Finite Group Databasebeta

← #14788537

Subgroups — #14788537

Order 2816.

1118 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622696C211yesmaximal, characteristic
2C2×C4×#4325C211yesmaximal, characteristic
3#13073534C211yesmaximal, characteristic
4#13069859C212yesmaximal, complemented
5#13069699C212yesmaximal
6#13069553C211yesmaximal, characteristic, complemented
7#13069419C211yesmaximal, characteristic, complemented
8#13068971C212yesmaximal
9#13068884C212yesmaximal, complemented
10#13068621C211yesmaximal, characteristic, complemented
11C2×C11×#557C211yesmaximal, characteristic, complemented
12C11×#557—24no—
13C11×#557—24no—
14C2×C11×C4⋊Q8C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125—21no—
17C2×C11×#125—22no—
18C2×C4×Q8×C11—21no—
19C2×C4×Q8×C11C2212yes—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×#66999—21no—
23C22×#4325C2211yescharacteristic
24C22×#4325C2212yes—
25C2×C4×D44C2211yescharacteristic
26C2×#66899C2212yes—
27C2×#66899C2211yescharacteristic
28C2×#66899C2212yes—
29C2×#66899C2212yes—
30C2×#66899C2212yes—
31#10622696—24no—
32C4×#4325—24no—
33#10622607—22no—
34#10622600—21no—
35C2×#66873C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37#10622552C2212yes—
38#10622548C2211yescharacteristic
39#10622541C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2312yes—
47C22×Q8×C11C2311yescharacteristic
48C22×D44C2311yescharacteristic
49C22×C4×D11—21no—
50C11×C4⋊Q8—24no—
51C11×C4⋊Q8—24no—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8D414yes—
54C11×#125—216no—
55C11×#125—28no—
56C4×Q8×C11—28no—
57C4×Q8×C11—24no—
58C4×Q8×C11—24no—
59C4×Q8×C11—22no—
60C4×Q8×C11—22no—
61C4×Q8×C11—22no—
62C4×Q8×C11D414yes—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4D412yes—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11—22no—
73C2×C42×C11—21no—
74C2×C42×C11C2312yes—
75C2×C42×C11C2311yescharacteristic
76#66999—44no—
77C2×#4325—22no—
78C2×#4325—22no—
79C2×#4325—24no—
80C2×#4325—24no—
81C2×#4325—22no—
82C2×#4325—42no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2312yes—
90C2×Dic11⋊C4—22no—
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2312yes—
93C22×C11⋊C8C2311yescharacteristic
94C4×D44—22no—
95C4×D44—22no—
96#66899—22no—
97#66899—24no—
98#66899—24no—
99#66899—42no—
100#66899—42no—
101C11⋊#95—22no—
102#66873—22no—
103#66872—22no—
104C4⋊(C11⋊C8)—22no—
105C4×C11⋊C8—22no—
106#24187—111nomaximal, Sylow
107C23×D11—21no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—21no—
114C2×Q8×C11—22no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—22no—
118C2×Q8×C11—21no—
119C2×Q8×C11—22no—
120C2×Q8×C11SD1614yescomplemented
121C2×Q8×C11C2×D414yes—
122C2×Q8×C11C2×D412yes—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—21no—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2411yescharacteristic
131C22×Dic11—21no—
132C22×Dic11—22no—
133C2×D44—21no—
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44#4112yes—
139C2×C4×D11—42no—
140C2×C4×D11—42no—
141C2×C4×D11—42no—
142C11×C4⋊C4—28no—
143C11×C4⋊C4—28no—
144C11×C4⋊C4—28no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4C2×D412yes—
152C42×C11—28no—
153C42×C11—24no—
154C42×C11—22no—
155C42×C11—22no—
156C42×C11C2×D412yes—
157C42×C11C2×D412yes—
158#4325—28no—
159#4325—48no—
160(C2×D11)⋊C4—42no—
161(C2×D11)⋊C4—44no—
162(C2×D11)⋊C4—82no—
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167C4⋊Dic11—42no—
168C4⋊Dic11—81no—
169Dic11⋊C4—44no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8#4112yes—
179C2×#557D1111yescharacteristic, complemented
180C2×#461—111no—
181C2×C4×SD16—111no—
182#2538—111no—
183#2043—112no—
184#2013—112no—
185#1984—111no—
186#1956—111no—
187#1880—112no—
188#1865—112no—
189#1803—111no—
190C23×C11C22×D411yescharacteristic
191C22×D11—22no—
192C22×D11—41no—
193C22×D11—41no—
194C22×D11—41no—
195C22×D11—41no—
196C22×D11—41no—
197C22×D11—41no—
198Q8×C11—28no—
199Q8×C11—22no—
200Q8×C11—22no—
201Q8×C11—24no—
202Q8×C11—24no—
203Q8×C11—42no—
204Q8×C11—42no—
205Q8×C11—41no—
206Q8×C11—41no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11#12012yes—
224C2×C4×C11#12012yes—
225C2×C4×C11C2×SD1614yes—
226C2×C4×C11C2×SD1612yes—
227C2×C4×C11#13712yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11H(5,𝔽2)11yescharacteristic
233C2×C4×C112−1+411yescharacteristic
234C2×Dic11—41no—
235C2×Dic11—42no—
236C2×Dic11—41no—
237C2×Dic11—42no—
238C2×Dic11—41no—
239C2×Dic11—42no—
240D44—22no—
241D44—22no—
242D44—41no—
243D44—41no—
244C4×D11—84no—
245C11⋊C8—22no—
246C11⋊C8—41no—
247C11⋊C8—42no—
248C22×SD16—111no—
249C22×SD16—112no—
250#557—24no—
251#557—24no—
252C2×C4⋊Q8C2×D1112yes—
253C2×C4⋊Q8C2×D1111yescharacteristic
254C2×#125—21no—
255C2×#125—22no—
256C2×C22⋊Q8—221no—
257C2×C4×Q8—21no—
258C2×C4×Q8C2×D1112yes—
259C2×C4×Q8C2×D1111yescharacteristic
260C2×C4×Q8C2×D1111yescharacteristic
261C2×C4×D4—111no—
262#461—224no—
263C4×SD16—224no—
264C2×#106—111no—
265C2×C4⋊C8—111no—
266C2×#103—112no—
267C2×#103—112no—
268C2×#103—111no—
269C2×#103—112no—
270C2×#103—112no—
271C2×#102—111no—
272C2×C4×C8—111no—
273#396—222no—
274#390—112no—
275#389—112no—
276#384—111no—
277#380—221no—
278#340—112no—
279#336—112no—
280#336—112no—
281C22×C11C2×#12011yescharacteristic
282C22×C11#54811yescharacteristic
283C22×C11#55011yescharacteristic
284C22×C11C22×SD1611yescharacteristic
285C22×C11C2×#13711yescharacteristic
286C22×C11#57711yescharacteristic
287C22×C11#57811yescharacteristic
288C2×D11—42no—
289C2×D11—42no—
290C2×D11—42no—
291C2×D11—81no—
292C2×D11—81no—
293C2×D11—81no—
294C2×D11—81no—
295C4×C11—24no—
296C4×C11—22no—
297C4×C11—42no—
298C4×C11—44no—
299C4×C11—42no—
300C4×C11—42no—
301C4×C11#44814yes—
302C4×C11#52511yescharacteristic
303C4×C11#53711yescharacteristic
304C4×C11#54611yescharacteristic
305C4×C11#54711yescharacteristic
306Dic11—82no—
307Dic11—81no—
308C22×Q8C22⋊D1111yescharacteristic
309C22×Q8C22×D1112yes—
310C22×Q8C22×D1111yescharacteristic
311C22×D4—111no—
312C23×C4—221no—
313C2×SD16—222no—
314C2×SD16—222no—
315C2×SD16—222no—
316C2×SD16—224no—
317C2×SD16—224no—
318C2×SD16—442no—
319C22×C8—111no—
320C22×C8—112no—
321C22×C8—111no—
322C4⋊Q8—24no—
323C4⋊Q8—24no—
324C4⋊Q8—22no—
325C4⋊Q8C22⋊D1114yes—
326#125—216no—
327#125—28no—
328C22⋊Q8—444no—
329C4×Q8—28no—
330C4×Q8—24no—
331C4×Q8—24no—
332C4×Q8—22no—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×Q8C22⋊D1114yes—
336C4×D4—222no—
337C4×D4—222no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—111no—
345C2×C4⋊C4—112no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—221no—
349C2×C4⋊C4C22⋊D1111yescharacteristic
350C2×C4⋊C4C22⋊D1112yes—
351C2×C4⋊C4C22×D1111yescharacteristic
352C2×C22⋊C4—221no—
353C2×C22⋊C4—222no—
354C2×C22⋊C4—222no—
355C2×C42—22no—
356C2×C42—21no—
357C2×C42C22×D1112yes—
358C2×C42C22×D1111yescharacteristic
359#106—222no—
360C4⋊C8—222no—
361#103—224no—
362#103—222no—
363#103—224no—
364#103—442no—
365#103—442no—
366#102—222no—
367C4×C8—222no—
368#95—222no—
369C2×C11#240711yescharacteristic
370C2×C11C2×#44811yescharacteristic
371C2×C11#301311yescharacteristic
372C2×C11#335911yescharacteristic
373C2×C11#337211yescharacteristic
374C2×C11#339211yescharacteristic
375C2×C11#339811yescharacteristic
376D11—82no—
377C24—221no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—21no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—21no—
384C2×Q8—22no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—21no—
390C2×Q8#432514yescomplemented
391C2×Q8C2×C22⋊D1114yes—
392C2×Q8C2×C22⋊D1112yes—
393C2×D4—112no—
394C2×D4—221no—
395C2×D4—221no—
396C2×D4—221no—
397C2×D4—221no—
398C2×D4—221no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—221no—
403C22×C4—222no—
404C22×C4—442no—
405C22×C4—442no—
406C22×C4—442no—
407C22×C4C2×C22⋊D1112yes—
408C22×C4C2×C22⋊D1112yes—
409C22×C4C2×C22⋊D1111yescharacteristic
410C22×C4C2×C22⋊D1111yescharacteristic
411C22×C4C23×D1111yescharacteristic
412SD16—228no—
413SD16—448no—
414C2×C8—112no—
415C2×C8—221no—
416C2×C8—221no—
417C2×C8—222no—
418C2×C8—221no—
419C2×C8—222no—
420C2×C8—221no—
421C2×C8—221no—
422C2×C8—222no—
423C4⋊C4—28no—
424C4⋊C4—28no—
425C4⋊C4—28no—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—24no—
429C4⋊C4—24no—
430C4⋊C4—22no—
431C4⋊C4—21no—
432C4⋊C4—222no—
433C4⋊C4—222no—
434C4⋊C4—221no—
435C4⋊C4—221no—
436C4⋊C4—444no—
437C4⋊C4—442no—
438C4⋊C4—881no—
439C4⋊C4C2×C22⋊D1112yes—
440C22⋊C4—444no—
441C22⋊C4—442no—
442C22⋊C4—882no—
443C42—28no—
444C42—24no—
445C42—22no—
446C42—22no—
447C42C2×C22⋊D1112yes—
448C42C2×C22⋊D1112yes—
449C11#2418711yescharacteristic, complemented, Sylow
450C23—222no—
451C23—441no—
452C23—441no—
453C23—441no—
454C23—441no—
455C23—441no—
456C23—441no—
457C23C22×C22⋊D1111yescharacteristic
458Q8—28no—
459Q8—24no—
460Q8—22no—
461Q8—24no—
462Q8—22no—
463Q8—41no—
464Q8—42no—
465Q8—41no—
466Q8—42no—
467D4—222no—
468D4—222no—
469D4—441no—
470D4—441no—
471C2×C4—22no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—42no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—442no—
488C2×C4—441no—
489C2×C4—441no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4—441no—
493C2×C4—884no—
494C2×C4C2×#432514yes—
495C2×C4C2×#432512yes—
496C2×C4#6699512yes—
497C2×C4#6700612yes—
498C2×C4#6700612yes—
499C2×C4#41×D1111yescharacteristic
500C2×C4#41×D1111yescharacteristic
501C2×C4#6704211yescharacteristic
502C2×C4#6704311yescharacteristic
503C2×C4C22×C22⋊D1111yescharacteristic
504C2×C4C22×C22⋊D1111yescharacteristic
505C8—222no—
506C8—442no—
507C8—441no—
508C22—442no—
509C22—442no—
510C22—442no—
511C22—881no—
512C22—881no—
513C22—881no—
514C22—881no—
515C22C22×#432511yescharacteristic
516C22C2×#6699511yescharacteristic
517C22#1062336211yescharacteristic
518C22#1062336511yescharacteristic
519C22#1062336811yescharacteristic
520C22#1062336911yescharacteristic
521C22C2×#6700611yescharacteristic
522C4—24no—
523C4—22no—
524C4—44no—
525C4—42no—
526C4—42no—
527C4—42no—
528C4—881no—
529C4—882no—
530C4#1062284014yes—
531C4#1062335511yescharacteristic
532C4#1062335911yescharacteristic
533C4#1062336011yescharacteristic
534C4#1062336411yescharacteristic
535C2—882no—
536C2#1307195511yescharacteristic
537C2C2×#1062284011yescharacteristic
538C2#1307793111yescharacteristic
539C2#1308125411yescharacteristic
540C2#1308139311yescharacteristic
541C2#1308159311yescharacteristic
542C2#1308164311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#557C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×#557D11
hypocenterC11#24187
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
4. #13069859C2semidirect
6. #13069553C2semidirect
7. #13069419C2semidirect
9. #13068884C2semidirect
10. #13068621C2semidirect
11. C2×C11×#557C2semidirect
120. C2×Q8×C11SD16semidirect
179. C2×#557D11semidirect
390. C2×Q8#4325semidirect
449. C11#24187semidirect

Maximal subgroups

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

subgroupindex
C2×#106226962
C2×C4×#43252
#130735342
#130698592
#130696992
#130695532
#130694192
#130689712
#130688842
#130686212
C2×C11×#5572
#2418711