Finite Group Databasebeta

← C2×#10590508 #11866979

Subgroups — C2×#10590508 #11866979

Order 1152.

1405 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64104C211yesmaximal, characteristic, complemented
2C2×#63916C211yesmaximal, characteristic, complemented
3C22×#3714C211yesmaximal, characteristic, complemented
4C22×#3712C211yesmaximal, characteristic, complemented
5C2×C3×#809C211yesmaximal, characteristic, complemented
6C2×C3×#808C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic, complemented
8#10590508C218yesmaximal, direct product factor
9C2×#4865—31nomaximal
10C2×#4782—31nomaximal
11C22×C4⋊(C3⋊D3)—21no—
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C22×#626—21no—
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×#3752—21no—
18#64104—22no—
19#64104C2214yescomplemented
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×(C2×D3)⋊Dic3—21no—
24#63916—22no—
25#63916C2214yescomplemented
26C2×#3714—24no—
27C2×#3714C2214yescomplemented
28C2×#3712—24no—
29C2×#3712C2214yescomplemented
30C3×#809C2214yescomplemented
31C3×#808C2214yescomplemented
32#63564C2214yescomplemented
33C2×#938—31no—
34C22×#213—31no—
35C22×D24—31no—
36C22×ΓL(1,𝔽25)—31no—
37C22×ΓL(1,𝔽25)—31no—
38C2×#895—31no—
39C2×#895—31no—
40C2×#895—31no—
41C2×#895—61no—
42C2×C3×#106—31no—
43C2×C3×#102—31no—
44C2×#821—31no—
45C2×#809—31no—
46C2×#809D311yescharacteristic, complemented
47C2×#808D311yescharacteristic, complemented
48#4865—38no—
49#4782—38no—
50C23×C3⋊D3—21no—
51C23×C3⋊D3D411yescharacteristic
52C23×C3×D3—21no—
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3D411yescharacteristic
56C2×C4⋊(C3⋊D3)—22no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)—24no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)—44no—
61C2×C4⋊(C3⋊D3)C2312yes—
62C2×C4×C3⋊D3—22no—
63C2×C4×C3⋊D3—22no—
64C2×C4×C3⋊D3D412yes—
65C2×C4×C3⋊D3C2312yes—
66C22×C3×Dic3—21no—
67C2×C3×D12—22no—
68C2×C3×D12—22no—
69C2×C3×D12—21no—
70C2×C3×D12C2312yes—
71C2×#626—24no—
72C2×#626—44no—
73C32×C4⋊C4—21no—
74C32×C4⋊C4C2312yes—
75#3752—24no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3C2312yes—
78C2×C3×C3⋊C8—22no—
79C2×C3×C3⋊C8D414yescomplemented
80C2×C3×C3⋊C8C2312yes—
81C2×C3×C3⋊C8C2312yes—
82(C2×D3)⋊Dic3—24no—
83#3714—28no—
84#3712—28no—
85C2×#469—91noSylow
86C22×C3×D4—31no—
87C22×#67—61no—
88C22×D12—31no—
89C22×D12—31no—
90C22×D12—61no—
91C22×D12—61no—
92C22×D12—61no—
93C22×D12—62no—
94C22×D12—61no—
95C22×D12C2×D311yescharacteristic
96C22×C4×D3—31no—
97C22×C4×D3—31no—
98C22×C4×D3—61no—
99C22×C3×C8—31no—
100C22×C3×C8—31no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4—31no—
103C2×C3×C4⋊C4C2×D311yescharacteristic
104C2×C3×C4⋊C4C2×D311yescharacteristic
105C2×#217—61no—
106#938—34no—
107#938—62no—
108C2×#213—34no—
109C2×#213—64no—
110C2×(C2×D3)⋊C4—61no—
111C2×(C2×D3)⋊C4—61no—
112C2×(C2×D3)⋊C4—61no—
113C2×(C2×D3)⋊C4—62no—
114C2×C4⋊Dic3C2×D311yescharacteristic
115C22×C3⋊C8C2×D311yescharacteristic
116C22×C3⋊C8C2×D311yescharacteristic
117C2×D24—34no—
118C2×D24—64no—
119C2×ΓL(1,𝔽25)—34no—
120C2×ΓL(1,𝔽25)—34no—
121C2×ΓL(1,𝔽25)—64no—
122C2×ΓL(1,𝔽25)—64no—
123#895—34no—
124#895—34no—
125#895—34no—
126#895—64no—
127#895—62no—
128#895—62no—
129#895—64no—
130#895—62no—
131C3×#106—34no—
132C3×#102—34no—
133#821—34no—
134#809—34no—
135#809C2×D314yescomplemented
136#808C2×D314yescomplemented
137C23×C32C2×D411yescharacteristic
138C22×C3⋊D3—22no—
139C22×C3⋊D3—22no—
140C22×C3⋊D3—22no—
141C22×C3⋊D3—22no—
142C22×C3⋊D3—42no—
143C22×C3⋊D3—42no—
144C22×C3⋊D3—42no—
145C22×C3⋊D3C2×D412yes—
146C22×C3×D3—22no—
147C22×C3×D3—42no—
148C22×C3×D3—42no—
149C22×C3×D3—42no—
150C2×C32×C4—22no—
151C2×C32×C4—42no—
152C2×C32×C4C2×D412yes—
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4#4112yes—
155C2×C32×C4C2411yescharacteristic
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3C2×D412yes—
158C4⋊(C3⋊D3)—22no—
159C4⋊(C3⋊D3)—22no—
160C4⋊(C3⋊D3)—48no—
161C4⋊(C3⋊D3)—42no—
162C4×C3⋊D3—24no—
163C4×C3⋊D3—22no—
164C4×C3⋊D3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—42no—
167C3×D12—22no—
168C3×D12—22no—
169C3×D12—42no—
170#626—48no—
171C3×C3⋊C8—22no—
172C3×C3⋊C8C2×D414yescomplemented
173C22×D8—91no—
174C22×M16—91no—
175C2×#121—91no—
176C2×#121—91no—
177#469—98no—
178C2×#106—31no—
179C2×#102—31no—
180C2×#102—91no—
181C24×C3—61no—
182C23×D3—21no—
183C23×D3—31no—
184C23×D3—31no—
185C23×D3—61no—
186C23×D3—62no—
187C23×D3—61no—
188C23×D3—61no—
189C2×C3×D4—32no—
190C2×C3×D4—62no—
191C2×C3×D4—61no—
192C2×C3×D4—62no—
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
200C2×#67—64no—
201C2×#67—124no—
202C22×Dic3—21no—
203C22×Dic3—31no—
204C22×Dic3—31no—
205C22×Dic3—61no—
206C2×D12—22no—
207C2×D12—22no—
208C2×D12—21no—
209C2×D12—32no—
210C2×D12—32no—
211C2×D12—62no—
212C2×D12—62no—
213C2×D12—62no—
214C2×D12—62no—
215C2×D12—62no—
216C2×D12—64no—
217C2×D12—64no—
218C2×D12—68no—
219C2×D12—62no—
220C2×D12—64no—
221C2×D12—61no—
222C2×D12—61no—
223C2×D12—122no—
224C2×D12—122no—
225C2×D12—128no—
226C2×D12—124no—
227C2×D12—124no—
228C2×D12—124no—
229C2×D12C22×D312yes—
230C2×C4×D3—32no—
231C2×C4×D3—32no—
232C2×C4×D3—32no—
233C2×C4×D3—32no—
234C2×C4×D3—62no—
235C2×C4×D3—62no—
236C2×C4×D3—62no—
237C2×C4×D3—62no—
238C2×C4×D3—62no—
239C2×C4×D3—62no—
240C2×C4×D3—122no—
241C2×C4×D3—122no—
242C2×C3×C8—34no—
243C2×C3×C8—32no—
244C2×C3×C8—32no—
245C2×C3×C8—62no—
246C3×C4⋊C4—22no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—22no—
250C3×C4⋊C4—32no—
251C3×C4⋊C4—61no—
252C3×C4⋊C4C22×D312yes—
253C3×C4⋊C4C22×D312yes—
254#217—64no—
255#213—68no—
256(C2×D3)⋊C4—64no—
257(C2×D3)⋊C4—64no—
258(C2×D3)⋊C4—64no—
259(C2×D3)⋊C4—68no—
260C4⋊Dic3—21no—
261C4⋊Dic3C22×D312yes—
262C2×C3⋊C8—22no—
263C2×C3⋊C8D1214yescomplemented
264C2×C3⋊C8C22×D312yes—
265C2×C3⋊C8C22×D312yes—
266D24—68no—
267ΓL(1,𝔽25)—68no—
268ΓL(1,𝔽25)—68no—
269C22×C32#12112yes—
270C22×C32AGL(1,ℤ/8)12yes—
271C22×C32AGL(1,ℤ/8)12yes—
272C22×C32C22×D411yescharacteristic
273C2×C3⋊D3—22no—
274C2×C3⋊D3—22no—
275C2×C3⋊D3—22no—
276C2×C3⋊D3—44no—
277C2×C3⋊D3—42no—
278C2×C3⋊D3—42no—
279C2×C3⋊D3—42no—
280C2×C3⋊D3—84no—
281C2×C3×D3—42no—
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C2×C3×D3—84no—
285C32×C4—42no—
286C32×C4#12112yes—
287C32×C4C22×D411yescharacteristic
288C32×C4C2×#4111yescharacteristic
289C3⋊Dic3—22no—
290C3×Dic3—42no—
291C22×D4—31no—
292C22×D4—91no—
293C22×D4—181no—
294C22×D4—181no—
295C23×C4—91no—
296C2×D8—94no—
297C2×D8—184no—
298C2×M16—94no—
299C2×M16—184no—
300C22×C8—31no—
301C22×C8—31no—
302#121—94no—
303#121—94no—
304#121—182no—
305#121—182no—
306C2×C4⋊C4—31no—
307C2×C4⋊C4D3211yescharacteristic
308C2×C22⋊C4—181no—
309C2×C22⋊C4—181no—
310#106—34no—
311#102—34no—
312#102—94no—
313C23×C3—21no—
314C23×C3—62no—
315C23×C3—122no—
316C23×C3—122no—
317C23×C3—122no—
318C23×C3D3×D411yescharacteristic
319C23×C3D3×D411yescharacteristic
320C22×D3—22no—
321C22×D3—32no—
322C22×D3—32no—
323C22×D3—42no—
324C22×D3—42no—
325C22×D3—42no—
326C22×D3—62no—
327C22×D3—64no—
328C22×D3—62no—
329C22×D3—62no—
330C22×D3—62no—
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—62no—
334C22×D3—64no—
335C22×D3—62no—
336C22×D3—62no—
337C22×D3—122no—
338C22×D3—122no—
339C22×D3—124no—
340C22×D3—124no—
341C22×D3—124no—
342C22×D3—122no—
343C22×D3—122no—
344C22×D3—122no—
345C22×D3—122no—
346C22×D3—122no—
347C22×D3—122no—
348C3×D4—62no—
349C3×D4—62no—
350C3×D4—122no—
351C2×C3×C4—24no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—21no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—21no—
358C2×C3×C4—44no—
359C2×C3×C4—42no—
360C2×C3×C4—42no—
361C2×C3×C4—62no—
362C2×C3×C4—122no—
363C2×C3×C4C2×D1212yes—
364C2×C3×C4#23512yes—
365C2×C3×C4D3×D412yes—
366C2×C3×C4D3×D411yescharacteristic
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4#23912yes—
369C2×C3×C4C23×D311yescharacteristic
370C2×C3×C4C23×D311yescharacteristic
371#67—128no—
372C2×Dic3—22no—
373C2×Dic3—32no—
374C2×Dic3—32no—
375C2×Dic3—42no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—122no—
380D12—22no—
381D12—22no—
382D12—42no—
383D12—62no—
384D12—62no—
385D12—62no—
386D12—62no—
387D12—122no—
388D12—122no—
389D12—124no—
390D12—1216no—
391D12—128no—
392D12—128no—
393D12—128no—
394D12—122no—
395D12—122no—
396C4×D3—64no—
397C4×D3—64no—
398C4×D3—62no—
399C4×D3—62no—
400C4×D3—62no—
401C4×D3—62no—
402C4×D3—122no—
403C4×D3—122no—
404C4×D3—124no—
405C3×C8—34no—
406C3×C8—62no—
407C3⋊C8—22no—
408C3⋊C8C2×D1214yescomplemented
409C2×C32#46914yescomplemented
410C2×C32C2×#12111yescharacteristic
411C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
412C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
413C3⋊D3—42no—
414C3⋊D3—82no—
415C3×D3—82no—
416C24—61no—
417C24—91no—
418C24—181no—
419C2×D4—32no—
420C2×D4—62no—
421C2×D4—62no—
422C2×D4—61no—
423C2×D4—92no—
424C2×D4—184no—
425C2×D4—184no—
426C2×D4—182no—
427C2×D4—182no—
428C2×D4—181no—
429C2×D4—364no—
430C2×D4—364no—
431C22×C4—21no—
432C22×C4—61no—
433C22×C4—91no—
434C22×C4—92no—
435C22×C4—92no—
436C22×C4—182no—
437C22×C4—182no—
438C22×C4C2×D3211yescharacteristic
439D8—188no—
440M16—188no—
441C2×C8—32no—
442C2×C8—34no—
443C2×C8—32no—
444C2×C8—62no—
445C4⋊C4—21no—
446C4⋊C4—32no—
447C4⋊C4—61no—
448C4⋊C4C2×D3212yes—
449C22⋊C4—184no—
450C22⋊C4—184no—
451C22×C3—21no—
452C22×C3—22no—
453C22×C3—22no—
454C22×C3—22no—
455C22×C3—122no—
456C22×C3—122no—
457C22×C3—122no—
458C22×C3—244no—
459C22×C3#88412yes—
460C22×C3#89512yes—
461C22×C3#91112yes—
462C22×C3#91412yes—
463C22×C3#91412yes—
464C22×C3#91412yes—
465C22×C3C2×D3×D411yescharacteristic
466C22×C3C2×D3×D411yescharacteristic
467C2×D3—42no—
468C2×D3—42no—
469C2×D3—42no—
470C2×D3—64no—
471C2×D3—62no—
472C2×D3—62no—
473C2×D3—62no—
474C2×D3—62no—
475C2×D3—62no—
476C2×D3—62no—
477C2×D3—84no—
478C2×D3—122no—
479C2×D3—122no—
480C2×D3—128no—
481C2×D3—124no—
482C2×D3—124no—
483C2×D3—124no—
484C2×D3—124no—
485C2×D3—124no—
486C2×D3—122no—
487C2×D3—122no—
488C2×D3—122no—
489C2×D3—122no—
490C2×D3—122no—
491C2×D3—122no—
492C2×D3—248no—
493C2×D3—244no—
494C2×D3—244no—
495C3×C4—21no—
496C3×C4—21no—
497C3×C4—22no—
498C3×C4—44no—
499C3×C4—42no—
500C3×C4—42no—
501C3×C4—122no—
502C3×C4#88412yes—
503C3×C4#89512yes—
504C3×C4C22×D1211yescharacteristic
505C3×C4C2×#23511yescharacteristic
506C3×C4C2×D3×D411yescharacteristic
507C3×C4C2×#23911yescharacteristic
508Dic3—42no—
509Dic3—62no—
510Dic3—62no—
511Dic3—122no—
512C32C2×#46911yescharacteristic, complemented, Sylow
513C23—62no—
514C23—92no—
515C23—122no—
516C23—122no—
517C23—122no—
518C23—182no—
519C23—182no—
520C23—182no—
521C23—182no—
522C23—362no—
523C23—362no—
524C23—362no—
525C23#381111yescharacteristic
526D4—62no—
527D4—62no—
528D4—122no—
529D4—182no—
530D4—182no—
531D4—368no—
532D4—368no—
533D4—362no—
534C2×C4—22no—
535C2×C4—42no—
536C2×C4—62no—
537C2×C4—92no—
538C2×C4—122no—
539C2×C4—182no—
540C2×C4—182no—
541C2×C4—182no—
542C2×C4—184no—
543C2×C4#379912yes—
544C2×C4D3×D1212yes—
545C2×C4#381111yescharacteristic
546C2×C4C22×D3211yescharacteristic
547C8—34no—
548C8—62no—
549C2×C3—21no—
550C2×C3—24no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—242no—
554C2×C3#478214yescomplemented
555C2×C3#486514yescomplemented
556C2×C3C2×#88411yescharacteristic
557C2×C3C2×#89511yescharacteristic
558C2×C3C2×#91111yescharacteristic
559C2×C3C2×#91411yescharacteristic
560C2×C3C2×#91411yescharacteristic
561C2×C3C2×#91411yescharacteristic
562D3—82no—
563D3—124no—
564D3—122no—
565D3—122no—
566D3—244no—
567D3—242no—
568D3—242no—
569C22—122no—
570C22—122no—
571C22—122no—
572C22—182no—
573C22—182no—
574C22—182no—
575C22—244no—
576C22—364no—
577C22—362no—
578C22—362no—
579C22—362no—
580C22—724no—
581C22#6391012yes—
582C22#6393712yes—
583C22#6394112yes—
584C22C2×#381111yescharacteristic
585C4—42no—
586C4—122no—
587C4—182no—
588C4#6391012yes—
589C4C2×#379911yescharacteristic
590C4C2×D3×D1211yescharacteristic
591C3—21no—
592C3C2×#478211yescharacteristic, complemented
593C3C2×#486511yescharacteristic, complemented
594C2—242no—
595C2—362no—
596C2—722no—
597C2#1059050814yesdirect product factor
598C2C2×#6391011yescharacteristic
599C2C2×#6393711yescharacteristic
600C2C2×#6394111yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#469
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64104C2semidirect
2. C2×#63916C2semidirect
3. C22×#3714C2semidirect
4. C22×#3712C2semidirect
5. C2×C3×#809C2semidirect
6. C2×C3×#808C2semidirect
7. C2×#63564C2semidirect
8. #10590508C2direct (N × H)
19. #64104C22semidirect
25. #63916C22semidirect
27. C2×#3714C22semidirect
29. C2×#3712C22semidirect
30. C3×#809C22semidirect
31. C3×#808C22semidirect
32. #63564C22semidirect
46. C2×#809D3semidirect
47. C2×#808D3semidirect
79. C2×C3×C3⋊C8D4semidirect
135. #809C2×D3semidirect
136. #808C2×D3semidirect
172. C3×C3⋊C8C2×D4semidirect
263. C2×C3⋊C8D12semidirect
408. C3⋊C8C2×D12semidirect
409. C2×C32#469semidirect
512. C32C2×#469semidirect
554. C2×C3#4782semidirect
555. C2×C3#4865semidirect
592. C3C2×#4782semidirect
593. C3C2×#4865semidirect
597. C2#10590508direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641042
C2×#639162
C22×#37142
C22×#37122
C2×C3×#8092
C2×C3×#8082
C2×#635642
#105905082
C2×#48653
C2×#47823