Finite Group Databasebeta

← C2×#13078769 #15621901

Subgroups — C2×#13078769 #15621901

Order 2816.

2430 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623256C211yesmaximal, characteristic, complemented
2C2×C4×#4341C211yesmaximal, characteristic, complemented
3#13078769C2116yesmaximal, direct product factor
4C2×#10622498C212yesmaximal, complemented
5C2×#10622707C211yesmaximal, characteristic, complemented
6C2×#10622461C211yesmaximal, characteristic, complemented
7C2×#10622628C211yesmaximal, characteristic, complemented
8C2×#10622394C212yesmaximal, complemented
9C2×#10622398C212yesmaximal, complemented
10C2×#10622502C212yesmaximal, complemented
11C2×#10622448C211yesmaximal, characteristic, complemented
12C2×C11×#474C211yesmaximal, characteristic, complemented
13C22×#4343—21no—
14C22×#4341C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#67000—21no—
18C2×D4×Dic11C2211yescharacteristic
19C22×#4323C2212yes—
20C2×C4×C22⋊D11—21no—
21C22×C4×Dic11—21no—
22C22×#4314C2212yes—
23#10623256—24no—
24#10623256C2218yescomplemented
25C4×#4341—24no—
26C4×#4341C2218yescomplemented
27C2×#66948—21no—
28C2×#66948C2212yes—
29C2×#66946—21no—
30C2×#66946C2212yes—
31C2×#66945C2211yescharacteristic
32C2×#66940C2211yescharacteristic
33C2×(C22⋊D11)⋊C4—21no—
34C2×#66930—21no—
35C2×#66927C2211yescharacteristic
36C2×C42×D11C2211yescharacteristic
37C2×C4×Dic22C2211yescharacteristic
38C11×#474C2218yescomplemented
39C2×C11×#107C2212yes—
40C2×C11×C4⋊C8C2211yescharacteristic
41C2×C11×#102C2212yes—
42C2×#66885C2212yes—
43C2×(C2×D11)⋊C8C2212yes—
44C2×#66879C2212yes—
45#10622707C2218yescomplemented
46#10622628C2218yescomplemented
47C2×#66874C2212yes—
48C2×#66873C2212yes—
49C2×#66872C2212yes—
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622502C22116yescomplemented
52#10622498C22116yescomplemented
53#10622461C2218yescomplemented
54#10622448C2218yescomplemented
55#10622398C22116yescomplemented
56#10622394C22116yescomplemented
57C22×Q8×C11—21no—
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C22×C22⋊D11—21no—
61C23×Dic11—21no—
62C23×Dic11—21no—
63C2×#4343—28no—
64C2×#4343—48no—
65C2×#4341—24no—
66C2×#4341—22no—
67C2×#4341—24no—
68C2×#4341C2314yes—
69C22×D44—22no—
70C22×D44—21no—
71C22×D44—21no—
72C22×D44C2312yes—
73C22×C4×D11—22no—
74C22×C4×D11D411yescharacteristic
75C22×C4×D11D411yescharacteristic
76C22×C4×D11C2311yescharacteristic
77C22×Dic22C2311yescharacteristic
78C22×C8×C11C2312yes—
79C11×C4⋊Q8—22no—
80C11×C4⋊Q8C2314yes—
81C4×D4×C11—22no—
82C4×D4×C11C2314yes—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C22⋊C4—21no—
87C2×C42×C11C2311yescharacteristic
88C2×C22⋊Dic11—21no—
89#67000—28no—
90D4×Dic11—22no—
91D4×Dic11C2314yes—
92C2×#4323—28no—
93C2×#4323C2318yes—
94C4×C22⋊D11—28no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—22no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—28no—
105C2×C4×Dic11D411yescharacteristic
106C2×C4×Dic11D411yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C22×C11⋊C8C2312yes—
109C2×#4314—28no—
110C2×#4314C2318yes—
111#66948—24no—
112#66948—28no—
113#66948C2318yes—
114#66946—24no—
115#66946—28no—
116#66946C2318yes—
117#66945—22no—
118#66945C2314yes—
119#66940—22no—
120#66940C2314yes—
121(C22⋊D11)⋊C4—28no—
122#66930—28no—
123#66927—22no—
124#66927C2314yes—
125C42×D11D414yes—
126C42×D11C2314yes—
127C4×Dic22—22no—
128C4×Dic22C2314yes—
129C11×#107C2318yes—
130C11×C4⋊C8C2314yes—
131C11×#102C2318yes—
132#66885C2318yes—
133(C2×D11)⋊C8C2318yes—
134#66879C2318yes—
135#66874C2318yes—
136#66873C2318yes—
137#66872C2318yes—
138C4⋊(C11⋊C8)C2314yes—
139C2×#3115—111nomaximal, Sylow
140C24×C11—21no—
141C23×D11—22no—
142C23×D11C2×D411yescharacteristic
143C2×Q8×C11—24no—
144C2×Q8×C11—44no—
145C2×D4×C11—21no—
146C2×D4×C11—22no—
147C2×D4×C11#4114yescomplemented
148C2×D4×C11C2412yes—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—24no—
152C22×C4×C11—44no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C2×C22⋊D11—28no—
157C2×C22⋊D11—24no—
158C22×Dic11—28no—
159C22×Dic11—24no—
160C22×Dic11—24no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—44no—
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167#4343—432no—
168#4341—216no—
169#4341—28no—
170#4341—28no—
171C2×D44—28no—
172C2×D44—22no—
173C2×D44—24no—
174C2×D44—24no—
175C2×D44—24no—
176C2×D44—24no—
177C2×D44—44no—
178C2×D44—48no—
179C2×D44—44no—
180C2×D44C2414yes—
181C2×C4×D11—28no—
182C2×C4×D11—24no—
183C2×C4×D11—22no—
184C2×C4×D11—22no—
185C2×C4×D11—42no—
186C2×C4×D11—48no—
187C2×C4×D11C2×D412yes—
188C2×C4×D11C2×D414yes—
189C2×C4×D11C2×D414yes—
190C2×C4×D11C2412yes—
191C2×Dic22—21no—
192C2×Dic22—22no—
193C2×Dic22#4114yescomplemented
194C2×Dic22C2412yes—
195C2×C8×C11—24no—
196C2×C8×C11C2414yes—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—24no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4C2414yes—
201C11×C4⋊C4C2412yes—
202C11×C22⋊C4—24no—
203C42×C11C2×D412yes—
204C42×C11C2412yes—
205C22⋊Dic11—24no—
206#4323—216no—
207(C2×D11)⋊C4—28no—
208(C2×D11)⋊C4—28no—
209(C2×D11)⋊C4—24no—
210C4⋊Dic11—21no—
211C4⋊Dic11C2412yes—
212Dic11⋊C4—24no—
213Dic11⋊C4—24no—
214C4×Dic11—24no—
215C4×Dic11—24no—
216C4×Dic11—24no—
217C4×Dic11C2×D412yes—
218C4×Dic11C2×D414yes—
219C4×Dic11C2×D414yes—
220C4×Dic11C2412yes—
221C2×C11⋊C8—24no—
222C2×C11⋊C8C2414yes—
223#4314—216no—
224C2×#532—111no—
225C2×C4×#41—111no—
226#3115—1116no—
227C2×#482—112no—
228C2×#475—111no—
229C2×#474D1111yescharacteristic, complemented
230C2×#460—111no—
231C2×#459—111no—
232C2×#449—112no—
233C2×#442—112no—
234C2×#440—112no—
235C2×#432—111no—
236C23×C11—24no—
237C23×C11—22no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11C22×D411yescharacteristic
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—22no—
244C22×D11—24no—
245C22×D11—44no—
246C22×D11—44no—
247C22×D11—44no—
248C22×D11C22×D412yes—
249Q8×C11—48no—
250D4×C11—24no—
251D4×C11—22no—
252D4×C11C2×#4114yescomplemented
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—24no—
256C2×C4×C11—44no—
257C2×C4×C11—42no—
258C2×C4×C11—48no—
259C2×C4×C11AGL(1,ℤ/8)14yes—
260C2×C4×C11C22×D412yes—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D412yes—
263C2×C4×C11C2×#4112yes—
264C2×C4×C11C2×#4112yes—
265C2×C4×C11C2511yescharacteristic
266C22⋊D11—216no—
267C2×Dic11—216no—
268C2×Dic11—24no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—48no—
275C2×Dic11—42no—
276C2×Dic11C22×D412yes—
277C2×Dic11C22×D412yes—
278C2×Dic11C22×D412yes—
279D44—24no—
280D44—24no—
281D44—48no—
282D44—416no—
283D44—44no—
284D44—48no—
285C4×D11—24no—
286C4×D11—28no—
287C4×D11—22no—
288C4×D11—22no—
289C4×D11—44no—
290C4×D11—416no—
291Dic22—24no—
292Dic22—22no—
293Dic22C2×#4114yescomplemented
294C8×C11—24no—
295C11⋊C8—24no—
296C22×#41—111no—
297C22×#41—221no—
298C22×SD16—112no—
299C22×D8—112no—
300#532—118no—
301#532—224no—
302C2×C4⋊Q8C2×D1111yescharacteristic
303C2×#127—111no—
304C2×#124—221no—
305C2×#121—112no—
306C2×#121—221no—
307C4×#41—118no—
308C4×#41—224no—
309C2×C4×Q8—111no—
310C2×C4×Q8—111no—
311C2×C4×D4—111no—
312C2×C4×D4—112no—
313C2×C4×D4—221no—
314C2×C4×D4—221no—
315C2×C4×D4—221no—
316C2×C4×D4C2×D1111yescharacteristic
317C2×#117—111no—
318C2×#117—221no—
319C22×C42—111no—
320C22×C42—221no—
321#482—1116no—
322#475—118no—
323#474C2×D1118yescomplemented
324#460—118no—
325#459—118no—
326#449—1116no—
327#442—1116no—
328#440—1116no—
329#432—118no—
330C2×#107C2×D1112yes—
331C2×#106—112no—
332C2×C4⋊C8—111no—
333C2×C4⋊C8C2×D1111yescharacteristic
334C2×#103—112no—
335C2×#102—112no—
336C2×#102—112no—
337C2×#102C2×D1112yes—
338C2×C22⋊C8—112no—
339C2×#97—112no—
340C22×C11—24no—
341C22×C11—48no—
342C22×C11—42no—
343C22×C11—42no—
344C22×C11#52512yes—
345C22×C11C2×AGL(1,ℤ/8)12yes—
346C22×C11#57512yes—
347C22×C11C23×D411yescharacteristic
348C2×D11—22no—
349C2×D11—22no—
350C2×D11—22no—
351C2×D11—44no—
352C2×D11—44no—
353C2×D11—44no—
354C2×D11—44no—
355C2×D11—88no—
356C4×C11—22no—
357C4×C11—42no—
358C4×C11—44no—
359C4×C11#52512yes—
360C4×C11C2×AGL(1,ℤ/8)14yes—
361C4×C11C22×#4111yescharacteristic
362C4×C11C22×#4111yescharacteristic
363Dic11—24no—
364Dic11—22no—
365Dic11—22no—
366Dic11—22no—
367Dic11—42no—
368C2×#41—114no—
369C2×#41—222no—
370C2×#41—228no—
371C2×#41—224no—
372C2×#41—224no—
373C2×#41—448no—
374C22×Q8—21no—
375C22×Q8—111no—
376C22×D4—112no—
377C22×D4—222no—
378C22×D4—221no—
379C22×D4—221no—
380C22×D4—221no—
381C22×D4C22×D1111yescharacteristic
382C23×C4—21no—
383C23×C4—111no—
384C23×C4—111no—
385C23×C4—111no—
386C23×C4—222no—
387C23×C4—221no—
388C23×C4—221no—
389C2×SD16—118no—
390C2×SD16—228no—
391C2×D8—118no—
392C2×D8—228no—
393C22×C8—112no—
394C22×C8C22×D1112yes—
395C4⋊Q8—22no—
396C4⋊Q8C22×D1114yes—
397#127—114no—
398#127—222no—
399#124—228no—
400#121—118no—
401#121—224no—
402#121—228no—
403C4×Q8—114no—
404C4×Q8—114no—
405C4×Q8—222no—
406C4×Q8—222no—
407C4×D4—22no—
408C4×D4—114no—
409C4×D4—118no—
410C4×D4—224no—
411C4×D4—228no—
412C4×D4—222no—
413C4×D4—228no—
414C4×D4—228no—
415C4×D4C22×D1114yes—
416#117—114no—
417#117—228no—
418#117—222no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C4⋊C4C22×D1112yes—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—222no—
427C2×C22⋊C4—222no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C42—111no—
431C2×C42—111no—
432C2×C42—111no—
433C2×C42—114no—
434C2×C42—114no—
435C2×C42—228no—
436C2×C42—221no—
437C2×C42—221no—
438C2×C42—221no—
439C2×C42C22×D1111yescharacteristic
440#107C22×D1118yes—
441#106—118no—
442C4⋊C8—114no—
443C4⋊C8C22×D1114yes—
444#103—118no—
445#102—118no—
446#102—118no—
447#102C22×D1118yes—
448C22⋊C8—118no—
449#97—118no—
450C2×C11—44no—
451C2×C11#311514yescomplemented
452C2×C11C2×#52511yescharacteristic
453C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
454C2×C11C2×#57511yescharacteristic
455D11—42no—
456D11—84no—
457C24—21no—
458C24—111no—
459C24—222no—
460#41—228no—
461#41—2216no—
462#41—228no—
463#41—4432no—
464C2×Q8—24no—
465C2×Q8—44no—
466C2×Q8—114no—
467C2×Q8—112no—
468C2×Q8—221no—
469C2×Q8—222no—
470C2×D4—21no—
471C2×D4—22no—
472C2×D4—114no—
473C2×D4—228no—
474C2×D4—224no—
475C2×D4—228no—
476C2×D4—224no—
477C2×D4—222no—
478C2×D4—224no—
479C2×D4—224no—
480C2×D4—224no—
481C2×D4—444no—
482C2×D4—448no—
483C2×D4—444no—
484C2×D4#434314yescomplemented
485C2×D4C23×D1112yes—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—44no—
490C22×C4—111no—
491C22×C4—111no—
492C22×C4—111no—
493C22×C4—112no—
494C22×C4—114no—
495C22×C4—112no—
496C22×C4—114no—
497C22×C4—228no—
498C22×C4—224no—
499C22×C4—224no—
500C22×C4—228no—
501C22×C4—221no—
502C22×C4—224no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—221no—
506C22×C4—442no—
507C22×C4—448no—
508C22×C4—444no—
509C22×C4D4×D1111yescharacteristic
510C22×C4D4×D1111yescharacteristic
511C22×C4C23×D1111yescharacteristic
512SD16—2216no—
513D8—2216no—
514C2×C8—24no—
515C2×C8—114no—
516C2×C8—224no—
517C2×C8C23×D1114yes—
518C4⋊C4—24no—
519C4⋊C4—21no—
520C4⋊C4—22no—
521C4⋊C4—112no—
522C4⋊C4—224no—
523C4⋊C4—221no—
524C4⋊C4—224no—
525C4⋊C4C23×D1112yes—
526C4⋊C4C23×D1114yes—
527C22⋊C4—24no—
528C22⋊C4—228no—
529C22⋊C4—228no—
530C22⋊C4—224no—
531C22⋊C4—224no—
532C42—114no—
533C42—114no—
534C42—112no—
535C42—112no—
536C42—224no—
537C42—224no—
538C42—224no—
539C42D4×D1112yes—
540C42C23×D1112yes—
541C11C2×#311511yescharacteristic, complemented, Sylow
542C23—24no—
543C23—22no—
544C23—42no—
545C23—42no—
546C23—112no—
547C23—222no—
548C23—222no—
549C23—222no—
550C23—224no—
551C23—444no—
552C23—444no—
553C23—444no—
554C23C2×D4×D1111yescharacteristic
555Q8—48no—
556Q8—114no—
557Q8—224no—
558Q8—222no—
559D4—24no—
560D4—22no—
561D4—2216no—
562D4—224no—
563D4—224no—
564D4—448no—
565D4—4416no—
566D4—448no—
567D4—444no—
568D4C2×#434314yescomplemented
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—42no—
573C2×C4—44no—
574C2×C4—48no—
575C2×C4—112no—
576C2×C4—112no—
577C2×C4—112no—
578C2×C4—2216no—
579C2×C4—222no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—224no—
583C2×C4—222no—
584C2×C4—228no—
585C2×C4—224no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—444no—
590C2×C4—4416no—
591C2×C4—448no—
592C2×C4—442no—
593C2×C4#6696414yes—
594C2×C4C2×D4×D1112yes—
595C2×C4C2×D4×D1112yes—
596C2×C4C2×D4×D1111yescharacteristic
597C2×C4C2×#434312yes—
598C2×C4#41×D1112yes—
599C2×C4C24×D1111yescharacteristic
600C8—24no—
601C8—224no—
602C22—24no—
603C22—42no—
604C22—42no—
605C22—48no—
606C22—222no—
607C22—222no—
608C22—222no—
609C22—444no—
610C22—444no—
611C22—444no—
612C22—444no—
613C22—888no—
614C22#1062315812yes—
615C22C2×#6696412yes—
616C22#1062330812yes—
617C22C22×D4×D1111yescharacteristic
618C4—22no—
619C4—42no—
620C4—44no—
621C4—222no—
622C4—224no—
623C4—222no—
624C4—222no—
625C4—442no—
626C4#1062315812yes—
627C4C2×#6696414yes—
628C4C22×#434311yescharacteristic
629C4C2×#41×D1111yescharacteristic
630C2—44no—
631C2—442no—
632C2—884no—
633C2#1307876914yesdirect product factor
634C2C2×#1062315811yescharacteristic
635C2C22×#6696411yescharacteristic
636C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#474C2
socleC23×C11C22×D4
hypercenterC2×#474D11
hypocenterC11C2×#3115
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#10623256C2semidirect
2. C2×C4×#4341C2semidirect
3. #13078769C2direct (N × H)
4. C2×#10622498C2semidirect
5. C2×#10622707C2semidirect
6. C2×#10622461C2semidirect
7. C2×#10622628C2semidirect
8. C2×#10622394C2semidirect
9. C2×#10622398C2semidirect
10. C2×#10622502C2semidirect
11. C2×#10622448C2semidirect
12. C2×C11×#474C2semidirect
24. #10623256C22semidirect
26. C4×#4341C22semidirect
38. C11×#474C22semidirect
45. #10622707C22semidirect
46. #10622628C22semidirect
51. #10622502C22semidirect
52. #10622498C22semidirect
53. #10622461C22semidirect
54. #10622448C22semidirect
55. #10622398C22semidirect
56. #10622394C22semidirect
147. C2×D4×C11#41semidirect
193. C2×Dic22#41semidirect
229. C2×#474D11semidirect
252. D4×C11C2×#41semidirect
293. Dic22C2×#41semidirect
323. #474C2×D11semidirect
451. C2×C11#3115semidirect
484. C2×D4#4343semidirect
541. C11C2×#3115semidirect
568. D4C2×#4343semidirect
633. C2#13078769direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232562
C2×C4×#43412
#130787692
C2×#106224982
C2×#106227072
C2×#106224612
C2×#106226282
C2×#106223942
C2×#106223982
C2×#106225022
C2×#106224482
C2×C11×#4742
C2×#311511