Finite Group Databasebeta

← #14736601

Subgroups — #14736601

Order 2816.

696 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078612C211yesmaximal, characteristic
2C2×#10622697C211yesmaximal, characteristic, complemented
3M16×D44C211yesmaximal, characteristic, complemented
4#13068188C212yesmaximal, complemented
5#13068146C212yesmaximal, complemented
6#13068064C212yesmaximal, complemented
7#13068022C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9#13067297C211yesmaximal, characteristic, complemented
10#13067293C211yesmaximal, characteristic, complemented
11C11×#3141C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×M16×D11—21no—
15C2×C4×D44C2211yescharacteristic
16C11×#489—22no—
17C11×#487C2212yescomplemented
18C11×#486C2212yescomplemented
19C11×#417—21no—
20C11×#417—21no—
21C4×C11×M16C2211yescharacteristic
22#10622739—21no—
23#10622700C2211yescharacteristic
24#10622700C2211yescharacteristic
25#10622697—21no—
26#10622697—21no—
27#10622697C2212yes—
28#10622697C2212yes—
29#10622685C2211yescharacteristic
30#10622685C2211yescharacteristic
31#10622649—21no—
32#10622646—21no—
33C4×#4323—21no—
34C4×#4323—21no—
35C2×#66873—21no—
36C2×#66872—21no—
37#10622538C2211yescharacteristic
38#10622537C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40#10622319—22no—
41#10622301C2212yes—
42C8×D44C2212yes—
43#10622185C2212yescomplemented
44#10622184C2212yescomplemented
45#10622184C2212yescomplemented
46#10622182C2212yescomplemented
47#10622096C2212yescomplemented
48#10622095C2212yescomplemented
49C2×C11×#41—21no—
50C22×Q8×C11—21no—
51C22×D44D411yescharacteristic
52C22×C4×D11—21no—
53C2×C11×M16D411yescharacteristic
54C2×C11×M16D411yescharacteristic
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8—21no—
58C11×C4⋊Q8C2312yes—
59C11×C4⋊Q8C2311yescharacteristic
60C11×#127C2311yescharacteristic
61C11×#124—21no—
62C11×#121—21no—
63C11×#121—21no—
64C4×D4×C11—21no—
65C4×D4×C11—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C42×C11C2311yescharacteristic
69C2×#4323—21no—
70C2×#4323—21no—
71C2×(C2×D11)⋊C4—21no—
72C2×C4⋊Dic11D411yescharacteristic
73C2×#4318—21no—
74C22×C11⋊C8—21no—
75M16×D11—44no—
76C2×#4313—22no—
77C2×C8×D11—22no—
78C4×D44—21no—
79C4×D44—21no—
80C4×D44D411yescharacteristic
81C4×D44D411yescharacteristic
82C4×D44C2311yescharacteristic
83C4×D44C2311yescharacteristic
84C11×#103—22no—
85C11×#103—22no—
86C11×#102—22no—
87C11×#102—22no—
88C11×#97D412yes—
89C4×C8×C11C2312yes—
90#66896—21no—
91#66896—21no—
92C22⋊(C11⋊C8)—21no—
93(C2×D11)⋊C8—22no—
94(C2×D11)⋊C8—22no—
95#66873—22no—
96#66873—22no—
97#66873—21no—
98#66873—21no—
99#66872—22no—
100#66872—22no—
101#66871—21no—
102#66871—21no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)C2312yes—
106C4⋊(C11⋊C8)C2312yes—
107C4⋊(C11⋊C8)C2311yescharacteristic
108C4⋊(C11⋊C8)C2311yescharacteristic
109C4×C11⋊C8—21no—
110#19168—111nomaximal, Sylow
111C23×D11—21no—
112C11×#41—42no—
113C11×#41—42no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—41no—
117C2×Q8×C11—82no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—41no—
122C22×C4×C11—41no—
123C22×C4×C11—41no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11#4111yescharacteristic
127C22×Dic11—21no—
128C2×D44—22no—
129C2×D44—21no—
130C2×D44—41no—
131C2×D44C2×D411yescharacteristic
132C2×D44C2×D411yescharacteristic
133C2×C4×D11—21no—
134C2×C4×D11—21no—
135C2×C4×D11—21no—
136C2×C4×D11—21no—
137C2×C4×D11—42no—
138C2×C4×D11—42no—
139C11×M16—22no—
140C11×M16—22no—
141C2×C8×C11C2×D412yes—
142C2×C8×C11C2×D412yes—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—41no—
148C11×C4⋊C4—41no—
149C11×C22⋊C4—41no—
150C11×C22⋊C4—41no—
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11#4111yescharacteristic
154C42×C11C2411yescharacteristic
155#4323—42no—
156#4323—42no—
157(C2×D11)⋊C4—21no—
158(C2×D11)⋊C4—21no—
159(C2×D11)⋊C4—21no—
160(C2×D11)⋊C4—21no—
161C4⋊Dic11—21no—
162C4⋊Dic11C2×D411yescharacteristic
163C4⋊Dic11C2×D411yescharacteristic
164#4318—42no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—42no—
170#4313—44no—
171C8×D11—44no—
172#3141D1111yescharacteristic, complemented
173#3100—111no—
174C2×#476—111no—
175D4×M16—111no—
176#1703—112no—
177#1697—112no—
178#1683—112no—
179#1677—112no—
180#1565—111no—
181#1548—111no—
182#1547—111no—
183C23×C11—41no—
184C23×C11#12111yescharacteristic
185C22×D11—21no—
186C22×D11—21no—
187C22×D11—42no—
188C22×D11—42no—
189C22×D11—81no—
190Q8×C11—41no—
191Q8×C11—41no—
192Q8×C11—82no—
193Q8×C11—82no—
194D4×C11—41no—
195D4×C11—41no—
196D4×C11—41no—
197D4×C11—41no—
198D4×C11—81no—
199D4×C11—82no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—82no—
206C2×C4×C11—82no—
207C2×C4×C11#12111yescharacteristic
208C2×C4×C11#12111yescharacteristic
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11#13512yes—
211C2×C4×C11AGL(1,ℤ/8)12yes—
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×Dic11—21no—
216C2×Dic11—21no—
217C2×Dic11—42no—
218D44—21no—
219D44—21no—
220D44—21no—
221D44—42no—
222D44#13712yes—
223C4×D11—41no—
224C4×D11—41no—
225C4×D11—41no—
226C4×D11—41no—
227C4×D11—42no—
228C4×D11—42no—
229C8×C11—22no—
230C8×C11—22no—
231C11⋊C8—42no—
232C11⋊C8—41no—
233C11⋊C8—42no—
234C11⋊C8—41no—
235C22×M16—221no—
236#532C2×D1111yescharacteristic
237C2×C4⋊Q8C2×D1111yescharacteristic
238C2×C4×D4—111no—
239#489—22no—
240#487C2×D1112yescomplemented
241#486C2×D1112yescomplemented
242#480—221no—
243#476—112no—
244#476—112no—
245#476—221no—
246#476—221no—
247#474—111no—
248#474—111no—
249#459—111no—
250#459—111no—
251#447—221no—
252C4×D8—221no—
253C4×D8—221no—
254#436—112no—
255#435—222no—
256C8×D4—112no—
257#431—111no—
258C2×#106—221no—
259#423—111no—
260C2×C4⋊C8—111no—
261#417—21no—
262#417—21no—
263C2×#102—221no—
264#407—221no—
265C4×M16C2×D1111yescharacteristic
266#335—112no—
267#334—112no—
268#333—112no—
269#333—112no—
270#332—112no—
271#331—112no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—81no—
275C22×C11—81no—
276C22×C11—81no—
277C22×C11#46312yes—
278C22×C11C2×#12111yescharacteristic
279C2×D11—22no—
280C2×D11—41no—
281C2×D11—41no—
282C2×D11—41no—
283C2×D11—41no—
284C2×D11—41no—
285C2×D11—84no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—81no—
290C4×C11—82no—
291C4×C11#46312yes—
292C4×C11C2×#13511yescharacteristic
293C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
294C4×C11C2×#13711yescharacteristic
295C4×C11#57511yescharacteristic
296Dic11—41no—
297Dic11—41no—
298C2×#41—21no—
299C22×Q8—21no—
300C22×D4—111no—
301C23×C4—221no—
302C2×D8—221no—
303C2×D8—221no—
304C2×M16—221no—
305C2×M16—222no—
306C2×M16—444no—
307C2×M16C22⋊D1111yescharacteristic
308C2×M16C22⋊D1111yescharacteristic
309C22×C8—221no—
310C22×C8—222no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8C22×D1112yes—
315C4⋊Q8C22×D1111yescharacteristic
316#127C22×D1111yescharacteristic
317#124—21no—
318#121—21no—
319#121—21no—
320C4×D4—21no—
321C4×D4—21no—
322C4×D4—111no—
323C4×D4—111no—
324C4×D4—111no—
325C4×D4—111no—
326C4×D4—221no—
327C4×D4—221no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—111no—
331C2×C22⋊C4—221no—
332C2×C42C22×D1111yescharacteristic
333#107—221no—
334#107—221no—
335#106—222no—
336#106—222no—
337C4⋊C8—112no—
338C4⋊C8—112no—
339C4⋊C8—111no—
340C4⋊C8—111no—
341C4⋊C8—221no—
342C4⋊C8—221no—
343#103—22no—
344#103—22no—
345#102—22no—
346#102—22no—
347#102—222no—
348#102—222no—
349#102—221no—
350#102—221no—
351#102—221no—
352#102—221no—
353C22⋊C8—221no—
354C22⋊C8—222no—
355C22⋊C8—222no—
356#97C22⋊D1112yes—
357C4×C8—221no—
358C4×C8C22×D1112yes—
359C2×C11—22no—
360C2×C11—161no—
361C2×C11C2×#46311yescharacteristic
362C2×C11#305611yescharacteristic
363C2×C11#306811yescharacteristic
364D11—42no—
365D11—81no—
366C24—221no—
367#41—42no—
368#41—42no—
369C2×Q8—22no—
370C2×Q8—21no—
371C2×Q8—41no—
372C2×Q8—82no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—41no—
377C2×D4—111no—
378C2×D4—111no—
379C2×D4—222no—
380C2×D4—221no—
381C2×D4—441no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—221no—
385C22×C4—221no—
386C22×C4—221no—
387C22×C4—221no—
388C22×C4—221no—
389C22×C4—442no—
390C22×C4—442no—
391C22×C4D4×D1111yescharacteristic
392C22×C4#434111yescharacteristic
393C22×C4C2×C22⋊D1111yescharacteristic
394D8—442no—
395D8—442no—
396M16—22no—
397M16—22no—
398M16—444no—
399M16—442no—
400C2×C8—221no—
401C2×C8—221no—
402C2×C8—222no—
403C2×C8—222no—
404C2×C8—444no—
405C2×C8—442no—
406C2×C8C2×C22⋊D1112yes—
407C2×C8C2×C22⋊D1112yes—
408C4⋊C4—22no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—22no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C4⋊C4—111no—
415C4⋊C4—111no—
416C4⋊C4—221no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—221no—
420C22⋊C4—221no—
421C22⋊C4—221no—
422C22⋊C4—221no—
423C42D4×D1111yescharacteristic
424C42#434111yescharacteristic
425C42C2×C22⋊D1111yescharacteristic
426C42C23×D1111yescharacteristic
427C11#1916811yescharacteristic, complemented, Sylow
428C23—41no—
429C23—221no—
430C23—221no—
431C23—442no—
432C23—442no—
433C23—881no—
434C23#6699111yescharacteristic
435Q8—41no—
436Q8—41no—
437Q8—82no—
438Q8—82no—
439D4—41no—
440D4—41no—
441D4—41no—
442D4—41no—
443D4—81no—
444D4—82no—
445D4—112no—
446D4—221no—
447D4—221no—
448D4—221no—
449D4—442no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—82no—
456C2×C4—82no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—442no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4#6699111yescharacteristic
467C2×C4#6699111yescharacteristic
468C2×C4#6699111yescharacteristic
469C2×C4#6700212yes—
470C2×C4#6700312yes—
471C2×C4C2×D4×D1111yescharacteristic
472C2×C4C2×#434111yescharacteristic
473C2×C4C22×C22⋊D1111yescharacteristic
474C8—22no—
475C8—22no—
476C8—441no—
477C8—442no—
478C8—441no—
479C8—442no—
480C22—21no—
481C22—21no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22—222no—
486C22—441no—
487C22—441no—
488C22—441no—
489C22—441no—
490C22—441no—
491C22—884no—
492C22#1062267012yes—
493C22C2×#6699111yescharacteristic
494C4—21no—
495C4—21no—
496C4—21no—
497C4—81no—
498C4—82no—
499C4—441no—
500C4—441no—
501C4#1062267012yes—
502C4D11×#13711yescharacteristic
503C4#1062330811yescharacteristic
504C4C2×#6700211yescharacteristic
505C4C2×#6700311yescharacteristic
506C2—22no—
507C2—161no—
508C2—442no—
509C2—881no—
510C2C2×#1062267011yescharacteristic
511C2#1307824011yescharacteristic
512C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3141C2
socleC22×C11C2×#121
prime radical#13078612C2
hypercenter#3141D11
hypocenterC11#19168
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

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

NH ≅ G/Ntype
2. C2×#10622697C2semidirect
3. M16×D44C2semidirect
4. #13068188C2semidirect
5. #13068146C2semidirect
6. #13068064C2semidirect
7. #13068022C2semidirect
8. #13067368C2semidirect
9. #13067297C2semidirect
10. #13067293C2semidirect
11. C11×#3141C2semidirect
17. C11×#487C22semidirect
18. C11×#486C22semidirect
43. #10622185C22semidirect
44. #10622184C22semidirect
45. #10622184C22semidirect
46. #10622182C22semidirect
47. #10622096C22semidirect
48. #10622095C22semidirect
172. #3141D11semidirect
240. #487C2×D11semidirect
241. #486C2×D11semidirect
427. C11#19168semidirect

Maximal subgroups

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

subgroupindex
#130786122
C2×#106226972
M16×D442
#130681882
#130681462
#130680642
#130680222
#130673682
#130672972
#130672932
C11×#31412
#1916811