Finite Group Databasebeta

← C2×#13080973 #15632196

Subgroups — C2×#13080973 #15632196

Order 2816.

2158 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623074C211yesmaximal, characteristic, complemented
2#13080973C2116yesmaximal, direct product factor
3C2×#10622692C211yesmaximal, characteristic, complemented
4C2×#10622647C212yesmaximal, complemented
5C2×#10622584C212yesmaximal, complemented
6C2×#10622707C211yesmaximal, characteristic, complemented
7C2×#10622621C211yesmaximal, characteristic, complemented
8C2×#10622654C212yesmaximal, complemented
9C2×C4×#4324C211yesmaximal, characteristic, complemented
10C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
11C22×#66872C212yesmaximal, complemented
12C2×C11×#547C211yesmaximal, characteristic
13C22×C11×#41—21no—
14C11×#547—24no—
15C11×#547C2218yes—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#123—22no—
18C2×C11×C22⋊Q8—21no—
19C2×C11×#121C2212yes—
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C22×C11×C4⋊C4C2212yes—
23C2×D4×Dic11—21no—
24C22×#4324C2211yescharacteristic
25C22×C4⋊Dic11C2212yes—
26C2×#66977C2212yes—
27C23×C11⋊C8C2212yes—
28#10623074—24no—
29#10623074C2218yescomplemented
30C2×#66943—21no—
31C2×#66931—22no—
32C2×#66922C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C2×#66896C2212yes—
35C2×#66896C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622707C2218yescomplemented
38#10622692C2218yescomplemented
39#10622654C22116yescomplemented
40#10622647C22116yescomplemented
41C4×#4324C2218yescomplemented
42D4×C11⋊C8C2218yescomplemented
43#10622621C2218yescomplemented
44#10622584C22116yescomplemented
45C2×#66874C2212yes—
46C2×#66874C2211yescharacteristic
47C2×#66872C2212yes—
48C2×#66872C2212yes—
49C2×#66872C2212yes—
50C2×#66872C2212yes—
51C2×#66872C2211yescharacteristic
52C2×#66872C22116yescomplemented
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—
64C23×Dic11—22no—
65C22×Dic22—21no—
66C22×Dic22C2311yescharacteristic
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8C2314yes—
69C11×#123—216no—
70C11×C22⋊Q8—28no—
71C11×#121—24no—
72C11×#121C2318yes—
73C4×D4×C11—22no—
74C4×D4×C11D414yes—
75C4×D4×C11C2314yes—
76C4×D4×C11C2314yes—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2318yes—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4D412yes—
87C2×C42×C11C2311yescharacteristic
88C2×C22⋊Dic11—22no—
89D4×Dic11—28no—
90C2×#4324—24no—
91C2×#4324C2314yes—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11—24no—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2312yes—
97C2×C4⋊Dic11C2318yes—
98#66977—24no—
99#66977C2318yes—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—22no—
102C2×C4×Dic11—21no—
103C22×C11⋊C8—28no—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2312yes—
106C22×C11⋊C8C2318yes—
107C22×C11⋊C8C2311yescharacteristic
108#66943—28no—
109#66931—216no—
110#66922—22no—
111#66922C2314yes—
112C4×Dic22—22no—
113C4×Dic22C2314yes—
114#66896C2318yes—
115#66896C2314yes—
116C22⋊(C11⋊C8)C2318yes—
117#66874C2314yes—
118#66874C2318yes—
119#66872C2314yes—
120#66872C2318yes—
121#66872C2318yes—
122#66872C2318yes—
123#66872C2318yes—
124C4⋊(C11⋊C8)C2314yes—
125C4×C11⋊C8C2314yes—
126C2×#3335—111nomaximal, Sylow
127C24×C11—21no—
128C24×C11C2×D412yes—
129C11×#41—432no—
130C2×Q8×C11—24no—
131C2×Q8×C11—44no—
132C2×D4×C11—28no—
133C2×D4×C11—21no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—48no—
137C2×D4×C11SD1618yescomplemented
138C2×D4×C11C2×D414yes—
139C2×D4×C11C2412yes—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—28no—
145C22×C4×C11—24no—
146C22×C4×C11—48no—
147C22×C4×C11—44no—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D414yes—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2414yes—
153C22×C4×C11C2411yescharacteristic
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—22no—
157C22×Dic11—28no—
158C22×Dic11—84no—
159C2×Dic22—21no—
160C2×Dic22—24no—
161C2×Dic22—22no—
162C2×Dic22—22no—
163C2×Dic22—82no—
164C2×Dic22C2412yes—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—28no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4C2×D414yes—
170C11×C4⋊C4C2412yes—
171C11×C4⋊C4C2414yes—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—28no—
174C11×C22⋊C4C2×D418yes—
175C42×C11C2×D412yes—
176C42×C11C2412yes—
177C22⋊Dic11—28no—
178#4324—28no—
179C4⋊Dic11—21no—
180C4⋊Dic11—22no—
181C4⋊Dic11—24no—
182C4⋊Dic11—28no—
183C4⋊Dic11C2412yes—
184C4⋊Dic11C2414yes—
185Dic11⋊C4—24no—
186Dic11⋊C4—28no—
187C4×Dic11—24no—
188C2×C11⋊C8—216no—
189C2×C11⋊C8—24no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8#4114yescomplemented
192C2×C11⋊C8C2412yes—
193C2×C11⋊C8C2414yes—
194C2×C11⋊C8C2412yes—
195C2×#554—111no—
196C2×#547D1111yescharacteristic
197#3335—1116no—
198C2×#498—111no—
199C2×#481—112no—
200C2×#483—112no—
201C2×#475—111no—
202C2×#476—111no—
203C2×#465—112no—
204C2×C4×SD16—111no—
205C2×C8×D4—111no—
206C22×#106—112no—
207C23×C11—24no—
208C23×C11—24no—
209C23×C11—22no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11C2×SD1618yes—
214C23×C11C22×D414yes—
215C23×C11C22×D411yescharacteristic
216Q8×C11—48no—
217D4×C11—22no—
218D4×C11—22no—
219D4×C11—416no—
220D4×C11—42no—
221D4×C11C2×SD16116yescomplemented
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—28no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—42no—
230C2×C4×C11—44no—
231C2×C4×C11—416no—
232C2×C4×C11—48no—
233C2×C4×C11C2×SD1614yes—
234C2×C4×C11C22×D414yes—
235C2×C4×C11C22×D412yes—
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D412yes—
238C2×C4×C11C2×#4112yes—
239C2×C4×C112−1+412yes—
240C2×C4×C11C2511yescharacteristic
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—24no—
244C2×Dic11—42no—
245C2×Dic11—44no—
246C2×Dic11—42no—
247C2×Dic11—88no—
248Dic22—22no—
249Dic22—22no—
250Dic22—42no—
251Dic22—84no—
252C11⋊C8—24no—
253C11⋊C8—22no—
254C11⋊C8C2×#4114yescomplemented
255C22×#41—21no—
256C22×SD16—111no—
257C23×C8—112no—
258#554—118no—
259#554—224no—
260#547—24no—
261#547C2×D1118yes—
262C2×C4⋊Q8—111no—
263C2×C4⋊Q8C2×D1111yescharacteristic
264C2×#125—221no—
265C2×#123—22no—
266C2×C22⋊Q8—21no—
267C2×C22⋊Q8—112no—
268C2×C22⋊Q8—222no—
269C2×#121C2×D1112yes—
270C2×C4×Q8—111no—
271C2×C4×D4—221no—
272C2×C4×D4C2×D1111yescharacteristic
273C2×C4×D4C2×D1111yescharacteristic
274C22×C4⋊C4—112no—
275C22×C4⋊C4C2×D1112yes—
276#498—118no—
277#483—1116no—
278#481—1116no—
279#476—118no—
280#475—118no—
281#465—1116no—
282C4×SD16—118no—
283C8×D4—118no—
284C2×#106—112no—
285C2×#106—1116no—
286C2×#106—112no—
287C2×#106—112no—
288C2×#106—112no—
289C2×#106—111no—
290C2×C4⋊C8—111no—
291C2×#103—112no—
292C2×#103—111no—
293C2×#102—111no—
294C2×#102—112no—
295C2×C22⋊C8—112no—
296C2×C4×C8—111no—
297C22×C11—216no—
298C22×C11—24no—
299C22×C11—24no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—84no—
304C22×C11#54712yes—
305C22×C11C22×SD1618yes—
306C22×C11C22×SD1612yes—
307C22×C11#57712yes—
308C22×C11C23×D411yescharacteristic
309C4×C11—24no—
310C4×C11—22no—
311C4×C11—42no—
312C4×C11—44no—
313C4×C11#54712yes—
314C4×C11C22×SD1614yes—
315C4×C11C22×#4111yescharacteristic
316C4×C11C2×2−1+411yescharacteristic
317Dic11—42no—
318Dic11—44no—
319Dic11—42no—
320C2×#41—28no—
321C2×#41—48no—
322C22×Q8—21no—
323C22×Q8—111no—
324C22×Q8—221no—
325C22×D4—22no—
326C22×D4C22⋊D1111yescharacteristic
327C22×D4C22×D1111yescharacteristic
328C23×C4—22no—
329C23×C4—21no—
330C23×C4—222no—
331C23×C4C22×D1112yes—
332C2×SD16—114no—
333C2×SD16—224no—
334C22×C8—111no—
335C22×C8—112no—
336C22×C8—118no—
337C22×C8—111no—
338C22×C8—228no—
339C4⋊Q8—22no—
340C4⋊Q8—114no—
341C4⋊Q8—222no—
342C4⋊Q8C22×D1114yes—
343#125—228no—
344#123—216no—
345C22⋊Q8—28no—
346C22⋊Q8—118no—
347C22⋊Q8—224no—
348C22⋊Q8—2216no—
349#121—24no—
350#121C22×D1118yes—
351C4×Q8—114no—
352C4×Q8—222no—
353C4×D4—22no—
354C4×D4—228no—
355C4×D4C22⋊D1114yes—
356C4×D4C22×D1114yes—
357C4×D4C22×D1114yes—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—112no—
363C2×C4⋊C4—118no—
364C2×C4⋊C4—222no—
365C2×C4⋊C4—224no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4C22⋊D1111yescharacteristic
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C4⋊C4C22×D1112yes—
372C2×C4⋊C4C22×D1118yes—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—222no—
376C2×C22⋊C4C22⋊D1112yes—
377C2×C42—221no—
378C2×C42C22×D1111yescharacteristic
379#106—114no—
380#106—118no—
381#106—118no—
382#106—118no—
383#106—118no—
384C4⋊C8—114no—
385#103—114no—
386#103—118no—
387#102—114no—
388#102—118no—
389C22⋊C8—118no—
390C4×C8—114no—
391C2×C11—28no—
392C2×C11—82no—
393C2×C11#333514yescomplemented
394C2×C11C2×#54711yescharacteristic
395C2×C11C23×SD1611yescharacteristic
396C2×C11C2×#57711yescharacteristic
397C24—21no—
398C24C2×C22⋊D1112yes—
399#41—432no—
400C2×Q8—24no—
401C2×Q8—44no—
402C2×Q8—112no—
403C2×Q8—221no—
404C2×Q8—224no—
405C2×Q8—222no—
406C2×Q8—222no—
407C2×Q8—882no—
408C2×D4—28no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—21no—
412C2×D4—48no—
413C2×D4#432418yescomplemented
414C2×D4C2×C22⋊D1114yes—
415C2×D4C23×D1112yes—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—28no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—24no—
422C22×C4—48no—
423C22×C4—44no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—222no—
427C22×C4—228no—
428C22×C4—884no—
429C22×C4C2×C22⋊D1114yes—
430C22×C4C2×C22⋊D1111yescharacteristic
431C22×C4C2×C22⋊D1112yes—
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C23×D1114yes—
434C22×C4C23×D1111yescharacteristic
435SD16—228no—
436C2×C8—114no—
437C2×C8—112no—
438C2×C8—112no—
439C2×C8—114no—
440C2×C8—2216no—
441C2×C8—224no—
442C2×C8—222no—
443C4⋊C4—21no—
444C4⋊C4—22no—
445C4⋊C4—28no—
446C4⋊C4—24no—
447C4⋊C4—112no—
448C4⋊C4—114no—
449C4⋊C4—221no—
450C4⋊C4—228no—
451C4⋊C4—222no—
452C4⋊C4—224no—
453C4⋊C4—224no—
454C4⋊C4—228no—
455C4⋊C4C2×C22⋊D1114yes—
456C4⋊C4C23×D1112yes—
457C4⋊C4C23×D1114yes—
458C22⋊C4—24no—
459C22⋊C4—28no—
460C22⋊C4—228no—
461C22⋊C4C2×C22⋊D1118yes—
462C42—224no—
463C42C2×C22⋊D1112yes—
464C42C23×D1112yes—
465C11C2×#333511yescharacteristic, complemented, Sylow
466C23—24no—
467C23—24no—
468C23—22no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23C2×#432418yes—
473C23C22×C22⋊D1114yes—
474C23C22×C22⋊D1111yescharacteristic
475Q8—48no—
476Q8—222no—
477Q8—222no—
478Q8—442no—
479Q8—884no—
480D4—22no—
481D4—22no—
482D4—416no—
483D4—42no—
484D4C2×#4324116yescomplemented
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—28no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—24no—
492C2×C4—42no—
493C2×C4—44no—
494C2×C4—416no—
495C2×C4—48no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—224no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—444no—
502C2×C4—888no—
503C2×C4C2×#432414yes—
504C2×C4#41×D1112yes—
505C2×C4#6704312yes—
506C2×C4C22×C22⋊D1112yes—
507C2×C4C22×C22⋊D1114yes—
508C2×C4C22×C22⋊D1112yes—
509C2×C4C22×C22⋊D1111yescharacteristic
510C2×C4C24×D1111yescharacteristic
511C8—114no—
512C8—224no—
513C8—222no—
514C22—216no—
515C22—24no—
516C22—24no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—84no—
521C22C22×#432418yes—
522C22C22×#432412yes—
523C22#1062335512yes—
524C22#1062336812yes—
525C22C23×C22⋊D1111yescharacteristic
526C4—24no—
527C4—22no—
528C4—42no—
529C4—44no—
530C4—442no—
531C4—442no—
532C4—444no—
533C4C22×#432414yes—
534C4#1062335512yes—
535C4C2×#41×D1111yescharacteristic
536C4C2×#6704311yescharacteristic
537C2—28no—
538C2—82no—
539C2#1308097314yesdirect product factor
540C2C2×#1062335511yescharacteristic
541C2C23×#432411yescharacteristic
542C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#547C2
socleC23×C11C22×D4
hypercenterC2×#547D11
hypocenterC11C2×#3335
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×#10623074C2semidirect
2. #13080973C2direct (N × H)
3. C2×#10622692C2semidirect
4. C2×#10622647C2semidirect
5. C2×#10622584C2semidirect
6. C2×#10622707C2semidirect
7. C2×#10622621C2semidirect
8. C2×#10622654C2semidirect
9. C2×C4×#4324C2semidirect
10. C2×D4×C11⋊C8C2semidirect
11. C22×#66872C2semidirect
29. #10623074C22semidirect
37. #10622707C22semidirect
38. #10622692C22semidirect
39. #10622654C22semidirect
40. #10622647C22semidirect
41. C4×#4324C22semidirect
42. D4×C11⋊C8C22semidirect
43. #10622621C22semidirect
44. #10622584C22semidirect
52. C2×#66872C22semidirect
137. C2×D4×C11SD16semidirect
191. C2×C11⋊C8#41semidirect
221. D4×C11C2×SD16semidirect
254. C11⋊C8C2×#41semidirect
393. C2×C11#3335semidirect
413. C2×D4#4324semidirect
465. C11C2×#3335semidirect
484. D4C2×#4324semidirect
539. C2#13080973direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230742
#130809732
C2×#106226922
C2×#106226472
C2×#106225842
C2×#106227072
C2×#106226212
C2×#106226542
C2×C4×#43242
C2×D4×C11⋊C82
C22×#668722
C2×C11×#5472
C2×#333511