Finite Group Databasebeta

← C2×#10590592 #11857836

Subgroups — C2×#10590592 #11857836

Order 1152.

2117 conjugacy classes of subgroups.

The subgroup lattice has 613 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×D12C211yesmaximal, characteristic
2C2×C3×#892C211yesmaximal, characteristic, complemented
3C22×#3711C211yesmaximal, characteristic, complemented
4C2×#63636C211yesmaximal, characteristic, complemented
5C2×C3×#809C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic, complemented
8#10590592C218yesmaximal, direct product factor
9C2×#5001—31nomaximal
10C2×#4770—31nomaximal
11C23×D32—21no—
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×C4×D3C2211yescharacteristic
15C22×#626—21no—
16C2×D3×D12—24no—
17C2×D3×D12—22no—
18C2×D3×D12C418yescomplemented
19C2×D3×D12C2214yes—
20C2×C32×C4⋊C4C2211yescharacteristic, complemented
21C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
22C2×C3×(C2×D3)⋊C4—21no—
23C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
24C2×C3×C4×Dic3—21no—
25C22×C3×C3⋊C8C2211yescharacteristic, complemented
26C3×#892—22no—
27C3×#892C2214yescomplemented
28C2×#3711—24no—
29C2×#3711C2214yescomplemented
30#63636C2214yescomplemented
31C3×#809C2214yescomplemented
32#63564C2214yescomplemented
33#63562C2214yescomplemented
34C22×D3×D4—31no—
35C23×D12—31no—
36C2×C3×#117—31no—
37C22×#208—31no—
38C22×ΓL(1,𝔽25)—31no—
39C2×#892D311yescharacteristic, complemented
40C2×C3×#102—31no—
41C2×#832—31no—
42C2×#821—31no—
43#5001—38no—
44C2×#809—31no—
45C2×#809—31no—
46C2×#809—31no—
47C2×#809—31no—
48C2×#809—61no—
49C2×#809D311yescharacteristic, complemented
50#4770—38no—
51C23×C3⋊D3—21no—
52C23×C3×D3—21no—
53C23×C3×D3D411yescharacteristic
54C22×D32—28no—
55C22×D32—24no—
56C22×D32—44no—
57C22×D32—44no—
58C22×C32×C4—21no—
59C22×C32×C4C2311yescharacteristic
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)—22no—
62C2×C4⋊(C3⋊D3)C2×C414yes—
63C2×C4⋊(C3⋊D3)C2312yes—
64C22×C3×Dic3—21no—
65C22×C3×Dic3D411yescharacteristic
66C2×C3×D12—21no—
67C2×C3×D12—22no—
68C2×C3×D12C2×C414yes—
69C2×C3×D12C2312yes—
70C2×C3×C4×D3C2×C414yes—
71C2×C3×C4×D3D412yes—
72C2×C3×C4×D3D414yes—
73C2×C3×C4×D3C2312yes—
74C2×#626—28no—
75C2×#626—24no—
76D3×D12—216no—
77D3×D12—28no—
78D3×D12C2×C4116yescomplemented
79C32×C4⋊C4—21no—
80C32×C4⋊C4C2312yescomplemented
81C2×C3⋊(C3⋊C8)—22no—
82C2×C3⋊(C3⋊C8)C2312yescomplemented
83C3×(C2×D3)⋊C4—24no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3C2312yescomplemented
86C3×C4×Dic3—24no—
87C2×C3×C3⋊C8—22no—
88C2×C3×C3⋊C8C2312yescomplemented
89#3711—28no—
90C2×#418—91noSylow
91C24×D3—61no—
92C24×D3—61no—
93C22×C3×D4—31no—
94C23×C3×C4—31no—
95C22×#67—61no—
96C2×D3×D4—38no—
97C2×D3×D4—34no—
98C2×D3×D4—64no—
99C2×D3×D4—62no—
100C22×D12—31no—
101C22×D12—31no—
102C22×D12—38no—
103C22×D12—34no—
104C22×D12—61no—
105C22×D12—64no—
106C22×D12—62no—
107C22×D12—61no—
108C22×D12C2×D311yescharacteristic
109C22×C4×D3C2×D311yescharacteristic
110C22×C3×C8—31no—
111C3×#117—34no—
112C3×#117—62no—
113C2×C3×C4⋊C4—21no—
114C2×C3×C4⋊C4—31no—
115C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
116C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
117C2×C3×C22⋊C4—61no—
118C2×C3×C42—61no—
119C2×(C2×D3)⋊C4—21no—
120C2×C4⋊Dic3C2×D311yescharacteristic, complemented
121C2×C4×Dic3—21no—
122C2×#208—34no—
123C2×#208—64no—
124C22×C3⋊C8—31no—
125C22×C3⋊C8—31no—
126C22×C3⋊C8—61no—
127C22×C3⋊C8C2×D311yescharacteristic, complemented
128C2×ΓL(1,𝔽25)—34no—
129C2×ΓL(1,𝔽25)—64no—
130#892—22no—
131#892C2×D314yescomplemented
132C3×#102—34no—
133#832—34no—
134#821—34no—
135#809—34no—
136#809—34no—
137#809—34no—
138#809—34no—
139#809—64no—
140#809C2×D314yescomplemented
141C23×C32C2×D411yescharacteristic
142C22×C3⋊D3—24no—
143C22×C3⋊D3—22no—
144C22×C3⋊D3—42no—
145C22×C3⋊D3—42no—
146C22×C3×D3—22no—
147C22×C3×D3—22no—
148C22×C3×D3—24no—
149C22×C3×D3—22no—
150C22×C3×D3—42no—
151C22×C3×D3—42no—
152C22×C3×D3C22⋊C414yes—
153C22×C3×D3C2×D412yes—
154C2×D32—216no—
155C2×D32—48no—
156C2×D32—48no—
157C2×D32—432no—
158C2×C32×C4—22no—
159C2×C32×C4—42no—
160C2×C32×C4C22×C412yes—
161C2×C32×C4C2×D412yes—
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2411yescharacteristic
164C4⋊(C3⋊D3)—24no—
165C4⋊(C3⋊D3)—22no—
166C4⋊(C3⋊D3)C22×C414yes—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—42no—
169C2×C3×Dic3C22⋊C414yes—
170C2×C3×Dic3C2×D412yes—
171C3×D12—24no—
172C3×D12—22no—
173C3×D12C22×C414yes—
174C3×C4×D3C22⋊C418yes—
175C3×C4×D3C22×C414yes—
176C3×C4×D3C2×D414yes—
177#626—216no—
178C3⋊(C3⋊C8)—22no—
179C3×C3⋊C8—22no—
180C23×D4—91no—
181C22×M16—91no—
182C2×#117—31no—
183#418—98no—
184C2×#102—31no—
185C2×#102—91no—
186C2×#102—91no—
187C2×#102—91no—
188C24×C3—31no—
189C24×C3—61no—
190C23×D3—21no—
191C23×D3—68no—
192C23×D3—64no—
193C23×D3—61no—
194C23×D3—61no—
195C23×D3—68no—
196C23×D3—64no—
197C23×D3—121no—
198C23×D3—124no—
199C23×D3—124no—
200C23×D3—124no—
201C23×D3—124no—
202C23×D3#6711yescharacteristic
203C2×C3×D4—34no—
204C2×C3×D4—32no—
205C2×C3×D4—62no—
206C2×C3×D4—61no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—31no—
211C22×C3×C4—34no—
212C22×C3×C4—34no—
213C22×C3×C4—32no—
214C22×C3×C4—32no—
215C22×C3×C4—41no—
216C22×C3×C4—61no—
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C2×#67—68no—
220C2×#67—64no—
221C22×Dic3—21no—
222C22×Dic3#6711yescharacteristic
223D3×D4—316no—
224D3×D4—616no—
225D3×D4—68no—
226C2×D12—22no—
227C2×D12—21no—
228C2×D12—34no—
229C2×D12—34no—
230C2×D12—32no—
231C2×D12—32no—
232C2×D12—316no—
233C2×D12—62no—
234C2×D12—64no—
235C2×D12—616no—
236C2×D12—68no—
237C2×D12—68no—
238C2×D12—64no—
239C2×D12—62no—
240C2×D12—62no—
241C2×D12—61no—
242C2×D12—61no—
243C2×D12—122no—
244C2×D12—121no—
245C2×D12C4×D314yes—
246C2×D12C22×D312yes—
247C2×C4×D3C4×D314yes—
248C2×C4×D3D1214yes—
249C2×C4×D3#6712yes—
250C2×C4×D3C22×D312yes—
251C2×C3×C8—32no—
252C2×C3×C8—62no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—22no—
256C3×C4⋊C4—32no—
257C3×C4⋊C4—41no—
258C3×C4⋊C4—61no—
259C3×C4⋊C4C22×D312yescomplemented
260C3×C4⋊C4C22×D312yescomplemented
261C3×C22⋊C4—64no—
262C3×C42—64no—
263(C2×D3)⋊C4—24no—
264C4⋊Dic3—21no—
265C4⋊Dic3C22×D312yescomplemented
266C4×Dic3—24no—
267#208—68no—
268C2×C3⋊C8—22no—
269C2×C3⋊C8—32no—
270C2×C3⋊C8—32no—
271C2×C3⋊C8—62no—
272C2×C3⋊C8—62no—
273C2×C3⋊C8—62no—
274C2×C3⋊C8—122no—
275C2×C3⋊C8C22×D312yescomplemented
276ΓL(1,𝔽25)—68no—
277C22×C32C2×C22⋊C412yes—
278C22×C32AGL(1,ℤ/8)12yes—
279C22×C32AGL(1,ℤ/8)12yes—
280C22×C32C22×D411yescharacteristic
281C2×C3⋊D3—24no—
282C2×C3⋊D3—42no—
283C2×C3⋊D3—42no—
284C2×C3⋊D3—48no—
285C2×C3×D3—22no—
286C2×C3×D3—22no—
287C2×C3×D3—28no—
288C2×C3×D3—24no—
289C2×C3×D3—42no—
290C2×C3×D3—42no—
291C2×C3×D3—48no—
292C2×C3×D3C2×C22⋊C414yes—
293D32—432no—
294C32×C4—42no—
295C32×C4C2×C22⋊C412yes—
296C32×C4C23×C411yescharacteristic
297C32×C4C22×D411yescharacteristic
298C3×Dic3—42no—
299C3×Dic3C2×C22⋊C414yes—
300C25—181no—
301C22×D4—31no—
302C22×D4—94no—
303C22×D4—98no—
304C22×D4—91no—
305C22×D4—184no—
306C22×D4—182no—
307C22×D4—181no—
308C23×C4—31no—
309C2×M16—94no—
310C2×M16—184no—
311C22×C8—31no—
312C22×C8—91no—
313#117—34no—
314#117—62no—
315C2×C4⋊C4—31no—
316C2×C4⋊C4D3211yescharacteristic, complemented
317C2×C22⋊C4—61no—
318C2×C42—61no—
319#102—34no—
320#102—94no—
321#102—94no—
322#102—94no—
323C23×C3—21no—
324C23×C3—34no—
325C23×C3—32no—
326C23×C3—62no—
327C23×C3—62no—
328C23×C3—64no—
329C23×C3—62no—
330C23×C3—122no—
331C23×C3—122no—
332C23×C3D3×D411yescharacteristic
333C23×C3C2×#6711yescharacteristic
334C22×D3—22no—
335C22×D3—22no—
336C22×D3—24no—
337C22×D3—22no—
338C22×D3—42no—
339C22×D3—42no—
340C22×D3—616no—
341C22×D3—64no—
342C22×D3—64no—
343C22×D3—62no—
344C22×D3—62no—
345C22×D3—616no—
346C22×D3—122no—
347C22×D3—124no—
348C22×D3—1232no—
349C22×D3—128no—
350C22×D3—128no—
351C22×D3—128no—
352C22×D3—128no—
353C22×D3—1232no—
354C22×D3—122no—
355C22×D3—122no—
356C22×D3—122no—
357C22×D3—122no—
358C22×D3—242no—
359C22×D3—242no—
360C22×D3(C2×D3)⋊C414yes—
361C22×D3C2×#6712yes—
362C3×D4—34no—
363C3×D4—64no—
364C3×D4—62no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—21no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—21no—
371C2×C3×C4—34no—
372C2×C3×C4—32no—
373C2×C3×C4—38no—
374C2×C3×C4—34no—
375C2×C3×C4—34no—
376C2×C3×C4—42no—
377C2×C3×C4—42no—
378C2×C3×C4—42no—
379C2×C3×C4—62no—
380C2×C3×C4—82no—
381C2×C3×C4—122no—
382C2×C3×C4C2×C4×D312yes—
383C2×C3×C4C2×C4×D312yes—
384C2×C3×C4C2×D1212yes—
385C2×C3×C4D3×D412yes—
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4C2×#6711yescharacteristic
388C2×C3×C4C23×D311yescharacteristic
389C2×C3×C4C23×D311yescharacteristic
390#67—616no—
391C2×Dic3—22no—
392C2×Dic3—42no—
393C2×Dic3(C2×D3)⋊C414yes—
394C2×Dic3C2×#6712yes—
395D12—24no—
396D12—22no—
397D12—34no—
398D12—34no—
399D12—64no—
400D12—616no—
401D12—64no—
402D12—64no—
403D12—62no—
404D12—62no—
405D12—122no—
406D12—124no—
407D12C2×C4×D314yes—
408C4×D3(C2×D3)⋊C418yes—
409C4×D3C2×C4×D314yes—
410C4×D3C2×D1214yes—
411C3×C8—62no—
412C3⋊C8—22no—
413C3⋊C8—62no—
414C3⋊C8—62no—
415C3⋊C8—122no—
416C2×C32#41814yescomplemented
417C2×C32C22×C22⋊C411yescharacteristic
418C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
419C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
420C3⋊D3—44no—
421C3×D3—24no—
422C3×D3—44no—
423C24—31no—
424C24—61no—
425C24—184no—
426C24—188no—
427C24—181no—
428C24—364no—
429C24—364no—
430C2×D4—32no—
431C2×D4—34no—
432C2×D4—62no—
433C2×D4—61no—
434C2×D4—916no—
435C2×D4—92no—
436C2×D4—94no—
437C2×D4—188no—
438C2×D4—1816no—
439C2×D4—184no—
440C2×D4—188no—
441C2×D4—182no—
442C2×D4—181no—
443C22×C4—21no—
444C22×C4—31no—
445C22×C4—32no—
446C22×C4—34no—
447C22×C4—34no—
448C22×C4—32no—
449C22×C4—61no—
450C22×C4C2×D3211yescharacteristic
451M16—188no—
452C2×C8—32no—
453C2×C8—62no—
454C2×C8—92no—
455C2×C8—182no—
456C4⋊C4—21no—
457C4⋊C4—32no—
458C4⋊C4—61no—
459C4⋊C4C2×D3212yescomplemented
460C22⋊C4—64no—
461C42—64no—
462C22×C3—21no—
463C22×C3—22no—
464C22×C3—22no—
465C22×C3—22no—
466C22×C3—34no—
467C22×C3—62no—
468C22×C3—62no—
469C22×C3—68no—
470C22×C3—64no—
471C22×C3—128no—
472C22×C3—122no—
473C22×C3—122no—
474C22×C3D3×C22⋊C412yes—
475C22×C3#91112yes—
476C22×C3#91412yes—
477C22×C3C2×(C2×D3)⋊C412yes—
478C22×C3#94912yes—
479C22×C3#94912yes—
480C22×C3C2×D3×D411yescharacteristic
481C22×C3C22×#6711yescharacteristic
482C2×D3—28no—
483C2×D3—22no—
484C2×D3—22no—
485C2×D3—24no—
486C2×D3—42no—
487C2×D3—42no—
488C2×D3—48no—
489C2×D3—64no—
490C2×D3—64no—
491C2×D3—124no—
492C2×D3—1232no—
493C2×D3—1232no—
494C2×D3—122no—
495C2×D3—122no—
496C2×D3—128no—
497C2×D3—128no—
498C2×D3—122no—
499C2×D3—122no—
500C2×D3—242no—
501C2×D3—248no—
502C2×D3—242no—
503C2×D3C2×(C2×D3)⋊C414yes—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—22no—
507C3×C4—34no—
508C3×C4—42no—
509C3×C4—42no—
510C3×C4—82no—
511C3×C4—122no—
512C3×C4D3×C22⋊C412yes—
513C3×C4C2×(C2×D3)⋊C412yes—
514C3×C4C22×C4×D311yescharacteristic
515C3×C4C22×C4×D311yescharacteristic
516C3×C4C22×D1211yescharacteristic
517C3×C4C2×D3×D411yescharacteristic
518Dic3—42no—
519Dic3C2×(C2×D3)⋊C414yes—
520C32C2×#41811yescharacteristic, complemented, Sylow
521C23—32no—
522C23—34no—
523C23—62no—
524C23—62no—
525C23—62no—
526C23—64no—
527C23—122no—
528C23—122no—
529C23—1816no—
530C23—182no—
531C23—184no—
532C23—368no—
533C23—3632no—
534C23—368no—
535C23—362no—
536C23—362no—
537C23D3×#6711yescharacteristic
538D4—34no—
539D4—62no—
540D4—64no—
541D4—94no—
542D4—1816no—
543D4—182no—
544D4—184no—
545C2×C4—22no—
546C2×C4—32no—
547C2×C4—34no—
548C2×C4—34no—
549C2×C4—34no—
550C2×C4—38no—
551C2×C4—42no—
552C2×C4—62no—
553C2×C4—122no—
554C2×C4C4×D3212yes—
555C2×C4D3×D1212yes—
556C2×C4D3×#6711yescharacteristic
557C2×C4C22×D3211yescharacteristic
558C8—62no—
559C8—182no—
560C2×C3—21no—
561C2×C3—24no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—64no—
565C2×C3—124no—
566C2×C3#477014yescomplemented
567C2×C3#500114yescomplemented
568C2×C3C2×D3×C22⋊C411yescharacteristic
569C2×C3C2×#91111yescharacteristic
570C2×C3C2×#91411yescharacteristic
571C2×C3C22×(C2×D3)⋊C411yescharacteristic
572C2×C3C2×#94911yescharacteristic
573C2×C3C2×#94911yescharacteristic
574D3—24no—
575D3—44no—
576D3—124no—
577D3—124no—
578D3—244no—
579C22—34no—
580C22—62no—
581C22—68no—
582C22—62no—
583C22—64no—
584C22—122no—
585C22—128no—
586C22—122no—
587C22—184no—
588C22—3632no—
589C22—362no—
590C22—368no—
591C22—362no—
592C22D3×(C2×D3)⋊C412yes—
593C22#6392512yes—
594C22#6393912yes—
595C22C2×D3×#6711yescharacteristic
596C4—34no—
597C4—42no—
598C4—122no—
599C4D3×(C2×D3)⋊C412yes—
600C4C2×C4×D3211yescharacteristic
601C4C2×D3×D1211yescharacteristic
602C3—21no—
603C3C2×#477011yescharacteristic, complemented
604C3C2×#500111yescharacteristic, complemented
605C2—64no—
606C2—124no—
607C2—364no—
608C2#1059059214yesdirect product factor
609C2C2×D3×(C2×D3)⋊C411yescharacteristic
610C2C2×#6392511yescharacteristic
611C2C2×#6393911yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×D3×D12C2
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#418
LCSG ▷ 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
2. C2×C3×#892C2semidirect
3. C22×#3711C2semidirect
4. C2×#63636C2semidirect
5. C2×C3×#809C2semidirect
6. C2×#63564C2semidirect
7. C2×#63562C2semidirect
8. #10590592C2direct (N × H)
18. C2×D3×D12C4semidirect
20. C2×C32×C4⋊C4C22semidirect
21. C22×C3⋊(C3⋊C8)C22semidirect
23. C2×C3×C4⋊Dic3C22semidirect
25. C22×C3×C3⋊C8C22semidirect
27. C3×#892C22semidirect
29. C2×#3711C22semidirect
30. #63636C22semidirect
31. C3×#809C22semidirect
32. #63564C22semidirect
33. #63562C22semidirect
39. C2×#892D3semidirect
49. C2×#809D3semidirect
78. D3×D12C2×C4semidirect
80. C32×C4⋊C4C23semidirect
82. C2×C3⋊(C3⋊C8)C23semidirect
85. C3×C4⋊Dic3C23semidirect
88. C2×C3×C3⋊C8C23semidirect
115. C2×C3×C4⋊C4C2×D3semidirect
116. C2×C3×C4⋊C4C2×D3semidirect
120. C2×C4⋊Dic3C2×D3semidirect
127. C22×C3⋊C8C2×D3semidirect
131. #892C2×D3semidirect
140. #809C2×D3semidirect
259. C3×C4⋊C4C22×D3semidirect
260. C3×C4⋊C4C22×D3semidirect
265. C4⋊Dic3C22×D3semidirect
275. C2×C3⋊C8C22×D3semidirect
316. C2×C4⋊C4D32semidirect
416. C2×C32#418semidirect
459. C4⋊C4C2×D32semidirect
520. C32C2×#418semidirect
566. C2×C3#4770semidirect
567. C2×C3#5001semidirect
603. C3C2×#4770semidirect
604. C3C2×#5001semidirect
608. C2#10590592direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×D122
C2×C3×#8922
C22×#37112
C2×#636362
C2×C3×#8092
C2×#635642
C2×#635622
#105905922
C2×#50013
C2×#47703