Finite Group Databasebeta

← C2×#13080980 #15632204

Subgroups — C2×#13080980 #15632204

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×#10623044C212yesmaximal
2#13080980C2116yesmaximal, direct product factor
3C2×#10622491C211yesmaximal, characteristic, complemented
4C2×#10622501C212yesmaximal, complemented
5C2×#10622584C212yesmaximal, complemented
6C2×#10622490C212yesmaximal, complemented
7C2×#10622500C211yesmaximal, characteristic, complemented
8C2×#10622729C211yesmaximal, characteristic, complemented
9C2×#10622486C211yesmaximal, characteristic, complemented
10C2×C8×C22⋊D11C211yesmaximal, characteristic
11C2×#10622493C211yesmaximal, characteristic, complemented
12C22×C11×#107C211yesmaximal, characteristic, complemented
13C23×C8×C11C2211yescharacteristic
14C22×C11×C4⋊C4C2212yes—
15C2×#66982—22no—
16C2×C4×C22⋊D11C2211yescharacteristic
17C2×#66979—22no—
18C2×#66977C2212yes—
19C22×Dic44C2211yescharacteristic
20C22×C8×D11C2211yescharacteristic
21#10623044—28no—
22#10623044C22116yes—
23C2×#66951—22no—
24C2×#66950C2212yes—
25C2×#66945C2212yes—
26C2×#66943C2212yes—
27C2×#66942—22no—
28C2×#66940C2212yes—
29C2×C11×#107C2211yescharacteristic
30C2×C11×#107C2212yes—
31C2×C11×#107C2211yescharacteristic
32C2×C11×#107C2218yescomplemented
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34#10622729C2218yescomplemented
35C8×C22⋊D11C2218yes—
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×#66882C2211yescharacteristic
38C2×#66880C2212yes—
39C2×Dic11⋊C8C2211yescharacteristic
40C2×C8×Dic11C2211yescharacteristic
41#10622584C22116yescomplemented
42C2×#66874C2212yes—
43C2×#66874C2212yes—
44C2×#66872C2212yes—
45C2×#66872C2212yes—
46#10622501C22116yescomplemented
47#10622500C2218yescomplemented
48#10622493C2218yescomplemented
49#10622491C2218yescomplemented
50#10622490C22116yescomplemented
51#10622486C2218yescomplemented
52C23×C4×C11—22no—
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11D411yescharacteristic
55C22×C4×D11C2311yescharacteristic
56C22×Dic22C2312yes—
57C22×C8×C11—24no—
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2314yes—
60C22×C8×C11C2311yescharacteristic
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—24no—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2318yes—
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11D411yescharacteristic
68#66982—216no—
69C4×C22⋊D11D414yes—
70C4×C22⋊D11C2314yes—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4D411yescharacteristic
74#66979—216no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11C2312yes—
78#66977—24no—
79#66977C2318yes—
80C2×Dic11⋊C4—22no—
81C2×Dic11⋊C4—22no—
82C2×Dic11⋊C4—22no—
83C2×Dic11⋊C4D411yescharacteristic
84C2×C4×Dic11—22no—
85C2×C4×Dic11—22no—
86C2×C4×Dic11C2311yescharacteristic
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C2×Dic44—24no—
90C2×Dic44C2314yes—
91C2×C8×D11—24no—
92C2×C8×D11C2314yes—
93#66951—216no—
94#66950—24no—
95#66950C2318yes—
96#66945—24no—
97#66945C2318yes—
98#66943—24no—
99#66943C2318yes—
100#66942—216no—
101#66940—24no—
102#66940C2318yes—
103C11×#107C2314yes—
104C11×#107C2318yes—
105C11×#107C2314yes—
106C22⋊(C11⋊C8)C2314yes—
107(C2×D11)⋊C8C2314yes—
108#66882C2314yes—
109#66880C2318yes—
110Dic11⋊C8C2314yes—
111C8×Dic11C2314yes—
112#66874C2318yes—
113#66874C2318yes—
114#66872C2318yes—
115#66872C2318yes—
116C2×#3336—111nomaximal, Sylow
117C24×C11C2×D411yescharacteristic
118C23×D11C2×D411yescharacteristic
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—28no—
124C22×C4×C11—48no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2412yes—
128C22×C4×C11C2411yescharacteristic
129C2×C22⋊D11—24no—
130C2×C22⋊D11C2×D414yes—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×C4×D11C2×D412yes—
139C2×C4×D11C2412yes—
140C2×Dic22—22no—
141C2×Dic22—24no—
142C2×Dic22—24no—
143C2×Dic22C2414yes—
144C2×C8×C11—28no—
145C2×C8×C11—22no—
146C2×C8×C11#4114yes—
147C2×C8×C11C2412yes—
148C2×C8×C11C2412yes—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—28no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4C2414yes—
153C11×C4⋊C4C2414yes—
154C22⋊Dic11—28no—
155C22⋊Dic11C2×D414yes—
156(C2×D11)⋊C4—28no—
157(C2×D11)⋊C4—28no—
158(C2×D11)⋊C4C2×D414yes—
159C4⋊Dic11—28no—
160C4⋊Dic11—28no—
161C4⋊Dic11—22no—
162C4⋊Dic11C2414yes—
163Dic11⋊C4—28no—
164Dic11⋊C4—28no—
165Dic11⋊C4—28no—
166Dic11⋊C4C2×D414yes—
167C4×Dic11—28no—
168C4×Dic11—28no—
169C4×Dic11C2×D412yes—
170C4×Dic11C2412yes—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8C2412yes—
174C2×C11⋊C8C2412yes—
175Dic44—28no—
176C8×D11—28no—
177C2×#552—112no—
178#3336—1116no—
179C2×#499—111no—
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×#107D1111yescharacteristic, complemented
189C23×C11—22no—
190C23×C11—22no—
191C23×C11#13514yes—
192C23×C11C22×D412yes—
193C23×C11C22×D411yescharacteristic
194C22×D11—22no—
195C22×D11—22no—
196C22×D11—22no—
197C22×D11C22×D412yes—
198C2×C4×C11—22no—
199C2×C4×C11—24no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—416no—
205C2×C4×C11—44no—
206C2×C4×C11—44no—
207C2×C4×C11C22×D412yes—
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C2×#4112yes—
210C2×C4×C112−1+412yes—
211C2×C4×C11C2511yescharacteristic
212C22⋊D11—28no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—24no—
217C2×Dic11—24no—
218C2×Dic11—44no—
219C2×Dic11—44no—
220C2×Dic11C22×D412yes—
221C2×Dic11C22×D412yes—
222C2×Dic11C22×D412yes—
223C4×D11—24no—
224C4×D11—22no—
225C4×D11—22no—
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×C8C2×D1111yescharacteristic
236#552—1116no—
237#552—228no—
238C2×#126—222no—
239C2×#125—112no—
240C2×#125—222no—
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⋊C4C2×D1112yes—
249#499—118no—
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×#107C2×D1112yes—
260C2×#107C2×D1111yescharacteristic
261C2×#107C2×D1111yescharacteristic
262C2×#107C2×D1118yescomplemented
263C2×#106—112no—
264C2×#106—112no—
265C2×C4⋊C8—111no—
266C2×#103—112no—
267C2×#103—112no—
268C2×#103—112no—
269C2×C22⋊C8—111no—
270C2×C22⋊C8—111no—
271C2×C4×C8—111no—
272C22×C11—28no—
273C22×C11—22no—
274C22×C11—22no—
275C22×C11#54712yes—
276C22×C11C2×#13514yes—
277C22×C11C2×#13512yes—
278C22×C11#57812yes—
279C22×C11C23×D411yescharacteristic
280C2×D11—22no—
281C2×D11—22no—
282C2×D11—22no—
283C2×D11—44no—
284C4×C11—22no—
285C4×C11—44no—
286C4×C11—44no—
287C4×C11#54712yes—
288C4×C11C22×#4111yescharacteristic
289C4×C11C2×2−1+411yescharacteristic
290Dic11—22no—
291Dic11—22no—
292Dic11—22no—
293Dic11—44no—
294Dic11—44no—
295C22×Q8—112no—
296C22×D4—111no—
297C23×C4—22no—
298C23×C4—111no—
299C23×C4C22×D1111yescharacteristic
300C2×Q16—114no—
301C2×Q16—224no—
302C22×C8—24no—
303C22×C8—111no—
304C22×C8—111no—
305C22×C8—114no—
306C22×C8—224no—
307C22×C8C22×D1111yescharacteristic
308C22×C8C22×D1114yes—
309C22×C8C22×D1111yescharacteristic
310#126—2216no—
311#125—118no—
312#125—224no—
313#125—2216no—
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—24no—
328C2×C4⋊C4—111no—
329C2×C4⋊C4—112no—
330C2×C4⋊C4—222no—
331C2×C4⋊C4—222no—
332C2×C4⋊C4—222no—
333C2×C4⋊C4—222no—
334C2×C4⋊C4—222no—
335C2×C4⋊C4C22×D1112yes—
336C2×C4⋊C4C22×D1112yes—
337C2×C4⋊C4C22×D1118yes—
338C2×C22⋊C4—111no—
339C2×C22⋊C4—111no—
340C2×C22⋊C4—222no—
341C2×C22⋊C4—222no—
342C2×C22⋊C4—222no—
343C2×C42—111no—
344C2×C42—222no—
345C2×C42—222no—
346#107—114no—
347#107C22×D1114yes—
348#107C22×D1114yes—
349#107C22×D1118yes—
350#106—118no—
351#106—118no—
352C4⋊C8—114no—
353#103—118no—
354#103—118no—
355#103—118no—
356C22⋊C8—114no—
357C22⋊C8—114no—
358C4×C8—114no—
359C2×C11—24no—
360C2×C11#333614yescomplemented
361C2×C11C2×#54711yescharacteristic
362C2×C11C22×#13511yescharacteristic
363C2×C11C2×#57811yescharacteristic
364D11—42no—
365C24—111no—
366C24D4×D1111yescharacteristic
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—28no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—48no—
379C22×C4—111no—
380C22×C4—111no—
381C22×C4—111no—
382C22×C4—112no—
383C22×C4—112no—
384C22×C4—222no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4—222no—
388C22×C4D4×D1112yes—
389C22×C4D4×D1111yescharacteristic
390C22×C4C23×D1112yes—
391C22×C4C23×D1111yescharacteristic
392Q16—228no—
393C2×C8—22no—
394C2×C8—28no—
395C2×C8—112no—
396C2×C8—112no—
397C2×C8—222no—
398C2×C8—222no—
399C2×C8—228no—
400C2×C8#433914yes—
401C2×C8C23×D1112yes—
402C2×C8C23×D1112yes—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—28no—
406C4⋊C4—114no—
407C4⋊C4—114no—
408C4⋊C4—228no—
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—112no—
422C42—112no—
423C42—228no—
424C42—228no—
425C11C2×#333611yescharacteristic, complemented, Sylow
426C23—22no—
427C23—22no—
428C23—112no—
429C23—222no—
430C23—222no—
431C23—222no—
432C23#6696514yes—
433C23C2×D4×D1112yes—
434C23C2×D4×D1111yescharacteristic
435Q8—224no—
436Q8—224no—
437Q8—444no—
438D4—228no—
439C2×C4—22no—
440C2×C4—24no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—416no—
446C2×C4—44no—
447C2×C4—44no—
448C2×C4—112no—
449C2×C4—112no—
450C2×C4—112no—
451C2×C4—222no—
452C2×C4—222no—
453C2×C4—222no—
454C2×C4—224no—
455C2×C4—222no—
456C2×C4—222no—
457C2×C4—224no—
458C2×C4—224no—
459C2×C4—444no—
460C2×C4—444no—
461C2×C4C2×#433912yes—
462C2×C4C2×D4×D1112yes—
463C2×C4C2×D4×D1111yescharacteristic
464C2×C4#6704012yes—
465C2×C4C24×D1111yescharacteristic
466C8—22no—
467C8—222no—
468C8—222no—
469C8C2×#433914yes—
470C22—28no—
471C22—22no—
472C22—22no—
473C22—222no—
474C22—222no—
475C22—222no—
476C22—444no—
477C22#1062303812yes—
478C22C2×#6696514yes—
479C22C2×#6696512yes—
480C22#1062329712yes—
481C22C22×D4×D1111yescharacteristic
482C4—22no—
483C4—44no—
484C4—44no—
485C4—222no—
486C4—222no—
487C4—222no—
488C4—444no—
489C4—444no—
490C4#1062303812yes—
491C4C22×#433911yescharacteristic
492C4C2×#6704011yescharacteristic
493C2—24no—
494C2—442no—
495C2#1308098014yesdirect product factor
496C2C2×#1062303811yescharacteristic
497C2C22×#6696511yescharacteristic
498C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#107C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
hypercenterC22×#107D11
hypocenterC11C2×#3336
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
2. #13080980C2direct (N × H)
3. C2×#10622491C2semidirect
4. C2×#10622501C2semidirect
5. C2×#10622584C2semidirect
6. C2×#10622490C2semidirect
7. C2×#10622500C2semidirect
8. C2×#10622729C2semidirect
9. C2×#10622486C2semidirect
11. C2×#10622493C2semidirect
12. C22×C11×#107C2semidirect
32. C2×C11×#107C22semidirect
34. #10622729C22semidirect
41. #10622584C22semidirect
46. #10622501C22semidirect
47. #10622500C22semidirect
48. #10622493C22semidirect
49. #10622491C22semidirect
50. #10622490C22semidirect
51. #10622486C22semidirect
188. C22×#107D11semidirect
262. C2×#107C2×D11semidirect
360. C2×C11#3336semidirect
425. C11C2×#3336semidirect
495. C2#13080980direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230442
#130809802
C2×#106224912
C2×#106225012
C2×#106225842
C2×#106224902
C2×#106225002
C2×#106227292
C2×#106224862
C2×C8×C22⋊D112
C2×#106224932
C22×C11×#1072
C2×#333611