Finite Group Databasebeta

← C2×#13070267 #14906506

Subgroups — C2×#13070267 #14906506

Order 2816.

1406 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623361C211yesmaximal, characteristic
2C2×#10622853C211yesmaximal, characteristic, complemented
3#13070267C218yesmaximal, direct product factor
4C2×#10622113C214yesmaximal, complemented
5C2×C11×#413C211yesmaximal, characteristic, complemented
6C22×C11×#41C2211yescharacteristic
7C23×D44C411yescharacteristic, complemented
8C22×C11×M16—21no—
9#10623361—22no—
10#10623361—22no—
11#10623361C414yescomplemented
12#10623361C2214yes—
13C2×#67000—21no—
14C2×#66993—21no—
15C2×#66990C412yescomplemented
16C2×#66990C2212yes—
17C2×#66983—21no—
18C2×#66983—21no—
19C2×#66979—21no—
20C2×#66979C411yescharacteristic, complemented
21C11×#413—22no—
22C11×#413C2214yescomplemented
23C2×C11×#101—21no—
24C2×C11×#100C2212yes—
25#10622853—22no—
26#10622853C2214yescomplemented
27C2×#66898—21no—
28C2×#66898C2212yes—
29#10622113C22116yescomplemented
30C24×D11C2×C412yes—
31C2×C11×#41—41no—
32C2×C11×#41—41no—
33C2×C11×#41—42no—
34C2×C11×#41C2×C412yes—
35C2×C11×#41D412yes—
36C2×C11×#41D412yes—
37C2×C11×#41C2312yes—
38C22×Q8×C11D411yescharacteristic
39C22×D4×C11C2×C411yescharacteristic
40C22×D4×C11D411yescharacteristic
41C22×D4×C11C2311yescharacteristic
42C23×C4×C11C2×C411yescharacteristic
43C23×C4×C11D411yescharacteristic
44C23×C4×C11D411yescharacteristic
45C22×C22⋊D11—22no—
46C22×C22⋊D11—22no—
47C22×D44—21no—
48C22×D44—21no—
49C22×D44—22no—
50C22×D44—42no—
51C22×D44—41no—
52C22×D44—41no—
53C22×D44C2×C414yescomplemented
54C2×C11×M16—22no—
55C2×C11×M16—24no—
56C2×C11×M16—41no—
57C2×C11×M16—42no—
58C22×C8×C11—41no—
59C2×C22⋊Dic11—22no—
60C2×C22⋊Dic11C2×C412yes—
61#67000—24no—
62#67000—24no—
63#66993—24no—
64#66993—24no—
65#66990—24no—
66#66990—22no—
67#66990—22no—
68#66990C2×C414yes—
69#66990C2×C418yescomplemented
70#66990C2314yes—
71#66983—24no—
72#66983—24no—
73#66983—24no—
74#66983—24no—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77#66979—22no—
78#66979—24no—
79#66979—42no—
80#66979C2×C414yescomplemented
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—41no—
83C2×C4×Dic11—21no—
84C2×C4×Dic11—41no—
85C11×#101—24no—
86C11×#100—22no—
87C11×#100C2314yes—
88#66898—24no—
89#66898—22no—
90#66898C2314yes—
91C2×#2122—111nomaximal, Sylow
92C24×C11C22⋊C411yescharacteristic
93C24×C11C22×C411yescharacteristic
94C24×C11C2×D411yescharacteristic
95C23×D11—22no—
96C23×D11—22no—
97C23×D11—42no—
98C23×D11—42no—
99C23×D11—84no—
100C23×D11C22×C414yes—
101C11×#41—42no—
102C11×#41—42no—
103C11×#41—42no—
104C11×#41—42no—
105C11×#41—42no—
106C11×#41—42no—
107C11×#41—42no—
108C11×#41—42no—
109C2×Q8×C11—41no—
110C2×Q8×C11—41no—
111C2×Q8×C11C22⋊C412yes—
112C2×Q8×C11C2×D412yes—
113C2×D4×C11—41no—
114C2×D4×C11—41no—
115C2×D4×C11—41no—
116C2×D4×C11—41no—
117C2×D4×C11—41no—
118C2×D4×C11—41no—
119C2×D4×C11C22⋊C412yes—
120C2×D4×C11C22⋊C412yes—
121C2×D4×C11C22×C411yescharacteristic
122C2×D4×C11C22×C412yes—
123C2×D4×C11C2×D411yescharacteristic
124C2×D4×C11C2×D412yes—
125C2×D4×C11C2×D411yescharacteristic
126C2×D4×C11C2411yescharacteristic
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11C22⋊C411yescharacteristic
137C22×C4×C11C22⋊C412yes—
138C22×C4×C11C22⋊C411yescharacteristic
139C22×C4×C11C22⋊C412yes—
140C22×C4×C11C22⋊C412yes—
141C22×C4×C11C22⋊C411yescharacteristic
142C22×C4×C11C22×C412yes—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D412yes—
146C2×C22⋊D11—24no—
147C2×C22⋊D11—28no—
148C2×C22⋊D11—24no—
149C2×C22⋊D11—84no—
150C2×C22⋊D11—84no—
151C22×Dic11—22no—
152C22×Dic11—42no—
153C2×D44—24no—
154C2×D44—24no—
155C2×D44—44no—
156C2×D44—44no—
157C2×D44—42no—
158C2×D44—42no—
159C2×D44—44no—
160C2×D44—44no—
161C2×D44—42no—
162C2×D44—41no—
163C2×D44—41no—
164C11×M16—24no—
165C11×M16—42no—
166C11×M16—44no—
167C2×C8×C11—42no—
168C2×C8×C11—44no—
169C22⋊Dic11—22no—
170C22⋊Dic11—24no—
171C22⋊Dic11—42no—
172C22⋊Dic11C22×C414yes—
173(C2×D11)⋊C4—24no—
174(C2×D11)⋊C4—28no—
175(C2×D11)⋊C4—24no—
176C4⋊Dic11—24no—
177C4⋊Dic11—44no—
178C4×Dic11—24no—
179C4×Dic11—44no—
180C2×#535—111no—
181C2×#413D1111yescharacteristic, complemented
182C2×#410—111no—
183#2122—118no—
184C2×AΣL(1,𝔽16)—114no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11C2×C22⋊C411yescharacteristic
195C23×C11C2×C22⋊C411yescharacteristic
196C23×C11C2×C22⋊C411yescharacteristic
197C23×C11C2×C22⋊C412yes—
198C23×C11C23×C411yescharacteristic
199C23×C11C22×D411yescharacteristic
200C22×D11—24no—
201C22×D11—44no—
202C22×D11—44no—
203C22×D11—44no—
204C22×D11—42no—
205C22×D11—42no—
206C22×D11—44no—
207C22×D11—84no—
208C22×D11—84no—
209C22×D11—88no—
210C22×D11—88no—
211Q8×C11—42no—
212Q8×C11—42no—
213D4×C11—42no—
214D4×C11—42no—
215D4×C11—42no—
216D4×C11—41no—
217D4×C11—41no—
218D4×C11—42no—
219D4×C11—41no—
220D4×C11—41no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11#9912yes—
240C2×C4×C11#9911yescharacteristic
241C2×C4×C11#9911yescharacteristic
242C2×C4×C11C2×C22⋊C412yes—
243C2×C4×C11C2×C22⋊C412yes—
244C2×C4×C11C2×C22⋊C411yescharacteristic
245C2×C4×C11C2×C22⋊C412yes—
246C2×C4×C11C22×D411yescharacteristic
247C22⋊D11—84no—
248C22⋊D11—88no—
249C22⋊D11—84no—
250C2×Dic11—24no—
251C2×Dic11—44no—
252C2×Dic11—44no—
253C2×Dic11—84no—
254D44—48no—
255D44—44no—
256D44—44no—
257C8×C11—44no—
258C22×#41C2×D1111yescharacteristic
259C23×D4—111no—
260C22×M16—21no—
261#535—114no—
262#535—114no—
263#535—222no—
264#535—222no—
265C2×#127—221no—
266C2×#124—221no—
267C2×#121—221no—
268C2×#121—221no—
269C2×#120—112no—
270C2×#120—112no—
271C2×#117—111no—
272C2×#117—221no—
273#413—22no—
274#413C2×D1114yescomplemented
275C2×#101—21no—
276C2×#100C2×D1112yes—
277#410—114no—
278#410—222no—
279C2×#99—112no—
280C2×#99—221no—
281AΣL(1,𝔽16)—1116no—
282C22×C11—22no—
283C22×C11—21no—
284C22×C11—21no—
285C22×C11—22no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—41no—
289C22×C11—41no—
290C22×C11—42no—
291C22×C11—41no—
292C22×C11—41no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11C2×#9911yescharacteristic
300C22×C11C2×#9911yescharacteristic
301C22×C11C22×C22⋊C411yescharacteristic
302C2×D11—44no—
303C2×D11—44no—
304C2×D11—44no—
305C2×D11—84no—
306C2×D11—88no—
307C2×D11—84no—
308C2×D11—88no—
309C4×C11—21no—
310C4×C11—22no—
311C4×C11—22no—
312C4×C11—21no—
313C4×C11C2×#9912yes—
314C4×C11C2×#9912yes—
315Dic11—44no—
316Dic11—84no—
317C25—112no—
318C2×#41—41no—
319C2×#41—41no—
320C2×#41—42no—
321C2×#41C4×D1112yes—
322C2×#41D4412yes—
323C2×#41C22⋊D1112yes—
324C2×#41C22×D1112yes—
325C22×Q8C22⋊D1111yescharacteristic
326C22×D4—114no—
327C22×D4—222no—
328C22×D4—222no—
329C22×D4—221no—
330C22×D4—222no—
331C22×D4—221no—
332C22×D4—442no—
333C22×D4—441no—
334C22×D4—441no—
335C22×D4C4×D1111yescharacteristic
336C22×D4D4411yescharacteristic
337C22×D4C22×D1111yescharacteristic
338C23×C4C4×D1111yescharacteristic
339C23×C4D4411yescharacteristic
340C23×C4C22⋊D1111yescharacteristic
341C2×M16—22no—
342C2×M16—24no—
343C2×M16—41no—
344C2×M16—42no—
345C22×C8—41no—
346#127—224no—
347#127—224no—
348#124—224no—
349#124—224no—
350#121—224no—
351#121—224no—
352#121—224no—
353#121—224no—
354#120—114no—
355#120—118no—
356#120—114no—
357#120—224no—
358#120—222no—
359#120—222no—
360#117—114no—
361#117—222no—
362#117—224no—
363#117—442no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—441no—
366C2×C22⋊C4—112no—
367C2×C22⋊C4—222no—
368C2×C22⋊C4—222no—
369C2×C22⋊C4—222no—
370C2×C42—221no—
371C2×C42—441no—
372#101—24no—
373#100—22no—
374#100C22×D1114yes—
375#99—114no—
376#99—222no—
377#99—224no—
378C2×C11—21no—
379C2×C11—21no—
380C2×C11—41no—
381C2×C11—41no—
382C2×C11—41no—
383C2×C11—42no—
384C2×C11—41no—
385C2×C11#212212yescomplemented
386C2×C11C22×#9911yescharacteristic
387D11—84no—
388C24—114no—
389C24—222no—
390C24—222no—
391C24—442no—
392C24—442no—
393C24—884no—
394C24(C2×D11)⋊C411yescharacteristic
395C24C2×C4×D1111yescharacteristic
396C24C2×D4411yescharacteristic
397#41—42no—
398#41—42no—
399#41—42no—
400#41—42no—
401#41—42no—
402#41—42no—
403#41—42no—
404#41—42no—
405C2×Q8—41no—
406C2×Q8—41no—
407C2×Q8(C2×D11)⋊C412yes—
408C2×Q8C2×C22⋊D1112yes—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—224no—
416C2×D4—228no—
417C2×D4—224no—
418C2×D4—224no—
419C2×D4—224no—
420C2×D4—442no—
421C2×D4—442no—
422C2×D4—444no—
423C2×D4—444no—
424C2×D4—444no—
425C2×D4—444no—
426C2×D4—442no—
427C2×D4—441no—
428C2×D4—441no—
429C2×D4—884no—
430C2×D4—884no—
431C2×D4(C2×D11)⋊C412yes—
432C2×D4(C2×D11)⋊C412yes—
433C2×D4C2×C4×D1111yescharacteristic
434C2×D4C2×C4×D1112yes—
435C2×D4C2×D4411yescharacteristic
436C2×D4C2×D4412yes—
437C2×D4C2×C22⋊D1111yescharacteristic
438C2×D4C23×D1111yescharacteristic
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—222no—
449C22×C4—442no—
450C22×C4(C2×D11)⋊C411yescharacteristic
451C22×C4(C2×D11)⋊C411yescharacteristic
452C22×C4(C2×D11)⋊C412yes—
453C22×C4(C2×D11)⋊C412yes—
454C22×C4(C2×D11)⋊C412yes—
455C22×C4(C2×D11)⋊C411yescharacteristic
456C22×C4C2×C4×D1112yes—
457C22×C4C2×D4412yes—
458C22×C4C2×C22⋊D1111yescharacteristic
459C22×C4C2×C22⋊D1112yes—
460M16—24no—
461M16—42no—
462M16—44no—
463C2×C8—42no—
464C2×C8—44no—
465C4⋊C4—224no—
466C4⋊C4—444no—
467C22⋊C4—114no—
468C22⋊C4—222no—
469C22⋊C4—228no—
470C22⋊C4—224no—
471C22⋊C4—224no—
472C22⋊C4—224no—
473C22⋊C4—442no—
474C42—224no—
475C42—444no—
476C11C2×#212211yescharacteristic, complemented, Sylow
477C23—21no—
478C23—21no—
479C23—21no—
480C23—21no—
481C23—21no—
482C23—21no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—224no—
487C23—444no—
488C23—444no—
489C23—444no—
490C23—444no—
491C23—442no—
492C23—442no—
493C23—884no—
494C23—884no—
495C23—888no—
496C23—888no—
497C23C2×(C2×D11)⋊C411yescharacteristic
498C23C2×(C2×D11)⋊C411yescharacteristic
499C23C2×(C2×D11)⋊C411yescharacteristic
500C23C2×(C2×D11)⋊C412yes—
501C23C22×C4×D1111yescharacteristic
502C23C22×D4411yescharacteristic
503Q8—42no—
504Q8—42no—
505D4—42no—
506D4—42no—
507D4—41no—
508D4—42no—
509D4—42no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—448no—
514D4—444no—
515D4—444no—
516D4—888no—
517D4—884no—
518D4—884no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—224no—
538C2×C4—444no—
539C2×C4—444no—
540C2×C4—884no—
541C2×C4#6687012yes—
542C2×C4#6687011yescharacteristic
543C2×C4#6687011yescharacteristic
544C2×C4C2×(C2×D11)⋊C412yes—
545C2×C4C2×(C2×D11)⋊C412yes—
546C2×C4C2×(C2×D11)⋊C411yescharacteristic
547C2×C4C2×(C2×D11)⋊C412yes—
548C2×C4C22×C22⋊D1111yescharacteristic
549C8—44no—
550C22—22no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—22no—
555C22—21no—
556C22—42no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—81no—
566C22—81no—
567C22—444no—
568C22—444no—
569C22—444no—
570C22—884no—
571C22—888no—
572C22—888no—
573C22—884no—
574C22C2×#6687011yescharacteristic
575C22C2×#6687011yescharacteristic
576C22C22×(C2×D11)⋊C411yescharacteristic
577C4—21no—
578C4—22no—
579C4—21no—
580C4—22no—
581C4—444no—
582C4—884no—
583C4C2×#6687012yes—
584C4C2×#6687012yes—
585C2—21no—
586C2—21no—
587C2—41no—
588C2—41no—
589C2—41no—
590C2—41no—
591C2—42no—
592C2—884no—
593C2#1307026712yesdirect product factor
594C2C22×#6687011yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC23×C11C23×C4
FrattiniC2×D4C23×D11
FittingC2×C11×#413C2
socleC22×C11C2×#99
prime radicalC2×#10623361C2
cosocleC2×D4×C11C24
hypercenterC2×#413D11
hypocenterC11C2×#2122
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
2. C2×#10622853C2semidirect
3. #13070267C2direct (N × H)
4. C2×#10622113C2semidirect
5. C2×C11×#413C2semidirect
7. C23×D44C4semidirect
11. #10623361C4semidirect
15. C2×#66990C4semidirect
20. C2×#66979C4semidirect
22. C11×#413C22semidirect
26. #10622853C22semidirect
29. #10622113C22semidirect
53. C22×D44C2×C4semidirect
69. #66990C2×C4semidirect
80. #66979C2×C4semidirect
181. C2×#413D11semidirect
274. #413C2×D11semidirect
385. C2×C11#2122semidirect
476. C11C2×#2122semidirect
593. C2#13070267direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233612
C2×#106228532
#130702672
C2×#106221132
C2×C11×#4132
C2×#212211