Finite Group Databasebeta

← C2×#10591529 #11857528

Subgroups — C2×#10591529 #11857528

Order 1152.

2021 conjugacy classes of subgroups.

The subgroup lattice has 565 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3830C211yesmaximal, characteristic
2C2×#63957C212yesmaximal, complemented
3C2×C3×#834C212yesmaximal, complemented
4C2×#63581C212yesmaximal, complemented
5#10591529C218yesmaximal, direct product factor
6C2×#4740—32nomaximal
7C22×C32×D4C2211yescharacteristic
8C22×#638C411yescharacteristic, complemented
9C22×#638C2211yescharacteristic
10C23×C3⋊Dic3C411yescharacteristic, complemented
11C23×C3⋊Dic3C2211yescharacteristic
12C2×#3830—22no—
13C2×#3830—24no—
14C2×#3830—22no—
15C2×#3830C414yescomplemented
16C2×#3830C2214yes—
17C22×C4×C3⋊D3C411yescharacteristic, complemented
18C22×#634C411yescharacteristic, complemented
19C2×C3×#217C2214yes—
20C2×#3724—22no—
21#63957—24no—
22#63957C2218yescomplemented
23C2×Dic32—22no—
24C3×#834C2218yescomplemented
25#63581C2218yescomplemented
26C22×#237—32no—
27C22×#237—61no—
28C2×#877—34no—
29C2×C3×#99—32no—
30C2×#834D312yescomplemented
31C2×#806—34no—
32#4740—316no—
33C24×C32C2×C411yescharacteristic
34C24×C32C2311yescharacteristic
35C23×C3⋊D3C2×C411yescharacteristic
36C2×C32×D4—22no—
37C2×C32×D4—22no—
38C2×C32×D4C2×C412yes—
39C2×C32×D4C2312yes—
40C22×C32×C4C2×C411yescharacteristic
41C2×#638—22no—
42C2×#638—22no—
43C2×#638—22no—
44C2×#638—22no—
45C2×#638C2×C412yes—
46C2×#638C2×C414yescomplemented
47C2×#638C2312yes—
48C22×C3⋊Dic3—22no—
49C22×C3⋊Dic3—21no—
50C22×C3⋊Dic3—21no—
51C22×C3⋊Dic3C2×C411yescharacteristic
52C22×C3⋊Dic3C2×C411yescharacteristic
53C22×C3⋊Dic3C2×C411yescharacteristic
54C22×C3⋊Dic3C2×C412yes—
55C22×C3⋊Dic3C2×C414yescomplemented
56C22×C3⋊Dic3D412yes—
57C22×C3⋊Dic3D414yes—
58C22×C3⋊Dic3D412yes—
59C22×C3⋊Dic3C2312yes—
60#3830—28no—
61#3830—28no—
62#3830—28no—
63#3830—28no—
64C2×C4×C3⋊D3—22no—
65C2×C4×C3⋊D3—21no—
66C2×C4×C3⋊D3—21no—
67C2×C4×C3⋊D3C2×C414yescomplemented
68C2×#634—22no—
69C2×#634—22no—
70C2×#634C2×C414yescomplemented
71C22×C3×Dic3—24no—
72C3×#217—24no—
73C3×#217C2318yes—
74#3724—28no—
75Dic32—28no—
76C2×#410—91noSylow
77C22×C3×D4—21no—
78C22×C3×D4C2×D312yes—
79C22×#67—32no—
80C22×#67—32no—
81C22×#67—61no—
82C22×#67—61no—
83C23×Dic3—32no—
84C23×Dic3—32no—
85C23×Dic3—61no—
86C23×Dic3—61no—
87C2×#237—38no—
88C2×#237—38no—
89C2×#237—64no—
90C2×#237—64no—
91C2×#237—68no—
92C2×#237—64no—
93C2×#237—64no—
94C2×#237—64no—
95C2×#237—64no—
96C2×#237—68no—
97C22×C4×D3—32no—
98C22×C4×D3—61no—
99C22×Dic6—32no—
100C22×Dic6—61no—
101C2×C3×C22⋊C4—34no—
102C2×#217C2×D314yes—
103C2×Dic3⋊C4—64no—
104C2×C4×Dic3—64no—
105#877—316no—
106#877—68no—
107C3×#99—38no—
108#834C2×D318yescomplemented
109#806—316no—
110C23×C32—21no—
111C23×C32—21no—
112C23×C32—42no—
113C23×C32—42no—
114C23×C32C22×C411yescharacteristic
115C23×C32C22×C412yes—
116C23×C32C22×C411yescharacteristic
117C23×C32C2×D412yes—
118C23×C32C2×D412yes—
119C23×C32C2411yescharacteristic
120C22×C3⋊D3—21no—
121C22×C3⋊D3—21no—
122C22×C3⋊D3—42no—
123C22×C3⋊D3C22×C412yes—
124C32×D4—24no—
125C32×D4—24no—
126C2×C32×C4—21no—
127C2×C32×C4—21no—
128C2×C32×C4C22×C412yes—
129#638—24no—
130#638—24no—
131#638—28no—
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—24no—
135C2×C3⋊Dic3—24no—
136C2×C3⋊Dic3C22⋊C412yes—
137C2×C3⋊Dic3C22⋊C412yes—
138C2×C3⋊Dic3C22⋊C412yes—
139C2×C3⋊Dic3C22⋊C411yescharacteristic
140C2×C3⋊Dic3C22⋊C411yescharacteristic
141C2×C3⋊Dic3C22⋊C414yes—
142C2×C3⋊Dic3C22⋊C414yes—
143C2×C3⋊Dic3C22×C412yes—
144C2×C3⋊Dic3C22×C412yes—
145C2×C3⋊Dic3C22×C412yes—
146C2×C3⋊Dic3C2×D414yes—
147C2×C3⋊Dic3C2×D414yes—
148C4×C3⋊D3—24no—
149C4×C3⋊D3—24no—
150#634—28no—
151C2×C3×Dic3—28no—
152C2×C3×Dic3—48no—
153C22×#41—91no—
154C2×#117—92no—
155#410—98no—
156C2×#99—32no—
157C2×#99—92no—
158C24×C3—21no—
159C24×C3—21no—
160C24×C3C4×D312yes—
161C24×C3C22×D312yes—
162C23×D3—32no—
163C23×D3—61no—
164C2×C3×D4—24no—
165C2×C3×D4—24no—
166C2×C3×D4—24no—
167C2×C3×D4—24no—
168C2×C3×D4—22no—
169C2×C3×D4—22no—
170C2×C3×D4C4×D314yes—
171C2×C3×D4C22×D314yes—
172C22×C3×C4—21no—
173C22×C3×C4—64no—
174C22×C3×C4C4×D312yes—
175C2×#67—34no—
176C2×#67—38no—
177C2×#67—34no—
178C2×#67—62no—
179C2×#67—64no—
180C2×#67—62no—
181C2×#67—64no—
182C2×#67—64no—
183C2×#67—64no—
184C2×#67—64no—
185C2×#67—64no—
186C2×#67—64no—
187C2×#67—64no—
188C2×#67—64no—
189C22×Dic3—24no—
190C22×Dic3—32no—
191C22×Dic3—32no—
192C22×Dic3—34no—
193C22×Dic3—38no—
194C22×Dic3—34no—
195C22×Dic3—34no—
196C22×Dic3—34no—
197C22×Dic3—32no—
198C22×Dic3—38no—
199C22×Dic3—61no—
200C22×Dic3—61no—
201C22×Dic3—61no—
202C22×Dic3—62no—
203C22×Dic3—64no—
204C22×Dic3—62no—
205C22×Dic3—62no—
206C22×Dic3—64no—
207C22×Dic3—62no—
208C22×Dic3—64no—
209C22×Dic3—62no—
210C22×Dic3—62no—
211C22×Dic3—64no—
212C22×Dic3—62no—
213C22×Dic3—62no—
214#237—616no—
215#237—616no—
216#237—616no—
217#237—616no—
218#237—616no—
219#237—616no—
220#237—616no—
221#237—616no—
222C2×C4×D3—38no—
223C2×C4×D3—64no—
224C2×C4×D3—64no—
225C2×C4×D3—62no—
226C2×C4×D3—62no—
227C2×C4×D3—64no—
228C2×C4×D3—62no—
229C2×C4×D3—62no—
230C2×Dic6—38no—
231C2×Dic6—64no—
232C2×Dic6—64no—
233C2×Dic6—64no—
234C2×Dic6—64no—
235C2×Dic6—64no—
236C3×C22⋊C4—38no—
237C3×C22⋊C4—64no—
238#217—24no—
239#217C22×D318yes—
240Dic3⋊C4—616no—
241C4×Dic3—616no—
242C22×C32—22no—
243C22×C32—22no—
244C22×C32—24no—
245C22×C32—41no—
246C22×C32—42no—
247C22×C32—41no—
248C22×C32—42no—
249C22×C32—42no—
250C22×C32—42no—
251C22×C32C2×C22⋊C411yescharacteristic
252C22×C32C2×C22⋊C412yes—
253C22×C32C2×C22⋊C411yescharacteristic
254C22×C32C23×C411yescharacteristic
255C22×C32C22×D412yes—
256C2×C3⋊D3—22no—
257C2×C3⋊D3—42no—
258C2×C3⋊D3—42no—
259C2×C3⋊D3—42no—
260C32×C4—22no—
261C3⋊Dic3—22no—
262C3⋊Dic3C2×C22⋊C414yes—
263C3⋊Dic3C2×C22⋊C412yes—
264C3⋊Dic3C2×C22⋊C412yes—
265C3×Dic3—48no—
266C2×#41—94no—
267C2×#41—94no—
268C2×#41—182no—
269C2×#41—182no—
270C2×#41—184no—
271C22×Q8—91no—
272C22×D4—91no—
273C22×D4—91no—
274C22×D4D3211yescharacteristic
275C23×C4—91no—
276C23×C4—91no—
277C23×C4—91no—
278#117—98no—
279#117—184no—
280C2×C4⋊C4—182no—
281C2×C22⋊C4—34no—
282C2×C42—182no—
283#99—38no—
284#99—98no—
285C23×C3—22no—
286C23×C3—22no—
287C23×C3—22no—
288C23×C3—22no—
289C23×C3—21no—
290C23×C3—21no—
291C23×C3—22no—
292C23×C3—21no—
293C23×C3—22no—
294C23×C3—22no—
295C23×C3—44no—
296C23×C3—44no—
297C23×C3—44no—
298C23×C3—44no—
299C23×C3C2×C4×D312yes—
300C23×C3C2×C4×D314yes—
301C23×C3C2×C4×D312yes—
302C23×C3D3×D414yes—
303C23×C3D3×D414yes—
304C23×C3C23×D312yes—
305C22×D3—34no—
306C22×D3—62no—
307C22×D3—62no—
308C22×D3—62no—
309C22×D3—62no—
310C22×D3—62no—
311C22×D3—124no—
312C22×D3—124no—
313C3×D4—28no—
314C3×D4—28no—
315C3×D4—28no—
316C3×D4—28no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—68no—
323C2×C3×C4—128no—
324C2×C3×C4C2×C4×D314yes—
325#67—616no—
326#67—616no—
327#67—68no—
328#67—68no—
329#67—68no—
330#67—68no—
331C2×Dic3—28no—
332C2×Dic3—34no—
333C2×Dic3—34no—
334C2×Dic3—34no—
335C2×Dic3—32no—
336C2×Dic3—32no—
337C2×Dic3—38no—
338C2×Dic3—38no—
339C2×Dic3—34no—
340C2×Dic3—34no—
341C2×Dic3—38no—
342C2×Dic3—38no—
343C2×Dic3—34no—
344C2×Dic3—48no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—61no—
349C2×Dic3—61no—
350C2×Dic3—64no—
351C2×Dic3—64no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—64no—
356C2×Dic3—64no—
357C2×Dic3—68no—
358C2×Dic3—68no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—68no—
362C2×Dic3—68no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C4×D3—68no—
366C4×D3—68no—
367C4×D3—68no—
368C4×D3—68no—
369Dic6—616no—
370Dic6—616no—
371C2×C32—21no—
372C2×C32—21no—
373C2×C32—22no—
374C2×C32—22no—
375C2×C32—42no—
376C2×C32#41012yescomplemented
377C2×C32C22×C22⋊C411yescharacteristic
378C3⋊D3—42no—
379C24—91no—
380C24#62411yescharacteristic
381C24C2×D3211yescharacteristic
382#41—188no—
383#41—188no—
384#41—188no—
385#41—188no—
386C2×Q8—94no—
387C2×Q8—182no—
388C2×Q8—182no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—92no—
392C2×D4—94no—
393C2×D4—92no—
394C2×D4—182no—
395C2×D4—182no—
396C2×D4—182no—
397C2×D4—182no—
398C2×D4#62412yes—
399C2×D4C2×D3212yes—
400C22×C4—64no—
401C22×C4—92no—
402C22×C4—91no—
403C22×C4—91no—
404C22×C4—92no—
405C22×C4—92no—
406C22×C4—92no—
407C22×C4—94no—
408C22×C4—91no—
409C22×C4—94no—
410C22×C4—94no—
411C22×C4—182no—
412C22×C4—181no—
413C22×C4—181no—
414C22×C4—182no—
415C22×C4—181no—
416C22×C4—181no—
417C22×C4#62411yescharacteristic
418C4⋊C4—188no—
419C22⋊C4—38no—
420C22⋊C4—64no—
421C42—188no—
422C22×C3—24no—
423C22×C3—28no—
424C22×C3—24no—
425C22×C3—24no—
426C22×C3—24no—
427C22×C3—21no—
428C22×C3—22no—
429C22×C3—21no—
430C22×C3—22no—
431C22×C3—21no—
432C22×C3—44no—
433C22×C3—42no—
434C22×C3—44no—
435C22×C3—42no—
436C22×C3—44no—
437C22×C3—42no—
438C22×C3—42no—
439C22×C3—44no—
440C22×C3—44no—
441C22×C3—44no—
442C22×C3—44no—
443C22×C3—44no—
444C22×C3—44no—
445C22×C3D3×C22⋊C412yes—
446C22×C3D3×C22⋊C414yes—
447C22×C3D3×C22⋊C412yes—
448C22×C3C22×C4×D312yes—
449C22×C3C2×D3×D414yes—
450C2×D3—64no—
451C2×D3—64no—
452C2×D3—124no—
453C2×D3—124no—
454C2×D3—124no—
455C2×D3—124no—
456C2×D3—124no—
457C2×D3—124no—
458C3×C4—24no—
459C3×C4—24no—
460C3×C4—128no—
461Dic3—38no—
462Dic3—34no—
463Dic3—34no—
464Dic3—48no—
465Dic3—64no—
466Dic3—62no—
467Dic3—62no—
468Dic3—64no—
469Dic3—64no—
470C32C2×#41011yescharacteristic, complemented, Sylow
471C23—21no—
472C23—21no—
473C23—42no—
474C23—42no—
475C23—92no—
476C23—181no—
477C23—181no—
478C23—362no—
479C23C2×#62411yescharacteristic
480C23C2×#62412yes—
481C23C2×#62411yescharacteristic
482C23#381112yes—
483C23#381112yes—
484C23C22×D3211yescharacteristic
485Q8—188no—
486D4—24no—
487D4—24no—
488D4—188no—
489D4—184no—
490D4—184no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—68no—
494C2×C4—92no—
495C2×C4—92no—
496C2×C4—94no—
497C2×C4—94no—
498C2×C4—92no—
499C2×C4—92no—
500C2×C4—94no—
501C2×C4—94no—
502C2×C4—91no—
503C2×C4—91no—
504C2×C4—92no—
505C2×C4—92no—
506C2×C4—128no—
507C2×C4—184no—
508C2×C4—184no—
509C2×C4—184no—
510C2×C4—184no—
511C2×C4—181no—
512C2×C4—181no—
513C2×C4C2×#62412yes—
514C2×C3—22no—
515C2×C3—22no—
516C2×C3—24no—
517C2×C3—22no—
518C2×C3—22no—
519C2×C3—24no—
520C2×C3—22no—
521C2×C3—21no—
522C2×C3—42no—
523C2×C3—42no—
524C2×C3—44no—
525C2×C3—44no—
526C2×C3#474014yescomplemented
527C2×C3C2×D3×C22⋊C412yes—
528D3—124no—
529D3—124no—
530C22—24no—
531C22—22no—
532C22—22no—
533C22—41no—
534C22—41no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—182no—
540C22—362no—
541C22—362no—
542C22—362no—
543C22#6397411yescharacteristic
544C22#6397412yes—
545C22#6397411yescharacteristic
546C22C22×#62411yescharacteristic
547C22C2×#381112yes—
548C4—22no—
549C4—92no—
550C4—92no—
551C4—94no—
552C4—128no—
553C4—182no—
554C3—21no—
555C3C2×#474012yescomplemented
556C2—22no—
557C2—21no—
558C2—21no—
559C2—22no—
560C2—42no—
561C2—362no—
562C2#1059152912yesdirect product factor
563C2C2×#6397411yescharacteristic
subgroupG/H
centerC22#63974
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC22×C32×D4C22
socleC22×C32C2×C22⋊C4
prime radicalC22×#3830C2
cosocleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#410
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63957C2semidirect
3. C2×C3×#834C2semidirect
4. C2×#63581C2semidirect
5. #10591529C2direct (N × H)
8. C22×#638C4semidirect
10. C23×C3⋊Dic3C4semidirect
15. C2×#3830C4semidirect
17. C22×C4×C3⋊D3C4semidirect
18. C22×#634C4semidirect
22. #63957C22semidirect
24. C3×#834C22semidirect
25. #63581C22semidirect
30. C2×#834D3semidirect
46. C2×#638C2×C4semidirect
55. C22×C3⋊Dic3C2×C4semidirect
67. C2×C4×C3⋊D3C2×C4semidirect
70. C2×#634C2×C4semidirect
108. #834C2×D3semidirect
376. C2×C32#410semidirect
470. C32C2×#410semidirect
526. C2×C3#4740semidirect
555. C3C2×#4740semidirect
562. C2#10591529direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38302
C2×#639572
C2×C3×#8342
C2×#635812
#105915292
C2×#47403