Finite Group Databasebeta

← C2×#13079592 #15624993

Subgroups — C2×#13079592 #15624993

Order 2816.

2218 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623010C211yesmaximal, characteristic, complemented
2#13079592C2116yesmaximal, direct product factor
3C2×#10622672C212yesmaximal, complemented
4C2×#10622669C212yesmaximal, complemented
5C2×#10622703C211yesmaximal, characteristic, complemented
6C2×#10622688C211yesmaximal, characteristic, complemented
7C2×#10622696C211yesmaximal, characteristic, complemented
8C2×#10622685C211yesmaximal, characteristic, complemented
9C2×#10622852C212yesmaximal, complemented
10C2×#10622851C212yesmaximal, complemented
11C2×#10622538C211yesmaximal, characteristic, complemented
12C2×C11×#532C211yesmaximal, characteristic, complemented
13C22×C11×#41C2212yes—
14C11×#532—24no—
15C11×#532C2218yescomplemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#127C2211yescharacteristic
18C2×C11×#124C2212yes—
19C2×C11×#121—21no—
20C2×C11×#121—21no—
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11—21no—
23C22×C42×C11C2211yescharacteristic
24C22×#4326C2212yes—
25C22×#4325C2212yes—
26C22×#4324C2212yes—
27C22×#4323C2212yes—
28C2×#66983C2211yescharacteristic
29C2×#66982—21no—
30C2×C4×C22⋊D11—21no—
31C2×#66977C2211yescharacteristic
32#10623010—24no—
33#10623010C2218yescomplemented
34C2×#66929—21no—
35C2×#66928C2211yescharacteristic
36C2×C4×D44C2211yescharacteristic
37C2×#66925—21no—
38C2×#66923C2211yescharacteristic
39C2×C4×Dic22C2211yescharacteristic
40#10622852C22116yescomplemented
41#10622851C22116yescomplemented
42C2×#66899C2212yes—
43C2×#66899C2212yes—
44C2×#66896C2212yes—
45C2×#66896C2212yes—
46C2×C22⋊(C11⋊C8)C2212yes—
47#10622703C2218yescomplemented
48#10622696C2218yescomplemented
49#10622688C2218yescomplemented
50#10622685C2218yescomplemented
51#10622672C22116yescomplemented
52#10622669C22116yescomplemented
53#10622538C2218yescomplemented
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4×C11⋊C8C2212yes—
57C2×C11×#41—24no—
58C2×C11×#41—44no—
59C2×C11×#41—44no—
60C2×C11×#41C2318yes—
61C22×Q8×C11C2312yes—
62C22×D4×C11—22no—
63C22×D4×C11—21no—
64C22×D4×C11—21no—
65C22×D4×C11C2312yes—
66C23×C4×C11—22no—
67C23×C4×C11D411yescharacteristic
68C23×C4×C11D411yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C22×C22⋊D11—21no—
71C22×D44C2311yescharacteristic
72C22×C4×D11—21no—
73C22×Dic22C2311yescharacteristic
74C11×C4⋊Q8—22no—
75C11×C4⋊Q8C2314yes—
76C11×#127—22no—
77C11×#127C2314yes—
78C11×#124—24no—
79C11×#124C2318yes—
80C11×#121—28no—
81C11×#121—28no—
82C4×D4×C11—28no—
83C4×D4×C11—28no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C42×C11D411yescharacteristic
89C2×C42×C11D411yescharacteristic
90C2×C42×C11D414yes—
91C2×C42×C11C2311yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C2×C42×C11C2314yes—
94C2×C22⋊Dic11—21no—
95C2×#4326—44no—
96C2×#4326C2318yes—
97C2×#4325—44no—
98C2×#4325C2318yes—
99C2×#4324—44no—
100C2×#4324C2318yes—
101C2×#4323—44no—
102C2×#4323C2318yes—
103#66983—22no—
104#66983C2314yes—
105#66982—28no—
106C4×C22⋊D11—28no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4⋊Dic11C2311yescharacteristic
113#66977—22no—
114#66977C2314yes—
115C2×Dic11⋊C4—21no—
116C2×Dic11⋊C4—21no—
117C2×Dic11⋊C4—21no—
118C2×Dic11⋊C4—21no—
119C2×C4×Dic11—21no—
120C22×C11⋊C8C2312yes—
121C22×C11⋊C8C2312yes—
122#66929—28no—
123#66928—22no—
124#66928C2314yes—
125C4×D44—22no—
126C4×D44C2314yes—
127#66925—28no—
128#66923—22no—
129#66923C2314yes—
130C4×Dic22—22no—
131C4×Dic22C2314yes—
132#66899C2318yes—
133#66899C2318yes—
134#66896C2318yes—
135#66896C2318yes—
136C22⋊(C11⋊C8)C2318yes—
137C4⋊(C11⋊C8)C2314yes—
138C4⋊(C11⋊C8)C2314yes—
139C4×C11⋊C8C2318yes—
140C2×#3212—111nomaximal, Sylow
141C24×C11—22no—
142C24×C11C2×D411yescharacteristic
143C23×D11—21no—
144C11×#41—48no—
145C11×#41—48no—
146C11×#41—416no—
147C2×Q8×C11—22no—
148C2×Q8×C11—24no—
149C2×Q8×C11—24no—
150C2×Q8×C11C2414yes—
151C2×D4×C11—28no—
152C2×D4×C11—24no—
153C2×D4×C11—24no—
154C2×D4×C11—22no—
155C2×D4×C11—24no—
156C2×D4×C11—24no—
157C2×D4×C11—44no—
158C2×D4×C11—48no—
159C2×D4×C11—44no—
160C2×D4×C11C2414yes—
161C22×C4×C11—24no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—28no—
166C22×C4×C11—42no—
167C22×C4×C11—48no—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2×D414yes—
174C22×C4×C11C2×D414yes—
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2412yes—
177C22×C4×C11C2411yescharacteristic
178C2×C22⋊D11—24no—
179C2×C22⋊D11—44no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C2×D44—21no—
184C2×D44—22no—
185C2×D44—22no—
186C2×D44C2412yes—
187C2×C4×D11—24no—
188C2×C4×D11—44no—
189C2×Dic22—21no—
190C2×Dic22—22no—
191C2×Dic22—22no—
192C2×Dic22C2412yes—
193C11×C4⋊C4—24no—
194C11×C4⋊C4—24no—
195C11×C22⋊C4—28no—
196C11×C22⋊C4—28no—
197C42×C11C2×D412yes—
198C42×C11C2×D412yes—
199C42×C11C2×D414yes—
200C42×C11C2×D414yes—
201C42×C11C2412yes—
202C42×C11C2412yes—
203C22⋊Dic11—24no—
204#4326—48no—
205#4325—48no—
206#4324—48no—
207#4323—48no—
208(C2×D11)⋊C4—24no—
209(C2×D11)⋊C4—24no—
210(C2×D11)⋊C4—24no—
211(C2×D11)⋊C4—24no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11C2412yes—
215C4⋊Dic11C2412yes—
216Dic11⋊C4—24no—
217Dic11⋊C4—24no—
218Dic11⋊C4—24no—
219Dic11⋊C4—24no—
220C4×Dic11—24no—
221C2×C11⋊C8—24no—
222C2×C11⋊C8—24no—
223C2×C11⋊C8C2414yes—
224C2×C11⋊C8C2414yes—
225C2×#532D1111yescharacteristic, complemented
226C2×#529—111no—
227#3212—1116no—
228C2×#495—112no—
229C2×#488—112no—
230C2×#462—111no—
231C2×#460—111no—
232C2×#461—111no—
233C2×#459—111no—
234C2×#452—112no—
235C2×#449—112no—
236C2×#431—111no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—22no—
240C23×C11—24no—
241C23×C11—44no—
242C23×C11—44no—
243C23×C11—44no—
244C23×C11C22×D412yes—
245C23×C11C22×D411yescharacteristic
246C22×D11—22no—
247C22×D11—42no—
248C22×D11—42no—
249C22×D11—42no—
250Q8×C11—24no—
251Q8×C11—24no—
252Q8×C11—44no—
253D4×C11—24no—
254D4×C11—24no—
255D4×C11—48no—
256D4×C11—416no—
257D4×C11—44no—
258D4×C11—48no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—24no—
264C2×C4×C11—28no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—24no—
268C2×C4×C11—44no—
269C2×C4×C11—416no—
270C2×C4×C11—44no—
271C2×C4×C11#13514yes—
272C2×C4×C11C22×D412yes—
273C2×C4×C11C22×D412yes—
274C2×C4×C11C22×D412yes—
275C2×C4×C11C22×D412yes—
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C22×D412yes—
278C2×C4×C11H(5,𝔽2)12yes—
279C2×C4×C11H(5,𝔽2)12yes—
280C2×C4×C11C2511yescharacteristic
281C22⋊D11—48no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287C2×Dic11—42no—
288D44—22no—
289D44—22no—
290D44—42no—
291C4×D11—48no—
292Dic22—22no—
293Dic22—22no—
294Dic22—42no—
295C11⋊C8—24no—
296C11⋊C8—24no—
297C22×#41C2×D1112yes—
298C22×Q16—112no—
299C22×SD16—112no—
300C22×SD16—112no—
301C22×D8—112no—
302#532—24no—
303#532C2×D1118yescomplemented
304C2×C4⋊Q8C2×D1111yescharacteristic
305C2×#127C2×D1111yescharacteristic
306#529—118no—
307#529—224no—
308C2×#126—221no—
309C2×#125—111no—
310C2×#124—111no—
311C2×#124C2×D1112yes—
312C2×#123—221no—
313C2×C22⋊Q8—111no—
314C2×#121—21no—
315C2×#121—21no—
316C2×#121—111no—
317C2×C4×Q8—111no—
318C2×C4×D4—21no—
319C2×C4×D4—21no—
320C2×C4×D4—111no—
321C2×C4×D4—221no—
322C2×#117—221no—
323C22×C42C2×D1111yescharacteristic
324#495—1116no—
325#488—1116no—
326#462—118no—
327#461—118no—
328#460—118no—
329#459—118no—
330#452—1116no—
331#449—1116no—
332#431—118no—
333C2×C4⋊C8—111no—
334C2×C4⋊C8—111no—
335C2×#103—112no—
336C2×#103—112no—
337C2×#102—112no—
338C2×#102—112no—
339C2×C22⋊C8—112no—
340C2×C4×C8—112no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11—44no—
345C22×C11—44no—
346C22×C11—44no—
347C22×C11—44no—
348C22×C11—88no—
349C22×C11#53512yes—
350C22×C11C2×#13512yes—
351C22×C11#57512yes—
352C22×C11C23×D411yescharacteristic
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—42no—
356C2×D11—84no—
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—22no—
360C4×C11—22no—
361C4×C11—44no—
362C4×C11#53512yes—
363C4×C11C2×#13514yes—
364C4×C11C2×H(5,𝔽2)11yescharacteristic
365C4×C11C2×H(5,𝔽2)11yescharacteristic
366Dic11—42no—
367Dic11—42no—
368Dic11—42no—
369C2×#41—24no—
370C2×#41—44no—
371C2×#41—44no—
372C2×#41C22×D1118yes—
373C22×Q8—111no—
374C22×Q8C22×D1112yes—
375C22×D4—22no—
376C22×D4—21no—
377C22×D4—21no—
378C22×D4—111no—
379C22×D4—221no—
380C22×D4C22×D1112yes—
381C23×C4—22no—
382C23×C4—221no—
383C23×C4C22⋊D1111yescharacteristic
384C23×C4C22⋊D1111yescharacteristic
385C23×C4C22×D1111yescharacteristic
386C2×Q16—118no—
387C2×Q16—444no—
388C2×SD16—118no—
389C2×SD16—118no—
390C2×SD16—444no—
391C2×SD16—444no—
392C2×D8—118no—
393C2×D8—444no—
394C22×C8—112no—
395C22×C8—112no—
396C4⋊Q8—22no—
397C4⋊Q8C22×D1114yes—
398#127—22no—
399#127C22×D1114yes—
400#126—228no—
401#125—114no—
402#125—222no—
403#124—24no—
404#124—114no—
405#124—222no—
406#124C22×D1118yes—
407#123—228no—
408C22⋊Q8—114no—
409C22⋊Q8—222no—
410#121—28no—
411#121—28no—
412#121—114no—
413#121—222no—
414C4×Q8—114no—
415C4×Q8—222no—
416C4×D4—28no—
417C4×D4—28no—
418C4×D4—114no—
419C4×D4—228no—
420C4×D4—222no—
421#117—228no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C42—221no—
438C2×C42C22⋊D1111yescharacteristic
439C2×C42C22⋊D1111yescharacteristic
440C2×C42C22⋊D1114yes—
441C2×C42C22×D1111yescharacteristic
442C2×C42C22×D1111yescharacteristic
443C2×C42C22×D1114yes—
444C4⋊C8—114no—
445C4⋊C8—114no—
446#103—118no—
447#103—118no—
448#102—118no—
449#102—118no—
450C22⋊C8—118no—
451C4×C8—118no—
452C2×C11—42no—
453C2×C11—84no—
454C2×C11#321214yescomplemented
455C2×C11C2×#53511yescharacteristic
456C2×C11C22×#13511yescharacteristic
457C2×C11C2×#57511yescharacteristic
458D11—82no—
459C24—22no—
460C24—221no—
461C24C2×C22⋊D1111yescharacteristic
462#41—48no—
463#41—48no—
464#41—416no—
465C2×Q8—22no—
466C2×Q8—24no—
467C2×Q8—24no—
468C2×Q8—112no—
469C2×Q8—221no—
470C2×Q8—222no—
471C2×Q8—222no—
472C2×Q8C23×D1114yes—
473C2×D4—28no—
474C2×D4—24no—
475C2×D4—24no—
476C2×D4—24no—
477C2×D4—24no—
478C2×D4—22no—
479C2×D4—44no—
480C2×D4—48no—
481C2×D4—44no—
482C2×D4—112no—
483C2×D4—224no—
484C2×D4—222no—
485C2×D4—222no—
486C2×D4—221no—
487C2×D4—444no—
488C2×D4C23×D1114yes—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—28no—
494C22×C4—42no—
495C22×C4—48no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—224no—
500C22×C4—444no—
501C22×C4C2×C22⋊D1114yes—
502C22×C4C2×C22⋊D1112yes—
503C22×C4C2×C22⋊D1111yescharacteristic
504C22×C4C2×C22⋊D1111yescharacteristic
505C22×C4C2×C22⋊D1111yescharacteristic
506C22×C4C2×C22⋊D1111yescharacteristic
507C22×C4C2×C22⋊D1114yes—
508C22×C4C2×C22⋊D1111yescharacteristic
509C22×C4C23×D1112yes—
510C22×C4C23×D1111yescharacteristic
511Q16—448no—
512SD16—448no—
513SD16—448no—
514D8—448no—
515C2×C8—114no—
516C2×C8—114no—
517C2×C8—224no—
518C2×C8—224no—
519C4⋊C4—24no—
520C4⋊C4—24no—
521C4⋊C4—112no—
522C4⋊C4—112no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—224no—
526C4⋊C4—224no—
527C4⋊C4—224no—
528C4⋊C4—224no—
529C22⋊C4—28no—
530C22⋊C4—28no—
531C22⋊C4—224no—
532C22⋊C4—224no—
533C22⋊C4—224no—
534C22⋊C4—224no—
535C22⋊C4—224no—
536C42—224no—
537C42C2×C22⋊D1114yes—
538C42C2×C22⋊D1114yes—
539C42C2×C22⋊D1112yes—
540C42C2×C22⋊D1112yes—
541C42C23×D1112yes—
542C42C23×D1112yes—
543C11C2×#321211yescharacteristic, complemented, Sylow
544C23—22no—
545C23—22no—
546C23—22no—
547C23—24no—
548C23—44no—
549C23—44no—
550C23—44no—
551C23—222no—
552C23—442no—
553C23—442no—
554C23—442no—
555C23C22×C22⋊D1112yes—
556C23C22×C22⋊D1111yescharacteristic
557Q8—24no—
558Q8—24no—
559Q8—44no—
560Q8—222no—
561Q8—222no—
562Q8—442no—
563D4—24no—
564D4—24no—
565D4—48no—
566D4—416no—
567D4—44no—
568D4—48no—
569D4—222no—
570D4—222no—
571D4—448no—
572D4—442no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—28no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—44no—
583C2×C4—416no—
584C2×C4—44no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—442no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4—448no—
592C2×C4#6700314yes—
593C2×C4#6703712yes—
594C2×C4#6703712yes—
595C2×C4C22×C22⋊D1112yes—
596C2×C4C22×C22⋊D1112yes—
597C2×C4C22×C22⋊D1112yes—
598C2×C4C22×C22⋊D1112yes—
599C2×C4C22×C22⋊D1111yescharacteristic
600C2×C4C22×C22⋊D1112yes—
601C2×C4C24×D1111yescharacteristic
602C8—224no—
603C8—224no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—44no—
608C22—44no—
609C22—44no—
610C22—44no—
611C22—88no—
612C22—442no—
613C22—442no—
614C22—442no—
615C22—884no—
616C22#1062333612yes—
617C22C2×#6700312yes—
618C22#1062335312yes—
619C22C23×C22⋊D1111yescharacteristic
620C4—22no—
621C4—22no—
622C4—22no—
623C4—22no—
624C4—44no—
625C4—442no—
626C4—442no—
627C4—442no—
628C4#1062333612yes—
629C4C2×#6700314yes—
630C4C2×#6703711yescharacteristic
631C4C2×#6703711yescharacteristic
632C2—42no—
633C2—84no—
634C2—882no—
635C2#1307959214yesdirect product factor
636C2C2×#1062333611yescharacteristic
637C2C22×#6700311yescharacteristic
638C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#532C2
socleC23×C11C22×D4
hypercenterC2×#532D11
hypocenterC11C2×#3212
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. C2×#10623010C2semidirect
2. #13079592C2direct (N × H)
3. C2×#10622672C2semidirect
4. C2×#10622669C2semidirect
5. C2×#10622703C2semidirect
6. C2×#10622688C2semidirect
7. C2×#10622696C2semidirect
8. C2×#10622685C2semidirect
9. C2×#10622852C2semidirect
10. C2×#10622851C2semidirect
11. C2×#10622538C2semidirect
12. C2×C11×#532C2semidirect
15. C11×#532C22semidirect
33. #10623010C22semidirect
40. #10622852C22semidirect
41. #10622851C22semidirect
47. #10622703C22semidirect
48. #10622696C22semidirect
49. #10622688C22semidirect
50. #10622685C22semidirect
51. #10622672C22semidirect
52. #10622669C22semidirect
53. #10622538C22semidirect
225. C2×#532D11semidirect
303. #532C2×D11semidirect
454. C2×C11#3212semidirect
543. C11C2×#3212semidirect
635. C2#13079592direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230102
#130795922
C2×#106226722
C2×#106226692
C2×#106227032
C2×#106226882
C2×#106226962
C2×#106226852
C2×#106228522
C2×#106228512
C2×#106225382
C2×C11×#5322
C2×#321211