Finite Group Databasebeta

← #14721605

Subgroups — #14721605

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#13082478C211yesmaximal, characteristic
2#13077699C211yesmaximal, characteristic, complemented
3#13071536C211yesmaximal, characteristic, complemented
4#13067181C211yesmaximal, characteristic, complemented
5#13067176C211yesmaximal, characteristic
6#13067151C214yesmaximal, complemented
7#13067138C214yesmaximal, complemented
8#13067114C211yesmaximal, characteristic, complemented
9C11×#1502C211yesmaximal, characteristic
10C11×#532C2211yescharacteristic
11#10623358—21no—
12#10623356—21no—
13#10623252C412yescomplemented
14#10623244C412yescomplemented
15#10623202—22no—
16#10623133—22no—
17#10623131C2214yes—
18#10623074C412yescomplemented
19#10623073C412yescomplemented
20#10623072—22no—
21#10623001C2211yescharacteristic
22C2×C4×Dic22—21no—
23C2×C4×Dic22C2211yescharacteristic
24C11×#431C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26#10622585—22no—
27#10622549C2211yescharacteristic
28#10622541—21no—
29#10622538C2211yescharacteristic
30#10622444—22no—
31#10622332C2214yes—
32#10622292—22no—
33#10622263C2212yes—
34#10622262C2212yes—
35C11×#327C2212yes—
36C11×#327C2212yes—
37#10622175C2214yes—
38#10622105C2214yes—
39#10622090C2212yes—
40#10622090C2212yes—
41C2×C11×#41—21no—
42C22×Dic22D411yescharacteristic
43C11×C4⋊Q8C2×C411yescharacteristic
44C11×#127C2×C411yescharacteristic
45C11×#124—21no—
46C11×#121—21no—
47C11×#121C2312yes—
48C4×D4×C11—21no—
49C4×D4×C11C2×C412yes—
50C2×C11×C4⋊C4—21no—
51C2×C42×C11—21no—
52C2×C42×C11C2311yescharacteristic
53Q8×Dic11—22no—
54#66997—22no—
55#66989—22no—
56#66989C2×C414yes—
57#66988—24no—
58#66988—24no—
59D4×Dic11—24no—
60D4×Dic11—22no—
61D4×Dic11C2×C414yes—
62#66979—21no—
63#66979—22no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11D411yescharacteristic
67#66977—21no—
68#66977—22no—
69#66977—22no—
70#66977C2312yes—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4D412yes—
74C2×C4×Dic11—22no—
75C2×C4×Dic11C2312yes—
76#66943C2×C414yes—
77#66942—24no—
78#66940C2×C414yes—
79#66932—24no—
80#66932—24no—
81#66931—24no—
82#66930—24no—
83#66923—21no—
84#66922C2×C411yescharacteristic
85#66922C2×C411yescharacteristic
86C4×Dic22—21no—
87C4×Dic22—44no—
88C4×Dic22C2×C412yes—
89C4×Dic22C2×C412yes—
90C4×Dic22C2×C412yes—
91C4×Dic22D412yes—
92C4×Dic22D412yes—
93C11×C4⋊C8—21no—
94C11×C22⋊C8C2312yes—
95C4×C8×C11—21no—
96C11×#95C2311yescharacteristic
97C11×#95C2311yescharacteristic
98C11⋊#95—21no—
99C11⋊#95—22no—
100C11⋊#95C2312yes—
101C22⋊(C11⋊C8)C2312yes—
102#66879—24no—
103Dic11⋊C8—24no—
104C4⋊(C11⋊C8)—21no—
105C4×C11⋊C8—21no—
106#17628—111nomaximal, Sylow
107C11×#41—42no—
108C11×#41—42no—
109C2×Q8×C11—21no—
110C2×D4×C11—22no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11C22×C412yes—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2411yescharacteristic
120C22×Dic11—24no—
121C22×Dic11—22no—
122C22×Dic11C2×D412yes—
123C22×Dic11C2×D412yes—
124C2×Dic22—21no—
125C2×Dic22—22no—
126C2×Dic22—22no—
127C2×Dic22C22⋊C412yes—
128C2×Dic22C22⋊C412yes—
129C2×Dic22C22×C412yes—
130C2×C8×C11—22no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—42no—
133C11×C4⋊C4C22×C412yes—
134C11×C22⋊C4—22no—
135C11×C22⋊C4—22no—
136C42×C11—42no—
137C42×C11C22×C411yescharacteristic
138C42×C11C22×C411yescharacteristic
139C42×C11C2×D411yescharacteristic
140C42×C11C2×D411yescharacteristic
141C22⋊Dic11—24no—
142C22⋊Dic11—24no—
143C22⋊Dic11—24no—
144C22⋊Dic11—22no—
145C4⋊Dic11—24no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—42no—
150C4⋊Dic11C22⋊C412yes—
151C4⋊Dic11C22⋊C412yes—
152C4⋊Dic11C22×C412yes—
153Dic11⋊C4—24no—
154Dic11⋊C4—24no—
155Dic11⋊C4—22no—
156Dic11⋊C4—22no—
157Dic11⋊C4—44no—
158Dic11⋊C4—44no—
159Dic11⋊C4C22⋊C414yes—
160Dic11⋊C4C22⋊C414yes—
161C4×Dic11—24no—
162C4×Dic11—22no—
163C4×Dic11—44no—
164C4×Dic11C22×C414yes—
165C4×Dic11C2×D414yes—
166C2×C11⋊C8—22no—
167#3507—111no—
168#2983—111no—
169#2351—111no—
170#1518—111no—
171#1517—111no—
172#1512—114no—
173#1509—114no—
174#1503—111no—
175#1502D1111yescharacteristic
176C23×C11—22no—
177C23×C11C22×D411yescharacteristic
178Q8×C11—42no—
179D4×C11—42no—
180D4×C11—42no—
181D4×C11—42no—
182D4×C11—42no—
183D4×C11—81no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—44no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11C2×C22⋊C411yescharacteristic
195C2×C4×C11C2×C22⋊C411yescharacteristic
196C2×C4×C11C2×C22⋊C411yescharacteristic
197C2×C4×C11C2×C22⋊C411yescharacteristic
198C2×C4×C11AGL(1,ℤ/8)12yes—
199C2×C4×C11#13712yes—
200C2×C4×C11C23×C411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—84no—
211C2×Dic11C2×C22⋊C414yes—
212C2×Dic11C2×C22⋊C414yes—
213Dic22—24no—
214Dic22—24no—
215Dic22—42no—
216Dic22—81no—
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#533—111no—
228#532C2×D1111yescharacteristic
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—221no—
239#389—222no—
240#382—111no—
241#382—112no—
242C4×C4⋊C4—112no—
243C4×C4⋊C4C2×D1111yescharacteristic
244#328—114no—
245#328—112no—
246#328—112no—
247#327—114no—
248#327C2×D1112yes—
249#327C2×D1112yes—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—42no—
253C22×C11—42no—
254C22×C11—42no—
255C22×C11C22×C22⋊C411yescharacteristic
256C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
257C22×C11C2×#13711yescharacteristic
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—42no—
263C4×C11—42no—
264C4×C11—81no—
265C4×C11#41712yes—
266C4×C11#41712yes—
267Dic11—24no—
268Dic11—24no—
269Dic11—42no—
270Dic11—42no—
271Dic11—82no—
272C2×#41—21no—
273C22×Q8—111no—
274C4⋊Q8—111no—
275C4⋊Q8—111no—
276C4⋊Q8—222no—
277C4⋊Q8C4×D1111yescharacteristic
278#127C4×D1111yescharacteristic
279#126—224no—
280#126—224no—
281#125—114no—
282#125—224no—
283#125—221no—
284#124—21no—
285#124—114no—
286#124—222no—
287#123—224no—
288#123—224no—
289C22⋊Q8—112no—
290C22⋊Q8—224no—
291C22⋊Q8—222no—
292C22⋊Q8—222no—
293C22⋊Q8—221no—
294#121—21no—
295#121C22×D1112yes—
296C4×Q8—112no—
297C4×Q8—112no—
298C4×Q8—112no—
299C4×Q8—112no—
300C4×Q8—114no—
301C4×Q8—112no—
302C4×Q8—222no—
303C4×Q8—221no—
304C4×Q8—444no—
305C4×D4—21no—
306C4×D4—114no—
307C4×D4—222no—
308C4×D4—224no—
309C4×D4C4×D1112yes—
310#117—224no—
311#117—222no—
312#117—221no—
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—21no—
321C2×C42—112no—
322C2×C42—222no—
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—112no—
333#95—222no—
334#95—221no—
335#95C22×D1111yescharacteristic
336#95C22×D1111yescharacteristic
337C2×C11—21no—
338C2×C11—21no—
339C2×C11—82no—
340C2×C11#288411yescharacteristic
341C2×C11C2×#41711yescharacteristic
342C2×C11#290111yescharacteristic
343#41—42no—
344#41—42no—
345C2×Q8—21no—
346C2×Q8—112no—
347C2×Q8—112no—
348C2×Q8—112no—
349C2×Q8—221no—
350C2×Q8—222no—
351C2×Q8—222no—
352C2×D4—22no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4C2×C4×D1112yes—
356C22×C4—21no—
357C22×C4—22no—
358C22×C4—21no—
359C22×C4—112no—
360C22×C4—112no—
361C22×C4—224no—
362C22×C4—222no—
363C22×C4D4×D1111yescharacteristic
364C22×C4D4×D1111yescharacteristic
365C22×C4C23×D1111yescharacteristic
366C2×C8—22no—
367C2×C8—222no—
368C4⋊C4—21no—
369C4⋊C4—42no—
370C4⋊C4—112no—
371C4⋊C4—112no—
372C4⋊C4—114no—
373C4⋊C4—114no—
374C4⋊C4—112no—
375C4⋊C4—224no—
376C4⋊C4—224no—
377C4⋊C4—224no—
378C4⋊C4—221no—
379C4⋊C4—221no—
380C4⋊C4—222no—
381C4⋊C4—221no—
382C4⋊C4—222no—
383C4⋊C4—444no—
384C4⋊C4—444no—
385C4⋊C4—442no—
386C4⋊C4C2×C4×D1112yes—
387C22⋊C4—22no—
388C22⋊C4—22no—
389C22⋊C4—224no—
390C22⋊C4—224no—
391C22⋊C4—224no—
392C22⋊C4—222no—
393C42—42no—
394C42—114no—
395C42—114no—
396C42—224no—
397C42—222no—
398C42—444no—
399C42C2×C4×D1111yescharacteristic
400C42C2×C4×D1111yescharacteristic
401C42D4×D1111yescharacteristic
402C42D4×D1111yescharacteristic
403C11#1762811yescharacteristic, complemented, Sylow
404C23—22no—
405C23C2×D4×D1111yescharacteristic
406Q8—42no—
407Q8—224no—
408Q8—224no—
409Q8—442no—
410Q8—881no—
411D4—42no—
412D4—42no—
413D4—42no—
414D4—42no—
415D4—81no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—44no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—114no—
427C2×C4—114no—
428C2×C4—222no—
429C2×C4—222no—
430C2×C4—222no—
431C2×C4—222no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4—884no—
437C2×C4C22⋊C4×D1111yescharacteristic
438C2×C4C22⋊C4×D1111yescharacteristic
439C2×C4C22⋊C4×D1111yescharacteristic
440C2×C4C22⋊C4×D1111yescharacteristic
441C2×C4#6696412yes—
442C2×C4#6696812yes—
443C2×C4C22×C4×D1111yescharacteristic
444C2×C4C2×D4×D1111yescharacteristic
445C8—42no—
446C8—442no—
447C22—21no—
448C22—21no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22C2×C22⋊C4×D1111yescharacteristic
453C22C2×#6696411yescharacteristic
454C22C2×#6696811yescharacteristic
455C4—21no—
456C4—21no—
457C4—21no—
458C4—21no—
459C4—42no—
460C4—42no—
461C4—81no—
462C4—224no—
463C4—224no—
464C4—442no—
465C4—442no—
466C4—882no—
467C4#1062238412yes—
468C4#1062238412yes—
469C2—21no—
470C2—21no—
471C2—82no—
472C2#1307707811yescharacteristic
473C2C2×#1062238411yescharacteristic
474C2#1307716011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1502C2
socleC22×C11C22×C22⋊C4
prime radicalC11×#532C22
cosocleC22×C4×C11C24
hypercenter#1502D11
hypocenterC11#17628
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1502

Complements

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

NH ≅ G/Ntype
2. #13077699C2semidirect
3. #13071536C2semidirect
4. #13067181C2semidirect
6. #13067151C2semidirect
7. #13067138C2semidirect
8. #13067114C2semidirect
13. #10623252C4semidirect
14. #10623244C4semidirect
18. #10623074C4semidirect
19. #10623073C4semidirect
403. C11#17628semidirect

Maximal subgroups

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

subgroupindex
#130824782
#130776992
#130715362
#130671812
#130671762
#130671512
#130671382
#130671142
C11×#15022
#1762811