Finite Group Databasebeta

← C2×#10591423 #11869445

Subgroups — C2×#10591423 #11869445

Order 1152.

1037 conjugacy classes of subgroups.

The subgroup lattice has 509 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#938C211yesmaximal, characteristic
2C2×#63841C211yesmaximal, characteristic, complemented
3C2×#63659C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5#10591423C218yesmaximal, direct product factor
6C2×#63575C211yesmaximal, characteristic, complemented
7C2×#63574C211yesmaximal, characteristic, complemented
8C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
9C2×#5035—31nomaximal
10C2×#4784—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×C3×#67—21no—
13C22×C3×C4×D3C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×#217—21no—
17C3×#938—22no—
18C3×#938C2214yes—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×(C2×D3)⋊Dic3—21no—
23C2×Dic32—21no—
24#63841—22no—
25#63841C2214yescomplemented
26#63659C2214yescomplemented
27C3×#832C2214yescomplemented
28#63575C2214yescomplemented
29#63574C2214yescomplemented
30(C2×D3)⋊(C3⋊C8)C2214yescomplemented
31C2×C3×#121—31no—
32C2×#938D311yescharacteristic
33C2×#926—31no—
34C2×#892—31no—
35C2×C3×#102—31no—
36C2×#832—31no—
37C2×#832—31no—
38C2×#832—61no—
39C2×#832D311yescharacteristic, complemented
40C2×#830—31no—
41C2×(C2×D3)⋊C8—31no—
42C2×#818—31no—
43#5035—38no—
44C2×#808—31no—
45C2×#808—31no—
46C2×#807—31no—
47#4784—38no—
48C24×C32—21no—
49C23×C3×D3D411yescharacteristic
50C2×C32×D4—21no—
51C2×C32×D4—22no—
52C2×C32×D4—22no—
53C2×C32×D4C2312yes—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C2×C3×#67—24no—
57C2×C3×#67—44no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3D411yescharacteristic
61C2×C3×C4×D3—22no—
62C2×C3×C4×D3—22no—
63C2×C3×C4×D3D412yes—
64C2×C3×C4×D3C2312yes—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)C2312yes—
67C2×C3⋊(C3⋊C8)—22no—
68C2×C3⋊(C3⋊C8)C2312yes—
69C3×#217—24no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3C2312yes—
73C3×C4⋊Dic3C2312yes—
74C2×C3×C3⋊C8—22no—
75C2×C3×C3⋊C8C2312yes—
76(C2×D3)⋊Dic3—24no—
77Dic32—24no—
78C2×#482—91noSylow
79C22×C3×D4—21no—
80C22×C3×D4—61no—
81C22×C3×D4C2×D311yescharacteristic
82C22×C3×D4C2×D311yescharacteristic
83C23×C3×C4—31no—
84C22×#67—21no—
85C22×C4×D3C2×D311yescharacteristic
86C22×C3×C8—31no—
87C3×#121—34no—
88C3×#121—62no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C22⋊C4—61no—
92C2×#217—21no—
93C2×#217—61no—
94#938—22no—
95#938C2×D314yes—
96C2×(C2×D3)⋊C4—61no—
97#926—34no—
98#926—62no—
99C2×C4⋊Dic3—31no—
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—61no—
102C2×C4⋊Dic3C2×D311yescharacteristic
103C2×C4⋊Dic3C2×D311yescharacteristic
104C2×C4×Dic3—61no—
105C2×C4×Dic3—61no—
106C22×C3⋊C8—31no—
107C22×C3⋊C8—31no—
108C22×C3⋊C8—61no—
109C22×C3⋊C8C2×D311yescharacteristic
110#892—34no—
111#892—62no—
112C3×#102—34no—
113#832—34no—
114#832—34no—
115#832—64no—
116#832C2×D314yescomplemented
117#830—34no—
118(C2×D3)⋊C8—34no—
119#818—34no—
120#808—34no—
121#808—34no—
122#807—34no—
123C23×C32—22no—
124C23×C32—42no—
125C23×C32—42no—
126C23×C32—42no—
127C23×C32C2×D411yescharacteristic
128C22×C3×D3—22no—
129C22×C3×D3—22no—
130C22×C3×D3—22no—
131C22×C3×D3C2×D412yes—
132C32×D4—22no—
133C32×D4—22no—
134C32×D4—42no—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4#4112yes—
137C2×C32×C4#4112yes—
138C2×C32×C4C2411yescharacteristic
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—42no—
141C3×#67—48no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—42no—
146C2×C3×Dic3—42no—
147C2×C3×Dic3C2×D412yes—
148C3×C4×D3—24no—
149C3×C4×D3—22no—
150C3×C4×D3—22no—
151C3⋊(C3⋊C8)—22no—
152C3×C3⋊C8—22no—
153C2×#121—31no—
154C2×#117—91no—
155#482—98no—
156C2×#107—91no—
157C2×#106—91no—
158C2×#102—31no—
159C2×#102—91no—
160C2×C22⋊C8—91no—
161C24×C3—21no—
162C24×C3—21no—
163C24×C3—31no—
164C24×C3—41no—
165C23×D3#6711yescharacteristic
166C2×C3×D4—24no—
167C2×C3×D4—22no—
168C2×C3×D4—21no—
169C2×C3×D4—22no—
170C2×C3×D4—22no—
171C2×C3×D4—22no—
172C2×C3×D4—21no—
173C2×C3×D4—22no—
174C2×C3×D4—42no—
175C2×C3×D4—41no—
176C2×C3×D4—64no—
177C2×C3×D4—124no—
178C2×C3×D4C22×D312yes—
179C2×C3×D4C22×D312yes—
180C22×C3×C4—21no—
181C22×C3×C4—31no—
182C22×C3×C4—32no—
183C22×C3×C4—32no—
184C22×C3×C4—62no—
185C22×C3×C4—62no—
186C22×C3×C4—61no—
187C22×C3×C4—61no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C2×#67—24no—
191C2×#67—44no—
192C22×Dic3—21no—
193C22×Dic3—21no—
194C22×Dic3—61no—
195C22×Dic3—61no—
196C22×Dic3—121no—
197C22×Dic3#6711yescharacteristic
198C2×C4×D3—22no—
199C2×C4×D3—22no—
200C2×C4×D3#6712yes—
201C2×C4×D3C22×D312yes—
202C2×C3×C8—32no—
203C2×C3×C8—62no—
204C3×C4⋊C4—32no—
205C3×C4⋊C4—32no—
206C3×C4⋊C4—61no—
207C3×C4⋊C4—61no—
208C3×C22⋊C4—64no—
209#217—24no—
210#217—64no—
211(C2×D3)⋊C4—64no—
212C4⋊Dic3—21no—
213C4⋊Dic3—21no—
214C4⋊Dic3—32no—
215C4⋊Dic3—32no—
216C4⋊Dic3—62no—
217C4⋊Dic3—61no—
218C4⋊Dic3—61no—
219C4⋊Dic3—121no—
220C4⋊Dic3C22×D312yes—
221C4⋊Dic3C22×D312yes—
222C4×Dic3—64no—
223C4×Dic3—64no—
224C2×C3⋊C8—22no—
225C2×C3⋊C8—32no—
226C2×C3⋊C8—32no—
227C2×C3⋊C8—62no—
228C2×C3⋊C8—62no—
229C2×C3⋊C8—62no—
230C2×C3⋊C8—122no—
231C2×C3⋊C8C22×D312yes—
232C22×C32—42no—
233C22×C32—42no—
234C22×C32—42no—
235C22×C32—84no—
236C22×C32#12312yes—
237C22×C32#13512yes—
238C22×C32AGL(1,ℤ/8)12yes—
239C22×C32C22×D411yescharacteristic
240C2×C3×D3—22no—
241C2×C3×D3—22no—
242C2×C3×D3—22no—
243C2×C3×D3—44no—
244C32×C4#12312yes—
245C32×C4C2×#4111yescharacteristic
246C32×C4C2×#4111yescharacteristic
247C3⋊Dic3—42no—
248C3×Dic3—22no—
249C3×Dic3—42no—
250C3×Dic3—42no—
251C22×D4—61no—
252C22×D4D3211yescharacteristic
253C23×C4—31no—
254C22×C8—31no—
255C22×C8—91no—
256#121—34no—
257#121—62no—
258#117—94no—
259#117—182no—
260C2×C4⋊C4—31no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—91no—
263C2×C22⋊C4—61no—
264C2×C22⋊C4—181no—
265C2×C42—181no—
266#107—94no—
267#106—94no—
268#102—34no—
269#102—94no—
270C22⋊C8—94no—
271C23×C3—22no—
272C23×C3—22no—
273C23×C3—21no—
274C23×C3—32no—
275C23×C3—42no—
276C23×C3—44no—
277C23×C3—42no—
278C23×C3—42no—
279C23×C3—42no—
280C23×C3—42no—
281C23×C3—42no—
282C23×C3—42no—
283C23×C3—62no—
284C23×C3—62no—
285C23×C3—62no—
286C23×C3—82no—
287C23×C3—82no—
288C23×C3D3×D411yescharacteristic
289C23×C3C2×#6711yescharacteristic
290C22×D3—22no—
291C22×D3—22no—
292C22×D3—22no—
293C22×D3C2×#6712yes—
294C3×D4—24no—
295C3×D4—22no—
296C3×D4—22no—
297C3×D4—22no—
298C3×D4—22no—
299C3×D4—42no—
300C3×D4—44no—
301C3×D4—42no—
302C3×D4—42no—
303C3×D4—128no—
304C2×C3×C4—21no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—21no—
308C2×C3×C4—32no—
309C2×C3×C4—62no—
310C2×C3×C4—64no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—122no—
316C2×C3×C4—122no—
317C2×C3×C4#23512yes—
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4#23712yes—
320C2×C3×C4#23712yes—
321C2×C3×C4#23712yes—
322C2×C3×C4C2×#6711yescharacteristic
323C2×C3×C4C23×D311yescharacteristic
324C2×C3×C4C23×D311yescharacteristic
325#67—48no—
326C2×Dic3—22no—
327C2×Dic3—22no—
328C2×Dic3—22no—
329C2×Dic3—42no—
330C2×Dic3—42no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—122no—
334C2×Dic3—122no—
335C2×Dic3—122no—
336C2×Dic3—242no—
337C2×Dic3C2×#6712yes—
338C4×D3—24no—
339C4×D3—22no—
340C4×D3—22no—
341C3×C8—62no—
342C3⋊C8—22no—
343C3⋊C8—62no—
344C3⋊C8—62no—
345C3⋊C8—122no—
346C2×C32—82no—
347C2×C32#48214yescomplemented
348C2×C32C2×#12311yescharacteristic
349C2×C32C2×#13511yescharacteristic
350C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
351C3×D3—42no—
352C24—21no—
353C24—31no—
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—21no—
357C2×D4—64no—
358C2×D4—124no—
359C2×D4C2×D3212yes—
360C22×C4—31no—
361C22×C4—32no—
362C22×C4—32no—
363C22×C4—62no—
364C22×C4—62no—
365C22×C4—61no—
366C22×C4—61no—
367C22×C4—181no—
368C22×C4C2×D3211yescharacteristic
369C2×C8—32no—
370C2×C8—62no—
371C2×C8—92no—
372C2×C8—182no—
373C4⋊C4—32no—
374C4⋊C4—32no—
375C4⋊C4—61no—
376C4⋊C4—61no—
377C4⋊C4—92no—
378C4⋊C4—181no—
379C22⋊C4—64no—
380C22⋊C4—184no—
381C42—184no—
382C22×C3—21no—
383C22×C3—22no—
384C22×C3—22no—
385C22×C3—22no—
386C22×C3—44no—
387C22×C3—42no—
388C22×C3—42no—
389C22×C3—42no—
390C22×C3—42no—
391C22×C3—42no—
392C22×C3—42no—
393C22×C3—62no—
394C22×C3—62no—
395C22×C3—62no—
396C22×C3—82no—
397C22×C3—82no—
398C22×C3—88no—
399C22×C3—84no—
400C22×C3—84no—
401C22×C3—124no—
402C22×C3#88312yes—
403C22×C3#91212yes—
404C22×C3#91412yes—
405C22×C3#93212yes—
406C22×C3#93512yes—
407C22×C3#95012yes—
408C22×C3C2×D3×D411yescharacteristic
409C22×C3C22×#6711yescharacteristic
410C2×D3—22no—
411C2×D3—22no—
412C2×D3—22no—
413C2×D3—44no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—22no—
417C3×C4—62no—
418C3×C4—122no—
419C3×C4—122no—
420C3×C4#88312yes—
421C3×C4#93512yes—
422C3×C4C2×#23511yescharacteristic
423C3×C4C2×#23711yescharacteristic
424C3×C4C2×#23711yescharacteristic
425C3×C4C2×#23711yescharacteristic
426Dic3—22no—
427Dic3—42no—
428Dic3—42no—
429Dic3—122no—
430Dic3—122no—
431Dic3—242no—
432C32C2×#48211yescharacteristic, complemented, Sylow
433C23—22no—
434C23—32no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23—62no—
439C23—62no—
440C23—62no—
441C23D3×#6711yescharacteristic
442D4—22no—
443D4—22no—
444D4—42no—
445D4—128no—
446C2×C4—32no—
447C2×C4—62no—
448C2×C4—62no—
449C2×C4—62no—
450C2×C4—64no—
451C2×C4—62no—
452C2×C4—62no—
453C2×C4—122no—
454C2×C4—122no—
455C2×C4—182no—
456C2×C4—362no—
457C2×C4#380412yes—
458C2×C4#380512yes—
459C2×C4D3×#6711yescharacteristic
460C2×C4C22×D3211yescharacteristic
461C8—62no—
462C8—182no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—24no—
467C2×C3—84no—
468C2×C3—82no—
469C2×C3—82no—
470C2×C3—122no—
471C2×C3#478414yescomplemented
472C2×C3#503514yescomplemented
473C2×C3C2×#88311yescharacteristic
474C2×C3C2×#91211yescharacteristic
475C2×C3C2×#91411yescharacteristic
476C2×C3C2×#93211yescharacteristic
477C2×C3C2×#93511yescharacteristic
478C2×C3C2×#95011yescharacteristic
479D3—42no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—62no—
484C22—62no—
485C22—62no—
486C22—84no—
487C22—124no—
488C22#6393312yes—
489C22#6393412yes—
490C22#6396912yes—
491C22C2×D3×#6711yescharacteristic
492C4—62no—
493C4—122no—
494C4—122no—
495C4—362no—
496C4#6396912yes—
497C4C2×#380411yescharacteristic
498C4C2×#380511yescharacteristic
499C3—21no—
500C3C2×#478411yescharacteristic, complemented
501C3C2×#503511yescharacteristic, complemented
502C2—82no—
503C2—122no—
504C2#1059142314yesdirect product factor
505C2C2×#6393311yescharacteristic
506C2C2×#6393411yescharacteristic
507C2C2×#6396911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC2×C3×#938C2
hypercenterC22×D4D32
hypocenterC32C2×#482
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63841C2semidirect
3. C2×#63659C2semidirect
4. C2×C3×#832C2semidirect
5. #10591423C2direct (N × H)
6. C2×#63575C2semidirect
7. C2×#63574C2semidirect
8. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
25. #63841C22semidirect
26. #63659C22semidirect
27. C3×#832C22semidirect
28. #63575C22semidirect
29. #63574C22semidirect
30. (C2×D3)⋊(C3⋊C8)C22semidirect
39. C2×#832D3semidirect
116. #832C2×D3semidirect
347. C2×C32#482semidirect
432. C32C2×#482semidirect
471. C2×C3#4784semidirect
472. C2×C3#5035semidirect
500. C3C2×#4784semidirect
501. C3C2×#5035semidirect
504. C2#10591423direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9382
C2×#638412
C2×#636592
C2×C3×#8322
#105914232
C2×#635752
C2×#635742
C2×(C2×D3)⋊(C3⋊C8)2
C2×#50353
C2×#47843