Finite Group Databasebeta

← #14780879

Subgroups — #14780879

Order 2816.

1938 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66995C211yesmaximal, characteristic
2C2×#10623347C211yesmaximal, characteristic
3C2×#10622838C211yesmaximal, characteristic, complemented
4C2×#10622726C211yesmaximal, characteristic
5#13071202C211yesmaximal, characteristic, complemented
6#13069714C214yesmaximal, complemented
7#13069707C214yesmaximal, complemented
8#13068312C211yesmaximal, characteristic, complemented
9C23×C11×Q16C211yesmaximal, characteristic, complemented
10C23×Q8×C11C2211yescharacteristic
11C23×Q8×C11C2211yescharacteristic
12C22×#4339C2211yescharacteristic
13C22×C11×Q16—24no—
14C22×C11×Q16—24no—
15C22×C11×Q16—24no—
16C22×C11×Q16C2214yes—
17C23×C8×C11C2211yescharacteristic
18#10623347—24no—
19#10623347—24no—
20C2×#67000C2212yes—
21C2×#66999—22no—
22C2×#66997C2212yes—
23C22×#4326C2212yes—
24C2×#66995—24no—
25C2×#66995—24no—
26C2×#66995—24no—
27C22×#4325C2212yes—
28C2×#66982—22no—
29C2×#66979C2211yescharacteristic
30C2×#66979C2211yescharacteristic
31C22×#4318C2211yescharacteristic
32#10622843—22no—
33#10622843C2214yes—
34#10622838—24no—
35C2×#66899C2214yes—
36#10622824—22no—
37#10622726—24no—
38C2×#66885C2212yes—
39C2×#66880C2212yes—
40#10622188C2214yes—
41C22×Q8×C11—21no—
42C22×Q8×C11—22no—
43C22×Q8×C11—21no—
44C22×Q8×C11—22no—
45C22×Q8×C11—22no—
46C22×Q8×C11—22no—
47C22×Q8×C11—22no—
48C22×Q8×C11—22no—
49C22×Q8×C11—22no—
50C22×Q8×C11—22no—
51C22×Q8×C11—22no—
52C22×Q8×C11—22no—
53C22×Q8×C11D414yes—
54C22×Q8×C11D414yes—
55C22×Q8×C11C2312yes—
56C22×Q8×C11C2312yes—
57C23×C4×C11—21no—
58C23×C4×C11—21no—
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C2×#4339—22no—
62C2×#4339—22no—
63C2×#4339—22no—
64C2×#4339—22no—
65C2×#4339—22no—
66C2×#4339D414yes—
67C22×D44C2311yescharacteristic
68C22×C4×D11—21no—
69C22×Dic22C2311yescharacteristic
70C2×C11×Q16—232no—
71C2×C11×Q16—28no—
72C2×C11×Q16—28no—
73C2×C11×Q16—28no—
74C22×C8×C11—22no—
75C22×C8×C11—22no—
76C22×C8×C11D414yes—
77C22×C8×C11C2312yes—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11D412yes—
80#67000—24no—
81#67000—24no—
82#66999—216no—
83#66997—24no—
84#66997—24no—
85C2×#4326—24no—
86C2×#4326—24no—
87C2×#4326—24no—
88#66995—232no—
89C2×#4325—24no—
90C2×#4325—24no—
91C2×#4325—24no—
92#66982—216no—
93C2×(C2×D11)⋊C4—24no—
94#66979—22no—
95#66979—22no—
96#66979—22no—
97#66979—22no—
98C2×C4⋊Dic11D412yes—
99C2×C4⋊Dic11C2312yes—
100C2×Dic11⋊C4—24no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11C2312yes—
103C2×#4318—22no—
104C2×#4318—22no—
105C2×#4318D414yes—
106C22×C11⋊C8C2312yes—
107#66899—28no—
108C11⋊#95—28no—
109#66885—24no—
110#66880—24no—
111#23425—111nomaximal, Sylow
112C24×C11C2×D411yescharacteristic
113C23×D11—21no—
114C2×Q8×C11—24no—
115C2×Q8×C11—24no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—28no—
119C2×Q8×C11—28no—
120C2×Q8×C11—28no—
121C2×Q8×C11—28no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11—42no—
131C2×Q8×C11—44no—
132C2×Q8×C11—42no—
133C2×Q8×C11—44no—
134C2×Q8×C11—44no—
135C2×Q8×C11—44no—
136C2×Q8×C11—42no—
137C2×Q8×C11—42no—
138C2×Q8×C11C2×D414yes—
139C2×Q8×C11C2×D414yes—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D412yes—
154C22×C4×C11#4112yes—
155C22×C4×C11C2411yescharacteristic
156C2×C22⋊D11—24no—
157C2×C22⋊D11—42no—
158C2×C22⋊D11—42no—
159C22×Dic11—21no—
160C22×Dic11—22no—
161C22×Dic11C2×D414yes—
162#4339—28no—
163#4339—28no—
164#4339—44no—
165#4339—44no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—21no—
170C2×D44—21no—
171C2×D44C2×D412yes—
172C2×C4×D11—24no—
173C2×C4×D11—42no—
174C2×C4×D11—42no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C2×Dic22—21no—
180C2×Dic22C2×D412yes—
181C11×Q16—232no—
182C2×C8×C11—28no—
183C2×C8×C11—22no—
184C2×C8×C11—22no—
185C2×C8×C11C2×D414yes—
186C22⋊Dic11—24no—
187C22⋊Dic11—42no—
188#4326—216no—
189#4325—216no—
190(C2×D11)⋊C4—216no—
191C4⋊Dic11—24no—
192C4⋊Dic11—22no—
193C4⋊Dic11—22no—
194Dic11⋊C4—216no—
195C4×Dic11—22no—
196C4×Dic11—22no—
197C4×Dic11—42no—
198#4318—28no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8C2×D414yes—
202C22×#137—111no—
203C23×Q16D1111yescharacteristic, complemented
204C2×#536—111no—
205C2×#419—111no—
206C2×#416—111no—
207#2310—111no—
208#2016—114no—
209#2015—114no—
210#1729—111no—
211C23×C11—24no—
212C23×C11#12012yes—
213C23×C11#12112yes—
214C23×C11#12712yes—
215C23×C11C22×D411yescharacteristic
216C22×D11—22no—
217C22×D11—41no—
218C22×D11—41no—
219C22×D11—44no—
220Q8×C11—24no—
221Q8×C11—24no—
222Q8×C11—24no—
223Q8×C11—24no—
224Q8×C11—42no—
225Q8×C11—42no—
226Q8×C11—42no—
227Q8×C11—42no—
228Q8×C11—48no—
229Q8×C11—48no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—48no—
237C2×C4×C11—48no—
238C2×C4×C11#12014yes—
239C2×C4×C11#12012yes—
240C2×C4×C11#12014yes—
241C2×C4×C11#12114yes—
242C2×C4×C11#12114yes—
243C2×C4×C11#12112yes—
244C2×C4×C11#12712yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C22⋊D11—48no—
252C2×Dic11—24no—
253C2×Dic11—22no—
254C2×Dic11—28no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—42no—
258C2×Dic11—44no—
259D44—22no—
260D44—22no—
261D44—41no—
262D44—41no—
263C4×D11—48no—
264Dic22—22no—
265Dic22—22no—
266Dic22—41no—
267Dic22—41no—
268C8×C11—24no—
269C11⋊C8—24no—
270C22×#41—111no—
271C23×Q8C2×D1111yescharacteristic
272C23×Q8C2×D1111yescharacteristic
273C2×#137—224no—
274C2×#137—224no—
275C2×#137—224no—
276C22×Q16—24no—
277C22×Q16—24no—
278C22×Q16—24no—
279C22×Q16—112no—
280C22×Q16C2×D1114yes—
281C22×SD16—112no—
282C22×M16—111no—
283C23×C8C2×D1111yescharacteristic
284#536—224no—
285#536—224no—
286C2×C4⋊Q8—112no—
287C2×#124—112no—
288C2×#123—222no—
289C2×C22⋊Q8—222no—
290C2×#117—111no—
291C2×#117—111no—
292#419—224no—
293#416—224no—
294C2×#103—114no—
295C2×#103—112no—
296C2×#102—112no—
297#391—114no—
298#391—222no—
299#381—222no—
300#336—114no—
301C22×C11—24no—
302C22×C11—24no—
303C22×C11—24no—
304C22×C11#39214yes—
305C22×C11C2×#12011yescharacteristic
306C22×C11C2×#12111yescharacteristic
307C22×C11C2×#12711yescharacteristic
308C22×C11#57814yes—
309C2×D11—42no—
310C2×D11—44no—
311C2×D11—82no—
312C2×D11—82no—
313C4×C11—44no—
314C4×C11—44no—
315C4×C11#39214yes—
316C4×C11C2×#12011yescharacteristic
317C4×C11C2×#12011yescharacteristic
318C4×C11C2×#12111yescharacteristic
319C4×C11C2×#12111yescharacteristic
320Dic11—42no—
321Dic11—44no—
322Dic11—82no—
323C2×#41—114no—
324C2×#41—222no—
325C2×#41—222no—
326C2×#41—222no—
327C2×#41—222no—
328C2×#41—222no—
329C22×Q8—21no—
330C22×Q8—22no—
331C22×Q8—21no—
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—22no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8—22no—
340C22×Q8—22no—
341C22×Q8—111no—
342C22×Q8C22⋊D1114yes—
343C22×Q8C22⋊D1114yes—
344C22×Q8C22×D1112yes—
345C22×Q8C22×D1112yes—
346C22×D4—111no—
347C22×D4—221no—
348C23×C4—21no—
349C23×C4—21no—
350C23×C4—221no—
351C23×C4C22×D1111yescharacteristic
352#137—2232no—
353C2×Q16—232no—
354C2×Q16—28no—
355C2×Q16—28no—
356C2×Q16—28no—
357C2×Q16—224no—
358C2×Q16—224no—
359C2×Q16—224no—
360C2×SD16—224no—
361C2×SD16—224no—
362C2×SD16—224no—
363C2×M16—114no—
364C2×M16—222no—
365C2×M16—222no—
366C22×C8—22no—
367C22×C8—22no—
368C22×C8—112no—
369C22×C8C22⋊D1114yes—
370C22×C8C22×D1112yes—
371C4⋊Q8—224no—
372C4⋊Q8—224no—
373#124—224no—
374#124—224no—
375#123—2216no—
376C22⋊Q8—2216no—
377#117—222no—
378#117—222no—
379#117—222no—
380#117—222no—
381C2×C4⋊C4—112no—
382C2×C4⋊C4—112no—
383C2×C4⋊C4—224no—
384C2×C22⋊C4—112no—
385C2×C22⋊C4—224no—
386C2×C22⋊C4—221no—
387C2×C42—112no—
388C2×C42—221no—
389#103—228no—
390#103—224no—
391#102—224no—
392#95—228no—
393C2×C11—24no—
394C2×C11C2×#39211yescharacteristic
395C2×C11#301112yes—
396C2×C11#304412yes—
397C2×C11#315612yes—
398D11—82no—
399C24—221no—
400C24D4×D1111yescharacteristic
401#41—228no—
402#41—228no—
403#41—444no—
404#41—444no—
405C2×Q8—24no—
406C2×Q8—24no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—28no—
410C2×Q8—28no—
411C2×Q8—28no—
412C2×Q8—28no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—42no—
422C2×Q8—44no—
423C2×Q8—44no—
424C2×Q8—44no—
425C2×Q8—42no—
426C2×Q8—44no—
427C2×Q8—42no—
428C2×Q8—42no—
429C2×Q8—112no—
430C2×Q8—221no—
431C2×Q8—221no—
432C2×Q8—221no—
433C2×Q8—221no—
434C2×Q8—221no—
435C2×Q8C2×C22⋊D1114yes—
436C2×Q8C2×C22⋊D1114yes—
437C2×D4—112no—
438C2×D4—224no—
439C2×D4—221no—
440C2×D4—221no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—221no—
444C2×D4—442no—
445C2×D4—442no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—114no—
455C22×C4—221no—
456C22×C4—224no—
457C22×C4—222no—
458C22×C4—442no—
459C22×C4—442no—
460C22×C4D4×D1112yes—
461C22×C4D4×D1111yescharacteristic
462C22×C4D4×D1112yes—
463C22×C4#434112yes—
464C22×C4C2×C22⋊D1112yes—
465C22×C4C2×C22⋊D1112yes—
466C22×C4C2×C22⋊D1112yes—
467C22×C4C23×D1111yescharacteristic
468Q16—232no—
469Q16—2216no—
470SD16—2216no—
471M16—228no—
472C2×C8—28no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—114no—
476C2×C8—222no—
477C2×C8—222no—
478C2×C8C2×C22⋊D1114yes—
479C4⋊C4—2216no—
480C4⋊C4—224no—
481C4⋊C4—222no—
482C4⋊C4—222no—
483C22⋊C4—2216no—
484C22⋊C4—224no—
485C22⋊C4—442no—
486C42—222no—
487C42—222no—
488C42—442no—
489C11#2342511yescharacteristic, complemented, Sylow
490C23—24no—
491C23—222no—
492C23—444no—
493C23—441no—
494C23—441no—
495C23#6699012yes—
496C23#6699212yes—
497C23#6699312yes—
498C23C2×D4×D1111yescharacteristic
499Q8—24no—
500Q8—24no—
501Q8—24no—
502Q8—24no—
503Q8—42no—
504Q8—42no—
505Q8—42no—
506Q8—42no—
507Q8—48no—
508Q8—48no—
509Q8—222no—
510Q8—222no—
511Q8—441no—
512Q8—441no—
513D4—222no—
514D4—222no—
515D4—448no—
516D4—441no—
517D4—441no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—48no—
525C2×C4—48no—
526C2×C4—228no—
527C2×C4—224no—
528C2×C4—222no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—448no—
532C2×C4—444no—
533C2×C4—442no—
534C2×C4#6699014yes—
535C2×C4#6699012yes—
536C2×C4#6699114yes—
537C2×C4#6699214yes—
538C2×C4#6699212yes—
539C2×C4#6699312yes—
540C2×C4#6700614yes—
541C2×C4C2×D4×D1111yescharacteristic
542C2×C4C2×D4×D1111yescharacteristic
543C2×C4C2×#434111yescharacteristic
544C2×C4C22×C22⋊D1111yescharacteristic
545C2×C4C22×C22⋊D1111yescharacteristic
546C2×C4C22×C22⋊D1111yescharacteristic
547C8—24no—
548C8—224no—
549C22—24no—
550C22—24no—
551C22—24no—
552C22—444no—
553C22—442no—
554C22—882no—
555C22—882no—
556C22#1062283614yes—
557C22#1062329714yes—
558C22C2×#6699011yescharacteristic
559C22C2×#6699211yescharacteristic
560C22C2×#6699311yescharacteristic
561C4—44no—
562C4—44no—
563C4—444no—
564C4—442no—
565C4—882no—
566C4#1062283614yes—
567C4C2×#6699011yescharacteristic
568C4C2×#6699111yescharacteristic
569C4C2×#6699211yescharacteristic
570C4C2×#6700611yescharacteristic
571C2—24no—
572C2—882no—
573C2C2×#1062283611yescharacteristic
574C2#1307790712yes—
575C2#1307814312yes—
576C2#1307910512yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC23×C11×Q16C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenterC23×Q16D11
hypocenterC11#23425
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q16

Complements

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

NH ≅ G/Ntype
3. C2×#10622838C2semidirect
5. #13071202C2semidirect
6. #13069714C2semidirect
7. #13069707C2semidirect
8. #13068312C2semidirect
9. C23×C11×Q16C2semidirect
203. C23×Q16D11semidirect
489. C11#23425semidirect

Maximal subgroups

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

subgroupindex
C22×#669952
C2×#106233472
C2×#106228382
C2×#106227262
#130712022
#130697142
#130697072
#130683122
C23×C11×Q162
#2342511