Finite Group Databasebeta

← #14755400

Subgroups — #14755400

Order 2816.

1974 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081819C211yesmaximal, characteristic, complemented
2C2×#10622853C211yesmaximal, characteristic, complemented
3#13070999C212yesmaximal, complemented
4#13069030C214yesmaximal, complemented
5#13069025C214yesmaximal, complemented
6#13068348C212yesmaximal, complemented
7C2×C11×#525C211yesmaximal, characteristic
8C22×C11×#41C2211yescharacteristic
9C24×C4×C11C2211yescharacteristic
10C11×#525—24no—
11C11×#525C418yescomplemented
12C2×C11×#123C2212yes—
13C2×C11×C22⋊Q8—21no—
14C2×C11×#121—21no—
15C2×C11×#120C2212yes—
16C2×C4×D4×C11—22no—
17C2×C11×#117C2211yescharacteristic
18#10623358—24no—
19#41×Dic11—24no—
20#10623343—21no—
21#10623329—21no—
22#10623329C2214yes—
23C2×#66979—22no—
24C2×#66979C2212yes—
25C2×#66979C2212yes—
26#10622860C2214yes—
27#10622853—24no—
28C2×#66898C2214yes—
29#10622825—24no—
30#10622824C2214yes—
31C4×C22⋊Dic11—24no—
32#10622165C2218yes—
33C25×C11C2311yescharacteristic
34C2×C11×#41—22no—
35C2×C11×#41—22no—
36C2×C11×#41—24no—
37C2×C11×#41C2×C414yes—
38C2×C11×#41D414yes—
39C22×Q8×C11D411yescharacteristic
40C22×D4×C11—22no—
41C22×D4×C11D411yescharacteristic
42C22×D4×C11C2312yes—
43C23×C4×C11—22no—
44C23×C4×C11—22no—
45C23×C4×C11—21no—
46C23×C4×C11—21no—
47C23×C4×C11—22no—
48C23×C4×C11—24no—
49C23×C4×C11C2×C414yescomplemented
50C23×C4×C11D412yes—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C11×#123—24no—
54C11×#123C2×C418yescomplemented
55C11×C22⋊Q8—28no—
56C11×#121—28no—
57C11×#120—24no—
58C11×#120C2×C418yescomplemented
59C4×D4×C11—216no—
60C11×#117—22no—
61C11×#117C2×C414yescomplemented
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4C2312yes—
67C2×C42×C11—21no—
68C2×C22⋊Dic11—24no—
69C2×C22⋊Dic11—28no—
70C2×C22⋊Dic11C2314yes—
71C2×C22⋊Dic11C2314yes—
72Q8×Dic11—28no—
73D4×Dic11—28no—
74D4×Dic11—216no—
75#66979—24no—
76#66979—24no—
77#66979—22no—
78#66979—24no—
79#66979—22no—
80#66979—22no—
81#66979—22no—
82#66979—24no—
83#66979—24no—
84C2×C4⋊Dic11—24no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11D414yescomplemented
87C2×C4×Dic11—24no—
88C2×C4×Dic11—22no—
89C2×C4×Dic11D414yescomplemented
90#66898—28no—
91C11⋊#95—28no—
92#20959—111nomaximal, Sylow
93C24×C11—22no—
94C24×C11—21no—
95C24×C11—21no—
96C24×C11—22no—
97C24×C11—44no—
98C24×C11C22×C412yes—
99C24×C11C2×D412yes—
100C24×C11C2411yescharacteristic
101C11×#41—28no—
102C11×#41—28no—
103C11×#41—28no—
104C11×#41—28no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11C22⋊C414yescomplemented
108C2×D4×C11—24no—
109C2×D4×C11—24no—
110C2×D4×C11—28no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—48no—
114C2×D4×C11C22⋊C414yescomplemented
115C2×D4×C11C22×C414yes—
116C2×D4×C11C2×D414yes—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—28no—
128C22×C4×C11—28no—
129C22×C4×C11—42no—
130C22×C4×C11—41no—
131C22×C4×C11—41no—
132C22×C4×C11—44no—
133C22×C4×C11—44no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11C22⋊C418yescomplemented
137C22×C4×C11C22×C412yes—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D412yes—
145C22×C4×C11#4114yes—
146C22×Dic11—28no—
147C22×Dic11—24no—
148C22×Dic11C2×D418yes—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—28no—
151C11×C22⋊C4—28no—
152C11×C22⋊C4—22no—
153C11×C22⋊C4—28no—
154C11×C22⋊C4C22×C414yes—
155C42×C11—24no—
156C22⋊Dic11—28no—
157C22⋊Dic11—24no—
158C22⋊Dic11—24no—
159C22⋊Dic11—24no—
160C22⋊Dic11—24no—
161C22⋊Dic11—416no—
162C4⋊Dic11—28no—
163C4⋊Dic11—24no—
164C4⋊Dic11—24no—
165C4⋊Dic11—44no—
166C4×Dic11—28no—
167C4×Dic11—24no—
168C4×Dic11—24no—
169C4×Dic11—44no—
170C2×#525D1111yescharacteristic
171#3428—111no—
172C2×#410—111no—
173#2280—112no—
174#1890—114no—
175#1889—114no—
176#1740—112no—
177C23×C11—28no—
178C23×C11—24no—
179C23×C11—22no—
180C23×C11—24no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—44no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—44no—
187C23×C11—44no—
188C23×C11—48no—
189C23×C11—44no—
190C23×C11—41no—
191C23×C11—42no—
192C23×C11—41no—
193C23×C11C2×C22⋊C414yes—
194C23×C11C23×C411yescharacteristic
195C23×C11C22×D412yes—
196C23×C11C22×D411yescharacteristic
197C23×C11C22×D411yescharacteristic
198C23×C11C2×#4112yes—
199Q8×C11—28no—
200D4×C11—28no—
201D4×C11—28no—
202D4×C11—28no—
203D4×C11—416no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—28no—
207C2×C4×C11—28no—
208C2×C4×C11—24no—
209C2×C4×C11—22no—
210C2×C4×C11—24no—
211C2×C4×C11—44no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—44no—
216C2×C4×C11—44no—
217C2×C4×C11—48no—
218C2×C4×C11C2×C22⋊C414yes—
219C2×C4×C11C2×C22⋊C412yes—
220C2×C4×C11C2×C22⋊C412yes—
221C2×C4×C11C4×D414yes—
222C2×C4×C11C4×D414yes—
223C2×C4×C11#12012yes—
224C2×C4×C11#12011yescharacteristic
225C2×C4×C11#12011yescharacteristic
226C2×C4×C11#12114yes—
227C2×C4×C11#12114yes—
228C2×C4×C11#12312yes—
229C2×C4×C11#12312yes—
230C2×Dic11—28no—
231C2×Dic11—48no—
232C2×Dic11—48no—
233C2×Dic11—44no—
234C2×Dic11—88no—
235C22×#41C2×D1111yescharacteristic
236C24×C4C2×D1111yescharacteristic
237#525—24no—
238#525Dic1118yescomplemented
239C2×#123C2×D1112yes—
240C2×C22⋊Q8—21no—
241C2×#121—21no—
242C2×#120C2×D1112yes—
243#520—224no—
244#519—221no—
245#518—114no—
246#518—221no—
247C4×#41—224no—
248C2×C4×D4—22no—
249C2×#117—112no—
250C2×#117—112no—
251C2×#117—222no—
252C2×#117C2×D1111yescharacteristic
253#410—224no—
254C2×#99—114no—
255#381—114no—
256#380—224no—
257#379—114no—
258C4×C22⋊C4—224no—
259#342—118no—
260C22×C11—22no—
261C22×C11—24no—
262C22×C11—24no—
263C22×C11—28no—
264C22×C11—24no—
265C22×C11—41no—
266C22×C11—41no—
267C22×C11—42no—
268C22×C11—44no—
269C22×C11—48no—
270C22×C11—42no—
271C22×C11—44no—
272C22×C11—44no—
273C22×C11—44no—
274C22×C11—44no—
275C22×C11—42no—
276C22×C11—82no—
277C22×C11C22×C22⋊C411yescharacteristic
278C22×C11C2×C4×D412yes—
279C22×C11C2×#12011yescharacteristic
280C22×C11C2×#12112yes—
281C22×C11C2×#12311yescharacteristic
282C4×C11—24no—
283C4×C11—44no—
284C4×C11—42no—
285C4×C11#38612yes—
286C4×C11#38612yes—
287C4×C11#38614yes—
288Dic11—48no—
289Dic11—84no—
290C25C22×D1111yescharacteristic
291C2×#41—22no—
292C2×#41—22no—
293C2×#41—24no—
294C2×#41C2×Dic1114yes—
295C2×#41C22⋊D1114yes—
296C22×Q8C22⋊D1111yescharacteristic
297C22×D4—22no—
298C22×D4C22⋊D1111yescharacteristic
299C22×D4C22×D1112yes—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—24no—
303C23×C4—21no—
304C23×C4—21no—
305C23×C4—22no—
306C23×C4C2×Dic1114yescomplemented
307C23×C4C22⋊D1112yes—
308C23×C4C22×D1111yescharacteristic
309C23×C4C22×D1111yescharacteristic
310#123—24no—
311#123C2×Dic1118yescomplemented
312C22⋊Q8—28no—
313#121—28no—
314#120—24no—
315#120C2×Dic1118yescomplemented
316C4×Q8—228no—
317C4×D4—216no—
318C4×D4—2216no—
319C4×D4—228no—
320#117—22no—
321#117—224no—
322#117—224no—
323#117—222no—
324#117—222no—
325#117—222no—
326#117—222no—
327#117—224no—
328#117—224no—
329#117—224no—
330#117C2×Dic1114yescomplemented
331C2×C4⋊C4—21no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—114no—
334C2×C4⋊C4—224no—
335C2×C4⋊C4—222no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—114no—
339C2×C22⋊C4—114no—
340C2×C22⋊C4—224no—
341C2×C22⋊C4—228no—
342C2×C22⋊C4C22×D1112yes—
343C2×C42—21no—
344C2×C42—114no—
345C2×C42—224no—
346C2×C42—222no—
347#99—228no—
348#95—228no—
349C2×C11—22no—
350C2×C11—21no—
351C2×C11—22no—
352C2×C11—21no—
353C2×C11—44no—
354C2×C11—44no—
355C2×C11C2×#38611yescharacteristic
356C2×C11#302512yes—
357C24—22no—
358C24—21no—
359C24—22no—
360C24—21no—
361C24—44no—
362C24C22×Dic1112yes—
363C24C2×C22⋊D1112yes—
364C24C23×D1111yescharacteristic
365#41—28no—
366#41—28no—
367#41—28no—
368#41—28no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8C22⋊Dic1114yescomplemented
372C2×D4—24no—
373C2×D4—24no—
374C2×D4—28no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—48no—
378C2×D4C22⋊Dic1114yescomplemented
379C2×D4C22×Dic1114yes—
380C2×D4C2×C22⋊D1114yes—
381C22×C4—24no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—28no—
390C22×C4—28no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—42no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—44no—
399C22×C4—44no—
400C22×C4—118no—
401C22×C4—228no—
402C22×C4—224no—
403C22×C4C22⋊Dic1118yescomplemented
404C22×C4D4×D1112yes—
405C22×C4D4×D1112yes—
406C22×C4#434114yes—
407C22×C4C22×Dic1112yes—
408C22×C4C22×Dic1112yes—
409C22×C4C2×C22⋊D1112yes—
410C22×C4C2×C22⋊D1111yescharacteristic
411C22×C4C2×C22⋊D1111yescharacteristic
412C22×C4C2×C22⋊D1112yes—
413C4⋊C4—24no—
414C4⋊C4—28no—
415C4⋊C4—228no—
416C4⋊C4—224no—
417C4⋊C4—224no—
418C4⋊C4—444no—
419C22⋊C4—28no—
420C22⋊C4—22no—
421C22⋊C4—28no—
422C22⋊C4—228no—
423C22⋊C4—224no—
424C22⋊C4—224no—
425C22⋊C4—224no—
426C22⋊C4—224no—
427C22⋊C4—4416no—
428C22⋊C4C22×Dic1114yes—
429C42—24no—
430C42—228no—
431C42—224no—
432C42—224no—
433C42—444no—
434C11#2095911yescharacteristic, complemented, Sylow
435C23—28no—
436C23—24no—
437C23—24no—
438C23—22no—
439C23—22no—
440C23—22no—
441C23—44no—
442C23—42no—
443C23—42no—
444C23—44no—
445C23—44no—
446C23—48no—
447C23—44no—
448C23—41no—
449C23—41no—
450C23—42no—
451C23C2×C22⋊Dic1114yes—
452C23C2×D4×D1112yes—
453C23C2×#434112yes—
454C23C23×Dic1111yescharacteristic
455C23C22×C22⋊D1111yescharacteristic
456C23C22×C22⋊D1111yescharacteristic
457Q8—28no—
458D4—28no—
459D4—28no—
460D4—28no—
461D4—416no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—28no—
465C2×C4—28no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—44no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—44no—
474C2×C4—44no—
475C2×C4—48no—
476C2×C4—228no—
477C2×C4—448no—
478C2×C4—448no—
479C2×C4—444no—
480C2×C4—888no—
481C2×C4D4×Dic1114yes—
482C2×C4D4×Dic1114yes—
483C2×C4#6698812yes—
484C2×C4#6698812yes—
485C2×C4#6699012yes—
486C2×C4#6699011yescharacteristic
487C2×C4#6699011yescharacteristic
488C2×C4#6699214yes—
489C2×C4#6699214yes—
490C2×C4C2×C22⋊Dic1114yes—
491C2×C4C2×C22⋊Dic1112yes—
492C2×C4C2×C22⋊Dic1112yes—
493C22—22no—
494C22—24no—
495C22—24no—
496C22—28no—
497C22—24no—
498C22—42no—
499C22—41no—
500C22—41no—
501C22—44no—
502C22—42no—
503C22—48no—
504C22—44no—
505C22—44no—
506C22—42no—
507C22—44no—
508C22—44no—
509C22—82no—
510C22C2×D4×Dic1112yes—
511C22C2×#6698811yescharacteristic
512C22C2×#6699011yescharacteristic
513C22C2×#6699212yes—
514C22C22×C22⋊Dic1111yescharacteristic
515C4—24no—
516C4—44no—
517C4—42no—
518C4—448no—
519C4—884no—
520C4#1062283312yes—
521C4#1062283312yes—
522C4#1062283314yes—
523C2—21no—
524C2—22no—
525C2—22no—
526C2—21no—
527C2—44no—
528C2—44no—
529C2C2×#1062283311yescharacteristic
530C2#1307800712yes—
subgroupG/H
centerC2×C4#66990
commutatorC23×C11C23×C4
FrattiniC24C23×D11
Fitting, prime radicalC2×C11×#525C2
socleC22×C11C2×#120
cosocleC24×C11C24
hypercenterC2×#525D11
hypocenterC11#20959
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. #13081819C2semidirect
2. C2×#10622853C2semidirect
3. #13070999C2semidirect
4. #13069030C2semidirect
5. #13069025C2semidirect
6. #13068348C2semidirect
11. C11×#525C4semidirect
49. C23×C4×C11C2×C4semidirect
54. C11×#123C2×C4semidirect
58. C11×#120C2×C4semidirect
61. C11×#117C2×C4semidirect
86. C2×C4⋊Dic11D4semidirect
89. C2×C4×Dic11D4semidirect
107. C2×Q8×C11C22⋊C4semidirect
114. C2×D4×C11C22⋊C4semidirect
136. C22×C4×C11C22⋊C4semidirect
238. #525Dic11semidirect
306. C23×C4C2×Dic11semidirect
311. #123C2×Dic11semidirect
315. #120C2×Dic11semidirect
330. #117C2×Dic11semidirect
371. C2×Q8C22⋊Dic11semidirect
378. C2×D4C22⋊Dic11semidirect
403. C22×C4C22⋊Dic11semidirect
434. C11#20959semidirect

Maximal subgroups

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

subgroupindex
#130818192
C2×#106228532
#130709992
#130690302
#130690252
#130683482
C2×C11×#5252
#2095911