Finite Group Databasebeta

← C2×#13072115 #14922010

Subgroups — C2×#13072115 #14922010

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×Q8×Dic11C211yesmaximal, characteristic, complemented
2#13072115C2116yesmaximal, direct product factor
3C2×#10622599C212yesmaximal, complemented
4C2×#10622566C212yesmaximal
5C2×#10622843C211yesmaximal, characteristic, complemented
6C2×#10622586C211yesmaximal, characteristic, complemented
7C2×#10622557C212yesmaximal
8C2×#10622591C212yesmaximal, complemented
9C2×#10622590C211yesmaximal, characteristic, complemented
10C2×#10622825C211yesmaximal, characteristic
11C2×C4×C22⋊Dic11C211yesmaximal, characteristic
12C22×C11×C22⋊Q8C211yesmaximal, characteristic
13C23×Q8×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C2×C11×C22⋊Q8—28no—
16C2×C11×C22⋊Q8C2218yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2212yes—
19C22×C11×C22⋊C4C2212yes—
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C2×Q8×Dic11—28no—
24C2×Q8×Dic11C2218yescomplemented
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2212yes—
28C22×Dic11⋊C4C2212yes—
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2212yes—
32#10622843C2218yescomplemented
33#10622825C2218yes—
34C4×C22⋊Dic11C2218yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622599C22116yescomplemented
44#10622591C22116yescomplemented
45#10622590C2218yescomplemented
46#10622586C2218yescomplemented
47#10622566C22116yes—
48#10622557C22116yes—
49C25×C11C2311yescharacteristic
50C22×Q8×C11—24no—
51C22×Q8×C11—24no—
52C22×Q8×C11D418yes—
53C22×Q8×C11C2314yes—
54C23×C4×C11—24no—
55C23×C4×C11—24no—
56C23×C4×C11—24no—
57C23×C4×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2314yes—
60C23×C4×C11C2312yes—
61C23×C4×C11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2312yes—
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2312yes—
67C23×Dic11C2311yescharacteristic
68C11×C22⋊Q8—232no—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4—28no—
71C2×C11×C4⋊C4C2314yes—
72C2×C11×C4⋊C4C2318yes—
73C2×C11×C22⋊C4—28no—
74C2×C11×C22⋊C4C2318yes—
75C2×C22⋊Dic11—24no—
76C2×C22⋊Dic11—28no—
77C2×C22⋊Dic11—24no—
78C2×C22⋊Dic11C2314yes—
79C2×C22⋊Dic11C2318yes—
80C2×C22⋊Dic11C2314yes—
81Q8×Dic11—232no—
82C2×C4⋊Dic11—28no—
83C2×C4⋊Dic11—24no—
84C2×C4⋊Dic11—24no—
85C2×C4⋊Dic11C2318yes—
86C2×C4⋊Dic11C2314yes—
87C2×C4⋊Dic11C2314yes—
88C2×Dic11⋊C4—28no—
89C2×Dic11⋊C4C2318yes—
90C2×C4×Dic11—28no—
91C2×C4×Dic11—24no—
92C2×C4×Dic11—24no—
93C2×C4×Dic11C2318yes—
94C2×C4×Dic11C2314yes—
95C2×C4×Dic11C2314yes—
96C11⋊#95C2318yes—
97C11⋊#95C2318yes—
98C11⋊#95C2318yes—
99C11⋊#95C2318yes—
100C11⋊#95C2318yes—
101C11⋊#95C2314yes—
102C11⋊#95C2314yes—
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
114C2×Q8×C11—232no—
115C2×Q8×C11—28no—
116C2×Q8×C11—28no—
117C2×Q8×C11C2×D4116yes—
118C22×C4×C11—24no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—22no—
122C22×C4×C11—24no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—28no—
127C22×C4×C11—28no—
128C22×C4×C11—28no—
129C22×C4×C11—416no—
130C22×C4×C11C2×D418yes—
131C22×C4×C11C2×D414yes—
132C22×C4×C11#4114yes—
133C22×C4×C11#4114yes—
134C22×C4×C11C2412yes—
135C22×C4×C11C2414yes—
136C22×C4×C11C2414yes—
137C22×C4×C11C2412yes—
138C22×Dic11—22no—
139C22×Dic11—24no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11—22no—
147C22×Dic11—24no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—24no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11#4114yes—
156C22×Dic11C2412yes—
157C22×Dic11C2412yes—
158C22×Dic11C2414yes—
159C22×Dic11C2414yes—
160C22×Dic11C2412yes—
161C22×Dic11C2412yes—
162C11×C4⋊C4—28no—
163C11×C4⋊C4—216no—
164C11×C22⋊C4—216no—
165C22⋊Dic11—28no—
166C22⋊Dic11—216no—
167C22⋊Dic11—28no—
168C4⋊Dic11—216no—
169C4⋊Dic11—28no—
170C4⋊Dic11—28no—
171Dic11⋊C4—216no—
172C4×Dic11—216no—
173C4×Dic11—28no—
174C4×Dic11—28no—
175C22×C22⋊Q8D1111yescharacteristic
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⋊C4—111no—
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×#4112yes—
202C23×C11C2×#4112yes—
203C23×C11C2×#4114yes—
204C23×C11C2×#4112yes—
205C23×C11C2×#4112yes—
206C23×C112−1+412yes—
207C23×C112−1+412yes—
208C23×C11C2511yescharacteristic
209Q8×C11—232no—
210C2×C4×C11—216no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—24no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—44no—
220C2×C4×C11—48no—
221C2×C4×C11—416no—
222C2×C4×C11#123116yes—
223C2×C4×C11C22×D418yes—
224C2×C4×C11C22×D414yes—
225C2×C4×C11C2×#4114yes—
226C2×C4×C11C2×#4114yes—
227C2×Dic11—28no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—24no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—24no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—48no—
246C2×Dic11—48no—
247C2×Dic11—44no—
248C2×Dic11—44no—
249C2×Dic11—44no—
250C2×Dic11C2×#4114yes—
251C23×Q8C2×D1111yescharacteristic
252C24×C4C2×D1111yescharacteristic
253C2×C22⋊Q8—28no—
254C2×C22⋊Q8C2×D1118yes—
255C2×C4×Q8—118no—
256C2×C4×Q8—228no—
257C22×C4⋊C4—112no—
258C22×C4⋊C4—112no—
259C22×C4⋊C4—111no—
260C22×C4⋊C4—111no—
261C22×C4⋊C4C2×D1112yes—
262C22×C4⋊C4C2×D1111yescharacteristic
263C22×C22⋊C4—111no—
264C22×C22⋊C4—112no—
265C22×C22⋊C4—111no—
266C22×C22⋊C4C2×D1112yes—
267C22×C42—111no—
268C22×C42—112no—
269C22×C42—111no—
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⋊C4—118no—
279C2×#95—112no—
280C2×#95—112no—
281C2×#95—112no—
282C2×#95—111no—
283C2×#95—112no—
284C2×#95—112no—
285C2×#95—112no—
286C2×#95—111no—
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—28no—
310C4×C11—42no—
311C4×C11—44no—
312C4×C11C2×#12318yes—
313Dic11—24no—
314Dic11—44no—
315Dic11—44no—
316Dic11—42no—
317Dic11—42no—
318Dic11—42no—
319C25C22×D1111yescharacteristic
320C22×Q8—24no—
321C22×Q8—24no—
322C22×Q8C22⋊D1118yes—
323C22×Q8C22×D1114yes—
324C23×C4—24no—
325C23×C4—24no—
326C23×C4—24no—
327C23×C4—111no—
328C23×C4—112no—
329C23×C4—111no—
330C23×C4—112no—
331C23×C4—111no—
332C23×C4—111no—
333C23×C4C22×D1114yes—
334C23×C4C22×D1112yes—
335C23×C4C22×D1111yescharacteristic
336C23×C4C22×D1112yes—
337C23×C4C22×D1111yescharacteristic
338C22⋊Q8—232no—
339C4×Q8—2232no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—114no—
343C2×C4⋊C4—118no—
344C2×C4⋊C4—114no—
345C2×C4⋊C4—118no—
346C2×C4⋊C4—228no—
347C2×C4⋊C4—224no—
348C2×C4⋊C4—228no—
349C2×C4⋊C4—224no—
350C2×C4⋊C4C22×D1114yes—
351C2×C4⋊C4C22×D1118yes—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—114no—
354C2×C22⋊C4—114no—
355C2×C22⋊C4—118no—
356C2×C22⋊C4—224no—
357C2×C22⋊C4—224no—
358C2×C22⋊C4—228no—
359C2×C22⋊C4C22×D1118yes—
360C2×C42—114no—
361C2×C42—118no—
362C2×C42—114no—
363C2×C42—224no—
364C2×C42—228no—
365C2×C42—224no—
366#95—114no—
367#95—114no—
368#95—118no—
369#95—118no—
370#95—118no—
371#95—118no—
372#95—118no—
373#95—118no—
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#434314yes—
390C24C23×D1112yes—
391C24C23×D1111yescharacteristic
392C2×Q8—232no—
393C2×Q8—28no—
394C2×Q8—28no—
395C2×Q8C2×C22⋊D11116yes—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—22no—
404C22×C4—28no—
405C22×C4—28no—
406C22×C4—28no—
407C22×C4—416no—
408C22×C4—114no—
409C22×C4—112no—
410C22×C4—112no—
411C22×C4—112no—
412C22×C4—114no—
413C22×C4—112no—
414C22×C4—114no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—224no—
420C22×C4—222no—
421C22×C4—224no—
422C22×C4—224no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—224no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—224no—
429C22×C4—222no—
430C22×C4—224no—
431C22×C4—222no—
432C22×C4#434114yes—
433C22×C4#434114yes—
434C22×C4C2×C22⋊D1118yes—
435C22×C4C2×C22⋊D1114yes—
436C22×C4C23×D1112yes—
437C22×C4C23×D1114yes—
438C22×C4C23×D1114yes—
439C22×C4C23×D1112yes—
440C4⋊C4—28no—
441C4⋊C4—216no—
442C4⋊C4—2216no—
443C4⋊C4—228no—
444C4⋊C4—2216no—
445C4⋊C4—228no—
446C22⋊C4—216no—
447C22⋊C4—228no—
448C22⋊C4—228no—
449C22⋊C4—2216no—
450C42—228no—
451C42—2216no—
452C42—228no—
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×#434112yes—
468C23C2×#434112yes—
469C23C2×#434314yes—
470C23C2×#434312yes—
471C23#6704012yes—
472C23#41×D1112yes—
473C23#6704312yes—
474C23C22×C22⋊D1112yes—
475C23C24×D1111yescharacteristic
476Q8—232no—
477C2×C4—216no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—44no—
487C2×C4—48no—
488C2×C4—416no—
489C2×C4—114no—
490C2×C4—228no—
491C2×C4—222no—
492C2×C4—222no—
493C2×C4—222no—
494C2×C4—222no—
495C2×C4—224no—
496C2×C4—222no—
497C2×C4—224no—
498C2×C4—222no—
499C2×C4—224no—
500C2×C4—222no—
501C2×C4—222no—
502C2×C4—224no—
503C2×C4—222no—
504C2×C4—224no—
505C2×C4—222no—
506C2×C4—224no—
507C2×C4—222no—
508C2×C4—444no—
509C2×C4—448no—
510C2×C4—448no—
511C2×C4—444no—
512C2×C4—444no—
513C2×C4#66988116yes—
514C2×C4C2×#434114yes—
515C2×C4C2×#434114yes—
516C2×C4C22×C22⋊D1118yes—
517C2×C4C22×C22⋊D1114yes—
518C22—24no—
519C22—24no—
520C22—24no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—416no—
525C22—42no—
526C22#1062315514yes—
527C22#1062315614yes—
528C22#1062317214yes—
529C22#1062317314yes—
530C22C2×#6698814yes—
531C22#1062334814yes—
532C22#1062336214yes—
533C22C22×#434111yescharacteristic
534C22C22×#434111yescharacteristic
535C22C22×#434311yescharacteristic
536C22C2×#6704011yescharacteristic
537C22C2×#41×D1111yescharacteristic
538C22C2×#6704311yescharacteristic
539C22C23×C22⋊D1111yescharacteristic
540C4—28no—
541C4—44no—
542C4—42no—
543C4—224no—
544C4—442no—
545C4—444no—
546C4—442no—
547C4—442no—
548C4—444no—
549C4C2×#6698818yes—
550C2—44no—
551C2#1307211518yesdirect product factor
552C2C22×#6698811yescharacteristic
553C2C2×#1062315511yescharacteristic
554C2C2×#1062315611yescharacteristic
555C2C2×#1062336211yescharacteristic
556C2C2×#1062334811yescharacteristic
557C2C2×#1062317311yescharacteristic
558C2C2×#1062317211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×C22⋊Q8C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC22×C22⋊Q8D11
hypocenterC11C2×#2421
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×Q8×Dic11C2semidirect
2. #13072115C2direct (N × H)
3. C2×#10622599C2semidirect
5. C2×#10622843C2semidirect
6. C2×#10622586C2semidirect
8. C2×#10622591C2semidirect
9. C2×#10622590C2semidirect
24. C2×Q8×Dic11C22semidirect
32. #10622843C22semidirect
43. #10622599C22semidirect
44. #10622591C22semidirect
45. #10622590C22semidirect
46. #10622586C22semidirect
375. C2×C11#2421semidirect
453. C11C2×#2421semidirect
551. C2#13072115direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×Dic112
#130721152
C2×#106225992
C2×#106225662
C2×#106228432
C2×#106225862
C2×#106225572
C2×#106225912
C2×#106225902
C2×#106228252
C2×C4×C22⋊Dic112
C22×C11×C22⋊Q82
C2×#242111