Finite Group Databasebeta

← C2×#10590746 #11860171

Subgroups — C2×#10590746 #11860171

Order 1152.

1317 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63894C211yesmaximal, characteristic, complemented
2C2×Dic3×D12C211yesmaximal, characteristic, complemented
3C22×#3714C211yesmaximal, characteristic
4C2×#63648C211yesmaximal, characteristic, complemented
5C2×C3×#821C211yesmaximal, characteristic, complemented
6C2×C3×#815C211yesmaximal, characteristic, complemented
7C2×#63573C211yesmaximal, characteristic, complemented
8#10590746C218yesmaximal, direct product factor
9C2×#4785—31nomaximal
10C2×#4711—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×#624—21no—
14C22×D3×Dic3—21no—
15C22×C32×C8C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C2×#3722—21no—
21C2×(C2×D3)⋊Dic3—21no—
22#63894—22no—
23#63894C2214yescomplemented
24Dic3×D12—22no—
25Dic3×D12C2214yescomplemented
26C2×#3714C418yescomplemented
27C2×#3714C2214yes—
28#63648C2214yescomplemented
29C3×#821C2214yescomplemented
30C3×#815C2214yescomplemented
31#63573C2214yescomplemented
32C2×D4×Dic3—31no—
33C22×#213—31no—
34C22×D24—31no—
35C2×#893—31no—
36C2×C4×D12—31no—
37C2×C4×D12—31no—
38C2×C3×#102—31no—
39C2×C3×#97—31no—
40C2×#821—31no—
41C2×#821—31no—
42C2×#821—61no—
43C2×#821D311yescharacteristic, complemented
44C2×#817—31no—
45C2×#815D311yescharacteristic, complemented
46C2×#808—31no—
47#4785—38no—
48#4711—38no—
49C23×C3⋊D3—21no—
50C23×C3×D3—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)—22no—
55C2×C4⋊(C3⋊D3)C2×C414yescomplemented
56C2×C4⋊(C3⋊D3)C2312yes—
57C22×C3×Dic3—21no—
58C22×C3×Dic3D411yescharacteristic
59C22×C3×Dic3D411yescharacteristic
60C2×C3×D12—21no—
61C2×C3×D12—22no—
62C2×C3×D12C2×C414yescomplemented
63C2×C3×D12C2312yes—
64C2×#624—24no—
65C2×#624—44no—
66C2×D3×Dic3—24no—
67C2×D3×Dic3—44no—
68C2×C32×C8—22no—
69C2×C32×C8C2312yes—
70C4⋊(C3⋊Dic3)—21no—
71C4⋊(C3⋊Dic3)C2312yes—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3C2312yes—
74C3×C4×Dic3D412yes—
75C3×C4×Dic3C2312yes—
76C2×C3×C3⋊C8C2×C414yescomplemented
77C2×C3×C3⋊C8C2312yes—
78#3722—24no—
79(C2×D3)⋊Dic3—24no—
80#3714C2×C4116yescomplemented
81C2×#442—91noSylow
82C22×C3×D4—31no—
83C23×Dic3—61no—
84C22×D12—31no—
85C22×D12—31no—
86C22×D12—61no—
87C22×D12C2×D311yescharacteristic
88C22×C4×D3—61no—
89C22×C4×D3—61no—
90C22×C4×D3—61no—
91C22×C3×C8—21no—
92C22×C3×C8—31no—
93C22×C3×C8C2×D311yescharacteristic
94C22×C3×C8C2×D311yescharacteristic
95C2×C3×C4⋊C4—31no—
96C2×C3×C42—31no—
97C2×#217—61no—
98D4×Dic3—34no—
99D4×Dic3—62no—
100C2×#213—38no—
101C2×#213—34no—
102C2×(C2×D3)⋊C4—61no—
103C2×(C2×D3)⋊C4—61no—
104C2×(C2×D3)⋊C4—61no—
105C2×C4⋊Dic3—31no—
106C2×C4⋊Dic3—31no—
107C2×C4⋊Dic3—61no—
108C2×C4⋊Dic3C2×D311yescharacteristic
109C2×C4×Dic3C2×D311yescharacteristic
110C22×C3⋊C8C2×D311yescharacteristic
111C2×D24—38no—
112C2×D24—34no—
113#893—34no—
114#893—62no—
115C4×D12—34no—
116C4×D12—34no—
117C4×D12—62no—
118C4×D12—62no—
119C3×#102—34no—
120C3×#97—34no—
121#821—34no—
122#821—34no—
123#821—64no—
124#821C2×D314yescomplemented
125#817—34no—
126#815C2×D314yescomplemented
127#808—34no—
128C23×C32C2×D411yescharacteristic
129C22×C3⋊D3—24no—
130C22×C3⋊D3—22no—
131C22×C3⋊D3—42no—
132C22×C3⋊D3—42no—
133C22×C3×D3—24no—
134C22×C3×D3—22no—
135C22×C3×D3—42no—
136C22×C3×D3—42no—
137C2×C32×C4C22×C412yes—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4#4112yes—
140C2×C32×C4C2411yescharacteristic
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—42no—
143C4⋊(C3⋊D3)—24no—
144C4⋊(C3⋊D3)—22no—
145C4⋊(C3⋊D3)C22×C414yescomplemented
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—42no—
150C2×C3×Dic3C2×D412yes—
151C2×C3×Dic3C2×D412yes—
152C3×D12—24no—
153C3×D12—22no—
154C3×D12C22×C414yescomplemented
155#624—48no—
156D3×Dic3—48no—
157C32×C8—22no—
158C3×C3⋊C8C22×C414yescomplemented
159C22×D8—91no—
160C2×C4×D4—91no—
161C2×C4×D4—91no—
162#442—98no—
163C2×#106—91no—
164C2×#102—31no—
165C2×#102—91no—
166C2×#97—31no—
167C24×C3—61no—
168C23×D3—21no—
169C23×D3—61no—
170C23×D3—61no—
171C23×D3—121no—
172C2×C3×D4—34no—
173C2×C3×D4—32no—
174C2×C3×D4—61no—
175C2×C3×D4—62no—
176C22×C3×C4—21no—
177C22×C3×C4—31no—
178C22×C3×C4—31no—
179C22×C3×C4—61no—
180C22×C3×C4C22×D311yescharacteristic
181C22×C3×C4C22×D311yescharacteristic
182C22×Dic3—21no—
183C22×Dic3—61no—
184C22×Dic3—61no—
185C22×Dic3—64no—
186C22×Dic3—121no—
187C22×Dic3—124no—
188C22×Dic3D1211yescharacteristic
189C22×Dic3D1211yescharacteristic
190C2×D12—21no—
191C2×D12—22no—
192C2×D12—34no—
193C2×D12—34no—
194C2×D12—32no—
195C2×D12—32no—
196C2×D12—62no—
197C2×D12—64no—
198C2×D12—61no—
199C2×D12—62no—
200C2×D12—61no—
201C2×D12—62no—
202C2×D12—121no—
203C2×D12—122no—
204C2×D12C4×D314yescomplemented
205C2×D12C22×D312yes—
206C2×C4×D3—64no—
207C2×C4×D3—64no—
208C2×C4×D3—64no—
209C2×C4×D3—124no—
210C2×C4×D3—124no—
211C2×C4×D3—124no—
212C2×C3×C8—22no—
213C2×C3×C8—22no—
214C2×C3×C8—22no—
215C2×C3×C8—34no—
216C2×C3×C8—32no—
217C2×C3×C8—42no—
218C2×C3×C8C22×D312yes—
219C2×C3×C8C22×D312yes—
220C3×C4⋊C4—32no—
221C3×C4⋊C4—61no—
222C3×C42—32no—
223C3×C42—32no—
224#217—64no—
225#213—316no—
226(C2×D3)⋊C4—64no—
227(C2×D3)⋊C4—64no—
228(C2×D3)⋊C4—64no—
229C4⋊Dic3—21no—
230C4⋊Dic3—32no—
231C4⋊Dic3—32no—
232C4⋊Dic3—62no—
233C4⋊Dic3—61no—
234C4⋊Dic3—61no—
235C4⋊Dic3—121no—
236C4⋊Dic3C22×D312yes—
237C4×Dic3D1212yes—
238C4×Dic3C22×D312yes—
239C2×C3⋊C8C4×D314yescomplemented
240C2×C3⋊C8C22×D312yes—
241D24—316no—
242C22×C32C4×D412yes—
243C22×C32AGL(1,ℤ/8)12yes—
244C22×C32AGL(1,ℤ/8)12yes—
245C22×C32C22×D411yescharacteristic
246C2×C3⋊D3—24no—
247C2×C3⋊D3—42no—
248C2×C3⋊D3—42no—
249C2×C3⋊D3—48no—
250C2×C3×D3—24no—
251C2×C3×D3—42no—
252C2×C3×D3—42no—
253C2×C3×D3—48no—
254C32×C4C4×D412yes—
255C32×C4C23×C411yescharacteristic
256C32×C4C2×#4111yescharacteristic
257C3⋊Dic3—42no—
258C3×Dic3—22no—
259C3×Dic3—22no—
260C3×Dic3—42no—
261C22×D4—31no—
262C22×D4—91no—
263C23×C4—181no—
264C23×C4—181no—
265C2×D8—98no—
266C2×D8—94no—
267C22×C8—31no—
268C22×C8D3211yescharacteristic
269C4×D4—94no—
270C4×D4—94no—
271C4×D4—182no—
272C4×D4—182no—
273C2×C4⋊C4—31no—
274C2×C4⋊C4—91no—
275C2×C22⋊C4—181no—
276C2×C22⋊C4—181no—
277C2×C42—31no—
278#106—94no—
279#102—34no—
280#102—94no—
281#97—34no—
282C23×C3—21no—
283C23×C3—64no—
284C23×C3—62no—
285C23×C3—122no—
286C23×C3—122no—
287C23×C3C2×D1211yescharacteristic
288C23×C3D3×D411yescharacteristic
289C22×D3—24no—
290C22×D3—22no—
291C22×D3—42no—
292C22×D3—42no—
293C22×D3—64no—
294C22×D3—64no—
295C22×D3—62no—
296C22×D3—62no—
297C22×D3—122no—
298C22×D3—124no—
299C22×D3—122no—
300C22×D3—122no—
301C22×D3—122no—
302C22×D3—122no—
303C22×D3—242no—
304C22×D3—242no—
305C3×D4—34no—
306C3×D4—64no—
307C3×D4—62no—
308C2×C3×C4—21no—
309C2×C3×C4—22no—
310C2×C3×C4—21no—
311C2×C3×C4—22no—
312C2×C3×C4—32no—
313C2×C3×C4—32no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—122no—
318C2×C3×C4C2×C4×D312yes—
319C2×C3×C4C2×C4×D312yes—
320C2×C3×C4C2×D1211yescharacteristic
321C2×C3×C4#23512yes—
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4#23712yes—
324C2×C3×C4C23×D311yescharacteristic
325C2×C3×C4C23×D311yescharacteristic
326C2×Dic3—22no—
327C2×Dic3—22no—
328C2×Dic3—22no—
329C2×Dic3—42no—
330C2×Dic3—62no—
331C2×Dic3—62no—
332C2×Dic3—122no—
333C2×Dic3—128no—
334C2×Dic3—122no—
335C2×Dic3—122no—
336C2×Dic3—242no—
337C2×Dic3C2×D1212yes—
338C2×Dic3C2×D1212yes—
339D12—24no—
340D12—22no—
341D12—34no—
342D12—34no—
343D12—64no—
344D12—64no—
345D12—64no—
346D12—62no—
347D12—62no—
348D12—122no—
349D12—124no—
350D12C2×C4×D314yescomplemented
351C4×D3—128no—
352C4×D3—128no—
353C4×D3—128no—
354C3×C8—22no—
355C3×C8—22no—
356C3×C8—34no—
357C3×C8—42no—
358C3⋊C8C2×C4×D314yescomplemented
359C2×C32#44214yescomplemented
360C2×C32C2×C4×D411yescharacteristic
361C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
362C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
363C3⋊D3—44no—
364C3×D3—44no—
365C24—61no—
366C24—181no—
367C2×D4—32no—
368C2×D4—34no—
369C2×D4—61no—
370C2×D4—62no—
371C2×D4—92no—
372C2×D4—94no—
373C2×D4—181no—
374C2×D4—182no—
375C22×C4—31no—
376C22×C4—31no—
377C22×C4—61no—
378C22×C4—184no—
379C22×C4—184no—
380C22×C4—181no—
381C22×C4—364no—
382C22×C4—364no—
383C22×C4C2×D3211yescharacteristic
384D8—916no—
385C2×C8—22no—
386C2×C8—32no—
387C2×C8—34no—
388C2×C8C2×D3212yes—
389C4⋊C4—32no—
390C4⋊C4—61no—
391C4⋊C4—92no—
392C4⋊C4—181no—
393C22⋊C4—184no—
394C22⋊C4—184no—
395C42—32no—
396C42—32no—
397C22×C3—21no—
398C22×C3—22no—
399C22×C3—22no—
400C22×C3—22no—
401C22×C3—64no—
402C22×C3—128no—
403C22×C3—122no—
404C22×C3—122no—
405C22×C3C4×D1212yes—
406C22×C3#67⋊C412yes—
407C22×C3#90812yes—
408C22×C3#90812yes—
409C22×C3#91112yes—
410C22×C3#91412yes—
411C22×C3C22×D1211yescharacteristic
412C22×C3C2×D3×D411yescharacteristic
413C2×D3—24no—
414C2×D3—42no—
415C2×D3—42no—
416C2×D3—48no—
417C2×D3—64no—
418C2×D3—64no—
419C2×D3—124no—
420C2×D3—128no—
421C2×D3—122no—
422C2×D3—122no—
423C2×D3—122no—
424C2×D3—122no—
425C2×D3—128no—
426C2×D3—248no—
427C2×D3—242no—
428C2×D3—242no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—22no—
432C3×C4—62no—
433C3×C4—62no—
434C3×C4—122no—
435C3×C4C4×D1212yes—
436C3×C4#67⋊C412yes—
437C3×C4C22×C4×D311yescharacteristic
438C3×C4C22×C4×D311yescharacteristic
439C3×C4C2×#23511yescharacteristic
440C3×C4C2×#23711yescharacteristic
441Dic3—22no—
442Dic3—22no—
443Dic3—42no—
444Dic3—122no—
445Dic3—122no—
446Dic3—242no—
447C32C2×#44211yescharacteristic, complemented, Sylow
448C23—62no—
449C23—64no—
450C23—122no—
451C23—122no—
452C23—182no—
453C23—184no—
454C23—362no—
455C23—362no—
456C23D3×D1211yescharacteristic
457D4—34no—
458D4—62no—
459D4—64no—
460D4—94no—
461D4—182no—
462D4—184no—
463C2×C4—32no—
464C2×C4—32no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—122no—
469C2×C4—182no—
470C2×C4—368no—
471C2×C4—368no—
472C2×C4—362no—
473C2×C4C4×D3212yes—
474C2×C4D3×D1211yescharacteristic
475C2×C4#380412yes—
476C2×C4C22×D3211yescharacteristic
477C8—22no—
478C8—34no—
479C2×C3—24no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—124no—
484C2×C3#471114yescomplemented
485C2×C3#478514yescomplemented
486C2×C3C2×C4×D1211yescharacteristic
487C2×C3C2×#67⋊C411yescharacteristic
488C2×C3C2×#90811yescharacteristic
489C2×C3C2×#90811yescharacteristic
490C2×C3C2×#91111yescharacteristic
491C2×C3C2×#91411yescharacteristic
492D3—44no—
493D3—124no—
494D3—124no—
495D3—244no—
496C22—64no—
497C22—128no—
498C22—122no—
499C22—122no—
500C22—184no—
501C22—368no—
502C22—362no—
503C22—362no—
504C22#6379412yes—
505C22#6379512yes—
506C22#6388012yes—
507C22C2×D3×D1211yescharacteristic
508C4—62no—
509C4—62no—
510C4—122no—
511C4—362no—
512C4#6388012yes—
513C4C2×C4×D3211yescharacteristic
514C4C2×#380411yescharacteristic
515C3—21no—
516C3C2×#471111yescharacteristic, complemented
517C3C2×#478511yescharacteristic, complemented
518C2—124no—
519C2—364no—
520C2#1059074614yesdirect product factor
521C2C2×#6379411yescharacteristic
522C2C2×#6379511yescharacteristic
523C2C2×#6388011yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×#3714C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C2×#442
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
1. C2×#63894C2semidirect
2. C2×Dic3×D12C2semidirect
4. C2×#63648C2semidirect
5. C2×C3×#821C2semidirect
6. C2×C3×#815C2semidirect
7. C2×#63573C2semidirect
8. #10590746C2direct (N × H)
23. #63894C22semidirect
25. Dic3×D12C22semidirect
26. C2×#3714C4semidirect
28. #63648C22semidirect
29. C3×#821C22semidirect
30. C3×#815C22semidirect
31. #63573C22semidirect
43. C2×#821D3semidirect
45. C2×#815D3semidirect
55. C2×C4⋊(C3⋊D3)C2×C4semidirect
62. C2×C3×D12C2×C4semidirect
76. C2×C3×C3⋊C8C2×C4semidirect
80. #3714C2×C4semidirect
124. #821C2×D3semidirect
126. #815C2×D3semidirect
145. C4⋊(C3⋊D3)C22×C4semidirect
154. C3×D12C22×C4semidirect
158. C3×C3⋊C8C22×C4semidirect
204. C2×D12C4×D3semidirect
239. C2×C3⋊C8C4×D3semidirect
350. D12C2×C4×D3semidirect
358. C3⋊C8C2×C4×D3semidirect
359. C2×C32#442semidirect
447. C32C2×#442semidirect
484. C2×C3#4711semidirect
485. C2×C3#4785semidirect
516. C3C2×#4711semidirect
517. C3C2×#4785semidirect
520. C2#10590746direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#638942
C2×Dic3×D122
C22×#37142
C2×#636482
C2×C3×#8212
C2×C3×#8152
C2×#635732
#105907462
C2×#47853
C2×#47113