Finite Group Databasebeta

← C2×#13081006 #15632232

Subgroups — C2×#13081006 #15632232

Order 2816.

1942 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623042C212yesmaximal
2#13081006C2116yesmaximal, direct product factor
3C2×#10622487C211yesmaximal, characteristic, complemented
4C2×#10622497C212yesmaximal, complemented
5C2×#10622583C212yesmaximal, complemented
6C2×#10622488C212yesmaximal, complemented
7C2×#10622500C211yesmaximal, characteristic, complemented
8C2×#10622729C211yesmaximal, characteristic, complemented
9C2×#10622486C211yesmaximal, characteristic, complemented
10C2×C8×C22⋊D11C211yesmaximal, characteristic
11C2×D11×#107C211yesmaximal, characteristic, complemented
12C22×C11×#107C211yesmaximal, characteristic, complemented
13C23×C8×C11C2211yescharacteristic
14C22×C11×C4⋊C4C2212yes—
15C2×C4×C22⋊D11—22no—
16C2×C4×C22⋊D11C2211yescharacteristic
17C2×#66977—22no—
18C2×#66977C2212yes—
19C22×Dic44C2211yescharacteristic
20C22×C8×D11C2211yescharacteristic
21#10623042—28no—
22#10623042C22116yes—
23C2×#66950C2212yes—
24C2×#66949—22no—
25C2×C4⋊C4×D11C2212yes—
26C2×#66942—22no—
27C2×#66941C2212yes—
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#10622583C22116yescomplemented
42C2×#66874C2212yes—
43C2×#66874C2212yes—
44C2×#66871C2212yes—
45C2×#66871C2212yes—
46#10622500C2218yescomplemented
47#10622497C22116yescomplemented
48D11×#107C2218yescomplemented
49#10622488C22116yescomplemented
50#10622487C2218yescomplemented
51#10622486C2218yescomplemented
52C23×C4×C11—22no—
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11D411yescharacteristic
55C22×C4×D11—22no—
56C22×C4×D11C2311yescharacteristic
57C22×Dic22—22no—
58C22×Dic22C2312yes—
59C22×C8×C11—24no—
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2314yes—
62C22×C8×C11C2311yescharacteristic
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—24no—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2318yes—
68C2×C22⋊Dic11—22no—
69C2×C22⋊Dic11D411yescharacteristic
70C4×C22⋊D11—216no—
71C4×C22⋊D11D414yes—
72C4×C22⋊D11C2314yes—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4D411yescharacteristic
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11C2312yes—
77#66977—24no—
78#66977—216no—
79#66977C2318yes—
80C2×Dic11⋊C4—22no—
81C2×Dic11⋊C4—22no—
82C2×Dic11⋊C4—22no—
83C2×Dic11⋊C4—22no—
84C2×Dic11⋊C4D411yescharacteristic
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#66950—24no—
94#66950C2318yes—
95#66949—216no—
96C4⋊C4×D11—24no—
97C4⋊C4×D11C2318yes—
98#66942—216no—
99#66941—24no—
100#66941C2318yes—
101#66940—24no—
102#66940C2318yes—
103C11×#107C2314yes—
104C11×#107C2314yes—
105C11×#107C2318yes—
106C22⋊(C11⋊C8)C2314yes—
107(C2×D11)⋊C8C2314yes—
108#66882C2314yes—
109#66880C2318yes—
110Dic11⋊C8C2314yes—
111C8×Dic11C2314yes—
112#66874C2318yes—
113#66874C2318yes—
114#66871C2318yes—
115#66871C2318yes—
116C2×#3338—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—84no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2412yes—
128C22×C4×C11C2411yescharacteristic
129C2×C22⋊D11Q1618yescomplemented
130C2×C22⋊D11C2×D414yes—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C2×C4×D11—28no—
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11—84no—
140C2×C4×D11C2×D412yes—
141C2×C4×D11C2412yes—
142C2×Dic22—28no—
143C2×Dic22—22no—
144C2×Dic22—24no—
145C2×Dic22—24no—
146C2×Dic22—84no—
147C2×Dic22C2414yes—
148C2×C8×C11—28no—
149C2×C8×C11—22no—
150C2×C8×C11#4114yes—
151C2×C8×C11C2412yes—
152C2×C8×C11C2412yes—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—28no—
156C11×C4⋊C4C2414yes—
157C11×C4⋊C4C2414yes—
158C22⋊Dic11—28no—
159C22⋊Dic11C2×D414yes—
160(C2×D11)⋊C4—28no—
161(C2×D11)⋊C4C2×D414yes—
162C4⋊Dic11—28no—
163C4⋊Dic11—22no—
164C4⋊Dic11C2414yes—
165Dic11⋊C4—28no—
166Dic11⋊C4—28no—
167Dic11⋊C4—28no—
168Dic11⋊C4—28no—
169Dic11⋊C4C2×D414yes—
170C4×Dic11—28no—
171C4×Dic11C2×D412yes—
172C4×Dic11C2412yes—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8C2412yes—
176C2×C11⋊C8C2412yes—
177Dic44—28no—
178C8×D11—28no—
179C2×#554—112no—
180#3338—1116no—
181C2×#500—111no—
182C2×#484—112no—
183C2×#484—112no—
184C2×#477—112no—
185C2×#467—111no—
186C2×#467—111no—
187C2×C4×Q16—111no—
188C2×C8×D4—111no—
189C22×#107—111no—
190C22×#107D1111yescharacteristic, complemented
191C23×C11—22no—
192C23×C11—22no—
193C23×C11C2×Q1614yes—
194C23×C11C22×D412yes—
195C23×C11C22×D411yescharacteristic
196C22×D11—22no—
197C22×D11—22no—
198C22×D11C2×Q1614yes—
199C22×D11C22×D412yes—
200C2×C4×C11—22no—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—44no—
207C2×C4×C11—44no—
208C2×C4×C11—88no—
209C2×C4×C11C22×D412yes—
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C2×#4112yes—
212C2×C4×C112−1+412yes—
213C2×C4×C11C2511yescharacteristic
214C22⋊D11C2×Q16116yescomplemented
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—24no—
218C2×Dic11—24no—
219C2×Dic11—44no—
220C2×Dic11—44no—
221C2×Dic11C2×Q1614yes—
222C2×Dic11C22×D412yes—
223C2×Dic11C22×D412yes—
224C2×Dic11C22×D412yes—
225C4×D11—24no—
226C4×D11—22no—
227C4×D11—22no—
228C4×D11—88no—
229Dic22—24no—
230Dic22—24no—
231Dic22—44no—
232Dic22—88no—
233C8×C11—22no—
234C8×C11C2×#4114yes—
235C11⋊C8—22no—
236C11⋊C8—22no—
237C22×Q16—111no—
238C23×C8—111no—
239C23×C8C2×D1111yescharacteristic
240#554—1116no—
241#554—228no—
242C2×C4⋊Q8—112no—
243C2×#125—222no—
244C2×C22⋊Q8—112no—
245C2×C22⋊Q8—112no—
246C2×C22⋊Q8—222no—
247C2×C22⋊Q8—222no—
248C2×C4×Q8—112no—
249C2×C4×D4—111no—
250C2×C4×D4—222no—
251C22×C4⋊C4—112no—
252C22×C4⋊C4C2×D1112yes—
253#500—118no—
254#484—1116no—
255#484—1116no—
256#477—1116no—
257#467—118no—
258#467—118no—
259C4×Q16—118no—
260C8×D4—118no—
261C2×#107—111no—
262C2×#107—112no—
263C2×#107—112no—
264C2×#107—118no—
265C2×#107C2×D1112yes—
266C2×#107C2×D1111yescharacteristic
267C2×#107C2×D1111yescharacteristic
268C2×#107C2×D1118yescomplemented
269C2×C4⋊C8—111no—
270C2×#103—112no—
271C2×#103—112no—
272C2×#103—112no—
273C2×C22⋊C8—111no—
274C2×C22⋊C8—111no—
275C2×C4×C8—111no—
276C22×C11—28no—
277C22×C11—22no—
278C22×C11—22no—
279C22×C11#54712yes—
280C22×C11C22×Q1614yes—
281C22×C11C22×Q1612yes—
282C22×C11#57612yes—
283C22×C11C23×D411yescharacteristic
284C2×D11—28no—
285C2×D11—22no—
286C2×D11—22no—
287C2×D11C22×Q1614yes—
288C4×C11—22no—
289C4×C11—44no—
290C4×C11—44no—
291C4×C11#54712yes—
292C4×C11C22×#4111yescharacteristic
293C4×C11C2×2−1+411yescharacteristic
294Dic11—22no—
295Dic11—22no—
296Dic11—44no—
297Dic11—44no—
298Dic11C22×Q1614yes—
299C22×Q8—112no—
300C22×Q8—222no—
301C22×D4—111no—
302C23×C4—22no—
303C23×C4—111no—
304C23×C4—222no—
305C23×C4C22×D1111yescharacteristic
306C2×Q16—114no—
307C2×Q16—224no—
308C22×C8—24no—
309C22×C8—111no—
310C22×C8—111no—
311C22×C8—114no—
312C22×C8—224no—
313C22×C8C22×D1111yescharacteristic
314C22×C8C22×D1114yes—
315C22×C8C22×D1111yescharacteristic
316C4⋊Q8—118no—
317C4⋊Q8—224no—
318#125—2216no—
319C22⋊Q8—118no—
320C22⋊Q8—118no—
321C22⋊Q8—2216no—
322C22⋊Q8—2216no—
323C22⋊Q8—224no—
324C22⋊Q8—224no—
325C4×Q8—118no—
326C4×Q8—224no—
327C4×D4—114no—
328C4×D4—114no—
329C4×D4—2216no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—111no—
333C2×C4⋊C4—112no—
334C2×C4⋊C4—118no—
335C2×C4⋊C4—224no—
336C2×C4⋊C4—222no—
337C2×C4⋊C4—222no—
338C2×C4⋊C4—222no—
339C2×C4⋊C4—222no—
340C2×C4⋊C4—222no—
341C2×C4⋊C4C22×D1112yes—
342C2×C4⋊C4C22×D1112yes—
343C2×C4⋊C4C22×D1118yes—
344C2×C22⋊C4—111no—
345C2×C22⋊C4—111no—
346C2×C22⋊C4—222no—
347C2×C22⋊C4—222no—
348C2×C42—111no—
349C2×C42—222no—
350#107—114no—
351#107—118no—
352#107—118no—
353#107C22×D1114yes—
354#107C22×D1114yes—
355#107C22×D1118yes—
356C4⋊C8—114no—
357#103—118no—
358#103—118no—
359#103—118no—
360C22⋊C8—114no—
361C22⋊C8—114no—
362C4×C8—114no—
363C2×C11—24no—
364C2×C11#333814yescomplemented
365C2×C11C2×#54711yescharacteristic
366C2×C11C23×Q1611yescharacteristic
367C2×C11C2×#57611yescharacteristic
368D11—24no—
369C24—111no—
370C24D4×D1111yescharacteristic
371C2×Q8—114no—
372C2×Q8—228no—
373C2×Q8—222no—
374C2×Q8—224no—
375C2×Q8—224no—
376C2×Q8—884no—
377C2×D4—118no—
378C2×D4—114no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—28no—
384C22×C4—84no—
385C22×C4—111no—
386C22×C4—111no—
387C22×C4—111no—
388C22×C4—112no—
389C22×C4—112no—
390C22×C4—228no—
391C22×C4—222no—
392C22×C4—222no—
393C22×C4—222no—
394C22×C4—222no—
395C22×C4—884no—
396C22×C4D4×D1112yes—
397C22×C4D4×D1111yescharacteristic
398C22×C4C23×D1112yes—
399C22×C4C23×D1111yescharacteristic
400Q16—228no—
401C2×C8—22no—
402C2×C8—28no—
403C2×C8—112no—
404C2×C8—112no—
405C2×C8—222no—
406C2×C8—222no—
407C2×C8—228no—
408C2×C8#433914yes—
409C2×C8C23×D1112yes—
410C2×C8C23×D1112yes—
411C4⋊C4—22no—
412C4⋊C4—28no—
413C4⋊C4—22no—
414C4⋊C4—114no—
415C4⋊C4—114no—
416C4⋊C4—228no—
417C4⋊C4—228no—
418C4⋊C4—228no—
419C4⋊C4—228no—
420C4⋊C4—222no—
421C4⋊C4—228no—
422C4⋊C4C23×D1114yes—
423C4⋊C4C23×D1114yes—
424C22⋊C4—114no—
425C22⋊C4—114no—
426C22⋊C4—228no—
427C22⋊C4—228no—
428C42—112no—
429C42—112no—
430C42—228no—
431C11C2×#333811yescharacteristic, complemented, Sylow
432C23—22no—
433C23—22no—
434C23—114no—
435C23—112no—
436C23—222no—
437C23—222no—
438C23Q16×D1114yes—
439C23C2×D4×D1112yes—
440C23C2×D4×D1111yescharacteristic
441Q8—224no—
442Q8—224no—
443Q8—444no—
444Q8—888no—
445D4—1116no—
446C2×C4—22no—
447C2×C4—24no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—44no—
453C2×C4—44no—
454C2×C4—88no—
455C2×C4—114no—
456C2×C4—112no—
457C2×C4—112no—
458C2×C4—112no—
459C2×C4—222no—
460C2×C4—222no—
461C2×C4—224no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—224no—
465C2×C4—224no—
466C2×C4—444no—
467C2×C4—444no—
468C2×C4—888no—
469C2×C4C2×#433912yes—
470C2×C4C2×D4×D1112yes—
471C2×C4C2×D4×D1111yescharacteristic
472C2×C4#6704012yes—
473C2×C4C24×D1111yescharacteristic
474C8—22no—
475C8—222no—
476C8—222no—
477C8C2×#433914yes—
478C22—28no—
479C22—22no—
480C22—22no—
481C22—114no—
482C22—228no—
483C22—222no—
484C22—222no—
485C22#1062303812yes—
486C22#1062328812yes—
487C22C2×Q16×D1114yes—
488C22C2×Q16×D1112yes—
489C22C22×D4×D1111yescharacteristic
490C4—22no—
491C4—44no—
492C4—44no—
493C4—114no—
494C4—222no—
495C4—222no—
496C4—444no—
497C4—444no—
498C4#1062303812yes—
499C4C22×#433911yescharacteristic
500C4C2×#6704011yescharacteristic
501C2—24no—
502C2—224no—
503C2#1308100614yesdirect product factor
504C2C2×#1062303811yescharacteristic
505C2C22×Q16×D1111yescharacteristic
506C2C2×#1062328811yescharacteristic
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×#3338
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. #13081006C2direct (N × H)
3. C2×#10622487C2semidirect
4. C2×#10622497C2semidirect
5. C2×#10622583C2semidirect
6. C2×#10622488C2semidirect
7. C2×#10622500C2semidirect
8. C2×#10622729C2semidirect
9. C2×#10622486C2semidirect
11. C2×D11×#107C2semidirect
12. C22×C11×#107C2semidirect
32. C2×C11×#107C22semidirect
34. #10622729C22semidirect
41. #10622583C22semidirect
46. #10622500C22semidirect
47. #10622497C22semidirect
48. D11×#107C22semidirect
49. #10622488C22semidirect
50. #10622487C22semidirect
51. #10622486C22semidirect
129. C2×C22⋊D11Q16semidirect
190. C22×#107D11semidirect
214. C22⋊D11C2×Q16semidirect
268. C2×#107C2×D11semidirect
364. C2×C11#3338semidirect
431. C11C2×#3338semidirect
503. C2#13081006direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230422
#130810062
C2×#106224872
C2×#106224972
C2×#106225832
C2×#106224882
C2×#106225002
C2×#106227292
C2×#106224862
C2×C8×C22⋊D112
C2×D11×#1072
C22×C11×#1072
C2×#333811