Finite Group Databasebeta

← C2×C4×#67003 #15617795

Subgroups — C2×C4×#67003 #15617795

Order 2816.

2894 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67003C211yesmaximal, characteristic
2C2×C4×#4339C211yesmaximal, characteristic, complemented
3C4×#67003C2116yesmaximal, direct product factor
4C2×C4×#4326C212yesmaximal, complemented
5C2×C4×#4325C212yesmaximal, complemented
6C2×C4×#4324C212yesmaximal, complemented
7C2×C4×#4323C212yesmaximal, complemented
8C2×#10622611C211yesmaximal, characteristic, complemented
9C2×#10622846C211yesmaximal, characteristic, complemented
10C2×#10622615C211yesmaximal, characteristic, complemented
11C22×C4×C11⋊C8C211yesmaximal, characteristic, complemented
12C2×C4×C11×#41C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C4×C11×#41—24no—
16C4×C11×#41C2218yescomplemented
17C2×C4×Q8×C11C2212yes—
18C2×C4×D4×C11—22no—
19C2×C4×D4×C11C2212yes—
20C2×C11×#117—21no—
21C2×C11×#117C2211yescharacteristic
22C22×C42×C11—21no—
23C22×C42×C11C2211yescharacteristic
24C2×#67003C4116yesdirect product factor
25C2×#67003C2218yes—
26C22×#4326C2211yescharacteristic
27C22×#4325C2211yescharacteristic
28C22×#4324C2211yescharacteristic
29C22×#4323C2211yescharacteristic
30C2×C4×C22⋊D11—22no—
31C2×#66979C2211yescharacteristic
32C23×C11⋊C8C2211yescharacteristic
33C23×C11⋊C8C2211yescharacteristic
34C4×#4339—24no—
35C4×#4339C2218yescomplemented
36C2×C4×D44C2212yes—
37C2×#66925—21no—
38C2×C42×D11—21no—
39C2×C4×Dic22C2212yes—
40#10622846C2218yescomplemented
41C2×#66899C2212yes—
42C2×#66896C2212yes—
43C4×#4326C22116yescomplemented
44C4×#4325C22116yescomplemented
45C4×#4324C22116yescomplemented
46C4×#4323C22116yescomplemented
47#10622615C2218yescomplemented
48#10622611C2218yescomplemented
49C2×#66874C2212yes—
50C2×#66873C2212yes—
51C2×#66872C2212yes—
52C2×#66871C2212yes—
53C2×C4×C11⋊C8C2212yes—
54C2×C4×C11⋊C8C2212yes—
55C2×C4×C11⋊C8C2218yescomplemented
56C2×C11×#41—22no—
57C2×C11×#41—24no—
58C2×C11×#41C2×C418yescomplemented
59C2×C11×#41C2314yes—
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—22no—
65C23×C4×C11D412yes—
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—21no—
68C2×#4339—22no—
69C2×#4339—24no—
70C2×#4339C2×C418yescomplemented
71C2×#4339C2314yes—
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×C4×D11—22no—
75C22×Dic22C2311yescharacteristic
76C4×Q8×C11—24no—
77C4×Q8×C11C2318yes—
78C4×D4×C11—216no—
79C4×D4×C11—24no—
80C4×D4×C11C2318yes—
81C11×#117—22no—
82C11×#117—28no—
83C11×#117C2314yes—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—22no—
88C2×C42×C11—21no—
89C2×C42×C11—22no—
90C2×C42×C11—28no—
91C2×C42×C11D411yescharacteristic
92C2×C42×C11D414yes—
93C2×C42×C11D411yescharacteristic
94C2×C42×C11C2312yes—
95C2×C42×C11C2314yes—
96C2×C22⋊Dic11—21no—
97#67003C2×C4164yesdirect product factor
98C2×#4326C2×C418yescomplemented
99C2×#4326C2314yes—
100C2×#4325C2×C418yescomplemented
101C2×#4325C2314yes—
102C2×#4324C2×C418yescomplemented
103C2×#4324C2314yes—
104C2×#4323C2×C418yescomplemented
105C2×#4323C2314yes—
106C4×C22⋊D11—216no—
107C2×(C2×D11)⋊C4—22no—
108#66979—22no—
109#66979C2314yes—
110C2×C4⋊Dic11C2312yes—
111C2×Dic11⋊C4—22no—
112C2×C4×Dic11—22no—
113C2×C4×Dic11—21no—
114C22×C11⋊C8—24no—
115C22×C11⋊C8C2×C418yescomplemented
116C22×C11⋊C8C2312yes—
117C22×C11⋊C8C2314yes—
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2314yes—
121C4×D44—24no—
122C4×D44C2318yes—
123#66925—28no—
124C42×D11—28no—
125C4×Dic22—24no—
126C4×Dic22C2318yes—
127#66899C2318yes—
128#66896C2318yes—
129#66874C2318yes—
130#66873C2318yes—
131#66872C2318yes—
132#66871C2318yes—
133C4×C11⋊C8C2318yes—
134C4×C11⋊C8C2318yes—
135C2×C4×#135—111nomaximal, Sylow
136C24×C11—21no—
137C24×C11C2×D411yescharacteristic
138C23×D11—21no—
139C11×#41—216no—
140C11×#41—28no—
141C11×#41C22×C4116yescomplemented
142C2×Q8×C11—21no—
143C2×Q8×C11—22no—
144C2×Q8×C11C22×C414yes—
145C2×Q8×C11C2412yes—
146C2×D4×C11—28no—
147C2×D4×C11—24no—
148C2×D4×C11—21no—
149C2×D4×C11—22no—
150C2×D4×C11C22×C414yes—
151C2×D4×C11C2412yes—
152C22×C4×C11—21no—
153C22×C4×C11—28no—
154C22×C4×C11—28no—
155C22×C4×C11—24no—
156C22×C4×C11—22no—
157C22×C4×C11—28no—
158C22×C4×C11—48no—
159C22×C4×C11C22×C414yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D418yes—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D412yes—
165C22×C4×C11#4114yes—
166C22×C4×C11C2411yescharacteristic
167C22×C4×C11C2412yes—
168C2×C22⋊D11—28no—
169C2×C22⋊D11—24no—
170C22×Dic11—21no—
171C22×Dic11—22no—
172#4339—216no—
173#4339—28no—
174#4339C22×C4116yescomplemented
175C2×D44—21no—
176C2×D44—22no—
177C2×D44C22×C414yes—
178C2×D44C2412yes—
179C2×C4×D11—28no—
180C2×C4×D11—24no—
181C2×C4×D11—28no—
182C2×C4×D11—48no—
183C2×Dic22—21no—
184C2×Dic22—22no—
185C2×Dic22C22×C414yes—
186C2×Dic22C2412yes—
187C11×C4⋊C4—28no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4C2414yes—
190C11×C22⋊C4—24no—
191C11×C22⋊C4—28no—
192C42×C11—24no—
193C42×C11—28no—
194C42×C11C2×D414yes—
195C42×C11C2×D414yes—
196C42×C11C2×D414yes—
197C42×C11C2414yes—
198C22⋊Dic11—24no—
199#4326C22×C4116yescomplemented
200#4325C22×C4116yescomplemented
201#4324C22×C4116yescomplemented
202#4323C22×C4116yescomplemented
203(C2×D11)⋊C4—28no—
204C4⋊Dic11—22no—
205C4⋊Dic11C2414yes—
206Dic11⋊C4—28no—
207C4×Dic11—28no—
208C4×Dic11—24no—
209C2×C11⋊C8—24no—
210C2×C11⋊C8—28no—
211C2×C11⋊C8C22×C414yes—
212C2×C11⋊C8C22×C414yes—
213C2×C11⋊C8C22×C4116yescomplemented
214C2×C11⋊C8C2414yes—
215C2×C11⋊C8C2412yes—
216C2×C11⋊C8C2412yes—
217C22×#135—111no—
218C2×C4×#41—111no—
219C2×C4×#41D1111yescharacteristic, complemented
220C4×#135—1116no—
221C2×C4×Q16—112no—
222C2×C4×SD16—112no—
223C2×C4×SD16—112no—
224C2×C4×D8—112no—
225C2×#427—111no—
226C2×#416—111no—
227C2×#416—111no—
228C22×C4×C8—111no—
229C23×C11—24no—
230C23×C11—24no—
231C23×C11—22no—
232C23×C11—44no—
233C23×C11C4×D414yes—
234C23×C11C22×D412yes—
235C23×C11C22×D411yescharacteristic
236C22×D11—24no—
237C22×D11—22no—
238C22×D11—44no—
239Q8×C11—24no—
240Q8×C11—22no—
241Q8×C11C23×C414yes—
242D4×C11—216no—
243D4×C11—24no—
244D4×C11—22no—
245D4×C11C23×C414yes—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—22no—
249C2×C4×C11—216no—
250C2×C4×C11—216no—
251C2×C4×C11—24no—
252C2×C4×C11—44no—
253C2×C4×C11—416no—
254C2×C4×C11C4×D414yes—
255C2×C4×C11C4×D418yes—
256C2×C4×C11#13518yescomplemented
257C2×C4×C11C23×C412yes—
258C2×C4×C11C23×C414yes—
259C2×C4×C11C22×D414yes—
260C2×C4×C11C22×D412yes—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D414yes—
263C2×C4×C11C2×#4112yes—
264C2×C4×C11C2×#4114yes—
265C2×C4×C11C2511yescharacteristic
266C22⋊D11—216no—
267C2×Dic11—24no—
268C2×Dic11—22no—
269C2×Dic11—24no—
270C2×Dic11—44no—
271D44—24no—
272D44—22no—
273D44C23×C414yes—
274C4×D11—216no—
275C4×D11—416no—
276Dic22—24no—
277Dic22—22no—
278Dic22C23×C414yes—
279C11⋊C8—24no—
280C11⋊C8C23×C414yes—
281C11⋊C8C23×C414yes—
282C22×#41—111no—
283C22×#41C2×D1111yescharacteristic
284C2×#135—118no—
285C2×#135—1116no—
286C22×Q16—111no—
287C22×SD16—111no—
288C22×SD16—111no—
289C22×D8—111no—
290C23×C8—111no—
291C23×C8—111no—
292C4×#41—24no—
293C4×#41—118no—
294C4×#41—224no—
295C4×#41C2×D1118yescomplemented
296C2×C4×Q8—112no—
297C2×C4×Q8C2×D1112yes—
298C2×C4×D4—22no—
299C2×C4×D4—112no—
300C2×C4×D4—222no—
301C2×C4×D4C2×D1112yes—
302C2×#117—21no—
303C2×#117—111no—
304C2×#117—221no—
305C2×#117C2×D1111yescharacteristic
306C22×C42—21no—
307C22×C42—221no—
308C22×C42C2×D1111yescharacteristic
309C4×Q16—1116no—
310C4×SD16—1116no—
311C4×SD16—1116no—
312C4×D8—1116no—
313#427—118no—
314C2×#107—112no—
315C2×#106—112no—
316#416—118no—
317#416—118no—
318C2×#103—112no—
319C2×#103—112no—
320C2×#102—112no—
321C2×#102—112no—
322C2×C4×C8—112no—
323C2×C4×C8—112no—
324C2×C4×C8—118no—
325C22×C11—28no—
326C22×C11—24no—
327C22×C11—24no—
328C22×C11—48no—
329C22×C11—44no—
330C22×C11C2×C4×D414yes—
331C22×C11C2×C4×D412yes—
332C22×C11C2×#13514yes—
333C22×C11C23×D411yescharacteristic
334C2×D11—24no—
335C2×D11—48no—
336C2×D11—44no—
337C4×C11—24no—
338C4×C11—24no—
339C4×C11—44no—
340C4×C11C2×C4×D414yes—
341C4×C11C2×C4×D412yes—
342C4×C11C2×#13518yescomplemented
343C4×C11C24×C411yescharacteristic
344C4×C11C22×#4111yescharacteristic
345Dic11—24no—
346Dic11—44no—
347C2×#41—24no—
348C2×#41—22no—
349C2×#41—118no—
350C2×#41—114no—
351C2×#41—224no—
352C2×#41—222no—
353C2×#41C4×D1118yescomplemented
354C2×#41C22×D1114yes—
355C22×Q8—111no—
356C22×Q8C22×D1111yescharacteristic
357C22×D4—21no—
358C22×D4—111no—
359C22×D4—221no—
360C22×D4C22×D1111yescharacteristic
361C23×C4—21no—
362C23×C4—22no—
363C23×C4—221no—
364C23×C4—222no—
365C23×C4C22⋊D1112yes—
366C23×C4C22×D1111yescharacteristic
367#135—1164no—
368C2×Q16—118no—
369C2×Q16—114no—
370C2×SD16—118no—
371C2×SD16—114no—
372C2×SD16—118no—
373C2×SD16—114no—
374C2×D8—118no—
375C2×D8—114no—
376C22×C8—118no—
377C22×C8—111no—
378C22×C8—111no—
379C22×C8—114no—
380C22×C8—112no—
381C22×C8—114no—
382C22×C8—224no—
383C4×Q8—24no—
384C4×Q8—118no—
385C4×Q8—224no—
386C4×Q8C22×D1118yes—
387C4×D4—216no—
388C4×D4—24no—
389C4×D4—118no—
390C4×D4—2216no—
391C4×D4—224no—
392C4×D4C22×D1118yes—
393#117—22no—
394#117—28no—
395#117—114no—
396#117—222no—
397#117—228no—
398#117C22×D1114yes—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—112no—
401C2×C4⋊C4—222no—
402C2×C4⋊C4C22×D1112yes—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4—222no—
407C2×C42—21no—
408C2×C42—22no—
409C2×C42—28no—
410C2×C42—221no—
411C2×C42—222no—
412C2×C42—228no—
413C2×C42C22⋊D1111yescharacteristic
414C2×C42C22⋊D1114yes—
415C2×C42C22⋊D1111yescharacteristic
416C2×C42C22×D1112yes—
417C2×C42C22×D1114yes—
418#107—118no—
419#106—118no—
420#103—118no—
421#103—118no—
422#102—118no—
423#102—118no—
424C4×C8—118no—
425C4×C8—118no—
426C2×C11—24no—
427C2×C11—44no—
428C2×C11C4×#13514yescomplemented
429C2×C11C22×C4×D411yescharacteristic
430C2×C11C22×#13512yes—
431D11—44no—
432C24—21no—
433C24—221no—
434C24C2×C22⋊D1111yescharacteristic
435#41—216no—
436#41—28no—
437#41—1116no—
438#41—2216no—
439#41—228no—
440#41C2×C4×D11116yescomplemented
441C2×Q8—22no—
442C2×Q8—21no—
443C2×Q8—114no—
444C2×Q8—112no—
445C2×Q8—222no—
446C2×Q8—221no—
447C2×Q8C2×C4×D1114yes—
448C2×Q8C23×D1112yes—
449C2×D4—28no—
450C2×D4—24no—
451C2×D4—22no—
452C2×D4—21no—
453C2×D4—114no—
454C2×D4—112no—
455C2×D4—228no—
456C2×D4—224no—
457C2×D4—222no—
458C2×D4—221no—
459C2×D4C2×C4×D1114yes—
460C2×D4C23×D1112yes—
461C22×C4—21no—
462C22×C4—28no—
463C22×C4—28no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—28no—
467C22×C4—48no—
468C22×C4—221no—
469C22×C4—228no—
470C22×C4—224no—
471C22×C4—222no—
472C22×C4—228no—
473C22×C4—448no—
474C22×C4C2×C4×D1114yes—
475C22×C4#433914yes—
476C22×C4C2×C22⋊D1112yes—
477C22×C4C2×C22⋊D1118yes—
478C22×C4C2×C22⋊D1111yescharacteristic
479C22×C4C2×C22⋊D1112yes—
480C22×C4C2×C22⋊D1112yes—
481C22×C4C23×D1111yescharacteristic
482C22×C4C23×D1112yes—
483Q16—1116no—
484SD16—1116no—
485SD16—1116no—
486D8—1116no—
487C2×C8—114no—
488C2×C8—114no—
489C2×C8—1116no—
490C2×C8—112no—
491C2×C8—112no—
492C2×C8—114no—
493C2×C8—224no—
494C2×C8—228no—
495C4⋊C4—28no—
496C4⋊C4—22no—
497C4⋊C4—114no—
498C4⋊C4—222no—
499C4⋊C4—228no—
500C4⋊C4C23×D1114yes—
501C22⋊C4—24no—
502C22⋊C4—28no—
503C22⋊C4—224no—
504C22⋊C4—228no—
505C42—24no—
506C42—28no—
507C42—224no—
508C42—228no—
509C42C2×C22⋊D1114yes—
510C42C2×C22⋊D1114yes—
511C42C2×C22⋊D1114yes—
512C42C23×D1114yes—
513C11C2×C4×#13511yescharacteristic, complemented, Sylow
514C23—24no—
515C23—24no—
516C23—22no—
517C23—44no—
518C23—224no—
519C23—222no—
520C23—444no—
521C23C4×C22⋊D1114yes—
522C23C22×C22⋊D1112yes—
523C23C22×C22⋊D1111yescharacteristic
524Q8—24no—
525Q8—22no—
526Q8—114no—
527Q8—224no—
528Q8—222no—
529Q8C22×C4×D1114yes—
530D4—216no—
531D4—24no—
532D4—22no—
533D4—114no—
534D4—2216no—
535D4—224no—
536D4—222no—
537D4C22×C4×D1114yes—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—216no—
542C2×C4—216no—
543C2×C4—24no—
544C2×C4—44no—
545C2×C4—416no—
546C2×C4—224no—
547C2×C4—222no—
548C2×C4—2216no—
549C2×C4—224no—
550C2×C4—444no—
551C2×C4—4416no—
552C2×C4C4×C22⋊D1114yes—
553C2×C4C4×C22⋊D1118yes—
554C2×C4#6700318yesdirect product factor
555C2×C4C22×C4×D1112yes—
556C2×C4C22×C4×D1114yes—
557C2×C4C2×#433912yes—
558C2×C4C2×#433914yes—
559C2×C4C22×C22⋊D1114yes—
560C2×C4C22×C22⋊D1112yes—
561C2×C4C22×C22⋊D1111yescharacteristic
562C2×C4C22×C22⋊D1114yes—
563C2×C4C24×D1111yescharacteristic
564C8—114no—
565C8—114no—
566C8—224no—
567C22—28no—
568C22—24no—
569C22—24no—
570C22—48no—
571C22—44no—
572C22—224no—
573C22—448no—
574C22—444no—
575C22C2×C4×C22⋊D1114yes—
576C22C2×C4×C22⋊D1112yes—
577C22C2×#6700314yes—
578C22C23×C22⋊D1111yescharacteristic
579C4—24no—
580C4—24no—
581C4—44no—
582C4—224no—
583C4—444no—
584C4C2×C4×C22⋊D1114yes—
585C4C2×C4×C22⋊D1112yes—
586C4C2×#6700318yesdirect product factor
587C4C23×C4×D1111yescharacteristic
588C4C22×#433911yescharacteristic
589C2—24no—
590C2—44no—
591C2—444no—
592C2C4×#6700314yesdirect product factor
593C2C22×C4×C22⋊D1111yescharacteristic
594C2C22×#6700312yes—
subgroupG/H
centerC2×C42C22⋊D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C4×C11×#41C2
socleC23×C11C22×D4
prime radicalC22×#67003C2
cosocleC2×C4×C11C25
hypercenterC2×C4×#41D11
hypocenterC11C2×C4×#135
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C42 ◁ C22×C42 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4339C2semidirect
3. C4×#67003C2direct (N × H)
4. C2×C4×#4326C2semidirect
5. C2×C4×#4325C2semidirect
6. C2×C4×#4324C2semidirect
7. C2×C4×#4323C2semidirect
8. C2×#10622611C2semidirect
9. C2×#10622846C2semidirect
10. C2×#10622615C2semidirect
11. C22×C4×C11⋊C8C2semidirect
12. C2×C4×C11×#41C2semidirect
16. C4×C11×#41C22semidirect
24. C2×#67003C4direct (N × H)
35. C4×#4339C22semidirect
40. #10622846C22semidirect
43. C4×#4326C22semidirect
44. C4×#4325C22semidirect
45. C4×#4324C22semidirect
46. C4×#4323C22semidirect
47. #10622615C22semidirect
48. #10622611C22semidirect
55. C2×C4×C11⋊C8C22semidirect
58. C2×C11×#41C2×C4semidirect
70. C2×#4339C2×C4semidirect
97. #67003C2×C4direct (N × H)
98. C2×#4326C2×C4semidirect
100. C2×#4325C2×C4semidirect
102. C2×#4324C2×C4semidirect
104. C2×#4323C2×C4semidirect
115. C22×C11⋊C8C2×C4semidirect
141. C11×#41C22×C4semidirect
174. #4339C22×C4semidirect
199. #4326C22×C4semidirect
200. #4325C22×C4semidirect
201. #4324C22×C4semidirect
202. #4323C22×C4semidirect
213. C2×C11⋊C8C22×C4semidirect
219. C2×C4×#41D11semidirect
256. C2×C4×C11#135semidirect
295. C4×#41C2×D11semidirect
342. C4×C11C2×#135semidirect
353. C2×#41C4×D11semidirect
428. C2×C11C4×#135semidirect
440. #41C2×C4×D11semidirect
513. C11C2×C4×#135semidirect
554. C2×C4#67003direct (N × H)
586. C4C2×#67003direct (N × H)
592. C2C4×#67003direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670032
C2×C4×#43392
C4×#670032
C2×C4×#43262
C2×C4×#43252
C2×C4×#43242
C2×C4×#43232
C2×#106226112
C2×#106228462
C2×#106226152
C22×C4×C11⋊C82
C2×C4×C11×#412
C2×C4×#13511