Finite Group Databasebeta

← #14727674

Subgroups — #14727674

Order 2816.

1282 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 1282 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×#10623041C211yesmaximal, characteristic, complemented
2#13079364C212yesmaximal, complemented
3#13067618C214yesmaximal, complemented
4#13067550C214yesmaximal, complemented
5#13067183C212yesmaximal, complemented
6C2×#10622166C211yesmaximal, characteristic, complemented
7C11×#2618C211yesmaximal, characteristic, complemented
8C22×#4339—21no—
9C2×C11×#123—21no—
10C2×C11×#121C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C2×#66983—21no—
13C2×#66983C2212yes—
14#10623041—22no—
15#10623041—24no—
16#10623041C2214yes—
17C2×#66950—22no—
18C2×#66948—22no—
19C11×#398C2212yescomplemented
20C11×#396—22no—
21C11×#394C2212yescomplemented
22C11×#386—21no—
23C11×#380C2211yescharacteristic
24#10622830C2214yescomplemented
25C2×C22⋊(C11⋊C8)C2212yes—
26#10622651—24no—
27#10622649—22no—
28#10622646—22no—
29#10622580C2214yescomplemented
30#10622166C2214yescomplemented
31#10622089C2218yescomplemented
32C22×D4×C11—21no—
33C22×D4×C11C2311yescharacteristic
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C22×C22⋊D11—22no—
38C2×#4339—24no—
39C2×#4339—24no—
40C2×#4339—44no—
41C2×#4339—44no—
42C22×D44—21no—
43C22×D44—21no—
44C22×D44D412yes—
45C22×C4×D11—22no—
46C22×Dic22—21no—
47C11×#123—44no—
48C11×#121—22no—
49C11×#121—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D412yes—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4—21no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×#4323—24no—
62#66983—24no—
63#66983—22no—
64#66983—22no—
65#66983—24no—
66#66983D414yes—
67#66983C2314yes—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11D412yes—
72C22×C11⋊C8—22no—
73#66950—28no—
74#66950—28no—
75#66948—28no—
76#66948—28no—
77C11×#95—22no—
78C11×#95C2312yes—
79#66896—24no—
80C22⋊(C11⋊C8)—22no—
81C22⋊(C11⋊C8)C2314yes—
82#66873—24no—
83#66871—24no—
84#18292—111nomaximal, Sylow
85C24×C11—21no—
86C24×C11C2×D411yescharacteristic
87C23×D11—22no—
88C2×D4×C11—22no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—42no—
92C2×D4×C11—42no—
93C2×D4×C11—81no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—22no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—81no—
102C22×C4×C11—81no—
103C22×C4×C11D814yescomplemented
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2411yescharacteristic
110C2×C22⋊D11—24no—
111C2×C22⋊D11—24no—
112C2×C22⋊D11—44no—
113C2×C22⋊D11—44no—
114C22×Dic11—22no—
115#4339—48no—
116#4339—416no—
117#4339—48no—
118C2×D44—24no—
119C2×D44—24no—
120C2×D44—22no—
121C2×D44—44no—
122C2×D44—82no—
123C2×D44—82no—
124C2×D44C2×D414yes—
125C2×C4×D11—28no—
126C2×C4×D11—48no—
127C2×Dic22—24no—
128C2×Dic22—44no—
129C11×C4⋊C4—24no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—44no—
133C11×C4⋊C4—81no—
134C11×C22⋊C4—42no—
135C11×C22⋊C4—42no—
136C11×C22⋊C4—44no—
137C11×C22⋊C4—82no—
138#4323—84no—
139(C2×D11)⋊C4—28no—
140(C2×D11)⋊C4—24no—
141(C2×D11)⋊C4—24no—
142C4⋊Dic11—24no—
143C4⋊Dic11—22no—
144C4⋊Dic11C2×D414yes—
145C2×C11⋊C8—24no—
146C2×C11⋊C8—82no—
147C2×#537—111no—
148#3186—112no—
149#2618D1111yescharacteristic, complemented
150#1610—114no—
151#1598—114no—
152#1519—112no—
153C2×#324—111no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—42no—
157C23×C11—42no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11#12011yescharacteristic
162C23×C11#12011yescharacteristic
163C23×C11C2×D812yes—
164C23×C11AGL(1,ℤ/8)12yes—
165C23×C11C22×D411yescharacteristic
166C22×D11—24no—
167C22×D11—44no—
168C22×D11—44no—
169C22×D11—44no—
170D4×C11—44no—
171D4×C11—82no—
172D4×C11—82no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
177C2×C4×C11—22no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—81no—
191C2×C4×C11#12012yes—
192C2×C4×C11C2×D814yes—
193C2×C4×C11C22×D412yes—
194C22⋊D11—44no—
195C22⋊D11—44no—
196C22⋊D11—48no—
197C2×Dic11—24no—
198C2×Dic11—44no—
199D44—44no—
200D44—48no—
201D44—82no—
202D44—84no—
203C4×D11—416no—
204Dic22—48no—
205C11⋊C8—44no—
206C22×#41—221no—
207#537—114no—
208#537—224no—
209#537—222no—
210C2×#123—21no—
211C2×C22⋊Q8—222no—
212C2×#121—112no—
213C2×#121—222no—
214C2×#121—221no—
215C2×#121C2×D1111yescharacteristic
216C22×C4⋊C4C2×D1111yescharacteristic
217#480—114no—
218#480—222no—
219#466—224no—
220#447—114no—
221#447—222no—
222C2×C22⋊C8—112no—
223#398C2×D1112yescomplemented
224#396—22no—
225#394C2×D1112yescomplemented
226#386—21no—
227#380C2×D1111yescharacteristic
228#327—118no—
229#324—114no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—42no—
237C22×C11—42no—
238C22×C11—82no—
239C22×C11—82no—
240C22×C11—81no—
241C22×C11—81no—
242C22×C11—81no—
243C22×C11#44712yes—
244C22×C11#44712yes—
245C22×C11C2×#12011yescharacteristic
246C22×C11C22×D811yescharacteristic
247C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
248C2×D11—44no—
249C2×D11—44no—
250C2×D11—44no—
251C2×D11—88no—
252C4×C11—24no—
253C4×C11—22no—
254C4×C11—22no—
255C4×C11—42no—
256C4×C11—82no—
257C4×C11—81no—
258Dic11—44no—
259C2×#41—224no—
260C2×#41—224no—
261C2×#41—444no—
262C2×#41—444no—
263C22×Q8—221no—
264C22×D4—21no—
265C22×D4—112no—
266C22×D4—221no—
267C22×D4—221no—
268C22×D4—222no—
269C22×D4C22×D1111yescharacteristic
270C23×C4—222no—
271C23×C4C22⋊D1111yescharacteristic
272C23×C4C22⋊D1111yescharacteristic
273C23×C4C22×D1111yescharacteristic
274C2×D8—224no—
275C22×C8—222no—
276#123—44no—
277C22⋊Q8—228no—
278C22⋊Q8—228no—
279#121—22no—
280#121—22no—
281#121—114no—
282#121—114no—
283#121—228no—
284#121—228no—
285#121—224no—
286#121—222no—
287#121—222no—
288#121—224no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—112no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4C22⋊D1112yes—
296C2×C4⋊C4C22×D1111yescharacteristic
297C2×C4⋊C4C22×D1112yes—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—222no—
303C2×C22⋊C4—222no—
304#107—224no—
305#102—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—161no—
316C2×C11C2×#44711yescharacteristic
317C2×C11#302011yescharacteristic
318C2×C11#302611yescharacteristic
319D11—84no—
320C24—21no—
321C24—222no—
322C24C2×C22⋊D1111yescharacteristic
323#41—448no—
324#41—4416no—
325#41—448no—
326C2×Q8—224no—
327C2×Q8—444no—
328C2×D4—22no—
329C2×D4—42no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—42no—
333C2×D4—81no—
334C2×D4—114no—
335C2×D4—224no—
336C2×D4—224no—
337C2×D4—224no—
338C2×D4—224no—
339C2×D4—222no—
340C2×D4—444no—
341C2×D4—444no—
342C2×D4—444no—
343C2×D4—882no—
344C2×D4—882no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—81no—
353C22×C4—81no—
354C22×C4—228no—
355C22×C4—222no—
356C22×C4—448no—
357C22×C4#432314yescomplemented
358C22×C4D4×D1112yes—
359C22×C4D4×D1112yes—
360C22×C4C2×C22⋊D1112yes—
361C22×C4C2×C22⋊D1112yes—
362C22×C4C2×C22⋊D1111yescharacteristic
363C22×C4C23×D1111yescharacteristic
364D8—884no—
365C2×C8—224no—
366C2×C8—882no—
367C4⋊C4—24no—
368C4⋊C4—24no—
369C4⋊C4—22no—
370C4⋊C4—44no—
371C4⋊C4—81no—
372C4⋊C4—114no—
373C4⋊C4—224no—
374C4⋊C4—222no—
375C22⋊C4—42no—
376C22⋊C4—44no—
377C22⋊C4—42no—
378C22⋊C4—82no—
379C22⋊C4—228no—
380C22⋊C4—224no—
381C22⋊C4—224no—
382C11#1829211yescharacteristic, complemented, Sylow
383C23—41no—
384C23—41no—
385C23—42no—
386C23—42no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—224no—
391C23—444no—
392C23—444no—
393C23—444no—
394C23C2×#432312yes—
395C23#6699011yescharacteristic
396C23#6699011yescharacteristic
397C23#6700212yes—
398C23C22×C22⋊D1111yescharacteristic
399Q8—448no—
400D4—44no—
401D4—82no—
402D4—82no—
403D4—444no—
404D4—448no—
405D4—444no—
406D4—444no—
407D4—448no—
408D4—882no—
409D4—884no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—22no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—81no—
428C2×C4—224no—
429C2×C4—4416no—
430C2×C4—444no—
431C2×C4C2×#432314yes—
432C2×C4#6699012yes—
433C2×C4C2×D4×D1112yes—
434C8—444no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—42no—
442C22—42no—
443C22—82no—
444C22—82no—
445C22—81no—
446C22—81no—
447C22—81no—
448C22—444no—
449C22—444no—
450C22—444no—
451C22—888no—
452C22#1062264912yes—
453C22#1062264912yes—
454C22C22×#432311yescharacteristic
455C22C2×#6699011yescharacteristic
456C22C2×#6700211yescharacteristic
457C4—24no—
458C4—22no—
459C4—22no—
460C4—42no—
461C4—82no—
462C4—81no—
463C4—444no—
464C2—21no—
465C2—21no—
466C2—22no—
467C2—22no—
468C2—161no—
469C2—884no—
470C2C2×#1062264911yescharacteristic
471C2#1307797911yescharacteristic
472C2#1307801211yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2618C2
socleC22×C11C2×#120
hypercenter#2618D11
hypocenterC11#18292
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2618

Complements

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

NH ≅ G/Ntype
1. C2×#10623041C2semidirect
2. #13079364C2semidirect
3. #13067618C2semidirect
4. #13067550C2semidirect
5. #13067183C2semidirect
6. C2×#10622166C2semidirect
7. C11×#2618C2semidirect
19. C11×#398C22semidirect
21. C11×#394C22semidirect
24. #10622830C22semidirect
29. #10622580C22semidirect
30. #10622166C22semidirect
31. #10622089C22semidirect
103. C22×C4×C11D8semidirect
149. #2618D11semidirect
223. #398C2×D11semidirect
225. #394C2×D11semidirect
357. C22×C4#4323semidirect
382. C11#18292semidirect

Maximal subgroups

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

subgroupindex
C2×#106230412
#130793642
#130676182
#130675502
#130671832
C2×#106221662
C11×#26182
#1829211