Finite Group Databasebeta

← #14803896

Subgroups — #14803896

Order 2816.

958 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622697C211yesmaximal, characteristic, complemented
2C2×C8×D44C211yesmaximal, characteristic, complemented
3#13073790C211yesmaximal, characteristic, complemented
4#13073532C211yesmaximal, characteristic
5#13070055C212yesmaximal, complemented
6#13069808C212yesmaximal, complemented
7#13069377C211yesmaximal, characteristic, complemented
8#13069043C212yesmaximal, complemented
9#13068640C212yesmaximal, complemented
10C4×#66885C211yesmaximal, characteristic, complemented
11C11×#1990C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C22×C8×D11C2212yes—
14C2×#66948—21no—
15C2×#66948C2212yes—
16C2×C4×D44C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C2×C4×C8×C11C2211yescharacteristic
19C11×#384C2211yescharacteristic
20#10622844—22no—
21C2×#66885C2211yescharacteristic
22C2×#66885C2211yescharacteristic
23C2×(C2×D11)⋊C8C2212yes—
24#10622697—24no—
25#10622604—22no—
26#10622601—21no—
27#10622600—21no—
28#10622600C2212yes—
29#10622600C2212yes—
30#10622600C2212yes—
31#10622590—21no—
32C2×#66873C2212yes—
33C2×#66872C2212yes—
34C2×#66872C2212yes—
35C4×C4⋊Dic11C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C8×D44—24no—
38C11×#340C2212yes—
39C11×#340C2212yes—
40#10622189C2211yescharacteristic
41#10622189C2211yescharacteristic
42#10622167C2212yes—
43C22×Q8×C11—21no—
44C22×D44—22no—
45C22×D44D411yescharacteristic
46C22×D44C2311yescharacteristic
47C22×C4×D11—21no—
48C22×C4×D11C2312yes—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8—22no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C42×C11C2311yescharacteristic
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—21no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4D412yes—
65C2×C4⋊Dic11D411yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4×Dic11—21no—
70C22×C11⋊C8C2312yes—
71C2×C8×D11—24no—
72C2×C8×D11—24no—
73C2×C8×D11—42no—
74#66948—24no—
75#66948—42no—
76#66948—44no—
77C4×D44—22no—
78C4×D44—22no—
79C4×D44—22no—
80C4×D44—22no—
81C4×C8×C11—22no—
82C11⋊#95—21no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86#66885—22no—
87#66885—22no—
88(C2×D11)⋊C8—24no—
89#66873—24no—
90#66872—24no—
91#66872—42no—
92C4⋊(C11⋊C8)D414yescomplemented
93#25339—111nomaximal, Sylow
94C23×D11—21no—
95C23×D11C2×D412yes—
96C2×Q8×C11—42no—
97C2×Q8×C11—81no—
98C2×Q8×C11—81no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2411yescharacteristic
104C22×Dic11—21no—
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11C2×D412yes—
108C2×D44—22no—
109C2×D44—22no—
110C2×D44—21no—
111C2×D44—21no—
112C2×D44—21no—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44—44no—
116C2×D44—44no—
117C2×D44—82no—
118C2×D44SD1614yes—
119C2×D44#4112yes—
120C2×C4×D11—22no—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×C4×D11—42no—
127C2×C4×D11—42no—
128C2×C4×D11—42no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11#4112yes—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—42no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4—81no—
142C42×C11C2×D412yes—
143C42×C11#4112yes—
144(C2×D11)⋊C4—24no—
145(C2×D11)⋊C4—44no—
146(C2×D11)⋊C4—44no—
147(C2×D11)⋊C4—42no—
148(C2×D11)⋊C4—82no—
149(C2×D11)⋊C4—82no—
150C4⋊Dic11—22no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4×Dic11—42no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8C2×D414yes—
161C8×D11—48no—
162C2×#476—111no—
163C2×C8×D4—111no—
164#2563—111no—
165#2537—111no—
166#2077—112no—
167#2034—112no—
168#1990D1111yescharacteristic, complemented
169#1948—111no—
170#1893—112no—
171#1807—112no—
172C4×#102—111no—
173C23×C11C22×D411yescharacteristic
174C22×D11—22no—
175C22×D11—22no—
176C22×D11—22no—
177C22×D11—22no—
178C22×D11—22no—
179C22×D11—22no—
180C22×D11—22no—
181C22×D11—41no—
182C22×D11—41no—
183C22×D11—41no—
184C22×D11—41no—
185C22×D11—41no—
186C22×D11—41no—
187C22×D11C2×SD1614yes—
188Q8×C11—84no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11#12112yes—
198C2×C4×C11#12112yes—
199C2×C4×C11C2×SD1612yes—
200C2×C4×C11#13512yes—
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11H(5,𝔽2)11yescharacteristic
206C2×C4×C112−1+411yescharacteristic
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—22no—
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—22no—
220D44—22no—
221D44—28no—
222D44—41no—
223D44—41no—
224D44—88no—
225C4×D11—42no—
226C4×D11—42no—
227C4×D11—42no—
228C4×D11—42no—
229C4×D11—84no—
230C8×C11—22no—
231C8×C11—41no—
232C11⋊C8—24no—
233C23×C8—112no—
234C2×C4⋊Q8C2×D1111yescharacteristic
235C2×#121—112no—
236C2×#121—221no—
237C2×C4×D4—111no—
238C2×C4×D4—111no—
239#476—224no—
240C8×D4—224no—
241C2×#106—112no—
242C2×#106—112no—
243C2×C4⋊C8—111no—
244C2×#102—111no—
245C2×#102—111no—
246C2×#102—112no—
247C2×C22⋊C8—112no—
248C2×C4×C8C2×D1111yescharacteristic
249#394—222no—
250#393—222no—
251#390—221no—
252#384C2×D1111yescharacteristic
253#382—221no—
254#380—112no—
255#380—112no—
256#380—112no—
257#380—221no—
258C4×C4⋊C4—111no—
259#340—111no—
260#340—111no—
261#340—112no—
262#340C2×D1112yes—
263#340C2×D1112yes—
264C22×C11C2×#12111yescharacteristic
265C22×C11#54611yescharacteristic
266C22×C11#54711yescharacteristic
267C22×C11C22×SD1611yescharacteristic
268C22×C11C2×#13511yescharacteristic
269C22×C11#57611yescharacteristic
270C22×C11#57711yescharacteristic
271C2×D11—24no—
272C2×D11—24no—
273C2×D11—24no—
274C2×D11—42no—
275C2×D11—42no—
276C2×D11—42no—
277C2×D11—42no—
278C2×D11—42no—
279C2×D11—42no—
280C2×D11—42no—
281C2×D11—81no—
282C2×D11—81no—
283C2×D11—81no—
284C2×D11—81no—
285C4×C11—22no—
286C4×C11—82no—
287C4×C11—82no—
288C4×C11#46514yes—
289C4×C11#52911yescharacteristic
290C4×C11#54211yescharacteristic
291C4×C11#54611yescharacteristic
292C4×C11#54811yescharacteristic
293Dic11—42no—
294Dic11—81no—
295Dic11—81no—
296Dic11—81no—
297C22×Q8—21no—
298C22×D4—111no—
299C22×D4—111no—
300C22×D4—222no—
301C23×C4—112no—
302C23×C4—221no—
303C22×C8—112no—
304C22×C8—224no—
305C22×C8—224no—
306C22×C8—442no—
307C22×C8C22×D1111yescharacteristic
308C22×C8C22×D1111yescharacteristic
309C4⋊Q8—22no—
310C4⋊Q8—22no—
311#121—224no—
312#121—442no—
313#121—444no—
314C4×D4—222no—
315C4×D4—222no—
316C4×D4—222no—
317C4×D4—222no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—111no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—111no—
325C2×C4⋊C4C22×D1112yes—
326C2×C4⋊C4C22×D1112yes—
327C2×C22⋊C4—112no—
328C2×C22⋊C4—222no—
329C2×C22⋊C4—222no—
330C2×C22⋊C4—221no—
331C2×C22⋊C4—222no—
332C2×C22⋊C4—222no—
333C2×C42—221no—
334C2×C42C22×D1111yescharacteristic
335#106—224no—
336#106—442no—
337C4⋊C8—114no—
338#102—224no—
339#102—222no—
340#102—222no—
341C22⋊C8—224no—
342C4×C8—22no—
343#95—222no—
344#95—222no—
345#95—222no—
346#95—221no—
347C2×C11#242711yescharacteristic
348C2×C11C2×#46511yescharacteristic
349C2×C11#306211yescharacteristic
350C2×C11#329511yescharacteristic
351C2×C11#330311yescharacteristic
352C2×C11#333511yescharacteristic
353C2×C11#334111yescharacteristic
354D11—44no—
355D11—82no—
356C24—112no—
357C24—221no—
358C2×Q8—42no—
359C2×Q8—81no—
360C2×Q8—81no—
361C2×D4—114no—
362C2×D4—112no—
363C2×D4—222no—
364C2×D4—222no—
365C2×D4—221no—
366C2×D4—221no—
367C2×D4—221no—
368C2×D4—221no—
369C2×D4—221no—
370C2×D4—444no—
371C2×D4—444no—
372C2×D4—882no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—112no—
376C22×C4—222no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—222no—
382C22×C4—221no—
383C22×C4—221no—
384C22×C4—221no—
385C22×C4—442no—
386C22×C4—442no—
387C22×C4—442no—
388C22×C4D4×D1111yescharacteristic
389C22×C4D4×D1111yescharacteristic
390C22×C4C23×D1111yescharacteristic
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8—21no—
395C2×C8—21no—
396C2×C8—114no—
397C2×C8—222no—
398C2×C8—222no—
399C2×C8—448no—
400C2×C8#434312yes—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—42no—
406C4⋊C4—42no—
407C4⋊C4—81no—
408C4⋊C4—222no—
409C4⋊C4—221no—
410C4⋊C4—221no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C4⋊C4—221no—
414C4⋊C4—221no—
415C22⋊C4—224no—
416C22⋊C4—444no—
417C22⋊C4—444no—
418C22⋊C4—442no—
419C22⋊C4—882no—
420C22⋊C4—882no—
421C42—442no—
422C42#433912yes—
423C42D4×D1112yes—
424C11#2533911yescharacteristic, complemented, Sylow
425C23—114no—
426C23—222no—
427C23—222no—
428C23—222no—
429C23—222no—
430C23—222no—
431C23—222no—
432C23—222no—
433C23—441no—
434C23—441no—
435C23—441no—
436C23—441no—
437C23—441no—
438C23—441no—
439C23C2×D4×D1111yescharacteristic
440Q8—84no—
441D4—222no—
442D4—222no—
443D4—228no—
444D4—441no—
445D4—441no—
446D4—888no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—222no—
456C2×C4—222no—
457C2×C4—222no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—884no—
472C2×C4#6693712yes—
473C2×C4#6693712yes—
474C2×C4SD16×D1112yes—
475C2×C4#6697212yes—
476C2×C4C2×#433911yescharacteristic
477C2×C4C2×D4×D1111yescharacteristic
478C2×C4C2×#434311yescharacteristic
479C2×C4#6704011yescharacteristic
480C2×C4#41×D1111yescharacteristic
481C2×C4#6704211yescharacteristic
482C8—22no—
483C8—41no—
484C8—224no—
485C22—224no—
486C22—224no—
487C22—224no—
488C22—442no—
489C22—442no—
490C22—442no—
491C22—442no—
492C22—442no—
493C22—442no—
494C22—442no—
495C22—881no—
496C22—881no—
497C22—881no—
498C22—881no—
499C22C2×#6693711yescharacteristic
500C22#1062320711yescharacteristic
501C22#1062325711yescharacteristic
502C22#1062328811yescharacteristic
503C22C2×SD16×D1111yescharacteristic
504C22#1062329311yescharacteristic
505C22C2×#6697211yescharacteristic
506C4—22no—
507C4—82no—
508C4—82no—
509C4—442no—
510C4—881no—
511C4—881no—
512C4—881no—
513C4#1062242014yes—
514C4#1062311111yescharacteristic
515C4#1062311311yescharacteristic
516C4#1062316111yescharacteristic
517C4#1062316411yescharacteristic
518C2—444no—
519C2—882no—
520C2#1307219411yescharacteristic
521C2C2×#1062242011yescharacteristic
522C2#1307829411yescharacteristic
523C2#1308043911yescharacteristic
524C2#1308054311yescharacteristic
525C2#1308097211yescharacteristic
526C2#1308103811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1990C2
socleC23×C11C22×D4
prime radical#13073532C2
hypercenter#1990D11
hypocenterC11#25339
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
1. C2×#10622697C2semidirect
2. C2×C8×D44C2semidirect
3. #13073790C2semidirect
5. #13070055C2semidirect
6. #13069808C2semidirect
7. #13069377C2semidirect
8. #13069043C2semidirect
9. #13068640C2semidirect
10. C4×#66885C2semidirect
11. C11×#1990C2semidirect
92. C4⋊(C11⋊C8)D4semidirect
168. #1990D11semidirect
424. C11#25339semidirect

Maximal subgroups

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

subgroupindex
C2×#106226972
C2×C8×D442
#130737902
#130735322
#130700552
#130698082
#130693772
#130690432
#130686402
C4×#668852
C11×#19902
#2533911