Finite Group Databasebeta

← C2×#10591550 #11857924

Subgroups — C2×#10591550 #11857924

Order 1152.

1713 conjugacy classes of subgroups.

The subgroup lattice has 567 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#239C211yesmaximal, characteristic
2C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C22×#3711C211yesmaximal, characteristic, complemented
4C2×#63662C211yesmaximal, characteristic, complemented
5C2×C3×#835C211yesmaximal, characteristic, complemented
6#10591550C218yesmaximal, direct product factor
7C2×#63563C211yesmaximal, characteristic, complemented
8C2×#63562C211yesmaximal, characteristic, complemented
9C2×#5232—31nomaximal
10C2×#4803—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
20C22×D3×Dic3—21no—
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×Dic3⋊Dic3—21no—
26D3×C4⋊Dic3—22no—
27D3×C4⋊Dic3C2214yescomplemented
28C2×#3711—24no—
29C2×#3711C2214yescomplemented
30#63662C2214yescomplemented
31C3×#835C2214yescomplemented
32#63563C2214yescomplemented
33#63562C2214yescomplemented
34C22×C3×#41—31no—
35C22×#239D311yescharacteristic
36C22×C4⋊Dic3—31no—
37C22×#208—31no—
38C22×ΓL(1,𝔽25)—31no—
39C2×D3×C4⋊C4—31no—
40C2×C3×#103—31no—
41#5232—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#4803—38no—
51C23×C3×D3—21no—
52C23×C3×D3D411yescharacteristic
53C2×C32×Q8—22no—
54C2×C32×Q8—21no—
55C2×C32×Q8C2×C414yescomplemented
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×C414yescomplemented
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—
77C2×D3×Dic3—24no—
78C2×D3×Dic3—44no—
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)C2312yes—
81C2×C3⋊(C3⋊C8)—22no—
82C2×C3⋊(C3⋊C8)C2312yes—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3C2312yes—
85C2×C3×C3⋊C8—22no—
86C2×C3×C3⋊C8C2312yes—
87Dic3⋊Dic3—24no—
88#3711—28no—
89C2×#417—91noSylow
90C2×C3×#41—38no—
91C2×C3×#41—34no—
92C2×C3×#41—64no—
93C2×C3×#41—62no—
94C22×C3×Q8—21no—
95C22×C3×Q8C2×D311yescharacteristic
96C22×C3×Q8C2×D311yescharacteristic
97C22×C3×D4—31no—
98C22×C3×D4—61no—
99C23×C3×C4—31no—
100C23×C3×C4—61no—
101C23×Dic3—61no—
102C2×#239—24no—
103C2×#239—22no—
104C2×#239Dic318yescomplemented
105C2×#239C2×D314yes—
106C22×D12—21no—
107C22×D12C2×D311yescharacteristic
108C22×C4×D3—21no—
109C22×C4×D3—61no—
110C22×C4×D3C2×D311yescharacteristic
111C22×C3×C8—31no—
112C2×C3×C4⋊C4—31no—
113C2×C4⋊Dic3—31no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—34no—
116C2×C4⋊Dic3—61no—
117C2×C4⋊Dic3—62no—
118C2×C4⋊Dic3—61no—
119C2×C4⋊Dic3C2×D311yescharacteristic
120C2×Dic3⋊C4—61no—
121C2×#208—34no—
122C2×#208—64no—
123C22×C3⋊C8—31no—
124C22×C3⋊C8—31no—
125C22×C3⋊C8—61no—
126C22×C3⋊C8C2×D311yescharacteristic
127C2×ΓL(1,𝔽25)—34no—
128C2×ΓL(1,𝔽25)—64no—
129D3×C4⋊C4—34no—
130D3×C4⋊C4—62no—
131C3×#103—34no—
132#835—34no—
133#835—34no—
134#835—64no—
135#835C2×D314yescomplemented
136#832—34no—
137#832—34no—
138#821—34no—
139#809—34no—
140C23×C32C2×D411yescharacteristic
141C22×C3×D3—22no—
142C22×C3×D3—22no—
143C22×C3×D3—24no—
144C22×C3×D3—22no—
145C22×C3×D3—42no—
146C22×C3×D3—42no—
147C22×C3×D3C22⋊C414yes—
148C22×C3×D3C2×D412yes—
149C32×Q8—24no—
150C32×Q8—22no—
151C32×Q8C22×C414yescomplemented
152C2×C32×C4—24no—
153C2×C32×C4—22no—
154C2×C32×C4C22×C412yes—
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D412yes—
157C2×C32×C4C2411yescharacteristic
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—42no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—42no—
162C2×C3×Dic3C22⋊C414yes—
163C2×C3×Dic3C2×D412yes—
164C3×D12—216no—
165C3×D12—24no—
166C3×D12—22no—
167C3×D12C22×C414yescomplemented
168C3×C4×D3—216no—
169C3×C4×D3C22⋊C418yes—
170C3×C4×D3C22×C414yes—
171C3×C4×D3C2×D414yes—
172D3×Dic3—48no—
173C3⋊(C3⋊C8)—22no—
174C3×C3⋊C8—22no—
175C22×#41—31no—
176C22×M16—91no—
177C22×C4⋊C4—91no—
178#417—98no—
179C2×#103—31no—
180C2×#103—91no—
181C2×#102—91no—
182C2×#102—91no—
183C24×C3—31no—
184C24×C3—61no—
185C23×D3—21no—
186C23×D3#6711yescharacteristic
187C3×#41—316no—
188C3×#41—616no—
189C3×#41—68no—
190C2×C3×Q8—22no—
191C2×C3×Q8—21no—
192C2×C3×Q8—22no—
193C2×C3×Q8—21no—
194C2×C3×Q8—24no—
195C2×C3×Q8—22no—
196C2×C3×Q8—42no—
197C2×C3×Q8—41no—
198C2×C3×Q8C4×D314yescomplemented
199C2×C3×Q8C2×Dic314yescomplemented
200C2×C3×Q8C22×D312yes—
201C2×C3×Q8C22×D312yes—
202C2×C3×D4—34no—
203C2×C3×D4—32no—
204C2×C3×D4—68no—
205C2×C3×D4—64no—
206C2×C3×D4—61no—
207C2×C3×D4—62no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—31no—
212C22×C3×C4—34no—
213C22×C3×C4—34no—
214C22×C3×C4—32no—
215C22×C3×C4—32no—
216C22×C3×C4—41no—
217C22×C3×C4—68no—
218C22×C3×C4—64no—
219C22×C3×C4—61no—
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C22×Dic3—21no—
223C22×Dic3—64no—
224C22×Dic3—61no—
225C22×Dic3—61no—
226C22×Dic3—121no—
227C22×Dic3—124no—
228C22×Dic3#6711yescharacteristic
229#239—216no—
230#239—28no—
231#239C2×Dic3116yescomplemented
232C2×D12—28no—
233C2×D12—24no—
234C2×D12—21no—
235C2×D12—22no—
236C2×D12C2×Dic314yescomplemented
237C2×D12C22×D312yes—
238C2×C4×D3—28no—
239C2×C4×D3—24no—
240C2×C4×D3—64no—
241C2×C4×D3—124no—
242C2×C4×D3C2×Dic314yes—
243C2×C4×D3#6712yes—
244C2×C4×D3#6714yes—
245C2×C4×D3C22×D312yes—
246C2×C3×C8—32no—
247C2×C3×C8—62no—
248C3×C4⋊C4—32no—
249C3×C4⋊C4—61no—
250C4⋊Dic3—21no—
251C4⋊Dic3—32no—
252C4⋊Dic3—32no—
253C4⋊Dic3—62no—
254C4⋊Dic3—64no—
255C4⋊Dic3—61no—
256C4⋊Dic3—61no—
257C4⋊Dic3—121no—
258C4⋊Dic3C22×D312yes—
259Dic3⋊C4—64no—
260#208—68no—
261C2×C3⋊C8—22no—
262C2×C3⋊C8—32no—
263C2×C3⋊C8—32no—
264C2×C3⋊C8—62no—
265C2×C3⋊C8—62no—
266C2×C3⋊C8—62no—
267C2×C3⋊C8—122no—
268C2×C3⋊C8C22×D312yes—
269ΓL(1,𝔽25)—68no—
270C22×C32C2×C22⋊C412yes—
271C22×C32AGL(1,ℤ/8)12yes—
272C22×C32#13712yes—
273C22×C32C22×D411yescharacteristic
274C2×C3×D3—22no—
275C2×C3×D3—22no—
276C2×C3×D3—28no—
277C2×C3×D3—24no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C2×C3×D3—48no—
281C2×C3×D3C2×C22⋊C414yes—
282C32×C4—24no—
283C32×C4C2×C22⋊C412yes—
284C32×C4C23×C411yescharacteristic
285C32×C4C22×D411yescharacteristic
286C3⋊Dic3—42no—
287C3×Dic3—42no—
288C3×Dic3C2×C22⋊C414yes—
289C2×#41—38no—
290C2×#41—34no—
291C2×#41—62no—
292C2×#41—64no—
293C22×Q8D3211yescharacteristic
294C22×D4—31no—
295C22×D4—61no—
296C23×C4—31no—
297C23×C4—61no—
298C23×C4—181no—
299C2×M16—94no—
300C2×M16—184no—
301C22×C8—31no—
302C22×C8—91no—
303C2×C4⋊C4—31no—
304C2×C4⋊C4—94no—
305C2×C4⋊C4—91no—
306C2×C4⋊C4—182no—
307C2×C4⋊C4—181no—
308#103—34no—
309#103—94no—
310#102—94no—
311#102—94no—
312C23×C3—21no—
313C23×C3—34no—
314C23×C3—32no—
315C23×C3—62no—
316C23×C3—62no—
317C23×C3—64no—
318C23×C3—62no—
319C23×C3—122no—
320C23×C3—122no—
321C23×C3D3×D411yescharacteristic
322C23×C3C2×#6711yescharacteristic
323C22×D3—22no—
324C22×D3—22no—
325C22×D3—24no—
326C22×D3—22no—
327C22×D3—42no—
328C22×D3—42no—
329C22×D3#21714yes—
330C22×D3C2×#6712yes—
331C3×Q8—24no—
332C3×Q8—24no—
333C3×Q8—22no—
334C3×Q8—22no—
335C3×Q8—24no—
336C3×Q8—42no—
337C3×Q8—44no—
338C3×Q8C2×C4×D314yescomplemented
339C3×Q8C22×Dic314yescomplemented
340C3×D4—34no—
341C3×D4—616no—
342C3×D4—64no—
343C3×D4—62no—
344C2×C3×C4—24no—
345C2×C3×C4—24no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—21no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—21no—
352C2×C3×C4—34no—
353C2×C3×C4—32no—
354C2×C3×C4—38no—
355C2×C3×C4—34no—
356C2×C3×C4—34no—
357C2×C3×C4—42no—
358C2×C3×C4—44no—
359C2×C3×C4—616no—
360C2×C3×C4—62no—
361C2×C3×C4—122no—
362C2×C3×C4C2×C4×D312yes—
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D412yes—
365C2×C3×C4C22×Dic312yes—
366C2×C3×C4C2×#6711yescharacteristic
367C2×C3×C4C2×#6712yes—
368C2×C3×C4C23×D311yescharacteristic
369C2×C3×C4C23×D311yescharacteristic
370C2×Dic3—22no—
371C2×Dic3—42no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—122no—
375C2×Dic3—128no—
376C2×Dic3—122no—
377C2×Dic3—122no—
378C2×Dic3—242no—
379C2×Dic3#21714yes—
380C2×Dic3C2×#6712yes—
381D12—216no—
382D12—24no—
383D12—22no—
384D12C22×Dic314yescomplemented
385C4×D3—216no—
386C4×D3—128no—
387C4×D3#21718yes—
388C4×D3C22×Dic314yes—
389C4×D3C2×#6714yes—
390C3×C8—62no—
391C3⋊C8—22no—
392C3⋊C8—62no—
393C3⋊C8—62no—
394C3⋊C8—122no—
395C2×C32#41714yescomplemented
396C2×C32C22×C22⋊C411yescharacteristic
397C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
398C2×C32C2×#13711yescharacteristic
399C3×D3—24no—
400C3×D3—44no—
401C24—31no—
402C24—61no—
403#41—316no—
404#41—68no—
405#41—616no—
406C2×Q8—21no—
407C2×Q8—22no—
408C2×Q8D3×Dic314yescomplemented
409C2×Q8C2×D3212yes—
410C2×D4—32no—
411C2×D4—34no—
412C2×D4—64no—
413C2×D4—68no—
414C2×D4—62no—
415C2×D4—61no—
416C22×C4—21no—
417C22×C4—31no—
418C22×C4—32no—
419C22×C4—34no—
420C22×C4—32no—
421C22×C4—34no—
422C22×C4—64no—
423C22×C4—68no—
424C22×C4—61no—
425C22×C4—184no—
426C22×C4—181no—
427C22×C4—364no—
428C22×C4C2×D3211yescharacteristic
429M16—188no—
430C2×C8—32no—
431C2×C8—62no—
432C2×C8—92no—
433C2×C8—182no—
434C4⋊C4—32no—
435C4⋊C4—61no—
436C4⋊C4—92no—
437C4⋊C4—184no—
438C4⋊C4—181no—
439C22×C3—21no—
440C22×C3—22no—
441C22×C3—22no—
442C22×C3—22no—
443C22×C3—34no—
444C22×C3—62no—
445C22×C3—62no—
446C22×C3—68no—
447C22×C3—64no—
448C22×C3—122no—
449C22×C3—122no—
450C22×C3—128no—
451C22×C3D3×C22⋊C412yes—
452C22×C3#91412yes—
453C22×C3#91812yes—
454C22×C3#94912yes—
455C22×C3#95112yes—
456C22×C3C2×#21712yes—
457C22×C3C2×D3×D411yescharacteristic
458C22×C3C22×#6711yescharacteristic
459C2×D3—28no—
460C2×D3—22no—
461C2×D3—22no—
462C2×D3—24no—
463C2×D3—48no—
464C2×D3—42no—
465C2×D3—42no—
466C2×D3C2×#21714yes—
467C3×C4—24no—
468C3×C4—24no—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—22no—
472C3×C4—34no—
473C3×C4—44no—
474C3×C4—122no—
475C3×C4D3×C22⋊C412yes—
476C3×C4C2×#21712yes—
477C3×C4C22×C4×D311yescharacteristic
478C3×C4C2×D3×D411yescharacteristic
479C3×C4C23×Dic311yescharacteristic
480C3×C4C22×#6711yescharacteristic
481Dic3—42no—
482Dic3—122no—
483Dic3—122no—
484Dic3—242no—
485Dic3C2×#21714yes—
486C32C2×#41711yescharacteristic, complemented, Sylow
487C23—32no—
488C23—34no—
489C23—62no—
490C23—62no—
491C23—62no—
492C23—64no—
493C23—122no—
494C23—122no—
495C23D3×#6711yescharacteristic
496Q8—22no—
497Q8—24no—
498Q8C2×D3×Dic314yescomplemented
499D4—34no—
500D4—616no—
501D4—62no—
502D4—64no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—32no—
506C2×C4—34no—
507C2×C4—34no—
508C2×C4—34no—
509C2×C4—38no—
510C2×C4—616no—
511C2×C4—62no—
512C2×C4—122no—
513C2×C4—182no—
514C2×C4—368no—
515C2×C4—362no—
516C2×C4C2×D3×Dic312yes—
517C2×C4D3×#6712yes—
518C2×C4D3×#6711yescharacteristic
519C2×C4C22×D3211yescharacteristic
520C8—62no—
521C8—182no—
522C2×C3—24no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—64no—
527C2×C3—124no—
528C2×C3#480314yescomplemented
529C2×C3#523214yescomplemented
530C2×C3C2×D3×C22⋊C411yescharacteristic
531C2×C3C2×#91411yescharacteristic
532C2×C3C2×#91811yescharacteristic
533C2×C3C2×#94911yescharacteristic
534C2×C3C2×#95111yescharacteristic
535C2×C3C22×#21711yescharacteristic
536D3—24no—
537D3—44no—
538C22—34no—
539C22—68no—
540C22—62no—
541C22—62no—
542C22—64no—
543C22—128no—
544C22—122no—
545C22—122no—
546C22#6393912yes—
547C22#6394312yes—
548C22D3×#21712yes—
549C22C2×D3×#6711yescharacteristic
550C4—24no—
551C4—34no—
552C4—122no—
553C4—362no—
554C4D3×#21712yes—
555C4C22×D3×Dic311yescharacteristic
556C4C2×D3×#6711yescharacteristic
557C3—21no—
558C3C2×#480311yescharacteristic, complemented
559C3C2×#523211yescharacteristic, complemented
560C2—64no—
561C2—124no—
562C2#1059155014yesdirect product factor
563C2C2×#6393911yescharacteristic
564C2C2×#6394311yescharacteristic
565C2C2×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×#417
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×D3×C4⋊Dic3C2semidirect
3. C22×#3711C2semidirect
4. C2×#63662C2semidirect
5. C2×C3×#835C2semidirect
6. #10591550C2direct (N × H)
7. C2×#63563C2semidirect
8. C2×#63562C2semidirect
14. C2×C3×#239C4semidirect
27. D3×C4⋊Dic3C22semidirect
29. C2×#3711C22semidirect
30. #63662C22semidirect
31. C3×#835C22semidirect
32. #63563C22semidirect
33. #63562C22semidirect
45. C2×#835D3semidirect
55. C2×C32×Q8C2×C4semidirect
64. C3×#239C2×C4semidirect
69. C2×C3×D12C2×C4semidirect
104. C2×#239Dic3semidirect
135. #835C2×D3semidirect
151. C32×Q8C22×C4semidirect
167. C3×D12C22×C4semidirect
198. C2×C3×Q8C4×D3semidirect
199. C2×C3×Q8C2×Dic3semidirect
231. #239C2×Dic3semidirect
236. C2×D12C2×Dic3semidirect
338. C3×Q8C2×C4×D3semidirect
339. C3×Q8C22×Dic3semidirect
384. D12C22×Dic3semidirect
395. C2×C32#417semidirect
408. C2×Q8D3×Dic3semidirect
486. C32C2×#417semidirect
498. Q8C2×D3×Dic3semidirect
528. C2×C3#4803semidirect
529. C2×C3#5232semidirect
558. C3C2×#4803semidirect
559. C3C2×#5232semidirect
562. C2#10591550direct (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×D3×C4⋊Dic32
C22×#37112
C2×#636622
C2×C3×#8352
#105915502
C2×#635632
C2×#635622
C2×#52323
C2×#48033