Finite Group Databasebeta

← #14755145

Subgroups — #14755145

Order 2816.

1802 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67004C211yesmaximal, characteristic
2C22×C4×Dic22C211yesmaximal, characteristic, complemented
3C2×#10622845C211yesmaximal, characteristic
4C2×#10622617C211yesmaximal, characteristic, complemented
5#13068974C214yesmaximal, complemented
6#13068960C214yesmaximal, complemented
7#13068337C211yesmaximal, characteristic, complemented
8#13068310C211yesmaximal, characteristic, complemented
9C11×#2297C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C2×#67004—24no—
15C2×#67004—24no—
16C2×#67004C418yescomplemented
17C22×#4326C2212yes—
18C22×#4324C2212yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4—21no—
21C22×C4×Dic11—21no—
22C22×#4318C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24C2×C4×Dic22—24no—
25C2×C4×Dic22—22no—
26C2×C4×Dic22—24no—
27C2×C4×Dic22C2214yes—
28C11×#391C2212yes—
29C11×#390C2212yes—
30C11×#386—21no—
31C11×#386—21no—
32C4×C11×C22⋊C4—22no—
33#10622845—24no—
34C2×#66899C2212yes—
35C2×#66896C2212yes—
36#10622617—24no—
37C2×#66874C2214yes—
38#10622167C2214yes—
39#10622162C2214yes—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41C2×C414yes—
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×Dic11—21no—
54C23×Dic11—21no—
55C22×Dic22—22no—
56C22×Dic22—21no—
57C22×Dic22—22no—
58C22×Dic22—22no—
59C22×Dic22C2×C414yes—
60C22×Dic22D414yes—
61C22×Dic22D414yes—
62C22×Dic22C2312yes—
63C11×#117—22no—
64C11×#117—22no—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C42×C11—22no—
70C2×C42×C11—22no—
71C2×C42×C11—21no—
72C2×C42×C11D412yes—
73C2×C42×C11C2312yes—
74#67004—232no—
75C2×#4326—24no—
76C2×#4326—24no—
77C2×#4326C2×C418yescomplemented
78C2×#4324—24no—
79C2×#4324—24no—
80C2×#4324C2×C418yescomplemented
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11D414yes—
84C2×C4⋊Dic11C2312yes—
85C2×Dic11⋊C4—28no—
86C2×Dic11⋊C4—24no—
87C2×C4×Dic11—28no—
88C2×C4×Dic11—24no—
89C2×#4318—22no—
90C2×#4318—22no—
91C2×#4318—22no—
92C2×#4318—22no—
93C2×#4318—22no—
94C2×#4318C2×C414yes—
95C22×C11⋊C8C2312yes—
96C22×C11⋊C8C2312yes—
97C4×Dic22—216no—
98C4×Dic22—28no—
99C4×Dic22—28no—
100C11×#95—22no—
101C11×#95—22no—
102#66899—24no—
103#66896—24no—
104#66874—28no—
105#20926—111nomaximal, Sylow
106C24×C11—21no—
107C24×C11C2×D411yescharacteristic
108C11×#41—28no—
109C11×#41—28no—
110C11×#41—44no—
111C11×#41—44no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11C22×C412yes—
118C2×D4×C11—24no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—42no—
125C2×D4×C11—42no—
126C2×D4×C11C22×C412yes—
127C22×C4×C11—22no—
128C22×C4×C11—24no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—24no—
132C22×C4×C11—22no—
133C22×C4×C11—42no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11C22×C412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D412yes—
143C22×C4×C11#4112yes—
144C22×C4×C11#4112yes—
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—44no—
153C2×Dic22—28no—
154C2×Dic22—24no—
155C2×Dic22—24no—
156C2×Dic22—28no—
157C2×Dic22—24no—
158C2×Dic22—28no—
159C2×Dic22—22no—
160C2×Dic22—22no—
161C2×Dic22—22no—
162C2×Dic22C22⋊C4116yescomplemented
163C2×Dic22C22×C414yes—
164C2×Dic22C2×D414yes—
165C2×Dic22C2×D414yes—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C22⋊C4—44no—
169C11×C22⋊C4—42no—
170C11×C22⋊C4—44no—
171C42×C11—24no—
172C42×C11—22no—
173C42×C11—22no—
174C42×C11—42no—
175#4326—216no—
176#4324—216no—
177C4⋊Dic11—24no—
178C4⋊Dic11—22no—
179C4⋊Dic11C2×D414yes—
180Dic11⋊C4—216no—
181C4×Dic11—216no—
182#4318—28no—
183#4318—44no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8C22×C414yes—
190C22×#137—111no—
191C22×C4×Q8—111no—
192C2×#417—111no—
193C2×#419—111no—
194#2297D1111yescharacteristic
195#1880—114no—
196#1878—114no—
197#1736—111no—
198#1728—111no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11C4×D412yes—
207C23×C11#12012yes—
208C23×C11#12112yes—
209C23×C11C22×D411yescharacteristic
210Q8×C11—22no—
211Q8×C11—22no—
212Q8×C11—41no—
213Q8×C11—41no—
214D4×C11—22no—
215D4×C11—22no—
216D4×C11—48no—
217D4×C11—41no—
218D4×C11—41no—
219C2×C4×C11—28no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—44no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—48no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11C2×C22⋊C414yes—
234C2×C4×C11C4×D414yes—
235C2×C4×C11C4×D412yes—
236C2×C4×C11#12012yes—
237C2×C4×C11#12114yes—
238C2×C4×C11#12112yes—
239C2×C4×C11#12314yes—
240C2×C4×C11#13714yescomplemented
241C2×C4×C11C23×C411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—216no—
251C2×Dic11—24no—
252C2×Dic11—48no—
253C2×Dic11—44no—
254Dic22—24no—
255Dic22—24no—
256Dic22—24no—
257Dic22—216no—
258Dic22C2×C22⋊C418yes—
259C11⋊C8—24no—
260C11⋊C8—42no—
261C22×#41C2×D1111yescharacteristic
262C23×Q8—111no—
263C2×#137—118no—
264C2×#137—224no—
265C2×#137—224no—
266C22×Q16—112no—
267C22×SD16—112no—
268C22×M16—111no—
269C22×M16—111no—
270C2×C4×Q8—114no—
271C2×C4×Q8—224no—
272C2×C4×Q8—224no—
273C2×C4×Q8—222no—
274C2×#117C2×D1111yescharacteristic
275C22×C4⋊C4—111no—
276C22×C4⋊C4—221no—
277C22×C42—221no—
278C22×C42C2×D1111yescharacteristic
279#419—224no—
280#417—224no—
281C2×#103—112no—
282C2×#103—114no—
283C2×#102—112no—
284#391C2×D1112yes—
285#390C2×D1112yes—
286#386—21no—
287#386—21no—
288C4×C22⋊C4—22no—
289#340—114no—
290#336—114no—
291C22×C11—24no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—24no—
295C22×C11—44no—
296C22×C11—42no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11—82no—
300C22×C11#38614yes—
301C22×C11C2×C4×D411yescharacteristic
302C22×C11C2×#12011yescharacteristic
303C22×C11C2×#12111yescharacteristic
304C22×C11C2×#13712yes—
305C22×C11#57512yes—
306C4×C11—24no—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11—82no—
310C4×C11#38614yes—
311C4×C11C22×C22⋊C411yescharacteristic
312C4×C11C2×C4×D411yescharacteristic
313C4×C11C2×#12111yescharacteristic
314C4×C11C2×#12311yescharacteristic
315Dic11—28no—
316Dic11—44no—
317C2×#41—22no—
318C2×#41—22no—
319C2×#41—22no—
320C2×#41—22no—
321C2×#41—22no—
322C2×#41C4×D1114yes—
323C22×Q8—114no—
324C22×Q8—114no—
325C22×Q8—114no—
326C22×Q8—112no—
327C22×Q8—222no—
328C22×Q8—222no—
329C22×Q8—222no—
330C22×Q8—221no—
331C22×Q8C22×D1111yescharacteristic
332C22×D4—21no—
333C22×D4C22×D1111yescharacteristic
334C23×C4—21no—
335C23×C4—221no—
336C23×C4—221no—
337C23×C4C22⋊D1111yescharacteristic
338C23×C4C22⋊D1111yescharacteristic
339C23×C4C22×D1111yescharacteristic
340#137—2232no—
341C2×Q16—118no—
342C2×Q16—224no—
343C2×Q16—224no—
344C2×SD16—118no—
345C2×SD16—224no—
346C2×SD16—224no—
347C2×M16—114no—
348C2×M16—222no—
349C2×M16—222no—
350C2×M16—222no—
351C2×M16—222no—
352C2×M16—222no—
353C22×C8—112no—
354C22×C8—112no—
355C4×Q8—228no—
356C4×Q8—228no—
357C4×Q8—2216no—
358#117—22no—
359#117—22no—
360C2×C4⋊C4—114no—
361C2×C4⋊C4—112no—
362C2×C4⋊C4—228no—
363C2×C4⋊C4—222no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—224no—
366C2×C4⋊C4C22×D1112yes—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—21no—
373C2×C42—228no—
374C2×C42—224no—
375C2×C42C22⋊D1112yes—
376C2×C42C22×D1112yes—
377#103—228no—
378#103—224no—
379#102—224no—
380#95—22no—
381#95—22no—
382C2×C11—24no—
383C2×C11—82no—
384C2×C11C2×#38611yescharacteristic
385C2×C11C4×#13712yes—
386C2×C11#300411yescharacteristic
387C2×C11#300511yescharacteristic
388C2×C11#303712yes—
389C24—21no—
390C24C2×C22⋊D1111yescharacteristic
391#41—28no—
392#41—28no—
393#41—44no—
394#41—44no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—1116no—
401C2×Q8—114no—
402C2×Q8—114no—
403C2×Q8—114no—
404C2×Q8—228no—
405C2×Q8—228no—
406C2×Q8—228no—
407C2×Q8—224no—
408C2×Q8—224no—
409C2×Q8—224no—
410C2×Q8—222no—
411C2×Q8—222no—
412C2×Q8—222no—
413C2×Q8C2×C4×D1112yes—
414C2×D4—24no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4C2×C4×D1112yes—
423C22×C4—22no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—224no—
433C22×C4—224no—
434C22×C4—224no—
435C22×C4—222no—
436C22×C4—224no—
437C22×C4—222no—
438C22×C4—444no—
439C22×C4C2×C4×D1112yes—
440C22×C4#433912yes—
441C22×C4D4×D1112yes—
442C22×C4D4×D1112yes—
443C22×C4D4×D1112yes—
444C22×C4#434112yes—
445C22×C4C2×C22⋊D1112yes—
446C22×C4C2×C22⋊D1112yes—
447C22×C4C2×C22⋊D1111yescharacteristic
448C22×C4C23×D1111yescharacteristic
449Q16—2216no—
450SD16—2216no—
451M16—228no—
452M16—444no—
453C2×C8—114no—
454C2×C8—222no—
455C2×C8—222no—
456C2×C8—222no—
457C2×C8—222no—
458C2×C8—222no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—114no—
462C4⋊C4—2216no—
463C4⋊C4—224no—
464C4⋊C4—222no—
465C22⋊C4—44no—
466C22⋊C4—42no—
467C22⋊C4—44no—
468C42—24no—
469C42—22no—
470C42—22no—
471C42—42no—
472C42—2216no—
473C11#2092611yescharacteristic, complemented, Sylow
474C23—22no—
475C23—22no—
476C23—22no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23—42no—
481C23C4×C22⋊D1112yes—
482C23#6699012yes—
483C23#6699112yes—
484C23C22×C22⋊D1111yescharacteristic
485Q8—22no—
486Q8—22no—
487Q8—41no—
488Q8—41no—
489Q8—118no—
490Q8—224no—
491Q8—224no—
492Q8—224no—
493Q8—2216no—
494D4—22no—
495D4—22no—
496D4—48no—
497D4—41no—
498D4—41no—
499C2×C4—28no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—44no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—48no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—224no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—2216no—
517C2×C4—224no—
518C2×C4—448no—
519C2×C4—444no—
520C2×C4C22⋊C4×D1114yes—
521C2×C4(C22⋊D11)⋊C414yes—
522C2×C4#6693614yes—
523C2×C4#6693714yes—
524C2×C4C4×C22⋊D1112yes—
525C2×C4#6699012yes—
526C2×C4#6699112yes—
527C2×C4#6700414yescomplemented
528C2×C4C22×C4×D1111yescharacteristic
529C2×C4C2×#433911yescharacteristic
530C2×C4C2×D4×D1111yescharacteristic
531C2×C4C2×D4×D1111yescharacteristic
532C2×C4C2×D4×D1111yescharacteristic
533C2×C4C2×#434111yescharacteristic
534C8—224no—
535C8—442no—
536C22—24no—
537C22—22no—
538C22—22no—
539C22—24no—
540C22—42no—
541C22—44no—
542C22—82no—
543C22—81no—
544C22—81no—
545C22#1062256914yes—
546C22C2×C4×C22⋊D1111yescharacteristic
547C22C2×#6699011yescharacteristic
548C22C2×#6699111yescharacteristic
549C22#1062335312yes—
550C22C2×#6700412yes—
551C4—24no—
552C4—42no—
553C4—42no—
554C4—82no—
555C4—228no—
556C4—444no—
557C4#1062256914yes—
558C4C2×C22⋊C4×D1111yescharacteristic
559C4C2×(C22⋊D11)⋊C411yescharacteristic
560C4C2×#6693611yescharacteristic
561C4C2×#6693711yescharacteristic
562C2—24no—
563C2—82no—
564C2C2×#1062256911yescharacteristic
565C2C4×#6700412yes—
566C2#1307784911yescharacteristic
567C2#1307785611yescharacteristic
568C2#1307808412yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2297C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenter#2297D11
hypocenterC11#20926
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2297

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic22C2semidirect
4. C2×#10622617C2semidirect
5. #13068974C2semidirect
6. #13068960C2semidirect
7. #13068337C2semidirect
8. #13068310C2semidirect
16. C2×#67004C4semidirect
77. C2×#4326C2×C4semidirect
80. C2×#4324C2×C4semidirect
162. C2×Dic22C22⋊C4semidirect
240. C2×C4×C11#137semidirect
473. C11#20926semidirect
527. C2×C4#67004semidirect

Maximal subgroups

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

subgroupindex
C22×#670042
C22×C4×Dic222
C2×#106228452
C2×#106226172
#130689742
#130689602
#130683372
#130683102
C11×#22972
#2092611