Finite Group Databasebeta

← #14727613

Subgroups — #14727613

Order 2816.

1408 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 1408 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×#10623024C211yesmaximal, characteristic
2#13079369C212yesmaximal, complemented
3#13067635C214yesmaximal, complemented
4#13067567C214yesmaximal, complemented
5#13067183C212yesmaximal, complemented
6C2×#10622163C211yesmaximal, characteristic, complemented
7C11×#2626C211yesmaximal, characteristic, complemented
8C23×C22⋊D11—21no—
9C2×C11×C22⋊Q8C2211yescharacteristic, complemented
10C22×C11×C22⋊C4C2211yescharacteristic
11C2×#66983—21no—
12C2×#66983C2212yes—
13#10623024—22no—
14#10623024—24no—
15#10623024C2214yes—
16C2×#66939—22no—
17C2×#66935—22no—
18C11×#399C2212yescomplemented
19C11×#396—22no—
20C11×#393C2212yescomplemented
21C11×#385—21no—
22C11×#380C2211yescharacteristic, complemented
23C11×#379—21no—
24#10622840C2214yescomplemented
25C2×C22⋊(C11⋊C8)C2212yescomplemented
26#10622661—24no—
27#10622659—22no—
28#10622656—22no—
29#10622581C2214yescomplemented
30#10622163C2214yescomplemented
31#10622089C2218yescomplemented
32C25×C11D411yescharacteristic
33C24×D11—21no—
34C22×Q8×C11C2311yescharacteristic, complemented
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C22×C22⋊D11—22no—
38C22×C22⋊D11—24no—
39C22×C22⋊D11—24no—
40C22×C22⋊D11—22no—
41C22×C22⋊D11—44no—
42C22×C22⋊D11—44no—
43C23×Dic11—21no—
44C22×D44—21no—
45C22×D44D412yes—
46C11×C22⋊Q8—22no—
47C11×C22⋊Q8—22no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4C2311yescharacteristic, complemented
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4—21no—
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4—22no—
57C2×C11×C22⋊C4—22no—
58C2×C11×C22⋊C4D412yes—
59C2×C11×C22⋊C4C2312yes—
60C2×#4325—24no—
61#66983—24no—
62#66983—22no—
63#66983—22no—
64#66983—24no—
65#66983D414yes—
66#66983C2314yes—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11D412yes—
71C22×C11⋊C8—22no—
72#66939—28no—
73#66939—28no—
74#66935—28no—
75#66935—28no—
76C11×#95—22no—
77C11×#95C2312yescomplemented
78#66899—24no—
79C22⋊(C11⋊C8)—22no—
80C22⋊(C11⋊C8)C2314yescomplemented
81#66873—24no—
82#66872—24no—
83#18285—111nomaximal, Sylow
84C24×C11—21no—
85C24×C11—21no—
86C24×C11—22no—
87C24×C11—81no—
88C24×C11—81no—
89C24×C11SD1614yescomplemented
90C24×C11C2×D412yes—
91C24×C11C2×D411yescharacteristic
92C23×D11—22no—
93C23×D11—24no—
94C23×D11—44no—
95C23×D11—82no—
96C23×D11—82no—
97C2×Q8×C11—22no—
98C2×Q8×C11—81no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—21no—
104C22×C4×C11—81no—
105C22×C4×C11—81no—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2411yescharacteristic
111C2×C22⋊D11—28no—
112C2×C22⋊D11—24no—
113C2×C22⋊D11—24no—
114C2×C22⋊D11—48no—
115C2×C22⋊D11—416no—
116C2×C22⋊D11—48no—
117C2×C22⋊D11—48no—
118C2×C22⋊D11—44no—
119C2×C22⋊D11—44no—
120C22×Dic11—24no—
121C22×Dic11—22no—
122C22×Dic11—44no—
123C2×D44—24no—
124C2×D44—22no—
125C2×D44—82no—
126C2×D44—82no—
127C2×D44C2×D414yes—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—42no—
130C11×C4⋊C4—81no—
131C11×C4⋊C4—82no—
132C11×C22⋊C4—24no—
133C11×C22⋊C4—24no—
134C11×C22⋊C4—41no—
135C11×C22⋊C4—41no—
136C11×C22⋊C4—42no—
137C11×C22⋊C4—82no—
138C11×C22⋊C4—82no—
139#4325—84no—
140(C2×D11)⋊C4—28no—
141(C2×D11)⋊C4—24no—
142(C2×D11)⋊C4—24no—
143C4⋊Dic11—24no—
144C4⋊Dic11—22no—
145C4⋊Dic11C2×D414yes—
146C2×C11⋊C8—24no—
147C2×C11⋊C8—82no—
148C2×#534—111no—
149#3187—112no—
150#2626D1111yescharacteristic, complemented
151#1613—114no—
152#1601—114no—
153#1519—112no—
154C2×#323—111no—
155C23×C11—22no—
156C23×C11—24no—
157C23×C11—22no—
158C23×C11—24no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11—42no—
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×C11AGL(1,ℤ/8)12yes—
174C23×C11C22×D411yescharacteristic
175C22×D11—24no—
176C22×D11—44no—
177C22×D11—44no—
178C22×D11—48no—
179C22×D11—44no—
180C22×D11—84no—
181C22×D11—84no—
182C22×D11—816no—
183Q8×C11—44no—
184C2×C4×C11—22no—
185C2×C4×C11—42no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11—81no—
199C2×C4×C11#12012yes—
200C2×C4×C11C22×D412yes—
201C22⋊D11—416no—
202C22⋊D11—44no—
203C22⋊D11—44no—
204C22⋊D11—48no—
205C2×Dic11—24no—
206C2×Dic11—48no—
207C2×Dic11—44no—
208D44—44no—
209D44—82no—
210D44—84no—
211C11⋊C8—44no—
212C23×D4—221no—
213#534—114no—
214#534—224no—
215#534—222no—
216C2×#123—222no—
217C2×C22⋊Q8C2×D1111yescharacteristic, complemented
218C2×#121—112no—
219C2×#121—221no—
220C2×#120—222no—
221C22×C22⋊C4C2×D1111yescharacteristic
222#483—222no—
223#481—114no—
224#465—224no—
225#450—222no—
226#448—114no—
227C2×C22⋊C8—112no—
228#399C2×D1112yescomplemented
229#396—22no—
230#393C2×D1112yescomplemented
231#385—21no—
232#380C2×D1111yescharacteristic, complemented
233#379—21no—
234#327—118no—
235#323—114no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—24no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11—44no—
246C22×C11—48no—
247C22×C11—42no—
248C22×C11—42no—
249C22×C11—82no—
250C22×C11—84no—
251C22×C11#45012yes—
252C22×C11#45012yes—
253C22×C11C2×#12011yescharacteristic
254C22×C11C22×SD1611yescharacteristic
255C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
256C2×D11—44no—
257C2×D11—44no—
258C2×D11—44no—
259C2×D11—88no—
260C2×D11—816no—
261C4×C11—22no—
262C4×C11—22no—
263C4×C11—42no—
264C4×C11—82no—
265C4×C11—81no—
266C4×C11—81no—
267Dic11—44no—
268C25—221no—
269C25C22⋊D1111yescharacteristic
270C22×Q8C22×D1111yescharacteristic, complemented
271C22×D4—112no—
272C22×D4—221no—
273C22×D4—222no—
274C22×D4—224no—
275C22×D4—222no—
276C22×D4—224no—
277C22×D4—444no—
278C22×D4—444no—
279C23×C4—221no—
280C23×C4C22⋊D1111yescharacteristic
281C23×C4C22×D1111yescharacteristic
282C2×SD16—224no—
283C22×C8—222no—
284#123—228no—
285#123—228no—
286C22⋊Q8—22no—
287C22⋊Q8—22no—
288#121—114no—
289#121—114no—
290#121—224no—
291#121—222no—
292#121—222no—
293#121—224no—
294#120—228no—
295#120—228no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—112no—
300C2×C4⋊C4—221no—
301C2×C4⋊C4C22×D1111yescharacteristic, complemented
302C2×C22⋊C4—22no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—222no—
309C2×C22⋊C4—222no—
310C2×C22⋊C4C22⋊D1112yes—
311C2×C22⋊C4C22×D1112yes—
312#106—224no—
313#103—224no—
314#102—224no—
315C22⋊C8—114no—
316C22⋊C8—222no—
317#95—22no—
318#95C22×D1112yescomplemented
319C2×C11—21no—
320C2×C11—22no—
321C2×C11—21no—
322C2×C11—22no—
323C2×C11—44no—
324C2×C11C2×#45011yescharacteristic
325C2×C11#301911yescharacteristic
326C2×C11#302611yescharacteristic
327D11—84no—
328C24—21no—
329C24—21no—
330C24—22no—
331C24—81no—
332C24—81no—
333C24—224no—
334C24—222no—
335C24—444no—
336C24—882no—
337C24—882no—
338C24#432514yescomplemented
339C24C2×C22⋊D1112yes—
340C24C2×C22⋊D1111yescharacteristic
341C2×Q8—22no—
342C2×Q8—81no—
343C2×D4—114no—
344C2×D4—224no—
345C2×D4—228no—
346C2×D4—224no—
347C2×D4—224no—
348C2×D4—222no—
349C2×D4—448no—
350C2×D4—4416no—
351C2×D4—448no—
352C2×D4—448no—
353C2×D4—444no—
354C2×D4—444no—
355C2×D4—882no—
356C2×D4—882no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—22no—
361C22×C4—21no—
362C22×C4—81no—
363C22×C4—81no—
364C22×C4—224no—
365C22×C4—222no—
366C22×C4—444no—
367C22×C4D4×D1112yes—
368C22×C4D4×D1112yes—
369C22×C4C2×C22⋊D1112yes—
370C22×C4C2×C22⋊D1111yescharacteristic
371C22×C4C23×D1111yescharacteristic
372SD16—884no—
373C2×C8—224no—
374C2×C8—882no—
375C4⋊C4—22no—
376C4⋊C4—42no—
377C4⋊C4—81no—
378C4⋊C4—82no—
379C4⋊C4—114no—
380C4⋊C4—224no—
381C4⋊C4—222no—
382C22⋊C4—24no—
383C22⋊C4—24no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—42no—
387C22⋊C4—82no—
388C22⋊C4—82no—
389C22⋊C4—228no—
390C22⋊C4—224no—
391C22⋊C4—224no—
392C11#1828511yescharacteristic, complemented, Sylow
393C23—22no—
394C23—24no—
395C23—22no—
396C23—24no—
397C23—41no—
398C23—41no—
399C23—42no—
400C23—42no—
401C23—42no—
402C23—42no—
403C23—81no—
404C23—81no—
405C23—84no—
406C23—84no—
407C23—224no—
408C23—448no—
409C23—444no—
410C23—444no—
411C23—444no—
412C23—884no—
413C23—884no—
414C23—8816no—
415C23#6699011yescharacteristic
416C23#6699011yescharacteristic
417C23C2×#432514yes—
418C23C2×#432512yes—
419C23#6700212yes—
420C23C22×C22⋊D1111yescharacteristic
421Q8—44no—
422D4—444no—
423D4—4416no—
424D4—444no—
425D4—444no—
426D4—448no—
427D4—882no—
428D4—884no—
429C2×C4—22no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—42no—
443C2×C4—81no—
444C2×C4—224no—
445C2×C4—448no—
446C2×C4—444no—
447C2×C4#6699012yes—
448C2×C4C2×D4×D1112yes—
449C8—444no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—24no—
457C22—42no—
458C22—42no—
459C22—44no—
460C22—48no—
461C22—42no—
462C22—42no—
463C22—82no—
464C22—84no—
465C22—444no—
466C22—444no—
467C22—444no—
468C22—888no—
469C22—8816no—
470C22#1062265912yes—
471C22#1062265912yes—
472C22C2×#6699011yescharacteristic
473C22C22×#432511yescharacteristic
474C22C2×#6700211yescharacteristic
475C4—22no—
476C4—22no—
477C4—42no—
478C4—82no—
479C4—81no—
480C4—81no—
481C4—444no—
482C2—21no—
483C2—22no—
484C2—21no—
485C2—22no—
486C2—44no—
487C2—884no—
488C2C2×#1062265911yescharacteristic
489C2#1307797211yescharacteristic
490C2#1307801211yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2626C2
socleC22×C11C2×#120
prime radicalC2×#10623024C2
hypercenter#2626D11
hypocenterC11#18285
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2626

Complements

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

NH ≅ G/Ntype
2. #13079369C2semidirect
3. #13067635C2semidirect
4. #13067567C2semidirect
5. #13067183C2semidirect
6. C2×#10622163C2semidirect
7. C11×#2626C2semidirect
9. C2×C11×C22⋊Q8C22semidirect
18. C11×#399C22semidirect
20. C11×#393C22semidirect
22. C11×#380C22semidirect
24. #10622840C22semidirect
25. C2×C22⋊(C11⋊C8)C22semidirect
29. #10622581C22semidirect
30. #10622163C22semidirect
31. #10622089C22semidirect
34. C22×Q8×C11C23semidirect
51. C2×C11×C4⋊C4C23semidirect
77. C11×#95C23semidirect
80. C22⋊(C11⋊C8)C23semidirect
89. C24×C11SD16semidirect
150. #2626D11semidirect
217. C2×C22⋊Q8C2×D11semidirect
228. #399C2×D11semidirect
230. #393C2×D11semidirect
232. #380C2×D11semidirect
270. C22×Q8C22×D11semidirect
301. C2×C4⋊C4C22×D11semidirect
318. #95C22×D11semidirect
338. C24#4325semidirect
392. C11#18285semidirect

Maximal subgroups

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

subgroupindex
C2×#106230242
#130793692
#130676352
#130675672
#130671832
C2×#106221632
C11×#26262
#1828511