Finite Group Databasebeta

← C2×#10591569 #11865488

Subgroups — C2×#10591569 #11865488

Order 1152.

1233 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64153C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic
3C2×#63898C211yesmaximal, characteristic
4C22×#3716C211yesmaximal, characteristic
5C2×C3×#835C211yesmaximal, characteristic, complemented
6#10591569C218yesmaximal, direct product factor
7C2×#63572C211yesmaximal, characteristic, complemented
8C2×#63567C211yesmaximal, characteristic, complemented
9C2×#5162—31nomaximal
10C2×#4818—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×D3×Dic3—21no—
15#64153—22no—
16#64153C2214yescomplemented
17C2×#3750—21no—
18C2×#3750—21no—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×#215—24no—
21C2×C3×#215C2214yes—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×(C2×D3)⋊Dic3—21no—
26#63898—22no—
27#63898C2214yes—
28C2×#3716—24no—
29C2×#3716C2214yes—
30C3×#835C2214yescomplemented
31#63572C2214yescomplemented
32#63567C2214yescomplemented
33C22×C3×SD16—31no—
34C2×#944—31no—
35C2×#944—31no—
36C2×#944—61no—
37C22×#215D311yescharacteristic
38C2×D4×Dic3—31no—
39C22×#214—31no—
40C22×#204—31no—
41C2×#893—31no—
42C2×C3×#103—31no—
43C2×#835D311yescharacteristic, complemented
44#5162—38no—
45C2×#816—31no—
46C2×Dic3⋊C8—31no—
47C2×Dic3⋊C8—31no—
48C2×#810—31no—
49#4818—38no—
50C23×C3×D3—21no—
51C2×C32×Q8—21no—
52C2×C32×Q8—22no—
53C2×C32×Q8—22no—
54C2×C32×Q8C2312yes—
55C22×C32×C4—21no—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3—21no—
58C22×C3⋊Dic3D411yescharacteristic
59C22×C3⋊Dic3D411yescharacteristic
60C2×#634—22no—
61C2×#634—22no—
62C2×#634—21no—
63C2×#634C2312yes—
64C22×C3×Dic3—21no—
65C2×C3×D12—21no—
66C2×C3×D12—22no—
67C2×C3×D12D414yes—
68C2×C3×D12C2312yes—
69C2×D3×Dic3—24no—
70C2×D3×Dic3—44no—
71#3750—24no—
72#3750—24no—
73C4×C3⋊Dic3D412yes—
74C4×C3⋊Dic3C2312yes—
75C3×#215—28no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3C2312yes—
78C2×C3×C3⋊C8—22no—
79C2×C3×C3⋊C8—22no—
80C2×C3×C3⋊C8C2312yes—
81C2×C3×C3⋊C8C2312yes—
82(C2×D3)⋊Dic3—24no—
83#3716—28no—
84C2×#461—91noSylow
85C22×C3×Q8—21no—
86C22×C3×Q8C2×D311yescharacteristic
87C22×C3×Q8C2×D311yescharacteristic
88C22×C3×D4—31no—
89C23×Dic3—61no—
90C22×D12C2×D311yescharacteristic
91C22×C4×D3—61no—
92C22×Dic6—31no—
93C22×Dic6—31no—
94C22×Dic6—61no—
95C2×C3×SD16—34no—
96C2×C3×SD16—64no—
97C22×C3×C8—31no—
98C22×C3×C8—31no—
99C2×C3×C4⋊C4—31no—
100C2×#217—61no—
101#944—34no—
102#944—34no—
103#944—64no—
104#944—62no—
105#944—62no—
106#944—64no—
107C2×#215—24no—
108C2×#215C2×D314yes—
109D4×Dic3—34no—
110D4×Dic3—62no—
111C2×#214—34no—
112C2×#214—64no—
113C2×(C2×D3)⋊C4—61no—
114C2×C4⋊Dic3C2×D311yescharacteristic
115C2×Dic3⋊C4—61no—
116C2×Dic3⋊C4—61no—
117C2×Dic3⋊C4—61no—
118C2×Dic3⋊C4—61no—
119C2×Dic3⋊C4—62no—
120C2×Dic3⋊C4—62no—
121C2×C4×Dic3—31no—
122C2×C4×Dic3—31no—
123C2×C4×Dic3—61no—
124C22×C3⋊C8C2×D311yescharacteristic
125C22×C3⋊C8C2×D311yescharacteristic
126C2×#204—34no—
127C2×#204—64no—
128#893—34no—
129#893—62no—
130C3×#103—34no—
131#835C2×D314yescomplemented
132#816—34no—
133Dic3⋊C8—34no—
134Dic3⋊C8—34no—
135#810—34no—
136C23×C32C2×D411yescharacteristic
137C22×C3×D3—24no—
138C22×C3×D3—22no—
139C22×C3×D3—42no—
140C22×C3×D3—42no—
141C32×Q8—22no—
142C32×Q8—22no—
143C32×Q8—42no—
144C2×C32×C4—22no—
145C2×C32×C4—42no—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D412yes—
148C2×C32×C4#4112yes—
149C2×C32×C4C2411yescharacteristic
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—42no—
153C2×C3⋊Dic3SD1614yescomplemented
154C2×C3⋊Dic3C2×D412yes—
155C2×C3⋊Dic3C2×D412yes—
156#634—22no—
157#634—22no—
158#634—42no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—42no—
161C3×D12—24no—
162C3×D12—22no—
163C3×D12C2×D414yes—
164D3×Dic3—48no—
165C3×C3⋊C8—22no—
166C3×C3⋊C8—22no—
167C22×SD16—31no—
168C22×SD16—91no—
169C2×C4⋊Q8—91no—
170C2×C4×D4—91no—
171#461—98no—
172C2×C4⋊C8—91no—
173C2×#103—31no—
174C2×#103—91no—
175C24×C3—61no—
176C23×D3—21no—
177C2×C3×Q8—22no—
178C2×C3×Q8—21no—
179C2×C3×Q8—21no—
180C2×C3×Q8—22no—
181C2×C3×Q8—22no—
182C2×C3×Q8—22no—
183C2×C3×Q8—22no—
184C2×C3×Q8—22no—
185C2×C3×Q8—42no—
186C2×C3×Q8—42no—
187C2×C3×Q8C22×D312yes—
188C2×C3×Q8C22×D312yes—
189C2×C3×D4—34no—
190C2×C3×D4—32no—
191C2×C3×D4—62no—
192C2×C3×D4—61no—
193C22×C3×C4—22no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—61no—
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C22×D311yescharacteristic
200C22×Dic3—21no—
201C22×Dic3—31no—
202C22×Dic3—31no—
203C22×Dic3—31no—
204C22×Dic3—31no—
205C22×Dic3—61no—
206C22×Dic3—61no—
207C22×Dic3—64no—
208C22×Dic3—62no—
209C22×Dic3—61no—
210C22×Dic3—61no—
211C22×Dic3—124no—
212C2×D12—21no—
213C2×D12—22no—
214C2×D12#6714yes—
215C2×D12C22×D312yes—
216C2×C4×D3—64no—
217C2×C4×D3—124no—
218C2×Dic6—32no—
219C2×Dic6—32no—
220C2×Dic6—62no—
221C2×Dic6—62no—
222C2×Dic6—62no—
223C2×Dic6—62no—
224C2×Dic6—62no—
225C2×Dic6—62no—
226C2×Dic6—61no—
227C2×Dic6—61no—
228C2×Dic6—122no—
229C2×Dic6—122no—
230C3×SD16—68no—
231C2×C3×C8—32no—
232C2×C3×C8—32no—
233C2×C3×C8—62no—
234C2×C3×C8—62no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—61no—
237#217—64no—
238#215—28no—
239#214—68no—
240(C2×D3)⋊C4—64no—
241C4⋊Dic3—21no—
242C4⋊Dic3C22×D312yes—
243Dic3⋊C4—64no—
244Dic3⋊C4—64no—
245Dic3⋊C4—64no—
246Dic3⋊C4—64no—
247Dic3⋊C4—68no—
248Dic3⋊C4—68no—
249C4×Dic3—32no—
250C4×Dic3—32no—
251C4×Dic3—32no—
252C4×Dic3—32no—
253C4×Dic3—62no—
254C4×Dic3—62no—
255C2×C3⋊C8—22no—
256C2×C3⋊C8—22no—
257C2×C3⋊C8C22×D312yes—
258C2×C3⋊C8C22×D312yes—
259#204—68no—
260C22×C32#12112yes—
261C22×C32C2×SD1612yes—
262C22×C32#13712yes—
263C22×C32C22×D411yescharacteristic
264C2×C3×D3—24no—
265C2×C3×D3—42no—
266C2×C3×D3—42no—
267C2×C3×D3—48no—
268C32×C4—42no—
269C32×C4#12112yes—
270C32×C4C22×D411yescharacteristic
271C32×C4C2×#4111yescharacteristic
272C3⋊Dic3—22no—
273C3⋊Dic3—42no—
274C3⋊Dic3C2×SD1614yescomplemented
275C3×Dic3—42no—
276C22×Q8—91no—
277C22×Q8D3211yescharacteristic
278C22×D4—31no—
279C23×C4—181no—
280C2×SD16—34no—
281C2×SD16—64no—
282C2×SD16—94no—
283C2×SD16—184no—
284C22×C8—31no—
285C22×C8—31no—
286C4⋊Q8—94no—
287C4⋊Q8—182no—
288C4×D4—94no—
289C4×D4—182no—
290C2×C4⋊C4—31no—
291C2×C4⋊C4—181no—
292C2×C4⋊C4—181no—
293C2×C22⋊C4—181no—
294C2×C42—91no—
295C4⋊C8—94no—
296#103—34no—
297#103—94no—
298C23×C3—21no—
299C23×C3—64no—
300C23×C3—62no—
301C23×C3—122no—
302C23×C3—122no—
303C23×C3D3×D411yescharacteristic
304C23×C3D3×D411yescharacteristic
305C22×D3—24no—
306C22×D3—22no—
307C22×D3—42no—
308C22×D3—42no—
309C3×Q8—22no—
310C3×Q8—22no—
311C3×Q8—22no—
312C3×Q8—22no—
313C3×Q8—42no—
314C3×Q8—42no—
315C3×Q8—44no—
316C3×Q8—42no—
317C3×Q8—42no—
318C3×D4—34no—
319C3×D4—64no—
320C3×D4—62no—
321C2×C3×C4—24no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—21no—
328C2×C3×C4—44no—
329C2×C3×C4—42no—
330C2×C3×C4—42no—
331C2×C3×C4—62no—
332C2×C3×C4—122no—
333C2×C3×C4#23512yes—
334C2×C3×C4D3×D412yes—
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4#23712yes—
338C2×C3×C4C2×#6712yes—
339C2×C3×C4C23×D311yescharacteristic
340C2×C3×C4C23×D311yescharacteristic
341C2×Dic3—22no—
342C2×Dic3—34no—
343C2×Dic3—34no—
344C2×Dic3—32no—
345C2×Dic3—32no—
346C2×Dic3—32no—
347C2×Dic3—32no—
348C2×Dic3—42no—
349C2×Dic3—64no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—64no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—64no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—128no—
359C2×Dic3—124no—
360C2×Dic3—122no—
361C2×Dic3—122no—
362D12—24no—
363D12—22no—
364D12C2×#6714yes—
365C4×D3—128no—
366Dic6—62no—
367Dic6—62no—
368Dic6—62no—
369Dic6—62no—
370Dic6—122no—
371Dic6—122no—
372Dic6—124no—
373Dic6—122no—
374Dic6—122no—
375C3×C8—62no—
376C3×C8—62no—
377C3⋊C8—22no—
378C3⋊C8—22no—
379C2×C32#46114yescomplemented
380C2×C32C2×#12111yescharacteristic
381C2×C32C22×SD1611yescharacteristic
382C2×C32C2×#13711yescharacteristic
383C3×D3—44no—
384C24—61no—
385C2×Q8—21no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—92no—
389C2×Q8—181no—
390C2×Q8—182no—
391C2×Q8—182no—
392C2×Q8C2×D3212yes—
393C2×D4—32no—
394C2×D4—34no—
395C2×D4—62no—
396C2×D4—61no—
397C22×C4—21no—
398C22×C4—61no—
399C22×C4—91no—
400C22×C4—91no—
401C22×C4—184no—
402C22×C4—181no—
403C22×C4—364no—
404C22×C4C2×D3211yescharacteristic
405SD16—68no—
406SD16—188no—
407C2×C8—32no—
408C2×C8—32no—
409C2×C8—62no—
410C2×C8—62no—
411C4⋊C4—32no—
412C4⋊C4—61no—
413C4⋊C4—184no—
414C4⋊C4—184no—
415C22⋊C4—184no—
416C42—92no—
417C42—92no—
418C22×C3—21no—
419C22×C3—22no—
420C22×C3—22no—
421C22×C3—22no—
422C22×C3—64no—
423C22×C3—122no—
424C22×C3—122no—
425C22×C3—128no—
426C22×C3#88412yes—
427C22×C3D3×SD1612yes—
428C22×C3D3×SD1612yes—
429C22×C3#91512yes—
430C22×C3#91812yes—
431C22×C3#93912yes—
432C22×C3C2×D3×D411yescharacteristic
433C22×C3C2×D3×D411yescharacteristic
434C2×D3—24no—
435C2×D3—48no—
436C2×D3—42no—
437C2×D3—42no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—22no—
441C3×C4—44no—
442C3×C4—42no—
443C3×C4—42no—
444C3×C4—122no—
445C3×C4#88412yes—
446C3×C4#93912yes—
447C3×C4C2×#23511yescharacteristic
448C3×C4C2×D3×D411yescharacteristic
449C3×C4C2×#23711yescharacteristic
450C3×C4C22×#6711yescharacteristic
451Dic3—34no—
452Dic3—34no—
453Dic3—42no—
454Dic3—64no—
455Dic3—64no—
456Dic3—62no—
457Dic3—62no—
458Dic3—124no—
459Dic3—122no—
460Dic3—122no—
461C32C2×#46111yescharacteristic, complemented, Sylow
462C23—62no—
463C23—64no—
464C23—122no—
465C23—122no—
466C23#381111yescharacteristic
467Q8—22no—
468Q8—22no—
469Q8—42no—
470Q8—182no—
471Q8—182no—
472Q8—362no—
473D4—34no—
474D4—62no—
475D4—64no—
476C2×C4—22no—
477C2×C4—42no—
478C2×C4—62no—
479C2×C4—92no—
480C2×C4—94no—
481C2×C4—92no—
482C2×C4—122no—
483C2×C4—182no—
484C2×C4—182no—
485C2×C4—368no—
486C2×C4—362no—
487C2×C4#380412yes—
488C2×C4D3×#6712yes—
489C2×C4#381111yescharacteristic
490C2×C4C22×D3211yescharacteristic
491C8—62no—
492C8—62no—
493C2×C3—21no—
494C2×C3—24no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—124no—
498C2×C3#481814yescomplemented
499C2×C3#516214yescomplemented
500C2×C3C2×#88411yescharacteristic
501C2×C3C2×D3×SD1611yescharacteristic
502C2×C3C2×D3×SD1611yescharacteristic
503C2×C3C2×#91511yescharacteristic
504C2×C3C2×#91811yescharacteristic
505C2×C3C2×#93911yescharacteristic
506D3—44no—
507C22—64no—
508C22—122no—
509C22—128no—
510C22—122no—
511C22#6394012yes—
512C22#6395112yes—
513C22#6397112yes—
514C22C2×#381111yescharacteristic
515C4—42no—
516C4—94no—
517C4—122no—
518C4—182no—
519C4—362no—
520C4#6397112yes—
521C4C2×#380411yescharacteristic
522C4C2×D3×#6711yescharacteristic
523C3—21no—
524C3C2×#481811yescharacteristic, complemented
525C3C2×#516211yescharacteristic, complemented
526C2—124no—
527C2#1059156914yesdirect product factor
528C2C2×#6394011yescharacteristic
529C2C2×#6395111yescharacteristic
530C2C2×#6397111yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×Q8D32
hypocenterC32C2×#461
LCSG ▷ C2×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
1. C2×#64153C2semidirect
5. C2×C3×#835C2semidirect
6. #10591569C2direct (N × H)
7. C2×#63572C2semidirect
8. C2×#63567C2semidirect
16. #64153C22semidirect
30. C3×#835C22semidirect
31. #63572C22semidirect
32. #63567C22semidirect
43. C2×#835D3semidirect
131. #835C2×D3semidirect
153. C2×C3⋊Dic3SD16semidirect
274. C3⋊Dic3C2×SD16semidirect
379. C2×C32#461semidirect
461. C32C2×#461semidirect
498. C2×C3#4818semidirect
499. C2×C3#5162semidirect
524. C3C2×#4818semidirect
525. C3C2×#5162semidirect
527. C2#10591569direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641532
C22×C3×#2152
C2×#638982
C22×#37162
C2×C3×#8352
#105915692
C2×#635722
C2×#635672
C2×#51623
C2×#48183