Finite Group Databasebeta

← #14760950

Subgroups — #14760950

Order 2816.

1048 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622646C211yesmaximal, characteristic
2C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
3#13069240C212yesmaximal, complemented
4#13069205C212yesmaximal, complemented
5#13068934C211yesmaximal, characteristic
6#13068808C211yesmaximal, characteristic, complemented
7#13068700C211yesmaximal, characteristic, complemented
8#13068514C212yesmaximal, complemented
9#13068441C212yesmaximal, complemented
10#13068378C211yesmaximal, characteristic, complemented
11C4×C11×#121C211yesmaximal, characteristic
12C2×C11×#121C2211yescharacteristic
13C2×C4×D4×C11—21no—
14C2×C4×D4×C11C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4×Dic11—21no—
19C11×#390C2211yescharacteristic
20C11×#389C2211yescharacteristic
21C11×#388—21no—
22C11×#386—21no—
23C11×#380C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C4×C11×C22⋊C4—21no—
26C2×#66896C2212yes—
27C2×#66896C2212yes—
28C2×C11⋊#95—21no—
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31#10622646C418yescomplemented
32C2×#66872C2212yes—
33C2×#66871C2212yes—
34C4×C4⋊Dic11—21no—
35C4×C4⋊Dic11—21no—
36C4×C4⋊Dic11C2212yes—
37C4×C4⋊Dic11C2212yes—
38C2×#66867C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622162C2212yes—
44C22×D4×C11—21no—
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11D411yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×Dic11—21no—
51C23×Dic11—21no—
52C11×#121—22no—
53C11×#121C2×C414yes—
54C4×D4×C11—24no—
55C4×D4×C11—44no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C22⋊C4—21no—
61C2×C11×C22⋊C4—21no—
62C2×C11×C22⋊C4—21no—
63C2×C11×C22⋊C4—21no—
64C2×C11×C22⋊C4—21no—
65C2×C42×C11—24no—
66C2×C42×C11—21no—
67C2×C42×C11D411yescharacteristic
68C2×C42×C11D411yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—24no—
75C2×C4⋊Dic11C2×C414yescomplemented
76C2×C4⋊Dic11C2312yes—
77C2×C4⋊Dic11C2312yes—
78C2×C4×Dic11—22no—
79C2×C4×Dic11—22no—
80C2×C4×Dic11—44no—
81C22×C11⋊C8C2312yes—
82C22×C11⋊C8C2312yes—
83C11×#95—21no—
84C11×#95—21no—
85C11×#95—21no—
86#66896—24no—
87#66896C2×C418yescomplemented
88C11⋊#95—22no—
89C11⋊#95—22no—
90C22⋊(C11⋊C8)—22no—
91C22⋊(C11⋊C8)C2×C414yescomplemented
92#66872—24no—
93#66871C2×C418yescomplemented
94#66867—24no—
95#21578—111nomaximal, Sylow
96C24×C11—21no—
97C24×C11C2×D411yescharacteristic
98C2×D4×C11—24no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—21no—
102C2×D4×C11—42no—
103C2×D4×C11—42no—
104C2×D4×C11C22×C412yes—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—41no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11C22×C412yes—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11#4112yes—
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—24no—
128C22×Dic11—24no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—42no—
132C22×Dic11—42no—
133C22×Dic11—42no—
134C22×Dic11—42no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—42no—
139C11×C4⋊C4C22×C412yes—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—42no—
142C11×C22⋊C4—42no—
143C11×C22⋊C4—42no—
144C11×C22⋊C4—42no—
145C42×C11—22no—
146C42×C11—22no—
147C42×C11—22no—
148C42×C11—42no—
149C42×C11#4114yes—
150C4⋊Dic11—24no—
151C4⋊Dic11—24no—
152C4⋊Dic11—22no—
153C4⋊Dic11—22no—
154C4⋊Dic11C22×C414yes—
155C4⋊Dic11#4114yes—
156C4×Dic11—44no—
157C4×Dic11—44no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8C22×C414yes—
164C2×#480—111no—
165C4×#121D1111yescharacteristic
166C2×C4×C4⋊C4—111no—
167#1926—112no—
168#1921—112no—
169#1874—111no—
170#1853—111no—
171#1823—111no—
172#1776—112no—
173#1762—112no—
174#1749—111no—
175C23×C11—21no—
176C23×C11—21no—
177C23×C11—21no—
178C23×C11—21no—
179C23×C11—22no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11C4×D412yes—
187C23×C11AGL(1,ℤ/8)12yes—
188C23×C11AGL(1,ℤ/8)12yes—
189C23×C11C22×D411yescharacteristic
190D4×C11—24no—
191D4×C11—48no—
192D4×C11—42no—
193C2×C4×C11—28no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—44no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—84no—
218C2×C4×C11C4×D412yes—
219C2×C4×C11#12312yes—
220C2×C4×C11#12312yes—
221C2×C4×C11#13712yes—
222C2×C4×C11C23×C411yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11C2×#4112yes—
225C2×C4×C11C2×#4112yes—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—48no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—48no—
234C11⋊C8—24no—
235C11⋊C8—42no—
236C2×#121C2×D1111yescharacteristic
237C2×C4×D4—21no—
238C2×C4×D4C2×D1111yescharacteristic
239C22×C4⋊C4—111no—
240C22×C4⋊C4—111no—
241C22×C42—221no—
242C22×C42C2×D1111yescharacteristic
243#480—118no—
244C2×#107—112no—
245C2×#106—112no—
246C2×#102—112no—
247C2×#102—112no—
248C2×C22⋊C8—111no—
249C2×C22⋊C8—111no—
250C2×#97—112no—
251#390C2×D1111yescharacteristic
252#389C2×D1111yescharacteristic
253#388—21no—
254#386—21no—
255#380C2×D1111yescharacteristic
256C4×C4⋊C4—112no—
257C4×C4⋊C4—112no—
258C4×C4⋊C4—221no—
259C4×C4⋊C4—221no—
260C4×C4⋊C4C2×D1111yescharacteristic
261C4×C22⋊C4—21no—
262C2×#95—221no—
263#340—112no—
264#340—112no—
265#340—112no—
266#340—112no—
267#336—112no—
268C22×C11—22no—
269C22×C11—22no—
270C22×C11—22no—
271C22×C11—22no—
272C22×C11—22no—
273C22×C11—22no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11—81no—
278C22×C11—81no—
279C22×C11—81no—
280C22×C11—81no—
281C22×C11#44214yes—
282C22×C11C2×C4×D411yescharacteristic
283C22×C11C2×#12311yescharacteristic
284C22×C11#52511yescharacteristic
285C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
287C22×C11C2×#13711yescharacteristic
288C22×C11#57511yescharacteristic
289C4×C11—22no—
290C4×C11—22no—
291C4×C11—22no—
292C4×C11—22no—
293C4×C11—41no—
294C4×C11—42no—
295C4×C11—81no—
296C4×C11—81no—
297C4×C11C4×#4112yes—
298C4×C11#52912yes—
299Dic11—44no—
300Dic11—44no—
301C22×D4—21no—
302C22×D4C22×D1111yescharacteristic
303C23×C4—21no—
304C23×C4—221no—
305C23×C4—221no—
306C23×C4C22⋊D1111yescharacteristic
307C23×C4C22⋊D1111yescharacteristic
308C23×C4C22×D1111yescharacteristic
309C22×C8—112no—
310C22×C8—112no—
311#121—22no—
312#121C4×D1114yes—
313C4×D4—24no—
314C4×D4—44no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—114no—
317C2×C4⋊C4—112no—
318C2×C4⋊C4—112no—
319C2×C4⋊C4—224no—
320C2×C4⋊C4—222no—
321C2×C4⋊C4—221no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4C22×D1111yescharacteristic
324C2×C4⋊C4C22×D1111yescharacteristic
325C2×C4⋊C4C22×D1111yescharacteristic
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C42—24no—
332C2×C42—21no—
333C2×C42—222no—
334C2×C42—222no—
335C2×C42—444no—
336C2×C42C22⋊D1111yescharacteristic
337C2×C42C22⋊D1111yescharacteristic
338C2×C42C22×D1111yescharacteristic
339C2×C42C22×D1111yescharacteristic
340#107—118no—
341#106—224no—
342#102—118no—
343#102—224no—
344C22⋊C8—114no—
345C22⋊C8—222no—
346#97—224no—
347#95—21no—
348#95—21no—
349#95—21no—
350#95—222no—
351#95—222no—
352C2×C11—24no—
353C2×C11—82no—
354C2×C11C4×#12311yescharacteristic
355C2×C11C2×#44211yescharacteristic
356C2×C11C4×#13711yescharacteristic
357C2×C11#309211yescharacteristic
358C2×C11#309411yescharacteristic
359C2×C11#311211yescharacteristic
360C2×C11#311411yescharacteristic
361C24—21no—
362C24C2×C22⋊D1111yescharacteristic
363C2×D4—24no—
364C2×D4—21no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—42no—
368C2×D4—42no—
369C2×D4C2×C4×D1112yes—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—41no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—224no—
385C22×C4—224no—
386C22×C4—222no—
387C22×C4—222no—
388C22×C4—442no—
389C22×C4—442no—
390C22×C4—442no—
391C22×C4—442no—
392C22×C4C2×C4×D1112yes—
393C22×C4#433912yes—
394C22×C4C2×C22⋊D1111yescharacteristic
395C22×C4C2×C22⋊D1111yescharacteristic
396C22×C4C2×C22⋊D1111yescharacteristic
397C22×C4C2×C22⋊D1111yescharacteristic
398C22×C4C2×C22⋊D1111yescharacteristic
399C22×C4C23×D1111yescharacteristic
400C2×C8—114no—
401C2×C8—222no—
402C2×C8—222no—
403C2×C8—222no—
404C2×C8—222no—
405C2×C8—222no—
406C4⋊C4—21no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—42no—
410C4⋊C4—114no—
411C4⋊C4—114no—
412C4⋊C4—224no—
413C4⋊C4—224no—
414C4⋊C4—222no—
415C4⋊C4—222no—
416C4⋊C4C2×C4×D1112yes—
417C22⋊C4—24no—
418C22⋊C4—42no—
419C22⋊C4—42no—
420C22⋊C4—42no—
421C22⋊C4—42no—
422C42—22no—
423C42—22no—
424C42—22no—
425C42—42no—
426C42—444no—
427C42—444no—
428C42#434114yes—
429C11#2157811yescharacteristic, complemented, Sylow
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—22no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23C4×C22⋊D1112yes—
442C23#6698512yes—
443C23#6700212yes—
444C23C22×C22⋊D1111yescharacteristic
445D4—24no—
446D4—48no—
447D4—42no—
448C2×C4—28no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—44no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—84no—
473C2×C4—224no—
474C2×C4—224no—
475C2×C4—448no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4—442no—
480C2×C4—448no—
481C2×C4C4×C22⋊D1112yes—
482C2×C4#6698812yes—
483C2×C4#6698812yes—
484C2×C4#6700412yes—
485C2×C4C22×C4×D1111yescharacteristic
486C2×C4C2×#433911yescharacteristic
487C2×C4C2×#434112yes—
488C2×C4#41×D1112yes—
489C8—224no—
490C8—442no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22#1062262714yes—
505C22C2×C4×C22⋊D1111yescharacteristic
506C22C2×#6698511yescharacteristic
507C22C2×#6698811yescharacteristic
508C22C2×#6700211yescharacteristic
509C22#1062335311yescharacteristic
510C22C2×#6700411yescharacteristic
511C22#1062335911yescharacteristic
512C4—22no—
513C4—22no—
514C4—22no—
515C4—22no—
516C4—41no—
517C4—42no—
518C4—81no—
519C4—81no—
520C4—444no—
521C4—444no—
522C4C4×#434112yes—
523C4#1062306912yes—
524C2—24no—
525C2—82no—
526C2C4×#6698811yescharacteristic
527C2C2×#1062262711yescharacteristic
528C2C4×#6700411yescharacteristic
529C2#1307853611yescharacteristic
530C2#1307855211yescharacteristic
531C2#1307873411yescharacteristic
532C2#1307875011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#121C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
cosocleC22×C4×C11C24
hypercenterC4×#121D11
hypocenterC11#21578
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. C2×C4×C4⋊Dic11C2semidirect
3. #13069240C2semidirect
4. #13069205C2semidirect
6. #13068808C2semidirect
7. #13068700C2semidirect
8. #13068514C2semidirect
9. #13068441C2semidirect
10. #13068378C2semidirect
31. #10622646C4semidirect
75. C2×C4⋊Dic11C2×C4semidirect
87. #66896C2×C4semidirect
91. C22⋊(C11⋊C8)C2×C4semidirect
93. #66871C2×C4semidirect
429. C11#21578semidirect

Maximal subgroups

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

subgroupindex
C2×#106226462
C2×C4×C4⋊Dic112
#130692402
#130692052
#130689342
#130688082
#130687002
#130685142
#130684412
#130683782
C4×C11×#1212
#2157811