Finite Group Databasebeta

← C2×#13077210 #15617439

Subgroups — C2×#13077210 #15617439

Order 2816.

2766 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66960C211yesmaximal, characteristic
2C2×#10623035C211yesmaximal, characteristic
3C2×#10623054C211yesmaximal, characteristic
4#13077210C2116yesmaximal, direct product factor
5C2×#10622734C211yesmaximal, characteristic, complemented
6C2×#10622494C212yesmaximal, complemented
7C2×#10622474C212yesmaximal, complemented
8C2×#10622493C212yesmaximal, complemented
9C2×#10622611C211yesmaximal, characteristic, complemented
10C22×#66872C211yesmaximal, characteristic, complemented
11C2×D11×#106C212yesmaximal, complemented
12C2×C11×#428C211yesmaximal, characteristic, complemented
13C22×#4339C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C2×C4×C22⋊D11—22no—
18C2×#66979C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C2×#66960C4116yescomplemented
22C2×#66960C2218yes—
23C22×#4313C2212yes—
24C22×C8×D11C2212yes—
25#10623054—24no—
26#10623054C2218yes—
27#10623035—24no—
28#10623035C2218yes—
29C2×#66946—21no—
30C2×#66945C2212yes—
31C2×#66945C2212yes—
32C2×C4⋊C4×D11C2212yes—
33C2×C4⋊C4×D11C2212yes—
34C2×#66940—21no—
35C2×(C22⋊D11)⋊C4—22no—
36C2×C4×D44—21no—
37C2×C4×Dic22—21no—
38C11×#428C2218yescomplemented
39C2×C11×#107C2212yes—
40C2×C11×#106C2212yes—
41#10622734C2218yescomplemented
42C2×#66882C2212yes—
43C2×#66881C2212yes—
44#10622611C2218yescomplemented
45C2×#66872C2211yescharacteristic
46C2×#66872C2212yes—
47C2×#66872C2212yes—
48C2×#66872C2211yescharacteristic
49C2×#66872C2218yescomplemented
50C2×#66871C2211yescharacteristic
51C2×#66871C2211yescharacteristic
52#10622494C22116yescomplemented
53#10622493C22116yescomplemented
54#10622474C22116yescomplemented
55D11×#106C22116yescomplemented
56C23×C4×C11—21no—
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11D412yes—
59C23×Dic11—21no—
60C2×#4339C2×C418yes—
61C2×#4339D414yes—
62C2×#4339Q818yes—
63C2×#4339C2314yes—
64C22×D44D411yescharacteristic
65C22×C4×D11—22no—
66C22×C4×D11—22no—
67C22×C4×D11C2312yes—
68C22×Dic22D411yescharacteristic
69C2×C11×M16C2×C418yescomplemented
70C2×C11×M16C2314yes—
71C22×C8×C11C2312yes—
72C11×#117—22no—
73C11×#117C2314yes—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C22⋊C4—21no—
81C2×C42×C11—21no—
82C2×C22⋊Dic11—21no—
83C4×C22⋊D11—216no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86#66979—22no—
87#66979C2314yes—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11C2314yes—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2312yes—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—22no—
95C2×Dic11⋊C4—22no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—22no—
98C2×C4×Dic11—22no—
99C22×C11⋊C8C2×C418yescomplemented
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2314yes—
103#66960C2×C4164yescomplemented
104C2×#4313C2×C4116yescomplemented
105C2×#4313C2318yes—
106C2×C8×D11C2×C4116yescomplemented
107C2×C8×D11C2318yes—
108#66946—28no—
109#66945—24no—
110#66945—24no—
111#66945C2318yes—
112#66945C2318yes—
113C4⋊C4×D11—24no—
114C4⋊C4×D11—24no—
115C4⋊C4×D11C2318yes—
116C4⋊C4×D11C2318yes—
117#66940—28no—
118(C22⋊D11)⋊C4—216no—
119C4×D44—28no—
120C4×Dic22—28no—
121C11×#107C2318yes—
122C11×#106C2318yes—
123#66882C2318yes—
124#66881C2318yes—
125#66872C2314yes—
126#66872C2318yes—
127#66872C2318yes—
128#66872C2314yes—
129#66871C2314yes—
130#66871C2314yes—
131C2×#2912—111nomaximal, Sylow
132C24×C11C2×D411yescharacteristic
133C23×D11C2×D412yes—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—24no—
138C22×C4×C11—82no—
139C22×C4×C11C22×C414yes—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×Q814yes—
143C22×C4×C11C2411yescharacteristic
144C22×C4×C11C2412yes—
145C2×C22⋊D11C4⋊C4116yes—
146C2×C22⋊D11C2×D418yes—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—22no—
150C22×Dic11—24no—
151C22×Dic11—82no—
152C22×Dic11C2×D412yes—
153#4339C4⋊C4132yes—
154#4339C22×C4116yes—
155#4339C2×Q8116yes—
156C2×D44C4⋊C418yes—
157C2×D44C2×D414yes—
158C2×C4×D11—28no—
159C2×C4×D11—28no—
160C2×C4×D11—84no—
161C2×C4×D11—84no—
162C2×C4×D11C22×C418yes—
163C2×C4×D11C2×D414yes—
164C2×C4×D11C2×Q818yes—
165C2×C4×D11C2414yes—
166C2×Dic22C4⋊C418yes—
167C2×Dic22C2×D414yes—
168C11×M16C22×C4116yescomplemented
169C2×C8×C11C22×C418yes—
170C2×C8×C11C2414yes—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4C2412yes—
176C11×C4⋊C4C2412yes—
177C11×C4⋊C4C2414yes—
178C11×C22⋊C4—24no—
179C42×C11—24no—
180C22⋊Dic11—24no—
181(C2×D11)⋊C4—28no—
182(C2×D11)⋊C4—28no—
183C4⋊Dic11—24no—
184C4⋊Dic11—21no—
185C4⋊Dic11—22no—
186C4⋊Dic11—21no—
187C4⋊Dic11C2412yes—
188C4⋊Dic11C2412yes—
189C4⋊Dic11C2414yes—
190Dic11⋊C4—28no—
191Dic11⋊C4—28no—
192C4×Dic11—28no—
193C4×Dic11—28no—
194C4×Dic11—24no—
195C2×C11⋊C8C22×C414yes—
196C2×C11⋊C8C22×C414yes—
197C2×C11⋊C8C22×C4116yescomplemented
198C2×C11⋊C8C2412yes—
199C2×C11⋊C8C2412yes—
200#4313C22×C4132yescomplemented
201C8×D11C22×C4132yescomplemented
202C22×#131—111no—
203C2×#520—111no—
204C2×#520—111no—
205#2912—1116no—
206C2×#428—112no—
207C2×#428—112no—
208C2×#428—111no—
209C2×#428D1111yescharacteristic, complemented
210C2×#427—112no—
211C2×#427—111no—
212C22×#106—112no—
213C22×#106—111no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11C2×C4⋊C414yes—
217C23×C11C22×D412yes—
218C23×C11C22×D411yescharacteristic
219C22×D11—24no—
220C22×D11—24no—
221C22×D11C2×C4⋊C418yes—
222C22×D11C22×D414yes—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—42no—
227C2×C4×C11—44no—
228C2×C4×C11—42no—
229C2×C4×C11—84no—
230C2×C4×C11C2×C4⋊C414yes—
231C2×C4×C11C2×C4⋊C418yes—
232C2×C4×C11C23×C412yes—
233C2×C4×C11C23×C414yes—
234C2×C4×C11C22×D412yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×Q812yes—
237C2×C4×C11C22×Q814yes—
238C2×C4×C11C2511yescharacteristic
239C22⋊D11C2×C4⋊C4132yes—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—24no—
243C2×Dic11—42no—
244C2×Dic11—44no—
245C2×Dic11—42no—
246C2×Dic11—84no—
247C2×Dic11C2×C4⋊C418yes—
248C2×Dic11C22×D414yes—
249D44C2×C4⋊C4116yes—
250C4×D11—88no—
251C4×D11—88no—
252C4×D11C2×C4⋊C4116yes—
253C4×D11C23×C418yes—
254C4×D11C22×Q818yes—
255Dic22C2×C4⋊C4116yes—
256C8×C11C23×C418yes—
257C11⋊C8C23×C414yes—
258C11⋊C8C23×C414yes—
259C22×#41—111no—
260C2×#131—118no—
261C2×#131—1116no—
262C22×M16—112no—
263C22×M16C2×D1111yescharacteristic
264C23×C8—111no—
265C23×C8—112no—
266#520—118no—
267#520—118no—
268#520—224no—
269#520—224no—
270C2×C4×Q8—221no—
271C2×C4×Q8—221no—
272C2×C4×D4—221no—
273C2×C4×D4—222no—
274C2×C4×D4—221no—
275C2×C4×D4—222no—
276C2×#117—111no—
277C2×#117—112no—
278C2×#117—112no—
279C2×#117C2×D1111yescharacteristic
280C22×C4⋊C4—111no—
281C22×C4⋊C4—112no—
282C22×C4⋊C4—112no—
283C22×C4⋊C4C2×D1111yescharacteristic
284#428—118no—
285#428—1116no—
286#428—1116no—
287#428C2×D1118yescomplemented
288#427—118no—
289#427—1116no—
290C2×#107—112no—
291C2×#107—111no—
292C2×#107—111no—
293C2×#107C2×D1112yes—
294C2×#106—112no—
295C2×#106—111no—
296C2×#106—112no—
297C2×#106—112no—
298C2×#106—118no—
299C2×#106—111no—
300C2×#106—1116no—
301C2×#106C2×D1112yes—
302C22×C11—28no—
303C22×C11—22no—
304C22×C11—22no—
305C22×C11C22×C4⋊C414yes—
306C22×C11C22×C4⋊C412yes—
307C22×C11#57712yes—
308C22×C11#57712yes—
309C22×C11C23×D411yescharacteristic
310C2×D11—216no—
311C2×D11—24no—
312C2×D11—24no—
313C2×D11C22×C4⋊C418yes—
314C4×C11—42no—
315C4×C11—44no—
316C4×C11—42no—
317C4×C11C22×C4⋊C414yes—
318C4×C11C22×C4⋊C412yes—
319C4×C11C24×C411yescharacteristic
320C4×C11C23×Q811yescharacteristic
321Dic11—42no—
322Dic11—44no—
323Dic11—42no—
324Dic11C22×C4⋊C418yes—
325C2×#41—118no—
326C2×#41—114no—
327C2×#41—118no—
328C2×#41—114no—
329C22×Q8—111no—
330C22×D4—112no—
331C22×D4—111no—
332C23×C4—21no—
333C23×C4—112no—
334C23×C4—222no—
335C23×C4—222no—
336C23×C4—221no—
337C23×C4C22×D1111yescharacteristic
338#131—1164no—
339C2×M16—1116no—
340C2×M16—118no—
341C2×M16C4×D1118yescomplemented
342C2×M16C22×D1114yes—
343C22×C8—118no—
344C22×C8—111no—
345C22×C8—111no—
346C22×C8—114no—
347C22×C8—1116no—
348C22×C8—118no—
349C22×C8C22×D1112yes—
350C4×Q8—228no—
351C4×Q8—228no—
352C4×D4—228no—
353C4×D4—2216no—
354C4×D4—228no—
355C4×D4—2216no—
356#117—22no—
357#117—114no—
358#117—118no—
359#117—118no—
360#117—224no—
361#117—224no—
362#117—222no—
363#117C22×D1114yes—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—112no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—114no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—118no—
371C2×C4⋊C4—118no—
372C2×C4⋊C4—224no—
373C2×C4⋊C4—224no—
374C2×C4⋊C4—222no—
375C2×C4⋊C4—222no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C4⋊C4C22×D1112yes—
380C2×C4⋊C4C22×D1114yes—
381C2×C4⋊C4C22×D1111yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—222no—
384C2×C22⋊C4—222no—
385C2×C22⋊C4—221no—
386C2×C42—21no—
387C2×C42—222no—
388C2×C42—222no—
389C2×C42—221no—
390#107—118no—
391#107—114no—
392#107—114no—
393#107C22×D1118yes—
394#106—118no—
395#106—118no—
396#106—114no—
397#106—118no—
398#106—114no—
399#106C22×D1118yes—
400C2×C11—24no—
401C2×C11#291214yescomplemented
402C2×C11C23×C4⋊C411yescharacteristic
403C2×C11C2×#57711yescharacteristic
404C2×C11C2×#57711yescharacteristic
405D11—28no—
406C24—112no—
407C24D4×D1111yescharacteristic
408#41—1132no—
409#41—1116no—
410#41—1116no—
411C2×Q8—118no—
412C2×Q8—114no—
413C2×D4—1116no—
414C2×D4—118no—
415C2×D4—118no—
416C2×D4—114no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—24no—
421C22×C4—82no—
422C22×C4—112no—
423C22×C4—118no—
424C22×C4—114no—
425C22×C4—118no—
426C22×C4—114no—
427C22×C4—228no—
428C22×C4—228no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—222no—
432C22×C4—224no—
433C22×C4—884no—
434C22×C4—884no—
435C22×C4—882no—
436C22×C4C2×C4×D1114yes—
437C22×C4D4×D1112yes—
438C22×C4D4×D1111yescharacteristic
439C22×C4Q8×D1114yes—
440C22×C4C23×D1112yes—
441C22×C4C23×D1111yescharacteristic
442M16—1132no—
443M16C2×C4×D11116yescomplemented
444C2×C8—114no—
445C2×C8—114no—
446C2×C8—1116no—
447C2×C8—112no—
448C2×C8—112no—
449C2×C8—1132no—
450C2×C8C2×C4×D1118yes—
451C2×C8C23×D1114yes—
452C4⋊C4—22no—
453C4⋊C4—24no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—112no—
457C4⋊C4—114no—
458C4⋊C4—112no—
459C4⋊C4—228no—
460C4⋊C4—228no—
461C4⋊C4—221no—
462C4⋊C4—222no—
463C4⋊C4—224no—
464C4⋊C4—221no—
465C4⋊C4C23×D1114yes—
466C4⋊C4C23×D1112yes—
467C4⋊C4C23×D1112yes—
468C22⋊C4—24no—
469C22⋊C4—228no—
470C22⋊C4—228no—
471C22⋊C4—224no—
472C42—24no—
473C42—228no—
474C42—228no—
475C42—224no—
476C11C2×#291211yescharacteristic, complemented, Sylow
477C23—22no—
478C23—22no—
479C23—118no—
480C23—114no—
481C23—224no—
482C23—224no—
483C23C4⋊C4×D1114yes—
484C23C2×D4×D1112yes—
485C23C2×D4×D1111yescharacteristic
486Q8—1116no—
487D4—1132no—
488D4—1116no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—24no—
492C2×C4—42no—
493C2×C4—44no—
494C2×C4—42no—
495C2×C4—84no—
496C2×C4—118no—
497C2×C4—114no—
498C2×C4—1116no—
499C2×C4—118no—
500C2×C4—118no—
501C2×C4—222no—
502C2×C4—224no—
503C2×C4—222no—
504C2×C4—442no—
505C2×C4—444no—
506C2×C4—442no—
507C2×C4—888no—
508C2×C4—888no—
509C2×C4—884no—
510C2×C4C4⋊C4×D1114yes—
511C2×C4C4⋊C4×D1118yes—
512C2×C4C22×C4×D1112yes—
513C2×C4C22×C4×D1114yes—
514C2×C4C2×D4×D1112yes—
515C2×C4C2×D4×D1111yescharacteristic
516C2×C4C2×Q8×D1112yes—
517C2×C4C2×Q8×D1114yes—
518C2×C4C24×D1111yescharacteristic
519C8—114no—
520C8—114no—
521C8C22×C4×D1118yes—
522C22—28no—
523C22—22no—
524C22—22no—
525C22—118no—
526C22—2216no—
527C22—224no—
528C22—224no—
529C22C2×C4⋊C4×D1114yes—
530C22C2×C4⋊C4×D1112yes—
531C22#1062330612yes—
532C22#1062330912yes—
533C22C22×D4×D1111yescharacteristic
534C4—42no—
535C4—44no—
536C4—42no—
537C4—118no—
538C4—444no—
539C4—442no—
540C4—442no—
541C4C2×C4⋊C4×D1112yes—
542C4C2×C4⋊C4×D1114yes—
543C4C23×C4×D1111yescharacteristic
544C4C22×Q8×D1111yescharacteristic
545C2—24no—
546C2—228no—
547C2#1307721014yesdirect product factor
548C2C22×C4⋊C4×D1111yescharacteristic
549C2C2×#1062330911yescharacteristic
550C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#428C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC2×C4×C11C25
hypercenterC2×#428D11
hypocenterC11C2×#2912
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
4. #13077210C2direct (N × H)
5. C2×#10622734C2semidirect
6. C2×#10622494C2semidirect
7. C2×#10622474C2semidirect
8. C2×#10622493C2semidirect
9. C2×#10622611C2semidirect
10. C22×#66872C2semidirect
11. C2×D11×#106C2semidirect
12. C2×C11×#428C2semidirect
21. C2×#66960C4semidirect
38. C11×#428C22semidirect
41. #10622734C22semidirect
44. #10622611C22semidirect
49. C2×#66872C22semidirect
52. #10622494C22semidirect
53. #10622493C22semidirect
54. #10622474C22semidirect
55. D11×#106C22semidirect
69. C2×C11×M16C2×C4semidirect
99. C22×C11⋊C8C2×C4semidirect
103. #66960C2×C4semidirect
104. C2×#4313C2×C4semidirect
106. C2×C8×D11C2×C4semidirect
168. C11×M16C22×C4semidirect
197. C2×C11⋊C8C22×C4semidirect
200. #4313C22×C4semidirect
201. C8×D11C22×C4semidirect
209. C2×#428D11semidirect
287. #428C2×D11semidirect
341. C2×M16C4×D11semidirect
401. C2×C11#2912semidirect
443. M16C2×C4×D11semidirect
476. C11C2×#2912semidirect
547. C2#13077210direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669602
C2×#106230352
C2×#106230542
#130772102
C2×#106227342
C2×#106224942
C2×#106224742
C2×#106224932
C2×#106226112
C22×#668722
C2×D11×#1062
C2×C11×#4282
C2×#291211