Finite Group Databasebeta

← C2×#13079929 #15626552

Subgroups — C2×#13079929 #15626552

Order 2816.

2178 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic, complemented
2C2×#10623079C211yesmaximal, characteristic
3#13079929C2116yesmaximal, direct product factor
4C2×#10622404C212yesmaximal, complemented
5C2×#10622455C211yesmaximal, characteristic, complemented
6C2×#10622621C211yesmaximal, characteristic, complemented
7C2×#10622420C212yesmaximal, complemented
8C2×#10622784C212yesmaximal, complemented
9C2×#10622776C212yesmaximal, complemented
10C2×#10622696C211yesmaximal, characteristic, complemented
11C2×D11×C4⋊C8C211yesmaximal, characteristic, complemented
12C2×C11×#461C211yesmaximal, characteristic, complemented
13C22×#4339—21no—
14C22×C11×SD16C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66999C2212yes—
18C2×Q8×Dic11C2212yes—
19C22×#4325C2212yes—
20C2×#66993C2211yescharacteristic
21C2×#66991C2211yescharacteristic
22C2×C4×C22⋊D11—21no—
23C22×C8×D11C2212yes—
24#10623259—24no—
25#10623259C2218yescomplemented
26#10623079—24no—
27#10623079C2218yes—
28C2×#66950—21no—
29C2×#66948C2211yescharacteristic
30C2×#66945—21no—
31C2×#66943—21no—
32C2×#66941C2211yescharacteristic
33C2×#66940—21no—
34C2×#66938—21no—
35C2×#66937—21no—
36C2×C4×D44C2211yescharacteristic
37C2×C42×D11C2211yescharacteristic
38C2×#66922C2211yescharacteristic
39C11×#461C2218yescomplemented
40C2×C11×C4⋊C8C2211yescharacteristic
41C2×C11×#103C2212yes—
42C2×#66899C2212yes—
43C2×#66896C2212yes—
44#10622784C22116yescomplemented
45#10622776C22116yescomplemented
46C2×#66885C2212yes—
47C2×#66881C2212yes—
48C2×Dic11⋊C8C2212yes—
49#10622696C2218yescomplemented
50#10622621C2218yescomplemented
51C2×#66872C2212yes—
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53#10622455C2218yescomplemented
54D11×C4⋊C8C2218yescomplemented
55#10622420C22116yescomplemented
56#10622404C22116yescomplemented
57C22×Q8×C11C2312yes—
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C22×C22⋊D11—21no—
61C22×C22⋊D11—21no—
62C22×C22⋊D11—21no—
63C2×#4339—28no—
64C2×#4339—48no—
65C22×D44—21no—
66C22×D44C2311yescharacteristic
67C22×C4×D11—21no—
68C22×C4×D11D411yescharacteristic
69C22×C4×D11D411yescharacteristic
70C22×C4×D11C2311yescharacteristic
71C22×Dic22—21no—
72C22×Dic22—21no—
73C2×C11×SD16—44no—
74C2×C11×SD16C2318yes—
75C22×C8×C11C2312yes—
76C11×C4⋊Q8—22no—
77C11×C4⋊Q8C2314yes—
78C4×D4×C11—22no—
79C4×D4×C11C2314yes—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C22⋊Dic11—21no—
86#66999—24no—
87#66999C2318yes—
88Q8×Dic11—24no—
89Q8×Dic11C2318yes—
90C2×#4325—44no—
91C2×#4325C2318yes—
92#66993—22no—
93#66993C2314yes—
94#66991—22no—
95#66991C2314yes—
96C4×C22⋊D11—28no—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11C2312yes—
103C2×C4⋊Dic11C2311yescharacteristic
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—22no—
106C2×C4×Dic11—22no—
107C2×C4×Dic11D411yescharacteristic
108C2×C4×Dic11D411yescharacteristic
109C2×C4×Dic11C2311yescharacteristic
110C22×C11⋊C8C2312yes—
111C2×C8×D11—44no—
112C2×C8×D11C2318yes—
113#66950—28no—
114#66948—22no—
115#66948C2314yes—
116#66945—28no—
117#66943—28no—
118#66941—22no—
119#66941C2314yes—
120#66940—28no—
121#66938—28no—
122#66937—28no—
123C4×D44—22no—
124C4×D44C2314yes—
125C42×D11D414yes—
126C42×D11C2314yes—
127#66922—22no—
128#66922C2314yes—
129C11×C4⋊C8C2314yes—
130C11×#103C2318yes—
131#66899C2318yes—
132#66896C2318yes—
133#66885C2318yes—
134#66881C2318yes—
135Dic11⋊C8C2318yes—
136#66872C2318yes—
137C4⋊(C11⋊C8)C2314yes—
138C2×#3246—111nomaximal, Sylow
139C24×C11—21no—
140C23×D11—21no—
141C23×D11C2×D411yescharacteristic
142C2×Q8×C11—22no—
143C2×Q8×C11—24no—
144C2×Q8×C11—24no—
145C2×Q8×C11C2414yes—
146C2×D4×C11—21no—
147C2×D4×C11—22no—
148C2×D4×C11—22no—
149C2×D4×C11C2412yes—
150C22×C4×C11—22no—
151C22×C4×C11—21no—
152C22×C4×C11—24no—
153C22×C4×C11—44no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—24no—
158C2×C22⋊D11—24no—
159C2×C22⋊D11—24no—
160C2×C22⋊D11—44no—
161C2×C22⋊D11—44no—
162C2×C22⋊D11—44no—
163C22×Dic11—22no—
164C22×Dic11—21no—
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168#4339—432no—
169C2×D44—24no—
170C2×D44—21no—
171C2×D44—22no—
172C2×D44—22no—
173C2×D44—44no—
174C2×D44C2412yes—
175C2×C4×D11—24no—
176C2×C4×D11—22no—
177C2×C4×D11—22no—
178C2×C4×D11—42no—
179C2×C4×D11—44no—
180C2×C4×D11SD1618yescomplemented
181C2×C4×D11C2×D412yes—
182C2×C4×D11C2×D414yes—
183C2×C4×D11C2×D414yes—
184C2×C4×D11C2412yes—
185C2×Dic22—24no—
186C2×Dic22—24no—
187C2×Dic22—44no—
188C2×Dic22—44no—
189C11×SD16—48no—
190C2×C8×C11—24no—
191C2×C8×C11C2414yes—
192C11×C4⋊C4—24no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—24no—
195C11×C4⋊C4C2412yes—
196C11×C22⋊C4—24no—
197C42×C11C2×D412yes—
198C42×C11C2412yes—
199C22⋊Dic11—24no—
200#4325—48no—
201(C2×D11)⋊C4—24no—
202(C2×D11)⋊C4—28no—
203(C2×D11)⋊C4—24no—
204C4⋊Dic11—28no—
205C4⋊Dic11—22no—
206C4⋊Dic11—24no—
207C4⋊Dic11—21no—
208C4⋊Dic11C2414yes—
209C4⋊Dic11C2412yes—
210Dic11⋊C4—24no—
211Dic11⋊C4—28no—
212C4×Dic11—28no—
213C4×Dic11C2×D412yes—
214C4×Dic11C2×D414yes—
215C4×Dic11C2×D414yes—
216C4×Dic11C2412yes—
217C2×C11⋊C8—24no—
218C2×C11⋊C8C2414yes—
219C8×D11—48no—
220C2×#533—111no—
221C2×#532—111no—
222#3246—1116no—
223C2×#475—112no—
224C2×#476—111no—
225C2×#476—111no—
226C2×#465—112no—
227C2×#465—112no—
228C2×#460—112no—
229C2×#461—111no—
230C2×#461D1111yescharacteristic, complemented
231C22×C4⋊C8—111no—
232C23×C11—22no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11C22×D411yescharacteristic
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—42no—
241C22×D11—42no—
242C22×D11—42no—
243C22×D11C2×SD1614yes—
244C22×D11C22×D412yes—
245Q8×C11—24no—
246Q8×C11—24no—
247Q8×C11—44no—
248D4×C11—22no—
249D4×C11—22no—
250D4×C11—42no—
251C2×C4×C11—22no—
252C2×C4×C11—24no—
253C2×C4×C11—22no—
254C2×C4×C11—44no—
255C2×C4×C11—42no—
256C2×C4×C11—48no—
257C2×C4×C11C2×SD1614yes—
258C2×C4×C11C22×D412yes—
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D412yes—
261C2×C4×C11H(5,𝔽2)12yes—
262C2×C4×C112−1+412yes—
263C2×C4×C11C2511yescharacteristic
264C22⋊D11—48no—
265C22⋊D11—48no—
266C22⋊D11—48no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—24no—
270C2×Dic11—22no—
271C2×Dic11—42no—
272C2×Dic11—44no—
273C2×Dic11C2×SD1614yes—
274C2×Dic11C22×D412yes—
275C2×Dic11C22×D412yes—
276C2×Dic11C22×D412yes—
277D44—22no—
278D44—22no—
279D44—48no—
280D44—42no—
281C4×D11—24no—
282C4×D11—22no—
283C4×D11—22no—
284C4×D11—44no—
285C4×D11—48no—
286C4×D11C2×SD16116yescomplemented
287Dic22—48no—
288Dic22—48no—
289C8×C11—24no—
290C11⋊C8—24no—
291C22×#41—221no—
292C22×SD16—112no—
293C22×SD16C2×D1112yes—
294C23×C8—112no—
295#533—118no—
296#533—224no—
297#532—118no—
298#532—224no—
299C2×C4⋊Q8—111no—
300C2×C4⋊Q8—111no—
301C2×C4⋊Q8C2×D1111yescharacteristic
302C2×#127—111no—
303C2×#125—221no—
304C2×#124—221no—
305C2×C22⋊Q8—112no—
306C2×C22⋊Q8—221no—
307C2×#121—111no—
308C2×#121—111no—
309C2×#121—221no—
310C2×C4×Q8—112no—
311C2×C4×Q8—221no—
312C2×C4×D4—111no—
313C2×C4×D4—221no—
314C2×C4×D4C2×D1111yescharacteristic
315C2×#117—221no—
316C22×C42—111no—
317#476—118no—
318#476—118no—
319#475—1116no—
320#465—1116no—
321#465—1116no—
322#461—118no—
323#461C2×D1118yescomplemented
324#460—1116no—
325C2×#106—112no—
326C2×#106—112no—
327C2×C4⋊C8—112no—
328C2×C4⋊C8—111no—
329C2×C4⋊C8—118no—
330C2×C4⋊C8C2×D1111yescharacteristic
331C2×#103—112no—
332C2×#103C2×D1112yes—
333C2×#102—112no—
334C2×#102—112no—
335C22×C11—42no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—84no—
339C22×C11#53712yes—
340C22×C11C22×SD1612yes—
341C22×C11#57512yes—
342C22×C11C23×D411yescharacteristic
343C2×D11—22no—
344C2×D11—28no—
345C2×D11—22no—
346C2×D11—42no—
347C2×D11—42no—
348C2×D11—42no—
349C2×D11—84no—
350C2×D11C22×SD1614yes—
351C4×C11—22no—
352C4×C11—44no—
353C4×C11—42no—
354C4×C11#53712yes—
355C4×C11C22×SD1614yes—
356C4×C11C2×H(5,𝔽2)11yescharacteristic
357C4×C11C2×2−1+411yescharacteristic
358Dic11—22no—
359Dic11—22no—
360Dic11—42no—
361Dic11—44no—
362Dic11C22×SD1614yes—
363C2×#41—228no—
364C2×#41—448no—
365C22×Q8—221no—
366C22×Q8—221no—
367C22×Q8C22×D1112yes—
368C22×D4—111no—
369C22×D4—221no—
370C22×D4—221no—
371C22×D4—221no—
372C22×D4—221no—
373C22×D4C22×D1111yescharacteristic
374C23×C4—21no—
375C23×C4—111no—
376C23×C4—111no—
377C23×C4—111no—
378C23×C4—221no—
379C2×SD16—44no—
380C2×SD16—118no—
381C2×SD16—444no—
382C2×SD16C22×D1118yes—
383C22×C8—112no—
384C22×C8—118no—
385C22×C8—444no—
386C22×C8C22×D1112yes—
387C4⋊Q8—22no—
388C4⋊Q8—114no—
389C4⋊Q8—114no—
390C4⋊Q8—222no—
391C4⋊Q8—222no—
392C4⋊Q8C22×D1114yes—
393#127—114no—
394#127—222no—
395#125—228no—
396#124—228no—
397C22⋊Q8—118no—
398C22⋊Q8—228no—
399C22⋊Q8—224no—
400#121—114no—
401#121—114no—
402#121—228no—
403#121—222no—
404#121—222no—
405C4×Q8—118no—
406C4×Q8—228no—
407C4×Q8—224no—
408C4×D4—22no—
409C4×D4—114no—
410C4×D4—228no—
411C4×D4—222no—
412C4×D4C22×D1114yes—
413#117—228no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—112no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—222no—
420C2×C4⋊C4—222no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—222no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C42—111no—
429C2×C42—111no—
430C2×C42—111no—
431C2×C42—114no—
432C2×C42—114no—
433C2×C42—222no—
434C2×C42C22×D1111yescharacteristic
435#106—118no—
436#106—118no—
437C4⋊C8—118no—
438C4⋊C8—114no—
439C4⋊C8C22×D1114yes—
440#103—118no—
441#103C22×D1118yes—
442#102—118no—
443#102—118no—
444C2×C11—82no—
445C2×C11#324614yescomplemented
446C2×C11C2×#53711yescharacteristic
447C2×C11C23×SD1611yescharacteristic
448C2×C11C2×#57511yescharacteristic
449D11—24no—
450D11—82no—
451C24—21no—
452C24—111no—
453C24—221no—
454#41—4432no—
455C2×Q8—22no—
456C2×Q8—24no—
457C2×Q8—24no—
458C2×Q8—224no—
459C2×Q8—224no—
460C2×Q8—444no—
461C2×Q8—444no—
462C2×Q8C23×D1114yes—
463C2×D4—21no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—112no—
467C2×D4—224no—
468C2×D4—224no—
469C2×D4—224no—
470C2×D4—224no—
471C2×D4—221no—
472C2×D4—222no—
473C2×D4—222no—
474C2×D4—444no—
475C2×D4—444no—
476C2×D4—444no—
477C2×D4—444no—
478C2×D4C23×D1112yes—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—24no—
482C22×C4—44no—
483C22×C4—111no—
484C22×C4—118no—
485C22×C4—114no—
486C22×C4—111no—
487C22×C4—111no—
488C22×C4—112no—
489C22×C4—112no—
490C22×C4—114no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—221no—
495C22×C4—224no—
496C22×C4—442no—
497C22×C4—444no—
498C22×C4D4×D1111yescharacteristic
499C22×C4D4×D1111yescharacteristic
500C22×C4C23×D1111yescharacteristic
501SD16—48no—
502SD16—448no—
503C2×C8—24no—
504C2×C8—114no—
505C2×C8—224no—
506C2×C8—448no—
507C2×C8C23×D1114yes—
508C4⋊C4—24no—
509C4⋊C4—24no—
510C4⋊C4—21no—
511C4⋊C4—114no—
512C4⋊C4—112no—
513C4⋊C4—224no—
514C4⋊C4—228no—
515C4⋊C4—228no—
516C4⋊C4—221no—
517C4⋊C4—222no—
518C4⋊C4—224no—
519C4⋊C4C23×D1112yes—
520C22⋊C4—24no—
521C22⋊C4—224no—
522C22⋊C4—228no—
523C22⋊C4—224no—
524C22⋊C4—224no—
525C42—114no—
526C42—114no—
527C42—112no—
528C42—112no—
529C42—228no—
530C42D4×D1112yes—
531C42C23×D1112yes—
532C11C2×#324611yescharacteristic, complemented, Sylow
533C23—22no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—114no—
538C23—112no—
539C23—222no—
540C23—222no—
541C23—222no—
542C23—442no—
543C23—442no—
544C23—442no—
545C23C2×D4×D1111yescharacteristic
546Q8—24no—
547Q8—24no—
548Q8—44no—
549Q8—448no—
550Q8—448no—
551D4—22no—
552D4—22no—
553D4—42no—
554D4—222no—
555D4—222no—
556D4—448no—
557D4—448no—
558D4—448no—
559D4—448no—
560D4—442no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—42no—
565C2×C4—44no—
566C2×C4—48no—
567C2×C4—114no—
568C2×C4—112no—
569C2×C4—1116no—
570C2×C4—112no—
571C2×C4—112no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—224no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—224no—
578C2×C4—222no—
579C2×C4—444no—
580C2×C4—442no—
581C2×C4—444no—
582C2×C4—448no—
583C2×C4SD16×D1114yes—
584C2×C4C2×D4×D1112yes—
585C2×C4C2×D4×D1112yes—
586C2×C4C2×D4×D1111yescharacteristic
587C2×C4#6703712yes—
588C2×C4#6704312yes—
589C2×C4C24×D1111yescharacteristic
590C8—24no—
591C8—224no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—84no—
596C22—114no—
597C22—222no—
598C22—228no—
599C22—222no—
600C22—442no—
601C22—442no—
602C22—442no—
603C22—884no—
604C22#1062313912yes—
605C22C2×SD16×D1112yes—
606C22#1062330812yes—
607C22C22×D4×D1111yescharacteristic
608C4—22no—
609C4—44no—
610C4—42no—
611C4—114no—
612C4—222no—
613C4—222no—
614C4—442no—
615C4—444no—
616C4#1062313912yes—
617C4C2×SD16×D1114yes—
618C4C2×#6703711yescharacteristic
619C4C2×#6704311yescharacteristic
620C2—82no—
621C2—224no—
622C2—882no—
623C2#1307992914yesdirect product factor
624C2C2×#1062313911yescharacteristic
625C2C22×SD16×D1111yescharacteristic
626C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#461C2
socleC23×C11C22×D4
prime radicalC2×#10623079C2
hypercenterC2×#461D11
hypocenterC11C2×#3246
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#10623259C2semidirect
3. #13079929C2direct (N × H)
4. C2×#10622404C2semidirect
5. C2×#10622455C2semidirect
6. C2×#10622621C2semidirect
7. C2×#10622420C2semidirect
8. C2×#10622784C2semidirect
9. C2×#10622776C2semidirect
10. C2×#10622696C2semidirect
11. C2×D11×C4⋊C8C2semidirect
12. C2×C11×#461C2semidirect
25. #10623259C22semidirect
39. C11×#461C22semidirect
44. #10622784C22semidirect
45. #10622776C22semidirect
49. #10622696C22semidirect
50. #10622621C22semidirect
53. #10622455C22semidirect
54. D11×C4⋊C8C22semidirect
55. #10622420C22semidirect
56. #10622404C22semidirect
180. C2×C4×D11SD16semidirect
230. C2×#461D11semidirect
286. C4×D11C2×SD16semidirect
323. #461C2×D11semidirect
445. C2×C11#3246semidirect
532. C11C2×#3246semidirect
623. C2#13079929direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106230792
#130799292
C2×#106224042
C2×#106224552
C2×#106226212
C2×#106224202
C2×#106227842
C2×#106227762
C2×#106226962
C2×D11×C4⋊C82
C2×C11×#4612
C2×#324611