Finite Group Databasebeta

← #14645895

Subgroups — #14645895

Order 2816.

868 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623094C211yesmaximal, characteristic
2#13069418C211yesmaximal, characteristic, complemented
3#13068617C211yesmaximal, characteristic, complemented
4#13068616C211yesmaximal, characteristic, complemented
5C2×#10622119C211yesmaximal, characteristic, complemented
6C2×#10622097C211yesmaximal, characteristic, complemented
7C2×C11×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×C4×D4×C11C2211yescharacteristic
9C2×#66991—21no—
10C2×#66983—21no—
11C2×#66979—21no—
12#10623094—22no—
13#10623094—22no—
14#10623094—22no—
15#10623094C414yescomplemented
16C2×#66945—21no—
17C2×#66938—22no—
18C2×C4×D44C2211yescharacteristic
19C2×#66922C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C4×C8×C11C2211yescharacteristic
22C2×#66896—21no—
23C2×#66885—21no—
24C2×#66880—22no—
25#10622548C2211yescharacteristic
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27C11×D4⋊C8—22no—
28#10622189—21no—
29#10622167—21no—
30#10622119—22no—
31#10622097—22no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C22×C22⋊D11—22no—
35C22×D44D411yescharacteristic
36C22×C4×D11—21no—
37C22×Dic22D412yes—
38C22×C8×C11—21no—
39C22×C8×C11—21no—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C4×D4×C11C2×C412yes—
43C4×D4×C11D412yes—
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C11×C22⋊C4—21no—
46C2×C42×C11C2311yescharacteristic
47C2×C22⋊Dic11—22no—
48#66991—24no—
49#66991—24no—
50#66983—24no—
51#66983—24no—
52C2×(C2×D11)⋊C4—22no—
53C2×(C2×D11)⋊C4—21no—
54#66979—24no—
55#66979—24no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11D411yescharacteristic
62C2×C4×Dic11—22no—
63C22×C11⋊C8—21no—
64#66945—24no—
65#66945—24no—
66#66938—28no—
67#66938—28no—
68C4×D44—21no—
69C4×D44—21no—
70C4×D44C2×C412yes—
71C4×D44D412yes—
72#66922—21no—
73#66922—21no—
74#66922C2×C412yes—
75#66922D412yes—
76C11×C4⋊C8—21no—
77C11×C4⋊C8—21no—
78C4×C8×C11—21no—
79C4×C8×C11—21no—
80#66896—42no—
81#66885—42no—
82#66880—44no—
83C4⋊(C11⋊C8)—21no—
84C4⋊(C11⋊C8)—21no—
85#8452—111nomaximal, Sylow
86C24×C11—21no—
87C23×D11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11C22⋊C412yes—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C2×C22⋊D11—28no—
105C2×C22⋊D11—82no—
106C2×C22⋊D11—82no—
107C22×Dic11—21no—
108C22×Dic11—22no—
109C22×Dic11—41no—
110C2×D44—21no—
111C2×D44—21no—
112C2×D44—21no—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44C22⋊C412yes—
116C2×C4×D11—22no—
117C2×C4×D11—22no—
118C2×C4×D11—41no—
119C2×C4×D11—41no—
120C2×C4×D11—41no—
121C2×C4×D11—41no—
122C2×Dic22—22no—
123C2×Dic22—42no—
124C2×Dic22—42no—
125C2×Dic22C22⋊C414yes—
126C2×C8×C11—22no—
127C2×C8×C11—41no—
128C2×C8×C11—41no—
129C2×C8×C11—41no—
130C2×C8×C11—41no—
131C2×C8×C11—41no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4C22⋊C412yes—
134C11×C22⋊C4—22no—
135C11×C22⋊C4—22no—
136C42×C11C22×C411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11C2×D411yescharacteristic
139C42×C11C2×D411yescharacteristic
140C22⋊Dic11—28no—
141(C2×D11)⋊C4—28no—
142(C2×D11)⋊C4—22no—
143(C2×D11)⋊C4—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11—22no—
147C4⋊Dic11—22no—
148C4⋊Dic11—21no—
149C4⋊Dic11—42no—
150C4⋊Dic11—41no—
151C4⋊Dic11—41no—
152C4⋊Dic11—41no—
153C4⋊Dic11—41no—
154C4⋊Dic11C22⋊C412yes—
155C4×Dic11—28no—
156C2×C11⋊C8—41no—
157C2×C11⋊C8—41no—
158C2×C11⋊C8—41no—
159C2×#555—111no—
160#1956—111no—
161#1802—111no—
162#1802—111no—
163C2×#333—111no—
164C2×D4⋊C8—111no—
165C2×D4⋊C8D1111yescharacteristic, complemented
166C23×C11—22no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11#12011yescharacteristic
174C22×D11—22no—
175C22×D11—41no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11—41no—
180C22×D11—41no—
181D4×C11—22no—
182D4×C11—22no—
183D4×C11—41no—
184D4×C11—41no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—22no—
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×C11C2×C22⋊C411yescharacteristic
195C2×C4×C11C2×C22⋊C411yescharacteristic
196C2×C4×C11C2×C22⋊C411yescharacteristic
197C2×C4×C11#12011yescharacteristic
198C2×C4×C11#12011yescharacteristic
199C2×C4×C11#12011yescharacteristic
200C2×C4×C11#13511yescharacteristic
201C2×C4×C11#13511yescharacteristic
202C2×C4×C11#13511yescharacteristic
203C2×C4×C11#13511yescharacteristic
204C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
205C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
206C2×C4×C11#13711yescharacteristic
207C2×C4×C11#13711yescharacteristic
208C22⋊D11—88no—
209C2×Dic11—22no—
210C2×Dic11—24no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—81no—
216C2×Dic11—81no—
217C2×Dic11—81no—
218D44—22no—
219D44—22no—
220D44—41no—
221D44—41no—
222C4×D11—42no—
223C4×D11—42no—
224C4×D11—42no—
225C4×D11—42no—
226Dic22—44no—
227Dic22—82no—
228C8×C11—42no—
229C8×C11—81no—
230C11⋊C8—81no—
231#555—114no—
232#555—222no—
233#555—222no—
234#555—222no—
235C2×C4⋊Q8—111no—
236C2×#124—222no—
237C2×#121—221no—
238C2×#121—221no—
239C2×C4×D4—111no—
240C2×C4×D4C2×D1111yescharacteristic
241C2×#117—221no—
242C2×#117—221no—
243C2×C4⋊C8—111no—
244C2×C4⋊C8C2×D1111yescharacteristic
245C2×#103—222no—
246C2×#102—221no—
247C2×#102—221no—
248C2×C4×C8C2×D1111yescharacteristic
249#384—111no—
250#340—221no—
251#340—221no—
252#333—222no—
253D4⋊C8—22no—
254D4⋊C8—222no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11—81no—
259C22×C11—81no—
260C22×C11—81no—
261C22×C11—81no—
262C22×C11#37911yescharacteristic
263C22×C11#44911yescharacteristic
264C22×C11#44911yescharacteristic
265C22×C11#45211yescharacteristic
266C22×C11#45211yescharacteristic
267C22×C11#45311yescharacteristic
268C22×C11#45511yescharacteristic
269C2×D11—42no—
270C2×D11—42no—
271C2×D11—42no—
272C2×D11—81no—
273C2×D11—81no—
274C2×D11—81no—
275C2×D11—81no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—42no—
279C4×C11#41611yescharacteristic
280C4×C11#41611yescharacteristic
281C4×C11#41711yescharacteristic
282C4×C11#41711yescharacteristic
283C4×C11#44911yescharacteristic
284C4×C11#44911yescharacteristic
285C4×C11#45211yescharacteristic
286C4×C11#45211yescharacteristic
287Dic11—44no—
288Dic11—42no—
289Dic11—161no—
290C22×Q8—112no—
291C22×D4—111no—
292C22×D4—222no—
293C22×D4D4411yescharacteristic
294C23×C4—21no—
295C23×C4—221no—
296C22×C8—21no—
297C22×C8—21no—
298C22×C8—221no—
299C4⋊Q8—112no—
300C4⋊Q8—112no—
301C4⋊Q8—221no—
302C4⋊Q8—221no—
303#124—228no—
304#124—228no—
305#121—224no—
306#121—224no—
307#121—224no—
308#121—224no—
309C4×D4—21no—
310C4×D4—21no—
311C4×D4—112no—
312C4×D4—112no—
313C4×D4—221no—
314C4×D4—221no—
315C4×D4C4×D1112yes—
316C4×D4C22⋊D1112yes—
317#117—224no—
318#117—224no—
319#117—224no—
320#117—224no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4D4411yescharacteristic
328C2×C22⋊C4—21no—
329C2×C22⋊C4—222no—
330C2×C22⋊C4—222no—
331C2×C22⋊C4—221no—
332C2×C42—222no—
333C2×C42C22×D1111yescharacteristic
334C4⋊C8—21no—
335C4⋊C8—21no—
336C4⋊C8—221no—
337C4⋊C8—221no—
338#103—444no—
339#102—442no—
340#102—442no—
341C4×C8—21no—
342C4×C8—21no—
343C2×C11—82no—
344C2×C11#162411yescharacteristic
345C2×C11#163411yescharacteristic
346C2×C11#164611yescharacteristic
347C2×C11#164611yescharacteristic
348C2×C11#178811yescharacteristic
349C2×C11#178811yescharacteristic
350C2×C11#179211yescharacteristic
351D11—82no—
352C24—21no—
353C24—221no—
354C2×Q8—114no—
355C2×Q8—222no—
356C2×Q8—442no—
357C2×Q8—442no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—112no—
364C2×D4—228no—
365C2×D4—221no—
366C2×D4—221no—
367C2×D4—221no—
368C2×D4—221no—
369C2×D4—221no—
370C2×D4—882no—
371C2×D4—882no—
372C2×D4(C2×D11)⋊C412yes—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—221no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—441no—
385C22×C4—441no—
386C22×C4—441no—
387C22×C4—441no—
388C22×C4—441no—
389C22×C4C2×D4411yescharacteristic
390C22×C4D4×D1111yescharacteristic
391C22×C4D4×D1111yescharacteristic
392C2×C8—22no—
393C2×C8—41no—
394C2×C8—41no—
395C2×C8—41no—
396C2×C8—41no—
397C2×C8—41no—
398C2×C8—441no—
399C2×C8—441no—
400C2×C8—441no—
401C4⋊C4—21no—
402C4⋊C4—112no—
403C4⋊C4—222no—
404C4⋊C4—222no—
405C4⋊C4—222no—
406C4⋊C4—221no—
407C4⋊C4—222no—
408C4⋊C4—442no—
409C4⋊C4—441no—
410C4⋊C4—441no—
411C4⋊C4—441no—
412C4⋊C4—441no—
413C4⋊C4(C2×D11)⋊C412yes—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C22⋊C4—228no—
417C22⋊C4—228no—
418C22⋊C4—222no—
419C22⋊C4—222no—
420C42—228no—
421C42C2×C4×D1111yescharacteristic
422C42D4×D1111yescharacteristic
423C42D4×D1111yescharacteristic
424C42C2×C22⋊D1111yescharacteristic
425C11#845211yescharacteristic, complemented, Sylow
426C23—22no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—222no—
434C23—441no—
435C23—441no—
436C23—441no—
437C23—441no—
438C23—441no—
439C23—441no—
440C23#6693511yescharacteristic
441Q8—444no—
442Q8—882no—
443D4—22no—
444D4—22no—
445D4—41no—
446D4—41no—
447D4—222no—
448D4—222no—
449D4—441no—
450D4—441no—
451D4—888no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—22no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—222no—
462C2×C4—224no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—442no—
471C2×C4—881no—
472C2×C4—881no—
473C2×C4—881no—
474C2×C4C22⋊C4×D1111yescharacteristic
475C2×C4C22⋊C4×D1111yescharacteristic
476C2×C4#6693511yescharacteristic
477C2×C4#6695711yescharacteristic
478C2×C4#6695711yescharacteristic
479C2×C4#6696111yescharacteristic
480C2×C4#6696211yescharacteristic
481C2×C4#6696411yescharacteristic
482C2×C4#6696511yescharacteristic
483C2×C4#6696811yescharacteristic
484C2×C4#6696911yescharacteristic
485C2×C4C2×(C2×D11)⋊C411yescharacteristic
486C2×C4#6699011yescharacteristic
487C2×C4#6699011yescharacteristic
488C8—42no—
489C8—81no—
490C8—881no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—81no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—442no—
499C22—442no—
500C22—442no—
501C22—881no—
502C22—881no—
503C22—881no—
504C22—881no—
505C22#1062234611yescharacteristic
506C22#1062234711yescharacteristic
507C22#1062239411yescharacteristic
508C22#1062239611yescharacteristic
509C22#1062243511yescharacteristic
510C22#1062243811yescharacteristic
511C22#1062256811yescharacteristic
512C4—21no—
513C4—21no—
514C4—42no—
515C4—442no—
516C4—444no—
517C4—1761no—
518C4#1062234611yescharacteristic
519C4#1062234711yescharacteristic
520C4#1062238411yescharacteristic
521C4#1062238511yescharacteristic
522C4#1062272611yescharacteristic
523C4#1062274611yescharacteristic
524C4#1062277111yescharacteristic
525C4#1062278611yescharacteristic
526C2—82no—
527C2—882no—
528C2#1306770111yescharacteristic
529C2#1306776311yescharacteristic
530C2#1306784611yescharacteristic
531C2#1306784711yescharacteristic
532C2#1306855311yescharacteristic
533C2#1306855711yescharacteristic
534C2#1306857111yescharacteristic
subgroupG/H
centerC23#66935
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×D4⋊C8C2
socleC23×C11#120
prime radicalC2×#10623094C2
cosocleC2×C42×C11C23
hypercenterC2×D4⋊C8D11
hypocenterC11#8452
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #13069418C2semidirect
3. #13068617C2semidirect
4. #13068616C2semidirect
5. C2×#10622119C2semidirect
6. C2×#10622097C2semidirect
7. C2×C11×D4⋊C8C2semidirect
15. #10623094C4semidirect
165. C2×D4⋊C8D11semidirect
425. C11#8452semidirect

Maximal subgroups

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

subgroupindex
C2×#106230942
#130694182
#130686172
#130686162
C2×#106221192
C2×#106220972
C2×C11×D4⋊C82
#845211