Finite Group Databasebeta

← C2×#10590827 #11866981

Subgroups — C2×#10590827 #11866981

Order 1152.

1293 conjugacy classes of subgroups.

The subgroup lattice has 577 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×#63909C211yesmaximal, characteristic, complemented
3C2×#63908C211yesmaximal, characteristic, complemented
4C22×#3714C211yesmaximal, characteristic, complemented
5C2×#63648C211yesmaximal, characteristic, complemented
6C2×C3×#821C211yesmaximal, characteristic, complemented
7C2×#63573C211yesmaximal, characteristic, complemented
8#10590827C218yesmaximal, direct product factor
9C2×#5135—31nomaximal
10C2×#4782—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×#626—21no—
15C22×#625—21no—
16C22×C32×C8C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C2×C3×ΓL(1,𝔽25)—24no—
21C2×C3×ΓL(1,𝔽25)C2214yescomplemented
22C2×#3722—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63909—22no—
25#63909C2214yescomplemented
26#63908—22no—
27#63908C2214yescomplemented
28C2×#3714—24no—
29C2×#3714C2214yescomplemented
30#63648C2214yescomplemented
31C3×#821C2214yescomplemented
32#63573C2214yescomplemented
33C22×C3×M16—31no—
34C2×#938—31no—
35C22×#213—31no—
36C2×#930—31no—
37C2×#930—31no—
38C22×D24—31no—
39C22×ΓL(1,𝔽25)D311yescharacteristic, complemented
40C2×#895—31no—
41C2×C3×#102—31no—
42#5135—38no—
43C2×#821—31no—
44C2×#821—31no—
45C2×#821—61no—
46C2×#821D311yescharacteristic, complemented
47C2×#817—31no—
48C2×#808—31no—
49#4782—38no—
50C23×C3⋊D3—21no—
51C23×C3×D3—21no—
52C23×C3×D3D411yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—21no—
55C2×C4⋊(C3⋊D3)—22no—
56C2×C4⋊(C3⋊D3)—22no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)C2312yes—
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×#626—24no—
70C2×#626—44no—
71C2×#625—24no—
72C2×#625—44no—
73C2×C32×C8—22no—
74C2×C32×C8C2312yes—
75C4⋊(C3⋊Dic3)—21no—
76C4⋊(C3⋊Dic3)C2312yes—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3C2312yes—
79C2×C3×C3⋊C8D414yescomplemented
80C2×C3×C3⋊C8C2312yes—
81C3×ΓL(1,𝔽25)—28no—
82#3722—24no—
83(C2×D3)⋊Dic3—24no—
84#3714—28no—
85C2×#469—91noSylow
86C22×C3×D4—31no—
87C23×C3×C4—31no—
88C22×#67—61no—
89C22×#67—61no—
90C22×#67—61no—
91C22×D12—31no—
92C22×D12—31no—
93C22×D12—61no—
94C22×D12—61no—
95C22×D12C2×D311yescharacteristic
96C22×C4×D3C2×D311yescharacteristic
97C2×C3×M16—34no—
98C2×C3×M16—64no—
99C22×C3×C8—21no—
100C22×C3×C8—31no—
101C22×C3×C8C2×D311yescharacteristic
102C22×C3×C8C2×D311yescharacteristic
103C2×C3×C4⋊C4—31no—
104C2×#217—61no—
105#938—34no—
106#938—62no—
107C2×#213—34no—
108C2×#213—64no—
109#930—34no—
110#930—34no—
111#930—62no—
112#930—62no—
113C2×(C2×D3)⋊C4—61no—
114C2×(C2×D3)⋊C4—61no—
115C2×(C2×D3)⋊C4—61no—
116C2×C4⋊Dic3—31no—
117C2×C4⋊Dic3—31no—
118C2×C4⋊Dic3—61no—
119C2×C4⋊Dic3C2×D311yescharacteristic
120C22×C3⋊C8C2×D311yescharacteristic
121C2×D24—34no—
122C2×D24—64no—
123C2×ΓL(1,𝔽25)—24no—
124C2×ΓL(1,𝔽25)C2×D314yescomplemented
125#895—34no—
126#895—62no—
127C3×#102—34no—
128#821—34no—
129#821—34no—
130#821—64no—
131#821C2×D314yescomplemented
132#817—34no—
133#808—34no—
134C23×C32C2×D411yescharacteristic
135C22×C3⋊D3—22no—
136C22×C3⋊D3—42no—
137C22×C3⋊D3—42no—
138C22×C3⋊D3—42no—
139C22×C3×D3—22no—
140C22×C3×D3—22no—
141C22×C3×D3—22no—
142C22×C3×D3—22no—
143C22×C3×D3—42no—
144C22×C3×D3—42no—
145C22×C3×D3—42no—
146C22×C3×D3C2×D412yes—
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D412yes—
149C2×C32×C4#4112yes—
150C2×C32×C4C2411yescharacteristic
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—42no—
153C4⋊(C3⋊D3)—22no—
154C4⋊(C3⋊D3)—22no—
155C4⋊(C3⋊D3)—42no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—42no—
159C2×C3×Dic3C2×D412yes—
160C3×D12—22no—
161C3×D12—22no—
162C3×D12—42no—
163C3×C4×D3—24no—
164C3×C4×D3—22no—
165C3×C4×D3—22no—
166#626—48no—
167#625—48no—
168C32×C8—22no—
169C3×C3⋊C8C2×D414yescomplemented
170C22×D8—91no—
171C22×M16—31no—
172C2×#121—91no—
173C2×#121—91no—
174#469—98no—
175C2×#106—91no—
176C2×#102—31no—
177C2×#102—91no—
178C24×C3—31no—
179C24×C3—61no—
180C23×D3—21no—
181C23×D3—61no—
182C23×D3—61no—
183C23×D3—121no—
184C23×D3D1211yescharacteristic
185C2×C3×D4—32no—
186C2×C3×D4—61no—
187C2×C3×D4—62no—
188C2×C3×D4—62no—
189C22×C3×C4—21no—
190C22×C3×C4—31no—
191C22×C3×C4—32no—
192C22×C3×C4—32no—
193C22×C3×C4—62no—
194C22×C3×C4—62no—
195C22×C3×C4—61no—
196C22×C3×C4C22×D311yescharacteristic
197C22×C3×C4C22×D311yescharacteristic
198C2×#67—64no—
199C2×#67—64no—
200C2×#67—64no—
201C2×#67—124no—
202C2×#67—124no—
203C2×#67—124no—
204C22×Dic3—21no—
205C22×Dic3—61no—
206C22×Dic3—61no—
207C22×Dic3—121no—
208C22×Dic3D1211yescharacteristic
209C2×D12—22no—
210C2×D12—22no—
211C2×D12—21no—
212C2×D12—32no—
213C2×D12—32no—
214C2×D12—62no—
215C2×D12—64no—
216C2×D12—62no—
217C2×D12—62no—
218C2×D12—62no—
219C2×D12—62no—
220C2×D12—64no—
221C2×D12—61no—
222C2×D12—61no—
223C2×D12—121no—
224C2×D12—122no—
225C2×D12—124no—
226C2×D12C22×D312yes—
227C2×C4×D3—22no—
228C2×C4×D3—22no—
229C2×C4×D3D1212yes—
230C2×C4×D3C22×D312yes—
231C3×M16—68no—
232C2×C3×C8—22no—
233C2×C3×C8—22no—
234C2×C3×C8—22no—
235C2×C3×C8—34no—
236C2×C3×C8—32no—
237C2×C3×C8—42no—
238C2×C3×C8C22×D312yes—
239C2×C3×C8C22×D312yes—
240C3×C4⋊C4—32no—
241C3×C4⋊C4—61no—
242#217—64no—
243#213—68no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—64no—
246(C2×D3)⋊C4—64no—
247C4⋊Dic3—21no—
248C4⋊Dic3—32no—
249C4⋊Dic3—32no—
250C4⋊Dic3—62no—
251C4⋊Dic3—61no—
252C4⋊Dic3—61no—
253C4⋊Dic3—121no—
254C4⋊Dic3C22×D312yes—
255C2×C3⋊C8#6714yescomplemented
256C2×C3⋊C8C22×D312yes—
257D24—68no—
258ΓL(1,𝔽25)—28no—
259C22×C32#12112yes—
260C22×C32AGL(1,ℤ/8)12yes—
261C22×C32AGL(1,ℤ/8)12yes—
262C22×C32C22×D411yescharacteristic
263C2×C3⋊D3—42no—
264C2×C3⋊D3—42no—
265C2×C3⋊D3—42no—
266C2×C3⋊D3—84no—
267C2×C3×D3—22no—
268C2×C3×D3—22no—
269C2×C3×D3—22no—
270C2×C3×D3—44no—
271C2×C3×D3—42no—
272C2×C3×D3—42no—
273C2×C3×D3—42no—
274C2×C3×D3—84no—
275C32×C4#12112yes—
276C32×C4C22×D411yescharacteristic
277C32×C4C2×#4111yescharacteristic
278C3⋊Dic3—42no—
279C3×Dic3—22no—
280C3×Dic3—42no—
281C22×D4—31no—
282C22×D4—91no—
283C22×D4—181no—
284C22×D4—181no—
285C23×C4—31no—
286C2×D8—94no—
287C2×D8—184no—
288C2×M16—34no—
289C2×M16—64no—
290C22×C8—31no—
291C22×C8D3211yescharacteristic
292#121—94no—
293#121—94no—
294#121—182no—
295#121—182no—
296C2×C4⋊C4—31no—
297C2×C4⋊C4—91no—
298C2×C22⋊C4—181no—
299C2×C22⋊C4—181no—
300#106—94no—
301#102—34no—
302#102—94no—
303C23×C3—21no—
304C23×C3—32no—
305C23×C3—62no—
306C23×C3—62no—
307C23×C3—62no—
308C23×C3—62no—
309C23×C3—122no—
310C23×C3—122no—
311C23×C3—122no—
312C23×C3C2×D1211yescharacteristic
313C23×C3D3×D411yescharacteristic
314C22×D3—22no—
315C22×D3—22no—
316C22×D3—22no—
317C22×D3—22no—
318C22×D3—42no—
319C22×D3—42no—
320C22×D3—42no—
321C22×D3—62no—
322C22×D3—62no—
323C22×D3—122no—
324C22×D3—124no—
325C22×D3—122no—
326C22×D3—122no—
327C22×D3—122no—
328C22×D3—122no—
329C22×D3—122no—
330C22×D3—122no—
331C22×D3—242no—
332C22×D3—242no—
333C22×D3C2×D1212yes—
334C3×D4—62no—
335C3×D4—62no—
336C3×D4—122no—
337C2×C3×C4—21no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—22no—
341C2×C3×C4—32no—
342C2×C3×C4—62no—
343C2×C3×C4—64no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—122no—
348C2×C3×C4C2×D1211yescharacteristic
349C2×C3×C4#23512yes—
350C2×C3×C4#23512yes—
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D412yes—
353C2×C3×C4C2×#6712yes—
354C2×C3×C4C23×D311yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356#67—128no—
357#67—128no—
358#67—128no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—42no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—122no—
365C2×Dic3—122no—
366C2×Dic3—122no—
367C2×Dic3—242no—
368C2×Dic3C2×D1212yes—
369D12—22no—
370D12—22no—
371D12—42no—
372D12—64no—
373D12—62no—
374D12—62no—
375D12—62no—
376D12—62no—
377D12—122no—
378D12—124no—
379D12—128no—
380D12—122no—
381D12—122no—
382C4×D3—24no—
383C4×D3—22no—
384C4×D3—22no—
385C3×C8—22no—
386C3×C8—22no—
387C3×C8—34no—
388C3×C8—42no—
389C3⋊C8C2×#6714yescomplemented
390C2×C32#46914yescomplemented
391C2×C32C2×#12111yescharacteristic
392C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
393C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
394C3⋊D3—82no—
395C3×D3—42no—
396C3×D3—82no—
397C24—31no—
398C24—61no—
399C24—181no—
400C2×D4—32no—
401C2×D4—62no—
402C2×D4—61no—
403C2×D4—62no—
404C2×D4—92no—
405C2×D4—184no—
406C2×D4—184no—
407C2×D4—182no—
408C2×D4—181no—
409C2×D4—182no—
410C2×D4—364no—
411C2×D4—364no—
412C22×C4—31no—
413C22×C4—32no—
414C22×C4—32no—
415C22×C4—62no—
416C22×C4—62no—
417C22×C4—61no—
418C22×C4—181no—
419C22×C4C2×D3211yescharacteristic
420D8—188no—
421M16—68no—
422C2×C8—22no—
423C2×C8—32no—
424C2×C8—34no—
425C2×C8C2×D3212yes—
426C4⋊C4—32no—
427C4⋊C4—61no—
428C4⋊C4—92no—
429C4⋊C4—181no—
430C22⋊C4—184no—
431C22⋊C4—184no—
432C22×C3—21no—
433C22×C3—22no—
434C22×C3—22no—
435C22×C3—22no—
436C22×C3—62no—
437C22×C3—62no—
438C22×C3—62no—
439C22×C3—124no—
440C22×C3—122no—
441C22×C3—122no—
442C22×C3—122no—
443C22×C3—244no—
444C22×C3#88412yes—
445C22×C3#90812yes—
446C22×C3#90812yes—
447C22×C3#91112yes—
448C22×C3#91412yes—
449C22×C3#93012yes—
450C22×C3C22×D1211yescharacteristic
451C22×C3C2×D3×D411yescharacteristic
452C2×D3—22no—
453C2×D3—22no—
454C2×D3—22no—
455C2×D3—44no—
456C2×D3—42no—
457C2×D3—42no—
458C2×D3—42no—
459C2×D3—84no—
460C2×D3—124no—
461C2×D3—122no—
462C2×D3—122no—
463C2×D3—122no—
464C2×D3—122no—
465C2×D3—122no—
466C2×D3—122no—
467C2×D3—242no—
468C2×D3—242no—
469C2×D3—248no—
470C2×D3—244no—
471C2×D3—244no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—22no—
475C3×C4—62no—
476C3×C4—122no—
477C3×C4#88412yes—
478C3×C4#93012yes—
479C3×C4C2×#23511yescharacteristic
480C3×C4C2×#23511yescharacteristic
481C3×C4C2×D3×D411yescharacteristic
482C3×C4C22×#6711yescharacteristic
483Dic3—22no—
484Dic3—42no—
485Dic3—122no—
486Dic3—122no—
487Dic3—242no—
488C32C2×#46911yescharacteristic, complemented, Sylow
489C23—32no—
490C23—62no—
491C23—62no—
492C23—62no—
493C23—62no—
494C23—122no—
495C23—122no—
496C23—122no—
497C23—182no—
498C23—362no—
499C23—362no—
500C23—362no—
501C23D3×D1211yescharacteristic
502D4—62no—
503D4—62no—
504D4—122no—
505D4—182no—
506D4—182no—
507D4—368no—
508D4—368no—
509D4—362no—
510C2×C4—32no—
511C2×C4—62no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—64no—
515C2×C4—62no—
516C2×C4—122no—
517C2×C4—182no—
518C2×C4—362no—
519C2×C4#379812yes—
520C2×C4D3×D1211yescharacteristic
521C2×C4D3×#6712yes—
522C2×C4C22×D3211yescharacteristic
523C8—22no—
524C8—34no—
525C2×C3—24no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—122no—
530C2×C3—242no—
531C2×C3#478214yescomplemented
532C2×C3#513514yescomplemented
533C2×C3C2×#88411yescharacteristic
534C2×C3C2×#90811yescharacteristic
535C2×C3C2×#90811yescharacteristic
536C2×C3C2×#91111yescharacteristic
537C2×C3C2×#91411yescharacteristic
538C2×C3C2×#93011yescharacteristic
539D3—42no—
540D3—82no—
541D3—244no—
542D3—242no—
543D3—242no—
544C22—62no—
545C22—62no—
546C22—62no—
547C22—124no—
548C22—122no—
549C22—122no—
550C22—122no—
551C22—244no—
552C22—362no—
553C22—362no—
554C22—362no—
555C22—724no—
556C22#6379412yes—
557C22#6379512yes—
558C22#6390612yes—
559C22C2×D3×D1211yescharacteristic
560C4—62no—
561C4—122no—
562C4—362no—
563C4#6390612yes—
564C4C2×#379811yescharacteristic
565C4C2×D3×#6711yescharacteristic
566C3—21no—
567C3C2×#478211yescharacteristic, complemented
568C3C2×#513511yescharacteristic, complemented
569C2—122no—
570C2—242no—
571C2—722no—
572C2#1059082714yesdirect product factor
573C2C2×#6379411yescharacteristic
574C2C2×#6379511yescharacteristic
575C2C2×#6390611yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
hypercenterC22×C8D32
hypocenterC32C2×#469
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
2. C2×#63909C2semidirect
3. C2×#63908C2semidirect
4. C22×#3714C2semidirect
5. C2×#63648C2semidirect
6. C2×C3×#821C2semidirect
7. C2×#63573C2semidirect
8. #10590827C2direct (N × H)
21. C2×C3×ΓL(1,𝔽25)C22semidirect
25. #63909C22semidirect
27. #63908C22semidirect
29. C2×#3714C22semidirect
30. #63648C22semidirect
31. C3×#821C22semidirect
32. #63573C22semidirect
39. C22×ΓL(1,𝔽25)D3semidirect
46. C2×#821D3semidirect
79. C2×C3×C3⋊C8D4semidirect
124. C2×ΓL(1,𝔽25)C2×D3semidirect
131. #821C2×D3semidirect
169. C3×C3⋊C8C2×D4semidirect
255. C2×C3⋊C8#67semidirect
389. C3⋊C8C2×#67semidirect
390. C2×C32#469semidirect
488. C32C2×#469semidirect
531. C2×C3#4782semidirect
532. C2×C3#5135semidirect
567. C3C2×#4782semidirect
568. C3C2×#5135semidirect
572. C2#10590827direct (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×#639092
C2×#639082
C22×#37142
C2×#636482
C2×C3×#8212
C2×#635732
#105908272
C2×#51353
C2×#47823