Finite Group Databasebeta

← #14650347

Subgroups — #14650347

Order 2816.

648 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079367C211yesmaximal, characteristic
2#13071663C211yesmaximal, characteristic, complemented
3#13069451C211yesmaximal, characteristic, complemented
4#13067183C211yesmaximal, characteristic, complemented
5C2×#10622089C211yesmaximal, characteristic, complemented
6#13066462C211yesmaximal, characteristic, complemented
7C11×#1294C211yesmaximal, characteristic, complemented
8C2×#66983C2211yescharacteristic
9C2×#66983C2211yescharacteristic
10C2×C4×C22⋊D11—21no—
11C2×C11×C22⋊C8C2211yescharacteristic
12C11×#380C2211yescharacteristic
13C2×C11×#95C2211yescharacteristic
14#10622826—21no—
15C4×C22⋊Dic11C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17#10622728—22no—
18C2×#66870—21no—
19C2×#66870—21no—
20#10622349—21no—
21#10622349C412yescomplemented
22#10622345—21no—
23#10622345C412yescomplemented
24#10622282—21no—
25#10622279—21no—
26#10622278—21no—
27#10622267—21no—
28#10622089—22no—
29#10622089—21no—
30#10622089—21no—
31C23×C4×C11—21no—
32C23×C4×C11C2311yescharacteristic
33C22×C22⋊D11—21no—
34C22×C22⋊D11—21no—
35C22×D44C2×C411yescharacteristic, complemented
36C22×D44D411yescharacteristic
37C22×C4×D11—21no—
38C22×C8×C11—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C22⋊Dic11D411yescharacteristic
42C2×C22⋊Dic11D411yescharacteristic
43#66983—21no—
44#66983—21no—
45#66983—21no—
46#66983—21no—
47#66983—21no—
48#66983—21no—
49#66983C2×C412yes—
50#66983D412yes—
51C4×C22⋊D11—42no—
52C4×C22⋊D11—42no—
53C2×(C2×D11)⋊C4—21no—
54C2×(C2×D11)⋊C4—21no—
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—21no—
57C2×(C2×D11)⋊C4—21no—
58C2×C4⋊Dic11C2×C411yescharacteristic, complemented
59C2×C4⋊Dic11D411yescharacteristic
60C2×Dic11⋊C4—21no—
61C2×C4×Dic11—21no—
62C2×C4×Dic11—21no—
63C22×C11⋊C8—21no—
64C2×D88—22no—
65C11×C22⋊C8—21no—
66C11×C22⋊C8C2×C412yescomplemented
67C11×#95—21no—
68C11×#95—21no—
69C11×#95D411yescharacteristic
70C11×#95D411yescharacteristic
71C11⋊#95—21no—
72C11⋊#95—21no—
73C11⋊#95—21no—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)—21no—
76#66885—22no—
77#66885—22no—
78#66882—22no—
79#66870—42no—
80#66870—42no—
81#9277—111nomaximal, Sylow
82C24×C11C2×D411yescharacteristic
83C23×D11—21no—
84C23×D11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—42no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—81no—
92C22×C4×C11—81no—
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C22×C4×C11#4111yescharacteristic
99C2×C22⋊D11—22no—
100C2×C22⋊D11—22no—
101C2×C22⋊D11—41no—
102C2×C22⋊D11—41no—
103C2×C22⋊D11—41no—
104C2×C22⋊D11—41no—
105C2×C22⋊D11—41no—
106C2×C22⋊D11—41no—
107C2×C22⋊D11—41no—
108C2×C22⋊D11—41no—
109C2×C22⋊D11—41no—
110C2×C22⋊D11—41no—
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—21no—
115C2×D44—21no—
116C2×D44—21no—
117C2×D44—21no—
118C2×D44—81no—
119C2×D44—81no—
120C2×D44C22⋊C412yes—
121C2×C4×D11—42no—
122C2×C4×D11—42no—
123C2×C4×D11—81no—
124C2×C8×C11—22no—
125C2×C8×C11—81no—
126C11×C4⋊C4—81no—
127C11×C22⋊C4—41no—
128C11×C22⋊C4—41no—
129C22⋊Dic11—21no—
130C22⋊Dic11—21no—
131C22⋊Dic11—21no—
132C22⋊Dic11D812yescomplemented
133(C2×D11)⋊C4—22no—
134(C2×D11)⋊C4—22no—
135(C2×D11)⋊C4—42no—
136(C2×D11)⋊C4—42no—
137(C2×D11)⋊C4—41no—
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4—81no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11C22⋊C412yes—
144Dic11⋊C4—42no—
145C4×Dic11—42no—
146C4×Dic11—81no—
147C2×C11⋊C8—41no—
148C2×C11⋊C8—81no—
149D88—82no—
150#3186—111no—
151#2364—111no—
152#1964—111no—
153#1519—111no—
154C2×#327—111no—
155#1294D1111yescharacteristic, complemented
156#1282—111no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11C4×D411yescharacteristic
160C23×C11#12011yescharacteristic
161C23×C11#12111yescharacteristic
162C23×C11C2×D811yescharacteristic
163C23×C11#13511yescharacteristic
164C23×C11AGL(1,ℤ/8)11yescharacteristic
165C23×C11AGL(1,ℤ/8)11yescharacteristic
166C22×D11—22no—
167C22×D11—41no—
168C22×D11—41no—
169C22×D11—41no—
170C22×D11—41no—
171C22×D11—41no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175C22×D11—41no—
176C22×D11—81no—
177C22×D11—81no—
178C2×C4×C11—22no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—82no—
191C2×C4×C11—82no—
192C2×C4×C11—81no—
193C2×C4×C11—81no—
194C2×C4×C11—81no—
195C2×C4×C11C2×C22⋊C411yescharacteristic
196C2×C4×C11C4×D411yescharacteristic
197C2×C4×C11#12111yescharacteristic
198C2×C4×C11#12311yescharacteristic
199C22⋊D11—42no—
200C22⋊D11—42no—
201C22⋊D11—42no—
202C22⋊D11—42no—
203C22⋊D11—81no—
204C22⋊D11—81no—
205C22⋊D11—81no—
206C22⋊D11—81no—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219D44—42no—
220D44—42no—
221D44—81no—
222D44—81no—
223C4×D11—84no—
224C8×C11—42no—
225C11⋊C8—81no—
226C2×#121—111no—
227C2×#121—111no—
228C2×C4×D4—221no—
229#480—112no—
230#480—221no—
231#466—222no—
232#447—112no—
233#447—221no—
234C2×#99—221no—
235C2×#99—221no—
236C2×C22⋊C8—111no—
237C2×C22⋊C8C2×D1111yescharacteristic
238#388—221no—
239#387—221no—
240#386—221no—
241#386—221no—
242#380C2×D1111yescharacteristic
243C4×C22⋊C4—111no—
244C4×C22⋊C4—221no—
245C2×#95C2×D1111yescharacteristic
246#327—222no—
247#327—221no—
248#327—221no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—41no—
256C22×C11—41no—
257C22×C11—41no—
258C22×C11—41no—
259C22×C11#38611yescharacteristic
260C22×C11C4×D811yescharacteristic
261C22×C11#44211yescharacteristic
262C22×C11#44711yescharacteristic
263C22×C11#44911yescharacteristic
264C22×C11#45911yescharacteristic
265C22×C11#46311yescharacteristic
266C2×D11—42no—
267C2×D11—42no—
268C2×D11—42no—
269C2×D11—81no—
270C2×D11—81no—
271C2×D11—81no—
272C2×D11—81no—
273C2×D11—81no—
274C2×D11—81no—
275C2×D11—81no—
276C2×D11—161no—
277C2×D11—161no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—42no—
283C4×C11—81no—
284C4×C11—161no—
285Dic11—42no—
286Dic11—42no—
287Dic11—81no—
288Dic11—81no—
289C22×D4—111no—
290C22×D4—111no—
291C22×D4—221no—
292C22×D4—221no—
293C23×C4—21no—
294C23×C4—221no—
295C23×C4C22×D1111yescharacteristic
296C2×D8—222no—
297C22×C8—21no—
298C22×C8—221no—
299#121—112no—
300#121—112no—
301#121—221no—
302#121—221no—
303#121—221no—
304#121—221no—
305#121—221no—
306#121—221no—
307C4×D4—442no—
308C4×D4—442no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—111no—
311C2×C4⋊C4—111no—
312C2×C4⋊C4—221no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—111no—
315C2×C22⋊C4—111no—
316C2×C22⋊C4—221no—
317C2×C22⋊C4—221no—
318C2×C22⋊C4—221no—
319C2×C22⋊C4—221no—
320C2×C22⋊C4—221no—
321C2×C42—221no—
322C2×C42—221no—
323#107—222no—
324#102—222no—
325#102—222no—
326#99—442no—
327#99—442no—
328C22⋊C8—21no—
329C22⋊C8—221no—
330C22⋊C8—221no—
331C22⋊C8C4×D1112yescomplemented
332#95—21no—
333#95—21no—
334#95—221no—
335#95—221no—
336#95—221no—
337#95D4411yescharacteristic
338#95D4411yescharacteristic
339C2×C11—21no—
340C2×C11—21no—
341C2×C11—21no—
342C2×C11—21no—
343C2×C11—21no—
344C2×C11—21no—
345C2×C11#187911yescharacteristic
346C2×C11#190611yescharacteristic
347C2×C11#191311yescharacteristic
348D11—82no—
349D11—161no—
350C24—221no—
351C24—221no—
352C24D4×D1111yescharacteristic
353C2×D4—112no—
354C2×D4—222no—
355C2×D4—222no—
356C2×D4—221no—
357C2×D4—221no—
358C2×D4—221no—
359C2×D4—441no—
360C2×D4—441no—
361C2×D4—441no—
362C2×D4—441no—
363C2×D4—441no—
364C2×D4—441no—
365C2×D4—441no—
366C2×D4—441no—
367C2×D4—441no—
368C2×D4—441no—
369C2×D4—881no—
370C2×D4—881no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—42no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—81no—
378C22×C4—81no—
379C22×C4—221no—
380C22×C4—221no—
381C22×C4—221no—
382C22×C4—221no—
383C22×C4—442no—
384C22×C4—442no—
385C22×C4—881no—
386C22×C4C2×C4×D1111yescharacteristic
387C22×C4C2×D4411yescharacteristic
388C22×C4#433911yescharacteristic
389C22×C4D4×D1111yescharacteristic
390C22×C4D4×D1111yescharacteristic
391C22×C4#434311yescharacteristic
392D8—882no—
393C2×C8—22no—
394C2×C8—81no—
395C2×C8—441no—
396C2×C8—881no—
397C4⋊C4—81no—
398C4⋊C4—112no—
399C4⋊C4—221no—
400C4⋊C4—221no—
401C4⋊C4—221no—
402C4⋊C4—442no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4—112no—
406C22⋊C4—221no—
407C22⋊C4—222no—
408C22⋊C4—222no—
409C22⋊C4—221no—
410C22⋊C4—221no—
411C22⋊C4—442no—
412C22⋊C4—442no—
413C22⋊C4—441no—
414C22⋊C4—441no—
415C22⋊C4—881no—
416C42—442no—
417C42—881no—
418C11#927711yescharacteristic, complemented, Sylow
419C23—41no—
420C23—41no—
421C23—222no—
422C23—441no—
423C23—441no—
424C23—441no—
425C23—441no—
426C23—441no—
427C23—441no—
428C23—441no—
429C23—441no—
430C23—441no—
431C23—881no—
432C23—881no—
433C23#6693511yescharacteristic
434C23#6693711yescharacteristic
435C23#6694611yescharacteristic
436C23D8×D1111yescharacteristic
437C23#6696711yescharacteristic
438C23#6696711yescharacteristic
439C23#6697211yescharacteristic
440D4—442no—
441D4—442no—
442D4—442no—
443D4—442no—
444D4—442no—
445D4—442no—
446D4—881no—
447D4—881no—
448D4—881no—
449D4—881no—
450D4—881no—
451D4—881no—
452C2×C4—22no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—82no—
465C2×C4—82no—
466C2×C4—81no—
467C2×C4—81no—
468C2×C4—81no—
469C2×C4—222no—
470C2×C4—222no—
471C2×C4—441no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—884no—
482C2×C4C4×D4411yescharacteristic
483C2×C4C22⋊C4×D1111yescharacteristic
484C2×C4#6694711yescharacteristic
485C2×C4#6694811yescharacteristic
486C8—42no—
487C8—881no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—442no—
499C22—442no—
500C22—442no—
501C22—881no—
502C22—881no—
503C22—881no—
504C22—881no—
505C22—881no—
506C22—881no—
507C22—881no—
508C22—1761no—
509C22—1761no—
510C22#1062227811yescharacteristic
511C22#1062238611yescharacteristic
512C22#1062239911yescharacteristic
513C22#1062242411yescharacteristic
514C22#1062243211yescharacteristic
515C22#1062248211yescharacteristic
516C22#1062248511yescharacteristic
517C4—21no—
518C4—21no—
519C4—21no—
520C4—21no—
521C4—42no—
522C4—81no—
523C4—161no—
524C4—442no—
525C4—442no—
526C4—881no—
527C4—881no—
528C2—21no—
529C2—21no—
530C2—21no—
531C2—21no—
532C2—21no—
533C2—21no—
534C2—882no—
535C2—1761no—
536C2#1306896511yescharacteristic
537C2#1306911611yescharacteristic
538C2#1306915711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC22×C11#386
prime radical#13079367C2
cosocleC23×C4×C11C23
hypercenter#1294D11
hypocenterC11#9277
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
2. #13071663C2semidirect
3. #13069451C2semidirect
4. #13067183C2semidirect
5. C2×#10622089C2semidirect
6. #13066462C2semidirect
7. C11×#1294C2semidirect
21. #10622349C4semidirect
23. #10622345C4semidirect
35. C22×D44C2×C4semidirect
58. C2×C4⋊Dic11C2×C4semidirect
66. C11×C22⋊C8C2×C4semidirect
132. C22⋊Dic11D8semidirect
155. #1294D11semidirect
331. C22⋊C8C4×D11semidirect
418. C11#9277semidirect

Maximal subgroups

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

subgroupindex
#130793672
#130716632
#130694512
#130671832
C2×#106220892
#130664622
C11×#12942
#927711