Finite Group Databasebeta

← C2×#13079161 #15623421

Subgroups — C2×#13079161 #15623421

Order 2816.

2118 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623219C211yesmaximal, characteristic
2C2×D11×C4⋊Q8C211yesmaximal, characteristic
3#13079161C2116yesmaximal, direct product factor
4C2×#10622678C211yesmaximal, characteristic, complemented
5C2×#10622315C211yesmaximal, characteristic, complemented
6C2×#10622693C211yesmaximal, characteristic, complemented
7C2×#10622487C212yesmaximal, complemented
8C2×#10622468C212yesmaximal, complemented
9C2×#10622494C212yesmaximal
10C2×#10622474C212yesmaximal
11C2×#10622320C211yesmaximal, characteristic
12C2×C11×#501C211yesmaximal, characteristic, complemented
13C22×Q8×D11—21no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#125C2211yescharacteristic
16C2×#66997—21no—
17C22×#4313C2212yes—
18D11×C4⋊Q8—24no—
19D11×C4⋊Q8C2218yes—
20#10623219—24no—
21#10623219C2218yes—
22C2×#66949—21no—
23C2×#66949—21no—
24C2×#66945C2211yescharacteristic
25C2×#66945C2211yescharacteristic
26C2×C4⋊C4×D11—21no—
27C2×C4⋊C4×D11C2212yes—
28C2×#66941—21no—
29C2×#66941C2212yes—
30C2×#66941C2211yescharacteristic
31C2×#66941C2211yescharacteristic
32C2×#66940—21no—
33C2×#66940—21no—
34C2×C42×D11C2211yescharacteristic
35C2×#66923C2211yescharacteristic
36C2×#66922C2211yescharacteristic
37C11×#501C2218yescomplemented
38C2×C11×#107C2212yes—
39C2×C11×#106C2212yes—
40C2×C11×#97C2211yescharacteristic
41C2×#66882C2212yes—
42C2×#66881C2212yes—
43C2×C8×Dic11C2212yes—
44#10622693C2218yescomplemented
45#10622678C2218yescomplemented
46C2×#66872C2212yes—
47C2×#66872C2212yes—
48C2×#66871C2212yes—
49C2×#66871C2212yes—
50C2×#66867C2211yescharacteristic
51#10622494C22116yes—
52#10622487C22116yescomplemented
53#10622474C22116yes—
54#10622468C22116yescomplemented
55#10622320C2218yes—
56#10622315C2218yescomplemented
57C22×Q8×C11—21no—
58C2×Q8×D11—28no—
59C2×Q8×D11—48no—
60C22×C4×D11—22no—
61C22×C4×D11D411yescharacteristic
62C22×C4×D11D411yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×Dic22—21no—
65C22×Dic22—21no—
66C22×Dic22—21no—
67C22×Dic22—22no—
68C22×C8×C11C2312yes—
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8C2314yes—
71C11×#125—22no—
72C11×#125C2314yes—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80#66997—28no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11C2312yes—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—22no—
92C2×Dic11⋊C4—22no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11D411yescharacteristic
96C2×C4×Dic11D411yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C22×C11⋊C8C2312yes—
99C2×#4313Q8116yescomplemented
100C2×#4313C2318yes—
101#66949—28no—
102#66949—28no—
103#66945—22no—
104#66945—22no—
105#66945C2314yes—
106#66945C2314yes—
107C4⋊C4×D11—24no—
108C4⋊C4×D11—28no—
109C4⋊C4×D11C2318yes—
110#66941—24no—
111#66941—28no—
112#66941—22no—
113#66941—22no—
114#66941C2314yes—
115#66941C2318yes—
116#66941C2314yes—
117#66940—28no—
118#66940—28no—
119C42×D11D414yes—
120C42×D11C2314yes—
121#66923—22no—
122#66923C2314yes—
123#66922—22no—
124#66922C2314yes—
125C11×#107C2318yes—
126C11×#106C2318yes—
127C11×#97C2314yes—
128#66882C2318yes—
129#66881C2318yes—
130C8×Dic11C2318yes—
131#66872C2318yes—
132#66872C2318yes—
133#66871C2318yes—
134#66871C2318yes—
135#66867C2314yes—
136C2×#3165—111nomaximal, Sylow
137C23×D11C2×D411yescharacteristic
138C2×Q8×C11—24no—
139C2×Q8×C11—44no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—22no—
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152Q8×D11—432no—
153C2×C4×D11—24no—
154C2×C4×D11—24no—
155C2×C4×D11—28no—
156C2×C4×D11—48no—
157C2×C4×D11C2×D414yes—
158C2×C4×D11C2×D414yes—
159C2×C4×D11C2×D412yes—
160C2×C4×D11C2×Q818yes—
161C2×C4×D11C2412yes—
162C2×Dic22—24no—
163C2×Dic22—24no—
164C2×Dic22—28no—
165C2×Dic22—24no—
166C2×Dic22—44no—
167C2×Dic22—44no—
168C2×Dic22—48no—
169C2×Dic22—44no—
170C2×C8×C11C2×Q818yescomplemented
171C2×C8×C11C2414yes—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C2412yes—
179C11×C4⋊C4C2414yes—
180C11×C4⋊C4C2412yes—
181C42×C11C2×D412yes—
182C42×C11C2412yes—
183(C2×D11)⋊C4—24no—
184(C2×D11)⋊C4—24no—
185C4⋊Dic11—22no—
186C4⋊Dic11—24no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11C2412yes—
190C4⋊Dic11C2414yes—
191C4⋊Dic11C2412yes—
192Dic11⋊C4—24no—
193Dic11⋊C4—24no—
194Dic11⋊C4—28no—
195Dic11⋊C4—28no—
196Dic11⋊C4—24no—
197Dic11⋊C4—24no—
198C4×Dic11—24no—
199C4×Dic11—24no—
200C4×Dic11C2×D412yes—
201C4×Dic11C2×D414yes—
202C4×Dic11C2×D414yes—
203C4×Dic11C2412yes—
204C2×C11⋊C8C2×Q818yescomplemented
205C2×C11⋊C8C2414yes—
206#4313C2×Q8132yescomplemented
207C2×#533—111no—
208C22×C4⋊Q8—111no—
209#3165—1116no—
210C2×#501—111no—
211C2×#501—111no—
212C2×#501—111no—
213C2×#501D1111yescharacteristic, complemented
214C2×#500—112no—
215C2×#498—112no—
216C2×#428—112no—
217C2×#428—112no—
218C2×C4×M16—111no—
219C23×C11C22×D411yescharacteristic
220C22×D11—22no—
221C22×D11—22no—
222C22×D11C4⋊Q814yes—
223C22×D11C22×D412yes—
224Q8×C11—48no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—44no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11C22×D412yes—
234C2×C4×C11C22×D412yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×Q814yes—
237C2×C4×C11C2511yescharacteristic
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—24no—
241C2×Dic11—44no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11C4⋊Q814yes—
245C2×Dic11AGL(1,ℤ/8)14yes—
246C2×Dic11#13714yes—
247C2×Dic11C22×D412yes—
248C2×Dic11C22×D412yes—
249C2×Dic11C22×D412yes—
250C4×D11—28no—
251C4×D11—28no—
252C4×D11—416no—
253C4×D11C4⋊Q818yes—
254C4×D11C22×Q818yes—
255Dic22—48no—
256Dic22—48no—
257Dic22—416no—
258Dic22—48no—
259C8×C11C22×Q818yescomplemented
260C11⋊C8C22×Q818yescomplemented
261C23×Q8—221no—
262C22×M16—112no—
263#533—118no—
264#533—224no—
265C2×C4⋊Q8—118no—
266C2×C4⋊Q8—111no—
267C2×C4⋊Q8—112no—
268C2×C4⋊Q8—111no—
269C2×C4⋊Q8—111no—
270C2×C4⋊Q8—221no—
271C2×C4⋊Q8—224no—
272C2×C4⋊Q8—221no—
273C2×C4⋊Q8C2×D1111yescharacteristic
274C2×#125—111no—
275C2×#125C2×D1111yescharacteristic
276C2×C22⋊Q8—221no—
277C2×C22⋊Q8—221no—
278C2×C4×Q8—221no—
279C2×C4×Q8—221no—
280C2×#117—111no—
281C2×#117—111no—
282C22×C4⋊C4—112no—
283C22×C4⋊C4—221no—
284C22×C42—111no—
285#501—118no—
286#501—118no—
287#501—118no—
288#501C2×D1118yescomplemented
289#500—1116no—
290#498—1116no—
291#428—1116no—
292#428—1116no—
293C2×#107—112no—
294C2×#107—112no—
295C2×#107—112no—
296C2×#107C2×D1112yes—
297C2×#106—112no—
298C2×#106—112no—
299C2×#106—112no—
300C2×#106C2×D1112yes—
301C4×M16—118no—
302C2×#97—111no—
303C2×#97C2×D1111yescharacteristic
304C2×C4×C8—112no—
305C22×C11C2×C4⋊Q812yes—
306C22×C11C2×AGL(1,ℤ/8)12yes—
307C22×C11C2×#13712yes—
308C22×C11C23×D411yescharacteristic
309C2×D11—28no—
310C2×D11—22no—
311C2×D11—22no—
312C2×D11C2×C4⋊Q814yes—
313C4×C11—22no—
314C4×C11—22no—
315C4×C11—44no—
316C4×C11—42no—
317C4×C11—42no—
318C4×C11C2×C4⋊Q812yes—
319C4×C11C23×Q812yes—
320Dic11—44no—
321Dic11—42no—
322Dic11—42no—
323Dic11C2×C4⋊Q814yes—
324Dic11C2×AGL(1,ℤ/8)14yes—
325Dic11C2×#13714yes—
326C22×Q8—21no—
327C22×Q8—221no—
328C22×Q8—221no—
329C22×Q8—222no—
330C22×Q8—228no—
331C22×Q8—221no—
332C22×Q8—448no—
333C23×C4—111no—
334C23×C4—111no—
335C23×C4—111no—
336C23×C4—222no—
337C2×M16—1116no—
338C2×M16—118no—
339C22×C8—112no—
340C22×C8C22×D1112yes—
341C4⋊Q8—22no—
342C4⋊Q8—118no—
343C4⋊Q8—114no—
344C4⋊Q8—114no—
345C4⋊Q8—114no—
346C4⋊Q8—228no—
347C4⋊Q8—224no—
348C4⋊Q8—222no—
349C4⋊Q8—222no—
350C4⋊Q8—228no—
351C4⋊Q8—222no—
352C4⋊Q8C22×D1114yes—
353#125—22no—
354#125—114no—
355#125—222no—
356#125C22×D1114yes—
357C22⋊Q8—228no—
358C22⋊Q8—228no—
359C4×Q8—228no—
360C4×Q8—228no—
361#117—114no—
362#117—114no—
363#117—222no—
364#117—222no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—112no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—118no—
372C2×C4⋊C4—224no—
373C2×C4⋊C4—228no—
374C2×C4⋊C4—222no—
375C2×C4⋊C4—222no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4C22×D1112yes—
382C2×C4⋊C4C22×D1111yescharacteristic
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C22⋊C4—221no—
385C2×C22⋊C4—221no—
386C2×C42—111no—
387C2×C42—111no—
388C2×C42—111no—
389C2×C42—114no—
390C2×C42—114no—
391C2×C42—221no—
392C2×C42—221no—
393C2×C42C22×D1111yescharacteristic
394#107—118no—
395#107—118no—
396#107—118no—
397#107C22×D1118yes—
398#106—118no—
399#106—118no—
400#106—118no—
401#106C22×D1118yes—
402#97—114no—
403#97C22×D1114yes—
404C4×C8—118no—
405C2×C11#316514yescomplemented
406C2×C11C22×C4⋊Q811yescharacteristic
407C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
408C2×C11C22×#13711yescharacteristic
409D11—24no—
410C24—111no—
411C2×Q8—24no—
412C2×Q8—44no—
413C2×Q8—224no—
414C2×Q8—224no—
415C2×Q8—228no—
416C2×Q8—224no—
417C2×Q8—444no—
418C2×Q8—448no—
419C2×Q8—444no—
420C2×Q8—444no—
421C2×Q8—4432no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—111no—
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—112no—
429C22×C4—118no—
430C22×C4—112no—
431C22×C4—114no—
432C22×C4—114no—
433C22×C4—224no—
434C22×C4—224no—
435C22×C4—228no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—222no—
439C22×C4—448no—
440C22×C4D4×D1111yescharacteristic
441C22×C4D4×D1111yescharacteristic
442C22×C4C23×D1111yescharacteristic
443M16—1132no—
444C2×C8—118no—
445C2×C8—114no—
446C2×C8Q8×D1118yescomplemented
447C2×C8C23×D1114yes—
448C4⋊C4—24no—
449C4⋊C4—24no—
450C4⋊C4—24no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—112no—
455C4⋊C4—114no—
456C4⋊C4—112no—
457C4⋊C4—228no—
458C4⋊C4—228no—
459C4⋊C4—224no—
460C4⋊C4—224no—
461C4⋊C4—222no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—224no—
465C4⋊C4—224no—
466C4⋊C4—224no—
467C4⋊C4C23×D1112yes—
468C4⋊C4C23×D1114yes—
469C4⋊C4C23×D1112yes—
470C22⋊C4—224no—
471C22⋊C4—224no—
472C42—114no—
473C42—114no—
474C42—112no—
475C42—112no—
476C42—224no—
477C42—224no—
478C42D4×D1112yes—
479C42C23×D1112yes—
480C11C2×#316511yescharacteristic, complemented, Sylow
481C23—114no—
482C23—112no—
483C23—222no—
484C23—222no—
485C23C2×D4×D1111yescharacteristic
486Q8—48no—
487Q8—448no—
488Q8—4416no—
489Q8—448no—
490Q8—448no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—44no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—114no—
500C2×C4—114no—
501C2×C4—114no—
502C2×C4—112no—
503C2×C4—112no—
504C2×C4—112no—
505C2×C4—118no—
506C2×C4—118no—
507C2×C4—228no—
508C2×C4—228no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—224no—
512C2×C4—4416no—
513C2×C4—444no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4C2×D4×D1112yes—
517C2×C4C2×D4×D1112yes—
518C2×C4C2×D4×D1111yescharacteristic
519C2×C4C2×Q8×D1114yes—
520C2×C4C24×D1111yescharacteristic
521C8—118no—
522C8C2×Q8×D1118yescomplemented
523C22—114no—
524C22—228no—
525C22—222no—
526C22—222no—
527C22D11×C4⋊Q812yes—
528C22D11×AGL(1,ℤ/8)12yes—
529C22D11×#13712yes—
530C22C22×D4×D1111yescharacteristic
531C4—22no—
532C4—22no—
533C4—44no—
534C4—42no—
535C4—42no—
536C4—114no—
537C4—114no—
538C4—114no—
539C4—444no—
540C4—442no—
541C4—442no—
542C4D11×C4⋊Q812yes—
543C4C22×Q8×D1112yes—
544C2—224no—
545C2#1307916114yesdirect product factor
546C2C2×D11×C4⋊Q811yescharacteristic
547C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
548C2C2×D11×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#501C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#501D11
hypocenterC11C2×#3165
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
3. #13079161C2direct (N × H)
4. C2×#10622678C2semidirect
5. C2×#10622315C2semidirect
6. C2×#10622693C2semidirect
7. C2×#10622487C2semidirect
8. C2×#10622468C2semidirect
12. C2×C11×#501C2semidirect
37. C11×#501C22semidirect
44. #10622693C22semidirect
45. #10622678C22semidirect
52. #10622487C22semidirect
54. #10622468C22semidirect
56. #10622315C22semidirect
99. C2×#4313Q8semidirect
170. C2×C8×C11C2×Q8semidirect
204. C2×C11⋊C8C2×Q8semidirect
206. #4313C2×Q8semidirect
213. C2×#501D11semidirect
259. C8×C11C22×Q8semidirect
260. C11⋊C8C22×Q8semidirect
288. #501C2×D11semidirect
405. C2×C11#3165semidirect
446. C2×C8Q8×D11semidirect
480. C11C2×#3165semidirect
522. C8C2×Q8×D11semidirect
545. C2#13079161direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232192
C2×D11×C4⋊Q82
#130791612
C2×#106226782
C2×#106223152
C2×#106226932
C2×#106224872
C2×#106224682
C2×#106224942
C2×#106224742
C2×#106223202
C2×C11×#5012
C2×#316511