Finite Group Databasebeta

← C2×#13069697 #14780828

Subgroups — C2×#13069697 #14780828

Order 2816.

2254 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4324C211yesmaximal, characteristic
2C22×#66997C211yesmaximal, characteristic, complemented
3C22×#66880C211yesmaximal, characteristic, complemented
4C22×#66899C211yesmaximal, characteristic, complemented
5C2×#10622834C211yesmaximal, characteristic
6#13069697C218yesmaximal, direct product factor
7C2×#10622188C211yesmaximal, characteristic, complemented
8C23×C11×SD16C211yesmaximal, characteristic
9C23×Q8×C11C2211yescharacteristic
10C23×D4×C11C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C22×C11×SD16—24no—
13C22×C11×SD16—24no—
14C22×C11×SD16—24no—
15C22×C11×SD16C2214yes—
16C23×C8×C11C2211yescharacteristic
17C22×C22⋊Dic11—22no—
18C2×#66997—24no—
19C2×#66997—24no—
20C2×#66997—22no—
21C2×#66997C2214yescomplemented
22C22×#4324—24no—
23C22×#4324—24no—
24C22×#4324—24no—
25C22×#4324C2214yes—
26C22×C4⋊Dic11C2211yescharacteristic
27C22×Dic11⋊C4—22no—
28C22×C4×Dic11C2211yescharacteristic
29C23×C11⋊C8C2211yescharacteristic
30C2×#66899—24no—
31C2×#66899C2214yescomplemented
32#10622834—22no—
33#10622834C2214yes—
34C2×#66880—24no—
35C2×#66880C2214yescomplemented
36#10622188C2214yescomplemented
37C25×C11—21no—
38C22×Q8×C11—22no—
39C22×Q8×C11—21no—
40C22×Q8×C11—22no—
41C22×Q8×C11—22no—
42C22×Q8×C11—22no—
43C22×Q8×C11—22no—
44C22×Q8×C11D414yes—
45C22×Q8×C11C2312yes—
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11—21no—
51C22×D4×C11—22no—
52C22×D4×C11D414yes—
53C22×D4×C11C2312yes—
54C23×C4×C11—21no—
55C23×C4×C11C2311yescharacteristic
56C23×Dic11—21no—
57C23×Dic11—21no—
58C23×Dic11D412yes—
59C22×Dic22—22no—
60C22×Dic22—22no—
61C22×Dic22—22no—
62C22×Dic22—22no—
63C22×Dic22—21no—
64C22×Dic22—22no—
65C22×Dic22D414yes—
66C22×Dic22C2312yes—
67C2×C11×SD16—232no—
68C2×C11×SD16—28no—
69C2×C11×SD16—28no—
70C2×C11×SD16—28no—
71C22×C8×C11—22no—
72C22×C8×C11—22no—
73C22×C8×C11D414yes—
74C22×C8×C11C2312yes—
75C2×C22⋊Dic11—28no—
76C2×C22⋊Dic11—48no—
77#66997—216no—
78#66997—28no—
79#66997—28no—
80C2×#4324—232no—
81C2×#4324—28no—
82C2×#4324—28no—
83C2×#4324—28no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11C2312yes—
88C2×Dic11⋊C4—216no—
89C2×Dic11⋊C4—28no—
90C2×C4×Dic11—22no—
91C2×C4×Dic11—22no—
92C2×C4×Dic11D412yes—
93C2×C4×Dic11C2312yes—
94C22×C11⋊C8—22no—
95C22×C11⋊C8—22no—
96C22×C11⋊C8D414yes—
97C22×C11⋊C8C2312yes—
98#66899—28no—
99#66880—28no—
100C2×#2013—111nomaximal, Sylow
101C24×C11—24no—
102C24×C11—22no—
103C24×C11—42no—
104C24×C11—42no—
105C24×C11—44no—
106C24×C11—44no—
107C24×C11C2×D411yescharacteristic
108C2×Q8×C11—24no—
109C2×Q8×C11—22no—
110C2×Q8×C11—28no—
111C2×Q8×C11—28no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—44no—
117C2×Q8×C11—42no—
118C2×Q8×C11—44no—
119C2×Q8×C11—42no—
120C2×Q8×C11C2×D414yes—
121C2×D4×C11—28no—
122C2×D4×C11—28no—
123C2×D4×C11—24no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—42no—
130C2×D4×C11—44no—
131C2×D4×C11—44no—
132C2×D4×C11—42no—
133C2×D4×C11C2×D414yes—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D412yes—
144C22×C4×C11#4112yes—
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—42no—
152C22×Dic11—42no—
153C22×Dic11—42no—
154C22×Dic11—44no—
155C22×Dic11SD1618yescomplemented
156C22×Dic11C2×D414yes—
157C2×Dic22—28no—
158C2×Dic22—24no—
159C2×Dic22—28no—
160C2×Dic22—22no—
161C2×Dic22—22no—
162C2×Dic22—22no—
163C2×Dic22—22no—
164C2×Dic22—22no—
165C2×Dic22—44no—
166C2×Dic22—44no—
167C2×Dic22—42no—
168C2×Dic22—42no—
169C2×Dic22C2×D414yes—
170C11×SD16—232no—
171C2×C8×C11—28no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11C2×D414yes—
175C22⋊Dic11—416no—
176#4324—232no—
177C4⋊Dic11—22no—
178C4⋊Dic11—22no—
179C4⋊Dic11—42no—
180Dic11⋊C4—232no—
181C4×Dic11—24no—
182C4×Dic11—22no—
183C4×Dic11—22no—
184C2×C11⋊C8—28no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8C2×D414yes—
188C23×SD16—111no—
189C23×SD16D1111yescharacteristic
190C22×C4⋊Q8—111no—
191C22×#103—111no—
192C22×#103—111no—
193C2×#390—111no—
194#2013—118no—
195C2×#336—111no—
196C23×C11—24no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—44no—
200C23×C11—44no—
201C23×C11—48no—
202C23×C11—416no—
203C23×C11—88no—
204C23×C11—84no—
205C23×C11—84no—
206C23×C11#12012yes—
207C23×C11#12112yes—
208C23×C11#12712yes—
209C23×C11C2×SD1614yes—
210C23×C11#13714yes—
211C23×C11C22×D411yescharacteristic
212Q8×C11—24no—
213Q8×C11—24no—
214Q8×C11—42no—
215Q8×C11—42no—
216Q8×C11—48no—
217D4×C11—24no—
218D4×C11—24no—
219D4×C11—42no—
220D4×C11—42no—
221D4×C11—48no—
222C2×C4×C11—24no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—48no—
226C2×C4×C11#12014yes—
227C2×C4×C11#12012yes—
228C2×C4×C11#12014yes—
229C2×C4×C11#12114yes—
230C2×C4×C11#12114yes—
231C2×C4×C11#12112yes—
232C2×C4×C11#12712yes—
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—216no—
242C2×Dic11—24no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—48no—
246C2×Dic11—42no—
247C2×Dic11—44no—
248C2×Dic11—84no—
249C2×Dic11C2×SD1618yescomplemented
250Dic22—24no—
251Dic22—24no—
252Dic22—42no—
253Dic22—42no—
254Dic22—48no—
255C8×C11—24no—
256C11⋊C8—24no—
257C23×Q8—111no—
258C23×Q8C2×D1111yescharacteristic
259C23×D4C2×D1111yescharacteristic
260C22×SD16—24no—
261C22×SD16—24no—
262C22×SD16—24no—
263C22×SD16—114no—
264C22×SD16—224no—
265C22×SD16—224no—
266C22×SD16—224no—
267C22×SD16C2×D1114yes—
268C23×C8—111no—
269C23×C8C2×D1111yescharacteristic
270C2×C4⋊Q8—114no—
271C2×C4⋊Q8—222no—
272C2×C4⋊Q8—224no—
273C2×C4⋊Q8—224no—
274C22×C4⋊C4—111no—
275C22×C4⋊C4—222no—
276C22×C22⋊C4—222no—
277C22×C42—111no—
278C2×#103—114no—
279C2×#103—114no—
280C2×#103—224no—
281C2×#103—224no—
282#390—114no—
283#390—222no—
284#336—114no—
285C22×C11—44no—
286C22×C11—48no—
287C22×C11—82no—
288C22×C11—82no—
289C22×C11—84no—
290C22×C11—816no—
291C22×C11#39214yes—
292C22×C11#44818yes—
293C22×C11#46118yes—
294C22×C11#49214yes—
295C22×C11#49714yes—
296C22×C11C2×#12011yescharacteristic
297C22×C11C2×#12111yescharacteristic
298C22×C11C2×#12711yescharacteristic
299C22×C11C22×SD1612yes—
300C22×C11C2×#13712yes—
301C4×C11—44no—
302C4×C11#39214yes—
303C4×C11C2×#12011yescharacteristic
304C4×C11C2×#12011yescharacteristic
305C4×C11C2×#12111yescharacteristic
306C4×C11C2×#12111yescharacteristic
307Dic11—28no—
308Dic11—44no—
309Dic11—82no—
310C25—21no—
311C22×Q8—22no—
312C22×Q8—21no—
313C22×Q8—22no—
314C22×Q8—22no—
315C22×Q8—22no—
316C22×Q8—22no—
317C22×Q8—114no—
318C22×Q8—112no—
319C22×Q8—221no—
320C22×Q8—222no—
321C22×Q8—222no—
322C22×Q8—222no—
323C22×Q8—222no—
324C22×Q8—222no—
325C22×Q8C22⋊D1114yes—
326C22×Q8C22×D1112yes—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—21no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4C22⋊D1114yes—
334C22×D4C22×D1112yes—
335C23×C4—21no—
336C23×C4—112no—
337C23×C4—221no—
338C23×C4—221no—
339C23×C4C22×D1111yescharacteristic
340C2×SD16—232no—
341C2×SD16—28no—
342C2×SD16—28no—
343C2×SD16—28no—
344C2×SD16—228no—
345C2×SD16—228no—
346C2×SD16—2232no—
347C2×SD16—228no—
348C22×C8—22no—
349C22×C8—22no—
350C22×C8—114no—
351C22×C8—112no—
352C22×C8—222no—
353C22×C8—222no—
354C22×C8C22⋊D1114yes—
355C22×C8C22×D1112yes—
356C4⋊Q8—228no—
357C4⋊Q8—2216no—
358C4⋊Q8—228no—
359C2×C4⋊C4—112no—
360C2×C4⋊C4—228no—
361C2×C4⋊C4—2216no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4—222no—
364C2×C4⋊C4—221no—
365C2×C22⋊C4—228no—
366C2×C22⋊C4—448no—
367C2×C42—112no—
368C2×C42—112no—
369C2×C42—222no—
370C2×C42—222no—
371#103—228no—
372#103—228no—
373C2×C11—84no—
374C2×C11#201318yescomplemented
375C2×C11C2×#39211yescharacteristic
376C2×C11C2×#44812yes—
377C2×C11C2×#46112yes—
378C2×C11C2×#49211yescharacteristic
379C2×C11C2×#49711yescharacteristic
380C24—24no—
381C24—22no—
382C24—44no—
383C24—44no—
384C24—42no—
385C24—42no—
386C24D4×D1111yescharacteristic
387C2×Q8—24no—
388C2×Q8—22no—
389C2×Q8—28no—
390C2×Q8—28no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—44no—
396C2×Q8—44no—
397C2×Q8—42no—
398C2×Q8—42no—
399C2×Q8—114no—
400C2×Q8—224no—
401C2×Q8—222no—
402C2×Q8—228no—
403C2×Q8—228no—
404C2×Q8—222no—
405C2×Q8—222no—
406C2×Q8—222no—
407C2×Q8—222no—
408C2×Q8—442no—
409C2×Q8—444no—
410C2×Q8—442no—
411C2×Q8—444no—
412C2×Q8C2×C22⋊D1114yes—
413C2×D4—28no—
414C2×D4—24no—
415C2×D4—28no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—42no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—42no—
425C2×D4C2×C22⋊D1114yes—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—118no—
431C22×C4—114no—
432C22×C4—224no—
433C22×C4—224no—
434C22×C4—224no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—442no—
438C22×C4—442no—
439C22×C4—444no—
440C22×C4—442no—
441C22×C4D4×D1112yes—
442C22×C4D4×D1111yescharacteristic
443C22×C4D4×D1112yes—
444C22×C4#434112yes—
445C22×C4C2×C22⋊D1112yes—
446C22×C4C2×C22⋊D1112yes—
447C22×C4C2×C22⋊D1112yes—
448C22×C4C23×D1111yescharacteristic
449SD16—232no—
450SD16—2232no—
451C2×C8—28no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—114no—
455C2×C8—228no—
456C2×C8—222no—
457C2×C8—222no—
458C2×C8C2×C22⋊D1114yes—
459C4⋊C4—2232no—
460C4⋊C4—222no—
461C4⋊C4—222no—
462C4⋊C4—442no—
463C22⋊C4—4416no—
464C42—224no—
465C42—222no—
466C42—222no—
467C11C2×#201311yescharacteristic, complemented, Sylow
468C23—24no—
469C23—416no—
470C23—44no—
471C23—44no—
472C23—42no—
473C23—42no—
474C23—48no—
475C23—84no—
476C23—88no—
477C23—84no—
478C23SD16×D1114yes—
479C23#6696814yes—
480C23#6699012yes—
481C23#6699212yes—
482C23#6699312yes—
483C23C2×D4×D1111yescharacteristic
484Q8—24no—
485Q8—24no—
486Q8—42no—
487Q8—42no—
488Q8—48no—
489Q8—224no—
490Q8—224no—
491Q8—442no—
492Q8—448no—
493Q8—442no—
494D4—24no—
495D4—24no—
496D4—42no—
497D4—42no—
498D4—48no—
499C2×C4—24no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—48no—
503C2×C4—118no—
504C2×C4—224no—
505C2×C4—2216no—
506C2×C4—224no—
507C2×C4—224no—
508C2×C4—442no—
509C2×C4—442no—
510C2×C4—448no—
511C2×C4—444no—
512C2×C4—442no—
513C2×C4—884no—
514C2×C4#6699014yes—
515C2×C4#6699012yes—
516C2×C4#6699114yes—
517C2×C4#6699214yes—
518C2×C4#6699212yes—
519C2×C4#6699312yes—
520C2×C4#6700614yes—
521C2×C4C2×D4×D1111yescharacteristic
522C2×C4C2×D4×D1111yescharacteristic
523C2×C4C2×#434111yescharacteristic
524C2×C4C22×C22⋊D1111yescharacteristic
525C2×C4C22×C22⋊D1111yescharacteristic
526C2×C4C22×C22⋊D1111yescharacteristic
527C8—24no—
528C8—224no—
529C22—48no—
530C22—44no—
531C22—82no—
532C22—84no—
533C22—816no—
534C22—82no—
535C22#1062277518yes—
536C22#1062278014yes—
537C22#1062278318yes—
538C22#1062278814yes—
539C22#1062283614yes—
540C22C2×SD16×D1112yes—
541C22C2×#6696812yes—
542C22C2×#6699011yescharacteristic
543C22C2×#6699211yescharacteristic
544C22C2×#6699311yescharacteristic
545C4—44no—
546C4—228no—
547C4—444no—
548C4—882no—
549C4#1062283614yes—
550C4C2×#6699011yescharacteristic
551C4C2×#6699111yescharacteristic
552C4C2×#6699211yescharacteristic
553C4C2×#6700611yescharacteristic
554C2—84no—
555C2#1306969718yesdirect product factor
556C2C2×#1062283611yescharacteristic
557C2C2×#1062278312yes—
558C2C2×#1062277512yes—
559C2C2×#1062278811yescharacteristic
560C2C2×#1062278011yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC23×C11×SD16C2
socleC24×C11C2×D4
prime radicalC23×D4×C11C22
hypercenterC23×SD16D11
hypocenterC11C2×#2013
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×SD16

Complements

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

NH ≅ G/Ntype
2. C22×#66997C2semidirect
3. C22×#66880C2semidirect
4. C22×#66899C2semidirect
6. #13069697C2direct (N × H)
7. C2×#10622188C2semidirect
21. C2×#66997C22semidirect
31. C2×#66899C22semidirect
35. C2×#66880C22semidirect
36. #10622188C22semidirect
155. C22×Dic11SD16semidirect
249. C2×Dic11C2×SD16semidirect
374. C2×C11#2013semidirect
467. C11C2×#2013semidirect
555. C2#13069697direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43242
C22×#669972
C22×#668802
C22×#668992
C2×#106228342
#130696972
C2×#106221882
C23×C11×SD162
C2×#201311