Finite Group Databasebeta

← C2×#13080954 #15630718

Subgroups — C2×#13080954 #15630718

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×#10623074C211yesmaximal, characteristic, complemented
2#13080954C2116yesmaximal, direct product factor
3C2×#10622683C211yesmaximal, characteristic, complemented
4C2×#10622646C212yesmaximal, complemented
5C2×#10622634C211yesmaximal, characteristic, complemented
6C2×#10622655C212yesmaximal, complemented
7C2×#10622688C211yesmaximal, characteristic, complemented
8C2×#10622852C212yesmaximal, complemented
9C2×C4×#4326C211yesmaximal, characteristic, complemented
10C2×#10622625C211yesmaximal, characteristic, complemented
11C2×#10622845C212yesmaximal, complemented
12C2×C11×#550C211yesmaximal, characteristic
13C22×C11×#41C2212yes—
14C11×#550—24no—
15C11×#550C2218yes—
16C2×C11×#127—21no—
17C2×C11×#127C2211yescharacteristic
18C2×C11×#121—22no—
19C2×C11×#121C2212yes—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11C2211yescharacteristic
23C22×#4326C2211yescharacteristic
24C2×D4×Dic11—21no—
25C22×#4324C2212yes—
26C22×C4⋊Dic11C2212yes—
27C2×#66977C2212yes—
28C22×#4318C2212yes—
29#10623074—24no—
30#10623074C2218yescomplemented
31C2×#66943—21no—
32C2×#66931—22no—
33C2×#66922C2211yescharacteristic
34C2×C4×Dic22C2211yescharacteristic
35#10622852C22116yescomplemented
36#10622845C22116yescomplemented
37C2×#66899C2212yes—
38C2×#66899C2211yescharacteristic
39C2×#66896C2212yes—
40C2×#66896C2212yes—
41C2×#66896C2212yes—
42C2×C22⋊(C11⋊C8)C2212yes—
43#10622688C2218yescomplemented
44#10622683C2218yescomplemented
45#10622655C22116yescomplemented
46#10622646C22116yescomplemented
47C4×#4326C2218yescomplemented
48#10622634C2218yescomplemented
49#10622625C2218yescomplemented
50C2×#66874C2211yescharacteristic
51C2×#66871C2212yes—
52C2×#66871C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55C2×C11×#41—24no—
56C2×C11×#41—28no—
57C2×C11×#41—44no—
58C2×C11×#41C2318yes—
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11—22no—
61C22×D4×C11—22no—
62C22×D4×C11—21no—
63C22×D4×C11—21no—
64C22×D4×C11D411yescharacteristic
65C22×D4×C11C2312yes—
66C23×C4×C11—22no—
67C23×C4×C11C2312yes—
68C23×Dic11—22no—
69C22×Dic22—21no—
70C22×Dic22C2311yescharacteristic
71C11×#127—28no—
72C11×#127—22no—
73C11×#127C2314yes—
74C11×#121—24no—
75C11×#121—216no—
76C11×#121C2318yes—
77C4×Q8×C11—22no—
78C4×Q8×C11C2314yes—
79C4×D4×C11—28no—
80C4×D4×C11D414yes—
81C4×D4×C11C2314yes—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4D412yes—
87C2×C42×C11—21no—
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11—22no—
90C2×#4326—24no—
91C2×#4326C2314yes—
92D4×Dic11—28no—
93C2×#4324—44no—
94C2×#4324C2318yes—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—22no—
97C2×C4⋊Dic11—24no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2312yes—
100C2×C4⋊Dic11C2318yes—
101#66977—24no—
102#66977C2318yes—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—22no—
105C2×C4×Dic11—21no—
106C2×#4318—44no—
107C2×#4318C2318yes—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2312yes—
111#66943—28no—
112#66931—216no—
113#66922—22no—
114#66922C2314yes—
115C4×Dic22—22no—
116C4×Dic22C2314yes—
117#66899C2314yes—
118#66899C2318yes—
119#66896C2318yes—
120#66896C2318yes—
121#66896C2318yes—
122C22⋊(C11⋊C8)C2318yes—
123#66874C2314yes—
124#66871C2318yes—
125#66871C2314yes—
126C4⋊(C11⋊C8)C2314yes—
127C4×C11⋊C8C2314yes—
128C2×#3333—111nomaximal, Sylow
129C24×C11—22no—
130C24×C11C2×D412yes—
131C11×#41—216no—
132C11×#41—48no—
133C11×#41—416no—
134C2×Q8×C11—21no—
135C2×Q8×C11—22no—
136C2×Q8×C11#4114yes—
137C2×Q8×C11C2412yes—
138C2×D4×C11—28no—
139C2×D4×C11—28no—
140C2×D4×C11—24no—
141C2×D4×C11—24no—
142C2×D4×C11—22no—
143C2×D4×C11—24no—
144C2×D4×C11—24no—
145C2×D4×C11—24no—
146C2×D4×C11—48no—
147C2×D4×C11—44no—
148C2×D4×C11—82no—
149C2×D4×C11—84no—
150C2×D4×C11C2×D414yes—
151C2×D4×C11C2414yes—
152C22×C4×C11—21no—
153C22×C4×C11—24no—
154C22×C4×C11—24no—
155C22×C4×C11—21no—
156C22×C4×C11—28no—
157C22×C4×C11—48no—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D414yes—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2414yes—
163C22×C4×C11C2411yescharacteristic
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—22no—
167C22×Dic11—28no—
168C22×Dic11—84no—
169C2×Dic22—21no—
170C2×Dic22—24no—
171C2×Dic22—22no—
172C2×Dic22—22no—
173C2×Dic22—82no—
174C2×Dic22C2412yes—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4C2×D414yes—
178C11×C4⋊C4C2412yes—
179C11×C22⋊C4—28no—
180C11×C22⋊C4C2×D418yes—
181C42×C11—24no—
182C42×C11C2×D412yes—
183C42×C11C2412yes—
184C22⋊Dic11—28no—
185#4326—28no—
186#4324—48no—
187C4⋊Dic11—21no—
188C4⋊Dic11—22no—
189C4⋊Dic11—24no—
190C4⋊Dic11—28no—
191C4⋊Dic11C2412yes—
192C4⋊Dic11C2414yes—
193Dic11⋊C4—24no—
194Dic11⋊C4—28no—
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×#554—111no—
204C2×#550D1111yescharacteristic
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×C11—24no—
219C23×C11—44no—
220C23×C11—44no—
221C23×C11—44no—
222C23×C11C22×D414yes—
223C23×C11C22×D411yescharacteristic
224Q8×C11—24no—
225Q8×C11—22no—
226Q8×C11C2×#4114yes—
227D4×C11—28no—
228D4×C11—24no—
229D4×C11—24no—
230D4×C11—416no—
231D4×C11—44no—
232D4×C11—48no—
233D4×C11—84no—
234D4×C11—88no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—28no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—22no—
243C2×C4×C11—416no—
244C2×C4×C11—42no—
245C2×C4×C11#13714yes—
246C2×C4×C11C22×D414yes—
247C2×C4×C11C22×D412yes—
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D412yes—
250C2×C4×C11C2×#4112yes—
251C2×C4×C11H(5,𝔽2)12yes—
252C2×C4×C11C2511yescharacteristic
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—24no—
256C2×Dic11—42no—
257C2×Dic11—44no—
258C2×Dic11—42no—
259C2×Dic11—88no—
260Dic22—22no—
261Dic22—22no—
262Dic22—42no—
263Dic22—84no—
264C11⋊C8—22no—
265C11⋊C8—22no—
266C11⋊C8—24no—
267C22×#41C2×D1112yes—
268C22×Q16—111no—
269C22×SD16—112no—
270C22×M16—112no—
271#554—118no—
272#554—224no—
273#550—24no—
274#550C2×D1118yes—
275C2×C4⋊Q8—111no—
276C2×#127—21no—
277C2×#127C2×D1111yescharacteristic
278C2×#125—221no—
279C2×C22⋊Q8—112no—
280C2×C22⋊Q8—222no—
281C2×#121—22no—
282C2×#121C2×D1112yes—
283C2×C4×Q8—111no—
284C2×C4×Q8C2×D1111yescharacteristic
285C2×C4×D4—21no—
286C2×C4×D4—221no—
287C2×C4×D4C2×D1111yescharacteristic
288C22×C4⋊C4—112no—
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—112no—
302C2×#103—111no—
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—44no—
314C22×C11—44no—
315C22×C11—44no—
316C22×C11—88no—
317C22×C11#54612yes—
318C22×C11C2×#13712yes—
319C22×C11#57612yes—
320C22×C11C23×D411yescharacteristic
321C4×C11—24no—
322C4×C11—24no—
323C4×C11—22no—
324C4×C11—42no—
325C4×C11#54612yes—
326C4×C11C2×#13714yes—
327C4×C11C22×#4111yescharacteristic
328C4×C11C2×H(5,𝔽2)11yescharacteristic
329Dic11—42no—
330Dic11—44no—
331Dic11—42no—
332C2×#41—24no—
333C2×#41—28no—
334C2×#41—44no—
335C2×#41C22×D1118yes—
336C22×Q8—111no—
337C22×Q8—221no—
338C22×Q8C22×D1111yescharacteristic
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—21no—
342C22×D4—21no—
343C22×D4C22⋊D1111yescharacteristic
344C22×D4C22×D1112yes—
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—114no—
358C4⋊Q8—222no—
359#127—28no—
360#127—22no—
361#127C22×D1114yes—
362#125—228no—
363C22⋊Q8—118no—
364C22⋊Q8—224no—
365C22⋊Q8—2216no—
366#121—24no—
367#121—216no—
368#121C22×D1118yes—
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—21no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—112no—
380C2×C4⋊C4—118no—
381C2×C4⋊C4—222no—
382C2×C4⋊C4—224no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—222no—
386C2×C4⋊C4C22⋊D1111yescharacteristic
387C2×C4⋊C4C22×D1111yescharacteristic
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—118no—
399#103—114no—
400#102—118no—
401#102—118no—
402#102—118no—
403C22⋊C8—118no—
404C4×C8—114no—
405C2×C11—44no—
406C2×C11—84no—
407C2×C11#333314yescomplemented
408C2×C11C2×#54611yescharacteristic
409C2×C11C22×#13711yescharacteristic
410C2×C11C2×#57611yescharacteristic
411C24—22no—
412C24C2×C22⋊D1112yes—
413#41—216no—
414#41—48no—
415#41—416no—
416C2×Q8—22no—
417C2×Q8—21no—
418C2×Q8—112no—
419C2×Q8—221no—
420C2×Q8—224no—
421C2×Q8—222no—
422C2×Q8—222no—
423C2×Q8—882no—
424C2×Q8#434114yes—
425C2×Q8C23×D1112yes—
426C2×D4—28no—
427C2×D4—28no—
428C2×D4—24no—
429C2×D4—24no—
430C2×D4—24no—
431C2×D4—24no—
432C2×D4—22no—
433C2×D4—24no—
434C2×D4—48no—
435C2×D4—44no—
436C2×D4—82no—
437C2×D4—84no—
438C2×D4C2×C22⋊D1114yes—
439C2×D4C23×D1114yes—
440C22×C4—21no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—21no—
444C22×C4—28no—
445C22×C4—48no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—222no—
449C22×C4—228no—
450C22×C4—884no—
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—24no—
467C4⋊C4—21no—
468C4⋊C4—112no—
469C4⋊C4—114no—
470C4⋊C4—221no—
471C4⋊C4—228no—
472C4⋊C4—222no—
473C4⋊C4—224no—
474C4⋊C4—224no—
475C4⋊C4—228no—
476C4⋊C4C2×C22⋊D1114yes—
477C4⋊C4C23×D1112yes—
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—24no—
490C23—44no—
491C23—44no—
492C23—44no—
493C23C22×C22⋊D1114yes—
494C23C22×C22⋊D1111yescharacteristic
495Q8—24no—
496Q8—22no—
497Q8—222no—
498Q8—222no—
499Q8—442no—
500Q8—884no—
501Q8C2×#434114yes—
502D4—28no—
503D4—24no—
504D4—24no—
505D4—416no—
506D4—44no—
507D4—48no—
508D4—84no—
509D4—88no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—28no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—22no—
518C2×C4—416no—
519C2×C4—42no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4—224no—
523C2×C4—442no—
524C2×C4—442no—
525C2×C4—444no—
526C2×C4—888no—
527C2×C4#6700414yes—
528C2×C4C2×#434112yes—
529C2×C4#6703712yes—
530C2×C4C22×C22⋊D1112yes—
531C2×C4C22×C22⋊D1114yes—
532C2×C4C22×C22⋊D1111yescharacteristic
533C2×C4C22×C22⋊D1112yes—
534C2×C4C24×D1111yescharacteristic
535C8—222no—
536C8—222no—
537C8—224no—
538C22—24no—
539C22—24no—
540C22—24no—
541C22—48no—
542C22—44no—
543C22—44no—
544C22—44no—
545C22—88no—
546C22#1062333712yes—
547C22C2×#6700412yes—
548C22#1062336612yes—
549C22C23×C22⋊D1111yescharacteristic
550C4—24no—
551C4—24no—
552C4—22no—
553C4—42no—
554C4—442no—
555C4—442no—
556C4—444no—
557C4#1062333712yes—
558C4C2×#6700414yes—
559C4C22×#434111yescharacteristic
560C4C2×#6703711yescharacteristic
561C2—44no—
562C2—84no—
563C2#1308095414yesdirect product factor
564C2C2×#1062333711yescharacteristic
565C2C22×#6700411yescharacteristic
566C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#550C2
socleC23×C11C22×D4
hypercenterC2×#550D11
hypocenterC11C2×#3333
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#10623074C2semidirect
2. #13080954C2direct (N × H)
3. C2×#10622683C2semidirect
4. C2×#10622646C2semidirect
5. C2×#10622634C2semidirect
6. C2×#10622655C2semidirect
7. C2×#10622688C2semidirect
8. C2×#10622852C2semidirect
9. C2×C4×#4326C2semidirect
10. C2×#10622625C2semidirect
11. C2×#10622845C2semidirect
30. #10623074C22semidirect
35. #10622852C22semidirect
36. #10622845C22semidirect
43. #10622688C22semidirect
44. #10622683C22semidirect
45. #10622655C22semidirect
46. #10622646C22semidirect
47. C4×#4326C22semidirect
48. #10622634C22semidirect
49. #10622625C22semidirect
407. C2×C11#3333semidirect
485. C11C2×#3333semidirect
563. C2#13080954direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230742
#130809542
C2×#106226832
C2×#106226462
C2×#106226342
C2×#106226552
C2×#106226882
C2×#106228522
C2×C4×#43262
C2×#106226252
C2×#106228452
C2×C11×#5502
C2×#333311