Finite Group Databasebeta

← #14644656

Subgroups — #14644656

Order 2816.

712 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071122C211yesmaximal, characteristic
2#13068380C211yesmaximal, characteristic, complemented
3C2×#10622108C211yesmaximal, characteristic
4C2×#10622089C211yesmaximal, characteristic
5#13066841C211yesmaximal, characteristic, complemented
6#13066494C211yesmaximal, characteristic, complemented
7C11×#1294C211yesmaximal, characteristic, complemented
8C2×#66983C2211yescharacteristic
9C22×C4×Dic11C2211yescharacteristic
10C2×#66946C411yescharacteristic, complemented
11C2×(C22⋊D11)⋊C4—21no—
12C2×C11×C22⋊C8C2211yescharacteristic
13C11×#380C2211yescharacteristic
14C2×C11×#95C2211yescharacteristic
15C2×C11⋊#95—21no—
16C2×C11⋊#95—21no—
17C2×C11⋊#95C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19C2×#66879—21no—
20#10622601C411yescharacteristic, complemented
21C4⋊C4×Dic11C411yescharacteristic, complemented
22#10622586C411yescharacteristic, complemented
23#10622571—21no—
24#10622282—21no—
25#10622279—21no—
26#10622188—21no—
27#10622108C414yescomplemented
28#10622089C414yescomplemented
29C23×C4×C11—21no—
30C23×C4×C11C2311yescharacteristic
31C22×C22⋊D11—21no—
32C23×Dic11—21no—
33C23×Dic11D411yescharacteristic
34C23×Dic11D411yescharacteristic
35C22×D44C2×C411yescharacteristic
36C22×C4×D11—21no—
37C22×C8×C11—21no—
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4—21no—
41#66983—21no—
42#66983—21no—
43#66983C2×C412yes—
44#66983C2×C412yes—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×C4⋊Dic11C2×C411yescharacteristic
50C2×Dic11⋊C4—21no—
51C2×C4×Dic11—21no—
52C2×C4×Dic11—42no—
53C2×C4×Dic11C2×C411yescharacteristic
54C2×C4×Dic11C2×C411yescharacteristic
55C2×C4×Dic11D411yescharacteristic
56C2×C4×Dic11D411yescharacteristic
57C22×C11⋊C8—21no—
58#66946—42no—
59(C22⋊D11)⋊C4—42no—
60(C22⋊D11)⋊C4—42no—
61C11×C22⋊C8—21no—
62C11×C22⋊C8C2×C412yescomplemented
63C11×#95—21no—
64C11×#95—21no—
65C11×#95C2×C412yescomplemented
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—42no—
70C11⋊#95—42no—
71C11⋊#95C2×C412yescomplemented
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)C2×C412yescomplemented
74#66879—42no—
75#8216—111nomaximal, Sylow
76C24×C11C2×D411yescharacteristic
77C23×D11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—22no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C2×C22⋊D11—22no—
96C2×C22⋊D11—22no—
97C2×C22⋊D11—41no—
98C2×C22⋊D11—41no—
99C2×C22⋊D11—41no—
100C2×C22⋊D11—41no—
101C22×Dic11—22no—
102C22×Dic11—21no—
103C22×Dic11—22no—
104C22×Dic11—21no—
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11—21no—
108C22×Dic11—41no—
109C22×Dic11—41no—
110C22×Dic11—41no—
111C22×Dic11—41no—
112C22×Dic11—41no—
113C22×Dic11—41no—
114C22×Dic11—41no—
115C22×Dic11—41no—
116C22×Dic11—41no—
117C22×Dic11C22⋊C411yescharacteristic
118C22×Dic11C22⋊C411yescharacteristic
119C22×Dic11C22⋊C411yescharacteristic
120C22×Dic11C22⋊C411yescharacteristic
121C2×D44—21no—
122C2×D44—41no—
123C2×D44—41no—
124C2×D44C4212yes—
125C2×C4×D11—42no—
126C2×C4×D11—42no—
127C2×C4×D11—42no—
128C2×C8×C11—22no—
129C2×C8×C11—41no—
130C2×C8×C11—41no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—41no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135(C2×D11)⋊C4—22no—
136(C2×D11)⋊C4—22no—
137(C2×D11)⋊C4—42no—
138(C2×D11)⋊C4—42no—
139(C2×D11)⋊C4—42no—
140C4⋊Dic11—21no—
141C4⋊Dic11C4212yes—
142Dic11⋊C4—42no—
143C4×Dic11—22no—
144C4×Dic11—22no—
145C4×Dic11—41no—
146C4×Dic11—41no—
147C4×Dic11—42no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—41no—
150C2×C11⋊C8—41no—
151C4×#121—111no—
152#1749—111no—
153C2×#327—111no—
154C2×#327—111no—
155#1434—111no—
156#1294—111no—
157#1294D1111yescharacteristic, complemented
158C23×C11—21no—
159C23×C11—21no—
160C23×C11—21no—
161C23×C11—21no—
162C23×C11C2×C22⋊C411yescharacteristic
163C23×C11C4×D411yescharacteristic
164C23×C11C4×D411yescharacteristic
165C23×C11AGL(1,ℤ/8)11yescharacteristic
166C23×C11AGL(1,ℤ/8)11yescharacteristic
167C23×C11AGL(1,ℤ/8)11yescharacteristic
168C23×C11#13711yescharacteristic
169C22×D11—22no—
170C22×D11—41no—
171C22×D11—41no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175C22×D11—41no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—42no—
193C2×C4×C11—81no—
194C2×C4×C11—81no—
195C2×C4×C11—81no—
196C2×C4×C11—81no—
197C2×C4×C11C2×C4211yescharacteristic
198C2×C4×C11#11711yescharacteristic
199C2×C4×C11C4×D411yescharacteristic
200C2×C4×C11C4×D411yescharacteristic
201C22⋊D11—42no—
202C22⋊D11—42no—
203C22⋊D11—42no—
204C22⋊D11—42no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—22no—
208C2×Dic11—21no—
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—21no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—81no—
227C2×Dic11—81no—
228C2×Dic11—81no—
229C2×Dic11—81no—
230C2×Dic11#9912yes—
231D44—42no—
232D44—42no—
233C4×D11—84no—
234C8×C11—42no—
235C11⋊C8—42no—
236C2×#121—111no—
237C2×C4×D4—111no—
238C2×C4×D4—221no—
239C22×C42—111no—
240C2×C22⋊C8—111no—
241C2×C22⋊C8C2×D1111yescharacteristic
242C2×#97—221no—
243#390—111no—
244#389—111no—
245#388—221no—
246#386—221no—
247#380C2×D1111yescharacteristic
248C4×C4⋊C4—111no—
249C4×C22⋊C4—221no—
250C2×#95—111no—
251C2×#95—221no—
252C2×#95—221no—
253C2×#95C2×D1111yescharacteristic
254#336—221no—
255#327—114no—
256#327—114no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11C4×C22⋊C411yescharacteristic
270C22×C11C2×#9911yescharacteristic
271C22×C11#41011yescharacteristic
272C22×C11#41711yescharacteristic
273C22×C11#41811yescharacteristic
274C22×C11#42111yescharacteristic
275C22×C11#42111yescharacteristic
276C22×C11#44011yescharacteristic
277C22×C11#44011yescharacteristic
278C22×C11#44211yescharacteristic
279C22×C11#44211yescharacteristic
280C2×D11—42no—
281C2×D11—42no—
282C2×D11—42no—
283C2×D11—81no—
284C2×D11—81no—
285C2×D11—81no—
286C2×D11—81no—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—21no—
290C4×C11—21no—
291C4×C11—82no—
292C4×C11—81no—
293C4×C11—81no—
294Dic11—22no—
295Dic11—42no—
296Dic11—41no—
297Dic11—41no—
298Dic11—41no—
299Dic11—82no—
300C22×D4—111no—
301C22×D4—221no—
302C23×C4—21no—
303C23×C4—111no—
304C23×C4—111no—
305C23×C4—221no—
306C23×C4—221no—
307C23×C4C22×D1111yescharacteristic
308C22×C8—21no—
309C22×C8—221no—
310#121—112no—
311#121—112no—
312#121—221no—
313#121—221no—
314C4×D4—442no—
315C4×D4—442no—
316C4×D4—442no—
317C2×C4⋊C4—111no—
318C2×C4⋊C4—221no—
319C2×C4⋊C4C4×D1111yescharacteristic
320C2×C4⋊C4C4×D1111yescharacteristic
321C2×C22⋊C4—21no—
322C2×C22⋊C4—221no—
323C2×C22⋊C4—221no—
324C2×C22⋊C4—221no—
325C2×C22⋊C4—221no—
326C2×C42—111no—
327C2×C42—111no—
328C2×C42—111no—
329C2×C42—111no—
330C2×C42—221no—
331C2×C42—442no—
332C22⋊C8—21no—
333C22⋊C8—112no—
334C22⋊C8—221no—
335C22⋊C8C4×D1112yescomplemented
336#97—442no—
337#95—21no—
338#95—21no—
339#95—112no—
340#95—221no—
341#95—221no—
342#95—221no—
343#95—442no—
344#95—442no—
345#95C4×D1112yescomplemented
346C2×C11—21no—
347C2×C11—21no—
348C2×C11—21no—
349C2×C11—21no—
350C2×C11#151011yescharacteristic
351C2×C11#151211yescharacteristic
352C2×C11#151311yescharacteristic
353C2×C11#151411yescharacteristic
354C2×C11C4×#9911yescharacteristic
355C2×C11#175911yescharacteristic
356C2×C11#176211yescharacteristic
357D11—82no—
358C24—221no—
359C24D4×D1111yescharacteristic
360C2×D4—112no—
361C2×D4—222no—
362C2×D4—222no—
363C2×D4—221no—
364C2×D4—441no—
365C2×D4—441no—
366C2×D4—441no—
367C2×D4—441no—
368C2×D4—441no—
369C2×D4—441no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—111no—
382C22×C4—111no—
383C22×C4—111no—
384C22×C4—111no—
385C22×C4—222no—
386C22×C4—221no—
387C22×C4—221no—
388C22×C4—221no—
389C22×C4—221no—
390C22×C4—221no—
391C22×C4—222no—
392C22×C4—442no—
393C22×C4—442no—
394C22×C4—442no—
395C22×C4—441no—
396C22×C4—441no—
397C22×C4—441no—
398C22×C4—441no—
399C22×C4—441no—
400C22×C4—441no—
401C22×C4—441no—
402C22×C4—441no—
403C22×C4—441no—
404C22×C4C2×C4×D1111yescharacteristic
405C22×C4C2×C4×D1111yescharacteristic
406C22×C4C2×C4×D1111yescharacteristic
407C22×C4D4×D1111yescharacteristic
408C22×C4#434111yescharacteristic
409C22×C4#434311yescharacteristic
410C2×C8—22no—
411C2×C8—41no—
412C2×C8—41no—
413C2×C8—222no—
414C2×C8—441no—
415C2×C8—441no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—112no—
419C4⋊C4—221no—
420C4⋊C4—442no—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C22⋊C4—222no—
424C22⋊C4—222no—
425C22⋊C4—442no—
426C22⋊C4—442no—
427C22⋊C4—442no—
428C42—222no—
429C42—222no—
430C42—441no—
431C42—441no—
432C42—442no—
433C11#821611yescharacteristic, complemented, Sylow
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—222no—
439C23—441no—
440C23—441no—
441C23—441no—
442C23—441no—
443C23—441no—
444C23—441no—
445C23C22⋊C4×D1111yescharacteristic
446C23(C22⋊D11)⋊C411yescharacteristic
447C23#6694611yescharacteristic
448C23#6696411yescharacteristic
449C23#6696711yescharacteristic
450C23#6696711yescharacteristic
451C23#6697111yescharacteristic
452D4—442no—
453D4—442no—
454D4—442no—
455D4—442no—
456D4—442no—
457D4—442no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—81no—
476C2×C4—81no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4—112no—
480C2×C4—221no—
481C2×C4—221no—
482C2×C4—222no—
483C2×C4—221no—
484C2×C4—221no—
485C2×C4—221no—
486C2×C4—221no—
487C2×C4—221no—
488C2×C4—221no—
489C2×C4—221no—
490C2×C4—221no—
491C2×C4—221no—
492C2×C4—442no—
493C2×C4—442no—
494C2×C4—442no—
495C2×C4—442no—
496C2×C4—441no—
497C2×C4—441no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—884no—
502C2×C4—881no—
503C2×C4—881no—
504C2×C4—881no—
505C2×C4—881no—
506C2×C4C42×D1111yescharacteristic
507C2×C4(C22⋊D11)⋊C411yescharacteristic
508C2×C4#6694511yescharacteristic
509C2×C4#6694611yescharacteristic
510C8—42no—
511C8—442no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—442no—
525C22—442no—
526C22—442no—
527C22—881no—
528C22—881no—
529C22—881no—
530C22—881no—
531C22#1062227911yescharacteristic
532C22#1062235311yescharacteristic
533C22D11×#9911yescharacteristic
534C22#1062238311yescharacteristic
535C22#1062239811yescharacteristic
536C22#1062241611yescharacteristic
537C22#1062243011yescharacteristic
538C22#1062243411yescharacteristic
539C22#1062243411yescharacteristic
540C22#1062248211yescharacteristic
541C22#1062250211yescharacteristic
542C4—21no—
543C4—21no—
544C4—21no—
545C4—21no—
546C4—82no—
547C4—81no—
548C4—81no—
549C4—222no—
550C4—441no—
551C4—441no—
552C4—441no—
553C4—442no—
554C4—882no—
555C2—21no—
556C2—21no—
557C2—21no—
558C2—21no—
559C2—882no—
560C2#1306714311yescharacteristic
561C2#1306715311yescharacteristic
562C2#1306715811yescharacteristic
563C2#1306716111yescharacteristic
564C2#1306840311yescharacteristic
565C2#1306842511yescharacteristic
566C2#1306844011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1294D11
hypocenterC11#8216
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
2. #13068380C2semidirect
5. #13066841C2semidirect
6. #13066494C2semidirect
7. C11×#1294C2semidirect
10. C2×#66946C4semidirect
20. #10622601C4semidirect
21. C4⋊C4×Dic11C4semidirect
22. #10622586C4semidirect
27. #10622108C4semidirect
28. #10622089C4semidirect
62. C11×C22⋊C8C2×C4semidirect
65. C11×#95C2×C4semidirect
71. C11⋊#95C2×C4semidirect
73. C22⋊(C11⋊C8)C2×C4semidirect
157. #1294D11semidirect
335. C22⋊C8C4×D11semidirect
345. #95C4×D11semidirect
433. C11#8216semidirect

Maximal subgroups

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

subgroupindex
#130711222
#130683802
C2×#106221082
C2×#106220892
#130668412
#130664942
C11×#12942
#821611