Finite Group Databasebeta

← #14781757

Subgroups — #14781757

Order 2816.

1570 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67002C211yesmaximal, characteristic
2C2×#10622612C211yesmaximal, characteristic, complemented
3C2×#10622846C211yesmaximal, characteristic, complemented
4C22×#66873C211yesmaximal, characteristic, complemented
5#13071196C211yesmaximal, characteristic, complemented
6#13069931C214yesmaximal, complemented
7#13069926C214yesmaximal, complemented
8#13068335C211yesmaximal, characteristic, complemented
9C11×#2311C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×D44C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C2×#67002—24no—
15C2×#67002—24no—
16C2×#67002—24no—
17C22×#4325C2212yes—
18C22×#4323C2212yes—
19C2×#66979C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C11×#391C2212yescomplemented
23C11×#390C2212yescomplemented
24C11×#386—22no—
25C11×#380—22no—
26#10622846—24no—
27C2×#66899C2212yescomplemented
28C2×#66896C2212yescomplemented
29#10622612—24no—
30#10622601—22no—
31C2×#66873—24no—
32C2×#66873C2214yes—
33#10622568—22no—
34#10622552C2214yes—
35C2×C4⋊(C11⋊C8)C2214yescomplemented
36#10622167C2214yescomplemented
37C24×D11—21no—
38C2×C11×#41—22no—
39C2×C11×#41—22no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41D414yes—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11—21no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C23×C4×C11C2311yescharacteristic
50C22×D44—22no—
51C22×D44—22no—
52C22×D44—22no—
53C22×D44—22no—
54C22×D44—21no—
55C22×D44—22no—
56C22×D44D414yes—
57C22×D44C2312yes—
58C11×#117—22no—
59C11×#117—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4D412yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4D412yes—
67C2×C42×C11C2312yes—
68C2×C22⋊Dic11—21no—
69#67002—232no—
70C2×#4325—24no—
71C2×#4325—24no—
72C2×#4325—24no—
73C2×#4323—24no—
74C2×#4323—24no—
75C2×#4323—24no—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—24no—
78#66979—22no—
79#66979—22no—
80C2×C4⋊Dic11C2312yes—
81C2×C4×Dic11—21no—
82C2×#4318—22no—
83C2×#4318—22no—
84C2×#4318D414yes—
85C22×C11⋊C8—22no—
86C22×C11⋊C8—22no—
87C22×C11⋊C8—22no—
88C22×C11⋊C8C2312yes—
89C22×C11⋊C8C2312yes—
90C11×#95—24no—
91#66899—24no—
92#66896—24no—
93#66873—28no—
94C4⋊(C11⋊C8)—28no—
95#23544—111nomaximal, Sylow
96C24×C11—21no—
97C24×C11C2×D411yescharacteristic
98C23×D11—22no—
99C23×D11—24no—
100C23×D11—42no—
101C23×D11—42no—
102C23×D11—82no—
103C23×D11—82no—
104C11×#41—28no—
105C11×#41—28no—
106C11×#41—44no—
107C11×#41—44no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11C2×D412yes—
114C2×D4×C11—24no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—42no—
121C2×D4×C11—42no—
122C2×D4×C11C2×D412yes—
123C22×C4×C11—21no—
124C22×C4×C11—24no—
125C22×C4×C11—22no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11—82no—
130C22×C4×C11C2×D414yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11#4112yes—
136C22×C4×C11#4112yes—
137C22×C4×C11#4112yes—
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—22no—
140C2×D44—28no—
141C2×D44—24no—
142C2×D44—28no—
143C2×D44—22no—
144C2×D44—22no—
145C2×D44—22no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—42no—
149C2×D44—42no—
150C2×D44—44no—
151C2×D44—44no—
152C2×D44C2×D414yes—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—42no—
157C11×C22⋊C4—24no—
158C11×C22⋊C4—84no—
159C42×C11—22no—
160C42×C11—22no—
161C22⋊Dic11—42no—
162#4325—216no—
163#4323—216no—
164(C2×D11)⋊C4—84no—
165(C2×D11)⋊C4—84no—
166C4⋊Dic11—22no—
167C4⋊Dic11—22no—
168C4×Dic11—42no—
169#4318—28no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—44no—
176C2×C11⋊C8C2×D414yes—
177C22×AGL(1,ℤ/8)—111no—
178C2×#424—111no—
179C2×#416—111no—
180C22×#102—111no—
181#2311D1111yescharacteristic, complemented
182#2309—111no—
183#2055—114no—
184#2054—114no—
185#1736—111no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11#12112yes—
194C23×C11#12112yes—
195C23×C11#12112yes—
196C23×C11C22×D411yescharacteristic
197C22×D11—24no—
198C22×D11—42no—
199C22×D11—42no—
200C22×D11—44no—
201C22×D11—44no—
202C22×D11—48no—
203C22×D11—84no—
204C22×D11—84no—
205C22×D11—88no—
206C22×D11—88no—
207Q8×C11—22no—
208Q8×C11—22no—
209Q8×C11—41no—
210Q8×C11—41no—
211D4×C11—22no—
212D4×C11—22no—
213D4×C11—48no—
214D4×C11—41no—
215D4×C11—41no—
216C2×C4×C11—24no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—48no—
223C2×C4×C11—42no—
224C2×C4×C11—44no—
225C2×C4×C11—84no—
226C2×C4×C11#12014yes—
227C2×C4×C11#12112yes—
228C2×C4×C11#12112yes—
229C2×C4×C11#12112yes—
230C2×C4×C11#12314yes—
231C2×C4×C11#12314yes—
232C2×C4×C11#12414yes—
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242D44—24no—
243D44—24no—
244D44—42no—
245D44—42no—
246D44—48no—
247C11⋊C8—24no—
248C11⋊C8—42no—
249C22×#41C2×D1111yescharacteristic
250C23×D4—111no—
251C2×AGL(1,ℤ/8)—224no—
252C2×AGL(1,ℤ/8)—224no—
253C2×AGL(1,ℤ/8)—224no—
254C22×SD16—112no—
255C22×D8—112no—
256C22×M16—111no—
257C23×C8—111no—
258C2×#117—111no—
259C2×#117C2×D1111yescharacteristic
260C22×C4⋊C4C2×D1111yescharacteristic
261#424—224no—
262C2×C4⋊C8—114no—
263#416—224no—
264C2×#103—112no—
265C2×#102—112no—
266C2×#102—114no—
267C2×#102—224no—
268#391C2×D1112yescomplemented
269#390—114no—
270#390—222no—
271#390C2×D1112yescomplemented
272#386—22no—
273#380—22no—
274#379—222no—
275#340—114no—
276C22×C11—22no—
277C22×C11—22no—
278C22×C11—24no—
279C22×C11—24no—
280C22×C11—42no—
281C22×C11—44no—
282C22×C11—81no—
283C22×C11—81no—
284C22×C11—82no—
285C22×C11#39414yes—
286C22×C11C2×#12111yescharacteristic
287C22×C11C2×#12111yescharacteristic
288C22×C11C2×#12111yescharacteristic
289C22×C11#57612yes—
290C22×C11#57712yes—
291C2×D11—44no—
292C2×D11—44no—
293C2×D11—44no—
294C2×D11—816no—
295C2×D11—84no—
296C2×D11—84no—
297C4×C11—42no—
298C4×C11—44no—
299C4×C11—82no—
300C4×C11#39414yes—
301C4×C11C2×#12011yescharacteristic
302C4×C11C2×#12311yescharacteristic
303C4×C11C2×#12311yescharacteristic
304C4×C11C2×#12411yescharacteristic
305Dic11—82no—
306C25—221no—
307C2×#41—22no—
308C2×#41—22no—
309C2×#41—22no—
310C2×#41—22no—
311C2×#41—22no—
312C2×#41D4414yes—
313C22×Q8C22×D1111yescharacteristic
314C22×D4—21no—
315C22×D4—114no—
316C22×D4—112no—
317C22×D4—222no—
318C22×D4—222no—
319C22×D4—222no—
320C22×D4—222no—
321C22×D4—222no—
322C22×D4—221no—
323C22×D4C22×D1111yescharacteristic
324C23×C4—21no—
325C23×C4—21no—
326C23×C4C22×D1111yescharacteristic
327AGL(1,ℤ/8)—2232no—
328C2×SD16—224no—
329C2×SD16—224no—
330C2×SD16—224no—
331C2×D8—224no—
332C2×D8—224no—
333C2×D8—224no—
334C2×M16—114no—
335C2×M16—222no—
336C2×M16—222no—
337C22×C8—112no—
338C22×C8—112no—
339C22×C8—222no—
340C22×C8—222no—
341C22×C8—222no—
342#117—22no—
343#117—22no—
344#117—222no—
345#117—222no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—112no—
350C2×C4⋊C4C22⋊D1112yes—
351C2×C4⋊C4C22×D1112yes—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—221no—
354C2×C22⋊C4—224no—
355C2×C22⋊C4—224no—
356C2×C22⋊C4C22⋊D1112yes—
357C2×C42—221no—
358C2×C42C22×D1112yes—
359C4⋊C8—228no—
360#103—224no—
361#102—228no—
362#102—224no—
363#95—24no—
364C2×C11—24no—
365C2×C11—82no—
366C2×C11C2×#39411yescharacteristic
367C2×C11#304111yescharacteristic
368C2×C11#304211yescharacteristic
369C2×C11#304512yes—
370C2×C11#306212yes—
371D11—84no—
372C24—21no—
373C24—222no—
374C24—224no—
375C24—442no—
376C24—442no—
377C24—882no—
378C24—882no—
379C24C2×C22⋊D1111yescharacteristic
380#41—28no—
381#41—28no—
382#41—44no—
383#41—44no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8C2×D4412yes—
390C2×D4—24no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4—114no—
399C2×D4—228no—
400C2×D4—228no—
401C2×D4—224no—
402C2×D4—222no—
403C2×D4—222no—
404C2×D4—222no—
405C2×D4—222no—
406C2×D4—222no—
407C2×D4—444no—
408C2×D4—444no—
409C2×D4—442no—
410C2×D4—442no—
411C2×D4C2×D4412yes—
412C22×C4—21no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—82no—
419C22×C4—222no—
420C22×C4C2×D4412yes—
421C22×C4#433912yes—
422C22×C4D4×D1112yes—
423C22×C4D4×D1112yes—
424C22×C4#434112yes—
425C22×C4#434112yes—
426C22×C4C2×C22⋊D1114yes—
427C22×C4C2×C22⋊D1111yescharacteristic
428C22×C4C23×D1111yescharacteristic
429SD16—2216no—
430D8—2216no—
431M16—228no—
432C2×C8—114no—
433C2×C8—222no—
434C2×C8—222no—
435C2×C8—222no—
436C2×C8—222no—
437C2×C8—222no—
438C2×C8—444no—
439C4⋊C4—24no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—42no—
443C4⋊C4—222no—
444C4⋊C4—222no—
445C22⋊C4—24no—
446C22⋊C4—84no—
447C22⋊C4—442no—
448C22⋊C4—884no—
449C22⋊C4—884no—
450C42—22no—
451C42—22no—
452C42—442no—
453C11#2354411yescharacteristic, complemented, Sylow
454C23—22no—
455C23—22no—
456C23—22no—
457C23—41no—
458C23—41no—
459C23—42no—
460C23—42no—
461C23—224no—
462C23—442no—
463C23—442no—
464C23—448no—
465C23—444no—
466C23—444no—
467C23—884no—
468C23—884no—
469C23—888no—
470C23—888no—
471C23#6698312yes—
472C23#6699112yes—
473C23#6699212yes—
474C23C22×C22⋊D1111yescharacteristic
475Q8—22no—
476Q8—22no—
477Q8—41no—
478Q8—41no—
479D4—22no—
480D4—22no—
481D4—48no—
482D4—41no—
483D4—41no—
484D4—224no—
485D4—224no—
486D4—442no—
487D4—442no—
488D4—448no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—48no—
496C2×C4—42no—
497C2×C4—44no—
498C2×C4—84no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4#6693514yes—
503C2×C4#6693614yes—
504C2×C4#6693814yes—
505C2×C4#6693914yes—
506C2×C4#6698312yes—
507C2×C4#6699112yes—
508C2×C4#6699212yes—
509C2×C4C22×D4411yescharacteristic
510C2×C4C2×#433911yescharacteristic
511C2×C4C2×D4×D1111yescharacteristic
512C2×C4C2×D4×D1111yescharacteristic
513C2×C4C2×#434111yescharacteristic
514C2×C4C2×#434111yescharacteristic
515C8—224no—
516C8—442no—
517C22—24no—
518C22—22no—
519C22—22no—
520C22—24no—
521C22—44no—
522C22—42no—
523C22—82no—
524C22—81no—
525C22—81no—
526C22—444no—
527C22—444no—
528C22—444no—
529C22—8816no—
530C22—884no—
531C22—884no—
532C22#1062257414yes—
533C22C2×#6698311yescharacteristic
534C22C2×#6699111yescharacteristic
535C22C2×#6699211yescharacteristic
536C22#1062336612yes—
537C22#1062336812yes—
538C4—44no—
539C4—42no—
540C4—82no—
541C4—882no—
542C4#1062257414yes—
543C4C2×#6693511yescharacteristic
544C4C2×#6693611yescharacteristic
545C4C2×#6693811yescharacteristic
546C4C2×#6693911yescharacteristic
547C2—24no—
548C2—82no—
549C2—884no—
550C2C2×#1062257411yescharacteristic
551C2#1307811511yescharacteristic
552C2#1307812411yescharacteristic
553C2#1307815512yes—
554C2#1307829812yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2311C2
socleC23×C11C22×D4
prime radicalC22×#67002C2
hypercenter#2311D11
hypocenterC11#23544
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. C2×#10622612C2semidirect
3. C2×#10622846C2semidirect
4. C22×#66873C2semidirect
5. #13071196C2semidirect
6. #13069931C2semidirect
7. #13069926C2semidirect
8. #13068335C2semidirect
9. C11×#2311C2semidirect
22. C11×#391C22semidirect
23. C11×#390C22semidirect
27. C2×#66899C22semidirect
28. C2×#66896C22semidirect
35. C2×C4⋊(C11⋊C8)C22semidirect
36. #10622167C22semidirect
181. #2311D11semidirect
268. #391C2×D11semidirect
271. #390C2×D11semidirect
453. C11#23544semidirect

Maximal subgroups

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

subgroupindex
C22×#670022
C2×#106226122
C2×#106228462
C22×#668732
#130711962
#130699312
#130699262
#130683352
C11×#23112
#2354411