Finite Group Databasebeta

← #14738513

Subgroups — #14738513

Order 2816.

712 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079846C211yesmaximal, characteristic, complemented
2#13079634C211yesmaximal, characteristic
3#13077591C211yesmaximal, characteristic, complemented
4#13068085C212yesmaximal, complemented
5#13068078C212yesmaximal, complemented
6#13067961C212yesmaximal, complemented
7#13067954C212yesmaximal, complemented
8#13067379C211yesmaximal, characteristic, complemented
9#13067333C211yesmaximal, characteristic, complemented
10#13067330C211yesmaximal, characteristic, complemented
11C2×C11×#492C211yesmaximal, characteristic, complemented
12C22×C11×SD16—21no—
13C22×C11×SD16—21no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#127C2211yescharacteristic
16#10623010C2211yescharacteristic
17C11×#492—21no—
18C11×#492—21no—
19C11×#492C2212yes—
20C11×#492C2212yes—
21C2×C4×C8×C11C2211yescharacteristic
22#10622831—21no—
23#10622830—21no—
24#10622724—21no—
25C8×C22⋊D11—21no—
26#10622707C2212yescomplemented
27#10622702—21no—
28#10622700C2212yescomplemented
29#10622693—21no—
30#10622688C2212yes—
31#10622687—21no—
32#10622685C2212yes—
33#10622684—21no—
34#10622583—21no—
35#10622581—21no—
36#10622539C2211yescharacteristic
37#10622539C2211yescharacteristic
38#10622539C2211yescharacteristic
39#10622303—21no—
40#10622302—21no—
41#10622301C2211yescharacteristic, complemented
42C8×D44C2211yescharacteristic, complemented
43#10622292C2211yescharacteristic, complemented
44C8×Dic22C2211yescharacteristic, complemented
45#10622185C2212yescomplemented
46#10622185C2212yescomplemented
47#10622182C2212yes—
48#10622182C2212yes—
49#10622096C2212yescomplemented
50#10622095C2212yescomplemented
51C22×Q8×C11—21no—
52C22×D4×C11—21no—
53C22×D4×C11—21no—
54C22×D4×C11—21no—
55C2×C11×SD16—22no—
56C2×C11×SD16—22no—
57C2×C11×SD16—22no—
58C2×C11×SD16—22no—
59C2×C11×SD16—44no—
60C2×C11×SD16—44no—
61C22×C8×C11D411yescharacteristic
62C22×C8×C11D411yescharacteristic
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8—21no—
65C11×C4⋊Q8—21no—
66C11×C4⋊Q8C2312yes—
67C11×#127—21no—
68C11×#127—21no—
69C11×#127—21no—
70C11×#127C2312yes—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C42×C11C2311yescharacteristic
74C2×#4324—22no—
75C2×#4323—22no—
76#66983D411yescharacteristic
77#66982—21no—
78C4×C22⋊D11—21no—
79#66977D411yescharacteristic
80C2×#4313—21no—
81C2×C8×D11—21no—
82#66929—21no—
83#66928D411yescharacteristic
84C4×D44C2311yescharacteristic
85#66925—21no—
86#66923D411yescharacteristic
87C4×Dic22C2311yescharacteristic
88C4×C8×C11D411yescharacteristic
89C4×C8×C11D411yescharacteristic
90C4×C8×C11C2311yescharacteristic
91C4×C8×C11C2311yescharacteristic
92#66896—22no—
93#66896—22no—
94C22⋊(C11⋊C8)—21no—
95C22⋊(C11⋊C8)—21no—
96C22⋊(C11⋊C8)—21no—
97(C2×D11)⋊C8—21no—
98(C2×D11)⋊C8—21no—
99#66879—21no—
100Dic11⋊C8—21no—
101Dic11⋊C8—21no—
102C8×Dic11—21no—
103#66874—22no—
104#66873—22no—
105#66872—22no—
106#66871—22no—
107C4⋊(C11⋊C8)C2311yescharacteristic
108C4⋊(C11⋊C8)C2311yescharacteristic
109C4⋊(C11⋊C8)C2312yes—
110C4⋊(C11⋊C8)C2312yes—
111#66867—21no—
112#66867—21no—
113#66867—21no—
114#19352—111nomaximal, Sylow
115C24×C11—41no—
116C2×Q8×C11—22no—
117C2×Q8×C11—42no—
118C2×Q8×C11—42no—
119C2×Q8×C11—41no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—42no—
124C2×D4×C11—42no—
125C2×D4×C11—41no—
126C2×D4×C11—41no—
127C2×D4×C11—41no—
128C2×D4×C11—82no—
129C2×D4×C11—82no—
130C22×C4×C11—41no—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11#4111yescharacteristic
134C2×C22⋊D11—21no—
135C2×D44C2×D411yescharacteristic
136C2×C4×D11—21no—
137C2×Dic22C2×D411yescharacteristic
138C11×SD16—44no—
139C11×SD16—44no—
140C11×SD16—44no—
141C11×SD16—44no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11C2×D411yescharacteristic
147C2×C8×C11C2×D411yescharacteristic
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—41no—
151C11×C4⋊C4—41no—
152C42×C11C2×D411yescharacteristic
153C42×C11C2×D411yescharacteristic
154C42×C11#4111yescharacteristic
155C42×C11C2411yescharacteristic
156C22⋊Dic11—21no—
157#4324—82no—
158#4323—82no—
159(C2×D11)⋊C4—21no—
160(C2×D11)⋊C4—21no—
161(C2×D11)⋊C4—21no—
162(C2×D11)⋊C4—21no—
163C4⋊Dic11C2×D411yescharacteristic
164C4⋊Dic11C2×D411yescharacteristic
165Dic11⋊C4—21no—
166Dic11⋊C4—21no—
167Dic11⋊C4—21no—
168Dic11⋊C4—21no—
169C4×Dic11—21no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—22no—
174#4313—42no—
175C8×D11—42no—
176#3239—111no—
177#3217—111no—
178C2×#492D1111yescharacteristic, complemented
179#2966—111no—
180#1686—112no—
181#1685—112no—
182#1666—112no—
183#1665—112no—
184#1568—111no—
185#1556—111no—
186#1555—111no—
187C23×C11—42no—
188C23×C11—82no—
189C23×C11—82no—
190C23×C11—82no—
191C23×C11#12111yescharacteristic
192C22×D11—21no—
193Q8×C11—42no—
194Q8×C11—42no—
195Q8×C11—82no—
196D4×C11—42no—
197D4×C11—42no—
198D4×C11—42no—
199D4×C11—42no—
200D4×C11—82no—
201D4×C11—82no—
202D4×C11—82no—
203D4×C11—82no—
204C2×C4×C11—22no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—22no—
208C2×C4×C11—42no—
209C2×C4×C11—82no—
210C2×C4×C11#12111yescharacteristic
211C2×C4×C11#12111yescharacteristic
212C2×C4×C11#12111yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C22⋊D11—42no—
217C2×Dic11—21no—
218C2×Dic11—21no—
219C2×Dic11—21no—
220D44—22no—
221C4×D11—41no—
222C4×D11—41no—
223Dic22—22no—
224C8×C11—21no—
225C8×C11—21no—
226C8×C11AGL(1,ℤ/8)12yes—
227C8×C11AGL(1,ℤ/8)12yes—
228C11⋊C8—41no—
229C11⋊C8—41no—
230C11⋊C8—42no—
231C11⋊C8—42no—
232C22×SD16—21no—
233C22×SD16—21no—
234C2×C4⋊Q8C2×D1111yescharacteristic
235C2×#127C2×D1111yescharacteristic
236#529—111no—
237#501—221no—
238#496—221no—
239#492—21no—
240#492—21no—
241#492C2×D1112yes—
242#492C2×D1112yes—
243#490—221no—
244#489—221no—
245#484—221no—
246#481—221no—
247#475—112no—
248#474—112no—
249#460—112no—
250#459—112no—
251#450—221no—
252#447—221no—
253#446—111no—
254C8×Q8—111no—
255#436—111no—
256#435—221no—
257C8×D4—111no—
258C8×D4—221no—
259#433—221no—
260#432—111no—
261#432—111no—
262#432—111no—
263#405—221no—
264C2×C4×C8C2×D1111yescharacteristic
265#335—112no—
266#334—112no—
267#332—112no—
268#332—112no—
269#331—112no—
270#331—112no—
271C22×C11—21no—
272C22×C11—21no—
273C22×C11—82no—
274C22×C11—82no—
275C22×C11—82no—
276C22×C11—164no—
277C22×C11#47112yes—
278C22×C11C2×#12111yescharacteristic
279C2×D11—41no—
280C2×D11—41no—
281C2×D11—41no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—82no—
287C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
288C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
289C4×C11#57712yes—
290Dic11—41no—
291Dic11—41no—
292Dic11—41no—
293C22×Q8—21no—
294C22×D4—21no—
295C22×D4—21no—
296C22×D4—21no—
297C2×SD16—22no—
298C2×SD16—22no—
299C2×SD16—22no—
300C2×SD16—22no—
301C2×SD16—44no—
302C2×SD16—44no—
303C2×SD16—222no—
304C2×D8—222no—
305C2×M16—221no—
306C22×C8—221no—
307C22×C8C22⋊D1111yescharacteristic
308C22×C8C22⋊D1111yescharacteristic
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8—21no—
312C4⋊Q8C22×D1112yes—
313#127—21no—
314#127—21no—
315#127—21no—
316#127C22×D1112yes—
317#126—221no—
318#125—111no—
319#124—111no—
320#123—221no—
321C22⋊Q8—111no—
322#121—111no—
323C4×Q8—111no—
324C4×D4—111no—
325C4×D4—221no—
326#117—221no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C42C22×D1111yescharacteristic
330#107—222no—
331#106—222no—
332C4⋊C8—111no—
333C4⋊C8—111no—
334C4⋊C8—112no—
335C4⋊C8—112no—
336C4⋊C8—221no—
337C4⋊C8—221no—
338#103—222no—
339#102—222no—
340#102—222no—
341#102—222no—
342C22⋊C8—221no—
343C22⋊C8—221no—
344C22⋊C8—221no—
345C22⋊C8—221no—
346C22⋊C8—221no—
347#97—221no—
348#97—221no—
349#97—221no—
350#97—221no—
351C4×C8—221no—
352C4×C8C22⋊D1111yescharacteristic
353C4×C8C22⋊D1111yescharacteristic
354C4×C8C22×D1111yescharacteristic
355C4×C8C22×D1111yescharacteristic
356C2×C11—22no—
357C2×C11—162no—
358C2×C11#303811yescharacteristic
359C2×C11#305711yescharacteristic
360C2×C11C2×#47111yescharacteristic
361D11—81no—
362C24—41no—
363C2×Q8—22no—
364C2×Q8—42no—
365C2×Q8—42no—
366C2×Q8—41no—
367C2×Q8—111no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—42no—
372C2×D4—42no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—82no—
377C2×D4—82no—
378C2×D4—111no—
379C2×D4—221no—
380C22×C4—41no—
381C22×C4—221no—
382C22×C4D4×D1111yescharacteristic
383C22×C4#434111yescharacteristic
384C22×C4C2×C22⋊D1111yescharacteristic
385SD16—44no—
386SD16—44no—
387SD16—44no—
388SD16—44no—
389SD16—882no—
390D8—882no—
391M16—442no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—222no—
395C2×C8—222no—
396C2×C8—221no—
397C2×C8—221no—
398C2×C8—442no—
399C2×C8C2×C22⋊D1111yescharacteristic
400C2×C8C2×C22⋊D1111yescharacteristic
401C2×C8C2×C22⋊D1111yescharacteristic
402C2×C8C2×C22⋊D1111yescharacteristic
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—111no—
408C4⋊C4—111no—
409C4⋊C4—221no—
410C4⋊C4—221no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C22⋊C4—221no—
414C22⋊C4—221no—
415C22⋊C4—221no—
416C22⋊C4—221no—
417C22⋊C4—221no—
418C42—221no—
419C42D4×D1111yescharacteristic
420C42#434111yescharacteristic
421C42C2×C22⋊D1111yescharacteristic
422C42C23×D1111yescharacteristic
423C11#1935211yescharacteristic, complemented, Sylow
424C23—42no—
425C23—82no—
426C23—82no—
427C23—82no—
428C23—221no—
429C23#6699111yescharacteristic
430Q8—42no—
431Q8—42no—
432Q8—82no—
433Q8—222no—
434D4—42no—
435D4—42no—
436D4—42no—
437D4—42no—
438D4—82no—
439D4—82no—
440D4—82no—
441D4—82no—
442D4—222no—
443D4—442no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—42no—
449C2×C4—82no—
450C2×C4—221no—
451C2×C4—221no—
452C2×C4—221no—
453C2×C4—441no—
454C2×C4—441no—
455C2×C4#6699111yescharacteristic
456C2×C4#6699111yescharacteristic
457C2×C4#6699111yescharacteristic
458C2×C4C2×D4×D1111yescharacteristic
459C2×C4C2×#434111yescharacteristic
460C2×C4C22×C22⋊D1111yescharacteristic
461C8—21no—
462C8—21no—
463C8—442no—
464C8—442no—
465C8—441no—
466C8—441no—
467C8#6698512yes—
468C8#6698512yes—
469C22—21no—
470C22—21no—
471C22—82no—
472C22—82no—
473C22—82no—
474C22—164no—
475C22—441no—
476C22—441no—
477C22—441no—
478C22#1062279012yes—
479C22C2×#6699111yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—82no—
485C4—441no—
486C4—441no—
487C4—441no—
488C4#1062329312yes—
489C4C2×#6698511yescharacteristic
490C4C2×#6698511yescharacteristic
491C2—22no—
492C2—162no—
493C2—881no—
494C2#1307809211yescharacteristic
495C2#1307825111yescharacteristic
496C2C2×#1062279011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#492C2
socleC22×C11C2×#121
prime radical#13079634C2
hypercenterC2×#492D11
hypocenterC11#19352
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#492

Complements

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

NH ≅ G/Ntype
1. #13079846C2semidirect
3. #13077591C2semidirect
4. #13068085C2semidirect
5. #13068078C2semidirect
6. #13067961C2semidirect
7. #13067954C2semidirect
8. #13067379C2semidirect
9. #13067333C2semidirect
10. #13067330C2semidirect
11. C2×C11×#492C2semidirect
26. #10622707C22semidirect
28. #10622700C22semidirect
41. #10622301C22semidirect
42. C8×D44C22semidirect
43. #10622292C22semidirect
44. C8×Dic22C22semidirect
45. #10622185C22semidirect
46. #10622185C22semidirect
49. #10622096C22semidirect
50. #10622095C22semidirect
178. C2×#492D11semidirect
423. C11#19352semidirect

Maximal subgroups

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

subgroupindex
#130798462
#130796342
#130775912
#130680852
#130680782
#130679612
#130679542
#130673792
#130673332
#130673302
C2×C11×#4922
#1935211