Finite Group Databasebeta

← C2×#13078940 #15622977

Subgroups — C2×#13078940 #15622977

Order 2816.

2222 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic, complemented
2C2×#10623256C211yesmaximal, characteristic
3#13078940C2116yesmaximal, direct product factor
4C2×#10622413C214yesmaximal, complemented
5C2×#10622694C211yesmaximal, characteristic, complemented
6C2×#10622701C211yesmaximal, characteristic, complemented
7C2×#10622307C211yesmaximal, characteristic, complemented
8C2×#10622417C214yesmaximal, complemented
9C2×C4×C8×D11C211yesmaximal, characteristic, complemented
10C2×C11×#487C211yesmaximal, characteristic, complemented
11C22×#4343C2212yes—
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#67000C2212yes—
15C2×#66999—21no—
16C2×Q8×Dic11—21no—
17C22×C8×D11C2212yes—
18#10623259—24no—
19#10623259C2218yescomplemented
20#10623256—24no—
21#10623256C2218yes—
22C2×#66950—21no—
23C2×#66948—21no—
24C2×#66948—21no—
25C2×#66946—21no—
26C2×#66946—21no—
27C2×#66945C2212yes—
28C2×#66943C2212yes—
29C2×#66940—21no—
30C2×#66927C2211yescharacteristic
31C2×C42×D11C2211yescharacteristic
32C2×#66922C2211yescharacteristic
33C11×#487C2218yescomplemented
34C2×C11×#103C2214yes—
35C2×C4×C8×C11C2211yescharacteristic
36C2×#66899C2214yes—
37C2×#66885C2214yes—
38C2×C8×Dic11C2212yes—
39#10622701C2218yescomplemented
40#10622694C2218yescomplemented
41C2×#66873C2214yes—
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622417C22132yescomplemented
44#10622413C22132yescomplemented
45#10622307C2218yescomplemented
46C4×C8×D11C2218yescomplemented
47C22×Q8×C11—21no—
48C22×Q8×C11C2312yes—
49C2×#4343—24no—
50C2×#4343—216no—
51C2×#4343C2318yes—
52C22×D44—22no—
53C22×D44—21no—
54C22×D44—21no—
55C22×D44C2312yes—
56C22×C4×D11—22no—
57C22×C4×D11D411yescharacteristic
58C22×C4×D11D411yescharacteristic
59C22×C4×D11C2311yescharacteristic
60C22×Dic22—21no—
61C22×C8×C11C2312yes—
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8—22no—
64C11×C4⋊Q8C2314yes—
65C11×C4⋊Q8C2314yes—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2312yes—
70C2×C42×C11C2311yescharacteristic
71#67000—24no—
72#67000C2318yes—
73#66999—28no—
74Q8×Dic11—28no—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—22no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11C2312yes—
81C2×Dic11⋊C4—22no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11D411yescharacteristic
85C2×C4×Dic11C2311yescharacteristic
86C22×C11⋊C8C2312yes—
87C2×C8×D11—28no—
88C2×C8×D11C2318yes—
89#66950—28no—
90#66948—28no—
91#66948—28no—
92#66946—28no—
93#66946—28no—
94#66945—24no—
95#66945C2318yes—
96#66943—24no—
97#66943C2318yes—
98#66940—28no—
99#66927—22no—
100#66927C2314yes—
101C42×D11D414yes—
102C42×D11C2314yes—
103#66922—22no—
104#66922C2314yes—
105C11×#103C23116yes—
106C4×C8×C11C2314yes—
107#66899C23116yes—
108#66885C23116yes—
109C8×Dic11C2318yes—
110#66873C23116yes—
111C4×C11⋊C8C2314yes—
112C2×#3131—111nomaximal, Sylow
113C23×D11—22no—
114C23×D11C2×D411yescharacteristic
115C2×Q8×C11—24no—
116C2×Q8×C11—22no—
117C2×Q8×C11—28no—
118C2×Q8×C11—44no—
119C2×Q8×C11C2414yes—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C22×Dic11—22no—
126C22×Dic11C2×D411yescharacteristic
127C22×Dic11C2×D411yescharacteristic
128C22×Dic11C2×D411yescharacteristic
129#4343—232no—
130#4343—416no—
131C2×D44—28no—
132C2×D44—22no—
133C2×D44—24no—
134C2×D44—24no—
135C2×D44—28no—
136C2×D44—48no—
137C2×D44—44no—
138C2×D44—44no—
139C2×D44C2414yes—
140C2×C4×D11—28no—
141C2×C4×D11—24no—
142C2×C4×D11—24no—
143C2×C4×D11—48no—
144C2×C4×D11C2×D414yes—
145C2×C4×D11C2×D414yes—
146C2×C4×D11C2×D412yes—
147C2×C4×D11#4118yes—
148C2×C4×D11C2412yes—
149C2×Dic22—24no—
150C2×Dic22—44no—
151C2×C8×C11—24no—
152C2×C8×C11C2414yes—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4C2414yes—
158C42×C11C2×D412yes—
159C42×C11C2412yes—
160(C2×D11)⋊C4—28no—
161(C2×D11)⋊C4—28no—
162(C2×D11)⋊C4—28no—
163C4⋊Dic11—28no—
164C4⋊Dic11—22no—
165C4⋊Dic11—24no—
166C4⋊Dic11C2414yes—
167Dic11⋊C4—28no—
168C4×Dic11—28no—
169C4×Dic11C2×D412yes—
170C4×Dic11C2×D414yes—
171C4×Dic11C2×D414yes—
172C4×Dic11C2412yes—
173C2×C11⋊C8—24no—
174C2×C11⋊C8C2414yes—
175C8×D11—216no—
176C2×#533—111no—
177C2×#532—111no—
178#3131—1116no—
179C2×#488—114no—
180C2×#487—111no—
181C2×#487D1111yescharacteristic, complemented
182C2×#486—111no—
183C2×#486—111no—
184C2×#416—114no—
185C22×C4×C8—111no—
186C23×C11C22×D411yescharacteristic
187C22×D11—22no—
188C22×D11—22no—
189C22×D11—24no—
190C22×D11—44no—
191C22×D11—44no—
192C22×D11—44no—
193C22×D11#12414yes—
194C22×D11C22×D412yes—
195Q8×C11—28no—
196Q8×C11—44no—
197Q8×C11—48no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—44no—
201C2×C4×C11—44no—
202C2×C4×C11#13514yes—
203C2×C4×C11#13514yes—
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C22×D412yes—
206C2×C4×C11C22×D412yes—
207C2×C4×C11C2×#4114yes—
208C2×C4×C11C2511yescharacteristic
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—24no—
212C2×Dic11—44no—
213C2×Dic11#12414yes—
214C2×Dic11C22×D412yes—
215C2×Dic11C22×D412yes—
216C2×Dic11C22×D412yes—
217D44—28no—
218D44—416no—
219D44—44no—
220D44—48no—
221D44—48no—
222C4×D11—28no—
223C4×D11—28no—
224C4×D11—416no—
225C4×D11#12418yes—
226C4×D11C2×#4118yes—
227Dic22—48no—
228C8×C11—24no—
229C11⋊C8—24no—
230C22×#41—112no—
231C23×C8—112no—
232#533—118no—
233#533—224no—
234#532—118no—
235#532—224no—
236C2×C4⋊Q8—111no—
237C2×C4⋊Q8C2×D1111yescharacteristic
238C2×C4⋊Q8C2×D1111yescharacteristic
239C2×#127—111no—
240C2×#125—112no—
241C2×#124—112no—
242C2×C22⋊Q8—221no—
243C2×C22⋊Q8—221no—
244C2×#121—221no—
245C2×#121—221no—
246C2×C4×Q8—221no—
247C2×C4×Q8—221no—
248C2×C4×D4—221no—
249C2×C4×D4—221no—
250C2×#117—112no—
251C22×C42—111no—
252#488—1132no—
253#487—118no—
254#487C2×D1118yescomplemented
255#486—118no—
256#486—118no—
257#416—1132no—
258C2×#103—114no—
259C2×#103C2×D1114yes—
260C2×#102—114no—
261C2×#102—114no—
262C2×C4×C8—112no—
263C2×C4×C8—111no—
264C2×C4×C8—118no—
265C2×C4×C8C2×D1111yescharacteristic
266C22×C11C2×#12412yes—
267C22×C11C2×#13512yes—
268C22×C11C2×#13512yes—
269C22×C11C23×D411yescharacteristic
270C2×D11—28no—
271C2×D11—22no—
272C2×D11—22no—
273C2×D11—44no—
274C2×D11—44no—
275C2×D11—44no—
276C2×D11—88no—
277C2×D11C2×#12414yes—
278C4×C11—44no—
279C4×C11—44no—
280C4×C11C2×#12412yes—
281C4×C11C2×#13514yes—
282C4×C11C2×#13514yes—
283C4×C11C22×#4112yes—
284Dic11—22no—
285Dic11—22no—
286Dic11—44no—
287Dic11C2×#12414yes—
288C2×#41—118no—
289C2×#41—224no—
290C2×#41—2216no—
291C22×Q8—21no—
292C22×Q8—221no—
293C22×Q8C22×D1112yes—
294C22×D4—112no—
295C22×D4—222no—
296C22×D4—221no—
297C22×D4—221no—
298C23×C4—111no—
299C23×C4—111no—
300C23×C4—111no—
301C23×C4—222no—
302C22×C8—112no—
303C22×C8—118no—
304C22×C8—228no—
305C22×C8C22×D1112yes—
306C4⋊Q8—22no—
307C4⋊Q8—22no—
308C4⋊Q8—114no—
309C4⋊Q8—222no—
310C4⋊Q8C22×D1114yes—
311C4⋊Q8C22×D1114yes—
312#127—114no—
313#127—222no—
314#125—118no—
315#125—224no—
316#124—118no—
317#124—224no—
318C22⋊Q8—228no—
319C22⋊Q8—228no—
320#121—228no—
321#121—228no—
322C4×Q8—228no—
323C4×Q8—228no—
324C4×D4—228no—
325C4×D4—228no—
326#117—118no—
327#117—224no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—112no—
332C2×C4⋊C4—222no—
333C2×C4⋊C4—222no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4C22×D1112yes—
336C2×C22⋊C4—222no—
337C2×C22⋊C4—222no—
338C2×C22⋊C4—222no—
339C2×C42—111no—
340C2×C42—111no—
341C2×C42—111no—
342C2×C42—114no—
343C2×C42—114no—
344C2×C42—222no—
345C2×C42C22×D1111yescharacteristic
346#103—1116no—
347#103C22×D11116yes—
348#102—1116no—
349#102—1116no—
350C4×C8—118no—
351C4×C8—114no—
352C4×C8C22×D1114yes—
353C2×C11#313114yescomplemented
354C2×C11C22×#12411yescharacteristic
355C2×C11C22×#13511yescharacteristic
356C2×C11C22×#13511yescharacteristic
357D11—24no—
358D11—84no—
359C24—111no—
360C24—222no—
361#41—2232no—
362#41—4416no—
363C2×Q8—24no—
364C2×Q8—22no—
365C2×Q8—28no—
366C2×Q8—44no—
367C2×Q8—224no—
368C2×Q8—444no—
369C2×Q8C23×D1114yes—
370C2×D4—114no—
371C2×D4—228no—
372C2×D4—224no—
373C2×D4—224no—
374C2×D4—222no—
375C2×D4—228no—
376C2×D4—448no—
377C2×D4—444no—
378C2×D4—444no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—111no—
382C22×C4—112no—
383C22×C4—118no—
384C22×C4—112no—
385C22×C4—111no—
386C22×C4—111no—
387C22×C4—114no—
388C22×C4—114no—
389C22×C4—228no—
390C22×C4—224no—
391C22×C4—224no—
392C22×C4—222no—
393C22×C4—448no—
394C22×C4D4×D1111yescharacteristic
395C22×C4D4×D1111yescharacteristic
396C22×C4C23×D1111yescharacteristic
397C2×C8—24no—
398C2×C8—114no—
399C2×C8—2216no—
400C2×C8—224no—
401C2×C8C23×D1114yes—
402C4⋊C4—24no—
403C4⋊C4—24no—
404C4⋊C4—24no—
405C4⋊C4—22no—
406C4⋊C4—114no—
407C4⋊C4—228no—
408C4⋊C4—228no—
409C4⋊C4—222no—
410C4⋊C4—224no—
411C4⋊C4C23×D1114yes—
412C22⋊C4—228no—
413C22⋊C4—228no—
414C22⋊C4—228no—
415C42—114no—
416C42—114no—
417C42—112no—
418C42—112no—
419C42—228no—
420C42D4×D1112yes—
421C42C23×D1112yes—
422C11C2×#313111yescharacteristic, complemented, Sylow
423C23—112no—
424C23—114no—
425C23—222no—
426C23—222no—
427C23—224no—
428C23—444no—
429C23—444no—
430C23—444no—
431C23C2×D4×D1111yescharacteristic
432Q8—28no—
433Q8—48no—
434Q8—44no—
435Q8—448no—
436D4—228no—
437D4—4416no—
438D4—448no—
439D4—448no—
440D4—444no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—44no—
444C2×C4—44no—
445C2×C4—112no—
446C2×C4—114no—
447C2×C4—118no—
448C2×C4—118no—
449C2×C4—112no—
450C2×C4—112no—
451C2×C4—222no—
452C2×C4—222no—
453C2×C4—228no—
454C2×C4—228no—
455C2×C4—224no—
456C2×C4—4416no—
457C2×C4—444no—
458C2×C4#6696914yes—
459C2×C4#6697214yes—
460C2×C4C2×D4×D1112yes—
461C2×C4C2×D4×D1112yes—
462C2×C4C2×D4×D1111yescharacteristic
463C2×C4#41×D1114yes—
464C2×C4C24×D1111yescharacteristic
465C8—24no—
466C8—224no—
467C22—114no—
468C22—228no—
469C22—222no—
470C22—222no—
471C22—444no—
472C22—444no—
473C22—444no—
474C22—888no—
475C22D11×#12412yes—
476C22C2×#6696912yes—
477C22C2×#6697212yes—
478C22C22×D4×D1111yescharacteristic
479C4—44no—
480C4—44no—
481C4—114no—
482C4—222no—
483C4—222no—
484C4—444no—
485C4D11×#12412yes—
486C4C2×#6696914yes—
487C4C2×#6697214yes—
488C4C2×#41×D1112yes—
489C2—224no—
490C2—884no—
491C2#1307894014yesdirect product factor
492C2C2×D11×#12411yescharacteristic
493C2C22×#6696911yescharacteristic
494C2C22×#6697211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#487C2
socleC23×C11C22×D4
prime radicalC2×#10623256C2
hypercenterC2×#487D11
hypocenterC11C2×#3131
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
1. C2×#10623259C2semidirect
3. #13078940C2direct (N × H)
4. C2×#10622413C2semidirect
5. C2×#10622694C2semidirect
6. C2×#10622701C2semidirect
7. C2×#10622307C2semidirect
8. C2×#10622417C2semidirect
9. C2×C4×C8×D11C2semidirect
10. C2×C11×#487C2semidirect
19. #10623259C22semidirect
33. C11×#487C22semidirect
39. #10622701C22semidirect
40. #10622694C22semidirect
43. #10622417C22semidirect
44. #10622413C22semidirect
45. #10622307C22semidirect
46. C4×C8×D11C22semidirect
181. C2×#487D11semidirect
254. #487C2×D11semidirect
353. C2×C11#3131semidirect
422. C11C2×#3131semidirect
491. C2#13078940direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106232562
#130789402
C2×#106224132
C2×#106226942
C2×#106227012
C2×#106223072
C2×#106224172
C2×C4×C8×D112
C2×C11×#4872
C2×#313111