Finite Group Databasebeta

← C2×#13080555 #15630236

Subgroups — C2×#13080555 #15630236

Order 2816.

2198 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623073C211yesmaximal, characteristic, complemented
2#13080555C2116yesmaximal, direct product factor
3C2×#10622683C211yesmaximal, characteristic, complemented
4C2×#10622648C212yesmaximal, complemented
5C2×#10622633C211yesmaximal, characteristic, complemented
6C2×#10622654C212yesmaximal, complemented
7C2×#10622688C211yesmaximal, characteristic, complemented
8C2×#10622852C212yesmaximal, complemented
9C2×C4×#4326C211yesmaximal, characteristic, complemented
10C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
11C2×#10622846C212yesmaximal, 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×#66989—21no—
25C22×#4324C2212yes—
26C2×#66979C2212yes—
27C2×#66977C2212yes—
28C23×C11⋊C8C2212yes—
29#10623073—24no—
30#10623073C2218yescomplemented
31C2×#66940—21no—
32C2×#66932—22no—
33C2×#66922C2211yescharacteristic
34C2×C4×Dic22C2211yescharacteristic
35#10622852C22116yescomplemented
36#10622846C22116yescomplemented
37C2×#66899C2212yes—
38C2×#66899C2211yescharacteristic
39C2×#66896C2212yes—
40C2×#66896C2212yes—
41C2×#66896C2212yes—
42C2×C22⋊(C11⋊C8)C2212yes—
43#10622688C2218yescomplemented
44#10622683C2218yescomplemented
45#10622654C22116yescomplemented
46#10622648C22116yescomplemented
47C4×#4326C2218yescomplemented
48#10622633C2218yescomplemented
49D4×C11⋊C8C2218yescomplemented
50C2×#66874C2211yescharacteristic
51C2×#66872C2212yes—
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—
68C22×Dic22—21no—
69C22×Dic22C2311yescharacteristic
70C11×#127—28no—
71C11×#127—22no—
72C11×#127C2314yes—
73C11×#121—24no—
74C11×#121—216no—
75C11×#121C2318yes—
76C4×Q8×C11—22no—
77C4×Q8×C11C2314yes—
78C4×D4×C11—28no—
79C4×D4×C11D414yes—
80C4×D4×C11C2314yes—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4D412yes—
86C2×C42×C11—21no—
87C2×C42×C11C2311yescharacteristic
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—22no—
90C2×#4326—24no—
91C2×#4326C2314yes—
92#66989—28no—
93C2×#4324—44no—
94C2×#4324C2318yes—
95#66979—24no—
96#66979C2318yes—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2312yes—
100#66977—24no—
101#66977C2318yes—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—22no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—22no—
106C22×C11⋊C8—44no—
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2312yes—
110C22×C11⋊C8C2318yes—
111#66940—28no—
112#66932—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#66872C2318yes—
125#66871C2314yes—
126C4⋊(C11⋊C8)C2314yes—
127C4×C11⋊C8C2314yes—
128C2×#3304—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—
167C2×Dic22—21no—
168C2×Dic22—24no—
169C2×Dic22—22no—
170C2×Dic22—22no—
171C2×Dic22—44no—
172C2×Dic22C2412yes—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4C2×D414yes—
176C11×C4⋊C4C2412yes—
177C11×C22⋊C4—28no—
178C11×C22⋊C4C2×D418yes—
179C42×C11—24no—
180C42×C11C2×D412yes—
181C42×C11C2412yes—
182C22⋊Dic11—28no—
183C22⋊Dic11—28no—
184#4326—28no—
185#4324—48no—
186C4⋊Dic11—21no—
187C4⋊Dic11—22no—
188C4⋊Dic11—24no—
189C4⋊Dic11C2412yes—
190C4⋊Dic11C2414yes—
191Dic11⋊C4—24no—
192Dic11⋊C4—28no—
193C4×Dic11—24no—
194C4×Dic11—28no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—24no—
198C2×C11⋊C8—48no—
199C2×C11⋊C8C2412yes—
200C2×C11⋊C8C2412yes—
201C2×C11⋊C8C2414yes—
202C2×#556—111no—
203C2×#550D1111yescharacteristic
204#3304—1116no—
205C2×#486—111no—
206C2×#482—112no—
207C2×#475—111no—
208C2×#465—112no—
209C2×#460—111no—
210C2×#452—112no—
211C2×C4×Q16—111no—
212C2×C8×D4—111no—
213C2×#416—112no—
214C23×C11—24no—
215C23×C11—24no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—44no—
219C23×C11—44no—
220C23×C11—44no—
221C23×C11C22×D414yes—
222C23×C11C22×D411yescharacteristic
223Q8×C11—24no—
224Q8×C11—22no—
225Q8×C11C2×#4114yes—
226D4×C11—28no—
227D4×C11—24no—
228D4×C11—24no—
229D4×C11—416no—
230D4×C11—44no—
231D4×C11—48no—
232D4×C11—84no—
233D4×C11—88no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—28no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—22no—
242C2×C4×C11—416no—
243C2×C4×C11—42no—
244C2×C4×C11#13514yes—
245C2×C4×C11C22×D414yes—
246C2×C4×C11C22×D412yes—
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D412yes—
249C2×C4×C11C2×#4112yes—
250C2×C4×C11H(5,𝔽2)12yes—
251C2×C4×C11C2511yescharacteristic
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—24no—
255C2×Dic11—42no—
256C2×Dic11—44no—
257C2×Dic11—42no—
258Dic22—22no—
259Dic22—22no—
260Dic22—42no—
261Dic22—48no—
262C11⋊C8—22no—
263C11⋊C8—22no—
264C11⋊C8—24no—
265C22×#41C2×D1112yes—
266C22×Q16—111no—
267C22×SD16—112no—
268C23×C8—112no—
269#556—118no—
270#556—224no—
271#550—24no—
272#550C2×D1118yes—
273C2×C4⋊Q8—111no—
274C2×#127—21no—
275C2×#127C2×D1111yescharacteristic
276C2×#126—222no—
277C2×#124—221no—
278C2×C22⋊Q8—112no—
279C2×#121—22no—
280C2×#121C2×D1112yes—
281C2×C4×Q8—111no—
282C2×C4×Q8—221no—
283C2×C4×Q8C2×D1111yescharacteristic
284C2×C4×D4—21no—
285C2×C4×D4C2×D1111yescharacteristic
286C2×#117—112no—
287#486—118no—
288#482—1116no—
289#475—118no—
290#465—1116no—
291#460—118no—
292#452—1116no—
293C4×Q16—118no—
294C8×D4—118no—
295C2×#107—111no—
296C2×#106—112no—
297C2×C4⋊C8—111no—
298#416—1116no—
299C2×#103—112no—
300C2×#103—111no—
301C2×#103—111no—
302C2×#102—112no—
303C2×#102—112no—
304C2×#102—112no—
305C2×C22⋊C8—112no—
306C2×C4×C8—111no—
307C22×C11—24no—
308C22×C11—24no—
309C22×C11—24no—
310C22×C11—48no—
311C22×C11—44no—
312C22×C11—44no—
313C22×C11—44no—
314C22×C11—88no—
315C22×C11#54612yes—
316C22×C11C2×#13512yes—
317C22×C11#57712yes—
318C22×C11C23×D411yescharacteristic
319C4×C11—24no—
320C4×C11—24no—
321C4×C11—22no—
322C4×C11—42no—
323C4×C11#54612yes—
324C4×C11C2×#13514yes—
325C4×C11C22×#4111yescharacteristic
326C4×C11C2×H(5,𝔽2)11yescharacteristic
327Dic11—42no—
328Dic11—44no—
329Dic11—42no—
330C2×#41—24no—
331C2×#41—28no—
332C2×#41—44no—
333C2×#41C22×D1118yes—
334C22×Q8—111no—
335C22×Q8—221no—
336C22×Q8C22×D1111yescharacteristic
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—21no—
340C22×D4—21no—
341C22×D4C22⋊D1111yescharacteristic
342C22×D4C22×D1112yes—
343C23×C4—22no—
344C23×C4C22×D1112yes—
345C2×Q16—114no—
346C2×Q16—224no—
347C2×SD16—118no—
348C2×SD16—444no—
349C22×C8—111no—
350C22×C8—112no—
351C22×C8—111no—
352C22×C8—118no—
353C22×C8—444no—
354C4⋊Q8—114no—
355C4⋊Q8—222no—
356#127—28no—
357#127—22no—
358#127C22×D1114yes—
359#126—2216no—
360#124—228no—
361C22⋊Q8—118no—
362C22⋊Q8—224no—
363#121—24no—
364#121—216no—
365#121C22×D1118yes—
366C4×Q8—22no—
367C4×Q8—114no—
368C4×Q8—228no—
369C4×Q8—222no—
370C4×Q8C22×D1114yes—
371C4×D4—28no—
372C4×D4C22⋊D1114yes—
373C4×D4C22×D1114yes—
374#117—118no—
375#117—224no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—112no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—222no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4C22⋊D1111yescharacteristic
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C22⋊C4—22no—
385C2×C22⋊C4—222no—
386C2×C22⋊C4—222no—
387C2×C22⋊C4C22⋊D1112yes—
388C2×C42—21no—
389C2×C42—222no—
390C2×C42—221no—
391C2×C42C22×D1111yescharacteristic
392#107—114no—
393#106—118no—
394C4⋊C8—114no—
395#103—114no—
396#103—118no—
397#103—114no—
398#102—118no—
399#102—118no—
400#102—118no—
401C22⋊C8—118no—
402C4×C8—114no—
403C2×C11—44no—
404C2×C11—84no—
405C2×C11#330414yescomplemented
406C2×C11C2×#54611yescharacteristic
407C2×C11C22×#13511yescharacteristic
408C2×C11C2×#57711yescharacteristic
409C24—22no—
410C24C2×C22⋊D1112yes—
411#41—216no—
412#41—48no—
413#41—416no—
414C2×Q8—22no—
415C2×Q8—21no—
416C2×Q8—112no—
417C2×Q8—221no—
418C2×Q8—224no—
419C2×Q8—222no—
420C2×Q8—222no—
421C2×Q8—444no—
422C2×Q8#434114yes—
423C2×Q8C23×D1112yes—
424C2×D4—28no—
425C2×D4—28no—
426C2×D4—24no—
427C2×D4—24no—
428C2×D4—24no—
429C2×D4—24no—
430C2×D4—22no—
431C2×D4—24no—
432C2×D4—48no—
433C2×D4—44no—
434C2×D4—82no—
435C2×D4—84no—
436C2×D4C2×C22⋊D1114yes—
437C2×D4C23×D1114yes—
438C22×C4—21no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—21no—
442C22×C4—28no—
443C22×C4—48no—
444C22×C4—221no—
445C22×C4—222no—
446C22×C4—221no—
447C22×C4C2×C22⋊D1114yes—
448C22×C4C2×C22⋊D1112yes—
449C22×C4C2×C22⋊D1111yescharacteristic
450C22×C4C2×C22⋊D1111yescharacteristic
451C22×C4C23×D1114yes—
452C22×C4C23×D1111yescharacteristic
453Q16—228no—
454SD16—448no—
455C2×C8—112no—
456C2×C8—112no—
457C2×C8—114no—
458C2×C8—222no—
459C2×C8—222no—
460C2×C8—224no—
461C2×C8—448no—
462C4⋊C4—24no—
463C4⋊C4—21no—
464C4⋊C4—114no—
465C4⋊C4—112no—
466C4⋊C4—221no—
467C4⋊C4—222no—
468C4⋊C4—224no—
469C4⋊C4—228no—
470C4⋊C4—224no—
471C4⋊C4C2×C22⋊D1114yes—
472C4⋊C4C23×D1112yes—
473C22⋊C4—28no—
474C22⋊C4—228no—
475C22⋊C4—228no—
476C22⋊C4C2×C22⋊D1118yes—
477C42—24no—
478C42—228no—
479C42—224no—
480C42C2×C22⋊D1112yes—
481C42C23×D1112yes—
482C11C2×#330411yescharacteristic, complemented, Sylow
483C23—24no—
484C23—24no—
485C23—24no—
486C23—24no—
487C23—44no—
488C23—44no—
489C23—44no—
490C23C22×C22⋊D1114yes—
491C23C22×C22⋊D1111yescharacteristic
492Q8—24no—
493Q8—22no—
494Q8—222no—
495Q8—222no—
496Q8—442no—
497Q8—448no—
498Q8C2×#434114yes—
499D4—28no—
500D4—24no—
501D4—24no—
502D4—416no—
503D4—44no—
504D4—48no—
505D4—84no—
506D4—88no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—28no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—416no—
516C2×C4—42no—
517C2×C4—222no—
518C2×C4—224no—
519C2×C4—222no—
520C2×C4—442no—
521C2×C4—444no—
522C2×C4—442no—
523C2×C4#6700314yes—
524C2×C4C2×#434112yes—
525C2×C4#6703712yes—
526C2×C4C22×C22⋊D1114yes—
527C2×C4C22×C22⋊D1112yes—
528C2×C4C22×C22⋊D1111yescharacteristic
529C2×C4C22×C22⋊D1112yes—
530C2×C4C24×D1111yescharacteristic
531C8—222no—
532C8—222no—
533C8—224no—
534C22—24no—
535C22—24no—
536C22—24no—
537C22—48no—
538C22—44no—
539C22—44no—
540C22—44no—
541C22—88no—
542C22#1062333712yes—
543C22C2×#6700312yes—
544C22#1062336712yes—
545C22C23×C22⋊D1111yescharacteristic
546C4—24no—
547C4—24no—
548C4—22no—
549C4—42no—
550C4—444no—
551C4—442no—
552C4—442no—
553C4#1062333712yes—
554C4C2×#6700314yes—
555C4C22×#434111yescharacteristic
556C4C2×#6703711yescharacteristic
557C2—44no—
558C2—84no—
559C2#1308055514yesdirect product factor
560C2C2×#1062333711yescharacteristic
561C2C22×#6700311yescharacteristic
562C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#550C2
socleC23×C11C22×D4
hypercenterC2×#550D11
hypocenterC11C2×#3304
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×#10623073C2semidirect
2. #13080555C2direct (N × H)
3. C2×#10622683C2semidirect
4. C2×#10622648C2semidirect
5. C2×#10622633C2semidirect
6. C2×#10622654C2semidirect
7. C2×#10622688C2semidirect
8. C2×#10622852C2semidirect
9. C2×C4×#4326C2semidirect
10. C2×D4×C11⋊C8C2semidirect
11. C2×#10622846C2semidirect
30. #10623073C22semidirect
35. #10622852C22semidirect
36. #10622846C22semidirect
43. #10622688C22semidirect
44. #10622683C22semidirect
45. #10622654C22semidirect
46. #10622648C22semidirect
47. C4×#4326C22semidirect
48. #10622633C22semidirect
49. D4×C11⋊C8C22semidirect
405. C2×C11#3304semidirect
482. C11C2×#3304semidirect
559. C2#13080555direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230732
#130805552
C2×#106226832
C2×#106226482
C2×#106226332
C2×#106226542
C2×#106226882
C2×#106228522
C2×C4×#43262
C2×D4×C11⋊C82
C2×#106228462
C2×C11×#5502
C2×#330411