Finite Group Databasebeta

← C2×#13079752 #15625831

Subgroups — C2×#13079752 #15625831

Order 2816.

2058 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623008C211yesmaximal, characteristic
2#13079752C2116yesmaximal, direct product factor
3C2×#10622691C211yesmaximal, characteristic, complemented
4C2×#10622692C211yesmaximal, characteristic, complemented
5C2×#10622701C211yesmaximal, characteristic, complemented
6C2×#10622701C211yesmaximal, characteristic, complemented
7C2×#10622616C214yesmaximal, complemented
8C2×#10622679C214yesmaximal, complemented
9C2×#10622538C211yesmaximal, characteristic, complemented
10C2×C11×#533C211yesmaximal, characteristic, complemented
11C22×#4339—21no—
12C11×#533—24no—
13C11×#533C2218yescomplemented
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125C2212yes—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8—21no—
19C2×C4×Q8×C11—21no—
20C2×C4×Q8×C11—21no—
21C2×C11×#117C2212yes—
22C22×C42×C11C2211yescharacteristic
23C2×#66983—21no—
24C2×#66983C2212yes—
25#10623008—24no—
26#10623008C2218yes—
27C2×#66928—21no—
28C2×#66927C2211yescharacteristic
29C2×C4×D44—21no—
30C2×C4×D44C2212yes—
31C2×#66922C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2212yes—
33#10622701C2218yescomplemented
34#10622701C2218yescomplemented
35#10622692C2218yescomplemented
36#10622691C2218yescomplemented
37#10622679C22132yescomplemented
38#10622616C22132yescomplemented
39C2×#66873C2214yes—
40C2×#66873C2214yes—
41C2×#66872C2214yes—
42C2×#66871C2214yes—
43#10622538C2218yescomplemented
44C2×C4⋊(C11⋊C8)C2212yes—
45C2×C4×C11⋊C8C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47C22×Q8×C11—21no—
48C22×Q8×C11—21no—
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C22×C22⋊D11—22no—
53C2×#4339—28no—
54C2×#4339—48no—
55C22×D44—21no—
56C22×D44—21no—
57C22×D44C2312yes—
58C22×C4×D11—22no—
59C22×Dic22—21no—
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8C2314yes—
63C11×C4⋊Q8C2314yes—
64C11×#125—24no—
65C11×#125C2318yes—
66C11×C22⋊Q8—28no—
67C11×C22⋊Q8—28no—
68C4×Q8×C11—28no—
69C4×Q8×C11—28no—
70C11×#117—24no—
71C11×#117C2318yes—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C22⋊C4—22no—
79C2×C42×C11—22no—
80C2×C42×C11D411yescharacteristic
81C2×C42×C11D411yescharacteristic
82C2×C42×C11D414yes—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2314yes—
86#66983—24no—
87#66983—28no—
88#66983C2318yes—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2312yes—
93C22×C11⋊C8C2312yes—
94C22×C11⋊C8C2312yes—
95#66928—28no—
96#66927—22no—
97#66927C2314yes—
98C4×D44—28no—
99C4×D44—24no—
100C4×D44C2318yes—
101#66922—22no—
102#66922C2314yes—
103C22⋊(C11⋊C8)C2318yes—
104#66873C23116yes—
105#66873C23116yes—
106#66872C23116yes—
107#66871C23116yes—
108C4⋊(C11⋊C8)C2318yes—
109C4×C11⋊C8C2314yes—
110C4×C11⋊C8C2314yes—
111C2×#3228—111nomaximal, Sylow
112C24×C11C2×D411yescharacteristic
113C23×D11—22no—
114C2×Q8×C11—24no—
115C2×Q8×C11—24no—
116C2×Q8×C11—44no—
117C2×Q8×C11—44no—
118C22×C4×C11—24no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D414yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D414yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2412yes—
132C22×C4×C11C2411yescharacteristic
133C2×C22⋊D11—28no—
134C2×C22⋊D11—48no—
135C22×Dic11—22no—
136#4339—432no—
137C2×D44—22no—
138C2×D44—24no—
139C2×D44—24no—
140C2×D44—28no—
141C2×D44—44no—
142C2×D44—44no—
143C2×D44C2414yes—
144C2×C4×D11—28no—
145C2×C4×D11—48no—
146C2×Dic22—24no—
147C2×Dic22—44no—
148C11×C4⋊C4—28no—
149C11×C4⋊C4—28no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4C2414yes—
155C11×C4⋊C4C2414yes—
156C11×C22⋊C4—28no—
157C42×C11—28no—
158C42×C11C2×D412yes—
159C42×C11C2×D414yes—
160C42×C11C2×D412yes—
161C42×C11C2×D414yes—
162C42×C11C2412yes—
163C42×C11C2412yes—
164(C2×D11)⋊C4—28no—
165(C2×D11)⋊C4—28no—
166C4⋊Dic11—22no—
167C4⋊Dic11—24no—
168C4⋊Dic11C2414yes—
169C2×C11⋊C8—24no—
170C2×C11⋊C8—24no—
171C2×C11⋊C8C2414yes—
172C2×C11⋊C8C2414yes—
173C2×#533D1111yescharacteristic, complemented
174C2×#532—111no—
175#3228—1116no—
176C2×#500—111no—
177C2×#498—111no—
178C2×#486—111no—
179C2×#486—111no—
180C2×#482—114no—
181C2×#478—114no—
182C2×#431—111no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11C22×D412yes—
187C23×C11C22×D411yescharacteristic
188C22×D11—24no—
189C22×D11—44no—
190C22×D11—44no—
191C22×D11—44no—
192Q8×C11—48no—
193Q8×C11—48no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—28no—
199C2×C4×C11—28no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—44no—
204C2×C4×C11—44no—
205C2×C4×C11#13514yes—
206C2×C4×C11AGL(1,ℤ/8)14yes—
207C2×C4×C11C22×D412yes—
208C2×C4×C11C22×D412yes—
209C2×C4×C11C22×D412yes—
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C22×D412yes—
212C2×C4×C11C22×D412yes—
213C2×C4×C112−1+414yes—
214C2×C4×C11C2511yescharacteristic
215C22⋊D11—416no—
216C2×Dic11—24no—
217C2×Dic11—44no—
218D44—28no—
219D44—44no—
220D44—48no—
221D44—48no—
222C4×D11—416no—
223Dic22—48no—
224C11⋊C8—24no—
225C11⋊C8—24no—
226C22×#41—221no—
227#533—24no—
228#533C2×D1118yescomplemented
229#532—118no—
230#532—224no—
231C2×C4⋊Q8—111no—
232C2×C4⋊Q8C2×D1111yescharacteristic
233C2×C4⋊Q8C2×D1111yescharacteristic
234C2×#127—111no—
235C2×#125C2×D1112yes—
236C2×#124—221no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×#121—112no—
240C2×#121—221no—
241C2×C4×Q8—21no—
242C2×C4×Q8—21no—
243C2×C4×D4—112no—
244C2×C4×D4—221no—
245C2×#117C2×D1112yes—
246C22×C42C2×D1111yescharacteristic
247#500—118no—
248#498—118no—
249#486—118no—
250#486—118no—
251#482—1132no—
252#478—1132no—
253#431—118no—
254C2×#107—114no—
255C2×#106—114no—
256C2×C4⋊C8—112no—
257C2×#102—114no—
258C2×#102—114no—
259C2×C22⋊C8—112no—
260C2×C4×C8—111no—
261C2×C4×C8—111no—
262C22×C11—22no—
263C22×C11—22no—
264C22×C11—22no—
265C22×C11—44no—
266C22×C11#53612yes—
267C22×C11C2×#13512yes—
268C22×C11C2×AGL(1,ℤ/8)12yes—
269C22×C11C23×D411yescharacteristic
270C2×D11—44no—
271C2×D11—44no—
272C2×D11—44no—
273C2×D11—88no—
274C4×C11—22no—
275C4×C11—22no—
276C4×C11—22no—
277C4×C11—44no—
278C4×C11—44no—
279C4×C11#53612yes—
280C4×C11C2×#13514yes—
281C4×C11C2×AGL(1,ℤ/8)14yes—
282C4×C11C2×2−1+412yes—
283Dic11—44no—
284C2×#41—228no—
285C2×#41—448no—
286C22×Q8—21no—
287C22×Q8—21no—
288C22×Q8—221no—
289C22×D4—112no—
290C22×D4—222no—
291C22×D4—221no—
292C22×D4—221no—
293C23×C4—222no—
294C23×C4C22⋊D1111yescharacteristic
295C23×C4C22⋊D1111yescharacteristic
296C23×C4C22×D1111yescharacteristic
297C22×C8—112no—
298C22×C8—112no—
299C4⋊Q8—22no—
300C4⋊Q8—22no—
301C4⋊Q8—114no—
302C4⋊Q8—222no—
303C4⋊Q8C22×D1114yes—
304C4⋊Q8C22×D1114yes—
305#127—114no—
306#127—222no—
307#125—24no—
308#125C22×D1118yes—
309#124—228no—
310C22⋊Q8—28no—
311C22⋊Q8—28no—
312#121—118no—
313#121—224no—
314#121—228no—
315C4×Q8—28no—
316C4×Q8—28no—
317C4×D4—118no—
318C4×D4—224no—
319C4×D4—228no—
320#117—24no—
321#117C22×D1118yes—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—112no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4C22×D1112yes—
329C2×C4⋊C4C22×D1112yes—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—222no—
332C2×C22⋊C4—222no—
333C2×C42—22no—
334C2×C42C22⋊D1111yescharacteristic
335C2×C42C22⋊D1111yescharacteristic
336C2×C42C22⋊D1114yes—
337C2×C42C22×D1111yescharacteristic
338C2×C42C22×D1111yescharacteristic
339C2×C42C22×D1114yes—
340#107—1116no—
341#106—1116no—
342C4⋊C8—118no—
343#102—1116no—
344#102—1116no—
345C22⋊C8—118no—
346C4×C8—114no—
347C4×C8—114no—
348C2×C11—42no—
349C2×C11#322814yescomplemented
350C2×C11C2×#53611yescharacteristic
351C2×C11C22×#13511yescharacteristic
352C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
353D11—84no—
354C24—222no—
355C24C2×C22⋊D1111yescharacteristic
356#41—4432no—
357C2×Q8—24no—
358C2×Q8—24no—
359C2×Q8—44no—
360C2×Q8—44no—
361C2×Q8—224no—
362C2×Q8—444no—
363C2×D4—114no—
364C2×D4—228no—
365C2×D4—228no—
366C2×D4—224no—
367C2×D4—222no—
368C2×D4—224no—
369C2×D4—448no—
370C2×D4—444no—
371C2×D4—444no—
372C22×C4—24no—
373C22×C4—24no—
374C22×C4—24no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—222no—
378C22×C4—228no—
379C22×C4—448no—
380C22×C4C2×C22⋊D1114yes—
381C22×C4C2×C22⋊D1114yes—
382C22×C4C2×C22⋊D1112yes—
383C22×C4C2×C22⋊D1111yescharacteristic
384C22×C4C2×C22⋊D1111yescharacteristic
385C22×C4C2×C22⋊D1111yescharacteristic
386C22×C4C2×C22⋊D1111yescharacteristic
387C22×C4C2×C22⋊D1111yescharacteristic
388C22×C4C23×D1112yes—
389C22×C4C23×D1111yescharacteristic
390C2×C8—114no—
391C2×C8—114no—
392C2×C8—224no—
393C2×C8—224no—
394C4⋊C4—28no—
395C4⋊C4—28no—
396C4⋊C4—24no—
397C4⋊C4—24no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—114no—
401C4⋊C4—222no—
402C4⋊C4—224no—
403C4⋊C4C23×D1114yes—
404C4⋊C4C23×D1114yes—
405C22⋊C4—28no—
406C22⋊C4—228no—
407C22⋊C4—228no—
408C42—28no—
409C42C2×C22⋊D1114yes—
410C42C2×C22⋊D1112yes—
411C42C2×C22⋊D1114yes—
412C42C2×C22⋊D1112yes—
413C42C23×D1112yes—
414C42C23×D1112yes—
415C11C2×#322811yescharacteristic, complemented, Sylow
416C23—22no—
417C23—22no—
418C23—22no—
419C23—224no—
420C23—444no—
421C23—444no—
422C23—444no—
423C23C22×C22⋊D1112yes—
424C23C22×C22⋊D1111yescharacteristic
425Q8—48no—
426Q8—48no—
427Q8—448no—
428D4—228no—
429D4—4416no—
430D4—444no—
431D4—448no—
432D4—448no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—24no—
437C2×C4—28no—
438C2×C4—28no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—44no—
443C2×C4—44no—
444C2×C4—224no—
445C2×C4—4416no—
446C2×C4—444no—
447C2×C4#6700214yes—
448C2×C4#6700314yes—
449C2×C4#6704014yes—
450C2×C4C22×C22⋊D1112yes—
451C2×C4C22×C22⋊D1112yes—
452C2×C4C22×C22⋊D1112yes—
453C2×C4C22×C22⋊D1111yescharacteristic
454C2×C4C22×C22⋊D1112yes—
455C2×C4C22×C22⋊D1112yes—
456C2×C4C24×D1111yescharacteristic
457C8—224no—
458C8—224no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—44no—
463C22—444no—
464C22—444no—
465C22—444no—
466C22—888no—
467C22#1062334712yes—
468C22C2×#6700212yes—
469C22C2×#6700312yes—
470C22C23×C22⋊D1111yescharacteristic
471C4—22no—
472C4—22no—
473C4—22no—
474C4—44no—
475C4—44no—
476C4—444no—
477C4#1062334712yes—
478C4C2×#6700214yes—
479C4C2×#6700314yes—
480C4C2×#6704012yes—
481C2—42no—
482C2—884no—
483C2#1307975214yesdirect product factor
484C2C2×#1062334711yescharacteristic
485C2C22×#6700311yescharacteristic
486C2C22×#6700211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#533C2
socleC23×C11C22×D4
prime radicalC2×#10623008C2
hypercenterC2×#533D11
hypocenterC11C2×#3228
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
2. #13079752C2direct (N × H)
3. C2×#10622691C2semidirect
4. C2×#10622692C2semidirect
5. C2×#10622701C2semidirect
6. C2×#10622701C2semidirect
7. C2×#10622616C2semidirect
8. C2×#10622679C2semidirect
9. C2×#10622538C2semidirect
10. C2×C11×#533C2semidirect
13. C11×#533C22semidirect
33. #10622701C22semidirect
34. #10622701C22semidirect
35. #10622692C22semidirect
36. #10622691C22semidirect
37. #10622679C22semidirect
38. #10622616C22semidirect
43. #10622538C22semidirect
173. C2×#533D11semidirect
228. #533C2×D11semidirect
349. C2×C11#3228semidirect
415. C11C2×#3228semidirect
483. C2#13079752direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230082
#130797522
C2×#106226912
C2×#106226922
C2×#106227012
C2×#106226162
C2×#106226792
C2×#106225382
C2×C11×#5332
C2×#322811