Finite Group Databasebeta

← C2×#13079755 #15625834

Subgroups — C2×#13079755 #15625834

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×#10623259C211yesmaximal, characteristic, complemented
2C2×#10623256C211yesmaximal, characteristic
3#13079755C2116yesmaximal, direct product factor
4C2×#10622692C211yesmaximal, characteristic, complemented
5C2×#10622701C211yesmaximal, characteristic, complemented
6C2×#10622307C211yesmaximal, characteristic, complemented
7C2×#10622498C214yesmaximal, complemented
8C2×#10622504C214yesmaximal, complemented
9C2×#10622298C211yesmaximal, characteristic, complemented
10C2×C11×#500C211yesmaximal, characteristic, complemented
11C22×#4343—21no—
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#67000—21no—
15C2×#66999—21no—
16C2×Q8×Dic11—21no—
17#10623259—24no—
18#10623259C2218yescomplemented
19#10623256—24no—
20#10623256C2218yes—
21C2×#66950—21no—
22C2×#66948—21no—
23C2×#66948C2212yes—
24C2×#66946—21no—
25C2×#66946C2212yes—
26C2×#66945C2212yes—
27C2×#66943C2212yes—
28C2×#66940—21no—
29C2×#66927C2211yescharacteristic
30C2×C42×D11C2211yescharacteristic
31C2×#66922C2211yescharacteristic
32C11×#500C2218yescomplemented
33C2×C11×#107C2214yes—
34C2×C4×C8×C11C2211yescharacteristic
35C2×#66885C2214yes—
36C2×(C2×D11)⋊C8C2212yes—
37C2×Dic11⋊C8C2212yes—
38#10622701C2218yescomplemented
39#10622692C2218yescomplemented
40C2×#66873C2214yes—
41C2×#66872C2214yes—
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622504C22132yescomplemented
44#10622498C22132yescomplemented
45#10622307C2218yescomplemented
46#10622298C2218yescomplemented
47C22×Q8×C11—21no—
48C22×Q8×C11—21no—
49C2×#4343—28no—
50C2×#4343—48no—
51C22×D44—22no—
52C22×D44—21no—
53C22×D44—21no—
54C22×D44C2312yes—
55C22×C4×D11—22no—
56C22×C4×D11D411yescharacteristic
57C22×C4×D11D411yescharacteristic
58C22×C4×D11C2311yescharacteristic
59C22×Dic22—21no—
60C22×C8×C11C2312yes—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8C2314yes—
64C11×C4⋊Q8C2314yes—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2312yes—
69C2×C42×C11C2311yescharacteristic
70#67000—28no—
71#66999—28no—
72Q8×Dic11—28no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—22no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11C2312yes—
79C2×Dic11⋊C4—22no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C22×C11⋊C8C2312yes—
85#66950—28no—
86#66948—24no—
87#66948—28no—
88#66948C2318yes—
89#66946—24no—
90#66946—28no—
91#66946C2318yes—
92#66945—24no—
93#66945C2318yes—
94#66943—24no—
95#66943C2318yes—
96#66940—28no—
97#66927—22no—
98#66927C2314yes—
99C42×D11D414yes—
100C42×D11C2314yes—
101#66922—22no—
102#66922C2314yes—
103C11×#107C23116yes—
104C4×C8×C11C2314yes—
105#66885C23116yes—
106(C2×D11)⋊C8C2318yes—
107Dic11⋊C8C2318yes—
108#66873C23116yes—
109#66872C23116yes—
110C4×C11⋊C8C2314yes—
111C2×#3228—111nomaximal, Sylow
112C23×D11—22no—
113C23×D11C2×D411yescharacteristic
114C2×Q8×C11—24no—
115C2×Q8×C11—24no—
116C2×Q8×C11—44no—
117C2×Q8×C11—44no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C22×Dic11—22no—
124C22×Dic11C2×D411yescharacteristic
125C22×Dic11C2×D411yescharacteristic
126C22×Dic11C2×D411yescharacteristic
127#4343—432no—
128C2×D44—28no—
129C2×D44—22no—
130C2×D44—24no—
131C2×D44—24no—
132C2×D44—28no—
133C2×D44—48no—
134C2×D44—44no—
135C2×D44—44no—
136C2×D44C2414yes—
137C2×C4×D11—28no—
138C2×C4×D11—24no—
139C2×C4×D11—24no—
140C2×C4×D11—24no—
141C2×C4×D11—48no—
142C2×C4×D11C2×D412yes—
143C2×C4×D11C2×D414yes—
144C2×C4×D11C2×D414yes—
145C2×C4×D11C2412yes—
146C2×Dic22—24no—
147C2×Dic22—44no—
148C2×C8×C11—24no—
149C2×C8×C11C2414yes—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4C2414yes—
155C11×C4⋊C4C2414yes—
156C42×C11C2×D412yes—
157C42×C11C2412yes—
158(C2×D11)⋊C4—28no—
159(C2×D11)⋊C4—28no—
160(C2×D11)⋊C4—28no—
161C4⋊Dic11—28no—
162C4⋊Dic11—22no—
163C4⋊Dic11—24no—
164C4⋊Dic11C2414yes—
165Dic11⋊C4—28no—
166C4×Dic11—28no—
167C4×Dic11C2×D412yes—
168C4×Dic11C2×D414yes—
169C4×Dic11C2×D414yes—
170C4×Dic11C2412yes—
171C2×C11⋊C8—24no—
172C2×C11⋊C8C2414yes—
173C2×#533—111no—
174C2×#532—111no—
175#3228—1116no—
176C2×#500D1111yescharacteristic, complemented
177C2×#498—111no—
178C2×#486—111no—
179C2×#486—111no—
180C2×#482—114no—
181C2×#478—114no—
182C2×#431—111no—
183C23×C11C22×D411yescharacteristic
184C22×D11—22no—
185C22×D11—22no—
186C22×D11—22no—
187C22×D11—24no—
188C22×D11—44no—
189C22×D11—44no—
190C22×D11—44no—
191C22×D11C22×D412yes—
192Q8×C11—48no—
193Q8×C11—48no—
194C2×C4×C11—24no—
195C2×C4×C11—24no—
196C2×C4×C11—44no—
197C2×C4×C11—44no—
198C2×C4×C11#13514yes—
199C2×C4×C11AGL(1,ℤ/8)14yes—
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C22×D412yes—
202C2×C4×C11C22×D412yes—
203C2×C4×C112−1+414yes—
204C2×C4×C11C2511yescharacteristic
205C2×Dic11—22no—
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—24no—
209C2×Dic11—44no—
210C2×Dic11C22×D412yes—
211C2×Dic11C22×D412yes—
212C2×Dic11C22×D412yes—
213D44—28no—
214D44—416no—
215D44—44no—
216D44—48no—
217D44—48no—
218C4×D11—24no—
219C4×D11—28no—
220C4×D11—28no—
221C4×D11—24no—
222C4×D11—416no—
223Dic22—48no—
224C8×C11—24no—
225C11⋊C8—24no—
226C22×#41—221no—
227#533—118no—
228#533—224no—
229#532—118no—
230#532—224no—
231C2×C4⋊Q8—111no—
232C2×C4⋊Q8C2×D1111yescharacteristic
233C2×C4⋊Q8C2×D1111yescharacteristic
234C2×#127—111no—
235C2×#125—112no—
236C2×#124—221no—
237C2×C22⋊Q8—221no—
238C2×C22⋊Q8—221no—
239C2×#121—112no—
240C2×#121—221no—
241C2×C4×Q8—221no—
242C2×C4×Q8—221no—
243C2×C4×D4—112no—
244C2×C4×D4—221no—
245C2×#117—112no—
246C22×C42—111no—
247#500C2×D1118yescomplemented
248#498—118no—
249#486—118no—
250#486—118no—
251#482—1132no—
252#478—1132no—
253#431—118no—
254C2×#107C2×D1114yes—
255C2×#106—114no—
256C2×C4⋊C8—112no—
257C2×#102—114no—
258C2×#102—114no—
259C2×C22⋊C8—112no—
260C2×C4×C8—111no—
261C2×C4×C8C2×D1111yescharacteristic
262C22×C11#53612yes—
263C22×C11C2×#13512yes—
264C22×C11C2×AGL(1,ℤ/8)12yes—
265C22×C11C23×D411yescharacteristic
266C2×D11—22no—
267C2×D11—22no—
268C2×D11—22no—
269C2×D11—44no—
270C2×D11—44no—
271C2×D11—44no—
272C2×D11—44no—
273C2×D11—88no—
274C4×C11—44no—
275C4×C11—44no—
276C4×C11#53612yes—
277C4×C11C2×#13514yes—
278C4×C11C2×AGL(1,ℤ/8)14yes—
279C4×C11C2×2−1+412yes—
280Dic11—22no—
281Dic11—22no—
282Dic11—22no—
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—111no—
294C23×C4—111no—
295C23×C4—111no—
296C23×C4—222no—
297C22×C8—112no—
298C22×C8C22×D1112yes—
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—118no—
308#125—224no—
309#124—228no—
310C22⋊Q8—228no—
311C22⋊Q8—228no—
312#121—118no—
313#121—224no—
314#121—228no—
315C4×Q8—228no—
316C4×Q8—228no—
317C4×D4—118no—
318C4×D4—224no—
319C4×D4—228no—
320#117—118no—
321#117—224no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—112no—
325C2×C4⋊C4—222no—
326C2×C4⋊C4—222no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4C22×D1112yes—
329C2×C4⋊C4C22×D1112yes—
330C2×C22⋊C4—222no—
331C2×C22⋊C4—222no—
332C2×C22⋊C4—222no—
333C2×C42—111no—
334C2×C42—111no—
335C2×C42—111no—
336C2×C42—114no—
337C2×C42—114no—
338C2×C42—222no—
339C2×C42C22×D1111yescharacteristic
340#107C22×D11116yes—
341#106—1116no—
342C4⋊C8—118no—
343#102—1116no—
344#102—1116no—
345C22⋊C8—118no—
346C4×C8—114no—
347C4×C8C22×D1114yes—
348C2×C11#322814yescomplemented
349C2×C11C2×#53611yescharacteristic
350C2×C11C22×#13511yescharacteristic
351C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
352D11—42no—
353D11—84no—
354C24—111no—
355C24—222no—
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—224no—
366C2×D4—222no—
367C2×D4—224no—
368C2×D4—228no—
369C2×D4—448no—
370C2×D4—444no—
371C2×D4—444no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—111no—
375C22×C4—111no—
376C22×C4—111no—
377C22×C4—112no—
378C22×C4—114no—
379C22×C4—114no—
380C22×C4—112no—
381C22×C4—228no—
382C22×C4—224no—
383C22×C4—224no—
384C22×C4—224no—
385C22×C4—222no—
386C22×C4—448no—
387C22×C4D4×D1111yescharacteristic
388C22×C4D4×D1111yescharacteristic
389C22×C4C23×D1111yescharacteristic
390C2×C8—24no—
391C2×C8—114no—
392C2×C8—224no—
393C2×C8C23×D1114yes—
394C4⋊C4—24no—
395C4⋊C4—24no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—114no—
399C4⋊C4—228no—
400C4⋊C4—228no—
401C4⋊C4—222no—
402C4⋊C4—224no—
403C4⋊C4C23×D1114yes—
404C4⋊C4C23×D1114yes—
405C22⋊C4—228no—
406C22⋊C4—228no—
407C22⋊C4—228no—
408C42—114no—
409C42—112no—
410C42—114no—
411C42—112no—
412C42—228no—
413C42D4×D1112yes—
414C42C23×D1112yes—
415C11C2×#322811yescharacteristic, complemented, Sylow
416C23—112no—
417C23—222no—
418C23—222no—
419C23—222no—
420C23—224no—
421C23—444no—
422C23—444no—
423C23—444no—
424C23C2×D4×D1111yescharacteristic
425Q8—48no—
426Q8—48no—
427Q8—448no—
428D4—228no—
429D4—4416no—
430D4—444no—
431D4—448no—
432D4—448no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—44no—
436C2×C4—44no—
437C2×C4—112no—
438C2×C4—112no—
439C2×C4—112no—
440C2×C4—222no—
441C2×C4—222no—
442C2×C4—222no—
443C2×C4—224no—
444C2×C4—228no—
445C2×C4—228no—
446C2×C4—224no—
447C2×C4—224no—
448C2×C4—4416no—
449C2×C4—444no—
450C2×C4#6696414yes—
451C2×C4#6697214yes—
452C2×C4C2×D4×D1111yescharacteristic
453C2×C4C2×D4×D1112yes—
454C2×C4C2×D4×D1112yes—
455C2×C4#6704014yes—
456C2×C4C24×D1111yescharacteristic
457C8—24no—
458C8—224no—
459C22—222no—
460C22—222no—
461C22—222no—
462C22—444no—
463C22—444no—
464C22—444no—
465C22—444no—
466C22—888no—
467C22#1062325512yes—
468C22C2×#6696412yes—
469C22C2×#6697212yes—
470C22C22×D4×D1111yescharacteristic
471C4—44no—
472C4—44no—
473C4—222no—
474C4—222no—
475C4—222no—
476C4—444no—
477C4#1062325512yes—
478C4C2×#6696414yes—
479C4C2×#6697214yes—
480C4C2×#6704012yes—
481C2—442no—
482C2—884no—
483C2#1307975514yesdirect product factor
484C2C2×#1062325511yescharacteristic
485C2C22×#6697211yescharacteristic
486C2C22×#6696411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#500C2
socleC23×C11C22×D4
prime radicalC2×#10623256C2
hypercenterC2×#500D11
hypocenterC11C2×#3228
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
1. C2×#10623259C2semidirect
3. #13079755C2direct (N × H)
4. C2×#10622692C2semidirect
5. C2×#10622701C2semidirect
6. C2×#10622307C2semidirect
7. C2×#10622498C2semidirect
8. C2×#10622504C2semidirect
9. C2×#10622298C2semidirect
10. C2×C11×#500C2semidirect
18. #10623259C22semidirect
32. C11×#500C22semidirect
38. #10622701C22semidirect
39. #10622692C22semidirect
43. #10622504C22semidirect
44. #10622498C22semidirect
45. #10622307C22semidirect
46. #10622298C22semidirect
176. C2×#500D11semidirect
247. #500C2×D11semidirect
348. C2×C11#3228semidirect
415. C11C2×#3228semidirect
483. C2#13079755direct (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
#130797552
C2×#106226922
C2×#106227012
C2×#106223072
C2×#106224982
C2×#106225042
C2×#106222982
C2×C11×#5002
C2×#322811