Finite Group Databasebeta

← C2×#13073213 #14923255

Subgroups — C2×#13073213 #14923255

Order 2816.

2334 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073213C2116yesmaximal, direct product factor
2C2×#10622288C212yesmaximal, complemented
3C2×#10622606C212yesmaximal, complemented
4C2×#10622552C211yesmaximal, characteristic
5C2×#10622552C211yesmaximal, characteristic
6C2×#10622552C211yesmaximal, characteristic
7C2×#10622541C211yesmaximal, characteristic, complemented
8C2×#10622603C212yesmaximal, complemented
9C2×#10622282C212yesmaximal, complemented
10C2×#10622549C211yesmaximal, characteristic, complemented
11C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
12C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
13C23×D44C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×Dic11⋊C4C2212yes—
29C22×C4×Dic11C2212yes—
30C4×C11×C4⋊C4C2218yescomplemented
31C2×C11×#95C2211yescharacteristic
32C2×C11×#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37#10622606C22116yescomplemented
38#10622603C22116yescomplemented
39#10622552C2218yes—
40#10622552C2218yes—
41#10622552C2218yes—
42#10622549C2218yescomplemented
43C4×C4⋊Dic11C2218yescomplemented
44#10622541C2218yescomplemented
45#10622288C22116yescomplemented
46#10622282C22116yescomplemented
47C24×D11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×Dic11C2312yes—
56C23×Dic11C2312yes—
57C23×Dic11C2312yes—
58C22×D44—24no—
59C22×D44—24no—
60C22×D44—24no—
61C22×D44C2314yes—
62C2×C11×C4⋊C4—24no—
63C2×C11×C4⋊C4—24no—
64C2×C11×C4⋊C4C2314yes—
65C2×C11×C4⋊C4C2314yes—
66C2×C42×C11—24no—
67C2×C42×C11—24no—
68C2×C42×C11—24no—
69C2×C42×C11C2314yes—
70C2×C42×C11C2314yes—
71C2×C42×C11C2314yes—
72C2×(C2×D11)⋊C4—28no—
73C2×(C2×D11)⋊C4—28no—
74C2×(C2×D11)⋊C4—44no—
75C2×(C2×D11)⋊C4—44no—
76C2×(C2×D11)⋊C4—44no—
77C2×(C2×D11)⋊C4—44no—
78C2×(C2×D11)⋊C4C2318yes—
79C2×(C2×D11)⋊C4C2318yes—
80C2×(C2×D11)⋊C4C2318yes—
81C2×(C2×D11)⋊C4C2318yes—
82C2×(C2×D11)⋊C4C2318yes—
83C2×(C2×D11)⋊C4C2318yes—
84C2×C4⋊Dic11—24no—
85C2×C4⋊Dic11—24no—
86C2×C4⋊Dic11—24no—
87C2×C4⋊Dic11C2314yes—
88C2×C4⋊Dic11C2314yes—
89C2×C4⋊Dic11C2314yes—
90C2×Dic11⋊C4—44no—
91C2×Dic11⋊C4C2318yes—
92C2×C4×Dic11—44no—
93C2×C4×Dic11C2318yes—
94C11×#95C2314yes—
95C11×#95C2314yes—
96C11⋊#95C2318yes—
97C11⋊#95C2318yes—
98C11⋊#95C2318yes—
99C11⋊#95C2318yes—
100C2×#2513—111nomaximal, Sylow
101C24×C11C2411yescharacteristic
102C23×D11—24no—
103C23×D11—24no—
104C23×D11—24no—
105C23×D11—24no—
106C23×D11—24no—
107C23×D11—24no—
108C23×D11—24no—
109C23×D11C2414yes—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11#4114yes—
127C22×C4×C11#4114yes—
128C22×C4×C11#4114yes—
129C22×C4×C11#4114yes—
130C22×C4×C11#4114yes—
131C22×C4×C11C2412yes—
132C22×C4×C11C2412yes—
133C22×C4×C11C2412yes—
134C22×C4×C11C2412yes—
135C22×C4×C11C2412yes—
136C22×C4×C11C2412yes—
137C22×C4×C11C2412yes—
138C22×Dic11—24no—
139C22×Dic11—24no—
140C22×Dic11—24no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11C2414yes—
148C22×Dic11C2414yes—
149C22×Dic11C2414yes—
150C2×D44—28no—
151C2×D44—28no—
152C2×D44—28no—
153C2×D44—416no—
154C11×C4⋊C4—28no—
155C11×C4⋊C4—28no—
156C42×C11—28no—
157C42×C11—28no—
158C42×C11—28no—
159(C2×D11)⋊C4—216no—
160(C2×D11)⋊C4—216no—
161(C2×D11)⋊C4—48no—
162(C2×D11)⋊C4—48no—
163(C2×D11)⋊C4—48no—
164(C2×D11)⋊C4—48no—
165C4⋊Dic11—28no—
166C4⋊Dic11—28no—
167C4⋊Dic11—28no—
168Dic11⋊C4—48no—
169C4×Dic11—48no—
170#2513—1116no—
171C2×#397—112no—
172C2×#397—112no—
173C2×#390—111no—
174C2×#390—111no—
175C2×#390—111no—
176C2×#389—111no—
177C2×#388—112no—
178C2×#388—112no—
179C2×#382—111no—
180C2×C4×C4⋊C4—111no—
181C2×C4×C4⋊C4D1111yescharacteristic, complemented
182C23×C11C2×#4112yes—
183C23×C11C2×#4112yes—
184C23×C11C2×#4112yes—
185C23×C11C2×#4112yes—
186C23×C11C2×#4112yes—
187C23×C11H(5,𝔽2)12yes—
188C23×C11H(5,𝔽2)12yes—
189C23×C11C2511yescharacteristic
190C22×D11—24no—
191C22×D11—24no—
192C22×D11—24no—
193C22×D11—24no—
194C22×D11—24no—
195C22×D11—24no—
196C22×D11—24no—
197C22×D11—48no—
198C22×D11—48no—
199C22×D11—48no—
200C22×D11—48no—
201C22×D11—48no—
202C22×D11—48no—
203C22×D11—48no—
204C2×C4×C11—28no—
205C2×C4×C11—28no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—44no—
223C2×C4×C11—44no—
224C2×C4×C11—44no—
225C2×C4×C11—44no—
226C2×C4×C11#126116yes—
227C2×C4×C11C2×#4114yes—
228C2×C4×C11C2×#4114yes—
229C2×C4×C11C2×#4114yes—
230C2×C4×C11C2×#4114yes—
231C2×C4×C11C2×#4114yes—
232C2×Dic11—24no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—48no—
242C2×Dic11—48no—
243C2×Dic11—48no—
244D44—416no—
245C23×D4—111no—
246C22×C4⋊C4—111no—
247C22×C4⋊C4—111no—
248C22×C4⋊C4—111no—
249C22×C4⋊C4—112no—
250C22×C4⋊C4C2×D1111yescharacteristic
251C22×C4⋊C4C2×D1111yescharacteristic
252C22×C22⋊C4—112no—
253C22×C22⋊C4—112no—
254C22×C22⋊C4—112no—
255C22×C22⋊C4—112no—
256C22×C22⋊C4—112no—
257C22×C22⋊C4—112no—
258C22×C42—112no—
259C22×C42C2×D1111yescharacteristic
260C22×C42C2×D1111yescharacteristic
261C22×C42C2×D1111yescharacteristic
262#397—1116no—
263#397—1116no—
264#390—118no—
265#390—118no—
266#390—118no—
267#389—118no—
268#388—1116no—
269#388—1116no—
270#382—118no—
271C4×C4⋊C4—118no—
272C4×C4⋊C4C2×D1118yescomplemented
273C2×#95—112no—
274C2×#95—112no—
275C2×#95—112no—
276C2×#95—112no—
277C2×#95C2×D1111yescharacteristic
278C2×#95C2×D1111yescharacteristic
279C22×C11C2×#12614yes—
280C22×C11#52914yes—
281C22×C11#54014yes—
282C22×C11#55314yes—
283C22×C11#55514yes—
284C22×C11#55914yes—
285C22×C11#55914yes—
286C22×C11C22×#4111yescharacteristic
287C22×C11C22×#4111yescharacteristic
288C22×C11C22×#4111yescharacteristic
289C22×C11C22×#4111yescharacteristic
290C22×C11C22×#4111yescharacteristic
291C22×C11C2×H(5,𝔽2)11yescharacteristic
292C22×C11C2×H(5,𝔽2)11yescharacteristic
293C2×D11—44no—
294C2×D11—44no—
295C2×D11—44no—
296C2×D11—44no—
297C2×D11—44no—
298C2×D11—44no—
299C2×D11—44no—
300C2×D11—816no—
301C4×C11—24no—
302C4×C11—24no—
303C4×C11—42no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11—42no—
307C4×C11C2×#12618yes—
308Dic11—44no—
309Dic11—44no—
310Dic11—44no—
311C25—112no—
312C22×D4—114no—
313C22×D4—224no—
314C22×D4—224no—
315C22×D4—224no—
316C23×C4—112no—
317C23×C4—112no—
318C23×C4—112no—
319C23×C4C22×D1111yescharacteristic
320C23×C4C22×D1111yescharacteristic
321C23×C4C22×D1111yescharacteristic
322C23×C4C22×D1111yescharacteristic
323C23×C4C22×D1111yescharacteristic
324C23×C4C22×D1111yescharacteristic
325C23×C4C22×D1111yescharacteristic
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—114no—
329C2×C4⋊C4—114no—
330C2×C4⋊C4—114no—
331C2×C4⋊C4—118no—
332C2×C4⋊C4—224no—
333C2×C4⋊C4—224no—
334C2×C4⋊C4—224no—
335C2×C4⋊C4—444no—
336C2×C4⋊C4C22×D1114yes—
337C2×C4⋊C4C22×D1114yes—
338C2×C22⋊C4—118no—
339C2×C22⋊C4—118no—
340C2×C22⋊C4—118no—
341C2×C22⋊C4—118no—
342C2×C22⋊C4—118no—
343C2×C22⋊C4—118no—
344C2×C22⋊C4—228no—
345C2×C22⋊C4—228no—
346C2×C22⋊C4—444no—
347C2×C22⋊C4—444no—
348C2×C22⋊C4—444no—
349C2×C22⋊C4—444no—
350C2×C42—24no—
351C2×C42—24no—
352C2×C42—24no—
353C2×C42—118no—
354C2×C42—444no—
355C2×C42C22×D1114yes—
356C2×C42C22×D1114yes—
357C2×C42C22×D1114yes—
358#95—118no—
359#95—118no—
360#95—118no—
361#95—118no—
362#95C22×D1114yes—
363#95C22×D1114yes—
364C2×C11#251318yescomplemented
365C2×C11C22×#12611yescharacteristic
366C2×C11C2×#52911yescharacteristic
367C2×C11C2×#54011yescharacteristic
368C2×C11C2×#55311yescharacteristic
369C2×C11C2×#55511yescharacteristic
370C2×C11C2×#55911yescharacteristic
371C2×C11C2×#55911yescharacteristic
372D11—84no—
373C24—114no—
374C24—224no—
375C24—224no—
376C24—224no—
377C24—224no—
378C24—224no—
379C24—224no—
380C24—224no—
381C24C23×D1111yescharacteristic
382C2×D4—228no—
383C2×D4—228no—
384C2×D4—228no—
385C2×D4—4416no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—114no—
403C22×C4—114no—
404C22×C4—114no—
405C22×C4—224no—
406C22×C4—224no—
407C22×C4—224no—
408C22×C4—224no—
409C22×C4—224no—
410C22×C4—224no—
411C22×C4—224no—
412C22×C4—224no—
413C22×C4—224no—
414C22×C4#433914yes—
415C22×C4#433914yes—
416C22×C4#433914yes—
417C22×C4#434114yes—
418C22×C4#434314yes—
419C22×C4C23×D1112yes—
420C22×C4C23×D1112yes—
421C22×C4C23×D1112yes—
422C22×C4C23×D1112yes—
423C22×C4C23×D1112yes—
424C22×C4C23×D1112yes—
425C22×C4C23×D1112yes—
426C4⋊C4—28no—
427C4⋊C4—28no—
428C4⋊C4—228no—
429C4⋊C4—228no—
430C4⋊C4—228no—
431C4⋊C4—448no—
432C22⋊C4—2216no—
433C22⋊C4—2216no—
434C22⋊C4—448no—
435C22⋊C4—448no—
436C22⋊C4—448no—
437C22⋊C4—448no—
438C42—28no—
439C42—28no—
440C42—28no—
441C42—448no—
442C11C2×#251311yescharacteristic, complemented, Sylow
443C23—224no—
444C23—224no—
445C23—224no—
446C23—224no—
447C23—224no—
448C23—224no—
449C23—224no—
450C23—448no—
451C23—448no—
452C23—448no—
453C23—448no—
454C23—448no—
455C23—448no—
456C23—448no—
457C23C2×#433912yes—
458C23C2×#433912yes—
459C23C2×#433912yes—
460C23C2×#434112yes—
461C23C2×#434312yes—
462C23#6704212yes—
463C23#6704212yes—
464C23C24×D1111yescharacteristic
465D4—4416no—
466C2×C4—28no—
467C2×C4—28no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—44no—
485C2×C4—44no—
486C2×C4—44no—
487C2×C4—44no—
488C2×C4—224no—
489C2×C4—224no—
490C2×C4—224no—
491C2×C4—224no—
492C2×C4—224no—
493C2×C4—224no—
494C2×C4—224no—
495C2×C4—224no—
496C2×C4—224no—
497C2×C4—448no—
498C2×C4—448no—
499C2×C4—448no—
500C2×C4#66951116yes—
501C2×C4C2×#433914yes—
502C2×C4C2×#433914yes—
503C2×C4C2×#433914yes—
504C2×C4C2×#434114yes—
505C2×C4C2×#434314yes—
506C22—444no—
507C22—444no—
508C22—444no—
509C22—444no—
510C22—444no—
511C22—444no—
512C22—444no—
513C22—8816no—
514C22#1062301014yes—
515C22C2×#6695114yes—
516C22#1062306614yes—
517C22#1062309414yes—
518C22#1062309614yes—
519C22#1062311614yes—
520C22#1062311614yes—
521C22C22×#433911yescharacteristic
522C22C22×#433911yescharacteristic
523C22C22×#433911yescharacteristic
524C22C22×#434111yescharacteristic
525C22C22×#434311yescharacteristic
526C22C2×#6704211yescharacteristic
527C22C2×#6704211yescharacteristic
528C4—24no—
529C4—24no—
530C4—42no—
531C4—42no—
532C4—42no—
533C4—42no—
534C4—444no—
535C4—444no—
536C4—444no—
537C4C2×#6695118yes—
538C2—884no—
539C2#1307321318yesdirect product factor
540C2C22×#6695111yescharacteristic
541C2C2×#1062301011yescharacteristic
542C2C2×#1062306611yescharacteristic
543C2C2×#1062309611yescharacteristic
544C2C2×#1062309411yescharacteristic
545C2C2×#1062311611yescharacteristic
546C2C2×#1062311611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C4×C11×C4⋊C4C2
socleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×C4×C4⋊C4D11
hypocenterC11C2×#2513
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #13073213C2direct (N × H)
2. C2×#10622288C2semidirect
3. C2×#10622606C2semidirect
7. C2×#10622541C2semidirect
8. C2×#10622603C2semidirect
9. C2×#10622282C2semidirect
10. C2×#10622549C2semidirect
11. C2×C4×C4⋊Dic11C2semidirect
12. C2×C4×C11×C4⋊C4C2semidirect
30. C4×C11×C4⋊C4C22semidirect
37. #10622606C22semidirect
38. #10622603C22semidirect
42. #10622549C22semidirect
43. C4×C4⋊Dic11C22semidirect
44. #10622541C22semidirect
45. #10622288C22semidirect
46. #10622282C22semidirect
181. C2×C4×C4⋊C4D11semidirect
272. C4×C4⋊C4C2×D11semidirect
364. C2×C11#2513semidirect
442. C11C2×#2513semidirect
539. C2#13073213direct (N × H)

Maximal subgroups

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

subgroupindex
#130732132
C2×#106222882
C2×#106226062
C2×#106225522
C2×#106225412
C2×#106226032
C2×#106222822
C2×#106225492
C2×C4×C4⋊Dic112
C2×C4×C11×C4⋊C42
C2×#251311