6—62no—
118C3×#102—34no—
119C3×#97—34no—
120#821C2×D314yes—
121#818—34no—
122#816—34no—
123#816—34no—
124#816—64no—
125#815C2×D314yescomplemented
126#807—34no—
127C23×C32C2×D411yescharacteristic
128C22×C3×D3—24no—
129C22×C3×D3—22no—
130C22×C3×D3—42no—
131C22×C3×D3—42no—
132C2×C32×C4C22×C412yes—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4#4112yes—
135C2×C32×C4C2411yescharacteristic
136C2×C3⋊Dic3—24no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—42no—
140#634—24no—
141#634—22no—
142#634C22×C414yescomplemented
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—42no—
147C2×C3×Dic3C2×D412yes—
148C2×C3×Dic3C2×D412yes—
149C3×D12—24no—
150C3×D12—22no—
151C3×D12C22×C414yes—
152D3×Dic3—48no—
153C32×C8—22no—
154C3×C3⋊C8C22×C414yescomplemented
155C22×SD16—91no—
156C2×C4×Q8—91no—
157C2×C4×D4—91no—
158#440—98no—
159C2×#107—91no—
160C2×#103—91no—
161C2×#102—31no—
162C2×#97—31no—
163C24×C3—61no—
164C23×D3—21no—
165C2×C3×D4—34no—
166C2×C3×D4—32no—
167C2×C3×D4—61no—
168C2×C3×D4—62no—
169C22×C3×C4—21no—
170C22×C3×C4—31no—
171C22×C3×C4—31no—
172C22×C3×C4—61no—
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C22×Dic3—21no—
176C22×Dic3—61no—
177C22×Dic3—61no—
178C22×Dic3—61no—
179C22×Dic3—61no—
180C22×Dic3—64no—
181C22×Dic3—121no—
182C22×Dic3—121no—
183C22×Dic3—124no—
184C22×Dic3D1211yescharacteristic
185C22×Dic3D1211yescharacteristic
186C2×D12—21no—
187C2×D12—22no—
188C2×D12C4×D314yes—
189C2×D12C22×D312yes—
190C2×C4×D3—64no—
191C2×C4×D3—124no—
192C2×Dic6—34no—
193C2×Dic6—34no—
194C2×Dic6—32no—
195C2×Dic6—32no—
196C2×Dic6—62no—
197C2×Dic6—64no—
198C2×Dic6—61no—
199C2×Dic6—62no—
200C2×Dic6—61no—
201C2×Dic6—62no—
202C2×Dic6—121no—
203C2×Dic6—122no—
204C2×C3×C8—22no—
205C2×C3×C8—22no—
206C2×C3×C8—22no—
207C2×C3×C8—34no—
208C2×C3×C8—32no—
209C2×C3×C8—42no—
210C2×C3×C8C22×D312yes—
211C2×C3×C8C22×D312yes—
212C3×C4⋊C4—32no—
213C3×C4⋊C4—61no—
214C3×C42—32no—
215C3×C42—32no—
216#217—64no—
217#214—316no—
218(C2×D3)⋊C4—64no—
219C4⋊Dic3—21no—
220C4⋊Dic3—32no—
221C4⋊Dic3—32no—
222C4⋊Dic3—62no—
223C4⋊Dic3—61no—
224C4⋊Dic3—61no—
225C4⋊Dic3—121no—
226C4⋊Dic3C22×D312yes—
227Dic3⋊C4—64no—
228Dic3⋊C4—64no—
229C4×Dic3—64no—
230C4×Dic3—64no—
231C4×Dic3D1212yes—
232C4×Dic3C22×D312yes—
233C2×C3⋊C8C4×D314yescomplemented
234C2×C3⋊C8C22×D312yes—
235#204—316no—
236C22×C32C4×D412yes—
237C22×C32AGL(1,ℤ/8)12yes—
238C22×C32#13712yes—
239C22×C32C22×D411yescharacteristic
240C2×C3×D3—24no—
241C2×C3×D3—42no—
242C2×C3×D3—42no—
243C2×C3×D3—48no—
244C32×C4C4×D412yes—
245C32×C4C23×C411yescharacteristic
246C32×C4C2×#4111yescharacteristic
247C3⋊Dic3—24no—
248C3⋊Dic3—42no—
249C3×Dic3—22no—
250C3×Dic3—22no—
251C3×Dic3—42no—
252C22×Q8—91no—
253C22×D4—31no—
254C23×C4—181no—
255C2×SD16—98no—
256C2×SD16—94no—
257C22×C8—31no—
258C22×C8D3211yescharacteristic
259C4×Q8—94no—
260C4×Q8—182no—
261C4×D4—94no—
262C4×D4—182no—
263C2×C4⋊C4—31no—
264C2×C4⋊C4—91no—
265C2×C4⋊C4—181no—
266C2×C22⋊C4—181no—
267C2×C42—31no—
268C2×C42—181no—
269#107—94no—
270#103—94no—
271#102—34no—
272#97—34no—
273C23×C3—21no—
274C23×C3—64no—
275C23×C3—62no—
276C23×C3—122no—
277C23×C3—122no—
278C23×C3C2×D1211yescharacteristic
279C23×C3D3×D411yescharacteristic
280C22×D3—24no—
281C22×D3—22no—
282C22×D3—42no—
283C22×D3—42no—
284C3×D4—34no—
285C3×D4—64no—
286C3×D4—62no—
287C2×C3×C4—21no—
288C2×C3×C4—22no—
289C2×C3×C4—21no—
290C2×C3×C4—22no—
291C2×C3×C4—32no—
292C2×C3×C4—32no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—62no—
296C2×C3×C4—122no—
297C2×C3×C4C2×C4×D312yes—
298C2×C3×C4C2×C4×D312yes—
299C2×C3×C4C2×D1211yescharacteristic
300C2×C3×C4#23512yes—
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4#23712yes—
303C2×C3×C4C23×D311yescharacteristic
304C2×C3×C4C23×D311yescharacteristic
305C2×Dic3—22no—
306C2×Dic3—22no—
307C2×Dic3—22no—
308C2×Dic3—42no—
309C2×Dic3—64no—
310C2×Dic3—64no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—62no—
315C2×Dic3—122no—
316C2×Dic3—124no—
317C2×Dic3—122no—
318C2×Dic3—128no—
319C2×Dic3—122no—
320C2×Dic3—122no—
321C2×Dic3—242no—
322C2×Dic3C2×D1212yes—
323C2×Dic3C2×D1212yes—
324D12—24no—
325D12—22no—
326D12C2×C4×D314yes—
327C4×D3—128no—
328Dic6—34no—
329Dic6—34no—
330Dic6—64no—
331Dic6—64no—
332Dic6—64no—
333Dic6—62no—
334Dic6—62no—
335Dic6—122no—
336Dic6—124no—
337C3×C8—22no—
338C3×C8—22no—
339C3×C8—34no—
340C3×C8—42no—
341C3⋊C8C2×C4×D314yescomplemented
342C2×C32#44014yescomplemented
343C2×C32C2×C4×D411yescharacteristic
344C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
345C2×C32C2×#13711yescharacteristic
346C3×D3—44no—
347C24—61no—
348C2×Q8—92no—
349C2×Q8—94no—
350C2×Q8—181no—
351C2×Q8—182no—
352C2×D4—32no—
353C2×D4—34no—
354C2×D4—61no—
355C2×D4—62no—
356C22×C4—31no—
357C22×C4—31no—
358C22×C4—61no—
359C22×C4—184no—
360C22×C4—181no—
361C22×C4—181no—
362C22×C4—364no—
363C22×C4C2×D3211yescharacteristic
364SD16—916no—
365C2×C8—22no—
366C2×C8—32no—
367C2×C8—34no—
368C2×C8C2×D3212yes—
369C4⋊C4—32no—
370C4⋊C4—61no—
371C4⋊C4—92no—
372C4⋊C4—184no—
373C4⋊C4—181no—
374C22⋊C4—184no—
375C42—32no—
376C42—32no—
377C42—184no—
378C22×C3—21no—
379C22×C3—22no—
380C22×C3—22no—
381C22×C3—22no—
382C22×C3—64no—
383C22×C3—128no—
384C22×C3—122no—
385C22×C3—122no—
386C22×C3C4×D1212yes—
387C22×C3#67⋊C412yes—
388C22×C3#90812yes—
389C22×C3#90912yes—
390C22×C3#91112yes—
391C22×C3#91512yes—
392C22×C3C22×D1211yescharacteristic
393C22×C3C2×D3×D411yescharacteristic
394C2×D3—24no—
395C2×D3—42no—
396C2×D3—42no—
397C2×D3—48no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—22no—
401C3×C4—62no—
402C3×C4—62no—
403C3×C4—122no—
404C3×C4C4×D1212yes—
405C3×C4#67⋊C412yes—
406C3×C4C22×C4×D311yescharacteristic
407C3×C4C22×C4×D311yescharacteristic
408C3×C4C2×#23511yescharacteristic
409C3×C4C2×#23711yescharacteristic
410Dic3—22no—
411Dic3—22no—
412Dic3—42no—
413Dic3—64no—
414Dic3—64no—
415Dic3—124no—
416Dic3—122no—
417Dic3—122no—
418Dic3—242no—
419C32C2×#44011yescharacteristic, complemented, Sylow
420C23—62no—
421C23—64no—
422C23—122no—
423C23—122no—
424C23D3×D1211yescharacteristic
425Q8—94no—
426Q8—182no—
427Q8—184no—
428D4—34no—
429D4—62no—
430D4—64no—
431C2×C4—32no—
432C2×C4—32no—
433C2×C4—62no—
434C2×C4—62no—
435C2×C4—62no—
436C2×C4—122no—
437C2×C4—182no—
438C2×C4—184no—
439C2×C4—182no—
440C2×C4—368no—
441C2×C4—362no—
442C2×C4C4×D3212yes—
443C2×C4D3×D1211yescharacteristic
444C2×C4#380412yes—
445C2×C4C22×D3211yescharacteristic
446C8—22no—
447C8—34no—
448C2×C3—24no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—124no—
453C2×C3#471014yescomplemented
454C2×C3#475714yescomplemented
455C2×C3C2×C4×D1211yescharacteristic
456C2×C3C2×#67⋊C411yescharacteristic
457C2×C3C2×#90811yescharacteristic
458C2×C3C2×#90911yescharacteristic
459C2×C3C2×#91111yescharacteristic
460C2×C3C2×#91511yescharacteristic
461D3—44no—
462C22—64no—
463C22—128no—
464C22—122no—
465C22—122no—
466C22#6379512yes—
467C22#6380012yes—
468C22#6388012yes—
469C22C2×D3×D1211yescharacteristic
470C4—62no—
471C4—62no—
472C4—122no—
473C4—184no—
474C4—362no—
475C4#6388012yes—
476C4C2×C4×D3211yescharacteristic
477C4C2×#380411yescharacteristic
478C3—21no—
479C3C2×#471011yescharacteristic, complemented
480C3C2×#475711yescharacteristic, complemented
481C2—124no—
482C2#1059074714yesdirect product factor
483C2C2×#6379511yescharacteristic
484C2C2×#6380011yescharacteristic
485C2C2×#6388011yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C2×#440
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63844C2semidirect
4. C2×#63643C2semidirect
6. C2×C3×#815C2semidirect
7. C2×#63575C2semidirect
8. #10590747C2direct (N × H)
25. #63844C22semidirect
26. C2×#3716C4semidirect
28. #63643C22semidirect
30. C3×#815C22semidirect
31. #63575C22semidirect
45. C2×#815D3semidirect
55. C2×#634C2×C4semidirect
74. C2×C3×C3⋊C8C2×C4semidirect
79. #3716C2×C4semidirect
125. #815C2×D3semidirect
142. #634C22×C4semidirect
154. C3×C3⋊C8C22×C4semidirect
233. C2×C3⋊C8C4×D3semidirect
341. C3⋊C8C2×C4×D3semidirect
342. C2×C32#440semidirect
419. C32C2×#440semidirect
453. C2×C3#4710semidirect
454. C2×C3#4757semidirect
479. C3C2×#4710semidirect
480. C3C2×#4757semidirect
482. C2#10590747direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Dic3×D122
C2×#638442
C22×#37162
C2×#636432
C2×C3×#8212
C2×C3×#8152
C2×#635752
#105907472
C2×#47573
C2×#47103