Finite Group Databasebeta

← C2×#10590461 #11860065

Subgroups — C2×#10590461 #11860065

Order 1152.

1237 conjugacy classes of subgroups.

The subgroup lattice has 499 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic, complemented
2C2×#63898C211yesmaximal, characteristic
3C22×#3716C211yesmaximal, characteristic
4C2×C3×#809C211yesmaximal, characteristic
5C2×C3×#807C211yesmaximal, characteristic, complemented
6C2×#63567C211yesmaximal, characteristic, complemented
7C2×#63555C211yesmaximal, characteristic, complemented
8#10590461C218yesmaximal, direct product factor
9C2×#4889—31nomaximal
10C2×#4757—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×D3×Dic3—21no—
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×#3750—21no—
16C2×C4×C3⋊Dic3—21no—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18#64096—22no—
19#64096C2214yescomplemented
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×(C2×D3)⋊Dic3—21no—
24#63898—22no—
25#63898C2214yes—
26C2×#3716C418yescomplemented
27C2×#3716C2214yes—
28C3×#809C2214yes—
29C3×#807C2214yescomplemented
30#63567C2214yescomplemented
31#63555C2214yescomplemented
32C2×D4×Dic3—31no—
33C22×#214—31no—
34C22×#204—31no—
35C2×#893—31no—
36C2×#887—31no—
37C2×#887—31no—
38C2×#887—61no—
39C2×C3×#107—31no—
40C2×C3×#102—31no—
41C2×#816—31no—
42C2×#815—31no—
43C2×#815—31no—
44C2×#810—31no—
45C2×#809D311yescharacteristic
46C2×#807D311yescharacteristic, complemented
47#4889—38no—
48#4757—38no—
49C23×C3×D3—21no—
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C22×C3⋊Dic3D411yescharacteristic
54C22×C3⋊Dic3D411yescharacteristic
55C2×#634—21no—
56C2×#634—22no—
57C2×#634C2×C414yescomplemented
58C2×#634C2312yes—
59C22×C3×Dic3—21no—
60C2×C3×D12—21no—
61C2×C3×D12—22no—
62C2×C3×D12C2×C414yes—
63C2×C3×D12C2312yes—
64C2×D3×Dic3—24no—
65C2×D3×Dic3—44no—
66C32×C4⋊C4—21no—
67C32×C4⋊C4C2312yes—
68#3750—24no—
69C4×C3⋊Dic3—24no—
70C4×C3⋊Dic3D412yes—
71C4×C3⋊Dic3C2312yes—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3C2312yes—
74C2×C3×C3⋊C8—22no—
75C2×C3×C3⋊C8C2×C414yescomplemented
76C2×C3×C3⋊C8C2312yes—
77C2×C3×C3⋊C8C2312yes—
78(C2×D3)⋊Dic3—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—31no—
89C22×C3×C8—31no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4—31no—
92C2×C3×C4⋊C4C2×D311yescharacteristic
93C2×C3×C4⋊C4C2×D311yescharacteristic
94C2×#217—61no—
95D4×Dic3—34no—
96D4×Dic3—62no—
97C2×#214—38no—
98C2×#214—34no—
99C2×(C2×D3)⋊C4—61no—
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×Dic3⋊C4—61no—
102C2×Dic3⋊C4—61no—
103C2×Dic3⋊C4—62no—
104C2×C4×Dic3—31no—
105C2×C4×Dic3—31no—
106C2×C4×Dic3—61no—
107C2×C4×Dic3—61no—
108C2×C4×Dic3—61no—
109C2×C4×Dic3—62no—
110C22×C3⋊C8C2×D311yescharacteristic
111C22×C3⋊C8C2×D311yescharacteristic
112C2×#204—38no—
113C2×#204—34no—
114#893—34no—
115#893—62no—
116#887—34no—
117#887—34no—
118#887—64no—
119#887—62no—
120#887—62no—
121#887—64no—
122C3×#107—34no—
123C3×#102—34no—
124#816—34no—
125#815—34no—
126#815—34no—
127#810—34no—
128#809C2×D314yes—
129#807C2×D314yescomplemented
130C23×C32C2×D411yescharacteristic
131C22×C3×D3—24no—
132C22×C3×D3—22no—
133C22×C3×D3—42no—
134C22×C3×D3—42no—
135C2×C32×C4—22no—
136C2×C32×C4—42no—
137C2×C32×C4C22×C412yes—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4#4112yes—
140C2×C32×C4C2411yescharacteristic
141C2×C3⋊Dic3—24no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3C2×D412yes—
146C2×C3⋊Dic3C2×D412yes—
147#634—24no—
148#634—22no—
149#634C22×C414yescomplemented
150C2×C3×Dic3—22no—
151C2×C3×Dic3—42no—
152C3×D12—24no—
153C3×D12—22no—
154C3×D12C22×C414yes—
155D3×Dic3—48no—
156C3×C3⋊C8—22no—
157C3×C3⋊C8C22×C414yescomplemented
158C22×SD16—91no—
159C2×C4×Q8—91no—
160C2×C4×D4—91no—
161#440—98no—
162C2×#107—31no—
163C2×#103—91no—
164C2×#102—31no—
165C2×#97—91no—
166C24×C3—61no—
167C23×D3—21no—
168C2×C3×D4—34no—
169C2×C3×D4—32no—
170C2×C3×D4—61no—
171C2×C3×D4—62no—
172C22×C3×C4—22no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—61no—
177C22×C3×C4C22×D311yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C22×Dic3—21no—
180C22×Dic3—31no—
181C22×Dic3—31no—
182C22×Dic3—31no—
183C22×Dic3—31no—
184C22×Dic3—61no—
185C22×Dic3—61no—
186C22×Dic3—64no—
187C22×Dic3—62no—
188C22×Dic3—61no—
189C22×Dic3—61no—
190C22×Dic3—124no—
191C2×D12—21no—
192C2×D12—22no—
193C2×D12C4×D314yes—
194C2×D12C22×D312yes—
195C2×C4×D3—64no—
196C2×C4×D3—124no—
197C2×Dic6—34no—
198C2×Dic6—34no—
199C2×Dic6—32no—
200C2×Dic6—32no—
201C2×Dic6—62no—
202C2×Dic6—64no—
203C2×Dic6—62no—
204C2×Dic6—64no—
205C2×Dic6—61no—
206C2×Dic6—61no—
207C2×Dic6—62no—
208C2×Dic6—62no—
209C2×C3×C8—34no—
210C2×C3×C8—32no—
211C2×C3×C8—32no—
212C2×C3×C8—62no—
213C3×C4⋊C4—22no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—22no—
217C3×C4⋊C4—32no—
218C3×C4⋊C4—61no—
219C3×C4⋊C4C22×D312yes—
220C3×C4⋊C4C22×D312yes—
221#217—64no—
222#214—316no—
223(C2×D3)⋊C4—64no—
224C4⋊Dic3—21no—
225C4⋊Dic3C22×D312yes—
226Dic3⋊C4—64no—
227Dic3⋊C4—64no—
228Dic3⋊C4—68no—
229C4×Dic3—32no—
230C4×Dic3—32no—
231C4×Dic3—32no—
232C4×Dic3—32no—
233C4×Dic3—62no—
234C4×Dic3—62no—
235C4×Dic3—64no—
236C4×Dic3—64no—
237C4×Dic3—68no—
238C2×C3⋊C8—22no—
239C2×C3⋊C8C4×D314yescomplemented
240C2×C3⋊C8C22×D312yes—
241C2×C3⋊C8C22×D312yes—
242#204—316no—
243C22×C32C4×D412yes—
244C22×C32AGL(1,ℤ/8)12yes—
245C22×C32#13712yes—
246C22×C32C22×D411yescharacteristic
247C2×C3×D3—24no—
248C2×C3×D3—42no—
249C2×C3×D3—42no—
250C2×C3×D3—48no—
251C32×C4—42no—
252C32×C4C4×D412yes—
253C32×C4C23×C411yescharacteristic
254C32×C4C2×#4111yescharacteristic
255C3⋊Dic3—24no—
256C3⋊Dic3—22no—
257C3⋊Dic3—22no—
258C3×Dic3—42no—
259C22×Q8—91no—
260C22×D4—31no—
261C23×C4—181no—
262C2×SD16—98no—
263C2×SD16—94no—
264C22×C8—31no—
265C22×C8—31no—
266C4×Q8—94no—
267C4×Q8—182no—
268C4×D4—94no—
269C4×D4—182no—
270C2×C4⋊C4—31no—
271C2×C4⋊C4—181no—
272C2×C4⋊C4D3211yescharacteristic
273C2×C22⋊C4—181no—
274C2×C42—91no—
275C2×C42—181no—
276#107—34no—
277#103—94no—
278#102—34no—
279#97—94no—
280C23×C3—21no—
281C23×C3—64no—
282C23×C3—62no—
283C23×C3—122no—
284C23×C3—122no—
285C23×C3D3×D411yescharacteristic
286C23×C3D3×D411yescharacteristic
287C22×D3—24no—
288C22×D3—22no—
289C22×D3—42no—
290C22×D3—42no—
291C3×D4—34no—
292C3×D4—64no—
293C3×D4—62no—
294C2×C3×C4—24no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—21no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—21no—
301C2×C3×C4—44no—
302C2×C3×C4—42no—
303C2×C3×C4—42no—
304C2×C3×C4—62no—
305C2×C3×C4—122no—
306C2×C3×C4C2×C4×D312yes—
307C2×C3×C4C2×C4×D312yes—
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4D3×D411yescharacteristic
310C2×C3×C4#23712yes—
311C2×C3×C4#23912yes—
312C2×C3×C4C23×D311yescharacteristic
313C2×C3×C4C23×D311yescharacteristic
314C2×Dic3—22no—
315C2×Dic3—32no—
316C2×Dic3—32no—
317C2×Dic3—32no—
318C2×Dic3—32no—
319C2×Dic3—42no—
320C2×Dic3—62no—
321C2×Dic3—62no—
322C2×Dic3—64no—
323C2×Dic3—68no—
324C2×Dic3—64no—
325C2×Dic3—64no—
326C2×Dic3—64no—
327C2×Dic3—62no—
328C2×Dic3—62no—
329C2×Dic3—62no—
330C2×Dic3—62no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—122no—
334C2×Dic3—128no—
335D12—24no—
336D12—22no—
337D12C2×C4×D314yes—
338C4×D3—128no—
339Dic6—34no—
340Dic6—34no—
341Dic6—64no—
342Dic6—64no—
343Dic6—68no—
344Dic6—64no—
345Dic6—64no—
346Dic6—62no—
347Dic6—62no—
348C3×C8—34no—
349C3×C8—62no—
350C3⋊C8—22no—
351C3⋊C8C2×C4×D314yescomplemented
352C2×C32#44014yescomplemented
353C2×C32C2×C4×D411yescharacteristic
354C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
355C2×C32C2×#13711yescharacteristic
356C3×D3—44no—
357C24—61no—
358C2×Q8—92no—
359C2×Q8—94no—
360C2×Q8—182no—
361C2×Q8—181no—
362C2×D4—32no—
363C2×D4—34no—
364C2×D4—62no—
365C2×D4—61no—
366C22×C4—21no—
367C22×C4—61no—
368C22×C4—91no—
369C22×C4—91no—
370C22×C4—184no—
371C22×C4—181no—
372C22×C4—364no—
373C22×C4C2×D3211yescharacteristic
374SD16—916no—
375C2×C8—32no—
376C2×C8—34no—
377C2×C8—32no—
378C2×C8—62no—
379C4⋊C4—21no—
380C4⋊C4—32no—
381C4⋊C4—61no—
382C4⋊C4—184no—
383C4⋊C4C2×D3212yes—
384C22⋊C4—184no—
385C42—92no—
386C42—92no—
387C42—184no—
388C22×C3—21no—
389C22×C3—22no—
390C22×C3—22no—
391C22×C3—22no—
392C22×C3—64no—
393C22×C3—128no—
394C22×C3—122no—
395C22×C3—122no—
396C22×C3#67⋊C412yes—
397C22×C3#89312yes—
398C22×C3#91112yes—
399C22×C3#91112yes—
400C22×C3#91512yes—
401C22×C3#91812yes—
402C22×C3C2×D3×D411yescharacteristic
403C22×C3C2×D3×D411yescharacteristic
404C2×D3—24no—
405C2×D3—42no—
406C2×D3—42no—
407C2×D3—48no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—22no—
411C3×C4—44no—
412C3×C4—42no—
413C3×C4—42no—
414C3×C4—122no—
415C3×C4#67⋊C412yes—
416C3×C4#89312yes—
417C3×C4C22×C4×D311yescharacteristic
418C3×C4C22×C4×D311yescharacteristic
419C3×C4C2×#23711yescharacteristic
420C3×C4C2×#23911yescharacteristic
421Dic3—42no—
422Dic3—68no—
423Dic3—64no—
424Dic3—64no—
425Dic3—62no—
426Dic3—62no—
427Dic3—64no—
428Dic3—62no—
429Dic3—62no—
430Dic3—122no—
431C32C2×#44011yescharacteristic, complemented, Sylow
432C23—62no—
433C23—64no—
434C23—122no—
435C23—122no—
436C23#381111yescharacteristic
437Q8—94no—
438Q8—182no—
439Q8—184no—
440D4—34no—
441D4—62no—
442D4—64no—
443C2×C4—22no—
444C2×C4—42no—
445C2×C4—62no—
446C2×C4—92no—
447C2×C4—92no—
448C2×C4—122no—
449C2×C4—182no—
450C2×C4—184no—
451C2×C4—182no—
452C2×C4—182no—
453C2×C4—368no—
454C2×C4#379612yes—
455C2×C4C4×D3212yes—
456C2×C4#381111yescharacteristic
457C2×C4C22×D3211yescharacteristic
458C8—34no—
459C8—62no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—24no—
464C2×C3—124no—
465C2×C3#475714yescomplemented
466C2×C3#488914yescomplemented
467C2×C3C2×#67⋊C411yescharacteristic
468C2×C3C2×#89311yescharacteristic
469C2×C3C2×#91111yescharacteristic
470C2×C3C2×#91111yescharacteristic
471C2×C3C2×#91511yescharacteristic
472C2×C3C2×#91811yescharacteristic
473D3—44no—
474C22—64no—
475C22—122no—
476C22—122no—
477C22—128no—
478C22#6388112yes—
479C22#6392712yes—
480C22#6395112yes—
481C22C2×#381111yescharacteristic
482C4—42no—
483C4—122no—
484C4—182no—
485C4—182no—
486C4—184no—
487C4#6388112yes—
488C4C2×#379611yescharacteristic
489C4C2×C4×D3211yescharacteristic
490C3—21no—
491C3C2×#475711yescharacteristic, complemented
492C3C2×#488911yescharacteristic, complemented
493C2—124no—
494C2#1059046114yesdirect product factor
495C2C2×#6388111yescharacteristic
496C2C2×#6392711yescharacteristic
497C2C2×#6395111yescharacteristic
subgroupG/H
centerC23#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#440
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
1. C2×#64096C2semidirect
5. C2×C3×#807C2semidirect
6. C2×#63567C2semidirect
7. C2×#63555C2semidirect
8. #10590461C2direct (N × H)
19. #64096C22semidirect
26. C2×#3716C4semidirect
29. C3×#807C22semidirect
30. #63567C22semidirect
31. #63555C22semidirect
46. C2×#807D3semidirect
57. C2×#634C2×C4semidirect
75. C2×C3×C3⋊C8C2×C4semidirect
79. #3716C2×C4semidirect
129. #807C2×D3semidirect
149. #634C22×C4semidirect
157. C3×C3⋊C8C22×C4semidirect
239. C2×C3⋊C8C4×D3semidirect
351. C3⋊C8C2×C4×D3semidirect
352. C2×C32#440semidirect
431. C32C2×#440semidirect
465. C2×C3#4757semidirect
466. C2×C3#4889semidirect
491. C3C2×#4757semidirect
492. C3C2×#4889semidirect
494. C2#10590461direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640962
C2×#638982
C22×#37162
C2×C3×#8092
C2×C3×#8072
C2×#635672
C2×#635552
#105904612
C2×#48893
C2×#47573