Finite Group Databasebeta

← #14722700

Subgroups — #14722700

Order 2816.

868 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082503C211yesmaximal, characteristic
2#13077746C211yesmaximal, characteristic
3#13077742C211yesmaximal, characteristic
4#13067345C212yesmaximal, complemented
5#13067323C212yesmaximal, complemented
6#13067305C212yesmaximal, complemented
7#13067298C211yesmaximal, characteristic, complemented
8#13067298C211yesmaximal, characteristic, complemented
9#13067281C211yesmaximal, characteristic, complemented
10#13067272C212yesmaximal, complemented
11C11×#1561C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13#10623259C2212yes—
14#10623259C2212yes—
15#10623228C414yes—
16#10623173—22no—
17#10623173—22no—
18#10623115—21no—
19#10623115—21no—
20#10623101—21no—
21#10623101—21no—
22#10623057C412yes—
23#10623047C412yes—
24C4×#4339C2211yescharacteristic
25C2×#66922C2211yescharacteristic
26C11×#423C2211yescharacteristic
27C11×#423C2211yescharacteristic
28#10622741—22no—
29#10622740—22no—
30#10622538C2211yescharacteristic
31#10622538C2211yescharacteristic
32#10622451—21no—
33#10622450C2212yes—
34#10622448C2212yes—
35#10622447—21no—
36#10622446C2212yes—
37D11×C4⋊C8C2212yes—
38#10622444—21no—
39#10622443—21no—
40C11×#332C2212yes—
41C11×#332C2212yes—
42#10622185C2211yescharacteristic
43#10622185C2211yescharacteristic
44#10622185C2211yescharacteristic
45#10622185C2211yescharacteristic
46#10622119C2212yes—
47#10622119C2212yes—
48#10622119C2212yes—
49#10622119C2212yes—
50C2×#4339C2×C411yescharacteristic
51C22×Dic22C2×C412yes—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C11×C4⋊Q8C2311yescharacteristic
55C11×C4⋊Q8C2311yescharacteristic
56C11×#125C2×C412yes—
57C11×C22⋊Q8—21no—
58C11×C22⋊Q8—21no—
59C4×Q8×C11—21no—
60C4×Q8×C11—21no—
61C11×#117C2×C412yes—
62C2×C42×C11C2311yescharacteristic
63#66999—22no—
64#66999—22no—
65Q8×Dic11—22no—
66Q8×Dic11—22no—
67C4×C22⋊D11D412yes—
68C4×C22⋊D11D412yes—
69#66979C2×C411yescharacteristic
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—21no—
72C2×#4313—22no—
73C2×C8×D11—22no—
74#66951—24no—
75#66951—24no—
76#66950C2×C414yes—
77#66950C2×C414yes—
78#66945—22no—
79#66945—22no—
80#66943—24no—
81#66943—24no—
82#66943—22no—
83#66943—22no—
84#66940C2×C414yes—
85#66940C2×C414yes—
86#66939—24no—
87#66930—24no—
88#66928—22no—
89C4×D44D411yescharacteristic
90C4×D44D411yescharacteristic
91#66925C2×C412yes—
92C42×D11C2312yes—
93#66922—22no—
94#66922—21no—
95#66922—21no—
96#66922C2×C412yes—
97#66922C2312yes—
98C4×Dic22—22no—
99C4×Dic22—22no—
100C4×Dic22D411yescharacteristic
101C4×Dic22D411yescharacteristic
102C11×C4⋊C8—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8C2312yes—
105C11×C4⋊C8C2312yes—
106C22⋊(C11⋊C8)—21no—
107C22⋊(C11⋊C8)—21no—
108(C2×D11)⋊C8—22no—
109(C2×D11)⋊C8—22no—
110#66879—22no—
111Dic11⋊C8—22no—
112Dic11⋊C8—22no—
113C8×Dic11—22no—
114C4⋊(C11⋊C8)C2311yescharacteristic
115C4⋊(C11⋊C8)C2311yescharacteristic
116C4⋊(C11⋊C8)C2311yescharacteristic
117C4⋊(C11⋊C8)C2311yescharacteristic
118C4×C11⋊C8—21no—
119C4×C11⋊C8—21no—
120#17778—111nomaximal, Sylow
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C2×C22⋊D11C22⋊C412yes—
127C22×Dic11—22no—
128#4339—42no—
129C2×D44C22⋊C411yescharacteristic
130C2×C4×D11C22×C412yes—
131C2×C4×D11C2×D412yes—
132C2×C4×D11C2×D412yes—
133C2×Dic22—22no—
134C2×Dic22—44no—
135C2×Dic22C22⋊C411yescharacteristic
136C2×Dic22C22×C414yes—
137C11×M16—81no—
138C11×M16—81no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4C22×C412yes—
146C11×C4⋊C4C22×C412yes—
147C11×C22⋊C4—22no—
148C42×C11—22no—
149C42×C11C22×C411yescharacteristic
150C42×C11C2×D411yescharacteristic
151C42×C11C2×D411yescharacteristic
152C42×C11C2411yescharacteristic
153C22⋊Dic11C22⋊C412yes—
154(C2×D11)⋊C4—24no—
155(C2×D11)⋊C4—24no—
156(C2×D11)⋊C4C22⋊C412yes—
157(C2×D11)⋊C4C22⋊C412yes—
158C4⋊Dic11—24no—
159C4⋊Dic11—24no—
160C4⋊Dic11—22no—
161C4⋊Dic11—22no—
162C4⋊Dic11—22no—
163C4⋊Dic11—22no—
164C4⋊Dic11C22⋊C411yescharacteristic
165C4⋊Dic11C22⋊C411yescharacteristic
166Dic11⋊C4—24no—
167Dic11⋊C4—24no—
168Dic11⋊C4C22⋊C412yes—
169Dic11⋊C4C22⋊C412yes—
170C4×Dic11—24no—
171C4×Dic11—24no—
172C4×Dic11C22×C412yes—
173C4×Dic11C2×D412yes—
174C4×Dic11C2×D412yes—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—21no—
179#4313—82no—
180C8×D11—82no—
181#3509—111no—
182#2991—111no—
183#2990—111no—
184#1561D1111yescharacteristic, complemented
185#1559—112no—
186#1554—112no—
187#1550—112no—
188#1548—111no—
189#1548—111no—
190#1544—111no—
191#1542—112no—
192C23×C11C2×C22⋊C411yescharacteristic
193C22×D11C2×C22⋊C412yes—
194Q8×C11—41no—
195Q8×C11—41no—
196Q8×C11—41no—
197Q8×C11—41no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11C2×C22⋊C411yescharacteristic
206C2×C4×C11C2×C22⋊C411yescharacteristic
207C2×C4×C11C2×C22⋊C411yescharacteristic
208C2×C4×C11C23×C411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C22⋊D11—42no—
212C2×Dic11—24no—
213C2×Dic11—44no—
214C2×Dic11C2×C22⋊C412yes—
215C2×Dic11C2×C22⋊C412yes—
216C2×Dic11C2×C22⋊C412yes—
217D44—22no—
218C4×D11—22no—
219C4×D11—22no—
220C4×D11—22no—
221C4×D11—22no—
222C4×D11—42no—
223Dic22—22no—
224Dic22—44no—
225Dic22—44no—
226C8×C11—42no—
227C8×C11—42no—
228C11⋊C8—41no—
229C11⋊C8—41no—
230C11⋊C8—41no—
231C11⋊C8—41no—
232#557—221no—
233#557—221no—
234#556—221no—
235#556—221no—
236#552—222no—
237#552—222no—
238#541—114no—
239#536—112no—
240#533—112no—
241#533—112no—
242#533C2×D1111yescharacteristic
243C2×C4⋊Q8—111no—
244#519—112no—
245C4×#41—111no—
246#446—221no—
247C8×Q8—221no—
248#436—221no—
249#436—222no—
250#435—222no—
251C8×D4—221no—
252#432—112no—
253#431—111no—
254#431—111no—
255#431—112no—
256#423—112no—
257#423C2×D1111yescharacteristic
258#423C2×D1111yescharacteristic
259C2×C4⋊C8—112no—
260#333—112no—
261#333—112no—
262#333—112no—
263#333—112no—
264#332—111no—
265#332—111no—
266#332—111no—
267#332—111no—
268#332C2×D1112yes—
269#332C2×D1112yes—
270C22×C11—21no—
271C22×C11—21no—
272C22×C11—21no—
273C22×C11C22×C22⋊C411yescharacteristic
274C2×D11—22no—
275C2×D11—22no—
276C2×D11—22no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11#41312yes—
283C4×C11#57711yescharacteristic
284C4×C11#57711yescharacteristic
285C4×C11#57811yescharacteristic
286C4×C11#57811yescharacteristic
287Dic11—22no—
288Dic11—22no—
289Dic11—22no—
290Dic11—44no—
291C2×#41—111no—
292C22×Q8—112no—
293C2×M16—21no—
294C2×M16—21no—
295C2×M16—222no—
296C22×C8—222no—
297C4⋊Q8—112no—
298C4⋊Q8—112no—
299C4⋊Q8—222no—
300C4⋊Q8—221no—
301C4⋊Q8—221no—
302C4⋊Q8C22×D1111yescharacteristic
303C4⋊Q8C22×D1111yescharacteristic
304#126—224no—
305#126—224no—
306#125—222no—
307#125—222no—
308#125—224no—
309#125—224no—
310#125C4×D1112yes—
311#124—222no—
312#123—224no—
313C22⋊Q8—21no—
314C22⋊Q8—21no—
315C22⋊Q8—114no—
316C22⋊Q8—114no—
317C22⋊Q8—222no—
318C22⋊Q8—222no—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×Q8—111no—
322C4×Q8—111no—
323C4×Q8—114no—
324C4×Q8—114no—
325C4×Q8—222no—
326C4×Q8—222no—
327C4×Q8—222no—
328C4×Q8—222no—
329C4×D4—112no—
330C4×D4—112no—
331C4×D4—111no—
332C4×D4—111no—
333#117—111no—
334#117—112no—
335#117—224no—
336#117—222no—
337#117—222no—
338#117C4×D1112yes—
339C2×C4⋊C4—221no—
340C2×C4⋊C4—221no—
341C2×C42—112no—
342C2×C42C22×D1111yescharacteristic
343C4⋊C8—21no—
344C4⋊C8—21no—
345C4⋊C8—111no—
346C4⋊C8—111no—
347C4⋊C8—111no—
348C4⋊C8—111no—
349C4⋊C8—222no—
350C4⋊C8—222no—
351C4⋊C8C22×D1112yes—
352C4⋊C8C22×D1112yes—
353C22⋊C8—222no—
354C22⋊C8—222no—
355C22⋊C8—221no—
356C22⋊C8—221no—
357#97—222no—
358C4×C8—222no—
359C4×C8—221no—
360C4×C8—221no—
361C2×C11—41no—
362C2×C11C2×#41311yescharacteristic
363C2×C11#289811yescharacteristic
364C2×C11#289811yescharacteristic
365D11—42no—
366#41—442no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—111no—
370C2×Q8—114no—
371C2×Q8—222no—
372C2×Q8—444no—
373C2×D4—112no—
374C2×D4—111no—
375C22×C4—112no—
376C22×C4—112no—
377C22×C4—112no—
378C22×C4—222no—
379C22×C4C2×C4×D1111yescharacteristic
380C22×C4D4×D1111yescharacteristic
381C22×C4D4×D1111yescharacteristic
382M16—81no—
383M16—81no—
384M16—882no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—221no—
388C2×C8—221no—
389C2×C8—221no—
390C2×C8—221no—
391C2×C8—882no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—111no—
397C4⋊C4—111no—
398C4⋊C4—112no—
399C4⋊C4—112no—
400C4⋊C4—224no—
401C4⋊C4—224no—
402C4⋊C4—224no—
403C4⋊C4—224no—
404C4⋊C4—222no—
405C4⋊C4—222no—
406C4⋊C4—222no—
407C4⋊C4—222no—
408C4⋊C4C2×C4×D1112yes—
409C4⋊C4C2×C4×D1112yes—
410C22⋊C4—22no—
411C22⋊C4—112no—
412C22⋊C4—112no—
413C22⋊C4—112no—
414C22⋊C4—224no—
415C22⋊C4—224no—
416C42—22no—
417C42—112no—
418C42—112no—
419C42—112no—
420C42—224no—
421C42—224no—
422C42C2×C4×D1111yescharacteristic
423C42D4×D1111yescharacteristic
424C42D4×D1111yescharacteristic
425C42C23×D1111yescharacteristic
426C11#1777811yescharacteristic, complemented, Sylow
427C23—112no—
428C23C22⋊C4×D1111yescharacteristic
429Q8—41no—
430Q8—41no—
431Q8—41no—
432Q8—41no—
433Q8—222no—
434Q8—444no—
435Q8—444no—
436D4—222no—
437D4—442no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—112no—
446C2×C4—112no—
447C2×C4—112no—
448C2×C4—222no—
449C2×C4—222no—
450C2×C4—222no—
451C2×C4—222no—
452C2×C4—224no—
453C2×C4—442no—
454C2×C4—444no—
455C2×C4C22⋊C4×D1111yescharacteristic
456C2×C4C22⋊C4×D1111yescharacteristic
457C2×C4C22⋊C4×D1111yescharacteristic
458C2×C4C22×C4×D1111yescharacteristic
459C2×C4C2×D4×D1111yescharacteristic
460C2×C4C2×D4×D1111yescharacteristic
461C8—42no—
462C8—42no—
463C8—441no—
464C8—441no—
465C8—441no—
466C8—441no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—222no—
471C22—222no—
472C22—222no—
473C22C2×C22⋊C4×D1111yescharacteristic
474C4—21no—
475C4—21no—
476C4—21no—
477C4—42no—
478C4—42no—
479C4—222no—
480C4—222no—
481C4—222no—
482C4—444no—
483C4#1062236412yes—
484C4#1062330611yescharacteristic
485C4#1062330611yescharacteristic
486C4#1062331011yescharacteristic
487C4#1062331011yescharacteristic
488C2—41no—
489C2—442no—
490C2C2×#1062236411yescharacteristic
491C2#1307714711yescharacteristic
492C2#1307714711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1561C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#4339C2×C4
cosocleC42×C11C24
hypercenter#1561D11
hypocenterC11#17778
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1561

Complements

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

NH ≅ G/Ntype
4. #13067345C2semidirect
5. #13067323C2semidirect
6. #13067305C2semidirect
7. #13067298C2semidirect
8. #13067298C2semidirect
9. #13067281C2semidirect
10. #13067272C2semidirect
11. C11×#1561C2semidirect
184. #1561D11semidirect
426. C11#17778semidirect

Maximal subgroups

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

subgroupindex
#130825032
#130777462
#130777422
#130673452
#130673232
#130673052
#130672982
#130672812
#130672722
C11×#15612
#1777811