Finite Group Databasebeta

← C2×#13070270 #14906510

Subgroups — C2×#13070270 #14906510

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×#10622850C211yesmaximal, characteristic
2C2×#10622853C211yesmaximal, characteristic
3#13070270C218yesmaximal, direct product factor
4C2×#10622177C214yesmaximal, complemented
5C2×C11×#536C211yesmaximal, characteristic
6C22×C11×#41C2211yescharacteristic
7C23×Q8×C11C411yescharacteristic, complemented
8C11×#536—22no—
9C11×#536—22no—
10C11×#536C414yescomplemented
11C11×#536C2214yes—
12C2×C11×C4⋊Q8—21no—
13C2×C11×#124—21no—
14C2×C11×#123C412yescomplemented
15C2×C11×#123C2212yes—
16C2×C11×C22⋊Q8—21no—
17C2×C11×C22⋊Q8—21no—
18C2×C11×#117C411yescharacteristic, complemented
19C2×#66979—21no—
20C22×#4318—21no—
21#10622853—22no—
22#10622853C2214yes—
23#10622850—22no—
24#10622850C2214yes—
25C2×#66900—21no—
26C2×#66898—21no—
27C2×#66898C2212yes—
28C2×#66897C2212yes—
29#10622177C22116yescomplemented
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×C11—21no—
38C22×Q8×C11—21no—
39C22×Q8×C11—22no—
40C22×Q8×C11—42no—
41C22×Q8×C11—41no—
42C22×Q8×C11—41no—
43C22×Q8×C11C2×C414yescomplemented
44C22×Q8×C11D411yescharacteristic
45C22×D4×C11C2×C411yescharacteristic
46C22×D4×C11D411yescharacteristic
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11C2×C411yescharacteristic
49C23×C4×C11C2×C412yes—
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C11×C4⋊Q8—24no—
53C11×C4⋊Q8—24no—
54C11×#124—24no—
55C11×#124—24no—
56C11×#123—24no—
57C11×#123—22no—
58C11×#123—22no—
59C11×#123C2×C414yes—
60C11×#123C2×C418yescomplemented
61C11×#123C2314yes—
62C11×C22⋊Q8—24no—
63C11×C22⋊Q8—24no—
64C11×C22⋊Q8—24no—
65C11×C22⋊Q8—24no—
66C11×#117—22no—
67C11×#117C2×C414yescomplemented
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4C2×C412yes—
74C2×C42×C11—21no—
75C2×C22⋊Dic11—22no—
76#66979—24no—
77#66979—42no—
78C2×C4⋊Dic11—41no—
79C2×C4×Dic11—41no—
80C2×#4318—22no—
81C2×#4318—24no—
82C2×#4318—41no—
83C2×#4318—42no—
84C22×C11⋊C8—41no—
85#66900—24no—
86#66898—24no—
87#66898—22no—
88#66898C2314yes—
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—24no—
104C2×Q8×C11—24no—
105C2×Q8×C11—41no—
106C2×Q8×C11—41no—
107C2×Q8×C11—42no—
108C2×Q8×C11—42no—
109C2×Q8×C11—44no—
110C2×Q8×C11—44no—
111C2×Q8×C11—44no—
112C2×Q8×C11—44no—
113C2×Q8×C11—42no—
114C2×Q8×C11—41no—
115C2×Q8×C11—41no—
116C2×Q8×C11C22⋊C412yes—
117C2×Q8×C11C2×D412yes—
118C2×D4×C11—41no—
119C2×D4×C11—41no—
120C2×D4×C11—41no—
121C2×D4×C11—41no—
122C2×D4×C11—41no—
123C2×D4×C11—41no—
124C2×D4×C11C22⋊C412yes—
125C2×D4×C11C22⋊C412yes—
126C2×D4×C11C22×C411yescharacteristic
127C2×D4×C11C22×C412yes—
128C2×D4×C11C2×D411yescharacteristic
129C2×D4×C11C2×D412yes—
130C2×D4×C11C2×D411yescharacteristic
131C2×D4×C11C2411yescharacteristic
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11C22⋊C411yescharacteristic
147C22×C4×C11C22⋊C411yescharacteristic
148C22×C4×C11C22⋊C412yes—
149C22×C4×C11C22⋊C412yes—
150C22×C4×C11C22⋊C412yes—
151C22×C4×C11C22⋊C411yescharacteristic
152C22×C4×C11C22×C412yes—
153C22×C4×C11C22×C414yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D412yes—
157C22×Dic11—42no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—28no—
161C11×C4⋊C4—24no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—28no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—24no—
166C11×C22⋊C4C22×C414yes—
167C42×C11—24no—
168C22⋊Dic11—24no—
169C22⋊Dic11—42no—
170C4⋊Dic11—44no—
171C4×Dic11—44no—
172#4318—24no—
173#4318—42no—
174#4318—44no—
175C2×C11⋊C8—42no—
176C2×C11⋊C8—44no—
177C2×#536D1111yescharacteristic
178C2×#413—111no—
179C2×#410—111no—
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—
199Q8×C11—48no—
200Q8×C11—44no—
201Q8×C11—44no—
202D4×C11—42no—
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—41no—
206D4×C11—41no—
207D4×C11—42no—
208D4×C11—41no—
209D4×C11—41no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
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—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—44no—
231C2×C4×C11—44no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—44no—
235C2×C4×C11#9912yes—
236C2×C4×C11#9911yescharacteristic
237C2×C4×C11#9911yescharacteristic
238C2×C4×C11C2×C22⋊C412yes—
239C2×C4×C11C2×C22⋊C412yes—
240C2×C4×C11C2×C22⋊C411yescharacteristic
241C2×C4×C11C2×C22⋊C412yes—
242C2×C4×C11C22×D411yescharacteristic
243C2×Dic11—44no—
244C2×Dic11—84no—
245C11⋊C8—44no—
246C22×#41C2×D1111yescharacteristic
247C23×Q8Dic1111yescharacteristic, complemented
248C22×M16—221no—
249#536—22no—
250#536—22no—
251#536Dic1114yescomplemented
252#536C2×D1114yes—
253C2×C4⋊Q8—21no—
254C2×#124—21no—
255C2×#123Dic1112yescomplemented
256C2×#123C2×D1112yes—
257C2×C22⋊Q8—21no—
258C2×C22⋊Q8—21no—
259C2×#117—221no—
260C2×#117Dic1111yescharacteristic, complemented
261#413—114no—
262#413—222no—
263C2×#101—221no—
264C2×#100—112no—
265#410—114no—
266#410—222no—
267C2×#99—112no—
268C2×#99—221no—
269#352—1116no—
270C22×C11—22no—
271C22×C11—21no—
272C22×C11—21no—
273C22×C11—22no—
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—44no—
295C4×C11—44no—
296C4×C11C2×#9912yes—
297C4×C11C2×#9912yes—
298Dic11—84no—
299C2×#41—41no—
300C2×#41—41no—
301C2×#41—42no—
302C2×#41C2×Dic1112yes—
303C2×#41C22⋊D1112yes—
304C2×#41C22⋊D1112yes—
305C2×#41C22×D1112yes—
306C22×Q8—21no—
307C22×Q8—22no—
308C22×Q8—21no—
309C22×Q8—42no—
310C22×Q8—41no—
311C22×Q8—41no—
312C22×Q8C2×Dic1114yescomplemented
313C22×Q8C22⋊D1111yescharacteristic
314C22×D4C2×Dic1111yescharacteristic
315C22×D4C22⋊D1111yescharacteristic
316C22×D4C22×D1111yescharacteristic
317C23×C4C2×Dic1111yescharacteristic
318C23×C4C2×Dic1112yes—
319C23×C4C22⋊D1111yescharacteristic
320C23×C4C22⋊D1111yescharacteristic
321C2×M16—222no—
322C2×M16—224no—
323C2×M16—441no—
324C2×M16—442no—
325C22×C8—441no—
326C4⋊Q8—24no—
327C4⋊Q8—24no—
328#124—24no—
329#124—24no—
330#123—24no—
331#123—22no—
332#123—22no—
333#123C2×Dic1114yes—
334#123C2×Dic1118yescomplemented
335#123C22×D1114yes—
336C22⋊Q8—24no—
337C22⋊Q8—24no—
338C22⋊Q8—24no—
339C22⋊Q8—24no—
340#117—22no—
341#117—224no—
342#117—442no—
343#117C2×Dic1114yescomplemented
344C2×C4⋊C4—22no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—441no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—222no—
351C2×C22⋊C4C2×Dic1112yes—
352C2×C42—21no—
353C2×C42—441no—
354#101—224no—
355#100—114no—
356#100—222no—
357#99—114no—
358#99—222no—
359#99—224no—
360C2×C11—21no—
361C2×C11—21no—
362C2×C11—41no—
363C2×C11—41no—
364C2×C11—41no—
365C2×C11—42no—
366C2×C11—41no—
367C2×C11#212312yescomplemented
368C2×C11C22×#9911yescharacteristic
369C24C22⋊Dic1111yescharacteristic
370C24C22×Dic1111yescharacteristic
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—24no—
381C2×Q8—24no—
382C2×Q8—41no—
383C2×Q8—41no—
384C2×Q8—44no—
385C2×Q8—44no—
386C2×Q8—42no—
387C2×Q8—42no—
388C2×Q8—44no—
389C2×Q8—44no—
390C2×Q8—42no—
391C2×Q8—41no—
392C2×Q8—41no—
393C2×Q8C22⋊Dic1112yes—
394C2×Q8C2×C22⋊D1112yes—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4C22⋊Dic1112yes—
402C2×D4C22⋊Dic1112yes—
403C2×D4C22×Dic1111yescharacteristic
404C2×D4C22×Dic1112yes—
405C2×D4C2×C22⋊D1111yescharacteristic
406C2×D4C2×C22⋊D1112yes—
407C2×D4C2×C22⋊D1111yescharacteristic
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—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—442no—
424C22×C4C22⋊Dic1111yescharacteristic
425C22×C4C22⋊Dic1111yescharacteristic
426C22×C4C22⋊Dic1112yes—
427C22×C4C22⋊Dic1112yes—
428C22×C4C22⋊Dic1112yes—
429C22×C4C22⋊Dic1111yescharacteristic
430C22×C4C22×Dic1112yes—
431C22×C4C22×Dic1114yes—
432C22×C4C2×C22⋊D1112yes—
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C2×C22⋊D1112yes—
435M16—224no—
436M16—442no—
437M16—444no—
438C2×C8—442no—
439C2×C8—444no—
440C4⋊C4—24no—
441C4⋊C4—24no—
442C4⋊C4—28no—
443C4⋊C4—24no—
444C4⋊C4—444no—
445C22⋊C4—24no—
446C22⋊C4—28no—
447C22⋊C4—22no—
448C22⋊C4—24no—
449C22⋊C4—224no—
450C22⋊C4—442no—
451C22⋊C4C22×Dic1114yes—
452C42—24no—
453C42—444no—
454C11C2×#212311yescharacteristic, complemented, Sylow
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23C2×C22⋊Dic1111yescharacteristic
465C23C2×C22⋊Dic1111yescharacteristic
466C23C2×C22⋊Dic1112yes—
467C23C2×C22⋊Dic1111yescharacteristic
468C23C23×Dic1111yescharacteristic
469C23C22×C22⋊D1111yescharacteristic
470Q8—42no—
471Q8—42no—
472Q8—48no—
473Q8—44no—
474Q8—44no—
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—24no—
502C2×C4—24no—
503C2×C4—44no—
504C2×C4—44no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—44no—
508C2×C4—444no—
509C2×C4—884no—
510C2×C4#6689812yes—
511C2×C4#6689811yescharacteristic
512C2×C4#6689811yescharacteristic
513C2×C4C2×C22⋊Dic1112yes—
514C2×C4C2×C22⋊Dic1112yes—
515C2×C4C2×C22⋊Dic1111yescharacteristic
516C2×C4C2×C22⋊Dic1112yes—
517C2×C4C22×C22⋊D1111yescharacteristic
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×#6689811yescharacteristic
537C22C2×#6689811yescharacteristic
538C22C22×C22⋊Dic1111yescharacteristic
539C4—21no—
540C4—22no—
541C4—21no—
542C4—22no—
543C4—44no—
544C4—44no—
545C4—884no—
546C4C2×#6689812yes—
547C4C2×#6689812yes—
548C2—21no—
549C2—21no—
550C2—41no—
551C2—41no—
552C2—41no—
553C2—41no—
554C2—42no—
555C2#1307027012yesdirect product factor
556C2C22×#6689811yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC23×C11C23×C4
FrattiniC2×D4C23×D11
FittingC2×C11×#536C2
socleC22×C11C2×#99
prime radicalC22×C11×#41C22
cosocleC2×D4×C11C24
hypercenterC2×#536D11
hypocenterC11C2×#2123
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
3. #13070270C2direct (N × H)
4. C2×#10622177C2semidirect
7. C23×Q8×C11C4semidirect
10. C11×#536C4semidirect
14. C2×C11×#123C4semidirect
18. C2×C11×#117C4semidirect
29. #10622177C22semidirect
43. C22×Q8×C11C2×C4semidirect
60. C11×#123C2×C4semidirect
67. C11×#117C2×C4semidirect
247. C23×Q8Dic11semidirect
251. #536Dic11semidirect
255. C2×#123Dic11semidirect
260. C2×#117Dic11semidirect
312. C22×Q8C2×Dic11semidirect
334. #123C2×Dic11semidirect
343. #117C2×Dic11semidirect
367. C2×C11#2123semidirect
454. C11C2×#2123semidirect
555. C2#13070270direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106228502
C2×#106228532
#130702702
C2×#106221772
C2×C11×#5362
C2×#212311