Finite Group Databasebeta

← C2×#13079842 #15625901

Subgroups — C2×#13079842 #15625901

Order 2816.

2018 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#10623211C211yesmaximal, characteristic
3#13079842C2116yesmaximal, direct product factor
4C2×#10622315C211yesmaximal, characteristic, complemented
5C2×#10622693C211yesmaximal, characteristic, complemented
6C2×#10622668C211yesmaximal, characteristic, complemented
7C2×#10622422C212yesmaximal, complemented
8C2×#10622390C212yesmaximal
9C2×#10622404C212yesmaximal, complemented
10C2×#10622372C212yesmaximal, complemented
11C2×#10622318C211yesmaximal, characteristic, complemented
12C2×C11×#489C211yesmaximal, characteristic, complemented
13C22×Q8×D11—21no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#124C2211yescharacteristic
16C2×#66999C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×#66997—21no—
19C2×#66991C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21D11×C4⋊Q8—24no—
22D11×C4⋊Q8C2218yescomplemented
23#10623211—24no—
24#10623211C2218yes—
25C2×C4⋊C4×D11—21no—
26C2×C4⋊C4×D11C2212yes—
27C2×#66941—21no—
28C2×#66941C2212yes—
29C2×#66936—21no—
30C2×(C22⋊D11)⋊C4—21no—
31C2×#66932—21no—
32C2×#66930—21no—
33C2×C42×D11C2211yescharacteristic
34C2×#66923C2211yescharacteristic
35C2×#66922C2211yescharacteristic
36C11×#489C2218yescomplemented
37C2×C11×#103C2212yes—
38C2×C11×#102C2212yes—
39C2×C11×#97C2211yescharacteristic
40C2×#66899C2212yes—
41C2×#66896C2212yes—
42C2×(C2×D11)⋊C8C2212yes—
43C2×#66882C2212yes—
44C2×#66881C2212yes—
45C2×Dic11⋊C8C2212yes—
46#10622693C2218yescomplemented
47#10622668C2218yescomplemented
48C2×#66872C2212yes—
49C2×#66871C2212yes—
50C2×#66867C2211yescharacteristic
51#10622422C22116yescomplemented
52#10622404C22116yescomplemented
53#10622390C22116yes—
54#10622372C22116yescomplemented
55#10622318C2218yescomplemented
56#10622315C2218yescomplemented
57C22×Q8×C11—21no—
58C22×Q8×C11C2311yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C23×Dic11—21no—
62C2×Q8×D11—28no—
63C2×Q8×D11—48no—
64C22×C4×D11—22no—
65C22×C4×D11D411yescharacteristic
66C22×C4×D11D411yescharacteristic
67C22×C4×D11C2311yescharacteristic
68C22×Dic22—21no—
69C22×Dic22—22no—
70C22×C8×C11C2312yes—
71C11×C4⋊Q8—22no—
72C11×C4⋊Q8C2314yes—
73C11×#124—22no—
74C11×#124C2314yes—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C42×C11C2311yescharacteristic
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82#66999—22no—
83#66999C2314yes—
84Q8×Dic11—22no—
85Q8×Dic11C2314yes—
86#66997—28no—
87#66991—22no—
88#66991C2314yes—
89D4×Dic11—22no—
90D4×Dic11C2314yes—
91C2×(C2×D11)⋊C4—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11C2312yes—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—22no—
101C2×Dic11⋊C4—22no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11D411yescharacteristic
104C2×C4×Dic11D411yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C22×C11⋊C8C2312yes—
107C4⋊C4×D11—24no—
108C4⋊C4×D11—28no—
109C4⋊C4×D11C2318yes—
110#66941—24no—
111#66941—28no—
112#66941C2318yes—
113#66936—28no—
114(C22⋊D11)⋊C4—28no—
115#66932—28no—
116#66930—28no—
117C42×D11D414yes—
118C42×D11C2314yes—
119#66923—22no—
120#66923C2314yes—
121#66922—22no—
122#66922C2314yes—
123C11×#103C2318yes—
124C11×#102C2318yes—
125C11×#97C2314yes—
126#66899C2318yes—
127#66896C2318yes—
128(C2×D11)⋊C8C2318yes—
129#66882C2318yes—
130#66881C2318yes—
131Dic11⋊C8C2318yes—
132#66872C2318yes—
133#66871C2318yes—
134#66867C2314yes—
135C2×#3239—111nomaximal, Sylow
136C24×C11—21no—
137C23×D11C2×D411yescharacteristic
138C2×Q8×C11—24no—
139C2×Q8×C11—21no—
140C2×Q8×C11—24no—
141C2×Q8×C11—44no—
142C2×Q8×C11C2412yes—
143C2×D4×C11—21no—
144C2×D4×C11—24no—
145C2×D4×C11C2412yes—
146C22×C4×C11—21no—
147C22×C4×C11—22no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C2×C22⋊D11—24no—
152C2×C22⋊D11—44no—
153C22×Dic11—24no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—22no—
157C22×Dic11—44no—
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161Q8×D11—432no—
162C2×C4×D11—24no—
163C2×C4×D11—24no—
164C2×C4×D11—28no—
165C2×C4×D11—24no—
166C2×C4×D11—48no—
167C2×C4×D11C2×D412yes—
168C2×C4×D11C2×D414yes—
169C2×C4×D11C2×D414yes—
170C2×C4×D11C2412yes—
171C2×Dic22—28no—
172C2×Dic22—24no—
173C2×Dic22—44no—
174C2×Dic22—48no—
175C2×C8×C11—24no—
176C2×C8×C11C2414yes—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4C2414yes—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—24no—
182C42×C11C2×D412yes—
183C42×C11C2412yes—
184C22⋊Dic11—24no—
185C22⋊Dic11—24no—
186(C2×D11)⋊C4—24no—
187C4⋊Dic11—24no—
188C4⋊Dic11—22no—
189C4⋊Dic11—24no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11C2412yes—
193C4⋊Dic11C2412yes—
194C4⋊Dic11C2414yes—
195Dic11⋊C4—24no—
196Dic11⋊C4—28no—
197Dic11⋊C4—28no—
198Dic11⋊C4—24no—
199Dic11⋊C4—24no—
200C4×Dic11—24no—
201C4×Dic11C2×D412yes—
202C4×Dic11C2×D414yes—
203C4×Dic11C2×D414yes—
204C4×Dic11C2412yes—
205C2×C11⋊C8—24no—
206C2×C11⋊C8C2414yes—
207C22×C4⋊Q8—111no—
208C2×#529—111no—
209#3239—1116no—
210C2×#501—111no—
211C2×#501—111no—
212C2×#489—111no—
213C2×#489D1111yescharacteristic, complemented
214C2×#484—112no—
215C2×#481—112no—
216C2×#475—112no—
217C2×#474—112no—
218C2×#432—111no—
219C23×C11—22no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11C22×D411yescharacteristic
224C22×D11—22no—
225C22×D11—22no—
226C22×D11#13714yes—
227C22×D11C22×D412yes—
228Q8×C11—24no—
229Q8×C11—48no—
230Q8×C11—42no—
231D4×C11—24no—
232D4×C11—42no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—42no—
238C2×C4×C11—44no—
239C2×C4×C11C22×D412yes—
240C2×C4×C11C22×D412yes—
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C112−1+414yes—
243C2×C4×C11C2511yescharacteristic
244C22⋊D11—48no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—24no—
250C2×Dic11—44no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—48no—
254C2×Dic11AGL(1,ℤ/8)14yes—
255C2×Dic11C22×D412yes—
256C2×Dic11C22×D412yes—
257C2×Dic11C22×D412yes—
258C4×D11—28no—
259C4×D11—24no—
260C4×D11—24no—
261C4×D11—28no—
262C4×D11—416no—
263Dic22—48no—
264Dic22—416no—
265C8×C11—24no—
266C11⋊C8—24no—
267C23×Q8—221no—
268C2×C4⋊Q8—118no—
269C2×C4⋊Q8—112no—
270C2×C4⋊Q8—111no—
271C2×C4⋊Q8—221no—
272C2×C4⋊Q8—224no—
273C2×C4⋊Q8—221no—
274C2×C4⋊Q8C2×D1111yescharacteristic
275#529—118no—
276#529—224no—
277C2×#126—221no—
278C2×#125—111no—
279C2×#124C2×D1111yescharacteristic
280C2×#123—221no—
281C2×C22⋊Q8—111no—
282C2×#121—111no—
283C2×C4×Q8—111no—
284C2×C4×D4—111no—
285C2×C4×D4—221no—
286C2×#117—221no—
287C22×C4⋊C4—112no—
288C22×C4⋊C4—221no—
289C22×C42—111no—
290#501—118no—
291#501—118no—
292#489—118no—
293#489C2×D1118yescomplemented
294#484—1116no—
295#481—1116no—
296#475—1116no—
297#474—1116no—
298#432—118no—
299C2×#107—112no—
300C2×#107—112no—
301C2×#106—112no—
302C2×#106—112no—
303C2×C4⋊C8—112no—
304C2×#103—112no—
305C2×#103C2×D1112yes—
306C2×#102—112no—
307C2×#102C2×D1112yes—
308C2×C22⋊C8—112no—
309C2×#97—111no—
310C2×#97C2×D1111yescharacteristic
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—84no—
315C22×C11#53612yes—
316C22×C11C2×AGL(1,ℤ/8)12yes—
317C22×C11C2×#13712yes—
318C22×C11C23×D411yescharacteristic
319C2×D11—22no—
320C2×D11—28no—
321C2×D11—22no—
322C2×D11C2×#13714yes—
323C4×C11—22no—
324C4×C11—22no—
325C4×C11—42no—
326C4×C11—44no—
327C4×C11#53612yes—
328C4×C11C2×2−1+412yes—
329Dic11—22no—
330Dic11—22no—
331Dic11—44no—
332Dic11—42no—
333Dic11—42no—
334Dic11C2×AGL(1,ℤ/8)14yes—
335C22×Q8—21no—
336C22×Q8—222no—
337C22×Q8—228no—
338C22×Q8—221no—
339C22×Q8—448no—
340C22×Q8C22×D1111yescharacteristic
341C22×D4—221no—
342C22×D4C22×D1111yescharacteristic
343C23×C4—111no—
344C23×C4—111no—
345C23×C4—111no—
346C23×C4—222no—
347C23×C4—221no—
348C22×C8—112no—
349C22×C8C22×D1112yes—
350C4⋊Q8—22no—
351C4⋊Q8—118no—
352C4⋊Q8—114no—
353C4⋊Q8—228no—
354C4⋊Q8—224no—
355C4⋊Q8—228no—
356C4⋊Q8—222no—
357C4⋊Q8C22×D1114yes—
358#126—228no—
359#125—114no—
360#125—222no—
361#124—22no—
362#124C22×D1114yes—
363#123—228no—
364C22⋊Q8—114no—
365C22⋊Q8—222no—
366#121—114no—
367#121—222no—
368C4×Q8—114no—
369C4×Q8—222no—
370C4×D4—114no—
371C4×D4—222no—
372C4×D4—228no—
373#117—228no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—112no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—118no—
379C2×C4⋊C4—224no—
380C2×C4⋊C4—228no—
381C2×C4⋊C4—222no—
382C2×C4⋊C4—222no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4C22×D1112yes—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—221no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C42—111no—
395C2×C42—111no—
396C2×C42—111no—
397C2×C42—114no—
398C2×C42—114no—
399C2×C42—221no—
400C2×C42C22×D1111yescharacteristic
401#107—118no—
402#107—118no—
403#106—118no—
404#106—118no—
405C4⋊C8—118no—
406#103—118no—
407#103C22×D1118yes—
408#102—118no—
409#102C22×D1118yes—
410C22⋊C8—118no—
411#97—114no—
412#97C22×D1114yes—
413C2×C11—82no—
414C2×C11#323914yescomplemented
415C2×C11C2×#53611yescharacteristic
416C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
417C2×C11C22×#13711yescharacteristic
418D11—24no—
419C24—21no—
420C24—111no—
421C2×Q8—21no—
422C2×Q8—24no—
423C2×Q8—24no—
424C2×Q8—44no—
425C2×Q8—228no—
426C2×Q8—224no—
427C2×Q8—444no—
428C2×Q8—448no—
429C2×Q8—4432no—
430C2×Q8C23×D1112yes—
431C2×D4—21no—
432C2×D4—24no—
433C2×D4—224no—
434C2×D4—444no—
435C2×D4C23×D1112yes—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—111no—
439C22×C4—111no—
440C22×C4—111no—
441C22×C4—112no—
442C22×C4—114no—
443C22×C4—114no—
444C22×C4—112no—
445C22×C4—224no—
446C22×C4—224no—
447C22×C4—228no—
448C22×C4—224no—
449C22×C4—224no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—222no—
453C22×C4—448no—
454C22×C4—444no—
455C22×C4D4×D1111yescharacteristic
456C22×C4D4×D1111yescharacteristic
457C22×C4C23×D1111yescharacteristic
458C2×C8—24no—
459C2×C8—114no—
460C2×C8—224no—
461C2×C8C23×D1114yes—
462C4⋊C4—24no—
463C4⋊C4—22no—
464C4⋊C4—114no—
465C4⋊C4—112no—
466C4⋊C4—112no—
467C4⋊C4—228no—
468C4⋊C4—228no—
469C4⋊C4—224no—
470C4⋊C4—224no—
471C4⋊C4—222no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—224no—
475C4⋊C4—224no—
476C4⋊C4—224no—
477C4⋊C4C23×D1114yes—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—224no—
481C22⋊C4—224no—
482C22⋊C4—224no—
483C42—114no—
484C42—112no—
485C42—114no—
486C42—112no—
487C42—224no—
488C42D4×D1112yes—
489C42C23×D1112yes—
490C11C2×#323911yescharacteristic, complemented, Sylow
491C23—22no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—114no—
496C23—112no—
497C23—222no—
498C23—222no—
499C23C2×D4×D1111yescharacteristic
500Q8—24no—
501Q8—48no—
502Q8—42no—
503Q8—448no—
504Q8—4416no—
505D4—24no—
506D4—42no—
507D4—448no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—44no—
513C2×C4—42no—
514C2×C4—114no—
515C2×C4—112no—
516C2×C4—112no—
517C2×C4—112no—
518C2×C4—228no—
519C2×C4—228no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4—224no—
523C2×C4—224no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—224no—
527C2×C4—4416no—
528C2×C4—448no—
529C2×C4—444no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4C2×D4×D1112yes—
533C2×C4C2×D4×D1112yes—
534C2×C4C2×D4×D1111yescharacteristic
535C2×C4#6704314yes—
536C2×C4C24×D1111yescharacteristic
537C8—24no—
538C8—224no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—84no—
543C22—114no—
544C22—228no—
545C22—222no—
546C22—222no—
547C22#1062320612yes—
548C22D11×AGL(1,ℤ/8)12yes—
549C22D11×#13712yes—
550C22C22×D4×D1111yescharacteristic
551C4—22no—
552C4—22no—
553C4—42no—
554C4—44no—
555C4—114no—
556C4—222no—
557C4—222no—
558C4—444no—
559C4—442no—
560C4—442no—
561C4#1062320612yes—
562C4C2×#6704312yes—
563C2—82no—
564C2—224no—
565C2#1307984214yesdirect product factor
566C2C2×#1062320611yescharacteristic
567C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
568C2C2×D11×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#489C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenterC2×#489D11
hypocenterC11C2×#3239
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×D11×C4⋊Q8C2semidirect
3. #13079842C2direct (N × H)
4. C2×#10622315C2semidirect
5. C2×#10622693C2semidirect
6. C2×#10622668C2semidirect
7. C2×#10622422C2semidirect
9. C2×#10622404C2semidirect
10. C2×#10622372C2semidirect
11. C2×#10622318C2semidirect
12. C2×C11×#489C2semidirect
22. D11×C4⋊Q8C22semidirect
36. C11×#489C22semidirect
46. #10622693C22semidirect
47. #10622668C22semidirect
51. #10622422C22semidirect
52. #10622404C22semidirect
54. #10622372C22semidirect
55. #10622318C22semidirect
56. #10622315C22semidirect
213. C2×#489D11semidirect
293. #489C2×D11semidirect
414. C2×C11#3239semidirect
490. C11C2×#3239semidirect
565. C2#13079842direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
C2×#106232112
#130798422
C2×#106223152
C2×#106226932
C2×#106226682
C2×#106224222
C2×#106223902
C2×#106224042
C2×#106223722
C2×#106223182
C2×C11×#4892
C2×#323911