Finite Group Databasebeta

← C2×#13072119 #14922015

Subgroups — C2×#13072119 #14922015

Order 2816.

2702 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66977C211yesmaximal, characteristic
2C22×C4×Dic22C211yesmaximal, characteristic, complemented
3#13072119C2116yesmaximal, direct product factor
4C2×#10622271C212yesmaximal, complemented
5C2×#10622565C212yesmaximal
6C2×#10622542C211yesmaximal, characteristic, complemented
7C2×#10622541C211yesmaximal, characteristic, complemented
8C2×#10622558C212yesmaximal
9C2×#10622265C212yesmaximal, complemented
10C2×#10622549C211yesmaximal, characteristic, complemented
11C2×#10622825C211yesmaximal, characteristic
12C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
13C24×C4×C11C2211yescharacteristic
14C23×Dic22C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C2×#66977—28no—
25C2×#66977C2218yes—
26C22×Dic11⋊C4C2212yes—
27C22×Dic11⋊C4C2212yes—
28C22×Dic11⋊C4C2212yes—
29C22×C4×Dic11C2212yes—
30C2×C4×Dic22—28no—
31C2×C4×Dic22C2218yescomplemented
32C4×C11×C22⋊C4C2218yes—
33C2×C11×#95C2211yescharacteristic
34C2×C11×#95C2211yescharacteristic
35#10622825C2218yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622565C22116yes—
43#10622558C22116yes—
44#10622549C2218yescomplemented
45#10622542C2218yescomplemented
46#10622541C2218yescomplemented
47#10622271C22116yescomplemented
48#10622265C22116yescomplemented
49C25×C11C2311yescharacteristic
50C23×C4×C11—24no—
51C23×C4×C11—24no—
52C23×C4×C11—24no—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2314yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×Dic11C2312yes—
61C23×Dic11C2312yes—
62C23×Dic11C2312yes—
63C23×Dic11C2312yes—
64C22×Dic22—24no—
65C22×Dic22—24no—
66C22×Dic22D418yes—
67C22×Dic22C2314yes—
68C2×C11×C22⋊C4—24no—
69C2×C11×C22⋊C4—24no—
70C2×C11×C22⋊C4C2314yes—
71C2×C11×C22⋊C4C2314yes—
72C2×C42×C11—24no—
73C2×C42×C11—24no—
74C2×C42×C11C2314yes—
75C2×C42×C11C2314yes—
76C2×C22⋊Dic11—28no—
77C2×C22⋊Dic11—28no—
78C2×C22⋊Dic11C2318yes—
79C2×C22⋊Dic11C2318yes—
80C2×C4⋊Dic11—24no—
81C2×C4⋊Dic11—24no—
82C2×C4⋊Dic11—24no—
83C2×C4⋊Dic11C2314yes—
84C2×C4⋊Dic11C2314yes—
85C2×C4⋊Dic11C2314yes—
86#66977—232no—
87C2×Dic11⋊C4—28no—
88C2×Dic11⋊C4—28no—
89C2×Dic11⋊C4—28no—
90C2×Dic11⋊C4C2318yes—
91C2×Dic11⋊C4C2318yes—
92C2×Dic11⋊C4C2318yes—
93C2×C4×Dic11—28no—
94C2×C4×Dic11C2318yes—
95C4×Dic22—232no—
96C11×#95C2314yes—
97C11×#95C2314yes—
98C11⋊#95C2318yes—
99C11⋊#95C2318yes—
100C11⋊#95C2318yes—
101C11⋊#95C2318yes—
102C11⋊#95C2318yes—
103C11⋊#95C2318yes—
104C2×#2421—111nomaximal, Sylow
105C24×C11—22no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11#4114yes—
112C24×C11C2412yes—
113C24×C11C2411yescharacteristic
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—22no—
127C22×C4×C11—22no—
128C22×C4×C11—28no—
129C22×C4×C11—28no—
130C22×C4×C11—28no—
131C22×C4×C11—416no—
132C22×C4×C11C2×D414yes—
133C22×C4×C11#4114yes—
134C22×C4×C11#4114yes—
135C22×C4×C11#4114yes—
136C22×C4×C11C2412yes—
137C22×C4×C11C2412yes—
138C22×C4×C11C2412yes—
139C22×C4×C11C2412yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2412yes—
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11C2×D418yes—
154C22×Dic11C2414yes—
155C22×Dic11C2414yes—
156C22×Dic11C2414yes—
157C22×Dic11C2414yes—
158C2×Dic22—232no—
159C2×Dic22—28no—
160C2×Dic22—28no—
161C2×Dic22C2×D4116yes—
162C11×C22⋊C4—28no—
163C11×C22⋊C4—28no—
164C42×C11—28no—
165C42×C11—28no—
166C22⋊Dic11—216no—
167C22⋊Dic11—216no—
168C4⋊Dic11—28no—
169C4⋊Dic11—28no—
170C4⋊Dic11—28no—
171Dic11⋊C4—216no—
172Dic11⋊C4—216no—
173Dic11⋊C4—216no—
174C4×Dic11—216no—
175C22×C22⋊Q8—111no—
176C22×C4×Q8—111no—
177#2421—1116no—
178C2×#400—112no—
179C2×#397—112no—
180C2×#391—111no—
181C2×#389—111no—
182C2×#388—112no—
183C2×#387—112no—
184C2×#382—111no—
185C2×#380—111no—
186C2×C4×C22⋊C4D1111yescharacteristic
187C23×C11—28no—
188C23×C11—28no—
189C23×C11—28no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—44no—
197C23×C11—44no—
198C23×C11—44no—
199C23×C11—44no—
200C23×C11C22×D412yes—
201C23×C11C2×#4114yes—
202C23×C11C2×#4112yes—
203C23×C11C2×#4112yes—
204C23×C11C2×#4112yes—
205C23×C11C2×#4112yes—
206C23×C112−1+412yes—
207C23×C112−1+412yes—
208C23×C11C2511yescharacteristic
209C2×C4×C11—28no—
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—22no—
223C2×C4×C11—22no—
224C2×C4×C11—44no—
225C2×C4×C11—44no—
226C2×C4×C11—44no—
227C2×C4×C11—44no—
228C2×C4×C11—416no—
229C2×C4×C11#123116yes—
230C2×C4×C11C22×D414yes—
231C2×C4×C11C2×#4114yes—
232C2×C4×C11C2×#4114yes—
233C2×C4×C11C2×#4114yes—
234C2×Dic11—216no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—48no—
247C2×Dic11—48no—
248C2×Dic11—48no—
249C2×Dic11C22×D418yes—
250Dic22—232no—
251C23×Q8—111no—
252C24×C4C2×D1111yescharacteristic
253C2×C22⋊Q8—118no—
254C2×C22⋊Q8—228no—
255C2×C4×Q8—118no—
256C2×C4×Q8—228no—
257C22×C4⋊C4—112no—
258C22×C4⋊C4—112no—
259C22×C4⋊C4—112no—
260C22×C4⋊C4—111no—
261C22×C4⋊C4—111no—
262C22×C4⋊C4—111no—
263C22×C22⋊C4—112no—
264C22×C22⋊C4—112no—
265C22×C22⋊C4C2×D1111yescharacteristic
266C22×C22⋊C4C2×D1111yescharacteristic
267C22×C42—112no—
268C22×C42C2×D1111yescharacteristic
269C22×C42C2×D1111yescharacteristic
270#400—1116no—
271#397—1116no—
272#391—118no—
273#389—118no—
274#388—1116no—
275#387—1116no—
276#382—118no—
277#380—118no—
278C4×C22⋊C4C2×D1118yes—
279C2×#95—112no—
280C2×#95—112no—
281C2×#95—112no—
282C2×#95—112no—
283C2×#95—112no—
284C2×#95—112no—
285C2×#95C2×D1111yescharacteristic
286C2×#95C2×D1111yescharacteristic
287C22×C11—24no—
288C22×C11—24no—
289C22×C11—24no—
290C22×C11—42no—
291C22×C11—416no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11C2×#12314yes—
296C22×C11#52914yes—
297C22×C11#54114yes—
298C22×C11#54814yes—
299C22×C11#54814yes—
300C22×C11#55214yes—
301C22×C11#55614yes—
302C22×C11C23×D411yescharacteristic
303C22×C11C22×#4111yescharacteristic
304C22×C11C22×#4111yescharacteristic
305C22×C11C22×#4111yescharacteristic
306C22×C11C22×#4111yescharacteristic
307C22×C11C2×2−1+411yescharacteristic
308C22×C11C2×2−1+411yescharacteristic
309C4×C11—24no—
310C4×C11—42no—
311C4×C11—42no—
312C4×C11—42no—
313C4×C11—42no—
314C4×C11C2×#12318yes—
315Dic11—28no—
316Dic11—44no—
317Dic11—44no—
318Dic11—44no—
319C25C22×D1111yescharacteristic
320C22×Q8—118no—
321C22×Q8—114no—
322C22×Q8—224no—
323C22×Q8—224no—
324C23×C4—24no—
325C23×C4—24no—
326C23×C4—24no—
327C23×C4—112no—
328C23×C4—112no—
329C23×C4—112no—
330C23×C4—112no—
331C23×C4C22×D1114yes—
332C23×C4C22×D1111yescharacteristic
333C23×C4C22×D1111yescharacteristic
334C23×C4C22×D1111yescharacteristic
335C23×C4C22×D1111yescharacteristic
336C23×C4C22×D1111yescharacteristic
337C23×C4C22×D1111yescharacteristic
338C22⋊Q8—2232no—
339C4×Q8—2232no—
340C2×C4⋊C4—114no—
341C2×C4⋊C4—118no—
342C2×C4⋊C4—114no—
343C2×C4⋊C4—118no—
344C2×C4⋊C4—114no—
345C2×C4⋊C4—118no—
346C2×C4⋊C4—228no—
347C2×C4⋊C4—228no—
348C2×C4⋊C4—228no—
349C2×C4⋊C4—224no—
350C2×C4⋊C4—224no—
351C2×C4⋊C4—224no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—118no—
355C2×C22⋊C4—118no—
356C2×C22⋊C4—228no—
357C2×C22⋊C4—228no—
358C2×C22⋊C4C22×D1114yes—
359C2×C22⋊C4C22×D1114yes—
360C2×C42—24no—
361C2×C42—24no—
362C2×C42—118no—
363C2×C42—228no—
364C2×C42C22×D1114yes—
365C2×C42C22×D1114yes—
366#95—118no—
367#95—118no—
368#95—118no—
369#95—118no—
370#95—118no—
371#95—118no—
372#95C22×D1114yes—
373#95C22×D1114yes—
374C2×C11—44no—
375C2×C11#242118yescomplemented
376C2×C11C22×#12311yescharacteristic
377C2×C11C2×#52911yescharacteristic
378C2×C11C2×#54111yescharacteristic
379C2×C11C2×#54811yescharacteristic
380C2×C11C2×#54811yescharacteristic
381C2×C11C2×#55211yescharacteristic
382C2×C11C2×#55611yescharacteristic
383C24—22no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24#433914yes—
390C24C23×D1112yes—
391C24C23×D1111yescharacteristic
392C2×Q8—1116no—
393C2×Q8—2232no—
394C2×Q8—228no—
395C2×Q8—228no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—28no—
411C22×C4—28no—
412C22×C4—28no—
413C22×C4—416no—
414C22×C4—118no—
415C22×C4—114no—
416C22×C4—114no—
417C22×C4—114no—
418C22×C4—114no—
419C22×C4—224no—
420C22×C4—224no—
421C22×C4—224no—
422C22×C4—224no—
423C22×C4—224no—
424C22×C4—224no—
425C22×C4—224no—
426C22×C4—224no—
427C22×C4—224no—
428C22×C4—224no—
429C22×C4—224no—
430C22×C4#433914yes—
431C22×C4#433914yes—
432C22×C4D4×D1114yes—
433C22×C4#434114yes—
434C22×C4C23×D1112yes—
435C22×C4C23×D1112yes—
436C22×C4C23×D1112yes—
437C22×C4C23×D1112yes—
438C22×C4C23×D1112yes—
439C22×C4C23×D1112yes—
440C4⋊C4—2216no—
441C4⋊C4—2216no—
442C4⋊C4—2216no—
443C4⋊C4—228no—
444C4⋊C4—228no—
445C4⋊C4—228no—
446C22⋊C4—28no—
447C22⋊C4—28no—
448C22⋊C4—2216no—
449C22⋊C4—2216no—
450C42—28no—
451C42—28no—
452C42—2216no—
453C11C2×#242111yescharacteristic, complemented, Sylow
454C23—28no—
455C23—28no—
456C23—28no—
457C23—22no—
458C23—22no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—44no—
464C23—44no—
465C23—44no—
466C23—44no—
467C23C2×#433914yes—
468C23C2×#433912yes—
469C23C2×#433912yes—
470C23C2×#433912yes—
471C23C2×D4×D1112yes—
472C23C2×#434112yes—
473C23#6704312yes—
474C23#6704312yes—
475C23C24×D1111yescharacteristic
476Q8—2232no—
477C2×C4—28no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—44no—
493C2×C4—44no—
494C2×C4—44no—
495C2×C4—44no—
496C2×C4—416no—
497C2×C4—118no—
498C2×C4—2216no—
499C2×C4—224no—
500C2×C4—224no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—224no—
504C2×C4—224no—
505C2×C4—224no—
506C2×C4—224no—
507C2×C4—224no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—448no—
511C2×C4—448no—
512C2×C4—448no—
513C2×C4#66936116yes—
514C2×C4C2×#433914yes—
515C2×C4C2×#433914yes—
516C2×C4C2×D4×D1114yes—
517C2×C4C2×#434114yes—
518C22—24no—
519C22—24no—
520C22—24no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—416no—
525C22—42no—
526C22#1062301014yes—
527C22C2×#6693614yes—
528C22#1062304914yes—
529C22#1062307214yes—
530C22#1062307314yes—
531C22#1062308314yes—
532C22#1062308314yes—
533C22C22×#433911yescharacteristic
534C22C22×#433911yescharacteristic
535C22C22×#433911yescharacteristic
536C22C22×D4×D1111yescharacteristic
537C22C22×#434111yescharacteristic
538C22C2×#6704311yescharacteristic
539C22C2×#6704311yescharacteristic
540C4—24no—
541C4—42no—
542C4—42no—
543C4—42no—
544C4—42no—
545C4—228no—
546C4—444no—
547C4—444no—
548C4—444no—
549C4C2×#6693618yes—
550C2—44no—
551C2#1307211918yesdirect product factor
552C2C22×#6693611yescharacteristic
553C2C2×#1062301011yescharacteristic
554C2C2×#1062304911yescharacteristic
555C2C2×#1062308311yescharacteristic
556C2C2×#1062308311yescharacteristic
557C2C2×#1062307211yescharacteristic
558C2C2×#1062307311yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C2×#2421
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic22C2semidirect
3. #13072119C2direct (N × H)
4. C2×#10622271C2semidirect
6. C2×#10622542C2semidirect
7. C2×#10622541C2semidirect
9. C2×#10622265C2semidirect
10. C2×#10622549C2semidirect
31. C2×C4×Dic22C22semidirect
44. #10622549C22semidirect
45. #10622542C22semidirect
46. #10622541C22semidirect
47. #10622271C22semidirect
48. #10622265C22semidirect
375. C2×C11#2421semidirect
453. C11C2×#2421semidirect
551. C2#13072119direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669772
C22×C4×Dic222
#130721192
C2×#106222712
C2×#106225652
C2×#106225422
C2×#106225412
C2×#106225582
C2×#106222652
C2×#106225492
C2×#106228252
C2×C4×C11×C22⋊C42
C2×#242111