Finite Group Databasebeta

← #14727620

Subgroups — #14727620

Order 2816.

1142 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 1142 conjugacy classes of subgroups — too many to draw. Only its 187 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
1C2×#10623014C211yesmaximal, characteristic, complemented
2#13079373C212yesmaximal, complemented
3#13067606C214yesmaximal, complemented
4#13067538C214yesmaximal, complemented
5#13067187C212yesmaximal, complemented
6C2×#10622163C211yesmaximal, characteristic, complemented
7C11×#2617C211yesmaximal, characteristic
8C2×C11×#121C2211yescharacteristic
9C2×C11×#120—21no—
10C22×C11×C22⋊C4C2211yescharacteristic
11C22×C22⋊Dic11—21no—
12C2×#66977—21no—
13C2×#66977C2212yes—
14#10623014—22no—
15#10623014—24no—
16#10623014C2214yes—
17C2×#66931—22no—
18C2×#66931—22no—
19C11×#397C2212yes—
20C11×#394—22no—
21C11×#392C2212yes—
22C11×#386—21no—
23C11×#380C2211yescharacteristic
24#10622831C2214yescomplemented
25C2×C22⋊(C11⋊C8)C2212yes—
26#10622654—24no—
27#10622653—22no—
28#10622647—22no—
29#10622584C2214yescomplemented
30#10622163C2214yes—
31#10622090C2218yescomplemented
32C25×C11D411yescharacteristic
33C22×D4×C11—21no—
34C22×D4×C11—22no—
35C22×D4×C11C2311yescharacteristic
36C23×C4×C11D411yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C23×Dic11—21no—
39C23×Dic11—21no—
40C22×Dic22—21no—
41C22×Dic22D412yescomplemented
42C11×#121—22no—
43C11×#121—22no—
44C11×#120—44no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4C2311yescharacteristic
47C2×C11×C22⋊C4—22no—
48C2×C11×C22⋊C4—22no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4D412yes—
54C2×C11×C22⋊C4C2312yes—
55C2×C22⋊Dic11—22no—
56C2×C22⋊Dic11—24no—
57C2×C22⋊Dic11—24no—
58C2×C22⋊Dic11—22no—
59C2×#4324—24no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11D412yescomplemented
62#66977—24no—
63#66977—22no—
64#66977—22no—
65#66977—24no—
66#66977D414yescomplemented
67#66977C2314yes—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4—22no—
70C22×C11⋊C8—22no—
71#66931—28no—
72#66931—28no—
73#66931—28no—
74#66931—28no—
75C11×#95—22no—
76C11×#95C2312yes—
77#66896—24no—
78C22⋊(C11⋊C8)—22no—
79C22⋊(C11⋊C8)C2314yes—
80#66874—24no—
81#66872—24no—
82#18286—111nomaximal, Sylow
83C24×C11—21no—
84C24×C11—21no—
85C24×C11—22no—
86C24×C11—21no—
87C24×C11—81no—
88C24×C11—81no—
89C24×C11SD1614yescomplemented
90C24×C11C2×D412yes—
91C24×C11C2×D411yescharacteristic
92C2×D4×C11—22no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—44no—
96C2×D4×C11—42no—
97C2×D4×C11—42no—
98C2×D4×C11—81no—
99C2×D4×C11—82no—
100C2×D4×C11—82no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—81no—
106C22×C4×C11—81no—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2411yescharacteristic
112C22×Dic11—24no—
113C22×Dic11—24no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—82no—
117C22×Dic11—82no—
118C2×Dic22—24no—
119C2×Dic22—22no—
120C2×Dic22—82no—
121C2×Dic22—82no—
122C2×Dic22C2×D414yes—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—81no—
125C11×C22⋊C4—24no—
126C11×C22⋊C4—24no—
127C11×C22⋊C4—44no—
128C11×C22⋊C4—42no—
129C11×C22⋊C4—42no—
130C11×C22⋊C4—82no—
131C22⋊Dic11—28no—
132C22⋊Dic11—24no—
133C22⋊Dic11—24no—
134#4324—84no—
135C4⋊Dic11—24no—
136C4⋊Dic11—22no—
137C4⋊Dic11C2×D414yes—
138Dic11⋊C4—28no—
139Dic11⋊C4—24no—
140Dic11⋊C4—24no—
141C2×C11⋊C8—24no—
142C2×C11⋊C8—82no—
143C2×#543—111no—
144#3187—112no—
145#2617D1111yescharacteristic
146#1608—114no—
147#1596—114no—
148#1520—112no—
149C2×#323—111no—
150C23×C11—22no—
151C23×C11—24no—
152C23×C11—22no—
153C23×C11—24no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—42no—
157C23×C11—42no—
158C23×C11—42no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11—81no—
166C23×C11—81no—
167C23×C11—84no—
168C23×C11—84no—
169C23×C11#12011yescharacteristic
170C23×C11#12011yescharacteristic
171C23×C11C2×SD1614yes—
172C23×C11C2×SD1612yes—
173C23×C11#13712yes—
174C23×C11C22×D411yescharacteristic
175D4×C11—44no—
176D4×C11—88no—
177D4×C11—82no—
178D4×C11—82no—
179C2×C4×C11—22no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—81no—
193C2×C4×C11#12012yes—
194C2×C4×C11C22×D412yes—
195C2×Dic11—24no—
196C2×Dic11—24no—
197C2×Dic11—44no—
198C2×Dic11—44no—
199C2×Dic11—84no—
200C2×Dic11—84no—
201Dic22—44no—
202Dic22—82no—
203Dic22—84no—
204C11⋊C8—44no—
205#543—114no—
206#543—224no—
207#543—222no—
208C2×C22⋊Q8—112no—
209C2×C22⋊Q8—222no—
210C2×C22⋊Q8—222no—
211C2×C22⋊Q8—221no—
212C2×#121C2×D1111yescharacteristic
213C2×#120—21no—
214C22×C22⋊C4—221no—
215C22×C22⋊C4C2×D1111yescharacteristic
216#483—114no—
217#481—222no—
218#465—224no—
219#450—114no—
220#448—222no—
221C2×C22⋊C8—112no—
222#397C2×D1112yes—
223#394—22no—
224#392C2×D1112yes—
225#386—21no—
226#380C2×D1111yescharacteristic
227#328—118no—
228#323—114no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—24no—
236C22×C11—42no—
237C22×C11—42no—
238C22×C11—44no—
239C22×C11—48no—
240C22×C11—42no—
241C22×C11—42no—
242C22×C11—82no—
243C22×C11—84no—
244C22×C11—82no—
245C22×C11—82no—
246C22×C11—81no—
247C22×C11—81no—
248C22×C11—81no—
249C22×C11#44812yes—
250C22×C11#44812yes—
251C22×C11C2×#12011yescharacteristic
252C22×C11C22×SD1611yescharacteristic
253C22×C11C2×#13711yescharacteristic
254C4×C11—22no—
255C4×C11—22no—
256C4×C11—42no—
257C4×C11—82no—
258C4×C11—81no—
259Dic11—44no—
260Dic11—44no—
261C25C22⋊D1111yescharacteristic
262C22×Q8—112no—
263C22×Q8—221no—
264C22×D4—21no—
265C22×D4—22no—
266C22×D4C22×D1111yescharacteristic
267C23×C4—221no—
268C23×C4—221no—
269C23×C4C22⋊D1111yescharacteristic
270C23×C4C22×D1111yescharacteristic
271C2×SD16—224no—
272C22×C8—222no—
273C22⋊Q8—114no—
274C22⋊Q8—114no—
275C22⋊Q8—228no—
276C22⋊Q8—228no—
277C22⋊Q8—228no—
278C22⋊Q8—228no—
279C22⋊Q8—224no—
280C22⋊Q8—222no—
281C22⋊Q8—222no—
282C22⋊Q8—224no—
283#121—22no—
284#121—22no—
285#120—44no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—112no—
288C2×C4⋊C4—222no—
289C2×C4⋊C4—221no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4C22×D1111yescharacteristic
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—222no—
299C2×C22⋊C4—224no—
300C2×C22⋊C4—222no—
301C2×C22⋊C4—224no—
302C2×C22⋊C4C22⋊D1112yes—
303C2×C22⋊C4C22×D1112yes—
304#106—224no—
305#103—224no—
306#102—224no—
307C22⋊C8—114no—
308C22⋊C8—222no—
309#95—22no—
310#95C22×D1112yes—
311C2×C11—21no—
312C2×C11—22no—
313C2×C11—21no—
314C2×C11—22no—
315C2×C11—44no—
316C2×C11—161no—
317C2×C11C2×#44811yescharacteristic
318C2×C11#301911yescharacteristic
319C2×C11#302611yescharacteristic
320C24—21no—
321C24—21no—
322C24—22no—
323C24—21no—
324C24—81no—
325C24—81no—
326C24#432414yescomplemented
327C24C2×C22⋊D1112yes—
328C24C2×C22⋊D1111yescharacteristic
329C2×Q8—114no—
330C2×Q8—224no—
331C2×Q8—222no—
332C2×Q8—882no—
333C2×Q8—882no—
334C2×D4—22no—
335C2×D4—44no—
336C2×D4—42no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—42no—
340C2×D4—81no—
341C2×D4—82no—
342C2×D4—82no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—22no—
347C22×C4—81no—
348C22×C4—81no—
349C22×C4—222no—
350C22×C4—222no—
351C22×C4—224no—
352C22×C4—224no—
353C22×C4—882no—
354C22×C4—882no—
355C22×C4D4×D1112yes—
356C22×C4D4×D1112yes—
357C22×C4C2×C22⋊D1112yes—
358C22×C4C2×C22⋊D1111yescharacteristic
359C22×C4C23×D1111yescharacteristic
360SD16—884no—
361C2×C8—224no—
362C2×C8—882no—
363C4⋊C4—22no—
364C4⋊C4—81no—
365C4⋊C4—114no—
366C4⋊C4—228no—
367C4⋊C4—224no—
368C4⋊C4—222no—
369C4⋊C4—224no—
370C4⋊C4—224no—
371C22⋊C4—24no—
372C22⋊C4—24no—
373C22⋊C4—44no—
374C22⋊C4—42no—
375C22⋊C4—42no—
376C22⋊C4—82no—
377C22⋊C4—228no—
378C22⋊C4—224no—
379C22⋊C4—224no—
380C11#1828611yescharacteristic, complemented, Sylow
381C23—22no—
382C23—24no—
383C23—22no—
384C23—24no—
385C23—41no—
386C23—41no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—81no—
397C23—81no—
398C23—84no—
399C23—84no—
400C23C2×#432414yes—
401C23C2×#432412yes—
402C23#6699011yescharacteristic
403C23#6699011yescharacteristic
404C23#6700412yes—
405C23C22×C22⋊D1111yescharacteristic
406Q8—444no—
407Q8—882no—
408Q8—884no—
409D4—44no—
410D4—88no—
411D4—82no—
412D4—82no—
413C2×C4—22no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—81no—
427C2×C4—224no—
428C2×C4—224no—
429C2×C4—444no—
430C2×C4—444no—
431C2×C4—884no—
432C2×C4—884no—
433C2×C4#6699012yes—
434C2×C4C2×D4×D1112yes—
435C8—444no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—24no—
443C22—42no—
444C22—42no—
445C22—44no—
446C22—48no—
447C22—42no—
448C22—42no—
449C22—82no—
450C22—84no—
451C22—82no—
452C22—82no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22#1062265312yes—
457C22#1062265312yes—
458C22C22×#432411yescharacteristic
459C22C2×#6699011yescharacteristic
460C22C2×#6700411yescharacteristic
461C4—22no—
462C4—22no—
463C4—42no—
464C4—82no—
465C4—81no—
466C4—444no—
467C4—444no—
468C2—21no—
469C2—22no—
470C2—21no—
471C2—22no—
472C2—44no—
473C2—161no—
474C2C2×#1062265311yescharacteristic
475C2#1307797211yescharacteristic
476C2#1307801211yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2617C2
socleC22×C11C2×#120
hypercenter#2617D11
hypocenterC11#18286
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2617

Complements

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

NH ≅ G/Ntype
1. C2×#10623014C2semidirect
2. #13079373C2semidirect
3. #13067606C2semidirect
4. #13067538C2semidirect
5. #13067187C2semidirect
6. C2×#10622163C2semidirect
24. #10622831C22semidirect
29. #10622584C22semidirect
31. #10622090C22semidirect
41. C22×Dic22D4semidirect
61. C2×C4⋊Dic11D4semidirect
66. #66977D4semidirect
89. C24×C11SD16semidirect
326. C24#4324semidirect
380. C11#18286semidirect

Maximal subgroups

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

subgroupindex
C2×#106230142
#130793732
#130676062
#130675382
#130671872
C2×#106221632
C11×#26172
#1828611