Finite Group Databasebeta

← #14669299

Subgroups — #14669299

Order 2816.

1186 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 1186 conjugacy classes of subgroups — too many to draw. Only its 135 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#13070262C214yesmaximal, complemented
2#13068537C211yesmaximal, characteristic, complemented
3#13068531C211yesmaximal, characteristic, complemented
4C11×#3484C211yesmaximal, characteristic
5C2×C11×H(5,𝔽2)C411yescharacteristic, complemented
6C23×D4×C11C2211yescharacteristic
7C11×#546—24no—
8D42×C11—24no—
9C11×#535—21no—
10C11×#534—21no—
11C11×#534C2212yes—
12C11×#525—21no—
13C2×C11×#120—21no—
14C2×C11×#120C412yescomplemented
15C11×#518C411yescharacteristic, complemented
16#10622860—21no—
17C2×#66898—21no—
18C2×#66898C2212yescomplemented
19C2×#66897—21no—
20C2×#66897C2212yescomplemented
21#10622820—21no—
22#10622177—24no—
23#10622174—24no—
24C25×C11C2×C411yescharacteristic
25C25×C11D411yescharacteristic
26C11×H(5,𝔽2)—42no—
27C11×H(5,𝔽2)—42no—
28C2×C11×#41—21no—
29C2×C11×#41—22no—
30C22×D4×C11—21no—
31C22×D4×C11—22no—
32C22×D4×C11—22no—
33C22×D4×C11—22no—
34C22×D4×C11—24no—
35C22×D4×C11—42no—
36C22×D4×C11—42no—
37C22×D4×C11C2×C411yescharacteristic
38C22×D4×C11C2×C412yes—
39C22×D4×C11D411yescharacteristic
40C22×D4×C11D411yescharacteristic
41C22×D4×C11C2311yescharacteristic
42C23×C4×C11D411yescharacteristic
43C11×#127—22no—
44C11×#124—22no—
45C11×#123—22no—
46C11×#123—22no—
47C11×#123D414yes—
48C11×C22⋊Q8—22no—
49C11×#121—22no—
50C11×#121—24no—
51C11×#121—24no—
52C11×#121—24no—
53C11×#120—24no—
54C11×#120—22no—
55C11×#120—22no—
56C11×#120—22no—
57C11×#120—22no—
58C11×#120—24no—
59C11×#120D414yes—
60C4×D4×C11—24no—
61C4×D4×C11—24no—
62C11×#117—21no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—21no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4C2×C412yes—
67C2×C22⋊Dic11—22no—
68C2×C22⋊Dic11—42no—
69C2×#4318—22no—
70#66898—24no—
71#66898—42no—
72#66897—24no—
73#66897—42no—
74C22⋊(C11⋊C8)—42no—
75#12705—111nomaximal, Sylow
76C24×C11—21no—
77C24×C11—22no—
78C24×C11—22no—
79C24×C11—22no—
80C24×C11—41no—
81C24×C11—41no—
82C24×C11—41no—
83C24×C11—82no—
84C24×C11—82no—
85C24×C11C22⋊C411yescharacteristic
86C24×C11C22⋊C411yescharacteristic
87C24×C11C22⋊C411yescharacteristic
88C24×C11C22⋊C412yescomplemented
89C24×C11C22×C411yescharacteristic
90C24×C11C2×D411yescharacteristic
91C11×#41—42no—
92C11×#41—48no—
93C11×#41—42no—
94C2×Q8×C11—21no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—24no—
98C2×D4×C11—22no—
99C2×D4×C11—21no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—24no—
105C2×D4×C11—24no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—41no—
110C2×D4×C11—41no—
111C2×D4×C11—41no—
112C2×D4×C11—41no—
113C2×D4×C11—416no—
114C2×D4×C11—48no—
115C2×D4×C11—42no—
116C2×D4×C11—42no—
117C2×D4×C11—42no—
118C2×D4×C11—42no—
119C2×D4×C11—84no—
120C2×D4×C11—84no—
121C2×D4×C11C2×D414yes—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—41no—
129C22×C4×C11C22⋊C411yescharacteristic
130C22×C4×C11C22⋊C412yescomplemented
131C22×C4×C11C2×D411yescharacteristic
132C22×Dic11—42no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—24no—
135C11×C22⋊C4—24no—
136C11×C22⋊C4—22no—
137C11×C22⋊C4—24no—
138C11×C22⋊C4—22no—
139C11×C22⋊C4—24no—
140C11×C22⋊C4—24no—
141C11×C22⋊C4C22⋊C414yescomplemented
142C42×C11—22no—
143C22⋊Dic11—42no—
144C22⋊Dic11—42no—
145C22⋊Dic11—84no—
146#4318—42no—
147#4318—42no—
148C2×C11⋊C8—42no—
149#3484D1111yescharacteristic
150#2121—114no—
151#1783—111no—
152#1781—111no—
153C23×C11—21no—
154C23×C11—21no—
155C23×C11—21no—
156C23×C11—21no—
157C23×C11—21no—
158C23×C11—21no—
159C23×C11—21no—
160C23×C11—21no—
161C23×C11—21no—
162C23×C11—21no—
163C23×C11—22no—
164C23×C11—21no—
165C23×C11—21no—
166C23×C11—42no—
167C23×C11—44no—
168C23×C11—44no—
169C23×C11—44no—
170C23×C11—44no—
171C23×C11—44no—
172C23×C11—42no—
173C23×C11—42no—
174C23×C11—82no—
175C23×C11—82no—
176C23×C11—82no—
177C23×C11—81no—
178C23×C11—81no—
179C23×C11—81no—
180C23×C11—81no—
181C23×C11—82no—
182C23×C11—82no—
183C23×C11—82no—
184C23×C11—82no—
185C23×C11—82no—
186C23×C11—82no—
187C23×C11—82no—
188C23×C11—82no—
189C23×C11#9912yes—
190C23×C11C2×C22⋊C412yes—
191C23×C11C2×C22⋊C411yescharacteristic
192C23×C11#12012yes—
193Q8×C11—42no—
194D4×C11—28no—
195D4×C11—44no—
196D4×C11—44no—
197D4×C11—44no—
198D4×C11—42no—
199D4×C11—44no—
200D4×C11—44no—
201D4×C11—48no—
202D4×C11—42no—
203D4×C11—42no—
204D4×C11—84no—
205D4×C11—84no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—24no—
211C2×C4×C11—22no—
212C2×C4×C11—44no—
213C2×C4×C11—44no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—82no—
217C2×C4×C11—82no—
218C2×C4×C11#9912yes—
219C2×C4×C11#12012yes—
220C2×Dic11—82no—
221C2×Dic11—84no—
222C11⋊C8—82no—
223C2×H(5,𝔽2)Dic1111yescharacteristic, complemented
224C23×D4C2×D1111yescharacteristic
225#546—24no—
226D42—24no—
227#535—21no—
228#534—21no—
229#534C2×D1112yes—
230#525—21no—
231C2×#120—21no—
232C2×#120Dic1112yescomplemented
233#518Dic1111yescharacteristic, complemented
234C2×#100—112no—
235C2×#100—221no—
236C2×#99—112no—
237C2×#99—221no—
238#407—221no—
239#379—221no—
240#352—224no—
241AΣL(1,𝔽16)—224no—
242C22×C11—22no—
243C22×C11—22no—
244C22×C11—22no—
245C22×C11—22no—
246C22×C11—22no—
247C22×C11—22no—
248C22×C11—41no—
249C22×C11—42no—
250C22×C11—42no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—41no—
254C22×C11—41no—
255C22×C11—41no—
256C22×C11—42no—
257C22×C11—44no—
258C22×C11—42no—
259C22×C11—41no—
260C22×C11—42no—
261C22×C11—41no—
262C22×C11—81no—
263C22×C11—81no—
264C22×C11—81no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11—88no—
269C22×C11—88no—
270C22×C11—162no—
271C22×C11—162no—
272C22×C11#37911yescharacteristic
273C22×C11C2×#9911yescharacteristic
274C22×C11C2×#9911yescharacteristic
275C4×C11—22no—
276C4×C11—22no—
277C4×C11—44no—
278C4×C11—42no—
279Dic11—162no—
280C25C2×Dic1111yescharacteristic
281C25C22⋊D1111yescharacteristic
282H(5,𝔽2)—42no—
283H(5,𝔽2)—42no—
284C2×#41—21no—
285C2×#41—22no—
286C22×D4—21no—
287C22×D4—22no—
288C22×D4—22no—
289C22×D4—22no—
290C22×D4—24no—
291C22×D4—42no—
292C22×D4—42no—
293C22×D4C2×Dic1111yescharacteristic
294C22×D4C2×Dic1112yes—
295C22×D4C22⋊D1111yescharacteristic
296C22×D4C22⋊D1111yescharacteristic
297C22×D4C22×D1111yescharacteristic
298C23×C4C22⋊D1111yescharacteristic
299C2×M16—222no—
300#127—22no—
301#124—22no—
302#123—22no—
303#123—22no—
304#123C22⋊D1114yes—
305C22⋊Q8—22no—
306#121—22no—
307#121—24no—
308#121—24no—
309#121—24no—
310#120—24no—
311#120—22no—
312#120—22no—
313#120—22no—
314#120—22no—
315#120—24no—
316#120C22⋊D1114yes—
317C4×D4—24no—
318C4×D4—24no—
319#117—21no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—222no—
324C2×C22⋊C4—442no—
325C2×C22⋊C4C2×Dic1112yes—
326#100—224no—
327#100—442no—
328#99—224no—
329#99—442no—
330C22⋊C8—442no—
331C2×C11—21no—
332C2×C11—21no—
333C2×C11—21no—
334C2×C11—42no—
335C2×C11—42no—
336C2×C11—42no—
337C2×C11—42no—
338C2×C11—81no—
339C2×C11—82no—
340C2×C11#178111yescharacteristic
341C24—21no—
342C24—22no—
343C24—22no—
344C24—22no—
345C24—41no—
346C24—41no—
347C24—41no—
348C24—82no—
349C24—82no—
350C24C22⋊Dic1111yescharacteristic
351C24C22⋊Dic1111yescharacteristic
352C24C22⋊Dic1111yescharacteristic
353C24C22⋊Dic1112yescomplemented
354C24C22×Dic1111yescharacteristic
355C24C2×C22⋊D1111yescharacteristic
356#41—42no—
357#41—48no—
358#41—42no—
359C2×Q8—21no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—24no—
363C2×D4—22no—
364C2×D4—21no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—24no—
370C2×D4—24no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—41no—
378C2×D4—416no—
379C2×D4—48no—
380C2×D4—42no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—84no—
385C2×D4—84no—
386C2×D4C2×C22⋊D1114yes—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—41no—
394C22×C4—442no—
395C22×C4C22⋊Dic1111yescharacteristic
396C22×C4C22⋊Dic1112yescomplemented
397C22×C4C2×C22⋊D1111yescharacteristic
398M16—442no—
399M16—442no—
400C2×C8—442no—
401C4⋊C4—22no—
402C4⋊C4—24no—
403C22⋊C4—24no—
404C22⋊C4—22no—
405C22⋊C4—24no—
406C22⋊C4—22no—
407C22⋊C4—24no—
408C22⋊C4—24no—
409C22⋊C4—442no—
410C22⋊C4—442no—
411C22⋊C4—884no—
412C22⋊C4C22⋊Dic1114yescomplemented
413C42—22no—
414C11#1270511yescharacteristic, complemented, Sylow
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—22no—
426C23—21no—
427C23—21no—
428C23—42no—
429C23—44no—
430C23—44no—
431C23—44no—
432C23—44no—
433C23—44no—
434C23—42no—
435C23—42no—
436C23—82no—
437C23—82no—
438C23—82no—
439C23—81no—
440C23—81no—
441C23—81no—
442C23—81no—
443C23—82no—
444C23—82no—
445C23—82no—
446C23—82no—
447C23—82no—
448C23—82no—
449C23—82no—
450C23—82no—
451C23#6689812yes—
452C23C2×C22⋊Dic1112yes—
453C23C2×C22⋊Dic1111yescharacteristic
454C23#6700612yes—
455Q8—42no—
456D4—28no—
457D4—44no—
458D4—44no—
459D4—44no—
460D4—42no—
461D4—44no—
462D4—44no—
463D4—48no—
464D4—42no—
465D4—42no—
466D4—84no—
467D4—84no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—44no—
475C2×C4—44no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—82no—
479C2×C4—82no—
480C2×C4—882no—
481C2×C4—884no—
482C2×C4#6689812yes—
483C2×C4#6700612yes—
484C8—882no—
485C22—22no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—41no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—44no—
501C22—42no—
502C22—41no—
503C22—42no—
504C22—41no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—88no—
512C22—88no—
513C22—162no—
514C22—162no—
515C22C2×#6689811yescharacteristic
516C22C2×#6689811yescharacteristic
517C22#1062286011yescharacteristic
518C4—22no—
519C4—22no—
520C4—44no—
521C4—42no—
522C4—1762no—
523C2—21no—
524C2—21no—
525C2—21no—
526C2—42no—
527C2—42no—
528C2—42no—
529C2—42no—
530C2—81no—
531C2—82no—
532C2#1306853111yescharacteristic
subgroupG/H
centerC2#13068531
commutatorC24×C11C22×C4
FrattiniC22×D4C22×D11
Fitting, prime radicalC11×#3484C2
socleC2×C11#1781
cosocleC22×D4×C11C23
hypercenter#3484D11
hypocenterC11#12705
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C23 ◁ C23×D4 ◁ #3484

Complements

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

NH ≅ G/Ntype
1. #13070262C2semidirect
2. #13068537C2semidirect
3. #13068531C2semidirect
5. C2×C11×H(5,𝔽2)C4semidirect
14. C2×C11×#120C4semidirect
15. C11×#518C4semidirect
18. C2×#66898C22semidirect
20. C2×#66897C22semidirect
88. C24×C11C22⋊C4semidirect
130. C22×C4×C11C22⋊C4semidirect
141. C11×C22⋊C4C22⋊C4semidirect
223. C2×H(5,𝔽2)Dic11semidirect
232. C2×#120Dic11semidirect
233. #518Dic11semidirect
353. C24C22⋊Dic11semidirect
396. C22×C4C22⋊Dic11semidirect
412. C22⋊C4C22⋊Dic11semidirect
414. C11#12705semidirect

Maximal subgroups

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

subgroupindex
#130702622
#130685372
#130685312
C11×#34842
#1270511