Finite Group Databasebeta

← #14672064

Subgroups — #14672064

Order 2816.

624 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073503C211yesmaximal, characteristic
2C2×#10622114C211yesmaximal, characteristic, complemented
3C2×#10622110C211yesmaximal, characteristic, complemented
4C2×#10622174C211yesmaximal, characteristic
5#13068602C211yesmaximal, characteristic, complemented
6#100×Dic11C211yesmaximal, characteristic, complemented
7C2×C11×AΣL(1,𝔽16)C211yesmaximal, characteristic
8C2×C11×#120C2211yescharacteristic
9C22×C22⋊Dic11C411yescharacteristic, complemented
10C2×#66988C2211yescharacteristic
11C2×D4×Dic11C2211yescharacteristic
12C2×C11×#100C2211yescharacteristic
13C2×C11×#99C2211yescharacteristic
14#10622860C411yescharacteristic, complemented
15#10622835—21no—
16#10622833—21no—
17C2×#66898C2211yescharacteristic
18C2×#66897C2211yescharacteristic
19M16×Dic11—21no—
20#10622561—21no—
21#10622558—21no—
22#10622556C411yescharacteristic, complemented
23#10622555—21no—
24#10622555C411yescharacteristic, complemented
25C11×AΣL(1,𝔽16)—22no—
26#10622192—21no—
27#10622174—22no—
28#10622165—21no—
29#10622114—22no—
30#10622110—22no—
31C25×C11C2×C411yescharacteristic
32C22×D4×C11—21no—
33C22×D4×C11C2311yescharacteristic
34C23×Dic11C2×C411yescharacteristic
35C23×Dic11C2×C411yescharacteristic
36C23×Dic11D411yescharacteristic
37C2×C11×M16—21no—
38C11×#120—21no—
39C11×#120—21no—
40C11×#120—21no—
41C11×#120—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4C2×C411yescharacteristic
45C2×C22⋊Dic11—21no—
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11—21no—
48C2×C22⋊Dic11—21no—
49C2×C22⋊Dic11—21no—
50C2×C22⋊Dic11—21no—
51C2×C22⋊Dic11—41no—
52C2×C22⋊Dic11—41no—
53C2×C22⋊Dic11C2×C411yescharacteristic
54C2×C22⋊Dic11C2×C411yescharacteristic
55C2×C22⋊Dic11D411yescharacteristic
56#66988—21no—
57#66988—21no—
58#66988—21no—
59#66988—21no—
60D4×Dic11—41no—
61D4×Dic11—41no—
62C2×C4⋊Dic11D411yescharacteristic
63C2×Dic11⋊C4—21no—
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—41no—
66C2×C4×Dic11D411yescharacteristic
67C2×#4318—21no—
68C11×#100—21no—
69C11×#100D412yes—
70C11×#99—21no—
71C11×#99—21no—
72#66898—21no—
73#66898—21no—
74#66897—21no—
75#66897D412yes—
76C11⋊#95—21no—
77C11⋊#95—21no—
78C11⋊#95—21no—
79C11⋊#95—41no—
80#66879—41no—
81C8×Dic11—41no—
82#13219—111nomaximal, Sylow
83C24×C11—21no—
84C24×C11—21no—
85C24×C11—21no—
86C24×C11—41no—
87C24×C11—42no—
88C24×C11—41no—
89C24×C11—81no—
90C24×C11C22×C411yescharacteristic
91C24×C11C2×D411yescharacteristic
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—42no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—81no—
98C2×D4×C11C2×D411yescharacteristic
99C2×D4×C11C2×D411yescharacteristic
100C2×D4×C11#4111yescharacteristic
101C2×D4×C11#4111yescharacteristic
102C22×C4×C11—21no—
103C22×C4×C11—41no—
104C22×C4×C11C2×D411yescharacteristic
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11—21no—
108C22×Dic11—21no—
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—41no—
114C22×Dic11—41no—
115C22×Dic11—41no—
116C22×Dic11—81no—
117C22×Dic11—81no—
118C22×Dic11C22⋊C411yescharacteristic
119C22×Dic11C22⋊C411yescharacteristic
120C22×Dic11C22⋊C411yescharacteristic
121C22×Dic11C22⋊C411yescharacteristic
122C11×M16—22no—
123C11×M16—41no—
124C2×C8×C11—41no—
125C11×C22⋊C4—21no—
126C11×C22⋊C4—21no—
127C11×C22⋊C4—41no—
128C11×C22⋊C4—41no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4—41no—
131C22⋊Dic11—21no—
132C22⋊Dic11—21no—
133C22⋊Dic11—41no—
134C22⋊Dic11—41no—
135C22⋊Dic11—42no—
136C22⋊Dic11—41no—
137C22⋊Dic11—42no—
138C22⋊Dic11—41no—
139C22⋊Dic11—41no—
140C22⋊Dic11—41no—
141C22⋊Dic11—41no—
142C22⋊Dic11—41no—
143C22⋊Dic11—81no—
144C4⋊Dic11—41no—
145Dic11⋊C4—41no—
146Dic11⋊C4—41no—
147Dic11⋊C4—81no—
148Dic11⋊C4—82no—
149C4×Dic11—21no—
150C4×Dic11—21no—
151#4318—22no—
152#4318—41no—
153C2×C11⋊C8—41no—
154#2534—111no—
155C2×#352—111no—
156C2×#352—111no—
157C2×AΣL(1,𝔽16)—111no—
158C2×AΣL(1,𝔽16)D1111yescharacteristic
159#1799—111no—
160C4×#100—111no—
161C23×C11—21no—
162C23×C11—21no—
163C23×C11—21no—
164C23×C11—21no—
165C23×C11—22no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—81no—
179C23×C11—81no—
180C23×C11—82no—
181C23×C11—82no—
182C23×C11—84no—
183C23×C11—81no—
184C23×C11—81no—
185C23×C11C2×C22⋊C411yescharacteristic
186C23×C11C4×D411yescharacteristic
187C23×C11C4×D411yescharacteristic
188C23×C11#12411yescharacteristic
189C23×C11#12711yescharacteristic
190D4×C11—41no—
191D4×C11—41no—
192D4×C11—41no—
193D4×C11—41no—
194D4×C11—82no—
195D4×C11—82no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—81no—
202C2×C4×C11—81no—
203C2×C4×C11—81no—
204C2×C4×C11#12111yescharacteristic
205C2×C4×C11#12111yescharacteristic
206C2×Dic11—21no—
207C2×Dic11—21no—
208C2×Dic11—21no—
209C2×Dic11—41no—
210C2×Dic11—42no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—81no—
221C2×Dic11—81no—
222C2×Dic11—81no—
223C2×Dic11—81no—
224C2×Dic11—81no—
225C2×Dic11—81no—
226C2×Dic11—81no—
227C2×Dic11—81no—
228C2×Dic11#9911yescharacteristic
229C2×Dic11#9911yescharacteristic
230C8×C11—42no—
231C11⋊C8—42no—
232C2×#123—111no—
233C2×#120C2×D1111yescharacteristic
234C2×C4×D4—111no—
235C22×C22⋊C4—111no—
236C2×#100—111no—
237C2×#100C2×D1111yescharacteristic
238C2×#99—111no—
239C2×#99C2×D1111yescharacteristic
240C4×M16—221no—
241#396—221no—
242#394—221no—
243#388—221no—
244#386—221no—
245#381—111no—
246#380—111no—
247#380—221no—
248#379—111no—
249#352—222no—
250#352—222no—
251AΣL(1,𝔽16)—22no—
252AΣL(1,𝔽16)—222no—
253#343—221no—
254#342—221no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—21no—
261C22×C11—41no—
262C22×C11—41no—
263C22×C11—41no—
264C22×C11—41no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—41no—
269C22×C11—41no—
270C22×C11—41no—
271C22×C11—41no—
272C22×C11—42no—
273C22×C11—81no—
274C22×C11—81no—
275C22×C11—81no—
276C22×C11—82no—
277C22×C11—82no—
278C22×C11—82no—
279C22×C11—82no—
280C22×C11—81no—
281C22×C11—81no—
282C22×C11#39011yescharacteristic
283C22×C11C2×#9911yescharacteristic
284C22×C11#41011yescharacteristic
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—81no—
288C4×C11—161no—
289Dic11—21no—
290Dic11—21no—
291Dic11—41no—
292Dic11—41no—
293Dic11—41no—
294Dic11—81no—
295Dic11—81no—
296Dic11—161no—
297C25C4×D1111yescharacteristic
298C22×D4—21no—
299C22×D4C22×D1111yescharacteristic
300C23×C4—111no—
301C23×C4—111no—
302C23×C4—111no—
303C2×M16—21no—
304C2×M16—221no—
305#123—221no—
306#123—221no—
307#123—221no—
308#123—221no—
309#120—21no—
310#120—21no—
311#120—21no—
312#120—21no—
313C4×D4—441no—
314C4×D4—441no—
315C2×C4⋊C4—111no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4—441no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—111no—
322C2×C22⋊C4—111no—
323C2×C22⋊C4—111no—
324C2×C22⋊C4—221no—
325C2×C22⋊C4—221no—
326C2×C22⋊C4—221no—
327C2×C22⋊C4—221no—
328C2×C22⋊C4—221no—
329C2×C22⋊C4—221no—
330C2×C22⋊C4—441no—
331C2×C22⋊C4—441no—
332C2×C22⋊C4C4×D1111yescharacteristic
333C2×C42—111no—
334#100—21no—
335#100—112no—
336#100—221no—
337#100C22⋊D1112yes—
338#99—21no—
339#99—21no—
340#99—221no—
341#99—221no—
342#97—441no—
343C4×C8—441no—
344#95—221no—
345#95—221no—
346#95—221no—
347#95—441no—
348C2×C11—21no—
349C2×C11—21no—
350C2×C11—41no—
351C2×C11—41no—
352C2×C11—41no—
353C2×C11—41no—
354C2×C11—82no—
355C2×C11#196411yescharacteristic
356C2×C11#212011yescharacteristic
357C2×C11#212111yescharacteristic
358C24—21no—
359C24—21no—
360C24—21no—
361C24—41no—
362C24—42no—
363C24—41no—
364C24—81no—
365C24C2×C4×D1111yescharacteristic
366C24D4×D1111yescharacteristic
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—42no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—81no—
373C2×D4#433911yescharacteristic
374C2×D4D4×D1111yescharacteristic
375C2×D4#434111yescharacteristic
376C2×D4C2×C22⋊D1111yescharacteristic
377C22×C4—21no—
378C22×C4—41no—
379C22×C4—111no—
380C22×C4—111no—
381C22×C4—111no—
382C22×C4—111no—
383C22×C4—221no—
384C22×C4—221no—
385C22×C4—221no—
386C22×C4—221no—
387C22×C4—221no—
388C22×C4—221no—
389C22×C4—221no—
390C22×C4—221no—
391C22×C4—441no—
392C22×C4—441no—
393C22×C4—441no—
394C22×C4—881no—
395C22×C4—881no—
396C22×C4D4×D1111yescharacteristic
397M16—22no—
398M16—41no—
399M16—222no—
400M16—441no—
401C2×C8—41no—
402C2×C8—441no—
403C4⋊C4—441no—
404C4⋊C4—441no—
405C4⋊C4—441no—
406C4⋊C4—881no—
407C4⋊C4—882no—
408C22⋊C4—21no—
409C22⋊C4—21no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—221no—
415C22⋊C4—221no—
416C22⋊C4—441no—
417C22⋊C4—441no—
418C22⋊C4—441no—
419C22⋊C4—441no—
420C22⋊C4—442no—
421C22⋊C4—442no—
422C22⋊C4—441no—
423C22⋊C4—441no—
424C22⋊C4—441no—
425C22⋊C4—441no—
426C22⋊C4—881no—
427C42—221no—
428C42—221no—
429C11#1321911yescharacteristic, complemented, Sylow
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—22no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—42no—
443C23—42no—
444C23—41no—
445C23—41no—
446C23—41no—
447C23—81no—
448C23—81no—
449C23—82no—
450C23—82no—
451C23—84no—
452C23—81no—
453C23—81no—
454C23C22⋊C4×D1111yescharacteristic
455C23(C22⋊D11)⋊C411yescharacteristic
456C23#6693811yescharacteristic
457C23C4×C22⋊D1111yescharacteristic
458C23#6699311yescharacteristic
459D4—41no—
460D4—41no—
461D4—41no—
462D4—41no—
463D4—82no—
464D4—82no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—81no—
471C2×C4—81no—
472C2×C4—81no—
473C2×C4—111no—
474C2×C4—111no—
475C2×C4—221no—
476C2×C4—221no—
477C2×C4—221no—
478C2×C4—441no—
479C2×C4—442no—
480C2×C4—441no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4—441no—
485C2×C4—441no—
486C2×C4—441no—
487C2×C4—441no—
488C2×C4—441no—
489C2×C4—881no—
490C2×C4—881no—
491C2×C4—881no—
492C2×C4—881no—
493C2×C4—881no—
494C2×C4—881no—
495C2×C4—881no—
496C2×C4—881no—
497C2×C4#6693711yescharacteristic
498C2×C4#6699211yescharacteristic
499C8—42no—
500C8—442no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—41no—
518C22—42no—
519C22—81no—
520C22—81no—
521C22—81no—
522C22—82no—
523C22—82no—
524C22—82no—
525C22—82no—
526C22—81no—
527C22—81no—
528C22#1062235311yescharacteristic
529C22D11×#9911yescharacteristic
530C22#1062257011yescharacteristic
531C4—21no—
532C4—21no—
533C4—81no—
534C4—161no—
535C4—221no—
536C4—221no—
537C4—441no—
538C4—441no—
539C4—441no—
540C4—881no—
541C4—881no—
542C4—1761no—
543C2—21no—
544C2—21no—
545C2—41no—
546C2—41no—
547C2—41no—
548C2—41no—
549C2—82no—
550C2#1306945011yescharacteristic
551C2#1307025411yescharacteristic
552C2#1307025911yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC24×C11C22×C4
FrattiniC22×D4C22×D11
FittingC2×C11×AΣL(1,𝔽16)C2
socleC22×C11C2×#99
prime radicalC2×C11×#120C22
cosocleC22×D4×C11C23
hypercenterC2×AΣL(1,𝔽16)D11
hypocenterC11#13219
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×AΣL(1,𝔽16)

Complements

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

NH ≅ G/Ntype
2. C2×#10622114C2semidirect
3. C2×#10622110C2semidirect
5. #13068602C2semidirect
6. #100×Dic11C2semidirect
9. C22×C22⋊Dic11C4semidirect
14. #10622860C4semidirect
22. #10622556C4semidirect
24. #10622555C4semidirect
429. C11#13219semidirect

Maximal subgroups

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

subgroupindex
#130735032
C2×#106221142
C2×#106221102
C2×#106221742
#130686022
#100×Dic112
C2×C11×AΣL(1,𝔽16)2
#1321911