Finite Group Databasebeta

← C2×#13079507 #15624469

Subgroups — C2×#13079507 #15624469

Order 2816.

2122 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623356C211yesmaximal, characteristic
2#13079507C2116yesmaximal, direct product factor
3C2×#10622609C212yesmaximal, complemented
4C2×#10622658C212yesmaximal, complemented
5C2×#10622665C212yesmaximal, complemented
6C2×#10622664C212yesmaximal, complemented
7C2×#10622841C212yesmaximal, complemented
8C2×#10622663C212yesmaximal, complemented
9C2×#10622847C211yesmaximal, characteristic
10C2×C11×#536C211yesmaximal, characteristic
11C22×C11×#41C2211yescharacteristic
12C23×Q8×C11C2211yescharacteristic
13C23×Dic22C2211yescharacteristic
14C11×#536—24no—
15C11×#536C2218yes—
16C2×C11×C4⋊Q8—21no—
17C2×C11×#124—21no—
18C2×C11×#123—21no—
19C2×C11×#123—21no—
20C2×C11×C22⋊Q8C2212yes—
21C2×C11×C22⋊Q8C2212yes—
22C2×C11×#117C2211yescharacteristic
23#10623356—24no—
24#10623356C2218yes—
25C2×#66997—21no—
26C22×#4326C2212yes—
27C22×#4326C2212yes—
28C2×#66989—21no—
29C2×#66988—21no—
30C2×#66988—21no—
31C2×#66979C2211yescharacteristic
32C2×#66977C2212yes—
33C2×#66977C2212yes—
34C22×#4318C2211yescharacteristic
35C23×C11⋊C8C2211yescharacteristic
36#10622847C2218yes—
37#10622841C22116yescomplemented
38C2×#66899C2212yes—
39C2×#66899C2212yes—
40C2×C22⋊(C11⋊C8)C2212yes—
41C2×C22⋊(C11⋊C8)C2212yes—
42#10622665C22116yescomplemented
43#10622664C22116yescomplemented
44#10622663C22116yescomplemented
45#10622658C22116yescomplemented
46#10622609C22116yescomplemented
47C2×#66874C2212yes—
48C2×#66874C2212yes—
49C2×#66872C2212yes—
50C2×#66871C2212yes—
51C2×C11×#41—42no—
52C2×C11×#41—42no—
53C2×C11×#41D414yes—
54C2×C11×#41C2314yes—
55C22×Q8×C11—21no—
56C22×Q8×C11—22no—
57C22×Q8×C11—42no—
58C22×Q8×C11—42no—
59C22×Q8×C11D411yescharacteristic
60C22×Q8×C11C2312yes—
61C22×Q8×C11C2314yes—
62C22×D4×C11D411yescharacteristic
63C22×D4×C11D411yescharacteristic
64C22×D4×C11D411yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×Dic11—21no—
70C22×Dic22—21no—
71C22×Dic22—22no—
72C22×Dic22—42no—
73C22×Dic22—42no—
74C22×Dic22C2312yes—
75C22×Dic22C2314yes—
76C11×C4⋊Q8—28no—
77C11×#124—28no—
78C11×#123—28no—
79C11×#123—28no—
80C11×C22⋊Q8—24no—
81C11×C22⋊Q8—24no—
82C11×C22⋊Q8C2318yes—
83C11×C22⋊Q8C2318yes—
84C11×#117—22no—
85C11×#117C2314yes—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C42×C11—21no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—21no—
96#66997—28no—
97C2×#4326—44no—
98C2×#4326—44no—
99C2×#4326C2318yes—
100C2×#4326C2318yes—
101#66989—28no—
102#66988—28no—
103#66988—28no—
104#66979—22no—
105#66979C2314yes—
106C2×C4⋊Dic11C2312yes—
107#66977—24no—
108#66977—24no—
109#66977C2318yes—
110#66977C2318yes—
111C2×Dic11⋊C4—22no—
112C2×Dic11⋊C4—22no—
113C2×C4×Dic11—21no—
114C2×#4318—42no—
115C2×#4318C2314yes—
116C22×C11⋊C8—42no—
117C22×C11⋊C8C2312yes—
118C22×C11⋊C8C2312yes—
119C22×C11⋊C8C2314yes—
120#66899C2318yes—
121#66899C2318yes—
122C22⋊(C11⋊C8)C2318yes—
123C22⋊(C11⋊C8)C2318yes—
124#66874C2318yes—
125#66874C2318yes—
126#66872C2318yes—
127#66871C2318yes—
128C2×#3202—111nomaximal, Sylow
129C24×C11C2×D411yescharacteristic
130C24×C11C2×D411yescharacteristic
131C24×C11C2×D411yescharacteristic
132C11×#41—48no—
133C11×#41—44no—
134C11×#41—44no—
135C2×Q8×C11—22no—
136C2×Q8×C11—24no—
137C2×Q8×C11—24no—
138C2×Q8×C11—24no—
139C2×Q8×C11—42no—
140C2×Q8×C11—44no—
141C2×Q8×C11—44no—
142C2×Q8×C11—44no—
143C2×Q8×C11—48no—
144C2×Q8×C11C2×D414yes—
145C2×Q8×C11C2414yes—
146C2×D4×C11—42no—
147C2×D4×C11—42no—
148C2×D4×C11—42no—
149C2×D4×C11C2×D414yes—
150C2×D4×C11C2×D414yes—
151C2×D4×C11C2×D414yes—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—24no—
161C22×C4×C11—44no—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2412yes—
169C22×C4×C11C2412yes—
170C22×C4×C11C2412yes—
171C22×C4×C11C2411yescharacteristic
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—24no—
175C22×Dic11—44no—
176C2×Dic22—22no—
177C2×Dic22—24no—
178C2×Dic22—24no—
179C2×Dic22—24no—
180C2×Dic22—44no—
181C2×Dic22—44no—
182C2×Dic22—44no—
183C2×Dic22—48no—
184C2×Dic22C2414yes—
185C11×C4⋊C4—28no—
186C11×C4⋊C4—28no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4C2414yes—
189C11×C22⋊C4—24no—
190C11×C22⋊C4—28no—
191C11×C22⋊C4—28no—
192C42×C11—24no—
193C22⋊Dic11—28no—
194C22⋊Dic11—28no—
195C22⋊Dic11—24no—
196#4326—48no—
197#4326—48no—
198C4⋊Dic11—22no—
199C4⋊Dic11C2414yes—
200Dic11⋊C4—28no—
201Dic11⋊C4—28no—
202C4×Dic11—24no—
203#4318—44no—
204C2×C11⋊C8—24no—
205C2×C11⋊C8—24no—
206C2×C11⋊C8—44no—
207C2×C11⋊C8C2414yes—
208C2×C11⋊C8C2414yes—
209C2×#536—111no—
210C2×#536D1111yescharacteristic
211#3202—1116no—
212C2×#485—112no—
213C2×#485—112no—
214C2×#470—112no—
215C2×#467—112no—
216C2×#451—112no—
217C2×#451—112no—
218C2×#408—111no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11C22×D412yes—
226C23×C11C22×D412yes—
227C23×C11C22×D412yes—
228C23×C11C22×D411yescharacteristic
229Q8×C11—24no—
230Q8×C11—24no—
231Q8×C11—44no—
232Q8×C11—48no—
233Q8×C11—44no—
234D4×C11—44no—
235D4×C11—44no—
236D4×C11—44no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—48no—
252C2×C4×C11—44no—
253C2×C4×C11—44no—
254C2×C4×C11C22×D412yes—
255C2×C4×C11C22×D412yes—
256C2×C4×C11C22×D412yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11H(5,𝔽2)12yes—
259C2×C4×C11H(5,𝔽2)12yes—
260C2×C4×C11C2511yescharacteristic
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—48no—
264C2×Dic11—44no—
265C2×Dic11—44no—
266Dic22—24no—
267Dic22—24no—
268Dic22—48no—
269Dic22—44no—
270C11⋊C8—24no—
271C11⋊C8—24no—
272C22×#41C2×D1111yescharacteristic
273C23×Q8—111no—
274C23×Q8C2×D1111yescharacteristic
275C22×Q16—112no—
276C22×Q16—112no—
277C22×M16—111no—
278C23×C8—111no—
279#536—24no—
280#536—118no—
281#536—224no—
282#536C2×D1118yes—
283C2×C4⋊Q8—21no—
284C2×C4⋊Q8—221no—
285C2×#124—21no—
286C2×#124—221no—
287C2×#123—21no—
288C2×#123—21no—
289C2×#123—221no—
290C2×#123—221no—
291C2×C22⋊Q8—112no—
292C2×C22⋊Q8—112no—
293C2×C22⋊Q8C2×D1112yes—
294C2×C22⋊Q8C2×D1112yes—
295C2×#117—111no—
296C2×#117C2×D1111yescharacteristic
297#485—1116no—
298#485—1116no—
299#470—1116no—
300#467—1116no—
301#451—1116no—
302#451—1116no—
303C2×#107—112no—
304C2×#106—112no—
305C2×#103—112no—
306C2×#103—112no—
307C2×#103—112no—
308C2×#103—112no—
309#408—118no—
310C2×C22⋊C8—112no—
311C2×C22⋊C8—112no—
312C22×C11—22no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—24no—
316C22×C11—24no—
317C22×C11—24no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—44no—
321C22×C11#53412yes—
322C22×C11#57814yes—
323C22×C11C23×D411yescharacteristic
324C4×C11—22no—
325C4×C11—22no—
326C4×C11—22no—
327C4×C11—44no—
328C4×C11—44no—
329C4×C11#53412yes—
330C4×C11C2×H(5,𝔽2)11yescharacteristic
331C4×C11C2×H(5,𝔽2)11yescharacteristic
332Dic11—44no—
333Dic11—44no—
334C2×#41—42no—
335C2×#41—42no—
336C2×#41C22⋊D1114yes—
337C2×#41C22×D1114yes—
338C22×Q8—21no—
339C22×Q8—22no—
340C22×Q8—42no—
341C22×Q8—42no—
342C22×Q8—112no—
343C22×Q8—114no—
344C22×Q8—221no—
345C22×Q8—222no—
346C22×Q8—442no—
347C22×Q8—442no—
348C22×Q8C22⋊D1111yescharacteristic
349C22×Q8C22×D1112yes—
350C22×Q8C22×D1114yes—
351C22×D4C22⋊D1111yescharacteristic
352C22×D4C22⋊D1111yescharacteristic
353C22×D4C22⋊D1111yescharacteristic
354C23×C4—21no—
355C23×C4—221no—
356C23×C4C22×D1111yescharacteristic
357C23×C4C22×D1111yescharacteristic
358C23×C4C22×D1111yescharacteristic
359C2×Q16—118no—
360C2×Q16—118no—
361C2×Q16—444no—
362C2×Q16—444no—
363C2×M16—114no—
364C2×M16—442no—
365C22×C8—112no—
366C22×C8—112no—
367C22×C8—114no—
368C22×C8—442no—
369C4⋊Q8—28no—
370C4⋊Q8—228no—
371#124—28no—
372#124—228no—
373#123—28no—
374#123—28no—
375#123—228no—
376#123—228no—
377C22⋊Q8—24no—
378C22⋊Q8—24no—
379C22⋊Q8—118no—
380C22⋊Q8—118no—
381C22⋊Q8—224no—
382C22⋊Q8—224no—
383C22⋊Q8C22×D1118yes—
384C22⋊Q8C22×D1118yes—
385#117—22no—
386#117—114no—
387#117—222no—
388#117C22×D1114yes—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—112no—
392C2×C4⋊C4—222no—
393C2×C4⋊C4—222no—
394C2×C4⋊C4C22×D1112yes—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—221no—
399C2×C22⋊C4—222no—
400C2×C22⋊C4—222no—
401C2×C42—21no—
402C2×C42—221no—
403#107—118no—
404#106—118no—
405#103—118no—
406#103—118no—
407#103—118no—
408#103—118no—
409C22⋊C8—118no—
410C22⋊C8—118no—
411C2×C11—42no—
412C2×C11—42no—
413C2×C11—42no—
414C2×C11#320214yescomplemented
415C2×C11C2×#53411yescharacteristic
416C2×C11C2×#57812yes—
417C24C2×C22⋊D1111yescharacteristic
418C24C2×C22⋊D1111yescharacteristic
419C24C2×C22⋊D1111yescharacteristic
420#41—44no—
421#41—44no—
422#41—48no—
423C2×Q8—22no—
424C2×Q8—24no—
425C2×Q8—24no—
426C2×Q8—24no—
427C2×Q8—42no—
428C2×Q8—44no—
429C2×Q8—44no—
430C2×Q8—44no—
431C2×Q8—48no—
432C2×Q8—114no—
433C2×Q8—222no—
434C2×Q8—224no—
435C2×Q8—224no—
436C2×Q8—224no—
437C2×Q8—444no—
438C2×Q8—444no—
439C2×Q8—444no—
440C2×Q8—448no—
441C2×Q8C2×C22⋊D1114yes—
442C2×Q8C23×D1114yes—
443C2×D4—42no—
444C2×D4—42no—
445C2×D4—42no—
446C2×D4C2×C22⋊D1114yes—
447C2×D4C2×C22⋊D1114yes—
448C2×D4C2×C22⋊D1114yes—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—24no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—44no—
459C22×C4—224no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—444no—
463C22×C4C2×C22⋊D1112yes—
464C22×C4C2×C22⋊D1112yes—
465C22×C4C2×C22⋊D1112yes—
466C22×C4C2×C22⋊D1111yescharacteristic
467C22×C4C2×C22⋊D1111yescharacteristic
468C22×C4C2×C22⋊D1111yescharacteristic
469C22×C4C23×D1112yes—
470C22×C4C23×D1112yes—
471C22×C4C23×D1112yes—
472C22×C4C23×D1111yescharacteristic
473Q16—448no—
474Q16—448no—
475M16—444no—
476C2×C8—114no—
477C2×C8—114no—
478C2×C8—224no—
479C2×C8—224no—
480C2×C8—444no—
481C4⋊C4—28no—
482C4⋊C4—28no—
483C4⋊C4—22no—
484C4⋊C4—114no—
485C4⋊C4—222no—
486C4⋊C4—228no—
487C4⋊C4—228no—
488C4⋊C4C23×D1114yes—
489C22⋊C4—24no—
490C22⋊C4—28no—
491C22⋊C4—28no—
492C22⋊C4—224no—
493C22⋊C4—228no—
494C22⋊C4—228no—
495C42—24no—
496C42—224no—
497C11C2×#320211yescharacteristic, complemented, Sylow
498C23—22no—
499C23—22no—
500C23—22no—
501C23—24no—
502C23—24no—
503C23—24no—
504C23C22×C22⋊D1112yes—
505C23C22×C22⋊D1112yes—
506C23C22×C22⋊D1112yes—
507C23C22×C22⋊D1111yescharacteristic
508Q8—24no—
509Q8—24no—
510Q8—44no—
511Q8—48no—
512Q8—44no—
513Q8—224no—
514Q8—224no—
515Q8—448no—
516Q8—444no—
517D4—44no—
518D4—44no—
519D4—44no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—48no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—224no—
538C2×C4—224no—
539C2×C4—448no—
540C2×C4—444no—
541C2×C4—444no—
542C2×C4#6703712yes—
543C2×C4#6703712yes—
544C2×C4C22×C22⋊D1112yes—
545C2×C4C22×C22⋊D1112yes—
546C2×C4C22×C22⋊D1112yes—
547C2×C4C22×C22⋊D1111yescharacteristic
548C2×C4C24×D1111yescharacteristic
549C8—224no—
550C8—224no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—24no—
555C22—24no—
556C22—24no—
557C22—44no—
558C22—44no—
559C22—44no—
560C22#1062333512yes—
561C22#1062336914yes—
562C22C23×C22⋊D1111yescharacteristic
563C4—22no—
564C4—22no—
565C4—22no—
566C4—44no—
567C4—44no—
568C4—444no—
569C4—444no—
570C4#1062333512yes—
571C4C2×#6703711yescharacteristic
572C4C2×#6703711yescharacteristic
573C2—42no—
574C2—42no—
575C2—42no—
576C2#1307950714yesdirect product factor
577C2C2×#1062333511yescharacteristic
578C2C2×#1062336912yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#536C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenterC2×#536D11
hypocenterC11C2×#3202
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
2. #13079507C2direct (N × H)
3. C2×#10622609C2semidirect
4. C2×#10622658C2semidirect
5. C2×#10622665C2semidirect
6. C2×#10622664C2semidirect
7. C2×#10622841C2semidirect
8. C2×#10622663C2semidirect
37. #10622841C22semidirect
42. #10622665C22semidirect
43. #10622664C22semidirect
44. #10622663C22semidirect
45. #10622658C22semidirect
46. #10622609C22semidirect
414. C2×C11#3202semidirect
497. C11C2×#3202semidirect
576. C2#13079507direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233562
#130795072
C2×#106226092
C2×#106226582
C2×#106226652
C2×#106226642
C2×#106228412
C2×#106226632
C2×#106228472
C2×C11×#5362
C2×#320211