Finite Group Databasebeta

← C2×#13074417 #14920848

Subgroups — C2×#13074417 #14920848

Order 2816.

2590 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66949C211yesmaximal, characteristic
2C22×#66945C211yesmaximal, characteristic
3#13074417C2116yesmaximal, direct product factor
4C2×#10622595C211yesmaximal, characteristic, complemented
5C2×#10622274C211yesmaximal, characteristic, complemented
6C2×#10622596C211yesmaximal, characteristic, complemented
7C2×#10622288C212yesmaximal
8C2×#10622287C212yesmaximal
9C2×#10622259C212yesmaximal, complemented
10C2×#10622260C212yesmaximal, complemented
11C2×#10622280C211yesmaximal, characteristic
12C2×C11×#400C211yesmaximal, characteristic, complemented
13C23×C4×D11C2211yescharacteristic
14C23×Dic22C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2212yes—
23C22×Dic11⋊C4C2212yes—
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2212yes—
27C22×C4×Dic11C2212yes—
28C2×#66949—28no—
29C2×#66949C2218yes—
30C2×#66945—28no—
31C2×#66945C2218yes—
32C11×#400C2218yescomplemented
33C2×C11×#95C2211yescharacteristic
34C2×C11×#95C2212yes—
35C2×C11×#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622596C2218yescomplemented
42#10622595C2218yescomplemented
43#10622288C22116yes—
44#10622287C22116yes—
45#10622280C2218yes—
46#10622274C2218yescomplemented
47#10622260C22116yescomplemented
48#10622259C22116yescomplemented
49C24×D11C2311yescharacteristic
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×Dic11C2312yes—
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C22×C4×D11—28no—
61C22×C4×D11D418yes—
62C22×C4×D11C2314yes—
63C22×Dic22—24no—
64C22×Dic22—28no—
65C22×Dic22C2314yes—
66C2×C11×C4⋊C4—24no—
67C2×C11×C4⋊C4—24no—
68C2×C11×C4⋊C4C2314yes—
69C2×C11×C4⋊C4C2314yes—
70C2×(C2×D11)⋊C4—28no—
71C2×(C2×D11)⋊C4—24no—
72C2×(C2×D11)⋊C4—24no—
73C2×(C2×D11)⋊C4—44no—
74C2×(C2×D11)⋊C4C2318yes—
75C2×(C2×D11)⋊C4C2314yes—
76C2×(C2×D11)⋊C4C2314yes—
77C2×(C2×D11)⋊C4C2318yes—
78C2×C4⋊Dic11—24no—
79C2×C4⋊Dic11—44no—
80C2×C4⋊Dic11C2314yes—
81C2×C4⋊Dic11C2318yes—
82C2×Dic11⋊C4—24no—
83C2×Dic11⋊C4—24no—
84C2×Dic11⋊C4—28no—
85C2×Dic11⋊C4—44no—
86C2×Dic11⋊C4C2318yes—
87C2×Dic11⋊C4C2314yes—
88C2×Dic11⋊C4C2314yes—
89C2×Dic11⋊C4C2318yes—
90C2×C4×Dic11—28no—
91C2×C4×Dic11C2318yes—
92#66949—232no—
93#66945—232no—
94C11×#95C2318yes—
95C11×#95C2318yes—
96C11×#95C2314yes—
97C11⋊#95C2318yes—
98C11⋊#95C2318yes—
99C11⋊#95C2318yes—
100C11⋊#95C2318yes—
101C11⋊#95C2314yes—
102C2×#2625—111nomaximal, Sylow
103C24×C11C2411yescharacteristic
104C23×D11—24no—
105C23×D11—22no—
106C23×D11—24no—
107C23×D11—22no—
108C23×D11C2×D414yes—
109C23×D11C2412yes—
110C22×C4×C11—24no—
111C22×C4×C11—24no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—24no—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—24no—
118C22×C4×C11—28no—
119C22×C4×C11—22no—
120C22×C4×C11—24no—
121C22×C4×C11C2×D414yes—
122C22×C4×C11C2414yes—
123C22×C4×C11C2412yes—
124C22×C4×C11C2414yes—
125C22×C4×C11C2412yes—
126C22×C4×C11C2412yes—
127C22×Dic11—24no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—24no—
131C22×Dic11—24no—
132C22×Dic11—24no—
133C22×Dic11—24no—
134C22×Dic11—22no—
135C22×Dic11—24no—
136C22×Dic11—22no—
137C22×Dic11—24no—
138C22×Dic11C2×D414yes—
139C22×Dic11#4118yes—
140C22×Dic11C2414yes—
141C22×Dic11C2412yes—
142C22×Dic11C2414yes—
143C22×Dic11C2412yes—
144C22×Dic11C2412yes—
145C2×C4×D11—232no—
146C2×C4×D11—216no—
147C2×C4×D11C2×D4116yes—
148C2×Dic22—28no—
149C2×Dic22—216no—
150C2×Dic22—416no—
151C11×C4⋊C4—28no—
152C11×C4⋊C4—28no—
153(C2×D11)⋊C4—216no—
154(C2×D11)⋊C4—28no—
155(C2×D11)⋊C4—28no—
156(C2×D11)⋊C4—48no—
157C4⋊Dic11—28no—
158C4⋊Dic11—48no—
159Dic11⋊C4—28no—
160Dic11⋊C4—216no—
161Dic11⋊C4—28no—
162Dic11⋊C4—48no—
163C4×Dic11—216no—
164C22×C22⋊Q8—111no—
165C22×#117—111no—
166#2625—1116no—
167C2×#400—111no—
168C2×#400D1111yescharacteristic, complemented
169C2×#398—111no—
170C2×#398—111no—
171C2×#397—112no—
172C2×#397—112no—
173C2×#391—112no—
174C2×#389—112no—
175C2×#380—111no—
176C23×C11C22×D412yes—
177C23×C11C2×#4114yes—
178C23×C11H(5,𝔽2)12yes—
179C23×C112−1+412yes—
180C23×C112−1+414yes—
181C23×C11C2511yescharacteristic
182C22×D11—28no—
183C22×D11—28no—
184C22×D11—28no—
185C22×D11—24no—
186C22×D11—22no—
187C22×D11—22no—
188C22×D11—24no—
189C22×D11—48no—
190C22×D11—48no—
191C22×D11C22×D414yes—
192C2×C4×C11—28no—
193C2×C4×C11—24no—
194C2×C4×C11—24no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—22no—
202C2×C4×C11—28no—
203C2×C4×C11—24no—
204C2×C4×C11—44no—
205C2×C4×C11—48no—
206C2×C4×C11—44no—
207C2×C4×C11—48no—
208C2×C4×C11C22×D414yes—
209C2×Dic11—24no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—24no—
213C2×Dic11—24no—
214C2×Dic11—24no—
215C2×Dic11—24no—
216C2×Dic11—22no—
217C2×Dic11—24no—
218C2×Dic11—22no—
219C2×Dic11—24no—
220C2×Dic11—44no—
221C2×Dic11—48no—
222C2×Dic11—44no—
223C2×Dic11—48no—
224C2×Dic11#123116yes—
225C2×Dic11C22×D414yes—
226C2×Dic11C2×#4118yes—
227C4×D11—232no—
228Dic22—416no—
229C23×Q8—111no—
230C24×C4—111no—
231C2×C22⋊Q8—118no—
232C2×C22⋊Q8—228no—
233C2×#117—118no—
234C2×#117—228no—
235C22×C4⋊C4—111no—
236C22×C4⋊C4—111no—
237C22×C4⋊C4—112no—
238C22×C4⋊C4—111no—
239C22×C4⋊C4—112no—
240C22×C4⋊C4—112no—
241C22×C4⋊C4C2×D1111yescharacteristic
242C22×C4⋊C4C2×D1111yescharacteristic
243C22×C22⋊C4—112no—
244C22×C22⋊C4—111no—
245C22×C22⋊C4—111no—
246C22×C22⋊C4—112no—
247C22×C42—112no—
248#400—118no—
249#400C2×D1118yescomplemented
250#398—118no—
251#398—118no—
252#397—1116no—
253#397—1116no—
254#391—1116no—
255#389—1116no—
256#380—118no—
257C2×#95—112no—
258C2×#95—112no—
259C2×#95—112no—
260C2×#95—112no—
261C2×#95—111no—
262C2×#95C2×D1112yes—
263C2×#95C2×D1112yes—
264C2×#95C2×D1111yescharacteristic
265C22×C11C2×#12314yes—
266C22×C11#53614yes—
267C22×C11#53714yes—
268C22×C11#54118yes—
269C22×C11#54218yes—
270C22×C11C23×D411yescharacteristic
271C22×C11C22×#4112yes—
272C22×C11C2×H(5,𝔽2)11yescharacteristic
273C22×C11C2×2−1+411yescharacteristic
274C22×C11C2×2−1+412yes—
275C2×D11—24no—
276C2×D11—24no—
277C2×D11—24no—
278C2×D11—416no—
279C2×D11—44no—
280C2×D11—44no—
281C4×C11—24no—
282C4×C11—42no—
283C4×C11—44no—
284C4×C11—42no—
285C4×C11—44no—
286Dic11—42no—
287Dic11—44no—
288Dic11—42no—
289Dic11—44no—
290Dic11C2×#12318yes—
291C25—111no—
292C22×Q8—114no—
293C22×Q8—224no—
294C22×Q8—228no—
295C23×C4—111no—
296C23×C4—118no—
297C23×C4—114no—
298C23×C4—111no—
299C23×C4—112no—
300C23×C4—112no—
301C23×C4—111no—
302C23×C4—228no—
303C23×C4C22×D1111yescharacteristic
304C23×C4C22×D1112yes—
305C23×C4C22×D1111yescharacteristic
306C23×C4C22×D1112yes—
307C23×C4C22×D1111yescharacteristic
308C22⋊Q8—2232no—
309#117—2232no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—114no—
313C2×C4⋊C4—114no—
314C2×C4⋊C4—114no—
315C2×C4⋊C4—118no—
316C2×C4⋊C4—118no—
317C2×C4⋊C4—118no—
318C2×C4⋊C4—224no—
319C2×C4⋊C4—228no—
320C2×C4⋊C4—224no—
321C2×C4⋊C4—224no—
322C2×C4⋊C4—444no—
323C2×C4⋊C4—444no—
324C2×C4⋊C4C22×D1114yes—
325C2×C4⋊C4C22×D1114yes—
326C2×C22⋊C4—118no—
327C2×C22⋊C4—114no—
328C2×C22⋊C4—114no—
329C2×C22⋊C4—118no—
330C2×C22⋊C4—228no—
331C2×C22⋊C4—224no—
332C2×C22⋊C4—224no—
333C2×C22⋊C4—444no—
334C2×C42—118no—
335C2×C42—228no—
336#95—114no—
337#95—118no—
338#95—118no—
339#95—118no—
340#95—118no—
341#95C22×D1114yes—
342#95C22×D1118yes—
343#95C22×D1118yes—
344C2×C11#262518yescomplemented
345C2×C11C22×#12311yescharacteristic
346C2×C11C2×#53611yescharacteristic
347C2×C11C2×#53711yescharacteristic
348C2×C11C2×#54112yes—
349C2×C11C2×#54212yes—
350D11—44no—
351C24—114no—
352C24—112no—
353C24—222no—
354C24—224no—
355C24—222no—
356C24—224no—
357C24C23×D1111yescharacteristic
358C2×Q8—228no—
359C2×Q8—2216no—
360C2×Q8—4416no—
361C22×C4—24no—
362C22×C4—24no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—22no—
370C22×C4—24no—
371C22×C4—28no—
372C22×C4—114no—
373C22×C4—118no—
374C22×C4—112no—
375C22×C4—1116no—
376C22×C4—114no—
377C22×C4—112no—
378C22×C4—114no—
379C22×C4—112no—
380C22×C4—2232no—
381C22×C4—2216no—
382C22×C4—224no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4—222no—
386C22×C4—224no—
387C22×C4—224no—
388C22×C4—224no—
389C22×C4—224no—
390C22×C4—224no—
391C22×C4—222no—
392C22×C4—224no—
393C22×C4D4×D1114yes—
394C22×C4C23×D1114yes—
395C22×C4C23×D1112yes—
396C22×C4C23×D1114yes—
397C22×C4C23×D1112yes—
398C22×C4C23×D1112yes—
399C4⋊C4—28no—
400C4⋊C4—28no—
401C4⋊C4—228no—
402C4⋊C4—2216no—
403C4⋊C4—228no—
404C4⋊C4—228no—
405C4⋊C4—448no—
406C4⋊C4—448no—
407C22⋊C4—2216no—
408C22⋊C4—228no—
409C22⋊C4—228no—
410C22⋊C4—448no—
411C42—2216no—
412C11C2×#262511yescharacteristic, complemented, Sylow
413C23—114no—
414C23—228no—
415C23—228no—
416C23—222no—
417C23—224no—
418C23—222no—
419C23—224no—
420C23—228no—
421C23—448no—
422C23—448no—
423C23C2×D4×D1112yes—
424C23#6704012yes—
425C23#41×D1114yes—
426C23#6704212yes—
427C23#6704314yes—
428C23C24×D1111yescharacteristic
429Q8—4416no—
430C2×C4—28no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—24no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—22no—
440C2×C4—28no—
441C2×C4—24no—
442C2×C4—48no—
443C2×C4—44no—
444C2×C4—44no—
445C2×C4—48no—
446C2×C4—1116no—
447C2×C4—114no—
448C2×C4—118no—
449C2×C4—2232no—
450C2×C4—224no—
451C2×C4—222no—
452C2×C4—222no—
453C2×C4—224no—
454C2×C4—222no—
455C2×C4—224no—
456C2×C4—224no—
457C2×C4—224no—
458C2×C4—224no—
459C2×C4—222no—
460C2×C4—224no—
461C2×C4—448no—
462C2×C4—448no—
463C2×C4—444no—
464C2×C4—444no—
465C2×C4C2×D4×D1114yes—
466C22—224no—
467C22—224no—
468C22—224no—
469C22—444no—
470C22—444no—
471C22—4416no—
472C22#1062316014yes—
473C22D11×#12314yes—
474C22#1062320614yes—
475C22#1062322718yes—
476C22#1062324118yes—
477C22C22×D4×D1111yescharacteristic
478C22C2×#6704011yescharacteristic
479C22C2×#41×D1112yes—
480C22C2×#6704211yescharacteristic
481C22C2×#6704312yes—
482C4—24no—
483C4—44no—
484C4—42no—
485C4—44no—
486C4—42no—
487C4—118no—
488C4—444no—
489C4—442no—
490C4—444no—
491C4—442no—
492C2—444no—
493C2#1307441718yesdirect product factor
494C2C2×D11×#12311yescharacteristic
495C2C2×#1062320611yescharacteristic
496C2C2×#1062316011yescharacteristic
497C2C2×#1062322712yes—
498C2C2×#1062324112yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#400C2
socleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#400D11
hypocenterC11C2×#2625
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
3. #13074417C2direct (N × H)
4. C2×#10622595C2semidirect
5. C2×#10622274C2semidirect
6. C2×#10622596C2semidirect
9. C2×#10622259C2semidirect
10. C2×#10622260C2semidirect
12. C2×C11×#400C2semidirect
32. C11×#400C22semidirect
41. #10622596C22semidirect
42. #10622595C22semidirect
46. #10622274C22semidirect
47. #10622260C22semidirect
48. #10622259C22semidirect
168. C2×#400D11semidirect
249. #400C2×D11semidirect
344. C2×C11#2625semidirect
412. C11C2×#2625semidirect
493. C2#13074417direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669492
C22×#669452
#130744172
C2×#106225952
C2×#106222742
C2×#106225962
C2×#106222882
C2×#106222872
C2×#106222592
C2×#106222602
C2×#106222802
C2×C11×#4002
C2×#262511