Finite Group Databasebeta

← #14650239

Subgroups — #14650239

Order 2816.

750 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
1C2×#10622840C211yesmaximal, characteristic
2Q8×C22⋊Dic11C211yesmaximal, characteristic, complemented
3#13069451C211yesmaximal, characteristic
4#13067185C211yesmaximal, characteristic
5#13066483C211yesmaximal, characteristic, complemented
6#13066462C211yesmaximal, characteristic, complemented
7C11×#1787C211yesmaximal, characteristic, complemented
8C23×Q8×C11C2211yescharacteristic
9C2×Q8×Dic11—21no—
10C22×#4325C412yescomplemented
11C2×#66983C2211yescharacteristic
12C2×C11×#103—22no—
13C2×C11×C22⋊C8C2211yescharacteristic
14C11×#380C2211yescharacteristic
15#10622843—21no—
16#10622843—22no—
17#10622840—21no—
18#10622840—21no—
19#10622840—22no—
20C2×#66899C412yescomplemented
21#10622825—21no—
22#10622825C2211yescharacteristic
23C4×C22⋊Dic11—21no—
24C4×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×#66870—21no—
27C2×#66870—21no—
28#10622108—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11—21no—
31C22×Q8×C11—21no—
32C22×Q8×C11—44no—
33C22×Q8×C11C2×C412yes—
34C22×Q8×C11D411yescharacteristic
35C22×Q8×C11D411yescharacteristic
36C22×Q8×C11D412yes—
37C23×C4×C11—21no—
38C23×C4×C11C2311yescharacteristic
39C22×C22⋊D11—21no—
40C22×D44C2×C411yescharacteristic
41C22×C8×C11—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C22⋊Dic11—21no—
45C2×C22⋊Dic11D411yescharacteristic
46C2×C22⋊Dic11D411yescharacteristic
47Q8×Dic11—44no—
48C2×#4325—22no—
49C2×#4325—22no—
50C2×#4325—44no—
51#66983—21no—
52#66983—21no—
53#66983—21no—
54#66983—21no—
55C2×(C2×D11)⋊C4—21no—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11C2×C411yescharacteristic
59C2×C4×Dic11—22no—
60C2×C4×Dic11—21no—
61C22×C11⋊C8C2×C412yes—
62C11×#103—44no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8—21no—
65C11×#95—21no—
66#66899—22no—
67#66899—22no—
68C11⋊#95—22no—
69C11⋊#95—22no—
70C11⋊#95—21no—
71C11⋊#95D412yes—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74#66870—42no—
75#66870—42no—
76#9262—111nomaximal, Sylow
77C24×C11C2×D411yescharacteristic
78C23×D11—21no—
79C2×Q8×C11—24no—
80C2×Q8×C11—22no—
81C2×Q8×C11—22no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—24no—
85C2×Q8×C11—24no—
86C2×Q8×C11—42no—
87C2×Q8×C11—42no—
88C2×Q8×C11—42no—
89C2×Q8×C11—44no—
90C2×Q8×C11—44no—
91C2×Q8×C11—44no—
92C2×Q8×C11C22⋊C412yes—
93C2×Q8×C11C22⋊C412yes—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—42no—
99C22×C4×C11—44no—
100C22×C4×C11—41no—
101C22×C4×C11C22×C411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11#4111yescharacteristic
106C22×C4×C11#4111yescharacteristic
107C2×C22⋊D11—41no—
108C2×C22⋊D11—41no—
109C2×C22⋊D11—41no—
110C2×C22⋊D11—41no—
111C2×C22⋊D11—41no—
112C2×C22⋊D11—41no—
113C22×Dic11—21no—
114C22×Dic11—21no—
115C22×Dic11—21no—
116C22×Dic11—22no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44—42no—
120C2×C8×C11—42no—
121C2×C8×C11—41no—
122C11×C4⋊C4—42no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C22⋊Dic11—21no—
126C22⋊Dic11—21no—
127C22⋊Dic11—21no—
128C22⋊Dic11—41no—
129C22⋊Dic11—41no—
130C22⋊Dic11SD1612yescomplemented
131#4325—44no—
132#4325—44no—
133(C2×D11)⋊C4—41no—
134(C2×D11)⋊C4—41no—
135C4⋊Dic11—21no—
136C4⋊Dic11—21no—
137C4⋊Dic11—44no—
138C4⋊Dic11—42no—
139C4×Dic11—44no—
140C4×Dic11—42no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—42no—
143C2×#448—111no—
144Q8×C22⋊C4—111no—
145#1964—111no—
146#1787D1111yescharacteristic, complemented
147#1519—111no—
148#1289—111no—
149#1282—111no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11C4×D411yescharacteristic
153C23×C11#12011yescharacteristic
154C23×C11#12111yescharacteristic
155C23×C11C2×SD1611yescharacteristic
156C23×C11#13511yescharacteristic
157C23×C11AGL(1,ℤ/8)11yescharacteristic
158C23×C11#13711yescharacteristic
159C22×D11—41no—
160C22×D11—41no—
161C22×D11—41no—
162C22×D11—81no—
163C22×D11—81no—
164Q8×C11—24no—
165Q8×C11—22no—
166Q8×C11—22no—
167Q8×C11—22no—
168Q8×C11—44no—
169Q8×C11—44no—
170Q8×C11—42no—
171Q8×C11#9914yescomplemented
172C2×C4×C11—24no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—44no—
182C2×C4×C11—44no—
183C2×C4×C11—42no—
184C2×C4×C11—81no—
185C2×C4×C11—81no—
186C2×C4×C11—81no—
187C2×C4×C11C2×C22⋊C411yescharacteristic
188C2×C4×C11C4×D411yescharacteristic
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11#12311yescharacteristic
191C22⋊D11—81no—
192C22⋊D11—81no—
193C22⋊D11—81no—
194C22⋊D11—81no—
195C2×Dic11—22no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—42no—
200C2×Dic11—41no—
201C2×Dic11—42no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—42no—
207D44—42no—
208D44—81no—
209C8×C11—81no—
210C11⋊C8—42no—
211C23×Q8C2×D1111yescharacteristic
212C22×SD16—112no—
213C2×#121—111no—
214C2×C4×Q8—221no—
215#448—221no—
216#448—221no—
217#448—222no—
218C2×#103—22no—
219C2×#103—112no—
220C2×#99—221no—
221C2×#99—221no—
222C2×C22⋊C8—111no—
223C2×C22⋊C8C2×D1111yescharacteristic
224#391—222no—
225#391—221no—
226#380—111no—
227#380—221no—
228#380C2×D1111yescharacteristic
229C4×C22⋊C4—111no—
230C4×C22⋊C4—221no—
231#327—222no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11—41no—
241C22×C11—41no—
242C22×C11#38611yescharacteristic
243C22×C11C4×SD1611yescharacteristic
244C22×C11#44011yescharacteristic
245C22×C11#44811yescharacteristic
246C22×C11#44911yescharacteristic
247C22×C11#46011yescharacteristic
248C22×C11#46411yescharacteristic
249C2×D11—81no—
250C2×D11—81no—
251C2×D11—81no—
252C2×D11—161no—
253C2×D11—161no—
254C4×C11—24no—
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—21no—
258C4×C11—42no—
259C4×C11—161no—
260C4×C11C2×#9912yes—
261Dic11—42no—
262Dic11—81no—
263Dic11—82no—
264Dic11—81no—
265C22×Q8—21no—
266C22×Q8—21no—
267C22×Q8—21no—
268C22×Q8—44no—
269C22×Q8C4×D1112yes—
270C22×Q8D4411yescharacteristic
271C22×Q8D4411yescharacteristic
272C22×Q8C22⋊D1112yes—
273C22×D4—111no—
274C22×D4—221no—
275C23×C4—21no—
276C23×C4C22×D1111yescharacteristic
277C2×SD16—222no—
278C2×SD16—222no—
279C2×SD16—444no—
280C22×C8—21no—
281C22×C8—112no—
282#121—221no—
283#121—221no—
284#121—221no—
285#121—221no—
286C4×Q8—444no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—222no—
290C2×C4⋊C4—221no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—111no—
293C2×C22⋊C4—111no—
294C2×C22⋊C4—221no—
295C2×C22⋊C4—221no—
296C2×C42—222no—
297C2×C42—221no—
298#103—44no—
299#103—222no—
300#103—222no—
301#99—442no—
302#99—442no—
303C22⋊C8—21no—
304C22⋊C8—21no—
305C22⋊C8—221no—
306C22⋊C8—221no—
307#95—21no—
308#95—112no—
309#95—222no—
310#95—222no—
311#95—221no—
312C2×C11—21no—
313C2×C11—21no—
314C2×C11—21no—
315C2×C11—21no—
316C2×C11—21no—
317C2×C11—21no—
318C2×C11#188011yescharacteristic
319C2×C11#189811yescharacteristic
320C2×C11#190511yescharacteristic
321D11—161no—
322C24—221no—
323C24D4×D1111yescharacteristic
324C2×Q8—24no—
325C2×Q8—22no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8—22no—
329C2×Q8—24no—
330C2×Q8—24no—
331C2×Q8—42no—
332C2×Q8—42no—
333C2×Q8—42no—
334C2×Q8—44no—
335C2×Q8—44no—
336C2×Q8—44no—
337C2×Q8(C2×D11)⋊C412yes—
338C2×Q8(C2×D11)⋊C412yes—
339C2×D4—221no—
340C2×D4—221no—
341C2×D4—442no—
342C2×D4—441no—
343C2×D4—441no—
344C2×D4—441no—
345C2×D4—441no—
346C2×D4—441no—
347C2×D4—441no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—42no—
353C22×C4—44no—
354C22×C4—41no—
355C22×C4—221no—
356C22×C4—221no—
357C22×C4—222no—
358C22×C4—221no—
359C22×C4C2×C4×D1111yescharacteristic
360C22×C4C2×D4411yescharacteristic
361C22×C4D4×D1111yescharacteristic
362C22×C4#434111yescharacteristic
363C22×C4#434111yescharacteristic
364C22×C4C2×C22⋊D1111yescharacteristic
365SD16—444no—
366SD16—444no—
367C2×C8—42no—
368C2×C8—41no—
369C2×C8—222no—
370C2×C8—442no—
371C4⋊C4—42no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4—444no—
375C4⋊C4—442no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—112no—
379C22⋊C4—221no—
380C22⋊C4—221no—
381C22⋊C4—221no—
382C22⋊C4—441no—
383C22⋊C4—441no—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C42—444no—
387C42—442no—
388C11#926211yescharacteristic, complemented, Sylow
389C23—41no—
390C23—41no—
391C23—441no—
392C23—441no—
393C23—441no—
394C23—881no—
395C23—881no—
396C23(C22⋊D11)⋊C411yescharacteristic
397C23#6693511yescharacteristic
398C23SD16×D1111yescharacteristic
399C23#6696711yescharacteristic
400C23#6697111yescharacteristic
401C23#6697211yescharacteristic
402C23#6699211yescharacteristic
403Q8—24no—
404Q8—22no—
405Q8—22no—
406Q8—22no—
407Q8—44no—
408Q8—44no—
409Q8—42no—
410Q8#6687014yescomplemented
411D4—442no—
412D4—881no—
413D4—881no—
414D4—881no—
415D4—881no—
416D4—881no—
417C2×C4—24no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—44no—
427C2×C4—44no—
428C2×C4—42no—
429C2×C4—81no—
430C2×C4—81no—
431C2×C4—81no—
432C2×C4—222no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—442no—
436C2×C4—441no—
437C2×C4—442no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—442no—
443C2×C4—441no—
444C2×C4(C22⋊D11)⋊C411yescharacteristic
445C2×C4#6693911yescharacteristic
446C2×C4C2×(C2×D11)⋊C411yescharacteristic
447C2×C4#6699211yescharacteristic
448C8—81no—
449C8—442no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—881no—
461C22—881no—
462C22—881no—
463C22—1761no—
464C22—1761no—
465C22#1062240111yescharacteristic
466C22#1062241911yescharacteristic
467C22#1062242411yescharacteristic
468C22#1062243011yescharacteristic
469C22#1062257111yescharacteristic
470C22#1062277611yescharacteristic
471C22#1062279811yescharacteristic
472C4—21no—
473C4—24no—
474C4—21no—
475C4—21no—
476C4—42no—
477C4—161no—
478C4—442no—
479C4—881no—
480C4—882no—
481C4—881no—
482C4C2×#6687012yes—
483C2—21no—
484C2—21no—
485C2—21no—
486C2—21no—
487C2—21no—
488C2—21no—
489C2—1761no—
490C2#1306896911yescharacteristic
491C2#1306906711yescharacteristic
492C2#1306910811yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1787C2
socleC22×C11#386
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1787D11
hypocenterC11#9262
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
2. Q8×C22⋊Dic11C2semidirect
5. #13066483C2semidirect
6. #13066462C2semidirect
7. C11×#1787C2semidirect
10. C22×#4325C4semidirect
20. C2×#66899C4semidirect
130. C22⋊Dic11SD16semidirect
146. #1787D11semidirect
171. Q8×C11#99semidirect
388. C11#9262semidirect
410. Q8#66870semidirect

Maximal subgroups

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

subgroupindex
C2×#106228402
Q8×C22⋊Dic112
#130694512
#130671852
#130664832
#130664622
C11×#17872
#926211