Finite Group Databasebeta

← #14810458

Subgroups — #14810458

Order 2816.

1078 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66943C211yesmaximal, characteristic
2C2×#10622410C212yesmaximal, complemented
3#13076964C211yesmaximal, characteristic
4#13069766C212yesmaximal, complemented
5#13069765C212yesmaximal, complemented
6#13069583C212yesmaximal, complemented
7#13068924C211yesmaximal, characteristic
8#13068923C211yesmaximal, characteristic
9#13068921C211yesmaximal, characteristic
10#13068380C211yesmaximal, characteristic
11C11×#1872C211yesmaximal, characteristic
12C2×C11×C22⋊Q8C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C2×#66997C2211yescharacteristic
15C22×C4⋊Dic11—21no—
16C22×C4⋊Dic11C2211yescharacteristic
17C2×#66977C2211yescharacteristic
18C22×Dic11⋊C4—21no—
19C22×C4×Dic11C2211yescharacteristic
20C2×#66943—21no—
21C2×#66943—21no—
22C2×#66943—28no—
23C2×#66943C2212yes—
24C2×#66943C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622843C2211yescharacteristic
28C2×#66899C2212yes—
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×#66880C2212yes—
31C2×#66879C2212yes—
32#10622589C2211yescharacteristic
33#10622587C2211yescharacteristic
34#10622585—21no—
35#10622585—21no—
36C2×#66874C2212yes—
37#10622555—21no—
38#10622555—21no—
39#10622410—28no—
40C11×#340C2212yes—
41#10622189C2212yes—
42#10622188C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11C2311yescharacteristic
48C23×Dic11—21no—
49C23×Dic11D411yescharacteristic
50C23×Dic11D411yescharacteristic
51C22×Dic22C2311yescharacteristic
52C22×C8×C11C2312yes—
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—24no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C22⋊C4—21no—
61C2×C22⋊Dic11—21no—
62#66997—24no—
63C2×C4⋊Dic11—28no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11—24no—
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2312yes—
70#66977—22no—
71#66977—22no—
72C2×Dic11⋊C4—28no—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—21no—
76C2×Dic11⋊C4—21no—
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—21no—
80C2×C4×Dic11—24no—
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C2×C4×Dic11C2311yescharacteristic
85C22×C11⋊C8C2312yes—
86#66943—28no—
87#66943—28no—
88#66943—24no—
89#66943—24no—
90#66943—24no—
91#66943D418yes—
92C11×#103—24no—
93C11×C22⋊C8—22no—
94#66899—24no—
95C11⋊#95—21no—
96C11⋊#95—21no—
97C11⋊#95—21no—
98C11⋊#95—21no—
99C22⋊(C11⋊C8)—22no—
100#66880—24no—
101#66879—24no—
102#66874—24no—
103#25912—111nomaximal, Sylow
104C24×C11C2×D411yescharacteristic
105C2×Q8×C11—22no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—24no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11#4112yes—
119C22×C4×C11#4112yes—
120C22×C4×C11C2411yescharacteristic
121C22×Dic11—24no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—41no—
130C22×Dic11—41no—
131C22×Dic11—42no—
132C22×Dic11—42no—
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C22×Dic11C2×D411yescharacteristic
137C2×Dic22—22no—
138C2×Dic22—21no—
139C2×Dic22—21no—
140C2×Dic22—22no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4C2×D414yes—
150C11×C22⋊C4—42no—
151C22⋊Dic11—42no—
152C4⋊Dic11—24no—
153C4⋊Dic11—28no—
154C4⋊Dic11—28no—
155C4⋊Dic11—22no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11C2×D414yes—
159Dic11⋊C4—28no—
160Dic11⋊C4—28no—
161Dic11⋊C4—42no—
162Dic11⋊C4—42no—
163Dic11⋊C4—42no—
164Dic11⋊C4—42no—
165Dic11⋊C4—42no—
166C4×Dic11—22no—
167C4×Dic11—22no—
168C4×Dic11—22no—
169C4×Dic11C2×D414yes—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C22×#125—111no—
174C2×#491—112no—
175#2857—111no—
176#2026—112no—
177#2026—112no—
178#1992—112no—
179#1872—111no—
180#1872—111no—
181#1872—111no—
182#1872D1111yescharacteristic
183#1749—111no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11#12412yes—
189C23×C11#13712yes—
190C23×C11#13712yes—
191C23×C11C22×D411yescharacteristic
192Q8×C11—42no—
193Q8×C11—42no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—48no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11#12412yes—
209C2×C4×C11C22×D412yes—
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C112−1+412yes—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—21no—
217C2×Dic11—21no—
218C2×Dic11—21no—
219C2×Dic11—24no—
220C2×Dic11—21no—
221C2×Dic11—21no—
222C2×Dic11—21no—
223C2×Dic11—21no—
224C2×Dic11—44no—
225C2×Dic11—44no—
226C2×Dic11—48no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11#12012yes—
236C2×Dic11#12012yes—
237Dic22—42no—
238Dic22—42no—
239C8×C11—42no—
240C11⋊C8—42no—
241C2×C4⋊Q8—111no—
242C2×#125—112no—
243C2×#125—112no—
244C2×#125—221no—
245C2×#125—221no—
246C2×#125—228no—
247C2×C22⋊Q8—111no—
248C2×C22⋊Q8C2×D1111yescharacteristic
249C22×C4⋊C4—111no—
250C22×C4⋊C4—221no—
251C22×C4⋊C4—221no—
252C22×C4⋊C4C2×D1111yescharacteristic
253C22×C42—111no—
254#491—228no—
255C2×#103—112no—
256C2×#103—112no—
257C2×#103—112no—
258C2×#103C2×D1112yes—
259C2×C22⋊C8—111no—
260C2×C22⋊C8C2×D1111yescharacteristic
261C2×#97—112no—
262#391—111no—
263#391—111no—
264#389—221no—
265#389—221no—
266#384—111no—
267#380—221no—
268#380—221no—
269#340—112no—
270#340—112no—
271#340—112no—
272#340C2×D1112yes—
273#336—112no—
274C22×C11—22no—
275C22×C11—22no—
276C22×C11—22no—
277C22×C11—22no—
278C22×C11—22no—
279C22×C11—22no—
280C22×C11#49114yescomplemented
281C22×C11C2×#12011yescharacteristic
282C22×C11C2×#12411yescharacteristic
283C22×C11#53611yescharacteristic
284C22×C11C2×#13711yescharacteristic
285C22×C11C2×#13711yescharacteristic
286C22×C11#57511yescharacteristic
287C22×C11#57511yescharacteristic
288C4×C11—22no—
289C4×C11—44no—
290C4×C11—81no—
291C4×C11—81no—
292C4×C11#54812yes—
293C4×C11#54812yes—
294Dic11—22no—
295Dic11—22no—
296Dic11—41no—
297Dic11—41no—
298Dic11—44no—
299Dic11—81no—
300Dic11—81no—
301C22×Q8—111no—
302C22×Q8C22×D1111yescharacteristic
303C23×C4—21no—
304C23×C4—111no—
305C23×C4—111no—
306C23×C4—221no—
307C23×C4C22×D1111yescharacteristic
308C22×C8—112no—
309C22×C8C22×D1112yes—
310C4⋊Q8—224no—
311#125—118no—
312#125—224no—
313#125—224no—
314#125—228no—
315#125—228no—
316#125—224no—
317C22⋊Q8—22no—
318C22⋊Q8—22no—
319C22⋊Q8—222no—
320C22⋊Q8—222no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—112no—
325C2×C4⋊C4—111no—
326C2×C4⋊C4—224no—
327C2×C4⋊C4—222no—
328C2×C4⋊C4—222no—
329C2×C4⋊C4—222no—
330C2×C4⋊C4—222no—
331C2×C4⋊C4—228no—
332C2×C4⋊C4—228no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4—221no—
336C2×C4⋊C4—221no—
337C2×C4⋊C4—221no—
338C2×C4⋊C4—221no—
339C2×C4⋊C4C22×D1111yescharacteristic
340C2×C4⋊C4C22×D1112yes—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—221no—
343C2×C42—111no—
344C2×C42—111no—
345C2×C42—111no—
346C2×C42—111no—
347C2×C42—224no—
348#103—24no—
349#103—224no—
350#103—224no—
351#103—224no—
352C22⋊C8—22no—
353C22⋊C8—222no—
354#97—224no—
355#95—221no—
356#95—221no—
357#95—221no—
358#95—221no—
359C2×C11—24no—
360C2×C11#243611yescharacteristic
361C2×C11#300711yescharacteristic
362C2×C11#300711yescharacteristic
363C2×C11C2×#49111yescharacteristic
364C2×C11#314211yescharacteristic
365C2×C11#323611yescharacteristic
366C2×C11#323611yescharacteristic
367C24D4×D1111yescharacteristic
368C2×Q8—21no—
369C2×Q8—22no—
370C2×Q8—21no—
371C2×Q8—22no—
372C2×Q8—221no—
373C2×Q8—222no—
374C2×Q8—221no—
375C2×Q8—222no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—24no—
379C22×C4—22no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—111no—
385C22×C4—111no—
386C22×C4—111no—
387C22×C4—111no—
388C22×C4—222no—
389C22×C4—222no—
390C22×C4—224no—
391C22×C4—222no—
392C22×C4—222no—
393C22×C4—222no—
394C22×C4—221no—
395C22×C4—221no—
396C22×C4—441no—
397C22×C4—441no—
398C22×C4—442no—
399C22×C4—442no—
400C22×C4#433912yes—
401C22×C4D4×D1111yescharacteristic
402C22×C4#434112yes—
403C22×C4C23×D1111yescharacteristic
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—222no—
408C2×C8—222no—
409C2×C8—222no—
410C4⋊C4—24no—
411C4⋊C4—22no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—42no—
415C4⋊C4—114no—
416C4⋊C4—228no—
417C4⋊C4—228no—
418C4⋊C4—228no—
419C4⋊C4—224no—
420C4⋊C4—228no—
421C4⋊C4—222no—
422C4⋊C4—221no—
423C4⋊C4—221no—
424C4⋊C4—442no—
425C4⋊C4—442no—
426C4⋊C4—442no—
427C4⋊C4—442no—
428C4⋊C4—442no—
429C4⋊C4D4×D1114yes—
430C22⋊C4—42no—
431C22⋊C4—442no—
432C42—114no—
433C42—222no—
434C42—222no—
435C42—222no—
436C11#2591211yescharacteristic, complemented, Sylow
437C23—21no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23#6693812yes—
442C23#6696812yes—
443C23#6697112yes—
444C23C2×D4×D1111yescharacteristic
445Q8—42no—
446Q8—42no—
447Q8—442no—
448Q8—442no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—24no—
454C2×C4—48no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—112no—
464C2×C4—112no—
465C2×C4—221no—
466C2×C4—221no—
467C2×C4—221no—
468C2×C4—221no—
469C2×C4—221no—
470C2×C4—221no—
471C2×C4—221no—
472C2×C4—221no—
473C2×C4—221no—
474C2×C4—221no—
475C2×C4—224no—
476C2×C4—444no—
477C2×C4—444no—
478C2×C4—448no—
479C2×C4—442no—
480C2×C4—442no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4—441no—
485C2×C4—441no—
486C2×C4—441no—
487C2×C4#6693812yes—
488C2×C4C2×#433911yescharacteristic
489C2×C4C2×D4×D1112yes—
490C2×C4C2×#434111yescharacteristic
491C2×C4#6704312yes—
492C8—42no—
493C8—442no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22#1062241014yescomplemented
501C22C2×#6693811yescharacteristic
502C22D11×#12011yescharacteristic
503C22#1062317911yescharacteristic
504C22C2×#6696811yescharacteristic
505C22C2×#6697111yescharacteristic
506C22#1062330411yescharacteristic
507C22#1062330811yescharacteristic
508C4—22no—
509C4—44no—
510C4—81no—
511C4—81no—
512C4—222no—
513C4—222no—
514C4—441no—
515C4—441no—
516C4—444no—
517C4—881no—
518C4—881no—
519C4#1062308312yes—
520C4#1062312912yes—
521C2—24no—
522C2#1307227211yescharacteristic
523C2#1307787111yescharacteristic
524C2#1307787511yescharacteristic
525C2C2×#1062241011yescharacteristic
526C2#1307901411yescharacteristic
527C2#1307981911yescharacteristic
528C2#1307982111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1872C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1872D11
hypocenterC11#25912
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
2. C2×#10622410C2semidirect
4. #13069766C2semidirect
5. #13069765C2semidirect
6. #13069583C2semidirect
280. C22×C11#491semidirect
436. C11#25912semidirect
500. C22#10622410semidirect

Maximal subgroups

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

subgroupindex
C22×#669432
C2×#106224102
#130769642
#130697662
#130697652
#130695832
#130689242
#130689232
#130689212
#130683802
C11×#18722
#2591211