Finite Group Databasebeta

← C2×#13080961 #15632183

Subgroups — C2×#13080961 #15632183

Order 2816.

2374 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623038C212yesmaximal, complemented
2#13080961C2116yesmaximal, direct product factor
3C2×#10622487C211yesmaximal, characteristic, complemented
4C2×#10622495C212yesmaximal, complemented
5C2×#10622580C212yesmaximal, complemented
6C2×#10622503C212yesmaximal, complemented
7C2×#10622496C211yesmaximal, characteristic, complemented
8C2×#10622728C211yesmaximal, characteristic, complemented
9C2×#10622485C211yesmaximal, characteristic, complemented
10C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
11C2×D11×#107C211yesmaximal, characteristic, complemented
12C22×C11×#107C211yesmaximal, characteristic, complemented
13C22×#4339—22no—
14C23×C8×C11C2211yescharacteristic
15C22×C11×C4⋊C4C2212yes—
16C2×#66983C2212yes—
17C2×#66982—22no—
18C2×C4×C22⋊D11C2211yescharacteristic
19C22×D88C2211yescharacteristic
20C22×C8×D11C2211yescharacteristic
21C2×#66949—22no—
22#10623038—28no—
23#10623038C22116yescomplemented
24C2×#66948C2212yes—
25C2×#66947—22no—
26C2×#66946C2212yes—
27C2×C4⋊C4×D11C2212yes—
28C2×#66941C2212yes—
29C2×C11×#107C2211yescharacteristic
30C2×C11×#107C2212yes—
31C2×C11×#107C2211yescharacteristic
32C2×C11×#107C2218yescomplemented
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34#10622728C2218yescomplemented
35C2×#66885C2212yes—
36C8×C22⋊D11C2218yescomplemented
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×#66882C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40C2×C8×Dic11C2211yescharacteristic
41#10622580C22116yescomplemented
42C2×#66873C2212yes—
43C2×#66873C2212yes—
44C2×#66871C2212yes—
45C2×#66871C2212yes—
46#10622503C22116yescomplemented
47#10622496C2218yescomplemented
48#10622495C22116yescomplemented
49D11×#107C2218yescomplemented
50#10622487C2218yescomplemented
51#10622485C2218yescomplemented
52C23×C4×C11—22no—
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11—22no—
55C22×C22⋊D11D411yescharacteristic
56C2×#4339—216no—
57C2×#4339—416no—
58C22×D44—22no—
59C22×D44C2312yes—
60C22×C4×D11—22no—
61C22×C4×D11—22no—
62C22×C4×D11C2311yescharacteristic
63C22×Dic22—22no—
64C22×C8×C11—24no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2314yes—
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C4⋊C4C2318yes—
73C2×C22⋊Dic11D411yescharacteristic
74#66983—24no—
75#66983C2318yes—
76#66982—216no—
77C4×C22⋊D11D414yes—
78C4×C22⋊D11C2314yes—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4D411yescharacteristic
83C2×C4⋊Dic11C2312yes—
84C2×Dic11⋊C4—22no—
85C2×Dic11⋊C4—22no—
86C2×Dic11⋊C4D411yescharacteristic
87C2×C4×Dic11C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C2×D88—24no—
91C2×D88C2314yes—
92C2×C8×D11—24no—
93C2×C8×D11C2314yes—
94#66949—216no—
95#66948—24no—
96#66948C2318yes—
97#66947—216no—
98#66946—24no—
99#66946C2318yes—
100C4⋊C4×D11—24no—
101C4⋊C4×D11C2318yes—
102#66941—24no—
103#66941C2318yes—
104C11×#107C2314yes—
105C11×#107C2314yes—
106C11×#107C2318yes—
107C22⋊(C11⋊C8)C2314yes—
108#66885C2318yes—
109(C2×D11)⋊C8C2314yes—
110#66882C2314yes—
111Dic11⋊C8C2314yes—
112C8×Dic11C2314yes—
113#66873C2318yes—
114#66873C2318yes—
115#66871C2318yes—
116#66871C2318yes—
117C2×#3334—111nomaximal, Sylow
118C24×C11C2×D411yescharacteristic
119C23×D11—22no—
120C23×D11C2×D411yescharacteristic
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—28no—
126C22×C4×C11—48no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2412yes—
130C22×C4×C11C2411yescharacteristic
131C2×C22⋊D11—28no—
132C2×C22⋊D11—48no—
133C2×C22⋊D11D818yescomplemented
134C2×C22⋊D11C2×D414yes—
135C22×Dic11—22no—
136C22×Dic11C2×D411yescharacteristic
137C22×Dic11C2×D411yescharacteristic
138C22×Dic11C2×D411yescharacteristic
139#4339—464no—
140C2×D44—28no—
141C2×D44—22no—
142C2×D44—24no—
143C2×D44—24no—
144C2×D44—48no—
145C2×D44C2414yes—
146C2×C4×D11—28no—
147C2×C4×D11—28no—
148C2×C4×D11—22no—
149C2×C4×D11—22no—
150C2×C4×D11—48no—
151C2×C4×D11—48no—
152C2×C4×D11C2×D412yes—
153C2×C4×D11C2412yes—
154C2×Dic22—28no—
155C2×Dic22—48no—
156C2×C8×C11—28no—
157C2×C8×C11—22no—
158C2×C8×C11#4114yescomplemented
159C2×C8×C11C2412yes—
160C2×C8×C11C2412yes—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—28no—
164C11×C4⋊C4C2414yes—
165C11×C4⋊C4C2414yes—
166C22⋊Dic11C2×D414yes—
167(C2×D11)⋊C4—28no—
168(C2×D11)⋊C4—28no—
169(C2×D11)⋊C4—28no—
170(C2×D11)⋊C4C2×D414yes—
171C4⋊Dic11—22no—
172C4⋊Dic11C2414yes—
173Dic11⋊C4—28no—
174Dic11⋊C4—28no—
175Dic11⋊C4C2×D414yes—
176C4×Dic11C2×D412yes—
177C4×Dic11C2412yes—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8C2412yes—
181C2×C11⋊C8C2412yes—
182D88—28no—
183C8×D11—28no—
184C2×#547—112no—
185#3334—1116no—
186C2×#500—111no—
187C2×#480—112no—
188C2×#480—112no—
189C2×#474—112no—
190C2×#466—111no—
191C2×#466—111no—
192C2×C4×D8—111no—
193C2×C8×D4—111no—
194C22×#107—111no—
195C22×#107D1111yescharacteristic, complemented
196C23×C11—22no—
197C23×C11—22no—
198C23×C11C2×D814yes—
199C23×C11C22×D412yes—
200C23×C11C22×D411yescharacteristic
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—24no—
204C22×D11—44no—
205C22×D11—44no—
206C22×D11—44no—
207C22×D11C2×D814yes—
208C22×D11C22×D412yes—
209C2×C4×C11—22no—
210C2×C4×C11—24no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—44no—
216C2×C4×C11—44no—
217C2×C4×C11—416no—
218C2×C4×C11C22×D412yes—
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C2×#4112yes—
221C2×C4×C112−1+412yes—
222C2×C4×C11C2511yescharacteristic
223C22⋊D11—416no—
224C22⋊D11C2×D8116yescomplemented
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—24no—
228C2×Dic11—44no—
229C2×Dic11C2×D814yes—
230C2×Dic11C22×D412yes—
231C2×Dic11C22×D412yes—
232C2×Dic11C22×D412yes—
233D44—24no—
234D44—24no—
235D44—416no—
236D44—44no—
237C4×D11—24no—
238C4×D11—22no—
239C4×D11—22no—
240C4×D11—416no—
241C4×D11—416no—
242Dic22—416no—
243C8×C11—22no—
244C8×C11C2×#4114yescomplemented
245C11⋊C8—22no—
246C11⋊C8—22no—
247C22×#41—222no—
248C22×D8—111no—
249C23×C8—111no—
250C23×C8C2×D1111yescharacteristic
251#547—1116no—
252#547—228no—
253C2×C4⋊Q8—112no—
254C2×#123—222no—
255C2×#123—222no—
256C2×C22⋊Q8—222no—
257C2×#121—112no—
258C2×#121—112no—
259C2×C4×D4—111no—
260C2×C4×D4—112no—
261C22×C4⋊C4—112no—
262C22×C4⋊C4C2×D1112yes—
263#500—118no—
264#480—1116no—
265#480—1116no—
266#474—1116no—
267#466—118no—
268#466—118no—
269C4×D8—118no—
270C8×D4—118no—
271C2×#107—111no—
272C2×#107—112no—
273C2×#107—112no—
274C2×#107—118no—
275C2×#107C2×D1112yes—
276C2×#107C2×D1111yescharacteristic
277C2×#107C2×D1111yescharacteristic
278C2×#107C2×D1118yescomplemented
279C2×C4⋊C8—111no—
280C2×#102—112no—
281C2×#102—112no—
282C2×#102—112no—
283C2×C22⋊C8—111no—
284C2×C22⋊C8—111no—
285C2×C4×C8—111no—
286C22×C11—28no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11#54712yes—
290C22×C11C22×D814yes—
291C22×C11C22×D812yes—
292C22×C11#57812yes—
293C22×C11C23×D411yescharacteristic
294C2×D11—28no—
295C2×D11—22no—
296C2×D11—22no—
297C2×D11—44no—
298C2×D11—44no—
299C2×D11—44no—
300C2×D11—88no—
301C2×D11C22×D814yes—
302C4×C11—22no—
303C4×C11—44no—
304C4×C11—44no—
305C4×C11#54712yes—
306C4×C11C22×#4111yescharacteristic
307C4×C11C2×2−1+411yescharacteristic
308Dic11—22no—
309Dic11—22no—
310Dic11—44no—
311Dic11C22×D814yes—
312C2×#41—2216no—
313C2×#41—4416no—
314C22×Q8—222no—
315C22×D4—111no—
316C22×D4—112no—
317C22×D4—222no—
318C22×D4—222no—
319C23×C4—22no—
320C23×C4—111no—
321C23×C4—222no—
322C23×C4—222no—
323C23×C4C22×D1111yescharacteristic
324C2×D8—114no—
325C2×D8—224no—
326C22×C8—24no—
327C22×C8—111no—
328C22×C8—111no—
329C22×C8—114no—
330C22×C8—224no—
331C22×C8C22×D1111yescharacteristic
332C22×C8C22×D1114yes—
333C22×C8C22×D1111yescharacteristic
334C4⋊Q8—118no—
335C4⋊Q8—224no—
336#123—2216no—
337#123—2216no—
338C22⋊Q8—2216no—
339#121—118no—
340#121—118no—
341#121—224no—
342#121—224no—
343C4×D4—114no—
344C4×D4—114no—
345C4×D4—118no—
346C4×D4—224no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—111no—
350C2×C4⋊C4—112no—
351C2×C4⋊C4—118no—
352C2×C4⋊C4—224no—
353C2×C4⋊C4—222no—
354C2×C4⋊C4—222no—
355C2×C4⋊C4C22×D1112yes—
356C2×C4⋊C4C22×D1112yes—
357C2×C4⋊C4C22×D1118yes—
358C2×C22⋊C4—111no—
359C2×C22⋊C4—111no—
360C2×C22⋊C4—222no—
361C2×C22⋊C4—222no—
362C2×C22⋊C4—222no—
363C2×C42—111no—
364#107—114no—
365#107—118no—
366#107—118no—
367#107C22×D1114yes—
368#107C22×D1114yes—
369#107C22×D1118yes—
370C4⋊C8—114no—
371#102—118no—
372#102—118no—
373#102—118no—
374C22⋊C8—114no—
375C22⋊C8—114no—
376C4×C8—114no—
377C2×C11—24no—
378C2×C11#333414yescomplemented
379C2×C11C2×#54711yescharacteristic
380C2×C11C23×D811yescharacteristic
381C2×C11C2×#57811yescharacteristic
382D11—24no—
383D11—84no—
384C24—111no—
385C24—222no—
386C24D4×D1111yescharacteristic
387#41—4464no—
388C2×Q8—228no—
389C2×Q8—448no—
390C2×D4—118no—
391C2×D4—114no—
392C2×D4—114no—
393C2×D4—228no—
394C2×D4—228no—
395C2×D4—224no—
396C2×D4—222no—
397C2×D4—224no—
398C2×D4—448no—
399C2×D4—448no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—28no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—48no—
406C22×C4—111no—
407C22×C4—111no—
408C22×C4—111no—
409C22×C4—112no—
410C22×C4—112no—
411C22×C4—228no—
412C22×C4—228no—
413C22×C4—222no—
414C22×C4—222no—
415C22×C4—222no—
416C22×C4—448no—
417C22×C4—448no—
418C22×C4D4×D1112yes—
419C22×C4D4×D1111yescharacteristic
420C22×C4C23×D1112yes—
421C22×C4C23×D1111yescharacteristic
422D8—228no—
423C2×C8—22no—
424C2×C8—28no—
425C2×C8—112no—
426C2×C8—112no—
427C2×C8—222no—
428C2×C8—222no—
429C2×C8—228no—
430C2×C8#433914yescomplemented
431C2×C8C23×D1112yes—
432C2×C8C23×D1112yes—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—28no—
436C4⋊C4—114no—
437C4⋊C4—114no—
438C4⋊C4—228no—
439C4⋊C4—228no—
440C4⋊C4—222no—
441C4⋊C4C23×D1114yes—
442C4⋊C4C23×D1114yes—
443C22⋊C4—114no—
444C22⋊C4—114no—
445C22⋊C4—228no—
446C22⋊C4—228no—
447C22⋊C4—228no—
448C42—112no—
449C42—112no—
450C11C2×#333411yescharacteristic, complemented, Sylow
451C23—22no—
452C23—22no—
453C23—114no—
454C23—112no—
455C23—222no—
456C23—222no—
457C23—224no—
458C23—444no—
459C23—444no—
460C23—444no—
461C23D8×D1114yes—
462C23C2×D4×D1112yes—
463C23C2×D4×D1111yescharacteristic
464Q8—4416no—
465D4—1116no—
466D4—224no—
467D4—224no—
468D4—4416no—
469D4—4416no—
470D4—444no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—44no—
478C2×C4—44no—
479C2×C4—416no—
480C2×C4—114no—
481C2×C4—112no—
482C2×C4—112no—
483C2×C4—112no—
484C2×C4—222no—
485C2×C4—222no—
486C2×C4—224no—
487C2×C4—222no—
488C2×C4—222no—
489C2×C4—224no—
490C2×C4—4416no—
491C2×C4—4416no—
492C2×C4—444no—
493C2×C4C2×#433912yes—
494C2×C4C2×D4×D1112yes—
495C2×C4C2×D4×D1111yescharacteristic
496C2×C4#6704012yes—
497C2×C4C24×D1111yescharacteristic
498C8—22no—
499C8—222no—
500C8—222no—
501C8C2×#433914yescomplemented
502C22—28no—
503C22—22no—
504C22—22no—
505C22—114no—
506C22—228no—
507C22—222no—
508C22—222no—
509C22—444no—
510C22—444no—
511C22—444no—
512C22—888no—
513C22#1062303812yes—
514C22C2×D8×D1114yes—
515C22C2×D8×D1112yes—
516C22#1062329712yes—
517C22C22×D4×D1111yescharacteristic
518C4—22no—
519C4—44no—
520C4—44no—
521C4—114no—
522C4—222no—
523C4—222no—
524C4—444no—
525C4#1062303812yes—
526C4C22×#433911yescharacteristic
527C4C2×#6704011yescharacteristic
528C2—24no—
529C2—224no—
530C2—884no—
531C2#1308096114yesdirect product factor
532C2C2×#1062303811yescharacteristic
533C2C22×D8×D1111yescharacteristic
534C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#107C2
socleC23×C11C22×D4
hypercenterC22×#107D11
hypocenterC11C2×#3334
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
1. C2×#10623038C2semidirect
2. #13080961C2direct (N × H)
3. C2×#10622487C2semidirect
4. C2×#10622495C2semidirect
5. C2×#10622580C2semidirect
6. C2×#10622503C2semidirect
7. C2×#10622496C2semidirect
8. C2×#10622728C2semidirect
9. C2×#10622485C2semidirect
10. C2×C8×C22⋊D11C2semidirect
11. C2×D11×#107C2semidirect
12. C22×C11×#107C2semidirect
23. #10623038C22semidirect
32. C2×C11×#107C22semidirect
34. #10622728C22semidirect
36. C8×C22⋊D11C22semidirect
41. #10622580C22semidirect
46. #10622503C22semidirect
47. #10622496C22semidirect
48. #10622495C22semidirect
49. D11×#107C22semidirect
50. #10622487C22semidirect
51. #10622485C22semidirect
133. C2×C22⋊D11D8semidirect
158. C2×C8×C11#41semidirect
195. C22×#107D11semidirect
224. C22⋊D11C2×D8semidirect
244. C8×C11C2×#41semidirect
278. C2×#107C2×D11semidirect
378. C2×C11#3334semidirect
430. C2×C8#4339semidirect
450. C11C2×#3334semidirect
501. C8C2×#4339semidirect
531. C2#13080961direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230382
#130809612
C2×#106224872
C2×#106224952
C2×#106225802
C2×#106225032
C2×#106224962
C2×#106227282
C2×#106224852
C2×C8×C22⋊D112
C2×D11×#1072
C22×C11×#1072
C2×#333411