Finite Group Databasebeta

← #14724085

Subgroups — #14724085

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078676C211yesmaximal, characteristic
2#13077583C211yesmaximal, characteristic, complemented
3#13077327C211yesmaximal, characteristic, complemented
4#13067527C212yesmaximal, complemented
5#13067521C212yesmaximal, complemented
6#13067455C212yesmaximal, complemented
7#13067448C212yesmaximal, complemented
8#13067407C211yesmaximal, characteristic, complemented
9#13067034C211yesmaximal, characteristic, complemented
10#13066903C211yesmaximal, characteristic, complemented
11C11×#1489C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13C2×#66960—21no—
14#10623008C2211yescharacteristic
15C11×#423C2211yescharacteristic
16C4×C11×M16C2211yescharacteristic
17#10622851C412yes—
18#10622742—21no—
19#10622640C411yescharacteristic
20C4×#4325C2212yes—
21#10622637C2211yescharacteristic
22#10622637C2211yescharacteristic
23#10622634C411yescharacteristic
24#10622628C411yescharacteristic
25C4×#4323C2212yes—
26#10622625C2211yescharacteristic
27#10622625C2211yescharacteristic
28#10622624—21no—
29#10622624—21no—
30#10622621C411yescharacteristic
31#10622616C412yes—
32#10622538—21no—
33#10622538C2211yescharacteristic
34#10622538C2211yescharacteristic
35C4×#4318—21no—
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622451—21no—
38#10622451C2212yes—
39#10622447—21no—
40#10622447C2212yes—
41C11×Q8⋊C8C2212yes—
42C11×D4⋊C8C2212yes—
43#10622118C2212yes—
44#10622117C2212yes—
45#10622097C2212yes—
46#10622097C2212yes—
47#10622092C2212yes—
48#10622092C2212yes—
49C2×C11×#41C2×C411yescharacteristic
50C2×#4339—21no—
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C4×Q8×C11C2×C411yescharacteristic
54C4×Q8×C11C2311yescharacteristic
55C4×D4×C11—21no—
56C4×D4×C11—21no—
57C4×D4×C11C2×C411yescharacteristic
58C4×D4×C11C2311yescharacteristic
59C11×#117—21no—
60C11×#117C2×C411yescharacteristic
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63C2×#4325C2×C412yes—
64C2×#4323C2×C412yes—
65#66983—21no—
66#66983C2×C412yes—
67C2×#4318—21no—
68C2×#4318—21no—
69C22×C11⋊C8D411yescharacteristic
70C22×C11⋊C8D411yescharacteristic
71#66960—44no—
72C2×#4313—22no—
73C2×C8×D11—22no—
74#66928—21no—
75#66927C2×C411yescharacteristic
76C4×D44—21no—
77C4×D44C2312yes—
78#66922C2×C411yescharacteristic
79C11×C4⋊C8—21no—
80C11×C4⋊C8C2312yes—
81C11×#97—21no—
82C4×C8×C11C2312yes—
83#66899C2×C412yes—
84#66896C2×C412yes—
85C22⋊(C11⋊C8)—21no—
86C22⋊(C11⋊C8)—21no—
87C22⋊(C11⋊C8)—21no—
88C22⋊(C11⋊C8)C2×C412yes—
89(C2×D11)⋊C8—22no—
90(C2×D11)⋊C8—22no—
91#66873C2×C412yes—
92#66873C2×C412yes—
93#66872C2×C412yes—
94#66871C2×C412yes—
95C4⋊(C11⋊C8)—21no—
96C4⋊(C11⋊C8)—21no—
97C4⋊(C11⋊C8)C2×C411yescharacteristic
98C4⋊(C11⋊C8)C2×C411yescharacteristic
99C4⋊(C11⋊C8)C2311yescharacteristic
100C4⋊(C11⋊C8)C2311yescharacteristic
101#66867—21no—
102#66867—21no—
103C4×C11⋊C8—21no—
104C4×C11⋊C8D411yescharacteristic
105C4×C11⋊C8D411yescharacteristic
106C4×C11⋊C8C2312yes—
107C4×C11⋊C8C2311yescharacteristic
108C4×C11⋊C8C2311yescharacteristic
109#17940—111nomaximal, Sylow
110C11×#41—41no—
111C11×#41—41no—
112C2×Q8×C11C22×C411yescharacteristic
113C2×D4×C11—21no—
114C2×D4×C11C22×C411yescharacteristic
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11C22×C411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11#4111yescharacteristic
121C2×C22⋊D11—22no—
122#4339—42no—
123#4339—42no—
124C2×D44—21no—
125C2×D44—21no—
126C2×D44C22×C412yes—
127C2×C4×D11—22no—
128C2×Dic22—21no—
129C11×M16—42no—
130C11×M16—42no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4C22×C411yescharacteristic
136C11×C4⋊C4C22×C411yescharacteristic
137C11×C22⋊C4—21no—
138C11×C22⋊C4—21no—
139C11×C22⋊C4—21no—
140C42×C11—21no—
141C42×C11—21no—
142C42×C11—21no—
143C42×C11C22×C411yescharacteristic
144C42×C11C2×D411yescharacteristic
145C42×C11#4111yescharacteristic
146C42×C11C2411yescharacteristic
147#4325—42no—
148#4323—42no—
149(C2×D11)⋊C4—22no—
150(C2×D11)⋊C4—22no—
151C4⋊Dic11—21no—
152C4⋊Dic11C22×C412yes—
153#4318—42no—
154#4318—42no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—41no—
159C2×C11⋊C8C22×C412yes—
160C2×C11⋊C8C22×C412yes—
161C2×C11⋊C8C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163C2×C11⋊C8C2×D411yescharacteristic
164C2×C11⋊C8C2×D411yescharacteristic
165#4313—44no—
166C8×D11—44no—
167#3106—111no—
168#2965—111no—
169#2931—111no—
170#1594—112no—
171#1592—112no—
172#1582—112no—
173#1581—112no—
174#1574—111no—
175#1489D1111yescharacteristic, complemented
176#1484—111no—
177#1451—111no—
178C23×C11—21no—
179C23×C11C4×D411yescharacteristic
180C22×D11—22no—
181Q8×C11—21no—
182Q8×C11—21no—
183D4×C11—21no—
184D4×C11—21no—
185D4×C11—42no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—22no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—42no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11C4×D411yescharacteristic
199C2×C4×C11C4×D411yescharacteristic
200C2×C4×C11C4×D411yescharacteristic
201C2×C4×C11C23×C411yescharacteristic
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C22⋊D11—44no—
205C2×Dic11—22no—
206D44—22no—
207D44—22no—
208D44—42no—
209D44—42no—
210C4×D11—42no—
211C4×D11—42no—
212Dic22—42no—
213C8×C11—42no—
214C8×C11—42no—
215C11⋊C8—22no—
216C11⋊C8—22no—
217C11⋊C8—21no—
218C11⋊C8—21no—
219C11⋊C8—21no—
220C11⋊C8—41no—
221C11⋊C8—41no—
222C11⋊C8AGL(1,ℤ/8)12yes—
223C2×#131—221no—
224#532—111no—
225C4×#41C2×D1111yescharacteristic
226#482—112no—
227#477—111no—
228#476—111no—
229#460—111no—
230#459—111no—
231#449—112no—
232#446—111no—
233#446—111no—
234C4×SD16—112no—
235C4×D8—112no—
236#436—111no—
237#436—111no—
238#436—112no—
239#436—221no—
240#435—221no—
241#435—221no—
242C8×D4—112no—
243C8×D4—221no—
244#431—111no—
245#431—111no—
246#431—221no—
247#423C2×D1111yescharacteristic
248#408—221no—
249C4×M16—221no—
250C4×M16C2×D1111yescharacteristic
251C2×C4×C8—111no—
252#335—112no—
253#334—112no—
254Q8⋊C8C2×D1112yes—
255D4⋊C8—112no—
256D4⋊C8—112no—
257D4⋊C8C2×D1112yes—
258#322—112no—
259#322—112no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—41no—
264C22×C11—41no—
265C22×C11—41no—
266C22×C11C2×C4×D411yescharacteristic
267C2×D11—42no—
268C2×D11—42no—
269C2×D11—42no—
270C4×C11—21no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—41no—
274C4×C11—41no—
275C4×C11—41no—
276C4×C11#44412yes—
277C4×C11#56811yescharacteristic
278C4×C11#56811yescharacteristic
279C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
280C4×C11#57511yescharacteristic
281Dic11—42no—
282C2×#41—221no—
283C2×#41C4×D1111yescharacteristic
284C2×SD16—112no—
285C2×D8—112no—
286#131—444no—
287C2×M16—21no—
288C2×M16—21no—
289C2×M16—222no—
290C2×M16—221no—
291C2×M16—221no—
292C22×C8—111no—
293C22×C8—111no—
294C22×C8—222no—
295C4⋊Q8—111no—
296#127—111no—
297#124—221no—
298#121—112no—
299#121—221no—
300C4×Q8C4×D1111yescharacteristic
301C4×Q8C22×D1111yescharacteristic
302C4×D4—21no—
303C4×D4—21no—
304C4×D4—112no—
305C4×D4—221no—
306C4×D4C4×D1111yescharacteristic
307C4×D4C22×D1111yescharacteristic
308#117—21no—
309#117C4×D1111yescharacteristic
310C2×C42—21no—
311C2×C42C22×D1111yescharacteristic
312#107—112no—
313#106—112no—
314C4⋊C8—21no—
315C4⋊C8—111no—
316C4⋊C8—111no—
317C4⋊C8—111no—
318C4⋊C8—111no—
319C4⋊C8—221no—
320C4⋊C8—221no—
321C4⋊C8C22×D1112yes—
322#103—112no—
323#102—112no—
324#102—112no—
325#102—112no—
326C22⋊C8—112no—
327C22⋊C8—222no—
328C22⋊C8—222no—
329C22⋊C8—221no—
330C22⋊C8—221no—
331C22⋊C8—221no—
332#97—21no—
333#97—221no—
334#97—221no—
335C4×C8—111no—
336C4×C8—111no—
337C4×C8—112no—
338C4×C8—111no—
339C4×C8—111no—
340C4×C8—221no—
341C4×C8C22×D1112yes—
342C2×C11—41no—
343C2×C11—81no—
344C2×C11#293011yescharacteristic
345C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
346C2×C11C2×#44411yescharacteristic
347D11—82no—
348#41—41no—
349#41—41no—
350#41—442no—
351#41—442no—
352C2×Q8—221no—
353C2×Q8C2×C4×D1111yescharacteristic
354C2×D4—21no—
355C2×D4—112no—
356C2×D4—222no—
357C2×D4—221no—
358C2×D4—221no—
359C2×D4C2×C4×D1111yescharacteristic
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—222no—
364C22×C4C2×C4×D1111yescharacteristic
365C22×C4D4×D1111yescharacteristic
366C22×C4#434111yescharacteristic
367SD16—442no—
368D8—442no—
369M16—42no—
370M16—42no—
371M16—444no—
372M16—442no—
373M16—442no—
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—111no—
377C2×C8—112no—
378C2×C8—112no—
379C2×C8—111no—
380C2×C8—111no—
381C2×C8—111no—
382C2×C8—222no—
383C2×C8—221no—
384C2×C8—221no—
385C2×C8—444no—
386C2×C8—441no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—112no—
390C4⋊C4—221no—
391C4⋊C4C2×C4×D1111yescharacteristic
392C4⋊C4C2×C4×D1111yescharacteristic
393C22⋊C4—21no—
394C22⋊C4—21no—
395C22⋊C4—21no—
396C22⋊C4—222no—
397C22⋊C4—222no—
398C42—21no—
399C42—21no—
400C42—21no—
401C42C2×C4×D1111yescharacteristic
402C42D4×D1111yescharacteristic
403C42#434111yescharacteristic
404C42C23×D1111yescharacteristic
405C11#1794011yescharacteristic, complemented, Sylow
406C23—21no—
407C23—222no—
408C23(C22⋊D11)⋊C411yescharacteristic
409Q8—21no—
410Q8—21no—
411Q8—442no—
412D4—21no—
413D4—21no—
414D4—42no—
415D4—222no—
416D4—222no—
417D4—442no—
418D4—444no—
419D4—442no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—222no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4(C22⋊D11)⋊C411yescharacteristic
436C2×C4(C22⋊D11)⋊C411yescharacteristic
437C2×C4(C22⋊D11)⋊C411yescharacteristic
438C2×C4C22×C4×D1111yescharacteristic
439C2×C4C2×D4×D1111yescharacteristic
440C2×C4C2×#434111yescharacteristic
441C8—42no—
442C8—42no—
443C8—112no—
444C8—222no—
445C8—222no—
446C8—221no—
447C8—221no—
448C8—221no—
449C8—441no—
450C8—441no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—442no—
458C22—442no—
459C22—442no—
460C22C2×(C22⋊D11)⋊C411yescharacteristic
461C4—21no—
462C4—21no—
463C4—21no—
464C4—41no—
465C4—41no—
466C4—41no—
467C4—442no—
468C4#1062243612yes—
469C4#1062327611yescharacteristic
470C4#1062327611yescharacteristic
471C4D11×AGL(1,ℤ/8)11yescharacteristic
472C4#1062330811yescharacteristic
473C2—41no—
474C2—81no—
475C2—882no—
476C2#1307731511yescharacteristic
477C2#1307742911yescharacteristic
478C2C2×#1062243611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1489C2
socleC22×C11C2×C4×D4
prime radical#13078676C2
cosocleC42×C11C24
hypercenter#1489D11
hypocenterC11#17940
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1489

Complements

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

NH ≅ G/Ntype
2. #13077583C2semidirect
3. #13077327C2semidirect
4. #13067527C2semidirect
5. #13067521C2semidirect
6. #13067455C2semidirect
7. #13067448C2semidirect
8. #13067407C2semidirect
9. #13067034C2semidirect
10. #13066903C2semidirect
11. C11×#1489C2semidirect
175. #1489D11semidirect
405. C11#17940semidirect

Maximal subgroups

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

subgroupindex
#130786762
#130775832
#130773272
#130675272
#130675212
#130674552
#130674482
#130674072
#130670342
#130669032
C11×#14892
#1794011