Finite Group Databasebeta

← C2×#13079324 #15623695

Subgroups — C2×#13079324 #15623695

Order 2816.

1998 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic, complemented
2C2×#10623222C211yesmaximal, characteristic
3#13079324C2116yesmaximal, direct product factor
4C2×#10622678C211yesmaximal, characteristic, complemented
5C2×#10622699C211yesmaximal, characteristic, complemented
6C2×#10622327C211yesmaximal, characteristic, complemented
7C2×#10622426C212yesmaximal, complemented
8C2×#10622420C212yesmaximal
9C2×#10622402C212yesmaximal, complemented
10C2×#10622430C212yesmaximal, complemented
11C2×D11×#97C211yesmaximal, characteristic, complemented
12C2×C11×#491C211yesmaximal, characteristic, complemented
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×#125C2211yescharacteristic
15C2×#66999C2212yes—
16C2×Q8×Dic11C2212yes—
17C22×#4326C2212yes—
18C22×#4325C2212yes—
19C22×C8×D11C2212yes—
20#10623259—24no—
21#10623259C2218yescomplemented
22#10623222—24no—
23#10623222C2218yes—
24C2×#66951—21no—
25C2×#66950—21no—
26C2×#66950C2211yescharacteristic
27C2×#66948C2211yescharacteristic
28C2×#66947—21no—
29C2×#66946—21no—
30C2×#66946C2211yescharacteristic
31C2×#66945—21no—
32C2×#66945—21no—
33C2×#66943—21no—
34C2×#66940—21no—
35C2×#66940C2211yescharacteristic
36C2×#66928C2211yescharacteristic
37C2×C42×D11C2211yescharacteristic
38C2×#66922C2211yescharacteristic
39C11×#491C2218yescomplemented
40C2×C11×#103C2212yes—
41C2×C11×#103C2212yes—
42C2×C11×#97C2211yescharacteristic
43C2×#66885C2212yes—
44C2×#66880C2212yes—
45C2×#66879C2212yes—
46#10622699C2218yescomplemented
47#10622678C2218yescomplemented
48C2×#66872C2212yes—
49C2×#66871C2212yes—
50C2×#66867C2211yescharacteristic
51#10622430C22116yescomplemented
52#10622426C22116yescomplemented
53#10622420C22116yes—
54#10622402C22116yescomplemented
55#10622327C2218yescomplemented
56D11×#97C2218yescomplemented
57C22×Q8×C11C2312yes—
58C22×D44—21no—
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×C4×D11D411yescharacteristic
62C22×C4×D11D411yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×Dic22—21no—
65C22×Dic22C2311yescharacteristic
66C22×C8×C11C2312yes—
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8C2314yes—
69C11×#125—22no—
70C11×#125C2314yes—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78#66999—24no—
79#66999C2318yes—
80Q8×Dic11—24no—
81Q8×Dic11C2318yes—
82C2×#4326—28no—
83C2×#4326C2318yes—
84C2×#4325—28no—
85C2×#4325C2318yes—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11C2312yes—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—22no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11D411yescharacteristic
101C2×C4×Dic11D411yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8C2312yes—
104C2×C8×D11—28no—
105C2×C8×D11C2318yes—
106#66951—28no—
107#66950—28no—
108#66950—22no—
109#66950C2314yes—
110#66948—22no—
111#66948C2314yes—
112#66947—28no—
113#66946—28no—
114#66946—22no—
115#66946C2314yes—
116#66945—28no—
117#66945—28no—
118#66943—28no—
119#66940—28no—
120#66940—22no—
121#66940C2314yes—
122#66928—22no—
123#66928C2314yes—
124C42×D11D414yes—
125C42×D11C2314yes—
126#66922—22no—
127#66922C2314yes—
128C11×#103C2318yes—
129C11×#103C2318yes—
130C11×#97C2314yes—
131#66885C2318yes—
132#66880C2318yes—
133#66879C2318yes—
134#66872C2318yes—
135#66871C2318yes—
136#66867C2314yes—
137C2×#3181—111nomaximal, Sylow
138C23×D11—21no—
139C23×D11C2×D411yescharacteristic
140C2×Q8×C11—22no—
141C2×Q8×C11—24no—
142C2×Q8×C11—24no—
143C2×Q8×C11C2414yes—
144C22×C4×C11—22no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—22no—
151C22×Dic11—21no—
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C2×D44—24no—
156C2×D44—21no—
157C2×D44—24no—
158C2×D44—44no—
159C2×D44C2412yes—
160C2×C4×D11—24no—
161C2×C4×D11—24no—
162C2×C4×D11—24no—
163C2×C4×D11—42no—
164C2×C4×D11—44no—
165C2×C4×D11C2×D412yes—
166C2×C4×D11C2×D414yes—
167C2×C4×D11C2×D414yes—
168C2×C4×D11C2412yes—
169C2×Dic22—24no—
170C2×Dic22—21no—
171C2×Dic22—24no—
172C2×Dic22—44no—
173C2×Dic22C2412yes—
174C2×C8×C11—24no—
175C2×C8×C11C2414yes—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—24no—
179C11×C4⋊C4—24no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4C2412yes—
183C11×C4⋊C4C2412yes—
184C42×C11C2×D412yes—
185C42×C11C2412yes—
186#4326—216no—
187#4325—216no—
188(C2×D11)⋊C4—24no—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—28no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—24no—
193(C2×D11)⋊C4—24no—
194C4⋊Dic11—28no—
195C4⋊Dic11—24no—
196C4⋊Dic11—22no—
197C4⋊Dic11—24no—
198C4⋊Dic11C2414yes—
199Dic11⋊C4—28no—
200Dic11⋊C4—24no—
201C4×Dic11—28no—
202C4×Dic11—24no—
203C4×Dic11C2×D412yes—
204C4×Dic11C2×D414yes—
205C4×Dic11C2×D414yes—
206C4×Dic11C2412yes—
207C2×C11⋊C8#4118yes—
208C2×C11⋊C8C2414yes—
209C8×D11—216no—
210C2×#533—111no—
211C2×#529—111no—
212#3181—1116no—
213C2×#501—111no—
214C2×#497—111no—
215C2×#491D1111yescharacteristic, complemented
216C2×#489—111no—
217C2×#467—112no—
218C2×#465—112no—
219C2×#441—112no—
220C2×#440—112no—
221C22×#97—111no—
222C23×C11C22×D411yescharacteristic
223C22×D11—22no—
224C22×D11—22no—
225C22×D11—22no—
226C22×D11—42no—
227C22×D11—42no—
228C22×D11—42no—
229C22×D11#13714yes—
230C22×D11C22×D412yes—
231Q8×C11—24no—
232Q8×C11—24no—
233Q8×C11—44no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—44no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11C22×D412yes—
243C2×C4×C11C22×D412yes—
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4114yes—
246C2×C4×C11C2511yescharacteristic
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—24no—
251C2×Dic11—22no—
252C2×Dic11—42no—
253C2×Dic11—44no—
254C2×Dic11C22×D412yes—
255C2×Dic11C22×D412yes—
256C2×Dic11C22×D412yes—
257D44—24no—
258D44—48no—
259D44—42no—
260C4×D11—28no—
261C4×D11—24no—
262C4×D11—24no—
263C4×D11—44no—
264C4×D11—48no—
265Dic22—24no—
266Dic22—48no—
267Dic22—42no—
268C8×C11—24no—
269C11⋊C8C2×#4118yes—
270C22×Q16—112no—
271C22×SD16—112no—
272C23×C8—112no—
273#533—118no—
274#533—224no—
275C2×C4⋊Q8—111no—
276C2×C4⋊Q8C2×D1111yescharacteristic
277#529—118no—
278#529—224no—
279C2×#126—221no—
280C2×#125—221no—
281C2×#125C2×D1111yescharacteristic
282C2×#124—111no—
283C2×#123—221no—
284C2×C22⋊Q8—112no—
285C2×C22⋊Q8—111no—
286C2×C22⋊Q8—221no—
287C2×#121—111no—
288C2×C4×Q8—112no—
289C2×C4×Q8—111no—
290C2×C4×Q8—221no—
291C2×C4×D4—111no—
292C2×C4×D4—221no—
293C2×#117—221no—
294C2×#117—221no—
295C22×C42—111no—
296#501—118no—
297#497—118no—
298#491C2×D1118yescomplemented
299#489—118no—
300#467—1116no—
301#465—1116no—
302#441—1116no—
303#440—1116no—
304C2×#107—112no—
305C2×#106—112no—
306C2×#103—112no—
307C2×#103C2×D1112yes—
308C2×#103C2×D1112yes—
309C2×#102—112no—
310C2×#97—112no—
311C2×#97—111no—
312C2×#97—118no—
313C2×#97C2×D1111yescharacteristic
314C22×C11#53212yes—
315C22×C11C2×#13712yes—
316C22×C11#57512yes—
317C22×C11C23×D411yescharacteristic
318C2×D11—28no—
319C2×D11—22no—
320C2×D11—22no—
321C2×D11—42no—
322C2×D11—42no—
323C2×D11—42no—
324C2×D11—84no—
325C2×D11C2×#13714yes—
326C4×C11—22no—
327C4×C11—22no—
328C4×C11—44no—
329C4×C11—42no—
330C4×C11—42no—
331C4×C11#53212yes—
332C4×C11C22×#4112yes—
333Dic11—22no—
334Dic11—22no—
335Dic11—22no—
336Dic11—42no—
337Dic11—44no—
338C22×Q8—111no—
339C22×Q8—221no—
340C22×Q8C22×D1112yes—
341C22×D4—111no—
342C22×D4—221no—
343C23×C4—111no—
344C23×C4—111no—
345C23×C4—111no—
346C23×C4—221no—
347C2×Q16—118no—
348C2×Q16—228no—
349C2×SD16—118no—
350C2×SD16—228no—
351C22×C8—112no—
352C22×C8—118no—
353C22×C8—228no—
354C22×C8C22×D1112yes—
355C4⋊Q8—22no—
356C4⋊Q8—114no—
357C4⋊Q8—222no—
358C4⋊Q8C22×D1114yes—
359#126—228no—
360#125—22no—
361#125—228no—
362#125C22×D1114yes—
363#124—114no—
364#124—222no—
365#123—228no—
366C22⋊Q8—118no—
367C22⋊Q8—114no—
368C22⋊Q8—222no—
369C22⋊Q8—228no—
370C22⋊Q8—224no—
371#121—114no—
372#121—222no—
373C4×Q8—118no—
374C4×Q8—114no—
375C4×Q8—222no—
376C4×Q8—228no—
377C4×Q8—224no—
378C4×D4—114no—
379C4×D4—222no—
380C4×D4—228no—
381#117—228no—
382#117—228no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—112no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—222no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—222no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C22⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4—222no—
398C2×C22⋊C4—221no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C42—111no—
402C2×C42—111no—
403C2×C42—111no—
404C2×C42—114no—
405C2×C42—114no—
406C2×C42—221no—
407C2×C42—222no—
408C2×C42C22×D1111yescharacteristic
409#107—118no—
410#106—118no—
411#103—118no—
412#103C22×D1118yes—
413#103C22×D1118yes—
414#102—118no—
415#97—118no—
416#97—114no—
417#97C22×D1114yes—
418C2×C11#318114yescomplemented
419C2×C11C2×#53211yescharacteristic
420C2×C11C22×#13711yescharacteristic
421C2×C11C2×#57511yescharacteristic
422D11—24no—
423D11—82no—
424C24—111no—
425C24—221no—
426C2×Q8—22no—
427C2×Q8—24no—
428C2×Q8—24no—
429C2×Q8—112no—
430C2×Q8—221no—
431C2×Q8—224no—
432C2×Q8—224no—
433C2×Q8—444no—
434C2×Q8C23×D1114yes—
435C2×D4—112no—
436C2×D4—224no—
437C2×D4—221no—
438C2×D4—224no—
439C2×D4—444no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—114no—
447C22×C4—112no—
448C22×C4—112no—
449C22×C4—114no—
450C22×C4—224no—
451C22×C4—224no—
452C22×C4—224no—
453C22×C4—221no—
454C22×C4—222no—
455C22×C4—442no—
456C22×C4—444no—
457C22×C4D4×D1111yescharacteristic
458C22×C4D4×D1111yescharacteristic
459C22×C4C23×D1111yescharacteristic
460Q16—2216no—
461SD16—2216no—
462C2×C8—24no—
463C2×C8—118no—
464C2×C8—114no—
465C2×C8—2216no—
466C2×C8C23×D1114yes—
467C4⋊C4—24no—
468C4⋊C4—24no—
469C4⋊C4—24no—
470C4⋊C4—24no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—114no—
474C4⋊C4—224no—
475C4⋊C4—228no—
476C4⋊C4—224no—
477C4⋊C4—228no—
478C4⋊C4—222no—
479C4⋊C4—224no—
480C4⋊C4C23×D1112yes—
481C4⋊C4C23×D1112yes—
482C22⋊C4—224no—
483C22⋊C4—224no—
484C22⋊C4—228no—
485C22⋊C4—224no—
486C22⋊C4—224no—
487C22⋊C4—224no—
488C42—114no—
489C42—112no—
490C42—114no—
491C42—112no—
492C42—224no—
493C42—228no—
494C42D4×D1112yes—
495C42C23×D1112yes—
496C11C2×#318111yescharacteristic, complemented, Sylow
497C23—114no—
498C23—112no—
499C23—222no—
500C23—222no—
501C23—222no—
502C23—442no—
503C23—442no—
504C23—442no—
505C23C2×D4×D1111yescharacteristic
506Q8—24no—
507Q8—24no—
508Q8—44no—
509Q8—224no—
510Q8—448no—
511Q8—442no—
512D4—224no—
513D4—448no—
514D4—442no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—44no—
523C2×C4—112no—
524C2×C4—112no—
525C2×C4—112no—
526C2×C4—228no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—222no—
530C2×C4—224no—
531C2×C4—224no—
532C2×C4—222no—
533C2×C4—224no—
534C2×C4—444no—
535C2×C4—448no—
536C2×C4—444no—
537C2×C4—442no—
538C2×C4C2×D4×D1112yes—
539C2×C4C2×D4×D1112yes—
540C2×C4C2×D4×D1111yescharacteristic
541C2×C4#41×D1114yes—
542C2×C4C24×D1111yescharacteristic
543C8—24no—
544C8—118no—
545C22—114no—
546C22—228no—
547C22—222no—
548C22—222no—
549C22—442no—
550C22—442no—
551C22—442no—
552C22—884no—
553C22#1062319912yes—
554C22D11×#13712yes—
555C22#1062330812yes—
556C22C22×D4×D1111yescharacteristic
557C4—22no—
558C4—22no—
559C4—44no—
560C4—42no—
561C4—42no—
562C4—222no—
563C4—222no—
564C4—222no—
565C4—442no—
566C4—444no—
567C4#1062319912yes—
568C4C2×#41×D1112yes—
569C2—224no—
570C2—882no—
571C2#1307932414yesdirect product factor
572C2C2×#1062319911yescharacteristic
573C2C2×D11×#13711yescharacteristic
574C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#491C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenterC2×#491D11
hypocenterC11C2×#3181
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
1. C2×#10623259C2semidirect
3. #13079324C2direct (N × H)
4. C2×#10622678C2semidirect
5. C2×#10622699C2semidirect
6. C2×#10622327C2semidirect
7. C2×#10622426C2semidirect
9. C2×#10622402C2semidirect
10. C2×#10622430C2semidirect
11. C2×D11×#97C2semidirect
12. C2×C11×#491C2semidirect
21. #10623259C22semidirect
39. C11×#491C22semidirect
46. #10622699C22semidirect
47. #10622678C22semidirect
51. #10622430C22semidirect
52. #10622426C22semidirect
54. #10622402C22semidirect
55. #10622327C22semidirect
56. D11×#97C22semidirect
215. C2×#491D11semidirect
298. #491C2×D11semidirect
418. C2×C11#3181semidirect
496. C11C2×#3181semidirect
571. C2#13079324direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106232222
#130793242
C2×#106226782
C2×#106226992
C2×#106223272
C2×#106224262
C2×#106224202
C2×#106224022
C2×#106224302
C2×D11×#972
C2×C11×#4912
C2×#318111