Finite Group Databasebeta

← C2×#13082216 #15660837

Subgroups — C2×#13082216 #15660837

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#13082216C2132yesmaximal, direct product factor
2C2×#10623116C213yesmaximal, complemented
3C2×#10623263C213yesmaximal, complemented
4C2×#10623226C216yesmaximal, complemented
5C2×#10623108C211yesmaximal, characteristic, complemented
6C2×#10623107C212yesmaximal, complemented
7C2×#10623256C213yesmaximal, complemented
8C2×#10623222C216yesmaximal, complemented
9C2×C4×#4343C212yesmaximal, complemented
10C2×C4×#4343C213yesmaximal, complemented
11C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
12C2×C11×#557C211yesmaximal, characteristic, complemented
13C22×#4343C2213yes—
14C22×#4343C2212yes—
15C22×Q8×D11C2211yescharacteristic
16C11×#557C22116yescomplemented
17C2×C11×C4⋊Q8C2213yes—
18C2×C11×#125C2216yes—
19C2×C4×Q8×C11C2213yes—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2212yes—
22C2×#67000C2216yes—
23C2×Q8×Dic11C2213yes—
24C2×Q8×Dic11C2211yescharacteristic
25#10623263C22148yescomplemented
26#10623256C22148yescomplemented
27#10623226C22196yescomplemented
28#10623222C22196yescomplemented
29#10623116C22148yescomplemented
30#10623108C22116yescomplemented
31#10623107C22132yescomplemented
32C4×#4343C22148yescomplemented
33C4×#4343C22132yescomplemented
34C4×Q8×D11C22116yescomplemented
35C2×#66951C22112yes—
36C2×#66950C2216yes—
37C2×#66948C2216yes—
38C2×#66948C2216yes—
39C2×#66948C2216yes—
40C2×#66947C22112yes—
41C2×#66946C2216yes—
42C2×#66946C2216yes—
43C2×#66946C2216yes—
44C2×#66946C2213yes—
45C2×#66945C2216yes—
46C2×#66945C2216yes—
47C2×#66945C2211yescharacteristic
48C2×C4⋊C4×D11C2213yes—
49C2×#66940C2213yes—
50C2×#66928C2216yes—
51C2×#66927C2213yes—
52C2×C4×D44C2216yes—
53C2×C4×D44C2216yes—
54C2×C4×D44C2213yes—
55C2×C42×D11C2216yes—
56C2×C42×D11C2213yes—
57C2×C4×Dic22C2213yes—
58C22×Q8×C11C2313yes—
59C22×Q8×C11C2311yescharacteristic
60C2×#4343—216no—
61C2×#4343—224no—
62C2×#4343C23124yes—
63C2×#4343C23116yes—
64C2×Q8×D11—28no—
65C2×Q8×D11C2318yes—
66C22×D44C2313yes—
67C22×D44C2316yes—
68C22×D44C2316yes—
69C22×D44C2316yes—
70C22×C4×D11C2313yes—
71C22×C4×D11C2316yes—
72C22×C4×D11C2316yes—
73C22×C4×D11C2316yes—
74C22×C4×D11C2313yes—
75C22×C4×D11C2311yescharacteristic
76C22×Dic22C2313yes—
77C11×C4⋊Q8C23124yes—
78C11×#125C23148yes—
79C4×Q8×C11C2318yes—
80C4×Q8×C11C23116yes—
81C4×Q8×C11C23124yes—
82C2×C11×C4⋊C4C2313yes—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2316yes—
85C2×C11×C4⋊C4C2316yes—
86C2×C11×C4⋊C4C2316yes—
87C2×C42×C11C2313yes—
88C2×C42×C11C2316yes—
89#67000C23148yes—
90Q8×Dic11C23124yes—
91Q8×Dic11C2318yes—
92C2×(C2×D11)⋊C4C2312yes—
93C2×(C2×D11)⋊C4C2316yes—
94C2×(C2×D11)⋊C4C23112yes—
95C2×(C2×D11)⋊C4C2316yes—
96C2×(C2×D11)⋊C4C23112yes—
97C2×C4⋊Dic11C2313yes—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2316yes—
100C2×Dic11⋊C4C2316yes—
101C2×C4×Dic11C2313yes—
102C2×C4×Dic11C2313yes—
103C2×C4×Dic11C2312yes—
104C2×C4×Dic11C2313yes—
105C2×C4×Dic11C2316yes—
106#66951C23196yes—
107#66950C23148yes—
108#66948C23148yes—
109#66948C23148yes—
110#66948C23148yes—
111#66947C23196yes—
112#66946C23148yes—
113#66946C23148yes—
114#66946C23124yes—
115#66946C23148yes—
116#66945C23148yes—
117#66945C2318yes—
118#66945C23148yes—
119C4⋊C4×D11C23124yes—
120#66940C23124yes—
121#66928C23148yes—
122#66927C23124yes—
123C4×D44C23124yes—
124C4×D44C23148yes—
125C4×D44C23148yes—
126C42×D11C23124yes—
127C42×D11C23148yes—
128C4×Dic22C23124yes—
129C2×#3480—111nomaximal, Sylow
130C23×D11C2416yes—
131C23×D11C2411yescharacteristic
132C2×Q8×C11—212no—
133C2×Q8×C11#4118yescomplemented
134C2×Q8×C11C24112yes—
135C2×Q8×C11C2414yes—
136C22×C4×C11C2413yes—
137C22×C4×C11C2416yes—
138C22×C4×C11C2412yes—
139C22×C4×C11C2411yescharacteristic
140C22×C4×C11C2413yes—
141C22×Dic11C2413yes—
142C22×Dic11C2412yes—
143C22×Dic11C2413yes—
144C22×Dic11C2411yescharacteristic
145#4343—296no—
146#4343—264no—
147Q8×D11—232no—
148C2×D44—224no—
149C2×D44—224no—
150C2×D44—212no—
151C2×D44—412no—
152C2×D44C24112yes—
153C2×D44C24124yes—
154C2×D44C24124yes—
155C2×D44C24124yes—
156C2×C4×D11—224no—
157C2×C4×D11—212no—
158C2×C4×D11—224no—
159C2×C4×D11—412no—
160C2×C4×D11—46no—
161C2×C4×D11#4118yescomplemented
162C2×C4×D11C24112yes—
163C2×C4×D11C24124yes—
164C2×C4×D11C24124yes—
165C2×C4×D11C24124yes—
166C2×C4×D11C24112yes—
167C2×C4×D11C2414yes—
168C2×Dic22—212no—
169C2×Dic22C24112yes—
170C11×C4⋊C4C24112yes—
171C11×C4⋊C4C2414yes—
172C11×C4⋊C4C24124yes—
173C11×C4⋊C4C24124yes—
174C11×C4⋊C4C24124yes—
175C42×C11C24112yes—
176C42×C11C24124yes—
177(C2×D11)⋊C4C2418yes—
178(C2×D11)⋊C4C24124yes—
179(C2×D11)⋊C4C24148yes—
180(C2×D11)⋊C4C24124yes—
181(C2×D11)⋊C4C24148yes—
182C4⋊Dic11C24112yes—
183C4⋊Dic11C2414yes—
184C4⋊Dic11C24124yes—
185Dic11⋊C4C24124yes—
186C4×Dic11C24112yes—
187C4×Dic11C24112yes—
188C4×Dic11C2418yes—
189C4×Dic11C24112yes—
190C4×Dic11C24124yes—
191#3480—1132no—
192C2×#559—113no—
193C2×#557D1111yescharacteristic, complemented
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×Q8—111no—
203C23×C11C2511yescharacteristic
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—212no—
207C22×D11—212no—
208C22×D11—212no—
209C22×D11C2×#4114yes—
210C22×D11C25112yes—
211C22×D11C2512yes—
212Q8×C11—224no—
213Q8×C11C2×#41116yescomplemented
214C2×C4×C11—212no—
215C2×C4×C11—24no—
216C2×C4×C11—26no—
217C2×C4×C11C2×#41112yes—
218C2×C4×C11C2×#4114yes—
219C2×C4×C11C2516yes—
220C2×C4×C11C25112yes—
221C2×C4×C11C2514yes—
222C2×C4×C11C2512yes—
223C2×C4×C11C2516yes—
224C2×Dic11—26no—
225C2×Dic11—24no—
226C2×Dic11—26no—
227C2×Dic11C2×#4114yes—
228C2×Dic11C2516yes—
229C2×Dic11C2514yes—
230C2×Dic11C2516yes—
231C2×Dic11C2512yes—
232D44—248no—
233D44—248no—
234D44—224no—
235D44—424no—
236C4×D11—224no—
237C4×D11—248no—
238C4×D11—248no—
239C4×D11—424no—
240C4×D11—412no—
241C4×D11C2×#41116yescomplemented
242Dic22—224no—
243C22×#41—113no—
244C22×#41—112no—
245C23×Q8—111no—
246#559—1148no—
247#557C2×D11116yescomplemented
248#556—1148no—
249#553—1196no—
250#550—1116no—
251#548—1132no—
252#532—1148no—
253C2×C4⋊Q8C2×D1113yes—
254C2×#127—113no—
255#529—1196no—
256C2×#126—1112no—
257C2×#125C2×D1116yes—
258C2×#124—116no—
259C2×#124—116no—
260C2×#123—1112no—
261C2×C22⋊Q8—116no—
262C2×#121—116no—
263C2×#121—116no—
264C2×#121—116no—
265C4×#41—1148no—
266C4×#41—1132no—
267C2×C4×Q8—111no—
268C2×C4×Q8—113no—
269C2×C4×Q8—1116no—
270C2×C4×Q8—113no—
271C2×C4×Q8—113no—
272C2×C4×Q8C2×D1111yescharacteristic
273C2×C4×Q8C2×D1112yes—
274C2×C4×Q8C2×D1113yes—
275C2×C4×D4—116no—
276C2×C4×D4—116no—
277C2×C4×D4—113no—
278C2×C4×D4—116no—
279C2×C4×D4—116no—
280C2×C4×D4—113no—
281C2×C4×D4—116no—
282C2×#117—111no—
283C2×#117—116no—
284C2×#117—116no—
285C22×C4⋊C4—113no—
286C22×C42—113no—
287C22×C42—116no—
288C22×C11C22×#4112yes—
289C22×C11C22×#4112yes—
290C22×C11#58512yes—
291C22×C11C2611yescharacteristic
292C2×D11—22no—
293C2×D11—22no—
294C2×D11—28no—
295C2×D11—212no—
296C2×D11—212no—
297C2×D11—212no—
298C2×D11—424no—
299C2×D11C22×#4114yes—
300C4×C11—212no—
301C4×C11—24no—
302C4×C11—26no—
303C4×C11C22×#41112yes—
304C4×C11C22×#4114yes—
305Dic11—26no—
306Dic11—24no—
307Dic11—26no—
308Dic11C22×#4114yes—
309C2×#41—1124no—
310C2×#41—1116no—
311C2×#41—2224no—
312C2×#41—2216no—
313C22×Q8—118no—
314C22×Q8—113no—
315C22×Q8—228no—
316C22×Q8C22×D1113yes—
317C22×Q8C22×D1111yescharacteristic
318C22×D4—116no—
319C22×D4—116no—
320C22×D4—113no—
321C22×D4—116no—
322C23×C4—111no—
323C23×C4—113no—
324C23×C4—116no—
325C23×C4—116no—
326C23×C4—113no—
327C23×C4—116no—
328C4⋊Q8C22×D11124yes—
329#127—1124no—
330#126—1196no—
331#125C22×D11148yes—
332#124—1148no—
333#124—1148no—
334#123—1196no—
335C22⋊Q8—1148no—
336#121—1148no—
337#121—1148no—
338#121—1148no—
339C4×Q8—118no—
340C4×Q8—1124no—
341C4×Q8—1124no—
342C4×Q8—1124no—
343C4×Q8C22×D1118yes—
344C4×Q8C22×D11116yes—
345C4×Q8C22×D11124yes—
346C4×D4—1148no—
347C4×D4—1148no—
348C4×D4—1124no—
349C4×D4—1148no—
350C4×D4—1148no—
351C4×D4—1124no—
352C4×D4—1148no—
353#117—118no—
354#117—1148no—
355#117—1148no—
356C2×C4⋊C4—113no—
357C2×C4⋊C4—116no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—116no—
360C2×C4⋊C4—1124no—
361C2×C4⋊C4C22×D1113yes—
362C2×C4⋊C4C22×D1111yescharacteristic
363C2×C4⋊C4C22×D1116yes—
364C2×C4⋊C4C22×D1116yes—
365C2×C4⋊C4C22×D1116yes—
366C2×C22⋊C4—112no—
367C2×C22⋊C4—116no—
368C2×C22⋊C4—1112no—
369C2×C22⋊C4—116no—
370C2×C22⋊C4—1112no—
371C2×C42—112no—
372C2×C42—113no—
373C2×C42—116no—
374C2×C42—113no—
375C2×C42—113no—
376C2×C42—1124no—
377C2×C42—1148no—
378C2×C42C22×D1116yes—
379C2×C42C22×D1113yes—
380C2×C11#348014yescomplemented
381C2×C11C23×#4111yescharacteristic
382C2×C11C23×#4111yescharacteristic
383C2×C11C2×#58511yescharacteristic
384D11—24no—
385D11—412no—
386C24—111no—
387C24—116no—
388#41—2296no—
389#41—2264no—
390C2×Q8—212no—
391C2×Q8—1112no—
392C2×Q8—2232no—
393C2×Q8—2212no—
394C2×Q8#434318yescomplemented
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—111no—
406C22×C4—118no—
407C22×C4—114no—
408C22×C4—112no—
409C22×C4—113no—
410C22×C4—113no—
411C22×C4—1112no—
412C22×C4—1124no—
413C22×C4—1124no—
414C22×C4—1112no—
415C22×C4—1124no—
416C22×C4—2224no—
417C22×C4—2212no—
418C22×C4—2224no—
419C22×C4—4412no—
420C22×C4—446no—
421C22×C4C23×D1112yes—
422C22×C4C23×D1116yes—
423C22×C4C23×D1113yes—
424C22×C4C23×D1113yes—
425C22×C4C23×D1111yescharacteristic
426C4⋊C4—1112no—
427C4⋊C4—1124no—
428C4⋊C4—114no—
429C4⋊C4—1124no—
430C4⋊C4C23×D11112yes—
431C4⋊C4C23×D1114yes—
432C4⋊C4C23×D11124yes—
433C4⋊C4C23×D11124yes—
434C4⋊C4C23×D11124yes—
435C22⋊C4—118no—
436C22⋊C4—1124no—
437C22⋊C4—1148no—
438C22⋊C4—1124no—
439C22⋊C4—1148no—
440C42—118no—
441C42—1112no—
442C42—1112no—
443C42—1124no—
444C42—1112no—
445C42C23×D11124yes—
446C42C23×D11112yes—
447C11C2×#348011yescharacteristic, complemented, Sylow
448C23—114no—
449C23—112no—
450C23—1112no—
451C23—222no—
452C23—222no—
453C23—2212no—
454C23—2212no—
455C23—2212no—
456C23C24×D1111yescharacteristic
457Q8—224no—
458Q8—2224no—
459Q8C2×#4343116yescomplemented
460D4—2248no—
461D4—2248no—
462D4—2224no—
463D4—4424no—
464C2×C4—212no—
465C2×C4—24no—
466C2×C4—26no—
467C2×C4—114no—
468C2×C4—112no—
469C2×C4—1116no—
470C2×C4—114no—
471C2×C4—116no—
472C2×C4—116no—
473C2×C4—2248no—
474C2×C4—224no—
475C2×C4—226no—
476C2×C4—226no—
477C2×C4—2224no—
478C2×C4—2248no—
479C2×C4—4424no—
480C2×C4—4412no—
481C2×C4C2×#4343112yes—
482C2×C4#41×D1114yes—
483C2×C4C24×D1114yes—
484C2×C4C24×D11112yes—
485C2×C4C24×D1116yes—
486C2×C4C24×D1116yes—
487C2×C4C24×D1112yes—
488C22—114no—
489C22—222no—
490C22—222no—
491C22—228no—
492C22—2212no—
493C22—2212no—
494C22—2212no—
495C22—4424no—
496C22C22×#434312yes—
497C22C2×#41×D1112yes—
498C22#1062345712yes—
499C22C25×D1111yescharacteristic
500C4—212no—
501C4—24no—
502C4—26no—
503C4—114no—
504C4—224no—
505C4—226no—
506C4—226no—
507C4C22×#4343112yes—
508C4C2×#41×D1114yes—
509C2—224no—
510C2—4412no—
511C2#1308221614yesdirect product factor
512C2C22×#41×D1111yescharacteristic
513C2C23×#434311yescharacteristic
514C2C2×#1062345711yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#557C2
socleC23×C11C25
hypercenterC2×#557D11
hypocenterC11C2×#3480
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #13082216C2direct (N × H)
2. C2×#10623116C2semidirect
3. C2×#10623263C2semidirect
4. C2×#10623226C2semidirect
5. C2×#10623108C2semidirect
6. C2×#10623107C2semidirect
7. C2×#10623256C2semidirect
8. C2×#10623222C2semidirect
9. C2×C4×#4343C2semidirect
10. C2×C4×#4343C2semidirect
11. C2×C4×Q8×D11C2semidirect
12. C2×C11×#557C2semidirect
16. C11×#557C22semidirect
25. #10623263C22semidirect
26. #10623256C22semidirect
27. #10623226C22semidirect
28. #10623222C22semidirect
29. #10623116C22semidirect
30. #10623108C22semidirect
31. #10623107C22semidirect
32. C4×#4343C22semidirect
33. C4×#4343C22semidirect
34. C4×Q8×D11C22semidirect
133. C2×Q8×C11#41semidirect
161. C2×C4×D11#41semidirect
193. C2×#557D11semidirect
213. Q8×C11C2×#41semidirect
241. C4×D11C2×#41semidirect
247. #557C2×D11semidirect
380. C2×C11#3480semidirect
394. C2×Q8#4343semidirect
447. C11C2×#3480semidirect
459. Q8C2×#4343semidirect
511. C2#13082216direct (N × H)

Maximal subgroups

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

subgroupindex
#130822162
C2×#106231162
C2×#106232632
C2×#106232262
C2×#106231082
C2×#106231072
C2×#106232562
C2×#106232222
C2×C4×#43432
C2×C4×Q8×D112
C2×C11×#5572
C2×#348011