Finite Group Databasebeta

← C2×#13081595 #15634672

Subgroups — C2×#13081595 #15634672

Order 2816.

2238 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623098C211yesmaximal, characteristic, complemented
2C2×#10623084C211yesmaximal, characteristic
3#13081595C2116yesmaximal, direct product factor
4C2×#10622306C211yesmaximal, characteristic, complemented
5C2×#10622788C212yesmaximal, complemented
6C2×#10622640C211yesmaximal, characteristic, complemented
7C2×#10622375C212yesmaximal, complemented
8C2×#10622632C211yesmaximal, characteristic, complemented
9C2×#10622431C212yesmaximal, complemented
10C2×C8×Dic22C211yesmaximal, characteristic, complemented
11C2×#10622465C212yesmaximal, complemented
12C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
13C22×#4339—21no—
14C22×C11×SD16C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66997C2212yes—
18C22×#4325C2212yes—
19C2×#66993C2212yes—
20C22×#4324C2212yes—
21C2×#66983—21no—
22C22×#4314C2212yes—
23C22×#4314C2212yes—
24#10623098—24no—
25#10623098C2218yescomplemented
26#10623084—24no—
27#10623084C2218yes—
28C2×#66946C2212yes—
29C2×#66942—22no—
30C2×#66940C2212yes—
31C2×#66937—22no—
32C2×#66927C2211yescharacteristic
33C2×#66923—21no—
34C2×#66922C2211yescharacteristic
35C2×C4×Dic22—21no—
36C2×C4×Dic22C2211yescharacteristic
37C4×C11×SD16C2218yescomplemented
38C2×C11×#106C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#102C2211yescharacteristic
41C2×C4×C8×C11C2211yescharacteristic
42#10622788C22116yescomplemented
43C2×Dic11⋊C8C2212yes—
44C2×C8×Dic11C2212yes—
45#10622640C2218yescomplemented
46#10622632C2218yescomplemented
47C2×#66874C2212yes—
48C2×#66873C2212yes—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622465C22116yescomplemented
51#10622431C22116yescomplemented
52#10622375C22116yescomplemented
53#10622306C2218yescomplemented
54C8×Dic22C2218yescomplemented
55C22×Q8×C11C2311yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C22×C22⋊D11—22no—
59C22×C22⋊D11—22no—
60C2×#4339—28no—
61C2×#4339—48no—
62C22×D44—21no—
63C22×D44—21no—
64C22×D44C2312yes—
65C22×C4×D11—22no—
66C22×Dic22D411yescharacteristic
67C22×Dic22C2312yes—
68C2×C11×SD16—24no—
69C2×C11×SD16C2314yes—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C4×Q8×C11—22no—
73C4×Q8×C11C2314yes—
74C4×D4×C11—22no—
75C4×D4×C11C2314yes—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82#66997—24no—
83#66997C2318yes—
84C2×#4325—44no—
85C2×#4325C2318yes—
86#66993—24no—
87#66993C2318yes—
88C2×#4324—44no—
89C2×#4324C2318yes—
90#66983—28no—
91C2×(C2×D11)⋊C4—22no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11D411yescharacteristic
95C2×Dic11⋊C4—22no—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4D412yes—
99C2×C4×Dic11—22no—
100C2×C4×Dic11C2312yes—
101C22×C11⋊C8C2312yes—
102C2×#4314—28no—
103C2×#4314—44no—
104C2×#4314C2318yes—
105C2×#4314C2318yes—
106#66946—24no—
107#66946C2318yes—
108#66942—216no—
109#66940—24no—
110#66940C2318yes—
111#66937—216no—
112#66927—22no—
113#66927C2314yes—
114#66923—28no—
115#66922—22no—
116#66922C2314yes—
117C4×Dic22—28no—
118C4×Dic22D414yes—
119C4×Dic22C2314yes—
120C11×#106C2314yes—
121C11×#103C2314yes—
122C11×#102C2314yes—
123C4×C8×C11C2314yes—
124Dic11⋊C8C2318yes—
125C8×Dic11C2318yes—
126#66874C2318yes—
127#66873C2318yes—
128C4⋊(C11⋊C8)C2314yes—
129C2×#3392—111nomaximal, Sylow
130C24×C11—21no—
131C23×D11—22no—
132C2×Q8×C11—21no—
133C2×Q8×C11—22no—
134C2×Q8×C11—22no—
135C2×Q8×C11C2412yes—
136C2×D4×C11—21no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11C2412yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—24no—
144C22×C4×C11—44no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C2×C22⋊D11—28no—
149C2×C22⋊D11—28no—
150C2×C22⋊D11—48no—
151C2×C22⋊D11—84no—
152C22×Dic11—22no—
153C22×Dic11C2×D412yes—
154C22×Dic11C2×D412yes—
155#4339—432no—
156C2×D44—22no—
157C2×D44—24no—
158C2×D44—24no—
159C2×D44—24no—
160C2×D44—24no—
161C2×D44—44no—
162C2×D44—82no—
163C2×D44C2414yes—
164C2×C4×D11—28no—
165C2×C4×D11—48no—
166C2×Dic22—22no—
167C2×Dic22—24no—
168C2×Dic22—24no—
169C2×Dic22SD1618yescomplemented
170C2×Dic22C2×D414yes—
171C2×Dic22C2414yes—
172C11×SD16—28no—
173C2×C8×C11—22no—
174C2×C8×C11#4114yescomplemented
175C2×C8×C11C2412yes—
176C2×C8×C11C2412yes—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—24no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4C2412yes—
181C11×C4⋊C4C2412yes—
182C11×C22⋊C4—24no—
183C42×C11—24no—
184C42×C11C2×D412yes—
185C42×C11C2412yes—
186#4325—48no—
187#4324—48no—
188(C2×D11)⋊C4—28no—
189C4⋊Dic11—24no—
190C4⋊Dic11—24no—
191C4⋊Dic11C2×D414yes—
192Dic11⋊C4—28no—
193Dic11⋊C4—28no—
194Dic11⋊C4—28no—
195Dic11⋊C4C2×D418yes—
196C4×Dic11—28no—
197C4×Dic11C2×D414yes—
198C4×Dic11C2414yes—
199C2×C11⋊C8—24no—
200C2×C11⋊C8C2414yes—
201#4314—216no—
202#4314—48no—
203C2×#557—111no—
204C2×#550—111no—
205#3392—1116no—
206C2×#492—111no—
207C2×#492—112no—
208C2×#460—112no—
209C2×#460—111no—
210C2×#461—112no—
211C2×#461—111no—
212C2×C8×Q8—111no—
213C2×C4×SD16—112no—
214C2×C4×SD16D1111yescharacteristic, complemented
215C23×C11—22no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11C22×D411yescharacteristic
220C22×D11—24no—
221C22×D11—44no—
222C22×D11—44no—
223C22×D11—44no—
224Q8×C11—22no—
225Q8×C11—22no—
226Q8×C11—42no—
227D4×C11—22no—
228D4×C11—22no—
229D4×C11—42no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—48no—
238C2×C4×C11C2×SD1614yes—
239C2×C4×C11C22×D412yes—
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C22×D412yes—
242C2×C4×C11C2×#4112yes—
243C2×C4×C11H(5,𝔽2)12yes—
244C2×C4×C11C2511yescharacteristic
245C22⋊D11—416no—
246C22⋊D11—88no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—44no—
250C2×Dic11C2×SD1618yes—
251C2×Dic11C22×D414yes—
252C2×Dic11C22×D414yes—
253D44—24no—
254D44—24no—
255D44—44no—
256D44—48no—
257D44—84no—
258C4×D11—416no—
259Dic22—24no—
260Dic22—24no—
261Dic22—44no—
262Dic22C2×SD16116yescomplemented
263C8×C11—22no—
264C8×C11C2×#4114yescomplemented
265C11⋊C8—24no—
266C22×#41—221no—
267C22×SD16—112no—
268C22×SD16—112no—
269C22×SD16—112no—
270C22×SD16—112no—
271C22×SD16C2×D1111yescharacteristic
272#557—118no—
273#557—224no—
274#550—118no—
275#550—224no—
276C2×C4⋊Q8—112no—
277C2×C4⋊Q8—111no—
278C2×#127—112no—
279C2×#127—111no—
280C2×#125—221no—
281C2×#125—222no—
282C2×#121—222no—
283C2×#121—221no—
284C2×C4×Q8—111no—
285C2×C4×Q8—112no—
286C2×C4×Q8—221no—
287C2×C4×Q8C2×D1111yescharacteristic
288C2×C4×D4—112no—
289C2×C4×D4C2×D1111yescharacteristic
290#492—1116no—
291#492—118no—
292#461—118no—
293#461—1116no—
294#460—118no—
295#460—1116no—
296C8×Q8—118no—
297C4×SD16—1116no—
298C4×SD16C2×D1118yescomplemented
299C2×#106C2×D1111yescharacteristic
300C2×C4⋊C8—112no—
301C2×C4⋊C8—111no—
302C2×#103—112no—
303C2×#103C2×D1111yescharacteristic
304C2×#102—112no—
305C2×#102C2×D1111yescharacteristic
306C2×C4×C8—112no—
307C2×C4×C8C2×D1111yescharacteristic
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—84no—
312C22×C11#55012yes—
313C22×C11C22×SD1612yes—
314C22×C11#57712yes—
315C22×C11C23×D411yescharacteristic
316C2×D11—44no—
317C2×D11—44no—
318C2×D11—44no—
319C2×D11—88no—
320C4×C11—22no—
321C4×C11—42no—
322C4×C11—42no—
323C4×C11—42no—
324C4×C11#55012yes—
325C4×C11C22×SD1614yes—
326C4×C11C22×#4111yescharacteristic
327C4×C11C2×H(5,𝔽2)11yescharacteristic
328Dic11—24no—
329Dic11—44no—
330Dic11C22×SD1618yes—
331C2×#41—228no—
332C2×#41—448no—
333C22×Q8—111no—
334C22×Q8—112no—
335C22×Q8C22×D1111yescharacteristic
336C22×D4—112no—
337C22×D4—222no—
338C22×D4—222no—
339C22×D4—221no—
340C22×D4—221no—
341C22×D4C22×D1111yescharacteristic
342C23×C4—21no—
343C23×C4—222no—
344C2×SD16—24no—
345C2×SD16—118no—
346C2×SD16—118no—
347C2×SD16—118no—
348C2×SD16—118no—
349C2×SD16—228no—
350C2×SD16—444no—
351C2×SD16—444no—
352C2×SD16—444no—
353C2×SD16C22×D1114yes—
354C22×C8—112no—
355C22×C8C22×D1111yescharacteristic
356C22×C8C22×D1111yescharacteristic
357C4⋊Q8—118no—
358C4⋊Q8—114no—
359C4⋊Q8—224no—
360C4⋊Q8—222no—
361#127—118no—
362#127—114no—
363#127—224no—
364#127—222no—
365#125—228no—
366#125—2216no—
367#121—2216no—
368#121—228no—
369C4×Q8—22no—
370C4×Q8—114no—
371C4×Q8—114no—
372C4×Q8—118no—
373C4×Q8—228no—
374C4×Q8—224no—
375C4×Q8C22×D1114yes—
376C4×D4—22no—
377C4×D4—118no—
378C4×D4—224no—
379C4×D4C22×D1114yes—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—112no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—222no—
384C2×C4⋊C4—222no—
385C2×C4⋊C4—222no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—222no—
392C2×C42—21no—
393C2×C42—112no—
394C2×C42—222no—
395C2×C42C22×D1111yescharacteristic
396#106C22×D1114yes—
397C4⋊C8—118no—
398C4⋊C8—114no—
399#103—118no—
400#103C22×D1114yes—
401#102—118no—
402#102C22×D1114yes—
403C4×C8—118no—
404C4×C8C22×D1114yes—
405C2×C11—82no—
406C2×C11#339214yescomplemented
407C2×C11C2×#55011yescharacteristic
408C2×C11C23×SD1611yescharacteristic
409C2×C11C2×#57711yescharacteristic
410D11—84no—
411C24—21no—
412C24—222no—
413#41—4432no—
414C2×Q8—21no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—118no—
418C2×Q8—114no—
419C2×Q8—114no—
420C2×Q8—222no—
421C2×Q8—224no—
422C2×Q8—224no—
423C2×Q8C23×D1112yes—
424C2×D4—22no—
425C2×D4—21no—
426C2×D4—22no—
427C2×D4—114no—
428C2×D4—228no—
429C2×D4—228no—
430C2×D4—224no—
431C2×D4—222no—
432C2×D4—224no—
433C2×D4—224no—
434C2×D4—224no—
435C2×D4—448no—
436C2×D4—444no—
437C2×D4—882no—
438C2×D4—884no—
439C2×D4C23×D1112yes—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—24no—
444C22×C4—44no—
445C22×C4—112no—
446C22×C4—112no—
447C22×C4—228no—
448C22×C4—222no—
449C22×C4—448no—
450C22×C4D4×D1111yescharacteristic
451C22×C4D4×D1111yescharacteristic
452C22×C4C23×D1111yescharacteristic
453SD16—28no—
454SD16—2216no—
455SD16—448no—
456SD16—448no—
457SD16—448no—
458C2×C8—22no—
459C2×C8—114no—
460C2×C8—224no—
461C2×C8#433914yescomplemented
462C2×C8C23×D1112yes—
463C2×C8C23×D1112yes—
464C4⋊C4—24no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—118no—
468C4⋊C4—114no—
469C4⋊C4—228no—
470C4⋊C4—228no—
471C4⋊C4—228no—
472C4⋊C4—224no—
473C4⋊C4—224no—
474C4⋊C4C23×D1112yes—
475C4⋊C4C23×D1112yes—
476C22⋊C4—24no—
477C22⋊C4—228no—
478C42—24no—
479C42—114no—
480C42—114no—
481C42—228no—
482C42D4×D1112yes—
483C42C23×D1112yes—
484C11C2×#339211yescharacteristic, complemented, Sylow
485C23—22no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—224no—
490C23—444no—
491C23—444no—
492C23—444no—
493C23C2×D4×D1111yescharacteristic
494Q8—22no—
495Q8—22no—
496Q8—42no—
497Q8—1116no—
498Q8—224no—
499Q8—224no—
500Q8—444no—
501D4—22no—
502D4—22no—
503D4—42no—
504D4—224no—
505D4—224no—
506D4—4416no—
507D4—448no—
508D4—444no—
509D4—884no—
510D4—888no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—48no—
519C2×C4—118no—
520C2×C4—114no—
521C2×C4—114no—
522C2×C4—224no—
523C2×C4—224no—
524C2×C4—4416no—
525C2×C4—444no—
526C2×C4SD16×D1114yes—
527C2×C4C2×#433912yes—
528C2×C4C2×D4×D1112yes—
529C2×C4C2×D4×D1112yes—
530C2×C4C2×D4×D1111yescharacteristic
531C2×C4#6704212yes—
532C2×C4C24×D1111yescharacteristic
533C8—22no—
534C8—224no—
535C8C2×#433914yescomplemented
536C22—42no—
537C22—42no—
538C22—42no—
539C22—84no—
540C22—444no—
541C22—444no—
542C22—444no—
543C22—888no—
544C22#1062308412yes—
545C22C2×SD16×D1112yes—
546C22#1062330112yes—
547C22C22×D4×D1111yescharacteristic
548C4—22no—
549C4—42no—
550C4—42no—
551C4—42no—
552C4—118no—
553C4—224no—
554C4—444no—
555C4#1062308412yes—
556C4C2×SD16×D1114yes—
557C4C22×#433911yescharacteristic
558C4C2×#6704211yescharacteristic
559C2—82no—
560C2—884no—
561C2#1308159514yesdirect product factor
562C2C2×#1062308411yescharacteristic
563C2C22×SD16×D1111yescharacteristic
564C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC2×#10623084C2
hypercenterC2×C4×SD16D11
hypocenterC11C2×#3392
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#10623098C2semidirect
3. #13081595C2direct (N × H)
4. C2×#10622306C2semidirect
5. C2×#10622788C2semidirect
6. C2×#10622640C2semidirect
7. C2×#10622375C2semidirect
8. C2×#10622632C2semidirect
9. C2×#10622431C2semidirect
10. C2×C8×Dic22C2semidirect
11. C2×#10622465C2semidirect
12. C2×C4×C11×SD16C2semidirect
25. #10623098C22semidirect
37. C4×C11×SD16C22semidirect
42. #10622788C22semidirect
45. #10622640C22semidirect
46. #10622632C22semidirect
50. #10622465C22semidirect
51. #10622431C22semidirect
52. #10622375C22semidirect
53. #10622306C22semidirect
54. C8×Dic22C22semidirect
169. C2×Dic22SD16semidirect
174. C2×C8×C11#41semidirect
214. C2×C4×SD16D11semidirect
262. Dic22C2×SD16semidirect
264. C8×C11C2×#41semidirect
298. C4×SD16C2×D11semidirect
406. C2×C11#3392semidirect
461. C2×C8#4339semidirect
484. C11C2×#3392semidirect
535. C8C2×#4339semidirect
561. C2#13081595direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230982
C2×#106230842
#130815952
C2×#106223062
C2×#106227882
C2×#106226402
C2×#106223752
C2×#106226322
C2×#106224312
C2×C8×Dic222
C2×#106224652
C2×C4×C11×SD162
C2×#339211