Finite Group Databasebeta

← C2×#13079565 #15624965

Subgroups — C2×#13079565 #15624965

Order 2816.

2134 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2C2×D11×C4⋊Q8C211yesmaximal, characteristic
3#13079565C2116yesmaximal, direct product factor
4C2×#10622312C211yesmaximal, characteristic, complemented
5C2×#10622705C211yesmaximal, characteristic, complemented
6C2×#10622706C211yesmaximal, characteristic, complemented
7C2×#10622406C214yesmaximal, complemented
8C2×#10622421C214yesmaximal
9C2×#10622298C211yesmaximal, characteristic
10C2×C11×#487C211yesmaximal, characteristic, complemented
11C22×Q8×D11C2212yes—
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#66999—21no—
15C2×Q8×Dic11—21no—
16C2×#66997C2212yes—
17C22×#4326C2214yes—
18C22×Dic44C2214yes—
19#10623259—24no—
20#10623259C2218yes—
21D11×C4⋊Q8—24no—
22D11×C4⋊Q8C2218yes—
23C2×#66950C2212yes—
24C2×#66945—21no—
25C2×C4⋊C4×D11—21no—
26C2×C4⋊C4×D11—21no—
27C2×#66943—21no—
28C2×#66941—21no—
29C2×#66941—21no—
30C2×#66940C2212yes—
31C2×C42×D11C2211yescharacteristic
32C2×#66922C2211yescharacteristic
33C2×#66922C2211yescharacteristic
34C11×#487C2218yescomplemented
35C2×C11×#103C2214yes—
36C2×C4×C8×C11C2211yescharacteristic
37C2×(C2×D11)⋊C8C2212yes—
38C2×Dic11⋊C8C2212yes—
39#10622706C2218yescomplemented
40#10622705C2218yescomplemented
41C2×#66874C2214yes—
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622421C22132yes—
44#10622406C22132yescomplemented
45#10622312C2218yescomplemented
46#10622298C2218yes—
47C22×Q8×C11—21no—
48C22×Q8×C11C2312yes—
49C2×Q8×D11—24no—
50C2×Q8×D11—48no—
51C2×Q8×D11C2318yes—
52C22×C4×D11—22no—
53C22×C4×D11D411yescharacteristic
54C22×C4×D11D411yescharacteristic
55C22×C4×D11C2311yescharacteristic
56C22×Dic22—22no—
57C22×Dic22C2312yes—
58C22×Dic22C2312yes—
59C22×C8×C11C2312yes—
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8C2314yes—
63C11×C4⋊Q8C2314yes—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2312yes—
68C2×C42×C11C2311yescharacteristic
69#66999—28no—
70Q8×Dic11—28no—
71#66997—24no—
72#66997C2318yes—
73C2×#4326—48no—
74C2×#4326C23116yes—
75C2×(C2×D11)⋊C4—22no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—22no—
81C2×Dic11⋊C4—22no—
82C2×Dic11⋊C4—22no—
83C2×Dic11⋊C4—22no—
84C2×C4×Dic11—22no—
85C2×C4×Dic11D411yescharacteristic
86C2×C4×Dic11D411yescharacteristic
87C2×C4×Dic11C2311yescharacteristic
88C22×C11⋊C8C2312yes—
89C2×Dic44—48no—
90C2×Dic44C23116yes—
91#66950—24no—
92#66950C2318yes—
93#66945—28no—
94C4⋊C4×D11—28no—
95C4⋊C4×D11—28no—
96#66943—28no—
97#66941—28no—
98#66941—28no—
99#66940—24no—
100#66940C2318yes—
101C42×D11D414yes—
102C42×D11C2314yes—
103#66922—22no—
104#66922—22no—
105#66922C2314yes—
106#66922C2314yes—
107C11×#103C23116yes—
108C4×C8×C11C2314yes—
109(C2×D11)⋊C8C2318yes—
110Dic11⋊C8C2318yes—
111#66874C23116yes—
112C4×C11⋊C8C2314yes—
113C2×#3209—111nomaximal, Sylow
114C23×D11C2×D411yescharacteristic
115C2×Q8×C11—22no—
116C2×Q8×C11—24no—
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×Dic11—22no—
127C22×Dic11C2×D411yescharacteristic
128C22×Dic11C2×D411yescharacteristic
129C22×Dic11C2×D411yescharacteristic
130Q8×D11—416no—
131Q8×D11—416no—
132C2×C4×D11—28no—
133C2×C4×D11—24no—
134C2×C4×D11—24no—
135C2×C4×D11—48no—
136C2×C4×D11Q1618yescomplemented
137C2×C4×D11C2×D412yes—
138C2×C4×D11C2×D414yes—
139C2×C4×D11C2×D414yes—
140C2×C4×D11C2412yes—
141C2×Dic22—28no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C2×Dic22—28no—
145C2×Dic22—28no—
146C2×Dic22—48no—
147C2×Dic22C2414yes—
148C2×Dic22C2414yes—
149C2×C8×C11—24no—
150C2×C8×C11C2414yes—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4C2414yes—
156C42×C11C2×D412yes—
157C42×C11C2412yes—
158#4326—416no—
159(C2×D11)⋊C4—28no—
160C4⋊Dic11—28no—
161C4⋊Dic11—24no—
162C4⋊Dic11—24no—
163C4⋊Dic11—24no—
164C4⋊Dic11—24no—
165Dic11⋊C4—28no—
166Dic11⋊C4—28no—
167Dic11⋊C4—28no—
168C4×Dic11—28no—
169C4×Dic11C2×D412yes—
170C4×Dic11C2×D414yes—
171C4×Dic11C2×D414yes—
172C4×Dic11C2412yes—
173C2×C11⋊C8—24no—
174C2×C11⋊C8C2414yes—
175Dic44—416no—
176C2×#533—111no—
177C22×C4⋊Q8—111no—
178#3209—1116no—
179C2×#494—111no—
180C2×#494—111no—
181C2×#487—111no—
182C2×#487D1111yescharacteristic, complemented
183C2×#462—114no—
184C2×#451—114no—
185C2×#431—111no—
186C23×C11C22×D411yescharacteristic
187C22×D11—22no—
188C22×D11—22no—
189C22×D11C2×Q1614yes—
190C22×D11C22×D412yes—
191Q8×C11—28no—
192Q8×C11—44no—
193Q8×C11—48no—
194C2×C4×C11—24no—
195C2×C4×C11—24no—
196C2×C4×C11—44no—
197C2×C4×C11—44no—
198C2×C4×C11C2×Q1614yes—
199C2×C4×C11#13714yes—
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C22×D412yes—
202C2×C4×C11C22×D412yes—
203C2×C4×C11H(5,𝔽2)14yes—
204C2×C4×C11C2511yescharacteristic
205C2×Dic11—22no—
206C2×Dic11—22no—
207C2×Dic11—24no—
208C2×Dic11—24no—
209C2×Dic11—44no—
210C2×Dic11—44no—
211C2×Dic11C2×Q1614yes—
212C2×Dic11C22×D412yes—
213C2×Dic11C22×D412yes—
214C2×Dic11C22×D412yes—
215C4×D11—24no—
216C4×D11—28no—
217C4×D11—24no—
218C4×D11—416no—
219C4×D11C2×Q16116yescomplemented
220Dic22—28no—
221Dic22—28no—
222Dic22—416no—
223Dic22—44no—
224Dic22—44no—
225C8×C11—24no—
226C11⋊C8—24no—
227C23×Q8—112no—
228C22×Q16—114no—
229C22×Q16—114no—
230#533—118no—
231#533—224no—
232C2×C4⋊Q8—112no—
233C2×C4⋊Q8—118no—
234C2×C4⋊Q8—111no—
235C2×C4⋊Q8—111no—
236C2×C4⋊Q8—221no—
237C2×C4⋊Q8—221no—
238C2×C4⋊Q8—224no—
239C2×C4⋊Q8C2×D1111yescharacteristic
240C2×C4⋊Q8C2×D1111yescharacteristic
241C2×#125—221no—
242C2×C22⋊Q8—112no—
243C2×C22⋊Q8—221no—
244C2×C4×Q8—112no—
245C2×C4×Q8—221no—
246C2×#117—221no—
247C22×C4⋊C4—221no—
248C22×C4⋊C4—221no—
249C22×C42—111no—
250#494—118no—
251#494—118no—
252#487—118no—
253#487C2×D1118yescomplemented
254#462—1132no—
255#451—1132no—
256#431—118no—
257C2×C4⋊C8—112no—
258C2×#103—114no—
259C2×#103C2×D1114yes—
260C2×C22⋊C8—112no—
261C2×C4×C8—111no—
262C2×C4×C8C2×D1111yescharacteristic
263C22×C11#53512yes—
264C22×C11C22×Q1612yes—
265C22×C11C2×#13712yes—
266C22×C11C23×D411yescharacteristic
267C2×D11—22no—
268C2×D11—28no—
269C2×D11—22no—
270C2×D11C22×Q1614yes—
271C4×C11—44no—
272C4×C11—44no—
273C4×C11#53512yes—
274C4×C11C22×Q1614yes—
275C4×C11C2×#13714yes—
276C4×C11C2×H(5,𝔽2)12yes—
277Dic11—22no—
278Dic11—22no—
279Dic11—44no—
280Dic11—44no—
281Dic11C22×Q1614yes—
282C22×Q8—21no—
283C22×Q8—118no—
284C22×Q8—112no—
285C22×Q8—112no—
286C22×Q8—222no—
287C22×Q8—224no—
288C22×Q8—448no—
289C22×Q8C22×D1112yes—
290C23×C4—111no—
291C23×C4—111no—
292C23×C4—111no—
293C23×C4—222no—
294C2×Q16—1116no—
295C2×Q16—1116no—
296C2×Q16—448no—
297C2×Q16—448no—
298C22×C8—112no—
299C22×C8C22×D1112yes—
300C4⋊Q8—22no—
301C4⋊Q8—22no—
302C4⋊Q8—118no—
303C4⋊Q8—114no—
304C4⋊Q8—114no—
305C4⋊Q8—228no—
306C4⋊Q8—228no—
307C4⋊Q8—224no—
308C4⋊Q8—222no—
309C4⋊Q8—222no—
310C4⋊Q8C22×D1114yes—
311C4⋊Q8C22×D1114yes—
312#125—228no—
313C22⋊Q8—118no—
314C22⋊Q8—224no—
315C22⋊Q8—228no—
316C4×Q8—118no—
317C4×Q8—224no—
318C4×Q8—228no—
319#117—228no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—228no—
324C2×C4⋊C4—228no—
325C2×C4⋊C4—222no—
326C2×C4⋊C4—222no—
327C2×C4⋊C4—222no—
328C2×C4⋊C4—222no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4—221no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4C22×D1112yes—
334C2×C22⋊C4—222no—
335C2×C42—111no—
336C2×C42—111no—
337C2×C42—111no—
338C2×C42—114no—
339C2×C42—114no—
340C2×C42—222no—
341C2×C42C22×D1111yescharacteristic
342C4⋊C8—118no—
343#103—1116no—
344#103C22×D11116yes—
345C22⋊C8—118no—
346C4×C8—114no—
347C4×C8C22×D1114yes—
348C2×C11#320914yescomplemented
349C2×C11C2×#53511yescharacteristic
350C2×C11C23×Q1611yescharacteristic
351C2×C11C22×#13711yescharacteristic
352D11—24no—
353C24—111no—
354C2×Q8—24no—
355C2×Q8—22no—
356C2×Q8—28no—
357C2×Q8—44no—
358C2×Q8—114no—
359C2×Q8—114no—
360C2×Q8—228no—
361C2×Q8—222no—
362C2×Q8—222no—
363C2×Q8—228no—
364C2×Q8—228no—
365C2×Q8—448no—
366C2×Q8—4416no—
367C2×Q8—4416no—
368C2×Q8C23×D1114yes—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—111no—
372C22×C4—118no—
373C22×C4—114no—
374C22×C4—111no—
375C22×C4—111no—
376C22×C4—114no—
377C22×C4—112no—
378C22×C4—112no—
379C22×C4—228no—
380C22×C4—224no—
381C22×C4—224no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—448no—
385C22×C4D4×D1111yescharacteristic
386C22×C4D4×D1111yescharacteristic
387C22×C4C23×D1111yescharacteristic
388Q16—4416no—
389Q16—4416no—
390C2×C8—24no—
391C2×C8—114no—
392C2×C8—224no—
393C2×C8C23×D1114yes—
394C4⋊C4—24no—
395C4⋊C4—24no—
396C4⋊C4—24no—
397C4⋊C4—22no—
398C4⋊C4—228no—
399C4⋊C4—228no—
400C4⋊C4—228no—
401C4⋊C4—228no—
402C4⋊C4—224no—
403C4⋊C4—224no—
404C4⋊C4—224no—
405C4⋊C4—224no—
406C4⋊C4C23×D1114yes—
407C22⋊C4—228no—
408C42—112no—
409C42—114no—
410C42—114no—
411C42—112no—
412C42—228no—
413C42D4×D1112yes—
414C42C23×D1112yes—
415C11C2×#320911yescharacteristic, complemented, Sylow
416C23—114no—
417C23—112no—
418C23—222no—
419C23—222no—
420C23C2×D4×D1111yescharacteristic
421Q8—28no—
422Q8—48no—
423Q8—44no—
424Q8—228no—
425Q8—228no—
426Q8—4416no—
427Q8—444no—
428Q8—444no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—44no—
432C2×C4—44no—
433C2×C4—114no—
434C2×C4—112no—
435C2×C4—1116no—
436C2×C4—112no—
437C2×C4—112no—
438C2×C4—222no—
439C2×C4—222no—
440C2×C4—228no—
441C2×C4—224no—
442C2×C4—224no—
443C2×C4—224no—
444C2×C4—224no—
445C2×C4—4416no—
446C2×C4—444no—
447C2×C4—444no—
448C2×C4#6696814yes—
449C2×C4Q16×D1114yes—
450C2×C4C2×D4×D1112yes—
451C2×C4C2×D4×D1112yes—
452C2×C4C2×D4×D1111yescharacteristic
453C2×C4#6704214yes—
454C2×C4C24×D1111yescharacteristic
455C8—24no—
456C8—224no—
457C22—114no—
458C22—228no—
459C22—222no—
460C22—222no—
461C22#1062320512yes—
462C22C2×#6696812yes—
463C22C2×Q16×D1112yes—
464C22C22×D4×D1111yescharacteristic
465C4—44no—
466C4—44no—
467C4—114no—
468C4—222no—
469C4—222no—
470C4—444no—
471C4—444no—
472C4#1062320512yes—
473C4C2×#6696814yes—
474C4C2×Q16×D1114yes—
475C4C2×#6704212yes—
476C2—224no—
477C2#1307956514yesdirect product factor
478C2C2×#1062320511yescharacteristic
479C2C22×Q16×D1111yescharacteristic
480C2C22×#6696811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#487C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#487D11
hypocenterC11C2×#3209
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
3. #13079565C2direct (N × H)
4. C2×#10622312C2semidirect
5. C2×#10622705C2semidirect
6. C2×#10622706C2semidirect
7. C2×#10622406C2semidirect
10. C2×C11×#487C2semidirect
34. C11×#487C22semidirect
39. #10622706C22semidirect
40. #10622705C22semidirect
44. #10622406C22semidirect
45. #10622312C22semidirect
136. C2×C4×D11Q16semidirect
182. C2×#487D11semidirect
219. C4×D11C2×Q16semidirect
253. #487C2×D11semidirect
348. C2×C11#3209semidirect
415. C11C2×#3209semidirect
477. C2#13079565direct (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×D11×C4⋊Q82
#130795652
C2×#106223122
C2×#106227052
C2×#106227062
C2×#106224062
C2×#106224212
C2×#106222982
C2×C11×#4872
C2×#320911