Finite Group Databasebeta

← C2×#13079594 #15624995

Subgroups — C2×#13079594 #15624995

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×#10623008C211yesmaximal, characteristic, complemented
2C2×#10623010C211yesmaximal, characteristic, complemented
3#13079594C2116yesmaximal, direct product factor
4C2×#10622309C212yesmaximal, complemented
5C2×#10622310C212yesmaximal, complemented
6C2×#10622462C211yesmaximal, characteristic, complemented
7C2×#10622461C211yesmaximal, characteristic, complemented
8C2×#10622454C211yesmaximal, characteristic, complemented
9C2×#10622456C211yesmaximal, characteristic, complemented
10C2×#10622346C212yesmaximal, complemented
11C2×#10622347C212yesmaximal, complemented
12C2×C11×#431C211yesmaximal, characteristic, complemented
13C22×#4339C2212yes—
14C22×C42×C11C2211yescharacteristic
15C2×#66983—21no—
16C2×#66983—21no—
17C2×#66983C2211yescharacteristic
18C2×#66982—21no—
19C2×C4×C22⋊D11—21no—
20C2×#66977C2211yescharacteristic
21C22×Dic44C2212yes—
22C22×D88C2212yes—
23C22×#4314C2212yes—
24C22×#4314C2212yes—
25#10623010—24no—
26#10623010C2218yescomplemented
27C2×#66929—21no—
28#10623008—24no—
29#10623008C2218yescomplemented
30C2×#66928C2211yescharacteristic
31C2×#66928C2212yes—
32C2×#66927C2211yescharacteristic
33C2×C4×D44—21no—
34C2×C4×D44—21no—
35C2×C4×D44C2211yescharacteristic
36C2×#66925—21no—
37C2×#66923C2211yescharacteristic
38C2×#66922C2211yescharacteristic
39C2×C4×Dic22C2211yescharacteristic
40C11×#431C2218yescomplemented
41C2×C11×C4⋊C8C2211yescharacteristic
42C2×C11×C4⋊C8C2211yescharacteristic
43C2×C11×C22⋊C8C2212yes—
44C2×C4×C8×C11C2212yes—
45C2×#66885C2212yes—
46C2×#66885C2212yes—
47C2×#66880C2212yes—
48C2×#66880C2212yes—
49#10622462C2218yescomplemented
50#10622461C2218yescomplemented
51#10622456C2218yescomplemented
52#10622454C2218yescomplemented
53#10622347C22116yescomplemented
54#10622346C22116yescomplemented
55#10622310C22116yescomplemented
56#10622309C22116yescomplemented
57C23×C4×C11D411yescharacteristic
58C23×C4×C11D411yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C22×C22⋊D11—22no—
62C2×#4339—24no—
63C2×#4339—44no—
64C2×#4339—44no—
65C2×#4339C2318yes—
66C22×D44—21no—
67C22×D44—21no—
68C22×D44C2312yes—
69C22×D44C2311yescharacteristic
70C22×C4×D11—21no—
71C22×C4×D11—22no—
72C22×Dic22C2311yescharacteristic
73C22×Dic22C2312yes—
74C22×C8×C11C2312yes—
75C22×C8×C11C2312yes—
76C2×C42×C11D411yescharacteristic
77C2×C42×C11D411yescharacteristic
78C2×C42×C11D414yes—
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2314yes—
82C2×C22⋊Dic11—21no—
83#66983—28no—
84#66983—28no—
85#66983—22no—
86#66983C2314yes—
87#66982—28no—
88C4×C22⋊D11—28no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99#66977—22no—
100#66977C2314yes—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×C4×Dic11—21no—
106C2×Dic44—44no—
107C2×Dic44C2318yes—
108C2×D88—44no—
109C2×D88C2318yes—
110C2×#4314—44no—
111C2×#4314—44no—
112C2×#4314C2318yes—
113C2×#4314C2318yes—
114#66929—28no—
115#66928—24no—
116#66928—22no—
117#66928C2318yes—
118#66928C2314yes—
119#66927—22no—
120#66927C2314yes—
121C4×D44—28no—
122C4×D44—28no—
123C4×D44—22no—
124C4×D44C2314yes—
125#66925—28no—
126#66923—22no—
127#66923C2314yes—
128#66922—22no—
129#66922C2314yes—
130C4×Dic22—22no—
131C4×Dic22C2314yes—
132C11×C4⋊C8C2314yes—
133C11×C4⋊C8C2314yes—
134C11×C22⋊C8C2318yes—
135C4×C8×C11C2318yes—
136#66885C2318yes—
137#66885C2318yes—
138#66880C2318yes—
139#66880C2318yes—
140C2×#3212—111nomaximal, Sylow
141C24×C11C2×D411yescharacteristic
142C23×D11—21no—
143C23×D11—22no—
144C22×C4×C11—24no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—42no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D414yes—
154C22×C4×C11C2×D414yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2412yes—
157C22×C4×C11C2411yescharacteristic
158C2×C22⋊D11—24no—
159C2×C22⋊D11—28no—
160C2×C22⋊D11—48no—
161C2×C22⋊D11—44no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—22no—
166#4339—48no—
167#4339—48no—
168#4339—416no—
169C2×D44—24no—
170C2×D44—24no—
171C2×D44—21no—
172C2×D44—22no—
173C2×D44—22no—
174C2×D44—24no—
175C2×D44—22no—
176C2×D44—24no—
177C2×D44—44no—
178C2×D44—44no—
179C2×D44C2414yes—
180C2×D44C2412yes—
181C2×C4×D11—24no—
182C2×C4×D11—28no—
183C2×C4×D11—48no—
184C2×C4×D11—44no—
185C2×Dic22—21no—
186C2×Dic22—22no—
187C2×Dic22—22no—
188C2×Dic22—24no—
189C2×Dic22—22no—
190C2×Dic22—24no—
191C2×Dic22C2414yes—
192C2×Dic22C2412yes—
193C2×C8×C11—24no—
194C2×C8×C11—24no—
195C2×C8×C11C2414yes—
196C2×C8×C11C2414yes—
197C42×C11C2×D412yes—
198C42×C11C2×D412yes—
199C42×C11C2×D414yes—
200C42×C11C2×D414yes—
201C42×C11C2412yes—
202C42×C11C2412yes—
203C22⋊Dic11—24no—
204(C2×D11)⋊C4—24no—
205(C2×D11)⋊C4—24no—
206(C2×D11)⋊C4—28no—
207(C2×D11)⋊C4—28no—
208(C2×D11)⋊C4—24no—
209(C2×D11)⋊C4—24no—
210C4⋊Dic11—21no—
211C4⋊Dic11—24no—
212C4⋊Dic11—24no—
213C4⋊Dic11—21no—
214C4⋊Dic11C2412yes—
215C4⋊Dic11C2412yes—
216Dic11⋊C4—24no—
217Dic11⋊C4—24no—
218Dic11⋊C4—24no—
219Dic11⋊C4—24no—
220C4×Dic11—24no—
221Dic44—48no—
222D88—48no—
223#4314—48no—
224#4314—48no—
225C2×#532—111no—
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×#431D1111yescharacteristic, complemented
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—22no—
240C23×C11C22×D412yes—
241C23×C11C22×D411yescharacteristic
242C22×D11—22no—
243C22×D11—24no—
244C22×D11—44no—
245C22×D11—42no—
246C22×D11—42no—
247C22×D11—44no—
248C22×D11—44no—
249C22×D11—42no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—24no—
255C2×C4×C11—28no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—44no—
259C2×C4×C11#13514yes—
260C2×C4×C11C22×D412yes—
261C2×C4×C11C22×D412yes—
262C2×C4×C11C22×D412yes—
263C2×C4×C11C22×D412yes—
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×D412yes—
266C2×C4×C11H(5,𝔽2)12yes—
267C2×C4×C11H(5,𝔽2)12yes—
268C2×C4×C11C2511yescharacteristic
269C22⋊D11—416no—
270C22⋊D11—48no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—24no—
275C2×Dic11—44no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279D44—22no—
280D44—24no—
281D44—22no—
282D44—24no—
283D44—48no—
284D44—42no—
285D44—44no—
286D44—48no—
287C4×D11—416no—
288C4×D11—48no—
289Dic22—22no—
290Dic22—24no—
291Dic22—22no—
292Dic22—24no—
293Dic22—42no—
294Dic22—44no—
295C8×C11—24no—
296C8×C11—24no—
297C22×#41—112no—
298C22×Q16—112no—
299C22×SD16—112no—
300C22×SD16—112no—
301C22×D8—112no—
302#532—118no—
303#532—224no—
304C2×C4⋊Q8—111no—
305C2×#127—111no—
306#529—118no—
307#529—224no—
308C2×#126—221no—
309C2×#125—111no—
310C2×#124—112no—
311C2×#124—111no—
312C2×#123—221no—
313C2×C22⋊Q8—111no—
314C2×#121—111no—
315C2×#121—221no—
316C2×#121—221no—
317C2×C4×Q8—111no—
318C2×C4×D4—111no—
319C2×C4×D4—221no—
320C2×C4×D4—221no—
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#431C2×D1118yescomplemented
333C2×C4⋊C8C2×D1111yescharacteristic
334C2×C4⋊C8C2×D1111yescharacteristic
335C2×#103—112no—
336C2×#103—112no—
337C2×#102—112no—
338C2×#102—112no—
339C2×C22⋊C8C2×D1112yes—
340C2×C4×C8C2×D1112yes—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11—44no—
345C22×C11#53512yes—
346C22×C11C2×#13512yes—
347C22×C11#57512yes—
348C22×C11C23×D411yescharacteristic
349C2×D11—44no—
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—44no—
353C2×D11—44no—
354C2×D11—42no—
355C2×D11—88no—
356C2×D11—84no—
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—22no—
360C4×C11—22no—
361C4×C11#53512yes—
362C4×C11C2×#13514yes—
363C4×C11C2×H(5,𝔽2)11yescharacteristic
364C4×C11C2×H(5,𝔽2)11yescharacteristic
365Dic11—44no—
366Dic11—42no—
367Dic11—42no—
368Dic11—42no—
369C2×#41—118no—
370C2×#41—224no—
371C2×#41—444no—
372C2×#41—444no—
373C22×Q8—111no—
374C22×Q8—112no—
375C22×D4—111no—
376C22×D4—112no—
377C22×D4—221no—
378C22×D4—222no—
379C22×D4—221no—
380C22×D4—221no—
381C23×C4—221no—
382C23×C4—222no—
383C23×C4D4411yescharacteristic
384C23×C4D4411yescharacteristic
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×C8C22×D1112yes—
395C22×C8C22×D1112yes—
396C4⋊Q8—114no—
397C4⋊Q8—222no—
398#127—114no—
399#127—222no—
400#126—228no—
401#125—114no—
402#125—222no—
403#124—114no—
404#124—118no—
405#124—222no—
406#124—224no—
407#123—228no—
408C22⋊Q8—114no—
409C22⋊Q8—222no—
410#121—114no—
411#121—222no—
412#121—228no—
413#121—228no—
414C4×Q8—114no—
415C4×Q8—222no—
416C4×D4—114no—
417C4×D4—228no—
418C4×D4—222no—
419C4×D4—228no—
420C4×D4—228no—
421#117—228no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—222no—
435C2×C22⋊C4—222no—
436C2×C22⋊C4—221no—
437C2×C42—221no—
438C2×C42D4411yescharacteristic
439C2×C42D4411yescharacteristic
440C2×C42D4414yes—
441C2×C42C22×D1111yescharacteristic
442C2×C42C22×D1111yescharacteristic
443C2×C42C22×D1114yes—
444C4⋊C8C22×D1114yes—
445C4⋊C8C22×D1114yes—
446#103—118no—
447#103—118no—
448#102—118no—
449#102—118no—
450C22⋊C8C22×D1118yes—
451C4×C8C22×D1118yes—
452C2×C11—42no—
453C2×C11#321214yescomplemented
454C2×C11C2×#53511yescharacteristic
455C2×C11C22×#13511yescharacteristic
456C2×C11C2×#57511yescharacteristic
457D11—84no—
458D11—82no—
459C24—221no—
460C24—222no—
461C24C2×D4411yescharacteristic
462#41—448no—
463#41—448no—
464#41—4416no—
465C2×Q8—114no—
466C2×Q8—112no—
467C2×Q8—221no—
468C2×Q8—222no—
469C2×Q8—222no—
470C2×Q8—224no—
471C2×Q8—222no—
472C2×Q8—224no—
473C2×D4—114no—
474C2×D4—112no—
475C2×D4—224no—
476C2×D4—228no—
477C2×D4—221no—
478C2×D4—224no—
479C2×D4—224no—
480C2×D4—222no—
481C2×D4—222no—
482C2×D4—224no—
483C2×D4—222no—
484C2×D4—224no—
485C2×D4—444no—
486C2×D4—448no—
487C2×D4—444no—
488C2×D4—444no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—42no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—222no—
497C22×C4—224no—
498C22×C4—228no—
499C22×C4—448no—
500C22×C4—444no—
501C22×C4C2×D4414yes—
502C22×C4C2×D4412yes—
503C22×C4C2×D4411yescharacteristic
504C22×C4C2×D4411yescharacteristic
505C22×C4C2×D4411yescharacteristic
506C22×C4C2×D4411yescharacteristic
507C22×C4C2×D4414yes—
508C22×C4C2×D4411yescharacteristic
509C22×C4C23×D1112yes—
510C22×C4C23×D1111yescharacteristic
511Q16—448no—
512SD16—448no—
513SD16—448no—
514D8—448no—
515C2×C8—24no—
516C2×C8—24no—
517C2×C8C23×D1114yes—
518C2×C8C23×D1114yes—
519C4⋊C4—112no—
520C4⋊C4—112no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—224no—
524C4⋊C4—224no—
525C4⋊C4—224no—
526C4⋊C4—224no—
527C4⋊C4—224no—
528C4⋊C4—224no—
529C22⋊C4—224no—
530C22⋊C4—224no—
531C22⋊C4—224no—
532C22⋊C4—224no—
533C22⋊C4—228no—
534C22⋊C4—228no—
535C22⋊C4—224no—
536C42—224no—
537C42C2×D4414yes—
538C42C2×D4414yes—
539C42C2×D4412yes—
540C42C2×D4412yes—
541C42C23×D1112yes—
542C42C23×D1112yes—
543C11C2×#321211yescharacteristic, complemented, Sylow
544C23—22no—
545C23—22no—
546C23—22no—
547C23—222no—
548C23—224no—
549C23—442no—
550C23—444no—
551C23—444no—
552C23—442no—
553C23—444no—
554C23—442no—
555C23C22×D4412yes—
556C23C22×D4411yescharacteristic
557Q8—222no—
558Q8—224no—
559Q8—222no—
560Q8—224no—
561Q8—444no—
562Q8—442no—
563D4—222no—
564D4—224no—
565D4—222no—
566D4—224no—
567D4—448no—
568D4—4416no—
569D4—448no—
570D4—448no—
571D4—444no—
572D4—442no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—28no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—44no—
582C2×C4—222no—
583C2×C4—222no—
584C2×C4—222no—
585C2×C4—224no—
586C2×C4—4416no—
587C2×C4—442no—
588C2×C4—442no—
589C2×C4—444no—
590C2×C4—442no—
591C2×C4—448no—
592C2×C4#6695714yes—
593C2×C4C22×D4412yes—
594C2×C4C22×D4412yes—
595C2×C4C22×D4412yes—
596C2×C4C22×D4412yes—
597C2×C4C22×D4412yes—
598C2×C4C22×D4411yescharacteristic
599C2×C4#6704212yes—
600C2×C4#6704212yes—
601C2×C4C24×D1111yescharacteristic
602C8—24no—
603C8—24no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—44no—
608C22—444no—
609C22—442no—
610C22—442no—
611C22—444no—
612C22—444no—
613C22—442no—
614C22—884no—
615C22—888no—
616C22#1062305612yes—
617C22C2×#6695712yes—
618C22#1062327912yes—
619C22C23×D4411yescharacteristic
620C4—22no—
621C4—22no—
622C4—22no—
623C4—22no—
624C4—444no—
625C4—442no—
626C4—442no—
627C4—442no—
628C4#1062305612yes—
629C4C2×#6695714yes—
630C4C2×#6704211yescharacteristic
631C4C2×#6704211yescharacteristic
632C2—42no—
633C2—884no—
634C2—882no—
635C2#1307959414yesdirect product factor
636C2C2×#1062305611yescharacteristic
637C2C22×#6695711yescharacteristic
638C2C2×#1062327911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#431C2
socleC23×C11C22×D4
hypercenterC2×#431D11
hypocenterC11C2×#3212
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
1. C2×#10623008C2semidirect
2. C2×#10623010C2semidirect
3. #13079594C2direct (N × H)
4. C2×#10622309C2semidirect
5. C2×#10622310C2semidirect
6. C2×#10622462C2semidirect
7. C2×#10622461C2semidirect
8. C2×#10622454C2semidirect
9. C2×#10622456C2semidirect
10. C2×#10622346C2semidirect
11. C2×#10622347C2semidirect
12. C2×C11×#431C2semidirect
26. #10623010C22semidirect
29. #10623008C22semidirect
40. C11×#431C22semidirect
49. #10622462C22semidirect
50. #10622461C22semidirect
51. #10622456C22semidirect
52. #10622454C22semidirect
53. #10622347C22semidirect
54. #10622346C22semidirect
55. #10622310C22semidirect
56. #10622309C22semidirect
236. C2×#431D11semidirect
332. #431C2×D11semidirect
453. C2×C11#3212semidirect
543. C11C2×#3212semidirect
635. C2#13079594direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230082
C2×#106230102
#130795942
C2×#106223092
C2×#106223102
C2×#106224622
C2×#106224612
C2×#106224542
C2×#106224562
C2×#106223462
C2×#106223472
C2×C11×#4312
C2×#321211