Finite Group Databasebeta

← C2×#13080983 #15632207

Subgroups — C2×#13080983 #15632207

Order 2816.

1866 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
1C2×#10623225C212yesmaximal
2#13080983C2116yesmaximal, direct product factor
3C2×#10622480C212yesmaximal, complemented
4C2×#10622475C212yesmaximal, complemented
5C2×#10622676C212yesmaximal, complemented
6C2×#10622500C211yesmaximal, characteristic, complemented
7C2×#10622500C211yesmaximal, characteristic, complemented
8C2×C4×Dic44C211yesmaximal, characteristic, complemented
9C2×C8×D44C211yesmaximal, characteristic
10C2×#10622493C211yesmaximal, characteristic, complemented
11C2×D11×#107C211yesmaximal, characteristic, complemented
12C2×C11×#499C211yesmaximal, characteristic, complemented
13C2×C11×#125C2212yes—
14C22×Dic44C2211yescharacteristic
15C22×C8×D11C2211yescharacteristic
16C22×C8×D11C2211yescharacteristic
17#10623225—28no—
18#10623225C22116yes—
19C2×#66951—22no—
20C2×#66950C2212yes—
21C2×#66950C2212yes—
22C2×#66947—22no—
23C2×#66945—22no—
24C2×#66945C2212yes—
25C2×C4⋊C4×D11C2212yes—
26C2×#66943—22no—
27C2×C4×D44C2211yescharacteristic
28C2×C4×Dic22C2212yes—
29C11×#499C2218yescomplemented
30C2×C11×#107C2211yescharacteristic
31C2×C11×#107C2211yescharacteristic
32C2×C11×#106C2212yes—
33C2×C4×C8×C11C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×#66882C2211yescharacteristic
37C2×#66880C2212yes—
38#10622676C22116yescomplemented
39C2×#66874C2212yes—
40C2×#66874C2212yes—
41C2×#66872C2212yes—
42C2×#66871C2212yes—
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44#10622500C2218yescomplemented
45#10622500C2218yescomplemented
46#10622493C2218yescomplemented
47D11×#107C2218yescomplemented
48#10622480C22116yescomplemented
49#10622475C22116yescomplemented
50C4×Dic44C2218yescomplemented
51C8×D44C2218yes—
52C22×D44D411yescharacteristic
53C22×C4×D11—22no—
54C22×C4×D11C2311yescharacteristic
55C22×C4×D11C2311yescharacteristic
56C22×Dic22C2312yes—
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2311yescharacteristic
59C11×#125—24no—
60C11×#125C2318yes—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C42×C11C2311yescharacteristic
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4D411yescharacteristic
70C2×(C2×D11)⋊C4D411yescharacteristic
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11D411yescharacteristic
74C2×C4⋊Dic11C2312yes—
75C2×Dic11⋊C4—22no—
76C2×Dic11⋊C4—22no—
77C2×C4×Dic11—22no—
78C2×C4×Dic11—22no—
79C22×C11⋊C8C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81C2×Dic44—24no—
82C2×Dic44C2314yes—
83C2×C8×D11—24no—
84C2×C8×D11—24no—
85C2×C8×D11C2314yes—
86C2×C8×D11C2314yes—
87#66951—216no—
88#66950—24no—
89#66950—24no—
90#66950C2318yes—
91#66950C2318yes—
92#66947—216no—
93#66945—24no—
94#66945—216no—
95#66945C2318yes—
96C4⋊C4×D11—24no—
97C4⋊C4×D11C2318yes—
98#66943—216no—
99C4×D44D414yes—
100C4×D44C2314yes—
101C4×Dic22—24no—
102C4×Dic22C2318yes—
103C11×#107C2314yes—
104C11×#107C2314yes—
105C11×#106C2318yes—
106C4×C8×C11C2314yes—
107(C2×D11)⋊C8C2314yes—
108(C2×D11)⋊C8C2314yes—
109#66882C2314yes—
110#66880C2318yes—
111#66874C2318yes—
112#66874C2318yes—
113#66872C2318yes—
114#66871C2318yes—
115C4⋊(C11⋊C8)C2314yes—
116C2×#3336—111nomaximal, Sylow
117C23×D11C2×D411yescharacteristic
118C23×D11C2×D411yescharacteristic
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11C2×D411yescharacteristic
127C22×Dic11C2×D411yescharacteristic
128C2×D44—24no—
129C2×D44C2×D414yes—
130C2×C4×D11—28no—
131C2×C4×D11—22no—
132C2×C4×D11—22no—
133C2×C4×D11—22no—
134C2×C4×D11—22no—
135C2×C4×D11—48no—
136C2×C4×D11C2×D412yes—
137C2×C4×D11C2×D412yes—
138C2×C4×D11C2412yes—
139C2×C4×D11C2412yes—
140C2×Dic22—22no—
141C2×Dic22—24no—
142C2×Dic22—24no—
143C2×Dic22C2414yes—
144C2×C8×C11—22no—
145C2×C8×C11#4114yes—
146C2×C8×C11C2412yes—
147C2×C8×C11C2412yes—
148C11×C4⋊C4—28no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—28no—
152C11×C4⋊C4C2414yes—
153C11×C4⋊C4C2414yes—
154C42×C11C2×D412yes—
155C42×C11C2412yes—
156(C2×D11)⋊C4—28no—
157(C2×D11)⋊C4—28no—
158(C2×D11)⋊C4—28no—
159(C2×D11)⋊C4C2×D414yes—
160(C2×D11)⋊C4C2×D414yes—
161C4⋊Dic11—28no—
162C4⋊Dic11—28no—
163C4⋊Dic11—22no—
164C4⋊Dic11C2×D414yes—
165C4⋊Dic11C2414yes—
166Dic11⋊C4—28no—
167Dic11⋊C4—28no—
168C4×Dic11—28no—
169C4×Dic11—28no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8C2412yes—
173C2×C11⋊C8C2412yes—
174Dic44—28no—
175C8×D11—28no—
176C8×D11—28no—
177C2×#552—112no—
178#3336—1116no—
179C2×#499D1111yescharacteristic, complemented
180C2×#485—112no—
181C2×#483—112no—
182C2×#479—112no—
183C2×#467—111no—
184C2×#467—111no—
185C2×C4×Q16—111no—
186C2×C8×D4—111no—
187C2×#427—111no—
188C22×#107—111no—
189C23×C11C22×D411yescharacteristic
190C22×D11—22no—
191C22×D11—22no—
192C22×D11—22no—
193C22×D11—22no—
194C22×D11—22no—
195C22×D11#13514yes—
196C22×D11C22×D412yes—
197C22×D11C22×D412yes—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—44no—
203C2×C4×C11—44no—
204C2×C4×C11C22×D412yes—
205C2×C4×C11C22×D412yes—
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C2×#4112yes—
208C2×C4×C112−1+412yes—
209C2×C4×C11C2511yescharacteristic
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—24no—
213C2×Dic11—24no—
214C2×Dic11—44no—
215C2×Dic11—44no—
216C2×Dic11C22×D412yes—
217C2×Dic11C22×D412yes—
218D44—28no—
219C4×D11—24no—
220C4×D11—24no—
221C4×D11—22no—
222C4×D11—22no—
223C4×D11—22no—
224C4×D11—22no—
225C4×D11—416no—
226Dic22—24no—
227Dic22—24no—
228Dic22—44no—
229C8×C11—22no—
230C8×C11C2×#4114yes—
231C11⋊C8—22no—
232C11⋊C8—22no—
233C22×Q16—111no—
234C23×C8—111no—
235C23×C8—111no—
236#552—1116no—
237#552—228no—
238C2×#126—222no—
239C2×#125—222no—
240C2×#125C2×D1112yes—
241C2×#123—222no—
242C2×C22⋊Q8—112no—
243C2×C22⋊Q8—112no—
244C2×C4×Q8—112no—
245C2×C4×D4—111no—
246C2×#117—112no—
247C2×#117—222no—
248C22×C4⋊C4—112no—
249#499C2×D1118yescomplemented
250#485—1116no—
251#483—1116no—
252#479—1116no—
253#467—118no—
254#467—118no—
255C4×Q16—118no—
256C8×D4—118no—
257#427—118no—
258C2×#107—111no—
259C2×#107—112no—
260C2×#107—118no—
261C2×#107C2×D1111yescharacteristic
262C2×#107C2×D1111yescharacteristic
263C2×#106—112no—
264C2×#106C2×D1112yes—
265C2×C4⋊C8—111no—
266C2×#103—112no—
267C2×#103—112no—
268C2×#103—112no—
269C2×C22⋊C8—111no—
270C2×C22⋊C8—111no—
271C2×C4×C8C2×D1111yescharacteristic
272C22×C11#54712yes—
273C22×C11C2×#13512yes—
274C22×C11#57812yes—
275C22×C11C23×D411yescharacteristic
276C2×D11—28no—
277C2×D11—22no—
278C2×D11—22no—
279C2×D11—22no—
280C2×D11—22no—
281C2×D11—22no—
282C2×D11—44no—
283C2×D11C2×#13514yes—
284C4×C11—22no—
285C4×C11—22no—
286C4×C11—44no—
287C4×C11—44no—
288C4×C11#54712yes—
289C4×C11C22×#4111yescharacteristic
290C4×C11C2×2−1+411yescharacteristic
291Dic11—22no—
292Dic11—22no—
293Dic11—44no—
294Dic11—44no—
295C22×Q8—112no—
296C22×D4—111no—
297C23×C4—111no—
298C23×C4—111no—
299C23×C4—222no—
300C2×Q16—114no—
301C2×Q16—224no—
302C22×C8—111no—
303C22×C8—111no—
304C22×C8—114no—
305C22×C8—114no—
306C22×C8—224no—
307C22×C8—224no—
308C22×C8C22×D1111yescharacteristic
309C22×C8C22×D1111yescharacteristic
310#126—2216no—
311#125—24no—
312#125—2216no—
313#125C22×D1118yes—
314#123—2216no—
315C22⋊Q8—118no—
316C22⋊Q8—118no—
317C22⋊Q8—224no—
318C22⋊Q8—224no—
319C4×Q8—118no—
320C4×Q8—224no—
321C4×D4—114no—
322C4×D4—114no—
323#117—118no—
324#117—2216no—
325#117—224no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—111no—
329C2×C4⋊C4—112no—
330C2×C4⋊C4—118no—
331C2×C4⋊C4—224no—
332C2×C4⋊C4—222no—
333C2×C4⋊C4—222no—
334C2×C4⋊C4—222no—
335C2×C4⋊C4—222no—
336C2×C4⋊C4C22×D1112yes—
337C2×C4⋊C4C22×D1112yes—
338C2×C22⋊C4—111no—
339C2×C22⋊C4—111no—
340C2×C22⋊C4—222no—
341C2×C22⋊C4—222no—
342C2×C22⋊C4—222no—
343C2×C42—222no—
344C2×C42—222no—
345C2×C42C22×D1111yescharacteristic
346#107—114no—
347#107—118no—
348#107C22×D1114yes—
349#107C22×D1114yes—
350#106—118no—
351#106C22×D1118yes—
352C4⋊C8—114no—
353#103—118no—
354#103—118no—
355#103—118no—
356C22⋊C8—114no—
357C22⋊C8—114no—
358C4×C8C22×D1114yes—
359C2×C11#333614yescomplemented
360C2×C11C2×#54711yescharacteristic
361C2×C11C22×#13511yescharacteristic
362C2×C11C2×#57811yescharacteristic
363D11—24no—
364D11—42no—
365C24—111no—
366C24—111no—
367C2×Q8—114no—
368C2×Q8—222no—
369C2×Q8—224no—
370C2×Q8—224no—
371C2×D4—114no—
372C2×D4—224no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—111no—
376C22×C4—111no—
377C22×C4—112no—
378C22×C4—112no—
379C22×C4—112no—
380C22×C4—112no—
381C22×C4—228no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4—222no—
388C22×C4—448no—
389C22×C4D4×D1111yescharacteristic
390C22×C4D4×D1111yescharacteristic
391C22×C4C23×D1111yescharacteristic
392Q16—228no—
393C2×C8—22no—
394C2×C8—112no—
395C2×C8—112no—
396C2×C8—222no—
397C2×C8—222no—
398C2×C8—228no—
399C2×C8—228no—
400C2×C8#434314yes—
401C2×C8C23×D1112yes—
402C2×C8C23×D1112yes—
403C4⋊C4—28no—
404C4⋊C4—28no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—114no—
408C4⋊C4—114no—
409C4⋊C4—228no—
410C4⋊C4—228no—
411C4⋊C4—228no—
412C4⋊C4—222no—
413C4⋊C4—228no—
414C4⋊C4C23×D1114yes—
415C4⋊C4C23×D1114yes—
416C22⋊C4—114no—
417C22⋊C4—114no—
418C22⋊C4—228no—
419C22⋊C4—228no—
420C22⋊C4—228no—
421C42—228no—
422C42—228no—
423C42D4×D1112yes—
424C42C23×D1112yes—
425C11C2×#333611yescharacteristic, complemented, Sylow
426C23—114no—
427C23—112no—
428C23—112no—
429C23—222no—
430C23—222no—
431C23—222no—
432C23—222no—
433C23—222no—
434C23C2×D4×D1111yescharacteristic
435Q8—224no—
436Q8—224no—
437Q8—444no—
438D4—228no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—44no—
444C2×C4—44no—
445C2×C4—112no—
446C2×C4—112no—
447C2×C4—222no—
448C2×C4—222no—
449C2×C4—224no—
450C2×C4—224no—
451C2×C4—222no—
452C2×C4—222no—
453C2×C4—222no—
454C2×C4—222no—
455C2×C4—224no—
456C2×C4—224no—
457C2×C4—4416no—
458C2×C4—444no—
459C2×C4—444no—
460C2×C4C2×D4×D1112yes—
461C2×C4C2×D4×D1112yes—
462C2×C4C2×D4×D1111yescharacteristic
463C2×C4C2×#434312yes—
464C2×C4#6704012yes—
465C2×C4C24×D1111yescharacteristic
466C8—22no—
467C8—222no—
468C8—222no—
469C8C2×#434314yes—
470C22—114no—
471C22—228no—
472C22—222no—
473C22—222no—
474C22—222no—
475C22—222no—
476C22—222no—
477C22—444no—
478C22#1062325712yes—
479C22D11×#13512yes—
480C22#1062330212yes—
481C22C22×D4×D1111yescharacteristic
482C4—22no—
483C4—22no—
484C4—44no—
485C4—44no—
486C4—222no—
487C4—222no—
488C4—444no—
489C4—444no—
490C4#1062325712yes—
491C4C22×#434311yescharacteristic
492C4C2×#6704011yescharacteristic
493C2—224no—
494C2—442no—
495C2#1308098314yesdirect product factor
496C2C2×#1062325711yescharacteristic
497C2C2×D11×#13511yescharacteristic
498C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#499C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenterC2×#499D11
hypocenterC11C2×#3336
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#499

Complements

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

NH ≅ G/Ntype
2. #13080983C2direct (N × H)
3. C2×#10622480C2semidirect
4. C2×#10622475C2semidirect
5. C2×#10622676C2semidirect
6. C2×#10622500C2semidirect
7. C2×#10622500C2semidirect
8. C2×C4×Dic44C2semidirect
10. C2×#10622493C2semidirect
11. C2×D11×#107C2semidirect
12. C2×C11×#499C2semidirect
29. C11×#499C22semidirect
38. #10622676C22semidirect
44. #10622500C22semidirect
45. #10622500C22semidirect
46. #10622493C22semidirect
47. D11×#107C22semidirect
48. #10622480C22semidirect
49. #10622475C22semidirect
50. C4×Dic44C22semidirect
179. C2×#499D11semidirect
249. #499C2×D11semidirect
359. C2×C11#3336semidirect
425. C11C2×#3336semidirect
495. C2#13080983direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232252
#130809832
C2×#106224802
C2×#106224752
C2×#106226762
C2×#106225002
C2×C4×Dic442
C2×C8×D442
C2×#106224932
C2×D11×#1072
C2×C11×#4992
C2×#333611