Finite Group Databasebeta

← C2×#13070269 #14906509

Subgroups — C2×#13070269 #14906509

Order 2816.

1214 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623356C211yesmaximal, characteristic
2C2×#10622850C211yesmaximal, characteristic
3#13070269C218yesmaximal, direct product factor
4C2×#10622110C214yesmaximal, complemented
5C2×C11×#410C211yesmaximal, characteristic
6C22×C11×#41C2211yescharacteristic
7C23×Dic22C411yescharacteristic, complemented
8C2×C11×#117—21no—
9#10623356—22no—
10#10623356—22no—
11#10623356C414yescomplemented
12#10623356C2214yes—
13C2×#66997—21no—
14C2×#66989—21no—
15C2×#66988C412yescomplemented
16C2×#66988C2212yes—
17C2×#66979C411yescharacteristic, complemented
18C2×#66977—21no—
19C2×#66977—21no—
20C22×#4318—21no—
21C11×#410—22no—
22C11×#410C2214yes—
23C2×C11×#99—21no—
24C2×C11×#99C2212yes—
25#10622850—22no—
26#10622850C2214yes—
27C2×#66900—21no—
28C2×#66897C2212yes—
29#10622110C22116yescomplemented
30C2×C11×#41—41no—
31C2×C11×#41—41no—
32C2×C11×#41—42no—
33C2×C11×#41C2×C412yes—
34C2×C11×#41D412yes—
35C2×C11×#41D412yes—
36C2×C11×#41C2312yes—
37C22×Q8×C11D411yescharacteristic
38C22×D4×C11C2×C411yescharacteristic
39C22×D4×C11D411yescharacteristic
40C22×D4×C11C2311yescharacteristic
41C23×C4×C11C2×C411yescharacteristic
42C23×C4×C11D411yescharacteristic
43C23×C4×C11D411yescharacteristic
44C23×Dic11C2×C412yes—
45C22×Dic22—21no—
46C22×Dic22—21no—
47C22×Dic22—22no—
48C22×Dic22—42no—
49C22×Dic22—41no—
50C22×Dic22—41no—
51C22×Dic22C2×C414yescomplemented
52C11×#117—24no—
53C11×#117—42no—
54C2×C11×C4⋊C4—41no—
55C2×C11×C22⋊C4—22no—
56C2×C42×C11—41no—
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—22no—
59C2×C22⋊Dic11C2×C412yes—
60#66997—24no—
61#66997—24no—
62#66989—24no—
63#66989—24no—
64#66988—24no—
65#66988—22no—
66#66988—22no—
67#66988C2×C414yes—
68#66988C2×C418yescomplemented
69#66988C2314yes—
70#66979—22no—
71#66979C2×C414yescomplemented
72C2×C4⋊Dic11—21no—
73#66977—24no—
74#66977—24no—
75#66977—24no—
76#66977—24no—
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C2×C4×Dic11—21no—
80C2×#4318—22no—
81C2×#4318—24no—
82C2×#4318—41no—
83C2×#4318—42no—
84C22×C11⋊C8—41no—
85C11×#99—24no—
86C11×#99—22no—
87C11×#99C2314yes—
88#66900—24no—
89#66897—22no—
90#66897C2314yes—
91C2×#2123—111nomaximal, Sylow
92C24×C11C22⋊C411yescharacteristic
93C24×C11C22×C411yescharacteristic
94C24×C11C2×D411yescharacteristic
95C11×#41—42no—
96C11×#41—42no—
97C11×#41—42no—
98C11×#41—42no—
99C11×#41—42no—
100C11×#41—42no—
101C11×#41—42no—
102C11×#41—42no—
103C2×Q8×C11—41no—
104C2×Q8×C11—41no—
105C2×Q8×C11C22⋊C412yes—
106C2×Q8×C11C2×D412yes—
107C2×D4×C11—41no—
108C2×D4×C11—41no—
109C2×D4×C11—41no—
110C2×D4×C11—41no—
111C2×D4×C11—41no—
112C2×D4×C11—41no—
113C2×D4×C11C22⋊C412yes—
114C2×D4×C11C22⋊C412yes—
115C2×D4×C11C22×C411yescharacteristic
116C2×D4×C11C22×C412yes—
117C2×D4×C11C2×D411yescharacteristic
118C2×D4×C11C2×D412yes—
119C2×D4×C11C2×D411yescharacteristic
120C2×D4×C11C2411yescharacteristic
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—42no—
131C22×C4×C11C22⋊C411yescharacteristic
132C22×C4×C11C22⋊C411yescharacteristic
133C22×C4×C11C22⋊C412yes—
134C22×C4×C11C22⋊C412yes—
135C22×C4×C11C22⋊C412yes—
136C22×C4×C11C22⋊C411yescharacteristic
137C22×C4×C11C22×C412yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D412yes—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—42no—
145C22×Dic11—42no—
146C22×Dic11C22×C414yes—
147C2×Dic22—24no—
148C2×Dic22—24no—
149C2×Dic22—42no—
150C2×Dic22—42no—
151C2×Dic22—44no—
152C2×Dic22—44no—
153C2×Dic22—44no—
154C2×Dic22—44no—
155C2×Dic22—42no—
156C2×Dic22—41no—
157C2×Dic22—41no—
158C11×C4⋊C4—44no—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—42no—
161C42×C11—44no—
162C22⋊Dic11—24no—
163C22⋊Dic11—28no—
164C22⋊Dic11—22no—
165C22⋊Dic11—24no—
166C22⋊Dic11C22×C414yes—
167C4⋊Dic11—24no—
168Dic11⋊C4—24no—
169Dic11⋊C4—28no—
170Dic11⋊C4—24no—
171C4×Dic11—24no—
172#4318—24no—
173#4318—42no—
174#4318—44no—
175C2×C11⋊C8—42no—
176C2×C11⋊C8—44no—
177C2×#536—111no—
178C2×#413—111no—
179C2×#410D1111yescharacteristic
180#2123—118no—
181C2×#352—114no—
182C23×C11—21no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11C2×C22⋊C411yescharacteristic
192C23×C11C2×C22⋊C411yescharacteristic
193C23×C11C2×C22⋊C412yes—
194C23×C11C2×C22⋊C411yescharacteristic
195C23×C11C23×C411yescharacteristic
196C23×C11C22×D411yescharacteristic
197Q8×C11—42no—
198Q8×C11—42no—
199D4×C11—42no—
200D4×C11—42no—
201D4×C11—42no—
202D4×C11—41no—
203D4×C11—41no—
204D4×C11—41no—
205D4×C11—42no—
206D4×C11—41no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—44no—
226C2×C4×C11—84no—
227C2×C4×C11#9912yes—
228C2×C4×C11#9911yescharacteristic
229C2×C4×C11#9911yescharacteristic
230C2×C4×C11C2×C22⋊C412yes—
231C2×C4×C11C2×C22⋊C412yes—
232C2×C4×C11C2×C22⋊C411yescharacteristic
233C2×C4×C11C2×C22⋊C412yes—
234C2×C4×C11C22×D411yescharacteristic
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—44no—
238C2×Dic11—44no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—44no—
242Dic22—48no—
243Dic22—44no—
244Dic22—44no—
245C11⋊C8—44no—
246C22×#41C2×D1111yescharacteristic
247C23×Q8—111no—
248C22×M16—221no—
249#536—114no—
250#536—114no—
251#536—222no—
252#536—222no—
253C2×C4⋊Q8—221no—
254C2×#124—221no—
255C2×#123—112no—
256C2×#123—112no—
257C2×C22⋊Q8—221no—
258C2×C22⋊Q8—221no—
259C2×#117—21no—
260C2×#117—111no—
261#413—114no—
262#413—222no—
263C2×#101—221no—
264C2×#100—112no—
265#410—22no—
266#410C2×D1114yes—
267C2×#99—21no—
268C2×#99C2×D1112yes—
269#352—1116no—
270C22×C11—22no—
271C22×C11—21no—
272C22×C11—22no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11—21no—
276C22×C11—41no—
277C22×C11—42no—
278C22×C11—41no—
279C22×C11—41no—
280C22×C11—41no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—81no—
286C22×C11—81no—
287C22×C11C2×#9911yescharacteristic
288C22×C11C2×#9911yescharacteristic
289C22×C11C22×C22⋊C411yescharacteristic
290C4×C11—21no—
291C4×C11—22no—
292C4×C11—22no—
293C4×C11—21no—
294C4×C11—84no—
295C4×C11C2×#9912yes—
296C4×C11C2×#9912yes—
297Dic11—44no—
298Dic11—44no—
299C2×#41—41no—
300C2×#41—41no—
301C2×#41—42no—
302C2×#41C4×D1112yes—
303C2×#41D4412yes—
304C2×#41C22⋊D1112yes—
305C2×#41C22×D1112yes—
306C22×Q8—114no—
307C22×Q8—221no—
308C22×Q8—222no—
309C22×Q8—221no—
310C22×Q8—442no—
311C22×Q8—441no—
312C22×Q8—441no—
313C22×Q8D4411yescharacteristic
314C22×D4C4×D1111yescharacteristic
315C22×D4C22⋊D1111yescharacteristic
316C22×D4C22×D1111yescharacteristic
317C23×C4—112no—
318C23×C4C4×D1111yescharacteristic
319C23×C4D4411yescharacteristic
320C23×C4C22⋊D1111yescharacteristic
321C2×M16—222no—
322C2×M16—224no—
323C2×M16—441no—
324C2×M16—442no—
325C22×C8—441no—
326C4⋊Q8—224no—
327C4⋊Q8—224no—
328#124—224no—
329#124—224no—
330#123—114no—
331#123—118no—
332#123—114no—
333#123—224no—
334#123—222no—
335#123—222no—
336C22⋊Q8—224no—
337C22⋊Q8—224no—
338C22⋊Q8—224no—
339C22⋊Q8—224no—
340#117—24no—
341#117—42no—
342#117—114no—
343#117—222no—
344C2×C4⋊C4—41no—
345C2×C4⋊C4—222no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4—222no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—112no—
350C2×C22⋊C4—222no—
351C2×C22⋊C4—222no—
352C2×C42—41no—
353C2×C42—221no—
354#101—224no—
355#100—114no—
356#100—222no—
357#99—24no—
358#99—22no—
359#99C22×D1114yes—
360C2×C11—21no—
361C2×C11—21no—
362C2×C11—41no—
363C2×C11—41no—
364C2×C11—41no—
365C2×C11—41no—
366C2×C11—42no—
367C2×C11#212312yescomplemented
368C2×C11C22×#9911yescharacteristic
369C24(C2×D11)⋊C411yescharacteristic
370C24C2×C4×D1111yescharacteristic
371C24C2×C22⋊D1111yescharacteristic
372#41—42no—
373#41—42no—
374#41—42no—
375#41—42no—
376#41—42no—
377#41—42no—
378#41—42no—
379#41—42no—
380C2×Q8—41no—
381C2×Q8—41no—
382C2×Q8—224no—
383C2×Q8—224no—
384C2×Q8—444no—
385C2×Q8—444no—
386C2×Q8—442no—
387C2×Q8—442no—
388C2×Q8—444no—
389C2×Q8—444no—
390C2×Q8—442no—
391C2×Q8—441no—
392C2×Q8—441no—
393C2×Q8(C2×D11)⋊C412yes—
394C2×Q8C2×D4412yes—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4(C2×D11)⋊C412yes—
402C2×D4(C2×D11)⋊C412yes—
403C2×D4C2×C4×D1111yescharacteristic
404C2×D4C2×C4×D1112yes—
405C2×D4C2×D4411yescharacteristic
406C2×D4C2×C22⋊D1111yescharacteristic
407C2×D4C2×C22⋊D1112yes—
408C2×D4C23×D1111yescharacteristic
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—42no—
419C22×C4—114no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—442no—
424C22×C4—442no—
425C22×C4(C2×D11)⋊C411yescharacteristic
426C22×C4(C2×D11)⋊C411yescharacteristic
427C22×C4(C2×D11)⋊C412yes—
428C22×C4(C2×D11)⋊C412yes—
429C22×C4(C2×D11)⋊C412yes—
430C22×C4(C2×D11)⋊C411yescharacteristic
431C22×C4C2×C4×D1112yes—
432C22×C4C2×D4411yescharacteristic
433C22×C4C2×D4412yes—
434C22×C4C2×C22⋊D1112yes—
435M16—224no—
436M16—442no—
437M16—444no—
438C2×C8—442no—
439C2×C8—444no—
440C4⋊C4—44no—
441C4⋊C4—224no—
442C4⋊C4—224no—
443C4⋊C4—228no—
444C4⋊C4—224no—
445C22⋊C4—24no—
446C22⋊C4—42no—
447C22⋊C4—114no—
448C22⋊C4—222no—
449C22⋊C4—224no—
450C22⋊C4—228no—
451C22⋊C4—224no—
452C42—44no—
453C42—224no—
454C11C2×#212311yescharacteristic, complemented, Sylow
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23C2×(C2×D11)⋊C411yescharacteristic
465C23C2×(C2×D11)⋊C411yescharacteristic
466C23C2×(C2×D11)⋊C412yes—
467C23C2×(C2×D11)⋊C411yescharacteristic
468C23C22×C4×D1111yescharacteristic
469C23C22×C22⋊D1111yescharacteristic
470Q8—42no—
471Q8—42no—
472Q8—448no—
473Q8—444no—
474Q8—444no—
475D4—42no—
476D4—42no—
477D4—41no—
478D4—42no—
479D4—41no—
480D4—42no—
481D4—41no—
482D4—41no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—44no—
502C2×C4—84no—
503C2×C4—224no—
504C2×C4—224no—
505C2×C4—444no—
506C2×C4—444no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4—444no—
510C2×C4#6687012yes—
511C2×C4#6687011yescharacteristic
512C2×C4#6687011yescharacteristic
513C2×C4C2×(C2×D11)⋊C412yes—
514C2×C4C2×(C2×D11)⋊C411yescharacteristic
515C2×C4C2×(C2×D11)⋊C412yes—
516C2×C4C2×(C2×D11)⋊C412yes—
517C2×C4C22×D4411yescharacteristic
518C8—444no—
519C22—22no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—22no—
524C22—21no—
525C22—41no—
526C22—42no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—81no—
535C22—81no—
536C22C2×#6687011yescharacteristic
537C22C2×#6687011yescharacteristic
538C22C22×(C2×D11)⋊C411yescharacteristic
539C4—21no—
540C4—22no—
541C4—21no—
542C4—22no—
543C4—84no—
544C4—444no—
545C4—444no—
546C4C2×#6687012yes—
547C4C2×#6687012yes—
548C2—21no—
549C2—21no—
550C2—41no—
551C2—41no—
552C2—41no—
553C2—41no—
554C2—42no—
555C2#1307026912yesdirect product factor
556C2C22×#6687011yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC23×C11C23×C4
FrattiniC2×D4C23×D11
FittingC2×C11×#410C2
socleC22×C11C2×#99
prime radicalC22×C11×#41C22
cosocleC2×D4×C11C24
hypercenterC2×#410D11
hypocenterC11C2×#2123
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
3. #13070269C2direct (N × H)
4. C2×#10622110C2semidirect
7. C23×Dic22C4semidirect
11. #10623356C4semidirect
15. C2×#66988C4semidirect
17. C2×#66979C4semidirect
29. #10622110C22semidirect
51. C22×Dic22C2×C4semidirect
68. #66988C2×C4semidirect
71. #66979C2×C4semidirect
367. C2×C11#2123semidirect
454. C11C2×#2123semidirect
555. C2#13070269direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233562
C2×#106228502
#130702692
C2×#106221102
C2×C11×#4102
C2×#212311