Finite Group Databasebeta

← C2×#13078766 #15621898

Subgroups — C2×#13078766 #15621898

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×#10623247C211yesmaximal, characteristic, complemented
2C2×C4×#4343C211yesmaximal, characteristic, complemented
3#13078766C2116yesmaximal, direct product factor
4C2×#10622397C212yesmaximal, complemented
5C2×#10622633C211yesmaximal, characteristic, complemented
6C2×#10622459C211yesmaximal, characteristic, complemented
7C2×#10622685C211yesmaximal, characteristic, complemented
8C2×#10622785C212yesmaximal, complemented
9C2×#10622398C212yesmaximal, complemented
10C2×#10622777C212yesmaximal, complemented
11C2×#10622448C211yesmaximal, characteristic, complemented
12C2×C11×#460C211yesmaximal, characteristic, complemented
13C22×#4343C2211yescharacteristic
14C22×#4341—21no—
15C22×C11×SD16C2212yes—
16C2×C11×#127C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×#66991—21no—
20C2×#66991C2212yes—
21C2×#66989—21no—
22C2×D4×Dic11—21no—
23C2×D4×Dic11C2212yes—
24C22×#4323C2212yes—
25#10623247—24no—
26#10623247C2218yescomplemented
27C4×#4343—24no—
28C4×#4343C2218yescomplemented
29C2×#66946—21no—
30C2×#66946C2211yescharacteristic
31C2×#66945—21no—
32C2×#66945C2211yescharacteristic
33C2×C4×D44—21no—
34C2×C4×D44C2211yescharacteristic
35C2×C42×D11—21no—
36C2×C42×D11C2211yescharacteristic
37C2×#66922C2211yescharacteristic
38C11×#460C2218yescomplemented
39C2×C11×C4⋊C8C2211yescharacteristic
40C2×C11×#102C2212yes—
41C2×#66899C2212yes—
42C2×#66896C2212yes—
43#10622785C22116yescomplemented
44#10622777C22116yescomplemented
45C2×#66885C2212yes—
46C2×(C2×D11)⋊C8C2212yes—
47C2×#66882C2212yes—
48C2×#66879C2212yes—
49#10622685C2218yescomplemented
50#10622633C2218yescomplemented
51C2×#66872C2212yes—
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53#10622459C2218yescomplemented
54#10622448C2218yescomplemented
55#10622398C22116yescomplemented
56#10622397C22116yescomplemented
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11—21no—
60C22×D4×C11C2312yes—
61C22×C22⋊D11—22no—
62C23×Dic11—22no—
63C2×#4343—24no—
64C2×#4343—24no—
65C2×#4343—22no—
66C2×#4343C2314yes—
67C2×#4341—28no—
68C2×#4341—48no—
69C22×D44—21no—
70C22×D44C2311yescharacteristic
71C22×C4×D11—21no—
72C22×C4×D11—21no—
73C22×C4×D11—21no—
74C22×C4×D11D411yescharacteristic
75C22×C4×D11D411yescharacteristic
76C22×C4×D11C2311yescharacteristic
77C22×Dic22—21no—
78C2×C11×SD16—28no—
79C2×C11×SD16C2318yes—
80C22×C8×C11C2312yes—
81C11×#127—22no—
82C11×#127C2314yes—
83C4×Q8×C11—22no—
84C4×Q8×C11C2314yes—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C42×C11—21no—
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—22no—
91Q8×Dic11—22no—
92Q8×Dic11C2314yes—
93#66991—24no—
94#66991—28no—
95#66991C2318yes—
96#66989—28no—
97D4×Dic11—24no—
98D4×Dic11—28no—
99D4×Dic11C2318yes—
100C2×#4323—28no—
101C2×#4323C2318yes—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×C4⋊Dic11—21no—
106C2×C4⋊Dic11—21no—
107C2×C4⋊Dic11C2312yes—
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4×Dic11—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11D411yescharacteristic
112C2×C4×Dic11D411yescharacteristic
113C2×C4×Dic11C2311yescharacteristic
114C22×C11⋊C8C2312yes—
115#66946—28no—
116#66946—22no—
117#66946C2314yes—
118#66945—22no—
119#66945—28no—
120#66945C2314yes—
121C4×D44—28no—
122C4×D44—22no—
123C4×D44C2314yes—
124C42×D11—28no—
125C42×D11D414yes—
126C42×D11C2314yes—
127#66922—22no—
128#66922C2314yes—
129C11×C4⋊C8C2314yes—
130C11×#102C2318yes—
131#66899C2318yes—
132#66896C2318yes—
133#66885C2318yes—
134(C2×D11)⋊C8C2318yes—
135#66882C2318yes—
136#66879C2318yes—
137#66872C2318yes—
138C4⋊(C11⋊C8)C2314yes—
139C2×#3115—111nomaximal, Sylow
140C24×C11—22no—
141C23×D11—21no—
142C23×D11C2×D411yescharacteristic
143C2×Q8×C11—21no—
144C2×Q8×C11—22no—
145C2×Q8×C11#4114yescomplemented
146C2×Q8×C11C2412yes—
147C2×D4×C11—22no—
148C2×D4×C11—24no—
149C2×D4×C11—24no—
150C2×D4×C11—24no—
151C2×D4×C11—24no—
152C2×D4×C11—44no—
153C2×D4×C11—44no—
154C2×D4×C11C2414yes—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—28no—
161C2×C22⋊D11—48no—
162C22×Dic11—28no—
163C22×Dic11—21no—
164C22×Dic11—22no—
165C22×Dic11—48no—
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169#4343—216no—
170#4343—28no—
171#4343—28no—
172#4341—432no—
173C2×D44—28no—
174C2×D44—24no—
175C2×D44—21no—
176C2×D44—22no—
177C2×D44#4114yescomplemented
178C2×D44C2412yes—
179C2×C4×D11—28no—
180C2×C4×D11—24no—
181C2×C4×D11—24no—
182C2×C4×D11—24no—
183C2×C4×D11—24no—
184C2×C4×D11—22no—
185C2×C4×D11—22no—
186C2×C4×D11—42no—
187C2×C4×D11—44no—
188C2×C4×D11—44no—
189C2×C4×D11C2×D412yes—
190C2×C4×D11C2×D414yes—
191C2×C4×D11C2×D414yes—
192C2×C4×D11C2412yes—
193C2×Dic22—24no—
194C2×Dic22—44no—
195C11×SD16—216no—
196C2×C8×C11—24no—
197C2×C8×C11C2414yes—
198C11×C4⋊C4—24no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4C2412yes—
201C42×C11—24no—
202C42×C11C2×D412yes—
203C42×C11C2412yes—
204C22⋊Dic11—28no—
205C22⋊Dic11—28no—
206#4323—216no—
207(C2×D11)⋊C4—24no—
208(C2×D11)⋊C4—24no—
209(C2×D11)⋊C4—24no—
210C4⋊Dic11—24no—
211C4⋊Dic11—22no—
212C4⋊Dic11—24no—
213C4⋊Dic11—21no—
214C4⋊Dic11C2414yes—
215C4⋊Dic11C2412yes—
216C4×Dic11—24no—
217C4×Dic11—24no—
218C4×Dic11C2×D414yes—
219C4×Dic11C2×D412yes—
220C4×Dic11C2×D414yes—
221C4×Dic11C2412yes—
222C2×C11⋊C8—24no—
223C2×C11⋊C8C2414yes—
224C2×#532—111no—
225C2×C4×#41—111no—
226#3115—1116no—
227C2×#482—112no—
228C2×#475—111no—
229C2×#474—111no—
230C2×#460D1111yescharacteristic, complemented
231C2×#459—111no—
232C2×#449—112no—
233C2×#442—112no—
234C2×#440—112no—
235C2×#432—111no—
236C23×C11—24no—
237C23×C11—44no—
238C23×C11—44no—
239C23×C11—44no—
240C23×C11C22×D411yescharacteristic
241C22×D11—22no—
242C22×D11—24no—
243C22×D11—22no—
244C22×D11—22no—
245C22×D11—22no—
246C22×D11—42no—
247C22×D11—42no—
248C22×D11C22×D412yes—
249Q8×C11—24no—
250Q8×C11—22no—
251Q8×C11C2×#4114yescomplemented
252D4×C11—24no—
253D4×C11—24no—
254D4×C11—48no—
255D4×C11—44no—
256D4×C11—48no—
257C2×C4×C11—24no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—42no—
262C2×C4×C11AGL(1,ℤ/8)14yes—
263C2×C4×C11C22×D412yes—
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×D412yes—
266C2×C4×C11C2×#4112yes—
267C2×C4×C11C2×#4112yes—
268C2×C4×C11C2511yescharacteristic
269C22⋊D11—416no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—24no—
275C2×Dic11—416no—
276C2×Dic11—44no—
277C2×Dic11—42no—
278C2×Dic11C22×D412yes—
279C2×Dic11C22×D412yes—
280C2×Dic11C22×D412yes—
281D44—216no—
282D44—24no—
283D44—22no—
284D44C2×#4114yescomplemented
285C4×D11—216no—
286C4×D11—24no—
287C4×D11—28no—
288C4×D11—22no—
289C4×D11—22no—
290C4×D11—44no—
291C4×D11—48no—
292C4×D11—48no—
293Dic22—48no—
294C8×C11—24no—
295C11⋊C8—24no—
296C22×#41—111no—
297C22×#41—221no—
298C22×SD16C2×D1112yes—
299C22×D8—112no—
300#532—118no—
301#532—224no—
302C2×C4⋊Q8—111no—
303C2×#127C2×D1111yescharacteristic
304C2×#124—221no—
305C2×#121—112no—
306C2×#121—221no—
307C4×#41—118no—
308C4×#41—224no—
309C2×C4×Q8—111no—
310C2×C4×Q8C2×D1111yescharacteristic
311C2×C4×D4—112no—
312C2×C4×D4—111no—
313C2×C4×D4—111no—
314C2×C4×D4—221no—
315C2×C4×D4—221no—
316C2×C4×D4—221no—
317C2×#117—111no—
318C2×#117—221no—
319C22×C42—111no—
320C22×C42—221no—
321#482—1116no—
322#475—118no—
323#474—118no—
324#460C2×D1118yescomplemented
325#459—118no—
326#449—1116no—
327#442—1116no—
328#440—1116no—
329#432—118no—
330C2×#107—112no—
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—44no—
341C22×C11—44no—
342C22×C11—44no—
343C22×C11—88no—
344C22×C11#52512yes—
345C22×C11C2×AGL(1,ℤ/8)12yes—
346C22×C11#57512yes—
347C22×C11C23×D411yescharacteristic
348C2×D11—24no—
349C2×D11—22no—
350C2×D11—22no—
351C2×D11—22no—
352C2×D11—44no—
353C2×D11—48no—
354C2×D11—42no—
355C2×D11—42no—
356C4×C11—24no—
357C4×C11—22no—
358C4×C11—42no—
359C4×C11#52512yes—
360C4×C11C2×AGL(1,ℤ/8)14yes—
361C4×C11C22×#4111yescharacteristic
362C4×C11C22×#4111yescharacteristic
363Dic11—22no—
364Dic11—22no—
365Dic11—22no—
366Dic11—44no—
367Dic11—42no—
368C2×#41—114no—
369C2×#41—228no—
370C2×#41—222no—
371C2×#41—224no—
372C2×#41—224no—
373C2×#41—448no—
374C22×Q8—221no—
375C22×Q8C22×D1111yescharacteristic
376C22×D4—21no—
377C22×D4—21no—
378C22×D4—111no—
379C22×D4—221no—
380C22×D4—222no—
381C22×D4C22×D1112yes—
382C23×C4—111no—
383C23×C4—111no—
384C23×C4—111no—
385C23×C4—221no—
386C23×C4—221no—
387C23×C4—222no—
388C23×C4—221no—
389C2×SD16—28no—
390C2×SD16C22×D1118yes—
391C2×D8—118no—
392C2×D8—228no—
393C22×C8—112no—
394C22×C8C22×D1112yes—
395C4⋊Q8—114no—
396C4⋊Q8—222no—
397#127—22no—
398#127C22×D1114yes—
399#124—228no—
400#121—118no—
401#121—224no—
402#121—228no—
403C4×Q8—22no—
404C4×Q8—114no—
405C4×Q8—222no—
406C4×Q8C22×D1114yes—
407C4×D4—118no—
408C4×D4—114no—
409C4×D4—114no—
410C4×D4—228no—
411C4×D4—222no—
412C4×D4—224no—
413C4×D4—228no—
414C4×D4—228no—
415C4×D4—222no—
416#117—114no—
417#117—228no—
418#117—222no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—112no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4C22×D1111yescharacteristic
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—222no—
428C2×C22⋊C4—222no—
429C2×C22⋊C4—221no—
430C2×C42—21no—
431C2×C42—111no—
432C2×C42—111no—
433C2×C42—111no—
434C2×C42—114no—
435C2×C42—114no—
436C2×C42—228no—
437C2×C42—221no—
438C2×C42—221no—
439C2×C42C22×D1111yescharacteristic
440#107—118no—
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—84no—
451C2×C11#311514yescomplemented
452C2×C11C2×#52511yescharacteristic
453C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
454C2×C11C2×#57511yescharacteristic
455D11—42no—
456D11—44no—
457C24—22no—
458C24—111no—
459C24—221no—
460#41—228no—
461#41—2216no—
462#41—228no—
463#41—4432no—
464C2×Q8—21no—
465C2×Q8—22no—
466C2×Q8—224no—
467C2×Q8—444no—
468C2×Q8#434114yescomplemented
469C2×Q8C23×D1112yes—
470C2×D4—22no—
471C2×D4—24no—
472C2×D4—24no—
473C2×D4—24no—
474C2×D4—24no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—114no—
478C2×D4—112no—
479C2×D4—224no—
480C2×D4—228no—
481C2×D4—228no—
482C2×D4—221no—
483C2×D4—222no—
484C2×D4—448no—
485C2×D4C23×D1114yes—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—111no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—112no—
492C22×C4—114no—
493C22×C4—112no—
494C22×C4—114no—
495C22×C4—224no—
496C22×C4—224no—
497C22×C4—228no—
498C22×C4—228no—
499C22×C4—224no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—221no—
503C22×C4—222no—
504C22×C4—224no—
505C22×C4—442no—
506C22×C4—444no—
507C22×C4—448no—
508C22×C4—444no—
509C22×C4D4×D1111yescharacteristic
510C22×C4D4×D1111yescharacteristic
511C22×C4C23×D1111yescharacteristic
512SD16—216no—
513D8—2216no—
514C2×C8—24no—
515C2×C8—114no—
516C2×C8—224no—
517C2×C8C23×D1114yes—
518C4⋊C4—24no—
519C4⋊C4—21no—
520C4⋊C4—112no—
521C4⋊C4—114no—
522C4⋊C4—224no—
523C4⋊C4—221no—
524C4⋊C4—222no—
525C4⋊C4—224no—
526C4⋊C4C23×D1112yes—
527C22⋊C4—224no—
528C22⋊C4—224no—
529C22⋊C4—228no—
530C22⋊C4—228no—
531C22⋊C4—224no—
532C42—24no—
533C42—114no—
534C42—114no—
535C42—112no—
536C42—112no—
537C42—224no—
538C42—224no—
539C42D4×D1112yes—
540C42C23×D1112yes—
541C11C2×#311511yescharacteristic, complemented, Sylow
542C23—24no—
543C23—44no—
544C23—44no—
545C23—44no—
546C23—112no—
547C23—222no—
548C23—222no—
549C23—224no—
550C23—222no—
551C23—222no—
552C23—442no—
553C23—442no—
554C23C2×D4×D1111yescharacteristic
555Q8—24no—
556Q8—22no—
557Q8—448no—
558Q8C2×#434114yescomplemented
559D4—24no—
560D4—24no—
561D4—48no—
562D4—48no—
563D4—44no—
564D4—114no—
565D4—2216no—
566D4—224no—
567D4—222no—
568D4—4416no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—42no—
574C2×C4—112no—
575C2×C4—112no—
576C2×C4—112no—
577C2×C4—2216no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—222no—
581C2×C4—228no—
582C2×C4—224no—
583C2×C4—222no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—224no—
587C2×C4—444no—
588C2×C4—448no—
589C2×C4—4416no—
590C2×C4—444no—
591C2×C4—442no—
592C2×C4—448no—
593C2×C4#6696714yes—
594C2×C4C2×D4×D1112yes—
595C2×C4C2×D4×D1112yes—
596C2×C4C2×D4×D1111yescharacteristic
597C2×C4C2×#434112yes—
598C2×C4#41×D1112yes—
599C2×C4C24×D1111yescharacteristic
600C8—24no—
601C8—224no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—88no—
606C22—224no—
607C22—222no—
608C22—222no—
609C22—222no—
610C22—442no—
611C22—442no—
612C22—444no—
613C22—448no—
614C22#1062313712yes—
615C22C2×#6696712yes—
616C22#1062330412yes—
617C22C22×D4×D1111yescharacteristic
618C4—24no—
619C4—22no—
620C4—42no—
621C4—222no—
622C4—222no—
623C4—222no—
624C4—444no—
625C4—442no—
626C4#1062313712yes—
627C4C2×#6696714yes—
628C4C22×#434111yescharacteristic
629C4C2×#41×D1111yescharacteristic
630C2—84no—
631C2—442no—
632C2—444no—
633C2#1307876614yesdirect product factor
634C2C2×#1062313711yescharacteristic
635C2C22×#6696711yescharacteristic
636C2C2×#1062330411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#460C2
socleC23×C11C22×D4
hypercenterC2×#460D11
hypocenterC11C2×#3115
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C2×#10623247C2semidirect
2. C2×C4×#4343C2semidirect
3. #13078766C2direct (N × H)
4. C2×#10622397C2semidirect
5. C2×#10622633C2semidirect
6. C2×#10622459C2semidirect
7. C2×#10622685C2semidirect
8. C2×#10622785C2semidirect
9. C2×#10622398C2semidirect
10. C2×#10622777C2semidirect
11. C2×#10622448C2semidirect
12. C2×C11×#460C2semidirect
26. #10623247C22semidirect
28. C4×#4343C22semidirect
38. C11×#460C22semidirect
43. #10622785C22semidirect
44. #10622777C22semidirect
49. #10622685C22semidirect
50. #10622633C22semidirect
53. #10622459C22semidirect
54. #10622448C22semidirect
55. #10622398C22semidirect
56. #10622397C22semidirect
145. C2×Q8×C11#41semidirect
177. C2×D44#41semidirect
230. C2×#460D11semidirect
251. Q8×C11C2×#41semidirect
284. D44C2×#41semidirect
324. #460C2×D11semidirect
451. C2×C11#3115semidirect
468. C2×Q8#4341semidirect
541. C11C2×#3115semidirect
558. Q8C2×#4341semidirect
633. C2#13078766direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232472
C2×C4×#43432
#130787662
C2×#106223972
C2×#106226332
C2×#106224592
C2×#106226852
C2×#106227852
C2×#106223982
C2×#106227772
C2×#106224482
C2×C11×#4602
C2×#311511