Finite Group Databasebeta

← C2×#13072492 #14921268

Subgroups — C2×#13072492 #14921268

Order 2816.

3894 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66988C212yesmaximal, complemented
2C22×D4×Dic11C212yesmaximal, complemented
3#13072492C2116yesmaximal, direct product factor
4C2×#10622562C211yesmaximal, characteristic, complemented
5C2×#10622835C212yesmaximal, complemented
6C2×#10622260C212yesmaximal, complemented
7C2×#10622558C212yesmaximal, complemented
8C2×#10622563C212yesmaximal, complemented
9C2×#10622559C211yesmaximal, characteristic, complemented
10C2×C11×#392C211yesmaximal, characteristic
11C23×D4×C11C2212yes—
12C23×D4×C11C2211yescharacteristic
13C24×Dic11C2211yescharacteristic
14C24×Dic11C2212yes—
15C22×C11×C22⋊C4C2212yes—
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2212yes—
22C2×#66988—216no—
23C2×#66988C22116yescomplemented
24C2×D4×Dic11—216no—
25C2×D4×Dic11C22116yescomplemented
26C22×C4⋊Dic11C2212yes—
27C22×C4⋊Dic11C2211yescharacteristic
28C22×Dic11⋊C4C2212yes—
29C22×Dic11⋊C4C2212yes—
30C22×Dic11⋊C4C2212yes—
31C22×C4×Dic11C2212yes—
32C11×#392C2218yes—
33C2×C11×#95C2211yescharacteristic
34#10622835C22116yescomplemented
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38#10622563C22116yescomplemented
39#10622562C2218yescomplemented
40#10622559C2218yescomplemented
41#10622558C22116yescomplemented
42#10622260C22116yescomplemented
43C25×C11C2312yes—
44C25×C11C2311yescharacteristic
45C22×D4×C11—28no—
46C22×D4×C11—28no—
47C22×D4×C11—28no—
48C22×D4×C11—28no—
49C22×D4×C11—42no—
50C22×D4×C11C2318yes—
51C22×D4×C11C2314yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2312yes—
55C23×Dic11—28no—
56C23×Dic11—28no—
57C23×Dic11—28no—
58C23×Dic11—42no—
59C23×Dic11—44no—
60C23×Dic11C2312yes—
61C23×Dic11C2312yes—
62C23×Dic11C2314yes—
63C23×Dic11C2318yes—
64C23×Dic11C2312yes—
65C23×Dic11C2312yes—
66C2×C11×C22⋊C4—28no—
67C2×C11×C22⋊C4—42no—
68C2×C11×C22⋊C4C2318yes—
69C2×C11×C22⋊C4C2314yes—
70C2×C22⋊Dic11—28no—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—28no—
73C2×C22⋊Dic11—28no—
74C2×C22⋊Dic11D4116yescomplemented
75C2×C22⋊Dic11C2318yes—
76C2×C22⋊Dic11C2318yes—
77C2×C22⋊Dic11C2314yes—
78C2×C22⋊Dic11C2318yes—
79C2×C22⋊Dic11C2318yes—
80#66988—264no—
81D4×Dic11—264no—
82C2×C4⋊Dic11—28no—
83C2×C4⋊Dic11—42no—
84C2×C4⋊Dic11C2318yes—
85C2×C4⋊Dic11C2314yes—
86C2×Dic11⋊C4—28no—
87C2×Dic11⋊C4—28no—
88C2×Dic11⋊C4—28no—
89C2×Dic11⋊C4C2318yes—
90C2×Dic11⋊C4C2318yes—
91C2×Dic11⋊C4C2318yes—
92C2×C4×Dic11—28no—
93C2×C4×Dic11C2318yes—
94C11×#95C2314yes—
95C11⋊#95C2318yes—
96C11⋊#95C2314yes—
97C11⋊#95C2318yes—
98C2×#2455—111nomaximal, Sylow
99C24×C11—24no—
100C24×C11—24no—
101C24×C11—24no—
102C24×C11—24no—
103C24×C11—24no—
104C24×C11—24no—
105C24×C11—22no—
106C24×C11—24no—
107C24×C11—22no—
108C24×C11—24no—
109C24×C11C2×D418yes—
110C24×C11#4114yes—
111C24×C11C2414yes—
112C24×C11C2412yes—
113C24×C11C2411yescharacteristic
114C2×D4×C11—264no—
115C2×D4×C11—216no—
116C2×D4×C11—216no—
117C2×D4×C11—216no—
118C2×D4×C11—216no—
119C2×D4×C11—44no—
120C2×D4×C11—416no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11#4118yes—
128C22×C4×C11C2412yes—
129C22×C4×C11C2412yes—
130C22×C4×C11C2414yes—
131C22×Dic11—216no—
132C22×Dic11—216no—
133C22×Dic11—24no—
134C22×Dic11—24no—
135C22×Dic11—24no—
136C22×Dic11—24no—
137C22×Dic11—216no—
138C22×Dic11—24no—
139C22×Dic11—24no—
140C22×Dic11—24no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11—44no—
145C22×Dic11—48no—
146C22×Dic11—432no—
147C22×Dic11—416no—
148C22×Dic11C2×D418yes—
149C22×Dic11C2×D418yes—
150C22×Dic11C2414yes—
151C22×Dic11C2414yes—
152C22×Dic11C2414yes—
153C22×Dic11C2414yes—
154C11×C22⋊C4—216no—
155C11×C22⋊C4—44no—
156C22⋊Dic11—216no—
157C22⋊Dic11—216no—
158C22⋊Dic11—216no—
159C22⋊Dic11—28no—
160C22⋊Dic11C2×D4132yescomplemented
161C4⋊Dic11—216no—
162C4⋊Dic11—44no—
163Dic11⋊C4—216no—
164Dic11⋊C4—216no—
165Dic11⋊C4—216no—
166C4×Dic11—216no—
167C22×#123—112no—
168C22×C4×D4—112no—
169#2455—1116no—
170C2×#399—111no—
171C2×#394—112no—
172C2×#392D1111yescharacteristic
173C2×#389—112no—
174C2×#388—112no—
175C2×#385—111no—
176C2×#385—112no—
177C23×C11—216no—
178C23×C11—216no—
179C23×C11—28no—
180C23×C11—216no—
181C23×C11—216no—
182C23×C11—24no—
183C23×C11—24no—
184C23×C11—24no—
185C23×C11—24no—
186C23×C11—24no—
187C23×C11—24no—
188C23×C11—22no—
189C23×C11—24no—
190C23×C11—22no—
191C23×C11—24no—
192C23×C11—48no—
193C23×C11—48no—
194C23×C11—44no—
195C23×C11—48no—
196C23×C11—48no—
197C23×C11—48no—
198C23×C11—44no—
199C23×C11C22×D418yes—
200C23×C11C22×D414yes—
201C23×C11C2×#4114yes—
202C23×C11C2×#4112yes—
203C23×C11C2×#4114yes—
204C23×C11H(5,𝔽2)12yes—
205C23×C112−1+412yes—
206C23×C11C2511yescharacteristic
207D4×C11—264no—
208D4×C11—416no—
209C2×C4×C11—216no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—44no—
217C2×C4×C11—44no—
218C2×C4×C11C2×#4118yes—
219C2×Dic11—216no—
220C2×Dic11—216no—
221C2×Dic11—24no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—24no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—24no—
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—416no—
232C2×Dic11—432no—
233C2×Dic11—48no—
234C2×Dic11—48no—
235C2×Dic11C22×D418yes—
236C2×Dic11C22×D418yes—
237C23×D4C2×D1112yes—
238C23×D4C2×D1111yescharacteristic
239C24×C4—111no—
240C24×C4—112no—
241C2×#123—1116no—
242C2×#123—2216no—
243C2×C4×D4—1116no—
244C2×C4×D4—2216no—
245C22×C4⋊C4—112no—
246C22×C4⋊C4—112no—
247C22×C4⋊C4—112no—
248C22×C4⋊C4—112no—
249C22×C4⋊C4—111no—
250C22×C22⋊C4—112no—
251C22×C22⋊C4—111no—
252C22×C22⋊C4—112no—
253C22×C22⋊C4—112no—
254C22×C22⋊C4—112no—
255C22×C22⋊C4C2×D1112yes—
256C22×C22⋊C4C2×D1111yescharacteristic
257C22×C42—112no—
258#399—118no—
259#394—1116no—
260#392C2×D1118yes—
261#389—1116no—
262#388—1116no—
263#385—118no—
264#385—1116no—
265C2×#95—112no—
266C2×#95—111no—
267C2×#95—112no—
268C2×#95C2×D1111yescharacteristic
269C22×C11—28no—
270C22×C11—28no—
271C22×C11—24no—
272C22×C11—28no—
273C22×C11—28no—
274C22×C11—44no—
275C22×C11—44no—
276C22×C11—42no—
277C22×C11—44no—
278C22×C11—44no—
279C22×C11—432no—
280C22×C11—416no—
281C22×C11—44no—
282C22×C11—42no—
283C22×C11#52518yes—
284C22×C11#53914yes—
285C22×C11D4214yes—
286C22×C11#54718yes—
287C22×C11#55914yes—
288C22×C11C23×D412yes—
289C22×C11C22×#4111yescharacteristic
290C22×C11C22×#4112yes—
291C22×C11C2×H(5,𝔽2)11yescharacteristic
292C22×C11C2×2−1+411yescharacteristic
293C4×C11—28no—
294C4×C11—42no—
295C4×C11—42no—
296Dic11—28no—
297Dic11—28no—
298Dic11—44no—
299Dic11—44no—
300C25C22×D1112yes—
301C25C22×D1111yescharacteristic
302C22×D4—28no—
303C22×D4—28no—
304C22×D4—28no—
305C22×D4—28no—
306C22×D4—42no—
307C22×D4C22×D1118yes—
308C22×D4C22×D1114yes—
309C23×C4—112no—
310C23×C4—112no—
311C23×C4—112no—
312C23×C4—112no—
313C23×C4—114no—
314C23×C4—118no—
315C23×C4—228no—
316C23×C4—228no—
317C23×C4—228no—
318C23×C4—442no—
319C23×C4—444no—
320C23×C4C22×D1111yescharacteristic
321C23×C4C22×D1111yescharacteristic
322C23×C4C22×D1112yes—
323#123—2264no—
324C4×D4—2264no—
325C2×C4⋊C4—118no—
326C2×C4⋊C4—118no—
327C2×C4⋊C4—118no—
328C2×C4⋊C4—118no—
329C2×C4⋊C4—114no—
330C2×C4⋊C4—228no—
331C2×C4⋊C4—228no—
332C2×C4⋊C4—228no—
333C2×C4⋊C4—228no—
334C2×C4⋊C4—442no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—1116no—
338C2×C22⋊C4—118no—
339C2×C22⋊C4—118no—
340C2×C22⋊C4—118no—
341C2×C22⋊C4—118no—
342C2×C22⋊C4—114no—
343C2×C22⋊C4—228no—
344C2×C22⋊C4—228no—
345C2×C22⋊C4—228no—
346C2×C22⋊C4—224no—
347C2×C22⋊C4C22×D1118yes—
348C2×C22⋊C4C22×D1114yes—
349C2×C42—118no—
350C2×C42—228no—
351#95—118no—
352#95—118no—
353#95—114no—
354#95C22×D1114yes—
355C2×C11—48no—
356C2×C11—44no—
357C2×C11#245518yescomplemented
358C2×C11C2×#52512yes—
359C2×C11C2×#53911yescharacteristic
360C2×C11C2×D4211yescharacteristic
361C2×C11C2×#54712yes—
362C2×C11C2×#55911yescharacteristic
363C24—24no—
364C24—24no—
365C24—24no—
366C24—24no—
367C24—24no—
368C24—24no—
369C24—22no—
370C24—24no—
371C24—22no—
372C24—24no—
373C24D4×D1118yes—
374C24#434114yes—
375C24C23×D1114yes—
376C24C23×D1112yes—
377C24C23×D1111yescharacteristic
378C2×D4—264no—
379C2×D4—216no—
380C2×D4—216no—
381C2×D4—216no—
382C2×D4—216no—
383C2×D4—44no—
384C2×D4—416no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—118no—
392C22×C4—118no—
393C22×C4—114no—
394C22×C4—114no—
395C22×C4—114no—
396C22×C4—114no—
397C22×C4—2216no—
398C22×C4—2216no—
399C22×C4—224no—
400C22×C4—224no—
401C22×C4—224no—
402C22×C4—224no—
403C22×C4—224no—
404C22×C4—224no—
405C22×C4—224no—
406C22×C4—2216no—
407C22×C4—224no—
408C22×C4—224no—
409C22×C4—224no—
410C22×C4—444no—
411C22×C4—448no—
412C22×C4—4416no—
413C22×C4—4432no—
414C22×C4#434118yes—
415C22×C4C23×D1112yes—
416C22×C4C23×D1112yes—
417C22×C4C23×D1114yes—
418C4⋊C4—2216no—
419C4⋊C4—2216no—
420C4⋊C4—2216no—
421C4⋊C4—2216no—
422C4⋊C4—444no—
423C22⋊C4—216no—
424C22⋊C4—44no—
425C22⋊C4—1132no—
426C22⋊C4—2216no—
427C22⋊C4—2216no—
428C22⋊C4—2216no—
429C22⋊C4—228no—
430C42—2216no—
431C11C2×#245511yescharacteristic, complemented, Sylow
432C23—216no—
433C23—216no—
434C23—216no—
435C23—28no—
436C23—216no—
437C23—24no—
438C23—24no—
439C23—24no—
440C23—24no—
441C23—24no—
442C23—24no—
443C23—22no—
444C23—24no—
445C23—22no—
446C23—24no—
447C23—48no—
448C23—44no—
449C23—48no—
450C23—44no—
451C23—48no—
452C23—48no—
453C23—48no—
454C23C2×D4×D1118yes—
455C23C2×D4×D1114yes—
456C23C2×#434114yes—
457C23C2×#434114yes—
458C23C2×#434112yes—
459C23#6703712yes—
460C23#6704312yes—
461C23C24×D1111yescharacteristic
462D4—264no—
463D4—416no—
464C2×C4—216no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—44no—
472C2×C4—44no—
473C2×C4—118no—
474C2×C4—118no—
475C2×C4—2216no—
476C2×C4—2216no—
477C2×C4—224no—
478C2×C4—224no—
479C2×C4—224no—
480C2×C4—224no—
481C2×C4—224no—
482C2×C4—224no—
483C2×C4—224no—
484C2×C4—224no—
485C2×C4—224no—
486C2×C4—224no—
487C2×C4—4416no—
488C2×C4—4432no—
489C2×C4—448no—
490C2×C4—448no—
491C2×C4C2×#434118yes—
492C22—24no—
493C22—28no—
494C22—28no—
495C22—28no—
496C22—28no—
497C22—44no—
498C22—42no—
499C22—432no—
500C22—416no—
501C22—44no—
502C22—42no—
503C22—44no—
504C22—44no—
505C22—44no—
506C22#1062311718yes—
507C22#1062312114yes—
508C22#1062313314yes—
509C22#1062314218yes—
510C22#1062324414yes—
511C22C22×D4×D1112yes—
512C22C22×#434112yes—
513C22C22×#434111yescharacteristic
514C22C2×#6703711yescharacteristic
515C22C2×#6704311yescharacteristic
516C4—28no—
517C4—42no—
518C4—42no—
519C4—228no—
520C4—228no—
521C4—444no—
522C4—444no—
523C2—44no—
524C2—48no—
525C2#1307249218yesdirect product factor
526C2C2×#1062311712yes—
527C2C2×#1062313311yescharacteristic
528C2C2×#1062312111yescharacteristic
529C2C2×#1062314212yes—
530C2C2×#1062324411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
Fitting, prime radicalC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2455
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#66988C2semidirect
2. C22×D4×Dic11C2semidirect
3. #13072492C2direct (N × H)
4. C2×#10622562C2semidirect
5. C2×#10622835C2semidirect
6. C2×#10622260C2semidirect
7. C2×#10622558C2semidirect
8. C2×#10622563C2semidirect
9. C2×#10622559C2semidirect
23. C2×#66988C22semidirect
25. C2×D4×Dic11C22semidirect
34. #10622835C22semidirect
38. #10622563C22semidirect
39. #10622562C22semidirect
40. #10622559C22semidirect
41. #10622558C22semidirect
42. #10622260C22semidirect
74. C2×C22⋊Dic11D4semidirect
160. C22⋊Dic11C2×D4semidirect
357. C2×C11#2455semidirect
431. C11C2×#2455semidirect
525. C2#13072492direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669882
C22×D4×Dic112
#130724922
C2×#106225622
C2×#106228352
C2×#106222602
C2×#106225582
C2×#106225632
C2×#106225592
C2×C11×#3922
C2×#245511