Finite Group Databasebeta

← C2×#13073018 #14923232

Subgroups — C2×#13073018 #14923232

Order 2816.

2182 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073018C2116yesmaximal, direct product factor
2C2×C11⋊#401C212yesmaximal, complemented
3C2×#10622566C212yesmaximal
4C2×#10622598C211yesmaximal, characteristic, complemented
5C2×#10622586C211yesmaximal, characteristic, complemented
6C2×#10622557C212yesmaximal
7C2×#10622268C212yesmaximal, complemented
8C2×#10622590C211yesmaximal, characteristic, complemented
9C2×#10622825C211yesmaximal, characteristic
10C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊Dic11C211yesmaximal, characteristic
12C2×C11×#380C211yesmaximal, characteristic
13C24×C4×C11C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2212yes—
23C22×Dic11⋊C4C2212yes—
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C22×C4×Dic11C2212yes—
27C11×#380C2218yes—
28C2×C11×#95C2212yes—
29#10622825C2218yes—
30C4×C22⋊Dic11C2218yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2212yes—
39#10622598C2218yescomplemented
40#10622590C2218yescomplemented
41C4⋊C4×Dic11C2218yescomplemented
42#10622586C2218yescomplemented
43#10622566C22116yes—
44#10622557C22116yes—
45C11⋊#401C22116yescomplemented
46#10622268C22116yescomplemented
47C25×C11C2311yescharacteristic
48C23×C4×C11—24no—
49C23×C4×C11—24no—
50C23×C4×C11—24no—
51C23×C4×C11C2312yes—
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2314yes—
55C23×C4×C11C2311yescharacteristic
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2312yes—
61C23×Dic11C2311yescharacteristic
62C2×C11×C4⋊C4—24no—
63C2×C11×C4⋊C4—24no—
64C2×C11×C4⋊C4C2314yes—
65C2×C11×C4⋊C4C2314yes—
66C2×C11×C22⋊C4—44no—
67C2×C11×C22⋊C4C2318yes—
68C2×C22⋊Dic11—24no—
69C2×C22⋊Dic11—28no—
70C2×C22⋊Dic11—24no—
71C2×C22⋊Dic11C2314yes—
72C2×C22⋊Dic11C2318yes—
73C2×C22⋊Dic11C2314yes—
74C2×C4⋊Dic11—24no—
75C2×C4⋊Dic11—24no—
76C2×C4⋊Dic11—44no—
77C2×C4⋊Dic11C2314yes—
78C2×C4⋊Dic11C2314yes—
79C2×C4⋊Dic11C2318yes—
80C2×Dic11⋊C4—28no—
81C2×Dic11⋊C4C2318yes—
82C2×C4×Dic11—24no—
83C2×C4×Dic11—24no—
84C2×C4×Dic11—44no—
85C2×C4×Dic11C2314yes—
86C2×C4×Dic11C2314yes—
87C2×C4×Dic11C2318yes—
88C11×#95C2318yes—
89C11⋊#95C2314yes—
90C11⋊#95C2318yes—
91C11⋊#95C2318yes—
92C11⋊#95C2314yes—
93C11⋊#95C2318yes—
94C11⋊#95C2318yes—
95C11⋊#95C2318yes—
96C11⋊#95C2318yes—
97C2×#2494—111nomaximal, Sylow
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—22no—
102C24×C11—22no—
103C24×C11—22no—
104C24×C11#4114yes—
105C24×C11C2412yes—
106C24×C11C2411yescharacteristic
107C22×C4×C11—24no—
108C22×C4×C11—24no—
109C22×C4×C11—24no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—24no—
114C22×C4×C11—24no—
115C22×C4×C11—24no—
116C22×C4×C11—28no—
117C22×C4×C11—28no—
118C22×C4×C11—28no—
119C22×C4×C11—416no—
120C22×C4×C11#4114yes—
121C22×C4×C11#4114yes—
122C22×C4×C11#4114yes—
123C22×C4×C11C2412yes—
124C22×C4×C11C2414yes—
125C22×C4×C11C2414yes—
126C22×C4×C11C2412yes—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—24no—
132C22×Dic11—24no—
133C22×Dic11—24no—
134C22×Dic11—24no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—24no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—24no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11#4114yes—
145C22×Dic11C2412yes—
146C22×Dic11C2412yes—
147C22×Dic11C2414yes—
148C22×Dic11C2412yes—
149C22×Dic11C2414yes—
150C22×Dic11C2412yes—
151C11×C4⋊C4—28no—
152C11×C4⋊C4—28no—
153C11×C22⋊C4—48no—
154C22⋊Dic11—28no—
155C22⋊Dic11—216no—
156C22⋊Dic11—28no—
157C4⋊Dic11—28no—
158C4⋊Dic11—28no—
159C4⋊Dic11—48no—
160Dic11⋊C4—216no—
161C4×Dic11—28no—
162C4×Dic11—28no—
163C4×Dic11—48no—
164#2494—1116no—
165C2×#401—112no—
166C2×#397—112no—
167C2×#389—111no—
168C2×#389—111no—
169C2×#388—112no—
170C2×#387—112no—
171C2×#382—111no—
172C2×#380—111no—
173C2×#380D1111yescharacteristic
174C2×C4×C4⋊C4—111no—
175C2×C4×C22⋊C4—111no—
176C23×C11—28no—
177C23×C11—28no—
178C23×C11—28no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—44no—
186C23×C11—44no—
187C23×C11—44no—
188C23×C11—44no—
189C23×C11C2×#4112yes—
190C23×C11C2×#4112yes—
191C23×C11C2×#4112yes—
192C23×C11C2×#4114yes—
193C23×C11C2×#4112yes—
194C23×C11C2×#4112yes—
195C23×C11H(5,𝔽2)12yes—
196C23×C112−1+412yes—
197C23×C11C2511yescharacteristic
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—44no—
208C2×C4×C11—48no—
209C2×C4×C11—48no—
210C2×C4×C11—416no—
211C2×C4×C11#126116yes—
212C2×C4×C11C2×#4114yes—
213C2×C4×C11C2×#4114yes—
214C2×C4×C11C2×#4114yes—
215C2×Dic11—28no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—24no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—24no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—24no—
228C2×Dic11—22no—
229C2×Dic11—24no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—48no—
234C2×Dic11—44no—
235C2×Dic11—44no—
236C2×Dic11—48no—
237C2×Dic11—44no—
238C2×Dic11C2×#4114yes—
239C24×C4C2×D1111yescharacteristic
240C22×C4⋊C4—112no—
241C22×C4⋊C4—111no—
242C22×C4⋊C4—111no—
243C22×C4⋊C4—112no—
244C22×C4⋊C4C2×D1111yescharacteristic
245C22×C4⋊C4C2×D1111yescharacteristic
246C22×C22⋊C4—111no—
247C22×C22⋊C4—112no—
248C22×C22⋊C4—111no—
249C22×C22⋊C4C2×D1112yes—
250C22×C42—111no—
251C22×C42—111no—
252C22×C42—112no—
253#401—1116no—
254#397—1116no—
255#389—118no—
256#389—118no—
257#388—1116no—
258#387—1116no—
259#382—118no—
260#380—118no—
261#380C2×D1118yes—
262C4×C4⋊C4—118no—
263C4×C22⋊C4—118no—
264C2×#95—112no—
265C2×#95—112no—
266C2×#95—112no—
267C2×#95—111no—
268C2×#95—112no—
269C2×#95—112no—
270C2×#95—112no—
271C2×#95—111no—
272C2×#95C2×D1112yes—
273C22×C11—24no—
274C22×C11—24no—
275C22×C11—24no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11—416no—
281C22×C11C2×#12614yes—
282C22×C11#52914yes—
283C22×C11#54214yes—
284C22×C11#55214yes—
285C22×C11#55314yes—
286C22×C11#55314yes—
287C22×C11#55614yes—
288C22×C11C22×#4111yescharacteristic
289C22×C11C22×#4111yescharacteristic
290C22×C11C22×#4111yescharacteristic
291C22×C11C22×#4111yescharacteristic
292C22×C11C22×#4111yescharacteristic
293C22×C11C2×H(5,𝔽2)11yescharacteristic
294C22×C11C2×2−1+411yescharacteristic
295C4×C11—42no—
296C4×C11—44no—
297C4×C11—44no—
298C4×C11C2×#12618yes—
299Dic11—24no—
300Dic11—44no—
301Dic11—42no—
302Dic11—42no—
303Dic11—44no—
304Dic11—42no—
305C25C22×D1111yescharacteristic
306C23×C4—24no—
307C23×C4—24no—
308C23×C4—24no—
309C23×C4—111no—
310C23×C4—112no—
311C23×C4—111no—
312C23×C4—112no—
313C23×C4—111no—
314C23×C4—111no—
315C23×C4C22×D1114yes—
316C23×C4C22×D1112yes—
317C23×C4C22×D1112yes—
318C23×C4C22×D1111yescharacteristic
319C23×C4C22×D1111yescharacteristic
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—114no—
323C2×C4⋊C4—114no—
324C2×C4⋊C4—118no—
325C2×C4⋊C4—118no—
326C2×C4⋊C4—228no—
327C2×C4⋊C4—224no—
328C2×C4⋊C4—224no—
329C2×C4⋊C4—444no—
330C2×C4⋊C4C22×D1114yes—
331C2×C4⋊C4C22×D1114yes—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—114no—
334C2×C22⋊C4—114no—
335C2×C22⋊C4—118no—
336C2×C22⋊C4—224no—
337C2×C22⋊C4—224no—
338C2×C22⋊C4—228no—
339C2×C22⋊C4C22×D1118yes—
340C2×C42—114no—
341C2×C42—114no—
342C2×C42—118no—
343C2×C42—224no—
344C2×C42—224no—
345C2×C42—444no—
346#95—114no—
347#95—114no—
348#95—118no—
349#95—118no—
350#95—118no—
351#95—118no—
352#95—118no—
353#95—118no—
354#95C22×D1118yes—
355C2×C11—44no—
356C2×C11#249418yescomplemented
357C2×C11C22×#12611yescharacteristic
358C2×C11C2×#52911yescharacteristic
359C2×C11C2×#54211yescharacteristic
360C2×C11C2×#55211yescharacteristic
361C2×C11C2×#55311yescharacteristic
362C2×C11C2×#55311yescharacteristic
363C2×C11C2×#55611yescharacteristic
364C24—22no—
365C24—22no—
366C24—22no—
367C24—22no—
368C24—22no—
369C24—22no—
370C24#434314yes—
371C24C23×D1112yes—
372C24C23×D1111yescharacteristic
373C22×C4—22no—
374C22×C4—24no—
375C22×C4—24no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—28no—
383C22×C4—28no—
384C22×C4—28no—
385C22×C4—416no—
386C22×C4—114no—
387C22×C4—112no—
388C22×C4—112no—
389C22×C4—112no—
390C22×C4—114no—
391C22×C4—112no—
392C22×C4—114no—
393C22×C4—222no—
394C22×C4—222no—
395C22×C4—222no—
396C22×C4—222no—
397C22×C4—224no—
398C22×C4—222no—
399C22×C4—224no—
400C22×C4—224no—
401C22×C4—222no—
402C22×C4—222no—
403C22×C4—224no—
404C22×C4—224no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—224no—
408C22×C4—222no—
409C22×C4—222no—
410C22×C4#433914yes—
411C22×C4#434114yes—
412C22×C4#434114yes—
413C22×C4C23×D1112yes—
414C22×C4C23×D1114yes—
415C22×C4C23×D1114yes—
416C22×C4C23×D1112yes—
417C4⋊C4—28no—
418C4⋊C4—28no—
419C4⋊C4—2216no—
420C4⋊C4—228no—
421C4⋊C4—228no—
422C4⋊C4—448no—
423C22⋊C4—48no—
424C22⋊C4—228no—
425C22⋊C4—228no—
426C22⋊C4—2216no—
427C42—228no—
428C42—228no—
429C42—448no—
430C11C2×#249411yescharacteristic, complemented, Sylow
431C23—28no—
432C23—28no—
433C23—28no—
434C23—22no—
435C23—22no—
436C23—22no—
437C23—22no—
438C23—22no—
439C23—22no—
440C23—44no—
441C23—44no—
442C23—44no—
443C23—44no—
444C23C2×#433912yes—
445C23C2×#434112yes—
446C23C2×#434112yes—
447C23#6703712yes—
448C23C2×#434314yes—
449C23C2×#434312yes—
450C23#41×D1112yes—
451C23#6704312yes—
452C23C24×D1111yescharacteristic
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—44no—
463C2×C4—48no—
464C2×C4—48no—
465C2×C4—416no—
466C2×C4—114no—
467C2×C4—228no—
468C2×C4—222no—
469C2×C4—222no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—224no—
473C2×C4—222no—
474C2×C4—224no—
475C2×C4—224no—
476C2×C4—222no—
477C2×C4—222no—
478C2×C4—222no—
479C2×C4—224no—
480C2×C4—224no—
481C2×C4—222no—
482C2×C4—224no—
483C2×C4—222no—
484C2×C4—222no—
485C2×C4—444no—
486C2×C4—448no—
487C2×C4—444no—
488C2×C4—448no—
489C2×C4—444no—
490C2×C4#66932116yes—
491C2×C4C2×#433914yes—
492C2×C4C2×#434114yes—
493C2×C4C2×#434114yes—
494C22—24no—
495C22—24no—
496C22—24no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—416no—
501C22—42no—
502C22C2×#6693214yes—
503C22#1062304514yes—
504C22#1062306414yes—
505C22#1062313414yes—
506C22#1062314514yes—
507C22#1062315514yes—
508C22#1062317314yes—
509C22C22×#433911yescharacteristic
510C22C22×#434111yescharacteristic
511C22C22×#434111yescharacteristic
512C22C2×#6703711yescharacteristic
513C22C22×#434311yescharacteristic
514C22C2×#41×D1111yescharacteristic
515C22C2×#6704311yescharacteristic
516C4—42no—
517C4—44no—
518C4—44no—
519C4—224no—
520C4—442no—
521C4—442no—
522C4—444no—
523C4—444no—
524C4—442no—
525C4C2×#6693218yes—
526C2—44no—
527C2#1307301818yesdirect product factor
528C2C22×#6693211yescharacteristic
529C2C2×#1062315511yescharacteristic
530C2C2×#1062313411yescharacteristic
531C2C2×#1062317311yescharacteristic
532C2C2×#1062314511yescharacteristic
533C2C2×#1062304511yescharacteristic
534C2C2×#1062306411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#380C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#380D11
hypocenterC11C2×#2494
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. #13073018C2direct (N × H)
2. C2×C11⋊#401C2semidirect
4. C2×#10622598C2semidirect
5. C2×#10622586C2semidirect
7. C2×#10622268C2semidirect
8. C2×#10622590C2semidirect
10. C2×C4⋊C4×Dic11C2semidirect
39. #10622598C22semidirect
40. #10622590C22semidirect
41. C4⋊C4×Dic11C22semidirect
42. #10622586C22semidirect
45. C11⋊#401C22semidirect
46. #10622268C22semidirect
356. C2×C11#2494semidirect
430. C11C2×#2494semidirect
527. C2#13073018direct (N × H)

Maximal subgroups

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

subgroupindex
#130730182
C2×C11⋊#4012
C2×#106225662
C2×#106225982
C2×#106225862
C2×#106225572
C2×#106222682
C2×#106225902
C2×#106228252
C2×C4⋊C4×Dic112
C2×C4×C22⋊Dic112
C2×C11×#3802
C2×#249411