Finite Group Databasebeta

← C2×#10590833 #11866920

Subgroups — C2×#10590833 #11866920

Order 1152.

1153 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic, complemented
2C22×C3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
3C2×#63908C211yesmaximal, characteristic
4C2×#63856C211yesmaximal, characteristic, complemented
5C2×#63645C211yesmaximal, characteristic, complemented
6C2×#63566C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic, complemented
8#10590833C218yesmaximal, direct product factor
9C2×#5174—31nomaximal
10C2×#5134—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×#625—21no—
15C22×C32×C8C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×C3×#204—24no—
20C2×C3×#204C2214yescomplemented
21C2×C3×ΓL(1,𝔽25)—24no—
22C2×C3×ΓL(1,𝔽25)C2214yescomplemented
23C2×#3724—21no—
24C2×(C2×D3)⋊Dic3—21no—
25C2×(C2×D3)⋊Dic3—21no—
26#63908—22no—
27#63908C2214yes—
28#63856—22no—
29#63856C2214yescomplemented
30#63645C2214yescomplemented
31#63566C2214yescomplemented
32#63563C2214yescomplemented
33C22×C3×SD16—31no—
34C22×C3×M16—31no—
35C2×#946—31no—
36C2×#938—31no—
37C2×#930—31no—
38C2×#924—31no—
39C22×#204D311yescharacteristic, complemented
40C22×ΓL(1,𝔽25)D311yescharacteristic, complemented
41C2×#835—31no—
42C2×#832—31no—
43#5174—38no—
44#5134—38no—
45C2×#821—31no—
46C2×#818—31no—
47C2×#818—31no—
48C2×#818—61no—
49C2×#816—31no—
50C23×C3×D3—21no—
51C23×C3×D3D411yescharacteristic
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3—21no—
54C22×C3⋊Dic3—21no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3D411yescharacteristic
57C2×C3×D12—22no—
58C2×C3×D12—22no—
59C2×C3×D12—21no—
60C2×C3×D12C2312yes—
61C2×C3×C4×D3—22no—
62C2×C3×C4×D3—22no—
63C2×C3×C4×D3D412yes—
64C2×C3×C4×D3C2312yes—
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6C2312yes—
69C2×#625—24no—
70C2×#625—44no—
71C2×C32×C8D414yescomplemented
72C2×C32×C8C2312yes—
73C4⋊(C3⋊Dic3)—21no—
74C4⋊(C3⋊Dic3)—21no—
75C4⋊(C3⋊Dic3)C2312yes—
76C4⋊(C3⋊Dic3)C2312yes—
77C2×C3×C3⋊C8—22no—
78C2×C3×C3⋊C8C2312yes—
79C3×#204—28no—
80C3×ΓL(1,𝔽25)—28no—
81#3724—24no—
82(C2×D3)⋊Dic3—24no—
83(C2×D3)⋊Dic3—24no—
84C2×#468—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—31no—
87C23×C3×C4—31no—
88C22×#67—61no—
89C22×#67—61no—
90C22×D12C2×D311yescharacteristic
91C22×C4×D3C2×D311yescharacteristic
92C22×Dic6C2×D311yescharacteristic
93C2×C3×SD16—34no—
94C2×C3×SD16—64no—
95C2×C3×M16—34no—
96C2×C3×M16—64no—
97C22×C3×C8—21no—
98C22×C3×C8—31no—
99C22×C3×C8C2×D311yescharacteristic
100C22×C3×C8C2×D311yescharacteristic
101C2×#217—61no—
102C2×#217—61no—
103#946—34no—
104#946—62no—
105#938—34no—
106#938—62no—
107#930—34no—
108#930—62no—
109C2×(C2×D3)⋊C4—61no—
110C2×(C2×D3)⋊C4—61no—
111C2×C4⋊Dic3—31no—
112C2×C4⋊Dic3—31no—
113C2×C4⋊Dic3—31no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—61no—
116C2×C4⋊Dic3—61no—
117#924—34no—
118#924—62no—
119C2×Dic3⋊C4—61no—
120C2×Dic3⋊C4—61no—
121C22×C3⋊C8C2×D311yescharacteristic
122C2×#204—24no—
123C2×#204C2×D314yescomplemented
124C2×ΓL(1,𝔽25)—24no—
125C2×ΓL(1,𝔽25)C2×D314yescomplemented
126#835—34no—
127#832—34no—
128#821—34no—
129#818—34no—
130#818—34no—
131#818—64no—
132#816—34no—
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—22no—
135C22×C3×D3—22no—
136C22×C3×D3—22no—
137C22×C3×D3—22no—
138C22×C3×D3—42no—
139C22×C3×D3—42no—
140C22×C3×D3—42no—
141C22×C3×D3C2×D412yes—
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D412yes—
144C2×C32×C4#4112yes—
145C2×C32×C4C2411yescharacteristic
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—42no—
149C2×C3⋊Dic3—42no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—42no—
153C2×C3×Dic3C2×D412yes—
154C3×D12—22no—
155C3×D12—22no—
156C3×D12—42no—
157C3×C4×D3—24no—
158C3×C4×D3—22no—
159C3×C4×D3—22no—
160C3×Dic6—22no—
161C3×Dic6—22no—
162C3×Dic6—42no—
163#625—48no—
164C32×C8C2×D414yescomplemented
165C3×C3⋊C8—22no—
166C22×SD16—31no—
167C22×M16—31no—
168C2×C22⋊Q8—91no—
169C2×#121—91no—
170#468—98no—
171C2×#107—91no—
172C2×#103—91no—
173C2×#102—91no—
174C24×C3—31no—
175C24×C3—61no—
176C23×D3—21no—
177C23×D3D1211yescharacteristic
178C2×C3×Q8—32no—
179C2×C3×Q8—61no—
180C2×C3×Q8—62no—
181C2×C3×Q8—62no—
182C2×C3×D4—32no—
183C2×C3×D4—61no—
184C2×C3×D4—62no—
185C2×C3×D4—62no—
186C22×C3×C4—21no—
187C22×C3×C4—31no—
188C22×C3×C4—32no—
189C22×C3×C4—32no—
190C22×C3×C4—62no—
191C22×C3×C4—62no—
192C22×C3×C4—61no—
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C2×#67—64no—
196C2×#67—64no—
197C2×#67—124no—
198C2×#67—124no—
199C22×Dic3—21no—
200C22×Dic3—61no—
201C22×Dic3—61no—
202C22×Dic3—61no—
203C22×Dic3—61no—
204C22×Dic3—121no—
205C22×Dic3—121no—
206C22×Dic3D1211yescharacteristic
207C2×D12—22no—
208C2×D12—22no—
209C2×D12—21no—
210C2×D12C22×D312yes—
211C2×C4×D3—22no—
212C2×C4×D3—22no—
213C2×C4×D3D1212yes—
214C2×C4×D3C22×D312yes—
215C2×Dic6—22no—
216C2×Dic6—22no—
217C2×Dic6—21no—
218C2×Dic6C22×D312yes—
219C3×SD16—68no—
220C3×M16—68no—
221C2×C3×C8—24no—
222C2×C3×C8—22no—
223C2×C3×C8—32no—
224C2×C3×C8—62no—
225C2×C3×C8#6714yescomplemented
226C2×C3×C8#6714yescomplemented
227C2×C3×C8C22×D312yes—
228C2×C3×C8C22×D312yes—
229#217—64no—
230#217—64no—
231(C2×D3)⋊C4—64no—
232(C2×D3)⋊C4—64no—
233C4⋊Dic3—32no—
234C4⋊Dic3—32no—
235C4⋊Dic3—32no—
236C4⋊Dic3—32no—
237C4⋊Dic3—62no—
238C4⋊Dic3—62no—
239C4⋊Dic3—61no—
240C4⋊Dic3—61no—
241C4⋊Dic3—61no—
242C4⋊Dic3—61no—
243C4⋊Dic3—121no—
244C4⋊Dic3—121no—
245Dic3⋊C4—64no—
246Dic3⋊C4—64no—
247C2×C3⋊C8—22no—
248C2×C3⋊C8C22×D312yes—
249#204—28no—
250ΓL(1,𝔽25)—28no—
251C22×C32#12112yes—
252C22×C32AGL(1,ℤ/8)12yes—
253C22×C32#13712yes—
254C22×C32C22×D411yescharacteristic
255C2×C3×D3—22no—
256C2×C3×D3—22no—
257C2×C3×D3—22no—
258C2×C3×D3—44no—
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C2×C3×D3—42no—
262C2×C3×D3—84no—
263C32×C4#12112yes—
264C32×C4C22×D411yescharacteristic
265C32×C4C2×#4111yescharacteristic
266C3⋊Dic3—42no—
267C3⋊Dic3—42no—
268C3×Dic3—22no—
269C3×Dic3—42no—
270C22×Q8—31no—
271C22×D4—31no—
272C22×D4—181no—
273C23×C4—31no—
274C2×SD16—34no—
275C2×SD16—64no—
276C2×M16—34no—
277C2×M16—64no—
278C22×C8—31no—
279C22×C8D3211yescharacteristic
280C22⋊Q8—94no—
281C22⋊Q8—182no—
282#121—94no—
283#121—182no—
284C2×C4⋊C4—91no—
285C2×C4⋊C4—91no—
286C2×C4⋊C4—181no—
287C2×C22⋊C4—181no—
288C2×C22⋊C4—181no—
289#107—94no—
290#103—94no—
291#102—94no—
292C23×C3—21no—
293C23×C3—32no—
294C23×C3—62no—
295C23×C3—62no—
296C23×C3—62no—
297C23×C3—62no—
298C23×C3—122no—
299C23×C3—122no—
300C23×C3—122no—
301C23×C3C2×D1211yescharacteristic
302C23×C3D3×D411yescharacteristic
303C22×D3—22no—
304C22×D3—22no—
305C22×D3—22no—
306C22×D3—22no—
307C22×D3—42no—
308C22×D3—42no—
309C22×D3—42no—
310C22×D3C2×D1212yes—
311C3×Q8—62no—
312C3×Q8—62no—
313C3×Q8—122no—
314C3×D4—62no—
315C3×D4—62no—
316C3×D4—122no—
317C2×C3×C4—21no—
318C2×C3×C4—22no—
319C2×C3×C4—21no—
320C2×C3×C4—22no—
321C2×C3×C4—32no—
322C2×C3×C4—62no—
323C2×C3×C4—64no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—122no—
328C2×C3×C4C2×D1211yescharacteristic
329C2×C3×C4#23512yes—
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4#23712yes—
332C2×C3×C4C2×#6712yes—
333C2×C3×C4C2×#6712yes—
334C2×C3×C4C23×D311yescharacteristic
335C2×C3×C4C23×D311yescharacteristic
336#67—128no—
337#67—128no—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—42no—
341C2×Dic3—62no—
342C2×Dic3—62no—
343C2×Dic3—62no—
344C2×Dic3—62no—
345C2×Dic3—122no—
346C2×Dic3—122no—
347C2×Dic3—122no—
348C2×Dic3—122no—
349C2×Dic3—122no—
350C2×Dic3—122no—
351C2×Dic3—242no—
352C2×Dic3—242no—
353C2×Dic3C2×D1212yes—
354D12—22no—
355D12—22no—
356D12—42no—
357C4×D3—24no—
358C4×D3—22no—
359C4×D3—22no—
360Dic6—22no—
361Dic6—22no—
362Dic6—42no—
363C3×C8—24no—
364C3×C8—62no—
365C3×C8C2×#6714yescomplemented
366C3×C8C2×#6714yescomplemented
367C3⋊C8—22no—
368C2×C32#46814yescomplemented
369C2×C32C2×#12111yescharacteristic
370C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
371C2×C32C2×#13711yescharacteristic
372C3×D3—42no—
373C3×D3—82no—
374C24—31no—
375C24—61no—
376C2×Q8—32no—
377C2×Q8—61no—
378C2×Q8—62no—
379C2×Q8—62no—
380C2×D4—32no—
381C2×D4—62no—
382C2×D4—61no—
383C2×D4—62no—
384C2×D4—184no—
385C2×D4—364no—
386C22×C4—31no—
387C22×C4—32no—
388C22×C4—32no—
389C22×C4—62no—
390C22×C4—62no—
391C22×C4—61no—
392C22×C4—181no—
393C22×C4—181no—
394C22×C4C2×D3211yescharacteristic
395SD16—68no—
396M16—68no—
397C2×C8—32no—
398C2×C8—62no—
399C2×C8#62514yescomplemented
400C2×C8C2×D3212yes—
401C4⋊C4—92no—
402C4⋊C4—92no—
403C4⋊C4—184no—
404C4⋊C4—181no—
405C4⋊C4—181no—
406C22⋊C4—184no—
407C22⋊C4—184no—
408C22×C3—21no—
409C22×C3—22no—
410C22×C3—22no—
411C22×C3—22no—
412C22×C3—62no—
413C22×C3—62no—
414C22×C3—62no—
415C22×C3—124no—
416C22×C3—122no—
417C22×C3—122no—
418C22×C3—122no—
419C22×C3—244no—
420C22×C3#90812yes—
421C22×C3#90912yes—
422C22×C3#91412yes—
423C22×C3#91512yes—
424C22×C3#93012yes—
425C22×C3#93812yes—
426C22×C3C22×D1211yescharacteristic
427C22×C3C2×D3×D411yescharacteristic
428C2×D3—22no—
429C2×D3—22no—
430C2×D3—22no—
431C2×D3—44no—
432C2×D3—42no—
433C2×D3—42no—
434C2×D3—42no—
435C2×D3—84no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—22no—
439C3×C4—62no—
440C3×C4—122no—
441C3×C4#93012yes—
442C3×C4#93812yes—
443C3×C4C2×#23511yescharacteristic
444C3×C4C2×#23711yescharacteristic
445C3×C4C22×#6711yescharacteristic
446C3×C4C22×#6711yescharacteristic
447Dic3—22no—
448Dic3—42no—
449Dic3—122no—
450Dic3—122no—
451Dic3—122no—
452Dic3—122no—
453Dic3—242no—
454Dic3—242no—
455C32C2×#46811yescharacteristic, complemented, Sylow
456C23—32no—
457C23—62no—
458C23—62no—
459C23—62no—
460C23—62no—
461C23—122no—
462C23—122no—
463C23—122no—
464C23D3×D1211yescharacteristic
465Q8—62no—
466Q8—62no—
467Q8—122no—
468D4—62no—
469D4—62no—
470D4—122no—
471D4—368no—
472C2×C4—32no—
473C2×C4—62no—
474C2×C4—62no—
475C2×C4—62no—
476C2×C4—64no—
477C2×C4—62no—
478C2×C4—122no—
479C2×C4—182no—
480C2×C4—182no—
481C2×C4—362no—
482C2×C4—362no—
483C2×C4#379512yes—
484C2×C4D3×D1211yescharacteristic
485C2×C4C2×#62512yes—
486C2×C4C22×D3211yescharacteristic
487C8—62no—
488C8C2×#62514yescomplemented
489C2×C3—24no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—122no—
494C2×C3—242no—
495C2×C3#513414yescomplemented
496C2×C3#517414yescomplemented
497C2×C3C2×#90811yescharacteristic
498C2×C3C2×#90911yescharacteristic
499C2×C3C2×#91411yescharacteristic
500C2×C3C2×#91511yescharacteristic
501C2×C3C2×#93011yescharacteristic
502C2×C3C2×#93811yescharacteristic
503D3—42no—
504D3—82no—
505C22—62no—
506C22—62no—
507C22—62no—
508C22—124no—
509C22—122no—
510C22—122no—
511C22—122no—
512C22—244no—
513C22#6379412yes—
514C22#6380012yes—
515C22#6390812yes—
516C22C2×D3×D1211yescharacteristic
517C4—62no—
518C4—122no—
519C4—362no—
520C4—362no—
521C4#6390812yes—
522C4C2×#379511yescharacteristic
523C4C22×#62511yescharacteristic
524C3—21no—
525C3C2×#513411yescharacteristic, complemented
526C3C2×#517411yescharacteristic, complemented
527C2—122no—
528C2—242no—
529C2#1059083314yesdirect product factor
530C2C2×#6379411yescharacteristic
531C2C2×#6380011yescharacteristic
532C2C2×#6390811yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC2×#63908C2
hypercenterC22×C8D32
hypocenterC32C2×#468
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×#204C2semidirect
2. C22×C3×ΓL(1,𝔽25)C2semidirect
4. C2×#63856C2semidirect
5. C2×#63645C2semidirect
6. C2×#63566C2semidirect
7. C2×#63563C2semidirect
8. #10590833C2direct (N × H)
20. C2×C3×#204C22semidirect
22. C2×C3×ΓL(1,𝔽25)C22semidirect
29. #63856C22semidirect
30. #63645C22semidirect
31. #63566C22semidirect
32. #63563C22semidirect
39. C22×#204D3semidirect
40. C22×ΓL(1,𝔽25)D3semidirect
71. C2×C32×C8D4semidirect
123. C2×#204C2×D3semidirect
125. C2×ΓL(1,𝔽25)C2×D3semidirect
164. C32×C8C2×D4semidirect
225. C2×C3×C8#67semidirect
226. C2×C3×C8#67semidirect
365. C3×C8C2×#67semidirect
366. C3×C8C2×#67semidirect
368. C2×C32#468semidirect
399. C2×C8#625semidirect
455. C32C2×#468semidirect
488. C8C2×#625semidirect
495. C2×C3#5134semidirect
496. C2×C3#5174semidirect
525. C3C2×#5134semidirect
526. C3C2×#5174semidirect
529. C2#10590833direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2042
C22×C3×ΓL(1,𝔽25)2
C2×#639082
C2×#638562
C2×#636452
C2×#635662
C2×#635632
#105908332
C2×#51743
C2×#51343