Finite Group Databasebeta

← C2×#10590828 #11866932

Subgroups — C2×#10590828 #11866932

Order 1152.

1169 conjugacy classes of subgroups.

The subgroup lattice has 539 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
2C2×#63908C211yesmaximal, characteristic
3C2×#63857C211yesmaximal, characteristic, complemented
4C22×#3716C211yesmaximal, characteristic, complemented
5C2×#63643C211yesmaximal, characteristic, complemented
6C2×C3×#821C211yesmaximal, characteristic, complemented
7C2×#63575C211yesmaximal, characteristic, complemented
8#10590828C218yesmaximal, direct product factor
9C2×#5134—31nomaximal
10C2×#4780—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×#625—21no—
15C22×C32×C8C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×C3×ΓL(1,𝔽25)—24no—
20C2×C3×ΓL(1,𝔽25)C2214yescomplemented
21C2×Dic3⋊Dic3—21no—
22C2×(C2×D3)⋊Dic3—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63908—22no—
25#63908C2214yes—
26#63857—22no—
27#63857C2214yescomplemented
28C2×#3716—24no—
29C2×#3716C2214yescomplemented
30#63643C2214yescomplemented
31C3×#821C2214yescomplemented
32#63575C2214yescomplemented
33C22×C3×M16—31no—
34C2×#938—31no—
35C22×#214—31no—
36C2×#930—31no—
37C2×#924—31no—
38C22×#204—31no—
39C22×ΓL(1,𝔽25)D311yescharacteristic, complemented
40C2×#897—31no—
41C2×C3×#102—31no—
42#5134—38no—
43C2×#821D311yescharacteristic, complemented
44C2×#818—31no—
45C2×#816—31no—
46C2×#816—31no—
47C2×#816—61no—
48C2×#807—31no—
49#4780—38no—
50C23×C3×D3—21no—
51C23×C3×D3D411yescharacteristic
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3—21no—
54C22×C3⋊Dic3—21no—
55C2×#634—22no—
56C2×#634—22no—
57C2×#634—21no—
58C2×#634C2312yes—
59C22×C3×Dic3—21no—
60C22×C3×Dic3D411yescharacteristic
61C2×C3×D12—22no—
62C2×C3×D12—22no—
63C2×C3×D12—21no—
64C2×C3×D12C2312yes—
65C2×C3×C4×D3—22no—
66C2×C3×C4×D3—22no—
67C2×C3×C4×D3D412yes—
68C2×C3×C4×D3C2312yes—
69C2×#625—24no—
70C2×#625—44no—
71C2×C32×C8—22no—
72C2×C32×C8C2312yes—
73C4⋊(C3⋊Dic3)—21no—
74C4⋊(C3⋊Dic3)C2312yes—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3C2312yes—
77C2×C3×C3⋊C8D414yescomplemented
78C2×C3×C3⋊C8C2312yes—
79C3×ΓL(1,𝔽25)—28no—
80Dic3⋊Dic3—24no—
81(C2×D3)⋊Dic3—24no—
82(C2×D3)⋊Dic3—24no—
83#3716—28no—
84C2×#468—91noSylow
85C22×C3×D4—31no—
86C23×C3×C4—31no—
87C22×#67—61no—
88C22×#67—61no—
89C22×D12C2×D311yescharacteristic
90C22×C4×D3C2×D311yescharacteristic
91C22×Dic6—31no—
92C22×Dic6—31no—
93C22×Dic6—61no—
94C2×C3×M16—34no—
95C2×C3×M16—64no—
96C22×C3×C8—21no—
97C22×C3×C8—31no—
98C22×C3×C8C2×D311yescharacteristic
99C22×C3×C8C2×D311yescharacteristic
100C2×C3×C4⋊C4—31no—
101C2×#217—61no—
102C2×#217—61no—
103#938—34no—
104#938—62no—
105C2×#214—34no—
106C2×#214—64no—
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—61no—
114C2×C4⋊Dic3—61no—
115C2×C4⋊Dic3C2×D311yescharacteristic
116#924—34no—
117#924—62no—
118C2×Dic3⋊C4—61no—
119C22×C3⋊C8C2×D311yescharacteristic
120C2×#204—34no—
121C2×#204—64no—
122C2×ΓL(1,𝔽25)—24no—
123C2×ΓL(1,𝔽25)C2×D314yescomplemented
124#897—34no—
125#897—62no—
126C3×#102—34no—
127#821C2×D314yescomplemented
128#818—34no—
129#816—34no—
130#816—34no—
131#816—64no—
132#807—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—
150#634—22no—
151#634—22no—
152#634—42no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—42no—
156C2×C3×Dic3C2×D412yes—
157C3×D12—22no—
158C3×D12—22no—
159C3×D12—42no—
160C3×C4×D3—24no—
161C3×C4×D3—22no—
162C3×C4×D3—22no—
163#625—48no—
164C32×C8—22no—
165C3×C3⋊C8C2×D414yescomplemented
166C22×SD16—91no—
167C22×M16—31no—
168C2×C22⋊Q8—91no—
169C2×#121—91no—
170#468—98no—
171C2×#107—91no—
172C2×#103—91no—
173C2×#102—31no—
174C24×C3—31no—
175C24×C3—61no—
176C23×D3—21no—
177C23×D3D1211yescharacteristic
178C2×C3×D4—32no—
179C2×C3×D4—61no—
180C2×C3×D4—62no—
181C2×C3×D4—62no—
182C22×C3×C4—21no—
183C22×C3×C4—31no—
184C22×C3×C4—32no—
185C22×C3×C4—32no—
186C22×C3×C4—62no—
187C22×C3×C4—62no—
188C22×C3×C4—61no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C2×#67—64no—
192C2×#67—64no—
193C2×#67—124no—
194C2×#67—124no—
195C22×Dic3—21no—
196C22×Dic3—61no—
197C22×Dic3—61no—
198C22×Dic3—61no—
199C22×Dic3—61no—
200C22×Dic3—121no—
201C22×Dic3—121no—
202C22×Dic3D1211yescharacteristic
203C2×D12—22no—
204C2×D12—22no—
205C2×D12—21no—
206C2×D12C22×D312yes—
207C2×C4×D3—22no—
208C2×C4×D3—22no—
209C2×C4×D3D1212yes—
210C2×C4×D3C22×D312yes—
211C2×Dic6—32no—
212C2×Dic6—32no—
213C2×Dic6—62no—
214C2×Dic6—64no—
215C2×Dic6—62no—
216C2×Dic6—62no—
217C2×Dic6—62no—
218C2×Dic6—62no—
219C2×Dic6—61no—
220C2×Dic6—61no—
221C2×Dic6—121no—
222C2×Dic6—122no—
223C3×M16—68no—
224C2×C3×C8—22no—
225C2×C3×C8—22no—
226C2×C3×C8—22no—
227C2×C3×C8—34no—
228C2×C3×C8—32no—
229C2×C3×C8—42no—
230C2×C3×C8C22×D312yes—
231C2×C3×C8C22×D312yes—
232C3×C4⋊C4—32no—
233C3×C4⋊C4—61no—
234#217—64no—
235#217—64no—
236#214—68no—
237(C2×D3)⋊C4—64no—
238(C2×D3)⋊C4—64no—
239C4⋊Dic3—21no—
240C4⋊Dic3—32no—
241C4⋊Dic3—32no—
242C4⋊Dic3—62no—
243C4⋊Dic3—61no—
244C4⋊Dic3—61no—
245C4⋊Dic3—64no—
246C4⋊Dic3—121no—
247C4⋊Dic3C22×D312yes—
248Dic3⋊C4—64no—
249C2×C3⋊C8#6714yescomplemented
250C2×C3⋊C8C22×D312yes—
251#204—68no—
252ΓL(1,𝔽25)—28no—
253C22×C32#12112yes—
254C22×C32AGL(1,ℤ/8)12yes—
255C22×C32#13712yes—
256C22×C32C22×D411yescharacteristic
257C2×C3×D3—22no—
258C2×C3×D3—22no—
259C2×C3×D3—22no—
260C2×C3×D3—44no—
261C2×C3×D3—42no—
262C2×C3×D3—42no—
263C2×C3×D3—42no—
264C2×C3×D3—84no—
265C32×C4#12112yes—
266C32×C4C22×D411yescharacteristic
267C32×C4C2×#4111yescharacteristic
268C3⋊Dic3—42no—
269C3⋊Dic3—42no—
270C3×Dic3—22no—
271C3×Dic3—42no—
272C22×Q8—91no—
273C22×D4—31no—
274C22×D4—181no—
275C23×C4—31no—
276C2×SD16—94no—
277C2×SD16—184no—
278C2×M16—34no—
279C2×M16—64no—
280C22×C8—31no—
281C22×C8D3211yescharacteristic
282C22⋊Q8—94no—
283C22⋊Q8—182no—
284#121—94no—
285#121—182no—
286C2×C4⋊C4—31no—
287C2×C4⋊C4—91no—
288C2×C4⋊C4—181no—
289C2×C22⋊C4—181no—
290C2×C22⋊C4—181no—
291#107—94no—
292#103—94no—
293#102—34no—
294C23×C3—21no—
295C23×C3—32no—
296C23×C3—62no—
297C23×C3—62no—
298C23×C3—62no—
299C23×C3—62no—
300C23×C3—122no—
301C23×C3—122no—
302C23×C3—122no—
303C23×C3C2×D1211yescharacteristic
304C23×C3D3×D411yescharacteristic
305C22×D3—22no—
306C22×D3—22no—
307C22×D3—22no—
308C22×D3—22no—
309C22×D3—42no—
310C22×D3—42no—
311C22×D3—42no—
312C22×D3C2×D1212yes—
313C3×D4—62no—
314C3×D4—62no—
315C3×D4—122no—
316C2×C3×C4—21no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—22no—
320C2×C3×C4—32no—
321C2×C3×C4—62no—
322C2×C3×C4—64no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—122no—
327C2×C3×C4C2×D1211yescharacteristic
328C2×C3×C4#23512yes—
329C2×C3×C4#23512yes—
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4D3×D412yes—
332C2×C3×C4C2×#6712yes—
333C2×C3×C4C23×D311yescharacteristic
334C2×C3×C4C23×D311yescharacteristic
335#67—128no—
336#67—128no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—42no—
340C2×Dic3—62no—
341C2×Dic3—62no—
342C2×Dic3—62no—
343C2×Dic3—62no—
344C2×Dic3—122no—
345C2×Dic3—122no—
346C2×Dic3—124no—
347C2×Dic3—122no—
348C2×Dic3—122no—
349C2×Dic3—122no—
350C2×Dic3—122no—
351C2×Dic3—242no—
352C2×Dic3C2×D1212yes—
353D12—22no—
354D12—22no—
355D12—42no—
356C4×D3—24no—
357C4×D3—22no—
358C4×D3—22no—
359Dic6—64no—
360Dic6—62no—
361Dic6—62no—
362Dic6—62no—
363Dic6—62no—
364Dic6—122no—
365Dic6—124no—
366Dic6—122no—
367Dic6—122no—
368C3×C8—22no—
369C3×C8—22no—
370C3×C8—34no—
371C3×C8—42no—
372C3⋊C8C2×#6714yescomplemented
373C2×C32#46814yescomplemented
374C2×C32C2×#12111yescharacteristic
375C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
376C2×C32C2×#13711yescharacteristic
377C3×D3—42no—
378C3×D3—82no—
379C24—31no—
380C24—61no—
381C2×Q8—92no—
382C2×Q8—181no—
383C2×Q8—182no—
384C2×Q8—182no—
385C2×D4—32no—
386C2×D4—62no—
387C2×D4—61no—
388C2×D4—62no—
389C2×D4—184no—
390C2×D4—364no—
391C22×C4—31no—
392C22×C4—32no—
393C22×C4—32no—
394C22×C4—62no—
395C22×C4—62no—
396C22×C4—61no—
397C22×C4—181no—
398C22×C4—181no—
399C22×C4C2×D3211yescharacteristic
400SD16—188no—
401M16—68no—
402C2×C8—22no—
403C2×C8—32no—
404C2×C8—34no—
405C2×C8C2×D3212yes—
406C4⋊C4—32no—
407C4⋊C4—61no—
408C4⋊C4—92no—
409C4⋊C4—184no—
410C4⋊C4—181no—
411C22⋊C4—184no—
412C22⋊C4—184no—
413C22×C3—21no—
414C22×C3—22no—
415C22×C3—22no—
416C22×C3—22no—
417C22×C3—62no—
418C22×C3—62no—
419C22×C3—62no—
420C22×C3—124no—
421C22×C3—122no—
422C22×C3—122no—
423C22×C3—122no—
424C22×C3—244no—
425C22×C3#88412yes—
426C22×C3#90812yes—
427C22×C3#90912yes—
428C22×C3#91112yes—
429C22×C3#91512yes—
430C22×C3#93012yes—
431C22×C3C22×D1211yescharacteristic
432C22×C3C2×D3×D411yescharacteristic
433C2×D3—22no—
434C2×D3—22no—
435C2×D3—22no—
436C2×D3—44no—
437C2×D3—42no—
438C2×D3—42no—
439C2×D3—42no—
440C2×D3—84no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—22no—
444C3×C4—62no—
445C3×C4—122no—
446C3×C4#88412yes—
447C3×C4#93012yes—
448C3×C4C2×#23511yescharacteristic
449C3×C4C2×#23511yescharacteristic
450C3×C4C2×D3×D411yescharacteristic
451C3×C4C22×#6711yescharacteristic
452Dic3—22no—
453Dic3—42no—
454Dic3—124no—
455Dic3—122no—
456Dic3—122no—
457Dic3—122no—
458Dic3—122no—
459Dic3—242no—
460C32C2×#46811yescharacteristic, complemented, Sylow
461C23—32no—
462C23—62no—
463C23—62no—
464C23—62no—
465C23—62no—
466C23—122no—
467C23—122no—
468C23—122no—
469C23D3×D1211yescharacteristic
470Q8—182no—
471Q8—182no—
472Q8—362no—
473D4—62no—
474D4—62no—
475D4—122no—
476D4—368no—
477C2×C4—32no—
478C2×C4—62no—
479C2×C4—62no—
480C2×C4—62no—
481C2×C4—64no—
482C2×C4—62no—
483C2×C4—122no—
484C2×C4—182no—
485C2×C4—182no—
486C2×C4—362no—
487C2×C4—362no—
488C2×C4#379812yes—
489C2×C4D3×D1211yescharacteristic
490C2×C4D3×#6712yes—
491C2×C4C22×D3211yescharacteristic
492C8—22no—
493C8—34no—
494C2×C3—24no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—122no—
499C2×C3—242no—
500C2×C3#478014yescomplemented
501C2×C3#513414yescomplemented
502C2×C3C2×#88411yescharacteristic
503C2×C3C2×#90811yescharacteristic
504C2×C3C2×#90911yescharacteristic
505C2×C3C2×#91111yescharacteristic
506C2×C3C2×#91511yescharacteristic
507C2×C3C2×#93011yescharacteristic
508D3—42no—
509D3—82no—
510C22—62no—
511C22—62no—
512C22—62no—
513C22—124no—
514C22—122no—
515C22—122no—
516C22—122no—
517C22—244no—
518C22#6379512yes—
519C22#6380012yes—
520C22#6390612yes—
521C22C2×D3×D1211yescharacteristic
522C4—62no—
523C4—122no—
524C4—362no—
525C4—362no—
526C4#6390612yes—
527C4C2×#379811yescharacteristic
528C4C2×D3×#6711yescharacteristic
529C3—21no—
530C3C2×#478011yescharacteristic, complemented
531C3C2×#513411yescharacteristic, complemented
532C2—122no—
533C2—242no—
534C2#1059082814yesdirect product factor
535C2C2×#6379511yescharacteristic
536C2C2×#6380011yescharacteristic
537C2C2×#6390611yescharacteristic
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×ΓL(1,𝔽25)C2semidirect
3. C2×#63857C2semidirect
4. C22×#3716C2semidirect
5. C2×#63643C2semidirect
6. C2×C3×#821C2semidirect
7. C2×#63575C2semidirect
8. #10590828C2direct (N × H)
20. C2×C3×ΓL(1,𝔽25)C22semidirect
27. #63857C22semidirect
29. C2×#3716C22semidirect
30. #63643C22semidirect
31. C3×#821C22semidirect
32. #63575C22semidirect
39. C22×ΓL(1,𝔽25)D3semidirect
43. C2×#821D3semidirect
77. C2×C3×C3⋊C8D4semidirect
123. C2×ΓL(1,𝔽25)C2×D3semidirect
127. #821C2×D3semidirect
165. C3×C3⋊C8C2×D4semidirect
249. C2×C3⋊C8#67semidirect
372. C3⋊C8C2×#67semidirect
373. C2×C32#468semidirect
460. C32C2×#468semidirect
500. C2×C3#4780semidirect
501. C2×C3#5134semidirect
530. C3C2×#4780semidirect
531. C3C2×#5134semidirect
534. C2#10590828direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×ΓL(1,𝔽25)2
C2×#639082
C2×#638572
C22×#37162
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C2×#635752
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C2×#47803