Finite Group Databasebeta

← C2×#10591556 #11857804

Subgroups — C2×#10591556 #11857804

Order 1152.

1665 conjugacy classes of subgroups.

The subgroup lattice has 559 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#239C211yesmaximal, characteristic
2C2×#63841C211yesmaximal, characteristic, complemented
3C22×D3×C3⋊C8C211yesmaximal, characteristic, complemented
4C2×#63662C211yesmaximal, characteristic, complemented
5C2×C3×#835C211yesmaximal, characteristic, complemented
6#10591556C218yesmaximal, direct product factor
7C2×#63563C211yesmaximal, characteristic, complemented
8C2×#63562C211yesmaximal, characteristic, complemented
9C2×#5233—31nomaximal
10C2×#4804—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C2×C3×#239—24no—
13C2×C3×#239—22no—
14C2×C3×#239C418yescomplemented
15C2×C3×#239C2214yes—
16C22×C3×D12—21no—
17C22×C3×D12C2211yescharacteristic
18C22×C3×C4×D3—21no—
19C22×C3×C4×D3C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×(C2×D3)⋊Dic3—21no—
25C2×Dic32—21no—
26#63841—22no—
27#63841C2214yescomplemented
28C2×D3×C3⋊C8—24no—
29C2×D3×C3⋊C8C2214yescomplemented
30#63662C2214yescomplemented
31C3×#835C2214yescomplemented
32#63563C2214yescomplemented
33#63562C2214yescomplemented
34C22×C3×#41—31no—
35C22×#239D311yescharacteristic
36C2×#926—31no—
37C23×C3⋊C8—31no—
38C22×D3×C8—31no—
39C2×#892—31no—
40C2×C3×#103—31no—
41#5233—38no—
42C2×#835—31no—
43C2×#835—31no—
44C2×#835—61no—
45C2×#835D311yescharacteristic, complemented
46C2×#832—31no—
47C2×#832—31no—
48C2×#821—31no—
49C2×#809—31no—
50#4804—38no—
51C23×C3×D3—21no—
52C23×C3×D3D411yescharacteristic
53C2×C32×Q8—22no—
54C2×C32×Q8—21no—
55C2×C32×Q8C2×C414yes—
56C2×C32×Q8C2312yes—
57C22×C32×C4—21no—
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3—21no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3D411yescharacteristic
62C3×#239—216no—
63C3×#239—28no—
64C3×#239C2×C4116yescomplemented
65C2×C3×D12—28no—
66C2×C3×D12—24no—
67C2×C3×D12—21no—
68C2×C3×D12—22no—
69C2×C3×D12C2×C414yes—
70C2×C3×D12C2312yes—
71C2×C3×C4×D3—28no—
72C2×C3×C4×D3—24no—
73C2×C3×C4×D3C2×C414yes—
74C2×C3×C4×D3D412yes—
75C2×C3×C4×D3D414yes—
76C2×C3×C4×D3C2312yes—
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)C2312yes—
79C2×C3⋊(C3⋊C8)—22no—
80C2×C3⋊(C3⋊C8)C2312yes—
81C3×C4⋊Dic3—21no—
82C3×C4⋊Dic3C2312yes—
83C2×C3×C3⋊C8—22no—
84C2×C3×C3⋊C8C2312yes—
85(C2×D3)⋊Dic3—24no—
86Dic32—24no—
87D3×C3⋊C8—28no—
88C2×#416—91noSylow
89C2×C3×#41—38no—
90C2×C3×#41—34no—
91C2×C3×#41—64no—
92C2×C3×#41—62no—
93C22×C3×Q8—21no—
94C22×C3×Q8C2×D311yescharacteristic
95C22×C3×Q8C2×D311yescharacteristic
96C22×C3×D4—31no—
97C22×C3×D4—61no—
98C23×C3×C4—31no—
99C23×C3×C4—61no—
100C2×#239—24no—
101C2×#239—22no—
102C2×#239Dic318yescomplemented
103C2×#239C2×D314yes—
104C22×D12—21no—
105C22×D12C2×D311yescharacteristic
106C22×C4×D3—21no—
107C22×C4×D3C2×D311yescharacteristic
108C22×C3×C8—31no—
109C2×C3×C4⋊C4—31no—
110C2×#217—61no—
111C2×(C2×D3)⋊C4—61no—
112#926—34no—
113#926—62no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—31no—
116C2×C4⋊Dic3—61no—
117C2×C4⋊Dic3C2×D311yescharacteristic
118C2×C4×Dic3—61no—
119C2×C4×Dic3—61no—
120C22×C3⋊C8—31no—
121C22×C3⋊C8—31no—
122C22×C3⋊C8—34no—
123C22×C3⋊C8—61no—
124C22×C3⋊C8—64no—
125C22×C3⋊C8C2×D311yescharacteristic
126C2×D3×C8—34no—
127C2×D3×C8—64no—
128#892—34no—
129#892—62no—
130C3×#103—34no—
131#835—34no—
132#835—34no—
133#835—64no—
134#835C2×D314yescomplemented
135#832—34no—
136#832—34no—
137#821—34no—
138#809—34no—
139C23×C32C2×D411yescharacteristic
140C22×C3×D3—22no—
141C22×C3×D3—22no—
142C22×C3×D3—24no—
143C22×C3×D3—22no—
144C22×C3×D3—42no—
145C22×C3×D3—42no—
146C22×C3×D3C22⋊C414yes—
147C22×C3×D3C2×D412yes—
148C32×Q8—24no—
149C32×Q8—22no—
150C32×Q8C22×C414yes—
151C2×C32×C4—24no—
152C2×C32×C4—22no—
153C2×C32×C4C22×C412yes—
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D412yes—
156C2×C32×C4C2411yescharacteristic
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—42no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—42no—
161C2×C3×Dic3C22⋊C414yes—
162C2×C3×Dic3C2×D412yes—
163C3×D12—216no—
164C3×D12—24no—
165C3×D12—22no—
166C3×D12C22×C414yes—
167C3×C4×D3—216no—
168C3×C4×D3C22⋊C418yes—
169C3×C4×D3C22×C414yes—
170C3×C4×D3C2×D414yes—
171C3⋊(C3⋊C8)—22no—
172C3×C3⋊C8—22no—
173C22×#41—31no—
174C23×C8—91no—
175C2×#117—91no—
176#416—98no—
177C2×#103—31no—
178C2×#103—91no—
179C2×#102—91no—
180C2×#102—91no—
181C24×C3—31no—
182C24×C3—61no—
183C23×D3—21no—
184C23×D3#6711yescharacteristic
185C3×#41—316no—
186C3×#41—616no—
187C3×#41—68no—
188C2×C3×Q8—22no—
189C2×C3×Q8—21no—
190C2×C3×Q8—22no—
191C2×C3×Q8—21no—
192C2×C3×Q8—24no—
193C2×C3×Q8—22no—
194C2×C3×Q8—42no—
195C2×C3×Q8—41no—
196C2×C3×Q8C4×D314yes—
197C2×C3×Q8C2×Dic314yes—
198C2×C3×Q8C22×D312yes—
199C2×C3×Q8C22×D312yes—
200C2×C3×D4—34no—
201C2×C3×D4—32no—
202C2×C3×D4—68no—
203C2×C3×D4—64no—
204C2×C3×D4—61no—
205C2×C3×D4—62no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—31no—
210C22×C3×C4—34no—
211C22×C3×C4—34no—
212C22×C3×C4—32no—
213C22×C3×C4—32no—
214C22×C3×C4—41no—
215C22×C3×C4—68no—
216C22×C3×C4—64no—
217C22×C3×C4—61no—
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C22×Dic3—21no—
221C22×Dic3—61no—
222C22×Dic3—61no—
223C22×Dic3—121no—
224C22×Dic3#6711yescharacteristic
225#239—216no—
226#239—28no—
227#239C2×Dic3116yescomplemented
228C2×D12—28no—
229C2×D12—24no—
230C2×D12—21no—
231C2×D12—22no—
232C2×D12C2×Dic314yes—
233C2×D12C22×D312yes—
234C2×C4×D3—28no—
235C2×C4×D3—24no—
236C2×C4×D3C2×Dic314yes—
237C2×C4×D3#6712yes—
238C2×C4×D3#6714yes—
239C2×C4×D3C22×D312yes—
240C2×C3×C8—32no—
241C2×C3×C8—62no—
242C3×C4⋊C4—32no—
243C3×C4⋊C4—61no—
244#217—64no—
245(C2×D3)⋊C4—64no—
246C4⋊Dic3—21no—
247C4⋊Dic3—32no—
248C4⋊Dic3—32no—
249C4⋊Dic3—62no—
250C4⋊Dic3—61no—
251C4⋊Dic3—61no—
252C4⋊Dic3—121no—
253C4⋊Dic3C22×D312yes—
254C4×Dic3—64no—
255C4×Dic3—64no—
256C2×C3⋊C8—22no—
257C2×C3⋊C8—32no—
258C2×C3⋊C8—32no—
259C2×C3⋊C8—62no—
260C2×C3⋊C8—68no—
261C2×C3⋊C8—62no—
262C2×C3⋊C8—62no—
263C2×C3⋊C8—122no—
264C2×C3⋊C8C22×D312yes—
265D3×C8—68no—
266C22×C32C2×C22⋊C412yes—
267C22×C32#13512yes—
268C22×C32#13512yes—
269C22×C32C22×D411yescharacteristic
270C2×C3×D3—22no—
271C2×C3×D3—22no—
272C2×C3×D3—28no—
273C2×C3×D3—24no—
274C2×C3×D3—42no—
275C2×C3×D3—42no—
276C2×C3×D3—48no—
277C2×C3×D3C2×C22⋊C414yes—
278C32×C4—24no—
279C32×C4C2×C22⋊C412yes—
280C32×C4C23×C411yescharacteristic
281C32×C4C22×D411yescharacteristic
282C3⋊Dic3—42no—
283C3×Dic3—42no—
284C3×Dic3C2×C22⋊C414yes—
285C2×#41—38no—
286C2×#41—34no—
287C2×#41—62no—
288C2×#41—64no—
289C22×Q8D3211yescharacteristic
290C22×D4—31no—
291C22×D4—61no—
292C23×C4—31no—
293C23×C4—61no—
294C22×C8—31no—
295C22×C8—94no—
296C22×C8—91no—
297C22×C8—184no—
298#117—94no—
299#117—182no—
300C2×C4⋊C4—31no—
301C2×C4⋊C4—91no—
302C2×C22⋊C4—181no—
303C2×C42—181no—
304#103—34no—
305#103—94no—
306#102—94no—
307#102—94no—
308C23×C3—21no—
309C23×C3—34no—
310C23×C3—32no—
311C23×C3—62no—
312C23×C3—62no—
313C23×C3—64no—
314C23×C3—62no—
315C23×C3—122no—
316C23×C3—122no—
317C23×C3D3×D411yescharacteristic
318C23×C3C2×#6711yescharacteristic
319C22×D3—22no—
320C22×D3—22no—
321C22×D3—24no—
322C22×D3—22no—
323C22×D3—42no—
324C22×D3—42no—
325C22×D3#21714yes—
326C22×D3C2×#6712yes—
327C3×Q8—24no—
328C3×Q8—24no—
329C3×Q8—22no—
330C3×Q8—22no—
331C3×Q8—24no—
332C3×Q8—42no—
333C3×Q8—44no—
334C3×Q8C2×C4×D314yes—
335C3×Q8C22×Dic314yes—
336C3×D4—34no—
337C3×D4—616no—
338C3×D4—64no—
339C3×D4—62no—
340C2×C3×C4—24no—
341C2×C3×C4—24no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—21no—
348C2×C3×C4—34no—
349C2×C3×C4—32no—
350C2×C3×C4—38no—
351C2×C3×C4—34no—
352C2×C3×C4—34no—
353C2×C3×C4—42no—
354C2×C3×C4—44no—
355C2×C3×C4—616no—
356C2×C3×C4—62no—
357C2×C3×C4—122no—
358C2×C3×C4C2×C4×D312yes—
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D412yes—
361C2×C3×C4C22×Dic312yes—
362C2×C3×C4C2×#6711yescharacteristic
363C2×C3×C4C2×#6712yes—
364C2×C3×C4C23×D311yescharacteristic
365C2×C3×C4C23×D311yescharacteristic
366C2×Dic3—22no—
367C2×Dic3—42no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—122no—
371C2×Dic3—122no—
372C2×Dic3—122no—
373C2×Dic3—242no—
374C2×Dic3#21714yes—
375C2×Dic3C2×#6712yes—
376D12—216no—
377D12—24no—
378D12—22no—
379D12C22×Dic314yes—
380C4×D3—216no—
381C4×D3#21718yes—
382C4×D3C22×Dic314yes—
383C4×D3C2×#6714yes—
384C3×C8—62no—
385C3⋊C8—22no—
386C3⋊C8—62no—
387C3⋊C8—62no—
388C3⋊C8—122no—
389C2×C32#41614yescomplemented
390C2×C32C22×C22⋊C411yescharacteristic
391C2×C32C2×#13511yescharacteristic
392C2×C32C2×#13511yescharacteristic
393C3×D3—24no—
394C3×D3—44no—
395C24—31no—
396C24—61no—
397#41—316no—
398#41—68no—
399#41—616no—
400C2×Q8—21no—
401C2×Q8—22no—
402C2×Q8D3×Dic314yes—
403C2×Q8C2×D3212yes—
404C2×D4—32no—
405C2×D4—34no—
406C2×D4—64no—
407C2×D4—68no—
408C2×D4—62no—
409C2×D4—61no—
410C22×C4—21no—
411C22×C4—31no—
412C22×C4—32no—
413C22×C4—34no—
414C22×C4—32no—
415C22×C4—34no—
416C22×C4—64no—
417C22×C4—68no—
418C22×C4—61no—
419C22×C4—181no—
420C22×C4C2×D3211yescharacteristic
421C2×C8—32no—
422C2×C8—62no—
423C2×C8—92no—
424C2×C8—188no—
425C2×C8—182no—
426C4⋊C4—32no—
427C4⋊C4—61no—
428C4⋊C4—92no—
429C4⋊C4—181no—
430C22⋊C4—184no—
431C42—184no—
432C22×C3—21no—
433C22×C3—22no—
434C22×C3—22no—
435C22×C3—22no—
436C22×C3—34no—
437C22×C3—62no—
438C22×C3—62no—
439C22×C3—68no—
440C22×C3—64no—
441C22×C3—122no—
442C22×C3—122no—
443C22×C3—128no—
444C22×C3D3×C22⋊C412yes—
445C22×C3#91612yes—
446C22×C3#91912yes—
447C22×C3#95012yes—
448C22×C3#95012yes—
449C22×C3C2×#21712yes—
450C22×C3C2×D3×D411yescharacteristic
451C22×C3C22×#6711yescharacteristic
452C2×D3—28no—
453C2×D3—22no—
454C2×D3—22no—
455C2×D3—24no—
456C2×D3—48no—
457C2×D3—42no—
458C2×D3—42no—
459C2×D3C2×#21714yes—
460C3×C4—24no—
461C3×C4—24no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—22no—
465C3×C4—34no—
466C3×C4—44no—
467C3×C4—122no—
468C3×C4D3×C22⋊C412yes—
469C3×C4C2×#21712yes—
470C3×C4C22×C4×D311yescharacteristic
471C3×C4C2×D3×D411yescharacteristic
472C3×C4C23×Dic311yescharacteristic
473C3×C4C22×#6711yescharacteristic
474Dic3—42no—
475Dic3—122no—
476Dic3—122no—
477Dic3—242no—
478Dic3C2×#21714yes—
479C32C2×#41611yescharacteristic, complemented, Sylow
480C23—32no—
481C23—34no—
482C23—62no—
483C23—62no—
484C23—62no—
485C23—64no—
486C23—122no—
487C23—122no—
488C23D3×#6711yescharacteristic
489Q8—22no—
490Q8—24no—
491Q8C2×D3×Dic314yes—
492D4—34no—
493D4—616no—
494D4—62no—
495D4—64no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—32no—
499C2×C4—34no—
500C2×C4—34no—
501C2×C4—34no—
502C2×C4—38no—
503C2×C4—616no—
504C2×C4—62no—
505C2×C4—122no—
506C2×C4—182no—
507C2×C4—362no—
508C2×C4C2×D3×Dic312yes—
509C2×C4D3×#6712yes—
510C2×C4D3×#6711yescharacteristic
511C2×C4C22×D3211yescharacteristic
512C8—62no—
513C8—182no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—24no—
517C2×C3—21no—
518C2×C3—64no—
519C2×C3—124no—
520C2×C3#480414yescomplemented
521C2×C3#523314yescomplemented
522C2×C3C2×D3×C22⋊C411yescharacteristic
523C2×C3C2×#91611yescharacteristic
524C2×C3C2×#91911yescharacteristic
525C2×C3C2×#95011yescharacteristic
526C2×C3C2×#95011yescharacteristic
527C2×C3C22×#21711yescharacteristic
528D3—24no—
529D3—44no—
530C22—34no—
531C22—62no—
532C22—62no—
533C22—68no—
534C22—64no—
535C22—122no—
536C22—122no—
537C22—128no—
538C22#6394712yes—
539C22#6394912yes—
540C22D3×#21712yes—
541C22C2×D3×#6711yescharacteristic
542C4—24no—
543C4—34no—
544C4—122no—
545C4—362no—
546C4D3×#21712yes—
547C4C22×D3×Dic311yescharacteristic
548C4C2×D3×#6711yescharacteristic
549C3—21no—
550C3C2×#480411yescharacteristic, complemented
551C3C2×#523311yescharacteristic, complemented
552C2—64no—
553C2—124no—
554C2#1059155614yesdirect product factor
555C2C2×#6394711yescharacteristic
556C2C2×#6394911yescharacteristic
557C2C2×D3×#21711yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C3×#239C2
cosocleC2×C32×C4C24
hypercenterC22×Q8D32
hypocenterC32C2×#416
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#63841C2semidirect
3. C22×D3×C3⋊C8C2semidirect
4. C2×#63662C2semidirect
5. C2×C3×#835C2semidirect
6. #10591556C2direct (N × H)
7. C2×#63563C2semidirect
8. C2×#63562C2semidirect
14. C2×C3×#239C4semidirect
27. #63841C22semidirect
29. C2×D3×C3⋊C8C22semidirect
30. #63662C22semidirect
31. C3×#835C22semidirect
32. #63563C22semidirect
33. #63562C22semidirect
45. C2×#835D3semidirect
64. C3×#239C2×C4semidirect
102. C2×#239Dic3semidirect
134. #835C2×D3semidirect
227. #239C2×Dic3semidirect
389. C2×C32#416semidirect
479. C32C2×#416semidirect
520. C2×C3#4804semidirect
521. C2×C3#5233semidirect
550. C3C2×#4804semidirect
551. C3C2×#5233semidirect
554. C2#10591556direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2392
C2×#638412
C22×D3×C3⋊C82
C2×#636622
C2×C3×#8352
#105915562
C2×#635632
C2×#635622
C2×#52333
C2×#48043