Finite Group Databasebeta

← C2×#13080951 #15630715

Subgroups — C2×#13080951 #15630715

Order 2816.

2210 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623261C211yesmaximal, characteristic, complemented
2C2×#10623108C211yesmaximal, characteristic
3#13080951C2116yesmaximal, direct product factor
4C2×#10622701C211yesmaximal, characteristic, complemented
5C2×#10622495C212yesmaximal, complemented
6C2×#10622499C212yesmaximal, complemented
7C2×#10622461C211yesmaximal, characteristic, complemented
8C2×#10622423C212yesmaximal, complemented
9C2×C4×#4326C211yesmaximal, characteristic, complemented
10C2×#10622451C211yesmaximal, characteristic, complemented
11C2×#10622416C212yesmaximal, complemented
12C2×C11×#477C211yesmaximal, characteristic, complemented
13C22×#4343C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C2×#66999—22no—
17C22×#4326C2211yescharacteristic
18C22×#4314C2212yes—
19C22×#4313C2212yes—
20#10623261—24no—
21#10623261C2218yescomplemented
22#10623108—24no—
23#10623108C2218yes—
24C2×#66950C2212yes—
25C2×#66948—22no—
26C2×#66948C2212yes—
27C2×#66946—21no—
28C2×C4⋊C4×D11C2212yes—
29C2×#66943—21no—
30C2×#66927—21no—
31C2×#66927C2211yescharacteristic
32C2×C4×D44—21no—
33C2×C4×D44C2211yescharacteristic
34C2×C4×Dic22C2211yescharacteristic
35C11×#477C2218yescomplemented
36C2×C11×#107C2212yes—
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#103C2212yes—
39C2×#66899C2211yescharacteristic
40C2×#66885C2212yes—
41C2×(C2×D11)⋊C8C2212yes—
42#10622701C2218yescomplemented
43C4×#4326C2218yescomplemented
44C2×#66874C2211yescharacteristic
45C2×#66873C2212yes—
46C2×#66873C2212yes—
47C2×#66871C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622499C22116yescomplemented
50#10622495C22116yescomplemented
51#10622461C2218yescomplemented
52#10622451C2218yescomplemented
53#10622423C22116yescomplemented
54#10622416C22116yescomplemented
55C22×Q8×C11—21no—
56C22×Q8×C11C2311yescharacteristic
57C2×#4343—24no—
58C2×#4343—28no—
59C2×#4343—44no—
60C2×#4343C2318yes—
61C22×D44—22no—
62C22×D44—21no—
63C22×D44—22no—
64C22×D44—21no—
65C22×D44D411yescharacteristic
66C22×D44C2312yes—
67C22×C4×D11—22no—
68C22×C4×D11—22no—
69C22×C4×D11C2312yes—
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⋊C4C2312yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82#66999—216no—
83C2×#4326—24no—
84C2×#4326C2314yes—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4D412yes—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11D411yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—22no—
93C2×C4×Dic11—21no—
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C2×#4314—44no—
97C2×#4314C2318yes—
98C2×#4313—44no—
99C2×#4313C2318yes—
100#66950—24no—
101#66950C2318yes—
102#66948—24no—
103#66948—216no—
104#66948C2318yes—
105#66946—28no—
106C4⋊C4×D11—24no—
107C4⋊C4×D11C2318yes—
108#66943—28no—
109#66927—28no—
110#66927—22no—
111#66927C2314yes—
112C4×D44—28no—
113C4×D44D414yes—
114C4×D44C2314yes—
115C4×Dic22—22no—
116C4×Dic22C2314yes—
117C11×#107C2318yes—
118C11×C4⋊C8C2314yes—
119C11×#103C2318yes—
120#66899C2314yes—
121#66885C2318yes—
122(C2×D11)⋊C8C2318yes—
123#66874C2314yes—
124#66873C2318yes—
125#66873C2318yes—
126#66871C2314yes—
127C4×C11⋊C8C2314yes—
128C2×#3333—111nomaximal, Sylow
129C23×D11—22no—
130C23×D11C2×D412yes—
131C2×Q8×C11—21no—
132C2×Q8×C11—24no—
133C2×Q8×C11—22no—
134C2×Q8×C11—82no—
135C2×Q8×C11#4114yes—
136C2×Q8×C11C2412yes—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11C2×D412yes—
146#4343—216no—
147#4343—48no—
148#4343—416no—
149C2×D44—28no—
150C2×D44—28no—
151C2×D44—24no—
152C2×D44—24no—
153C2×D44—22no—
154C2×D44—24no—
155C2×D44—24no—
156C2×D44—24no—
157C2×D44—48no—
158C2×D44—44no—
159C2×D44—82no—
160C2×D44—84no—
161C2×D44C2×D414yes—
162C2×D44C2414yes—
163C2×C4×D11—28no—
164C2×C4×D11—28no—
165C2×C4×D11—24no—
166C2×C4×D11—24no—
167C2×C4×D11—48no—
168C2×C4×D11—84no—
169C2×C4×D11C2×D414yes—
170C2×C4×D11C2414yes—
171C2×Dic22—21no—
172C2×Dic22—22no—
173C2×Dic22—22no—
174C2×Dic22C2412yes—
175C2×C8×C11—24no—
176C2×C8×C11C2414yes—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—24no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4C2412yes—
182C11×C4⋊C4C2414yes—
183C42×C11—24no—
184C42×C11C2×D412yes—
185C42×C11C2412yes—
186#4326—28no—
187(C2×D11)⋊C4—28no—
188(C2×D11)⋊C4—28no—
189(C2×D11)⋊C4C2×D418yes—
190C4⋊Dic11—28no—
191C4⋊Dic11—21no—
192C4⋊Dic11C2×D414yes—
193C4⋊Dic11C2412yes—
194Dic11⋊C4—28no—
195Dic11⋊C4—24no—
196C4×Dic11—24no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8C2412yes—
200C2×C11⋊C8C2412yes—
201#4314—48no—
202#4313—48no—
203C2×#554—111no—
204C2×#550—111no—
205#3333—1116no—
206C2×#486—111no—
207C2×#480—112no—
208C2×#477D1111yescharacteristic, complemented
209C2×#468—112no—
210C2×#460—111no—
211C2×#452—112no—
212C2×C4×Q16—111no—
213C2×#436—111no—
214C2×#417—112no—
215C23×C11C22×D411yescharacteristic
216C22×D11—24no—
217C22×D11—24no—
218C22×D11—24no—
219C22×D11—24no—
220C22×D11—44no—
221C22×D11—44no—
222C22×D11—44no—
223C22×D11C22×D414yes—
224Q8×C11—24no—
225Q8×C11—22no—
226Q8×C11—84no—
227Q8×C11C2×#4114yes—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—44no—
234C2×C4×C11—42no—
235C2×C4×C11#13714yes—
236C2×C4×C11C22×D412yes—
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D412yes—
239C2×C4×C11C2×#4112yes—
240C2×C4×C11H(5,𝔽2)12yes—
241C2×C4×C11C2511yescharacteristic
242C2×Dic11—24no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11C22×D414yes—
248D44—28no—
249D44—24no—
250D44—24no—
251D44—416no—
252D44—44no—
253D44—48no—
254D44—84no—
255D44—88no—
256C4×D11—28no—
257C4×D11—24no—
258C4×D11—24no—
259C4×D11—416no—
260C4×D11—88no—
261Dic22—22no—
262Dic22—22no—
263Dic22—42no—
264C8×C11—24no—
265C11⋊C8—22no—
266C11⋊C8—22no—
267C22×#41—112no—
268C22×Q16—111no—
269C22×SD16—112no—
270C22×M16—112no—
271#554—118no—
272#554—224no—
273#550—118no—
274#550—224no—
275C2×C4⋊Q8C2×D1111yescharacteristic
276C2×#127—111no—
277C2×#127—221no—
278C2×#125—221no—
279C2×C22⋊Q8—112no—
280C2×C22⋊Q8—222no—
281C2×#121—112no—
282C2×#121—222no—
283C2×C4×Q8—111no—
284C2×C4×Q8C2×D1111yescharacteristic
285C2×C4×D4—111no—
286C2×C4×D4—221no—
287C2×C4×D4—221no—
288C22×C4⋊C4—112no—
289#486—118no—
290#480—1116no—
291#477C2×D1118yescomplemented
292#468—1116no—
293#460—118no—
294#452—1116no—
295C4×Q16—118no—
296#436—118no—
297C2×#107—111no—
298C2×#107C2×D1112yes—
299C2×C4⋊C8C2×D1111yescharacteristic
300#417—1116no—
301C2×#103—111no—
302C2×#103—111no—
303C2×#103C2×D1112yes—
304C2×#102—112no—
305C2×#102—112no—
306C2×#102—112no—
307C2×C22⋊C8—112no—
308C2×C4×C8—111no—
309C22×C11#54612yes—
310C22×C11C2×#13712yes—
311C22×C11#57612yes—
312C22×C11C23×D411yescharacteristic
313C2×D11—24no—
314C2×D11—24no—
315C2×D11—24no—
316C2×D11—48no—
317C2×D11—44no—
318C2×D11—44no—
319C2×D11—44no—
320C2×D11—88no—
321C4×C11—24no—
322C4×C11—22no—
323C4×C11—44no—
324C4×C11—42no—
325C4×C11#54612yes—
326C4×C11C2×#13714yes—
327C4×C11C22×#4111yescharacteristic
328C4×C11C2×H(5,𝔽2)11yescharacteristic
329Dic11—24no—
330Dic11—42no—
331Dic11—42no—
332C2×#41—118no—
333C2×#41—224no—
334C2×#41—228no—
335C2×#41—444no—
336C22×Q8—21no—
337C22×Q8—111no—
338C22×Q8C22×D1111yescharacteristic
339C22×D4—111no—
340C22×D4—112no—
341C22×D4—222no—
342C22×D4—222no—
343C22×D4—221no—
344C22×D4—221no—
345C23×C4—112no—
346C23×C4—222no—
347C23×C4—222no—
348C2×Q16—114no—
349C2×Q16—224no—
350C2×SD16—118no—
351C2×SD16—444no—
352C2×M16—118no—
353C2×M16—444no—
354C22×C8—111no—
355C22×C8—111no—
356C22×C8C22×D1112yes—
357C4⋊Q8—22no—
358C4⋊Q8C22×D1114yes—
359#127—114no—
360#127—228no—
361#127—222no—
362#125—228no—
363C22⋊Q8—118no—
364C22⋊Q8—2216no—
365C22⋊Q8—224no—
366#121—118no—
367#121—2216no—
368#121—224no—
369C4×Q8—22no—
370C4×Q8—114no—
371C4×Q8—222no—
372C4×Q8C22×D1114yes—
373C4×D4—114no—
374C4×D4—114no—
375C4×D4—228no—
376C4×D4—228no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—118no—
382C2×C4⋊C4—224no—
383C2×C4⋊C4—222no—
384C2×C4⋊C4—222no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4C22×D1112yes—
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C22⋊C4—112no—
389C2×C22⋊C4—222no—
390C2×C22⋊C4—222no—
391C2×C42—21no—
392C2×C42—221no—
393C2×C42C22×D1111yescharacteristic
394#107—114no—
395#107C22×D1118yes—
396C4⋊C8C22×D1114yes—
397#103—114no—
398#103—114no—
399#103C22×D1118yes—
400#102—118no—
401#102—118no—
402#102—118no—
403C22⋊C8—118no—
404C4×C8—114no—
405C2×C11#333314yescomplemented
406C2×C11C2×#54611yescharacteristic
407C2×C11C22×#13711yescharacteristic
408C2×C11C2×#57611yescharacteristic
409D11—44no—
410D11—84no—
411C24—112no—
412C24—222no—
413#41—2216no—
414#41—448no—
415#41—4416no—
416C2×Q8—21no—
417C2×Q8—24no—
418C2×Q8—22no—
419C2×Q8—82no—
420C2×Q8—112no—
421C2×Q8—221no—
422C2×Q8—222no—
423C2×Q8—222no—
424C2×Q8#434314yes—
425C2×Q8C23×D1112yes—
426C2×D4—114no—
427C2×D4—114no—
428C2×D4—228no—
429C2×D4—228no—
430C2×D4—224no—
431C2×D4—224no—
432C2×D4—222no—
433C2×D4—224no—
434C2×D4—224no—
435C2×D4—224no—
436C2×D4—448no—
437C2×D4—444no—
438C2×D4—882no—
439C2×D4—884no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—112no—
444C22×C4—114no—
445C22×C4—114no—
446C22×C4—228no—
447C22×C4—228no—
448C22×C4—224no—
449C22×C4—224no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—448no—
453C22×C4—884no—
454C22×C4D4×D1111yescharacteristic
455C22×C4D4×D1111yescharacteristic
456C22×C4C23×D1111yescharacteristic
457Q16—228no—
458SD16—448no—
459M16—448no—
460C2×C8—24no—
461C2×C8—112no—
462C2×C8—112no—
463C2×C8—222no—
464C2×C8—222no—
465C2×C8C23×D1114yes—
466C4⋊C4—24no—
467C4⋊C4—24no—
468C4⋊C4—22no—
469C4⋊C4—21no—
470C4⋊C4—114no—
471C4⋊C4—112no—
472C4⋊C4—228no—
473C4⋊C4—228no—
474C4⋊C4—221no—
475C4⋊C4—224no—
476C4⋊C4C23×D1114yes—
477C4⋊C4C23×D1112yes—
478C22⋊C4—118no—
479C22⋊C4—228no—
480C22⋊C4—228no—
481C42—24no—
482C42—224no—
483C42D4×D1112yes—
484C42C23×D1112yes—
485C11C2×#333311yescharacteristic, complemented, Sylow
486C23—114no—
487C23—224no—
488C23—224no—
489C23—224no—
490C23—224no—
491C23—444no—
492C23—444no—
493C23—444no—
494C23C2×D4×D1111yescharacteristic
495Q8—24no—
496Q8—22no—
497Q8—84no—
498Q8—222no—
499Q8—222no—
500Q8—442no—
501Q8C2×#434314yes—
502D4—228no—
503D4—224no—
504D4—224no—
505D4—4416no—
506D4—448no—
507D4—444no—
508D4—884no—
509D4—888no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—44no—
516C2×C4—42no—
517C2×C4—114no—
518C2×C4—224no—
519C2×C4—228no—
520C2×C4—224no—
521C2×C4—224no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—4416no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—888no—
528C2×C4#6697114yes—
529C2×C4C2×D4×D1112yes—
530C2×C4C2×D4×D1112yes—
531C2×C4C2×D4×D1111yescharacteristic
532C2×C4C2×#434312yes—
533C2×C4#6704212yes—
534C2×C4C24×D1111yescharacteristic
535C8—24no—
536C8—222no—
537C8—222no—
538C22—224no—
539C22—224no—
540C22—224no—
541C22—448no—
542C22—444no—
543C22—444no—
544C22—444no—
545C22—888no—
546C22#1062316112yes—
547C22C2×#6697112yes—
548C22#1062330512yes—
549C22C22×D4×D1111yescharacteristic
550C4—24no—
551C4—22no—
552C4—44no—
553C4—42no—
554C4—224no—
555C4—442no—
556C4—442no—
557C4#1062316112yes—
558C4C2×#6697114yes—
559C4C22×#434311yescharacteristic
560C4C2×#6704211yescharacteristic
561C2—444no—
562C2—884no—
563C2#1308095114yesdirect product factor
564C2C2×#1062316111yescharacteristic
565C2C22×#6697111yescharacteristic
566C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#477C2
socleC23×C11C22×D4
prime radicalC2×#10623108C2
hypercenterC2×#477D11
hypocenterC11C2×#3333
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. C2×#10623261C2semidirect
3. #13080951C2direct (N × H)
4. C2×#10622701C2semidirect
5. C2×#10622495C2semidirect
6. C2×#10622499C2semidirect
7. C2×#10622461C2semidirect
8. C2×#10622423C2semidirect
9. C2×C4×#4326C2semidirect
10. C2×#10622451C2semidirect
11. C2×#10622416C2semidirect
12. C2×C11×#477C2semidirect
21. #10623261C22semidirect
35. C11×#477C22semidirect
42. #10622701C22semidirect
43. C4×#4326C22semidirect
49. #10622499C22semidirect
50. #10622495C22semidirect
51. #10622461C22semidirect
52. #10622451C22semidirect
53. #10622423C22semidirect
54. #10622416C22semidirect
208. C2×#477D11semidirect
291. #477C2×D11semidirect
405. C2×C11#3333semidirect
485. C11C2×#3333semidirect
563. C2#13080951direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232612
C2×#106231082
#130809512
C2×#106227012
C2×#106224952
C2×#106224992
C2×#106224612
C2×#106224232
C2×C4×#43262
C2×#106224512
C2×#106224162
C2×C11×#4772
C2×#333311