Finite Group Databasebeta

← #14737821

Subgroups — #14737821

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079198C211yesmaximal, characteristic, complemented
2#13078715C211yesmaximal, characteristic
3C2×#10622625C211yesmaximal, characteristic
4#13068165C212yesmaximal, complemented
5#13068161C212yesmaximal, complemented
6#13068127C212yesmaximal, complemented
7#13068103C212yesmaximal, complemented
8#13067377C211yesmaximal, characteristic, complemented
9#13067317C211yesmaximal, characteristic, complemented
10#13067316C211yesmaximal, characteristic, complemented
11C11×#3110C211yesmaximal, characteristic
12C11×#533C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C22×#4318—21no—
15#10623001C2211yescharacteristic
16C11×#484—21no—
17C11×#474C2212yes—
18C11×#461C2212yes—
19C11×#450—21no—
20C11×#440—22no—
21C11×#432C2211yescharacteristic
22#10622831—21no—
23C2×C22⋊(C11⋊C8)—21no—
24#10622706C2211yescharacteristic, complemented
25#10622705C2211yescharacteristic, complemented
26#10622694C2211yescharacteristic, complemented
27#10622691C2211yescharacteristic, complemented
28#10622664—21no—
29#10622664—21no—
30C4×#4326—21no—
31C4×#4326—21no—
32#10622632C2212yes—
33#10622631—22no—
34#10622625—21no—
35#10622625—21no—
36#10622625C2212yes—
37#10622625C2212yes—
38#10622620C2212yes—
39#10622583—21no—
40#10622539C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622185C2212yescomplemented
44#10622185C2212yescomplemented
45#10622124C2212yescomplemented
46#10622120C2212yescomplemented
47#10622118C2212yescomplemented
48#10622117C2212yescomplemented
49C22×D4×C11D411yescharacteristic
50C23×C4×C11—21no—
51C2×C11×SD16—22no—
52C11×C4⋊Q8C2311yescharacteristic
53C11×C4⋊Q8C2311yescharacteristic
54C11×#125—21no—
55C11×C22⋊Q8—21no—
56C11×C22⋊Q8—21no—
57C4×Q8×C11—21no—
58C4×Q8×C11—21no—
59C4×D4×C11—21no—
60C4×D4×C11—21no—
61C4×D4×C11D412yes—
62C4×D4×C11C2312yes—
63C11×#117—21no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C42×C11C2311yescharacteristic
67C2×#4326—21no—
68C2×#4326—21no—
69C2×#4324—22no—
70#66979—21no—
71#66977—21no—
72#66977—21no—
73C2×#4318—22no—
74C2×#4318—22no—
75C2×#4318—44no—
76C22×C11⋊C8—21no—
77C22×C11⋊C8D411yescharacteristic
78C22×C11⋊C8D411yescharacteristic
79#66923—21no—
80#66922C2311yescharacteristic
81#66922C2311yescharacteristic
82C4×Dic22—21no—
83C4×Dic22—21no—
84C11×#107—22no—
85C11×C4⋊C8C2312yes—
86C11×#103—22no—
87C11×#102—22no—
88C11×C22⋊C8—21no—
89C11×#97—21no—
90#66899—21no—
91#66899—21no—
92#66896—22no—
93C22⋊(C11⋊C8)—21no—
94C22⋊(C11⋊C8)—22no—
95C22⋊(C11⋊C8)—22no—
96#66874—22no—
97#66874—21no—
98#66874—21no—
99#66871—22no—
100#66871—21no—
101#66871—21no—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)C2312yes—
104C4⋊(C11⋊C8)C2312yes—
105#66867—21no—
106C4×C11⋊C8D411yescharacteristic
107C4×C11⋊C8D411yescharacteristic
108C4×C11⋊C8C2311yescharacteristic
109C4×C11⋊C8C2311yescharacteristic
110#19284—111nomaximal, Sylow
111C24×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—42no—
116C2×D4×C11C2×D412yes—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11#4111yescharacteristic
125C2×Dic22—21no—
126C2×Dic22—21no—
127C11×SD16—44no—
128C2×C8×C11—22no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—41no—
135C11×C4⋊C4—41no—
136C11×C4⋊C4C2×D412yes—
137C11×C22⋊C4—22no—
138C11×C22⋊C4—22no—
139C11×C22⋊C4—41no—
140C42×C11—41no—
141C42×C11C2×D411yescharacteristic
142C42×C11C2×D411yescharacteristic
143C42×C11#4111yescharacteristic
144C42×C11C2411yescharacteristic
145C22⋊Dic11—41no—
146#4326—42no—
147#4326—42no—
148#4324—44no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155C4×Dic11—41no—
156#4318—44no—
157#4318—44no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—41no—
162C2×C11⋊C8—42no—
163C2×C11⋊C8C2×D411yescharacteristic
164C2×C11⋊C8C2×D411yescharacteristic
165C2×C11⋊C8C2×D411yescharacteristic
166C2×C11⋊C8C2×D411yescharacteristic
167#3170—111no—
168#3110—111no—
169#3110D1111yescharacteristic
170C2×#436—111no—
171#1699—112no—
172#1699—112no—
173#1693—112no—
174#1689—112no—
175#1568—111no—
176#1552—111no—
177#1552—111no—
178C23×C11—22no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11#12111yescharacteristic
183Q8×C11—41no—
184Q8×C11—41no—
185Q8×C11—42no—
186D4×C11—22no—
187D4×C11—22no—
188D4×C11—42no—
189C2×C4×C11—22no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—44no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11#12111yescharacteristic
202C2×C4×C11#12111yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×Dic11—41no—
207C2×Dic11—41no—
208Dic22—41no—
209Dic22—42no—
210Dic22—41no—
211C8×C11—42no—
212C11⋊C8—21no—
213C11⋊C8—21no—
214C11⋊C8—21no—
215C11⋊C8—42no—
216C11⋊C8—42no—
217C11⋊C8AGL(1,ℤ/8)12yes—
218C22×M16—221no—
219#533—111no—
220#533C2×D1111yescharacteristic
221C2×C4×D4C2×D1111yescharacteristic
222#500—111no—
223#494—111no—
224#487—111no—
225#487—111no—
226#484—21no—
227#484—221no—
228#474—112no—
229#474C2×D1112yes—
230#467—221no—
231#467—221no—
232#461—112no—
233#461C2×D1112yes—
234#450—21no—
235#450—221no—
236#440—22no—
237#440—222no—
238C4×Q16—221no—
239C4×Q16—221no—
240#436—112no—
241#436—112no—
242#436—221no—
243#436—221no—
244#432—111no—
245#432C2×D1111yescharacteristic
246C2×C4⋊C8—111no—
247C2×C22⋊C8—221no—
248C2×C4×C8—111no—
249#335—112no—
250#334—112no—
251#332—112no—
252#332—112no—
253#332—112no—
254#332—112no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—84no—
261C22×C11#47312yes—
262C22×C11C2×#12111yescharacteristic
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—42no—
268C4×C11—81no—
269C4×C11—81no—
270C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
271C4×C11#57511yescharacteristic
272C4×C11#57512yes—
273Dic11—81no—
274Dic11—81no—
275C22×D4C22⋊D1111yescharacteristic
276C23×C4—21no—
277C2×Q16—221no—
278C2×Q16—221no—
279C2×SD16—22no—
280C2×SD16—222no—
281C2×M16—222no—
282C2×M16—222no—
283C2×M16—444no—
284C22×C8—111no—
285C22×C8—111no—
286C22×C8—221no—
287C4⋊Q8—111no—
288C4⋊Q8—111no—
289C4⋊Q8C22×D1111yescharacteristic
290C4⋊Q8C22×D1111yescharacteristic
291#125—21no—
292#125—221no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C22⋊Q8—221no—
296C22⋊Q8—221no—
297C4×Q8—21no—
298C4×Q8—21no—
299C4×Q8—221no—
300C4×Q8—221no—
301C4×D4—21no—
302C4×D4—21no—
303C4×D4C22⋊D1112yes—
304C4×D4C22×D1112yes—
305#117—21no—
306#117—221no—
307C2×C4⋊C4C22⋊D1111yescharacteristic
308C2×C22⋊C4—21no—
309C2×C42C22×D1111yescharacteristic
310#107—22no—
311#107—221no—
312#107—221no—
313#107—222no—
314C4⋊C8—112no—
315C4⋊C8—112no—
316C4⋊C8—221no—
317C4⋊C8C22×D1112yes—
318#103—22no—
319#103—221no—
320#103—221no—
321#103—221no—
322#103—221no—
323#103—222no—
324#102—22no—
325#102—222no—
326C22⋊C8—21no—
327C22⋊C8—222no—
328C22⋊C8—222no—
329C22⋊C8—221no—
330#97—21no—
331#97—221no—
332C4×C8—111no—
333C4×C8—111no—
334C4×C8—111no—
335C4×C8—111no—
336C2×C11—22no—
337C2×C11—82no—
338C2×C11#303611yescharacteristic
339C2×C11#305411yescharacteristic
340C2×C11C2×#47311yescharacteristic
341C24—21no—
342C2×Q8—21no—
343C2×Q8—21no—
344C2×Q8—221no—
345C2×Q8—221no—
346C2×D4—21no—
347C2×D4—42no—
348C2×D4C2×C22⋊D1112yes—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4D4×D1111yescharacteristic
355C22×C4#434111yescharacteristic
356C22×C4C2×C22⋊D1111yescharacteristic
357Q16—442no—
358Q16—442no—
359SD16—44no—
360SD16—444no—
361M16—444no—
362M16—444no—
363C2×C8—22no—
364C2×C8—111no—
365C2×C8—111no—
366C2×C8—111no—
367C2×C8—111no—
368C2×C8—222no—
369C2×C8—222no—
370C2×C8—222no—
371C2×C8—441no—
372C2×C8—442no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—221no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—221no—
384C4⋊C4—441no—
385C4⋊C4—441no—
386C4⋊C4C2×C22⋊D1112yes—
387C22⋊C4—22no—
388C22⋊C4—22no—
389C22⋊C4—41no—
390C22⋊C4—441no—
391C42—41no—
392C42—441no—
393C42D4×D1111yescharacteristic
394C42#434111yescharacteristic
395C42C2×C22⋊D1111yescharacteristic
396C42C23×D1111yescharacteristic
397C11#1928411yescharacteristic, complemented, Sylow
398C23—22no—
399C23—42no—
400C23—42no—
401C23—42no—
402C23#6699211yescharacteristic
403Q8—41no—
404Q8—41no—
405Q8—42no—
406Q8—441no—
407Q8—441no—
408Q8—442no—
409D4—22no—
410D4—22no—
411D4—42no—
412C2×C4—22no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—44no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4#6699211yescharacteristic
426C2×C4#6699211yescharacteristic
427C2×C4#6699211yescharacteristic
428C2×C4C2×D4×D1111yescharacteristic
429C2×C4C2×#434111yescharacteristic
430C2×C4C22×C22⋊D1111yescharacteristic
431C8—42no—
432C8—112no—
433C8—221no—
434C8—221no—
435C8—221no—
436C8—442no—
437C8—442no—
438C22—21no—
439C22—21no—
440C22—42no—
441C22—42no—
442C22—42no—
443C22—84no—
444C22#1062281712yes—
445C22C2×#6699211yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—42no—
451C4—81no—
452C4—81no—
453C4—881no—
454C4—881no—
455C4D11×AGL(1,ℤ/8)11yescharacteristic
456C4#1062330411yescharacteristic
457C4#1062335312yes—
458C2—22no—
459C2—82no—
460C2#1307807711yescharacteristic
461C2#1307822211yescharacteristic
462C2C2×#1062281711yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3110C2
socleC22×C11C2×#121
prime radicalC22×D4×C11D4
hypercenter#3110D11
hypocenterC11#19284
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3110

Complements

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

NH ≅ G/Ntype
1. #13079198C2semidirect
4. #13068165C2semidirect
5. #13068161C2semidirect
6. #13068127C2semidirect
7. #13068103C2semidirect
8. #13067377C2semidirect
9. #13067317C2semidirect
10. #13067316C2semidirect
24. #10622706C22semidirect
25. #10622705C22semidirect
26. #10622694C22semidirect
27. #10622691C22semidirect
43. #10622185C22semidirect
44. #10622185C22semidirect
45. #10622124C22semidirect
46. #10622120C22semidirect
47. #10622118C22semidirect
48. #10622117C22semidirect
397. C11#19284semidirect

Maximal subgroups

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

subgroupindex
#130791982
#130787152
C2×#106226252
#130681652
#130681612
#130681272
#130681032
#130673772
#130673172
#130673162
C11×#31102
#1928411