Finite Group Databasebeta

← C2×#10591557 #11857875

Subgroups — C2×#10591557 #11857875

Order 1152.

1585 conjugacy classes of subgroups.

The subgroup lattice has 535 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×Q8C211yesmaximal, characteristic
2C2×#63841C211yesmaximal, characteristic
3C22×#3711C211yesmaximal, characteristic
4C2×#63662C211yesmaximal, characteristic, complemented
5C2×C3×#835C211yesmaximal, characteristic, complemented
6#10591557C218yesmaximal, direct product factor
7C2×#63566C211yesmaximal, characteristic, complemented
8C2×#63565C211yesmaximal, characteristic, complemented
9C2×#5225—31nomaximal
10C2×#4802—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C2×C3×D3×Q8—24no—
13C2×C3×D3×Q8—22no—
14C2×C3×D3×Q8C418yescomplemented
15C2×C3×D3×Q8C2214yes—
16C22×C3×C4×D3—21no—
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×Dic6—21no—
19C22×C3×Dic6C2211yescharacteristic
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#63841C2214yes—
28C2×#3711—24no—
29C2×#3711C2214yes—
30#63662C2214yescomplemented
31C3×#835C2214yescomplemented
32#63566C2214yescomplemented
33#63565C2214yescomplemented
34C23×C3×Q8—31no—
35C22×D3×Q8D311yescharacteristic
36C2×#926—31no—
37C22×#208—31no—
38C22×ΓL(1,𝔽25)—31no—
39C2×#892—31no—
40C2×C3×#103—31no—
41#5225—38no—
42C2×#835—31no—
43C2×#835—31no—
44C2×#835—31no—
45C2×#835—31no—
46C2×#835—61no—
47C2×#835D311yescharacteristic, complemented
48C2×#816—31no—
49C2×#810—31no—
50#4802—38no—
51C23×C3×D3D411yescharacteristic
52C2×C32×Q8—22no—
53C2×C32×Q8—21no—
54C2×C32×Q8C2×C414yes—
55C2×C32×Q8C2312yes—
56C22×C32×C4—21no—
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3—21no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3D411yescharacteristic
62C3×D3×Q8—216no—
63C3×D3×Q8—28no—
64C3×D3×Q8C2×C4116yescomplemented
65C2×C3×C4×D3—28no—
66C2×C3×C4×D3—24no—
67C2×C3×C4×D3C2×C414yes—
68C2×C3×C4×D3D412yes—
69C2×C3×C4×D3D414yes—
70C2×C3×C4×D3C2312yes—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6—28no—
74C2×C3×Dic6—24no—
75C2×C3×Dic6C2×C414yes—
76C2×C3×Dic6C2312yes—
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—
87#3711—28no—
88C2×#419—91noSylow
89C22×C3×Q8—21no—
90C22×C3×Q8—38no—
91C22×C3×Q8—34no—
92C22×C3×Q8—31no—
93C22×C3×Q8—61no—
94C22×C3×Q8—64no—
95C22×C3×Q8—62no—
96C22×C3×Q8C2×D311yescharacteristic
97C22×C3×Q8C2×D311yescharacteristic
98C23×C3×C4—31no—
99C23×C3×C4—61no—
100C2×D3×Q8—24no—
101C2×D3×Q8—22no—
102C2×D3×Q8Dic318yescomplemented
103C2×D3×Q8C2×D314yes—
104C22×C4×D3—21no—
105C22×C4×D3C2×D311yescharacteristic
106C22×Dic6—21no—
107C22×Dic6C2×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—
120C2×#208—34no—
121C2×#208—64no—
122C22×C3⋊C8—31no—
123C22×C3⋊C8—31no—
124C22×C3⋊C8—61no—
125C22×C3⋊C8C2×D311yescharacteristic
126C2×ΓL(1,𝔽25)—34no—
127C2×ΓL(1,𝔽25)—64no—
128#892—34no—
129#892—62no—
130C3×#103—34no—
131#835—34no—
132#835—34no—
133#835—34no—
134#835—34no—
135#835—64no—
136#835C2×D314yescomplemented
137#816—34no—
138#810—34no—
139C23×C32C2×D411yescharacteristic
140C22×C3×D3—22no—
141C22×C3×D3—22no—
142C22×C3×D3C22⋊C414yes—
143C22×C3×D3C2×D412yes—
144C32×Q8—24no—
145C32×Q8—22no—
146C32×Q8C22×C414yes—
147C2×C32×C4—24no—
148C2×C32×C4—22no—
149C2×C32×C4C22×C412yes—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D412yes—
152C2×C32×C4C2411yescharacteristic
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—42no—
155C2×C3×Dic3—24no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—42no—
159C2×C3×Dic3C22⋊C414yes—
160C2×C3×Dic3C2×D412yes—
161C3×C4×D3—216no—
162C3×C4×D3C22⋊C418yes—
163C3×C4×D3C22×C414yes—
164C3×C4×D3C2×D414yes—
165C3×Dic6—24no—
166C3×Dic6—22no—
167C3×Dic6—216no—
168C3×Dic6C22×C414yes—
169C3⋊(C3⋊C8)—22no—
170C3×C3⋊C8—22no—
171C23×Q8—31no—
172C22×M16—91no—
173C2×#117—91no—
174#419—98no—
175C2×#103—31no—
176C2×#103—91no—
177C2×#103—91no—
178C2×#103—91no—
179C24×C3—31no—
180C23×D3#6711yescharacteristic
181C2×C3×Q8—22no—
182C2×C3×Q8—21no—
183C2×C3×Q8—22no—
184C2×C3×Q8—21no—
185C2×C3×Q8—24no—
186C2×C3×Q8—22no—
187C2×C3×Q8—316no—
188C2×C3×Q8—34no—
189C2×C3×Q8—32no—
190C2×C3×Q8—42no—
191C2×C3×Q8—41no—
192C2×C3×Q8—68no—
193C2×C3×Q8—64no—
194C2×C3×Q8—616no—
195C2×C3×Q8—68no—
196C2×C3×Q8—62no—
197C2×C3×Q8—61no—
198C2×C3×Q8C4×D314yes—
199C2×C3×Q8C2×Dic314yes—
200C2×C3×Q8C22×D312yes—
201C2×C3×Q8C22×D312yes—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—31no—
206C22×C3×C4—34no—
207C22×C3×C4—34no—
208C22×C3×C4—32no—
209C22×C3×C4—32no—
210C22×C3×C4—41no—
211C22×C3×C4—68no—
212C22×C3×C4—64no—
213C22×C3×C4—61no—
214C22×C3×C4—61no—
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C22×D311yescharacteristic
217C22×Dic3—21no—
218C22×Dic3—21no—
219C22×Dic3—61no—
220C22×Dic3—61no—
221C22×Dic3—121no—
222C22×Dic3#6711yescharacteristic
223D3×Q8—216no—
224D3×Q8—28no—
225D3×Q8C2×Dic3116yescomplemented
226C2×C4×D3—28no—
227C2×C4×D3—24no—
228C2×C4×D3C2×Dic314yes—
229C2×C4×D3#6712yes—
230C2×C4×D3#6714yes—
231C2×C4×D3C22×D312yes—
232C2×Dic6—21no—
233C2×Dic6—22no—
234C2×Dic6—28no—
235C2×Dic6—24no—
236C2×Dic6C2×Dic314yes—
237C2×Dic6C22×D312yes—
238C2×C3×C8—32no—
239C2×C3×C8—62no—
240C3×C4⋊C4—32no—
241C3×C4⋊C4—61no—
242#217—64no—
243(C2×D3)⋊C4—64no—
244C4⋊Dic3—21no—
245C4⋊Dic3—32no—
246C4⋊Dic3—32no—
247C4⋊Dic3—62no—
248C4⋊Dic3—61no—
249C4⋊Dic3—61no—
250C4⋊Dic3—121no—
251C4⋊Dic3C22×D312yes—
252C4×Dic3—64no—
253C4×Dic3—64no—
254#208—68no—
255C2×C3⋊C8—22no—
256C2×C3⋊C8—32no—
257C2×C3⋊C8—32no—
258C2×C3⋊C8—62no—
259C2×C3⋊C8—62no—
260C2×C3⋊C8—62no—
261C2×C3⋊C8—122no—
262C2×C3⋊C8C22×D312yes—
263ΓL(1,𝔽25)—68no—
264C22×C32C2×C22⋊C412yes—
265C22×C32#13712yes—
266C22×C32#13712yes—
267C22×C32C22×D411yescharacteristic
268C2×C3×D3—22no—
269C2×C3×D3—22no—
270C2×C3×D3—28no—
271C2×C3×D3C2×C22⋊C414yes—
272C32×C4—24no—
273C32×C4C2×C22⋊C412yes—
274C32×C4C23×C411yescharacteristic
275C32×C4C22×D411yescharacteristic
276C3⋊Dic3—42no—
277C3×Dic3—24no—
278C3×Dic3—42no—
279C3×Dic3C2×C22⋊C414yes—
280C22×Q8—38no—
281C22×Q8—34no—
282C22×Q8—31no—
283C22×Q8—61no—
284C22×Q8—62no—
285C22×Q8—64no—
286C22×Q8D3211yescharacteristic
287C23×C4—31no—
288C23×C4—61no—
289C2×M16—94no—
290C2×M16—184no—
291C22×C8—31no—
292C22×C8—91no—
293#117—94no—
294#117—182no—
295C2×C4⋊C4—31no—
296C2×C4⋊C4—91no—
297C2×C22⋊C4—181no—
298C2×C42—181no—
299#103—34no—
300#103—94no—
301#103—94no—
302#103—94no—
303C23×C3—21no—
304C23×C3—34no—
305C23×C3—32no—
306C23×C3—62no—
307C23×C3—62no—
308C23×C3D3×D411yescharacteristic
309C23×C3C2×#6711yescharacteristic
310C22×D3—22no—
311C22×D3—22no—
312C22×D3#21714yes—
313C22×D3C2×#6712yes—
314C3×Q8—24no—
315C3×Q8—24no—
316C3×Q8—22no—
317C3×Q8—22no—
318C3×Q8—24no—
319C3×Q8—34no—
320C3×Q8—42no—
321C3×Q8—44no—
322C3×Q8—616no—
323C3×Q8—64no—
324C3×Q8—62no—
325C3×Q8C2×C4×D314yes—
326C3×Q8C22×Dic314yes—
327C2×C3×C4—24no—
328C2×C3×C4—24no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—21no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—21no—
335C2×C3×C4—34no—
336C2×C3×C4—32no—
337C2×C3×C4—38no—
338C2×C3×C4—34no—
339C2×C3×C4—34no—
340C2×C3×C4—42no—
341C2×C3×C4—44no—
342C2×C3×C4—616no—
343C2×C3×C4—64no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4—122no—
347C2×C3×C4C2×C4×D312yes—
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D412yes—
350C2×C3×C4C22×Dic312yes—
351C2×C3×C4C2×#6711yescharacteristic
352C2×C3×C4C2×#6712yes—
353C2×C3×C4C23×D311yescharacteristic
354C2×C3×C4C23×D311yescharacteristic
355C2×Dic3—24no—
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—42no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—122no—
362C2×Dic3—122no—
363C2×Dic3—122no—
364C2×Dic3—242no—
365C2×Dic3#21714yes—
366C2×Dic3C2×#6712yes—
367C4×D3—216no—
368C4×D3#21718yes—
369C4×D3C22×Dic314yes—
370C4×D3C2×#6714yes—
371Dic6—24no—
372Dic6—22no—
373Dic6—216no—
374Dic6C22×Dic314yes—
375C3×C8—62no—
376C3⋊C8—22no—
377C3⋊C8—62no—
378C3⋊C8—62no—
379C3⋊C8—122no—
380C2×C32#41914yescomplemented
381C2×C32C22×C22⋊C411yescharacteristic
382C2×C32C2×#13711yescharacteristic
383C2×C32C2×#13711yescharacteristic
384C3×D3—24no—
385C24—31no—
386C2×Q8—21no—
387C2×Q8—22no—
388C2×Q8—316no—
389C2×Q8—32no—
390C2×Q8—34no—
391C2×Q8—64no—
392C2×Q8—68no—
393C2×Q8—68no—
394C2×Q8—616no—
395C2×Q8—61no—
396C2×Q8—62no—
397C2×Q8D3×Dic314yes—
398C2×Q8C2×D3212yes—
399C22×C4—21no—
400C22×C4—31no—
401C22×C4—32no—
402C22×C4—34no—
403C22×C4—32no—
404C22×C4—34no—
405C22×C4—64no—
406C22×C4—68no—
407C22×C4—61no—
408C22×C4—61no—
409C22×C4—181no—
410C22×C4C2×D3211yescharacteristic
411M16—188no—
412C2×C8—32no—
413C2×C8—62no—
414C2×C8—92no—
415C2×C8—182no—
416C4⋊C4—32no—
417C4⋊C4—61no—
418C4⋊C4—92no—
419C4⋊C4—181no—
420C22⋊C4—184no—
421C42—184no—
422C22×C3—21no—
423C22×C3—22no—
424C22×C3—22no—
425C22×C3—22no—
426C22×C3—34no—
427C22×C3—62no—
428C22×C3—62no—
429C22×C3—68no—
430C22×C3D3×C22⋊C412yes—
431C22×C3#91512yes—
432C22×C3#91812yes—
433C22×C3#94212yes—
434C22×C3#94212yes—
435C22×C3C2×#21712yes—
436C22×C3C2×D3×D411yescharacteristic
437C22×C3C22×#6711yescharacteristic
438C2×D3—28no—
439C2×D3—22no—
440C2×D3—22no—
441C2×D3C2×#21714yes—
442C3×C4—24no—
443C3×C4—24no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—22no—
447C3×C4—34no—
448C3×C4—44no—
449C3×C4—64no—
450C3×C4—122no—
451C3×C4D3×C22⋊C412yes—
452C3×C4C2×#21712yes—
453C3×C4C22×C4×D311yescharacteristic
454C3×C4C2×D3×D411yescharacteristic
455C3×C4C23×Dic311yescharacteristic
456C3×C4C22×#6711yescharacteristic
457Dic3—24no—
458Dic3—42no—
459Dic3—122no—
460Dic3—122no—
461Dic3—242no—
462Dic3C2×#21714yes—
463C32C2×#41911yescharacteristic, complemented, Sylow
464C23—32no—
465C23—34no—
466C23—62no—
467C23—62no—
468C23D3×#6711yescharacteristic
469Q8—22no—
470Q8—24no—
471Q8—34no—
472Q8—616no—
473Q8—62no—
474Q8—64no—
475Q8C2×D3×Dic314yes—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—32no—
479C2×C4—34no—
480C2×C4—34no—
481C2×C4—34no—
482C2×C4—38no—
483C2×C4—616no—
484C2×C4—62no—
485C2×C4—64no—
486C2×C4—62no—
487C2×C4—122no—
488C2×C4—182no—
489C2×C4—362no—
490C2×C4C2×D3×Dic312yes—
491C2×C4D3×#6712yes—
492C2×C4D3×#6711yescharacteristic
493C2×C4C22×D3211yescharacteristic
494C8—62no—
495C8—182no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—24no—
499C2×C3—21no—
500C2×C3—64no—
501C2×C3#480214yescomplemented
502C2×C3#522514yescomplemented
503C2×C3C2×D3×C22⋊C411yescharacteristic
504C2×C3C2×#91511yescharacteristic
505C2×C3C2×#91811yescharacteristic
506C2×C3C2×#94211yescharacteristic
507C2×C3C2×#94211yescharacteristic
508C2×C3C22×#21711yescharacteristic
509D3—24no—
510C22—34no—
511C22—62no—
512C22—62no—
513C22—68no—
514C22#6394612yes—
515C22#6394812yes—
516C22D3×#21712yes—
517C22C2×D3×#6711yescharacteristic
518C4—24no—
519C4—34no—
520C4—64no—
521C4—122no—
522C4—362no—
523C4D3×#21712yes—
524C4C22×D3×Dic311yescharacteristic
525C4C2×D3×#6711yescharacteristic
526C3—21no—
527C3C2×#480211yescharacteristic, complemented
528C3C2×#522511yescharacteristic, complemented
529C2—64no—
530C2#1059155714yesdirect product factor
531C2C2×#6394611yescharacteristic
532C2C2×#6394811yescharacteristic
533C2C2×D3×#21711yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
cosocleC2×C32×C4C24
hypercenterC22×Q8D32
hypocenterC32C2×#419
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
4. C2×#63662C2semidirect
5. C2×C3×#835C2semidirect
6. #10591557C2direct (N × H)
7. C2×#63566C2semidirect
8. C2×#63565C2semidirect
14. C2×C3×D3×Q8C4semidirect
30. #63662C22semidirect
31. C3×#835C22semidirect
32. #63566C22semidirect
33. #63565C22semidirect
47. C2×#835D3semidirect
64. C3×D3×Q8C2×C4semidirect
102. C2×D3×Q8Dic3semidirect
136. #835C2×D3semidirect
225. D3×Q8C2×Dic3semidirect
380. C2×C32#419semidirect
463. C32C2×#419semidirect
501. C2×C3#4802semidirect
502. C2×C3#5225semidirect
527. C3C2×#4802semidirect
528. C3C2×#5225semidirect
530. C2#10591557direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×Q82
C2×#638412
C22×#37112
C2×#636622
C2×C3×#8352
#105915572
C2×#635662
C2×#635652
C2×#52253
C2×#48023