Finite Group Databasebeta

← C2×#13082215 #15660832

Subgroups — C2×#13082215 #15660832

Order 2816.

7802 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082215C2132yesmaximal, direct product factor
2C2×#10623244C213yesmaximal, complemented
3C2×#10623101C211yesmaximal, characteristic, complemented
4C2×#10623073C213yesmaximal, complemented
5C2×#10623145C216yesmaximal, complemented
6C2×#10623362C212yesmaximal, complemented
7C2×#10623247C213yesmaximal, complemented
8C2×#10623131C216yesmaximal, complemented
9C2×#41×Dic11C212yesmaximal, complemented
10C2×C4×#4341C213yesmaximal, complemented
11C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
12C2×C11×#550C211yesmaximal, characteristic, complemented
13C22×C11×#41C2212yes—
14C22×Q8×D11C2211yescharacteristic
15C22×#4341C2213yes—
16C11×#550C22116yescomplemented
17C2×C11×#127C2213yes—
18C2×C11×#121C2216yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2213yes—
21#10623362C22132yescomplemented
22#41×Dic11C22132yescomplemented
23C2×Q8×Dic11C2212yes—
24C2×Q8×Dic11C2211yescharacteristic
25C2×#66991C2216yes—
26C2×#66991C2216yes—
27C2×#66989C2216yes—
28C2×#66989C2216yes—
29C2×#66988C22112yes—
30C2×D4×Dic11C2216yes—
31C2×D4×Dic11C2216yes—
32C2×D4×Dic11C2216yes—
33C2×D4×Dic11C2213yes—
34C2×C4×C22⋊D11C2216yes—
35C2×#66979C2216yes—
36C2×#66977C2216yes—
37C22×C4×Dic11C2216yes—
38#10623247C22148yescomplemented
39#10623244C22148yescomplemented
40#10623145C22196yescomplemented
41#10623131C22196yescomplemented
42C4×Q8×D11C22116yescomplemented
43#10623101C22116yescomplemented
44#10623073C22148yescomplemented
45C4×#4341C22148yescomplemented
46C2×#66945C2211yescharacteristic
47C2×C4⋊C4×D11C2213yes—
48C2×#66943C2216yes—
49C2×#66940C2213yes—
50C2×#66940C2213yes—
51C2×(C22⋊D11)⋊C4C2216yes—
52C2×#66932C22112yes—
53C2×#66930C2216yes—
54C2×C42×D11C2213yes—
55C2×#66922C2213yes—
56C2×C4×Dic22C2213yes—
57C2×C4×Dic22C2213yes—
58C2×C11×#41—216no—
59C2×C11×#41C23116yes—
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11C2316yes—
62C22×D4×C11C2313yes—
63C22×D4×C11C2316yes—
64C23×C4×C11C2316yes—
65C22×C22⋊D11C2316yes—
66C23×Dic11C2316yes—
67C23×Dic11C2316yes—
68C2×Q8×D11—28no—
69C2×Q8×D11C2318yes—
70C2×#4341—224no—
71C2×#4341C23124yes—
72C22×C4×D11C2313yes—
73C22×C4×D11C2313yes—
74C22×C4×D11C2311yescharacteristic
75C22×Dic22C2313yes—
76C22×Dic22C2313yes—
77C11×#127C23124yes—
78C11×#121C23148yes—
79C4×Q8×C11C2318yes—
80C4×D4×C11C23124yes—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2313yes—
83C2×C11×C22⋊C4C2316yes—
84C2×C42×C11C2313yes—
85C2×C22⋊Dic11C2316yes—
86C2×C22⋊Dic11C23112yes—
87C2×C22⋊Dic11C23112yes—
88Q8×Dic11C23116yes—
89Q8×Dic11C2318yes—
90#66991C23148yes—
91#66991C23148yes—
92#66989C23148yes—
93#66989C23148yes—
94#66988C23196yes—
95D4×Dic11C23124yes—
96D4×Dic11C23148yes—
97D4×Dic11C23148yes—
98D4×Dic11C23148yes—
99C4×C22⋊D11C23148yes—
100C2×(C2×D11)⋊C4C2312yes—
101#66979C23148yes—
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2313yes—
104C2×C4⋊Dic11C2316yes—
105C2×C4⋊Dic11C2316yes—
106#66977C23148yes—
107C2×Dic11⋊C4C2316yes—
108C2×Dic11⋊C4C2316yes—
109C2×Dic11⋊C4C2316yes—
110C2×C4×Dic11C2313yes—
111C2×C4×Dic11C2316yes—
112C2×C4×Dic11C2313yes—
113C2×C4×Dic11C2313yes—
114C2×C4×Dic11C2312yes—
115C2×C4×Dic11C2316yes—
116C2×C4×Dic11C23148yes—
117#66945C2318yes—
118C4⋊C4×D11C23124yes—
119#66943C23148yes—
120#66940C23124yes—
121#66940C23124yes—
122(C22⋊D11)⋊C4C23148yes—
123#66932C23196yes—
124#66930C23148yes—
125C42×D11C23124yes—
126#66922C23124yes—
127C4×Dic22C23124yes—
128C4×Dic22C23124yes—
129C2×#3480—111nomaximal, Sylow
130C24×C11C2416yes—
131C23×D11C2411yescharacteristic
132C11×#41—264no—
133C2×Q8×C11#4118yescomplemented
134C2×Q8×C11C2414yes—
135C2×D4×C11—212no—
136C2×D4×C11—224no—
137C2×D4×C11—412no—
138C2×D4×C11C24124yes—
139C2×D4×C11C24112yes—
140C2×D4×C11C24124yes—
141C22×C4×C11—224no—
142C22×C4×C11C2412yes—
143C22×C4×C11C24124yes—
144C22×C4×C11C2413yes—
145C22×C4×C11C2413yes—
146C22×C4×C11C2411yescharacteristic
147C2×C22⋊D11—224no—
148C2×C22⋊D11C24124yes—
149C22×Dic11—224no—
150C22×Dic11—412no—
151C22×Dic11C24124yes—
152C22×Dic11C2412yes—
153C22×Dic11C2413yes—
154C22×Dic11C2413yes—
155C22×Dic11C2416yes—
156C22×Dic11C24124yes—
157C22×Dic11C2411yescharacteristic
158Q8×D11—232no—
159#4341—296no—
160C2×C4×D11—212no—
161C2×C4×D11—46no—
162C2×C4×D11#4118yescomplemented
163C2×C4×D11C24112yes—
164C2×C4×D11C24112yes—
165C2×C4×D11C2414yes—
166C2×Dic22—212no—
167C2×Dic22—212no—
168C2×Dic22C24112yes—
169C2×Dic22C24112yes—
170C11×C4⋊C4C2414yes—
171C11×C4⋊C4C24112yes—
172C11×C22⋊C4C24124yes—
173C42×C11C24112yes—
174C22⋊Dic11C24124yes—
175C22⋊Dic11C24148yes—
176C22⋊Dic11C24148yes—
177(C2×D11)⋊C4C2418yes—
178C4⋊Dic11C2414yes—
179C4⋊Dic11C24112yes—
180C4⋊Dic11C24124yes—
181C4⋊Dic11C24124yes—
182Dic11⋊C4C24124yes—
183Dic11⋊C4C24124yes—
184Dic11⋊C4C24124yes—
185C4×Dic11C24112yes—
186C4×Dic11C24124yes—
187C4×Dic11C24112yes—
188C4×Dic11C24112yes—
189C4×Dic11C2418yes—
190C4×Dic11C24124yes—
191#3480—1132no—
192C2×#559—113no—
193C2×#557—111no—
194C2×#556—113no—
195C2×#553—116no—
196C2×#550D1111yescharacteristic, complemented
197C2×#548—112no—
198C2×#532—113no—
199C2×#529—116no—
200C2×C4×#41—112no—
201C2×C4×#41—113no—
202C22×C4×Q8—111no—
203C23×C11—212no—
204C23×C11—212no—
205C23×C11—212no—
206C23×C11C25112yes—
207C23×C11C2511yescharacteristic
208C22×D11—22no—
209C22×D11—22no—
210C22×D11C2×#4114yes—
211C22×D11C2512yes—
212Q8×C11C2×#41116yescomplemented
213D4×C11—224no—
214D4×C11—248no—
215D4×C11—424no—
216C2×C4×C11—24no—
217C2×C4×C11—26no—
218C2×C4×C11—248no—
219C2×C4×C11C2×#41112yes—
220C2×C4×C11C2×#4114yes—
221C2×C4×C11C2514yes—
222C2×C4×C11C2516yes—
223C2×C4×C11C2516yes—
224C2×C4×C11C2512yes—
225C22⋊D11—248no—
226C2×Dic11—26no—
227C2×Dic11—212no—
228C2×Dic11—26no—
229C2×Dic11—24no—
230C2×Dic11—248no—
231C2×Dic11—424no—
232C2×Dic11C2×#4114yes—
233C2×Dic11C2514yes—
234C2×Dic11C2516yes—
235C2×Dic11C2516yes—
236C2×Dic11C25112yes—
237C2×Dic11C2512yes—
238C4×D11—224no—
239C4×D11—412no—
240C4×D11C2×#41116yescomplemented
241Dic22—224no—
242Dic22—224no—
243C22×#41—113no—
244C22×#41C2×D1112yes—
245C23×Q8—111no—
246#559—1148no—
247#557—1116no—
248#556—1148no—
249#553—1196no—
250#550C2×D11116yescomplemented
251#548—1132no—
252#532—1148no—
253C2×C4⋊Q8—113no—
254C2×#127C2×D1113yes—
255#529—1196no—
256C2×#126—1112no—
257C2×#125—116no—
258C2×#124—116no—
259C2×#124—116no—
260C2×#123—1112no—
261C2×C22⋊Q8—116no—
262C2×#121—116no—
263C2×#121—116no—
264C2×#121C2×D1116yes—
265C4×#41—1132no—
266C4×#41—1148no—
267C2×C4×Q8—111no—
268C2×C4×Q8—112no—
269C2×C4×Q8—1116no—
270C2×C4×Q8—113no—
271C2×C4×Q8—113no—
272C2×C4×Q8—113no—
273C2×C4×Q8—113no—
274C2×C4×Q8C2×D1111yescharacteristic
275C2×C4×D4—116no—
276C2×C4×D4—116no—
277C2×C4×D4—113no—
278C2×C4×D4—116no—
279C2×C4×D4—116no—
280C2×C4×D4—116no—
281C2×C4×D4C2×D1113yes—
282C2×#117—116no—
283C2×#117—111no—
284C2×#117—116no—
285C22×C4⋊C4—113no—
286C22×C42—116no—
287C22×C42—113no—
288C22×C11—212no—
289C22×C11—212no—
290C22×C11—212no—
291C22×C11—424no—
292C22×C11C22×#4112yes—
293C22×C11C22×#4112yes—
294C22×C11#58512yes—
295C22×C11C2611yescharacteristic
296C2×D11—22no—
297C2×D11—22no—
298C2×D11—28no—
299C2×D11C22×#4114yes—
300C4×C11—24no—
301C4×C11—26no—
302C4×C11C22×#41112yes—
303C4×C11C22×#4114yes—
304Dic11—26no—
305Dic11—212no—
306Dic11—26no—
307Dic11—24no—
308Dic11C22×#4114yes—
309C2×#41—216no—
310C2×#41—1124no—
311C2×#41—2224no—
312C2×#41C22×D11116yes—
313C22×Q8—118no—
314C22×Q8—113no—
315C22×Q8—113no—
316C22×Q8—228no—
317C22×Q8C22×D1111yescharacteristic
318C22×D4—116no—
319C22×D4C22×D1116yes—
320C22×D4C22×D1113yes—
321C22×D4C22×D1116yes—
322C23×C4—111no—
323C23×C4—116no—
324C23×C4—116no—
325C23×C4—113no—
326C23×C4—113no—
327C23×C4C22×D1116yes—
328C4⋊Q8—1124no—
329#127C22×D11124yes—
330#126—1196no—
331#125—1148no—
332#124—1148no—
333#124—1148no—
334#123—1196no—
335C22⋊Q8—1148no—
336#121—1148no—
337#121—1148no—
338#121C22×D11148yes—
339C4×Q8—118no—
340C4×Q8—1116no—
341C4×Q8—1124no—
342C4×Q8—1124no—
343C4×Q8—1124no—
344C4×Q8—1124no—
345C4×Q8C22×D1118yes—
346C4×D4—1148no—
347C4×D4—1148no—
348C4×D4—1124no—
349C4×D4—1148no—
350C4×D4—1148no—
351C4×D4—1148no—
352C4×D4C22×D11124yes—
353#117—1148no—
354#117—118no—
355#117—1148no—
356C2×C4⋊C4—113no—
357C2×C4⋊C4—116no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—116no—
360C2×C4⋊C4—116no—
361C2×C4⋊C4—116no—
362C2×C4⋊C4—116no—
363C2×C4⋊C4—1124no—
364C2×C4⋊C4C22×D1113yes—
365C2×C4⋊C4C22×D1111yescharacteristic
366C2×C22⋊C4—1112no—
367C2×C22⋊C4—116no—
368C2×C22⋊C4—1112no—
369C2×C22⋊C4—112no—
370C2×C22⋊C4C22×D1116yes—
371C2×C42—112no—
372C2×C42—113no—
373C2×C42—116no—
374C2×C42—116no—
375C2×C42—113no—
376C2×C42—113no—
377C2×C42—1148no—
378C2×C42—1124no—
379C2×C42C22×D1113yes—
380C2×C11—412no—
381C2×C11#348014yescomplemented
382C2×C11C23×#4111yescharacteristic
383C2×C11C23×#4111yescharacteristic
384C2×C11C2×#58511yescharacteristic
385D11—24no—
386C24—111no—
387C24C23×D1116yes—
388#41—264no—
389#41—2296no—
390C2×Q8—1112no—
391C2×Q8—1112no—
392C2×Q8—2232no—
393C2×Q8—2212no—
394C2×Q8—2212no—
395C2×Q8#434118yescomplemented
396C2×Q8C23×D1114yes—
397C2×D4—224no—
398C2×D4—212no—
399C2×D4—412no—
400C2×D4—1124no—
401C2×D4—2224no—
402C2×D4C23×D11124yes—
403C2×D4C23×D11112yes—
404C2×D4C23×D11124yes—
405C22×C4—224no—
406C22×C4—111no—
407C22×C4—118no—
408C22×C4—114no—
409C22×C4—1124no—
410C22×C4—112no—
411C22×C4—113no—
412C22×C4—113no—
413C22×C4—116no—
414C22×C4—1124no—
415C22×C4—1112no—
416C22×C4—1112no—
417C22×C4—2224no—
418C22×C4—2212no—
419C22×C4—446no—
420C22×C4—4412no—
421C22×C4C23×D11124yes—
422C22×C4C23×D1112yes—
423C22×C4C23×D1113yes—
424C22×C4C23×D1113yes—
425C22×C4C23×D1111yescharacteristic
426C4⋊C4—1112no—
427C4⋊C4—1124no—
428C4⋊C4—114no—
429C4⋊C4—1124no—
430C4⋊C4—1124no—
431C4⋊C4—1124no—
432C4⋊C4—1124no—
433C4⋊C4C23×D11112yes—
434C4⋊C4C23×D1114yes—
435C22⋊C4—1148no—
436C22⋊C4—1124no—
437C22⋊C4—1148no—
438C22⋊C4—118no—
439C22⋊C4C23×D11124yes—
440C42—118no—
441C42—1112no—
442C42—1112no—
443C42—1124no—
444C42—1124no—
445C42—1112no—
446C42C23×D11112yes—
447C11C2×#348011yescharacteristic, complemented, Sylow
448C23—212no—
449C23—212no—
450C23—212no—
451C23—114no—
452C23—112no—
453C23—222no—
454C23—222no—
455C23C24×D11112yes—
456C23C24×D1111yescharacteristic
457Q8—2224no—
458Q8—2224no—
459Q8C2×#4341116yescomplemented
460D4—248no—
461D4—224no—
462D4—424no—
463D4—2248no—
464C2×C4—24no—
465C2×C4—26no—
466C2×C4—248no—
467C2×C4—114no—
468C2×C4—112no—
469C2×C4—1116no—
470C2×C4—114no—
471C2×C4—116no—
472C2×C4—116no—
473C2×C4—1112no—
474C2×C4—2248no—
475C2×C4—226no—
476C2×C4—2212no—
477C2×C4—226no—
478C2×C4—224no—
479C2×C4—2224no—
480C2×C4—4412no—
481C2×C4—4424no—
482C2×C4C2×#4341112yes—
483C2×C4#41×D1114yes—
484C2×C4C24×D1114yes—
485C2×C4C24×D1116yes—
486C2×C4C24×D1116yes—
487C2×C4C24×D1112yes—
488C22—212no—
489C22—212no—
490C22—212no—
491C22—424no—
492C22—114no—
493C22—222no—
494C22—222no—
495C22—228no—
496C22C22×#434112yes—
497C22C2×#41×D1112yes—
498C22#1062345512yes—
499C22C25×D1111yescharacteristic
500C4—24no—
501C4—26no—
502C4—114no—
503C4—2212no—
504C4—226no—
505C4—226no—
506C4—224no—
507C4C22×#4341112yes—
508C4C2×#41×D1114yes—
509C2—412no—
510C2—224no—
511C2#1308221514yesdirect product factor
512C2C22×#41×D1111yescharacteristic
513C2C23×#434111yescharacteristic
514C2C2×#1062345511yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#550C2
socleC23×C11C25
hypercenterC2×#550D11
hypocenterC11C2×#3480
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. #13082215C2direct (N × H)
2. C2×#10623244C2semidirect
3. C2×#10623101C2semidirect
4. C2×#10623073C2semidirect
5. C2×#10623145C2semidirect
6. C2×#10623362C2semidirect
7. C2×#10623247C2semidirect
8. C2×#10623131C2semidirect
9. C2×#41×Dic11C2semidirect
10. C2×C4×#4341C2semidirect
11. C2×C4×Q8×D11C2semidirect
12. C2×C11×#550C2semidirect
16. C11×#550C22semidirect
21. #10623362C22semidirect
22. #41×Dic11C22semidirect
38. #10623247C22semidirect
39. #10623244C22semidirect
40. #10623145C22semidirect
41. #10623131C22semidirect
42. C4×Q8×D11C22semidirect
43. #10623101C22semidirect
44. #10623073C22semidirect
45. C4×#4341C22semidirect
133. C2×Q8×C11#41semidirect
162. C2×C4×D11#41semidirect
196. C2×#550D11semidirect
212. Q8×C11C2×#41semidirect
240. C4×D11C2×#41semidirect
250. #550C2×D11semidirect
381. C2×C11#3480semidirect
395. C2×Q8#4341semidirect
447. C11C2×#3480semidirect
459. Q8C2×#4341semidirect
511. C2#13082215direct (N × H)

Maximal subgroups

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

subgroupindex
#130822152
C2×#106232442
C2×#106231012
C2×#106230732
C2×#106231452
C2×#106233622
C2×#106232472
C2×#106231312
C2×#41×Dic112
C2×C4×#43412
C2×C4×Q8×D112
C2×C11×#5502
C2×#348011