Finite Group Databasebeta

← C2×#13069874 #14781560

Subgroups — C2×#13069874 #14781560

Order 2816.

1458 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622715C211yesmaximal, characteristic, complemented
2C2×#10622838C211yesmaximal, characteristic, complemented
3C2×#10622828C211yesmaximal, characteristic
4C22×#66900C211yesmaximal, characteristic, complemented
5C22×#66897C211yesmaximal, characteristic
6#13069874C218yesmaximal, direct product factor
7C2×#10622190C211yesmaximal, characteristic, complemented
8C23×C11×SD16C211yesmaximal, characteristic
9C23×Q8×C11C2211yescharacteristic
10C23×D4×C11C2211yescharacteristic
11C22×C11×SD16—24no—
12C22×C11×SD16—24no—
13C22×C11×SD16—22no—
14C22×C11×SD16—22no—
15C22×C11×SD16C2214yes—
16C23×C8×C11C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C2×#66900—24no—
22C2×#66900C2214yescomplemented
23#10622838—22no—
24#10622838C2214yescomplemented
25C2×#66899—22no—
26C2×#66897—24no—
27C2×#66897C2214yes—
28#10622828—22no—
29#10622828C2214yes—
30C2×#66896—22no—
31#10622715—22no—
32#10622715C2214yescomplemented
33C2×Dic11⋊C8—22no—
34#10622190C2214yescomplemented
35C25×C11—21no—
36C22×Q8×C11—22no—
37C22×Q8×C11—21no—
38C22×Q8×C11—21no—
39C22×Q8×C11—21no—
40C22×Q8×C11—21no—
41C22×Q8×C11—21no—
42C22×Q8×C11—22no—
43C22×Q8×C11—22no—
44C22×Q8×C11D414yes—
45C22×Q8×C11C2312yes—
46C22×D4×C11—21no—
47C22×D4×C11—21no—
48C22×D4×C11—22no—
49C22×D4×C11—21no—
50C22×D4×C11—21no—
51C22×D4×C11—22no—
52C22×D4×C11—21no—
53C22×D4×C11—22no—
54C22×D4×C11D414yes—
55C22×D4×C11C2312yes—
56C23×C4×C11—21no—
57C23×C4×C11C2311yescharacteristic
58C2×C11×SD16—216no—
59C2×C11×SD16—216no—
60C2×C11×SD16—28no—
61C2×C11×SD16—28no—
62C2×C11×SD16—28no—
63C22×C8×C11—22no—
64C22×C8×C11—22no—
65C22×C8×C11D412yes—
66C22×C8×C11D412yes—
67C22×C8×C11C2312yes—
68C2×C22⋊Dic11—21no—
69#66979—21no—
70#66979—21no—
71#66979D412yes—
72#66979C2312yes—
73C2×C4⋊Dic11D412yes—
74C2×C4×Dic11—21no—
75C2×#4318—21no—
76C2×#4318—21no—
77C2×#4318—21no—
78C2×#4318—22no—
79C2×#4318—22no—
80C2×#4318—22no—
81C2×#4318—22no—
82C2×#4318—22no—
83C2×#4318—22no—
84C2×#4318C2312yes—
85C2×#4318C2312yes—
86C2×#4318C2312yes—
87C22×C11⋊C8—21no—
88C22×C11⋊C8—21no—
89C22×C11⋊C8—21no—
90#66900—28no—
91#66899—28no—
92#66897—28no—
93#66896—28no—
94Dic11⋊C8—28no—
95C2×#2046—111nomaximal, Sylow
96C24×C11—24no—
97C24×C11—22no—
98C24×C11—41no—
99C24×C11—41no—
100C24×C11—42no—
101C24×C11—84no—
102C24×C11#4111yescharacteristic
103C2×Q8×C11—24no—
104C2×Q8×C11—22no—
105C2×Q8×C11—24no—
106C2×Q8×C11—24no—
107C2×Q8×C11—24no—
108C2×Q8×C11—24no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—41no—
114C2×Q8×C11—41no—
115C2×Q8×C11—42no—
116C2×Q8×C11—42no—
117C2×Q8×C11—42no—
118C2×Q8×C11—42no—
119C2×Q8×C11—42no—
120C2×Q8×C11C2×D414yes—
121C2×D4×C11—24no—
122C2×D4×C11—24no—
123C2×D4×C11—24no—
124C2×D4×C11—24no—
125C2×D4×C11—24no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—41no—
132C2×D4×C11—41no—
133C2×D4×C11—42no—
134C2×D4×C11—42no—
135C2×D4×C11—42no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11C2×D414yes—
139C22×C4×C11—24no—
140C22×C4×C11—22no—
141C22×C4×C11—41no—
142C22×C4×C11—41no—
143C22×C4×C11—42no—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11#4111yescharacteristic
151C22×C4×C11#4112yes—
152C22×C4×C11#4112yes—
153C22×C4×C11C2411yescharacteristic
154C22×Dic11—22no—
155C11×SD16—232no—
156C2×C8×C11—24no—
157C2×C8×C11—24no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11C2×D414yes—
161C22⋊Dic11—22no—
162C22⋊Dic11—22no—
163C4⋊Dic11—22no—
164C4⋊Dic11C2×D414yes—
165C4×Dic11—22no—
166C4×Dic11—22no—
167#4318—22no—
168#4318—22no—
169#4318—22no—
170#4318—22no—
171#4318—22no—
172#4318—22no—
173#4318—42no—
174#4318—42no—
175#4318—42no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—42no—
180C2×C11⋊C8—42no—
181C2×C11⋊C8—42no—
182C23×SD16D1111yescharacteristic
183C2×#424—111no—
184C2×#419—111no—
185C2×#418—111no—
186C22×#101—111no—
187C22×#100—111no—
188#2046—118no—
189C2×#341—111no—
190C23×C11—24no—
191C23×C11—24no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—44no—
195C23×C11—44no—
196C23×C11—84no—
197C23×C11—88no—
198C23×C11—84no—
199C23×C11—88no—
200C23×C11—84no—
201C23×C11#12111yescharacteristic
202C23×C11#12111yescharacteristic
203C23×C11#12312yes—
204C23×C11#12312yes—
205C23×C11C2×#4111yescharacteristic
206Q8×C11—24no—
207Q8×C11—24no—
208Q8×C11—42no—
209Q8×C11—42no—
210Q8×C11—44no—
211Q8×C11—44no—
212D4×C11—24no—
213D4×C11—24no—
214D4×C11—42no—
215D4×C11—42no—
216D4×C11—44no—
217D4×C11—44no—
218C2×C4×C11—24no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—44no—
222C2×C4×C11—44no—
223C2×C4×C11#12012yes—
224C2×C4×C11#12012yes—
225C2×C4×C11#12111yescharacteristic
226C2×C4×C11#12111yescharacteristic
227C2×C4×C11#12112yes—
228C2×C4×C11#12112yes—
229C2×C4×C11#12112yes—
230C2×C4×C11#12112yes—
231C2×C4×C11#12312yes—
232C2×C4×C11#12312yes—
233C2×C4×C11#12412yes—
234C2×C4×C11#12412yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×Dic11—24no—
242C2×Dic11—44no—
243C8×C11—24no—
244C11⋊C8—42no—
245C11⋊C8—42no—
246C11⋊C8—42no—
247C23×Q8C2×D1111yescharacteristic
248C23×D4C2×D1111yescharacteristic
249C22×SD16—24no—
250C22×SD16—24no—
251C22×SD16—22no—
252C22×SD16—22no—
253C22×SD16C2×D1114yes—
254C22×M16—111no—
255C22×M16—111no—
256C22×M16—111no—
257C23×C8C2×D1111yescharacteristic
258C2×#117—111no—
259#424—114no—
260#424—222no—
261C2×C4⋊C8—222no—
262#419—114no—
263#419—222no—
264#418—114no—
265#418—222no—
266C2×#103—222no—
267C2×#102—222no—
268C2×#101—114no—
269C2×#101—224no—
270C2×#100—114no—
271C2×#100—224no—
272#341—114no—
273C22×C11—22no—
274C22×C11—22no—
275C22×C11—24no—
276C22×C11—24no—
277C22×C11—44no—
278C22×C11—84no—
279C22×C11—84no—
280C22×C11—88no—
281C22×C11—84no—
282C22×C11—88no—
283C22×C11#39412yes—
284C22×C11#39412yes—
285C22×C11#47114yes—
286C22×C11C2×#12111yescharacteristic
287C22×C11C2×#12311yescharacteristic
288C22×C11C2×#12311yescharacteristic
289C4×C11—44no—
290C4×C11#39412yes—
291C4×C11#39412yes—
292C4×C11C2×#12011yescharacteristic
293C4×C11C2×#12111yescharacteristic
294C4×C11C2×#12111yescharacteristic
295C4×C11C2×#12411yescharacteristic
296Dic11—44no—
297C25—21no—
298C22×Q8—22no—
299C22×Q8—21no—
300C22×Q8—21no—
301C22×Q8—21no—
302C22×Q8—22no—
303C22×Q8—22no—
304C22×Q8—21no—
305C22×Q8—21no—
306C22×Q8C22⋊D1114yes—
307C22×Q8C22×D1112yes—
308C22×D4—21no—
309C22×D4—21no—
310C22×D4—22no—
311C22×D4—21no—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4—21no—
315C22×D4—21no—
316C22×D4C22⋊D1114yes—
317C22×D4C22×D1112yes—
318C23×C4—21no—
319C23×C4C22×D1111yescharacteristic
320C2×SD16—216no—
321C2×SD16—216no—
322C2×SD16—28no—
323C2×SD16—28no—
324C2×SD16—28no—
325C2×M16—112no—
326C2×M16—112no—
327C2×M16—112no—
328C2×M16—221no—
329C2×M16—221no—
330C2×M16—221no—
331C2×M16—222no—
332C2×M16—222no—
333C2×M16—222no—
334C2×M16—222no—
335C2×M16—222no—
336C2×M16—222no—
337C22×C8—22no—
338C22×C8—22no—
339C22×C8—221no—
340C22×C8—221no—
341C22×C8—221no—
342C22×C8C22⋊D1112yes—
343C22×C8C22⋊D1112yes—
344C22×C8C22×D1112yes—
345#117—112no—
346#117—112no—
347#117—221no—
348#117—221no—
349C2×C4⋊C4—112no—
350C2×C22⋊C4—221no—
351C2×C42—221no—
352C4⋊C8—228no—
353#103—228no—
354#102—228no—
355#101—228no—
356#100—228no—
357C2×C11—21no—
358C2×C11—21no—
359C2×C11—22no—
360C2×C11—84no—
361C2×C11#204614yescomplemented
362C2×C11C2×#39411yescharacteristic
363C2×C11C2×#47112yes—
364C24—24no—
365C24—22no—
366C24—42no—
367C24—41no—
368C24—41no—
369C24—84no—
370C24#434111yescharacteristic
371C2×Q8—24no—
372C2×Q8—22no—
373C2×Q8—24no—
374C2×Q8—24no—
375C2×Q8—24no—
376C2×Q8—24no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—42no—
382C2×Q8—42no—
383C2×Q8—42no—
384C2×Q8—41no—
385C2×Q8—41no—
386C2×Q8—42no—
387C2×Q8—42no—
388C2×Q8C2×C22⋊D1114yes—
389C2×D4—24no—
390C2×D4—24no—
391C2×D4—24no—
392C2×D4—24no—
393C2×D4—24no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4—42no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—42no—
405C2×D4—42no—
406C2×D4C2×C22⋊D1114yes—
407C22×C4—24no—
408C22×C4—22no—
409C22×C4—42no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—222no—
413C22×C4D4×D1111yescharacteristic
414C22×C4D4×D1111yescharacteristic
415C22×C4#434111yescharacteristic
416C22×C4#434112yes—
417C22×C4#434112yes—
418C22×C4C2×C22⋊D1112yes—
419C22×C4C2×C22⋊D1112yes—
420C22×C4C2×C22⋊D1111yescharacteristic
421C22×C4C2×C22⋊D1111yescharacteristic
422C22×C4C23×D1111yescharacteristic
423SD16—232no—
424M16—222no—
425M16—222no—
426M16—222no—
427M16—222no—
428M16—222no—
429M16—222no—
430M16—442no—
431M16—442no—
432M16—442no—
433C2×C8—24no—
434C2×C8—24no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—222no—
438C2×C8—222no—
439C2×C8—222no—
440C2×C8—442no—
441C2×C8—442no—
442C2×C8—442no—
443C2×C8C2×C22⋊D1114yes—
444C4⋊C4—114no—
445C4⋊C4—222no—
446C22⋊C4—222no—
447C22⋊C4—222no—
448C42—222no—
449C42—222no—
450C11C2×#204611yescharacteristic, complemented, Sylow
451C23—24no—
452C23—24no—
453C23—42no—
454C23—42no—
455C23—44no—
456C23—44no—
457C23—84no—
458C23—88no—
459C23—84no—
460C23—88no—
461C23—84no—
462C23#6698812yes—
463C23#6698812yes—
464C23#6699111yescharacteristic
465C23#6699111yescharacteristic
466C23C2×#434111yescharacteristic
467Q8—24no—
468Q8—24no—
469Q8—42no—
470Q8—42no—
471Q8—44no—
472Q8—44no—
473D4—24no—
474D4—24no—
475D4—42no—
476D4—42no—
477D4—44no—
478D4—44no—
479C2×C4—24no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—44no—
483C2×C4—44no—
484C2×C4—224no—
485C2×C4—444no—
486C2×C4#6698812yes—
487C2×C4#6698812yes—
488C2×C4#6698912yes—
489C2×C4#6698912yes—
490C2×C4#6699111yescharacteristic
491C2×C4#6699111yescharacteristic
492C2×C4#6699212yes—
493C2×C4#6699212yes—
494C2×C4#6699212yes—
495C2×C4#6699212yes—
496C2×C4#6700612yes—
497C2×C4#6700612yes—
498C2×C4C2×D4×D1111yescharacteristic
499C2×C4C2×#434111yescharacteristic
500C2×C4C2×#434111yescharacteristic
501C2×C4C22×C22⋊D1111yescharacteristic
502C2×C4C22×C22⋊D1111yescharacteristic
503C2×C4C22×C22⋊D1111yescharacteristic
504C8—24no—
505C8—442no—
506C8—442no—
507C8—442no—
508C22—22no—
509C22—22no—
510C22—24no—
511C22—24no—
512C22—44no—
513C22—84no—
514C22—84no—
515C22—88no—
516C22—84no—
517C22—88no—
518C22#1062279014yes—
519C22#1062283512yes—
520C22#1062283512yes—
521C22C2×#6698811yescharacteristic
522C22C2×#6698811yescharacteristic
523C22C2×#6699111yescharacteristic
524C4—44no—
525C4—444no—
526C4#1062283512yes—
527C4#1062283512yes—
528C4C2×#6698911yescharacteristic
529C4C2×#6699211yescharacteristic
530C4C2×#6699211yescharacteristic
531C4C2×#6700611yescharacteristic
532C2—21no—
533C2—21no—
534C2—22no—
535C2—84no—
536C2#1306987414yesdirect product factor
537C2C2×#1062283511yescharacteristic
538C2C2×#1062279012yes—
subgroupG/H
centerC23#66991
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC23×C11×SD16C2
socleC23×C11#121
prime radicalC23×D4×C11C22
hypercenterC23×SD16D11
hypocenterC11C2×#2046
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#10622715C2semidirect
2. C2×#10622838C2semidirect
4. C22×#66900C2semidirect
6. #13069874C2direct (N × H)
7. C2×#10622190C2semidirect
22. C2×#66900C22semidirect
24. #10622838C22semidirect
32. #10622715C22semidirect
34. #10622190C22semidirect
361. C2×C11#2046semidirect
450. C11C2×#2046semidirect
536. C2#13069874direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106227152
C2×#106228382
C2×#106228282
C22×#669002
C22×#668972
#130698742
C2×#106221902
C23×C11×SD162
C2×#204611