Finite Group Databasebeta

← C2×#13080959 #15632181

Subgroups — C2×#13080959 #15632181

Order 2816.

2374 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623086C211yesmaximal, characteristic, complemented
2#13080959C2116yesmaximal, direct product factor
3C2×#10622691C211yesmaximal, characteristic, complemented
4C2×#10622580C212yesmaximal, complemented
5C2×#10622646C212yesmaximal, complemented
6C2×#10622620C211yesmaximal, characteristic, complemented
7C2×#10622700C211yesmaximal, characteristic, complemented
8C2×#10622651C212yesmaximal, complemented
9C2×C4×#4323C211yesmaximal, characteristic, complemented
10C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
11C22×#66871C212yesmaximal, complemented
12C2×C11×#547C211yesmaximal, characteristic, complemented
13C22×C11×#41—21no—
14C22×#4341—21no—
15C11×#547—24no—
16C11×#547C2218yescomplemented
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#123—22no—
19C2×C11×C22⋊Q8—21no—
20C2×C11×#121C2212yes—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C22×C11×C4⋊C4C2212yes—
24C22×#4323C2211yescharacteristic
25C2×#66983C2212yes—
26C22×C4⋊Dic11C2212yes—
27C23×C11⋊C8C2212yes—
28#10623086—24no—
29#10623086C2218yescomplemented
30C2×#66950—21no—
31C2×#66939—22no—
32C2×C4×D44C2211yescharacteristic
33C2×#66922C2211yescharacteristic
34C2×#66896C2212yes—
35C2×#66896C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622700C2218yescomplemented
38#10622691C2218yescomplemented
39#10622651C22116yescomplemented
40#10622646C22116yescomplemented
41C4×#4323C2218yescomplemented
42D4×C11⋊C8C2218yescomplemented
43#10622620C2218yescomplemented
44#10622580C22116yescomplemented
45C2×#66873C2212yes—
46C2×#66873C2211yescharacteristic
47C2×#66871C2212yes—
48C2×#66871C2212yes—
49C2×#66871C2212yes—
50C2×#66871C2212yes—
51C2×#66871C2211yescharacteristic
52C2×#66871C22116yescomplemented
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55C2×C11×#41—28no—
56C2×C11×#41—48no—
57C22×Q8×C11—21no—
58C22×D4×C11—22no—
59C22×D4×C11D411yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—22no—
62C23×C4×C11—21no—
63C23×C4×C11C2312yes—
64C22×C22⋊D11—22no—
65C23×Dic11—22no—
66C2×#4341—28no—
67C2×#4341—48no—
68C22×D44C2311yescharacteristic
69C22×C4×D11—21no—
70C22×Dic22—21no—
71C11×C4⋊Q8—22no—
72C11×C4⋊Q8C2314yes—
73C11×#123—216no—
74C11×C22⋊Q8—28no—
75C11×#121—24no—
76C11×#121C2318yes—
77C4×D4×C11—22no—
78C4×D4×C11D414yes—
79C4×D4×C11C2314yes—
80C4×D4×C11C2314yes—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—24no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C4⋊C4C2318yes—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4D412yes—
91C2×C42×C11C2311yescharacteristic
92C2×#4323—24no—
93C2×#4323C2314yes—
94#66983—24no—
95#66983C2318yes—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—22no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—22no—
100C2×C4⋊Dic11—24no—
101C2×C4⋊Dic11C2312yes—
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2318yes—
104C22×C11⋊C8—28no—
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2312yes—
107C22×C11⋊C8C2318yes—
108C22×C11⋊C8C2311yescharacteristic
109#66950—28no—
110#66939—216no—
111C4×D44—22no—
112C4×D44C2314yes—
113#66922—22no—
114#66922C2314yes—
115#66896C2318yes—
116#66896C2314yes—
117C22⋊(C11⋊C8)C2318yes—
118#66873C2314yes—
119#66873C2318yes—
120#66871C2314yes—
121#66871C2318yes—
122#66871C2318yes—
123#66871C2318yes—
124#66871C2318yes—
125C4⋊(C11⋊C8)C2314yes—
126C4×C11⋊C8C2314yes—
127C2×#3334—111nomaximal, Sylow
128C24×C11—21no—
129C24×C11C2×D412yes—
130C23×D11—21no—
131C11×#41—432no—
132C2×Q8×C11—24no—
133C2×Q8×C11—44no—
134C2×D4×C11—28no—
135C2×D4×C11—21no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—48no—
139C2×D4×C11D818yescomplemented
140C2×D4×C11C2×D414yes—
141C2×D4×C11C2412yes—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—21no—
145C22×C4×C11—22no—
146C22×C4×C11—28no—
147C22×C4×C11—24no—
148C22×C4×C11—48no—
149C22×C4×C11—44no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D414yes—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2414yes—
155C22×C4×C11C2411yescharacteristic
156C2×C22⋊D11—28no—
157C2×C22⋊D11—48no—
158C22×Dic11—28no—
159C22×Dic11—22no—
160C22×Dic11—21no—
161C22×Dic11—48no—
162#4341—432no—
163C2×D44—21no—
164C2×D44—22no—
165C2×D44—22no—
166C2×D44C2412yes—
167C2×C4×D11—24no—
168C2×C4×D11—44no—
169C2×Dic22—24no—
170C2×Dic22—44no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—28no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4C2×D414yes—
176C11×C4⋊C4C2412yes—
177C11×C4⋊C4C2414yes—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—28no—
180C11×C22⋊C4C2×D418yes—
181C42×C11C2×D412yes—
182C42×C11C2412yes—
183#4323—28no—
184(C2×D11)⋊C4—24no—
185(C2×D11)⋊C4—28no—
186C4⋊Dic11—22no—
187C4⋊Dic11—24no—
188C4⋊Dic11—21no—
189C4⋊Dic11—28no—
190C4⋊Dic11C2414yes—
191C4⋊Dic11C2412yes—
192C2×C11⋊C8—216no—
193C2×C11⋊C8—24no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8#4114yescomplemented
196C2×C11⋊C8C2412yes—
197C2×C11⋊C8C2414yes—
198C2×C11⋊C8C2412yes—
199C2×#547—111no—
200C2×#547D1111yescharacteristic, complemented
201#3334—1116no—
202C2×#500—111no—
203C2×#480—112no—
204C2×#480—112no—
205C2×#474—111no—
206C2×#474—111no—
207C2×#466—112no—
208C2×C4×D8—111no—
209C2×C8×D4—111no—
210C22×#107—112no—
211C23×C11—24no—
212C23×C11—24no—
213C23×C11—22no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11C2×D818yes—
218C23×C11C22×D414yes—
219C23×C11C22×D411yescharacteristic
220C22×D11—22no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224Q8×C11—48no—
225D4×C11—22no—
226D4×C11—22no—
227D4×C11—416no—
228D4×C11—42no—
229D4×C11C2×D8116yescomplemented
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—28no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—42no—
238C2×C4×C11—44no—
239C2×C4×C11—416no—
240C2×C4×C11—48no—
241C2×C4×C11C2×D814yes—
242C2×C4×C11C22×D412yes—
243C2×C4×C11C22×D414yes—
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D412yes—
246C2×C4×C11C2×#4112yes—
247C2×C4×C112−1+412yes—
248C2×C4×C11C2511yescharacteristic
249C22⋊D11—416no—
250C2×Dic11—24no—
251C2×Dic11—22no—
252C2×Dic11—44no—
253C2×Dic11—42no—
254C2×Dic11—416no—
255D44—22no—
256D44—22no—
257D44—42no—
258C4×D11—48no—
259Dic22—48no—
260C11⋊C8—24no—
261C11⋊C8—22no—
262C11⋊C8C2×#4114yescomplemented
263C22×#41—21no—
264C22×#41—221no—
265C22×D8—111no—
266C23×C8—112no—
267#547—24no—
268#547—118no—
269#547—224no—
270#547C2×D1118yescomplemented
271C2×C4⋊Q8—111no—
272C2×C4⋊Q8C2×D1111yescharacteristic
273C2×#123—22no—
274C2×#123—222no—
275C2×C22⋊Q8—21no—
276C2×C22⋊Q8—221no—
277C2×#121—112no—
278C2×#121C2×D1112yes—
279C2×C4×D4—111no—
280C2×C4×D4C2×D1111yescharacteristic
281C2×C4×D4C2×D1111yescharacteristic
282C22×C4⋊C4—112no—
283C22×C4⋊C4C2×D1112yes—
284#500—118no—
285#480—1116no—
286#480—1116no—
287#474—118no—
288#474—118no—
289#466—1116no—
290C4×D8—118no—
291C8×D4—118no—
292C2×#107—1116no—
293C2×#107—112no—
294C2×#107—112no—
295C2×#107—112no—
296C2×#107—112no—
297C2×#107—111no—
298C2×C4⋊C8—111no—
299C2×#102—111no—
300C2×#102—112no—
301C2×#102—111no—
302C2×#102—112no—
303C2×C22⋊C8—112no—
304C2×C4×C8—111no—
305C22×C11—216no—
306C22×C11—24no—
307C22×C11—24no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—84no—
312C22×C11#54712yes—
313C22×C11C22×D818yes—
314C22×C11C22×D812yes—
315C22×C11#57812yes—
316C22×C11C23×D411yescharacteristic
317C2×D11—42no—
318C2×D11—42no—
319C2×D11—42no—
320C2×D11—84no—
321C4×C11—24no—
322C4×C11—22no—
323C4×C11—42no—
324C4×C11—44no—
325C4×C11#54712yes—
326C4×C11C22×D814yes—
327C4×C11C22×#4111yescharacteristic
328C4×C11C2×2−1+411yescharacteristic
329Dic11—44no—
330Dic11—42no—
331C2×#41—28no—
332C2×#41—48no—
333C2×#41—228no—
334C2×#41—448no—
335C22×Q8—21no—
336C22×Q8—221no—
337C22×D4—22no—
338C22×D4—111no—
339C22×D4—222no—
340C22×D4C22⋊D1111yescharacteristic
341C22×D4C22×D1111yescharacteristic
342C23×C4—22no—
343C23×C4—21no—
344C23×C4—222no—
345C23×C4—221no—
346C23×C4C22×D1112yes—
347C2×D8—114no—
348C2×D8—224no—
349C22×C8—111no—
350C22×C8—112no—
351C22×C8—118no—
352C22×C8—111no—
353C22×C8—228no—
354C4⋊Q8—22no—
355C4⋊Q8—114no—
356C4⋊Q8—222no—
357C4⋊Q8C22×D1114yes—
358#123—216no—
359#123—2216no—
360C22⋊Q8—28no—
361C22⋊Q8—228no—
362#121—24no—
363#121—118no—
364#121—224no—
365#121C22×D1118yes—
366C4×D4—22no—
367C4×D4—114no—
368C4×D4—222no—
369C4×D4C22⋊D1114yes—
370C4×D4C22×D1114yes—
371C4×D4C22×D1114yes—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—112no—
377C2×C4⋊C4—118no—
378C2×C4⋊C4—222no—
379C2×C4⋊C4—224no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4C22⋊D1111yescharacteristic
382C2×C4⋊C4C22×D1111yescharacteristic
383C2×C4⋊C4C22×D1112yes—
384C2×C4⋊C4C22×D1118yes—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—221no—
388C2×C22⋊C4—222no—
389C2×C22⋊C4C22⋊D1112yes—
390C2×C42C22×D1111yescharacteristic
391#107—114no—
392#107—118no—
393#107—118no—
394#107—118no—
395#107—118no—
396C4⋊C8—114no—
397#102—114no—
398#102—118no—
399#102—114no—
400#102—118no—
401C22⋊C8—118no—
402C4×C8—114no—
403C2×C11—28no—
404C2×C11—82no—
405C2×C11#333414yescomplemented
406C2×C11C2×#54711yescharacteristic
407C2×C11C23×D811yescharacteristic
408C2×C11C2×#57811yescharacteristic
409D11—82no—
410C24—21no—
411C24—221no—
412C24C2×C22⋊D1112yes—
413#41—432no—
414#41—4432no—
415C2×Q8—24no—
416C2×Q8—44no—
417C2×Q8—224no—
418C2×Q8—444no—
419C2×D4—28no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—21no—
423C2×D4—48no—
424C2×D4—112no—
425C2×D4—228no—
426C2×D4—222no—
427C2×D4—222no—
428C2×D4—221no—
429C2×D4—448no—
430C2×D4#432318yescomplemented
431C2×D4C2×C22⋊D1114yes—
432C2×D4C23×D1112yes—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—28no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—24no—
439C22×C4—48no—
440C22×C4—44no—
441C22×C4—228no—
442C22×C4—221no—
443C22×C4—222no—
444C22×C4—224no—
445C22×C4—448no—
446C22×C4—444no—
447C22×C4C2×C22⋊D1114yes—
448C22×C4C2×C22⋊D1111yescharacteristic
449C22×C4C2×C22⋊D1112yes—
450C22×C4C2×C22⋊D1111yescharacteristic
451C22×C4C23×D1114yes—
452C22×C4C23×D1111yescharacteristic
453D8—228no—
454C2×C8—114no—
455C2×C8—112no—
456C2×C8—112no—
457C2×C8—114no—
458C2×C8—2216no—
459C2×C8—224no—
460C2×C8—222no—
461C4⋊C4—21no—
462C4⋊C4—22no—
463C4⋊C4—28no—
464C4⋊C4—24no—
465C4⋊C4—112no—
466C4⋊C4—114no—
467C4⋊C4—221no—
468C4⋊C4—222no—
469C4⋊C4—228no—
470C4⋊C4—224no—
471C4⋊C4C2×C22⋊D1114yes—
472C4⋊C4C23×D1112yes—
473C4⋊C4C23×D1114yes—
474C22⋊C4—24no—
475C22⋊C4—28no—
476C22⋊C4—224no—
477C22⋊C4—228no—
478C22⋊C4C2×C22⋊D1118yes—
479C42C2×C22⋊D1112yes—
480C42C23×D1112yes—
481C11C2×#333411yescharacteristic, complemented, Sylow
482C23—24no—
483C23—24no—
484C23—22no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—222no—
489C23—442no—
490C23—442no—
491C23—442no—
492C23C2×#432318yes—
493C23C22×C22⋊D1114yes—
494C23C22×C22⋊D1111yescharacteristic
495Q8—48no—
496Q8—448no—
497D4—22no—
498D4—22no—
499D4—416no—
500D4—42no—
501D4—222no—
502D4—222no—
503D4—4416no—
504D4—442no—
505D4C2×#4323116yescomplemented
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—28no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—42no—
514C2×C4—44no—
515C2×C4—416no—
516C2×C4—48no—
517C2×C4—222no—
518C2×C4—224no—
519C2×C4—442no—
520C2×C4—444no—
521C2×C4—4416no—
522C2×C4—448no—
523C2×C4C2×#432314yes—
524C2×C4#41×D1112yes—
525C2×C4#6704312yes—
526C2×C4C22×C22⋊D1112yes—
527C2×C4C22×C22⋊D1114yes—
528C2×C4C22×C22⋊D1112yes—
529C2×C4C22×C22⋊D1111yescharacteristic
530C2×C4C24×D1111yescharacteristic
531C8—114no—
532C8—224no—
533C8—222no—
534C22—216no—
535C22—24no—
536C22—24no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—84no—
541C22—442no—
542C22—442no—
543C22—442no—
544C22—884no—
545C22C22×#432318yes—
546C22C22×#432312yes—
547C22#1062335512yes—
548C22#1062336912yes—
549C22C23×C22⋊D1111yescharacteristic
550C4—24no—
551C4—22no—
552C4—42no—
553C4—44no—
554C4—442no—
555C4—444no—
556C4C22×#432314yes—
557C4#1062335512yes—
558C4C2×#41×D1111yescharacteristic
559C4C2×#6704311yescharacteristic
560C2—28no—
561C2—82no—
562C2—882no—
563C2#1308095914yesdirect product factor
564C2C2×#1062335511yescharacteristic
565C2C23×#432311yescharacteristic
566C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#547C2
socleC23×C11C22×D4
hypercenterC2×#547D11
hypocenterC11C2×#3334
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#10623086C2semidirect
2. #13080959C2direct (N × H)
3. C2×#10622691C2semidirect
4. C2×#10622580C2semidirect
5. C2×#10622646C2semidirect
6. C2×#10622620C2semidirect
7. C2×#10622700C2semidirect
8. C2×#10622651C2semidirect
9. C2×C4×#4323C2semidirect
10. C2×D4×C11⋊C8C2semidirect
11. C22×#66871C2semidirect
12. C2×C11×#547C2semidirect
16. C11×#547C22semidirect
29. #10623086C22semidirect
37. #10622700C22semidirect
38. #10622691C22semidirect
39. #10622651C22semidirect
40. #10622646C22semidirect
41. C4×#4323C22semidirect
42. D4×C11⋊C8C22semidirect
43. #10622620C22semidirect
44. #10622580C22semidirect
52. C2×#66871C22semidirect
139. C2×D4×C11D8semidirect
195. C2×C11⋊C8#41semidirect
200. C2×#547D11semidirect
229. D4×C11C2×D8semidirect
262. C11⋊C8C2×#41semidirect
270. #547C2×D11semidirect
405. C2×C11#3334semidirect
430. C2×D4#4323semidirect
481. C11C2×#3334semidirect
505. D4C2×#4323semidirect
563. C2#13080959direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230862
#130809592
C2×#106226912
C2×#106225802
C2×#106226462
C2×#106226202
C2×#106227002
C2×#106226512
C2×C4×#43232
C2×D4×C11⋊C82
C22×#668712
C2×C11×#5472
C2×#333411