Finite Group Databasebeta

← #14781673

Subgroups — #14781673

Order 2816.

1326 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×#66995C211yesmaximal, characteristic
2C2×#10622737C211yesmaximal, characteristic, complemented
3#13077136C211yesmaximal, characteristic
4C2×#10622838C211yesmaximal, characteristic, complemented
5#13077060C211yesmaximal, characteristic
6#13069915C218yesmaximal, complemented
7#13068354C211yesmaximal, characteristic, complemented
8C22×C11×#101C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C22×#4339C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C22×#4326—21no—
14C2×#66995—24no—
15C2×#66995—22no—
16C2×#66995—24no—
17C2×#66995C2214yes—
18C22×#4325—21no—
19C2×#66979C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C2×C11×#101—24no—
23C2×C11×#101C2214yescomplemented
24#10622838—22no—
25#10622838—22no—
26C2×#66899C2214yescomplemented
27#10622746C2214yes—
28#10622744—21no—
29#10622742C2214yes—
30#10622739—22no—
31#10622737—24no—
32C2×#66886C2214yescomplemented
33#10622733—21no—
34#10622726—22no—
35#10622723—22no—
36#10622192C2214yescomplemented
37C22×Q8×C11—22no—
38C22×Q8×C11—21no—
39C22×Q8×C11—21no—
40C22×Q8×C11—21no—
41C22×Q8×C11—22no—
42C22×Q8×C11—21no—
43C22×Q8×C11—21no—
44C22×Q8×C11—22no—
45C22×Q8×C11D414yes—
46C22×Q8×C11C2312yes—
47C23×C4×C11—21no—
48C23×C4×C11C2311yescharacteristic
49C22×C22⋊D11—21no—
50C2×#4339—21no—
51C2×#4339—21no—
52C2×#4339—22no—
53C2×#4339—22no—
54C2×#4339—22no—
55C2×#4339—22no—
56C2×#4339D412yes—
57C2×#4339C2312yes—
58C22×D44D411yescharacteristic
59C22×C4×D11—21no—
60C22×Dic22D411yescharacteristic
61C2×C11×M16—21no—
62C2×C11×M16—21no—
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C2×C11×M16—22no—
66C2×C11×M16—22no—
67C2×C11×M16C2312yes—
68C2×C11×M16C2312yes—
69C22×C8×C11—21no—
70C22×C8×C11—21no—
71C2×C22⋊Dic11—21no—
72C2×#4326—28no—
73C2×#4326—24no—
74#66995—216no—
75#66995—28no—
76#66995—28no—
77C2×#4325—28no—
78C2×#4325—24no—
79#66979—21no—
80#66979—21no—
81#66979—21no—
82#66979—21no—
83C2×C4⋊Dic11C2312yes—
84C2×C4×Dic11—21no—
85C2×#4318—22no—
86C2×#4318—21no—
87C2×#4318—22no—
88C2×#4318—22no—
89C2×#4318D414yes—
90C2×#4318D412yes—
91C2×#4318D412yes—
92C2×#4318C2312yes—
93C22×C11⋊C8—21no—
94C22×C11⋊C8C2312yes—
95C11×#101—28no—
96#66899—28no—
97#66886—28no—
98#66885—24no—
99(C2×D11)⋊C8—28no—
100#66880—24no—
101#23532—111nomaximal, Sylow
102C24×C11#4111yescharacteristic
103C23×D11—21no—
104C2×Q8×C11—24no—
105C2×Q8×C11—22no—
106C2×Q8×C11—24no—
107C2×Q8×C11—24no—
108C2×Q8×C11—24no—
109C2×Q8×C11—24no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—41no—
115C2×Q8×C11—41no—
116C2×Q8×C11—42no—
117C2×Q8×C11—42no—
118C2×Q8×C11—42no—
119C2×Q8×C11—42no—
120C2×Q8×C11—42no—
121C2×Q8×C11C2×D414yes—
122C22×C4×C11—24no—
123C22×C4×C11—22no—
124C22×C4×C11—41no—
125C22×C4×C11—41no—
126C22×C4×C11—42no—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11#4112yes—
134C22×C4×C11#4111yescharacteristic
135C22×C4×C11#4112yes—
136C22×C4×C11C2411yescharacteristic
137C2×C22⋊D11—22no—
138C2×C22⋊D11—22no—
139C2×C22⋊D11—42no—
140C2×C22⋊D11—42no—
141C22×Dic11—21no—
142C22×Dic11—22no—
143#4339—24no—
144#4339—24no—
145#4339—22no—
146#4339—22no—
147#4339—22no—
148#4339—22no—
149#4339—42no—
150#4339—42no—
151#4339—42no—
152#4339—42no—
153C2×D44—22no—
154C2×D44—21no—
155C2×D44—22no—
156C2×D44C2×D412yes—
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×C4×D11—42no—
160C2×C4×D11—42no—
161C2×Dic22—22no—
162C2×Dic22—21no—
163C2×Dic22—22no—
164C2×Dic22C2×D412yes—
165C11×M16—22no—
166C11×M16—22no—
167C11×M16—22no—
168C11×M16—22no—
169C11×M16—42no—
170C11×M16—42no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11—42no—
174C2×C8×C11—42no—
175C22⋊Dic11—41no—
176C22⋊Dic11—41no—
177#4326—216no—
178#4325—216no—
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181C4×Dic11—41no—
182C4×Dic11—41no—
183#4318—24no—
184#4318—24no—
185#4318—24no—
186#4318—22no—
187#4318C2×D414yes—
188C2×C11⋊C8—24no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8C2×D414yes—
193C22×#137—111no—
194C2×#430—111no—
195#2896—111no—
196C2×#419—111no—
197C22×#101D1111yescharacteristic, complemented
198#2879—111no—
199#2052—118no—
200#1742—111no—
201C23×C11—42no—
202C23×C11#12111yescharacteristic
203C23×C11#12111yescharacteristic
204C23×C11#12312yes—
205C23×C11#12412yes—
206C23×C11C2×#4111yescharacteristic
207C22×D11—22no—
208C22×D11—42no—
209C22×D11—82no—
210Q8×C11—24no—
211Q8×C11—24no—
212Q8×C11—42no—
213Q8×C11—42no—
214Q8×C11—44no—
215Q8×C11—44no—
216C2×C4×C11—24no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—44no—
220C2×C4×C11—44no—
221C2×C4×C11#12012yes—
222C2×C4×C11#12012yes—
223C2×C4×C11#12112yes—
224C2×C4×C11#12112yes—
225C2×C4×C11#12111yescharacteristic
226C2×C4×C11#12111yescharacteristic
227C2×C4×C11#12112yes—
228C2×C4×C11#12112yes—
229C2×C4×C11#12312yes—
230C2×C4×C11#12312yes—
231C2×C4×C11#12312yes—
232C2×C4×C11#12412yes—
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C22⋊D11—42no—
240C22⋊D11—42no—
241C22⋊D11—44no—
242C2×Dic11—22no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—82no—
246D44—22no—
247D44—22no—
248D44—42no—
249C4×D11—42no—
250C4×D11—42no—
251C4×D11—44no—
252Dic22—22no—
253Dic22—22no—
254Dic22—42no—
255C8×C11—42no—
256C8×C11—42no—
257C11⋊C8—24no—
258C11⋊C8—24no—
259C22×#41—111no—
260C23×Q8C2×D1111yescharacteristic
261C2×#137—114no—
262C2×#137—224no—
263C2×#137—222no—
264C2×#137—224no—
265C22×Q16—221no—
266C22×SD16—221no—
267C22×M16—111no—
268C22×M16—111no—
269C22×M16C2×D1111yescharacteristic
270C22×M16C2×D1111yescharacteristic
271C2×#117—111no—
272#430—224no—
273C2×#108—114no—
274#419—221no—
275#419—222no—
276#419—222no—
277#418—221no—
278#417—114no—
279#416—222no—
280C2×#103—114no—
281C2×#101—24no—
282C2×#101C2×D1114yescomplemented
283#408—114no—
284#408—222no—
285#407—222no—
286#343—114no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11#39412yes—
293C22×C11#39412yes—
294C22×C11C2×#12111yescharacteristic
295C22×C11C2×#12311yescharacteristic
296C22×C11C2×#12411yescharacteristic
297C2×D11—42no—
298C2×D11—44no—
299C2×D11—84no—
300C4×C11—44no—
301C4×C11#39412yes—
302C4×C11#39412yes—
303C4×C11C2×#12011yescharacteristic
304C4×C11C2×#12111yescharacteristic
305C4×C11C2×#12111yescharacteristic
306C4×C11C2×#12311yescharacteristic
307Dic11—42no—
308Dic11—82no—
309C2×#41—112no—
310C2×#41—112no—
311C2×#41—221no—
312C2×#41—221no—
313C2×#41—222no—
314C2×#41—222no—
315C2×#41—222no—
316C2×#41—222no—
317C22×Q8—22no—
318C22×Q8—21no—
319C22×Q8—21no—
320C22×Q8—21no—
321C22×Q8—22no—
322C22×Q8—21no—
323C22×Q8—21no—
324C22×Q8—22no—
325C22×Q8—111no—
326C22×Q8C22⋊D1114yes—
327C22×Q8C22×D1112yes—
328C22×D4—111no—
329C22×D4—221no—
330C23×C4—21no—
331C23×C4—221no—
332C23×C4C22×D1111yescharacteristic
333#137—228no—
334#137—2216no—
335#137—228no—
336C2×Q16—224no—
337C2×Q16—228no—
338C2×SD16—224no—
339C2×SD16—228no—
340C2×M16—21no—
341C2×M16—21no—
342C2×M16—22no—
343C2×M16—22no—
344C2×M16—22no—
345C2×M16—22no—
346C2×M16—112no—
347C2×M16—112no—
348C2×M16—114no—
349C2×M16—112no—
350C2×M16—222no—
351C2×M16—221no—
352C2×M16—222no—
353C2×M16—222no—
354C2×M16C22×D1112yes—
355C2×M16C22×D1112yes—
356C22×C8—21no—
357C22×C8—21no—
358C22×C8—112no—
359C22×C8—221no—
360#117—221no—
361#117—221no—
362#117—221no—
363#117—221no—
364C2×C4⋊C4—112no—
365C2×C22⋊C4—221no—
366C2×C42—221no—
367#108—228no—
368#103—224no—
369#103—228no—
370#102—224no—
371#101—28no—
372C22⋊C8—228no—
373C2×C11—22no—
374C2×C11—21no—
375C2×C11—21no—
376C2×C11—22no—
377C2×C11C2×#39411yescharacteristic
378C2×C11#306912yes—
379D11—82no—
380C24—221no—
381C24#433911yescharacteristic
382#41—224no—
383#41—224no—
384#41—222no—
385#41—222no—
386#41—222no—
387#41—222no—
388#41—442no—
389#41—442no—
390#41—442no—
391#41—442no—
392C2×Q8—24no—
393C2×Q8—22no—
394C2×Q8—24no—
395C2×Q8—24no—
396C2×Q8—24no—
397C2×Q8—24no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—42no—
403C2×Q8—42no—
404C2×Q8—41no—
405C2×Q8—41no—
406C2×Q8—42no—
407C2×Q8—42no—
408C2×Q8—42no—
409C2×Q8—112no—
410C2×Q8—221no—
411C2×Q8—222no—
412C2×Q8—222no—
413C2×Q8C2×C22⋊D1114yes—
414C2×D4—112no—
415C2×D4—222no—
416C2×D4—222no—
417C2×D4—222no—
418C2×D4—221no—
419C2×D4—222no—
420C2×D4—442no—
421C2×D4—442no—
422C22×C4—24no—
423C22×C4—22no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—42no—
427C22×C4—221no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—442no—
432C22×C4—442no—
433C22×C4#433912yes—
434C22×C4#433911yescharacteristic
435C22×C4D4×D1111yescharacteristic
436C22×C4D4×D1111yescharacteristic
437C22×C4D4×D1111yescharacteristic
438C22×C4D4×D1111yescharacteristic
439C22×C4D4×D1112yes—
440C22×C4#434112yes—
441C22×C4C2×C22⋊D1112yes—
442C22×C4C23×D1111yescharacteristic
443Q16—2216no—
444SD16—2216no—
445M16—22no—
446M16—22no—
447M16—22no—
448M16—22no—
449M16—42no—
450M16—42no—
451M16—114no—
452M16—224no—
453M16—224no—
454M16—224no—
455M16—222no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—42no—
459C2×C8—42no—
460C2×C8—114no—
461C2×C8—224no—
462C2×C8—222no—
463C2×C8—222no—
464C2×C8—222no—
465C4⋊C4—222no—
466C4⋊C4—222no—
467C22⋊C4—441no—
468C22⋊C4—441no—
469C42—441no—
470C42—441no—
471C11#2353211yescharacteristic, complemented, Sylow
472C23—42no—
473C23—222no—
474C23—442no—
475C23—882no—
476C23#6693711yescharacteristic
477C23#6693711yescharacteristic
478C23#6693812yes—
479C23#6698212yes—
480C23C2×#433911yescharacteristic
481Q8—24no—
482Q8—24no—
483Q8—42no—
484Q8—42no—
485Q8—44no—
486Q8—44no—
487Q8—222no—
488Q8—222no—
489Q8—442no—
490D4—222no—
491D4—222no—
492D4—442no—
493D4—442no—
494D4—444no—
495D4—442no—
496C2×C4—24no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—44no—
500C2×C4—44no—
501C2×C4—222no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—444no—
506C2×C4—442no—
507C2×C4—882no—
508C2×C4#6693612yes—
509C2×C4#6693612yes—
510C2×C4#6693712yes—
511C2×C4#6693712yes—
512C2×C4#6693711yescharacteristic
513C2×C4#6693711yescharacteristic
514C2×C4#6693812yes—
515C2×C4#6698212yes—
516C2×C4#6699012yes—
517C2×C4#6699012yes—
518C2×C4#6699212yes—
519C2×C4#6699212yes—
520C2×C4C2×#433911yescharacteristic
521C2×C4C2×D4×D1111yescharacteristic
522C2×C4C2×D4×D1111yescharacteristic
523C2×C4C2×D4×D1111yescharacteristic
524C2×C4C2×#434111yescharacteristic
525C2×C4C22×C22⋊D1111yescharacteristic
526C8—42no—
527C8—42no—
528C8—224no—
529C8—224no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—42no—
534C22—42no—
535C22—444no—
536C22—442no—
537C22—884no—
538C22#1062257212yes—
539C22#1062257212yes—
540C22C2×#6693711yescharacteristic
541C22C2×#6693811yescharacteristic
542C22C2×#6698211yescharacteristic
543C4—44no—
544C4—442no—
545C4—882no—
546C4#1062257212yes—
547C4#1062257212yes—
548C4C2×#6693611yescharacteristic
549C4C2×#6693711yescharacteristic
550C4C2×#6699011yescharacteristic
551C4C2×#6699211yescharacteristic
552C2—22no—
553C2—21no—
554C2—21no—
555C2—22no—
556C2—882no—
557C2C2×#1062257211yescharacteristic
558C2#1307835212yes—
subgroupG/H
centerC22C2×#66937
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#101C2
socleC22×C11C2×#121
prime radicalC22×#4339C22
hypercenterC22×#101D11
hypocenterC11#23532
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#101

Complements

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

NH ≅ G/Ntype
2. C2×#10622737C2semidirect
4. C2×#10622838C2semidirect
6. #13069915C2semidirect
7. #13068354C2semidirect
8. C22×C11×#101C2semidirect
23. C2×C11×#101C22semidirect
26. C2×#66899C22semidirect
32. C2×#66886C22semidirect
36. #10622192C22semidirect
197. C22×#101D11semidirect
282. C2×#101C2×D11semidirect
471. C11#23532semidirect

Maximal subgroups

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

subgroupindex
C22×#669952
C2×#106227372
#130771362
C2×#106228382
#130770602
#130699152
#130683542
C22×C11×#1012
#2353211