Finite Group Databasebeta

← C2×#13080893 #15630652

Subgroups — C2×#13080893 #15630652

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×D4×Dic22C211yesmaximal, characteristic
2#13080893C2116yesmaximal, direct product factor
3C2×#10622706C211yesmaximal, characteristic, complemented
4C2×#10622609C212yesmaximal, complemented
5C2×#10622707C211yesmaximal, characteristic, complemented
6C2×#10622665C212yesmaximal, complemented
7C2×#10622644C211yesmaximal, characteristic, complemented
8C2×#10622663C212yesmaximal, complemented
9C2×C4×#4326C211yesmaximal, characteristic, complemented
10C2×#10622625C211yesmaximal, characteristic
11C2×#10622617C212yesmaximal, complemented
12C2×C11×#556C211yesmaximal, characteristic
13C23×Dic22C2212yes—
14C11×#556—24no—
15C11×#556C2218yes—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#126—22no—
18C2×C11×#124—21no—
19C2×C11×C22⋊Q8C2212yes—
20C2×C4×Q8×C11—21no—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117C2212yes—
24C22×#4326C2211yescharacteristic
25C22×#4326C2212yes—
26C2×D4×Dic11—21no—
27C2×#66977C2212yes—
28C22×#4318C2212yes—
29D4×Dic22—24no—
30D4×Dic22C2218yes—
31C2×#66941—21no—
32C2×#66931—22no—
33C2×#66922C2211yescharacteristic
34C2×C4×Dic22C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622707C2218yescomplemented
38#10622706C2218yescomplemented
39#10622665C22116yescomplemented
40#10622663C22116yescomplemented
41#10622644C2218yescomplemented
42C4×#4326C2218yescomplemented
43#10622625C2218yes—
44#10622617C22116yescomplemented
45#10622609C22116yescomplemented
46C2×#66874C2212yes—
47C2×#66874C2212yes—
48C2×#66874C2212yes—
49C2×#66874C2211yescharacteristic
50C2×#66874C2212yes—
51C2×#66872C2212yes—
52C2×#66871C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55C22×Q8×C11—21no—
56C22×Q8×C11C2311yescharacteristic
57C22×D4×C11D411yescharacteristic
58C23×C4×C11C2312yes—
59C23×Dic11—22no—
60C22×Dic22—28no—
61C22×Dic22—22no—
62C22×Dic22—24no—
63C22×Dic22—44no—
64C22×Dic22C2312yes—
65C22×Dic22C2318yes—
66C22×Dic22C2311yescharacteristic
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8C2314yes—
69C11×#126—216no—
70C11×#124—28no—
71C11×C22⋊Q8—24no—
72C11×C22⋊Q8C2318yes—
73C4×Q8×C11—28no—
74C4×Q8×C11—22no—
75C4×Q8×C11C2314yes—
76C4×D4×C11D414yes—
77C4×D4×C11C2314yes—
78C11×#117—24no—
79C11×#117C2318yes—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4D412yes—
89C2×C42×C11—22no—
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92C2×C22⋊Dic11—22no—
93C2×#4326—24no—
94C2×#4326—44no—
95C2×#4326C2314yes—
96C2×#4326C2318yes—
97D4×Dic11—28no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11C2311yescharacteristic
101#66977—24no—
102#66977C2318yes—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—22no—
105C2×C4×Dic11—21no—
106C2×#4318—44no—
107C2×#4318C2318yes—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2312yes—
111#66941—28no—
112#66931—216no—
113#66922—22no—
114#66922C2314yes—
115C4×Dic22—22no—
116C4×Dic22C2314yes—
117#66899C2314yes—
118C22⋊(C11⋊C8)C2318yes—
119#66874C2318yes—
120#66874C2318yes—
121#66874C2314yes—
122#66874C2318yes—
123#66874C2318yes—
124#66872C2318yes—
125#66871C2314yes—
126C4⋊(C11⋊C8)C2314yes—
127C4×C11⋊C8C2314yes—
128C2×#3328—111nomaximal, Sylow
129C24×C11C2×D412yes—
130C2×Q8×C11—21no—
131C2×Q8×C11—24no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11—44no—
135C2×Q8×C11C2412yes—
136C2×D4×C11—24no—
137C2×D4×C11C2×D414yes—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D414yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2414yes—
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—21no—
150C22×Dic11—28no—
151C22×Dic11—21no—
152C22×Dic11—22no—
153C22×Dic11—48no—
154C2×Dic22—216no—
155C2×Dic22—21no—
156C2×Dic22—22no—
157C2×Dic22—28no—
158C2×Dic22—24no—
159C2×Dic22—22no—
160C2×Dic22—24no—
161C2×Dic22—48no—
162C2×Dic22—416no—
163C2×Dic22—48no—
164C2×Dic22#4114yes—
165C2×Dic22C2414yes—
166C2×Dic22C2412yes—
167C11×C4⋊C4—28no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—24no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4C2×D414yes—
173C11×C4⋊C4C2412yes—
174C11×C4⋊C4C2414yes—
175C11×C22⋊C4—28no—
176C11×C22⋊C4—28no—
177C11×C22⋊C4C2×D418yes—
178C42×C11—28no—
179C42×C11—24no—
180C42×C11C2×D412yes—
181C42×C11C2412yes—
182C22⋊Dic11—28no—
183#4326—28no—
184#4326—48no—
185C4⋊Dic11—21no—
186C4⋊Dic11—24no—
187C4⋊Dic11—24no—
188C4⋊Dic11C2412yes—
189Dic11⋊C4—24no—
190Dic11⋊C4—28no—
191C4×Dic11—24no—
192#4318—48no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—24no—
196C2×C11⋊C8C2412yes—
197C2×C11⋊C8C2412yes—
198C2×C11⋊C8C2414yes—
199C2×#556D1111yescharacteristic
200C2×D4×Q8—111no—
201#3328—1116no—
202C2×#487—111no—
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×C11—24no—
212C23×C11—24no—
213C23×C11—24no—
214C23×C11C22×D414yes—
215C23×C11C22×D411yescharacteristic
216Q8×C11—22no—
217Q8×C11—22no—
218Q8×C11—42no—
219Q8×C11—48no—
220D4×C11—28no—
221C2×C4×C11—24no—
222C2×C4×C11—22no—
223C2×C4×C11—28no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—42no—
230C2×C4×C11—44no—
231C2×C4×C11—42no—
232C2×C4×C11#13714yes—
233C2×C4×C11C22×D412yes—
234C2×C4×C11C22×D414yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D412yes—
237C2×C4×C11C2×#4112yes—
238C2×C4×C11H(5,𝔽2)12yes—
239C2×C4×C11C2511yescharacteristic
240C2×Dic11—24no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—24no—
244C2×Dic11—416no—
245C2×Dic11—44no—
246C2×Dic11—42no—
247Dic22—24no—
248Dic22—22no—
249Dic22—24no—
250Dic22—24no—
251Dic22—416no—
252Dic22—44no—
253Dic22C2×#4114yes—
254C11⋊C8—22no—
255C11⋊C8—22no—
256C11⋊C8—24no—
257C23×Q8—112no—
258C22×Q16—111no—
259C22×Q16—112no—
260C22×M16—112no—
261#556—24no—
262#556C2×D1118yes—
263D4×Q8—118no—
264D4×Q8—224no—
265C2×C4⋊Q8—111no—
266C2×C4⋊Q8—221no—
267C2×C4⋊Q8C2×D1111yescharacteristic
268C2×#126—22no—
269C2×#124—21no—
270C2×C22⋊Q8—112no—
271C2×C22⋊Q8—222no—
272C2×C22⋊Q8C2×D1112yes—
273C2×C4×Q8—21no—
274C2×C4×Q8—111no—
275C2×C4×Q8C2×D1111yescharacteristic
276C2×C4×D4—221no—
277C2×C4×D4C2×D1111yescharacteristic
278C2×#117C2×D1112yes—
279#487—118no—
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—111no—
292C2×#103—112no—
293C2×#103—112no—
294C2×#103—112no—
295C2×#103—112no—
296C2×#103—111no—
297C2×C22⋊C8—112no—
298C2×C4×C8—111no—
299C22×C11—24no—
300C22×C11—24no—
301C22×C11—24no—
302C22×C11—48no—
303C22×C11#54612yes—
304C22×C11C2×#13712yes—
305C22×C11#57812yes—
306C22×C11C23×D411yescharacteristic
307C4×C11—24no—
308C4×C11—22no—
309C4×C11—42no—
310C4×C11—44no—
311C4×C11—42no—
312C4×C11#54612yes—
313C4×C11C2×#13714yes—
314C4×C11C22×#4111yescharacteristic
315C4×C11C2×H(5,𝔽2)11yescharacteristic
316Dic11—24no—
317Dic11—44no—
318Dic11—42no—
319C22×Q8—21no—
320C22×Q8—111no—
321C22×Q8—112no—
322C22×Q8—118no—
323C22×Q8—228no—
324C22×Q8—222no—
325C22×Q8—224no—
326C22×Q8—444no—
327C22×Q8C22×D1111yescharacteristic
328C22×D4C22⋊D1111yescharacteristic
329C23×C4—222no—
330C23×C4C22×D1112yes—
331C2×Q16—114no—
332C2×Q16—118no—
333C2×Q16—224no—
334C2×Q16—444no—
335C2×M16—118no—
336C2×M16—444no—
337C22×C8—111no—
338C22×C8—112no—
339C22×C8—111no—
340C4⋊Q8—22no—
341C4⋊Q8—114no—
342C4⋊Q8—228no—
343C4⋊Q8—222no—
344C4⋊Q8C22×D1114yes—
345#126—216no—
346#124—28no—
347C22⋊Q8—24no—
348C22⋊Q8—118no—
349C22⋊Q8—224no—
350C22⋊Q8—2216no—
351C22⋊Q8C22×D1118yes—
352C4×Q8—28no—
353C4×Q8—22no—
354C4×Q8—114no—
355C4×Q8—222no—
356C4×Q8C22×D1114yes—
357C4×D4—228no—
358C4×D4C22⋊D1114yes—
359C4×D4C22×D1114yes—
360#117—24no—
361#117C22×D1118yes—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4C22⋊D1111yescharacteristic
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C4⋊C4C22×D1112yes—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—222no—
376C2×C22⋊C4C22⋊D1112yes—
377C2×C42—22no—
378C2×C42—21no—
379C2×C42—221no—
380C2×C42C22×D1111yescharacteristic
381#107—114no—
382#106—118no—
383C4⋊C8—114no—
384#103—114no—
385#103—114no—
386#103—118no—
387#103—118no—
388#103—118no—
389#103—118no—
390C22⋊C8—118no—
391C4×C8—114no—
392C2×C11—44no—
393C2×C11#332814yescomplemented
394C2×C11C2×#54611yescharacteristic
395C2×C11C22×#13711yescharacteristic
396C2×C11C2×#57811yescharacteristic
397C24C2×C22⋊D1112yes—
398C2×Q8—21no—
399C2×Q8—24no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—44no—
403C2×Q8—114no—
404C2×Q8—112no—
405C2×Q8—114no—
406C2×Q8—2216no—
407C2×Q8—222no—
408C2×Q8—221no—
409C2×Q8—228no—
410C2×Q8—222no—
411C2×Q8—224no—
412C2×Q8—224no—
413C2×Q8—448no—
414C2×Q8—448no—
415C2×Q8—4416no—
416C2×Q8C23×D1112yes—
417C2×D4—24no—
418C2×D4C2×C22⋊D1114yes—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—221no—
425C22×C4—228no—
426C22×C4—221no—
427C22×C4—222no—
428C22×C4—448no—
429C22×C4C2×C22⋊D1114yes—
430C22×C4C2×C22⋊D1112yes—
431C22×C4C2×C22⋊D1111yescharacteristic
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C23×D1114yes—
434C22×C4C23×D1111yescharacteristic
435Q16—228no—
436Q16—448no—
437M16—448no—
438C2×C8—112no—
439C2×C8—112no—
440C2×C8—114no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—224no—
444C4⋊C4—28no—
445C4⋊C4—24no—
446C4⋊C4—24no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—112no—
450C4⋊C4—221no—
451C4⋊C4—224no—
452C4⋊C4—224no—
453C4⋊C4—228no—
454C4⋊C4—224no—
455C4⋊C4C2×C22⋊D1114yes—
456C4⋊C4C23×D1114yes—
457C4⋊C4C23×D1112yes—
458C22⋊C4—28no—
459C22⋊C4—28no—
460C22⋊C4—228no—
461C22⋊C4C2×C22⋊D1118yes—
462C42—28no—
463C42—24no—
464C42—224no—
465C42C2×C22⋊D1112yes—
466C42C23×D1112yes—
467C11C2×#332811yescharacteristic, complemented, Sylow
468C23—24no—
469C23—24no—
470C23—24no—
471C23C22×C22⋊D1114yes—
472C23C22×C22⋊D1111yescharacteristic
473Q8—22no—
474Q8—22no—
475Q8—48no—
476Q8—42no—
477Q8—114no—
478Q8—224no—
479Q8—222no—
480Q8—224no—
481Q8—224no—
482Q8—4416no—
483Q8—444no—
484D4—28no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—28no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—44no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—224no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—224no—
500C2×C4—4416no—
501C2×C4—444no—
502C2×C4—442no—
503C2×C4#6700414yes—
504C2×C4#41×D1112yes—
505C2×C4#6704212yes—
506C2×C4C22×C22⋊D1114yes—
507C2×C4C22×C22⋊D1112yes—
508C2×C4C22×C22⋊D1112yes—
509C2×C4C22×C22⋊D1111yescharacteristic
510C2×C4C24×D1111yescharacteristic
511C8—222no—
512C8—222no—
513C8—224no—
514C22—24no—
515C22—24no—
516C22—24no—
517C22—48no—
518C22C2×#6700412yes—
519C22#1062336012yes—
520C22#1062336912yes—
521C22C23×C22⋊D1111yescharacteristic
522C4—24no—
523C4—22no—
524C4—42no—
525C4—44no—
526C4—42no—
527C4—224no—
528C4—444no—
529C4—442no—
530C4C2×#6700414yes—
531C4#1062336012yes—
532C4C2×#41×D1111yescharacteristic
533C4C2×#6704211yescharacteristic
534C2—44no—
535C2#1308089314yesdirect product factor
536C2C2×#1062336011yescharacteristic
537C2C22×#6700411yescharacteristic
538C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#556C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenterC2×#556D11
hypocenterC11C2×#3328
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
2. #13080893C2direct (N × H)
3. C2×#10622706C2semidirect
4. C2×#10622609C2semidirect
5. C2×#10622707C2semidirect
6. C2×#10622665C2semidirect
7. C2×#10622644C2semidirect
8. C2×#10622663C2semidirect
9. C2×C4×#4326C2semidirect
11. C2×#10622617C2semidirect
37. #10622707C22semidirect
38. #10622706C22semidirect
39. #10622665C22semidirect
40. #10622663C22semidirect
41. #10622644C22semidirect
42. C4×#4326C22semidirect
44. #10622617C22semidirect
45. #10622609C22semidirect
393. C2×C11#3328semidirect
467. C11C2×#3328semidirect
535. C2#13080893direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Dic222
#130808932
C2×#106227062
C2×#106226092
C2×#106227072
C2×#106226652
C2×#106226442
C2×#106226632
C2×C4×#43262
C2×#106226252
C2×#106226172
C2×C11×#5562
C2×#332811