Finite Group Databasebeta

← #14724142

Subgroups — #14724142

Order 2816.

670 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#13078670C211yesmaximal, characteristic
2#13077582C211yesmaximal, characteristic, complemented
3#13067504C212yesmaximal, complemented
4#13067499C212yesmaximal, complemented
5#13067480C212yesmaximal, complemented
6#13067473C212yesmaximal, complemented
7#13067407C211yesmaximal, characteristic, complemented
8#13067053C211yesmaximal, characteristic, complemented
9#13067033C211yesmaximal, characteristic, complemented
10C8×#4318C211yesmaximal, characteristic, complemented
11C11×#2931C211yesmaximal, characteristic, complemented
12C2×C11×#131—21no—
13C11×#532C2211yescharacteristic
14C4×#4339C2211yescharacteristic
15C11×#436—21no—
16C11×#436C2212yes—
17C8×D4×C11—21no—
18C8×D4×C11C2212yes—
19C11×#423C2211yescharacteristic
20C11×#408—21no—
21C2×C4×C8×C11C2211yescharacteristic
22#10622724—21no—
23#10622724—21no—
24#10622704C411yescharacteristic
25#10622697C411yescharacteristic
26#10622688C411yescharacteristic
27#10622685C411yescharacteristic
28#10622650C412yes—
29#10622648C412yes—
30C4×#4324C2212yes—
31C4×#4323C2212yes—
32#10622538C2211yescharacteristic
33#10622538C2211yescharacteristic
34C4×#4318C2211yescharacteristic
35#10622301C2211yescharacteristic
36#10622301C2211yescharacteristic
37C4×#4313—21no—
38#10622298—21no—
39#10622292C2211yescharacteristic
40#10622292C2211yescharacteristic
41D4⋊(C11⋊C8)C2212yes—
42D4⋊(C11⋊C8)C2212yes—
43#10622122C2212yes—
44#10622121C2212yes—
45#10622118C2212yes—
46#10622117C2212yes—
47#10622092C2212yes—
48C8×C11⋊C8C2212yes—
49C2×C11×#41—21no—
50C2×#4339C2×C411yescharacteristic
51C11×#131—44no—
52C2×C11×M16—21no—
53C2×C11×M16—22no—
54C22×C8×C11—22no—
55C22×C8×C11D411yescharacteristic
56C22×C8×C11D411yescharacteristic
57C11×C4⋊Q8C2×C411yescharacteristic
58C11×#127C2×C411yescharacteristic
59C11×#124—21no—
60C11×#121—21no—
61C11×#121C2×C412yes—
62C4×D4×C11—21no—
63C4×D4×C11C2312yes—
64C2×C42×C11C2311yescharacteristic
65C2×#4324C2×C412yes—
66C2×#4323C2×C412yes—
67C4×C22⋊D11—21no—
68C4×C22⋊D11—21no—
69#66979C2×C411yescharacteristic
70C2×#4318—21no—
71C2×#4313—21no—
72C2×#4313—21no—
73C4×D44C2×C411yescharacteristic
74C4×D44C2311yescharacteristic
75#66925—21no—
76C42×D11—21no—
77C4×Dic22C2×C411yescharacteristic
78C4×Dic22C2311yescharacteristic
79C11×C4⋊C8—21no—
80C11×C4⋊C8C2312yes—
81C11×C22⋊C8—22no—
82C11×C22⋊C8—22no—
83C4×C8×C11D411yescharacteristic
84C4×C8×C11D411yescharacteristic
85C4×C8×C11C2311yescharacteristic
86C4×C8×C11C2311yescharacteristic
87#66896C2×C412yes—
88#66896C2×C412yes—
89C22⋊(C11⋊C8)—21no—
90C22⋊(C11⋊C8)C2×C412yes—
91(C2×D11)⋊C8—21no—
92(C2×D11)⋊C8—21no—
93#66879—21no—
94#66879—21no—
95Dic11⋊C8—21no—
96Dic11⋊C8—21no—
97#66874C2×C412yes—
98#66873C2×C412yes—
99#66872C2×C412yes—
100#66871C2×C412yes—
101C4⋊(C11⋊C8)C2×C411yescharacteristic
102C4⋊(C11⋊C8)C2×C411yescharacteristic
103C4⋊(C11⋊C8)C2311yescharacteristic
104C4⋊(C11⋊C8)C2311yescharacteristic
105#66867—21no—
106C4×C11⋊C8—21no—
107C4×C11⋊C8C2312yes—
108C4×C11⋊C8C2312yes—
109#17945—111nomaximal, Sylow
110C11×#41—42no—
111C11×#41—42no—
112C2×Q8×C11—21no—
113C2×D4×C11—22no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11C22×C412yes—
117C22×C4×C11—22no—
118C22×C4×C11C22×C411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11#4111yescharacteristic
121C2×C22⋊D11—21no—
122#4339—41no—
123#4339—41no—
124C2×D44C22×C411yescharacteristic
125C2×C4×D11—21no—
126C2×C4×D11—21no—
127C2×C4×D11—21no—
128C2×Dic22C22×C411yescharacteristic
129C11×M16—42no—
130C11×M16—44no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11—41no—
134C2×C8×C11—44no—
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2×D411yescharacteristic
138C2×C8×C11C2×D411yescharacteristic
139C11×C4⋊C4—21no—
140C11×C4⋊C4C22×C412yes—
141C11×C22⋊C4—22no—
142C11×C22⋊C4—22no—
143C42×C11C22×C411yescharacteristic
144C42×C11C2×D411yescharacteristic
145C42×C11#4111yescharacteristic
146C42×C11C2411yescharacteristic
147C22⋊Dic11—21no—
148#4324—42no—
149#4323—42no—
150(C2×D11)⋊C4—21no—
151(C2×D11)⋊C4—21no—
152C4⋊Dic11C22×C411yescharacteristic
153C4⋊Dic11C22×C411yescharacteristic
154Dic11⋊C4—21no—
155Dic11⋊C4—21no—
156C4×Dic11—21no—
157C4×Dic11—21no—
158C4×Dic11—21no—
159#4318—24no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8C22×C412yes—
164C2×C11⋊C8C22×C412yes—
165#4313—42no—
166#4313—42no—
167#3106—111no—
168#2965—111no—
169#2931D1111yescharacteristic, complemented
170#1590—112no—
171#1589—112no—
172#1586—112no—
173#1585—112no—
174#1574—111no—
175#1489—111no—
176#1484—111no—
177C8×M16—111no—
178C23×C11—22no—
179C23×C11C4×D411yescharacteristic
180C22×D11—21no—
181Q8×C11—42no—
182D4×C11—22no—
183D4×C11—22no—
184D4×C11—42no—
185D4×C11—44no—
186D4×C11—42no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11C4×D411yescharacteristic
196C2×C4×C11C4×D411yescharacteristic
197C2×C4×C11C4×D411yescharacteristic
198C2×C4×C11C23×C411yescharacteristic
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C22⋊D11—42no—
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—21no—
205D44—21no—
206D44—21no—
207C4×D11—42no—
208C4×D11—41no—
209C4×D11—41no—
210C4×D11—42no—
211Dic22—21no—
212Dic22—21no—
213C8×C11—21no—
214C8×C11—21no—
215C8×C11—21no—
216C8×C11—42no—
217C8×C11AGL(1,ℤ/8)12yes—
218C11⋊C8—24no—
219C11⋊C8—22no—
220C11⋊C8—22no—
221C11⋊C8—41no—
222C11⋊C8—41no—
223C2×#131—21no—
224#532C2×D1111yescharacteristic
225C4×#41—111no—
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—21no—
237#436—111no—
238#436—111no—
239#436C2×D1112yes—
240#435—221no—
241#435—221no—
242C8×D4—21no—
243C8×D4C2×D1112yes—
244#431—111no—
245#431—111no—
246#431—221no—
247#423C2×D1111yescharacteristic
248#408—21no—
249C4×M16—111no—
250C4×M16—221no—
251C2×C4×C8C2×D1111yescharacteristic
252#335—112no—
253#334—112no—
254Q8⋊C8—112no—
255D4⋊C8—112no—
256D4⋊C8—112no—
257D4⋊C8—112no—
258#322—112no—
259C82—112no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11C2×C4×D411yescharacteristic
267C2×D11—41no—
268C2×D11—41no—
269C2×D11—41no—
270C4×C11—21no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—42no—
274C4×C11#44312yes—
275C4×C11#56811yescharacteristic
276C4×C11#56811yescharacteristic
277C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
278C4×C11#57511yescharacteristic
279Dic11—41no—
280Dic11—41no—
281Dic11—41no—
282C2×#41—21no—
283C2×#41—111no—
284C2×SD16—112no—
285C2×D8—112no—
286#131—44no—
287C2×M16—21no—
288C2×M16—22no—
289C2×M16—221no—
290C2×M16—221no—
291C2×M16—221no—
292C22×C8—22no—
293C22×C8C22⋊D1111yescharacteristic
294C22×C8C22⋊D1111yescharacteristic
295C4⋊Q8C4×D1111yescharacteristic
296#127C4×D1111yescharacteristic
297#124—21no—
298#121—21no—
299#121C4×D1112yes—
300C4×Q8—111no—
301C4×Q8—111no—
302C4×D4—21no—
303C4×D4—111no—
304C4×D4—111no—
305C4×D4—221no—
306C4×D4—221no—
307C4×D4C22×D1112yes—
308#117—111no—
309#117—221no—
310C2×C42—221no—
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—22no—
327C22⋊C8—22no—
328C22⋊C8—112no—
329C22⋊C8—221no—
330C22⋊C8—221no—
331C22⋊C8—221no—
332#97—221no—
333#97—221no—
334#97—221no—
335C4×C8—112no—
336C4×C8—112no—
337C4×C8—221no—
338C4×C8C22⋊D1111yescharacteristic
339C4×C8C22⋊D1111yescharacteristic
340C4×C8C22×D1111yescharacteristic
341C4×C8C22×D1111yescharacteristic
342C2×C11—41no—
343C2×C11—82no—
344C2×C11#293011yescharacteristic
345C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
346C2×C11C2×#44311yescharacteristic
347D11—81no—
348#41—42no—
349#41—42no—
350#41—441no—
351#41—441no—
352C2×Q8—21no—
353C2×Q8—111no—
354C2×D4—22no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—111no—
358C2×D4—221no—
359C2×D4C2×C4×D1112yes—
360C22×C4—22no—
361C22×C4—221no—
362C22×C4—221no—
363C22×C4—221no—
364C22×C4C2×C4×D1111yescharacteristic
365C22×C4#433911yescharacteristic
366C22×C4C2×C22⋊D1111yescharacteristic
367SD16—442no—
368D8—442no—
369M16—42no—
370M16—44no—
371M16—224no—
372M16—442no—
373M16—442no—
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—41no—
377C2×C8—44no—
378C2×C8—112no—
379C2×C8—112no—
380C2×C8—222no—
381C2×C8—221no—
382C2×C8—221no—
383C2×C8C2×C22⋊D1111yescharacteristic
384C2×C8C2×C22⋊D1111yescharacteristic
385C2×C8C2×C22⋊D1111yescharacteristic
386C2×C8C2×C22⋊D1111yescharacteristic
387C4⋊C4—21no—
388C4⋊C4—111no—
389C4⋊C4—111no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C4⋊C4C2×C4×D1112yes—
393C22⋊C4—22no—
394C22⋊C4—22no—
395C22⋊C4—221no—
396C22⋊C4—221no—
397C22⋊C4—221no—
398C42—221no—
399C42—221no—
400C42—221no—
401C42C2×C4×D1111yescharacteristic
402C42#433911yescharacteristic
403C42C2×C22⋊D1111yescharacteristic
404C42C23×D1111yescharacteristic
405C11#1794511yescharacteristic, complemented, Sylow
406C23—22no—
407C23—221no—
408C23C4×C22⋊D1111yescharacteristic
409Q8—42no—
410Q8—221no—
411Q8—221no—
412D4—22no—
413D4—22no—
414D4—42no—
415D4—44no—
416D4—42no—
417D4—221no—
418D4—221no—
419D4—442no—
420C2×C4—22no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—22no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—221no—
429C2×C4—221no—
430C2×C4—221no—
431C2×C4—442no—
432C2×C4—442no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4C4×C22⋊D1111yescharacteristic
436C2×C4C4×C22⋊D1111yescharacteristic
437C2×C4C4×C22⋊D1111yescharacteristic
438C2×C4C22×C4×D1111yescharacteristic
439C2×C4C2×#433911yescharacteristic
440C2×C4C22×C22⋊D1111yescharacteristic
441C8—21no—
442C8—21no—
443C8—21no—
444C8—42no—
445C8—224no—
446C8—222no—
447C8—222no—
448C8—441no—
449C8—441no—
450C8#6698512yes—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—42no—
455C22—42no—
456C22—42no—
457C22—441no—
458C22—441no—
459C22—441no—
460C22C2×C4×C22⋊D1111yescharacteristic
461C4—21no—
462C4—21no—
463C4—21no—
464C4—42no—
465C4—441no—
466C4—441no—
467C4—441no—
468C4#1062275712yes—
469C4#1062328111yescharacteristic
470C4#1062328111yescharacteristic
471C4C2×#6698511yescharacteristic
472C4#1062335311yescharacteristic
473C2—41no—
474C2—82no—
475C2—881no—
476C2#1307731711yescharacteristic
477C2C4×#6698511yescharacteristic
478C2C2×#1062275711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2931C2
socleC22×C11C2×C4×D4
prime radical#13078670C2
cosocleC42×C11C24
hypercenter#2931D11
hypocenterC11#17945
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ #2931

Complements

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

NH ≅ G/Ntype
2. #13077582C2semidirect
3. #13067504C2semidirect
4. #13067499C2semidirect
5. #13067480C2semidirect
6. #13067473C2semidirect
7. #13067407C2semidirect
8. #13067053C2semidirect
9. #13067033C2semidirect
10. C8×#4318C2semidirect
11. C11×#2931C2semidirect
169. #2931D11semidirect
405. C11#17945semidirect

Maximal subgroups

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

subgroupindex
#130786702
#130775822
#130675042
#130674992
#130674802
#130674732
#130674072
#130670532
#130670332
C8×#43182
C11×#29312
#1794511