Finite Group Databasebeta

← C2×#13080341 #15629021

Subgroups — C2×#13080341 #15629021

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×#66972C212yesmaximal, complemented
2C2×#10623108C211yesmaximal, characteristic, complemented
3C2×#10623257C211yesmaximal, characteristic, complemented
4#13080341C2116yesmaximal, direct product factor
5C2×#10622698C211yesmaximal, characteristic, complemented
6C2×#10622420C212yesmaximal, complemented
7C2×#10622456C211yesmaximal, characteristic, complemented
8C2×#10622800C212yesmaximal, complemented
9C2×#10622424C212yesmaximal, complemented
10C2×C4×#4325C211yesmaximal, characteristic, complemented
11C2×#10622447C211yesmaximal, characteristic, complemented
12C2×C11×#462C211yesmaximal, characteristic, complemented
13C22×#4343C2212yes—
14C22×#4343C2212yes—
15C22×C11×Q16C2212yes—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×#66999C2212yes—
19C22×#4325C2212yes—
20C22×#4325C2212yes—
21C22×#4325C2211yescharacteristic
22C2×#66972—216no—
23C2×#66972C22116yescomplemented
24C22×D88C2212yes—
25C22×C8×D11C2212yes—
26#10623257—24no—
27#10623257C2218yescomplemented
28#10623108—24no—
29#10623108C2218yescomplemented
30C2×#66948—21no—
31C2×#66948—22no—
32C2×#66948C2212yes—
33C2×#66947—22no—
34C2×C4⋊C4×D11—21no—
35C2×#66927—21no—
36C2×#66927C2211yescharacteristic
37C2×C4×D44—21no—
38C2×C4×D44C2211yescharacteristic
39C2×C4×D44C2211yescharacteristic
40C11×#462C2218yescomplemented
41C2×C11×C4⋊C8C2211yescharacteristic
42C2×C11×#103C2212yes—
43C2×#66899C2211yescharacteristic
44#10622800C22116yescomplemented
45C2×#66885C2212yes—
46C2×(C2×D11)⋊C8C2212yes—
47#10622698C2218yescomplemented
48C4×#4325C2218yescomplemented
49C2×#66873C2211yescharacteristic
50C2×#66872C2211yescharacteristic
51C2×C4×C11⋊C8C2211yescharacteristic
52#10622456C2218yescomplemented
53#10622447C2218yescomplemented
54#10622424C22116yescomplemented
55#10622420C22116yescomplemented
56C22×Q8×C11C2312yes—
57C22×Q8×C11C2311yescharacteristic
58C2×#4343—24no—
59C2×#4343—24no—
60C2×#4343—28no—
61C2×#4343—28no—
62C2×#4343—44no—
63C2×#4343—44no—
64C2×#4343C2318yes—
65C2×#4343C2318yes—
66C22×D44—22no—
67C22×D44—22no—
68C22×D44—21no—
69C22×D44—22no—
70C22×D44—21no—
71C22×D44D411yescharacteristic
72C22×D44C2312yes—
73C22×D44C2311yescharacteristic
74C22×C4×D11—21no—
75C22×C4×D11—22no—
76C22×C4×D11—22no—
77C22×C4×D11C2312yes—
78C2×C11×Q16—28no—
79C2×C11×Q16C2318yes—
80C22×C8×C11C2312yes—
81C11×C4⋊Q8—22no—
82C11×C4⋊Q8C2314yes—
83C4×Q8×C11—22no—
84C4×Q8×C11C2314yes—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C42×C11—21no—
90C2×C42×C11C2311yescharacteristic
91#66999—24no—
92#66999C2318yes—
93C2×#4325—28no—
94C2×#4325—44no—
95C2×#4325D418yescomplemented
96C2×#4325C2318yes—
97C2×#4325C2318yes—
98C2×#4325C2314yes—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4D412yes—
103C2×C4⋊Dic11D411yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×Dic11⋊C4—22no—
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108#66972—264no—
109C2×D88—28no—
110C2×D88C2318yes—
111C2×C8×D11—28no—
112C2×C8×D11C2318yes—
113#66948—28no—
114#66948—24no—
115#66948—216no—
116#66948C2318yes—
117#66947—216no—
118C4⋊C4×D11—28no—
119#66927—28no—
120#66927—22no—
121#66927C2314yes—
122C4×D44—22no—
123C4×D44—28no—
124C4×D44D414yes—
125C4×D44C2314yes—
126C4×D44C2314yes—
127C11×C4⋊C8C2314yes—
128C11×#103C2318yes—
129#66899C2314yes—
130#66885C2318yes—
131(C2×D11)⋊C8C2318yes—
132#66873C2314yes—
133#66872C2314yes—
134C4×C11⋊C8C2314yes—
135C2×#3284—111nomaximal, Sylow
136C23×D11—21no—
137C23×D11—22no—
138C23×D11C2×D412yes—
139C2×Q8×C11—21no—
140C2×Q8×C11—22no—
141C2×Q8×C11—22no—
142C2×Q8×C11—24no—
143C2×Q8×C11—24no—
144C2×Q8×C11C2×D414yes—
145C2×Q8×C11C2414yes—
146C2×Q8×C11C2412yes—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11—21no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11C2×D412yes—
155#4343—216no—
156#4343—216no—
157#4343—48no—
158#4343—48no—
159#4343—416no—
160#4343—416no—
161C2×D44—28no—
162C2×D44—28no—
163C2×D44—28no—
164C2×D44—24no—
165C2×D44—21no—
166C2×D44—24no—
167C2×D44—22no—
168C2×D44—24no—
169C2×D44—24no—
170C2×D44—22no—
171C2×D44—24no—
172C2×D44—48no—
173C2×D44—48no—
174C2×D44—44no—
175C2×D44—82no—
176C2×D44—84no—
177C2×D44C2×D414yes—
178C2×D44C2×D414yes—
179C2×D44C2414yes—
180C2×D44C2412yes—
181C2×C4×D11—28no—
182C2×C4×D11—28no—
183C2×C4×D11—24no—
184C2×C4×D11—24no—
185C2×C4×D11—24no—
186C2×C4×D11—48no—
187C2×C4×D11—48no—
188C2×C4×D11—44no—
189C2×C4×D11C2×D414yes—
190C2×C4×D11C2414yes—
191C11×Q16—216no—
192C2×C8×C11—24no—
193C2×C8×C11C2414yes—
194C11×C4⋊C4—24no—
195C11×C4⋊C4—24no—
196C11×C4⋊C4—24no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4C2412yes—
199C42×C11—24no—
200C42×C11C2×D412yes—
201C42×C11C2412yes—
202#4325—216no—
203#4325—48no—
204#4325C2×D4116yescomplemented
205(C2×D11)⋊C4—28no—
206(C2×D11)⋊C4—28no—
207(C2×D11)⋊C4—24no—
208(C2×D11)⋊C4C2×D418yes—
209C4⋊Dic11—21no—
210C4⋊Dic11C2×D414yes—
211C4⋊Dic11C2412yes—
212Dic11⋊C4—28no—
213C2×C11⋊C8—22no—
214C2×C11⋊C8C2×D414yes—
215C2×C11⋊C8C2412yes—
216C2×C11⋊C8C2412yes—
217D88—216no—
218C8×D11—216no—
219C22×#135—112no—
220C2×#550—111no—
221C2×#547—111no—
222#3284—1116no—
223C2×#492—111no—
224C2×#465—112no—
225C2×#462D1111yescharacteristic, complemented
226C2×#459—111no—
227C2×#452—112no—
228C2×#449—112no—
229C2×C4×SD16—111no—
230C2×C8×D4—111no—
231C23×C11C22×D411yescharacteristic
232C22×D11—24no—
233C22×D11—24no—
234C22×D11—24no—
235C22×D11—24no—
236C22×D11—22no—
237C22×D11—24no—
238C22×D11—42no—
239C22×D11—42no—
240C22×D11—44no—
241C22×D11—44no—
242C22×D11—44no—
243C22×D11C22×D414yes—
244Q8×C11—24no—
245Q8×C11—22no—
246Q8×C11—24no—
247Q8×C11—24no—
248Q8×C11—44no—
249Q8×C11C22×D414yes—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—22no—
255C2×C4×C11—44no—
256C2×C4×C11—42no—
257C2×C4×C11#13514yescomplemented
258C2×C4×C11C22×D412yes—
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D412yes—
261C2×C4×C11C22×D412yes—
262C2×C4×C11H(5,𝔽2)12yes—
263C2×C4×C11C2511yescharacteristic
264C2×Dic11—24no—
265C2×Dic11—22no—
266C2×Dic11—42no—
267C2×Dic11C22×D414yes—
268D44—24no—
269D44—28no—
270D44—24no—
271D44—22no—
272D44—24no—
273D44—416no—
274D44—416no—
275D44—44no—
276D44—48no—
277D44—84no—
278D44—88no—
279D44C22×D414yes—
280C4×D11—28no—
281C4×D11—24no—
282C4×D11—24no—
283C4×D11—416no—
284C4×D11—416no—
285C4×D11—48no—
286C8×C11—24no—
287C11⋊C8—22no—
288C11⋊C8C22×D414yes—
289C22×#41—112no—
290C22×#41—112no—
291C2×#135—1116no—
292C2×#135—2216no—
293C22×Q16C2×D1112yes—
294C22×SD16—111no—
295C22×SD16—112no—
296C22×SD16—112no—
297C22×D8—112no—
298C23×C8—112no—
299#550—118no—
300#550—224no—
301#547—118no—
302#547—224no—
303C2×C4⋊Q8C2×D1111yescharacteristic
304C2×#127—111no—
305C2×#127—221no—
306C2×#123—222no—
307C2×C22⋊Q8—112no—
308C2×#121—112no—
309C2×#121—222no—
310C2×#121—221no—
311C2×C4×Q8C2×D1111yescharacteristic
312C2×C4×D4—111no—
313C2×C4×D4—111no—
314C2×C4×D4—221no—
315C22×C4⋊C4—221no—
316#492—118no—
317#465—1116no—
318#462C2×D1118yescomplemented
319#459—118no—
320#452—1116no—
321#449—1116no—
322C4×SD16—118no—
323C8×D4—118no—
324C2×#106—111no—
325C2×C4⋊C8C2×D1111yescharacteristic
326C2×#103—111no—
327C2×#103C2×D1112yes—
328C2×#102—112no—
329C2×#102—111no—
330C2×C22⋊C8—112no—
331C2×C4×C8—111no—
332C22×C11D4212yes—
333C22×C11C2×#13512yes—
334C22×C11#57712yes—
335C22×C11C23×D411yescharacteristic
336C2×D11—24no—
337C2×D11—24no—
338C2×D11—24no—
339C2×D11—24no—
340C2×D11—48no—
341C2×D11—48no—
342C2×D11—42no—
343C2×D11—42no—
344C2×D11—44no—
345C2×D11—44no—
346C2×D11—44no—
347C2×D11—88no—
348C4×C11—24no—
349C4×C11—22no—
350C4×C11—44no—
351C4×C11—42no—
352C4×C11D4212yes—
353C4×C11C2×#13514yescomplemented
354C4×C11C23×D411yescharacteristic
355C4×C11C2×H(5,𝔽2)11yescharacteristic
356Dic11—24no—
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×Q8C22×D1112yes—
367C22×Q8C22×D1111yescharacteristic
368C22×D4—111no—
369C22×D4—111no—
370C22×D4—112no—
371C22×D4—222no—
372C22×D4—222no—
373C22×D4—222no—
374C22×D4—221no—
375C22×D4—221no—
376C23×C4—112no—
377C23×C4—222no—
378C23×C4—222no—
379C23×C4—221no—
380#135—2264no—
381C2×Q16—28no—
382C2×Q16C22×D1118yes—
383C2×SD16—118no—
384C2×SD16—114no—
385C2×SD16—118no—
386C2×SD16—118no—
387C2×SD16—228no—
388C2×SD16—444no—
389C2×D8—118no—
390C2×D8—228no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8—118no—
394C22×C8—228no—
395C22×C8C22×D1112yes—
396C4⋊Q8—22no—
397C4⋊Q8C22×D1114yes—
398#127—114no—
399#127—228no—
400#127—222no—
401#123—2216no—
402C22⋊Q8—118no—
403C22⋊Q8—224no—
404#121—118no—
405#121—2216no—
406#121—224no—
407#121—228no—
408C4×Q8—22no—
409C4×Q8C22×D1114yes—
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—21no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—228no—
421C2×C4⋊C4—222no—
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C22⋊C4—112no—
424C2×C22⋊C4—222no—
425C2×C22⋊C4—222no—
426C2×C22⋊C4—221no—
427C2×C42—21no—
428C2×C42C22×D1111yescharacteristic
429#106—114no—
430C4⋊C8C22×D1114yes—
431#103—114no—
432#103C22×D1118yes—
433#102—118no—
434#102—114no—
435C22⋊C8—118no—
436C4×C8—114no—
437C2×C11#328414yescomplemented
438C2×C11C2×D4211yescharacteristic
439C2×C11C22×#13511yescharacteristic
440C2×C11C2×#57711yescharacteristic
441D11—44no—
442D11—44no—
443D11—84no—
444C24—112no—
445C24—221no—
446C24—222no—
447#41—2216no—
448#41—2216no—
449#41—448no—
450#41—448no—
451#41—4416no—
452#41—4416no—
453C2×Q8—21no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—24no—
457C2×Q8—24no—
458C2×Q8D4×D1114yes—
459C2×Q8C23×D1114yes—
460C2×Q8C23×D1112yes—
461C2×D4—114no—
462C2×D4—114no—
463C2×D4—112no—
464C2×D4—114no—
465C2×D4—228no—
466C2×D4—228no—
467C2×D4—228no—
468C2×D4—224no—
469C2×D4—221no—
470C2×D4—224no—
471C2×D4—224no—
472C2×D4—222no—
473C2×D4—224no—
474C2×D4—222no—
475C2×D4—224no—
476C2×D4—448no—
477C2×D4—448no—
478C2×D4—444no—
479C2×D4—882no—
480C2×D4—884no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—112no—
485C22×C4—114no—
486C22×C4—114no—
487C22×C4—228no—
488C22×C4—228no—
489C22×C4—224no—
490C22×C4—224no—
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—216no—
500SD16—1116no—
501SD16—2216no—
502SD16—448no—
503D8—2216no—
504C2×C8—24no—
505C2×C8—114no—
506C2×C8—112no—
507C2×C8—112no—
508C2×C8—2216no—
509C2×C8—222no—
510C2×C8C23×D1114yes—
511C4⋊C4—24no—
512C4⋊C4—24no—
513C4⋊C4—24no—
514C4⋊C4—21no—
515C4⋊C4—114no—
516C4⋊C4—112no—
517C4⋊C4—228no—
518C4⋊C4—221no—
519C4⋊C4C23×D1112yes—
520C22⋊C4—118no—
521C22⋊C4—228no—
522C22⋊C4—228no—
523C22⋊C4—224no—
524C42—24no—
525C42D4×D1112yes—
526C42C23×D1112yes—
527C11C2×#328411yescharacteristic, complemented, Sylow
528C23—114no—
529C23—224no—
530C23—224no—
531C23—224no—
532C23—224no—
533C23—222no—
534C23—224no—
535C23—442no—
536C23—442no—
537C23—444no—
538C23—444no—
539C23—444no—
540C23C2×D4×D1111yescharacteristic
541Q8—24no—
542Q8—22no—
543Q8—24no—
544Q8—24no—
545Q8—44no—
546Q8C2×D4×D1114yes—
547D4—114no—
548D4—228no—
549D4—224no—
550D4—224no—
551D4—222no—
552D4—224no—
553D4—4416no—
554D4—4416no—
555D4—448no—
556D4—444no—
557D4—884no—
558D4—888no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—42no—
565C2×C4—44no—
566C2×C4—114no—
567C2×C4—224no—
568C2×C4—228no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—222no—
572C2×C4—4416no—
573C2×C4—4416no—
574C2×C4—442no—
575C2×C4—448no—
576C2×C4#6697214yescomplemented
577C2×C4C2×D4×D1112yes—
578C2×C4C2×D4×D1112yes—
579C2×C4C2×D4×D1111yescharacteristic
580C2×C4C2×D4×D1112yes—
581C2×C4#6704212yes—
582C2×C4C24×D1111yescharacteristic
583C8—24no—
584C8—114no—
585C8—222no—
586C22—224no—
587C22—224no—
588C22—224no—
589C22—224no—
590C22—448no—
591C22—448no—
592C22—442no—
593C22—442no—
594C22—444no—
595C22—444no—
596C22—444no—
597C22—888no—
598C22#1062314012yes—
599C22C2×#6697212yes—
600C22#1062330912yes—
601C22C22×D4×D1111yescharacteristic
602C4—24no—
603C4—22no—
604C4—44no—
605C4—42no—
606C4—224no—
607C4—442no—
608C4#1062314012yes—
609C4C2×#6697214yescomplemented
610C4C22×D4×D1111yescharacteristic
611C4C2×#6704211yescharacteristic
612C2—444no—
613C2—444no—
614C2—884no—
615C2#1308034114yesdirect product factor
616C2C2×#1062314011yescharacteristic
617C2C22×#6697211yescharacteristic
618C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#462C2
socleC23×C11C22×D4
hypercenterC2×#462D11
hypocenterC11C2×#3284
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
1. C22×#66972C2semidirect
2. C2×#10623108C2semidirect
3. C2×#10623257C2semidirect
4. #13080341C2direct (N × H)
5. C2×#10622698C2semidirect
6. C2×#10622420C2semidirect
7. C2×#10622456C2semidirect
8. C2×#10622800C2semidirect
9. C2×#10622424C2semidirect
10. C2×C4×#4325C2semidirect
11. C2×#10622447C2semidirect
12. C2×C11×#462C2semidirect
23. C2×#66972C22semidirect
27. #10623257C22semidirect
29. #10623108C22semidirect
40. C11×#462C22semidirect
44. #10622800C22semidirect
47. #10622698C22semidirect
48. C4×#4325C22semidirect
52. #10622456C22semidirect
53. #10622447C22semidirect
54. #10622424C22semidirect
55. #10622420C22semidirect
95. C2×#4325D4semidirect
204. #4325C2×D4semidirect
225. C2×#462D11semidirect
257. C2×C4×C11#135semidirect
318. #462C2×D11semidirect
353. C4×C11C2×#135semidirect
437. C2×C11#3284semidirect
527. C11C2×#3284semidirect
576. C2×C4#66972semidirect
609. C4C2×#66972semidirect
615. C2#13080341direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669722
C2×#106231082
C2×#106232572
#130803412
C2×#106226982
C2×#106224202
C2×#106224562
C2×#106228002
C2×#106224242
C2×C4×#43252
C2×#106224472
C2×C11×#4622
C2×#328411