Finite Group Databasebeta

← C2×#10591136 #11869446

Subgroups — C2×#10591136 #11869446

Order 1152.

1149 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64139C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic, complemented
3C2×C3×#830C211yesmaximal, characteristic, complemented
4#10591136C218yesmaximal, direct product factor
5C2×#63575C211yesmaximal, characteristic, complemented
6C2×#63573C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic, complemented
8C2×#63564C211yesmaximal, characteristic, complemented
9C2×#5003—31nomaximal
10C2×#4737—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×#638—21no—
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14#64139—22no—
15#64139C2214yes—
16C2×#3752—21no—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C3×#217—21no—
19C3×#926—22no—
20C3×#926C2214yescomplemented
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4×Dic3—21no—
24C22×C3×C3⋊C8C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C3×#830C2214yescomplemented
27#63575C2214yescomplemented
28#63573C2214yescomplemented
29#63564C2214yescomplemented
30#63564C2214yescomplemented
31C2×C3×#117—31no—
32C2×#930—31no—
33C2×#930—31no—
34C2×#930—61no—
35C2×#926D311yescharacteristic, complemented
36C2×C3×C22⋊C8—31no—
37C2×#830D311yescharacteristic, complemented
38C2×#821—31no—
39C2×#821—31no—
40C2×#818—31no—
41C2×#817—31no—
42#5003—38no—
43C2×#809—31no—
44C2×#809—31no—
45C2×#808—31no—
46C2×#807—31no—
47#4737—38no—
48C24×C32D411yescharacteristic
49C23×C3⋊D3—21no—
50C22×C32×C4—22no—
51C22×C32×C4—22no—
52C22×C32×C4D411yescharacteristic
53C22×C32×C4D412yes—
54C22×C32×C4C2312yes—
55C22×C32×C4C2311yescharacteristic
56C2×#638—24no—
57C2×#638—44no—
58C22×C3⋊Dic3—21no—
59C2×C4⋊(C3⋊D3)—22no—
60C2×C4⋊(C3⋊D3)—22no—
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)C2312yes—
63C22×C3×Dic3—21no—
64C22×C3×Dic3—21no—
65#3752—24no—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)C2312yes—
68C3×#217—24no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3C2312yes—
72C3×C4⋊Dic3C2312yes—
73C3×C4×Dic3—24no—
74C2×C3×C3⋊C8—22no—
75C2×C3×C3⋊C8—22no—
76C2×C3×C3⋊C8C2312yes—
77C2×C3×C3⋊C8C2312yes—
78C2×#482—91noSylow
79C23×C3×C4—21no—
80C23×C3×C4C2×D311yescharacteristic
81C23×C3×C4C2×D311yescharacteristic
82C22×#67—62no—
83C22×#67—61no—
84C22×#67—61no—
85C22×D12—31no—
86C22×D12—31no—
87C22×D12—61no—
88C22×C3×C8—31no—
89C22×C3×C8—31no—
90C3×#117—34no—
91C3×#117—62no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C22⋊C4—61no—
95C2×C3×C42—61no—
96C2×#217—21no—
97#930—34no—
98#930—34no—
99#930—64no—
100#930—64no—
101#930—62no—
102#930—62no—
103C2×(C2×D3)⋊C4—62no—
104C2×(C2×D3)⋊C4—61no—
105C2×(C2×D3)⋊C4—61no—
106#926—22no—
107#926C2×D314yescomplemented
108C2×C4⋊Dic3—31no—
109C2×C4⋊Dic3—31no—
110C2×C4⋊Dic3—61no—
111C2×C4⋊Dic3C2×D311yescharacteristic
112C2×C4⋊Dic3C2×D311yescharacteristic
113C2×C4×Dic3—21no—
114C22×C3⋊C8C2×D311yescharacteristic
115C22×C3⋊C8C2×D311yescharacteristic
116C3×C22⋊C8—34no—
117#830C2×D314yescomplemented
118#821—34no—
119#821—34no—
120#818—34no—
121#817—34no—
122#809—34no—
123#809—34no—
124#808—34no—
125#807—34no—
126C23×C32—22no—
127C23×C32—22no—
128C23×C32—22no—
129C23×C32C2×D412yes—
130C23×C32C2×D411yescharacteristic
131C22×C3⋊D3—22no—
132C22×C3⋊D3—42no—
133C22×C3⋊D3—42no—
134C22×C3⋊D3—42no—
135C2×C32×C4—22no—
136C2×C32×C4—24no—
137C2×C32×C4—22no—
138C2×C32×C4—22no—
139C2×C32×C4C2×D412yes—
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4112yes—
142C2×C32×C4#4112yes—
143C2×C32×C4C2411yescharacteristic
144#638—48no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—42no—
147C4⋊(C3⋊D3)—22no—
148C4⋊(C3⋊D3)—22no—
149C4⋊(C3⋊D3)—42no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—42no—
153C2×C3×Dic3—42no—
154C3×C3⋊C8—22no—
155C3×C3⋊C8—22no—
156C2×#121—91no—
157C2×#117—31no—
158#482—98no—
159C2×#107—91no—
160C2×#106—91no—
161C2×#102—91no—
162C2×#102—91no—
163C2×C22⋊C8—31no—
164C24×C3—21no—
165C24×C3D1211yescharacteristic
166C24×C3#6711yescharacteristic
167C23×D3—62no—
168C23×D3—61no—
169C23×D3—61no—
170C22×C3×C4—22no—
171C22×C3×C4—22no—
172C22×C3×C4—22no—
173C22×C3×C4—22no—
174C22×C3×C4—21no—
175C22×C3×C4—22no—
176C22×C3×C4—21no—
177C22×C3×C4—22no—
178C22×C3×C4—42no—
179C22×C3×C4—42no—
180C22×C3×C4—61no—
181C22×C3×C4—61no—
182C22×C3×C4D1211yescharacteristic
183C22×C3×C4D1212yes—
184C22×C3×C4#6711yescharacteristic
185C22×C3×C4#6712yes—
186C22×C3×C4C22×D312yes—
187C22×C3×C4C22×D312yes—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C2×#67—68no—
191C2×#67—64no—
192C2×#67—64no—
193C2×#67—128no—
194C2×#67—124no—
195C2×#67—124no—
196C22×Dic3—21no—
197C22×Dic3—21no—
198C22×Dic3—62no—
199C22×Dic3—61no—
200C22×Dic3—61no—
201C2×D12—32no—
202C2×D12—32no—
203C2×D12—62no—
204C2×D12—62no—
205C2×D12—62no—
206C2×D12—62no—
207C2×D12—62no—
208C2×D12—62no—
209C2×D12—61no—
210C2×D12—61no—
211C2×D12—122no—
212C2×D12—122no—
213C2×C3×C8—32no—
214C2×C3×C8—32no—
215C2×C3×C8—62no—
216C2×C3×C8—62no—
217C3×C4⋊C4—32no—
218C3×C4⋊C4—32no—
219C3×C4⋊C4—61no—
220C3×C4⋊C4—61no—
221C3×C22⋊C4—64no—
222C3×C42—64no—
223#217—24no—
224(C2×D3)⋊C4—68no—
225(C2×D3)⋊C4—64no—
226(C2×D3)⋊C4—64no—
227C4⋊Dic3—21no—
228C4⋊Dic3—21no—
229C4⋊Dic3—32no—
230C4⋊Dic3—32no—
231C4⋊Dic3—62no—
232C4⋊Dic3—62no—
233C4⋊Dic3—61no—
234C4⋊Dic3—61no—
235C4⋊Dic3C22×D312yes—
236C4⋊Dic3C22×D312yes—
237C4×Dic3—24no—
238C2×C3⋊C8—22no—
239C2×C3⋊C8—22no—
240C2×C3⋊C8C22×D312yes—
241C2×C3⋊C8C22×D312yes—
242C22×C32—22no—
243C22×C32—22no—
244C22×C32—22no—
245C22×C32—44no—
246C22×C32#12312yes—
247C22×C32#13512yes—
248C22×C32AGL(1,ℤ/8)12yes—
249C22×C32C22×D411yescharacteristic
250C2×C3⋊D3—42no—
251C2×C3⋊D3—42no—
252C2×C3⋊D3—42no—
253C2×C3⋊D3—84no—
254C32×C4—22no—
255C32×C4#12312yes—
256C32×C4C2×#4111yescharacteristic
257C32×C4C2×#4111yescharacteristic
258C3⋊Dic3—42no—
259C3×Dic3—42no—
260C3×Dic3—42no—
261C22×D4—91no—
262C22×D4—181no—
263C23×C4D3211yescharacteristic
264C22×C8—31no—
265C22×C8—31no—
266#121—94no—
267#121—182no—
268#117—34no—
269#117—62no—
270C2×C4⋊C4—31no—
271C2×C4⋊C4—31no—
272C2×C4⋊C4—91no—
273C2×C22⋊C4—61no—
274C2×C22⋊C4—181no—
275C2×C42—61no—
276#107—94no—
277#106—94no—
278#102—94no—
279#102—94no—
280C22⋊C8—34no—
281C23×C3—24no—
282C23×C3—22no—
283C23×C3—22no—
284C23×C3—22no—
285C23×C3—22no—
286C23×C3—22no—
287C23×C3—22no—
288C23×C3—22no—
289C23×C3—21no—
290C23×C3—42no—
291C23×C3—42no—
292C23×C3C2×D1212yes—
293C23×C3C2×D1211yescharacteristic
294C23×C3C2×#6712yes—
295C23×C3C2×#6711yescharacteristic
296C22×D3—64no—
297C22×D3—62no—
298C22×D3—62no—
299C22×D3—124no—
300C22×D3—124no—
301C22×D3—124no—
302C22×D3—122no—
303C22×D3—122no—
304C22×D3—122no—
305C22×D3—122no—
306C22×D3—122no—
307C22×D3—122no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—24no—
311C2×C3×C4—24no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—21no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—21no—
320C2×C3×C4—22no—
321C2×C3×C4—42no—
322C2×C3×C4—42no—
323C2×C3×C4—44no—
324C2×C3×C4—42no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—122no—
328C2×C3×C4—122no—
329C2×C3×C4C2×D1212yes—
330C2×C3×C4C2×D1211yescharacteristic
331C2×C3×C4#23512yes—
332C2×C3×C4#23512yes—
333C2×C3×C4#23712yes—
334C2×C3×C4#23712yes—
335C2×C3×C4C2×#6712yes—
336C2×C3×C4C2×#6711yescharacteristic
337C2×C3×C4C23×D311yescharacteristic
338C2×C3×C4C23×D311yescharacteristic
339#67—1216no—
340#67—128no—
341#67—128no—
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—42no—
345C2×Dic3—42no—
346C2×Dic3—64no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—124no—
350C2×Dic3—122no—
351C2×Dic3—122no—
352D12—62no—
353D12—62no—
354D12—62no—
355D12—62no—
356D12—122no—
357D12—122no—
358D12—124no—
359D12—122no—
360D12—122no—
361C3×C8—62no—
362C3×C8—62no—
363C3⋊C8—22no—
364C3⋊C8—22no—
365C2×C32—42no—
366C2×C32#48214yescomplemented
367C2×C32C2×#12311yescharacteristic
368C2×C32C2×#13511yescharacteristic
369C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
370C3⋊D3—82no—
371C24—181no—
372C24#62611yescharacteristic
373C2×D4—92no—
374C2×D4—184no—
375C2×D4—182no—
376C2×D4—182no—
377C2×D4—181no—
378C2×D4—364no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—61no—
382C22×C4—61no—
383C22×C4—181no—
384C22×C4#62612yes—
385C22×C4#62611yescharacteristic
386C22×C4C2×D3212yes—
387C22×C4C2×D3211yescharacteristic
388C2×C8—32no—
389C2×C8—32no—
390C2×C8—62no—
391C2×C8—62no—
392C4⋊C4—32no—
393C4⋊C4—32no—
394C4⋊C4—61no—
395C4⋊C4—61no—
396C4⋊C4—92no—
397C4⋊C4—181no—
398C22⋊C4—64no—
399C22⋊C4—184no—
400C42—64no—
401C22×C3—24no—
402C22×C3—22no—
403C22×C3—22no—
404C22×C3—22no—
405C22×C3—22no—
406C22×C3—22no—
407C22×C3—22no—
408C22×C3—21no—
409C22×C3—22no—
410C22×C3—22no—
411C22×C3—22no—
412C22×C3—42no—
413C22×C3—42no—
414C22×C3—48no—
415C22×C3—44no—
416C22×C3—44no—
417C22×C3#88612yes—
418C22×C3#90412yes—
419C22×C3#90812yes—
420C22×C3#92912yes—
421C22×C3#94912yes—
422C22×C3#95012yes—
423C22×C3C22×D1211yescharacteristic
424C22×C3C22×#6711yescharacteristic
425C2×D3—124no—
426C2×D3—124no—
427C2×D3—124no—
428C2×D3—122no—
429C2×D3—122no—
430C2×D3—122no—
431C2×D3—122no—
432C2×D3—122no—
433C2×D3—122no—
434C2×D3—248no—
435C2×D3—244no—
436C2×D3—244no—
437C3×C4—22no—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—22no—
442C3×C4—42no—
443C3×C4—122no—
444C3×C4—122no—
445C3×C4#88612yes—
446C3×C4#92912yes—
447C3×C4C2×#23511yescharacteristic
448C3×C4C2×#23511yescharacteristic
449C3×C4C2×#23711yescharacteristic
450C3×C4C2×#23711yescharacteristic
451Dic3—42no—
452Dic3—42no—
453Dic3—124no—
454Dic3—122no—
455Dic3—122no—
456C32C2×#48211yescharacteristic, complemented, Sylow
457C23—22no—
458C23—22no—
459C23—22no—
460C23—182no—
461C23—362no—
462C23—362no—
463C23—362no—
464C23C2×#62612yes—
465C23C2×#62611yescharacteristic
466D4—182no—
467D4—182no—
468D4—368no—
469D4—362no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—62no—
475C2×C4—62no—
476C2×C4—122no—
477C2×C4—122no—
478C2×C4—182no—
479C2×C4—362no—
480C2×C4#380412yes—
481C2×C4#380412yes—
482C2×C4C2×#62612yes—
483C2×C4C2×#62611yescharacteristic
484C2×C4C22×D3211yescharacteristic
485C8—62no—
486C8—62no—
487C2×C3—24no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—44no—
492C2×C3—42no—
493C2×C3—42no—
494C2×C3#473714yescomplemented
495C2×C3#500314yescomplemented
496C2×C3C2×#88611yescharacteristic
497C2×C3C2×#90411yescharacteristic
498C2×C3C2×#90811yescharacteristic
499C2×C3C2×#92911yescharacteristic
500C2×C3C2×#94911yescharacteristic
501C2×C3C2×#95011yescharacteristic
502D3—244no—
503D3—242no—
504D3—242no—
505C22—22no—
506C22—22no—
507C22—22no—
508C22—44no—
509C22—362no—
510C22—362no—
511C22—362no—
512C22—724no—
513C22#6382512yes—
514C22#6382912yes—
515C22#6396612yes—
516C22C22×#62611yescharacteristic
517C4—22no—
518C4—122no—
519C4—122no—
520C4—362no—
521C4#6396612yes—
522C4C2×#380411yescharacteristic
523C4C2×#380411yescharacteristic
524C3—21no—
525C3C2×#473711yescharacteristic, complemented
526C3C2×#500311yescharacteristic, complemented
527C2—42no—
528C2—722no—
529C2#1059113614yesdirect product factor
530C2C2×#6382511yescharacteristic
531C2C2×#6382911yescharacteristic
532C2C2×#6396611yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC2×#64139C2
hypercenterC23×C4D32
hypocenterC32C2×#482
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#926C2semidirect
3. C2×C3×#830C2semidirect
4. #10591136C2direct (N × H)
5. C2×#63575C2semidirect
6. C2×#63573C2semidirect
7. C2×#63564C2semidirect
8. C2×#63564C2semidirect
20. C3×#926C22semidirect
26. C3×#830C22semidirect
27. #63575C22semidirect
28. #63573C22semidirect
29. #63564C22semidirect
30. #63564C22semidirect
35. C2×#926D3semidirect
37. C2×#830D3semidirect
107. #926C2×D3semidirect
117. #830C2×D3semidirect
366. C2×C32#482semidirect
456. C32C2×#482semidirect
494. C2×C3#4737semidirect
495. C2×C3#5003semidirect
525. C3C2×#4737semidirect
526. C3C2×#5003semidirect
529. C2#10591136direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641392
C2×C3×#9262
C2×C3×#8302
#105911362
C2×#635752
C2×#635732
C2×#635642
C2×#50033
C2×#47373