Finite Group Databasebeta

← C2×#13081471 #15634190

Subgroups — C2×#13081471 #15634190

Order 2816.

2058 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623253C211yesmaximal, characteristic, complemented
2C2×D4×Dic22C211yesmaximal, characteristic
3#13081471C2116yesmaximal, direct product factor
4C2×#10622468C212yesmaximal, complemented
5C2×#10622692C211yesmaximal, characteristic, complemented
6C2×#10622464C211yesmaximal, characteristic, complemented
7C2×#10622467C212yesmaximal, complemented
8C2×#10622374C212yesmaximal
9C2×#10622443C211yesmaximal, characteristic, complemented
10C2×#10622371C212yesmaximal
11C2×C4×#4324C211yesmaximal, characteristic
12C2×C11×#476C211yesmaximal, characteristic
13C23×Dic22—21no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×#66997—22no—
17C2×D4×Dic11C2212yes—
18C22×#4324C2211yescharacteristic
19C2×#66977—21no—
20#10623253—24no—
21#10623253C2218yescomplemented
22D4×Dic22—24no—
23D4×Dic22C2218yes—
24C2×#66941—21no—
25C2×#66941C2212yes—
26C2×#66941C2212yes—
27C2×#66940—21no—
28C2×#66940C2212yes—
29C2×#66931—22no—
30C2×#66922C2211yescharacteristic
31C2×C4×Dic22C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C11×#476C2218yes—
34C2×C11×#106C2212yes—
35C2×C11×C4⋊C8C2211yescharacteristic
36C2×C11×#102C2212yes—
37C2×#66896C2211yescharacteristic
38C2×#66881C2212yes—
39C2×#66880C2212yes—
40C2×Dic11⋊C8C2212yes—
41C2×C8×Dic11C2212yes—
42#10622692C2218yescomplemented
43C4×#4324C2218yes—
44C2×#66874C2211yescharacteristic
45C2×#66872C2212yes—
46C2×#66872C2212yes—
47C2×#66872C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622468C22116yescomplemented
50#10622467C22116yescomplemented
51#10622464C2218yescomplemented
52#10622443C2218yescomplemented
53#10622374C22116yes—
54#10622371C22116yes—
55C22×Q8×C11—21no—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C23×Dic11—22no—
59C22×Dic22—21no—
60C22×Dic22—22no—
61C22×Dic22—22no—
62C22×Dic22—28no—
63C22×Dic22—48no—
64C22×Dic22D411yescharacteristic
65C22×Dic22C2311yescharacteristic
66C22×C8×C11C2312yes—
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8C2314yes—
69C4×D4×C11—22no—
70C4×D4×C11C2314yes—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C42×C11C2311yescharacteristic
76C2×C22⋊Dic11—22no—
77#66997—216no—
78D4×Dic11—24no—
79D4×Dic11C2318yes—
80C2×#4324Q818yescomplemented
81C2×#4324C2314yes—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11D411yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2312yes—
86#66977—28no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4D412yes—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—22no—
94C2×C4×Dic11C2312yes—
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97#66941—28no—
98#66941—24no—
99#66941—24no—
100#66941C2318yes—
101#66941C2318yes—
102#66940—28no—
103#66940—24no—
104#66940C2318yes—
105#66931—216no—
106#66922—22no—
107#66922C2314yes—
108C4×Dic22—22no—
109C4×Dic22D414yes—
110C4×Dic22C2314yes—
111C4×Dic22C2314yes—
112C11×#106C2318yes—
113C11×C4⋊C8C2314yes—
114C11×#102C2318yes—
115#66896C2314yes—
116#66881C2318yes—
117#66880C2318yes—
118Dic11⋊C8C2318yes—
119C8×Dic11C2318yes—
120#66874C2314yes—
121#66872C2318yes—
122#66872C2314yes—
123#66872C2318yes—
124C4×C11⋊C8C2314yes—
125C2×Q8×SD16—111nomaximal, Sylow
126C24×C11—21no—
127C2×Q8×C11—24no—
128C2×Q8×C11—82no—
129C2×D4×C11—21no—
130C2×D4×C11—22no—
131C2×D4×C11C2×Q814yes—
132C2×D4×C11C2412yes—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—24no—
136C22×C4×C11—44no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—28no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—22no—
144C22×Dic11—48no—
145C22×Dic11C2×D412yes—
146C22×Dic11C2×D412yes—
147C2×Dic22—28no—
148C2×Dic22—28no—
149C2×Dic22—21no—
150C2×Dic22—24no—
151C2×Dic22—22no—
152C2×Dic22—48no—
153C2×Dic22—432no—
154C2×Dic22—44no—
155C2×Dic22—84no—
156C2×Dic22SD1618yescomplemented
157C2×Dic22C2×D414yes—
158C2×Dic22C2×Q814yescomplemented
159C2×Dic22C2412yes—
160C2×C8×C11—24no—
161C2×C8×C11C2414yes—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4C2414yes—
166C11×C4⋊C4C2412yes—
167C11×C22⋊C4—24no—
168C42×C11C2×D412yes—
169C42×C11C2412yes—
170C22⋊Dic11—28no—
171#4324C2×Q8116yescomplemented
172C4⋊Dic11—21no—
173C4⋊Dic11—22no—
174C4⋊Dic11—24no—
175C4⋊Dic11C2×D414yes—
176C4⋊Dic11C2414yes—
177C4⋊Dic11C2412yes—
178Dic11⋊C4—28no—
179Dic11⋊C4—28no—
180Dic11⋊C4—28no—
181Dic11⋊C4—24no—
182Dic11⋊C4C2×D418yes—
183C4×Dic11—28no—
184C4×Dic11—24no—
185C4×Dic11C2×D414yes—
186C4×Dic11C2414yes—
187C2×C11⋊C8—22no—
188C2×C11⋊C8C2×Q814yescomplemented
189C2×C11⋊C8C2412yes—
190C2×C11⋊C8C2412yes—
191C2×Q82—111no—
192C2×D4×Q8—111no—
193Q8×SD16—1116no—
194C2×#498—112no—
195C2×#498—111no—
196C2×#475—112no—
197C2×#475—111no—
198C2×#476—112no—
199C2×#476D1111yescharacteristic
200C2×C8×Q8—111no—
201C2×C4×SD16—112no—
202C2×C4×SD16—111no—
203C23×C11—24no—
204C23×C11—22no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11C22×D411yescharacteristic
208Q8×C11—84no—
209D4×C11—24no—
210D4×C11—22no—
211D4×C11C22×Q814yes—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—42no—
216C2×C4×C11—44no—
217C2×C4×C11—48no—
218C2×C4×C11C2×SD1614yes—
219C2×C4×C11C22×D412yes—
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D412yes—
222C2×C4×C11C22×Q812yes—
223C2×C4×C112−1+412yes—
224C2×C4×C11C2511yescharacteristic
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—24no—
230C2×Dic11—44no—
231C2×Dic11—42no—
232C2×Dic11—416no—
233C2×Dic11C2×SD1618yes—
234C2×Dic11C22×D414yes—
235C2×Dic11C22×D414yes—
236Dic22—24no—
237Dic22—22no—
238Dic22—48no—
239Dic22—416no—
240Dic22—88no—
241Dic22C2×SD16116yescomplemented
242Dic22C22×Q814yescomplemented
243C8×C11—24no—
244C11⋊C8—22no—
245C11⋊C8C22×Q814yescomplemented
246C23×Q8—221no—
247C22×SD16—111no—
248Q82—118no—
249Q82—224no—
250D4×Q8—118no—
251D4×Q8—224no—
252C2×C4⋊Q8—112no—
253C2×C4⋊Q8—112no—
254C2×C4⋊Q8—111no—
255C2×C4⋊Q8—221no—
256C2×C4⋊Q8—222no—
257C2×C4⋊Q8C2×D1111yescharacteristic
258C2×C22⋊Q8—222no—
259C2×C22⋊Q8—221no—
260C2×C4×Q8—111no—
261C2×C4×Q8—112no—
262C2×C4×Q8—111no—
263C2×C4×Q8—221no—
264C2×C4×D4—112no—
265C2×C4×D4C2×D1111yescharacteristic
266#498—118no—
267#498—1116no—
268#476—1116no—
269#476C2×D1118yes—
270#475—1116no—
271#475—118no—
272C8×Q8—118no—
273C4×SD16—118no—
274C4×SD16—1116no—
275C2×#106—112no—
276C2×#106—112no—
277C2×#106—112no—
278C2×#106—111no—
279C2×#106C2×D1112yes—
280C2×C4⋊C8—112no—
281C2×C4⋊C8C2×D1111yescharacteristic
282C2×#103—112no—
283C2×#103—111no—
284C2×#102—111no—
285C2×#102C2×D1112yes—
286C2×C4×C8—112no—
287C2×C4×C8—111no—
288C22×C11—24no—
289C22×C11—48no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11D4×Q812yes—
293C22×C11C22×SD1612yes—
294C22×C11#57712yes—
295C22×C11C23×D411yescharacteristic
296C4×C11—22no—
297C4×C11—42no—
298C4×C11—44no—
299C4×C11D4×Q812yes—
300C4×C11C22×SD1614yes—
301C4×C11C23×Q811yescharacteristic
302C4×C11C2×2−1+411yescharacteristic
303Dic11—24no—
304Dic11—24no—
305Dic11—44no—
306Dic11—42no—
307Dic11C22×SD1618yes—
308C22×Q8—21no—
309C22×Q8—111no—
310C22×Q8—111no—
311C22×Q8—222no—
312C22×Q8—222no—
313C22×Q8—228no—
314C22×Q8—221no—
315C22×Q8—448no—
316C22×D4C22×D1111yescharacteristic
317C23×C4—21no—
318C23×C4—222no—
319C2×SD16—118no—
320C2×SD16—114no—
321C22×C8—111no—
322C22×C8—111no—
323C22×C8C22×D1112yes—
324C4⋊Q8—22no—
325C4⋊Q8—118no—
326C4⋊Q8—118no—
327C4⋊Q8—114no—
328C4⋊Q8—224no—
329C4⋊Q8—224no—
330C4⋊Q8—228no—
331C4⋊Q8—2216no—
332C4⋊Q8—222no—
333C4⋊Q8C22×D1114yes—
334C22⋊Q8—2216no—
335C22⋊Q8—228no—
336C4×Q8—114no—
337C4×Q8—114no—
338C4×Q8—118no—
339C4×Q8—114no—
340C4×Q8—224no—
341C4×Q8—228no—
342C4×Q8—222no—
343C4×D4—22no—
344C4×D4—118no—
345C4×D4—224no—
346C4×D4C22×D1114yes—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—112no—
349C2×C4⋊C4—111no—
350C2×C4⋊C4—112no—
351C2×C4⋊C4—111no—
352C2×C4⋊C4—222no—
353C2×C4⋊C4—222no—
354C2×C4⋊C4—222no—
355C2×C4⋊C4—221no—
356C2×C4⋊C4—221no—
357C2×C4⋊C4C22×D1111yescharacteristic
358C2×C4⋊C4C22×D1112yes—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—222no—
361C2×C42—112no—
362C2×C42—222no—
363C2×C42—221no—
364C2×C42C22×D1111yescharacteristic
365#106—118no—
366#106—114no—
367#106—118no—
368#106—118no—
369#106C22×D1118yes—
370C4⋊C8—118no—
371C4⋊C8C22×D1114yes—
372#103—118no—
373#103—114no—
374#102—114no—
375#102C22×D1118yes—
376C4×C8—118no—
377C4×C8—114no—
378C2×C11—44no—
379C2×C11Q8×SD1614yescomplemented
380C2×C11C2×D4×Q811yescharacteristic
381C2×C11C23×SD1611yescharacteristic
382C2×C11C2×#57711yescharacteristic
383C24—21no—
384C2×Q8—24no—
385C2×Q8—82no—
386C2×Q8—118no—
387C2×Q8—114no—
388C2×Q8—114no—
389C2×Q8—112no—
390C2×Q8—228no—
391C2×Q8—228no—
392C2×Q8—221no—
393C2×Q8—224no—
394C2×Q8—222no—
395C2×Q8—448no—
396C2×Q8—4432no—
397C2×Q8—444no—
398C2×Q8—884no—
399C2×D4—21no—
400C2×D4—22no—
401C2×D4Q8×D1114yes—
402C2×D4C23×D1112yes—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—24no—
406C22×C4—44no—
407C22×C4—112no—
408C22×C4—112no—
409C22×C4—228no—
410C22×C4—221no—
411C22×C4—221no—
412C22×C4—222no—
413C22×C4—448no—
414C22×C4D4×D1111yescharacteristic
415C22×C4D4×D1111yescharacteristic
416C22×C4C23×D1111yescharacteristic
417SD16—1116no—
418C2×C8—24no—
419C2×C8—114no—
420C2×C8—112no—
421C2×C8—112no—
422C2×C8—222no—
423C2×C8C23×D1114yes—
424C4⋊C4—24no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—118no—
428C4⋊C4—114no—
429C4⋊C4—112no—
430C4⋊C4—114no—
431C4⋊C4—228no—
432C4⋊C4—228no—
433C4⋊C4—228no—
434C4⋊C4—222no—
435C4⋊C4—221no—
436C4⋊C4—224no—
437C4⋊C4—224no—
438C4⋊C4C23×D1114yes—
439C4⋊C4C23×D1112yes—
440C22⋊C4—24no—
441C22⋊C4—228no—
442C42—114no—
443C42—114no—
444C42—228no—
445C42—224no—
446C42D4×D1112yes—
447C42C23×D1112yes—
448C11C2×Q8×SD1611yescharacteristic, complemented, Sylow
449C23—24no—
450C23—22no—
451C23—42no—
452C23—42no—
453C23C2×D4×D1111yescharacteristic
454Q8—84no—
455Q8—1116no—
456Q8—114no—
457Q8—224no—
458Q8—222no—
459Q8—4416no—
460Q8—448no—
461Q8—888no—
462D4—24no—
463D4—22no—
464D4C2×Q8×D1114yes—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—42no—
469C2×C4—44no—
470C2×C4—48no—
471C2×C4—118no—
472C2×C4—114no—
473C2×C4—114no—
474C2×C4—224no—
475C2×C4—224no—
476C2×C4—222no—
477C2×C4—222no—
478C2×C4—224no—
479C2×C4—4416no—
480C2×C4—444no—
481C2×C4—442no—
482C2×C4SD16×D1114yes—
483C2×C4C2×D4×D1112yes—
484C2×C4C2×D4×D1112yes—
485C2×C4C2×D4×D1111yescharacteristic
486C2×C4C2×Q8×D1112yes—
487C2×C4#6704312yes—
488C2×C4C24×D1111yescharacteristic
489C8—24no—
490C8—114no—
491C8—222no—
492C22—24no—
493C22—48no—
494C22—42no—
495C22—42no—
496C22#1062316312yes—
497C22C2×SD16×D1112yes—
498C22#1062330612yes—
499C22C22×D4×D1111yescharacteristic
500C4—22no—
501C4—42no—
502C4—44no—
503C4—118no—
504C4—224no—
505C4—224no—
506C4—444no—
507C4—442no—
508C4#1062316312yes—
509C4C2×SD16×D1114yes—
510C4C22×Q8×D1111yescharacteristic
511C4C2×#6704311yescharacteristic
512C2—44no—
513C2#1308147114yesdirect product factor
514C2C2×#1062316311yescharacteristic
515C2C22×SD16×D1111yescharacteristic
516C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#476C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#476D11
hypocenterC11C2×Q8×SD16
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#10623253C2semidirect
3. #13081471C2direct (N × H)
4. C2×#10622468C2semidirect
5. C2×#10622692C2semidirect
6. C2×#10622464C2semidirect
7. C2×#10622467C2semidirect
9. C2×#10622443C2semidirect
21. #10623253C22semidirect
42. #10622692C22semidirect
49. #10622468C22semidirect
50. #10622467C22semidirect
51. #10622464C22semidirect
52. #10622443C22semidirect
80. C2×#4324Q8semidirect
156. C2×Dic22SD16semidirect
158. C2×Dic22C2×Q8semidirect
171. #4324C2×Q8semidirect
188. C2×C11⋊C8C2×Q8semidirect
241. Dic22C2×SD16semidirect
242. Dic22C22×Q8semidirect
245. C11⋊C8C22×Q8semidirect
379. C2×C11Q8×SD16semidirect
448. C11C2×Q8×SD16semidirect
513. C2#13081471direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232532
C2×D4×Dic222
#130814712
C2×#106224682
C2×#106226922
C2×#106224642
C2×#106224672
C2×#106223742
C2×#106224432
C2×#106223712
C2×C4×#43242
C2×C11×#4762
C2×Q8×SD1611