Finite Group Databasebeta

← #14721612

Subgroups — #14721612

Order 2816.

942 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082483C211yesmaximal, characteristic
2#13077699C211yesmaximal, characteristic, complemented
3#13071533C211yesmaximal, characteristic, complemented
4#13067175C211yesmaximal, characteristic
5#13067153C214yesmaximal, complemented
6#13067140C214yesmaximal, complemented
7#13067115C211yesmaximal, characteristic, complemented
8#13067112C211yesmaximal, characteristic
9C11×#1518C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11#10623263C412yescomplemented
12#10623261C412yescomplemented
13#10623225—22no—
14#10623176—22no—
15#10623155C2214yes—
16#10623116C412yescomplemented
17#10623115—22no—
18#10623101C412yescomplemented
19#10623057—21no—
20#10623054—21no—
21C2×#66940—21no—
22#10623008C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C11×#431C2211yescharacteristic
25C11×#382C2211yescharacteristic
26#10622586—21no—
27C4×C4⋊Dic11C2211yescharacteristic
28#10622538C2211yescharacteristic
29#10622444—22no—
30#10622332C2214yes—
31#10622292—22no—
32#10622263C2212yes—
33#10622262C2212yes—
34#10622260—22no—
35C11×#328C2214yes—
36#10622176C2212yes—
37#10622176C2212yes—
38#10622108C2212yes—
39#10622108C2212yes—
40#10622089C2214yes—
41C2×#4339—21no—
42C22×Dic22D411yescharacteristic
43C11×C4⋊Q8C2×C411yescharacteristic
44C11×C4⋊Q8C2×C411yescharacteristic
45C11×#125—21no—
46C11×C22⋊Q8—21no—
47C11×C22⋊Q8C2312yes—
48C4×Q8×C11—21no—
49C4×Q8×C11C2×C412yes—
50C11×#117—21no—
51C2×C11×C4⋊C4—21no—
52C2×C42×C11C2311yescharacteristic
53#67000C2×C414yes—
54#66999—24no—
55Q8×Dic11C2×C414yes—
56#66983—21no—
57#66983C2312yes—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11D411yescharacteristic
60C2×Dic11⋊C4—22no—
61C2×Dic11⋊C4—22no—
62C2×Dic11⋊C4D412yes—
63C2×C4×Dic11—21no—
64C2×C4×Dic11—22no—
65C2×C4×Dic11C2312yes—
66#66951—24no—
67#66951—24no—
68#66950—22no—
69#66950—22no—
70#66947—24no—
71#66946C2×C414yes—
72#66945—22no—
73#66945—24no—
74C4⋊C4×D11—22no—
75#66943—24no—
76#66943C2×C414yes—
77#66940—44no—
78#66939—24no—
79(C22⋊D11)⋊C4—24no—
80#66928—22no—
81#66928—21no—
82#66927C2×C411yescharacteristic
83C4×D44—21no—
84C4×D44—22no—
85C4×D44C2×C412yes—
86#66922—22no—
87#66922C2×C411yescharacteristic
88C4×Dic22—22no—
89C4×Dic22C2×C412yes—
90C4×Dic22C2×C412yes—
91C4×Dic22D412yes—
92C4×Dic22D412yes—
93C11×C4⋊C8—21no—
94C11×C22⋊C8C2312yes—
95C4×C8×C11—21no—
96C11×#95—21no—
97C11×#95C2312yes—
98C11⋊#95—22no—
99C11⋊#95C2311yescharacteristic
100C11⋊#95C2311yescharacteristic
101C22⋊(C11⋊C8)C2312yes—
102#66879—24no—
103Dic11⋊C8—24no—
104C4⋊(C11⋊C8)—21no—
105C4×C11⋊C8—21no—
106#17628—111nomaximal, Sylow
107C2×Q8×C11—21no—
108C2×Q8×C11C22×C412yes—
109C22×C4×C11—22no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2411yescharacteristic
113C2×C22⋊D11—22no—
114C22×Dic11—21no—
115C22×Dic11—21no—
116C22×Dic11C2×D412yes—
117C22×Dic11C2×D412yes—
118#4339—42no—
119#4339—42no—
120C2×D44—21no—
121C2×D44—21no—
122C2×D44C22×C412yes—
123C2×C4×D11—24no—
124C2×C4×D11—22no—
125C2×Dic22—21no—
126C2×Dic22—22no—
127C2×Dic22—22no—
128C2×Dic22C22⋊C412yes—
129C2×Dic22C22⋊C412yes—
130C2×C8×C11—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—42no—
137C11×C4⋊C4C22×C412yes—
138C11×C22⋊C4—22no—
139C42×C11—22no—
140C42×C11C22×C411yescharacteristic
141C42×C11C22×C411yescharacteristic
142C42×C11C2×D411yescharacteristic
143C42×C11C2×D411yescharacteristic
144(C2×D11)⋊C4—24no—
145(C2×D11)⋊C4—24no—
146(C2×D11)⋊C4—24no—
147(C2×D11)⋊C4—22no—
148(C2×D11)⋊C4—22no—
149C4⋊Dic11—24no—
150C4⋊Dic11—24no—
151C4⋊Dic11—21no—
152C4⋊Dic11—42no—
153C4⋊Dic11C22⋊C412yes—
154C4⋊Dic11C22⋊C412yes—
155C4⋊Dic11C22×C412yes—
156Dic11⋊C4—24no—
157Dic11⋊C4—44no—
158Dic11⋊C4—44no—
159Dic11⋊C4C22⋊C414yes—
160Dic11⋊C4C22⋊C414yes—
161C4×Dic11—24no—
162C4×Dic11—44no—
163C4×Dic11—42no—
164C4×Dic11C22×C414yes—
165C4×Dic11C2×D414yes—
166C2×C11⋊C8—22no—
167#3507—111no—
168#2983—111no—
169#2351—111no—
170#1518D1111yescharacteristic, complemented
171#1517—111no—
172#1512—114no—
173#1509—114no—
174#1503—111no—
175#1502—111no—
176C23×C11C22×D411yescharacteristic
177C22×D11—22no—
178Q8×C11—42no—
179Q8×C11—81no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11C2×C22⋊C411yescharacteristic
188C2×C4×C11C2×C22⋊C411yescharacteristic
189C2×C4×C11C2×C22⋊C411yescharacteristic
190C2×C4×C11C2×C22⋊C411yescharacteristic
191C2×C4×C11AGL(1,ℤ/8)12yes—
192C2×C4×C11#13712yes—
193C2×C4×C11C23×C411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C22⋊D11—42no—
196C22⋊D11—42no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—42no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11C2×C22⋊C414yes—
208C2×Dic11C2×C22⋊C414yes—
209D44—42no—
210D44—42no—
211D44—81no—
212C4×D11—44no—
213C4×D11—84no—
214Dic22—24no—
215Dic22—24no—
216Dic22—42no—
217C8×C11—42no—
218C11⋊C8—42no—
219#559—112no—
220#557—112no—
221#556—112no—
222#556—222no—
223#554—112no—
224#552—222no—
225#539—222no—
226#536—221no—
227#533C2×D1111yescharacteristic
228#532—111no—
229#529—114no—
230#520—221no—
231C2×C4×Q8—111no—
232C2×C4×Q8—221no—
233#446—222no—
234#446—222no—
235#432—114no—
236#431—111no—
237#431C2×D1111yescharacteristic
238#389—222no—
239#389—221no—
240#382—112no—
241#382C2×D1111yescharacteristic
242C4×C4⋊C4—111no—
243C4×C4⋊C4—112no—
244#328—112no—
245#328—112no—
246#328C2×D1114yes—
247#327—112no—
248#327—112no—
249#327—114no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11C22×C22⋊C411yescharacteristic
253C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
254C22×C11C2×#13711yescharacteristic
255C2×D11—42no—
256C2×D11—42no—
257C2×D11—42no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—42no—
263C4×C11—42no—
264C4×C11—82no—
265C4×C11#41712yes—
266C4×C11#41712yes—
267Dic11—24no—
268Dic11—24no—
269Dic11—42no—
270Dic11—42no—
271Dic11—81no—
272C2×#41—221no—
273C22×Q8—111no—
274C4⋊Q8—111no—
275C4⋊Q8—222no—
276C4⋊Q8C4×D1111yescharacteristic
277C4⋊Q8C4×D1111yescharacteristic
278#127—111no—
279#126—224no—
280#126—224no—
281#125—21no—
282#125—114no—
283#125—224no—
284#124—114no—
285#124—222no—
286#124—221no—
287#123—224no—
288#123—224no—
289C22⋊Q8—21no—
290C22⋊Q8—222no—
291C22⋊Q8—222no—
292C22⋊Q8—224no—
293C22⋊Q8C22×D1112yes—
294#121—112no—
295#121—221no—
296C4×Q8—21no—
297C4×Q8—112no—
298C4×Q8—112no—
299C4×Q8—112no—
300C4×Q8—112no—
301C4×Q8—114no—
302C4×Q8—222no—
303C4×Q8—444no—
304C4×Q8C4×D1112yes—
305C4×D4—114no—
306C4×D4—112no—
307C4×D4—222no—
308C4×D4—224no—
309C4×D4—221no—
310#117—21no—
311#117—224no—
312#117—222no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—111no—
315C2×C4⋊C4—112no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4—222no—
318C2×C4⋊C4—222no—
319C2×C4⋊C4—221no—
320C2×C42—112no—
321C2×C42—222no—
322C2×C42—221no—
323C2×C42C22×D1111yescharacteristic
324C4⋊C8—21no—
325C4⋊C8—224no—
326C4⋊C8—221no—
327C22⋊C8—112no—
328C22⋊C8C22×D1112yes—
329#97—224no—
330C4×C8—21no—
331C4×C8—221no—
332#95—21no—
333#95—111no—
334#95—111no—
335#95—222no—
336#95C22×D1112yes—
337C2×C11—21no—
338C2×C11—21no—
339C2×C11#288411yescharacteristic
340C2×C11C2×#41711yescharacteristic
341C2×C11#290111yescharacteristic
342D11—82no—
343#41—442no—
344#41—442no—
345C2×Q8—21no—
346C2×Q8—112no—
347C2×Q8—112no—
348C2×Q8—221no—
349C2×Q8—222no—
350C2×Q8—222no—
351C2×Q8C2×C4×D1112yes—
352C2×D4—112no—
353C2×D4—222no—
354C2×D4—221no—
355C2×D4—221no—
356C22×C4—22no—
357C22×C4—112no—
358C22×C4—112no—
359C22×C4—224no—
360C22×C4—221no—
361C22×C4—222no—
362C22×C4—221no—
363C22×C4D4×D1111yescharacteristic
364C22×C4D4×D1111yescharacteristic
365C22×C4C23×D1111yescharacteristic
366C2×C8—22no—
367C2×C8—222no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—42no—
374C4⋊C4—112no—
375C4⋊C4—112no—
376C4⋊C4—114no—
377C4⋊C4—114no—
378C4⋊C4—112no—
379C4⋊C4—224no—
380C4⋊C4—224no—
381C4⋊C4—224no—
382C4⋊C4—221no—
383C4⋊C4—444no—
384C4⋊C4—444no—
385C4⋊C4—442no—
386C4⋊C4C2×C4×D1112yes—
387C22⋊C4—22no—
388C22⋊C4—224no—
389C22⋊C4—224no—
390C22⋊C4—224no—
391C22⋊C4—222no—
392C22⋊C4—222no—
393C42—22no—
394C42—114no—
395C42—114no—
396C42—224no—
397C42—444no—
398C42—442no—
399C42C2×C4×D1111yescharacteristic
400C42C2×C4×D1111yescharacteristic
401C42D4×D1111yescharacteristic
402C42D4×D1111yescharacteristic
403C11#1762811yescharacteristic, complemented, Sylow
404C23—222no—
405C23C2×D4×D1111yescharacteristic
406Q8—42no—
407Q8—81no—
408Q8—224no—
409Q8—224no—
410Q8—442no—
411D4—442no—
412D4—442no—
413D4—442no—
414D4—442no—
415D4—881no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—114no—
424C2×C4—114no—
425C2×C4—222no—
426C2×C4—222no—
427C2×C4—222no—
428C2×C4—222no—
429C2×C4—442no—
430C2×C4—441no—
431C2×C4—441no—
432C2×C4—444no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—884no—
437C2×C4C22⋊C4×D1111yescharacteristic
438C2×C4C22⋊C4×D1111yescharacteristic
439C2×C4C22⋊C4×D1111yescharacteristic
440C2×C4C22⋊C4×D1111yescharacteristic
441C2×C4#6696712yes—
442C2×C4#6697112yes—
443C2×C4C22×C4×D1111yescharacteristic
444C2×C4C2×D4×D1111yescharacteristic
445C8—42no—
446C8—442no—
447C22—21no—
448C22—21no—
449C22—442no—
450C22—442no—
451C22—442no—
452C22C2×C22⋊C4×D1111yescharacteristic
453C22C2×#6696711yescharacteristic
454C22C2×#6697111yescharacteristic
455C4—21no—
456C4—21no—
457C4—21no—
458C4—21no—
459C4—42no—
460C4—42no—
461C4—82no—
462C4—224no—
463C4—224no—
464C4—442no—
465C4—442no—
466C4—881no—
467C4#1062241612yes—
468C4#1062241612yes—
469C2—21no—
470C2—21no—
471C2—882no—
472C2#1307707811yescharacteristic
473C2C2×#1062241611yescharacteristic
474C2#1307716211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1518C2
socleC22×C11C22×C22⋊C4
prime radical#10623008C22
cosocleC22×C4×C11C24
hypercenter#1518D11
hypocenterC11#17628
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
2. #13077699C2semidirect
3. #13071533C2semidirect
5. #13067153C2semidirect
6. #13067140C2semidirect
7. #13067115C2semidirect
9. C11×#1518C2semidirect
11. #10623263C4semidirect
12. #10623261C4semidirect
16. #10623116C4semidirect
18. #10623101C4semidirect
170. #1518D11semidirect
403. C11#17628semidirect

Maximal subgroups

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

subgroupindex
#130824832
#130776992
#130715332
#130671752
#130671532
#130671402
#130671152
#130671122
C11×#15182
#1762811