Finite Group Databasebeta

← C2×#13074542 #14920179

Subgroups — C2×#13074542 #14920179

Order 2816.

2958 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66999C211yesmaximal, characteristic, complemented
2C22×#66946C211yesmaximal, characteristic
3#13074542C2116yesmaximal, direct product factor
4C2×#10622596C211yesmaximal, characteristic, complemented
5C2×#10622287C211yesmaximal, characteristic, complemented
6C2×#10622606C212yesmaximal, complemented
7C2×#10622285C212yesmaximal
8C2×#10622844C211yesmaximal, characteristic, complemented
9C2×#10622265C212yesmaximal, complemented
10C2×#10622602C212yesmaximal, complemented
11C2×#10622277C211yesmaximal, characteristic, complemented
12C2×C11×#395C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C23×D44C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C23×C4×D11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2212yes—
19C2×#66999—28no—
20C2×#66999C2218yescomplemented
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×C4⋊Dic11C2211yescharacteristic
28C22×Dic11⋊C4C2212yes—
29C22×Dic11⋊C4C2212yes—
30C22×C4×Dic11C2211yescharacteristic
31C2×#66946—28no—
32C2×#66946C2218yes—
33C11×#395C2218yescomplemented
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2212yes—
36#10622844C2218yescomplemented
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622606C22116yescomplemented
43#10622602C22116yescomplemented
44#10622596C2218yescomplemented
45#10622287C2218yescomplemented
46#10622285C22116yes—
47#10622277C2218yescomplemented
48#10622265C22116yescomplemented
49C24×D11C2311yescharacteristic
50C24×D11C2311yescharacteristic
51C22×Q8×C11—24no—
52C22×Q8×C11—44no—
53C22×Q8×C11C2314yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2312yes—
61C23×Dic11C2312yes—
62C23×Dic11C2311yescharacteristic
63C22×D44—24no—
64C22×D44—24no—
65C22×D44—24no—
66C22×D44C2314yes—
67C22×C4×D11—24no—
68C22×C4×D11—44no—
69C22×C4×D11—44no—
70C22×C4×D11D418yes—
71C22×C4×D11C2314yes—
72C22×C4×D11C2314yes—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4—44no—
75C2×C11×C4⋊C4C2314yes—
76C2×C11×C4⋊C4C2318yes—
77#66999—232no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—28no—
80C2×(C2×D11)⋊C4—28no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—44no—
83C2×(C2×D11)⋊C4—44no—
84C2×(C2×D11)⋊C4C2314yes—
85C2×(C2×D11)⋊C4C2314yes—
86C2×(C2×D11)⋊C4C2318yes—
87C2×(C2×D11)⋊C4C2318yes—
88C2×(C2×D11)⋊C4C2318yes—
89C2×(C2×D11)⋊C4C2318yes—
90C2×C4⋊Dic11—24no—
91C2×C4⋊Dic11C2314yes—
92C2×Dic11⋊C4—28no—
93C2×Dic11⋊C4—28no—
94C2×Dic11⋊C4C2318yes—
95C2×Dic11⋊C4C2318yes—
96C2×C4×Dic11—24no—
97C2×C4×Dic11C2314yes—
98#66946—232no—
99C11×#95C2318yes—
100C11×#95C2314yes—
101C11⋊#95C2318yes—
102C11⋊#95C2318yes—
103C11⋊#95C2318yes—
104C11⋊#95C2314yes—
105C11⋊#95C2318yes—
106C2×#2638—111nomaximal, Sylow
107C24×C11C2411yescharacteristic
108C23×D11—22no—
109C23×D11—22no—
110C23×D11—22no—
111C23×D11—22no—
112C23×D11—24no—
113C23×D11—24no—
114C23×D11—24no—
115C23×D11—24no—
116C23×D11C2×D414yes—
117C23×D11#4114yes—
118C23×D11C2412yes—
119C23×D11C2412yes—
120C2×Q8×C11—28no—
121C2×Q8×C11—48no—
122C2×Q8×C11—416no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—22no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11C2×D414yes—
135C22×C4×C11#4114yes—
136C22×C4×C11C2414yes—
137C22×C4×C11C2412yes—
138C22×C4×C11C2414yes—
139C22×C4×C11C2412yes—
140C22×C4×C11C2412yes—
141C22×Dic11—22no—
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×Dic11C2×D414yes—
151C22×Dic11C2412yes—
152C22×Dic11C2414yes—
153C22×Dic11C2414yes—
154C22×Dic11C2412yes—
155C2×D44—232no—
156C2×D44—28no—
157C2×D44—28no—
158C2×D44—28no—
159C2×C4×D11—28no—
160C2×C4×D11—416no—
161C2×C4×D11—48no—
162C2×C4×D11—48no—
163C2×C4×D11—416no—
164C2×C4×D11C2×D4116yes—
165C11×C4⋊C4—28no—
166C11×C4⋊C4—48no—
167(C2×D11)⋊C4—28no—
168(C2×D11)⋊C4—216no—
169(C2×D11)⋊C4—216no—
170(C2×D11)⋊C4—28no—
171(C2×D11)⋊C4—48no—
172(C2×D11)⋊C4—48no—
173C4⋊Dic11—28no—
174Dic11⋊C4—216no—
175Dic11⋊C4—216no—
176C4×Dic11—28no—
177C22×C22⋊Q8—111no—
178C22×C4×D4—111no—
179#2638—1116no—
180C2×#398—111no—
181C2×#397—111no—
182C2×#397—112no—
183C2×#395D1111yescharacteristic, complemented
184C2×#394—112no—
185C2×#393—111no—
186C2×#387—112no—
187C2×#385—112no—
188C2×#381—111no—
189C23×C11C22×D412yes—
190C23×C11C2×#4112yes—
191C23×C11C2×#4112yes—
192C23×C11H(5,𝔽2)14yes—
193C23×C112−1+414yes—
194C23×C11C2511yescharacteristic
195C22×D11—28no—
196C22×D11—28no—
197C22×D11—28no—
198C22×D11—28no—
199C22×D11—216no—
200C22×D11—22no—
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—24no—
205C22×D11—24no—
206C22×D11—24no—
207C22×D11—24no—
208C22×D11—44no—
209C22×D11—44no—
210C22×D11—48no—
211C22×D11—48no—
212C22×D11—48no—
213C22×D11C22×D414yes—
214C22×D11C2×#4114yes—
215Q8×C11—416no—
216C2×C4×C11—28no—
217C2×C4×C11—28no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—44no—
230C2×C4×C11—48no—
231C2×C4×C11—48no—
232C2×C4×C11C22×D414yes—
233C2×C4×C11C2×#4114yes—
234C2×Dic11—28no—
235C2×Dic11—24no—
236C2×Dic11—22no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—48no—
245C2×Dic11—44no—
246C2×Dic11—48no—
247C2×Dic11C22×D414yes—
248D44—232no—
249C4×D11—416no—
250C4×D11—416no—
251C23×Q8C2×D1111yescharacteristic
252C23×D4—111no—
253C24×C4—111no—
254C24×C4—111no—
255C2×C22⋊Q8—118no—
256C2×C22⋊Q8—228no—
257C2×C4×D4—118no—
258C2×C4×D4—228no—
259C22×C4⋊C4—112no—
260C22×C4⋊C4—112no—
261C22×C4⋊C4—111no—
262C22×C4⋊C4C2×D1111yescharacteristic
263C22×C4⋊C4C2×D1112yes—
264C22×C22⋊C4—111no—
265C22×C22⋊C4—112no—
266C22×C22⋊C4—112no—
267C22×C22⋊C4—111no—
268C22×C22⋊C4—112no—
269C22×C22⋊C4—112no—
270C22×C42—111no—
271#398—118no—
272#397—1116no—
273#397—118no—
274#395C2×D1118yescomplemented
275#394—1116no—
276#393—118no—
277#387—1116no—
278#385—1116no—
279#381—118no—
280C2×#95—112no—
281C2×#95—111no—
282C2×#95—112no—
283C2×#95—112no—
284C2×#95—112no—
285C2×#95C2×D1112yes—
286C2×#95C2×D1111yescharacteristic
287C22×C11#52514yes—
288C22×C11#53414yes—
289C22×C11#53614yes—
290C22×C11#53918yes—
291C22×C11#54218yes—
292C22×C11C23×D411yescharacteristic
293C22×C11C22×#4111yescharacteristic
294C22×C11C22×#4111yescharacteristic
295C22×C11C2×H(5,𝔽2)12yes—
296C22×C11C2×2−1+412yes—
297C2×D11—24no—
298C2×D11—24no—
299C2×D11—24no—
300C2×D11—24no—
301C2×D11—28no—
302C2×D11—416no—
303C2×D11—416no—
304C2×D11—42no—
305C2×D11—42no—
306C2×D11—44no—
307C2×D11—44no—
308C2×D11—44no—
309C4×C11—24no—
310C4×C11—24no—
311C4×C11—44no—
312C4×C11—42no—
313C4×C11—44no—
314Dic11—24no—
315Dic11—44no—
316Dic11—42no—
317Dic11—44no—
318C25—111no—
319C25—111no—
320C22×Q8—24no—
321C22×Q8—44no—
322C22×Q8C22×D1114yes—
323C22×D4—114no—
324C22×D4—224no—
325C22×D4—224no—
326C22×D4—224no—
327C23×C4—111no—
328C23×C4—118no—
329C23×C4—114no—
330C23×C4—112no—
331C23×C4—112no—
332C23×C4—111no—
333C23×C4—114no—
334C23×C4—224no—
335C23×C4—444no—
336C23×C4—444no—
337C23×C4C22×D1112yes—
338C23×C4C22×D1112yes—
339C23×C4C22×D1111yescharacteristic
340C23×C4C22×D1111yescharacteristic
341C23×C4C22×D1111yescharacteristic
342C22⋊Q8—2232no—
343C4×D4—2232no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—118no—
347C2×C4⋊C4—114no—
348C2×C4⋊C4—118no—
349C2×C4⋊C4—228no—
350C2×C4⋊C4—224no—
351C2×C4⋊C4—228no—
352C2×C4⋊C4C22×D1114yes—
353C2×C4⋊C4C22×D1118yes—
354C2×C22⋊C4—114no—
355C2×C22⋊C4—114no—
356C2×C22⋊C4—118no—
357C2×C22⋊C4—118no—
358C2×C22⋊C4—118no—
359C2×C22⋊C4—118no—
360C2×C22⋊C4—224no—
361C2×C22⋊C4—228no—
362C2×C22⋊C4—228no—
363C2×C22⋊C4—224no—
364C2×C22⋊C4—444no—
365C2×C22⋊C4—444no—
366C2×C42—114no—
367C2×C42—224no—
368#95—118no—
369#95—114no—
370#95—118no—
371#95—118no—
372#95—118no—
373#95C22×D1114yes—
374#95C22×D1118yes—
375C2×C11#263818yescomplemented
376C2×C11C2×#52511yescharacteristic
377C2×C11C2×#53411yescharacteristic
378C2×C11C2×#53611yescharacteristic
379C2×C11C2×#53912yes—
380C2×C11C2×#54212yes—
381D11—44no—
382D11—44no—
383C24—114no—
384C24—114no—
385C24—112no—
386C24—112no—
387C24—222no—
388C24—224no—
389C24—224no—
390C24—222no—
391C24—222no—
392C24—224no—
393C24—224no—
394C24—222no—
395C24C23×D1111yescharacteristic
396C2×Q8—28no—
397C2×Q8—48no—
398C2×Q8—416no—
399C2×D4—228no—
400C2×D4—228no—
401C2×D4—2232no—
402C2×D4—228no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—114no—
415C22×C4—112no—
416C22×C4—1116no—
417C22×C4—112no—
418C22×C4—114no—
419C22×C4—114no—
420C22×C4—228no—
421C22×C4—224no—
422C22×C4—222no—
423C22×C4—224no—
424C22×C4—224no—
425C22×C4—224no—
426C22×C4—224no—
427C22×C4—224no—
428C22×C4—224no—
429C22×C4—224no—
430C22×C4—4416no—
431C22×C4—448no—
432C22×C4—448no—
433C22×C4—4416no—
434C22×C4D4×D1114yes—
435C22×C4#434314yes—
436C22×C4C23×D1114yes—
437C22×C4C23×D1112yes—
438C22×C4C23×D1114yes—
439C22×C4C23×D1112yes—
440C22×C4C23×D1112yes—
441C4⋊C4—28no—
442C4⋊C4—48no—
443C4⋊C4—2216no—
444C4⋊C4—228no—
445C4⋊C4—2216no—
446C22⋊C4—228no—
447C22⋊C4—2216no—
448C22⋊C4—2216no—
449C22⋊C4—228no—
450C22⋊C4—448no—
451C22⋊C4—448no—
452C42—228no—
453C11C2×#263811yescharacteristic, complemented, Sylow
454C23—114no—
455C23—114no—
456C23—228no—
457C23—228no—
458C23—228no—
459C23—228no—
460C23—2216no—
461C23—222no—
462C23—224no—
463C23—224no—
464C23—222no—
465C23—222no—
466C23—224no—
467C23—224no—
468C23—222no—
469C23—444no—
470C23—448no—
471C23—448no—
472C23—444no—
473C23—448no—
474C23C2×D4×D1112yes—
475C23#6703714yes—
476C23C2×#434312yes—
477C23#6704014yes—
478C23#41×D1112yes—
479C23C24×D1111yescharacteristic
480Q8—416no—
481D4—2232no—
482C2×C4—28no—
483C2×C4—28no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—44no—
496C2×C4—48no—
497C2×C4—48no—
498C2×C4—114no—
499C2×C4—228no—
500C2×C4—224no—
501C2×C4—222no—
502C2×C4—224no—
503C2×C4—224no—
504C2×C4—224no—
505C2×C4—224no—
506C2×C4—224no—
507C2×C4—224no—
508C2×C4—224no—
509C2×C4—4416no—
510C2×C4—4416no—
511C2×C4—444no—
512C2×C4—448no—
513C2×C4—448no—
514C2×C4C2×D4×D1114yes—
515C2×C4C2×#434314yes—
516C22—224no—
517C22—224no—
518C22—224no—
519C22—224no—
520C22—228no—
521C22—442no—
522C22—442no—
523C22—4416no—
524C22—4416no—
525C22—444no—
526C22—444no—
527C22—444no—
528C22#1062312014yes—
529C22#1062315814yes—
530C22#1062316918yes—
531C22#1062325514yes—
532C22#1062326418yes—
533C22C22×D4×D1111yescharacteristic
534C22C2×#6703712yes—
535C22C22×#434311yescharacteristic
536C22C2×#6704012yes—
537C22C2×#41×D1111yescharacteristic
538C4—24no—
539C4—24no—
540C4—42no—
541C4—44no—
542C4—44no—
543C4—224no—
544C4—444no—
545C4—442no—
546C4—444no—
547C2—444no—
548C2—444no—
549C2#1307454218yesdirect product factor
550C2C2×#1062315811yescharacteristic
551C2C2×#1062312011yescharacteristic
552C2C2×#1062325511yescharacteristic
553C2C2×#1062316912yes—
554C2C2×#1062326412yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#395C2
socleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#395D11
hypocenterC11C2×#2638
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
1. C22×#66999C2semidirect
3. #13074542C2direct (N × H)
4. C2×#10622596C2semidirect
5. C2×#10622287C2semidirect
6. C2×#10622606C2semidirect
8. C2×#10622844C2semidirect
9. C2×#10622265C2semidirect
10. C2×#10622602C2semidirect
11. C2×#10622277C2semidirect
12. C2×C11×#395C2semidirect
20. C2×#66999C22semidirect
33. C11×#395C22semidirect
36. #10622844C22semidirect
42. #10622606C22semidirect
43. #10622602C22semidirect
44. #10622596C22semidirect
45. #10622287C22semidirect
47. #10622277C22semidirect
48. #10622265C22semidirect
183. C2×#395D11semidirect
274. #395C2×D11semidirect
375. C2×C11#2638semidirect
453. C11C2×#2638semidirect
549. C2#13074542direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669992
C22×#669462
#130745422
C2×#106225962
C2×#106222872
C2×#106226062
C2×#106222852
C2×#106228442
C2×#106222652
C2×#106226022
C2×#106222772
C2×C11×#3952
C2×#263811