Finite Group Databasebeta

← C2×#13080898 #15630657

Subgroups — C2×#13080898 #15630657

Order 2816.

2082 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623263C211yesmaximal, characteristic
2C2×#10623258C211yesmaximal, characteristic
3#13080898C2116yesmaximal, direct product factor
4C2×#10622427C212yesmaximal, complemented
5C2×#10622707C211yesmaximal, characteristic, complemented
6C2×#10622429C212yesmaximal, complemented
7C2×#10622703C211yesmaximal, characteristic, complemented
8C2×#10622421C212yesmaximal, complemented
9C2×C4×Dic44C211yesmaximal, characteristic, complemented
10C2×#10622301C211yesmaximal, characteristic
11C2×#10622415C212yesmaximal, complemented
12C2×C11×#487C211yesmaximal, characteristic, complemented
13C22×Q8×D11C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×#67000—21no—
17C2×#66999C2212yes—
18C2×Q8×Dic11—21no—
19C22×#4326C2212yes—
20C22×Dic44C2211yescharacteristic
21C22×#4313C2212yes—
22#10623263—24no—
23#10623263C2218yes—
24#10623258—24no—
25#10623258C2218yes—
26C2×#66951—22no—
27C2×#66950C2212yes—
28C2×#66949—22no—
29C2×#66946—21no—
30C2×#66945C2212yes—
31C2×#66941—21no—
32C2×C4×D44C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C2×C4×Dic22C2211yescharacteristic
35C11×#487C2218yescomplemented
36C2×C11×#103C2212yes—
37C2×C11×#103C2212yes—
38C2×C4×C8×C11C2211yescharacteristic
39C2×#66899C2212yes—
40C2×(C2×D11)⋊C8C2212yes—
41C2×#66882C2211yescharacteristic
42C2×#66880C2211yescharacteristic
43C2×#66880C2211yescharacteristic
44#10622707C2218yescomplemented
45#10622703C2218yescomplemented
46C2×#66874C2212yes—
47C2×#66872C2212yes—
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622429C22116yescomplemented
50#10622427C22116yescomplemented
51#10622421C22116yescomplemented
52#10622415C22116yescomplemented
53C4×Dic44C2218yescomplemented
54#10622301C2218yes—
55C22×Q8×C11—21no—
56C22×Q8×C11C2312yes—
57C2×Q8×D11—24no—
58C2×Q8×D11—28no—
59C2×Q8×D11—44no—
60C2×Q8×D11C2318yes—
61C22×D44D411yescharacteristic
62C22×C4×D11—22no—
63C22×C4×D11C2312yes—
64C22×Dic22—22no—
65C22×Dic22C2311yescharacteristic
66C22×Dic22C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8—22no—
71C11×C4⋊Q8C2314yes—
72C11×C4⋊Q8C2314yes—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2312yes—
77C2×C42×C11C2311yescharacteristic
78#67000—28no—
79#66999—24no—
80#66999C2318yes—
81Q8×Dic11—28no—
82C2×#4326—44no—
83C2×#4326C2318yes—
84C2×(C2×D11)⋊C4—22no—
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×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—22no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—22no—
98C22×C11⋊C8C2312yes—
99C2×Dic44—24no—
100C2×Dic44C2314yes—
101C2×#4313—44no—
102C2×#4313C2318yes—
103#66951—216no—
104#66950—24no—
105#66950C2318yes—
106#66949—216no—
107#66946—28no—
108#66945—24no—
109#66945C2318yes—
110#66941—28no—
111C4×D44D414yes—
112C4×D44C2314yes—
113C4×Dic22—22no—
114C4×Dic22—22no—
115C4×Dic22C2314yes—
116C4×Dic22C2314yes—
117C11×#103C2318yes—
118C11×#103C2318yes—
119C4×C8×C11C2314yes—
120#66899C2318yes—
121(C2×D11)⋊C8C2318yes—
122#66882C2314yes—
123#66880C2314yes—
124#66880C2314yes—
125#66874C2318yes—
126#66872C2318yes—
127C4⋊(C11⋊C8)C2314yes—
128C2×#3328—111nomaximal, Sylow
129C23×D11C2×D412yes—
130C2×Q8×C11—24no—
131C2×Q8×C11—22no—
132C2×Q8×C11—24no—
133C2×Q8×C11—24no—
134C2×Q8×C11—44no—
135C2×Q8×C11C2414yes—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11C2×D412yes—
146Q8×D11—216no—
147Q8×D11—48no—
148Q8×D11—416no—
149C2×D44—24no—
150C2×D44C2×D414yes—
151C2×C4×D11—28no—
152C2×C4×D11—24no—
153C2×C4×D11—24no—
154C2×C4×D11—48no—
155C2×C4×D11C2×D414yes—
156C2×C4×D11C2414yes—
157C2×Dic22—28no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—22no—
161C2×Dic22—22no—
162C2×Dic22—22no—
163C2×Dic22—48no—
164C2×Dic22#4114yes—
165C2×Dic22C2412yes—
166C2×Dic22C2412yes—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11C2412yes—
170C2×C8×C11C2412yes—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4C2414yes—
176C42×C11C2×D412yes—
177C42×C11C2412yes—
178#4326—48no—
179(C2×D11)⋊C4—28no—
180(C2×D11)⋊C4—28no—
181(C2×D11)⋊C4—28no—
182(C2×D11)⋊C4C2×D418yes—
183C4⋊Dic11—28no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11C2×D414yes—
187C4⋊Dic11C2412yes—
188C4⋊Dic11C2412yes—
189Dic11⋊C4—28no—
190Dic11⋊C4—24no—
191Dic11⋊C4—24no—
192C4×Dic11—28no—
193C4×Dic11—24no—
194C4×Dic11—24no—
195C2×C11⋊C8—24no—
196C2×C11⋊C8C2414yes—
197Dic44—28no—
198#4313—48no—
199C2×#556—111no—
200C2×D4×Q8—111no—
201#3328—1116no—
202C2×#487D1111yescharacteristic, complemented
203C2×#485—112no—
204C2×#475—111no—
205C2×#470—112no—
206C2×#462—111no—
207C2×#451—112no—
208C2×C4×Q16—111no—
209C2×#436—111no—
210C2×#419—112no—
211C23×C11C22×D411yescharacteristic
212C22×D11—24no—
213C22×D11—24no—
214C22×D11—24no—
215C22×D11C22×D414yes—
216Q8×C11—24no—
217Q8×C11—24no—
218Q8×C11—44no—
219Q8×C11—48no—
220C2×C4×C11—22no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—44no—
224C2×C4×C11—44no—
225C2×C4×C11#13714yes—
226C2×C4×C11C22×D412yes—
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D412yes—
229C2×C4×C11C2×#4112yes—
230C2×C4×C11H(5,𝔽2)12yes—
231C2×C4×C11C2511yescharacteristic
232C2×Dic11—24no—
233C2×Dic11—24no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11C22×D414yes—
242D44—28no—
243C4×D11—28no—
244C4×D11—24no—
245C4×D11—24no—
246C4×D11—416no—
247Dic22—24no—
248Dic22—22no—
249Dic22—22no—
250Dic22—22no—
251Dic22—416no—
252Dic22—42no—
253Dic22C2×#4114yes—
254C8×C11—22no—
255C8×C11—22no—
256C11⋊C8—24no—
257C23×Q8—112no—
258C22×Q16—112no—
259C22×Q16—111no—
260C22×M16—112no—
261#556—118no—
262#556—224no—
263D4×Q8—118no—
264D4×Q8—224no—
265C2×C4⋊Q8—221no—
266C2×C4⋊Q8C2×D1111yescharacteristic
267C2×C4⋊Q8C2×D1111yescharacteristic
268C2×#126—222no—
269C2×#124—221no—
270C2×C22⋊Q8—112no—
271C2×C22⋊Q8—112no—
272C2×C22⋊Q8—222no—
273C2×C4×Q8—111no—
274C2×C4×Q8—111no—
275C2×C4×Q8—221no—
276C2×C4×D4—111no—
277C2×C4×D4—221no—
278C2×#117—112no—
279#487C2×D1118yescomplemented
280#485—1116no—
281#475—118no—
282#470—1116no—
283#462—118no—
284#451—1116no—
285C4×Q16—118no—
286#436—118no—
287C2×#107—111no—
288C2×#106—112no—
289C2×C4⋊C8—111no—
290#419—1116no—
291C2×#103—112no—
292C2×#103—111no—
293C2×#103—111no—
294C2×#103—112no—
295C2×#103C2×D1112yes—
296C2×#103C2×D1112yes—
297C2×C22⋊C8—112no—
298C2×C4×C8C2×D1111yescharacteristic
299C22×C11#54612yes—
300C22×C11C2×#13712yes—
301C22×C11#57812yes—
302C22×C11C23×D411yescharacteristic
303C2×D11—24no—
304C2×D11—24no—
305C2×D11—24no—
306C2×D11—48no—
307C4×C11—22no—
308C4×C11—44no—
309C4×C11—44no—
310C4×C11#54612yes—
311C4×C11C2×#13714yes—
312C4×C11C22×#4111yescharacteristic
313C4×C11C2×H(5,𝔽2)11yescharacteristic
314Dic11—24no—
315Dic11—24no—
316Dic11—42no—
317Dic11—42no—
318Dic11—42no—
319C22×Q8—21no—
320C22×Q8—118no—
321C22×Q8—111no—
322C22×Q8—111no—
323C22×Q8—222no—
324C22×Q8—224no—
325C22×Q8—228no—
326C22×Q8—444no—
327C22×Q8C22×D1112yes—
328C22×D4—111no—
329C23×C4—112no—
330C23×C4—222no—
331C2×Q16—118no—
332C2×Q16—114no—
333C2×Q16—224no—
334C2×Q16—444no—
335C2×M16—118no—
336C2×M16—444no—
337C22×C8—112no—
338C22×C8C22×D1111yescharacteristic
339C22×C8C22×D1111yescharacteristic
340C4⋊Q8—22no—
341C4⋊Q8—22no—
342C4⋊Q8—228no—
343C4⋊Q8C22×D1114yes—
344C4⋊Q8C22×D1114yes—
345#126—2216no—
346#124—228no—
347C22⋊Q8—118no—
348C22⋊Q8—118no—
349C22⋊Q8—2216no—
350C22⋊Q8—224no—
351C22⋊Q8—224no—
352C4×Q8—114no—
353C4×Q8—114no—
354C4×Q8—228no—
355C4×Q8—222no—
356C4×Q8—222no—
357C4×D4—114no—
358C4×D4—114no—
359C4×D4—228no—
360#117—118no—
361#117—224no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4C22×D1112yes—
373C2×C22⋊C4—112no—
374C2×C22⋊C4—222no—
375C2×C22⋊C4—222no—
376C2×C22⋊C4—222no—
377C2×C42—222no—
378C2×C42—221no—
379C2×C42—221no—
380C2×C42C22×D1111yescharacteristic
381#107—114no—
382#106—118no—
383C4⋊C8—114no—
384#103—118no—
385#103—114no—
386#103—114no—
387#103—118no—
388#103C22×D1118yes—
389#103C22×D1118yes—
390C22⋊C8—118no—
391C4×C8C22×D1114yes—
392C2×C11#332814yescomplemented
393C2×C11C2×#54611yescharacteristic
394C2×C11C22×#13711yescharacteristic
395C2×C11C2×#57811yescharacteristic
396D11—44no—
397C24—112no—
398C2×Q8—24no—
399C2×Q8—22no—
400C2×Q8—24no—
401C2×Q8—24no—
402C2×Q8—44no—
403C2×Q8—114no—
404C2×Q8—112no—
405C2×Q8—112no—
406C2×Q8—228no—
407C2×Q8—221no—
408C2×Q8—221no—
409C2×Q8—222no—
410C2×Q8—2216no—
411C2×Q8—222no—
412C2×Q8—222no—
413C2×Q8—448no—
414C2×Q8—448no—
415C2×Q8—4416no—
416C2×Q8C23×D1114yes—
417C2×D4—114no—
418C2×D4—224no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—112no—
422C22×C4—114no—
423C22×C4—114no—
424C22×C4—228no—
425C22×C4—221no—
426C22×C4—224no—
427C22×C4—224no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—448no—
432C22×C4D4×D1111yescharacteristic
433C22×C4D4×D1111yescharacteristic
434C22×C4C23×D1111yescharacteristic
435Q16—228no—
436Q16—448no—
437M16—448no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—114no—
441C2×C8—224no—
442C2×C8C23×D1112yes—
443C2×C8C23×D1112yes—
444C4⋊C4—24no—
445C4⋊C4—24no—
446C4⋊C4—24no—
447C4⋊C4—22no—
448C4⋊C4—114no—
449C4⋊C4—112no—
450C4⋊C4—112no—
451C4⋊C4—228no—
452C4⋊C4—228no—
453C4⋊C4—221no—
454C4⋊C4—221no—
455C4⋊C4—224no—
456C4⋊C4—224no—
457C4⋊C4C23×D1114yes—
458C22⋊C4—118no—
459C22⋊C4—228no—
460C22⋊C4—228no—
461C22⋊C4—228no—
462C42—228no—
463C42—224no—
464C42—224no—
465C42D4×D1112yes—
466C42C23×D1112yes—
467C11C2×#332811yescharacteristic, complemented, Sylow
468C23—114no—
469C23—224no—
470C23—224no—
471C23—224no—
472C23C2×D4×D1111yescharacteristic
473Q8—24no—
474Q8—24no—
475Q8—48no—
476Q8—44no—
477Q8—114no—
478Q8—222no—
479Q8—224no—
480Q8—222no—
481Q8—222no—
482Q8—4416no—
483Q8—442no—
484D4—228no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—44no—
489C2×C4—44no—
490C2×C4—114no—
491C2×C4—222no—
492C2×C4—224no—
493C2×C4—224no—
494C2×C4—224no—
495C2×C4—224no—
496C2×C4—228no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—4416no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4#6696814yes—
505C2×C4C2×D4×D1112yes—
506C2×C4C2×D4×D1112yes—
507C2×C4C2×D4×D1111yescharacteristic
508C2×C4#41×D1112yes—
509C2×C4#6704212yes—
510C2×C4C24×D1111yescharacteristic
511C8—22no—
512C8—22no—
513C8—224no—
514C22—224no—
515C22—224no—
516C22—224no—
517C22—448no—
518C22#1062320712yes—
519C22C2×#6696812yes—
520C22#1062329712yes—
521C22C22×D4×D1111yescharacteristic
522C4—22no—
523C4—44no—
524C4—44no—
525C4—224no—
526C4—224no—
527C4—442no—
528C4—442no—
529C4—442no—
530C4#1062320712yes—
531C4C2×#6696814yes—
532C4C2×#41×D1111yescharacteristic
533C4C2×#6704211yescharacteristic
534C2—444no—
535C2#1308089814yesdirect product factor
536C2C2×#1062320711yescharacteristic
537C2C22×#6696811yescharacteristic
538C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#487C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenterC2×#487D11
hypocenterC11C2×#3328
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
3. #13080898C2direct (N × H)
4. C2×#10622427C2semidirect
5. C2×#10622707C2semidirect
6. C2×#10622429C2semidirect
7. C2×#10622703C2semidirect
8. C2×#10622421C2semidirect
9. C2×C4×Dic44C2semidirect
11. C2×#10622415C2semidirect
12. C2×C11×#487C2semidirect
35. C11×#487C22semidirect
44. #10622707C22semidirect
45. #10622703C22semidirect
49. #10622429C22semidirect
50. #10622427C22semidirect
51. #10622421C22semidirect
52. #10622415C22semidirect
53. C4×Dic44C22semidirect
202. C2×#487D11semidirect
279. #487C2×D11semidirect
392. C2×C11#3328semidirect
467. C11C2×#3328semidirect
535. C2#13080898direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232632
C2×#106232582
#130808982
C2×#106224272
C2×#106227072
C2×#106224292
C2×#106227032
C2×#106224212
C2×C4×Dic442
C2×#106223012
C2×#106224152
C2×C11×#4872
C2×#332811