Finite Group Databasebeta

← C2×#13082211 #15660836

Subgroups — C2×#13082211 #15660836

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#13082211C2132yesmaximal, direct product factor
2C2×#10623116C213yesmaximal, complemented
3C2×#10623101C211yesmaximal, characteristic, complemented
4C2×#10623115C213yesmaximal, complemented
5C2×#10623045C216yesmaximal, complemented
6C2×#10623108C211yesmaximal, characteristic, complemented
7C2×#10623348C212yesmaximal, complemented
8C2×#10623008C213yesmaximal, complemented
9C2×#10623111C216yesmaximal, complemented
10C2×C4×#4343C212yesmaximal, complemented
11C2×C4×#4339C213yesmaximal, complemented
12C22×C4×Q8×C11C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C22×#4343C2212yes—
15C22×#4339C2213yes—
16C2×C4×Q8×C11C2213yes—
17C2×C4×Q8×C11C2213yes—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×Q8×C11C22116yescomplemented
21C22×C11×C4⋊C4C2213yes—
22C22×C42×C11C2213yes—
23#10623348C22132yescomplemented
24C2×#67000C2216yes—
25C2×#66999C2216yes—
26C2×Q8×Dic11C2212yes—
27C2×#66983C2216yes—
28C2×#66983C2216yes—
29C2×C4×C22⋊D11C2216yes—
30C2×C4×C22⋊D11C2216yes—
31C2×#66979C2211yescharacteristic
32#10623116C22148yescomplemented
33#10623115C22148yescomplemented
34#10623111C22196yescomplemented
35#10623108C22116yescomplemented
36C4×#4343C22132yescomplemented
37#10623101C22116yescomplemented
38#10623045C22196yescomplemented
39C2×#66951C22112yes—
40C2×#66948C2216yes—
41C2×#66947C22112yes—
42C2×#66946C2216yes—
43C2×#66945C2216yes—
44C2×#66943C2216yes—
45#10623008C22148yescomplemented
46C2×#66928C2216yes—
47C2×#66927C2213yes—
48C4×#4339C22148yescomplemented
49C2×C4×D44C2216yes—
50C2×C4×D44C2216yes—
51C2×C4×D44C2213yes—
52C2×C4×D44C2213yes—
53C2×#66925C2216yes—
54C2×C42×D11C2216yes—
55C2×#66922C2213yes—
56C2×C4×Dic22C2213yes—
57C2×C4×Dic22C2213yes—
58C22×Q8×C11—28no—
59C22×Q8×C11C2313yes—
60C22×Q8×C11C2318yes—
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11C2313yes—
63C23×C4×C11C2313yes—
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11C2316yes—
66C2×#4343—216no—
67C2×#4343C23116yes—
68C2×#4339—224no—
69C2×#4339C23124yes—
70C22×D44C2313yes—
71C22×D44C2316yes—
72C22×D44C2316yes—
73C22×C4×D11C2316yes—
74C22×C4×D11C2316yes—
75C22×C4×D11C2316yes—
76C22×Dic22C2313yes—
77C4×Q8×C11C2318yes—
78C4×Q8×C11C2318yes—
79C4×Q8×C11C23124yes—
80C4×Q8×C11C23124yes—
81C2×C11×C4⋊C4C2313yes—
82C2×C11×C4⋊C4C2313yes—
83C2×C11×C4⋊C4C2316yes—
84C2×C11×C4⋊C4C23124yes—
85C2×C42×C11C2313yes—
86C2×C42×C11C2313yes—
87C2×C42×C11C2313yes—
88C2×C42×C11C2313yes—
89C2×C42×C11C23124yes—
90C2×C22⋊Dic11C2312yes—
91#67000C23148yes—
92#66999C23148yes—
93Q8×Dic11C23116yes—
94#66983C23148yes—
95#66983C23148yes—
96C4×C22⋊D11C23148yes—
97C4×C22⋊D11C23148yes—
98C2×(C2×D11)⋊C4C2316yes—
99C2×(C2×D11)⋊C4C2316yes—
100C2×(C2×D11)⋊C4C23112yes—
101C2×(C2×D11)⋊C4C23112yes—
102#66979C2318yes—
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2316yes—
106C2×C4⋊Dic11C2316yes—
107C2×Dic11⋊C4C2316yes—
108C2×Dic11⋊C4C2316yes—
109C2×C4×Dic11C2316yes—
110C2×C4×Dic11C2316yes—
111C2×C4×Dic11C2312yes—
112#66951C23196yes—
113#66948C23148yes—
114#66947C23196yes—
115#66946C23148yes—
116#66945C23148yes—
117#66943C23148yes—
118#66928C23148yes—
119#66927C23124yes—
120C4×D44C23124yes—
121C4×D44C23124yes—
122C4×D44C23148yes—
123C4×D44C23148yes—
124#66925C23148yes—
125C42×D11C23148yes—
126#66922C23124yes—
127C4×Dic22C23124yes—
128C4×Dic22C23124yes—
129C2×#3480—111nomaximal, Sylow
130C24×C11C2411yescharacteristic
131C23×D11C2416yes—
132C2×Q8×C11—232no—
133C2×Q8×C11—212no—
134C2×Q8×C11#4118yescomplemented
135C2×Q8×C11C24112yes—
136C2×Q8×C11C2414yes—
137C22×C4×C11—212no—
138C22×C4×C11—46no—
139C22×C4×C11#4118yescomplemented
140C22×C4×C11C2413yes—
141C22×C4×C11C2413yes—
142C22×C4×C11C2413yes—
143C22×C4×C11C24112yes—
144C22×C4×C11C24112yes—
145C22×C4×C11C2413yes—
146C22×C4×C11C2411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C22×C4×C11C2414yes—
149C2×C22⋊D11—224no—
150C2×C22⋊D11C24124yes—
151C22×Dic11C2412yes—
152C22×Dic11C2412yes—
153C22×Dic11C2416yes—
154#4343—264no—
155#4339—296no—
156C2×D44—212no—
157C2×D44—224no—
158C2×D44—412no—
159C2×D44C24112yes—
160C2×D44C24124yes—
161C2×D44C24124yes—
162C2×C4×D11—224no—
163C2×C4×D11—224no—
164C2×C4×D11—412no—
165C2×C4×D11C24124yes—
166C2×C4×D11C24124yes—
167C2×C4×D11C24124yes—
168C2×Dic22—212no—
169C2×Dic22C24112yes—
170C11×C4⋊C4C24112yes—
171C11×C4⋊C4C24112yes—
172C11×C4⋊C4C24124yes—
173C42×C11C24112yes—
174C42×C11C24112yes—
175C42×C11C24112yes—
176C42×C11C24112yes—
177C22⋊Dic11C2418yes—
178(C2×D11)⋊C4C24124yes—
179(C2×D11)⋊C4C24124yes—
180(C2×D11)⋊C4C24148yes—
181(C2×D11)⋊C4C24148yes—
182C4⋊Dic11C2414yes—
183C4⋊Dic11C2414yes—
184C4⋊Dic11C24124yes—
185C4⋊Dic11C24124yes—
186Dic11⋊C4C24124yes—
187Dic11⋊C4C24124yes—
188C4×Dic11C24124yes—
189C4×Dic11C24124yes—
190C4×Dic11C2418yes—
191#3480—1132no—
192C2×#559—113no—
193C2×#557—111no—
194C2×#556—113no—
195C2×#553—116no—
196C2×#550—111no—
197C2×#548—112no—
198C2×#532—113no—
199C2×#529—116no—
200C2×C4×#41—113no—
201C2×C4×#41—112no—
202C22×C4×Q8D1111yescharacteristic, complemented
203C23×C11—22no—
204C23×C11—22no—
205C23×C11C2×#4114yes—
206C23×C11C2512yes—
207C23×C11C2511yescharacteristic
208C22×D11—212no—
209C22×D11—212no—
210C22×D11—212no—
211C22×D11C25112yes—
212Q8×C11—224no—
213Q8×C11C2×#41116yescomplemented
214C2×C4×C11—26no—
215C2×C4×C11—26no—
216C2×C4×C11—26no—
217C2×C4×C11—224no—
218C2×C4×C11—412no—
219C2×C4×C11C2×#41112yes—
220C2×C4×C11C2×#4114yes—
221C2×C4×C11C2×#4114yes—
222C2×C4×C11C2×#41116yescomplemented
223C2×C4×C11C2516yes—
224C2×C4×C11C2516yes—
225C2×C4×C11C2516yes—
226C2×C4×C11C2516yes—
227C2×C4×C11C2512yes—
228C2×C4×C11C2512yes—
229C22⋊D11—248no—
230C2×Dic11—212no—
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11C2514yes—
234C2×Dic11C2514yes—
235C2×Dic11C25112yes—
236D44—224no—
237D44—248no—
238D44—424no—
239C4×D11—248no—
240C4×D11—248no—
241C4×D11—424no—
242Dic22—224no—
243C22×#41—112no—
244C22×#41—113no—
245C23×Q8C2×D1111yescharacteristic
246#559—1148no—
247#557—1116no—
248#556—1148no—
249#553—1196no—
250#550—1116no—
251#548—1132no—
252#532—1148no—
253C2×C4⋊Q8—113no—
254C2×#127—113no—
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×#121—116no—
265C4×#41—1132no—
266C4×#41—1148no—
267C2×C4×Q8—112no—
268C2×C4×Q8—113no—
269C2×C4×Q8—113no—
270C2×C4×Q8C2×D1111yescharacteristic
271C2×C4×Q8C2×D1113yes—
272C2×C4×Q8C2×D1111yescharacteristic
273C2×C4×Q8C2×D1113yes—
274C2×C4×Q8C2×D11116yescomplemented
275C2×C4×D4—116no—
276C2×C4×D4—116no—
277C2×C4×D4—116no—
278C2×C4×D4—116no—
279C2×C4×D4—113no—
280C2×C4×D4—113no—
281C2×C4×D4—116no—
282C2×#117—111no—
283C2×#117—116no—
284C2×#117—116no—
285C22×C4⋊C4C2×D1113yes—
286C22×C42—116no—
287C22×C42C2×D1113yes—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—28no—
291C22×C11C22×#4112yes—
292C22×C11C22×#4114yes—
293C22×C11C22×#4112yes—
294C22×C11#58512yes—
295C22×C11C2611yescharacteristic
296C2×D11—212no—
297C2×D11—212no—
298C2×D11—212no—
299C2×D11—424no—
300C4×C11—26no—
301C4×C11—26no—
302C4×C11—26no—
303C4×C11C22×#41112yes—
304C4×C11C22×#4114yes—
305C4×C11C22×#4114yes—
306Dic11—212no—
307Dic11—24no—
308Dic11—24no—
309C2×#41—1116no—
310C2×#41—1124no—
311C2×#41—2216no—
312C2×#41—2224no—
313C22×Q8—28no—
314C22×Q8—113no—
315C22×Q8C22×D1113yes—
316C22×Q8C22×D1118yes—
317C22×Q8C22×D1111yescharacteristic
318C22×D4—116no—
319C22×D4—116no—
320C22×D4—113no—
321C22×D4—116no—
322C23×C4—116no—
323C23×C4—116no—
324C23×C4—116no—
325C23×C4C22×D1113yes—
326C23×C4C22×D1113yes—
327C23×C4C22×D1111yescharacteristic
328C4⋊Q8—1124no—
329#127—1124no—
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#121—1148no—
339C4×Q8—1116no—
340C4×Q8—1124no—
341C4×Q8—1124no—
342C4×Q8C22×D1118yes—
343C4×Q8C22×D11124yes—
344C4×Q8C22×D1118yes—
345C4×Q8C22×D11124yes—
346C4×D4—1148no—
347C4×D4—1148no—
348C4×D4—1148no—
349C4×D4—1148no—
350C4×D4—1124no—
351C4×D4—1124no—
352C4×D4—1148no—
353#117—118no—
354#117—1148no—
355#117—1148no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—116no—
359C2×C4⋊C4—116no—
360C2×C4⋊C4—116no—
361C2×C4⋊C4—116no—
362C2×C4⋊C4C22×D1113yes—
363C2×C4⋊C4C22×D1113yes—
364C2×C4⋊C4C22×D1116yes—
365C2×C4⋊C4C22×D11124yes—
366C2×C22⋊C4—112no—
367C2×C22⋊C4—116no—
368C2×C22⋊C4—1112no—
369C2×C22⋊C4—116no—
370C2×C22⋊C4—1112no—
371C2×C42—116no—
372C2×C42—116no—
373C2×C42—112no—
374C2×C42—1148no—
375C2×C42C22×D1113yes—
376C2×C42C22×D1113yes—
377C2×C42C22×D11124yes—
378C2×C42C22×D1113yes—
379C2×C42C22×D1113yes—
380C2×C11—24no—
381C2×C11#348014yescomplemented
382C2×C11C23×#4111yescharacteristic
383C2×C11C23×#4111yescharacteristic
384C2×C11C2×#58511yescharacteristic
385D11—412no—
386C24—116no—
387C24C23×D1111yescharacteristic
388#41—2264no—
389#41—2296no—
390C2×Q8—232no—
391C2×Q8—212no—
392C2×Q8—1112no—
393C2×Q8—2212no—
394C2×Q8#433918yescomplemented
395C2×Q8C23×D11112yes—
396C2×Q8C23×D1114yes—
397C2×D4—1124no—
398C2×D4—1124no—
399C2×D4—1112no—
400C2×D4—1124no—
401C2×D4—2224no—
402C2×D4—2224no—
403C2×D4—2212no—
404C2×D4—4412no—
405C22×C4—212no—
406C22×C4—46no—
407C22×C4—112no—
408C22×C4—112no—
409C22×C4—116no—
410C22×C4—1124no—
411C22×C4—1124no—
412C22×C4—1124no—
413C22×C4—2224no—
414C22×C4—2224no—
415C22×C4—4412no—
416C22×C4#434318yescomplemented
417C22×C4C23×D1113yes—
418C22×C4C23×D1113yes—
419C22×C4C23×D1113yes—
420C22×C4C23×D11112yes—
421C22×C4C23×D11112yes—
422C22×C4C23×D1113yes—
423C22×C4C23×D1111yescharacteristic
424C22×C4C23×D1114yes—
425C22×C4C23×D1111yescharacteristic
426C4⋊C4—114no—
427C4⋊C4—114no—
428C4⋊C4—1124no—
429C4⋊C4—1124no—
430C4⋊C4—1124no—
431C4⋊C4—1124no—
432C4⋊C4C23×D11112yes—
433C4⋊C4C23×D11112yes—
434C4⋊C4C23×D11124yes—
435C22⋊C4—118no—
436C22⋊C4—1124no—
437C22⋊C4—1148no—
438C22⋊C4—1124no—
439C22⋊C4—1148no—
440C42—118no—
441C42—1124no—
442C42—1124no—
443C42C23×D11112yes—
444C42C23×D11112yes—
445C42C23×D11112yes—
446C42C23×D11112yes—
447C11C2×#348011yescharacteristic, complemented, Sylow
448C23—22no—
449C23—22no—
450C23—1112no—
451C23—2212no—
452C23—2212no—
453C23—2212no—
454C23C2×#434314yes—
455C23C24×D1112yes—
456C23C24×D1111yescharacteristic
457Q8—224no—
458Q8—2224no—
459Q8C2×#4339116yescomplemented
460D4—2248no—
461D4—2248no—
462D4—2224no—
463D4—4424no—
464C2×C4—26no—
465C2×C4—26no—
466C2×C4—26no—
467C2×C4—224no—
468C2×C4—412no—
469C2×C4—114no—
470C2×C4—114no—
471C2×C4—1112no—
472C2×C4—224no—
473C2×C4—2212no—
474C2×C4—224no—
475C2×C4—2248no—
476C2×C4—2248no—
477C2×C4—4424no—
478C2×C4C2×#4339112yes—
479C2×C4C2×#434314yes—
480C2×C4C2×#434314yes—
481C2×C4C2×#4343116yescomplemented
482C2×C4C24×D1116yes—
483C2×C4C24×D1116yes—
484C2×C4C24×D1116yes—
485C2×C4C24×D1116yes—
486C2×C4C24×D1112yes—
487C2×C4C24×D1112yes—
488C22—22no—
489C22—22no—
490C22—28no—
491C22—2212no—
492C22—2212no—
493C22—2212no—
494C22—4424no—
495C22C22×#433912yes—
496C22C22×#434314yes—
497C22C22×#434312yes—
498C22#1062345312yes—
499C22C25×D1111yescharacteristic
500C4—26no—
501C4—26no—
502C4—26no—
503C4—224no—
504C4—2212no—
505C4—224no—
506C4C22×#4339112yes—
507C4C22×#434314yes—
508C4C22×#434314yes—
509C2—24no—
510C2—4412no—
511C2#1308221114yesdirect product factor
512C2C23×#433911yescharacteristic
513C2C23×#434311yescharacteristic
514C2C2×#1062345311yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C4×Q8×C11C2
socleC23×C11C25
hypercenterC22×C4×Q8D11
hypocenterC11C2×#3480
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #13082211C2direct (N × H)
2. C2×#10623116C2semidirect
3. C2×#10623101C2semidirect
4. C2×#10623115C2semidirect
5. C2×#10623045C2semidirect
6. C2×#10623108C2semidirect
7. C2×#10623348C2semidirect
8. C2×#10623008C2semidirect
9. C2×#10623111C2semidirect
10. C2×C4×#4343C2semidirect
11. C2×C4×#4339C2semidirect
12. C22×C4×Q8×C11C2semidirect
20. C2×C4×Q8×C11C22semidirect
23. #10623348C22semidirect
32. #10623116C22semidirect
33. #10623115C22semidirect
34. #10623111C22semidirect
35. #10623108C22semidirect
36. C4×#4343C22semidirect
37. #10623101C22semidirect
38. #10623045C22semidirect
45. #10623008C22semidirect
48. C4×#4339C22semidirect
134. C2×Q8×C11#41semidirect
139. C22×C4×C11#41semidirect
202. C22×C4×Q8D11semidirect
213. Q8×C11C2×#41semidirect
222. C2×C4×C11C2×#41semidirect
274. C2×C4×Q8C2×D11semidirect
381. C2×C11#3480semidirect
394. C2×Q8#4339semidirect
416. C22×C4#4343semidirect
447. C11C2×#3480semidirect
459. Q8C2×#4339semidirect
481. C2×C4C2×#4343semidirect
511. C2#13082211direct (N × H)

Maximal subgroups

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

subgroupindex
#130822112
C2×#106231162
C2×#106231012
C2×#106231152
C2×#106230452
C2×#106231082
C2×#106233482
C2×#106230082
C2×#106231112
C2×C4×#43432
C2×C4×#43392
C22×C4×Q8×C112
C2×#348011