Finite Group Databasebeta

← C2×#13078748 #15621978

Subgroups — C2×#13078748 #15621978

Order 2816.

2118 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2C2×C4×Q8×D11C211yesmaximal, characteristic
3#13078748C2116yesmaximal, direct product factor
4C2×#10622475C212yesmaximal
5C2×#10622707C211yesmaximal, characteristic, complemented
6C2×#10622462C211yesmaximal, characteristic, complemented
7C2×#10622644C211yesmaximal, characteristic, complemented
8C2×#10622421C212yesmaximal
9C2×#10622466C212yesmaximal, complemented
10C2×#10622402C212yesmaximal, complemented
11C2×#10622448C211yesmaximal, characteristic
12C2×C11×#475C211yesmaximal, characteristic, complemented
13C22×Q8×D11C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C2×#66999—21no—
17C2×Q8×Dic11—21no—
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4326C2212yes—
20C22×Dic44C2212yes—
21#10623259—24no—
22#10623259C2218yes—
23C4×Q8×D11—24no—
24C4×Q8×D11C2218yes—
25C2×#66950C2212yes—
26C2×#66945—21no—
27C2×C4⋊C4×D11—21no—
28C2×C4⋊C4×D11C2211yescharacteristic
29C2×#66943—21no—
30C2×#66940—21no—
31C2×#66940C2212yes—
32C2×#66940C2211yescharacteristic
33C2×C42×D11—21no—
34C2×C42×D11C2211yescharacteristic
35C2×#66922C2211yescharacteristic
36C2×C4×Dic22—21no—
37C2×C4×Dic22C2211yescharacteristic
38C11×#475C2218yescomplemented
39C2×C11×#106C2212yes—
40C2×C11×C4⋊C8C2211yescharacteristic
41C2×C11×#103C2212yes—
42C2×(C2×D11)⋊C8C2212yes—
43C2×#66880C2212yes—
44C2×#66879C2212yes—
45#10622707C2218yescomplemented
46#10622644C2218yescomplemented
47C2×#66874C2212yes—
48C2×#66874C2212yes—
49C2×#66872C2212yes—
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622475C22116yes—
52#10622466C22116yescomplemented
53#10622462C2218yescomplemented
54#10622448C2218yes—
55#10622421C22116yes—
56#10622402C22116yescomplemented
57C22×Q8×C11—21no—
58C22×Q8×C11C2311yescharacteristic
59C2×Q8×D11—24no—
60C2×Q8×D11—22no—
61C2×Q8×D11—24no—
62C2×Q8×D11C2314yes—
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11D411yescharacteristic
66C22×C4×D11D411yescharacteristic
67C22×C4×D11C2311yescharacteristic
68C22×Dic22—21no—
69C22×Dic22C2312yes—
70C22×Dic22C2311yescharacteristic
71C22×C8×C11C2312yes—
72C11×C4⋊Q8—22no—
73C11×C4⋊Q8C2314yes—
74C4×Q8×C11—22no—
75C4×Q8×C11C2314yes—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2312yes—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82#66999—28no—
83Q8×Dic11—28no—
84Q8×Dic11—22no—
85Q8×Dic11C2314yes—
86C2×#4326—28no—
87C2×#4326C2318yes—
88C2×(C2×D11)⋊C4—22no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—22no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—22no—
102C2×C4×Dic11D411yescharacteristic
103C2×C4×Dic11D411yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8C2312yes—
106C2×Dic44—28no—
107C2×Dic44C2318yes—
108#66950—24no—
109#66950C2318yes—
110#66945—28no—
111C4⋊C4×D11—28no—
112C4⋊C4×D11—22no—
113C4⋊C4×D11C2314yes—
114#66943—28no—
115#66940—24no—
116#66940—28no—
117#66940—22no—
118#66940C2314yes—
119#66940C2318yes—
120C42×D11—28no—
121C42×D11D414yes—
122C42×D11C2314yes—
123#66922—22no—
124#66922C2314yes—
125C4×Dic22—22no—
126C4×Dic22—28no—
127C4×Dic22C2314yes—
128C11×#106C2318yes—
129C11×C4⋊C8C2314yes—
130C11×#103C2318yes—
131(C2×D11)⋊C8C2318yes—
132#66880C2318yes—
133#66879C2318yes—
134#66874C2318yes—
135#66874C2318yes—
136#66872C2318yes—
137C4⋊(C11⋊C8)C2314yes—
138C2×#3113—111nomaximal, Sylow
139C23×D11C2×D411yescharacteristic
140C2×Q8×C11—21no—
141C2×Q8×C11—24no—
142C2×Q8×C11—22no—
143C2×Q8×C11—44no—
144C2×Q8×C11#4114yes—
145C2×Q8×C11C2412yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—22no—
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158Q8×D11—216no—
159Q8×D11—28no—
160Q8×D11—28no—
161C2×C4×D11—28no—
162C2×C4×D11—24no—
163C2×C4×D11—24no—
164C2×C4×D11—24no—
165C2×C4×D11—24no—
166C2×C4×D11—22no—
167C2×C4×D11—22no—
168C2×C4×D11—44no—
169C2×C4×D11C2×D414yes—
170C2×C4×D11C2×D412yes—
171C2×C4×D11C2×D414yes—
172C2×C4×D11C2412yes—
173C2×Dic22—28no—
174C2×Dic22—24no—
175C2×Dic22—21no—
176C2×Dic22—22no—
177C2×Dic22—22no—
178C2×Dic22—24no—
179C2×Dic22—24no—
180C2×Dic22#4114yes—
181C2×Dic22C2414yes—
182C2×Dic22C2412yes—
183C2×C8×C11—24no—
184C2×C8×C11C2414yes—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—24no—
189C11×C4⋊C4C2414yes—
190C11×C4⋊C4C2412yes—
191C42×C11—24no—
192C42×C11C2×D412yes—
193C42×C11C2412yes—
194#4326—216no—
195(C2×D11)⋊C4—28no—
196C4⋊Dic11—24no—
197C4⋊Dic11—28no—
198C4⋊Dic11—21no—
199C4⋊Dic11—24no—
200C4⋊Dic11—24no—
201C4⋊Dic11C2412yes—
202Dic11⋊C4—24no—
203Dic11⋊C4—24no—
204Dic11⋊C4—28no—
205Dic11⋊C4—24no—
206C4×Dic11—24no—
207C4×Dic11—24no—
208C4×Dic11—28no—
209C4×Dic11—24no—
210C4×Dic11C2×D414yes—
211C4×Dic11C2×D412yes—
212C4×Dic11C2×D414yes—
213C4×Dic11C2412yes—
214C2×C11⋊C8—24no—
215C2×C11⋊C8C2414yes—
216Dic44—216no—
217C2×#533—111no—
218C22×C4×Q8—111no—
219#3113—1116no—
220C2×#483—112no—
221C2×#475—111no—
222C2×#475D1111yescharacteristic, complemented
223C2×#462—111no—
224C2×#462—111no—
225C2×#451—112no—
226C2×#441—112no—
227C2×#441—112no—
228C2×#432—111no—
229C23×C11C22×D411yescharacteristic
230C22×D11—22no—
231C22×D11—22no—
232C22×D11#13714yes—
233C22×D11C22×D412yes—
234Q8×C11—24no—
235Q8×C11—22no—
236Q8×C11—48no—
237Q8×C11C2×#4114yes—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—24no—
243C2×C4×C11—42no—
244C2×C4×C11—44no—
245C2×C4×C11#13714yes—
246C2×C4×C11C22×D412yes—
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D412yes—
249C2×C4×C11C2×#4112yes—
250C2×C4×C11C2×#4112yes—
251C2×C4×C11C2511yescharacteristic
252C2×Dic11—22no—
253C2×Dic11—24no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—24no—
259C2×Dic11—44no—
260C2×Dic11—42no—
261C2×Dic11C22×D412yes—
262C2×Dic11C22×D412yes—
263C2×Dic11C22×D412yes—
264C4×D11—216no—
265C4×D11—28no—
266C4×D11—24no—
267C4×D11—28no—
268C4×D11—22no—
269C4×D11—22no—
270C4×D11—48no—
271Dic22—216no—
272Dic22—24no—
273Dic22—22no—
274Dic22—24no—
275Dic22—24no—
276Dic22—44no—
277Dic22C2×#4114yes—
278C8×C11—24no—
279C11⋊C8—24no—
280C23×Q8—111no—
281C22×Q16—112no—
282C22×Q16—112no—
283#533—118no—
284#533—224no—
285C2×C4⋊Q8—111no—
286C2×C4⋊Q8C2×D1111yescharacteristic
287C2×#125—221no—
288C2×C22⋊Q8—112no—
289C2×C22⋊Q8—221no—
290C2×C4×Q8—111no—
291C2×C4×Q8—118no—
292C2×C4×Q8—111no—
293C2×C4×Q8—112no—
294C2×C4×Q8—111no—
295C2×C4×Q8—221no—
296C2×C4×Q8—221no—
297C2×C4×Q8—224no—
298C2×C4×Q8—221no—
299C2×C4×Q8C2×D1111yescharacteristic
300C2×#117—221no—
301C22×C4⋊C4—111no—
302C22×C4⋊C4—221no—
303C22×C42—111no—
304C22×C42—221no—
305#483—1116no—
306#475—118no—
307#475C2×D1118yescomplemented
308#462—118no—
309#462—118no—
310#451—1116no—
311#441—1116no—
312#441—1116no—
313#432—118no—
314C2×#106—112no—
315C2×#106C2×D1112yes—
316C2×C4⋊C8—111no—
317C2×C4⋊C8C2×D1111yescharacteristic
318C2×#103—112no—
319C2×#103—112no—
320C2×#103—112no—
321C2×#103C2×D1112yes—
322C2×C22⋊C8—112no—
323C2×#97—112no—
324C22×C11#52512yes—
325C22×C11C2×#13712yes—
326C22×C11C2×#13712yes—
327C22×C11C23×D411yescharacteristic
328C2×D11—28no—
329C2×D11—22no—
330C2×D11—22no—
331C2×D11C2×#13714yes—
332C4×C11—24no—
333C4×C11—22no—
334C4×C11—44no—
335C4×C11—42no—
336C4×C11#52512yes—
337C4×C11C2×#13714yes—
338C4×C11C22×#4111yescharacteristic
339C4×C11C22×#4111yescharacteristic
340Dic11—22no—
341Dic11—24no—
342Dic11—22no—
343Dic11—22no—
344Dic11—44no—
345Dic11—42no—
346C22×Q8—21no—
347C22×Q8—114no—
348C22×Q8—111no—
349C22×Q8—112no—
350C22×Q8—221no—
351C22×Q8—222no—
352C22×Q8—224no—
353C22×Q8—224no—
354C22×Q8C22×D1111yescharacteristic
355C23×C4—111no—
356C23×C4—111no—
357C23×C4—111no—
358C23×C4—221no—
359C23×C4—221no—
360C2×Q16—118no—
361C2×Q16—118no—
362C2×Q16—228no—
363C2×Q16—228no—
364C22×C8—112no—
365C22×C8C22×D1112yes—
366C4⋊Q8—22no—
367C4⋊Q8—114no—
368C4⋊Q8—222no—
369C4⋊Q8C22×D1114yes—
370#125—228no—
371C22⋊Q8—118no—
372C22⋊Q8—224no—
373C22⋊Q8—228no—
374C4×Q8—22no—
375C4×Q8—114no—
376C4×Q8—114no—
377C4×Q8—118no—
378C4×Q8—114no—
379C4×Q8—228no—
380C4×Q8—222no—
381C4×Q8—228no—
382C4×Q8—224no—
383C4×Q8—222no—
384C4×Q8—228no—
385C4×Q8—222no—
386C4×Q8C22×D1114yes—
387#117—228no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—114no—
392C2×C4⋊C4—222no—
393C2×C4⋊C4—228no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—222no—
398C2×C4⋊C4—222no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C4⋊C4C22×D1112yes—
404C2×C22⋊C4—222no—
405C2×C42—21no—
406C2×C42—111no—
407C2×C42—111no—
408C2×C42—111no—
409C2×C42—114no—
410C2×C42—114no—
411C2×C42—228no—
412C2×C42—222no—
413C2×C42—221no—
414C2×C42—221no—
415C2×C42—221no—
416C2×C42C22×D1111yescharacteristic
417#106—118no—
418#106C22×D1118yes—
419C4⋊C8—114no—
420C4⋊C8C22×D1114yes—
421#103—118no—
422#103—118no—
423#103—118no—
424#103C22×D1118yes—
425C22⋊C8—118no—
426#97—118no—
427C2×C11#311314yescomplemented
428C2×C11C2×#52511yescharacteristic
429C2×C11C22×#13711yescharacteristic
430C2×C11C22×#13711yescharacteristic
431D11—24no—
432C24—111no—
433C2×Q8—21no—
434C2×Q8—24no—
435C2×Q8—22no—
436C2×Q8—44no—
437C2×Q8—114no—
438C2×Q8—112no—
439C2×Q8—114no—
440C2×Q8—224no—
441C2×Q8—228no—
442C2×Q8—228no—
443C2×Q8—2216no—
444C2×Q8—228no—
445C2×Q8—221no—
446C2×Q8—222no—
447C2×Q8—222no—
448C2×Q8—224no—
449C2×Q8—224no—
450C2×Q8#434314yes—
451C2×Q8C23×D1112yes—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—114no—
459C22×C4—114no—
460C22×C4—112no—
461C22×C4—112no—
462C22×C4—224no—
463C22×C4—224no—
464C22×C4—228no—
465C22×C4—224no—
466C22×C4—221no—
467C22×C4—224no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—221no—
471C22×C4—222no—
472C22×C4—444no—
473C22×C4D4×D1111yescharacteristic
474C22×C4D4×D1111yescharacteristic
475C22×C4C23×D1111yescharacteristic
476Q16—2216no—
477Q16—2216no—
478C2×C8—24no—
479C2×C8—114no—
480C2×C8—224no—
481C2×C8C23×D1114yes—
482C4⋊C4—24no—
483C4⋊C4—24no—
484C4⋊C4—21no—
485C4⋊C4—22no—
486C4⋊C4—112no—
487C4⋊C4—224no—
488C4⋊C4—224no—
489C4⋊C4—224no—
490C4⋊C4—228no—
491C4⋊C4—228no—
492C4⋊C4—221no—
493C4⋊C4—224no—
494C4⋊C4—224no—
495C4⋊C4—224no—
496C4⋊C4C23×D1112yes—
497C4⋊C4C23×D1114yes—
498C22⋊C4—228no—
499C42—24no—
500C42—112no—
501C42—114no—
502C42—114no—
503C42—112no—
504C42—224no—
505C42—224no—
506C42—228no—
507C42—224no—
508C42D4×D1112yes—
509C42C23×D1112yes—
510C11C2×#311311yescharacteristic, complemented, Sylow
511C23—114no—
512C23—112no—
513C23—222no—
514C23—222no—
515C23C2×D4×D1111yescharacteristic
516Q8—24no—
517Q8—22no—
518Q8—48no—
519Q8—114no—
520Q8—2216no—
521Q8—224no—
522Q8—222no—
523Q8—224no—
524Q8—224no—
525Q8—444no—
526Q8C2×#434314yes—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—44no—
533C2×C4—42no—
534C2×C4—112no—
535C2×C4—112no—
536C2×C4—112no—
537C2×C4—228no—
538C2×C4—2216no—
539C2×C4—222no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—224no—
543C2×C4—222no—
544C2×C4—228no—
545C2×C4—224no—
546C2×C4—222no—
547C2×C4—222no—
548C2×C4—222no—
549C2×C4—224no—
550C2×C4—448no—
551C2×C4—442no—
552C2×C4—444no—
553C2×C4#6696814yes—
554C2×C4C2×D4×D1112yes—
555C2×C4C2×D4×D1112yes—
556C2×C4C2×D4×D1111yescharacteristic
557C2×C4C2×#434312yes—
558C2×C4#41×D1112yes—
559C2×C4C24×D1111yescharacteristic
560C8—24no—
561C8—224no—
562C22—114no—
563C22—222no—
564C22—222no—
565C22—228no—
566C22#1062315812yes—
567C22C2×#6696812yes—
568C22D11×#13712yes—
569C22C22×D4×D1111yescharacteristic
570C4—24no—
571C4—22no—
572C4—42no—
573C4—44no—
574C4—222no—
575C4—224no—
576C4—222no—
577C4—222no—
578C4—444no—
579C4—442no—
580C4#1062315812yes—
581C4C2×#6696814yes—
582C4C22×#434311yescharacteristic
583C4C2×#41×D1111yescharacteristic
584C2—224no—
585C2#1307874814yesdirect product factor
586C2C2×#1062315811yescharacteristic
587C2C2×D11×#13711yescharacteristic
588C2C22×#6696811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#475C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#475D11
hypocenterC11C2×#3113
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. #13078748C2direct (N × H)
5. C2×#10622707C2semidirect
6. C2×#10622462C2semidirect
7. C2×#10622644C2semidirect
9. C2×#10622466C2semidirect
10. C2×#10622402C2semidirect
12. C2×C11×#475C2semidirect
38. C11×#475C22semidirect
45. #10622707C22semidirect
46. #10622644C22semidirect
52. #10622466C22semidirect
53. #10622462C22semidirect
56. #10622402C22semidirect
222. C2×#475D11semidirect
307. #475C2×D11semidirect
427. C2×C11#3113semidirect
510. C11C2×#3113semidirect
585. C2#13078748direct (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×C4×Q8×D112
#130787482
C2×#106224752
C2×#106227072
C2×#106224622
C2×#106226442
C2×#106224212
C2×#106224662
C2×#106224022
C2×#106224482
C2×C11×#4752
C2×#311311