Finite Group Databasebeta

← #14657113

Subgroups — #14657113

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074550C211yesmaximal, characteristic
2#13068931C211yesmaximal, characteristic
3#13068924C211yesmaximal, characteristic, complemented
4C2×#10622089C211yesmaximal, characteristic
5#13066881C211yesmaximal, characteristic, complemented
6#13066458C211yesmaximal, characteristic, complemented
7C2×C11×#328C211yesmaximal, characteristic, complemented
8C2×C11×C22⋊Q8C2211yescharacteristic
9C2×#66983C2211yescharacteristic
10C22×C4⋊Dic11—21no—
11C22×C4⋊Dic11C2211yescharacteristic
12C2×C11×C22⋊C8C2211yescharacteristic
13C2×C11×#95C2211yescharacteristic
14#10622844—21no—
15C2×#66899—21no—
16C2×C11⋊#95—21no—
17C2×C11⋊#95C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19C2×#66885—21no—
20#10622606—21no—
21#10622604—21no—
22#10622599—21no—
23#10622571—21no—
24#10622571—21no—
25C11×#328—22no—
26#10622189—21no—
27#10622167—21no—
28#10622089—22no—
29C22×Q8×C11D411yescharacteristic
30C23×C4×C11—21no—
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11—21no—
33C23×Dic11—21no—
34C23×Dic11D411yescharacteristic
35C23×Dic11D411yescharacteristic
36C22×D44D411yescharacteristic
37C22×C8×C11—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4D411yescharacteristic
44C2×C11×C22⋊C4—21no—
45#66983—21no—
46#66983—21no—
47#66983—21no—
48#66983—21no—
49C2×(C2×D11)⋊C4—21no—
50C2×(C2×D11)⋊C4—21no—
51C2×(C2×D11)⋊C4—21no—
52C2×(C2×D11)⋊C4—21no—
53C2×(C2×D11)⋊C4—21no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—42no—
57C2×C4⋊Dic11—42no—
58C2×C4⋊Dic11—42no—
59C2×C4⋊Dic11—42no—
60C2×C4⋊Dic11D411yescharacteristic
61C22×C11⋊C8—21no—
62C11×C22⋊C8—21no—
63C11×C22⋊C8—21no—
64C11×#95—21no—
65C11×#95D412yes—
66#66899—42no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C11⋊#95—42no—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)—21no—
76#66885—42no—
77#10405—111nomaximal, Sylow
78C24×C11C2×D411yescharacteristic
79C23×D11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11#4111yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C22×C4×C11#4111yescharacteristic
101C2×C22⋊D11—41no—
102C2×C22⋊D11—41no—
103C2×C22⋊D11—41no—
104C2×C22⋊D11—41no—
105C2×C22⋊D11—41no—
106C2×C22⋊D11—41no—
107C22×Dic11—22no—
108C22×Dic11—21no—
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—21no—
115C22×Dic11—41no—
116C22×Dic11—41no—
117C22×Dic11—41no—
118C22×Dic11—41no—
119C22×Dic11—41no—
120C22×Dic11—41no—
121C22×Dic11—41no—
122C22×Dic11—41no—
123C22×Dic11—41no—
124C22×Dic11—41no—
125C2×D44—21no—
126C2×D44—21no—
127C2×D44—41no—
128C2×D44—41no—
129C2×C8×C11—41no—
130C2×C8×C11—41no—
131C2×C8×C11—41no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—41no—
135C11×C4⋊C4—41no—
136C11×C22⋊C4—41no—
137C11×C22⋊C4—41no—
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4—41no—
140(C2×D11)⋊C4—81no—
141(C2×D11)⋊C4—81no—
142(C2×D11)⋊C4—81no—
143(C2×D11)⋊C4—81no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—41no—
149C4⋊Dic11—41no—
150C4⋊Dic11—48no—
151C2×C11⋊C8—41no—
152C2×C11⋊C8—41no—
153C2×C11⋊C8—41no—
154#2639—111no—
155#1874—111no—
156#1872—111no—
157C2×#328D1111yescharacteristic, complemented
158C2×#327—111no—
159#1444—111no—
160#1280—111no—
161C23×C11—21no—
162C23×C11—21no—
163C23×C11—21no—
164C23×C11—21no—
165C23×C11#12011yescharacteristic
166C23×C11#12111yescharacteristic
167C23×C11#12411yescharacteristic
168C23×C11#13511yescharacteristic
169C23×C11#13511yescharacteristic
170C23×C11AGL(1,ℤ/8)11yescharacteristic
171C23×C11#13711yescharacteristic
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175C22×D11—41no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—41no—
179Q8×C11—42no—
180Q8×C11—81no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—24no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11#12111yescharacteristic
203C2×C4×C11#12111yescharacteristic
204C2×C4×C11#12311yescharacteristic
205C2×C4×C11#12311yescharacteristic
206C22⋊D11—81no—
207C22⋊D11—81no—
208C22⋊D11—81no—
209C22⋊D11—81no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—42no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—81no—
225C2×Dic11—81no—
226C2×Dic11—81no—
227C2×Dic11—81no—
228C2×Dic11—81no—
229C2×Dic11—81no—
230D44—42no—
231D44—81no—
232C8×C11—81no—
233C11⋊C8—81no—
234C2×C22⋊Q8C2×D1111yescharacteristic
235C2×#121—111no—
236C22×C4⋊C4—111no—
237C22×C4⋊C4—221no—
238C2×#103—221no—
239C2×#102—221no—
240C2×C22⋊C8—111no—
241C2×C22⋊C8C2×D1111yescharacteristic
242#400—221no—
243#397—221no—
244#394—221no—
245#393—221no—
246#386—221no—
247#386—221no—
248C2×#95—111no—
249C2×#95—221no—
250C2×#95C2×D1111yescharacteristic
251#340—221no—
252#340—221no—
253#328—22no—
254#327—222no—
255C22×C11—21no—
256C22×C11—21no—
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#39411yescharacteristic
268C22×C11#44911yescharacteristic
269C22×C11#45211yescharacteristic
270C22×C11#45311yescharacteristic
271C22×C11#45611yescharacteristic
272C22×C11B(4,𝔽2)11yescharacteristic
273C22×C11#45811yescharacteristic
274C22×C11#46311yescharacteristic
275C22×C11#46411yescharacteristic
276C22×C11#48811yescharacteristic
277C22×C11#48911yescharacteristic
278C2×D11—81no—
279C2×D11—81no—
280C2×D11—81no—
281C2×D11—81no—
282C2×D11—81no—
283C2×D11—81no—
284C2×D11—81no—
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—44no—
290C4×C11—81no—
291C4×C11—81no—
292Dic11—81no—
293Dic11—82no—
294Dic11—81no—
295Dic11—81no—
296C22×Q8D4411yescharacteristic
297C22×D4—111no—
298C22×D4—221no—
299C23×C4—21no—
300C23×C4—111no—
301C23×C4—111no—
302C23×C4—221no—
303C23×C4C22×D1111yescharacteristic
304C22×C8—21no—
305C22×C8—221no—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310#121—221no—
311#121—221no—
312#121—221no—
313#121—221no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—111no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4—442no—
319C2×C4⋊C4—442no—
320C2×C4⋊C4—442no—
321C2×C4⋊C4—442no—
322C2×C4⋊C4D4411yescharacteristic
323C2×C22⋊C4—21no—
324C2×C22⋊C4—221no—
325C2×C22⋊C4—221no—
326C2×C22⋊C4—221no—
327C2×C22⋊C4—221no—
328C2×C22⋊C4—221no—
329#103—442no—
330#102—442no—
331C22⋊C8—21no—
332C22⋊C8—21no—
333C22⋊C8—221no—
334C22⋊C8—221no—
335#95—21no—
336#95—221no—
337#95—221no—
338#95—221no—
339#95—221no—
340#95—221no—
341#95—221no—
342#95—442no—
343#95C22⋊D1112yes—
344C2×C11—21no—
345C2×C11—21no—
346C2×C11—21no—
347C2×C11—21no—
348C2×C11#160011yescharacteristic
349C2×C11#160311yescharacteristic
350C2×C11#160911yescharacteristic
351C2×C11#161811yescharacteristic
352C2×C11#203911yescharacteristic
353C2×C11#204211yescharacteristic
354C2×C11#204411yescharacteristic
355D11—161no—
356C24—221no—
357C24D4×D1111yescharacteristic
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—41no—
361C2×Q8—41no—
362C2×D4—221no—
363C2×D4—221no—
364C2×D4—441no—
365C2×D4—441no—
366C2×D4—441no—
367C2×D4—441no—
368C2×D4—441no—
369C2×D4—441no—
370C2×D4—441no—
371C2×D4—441no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—222no—
384C22×C4—221no—
385C22×C4—221no—
386C22×C4—221no—
387C22×C4—221no—
388C22×C4—221no—
389C22×C4—221no—
390C22×C4—221no—
391C22×C4—441no—
392C22×C4—441no—
393C22×C4—441no—
394C22×C4—441no—
395C22×C4—441no—
396C22×C4—441no—
397C22×C4—441no—
398C22×C4—441no—
399C22×C4—441no—
400C22×C4—441no—
401C22×C4C2×D4411yescharacteristic
402C22×C4#433911yescharacteristic
403C22×C4D4×D1111yescharacteristic
404C22×C4#434111yescharacteristic
405C22×C4#434111yescharacteristic
406C22×C4C2×C22⋊D1111yescharacteristic
407C2×C8—41no—
408C2×C8—41no—
409C2×C8—41no—
410C2×C8—441no—
411C2×C8—441no—
412C2×C8—441no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—222no—
418C4⋊C4—222no—
419C4⋊C4—221no—
420C4⋊C4—221no—
421C4⋊C4—441no—
422C4⋊C4—441no—
423C4⋊C4—448no—
424C22⋊C4—41no—
425C22⋊C4—41no—
426C22⋊C4—441no—
427C22⋊C4—441no—
428C22⋊C4—881no—
429C22⋊C4—881no—
430C22⋊C4—881no—
431C22⋊C4—881no—
432C11#1040511yescharacteristic, complemented, Sylow
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—441no—
438C23—441no—
439C23—441no—
440C23—441no—
441C23—441no—
442C23—441no—
443C23—441no—
444C23#6693511yescharacteristic
445C23#6693811yescharacteristic
446C23#6696711yescharacteristic
447C23#6696911yescharacteristic
448C23#6697111yescharacteristic
449C23#6697211yescharacteristic
450C23#6699211yescharacteristic
451Q8—42no—
452Q8—81no—
453D4—442no—
454D4—881no—
455D4—881no—
456D4—881no—
457D4—881no—
458D4—881no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—24no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—442no—
481C2×C4—442no—
482C2×C4—442no—
483C2×C4—442no—
484C2×C4—441no—
485C2×C4—441no—
486C2×C4—442no—
487C2×C4—441no—
488C2×C4—441no—
489C2×C4—441no—
490C2×C4—441no—
491C2×C4—441no—
492C2×C4—441no—
493C2×C4—441no—
494C2×C4—881no—
495C2×C4—881no—
496C2×C4—881no—
497C2×C4—881no—
498C2×C4—881no—
499C2×C4—881no—
500C2×C4#6693611yescharacteristic
501C2×C4#6693911yescharacteristic
502C2×C4#6698311yescharacteristic
503C2×C4#6699111yescharacteristic
504C8—81no—
505C8—881no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—881no—
519C22—881no—
520C22—881no—
521C22—881no—
522C22—881no—
523C22—881no—
524C22—881no—
525C22#1062235411yescharacteristic
526C22#1062235511yescharacteristic
527C22#1062240811yescharacteristic
528C22#1062241311yescharacteristic
529C22#1062242311yescharacteristic
530C22#1062242411yescharacteristic
531C22#1062243511yescharacteristic
532C22#1062243911yescharacteristic
533C22#1062257411yescharacteristic
534C22#1062277811yescharacteristic
535C22#1062279811yescharacteristic
536C4—21no—
537C4—21no—
538C4—21no—
539C4—21no—
540C4—44no—
541C4—81no—
542C4—81no—
543C4—881no—
544C4—881no—
545C4—882no—
546C4—881no—
547C2—21no—
548C2—21no—
549C2—21no—
550C2—21no—
551C2—1761no—
552C2#1306756511yescharacteristic
553C2#1306758211yescharacteristic
554C2#1306761611yescharacteristic
555C2#1306766711yescharacteristic
556C2#1306983911yescharacteristic
557C2#1306985411yescharacteristic
558C2#1306986611yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC2×C11×#328C2
socleC23×C11#120
prime radicalC2×#66983C22
hypercenterC2×#328D11
hypocenterC11#10405
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
3. #13068924C2semidirect
5. #13066881C2semidirect
6. #13066458C2semidirect
7. C2×C11×#328C2semidirect
157. C2×#328D11semidirect
432. C11#10405semidirect

Maximal subgroups

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

subgroupindex
#130745502
#130689312
#130689242
C2×#106220892
#130668812
#130664582
C2×C11×#3282
#1040511