Finite Group Databasebeta

← C2×#10591454 #11866971

Subgroups — C2×#10591454 #11866971

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×#64147C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic, complemented
3C2×#63916C211yesmaximal, characteristic, complemented
4C22×#3712C211yesmaximal, characteristic, complemented
5C2×C3×#832C211yesmaximal, characteristic, complemented
6#10591454C218yesmaximal, direct product factor
7C2×#63573C211yesmaximal, characteristic, complemented
8C2×#63563C211yesmaximal, characteristic, complemented
9C2×#5159—31nomaximal
10C2×#4782—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×#638—21no—
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C22×#626—21no—
16C2×#3757—21no—
17#64147—22no—
18#64147C2214yescomplemented
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C3×#213—24no—
21C2×C3×#213C2214yescomplemented
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×(C2×D3)⋊Dic3—21no—
26#63916—22no—
27#63916C2214yescomplemented
28C2×#3712—24no—
29C2×#3712C2214yescomplemented
30C3×#832C2214yescomplemented
31#63573C2214yescomplemented
32#63563C2214yescomplemented
33C22×C3×D8—31no—
34C2×#938—31no—
35C2×#938—31no—
36C2×#938—31no—
37C2×#938—61no—
38C22×#213D311yescharacteristic, complemented
39C22×ΓL(1,𝔽25)—31no—
40C22×ΓL(1,𝔽25)—31no—
41C2×#895—31no—
42C2×C3×#102—31no—
43C2×#832—31no—
44C2×#832D311yescharacteristic, complemented
45#5159—38no—
46C2×#821—31no—
47C2×#817—31no—
48C2×#808—31no—
49#4782—38no—
50C24×C32—21no—
51C23×C3⋊D3D411yescharacteristic
52C23×C3×D3—21no—
53C2×C32×D4—22no—
54C2×C32×D4—21no—
55C2×C32×D4—22no—
56C2×C32×D4C2312yes—
57C22×C32×C4C2311yescharacteristic
58C2×#638—24no—
59C2×#638—44no—
60C22×C3⋊Dic3—21no—
61C22×C3⋊Dic3D411yescharacteristic
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—
73#3757—24no—
74C4⋊(C3⋊Dic3)—21no—
75C4⋊(C3⋊Dic3)C2312yes—
76C3×#213—28no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3C2312yes—
79C2×C3×C3⋊C8—22no—
80C2×C3×C3⋊C8D414yescomplemented
81C2×C3×C3⋊C8C2312yes—
82C2×C3×C3⋊C8C2312yes—
83(C2×D3)⋊Dic3—24no—
84#3712—28no—
85C2×#469—91noSylow
86C22×C3×D4—21no—
87C22×C3×D4—31no—
88C22×C3×D4C2×D311yescharacteristic
89C22×C3×D4C2×D311yescharacteristic
90C22×#67—61no—
91C22×#67—61no—
92C22×#67—61no—
93C22×#67—62no—
94C22×D12—61no—
95C22×D12C2×D311yescharacteristic
96C22×C4×D3—31no—
97C22×C4×D3—31no—
98C22×C4×D3—61no—
99C2×C3×D8—34no—
100C2×C3×D8—64no—
101C22×C3×C8—31no—
102C22×C3×C8—31no—
103C2×C3×C4⋊C4—31no—
104C2×#217—61no—
105C2×#217—61no—
106C2×#217—61no—
107C2×#217—62no—
108#938—34no—
109#938—34no—
110#938—34no—
111#938—64no—
112#938—62no—
113#938—62no—
114#938—62no—
115#938—64no—
116C2×#213—24no—
117C2×#213C2×D314yescomplemented
118C2×(C2×D3)⋊C4—61no—
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3—31no—
121C2×C4⋊Dic3—61no—
122C2×C4⋊Dic3C2×D311yescharacteristic
123C22×C3⋊C8C2×D311yescharacteristic
124C22×C3⋊C8C2×D311yescharacteristic
125C2×ΓL(1,𝔽25)—34no—
126C2×ΓL(1,𝔽25)—34no—
127C2×ΓL(1,𝔽25)—64no—
128C2×ΓL(1,𝔽25)—64no—
129#895—34no—
130#895—62no—
131C3×#102—34no—
132#832—34no—
133#832C2×D314yescomplemented
134#821—34no—
135#817—34no—
136#808—34no—
137C23×C32—22no—
138C23×C32—42no—
139C23×C32—42no—
140C23×C32—42no—
141C23×C32C2×D411yescharacteristic
142C22×C3⋊D3—22no—
143C22×C3⋊D3—22no—
144C22×C3⋊D3—22no—
145C22×C3⋊D3C2×D412yes—
146C22×C3×D3—22no—
147C22×C3×D3—42no—
148C22×C3×D3—42no—
149C22×C3×D3—42no—
150C32×D4—22no—
151C32×D4—22no—
152C32×D4—42no—
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D412yes—
155C2×C32×C4#4112yes—
156C2×C32×C4C2411yescharacteristic
157#638—48no—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3—42no—
161C2×C3⋊Dic3C2×D412yes—
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—31no—
174C22×M16—91no—
175C2×#121—91no—
176C2×#121—91no—
177#469—98no—
178C2×#106—91no—
179C2×#102—31no—
180C2×#102—91no—
181C24×C3—22no—
182C24×C3—21no—
183C24×C3—21no—
184C24×C3—61no—
185C23×D3—21no—
186C23×D3—31no—
187C23×D3—31no—
188C23×D3—61no—
189C2×C3×D4—22no—
190C2×C3×D4—22no—
191C2×C3×D4—22no—
192C2×C3×D4—21no—
193C2×C3×D4—21no—
194C2×C3×D4—22no—
195C2×C3×D4—22no—
196C2×C3×D4—22no—
197C2×C3×D4—32no—
198C2×C3×D4—42no—
199C2×C3×D4—42no—
200C2×C3×D4—62no—
201C2×C3×D4—62no—
202C2×C3×D4—61no—
203C2×C3×D4C22×D312yes—
204C2×C3×D4C22×D312yes—
205C22×C3×C4—21no—
206C22×C3×C4—61no—
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C22×D311yescharacteristic
209C2×#67—64no—
210C2×#67—64no—
211C2×#67—64no—
212C2×#67—68no—
213C2×#67—124no—
214C2×#67—128no—
215C2×#67—124no—
216C2×#67—124no—
217C22×Dic3—21no—
218C22×Dic3—31no—
219C22×Dic3—31no—
220C22×Dic3—61no—
221C22×Dic3—62no—
222C22×Dic3—61no—
223C22×Dic3—61no—
224C2×D12—22no—
225C2×D12—22no—
226C2×D12—21no—
227C2×D12—64no—
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—
242C3×D8—68no—
243C2×C3×C8—34no—
244C2×C3×C8—32no—
245C2×C3×C8—32no—
246C2×C3×C8—62no—
247C3×C4⋊C4—32no—
248C3×C4⋊C4—61no—
249#217—64no—
250#217—64no—
251#217—64no—
252#217—68no—
253#213—28no—
254(C2×D3)⋊C4—64no—
255C4⋊Dic3—21no—
256C4⋊Dic3—32no—
257C4⋊Dic3—32no—
258C4⋊Dic3—62no—
259C4⋊Dic3—62no—
260C4⋊Dic3—61no—
261C4⋊Dic3—61no—
262C4⋊Dic3C22×D312yes—
263C2×C3⋊C8—22no—
264C2×C3⋊C8#6714yescomplemented
265C2×C3⋊C8C22×D312yes—
266C2×C3⋊C8C22×D312yes—
267ΓL(1,𝔽25)—68no—
268ΓL(1,𝔽25)—68no—
269C22×C32—42no—
270C22×C32—42no—
271C22×C32—42no—
272C22×C32—84no—
273C22×C32#12112yes—
274C22×C32AGL(1,ℤ/8)12yes—
275C22×C32AGL(1,ℤ/8)12yes—
276C22×C32C22×D411yescharacteristic
277C2×C3⋊D3—22no—
278C2×C3⋊D3—22no—
279C2×C3⋊D3—22no—
280C2×C3⋊D3—44no—
281C2×C3×D3—42no—
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C2×C3×D3—84no—
285C32×C4#12112yes—
286C32×C4C22×D411yescharacteristic
287C32×C4C2×#4111yescharacteristic
288C3⋊Dic3—22no—
289C3⋊Dic3—42no—
290C3×Dic3—42no—
291C22×D4—31no—
292C22×D4—181no—
293C22×D4—181no—
294C22×D4D3211yescharacteristic
295C23×C4—91no—
296C2×D8—34no—
297C2×D8—64no—
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⋊C4—91no—
308C2×C22⋊C4—181no—
309C2×C22⋊C4—181no—
310#106—94no—
311#102—34no—
312#102—94no—
313C23×C3—24no—
314C23×C3—22no—
315C23×C3—22no—
316C23×C3—21no—
317C23×C3—44no—
318C23×C3—44no—
319C23×C3—44no—
320C23×C3—42no—
321C23×C3—42no—
322C23×C3—42no—
323C23×C3—42no—
324C23×C3—42no—
325C23×C3—42no—
326C23×C3—62no—
327C23×C3—122no—
328C23×C3—122no—
329C23×C3—122no—
330C23×C3D3×D411yescharacteristic
331C23×C3D3×D411yescharacteristic
332C22×D3—22no—
333C22×D3—32no—
334C22×D3—32no—
335C22×D3—42no—
336C22×D3—42no—
337C22×D3—42no—
338C22×D3—62no—
339C22×D3—64no—
340C22×D3—62no—
341C22×D3—62no—
342C22×D3—62no—
343C22×D3—62no—
344C22×D3—62no—
345C22×D3—62no—
346C22×D3—122no—
347C22×D3—122no—
348C3×D4—22no—
349C3×D4—22no—
350C3×D4—22no—
351C3×D4—22no—
352C3×D4—42no—
353C3×D4—42no—
354C3×D4—44no—
355C3×D4—42no—
356C3×D4—42no—
357C3×D4—62no—
358C3×D4—62no—
359C3×D4—122no—
360C2×C3×C4—21no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—21no—
364C2×C3×C4—62no—
365C2×C3×C4—122no—
366C2×C3×C4#23512yes—
367C2×C3×C4D3×D412yes—
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4#23712yes—
371C2×C3×C4C2×#6712yes—
372C2×C3×C4C23×D311yescharacteristic
373C2×C3×C4C23×D311yescharacteristic
374#67—128no—
375#67—1216no—
376#67—128no—
377#67—128no—
378C2×Dic3—22no—
379C2×Dic3—32no—
380C2×Dic3—32no—
381C2×Dic3—42no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—64no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—122no—
389C2×Dic3—124no—
390C2×Dic3—122no—
391C2×Dic3—122no—
392D12—22no—
393D12—22no—
394D12—42no—
395D12—128no—
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×#6714yescomplemented
409C2×C32—82no—
410C2×C32#46914yescomplemented
411C2×C32C2×#12111yescharacteristic
412C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
413C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
414C3⋊D3—42no—
415C3×D3—82no—
416C24—21no—
417C24—61no—
418C24—91no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—21no—
422C2×D4—32no—
423C2×D4—62no—
424C2×D4—62no—
425C2×D4—61no—
426C2×D4—184no—
427C2×D4—184no—
428C2×D4—364no—
429C2×D4—364no—
430C2×D4C2×D3212yes—
431C22×C4—61no—
432C22×C4—91no—
433C22×C4—92no—
434C22×C4—92no—
435C22×C4—182no—
436C22×C4—182no—
437C22×C4—181no—
438C22×C4C2×D3211yescharacteristic
439D8—68no—
440M16—188no—
441C2×C8—32no—
442C2×C8—34no—
443C2×C8—32no—
444C2×C8—62no—
445C4⋊C4—32no—
446C4⋊C4—61no—
447C4⋊C4—92no—
448C4⋊C4—181no—
449C22⋊C4—184no—
450C22⋊C4—184no—
451C22×C3—21no—
452C22×C3—22no—
453C22×C3—22no—
454C22×C3—22no—
455C22×C3—44no—
456C22×C3—44no—
457C22×C3—44no—
458C22×C3—42no—
459C22×C3—42no—
460C22×C3—42no—
461C22×C3—42no—
462C22×C3—42no—
463C22×C3—42no—
464C22×C3—88no—
465C22×C3—84no—
466C22×C3—84no—
467C22×C3—122no—
468C22×C3—122no—
469C22×C3—122no—
470C22×C3—244no—
471C22×C3#88412yes—
472C22×C3#91112yes—
473C22×C3#91112yes—
474C22×C3#91112yes—
475C22×C3#91412yes—
476C22×C3#93812yes—
477C22×C3C2×D3×D411yescharacteristic
478C22×C3C2×D3×D411yescharacteristic
479C2×D3—42no—
480C2×D3—42no—
481C2×D3—42no—
482C2×D3—64no—
483C2×D3—62no—
484C2×D3—62no—
485C2×D3—62no—
486C2×D3—62no—
487C2×D3—62no—
488C2×D3—62no—
489C2×D3—84no—
490C2×D3—122no—
491C2×D3—122no—
492C2×D3—128no—
493C2×D3—124no—
494C2×D3—124no—
495C3×C4—21no—
496C3×C4—21no—
497C3×C4—22no—
498C3×C4—122no—
499C3×C4#88412yes—
500C3×C4#93812yes—
501C3×C4C2×#23511yescharacteristic
502C3×C4C2×D3×D411yescharacteristic
503C3×C4C2×#23711yescharacteristic
504C3×C4C22×#6711yescharacteristic
505Dic3—42no—
506Dic3—62no—
507Dic3—62no—
508Dic3—122no—
509Dic3—124no—
510Dic3—122no—
511Dic3—122no—
512C32C2×#46911yescharacteristic, complemented, Sylow
513C23—22no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—62no—
518C23—92no—
519C23—122no—
520C23—122no—
521C23—122no—
522C23—182no—
523C23—182no—
524C23—182no—
525C23#381111yescharacteristic
526D4—22no—
527D4—22no—
528D4—42no—
529D4—62no—
530D4—62no—
531D4—122no—
532D4—368no—
533D4—368no—
534C2×C4—62no—
535C2×C4—92no—
536C2×C4—122no—
537C2×C4—182no—
538C2×C4—182no—
539C2×C4—182no—
540C2×C4—184no—
541C2×C4—182no—
542C2×C4—362no—
543C2×C4#380412yes—
544C2×C4D3×#6712yes—
545C2×C4#381111yescharacteristic
546C2×C4C22×D3211yescharacteristic
547C8—34no—
548C8—62no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—24no—
553C2×C3—84no—
554C2×C3—82no—
555C2×C3—82no—
556C2×C3—242no—
557C2×C3#478214yescomplemented
558C2×C3#515914yescomplemented
559C2×C3C2×#88411yescharacteristic
560C2×C3C2×#91111yescharacteristic
561C2×C3C2×#91111yescharacteristic
562C2×C3C2×#91111yescharacteristic
563C2×C3C2×#91411yescharacteristic
564C2×C3C2×#93811yescharacteristic
565D3—82no—
566D3—124no—
567D3—122no—
568D3—122no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—84no—
573C22—122no—
574C22—122no—
575C22—122no—
576C22—182no—
577C22—182no—
578C22—182no—
579C22—244no—
580C22—364no—
581C22#6392712yes—
582C22#6393712yes—
583C22#6395812yes—
584C22C2×#381111yescharacteristic
585C4—122no—
586C4—182no—
587C4—362no—
588C4#6395812yes—
589C4C2×#380411yescharacteristic
590C4C2×D3×#6711yescharacteristic
591C3—21no—
592C3C2×#478211yescharacteristic, complemented
593C3C2×#515911yescharacteristic, complemented
594C2—82no—
595C2—242no—
596C2—362no—
597C2#1059145414yesdirect product factor
598C2C2×#6392711yescharacteristic
599C2C2×#6393711yescharacteristic
600C2C2×#6395811yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32C2×#469
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64147C2semidirect
2. C22×C3×#213C2semidirect
3. C2×#63916C2semidirect
4. C22×#3712C2semidirect
5. C2×C3×#832C2semidirect
6. #10591454C2direct (N × H)
7. C2×#63573C2semidirect
8. C2×#63563C2semidirect
18. #64147C22semidirect
21. C2×C3×#213C22semidirect
27. #63916C22semidirect
29. C2×#3712C22semidirect
30. C3×#832C22semidirect
31. #63573C22semidirect
32. #63563C22semidirect
38. C22×#213D3semidirect
44. C2×#832D3semidirect
80. C2×C3×C3⋊C8D4semidirect
117. C2×#213C2×D3semidirect
133. #832C2×D3semidirect
172. C3×C3⋊C8C2×D4semidirect
264. C2×C3⋊C8#67semidirect
408. C3⋊C8C2×#67semidirect
410. C2×C32#469semidirect
512. C32C2×#469semidirect
557. C2×C3#4782semidirect
558. C2×C3#5159semidirect
592. C3C2×#4782semidirect
593. C3C2×#5159semidirect
597. C2#10591454direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641472
C22×C3×#2132
C2×#639162
C22×#37122
C2×C3×#8322
#105914542
C2×#635732
C2×#635632
C2×#51593
C2×#47823