Finite Group Databasebeta

← C2×#13080948 #15630712

Subgroups — C2×#13080948 #15630712

Order 2816.

2210 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×#10623084C211yesmaximal, characteristic
2#13080948C2116yesmaximal, direct product factor
3C2×#10622701C211yesmaximal, characteristic, complemented
4C2×#10622580C212yesmaximal, complemented
5C2×#10622704C211yesmaximal, characteristic, complemented
6C2×#10622662C212yesmaximal, complemented
7C2×#10622640C211yesmaximal, characteristic, complemented
8C2×#10622660C212yesmaximal, complemented
9C2×C4×#4326C211yesmaximal, characteristic, complemented
10C2×#10622625C211yesmaximal, characteristic, complemented
11C2×#10622579C212yesmaximal, complemented
12C2×C11×#554C211yesmaximal, characteristic, complemented
13C22×#4339C2212yes—
14C11×#554—24no—
15C11×#554C2218yescomplemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#125—21no—
18C2×C11×C22⋊Q8—22no—
19C2×C11×C22⋊Q8C2212yes—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11C2211yescharacteristic
23C22×C11×C4⋊C4C2212yes—
24C22×#4326C2211yescharacteristic
25C22×#4325C2212yes—
26C2×#66993—21no—
27C2×#66983C2212yes—
28C22×#4318C2212yes—
29#10623084—24no—
30#10623084C2218yes—
31C2×#66946—21no—
32C2×#66937—22no—
33C2×#66927C2211yescharacteristic
34C2×C4×Dic22C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622704C2218yescomplemented
38#10622701C2218yescomplemented
39#10622662C22116yescomplemented
40#10622660C22116yescomplemented
41C4×#4326C2218yescomplemented
42#10622640C2218yescomplemented
43#10622625C2218yescomplemented
44C2×#66874C2212yes—
45C2×#66874C2211yescharacteristic
46#10622580C22116yescomplemented
47#10622579C22116yescomplemented
48C2×#66873C2212yes—
49C2×#66873C2212yes—
50C2×#66873C2212yes—
51C2×#66871C2212yes—
52C2×#66871C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55C22×Q8×C11—21no—
56C22×Q8×C11C2311yescharacteristic
57C22×D4×C11D411yescharacteristic
58C23×C4×C11—22no—
59C23×C4×C11C2312yes—
60C22×C22⋊D11—22no—
61C22×C22⋊D11—22no—
62C2×#4339—24no—
63C2×#4339—28no—
64C2×#4339—44no—
65C2×#4339C2318yes—
66C22×D44—21no—
67C22×D44—21no—
68C22×D44C2312yes—
69C22×C4×D11—22no—
70C22×Dic22C2311yescharacteristic
71C11×C4⋊Q8—22no—
72C11×C4⋊Q8C2314yes—
73C11×#125—28no—
74C11×C22⋊Q8—24no—
75C11×C22⋊Q8—216no—
76C11×C22⋊Q8C2318yes—
77C4×Q8×C11—22no—
78C4×Q8×C11C2314yes—
79C4×D4×C11—28no—
80C4×D4×C11D414yes—
81C4×D4×C11C2314yes—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—24no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4D411yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C4⋊C4C2318yes—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4D412yes—
93C2×C42×C11—21no—
94C2×C42×C11C2311yescharacteristic
95C2×#4326—24no—
96C2×#4326C2314yes—
97C2×#4325—44no—
98C2×#4325C2318yes—
99#66993—28no—
100#66983—24no—
101#66983C2318yes—
102C2×(C2×D11)⋊C4—22no—
103C2×C4⋊Dic11C2311yescharacteristic
104C2×Dic11⋊C4—21no—
105C2×C4×Dic11—21no—
106C2×#4318—44no—
107C2×#4318C2318yes—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2312yes—
111#66946—28no—
112#66937—216no—
113#66927—22no—
114#66927C2314yes—
115C4×Dic22—22no—
116C4×Dic22C2314yes—
117#66899C2314yes—
118C22⋊(C11⋊C8)C2318yes—
119#66874C2314yes—
120#66874C2318yes—
121#66873C2318yes—
122#66873C2318yes—
123#66873C2318yes—
124#66871C2314yes—
125#66871C2318yes—
126C4⋊(C11⋊C8)C2314yes—
127C4×C11⋊C8C2314yes—
128C2×#3333—111nomaximal, Sylow
129C24×C11C2×D412yes—
130C23×D11—22no—
131C2×Q8×C11—21no—
132C2×Q8×C11—24no—
133C2×Q8×C11—22no—
134C2×Q8×C11—22no—
135C2×Q8×C11—82no—
136C2×Q8×C11C2412yes—
137C2×D4×C11—24no—
138C2×D4×C11C2×D414yes—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—28no—
145C22×C4×C11—84no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D414yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2414yes—
151C22×C4×C11C2411yescharacteristic
152C2×C22⋊D11—28no—
153C2×C22⋊D11—28no—
154C2×C22⋊D11—48no—
155C2×C22⋊D11—84no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158#4339—216no—
159#4339—48no—
160#4339—416no—
161C2×D44—22no—
162C2×D44—24no—
163C2×D44—24no—
164C2×D44—24no—
165C2×D44—24no—
166C2×D44—44no—
167C2×D44—82no—
168C2×D44C2414yes—
169C2×C4×D11—28no—
170C2×C4×D11—48no—
171C2×Dic22—21no—
172C2×Dic22—22no—
173C2×Dic22#4114yes—
174C2×Dic22C2412yes—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—28no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—24no—
179C11×C4⋊C4—24no—
180C11×C4⋊C4—28no—
181C11×C4⋊C4C2×D414yes—
182C11×C4⋊C4C2412yes—
183C11×C4⋊C4C2414yes—
184C11×C22⋊C4—28no—
185C11×C22⋊C4C2×D418yes—
186C42×C11—24no—
187C42×C11C2×D412yes—
188C42×C11C2412yes—
189#4326—28no—
190#4325—48no—
191(C2×D11)⋊C4—28no—
192C4⋊Dic11—21no—
193C4⋊Dic11C2412yes—
194Dic11⋊C4—24no—
195C4×Dic11—24no—
196#4318—48no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—24no—
200C2×C11⋊C8C2412yes—
201C2×C11⋊C8C2412yes—
202C2×C11⋊C8C2414yes—
203C2×#554D1111yescharacteristic, complemented
204C2×#550—111no—
205#3333—1116no—
206C2×#486—111no—
207C2×#480—112no—
208C2×#477—111no—
209C2×#468—112no—
210C2×#460—111no—
211C2×#452—112no—
212C2×C4×Q16—111no—
213C2×#436—111no—
214C2×#417—112no—
215C23×C11—24no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11C22×D414yes—
219C23×C11C22×D411yescharacteristic
220C22×D11—24no—
221C22×D11—44no—
222C22×D11—44no—
223C22×D11—44no—
224Q8×C11—22no—
225Q8×C11—22no—
226Q8×C11—42no—
227Q8×C11—84no—
228D4×C11—28no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—28no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—44no—
240C2×C4×C11—88no—
241C2×C4×C11#13714yes—
242C2×C4×C11C22×D412yes—
243C2×C4×C11C22×D414yes—
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D412yes—
246C2×C4×C11C2×#4112yes—
247C2×C4×C11H(5,𝔽2)12yes—
248C2×C4×C11C2511yescharacteristic
249C22⋊D11—416no—
250C22⋊D11—88no—
251C2×Dic11—24no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—42no—
255D44—24no—
256D44—24no—
257D44—44no—
258D44—48no—
259D44—84no—
260C4×D11—416no—
261Dic22—24no—
262Dic22—22no—
263Dic22C2×#4114yes—
264C11⋊C8—22no—
265C11⋊C8—22no—
266C11⋊C8—24no—
267C22×#41—112no—
268C22×Q16—111no—
269C22×SD16—112no—
270C22×M16—112no—
271#554—24no—
272#554C2×D1118yescomplemented
273#550—118no—
274#550—224no—
275C2×C4⋊Q8C2×D1111yescharacteristic
276C2×#127—111no—
277C2×#127—221no—
278C2×#125—21no—
279C2×C22⋊Q8—22no—
280C2×C22⋊Q8C2×D1112yes—
281C2×#121—112no—
282C2×#121—222no—
283C2×C4×Q8—111no—
284C2×C4×Q8C2×D1111yescharacteristic
285C2×C4×D4—21no—
286C2×C4×D4—221no—
287C2×C4×D4C2×D1111yescharacteristic
288C22×C4⋊C4C2×D1112yes—
289#486—118no—
290#480—1116no—
291#477—118no—
292#468—1116no—
293#460—118no—
294#452—1116no—
295C4×Q16—118no—
296#436—118no—
297C2×#107—112no—
298C2×#107—111no—
299C2×C4⋊C8—111no—
300#417—1116no—
301C2×#103—111no—
302C2×#103—112no—
303C2×#103—111no—
304C2×#102—112no—
305C2×#102—112no—
306C2×#102—112no—
307C2×C22⋊C8—112no—
308C2×C4×C8—111no—
309C22×C11—24no—
310C22×C11—24no—
311C22×C11—24no—
312C22×C11—48no—
313C22×C11#54612yes—
314C22×C11C2×#13712yes—
315C22×C11#57612yes—
316C22×C11C23×D411yescharacteristic
317C2×D11—44no—
318C2×D11—44no—
319C2×D11—44no—
320C2×D11—88no—
321C4×C11—24no—
322C4×C11—22no—
323C4×C11—42no—
324C4×C11—42no—
325C4×C11—44no—
326C4×C11#54612yes—
327C4×C11C2×#13714yes—
328C4×C11C22×#4111yescharacteristic
329C4×C11C2×H(5,𝔽2)11yescharacteristic
330Dic11—24no—
331Dic11—42no—
332C2×#41—118no—
333C2×#41—228no—
334C2×#41—224no—
335C2×#41—444no—
336C22×Q8—21no—
337C22×Q8—111no—
338C22×Q8C22×D1111yescharacteristic
339C22×D4—112no—
340C22×D4—222no—
341C22×D4—222no—
342C22×D4—221no—
343C22×D4—221no—
344C22×D4C22⋊D1111yescharacteristic
345C23×C4—22no—
346C23×C4—222no—
347C23×C4C22×D1112yes—
348C2×Q16—114no—
349C2×Q16—224no—
350C2×SD16—118no—
351C2×SD16—444no—
352C2×M16—118no—
353C2×M16—444no—
354C22×C8—111no—
355C22×C8—112no—
356C22×C8—111no—
357C4⋊Q8—22no—
358C4⋊Q8C22×D1114yes—
359#127—114no—
360#127—228no—
361#127—222no—
362#125—28no—
363C22⋊Q8—24no—
364C22⋊Q8—216no—
365C22⋊Q8C22×D1118yes—
366#121—118no—
367#121—224no—
368#121—2216no—
369C4×Q8—22no—
370C4×Q8—114no—
371C4×Q8—222no—
372C4×Q8C22×D1114yes—
373C4×D4—28no—
374C4×D4—228no—
375C4×D4C22⋊D1114yes—
376C4×D4C22×D1114yes—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4C22⋊D1111yescharacteristic
385C2×C4⋊C4C22×D1111yescharacteristic
386C2×C4⋊C4C22×D1112yes—
387C2×C4⋊C4C22×D1118yes—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—222no—
390C2×C22⋊C4C22⋊D1112yes—
391C2×C42—21no—
392C2×C42—221no—
393C2×C42C22×D1111yescharacteristic
394#107—114no—
395#107—118no—
396C4⋊C8—114no—
397#103—114no—
398#103—114no—
399#103—118no—
400#102—118no—
401#102—118no—
402#102—118no—
403C22⋊C8—118no—
404C4×C8—114no—
405C2×C11—44no—
406C2×C11#333314yescomplemented
407C2×C11C2×#54611yescharacteristic
408C2×C11C22×#13711yescharacteristic
409C2×C11C2×#57611yescharacteristic
410D11—84no—
411C24—222no—
412C24C2×C22⋊D1112yes—
413#41—2216no—
414#41—448no—
415#41—4416no—
416C2×Q8—21no—
417C2×Q8—24no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—82no—
421C2×Q8—114no—
422C2×Q8—112no—
423C2×Q8—222no—
424C2×Q8—221no—
425C2×Q8C23×D1112yes—
426C2×D4—24no—
427C2×D4—114no—
428C2×D4—228no—
429C2×D4—228no—
430C2×D4—224no—
431C2×D4—224no—
432C2×D4—224no—
433C2×D4—222no—
434C2×D4—224no—
435C2×D4—448no—
436C2×D4—444no—
437C2×D4—882no—
438C2×D4—884no—
439C2×D4C2×C22⋊D1114yes—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—28no—
446C22×C4—84no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—228no—
450C22×C4—448no—
451C22×C4C2×C22⋊D1114yes—
452C22×C4C2×C22⋊D1111yescharacteristic
453C22×C4C2×C22⋊D1112yes—
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C23×D1114yes—
456C22×C4C23×D1111yescharacteristic
457Q16—228no—
458SD16—448no—
459M16—448no—
460C2×C8—112no—
461C2×C8—112no—
462C2×C8—114no—
463C2×C8—222no—
464C2×C8—222no—
465C2×C8—224no—
466C4⋊C4—21no—
467C4⋊C4—28no—
468C4⋊C4—22no—
469C4⋊C4—24no—
470C4⋊C4—24no—
471C4⋊C4—28no—
472C4⋊C4—112no—
473C4⋊C4—221no—
474C4⋊C4—224no—
475C4⋊C4C2×C22⋊D1114yes—
476C4⋊C4C23×D1112yes—
477C4⋊C4C23×D1114yes—
478C22⋊C4—28no—
479C22⋊C4—228no—
480C22⋊C4C2×C22⋊D1118yes—
481C42—24no—
482C42—224no—
483C42C2×C22⋊D1112yes—
484C42C23×D1112yes—
485C11C2×#333311yescharacteristic, complemented, Sylow
486C23—24no—
487C23—24no—
488C23—24no—
489C23—224no—
490C23—444no—
491C23—444no—
492C23—444no—
493C23C22×C22⋊D1114yes—
494C23C22×C22⋊D1111yescharacteristic
495Q8—22no—
496Q8—22no—
497Q8—42no—
498Q8—84no—
499Q8—114no—
500Q8—224no—
501Q8—222no—
502D4—28no—
503D4—224no—
504D4—224no—
505D4—4416no—
506D4—448no—
507D4—444no—
508D4—884no—
509D4—888no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—28no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—44no—
521C2×C4—88no—
522C2×C4—224no—
523C2×C4—222no—
524C2×C4—222no—
525C2×C4—4416no—
526C2×C4—442no—
527C2×C4#6699514yes—
528C2×C4#41×D1112yes—
529C2×C4#6704212yes—
530C2×C4C22×C22⋊D1112yes—
531C2×C4C22×C22⋊D1114yes—
532C2×C4C22×C22⋊D1112yes—
533C2×C4C22×C22⋊D1111yescharacteristic
534C2×C4C24×D1111yescharacteristic
535C8—222no—
536C8—222no—
537C8—224no—
538C22—24no—
539C22—24no—
540C22—24no—
541C22—48no—
542C22—444no—
543C22—444no—
544C22—444no—
545C22—888no—
546C22C2×#6699512yes—
547C22#1062336012yes—
548C22#1062336612yes—
549C22C23×C22⋊D1111yescharacteristic
550C4—24no—
551C4—22no—
552C4—42no—
553C4—42no—
554C4—44no—
555C4—224no—
556C4—442no—
557C4C2×#6699514yes—
558C4#1062336012yes—
559C4C2×#41×D1111yescharacteristic
560C4C2×#6704211yescharacteristic
561C2—44no—
562C2—884no—
563C2#1308094814yesdirect product factor
564C2C2×#1062336011yescharacteristic
565C2C22×#6699511yescharacteristic
566C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#554C2
socleC23×C11C22×D4
prime radicalC2×#10623084C2
hypercenterC2×#554D11
hypocenterC11C2×#3333
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. #13080948C2direct (N × H)
3. C2×#10622701C2semidirect
4. C2×#10622580C2semidirect
5. C2×#10622704C2semidirect
6. C2×#10622662C2semidirect
7. C2×#10622640C2semidirect
8. C2×#10622660C2semidirect
9. C2×C4×#4326C2semidirect
10. C2×#10622625C2semidirect
11. C2×#10622579C2semidirect
12. C2×C11×#554C2semidirect
15. C11×#554C22semidirect
37. #10622704C22semidirect
38. #10622701C22semidirect
39. #10622662C22semidirect
40. #10622660C22semidirect
41. C4×#4326C22semidirect
42. #10622640C22semidirect
43. #10622625C22semidirect
46. #10622580C22semidirect
47. #10622579C22semidirect
203. C2×#554D11semidirect
272. #554C2×D11semidirect
406. C2×C11#3333semidirect
485. C11C2×#3333semidirect
563. C2#13080948direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230842
#130809482
C2×#106227012
C2×#106225802
C2×#106227042
C2×#106226622
C2×#106226402
C2×#106226602
C2×C4×#43262
C2×#106226252
C2×#106225792
C2×C11×#5542
C2×#333311