Finite Group Databasebeta

← C2×#13074444 #14920792

Subgroups — C2×#13074444 #14920792

Order 2816.

2742 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66941C211yesmaximal, characteristic, complemented
2C22×#66945C211yesmaximal, characteristic
3#13074444C2116yesmaximal, direct product factor
4C2×#10622599C211yesmaximal, characteristic, complemented
5C2×#10622290C211yesmaximal, characteristic
6C2×#10622605C211yesmaximal, characteristic
7C2×#10622269C212yesmaximal, complemented
8C2×#10622286C212yesmaximal
9C2×#10622260C212yesmaximal, complemented
10C2×#10622263C211yesmaximal, characteristic, complemented
11C2×#10622280C212yesmaximal
12C2×C11×#400C211yesmaximal, characteristic, complemented
13C23×C4×D11C2211yescharacteristic
14C23×Dic22C2212yes—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2212yes—
24C22×Dic11⋊C4C2212yes—
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2212yes—
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C2×#66945—28no—
30C2×#66945C2218yes—
31C2×#66941—28no—
32C2×#66941C2218yescomplemented
33C11×#400C2218yescomplemented
34C2×C11×#95C2212yes—
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41#10622605C2218yes—
42#10622599C2218yescomplemented
43#10622290C2218yes—
44#10622286C22116yes—
45#10622280C22116yes—
46#10622269C22116yescomplemented
47#10622263C2218yescomplemented
48#10622260C22116yescomplemented
49C24×D11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×Dic11C2311yescharacteristic
56C23×Dic11C2312yes—
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C22×C4×D11—24no—
61C22×C4×D11—24no—
62C22×C4×D11Q818yescomplemented
63C22×C4×D11C2314yes—
64C22×Dic22—28no—
65C22×Dic22—44no—
66C22×Dic22—44no—
67C22×Dic22C2318yes—
68C2×C11×C4⋊C4—24no—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4C2314yes—
71C2×C11×C4⋊C4C2314yes—
72C2×(C2×D11)⋊C4—24no—
73C2×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4—44no—
75C2×(C2×D11)⋊C4—44no—
76C2×(C2×D11)⋊C4C2314yes—
77C2×(C2×D11)⋊C4C2314yes—
78C2×(C2×D11)⋊C4C2318yes—
79C2×(C2×D11)⋊C4C2318yes—
80C2×C4⋊Dic11—24no—
81C2×C4⋊Dic11—24no—
82C2×C4⋊Dic11—44no—
83C2×C4⋊Dic11C2314yes—
84C2×C4⋊Dic11C2314yes—
85C2×C4⋊Dic11C2318yes—
86C2×Dic11⋊C4—28no—
87C2×Dic11⋊C4—28no—
88C2×Dic11⋊C4—44no—
89C2×Dic11⋊C4C2318yes—
90C2×Dic11⋊C4C2318yes—
91C2×Dic11⋊C4C2318yes—
92C2×C4×Dic11—24no—
93C2×C4×Dic11D418yes—
94C2×C4×Dic11C2314yes—
95C2×C4×Dic11C2314yes—
96#66945—232no—
97#66941—232no—
98C11×#95C2318yes—
99C11×#95C2314yes—
100C11×#95C2318yes—
101C11⋊#95C2318yes—
102C11⋊#95C2318yes—
103C11⋊#95C2314yes—
104C11⋊#95C2318yes—
105C2×#2628—111nomaximal, Sylow
106C24×C11C2411yescharacteristic
107C23×D11—22no—
108C23×D11—22no—
109C23×D11—24no—
110C23×D11—24no—
111C23×D11C2×Q814yes—
112C23×D11C2412yes—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—24no—
118C22×C4×C11—24no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11C2×D414yes—
125C22×C4×C11C2×Q814yes—
126C22×C4×C11C2412yes—
127C22×C4×C11C2414yes—
128C22×C4×C11C2414yes—
129C22×C4×C11C2412yes—
130C22×C4×C11C2412yes—
131C22×Dic11—22no—
132C22×Dic11—24no—
133C22×Dic11—24no—
134C22×Dic11—24no—
135C22×Dic11—24no—
136C22×Dic11—24no—
137C22×Dic11—24no—
138C22×Dic11—24no—
139C22×Dic11—24no—
140C22×Dic11C2×D414yes—
141C22×Dic11C2×D414yes—
142C22×Dic11C2×Q814yes—
143C22×Dic11#4114yes—
144C22×Dic11C2414yes—
145C22×Dic11C2414yes—
146C22×Dic11C2412yes—
147C22×Dic11C2412yes—
148C22×Dic11C2412yes—
149C2×C4×D11—232no—
150C2×C4×D11—28no—
151C2×C4×D11—28no—
152C2×C4×D11C2×Q8116yescomplemented
153C2×Dic22—216no—
154C2×Dic22—48no—
155C2×Dic22—48no—
156C2×Dic22—432no—
157C11×C4⋊C4—28no—
158C11×C4⋊C4—28no—
159(C2×D11)⋊C4—28no—
160(C2×D11)⋊C4—28no—
161(C2×D11)⋊C4—48no—
162(C2×D11)⋊C4—48no—
163C4⋊Dic11—28no—
164C4⋊Dic11—28no—
165C4⋊Dic11—48no—
166Dic11⋊C4—216no—
167Dic11⋊C4—216no—
168Dic11⋊C4—48no—
169C4×Dic11—28no—
170C4×Dic11C2×D4116yes—
171C22×C4⋊Q8—111no—
172C22×#117—111no—
173#2628—1116no—
174C2×#400—111no—
175C2×#400D1111yescharacteristic, complemented
176C2×#399—111no—
177C2×#399—111no—
178C2×#395—112no—
179C2×#393—112no—
180C2×#389—112no—
181C2×#382—111no—
182C2×#380—112no—
183C23×C11C22×D412yes—
184C23×C11C22×Q812yes—
185C23×C11C2×#4112yes—
186C23×C11H(5,𝔽2)14yes—
187C23×C112−1+414yes—
188C23×C11C2511yescharacteristic
189C22×D11—28no—
190C22×D11—216no—
191C22×D11—22no—
192C22×D11—22no—
193C22×D11—24no—
194C22×D11—24no—
195C22×D11—44no—
196C22×D11—44no—
197C22×D11—48no—
198C22×D11C22×Q814yes—
199C2×C4×C11—28no—
200C2×C4×C11—28no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—48no—
213C2×C4×C11—44no—
214C2×C4×C11—48no—
215C2×C4×C11C22×D414yes—
216C2×C4×C11C22×Q814yes—
217C2×Dic11—28no—
218C2×Dic11—24no—
219C2×Dic11—22no—
220C2×Dic11—24no—
221C2×Dic11—24no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—24no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—48no—
228C2×Dic11—44no—
229C2×Dic11—48no—
230C2×Dic11C22⋊Q8116yes—
231C2×Dic11C22×D414yes—
232C2×Dic11C22×D414yes—
233C2×Dic11C22×Q814yes—
234C2×Dic11C2×#4114yes—
235C4×D11—232no—
236Dic22—432no—
237C23×Q8—112no—
238C24×C4—111no—
239C2×C4⋊Q8—118no—
240C2×C4⋊Q8—228no—
241C2×#117—118no—
242C2×#117—228no—
243C22×C4⋊C4—112no—
244C22×C4⋊C4—112no—
245C22×C4⋊C4—111no—
246C22×C4⋊C4—111no—
247C22×C4⋊C4—112no—
248C22×C4⋊C4—112no—
249C22×C4⋊C4C2×D1111yescharacteristic
250C22×C4⋊C4C2×D1111yescharacteristic
251C22×C22⋊C4—111no—
252C22×C22⋊C4—111no—
253C22×C22⋊C4—112no—
254C22×C22⋊C4—112no—
255C22×C42—111no—
256C22×C42—111no—
257#400—118no—
258#400C2×D1118yescomplemented
259#399—118no—
260#399—118no—
261#395—1116no—
262#393—1116no—
263#389—1116no—
264#382—118no—
265#380—1116no—
266C2×#95—112no—
267C2×#95—112no—
268C2×#95—112no—
269C2×#95—111no—
270C2×#95C2×D1112yes—
271C2×#95C2×D1112yes—
272C2×#95C2×D1111yescharacteristic
273C22×C11C2×C22⋊Q814yes—
274C22×C11#53514yes—
275C22×C11#53614yes—
276C22×C11#54218yes—
277C22×C11#54418yes—
278C22×C11C23×D411yescharacteristic
279C22×C11C23×Q811yescharacteristic
280C22×C11C22×#4111yescharacteristic
281C22×C11C2×H(5,𝔽2)12yes—
282C22×C11C2×2−1+412yes—
283C2×D11—24no—
284C2×D11—28no—
285C2×D11—416no—
286C2×D11—42no—
287C2×D11—42no—
288C2×D11—44no—
289C4×C11—24no—
290C4×C11—24no—
291C4×C11—44no—
292C4×C11—42no—
293C4×C11—44no—
294Dic11—24no—
295Dic11—44no—
296Dic11—42no—
297Dic11—44no—
298Dic11C2×C22⋊Q818yes—
299C25—111no—
300C22×Q8—118no—
301C22×Q8—228no—
302C22×Q8—444no—
303C22×Q8—444no—
304C23×C4—111no—
305C23×C4—111no—
306C23×C4—118no—
307C23×C4—114no—
308C23×C4—111no—
309C23×C4—112no—
310C23×C4—112no—
311C23×C4—224no—
312C23×C4—224no—
313C23×C4C22×D1112yes—
314C23×C4C22×D1112yes—
315C23×C4C22×D1111yescharacteristic
316C23×C4C22×D1111yescharacteristic
317C23×C4C22×D1111yescharacteristic
318C4⋊Q8—2232no—
319#117—2232no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—114no—
323C2×C4⋊C4—118no—
324C2×C4⋊C4—114no—
325C2×C4⋊C4—118no—
326C2×C4⋊C4—118no—
327C2×C4⋊C4—118no—
328C2×C4⋊C4—224no—
329C2×C4⋊C4—228no—
330C2×C4⋊C4—228no—
331C2×C4⋊C4—224no—
332C2×C4⋊C4—444no—
333C2×C4⋊C4—444no—
334C2×C4⋊C4C22×D1114yes—
335C2×C4⋊C4C22×D1114yes—
336C2×C22⋊C4—114no—
337C2×C22⋊C4—114no—
338C2×C22⋊C4—118no—
339C2×C22⋊C4—118no—
340C2×C22⋊C4—224no—
341C2×C22⋊C4—224no—
342C2×C22⋊C4—444no—
343C2×C22⋊C4—444no—
344C2×C42—118no—
345C2×C42—114no—
346C2×C42—114no—
347C2×C42—224no—
348#95—118no—
349#95—118no—
350#95—114no—
351#95—118no—
352#95C22×D1118yes—
353#95C22×D1114yes—
354#95C22×D1118yes—
355C2×C11#262818yescomplemented
356C2×C11C22×C22⋊Q811yescharacteristic
357C2×C11C2×#53511yescharacteristic
358C2×C11C2×#53611yescharacteristic
359C2×C11C2×#54212yes—
360C2×C11C2×#54412yes—
361D11—44no—
362C24—114no—
363C24—112no—
364C24—222no—
365C24—222no—
366C24—224no—
367C24—224no—
368C24C23×D1111yescharacteristic
369C2×Q8—2216no—
370C2×Q8—448no—
371C2×Q8—448no—
372C2×Q8—4432no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—24no—
376C22×C4—22no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—114no—
385C22×C4—114no—
386C22×C4—114no—
387C22×C4—112no—
388C22×C4—114no—
389C22×C4—112no—
390C22×C4—1116no—
391C22×C4—114no—
392C22×C4—114no—
393C22×C4—112no—
394C22×C4—228no—
395C22×C4—2232no—
396C22×C4—228no—
397C22×C4—224no—
398C22×C4—222no—
399C22×C4—224no—
400C22×C4—224no—
401C22×C4—224no—
402C22×C4—224no—
403C22×C4—224no—
404C22×C4—224no—
405C22×C4—224no—
406C22×C4D4×D1114yes—
407C22×C4Q8×D1114yes—
408C22×C4C23×D1112yes—
409C22×C4C23×D1114yes—
410C22×C4C23×D1114yes—
411C22×C4C23×D1112yes—
412C22×C4C23×D1112yes—
413C4⋊C4—28no—
414C4⋊C4—28no—
415C4⋊C4—228no—
416C4⋊C4—2216no—
417C4⋊C4—2216no—
418C4⋊C4—228no—
419C4⋊C4—448no—
420C4⋊C4—448no—
421C22⋊C4—228no—
422C22⋊C4—228no—
423C22⋊C4—448no—
424C22⋊C4—448no—
425C42—1116no—
426C42—228no—
427C11C2×#262811yescharacteristic, complemented, Sylow
428C23—114no—
429C23—228no—
430C23—222no—
431C23—222no—
432C23—224no—
433C23—224no—
434C23—2216no—
435C23—448no—
436C23—444no—
437C23—444no—
438C23C2×D4×D1112yes—
439C23C2×Q8×D1112yes—
440C23#41×D1112yes—
441C23#6704214yes—
442C23#6704314yes—
443C23C24×D1111yescharacteristic
444Q8—4432no—
445C2×C4—28no—
446C2×C4—28no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—24no—
450C2×C4—22no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—48no—
459C2×C4—44no—
460C2×C4—48no—
461C2×C4—1116no—
462C2×C4—114no—
463C2×C4—114no—
464C2×C4—114no—
465C2×C4—114no—
466C2×C4—2232no—
467C2×C4—224no—
468C2×C4—228no—
469C2×C4—222no—
470C2×C4—224no—
471C2×C4—224no—
472C2×C4—224no—
473C2×C4—224no—
474C2×C4—224no—
475C2×C4—224no—
476C2×C4—224no—
477C2×C4—448no—
478C2×C4—448no—
479C2×C4—444no—
480C2×C4C2×D4×D1114yes—
481C2×C4C2×Q8×D1114yes—
482C22—228no—
483C22—224no—
484C22—4416no—
485C22—442no—
486C22—442no—
487C22—444no—
488C22D11×C22⋊Q814yes—
489C22#1062317914yes—
490C22#1062320514yes—
491C22#1062322018yes—
492C22#1062324118yes—
493C22C22×D4×D1111yescharacteristic
494C22C22×Q8×D1111yescharacteristic
495C22C2×#41×D1111yescharacteristic
496C22C2×#6704212yes—
497C22C2×#6704312yes—
498C4—24no—
499C4—24no—
500C4—44no—
501C4—42no—
502C4—44no—
503C4—118no—
504C4—224no—
505C4—444no—
506C4—442no—
507C4—444no—
508C2—444no—
509C2#1307444418yesdirect product factor
510C2C2×D11×C22⋊Q811yescharacteristic
511C2C2×#1062320511yescharacteristic
512C2C2×#1062317911yescharacteristic
513C2C2×#1062324112yes—
514C2C2×#1062322012yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#400C2
socleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#400D11
hypocenterC11C2×#2628
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. C22×#66941C2semidirect
3. #13074444C2direct (N × H)
4. C2×#10622599C2semidirect
7. C2×#10622269C2semidirect
9. C2×#10622260C2semidirect
10. C2×#10622263C2semidirect
12. C2×C11×#400C2semidirect
32. C2×#66941C22semidirect
33. C11×#400C22semidirect
42. #10622599C22semidirect
46. #10622269C22semidirect
47. #10622263C22semidirect
48. #10622260C22semidirect
62. C22×C4×D11Q8semidirect
152. C2×C4×D11C2×Q8semidirect
175. C2×#400D11semidirect
258. #400C2×D11semidirect
355. C2×C11#2628semidirect
427. C11C2×#2628semidirect
509. C2#13074444direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669412
C22×#669452
#130744442
C2×#106225992
C2×#106222902
C2×#106226052
C2×#106222692
C2×#106222862
C2×#106222602
C2×#106222632
C2×#106222802
C2×C11×#4002
C2×#262811