Finite Group Databasebeta

← C2×#13080345 #15629025

Subgroups — C2×#13080345 #15629025

Order 2816.

2858 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66969C212yesmaximal, complemented
2C2×#10623249C211yesmaximal, characteristic, complemented
3C2×#10623257C211yesmaximal, characteristic, complemented
4#13080345C2116yesmaximal, direct product factor
5C2×#10622784C212yesmaximal, complemented
6C2×#10622703C211yesmaximal, characteristic, complemented
7C2×#10622685C211yesmaximal, characteristic, complemented
8C2×#10622786C212yesmaximal, complemented
9C2×#10622785C212yesmaximal, complemented
10C2×C4×#4314C211yesmaximal, characteristic, complemented
11C2×C8×D44C211yesmaximal, characteristic, complemented
12C2×C11×#492C211yesmaximal, characteristic, complemented
13C22×#4343C2212yes—
14C22×#4341C2212yes—
15C22×C11×SD16C2212yes—
16C22×C11×SD16C2212yes—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#127C2211yescharacteristic
19C2×#66999C2212yes—
20C22×#4326C2212yes—
21C2×#66993—21no—
22C2×#66992—22no—
23C2×#66991C2212yes—
24C2×D4×Dic11—21no—
25C22×#4323C2212yes—
26C2×#66969—216no—
27C2×#66969C22116yescomplemented
28C22×#4314C2211yescharacteristic
29C22×C8×D11C2212yes—
30#10623257—24no—
31#10623257C2218yescomplemented
32#10623249—24no—
33#10623249C2218yescomplemented
34C2×#66948—21no—
35C2×#66947—22no—
36C2×C4⋊C4×D11—21no—
37C2×C4×D44C2211yescharacteristic
38C2×C4×D44C2211yescharacteristic
39C2×C4×Dic22C2211yescharacteristic
40C11×#492C2218yescomplemented
41C2×C4×C8×C11C2211yescharacteristic
42C2×#66899C2212yes—
43C2×#66896C2212yes—
44#10622786C22116yescomplemented
45#10622785C22116yescomplemented
46#10622784C22116yescomplemented
47C2×#66885C2211yescharacteristic
48C2×(C2×D11)⋊C8C2212yes—
49C2×#66881C2211yescharacteristic
50C2×#66880C2211yescharacteristic
51#10622703C2218yescomplemented
52#10622685C2218yescomplemented
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C4×#4314C2218yescomplemented
55C8×D44C2218yescomplemented
56C22×Q8×C11C2312yes—
57C22×D4×C11—21no—
58C22×D4×C11—21no—
59C22×D4×C11C2312yes—
60C22×C22⋊D11—22no—
61C22×C22⋊D11—22no—
62C23×Dic11—22no—
63C2×#4343—24no—
64C2×#4343—28no—
65C2×#4343—44no—
66C2×#4343C2318yes—
67C2×#4341—24no—
68C2×#4341—28no—
69C2×#4341—44no—
70C2×#4341C2318yes—
71C22×D44—22no—
72C22×D44D411yescharacteristic
73C22×D44C2311yescharacteristic
74C22×C4×D11—21no—
75C22×C4×D11—22no—
76C22×C4×D11C2312yes—
77C22×Dic22C2311yescharacteristic
78C2×C11×SD16—28no—
79C2×C11×SD16—44no—
80C2×C11×SD16C2318yes—
81C2×C11×SD16C2318yes—
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C11×C4⋊Q8—22no—
85C11×C4⋊Q8C2314yes—
86C11×#127—22no—
87C11×#127C2314yes—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C42×C11C2311yescharacteristic
91C2×C22⋊Dic11—22no—
92#66999—24no—
93#66999C2318yes—
94C2×#4326—28no—
95C2×#4326C2318yes—
96#66993—28no—
97#66992—216no—
98#66991—24no—
99#66991C2318yes—
100D4×Dic11—28no—
101C2×#4323—28no—
102C2×#4323C2318yes—
103C2×(C2×D11)⋊C4—22no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4D412yes—
106C2×C4⋊Dic11D411yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×Dic11⋊C4—21no—
110C2×Dic11⋊C4—22no—
111C2×C4×Dic11—21no—
112C22×C11⋊C8C2312yes—
113#66969—264no—
114C2×#4314D418yescomplemented
115C2×#4314C2314yes—
116C2×C8×D11—28no—
117C2×C8×D11C2318yes—
118#66948—28no—
119#66947—216no—
120C4⋊C4×D11—28no—
121C4×D44—22no—
122C4×D44D414yes—
123C4×D44C2314yes—
124C4×D44C2314yes—
125C4×Dic22—22no—
126C4×Dic22C2314yes—
127C4×C8×C11C2314yes—
128#66899C2318yes—
129#66896C2318yes—
130#66885C2314yes—
131(C2×D11)⋊C8C2318yes—
132#66881C2314yes—
133#66880C2314yes—
134C4⋊(C11⋊C8)C2314yes—
135C2×#3284—111nomaximal, Sylow
136C24×C11—22no—
137C23×D11—21no—
138C23×D11C2×D412yes—
139C2×Q8×C11—22no—
140C2×Q8×C11—24no—
141C2×Q8×C11—24no—
142C2×Q8×C11C2414yes—
143C2×D4×C11—24no—
144C2×D4×C11—24no—
145C2×D4×C11—22no—
146C2×D4×C11—24no—
147C2×D4×C11—24no—
148C2×D4×C11—44no—
149C2×D4×C11—82no—
150C2×D4×C11C2414yes—
151C22×C4×C11—22no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C2×C22⋊D11—28no—
156C2×C22⋊D11—28no—
157C2×C22⋊D11—48no—
158C2×C22⋊D11—84no—
159C22×Dic11—28no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—48no—
164C22×Dic11C2×D412yes—
165#4343—216no—
166#4343—48no—
167#4343—416no—
168#4341—216no—
169#4341—48no—
170#4341—416no—
171C2×D44—28no—
172C2×D44—24no—
173C2×D44—21no—
174C2×D44—22no—
175C2×D44—48no—
176C2×D44C2×D414yes—
177C2×D44C2×D414yes—
178C2×D44C2412yes—
179C2×C4×D11—28no—
180C2×C4×D11—24no—
181C2×C4×D11—24no—
182C2×C4×D11—24no—
183C2×C4×D11—48no—
184C2×C4×D11—44no—
185C2×C4×D11C2×D414yes—
186C2×C4×D11C2414yes—
187C2×Dic22—21no—
188C2×Dic22—22no—
189C2×Dic22C2×D414yes—
190C2×Dic22C2412yes—
191C11×SD16—216no—
192C11×SD16—48no—
193C2×C8×C11—22no—
194C2×C8×C11C2×D414yes—
195C2×C8×C11C2412yes—
196C2×C8×C11C2412yes—
197C11×C4⋊C4—24no—
198C11×C4⋊C4—24no—
199C42×C11C2×D412yes—
200C42×C11C2412yes—
201C22⋊Dic11—28no—
202#4326—216no—
203#4323—216no—
204(C2×D11)⋊C4—28no—
205(C2×D11)⋊C4—24no—
206(C2×D11)⋊C4C2×D418yes—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11C2×D414yes—
210C4⋊Dic11C2412yes—
211C4⋊Dic11C2412yes—
212Dic11⋊C4—28no—
213Dic11⋊C4—24no—
214C4×Dic11—24no—
215C2×C11⋊C8—24no—
216C2×C11⋊C8C2414yes—
217#4314C2×D4116yescomplemented
218C8×D11—216no—
219C22×#135—112no—
220C2×#550—111no—
221C2×#547—111no—
222#3284—1116no—
223C2×#492D1111yescharacteristic, complemented
224C2×#465—112no—
225C2×#462—111no—
226C2×#459—111no—
227C2×#452—112no—
228C2×#449—112no—
229C2×C4×SD16—111no—
230C2×C8×D4—111no—
231C23×C11—24no—
232C23×C11—44no—
233C23×C11—44no—
234C23×C11—44no—
235C23×C11C22×D411yescharacteristic
236C22×D11—24no—
237C22×D11—24no—
238C22×D11—24no—
239C22×D11—24no—
240C22×D11—22no—
241C22×D11—42no—
242C22×D11—42no—
243C22×D11C22×D414yes—
244Q8×C11—24no—
245Q8×C11—24no—
246Q8×C11—44no—
247D4×C11—24no—
248D4×C11—24no—
249D4×C11—44no—
250D4×C11—48no—
251D4×C11—84no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—44no—
255C2×C4×C11#13514yescomplemented
256C2×C4×C11C22×D412yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D412yes—
259C2×C4×C11C22×D412yes—
260C2×C4×C11H(5,𝔽2)12yes—
261C2×C4×C11C2511yescharacteristic
262C22⋊D11—416no—
263C22⋊D11—88no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—416no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11C22×D414yes—
273D44—24no—
274D44—28no—
275D44—22no—
276D44—416no—
277D44C22×D414yes—
278C4×D11—28no—
279C4×D11—24no—
280C4×D11—24no—
281C4×D11—416no—
282C4×D11—48no—
283Dic22—24no—
284Dic22—22no—
285Dic22C22×D414yes—
286C8×C11—22no—
287C8×C11C22×D414yes—
288C11⋊C8—24no—
289C22×#41—112no—
290C22×#41—112no—
291C2×#135—1116no—
292C2×#135—2216no—
293C22×Q16—112no—
294C22×SD16—111no—
295C22×SD16C2×D1112yes—
296C22×SD16C2×D1112yes—
297C22×D8—112no—
298C23×C8—112no—
299#550—118no—
300#550—224no—
301#547—118no—
302#547—224no—
303C2×C4⋊Q8C2×D1111yescharacteristic
304C2×#127—221no—
305C2×#127C2×D1111yescharacteristic
306C2×#123—222no—
307C2×C22⋊Q8—112no—
308C2×#121—112no—
309C2×#121—222no—
310C2×#121—221no—
311C2×C4×Q8—111no—
312C2×C4×D4—111no—
313C2×C4×D4—111no—
314C2×C4×D4—221no—
315C22×C4⋊C4—221no—
316#492C2×D1118yescomplemented
317#465—1116no—
318#462—118no—
319#459—118no—
320#452—1116no—
321#449—1116no—
322C4×SD16—118no—
323C8×D4—118no—
324C2×#106—111no—
325C2×C4⋊C8—111no—
326C2×#103—112no—
327C2×#103—111no—
328C2×#102—112no—
329C2×#102—111no—
330C2×C22⋊C8—112no—
331C2×C4×C8C2×D1111yescharacteristic
332C22×C11—44no—
333C22×C11—44no—
334C22×C11—44no—
335C22×C11—88no—
336C22×C11D4212yes—
337C22×C11C2×#13512yes—
338C22×C11#57712yes—
339C22×C11C23×D411yescharacteristic
340C2×D11—24no—
341C2×D11—24no—
342C2×D11—24no—
343C2×D11—24no—
344C2×D11—48no—
345C2×D11—48no—
346C2×D11—42no—
347C2×D11—42no—
348C4×C11—22no—
349C4×C11—44no—
350C4×C11D4212yes—
351C4×C11C2×#13514yescomplemented
352C4×C11C23×D411yescharacteristic
353C4×C11C2×H(5,𝔽2)11yescharacteristic
354Dic11—24no—
355Dic11—24no—
356Dic11—42no—
357Dic11—42no—
358C2×#41—118no—
359C2×#41—118no—
360C2×#41—224no—
361C2×#41—224no—
362C2×#41—228no—
363C2×#41—228no—
364C2×#41—444no—
365C2×#41—444no—
366C22×Q8—111no—
367C22×Q8C22×D1112yes—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—111no—
371C22×D4—111no—
372C22×D4—222no—
373C22×D4—222no—
374C22×D4—222no—
375C22×D4C22×D1112yes—
376C23×C4—112no—
377C23×C4—222no—
378C23×C4—222no—
379C23×C4—221no—
380#135—2264no—
381C2×Q16—118no—
382C2×Q16—228no—
383C2×SD16—28no—
384C2×SD16—44no—
385C2×SD16—118no—
386C2×SD16—114no—
387C2×SD16C22×D1118yes—
388C2×SD16C22×D1118yes—
389C2×D8—118no—
390C2×D8—228no—
391C22×C8—112no—
392C22×C8—118no—
393C22×C8—228no—
394C22×C8C22×D1111yescharacteristic
395C22×C8C22×D1111yescharacteristic
396C4⋊Q8—22no—
397C4⋊Q8C22×D1114yes—
398#127—22no—
399#127—228no—
400#127C22×D1114yes—
401#123—2216no—
402C22⋊Q8—118no—
403C22⋊Q8—224no—
404#121—118no—
405#121—2216no—
406#121—228no—
407#121—224no—
408C4×Q8—114no—
409C4×Q8—222no—
410C4×D4—114no—
411C4×D4—114no—
412C4×D4—114no—
413C4×D4—228no—
414C4×D4—222no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—228no—
421C2×C4⋊C4—222no—
422C2×C4⋊C4—221no—
423C2×C22⋊C4—112no—
424C2×C22⋊C4—222no—
425C2×C22⋊C4—222no—
426C2×C22⋊C4—221no—
427C2×C42—221no—
428C2×C42C22×D1111yescharacteristic
429#106—114no—
430C4⋊C8—114no—
431#103—118no—
432#103—114no—
433#102—118no—
434#102—114no—
435C22⋊C8—118no—
436C4×C8C22×D1114yes—
437C2×C11—84no—
438C2×C11#328414yescomplemented
439C2×C11C2×D4211yescharacteristic
440C2×C11C22×#13511yescharacteristic
441C2×C11C2×#57711yescharacteristic
442D11—44no—
443D11—44no—
444C24—22no—
445C24—112no—
446C24—221no—
447#41—2216no—
448#41—2216no—
449#41—448no—
450#41—4416no—
451#41—448no—
452#41—4416no—
453C2×Q8—22no—
454C2×Q8—24no—
455C2×Q8—24no—
456C2×Q8—114no—
457C2×Q8—112no—
458C2×Q8—221no—
459C2×Q8—222no—
460C2×Q8C23×D1114yes—
461C2×D4—24no—
462C2×D4—24no—
463C2×D4—22no—
464C2×D4—24no—
465C2×D4—24no—
466C2×D4—44no—
467C2×D4—82no—
468C2×D4—114no—
469C2×D4—114no—
470C2×D4—112no—
471C2×D4—228no—
472C2×D4—228no—
473C2×D4—228no—
474C2×D4—224no—
475C2×D4—221no—
476C2×D4—222no—
477C2×D4—448no—
478C2×D4—448no—
479C2×D4—884no—
480C2×D4C23×D1114yes—
481C22×C4—22no—
482C22×C4—112no—
483C22×C4—114no—
484C22×C4—114no—
485C22×C4—228no—
486C22×C4—228no—
487C22×C4—221no—
488C22×C4—224no—
489C22×C4—224no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—224no—
493C22×C4—448no—
494C22×C4—448no—
495C22×C4—444no—
496C22×C4D4×D1111yescharacteristic
497C22×C4D4×D1111yescharacteristic
498C22×C4C23×D1111yescharacteristic
499Q16—2216no—
500SD16—216no—
501SD16—48no—
502SD16—1116no—
503D8—2216no—
504C2×C8—22no—
505C2×C8—114no—
506C2×C8—224no—
507C2×C8—2216no—
508C2×C8D4×D1114yes—
509C2×C8C23×D1112yes—
510C2×C8C23×D1112yes—
511C4⋊C4—24no—
512C4⋊C4—24no—
513C4⋊C4—114no—
514C4⋊C4—112no—
515C4⋊C4—112no—
516C4⋊C4—228no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—224no—
520C22⋊C4—118no—
521C22⋊C4—228no—
522C22⋊C4—228no—
523C22⋊C4—224no—
524C42—224no—
525C42D4×D1112yes—
526C42C23×D1112yes—
527C11C2×#328411yescharacteristic, complemented, Sylow
528C23—24no—
529C23—44no—
530C23—44no—
531C23—44no—
532C23—114no—
533C23—224no—
534C23—224no—
535C23—224no—
536C23—224no—
537C23—222no—
538C23—442no—
539C23—442no—
540C23C2×D4×D1111yescharacteristic
541Q8—24no—
542Q8—24no—
543Q8—44no—
544Q8—114no—
545Q8—224no—
546Q8—222no—
547D4—24no—
548D4—24no—
549D4—44no—
550D4—48no—
551D4—84no—
552D4—114no—
553D4—224no—
554D4—228no—
555D4—222no—
556D4—4416no—
557D4—4416no—
558D4—888no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—44no—
562C2×C4—114no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—222no—
566C2×C4—228no—
567C2×C4—224no—
568C2×C4—224no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—4416no—
572C2×C4—4416no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—448no—
576C2×C4#6696914yescomplemented
577C2×C4C2×D4×D1112yes—
578C2×C4C2×D4×D1111yescharacteristic
579C2×C4C2×D4×D1112yes—
580C2×C4C2×D4×D1112yes—
581C2×C4#6703712yes—
582C2×C4C24×D1111yescharacteristic
583C8—22no—
584C8—224no—
585C8C2×D4×D1114yes—
586C22—44no—
587C22—44no—
588C22—44no—
589C22—88no—
590C22—224no—
591C22—224no—
592C22—224no—
593C22—224no—
594C22—448no—
595C22—448no—
596C22—442no—
597C22—442no—
598C22#1062324812yes—
599C22C2×#6696912yes—
600C22#1062329312yes—
601C22C22×D4×D1111yescharacteristic
602C4—22no—
603C4—44no—
604C4—224no—
605C4—224no—
606C4—442no—
607C4—442no—
608C4#1062324812yes—
609C4C2×#6696914yescomplemented
610C4C22×D4×D1111yescharacteristic
611C4C2×#6703711yescharacteristic
612C2—84no—
613C2—444no—
614C2—444no—
615C2#1308034514yesdirect product factor
616C2C2×#1062324811yescharacteristic
617C2C22×#6696911yescharacteristic
618C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#492C2
socleC23×C11C22×D4
hypercenterC2×#492D11
hypocenterC11C2×#3284
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#492

Complements

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

NH ≅ G/Ntype
1. C22×#66969C2semidirect
2. C2×#10623249C2semidirect
3. C2×#10623257C2semidirect
4. #13080345C2direct (N × H)
5. C2×#10622784C2semidirect
6. C2×#10622703C2semidirect
7. C2×#10622685C2semidirect
8. C2×#10622786C2semidirect
9. C2×#10622785C2semidirect
10. C2×C4×#4314C2semidirect
11. C2×C8×D44C2semidirect
12. C2×C11×#492C2semidirect
27. C2×#66969C22semidirect
31. #10623257C22semidirect
33. #10623249C22semidirect
40. C11×#492C22semidirect
44. #10622786C22semidirect
45. #10622785C22semidirect
46. #10622784C22semidirect
51. #10622703C22semidirect
52. #10622685C22semidirect
54. C4×#4314C22semidirect
55. C8×D44C22semidirect
114. C2×#4314D4semidirect
217. #4314C2×D4semidirect
223. C2×#492D11semidirect
255. C2×C4×C11#135semidirect
316. #492C2×D11semidirect
351. C4×C11C2×#135semidirect
438. C2×C11#3284semidirect
527. C11C2×#3284semidirect
576. C2×C4#66969semidirect
609. C4C2×#66969semidirect
615. C2#13080345direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669692
C2×#106232492
C2×#106232572
#130803452
C2×#106227842
C2×#106227032
C2×#106226852
C2×#106227862
C2×#106227852
C2×C4×#43142
C2×C8×D442
C2×C11×#4922
C2×#328411