Finite Group Databasebeta

← #14804518

Subgroups — #14804518

Order 2816.

1018 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622664C212yesmaximal, complemented
2C2×#10622644C211yesmaximal, characteristic, complemented
3C2×D4×C11⋊C8C211yesmaximal, characteristic
4#13073569C211yesmaximal, characteristic
5#13069819C212yesmaximal, complemented
6#13069624C212yesmaximal, complemented
7#13069417C211yesmaximal, characteristic, complemented
8#13069372C211yesmaximal, characteristic, complemented
9#13069037C212yesmaximal, complemented
10C4×#66899C211yesmaximal, characteristic, complemented
11C11×#2538C211yesmaximal, characteristic
12C2×C11×C22⋊Q8C2212yes—
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C22×#4326C2212yes—
16C2×#66977C2212yes—
17C2×#66977C2212yes—
18C23×C11⋊C8C2212yes—
19C2×#66922C2211yescharacteristic
20C11×#396—22no—
21C11×#390—21no—
22C11×#389—21no—
23C11×#384C2211yescharacteristic
24C11×#380C2212yes—
25C2×#66899C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27#10622834—21no—
28C2×C22⋊(C11⋊C8)C2212yes—
29#10622664—28no—
30#10622644—24no—
31D4×C11⋊C8—24no—
32#10622589—21no—
33C2×#66874C2212yes—
34C2×#66874C2212yes—
35C2×#66874C2212yes—
36C2×#66871C2212yes—
37#10622562—22no—
38C4×C4⋊Dic11C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622167C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11D411yescharacteristic
46C23×C4×C11C2312yes—
47C22×Dic22C2312yes—
48C11×C22⋊Q8—24no—
49C11×C22⋊Q8—42no—
50C4×Q8×C11—22no—
51C4×Q8×C11—22no—
52C4×D4×C11—22no—
53C4×D4×C11—22no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4D412yes—
64C2×C42×C11—21no—
65C2×C42×C11C2311yescharacteristic
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11—22no—
68C2×#4326—24no—
69C2×#4326—24no—
70C2×#4326—42no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4⋊Dic11C2311yescharacteristic
75#66977—24no—
76#66977—24no—
77#66977—42no—
78#66977—42no—
79C2×Dic11⋊C4—22no—
80C2×Dic11⋊C4—22no—
81C2×C4×Dic11—21no—
82C22×C11⋊C8—24no—
83C22×C11⋊C8—24no—
84C22×C11⋊C8—42no—
85C22×C11⋊C8C2311yescharacteristic
86C22×C11⋊C8C2311yescharacteristic
87C22×C11⋊C8C2312yes—
88#66922—22no—
89#66922—22no—
90C11×#95—22no—
91#66899—22no—
92#66899D414yescomplemented
93C11⋊#95—21no—
94C22⋊(C11⋊C8)—24no—
95#66874—24no—
96#66874—24no—
97#66874—42no—
98#66871—24no—
99C4⋊(C11⋊C8)D414yes—
100C4×C11⋊C8—22no—
101#25386—111nomaximal, Sylow
102C24×C11C2×D412yes—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11C2×D412yes—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11Q1614yescomplemented
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C22×Dic11—21no—
126C22×Dic11—21no—
127C22×Dic11—22no—
128C2×Dic22—22no—
129C2×Dic22—22no—
130C2×Dic22—22no—
131C2×Dic22—22no—
132C2×Dic22—22no—
133C2×Dic22—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—44no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4—42no—
142C11×C4⋊C4—81no—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—44no—
145C11×C22⋊C4—82no—
146C42×C11—42no—
147C42×C11C2×D412yes—
148C42×C11#4112yes—
149C22⋊Dic11—44no—
150C22⋊Dic11—44no—
151#4326—48no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—42no—
155C4⋊Dic11—42no—
156C4⋊Dic11C2×D412yes—
157C4⋊Dic11#4112yes—
158Dic11⋊C4—44no—
159Dic11⋊C4—44no—
160C4×Dic11—42no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—48no—
169C2×C11⋊C8C2×D414yes—
170C2×C11⋊C8C2×D412yes—
171C2×#467—112no—
172C2×#462—111no—
173C2×C8×D4—111no—
174#2542—111no—
175#2538D1111yescharacteristic
176#2036—112no—
177#2001—112no—
178#1956—111no—
179#1947—111no—
180#1892—112no—
181C4×#103—111no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11C2×Q1614yes—
189C23×C11C22×D411yescharacteristic
190Q8×C11—22no—
191Q8×C11—22no—
192Q8×C11—41no—
193Q8×C11—41no—
194D4×C11—28no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—41no—
213C2×C4×C11#12112yes—
214C2×C4×C11#12112yes—
215C2×C4×C11C2×Q1612yes—
216C2×C4×C11#13512yes—
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11H(5,𝔽2)11yescharacteristic
222C2×C4×C11H(5,𝔽2)11yescharacteristic
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232Dic22—42no—
233Dic22—42no—
234Dic22—42no—
235Dic22—42no—
236C11⋊C8—22no—
237C11⋊C8—24no—
238C11⋊C8—41no—
239C22×Q16—112no—
240C23×C8—112no—
241C2×C4⋊Q8—111no—
242C2×C22⋊Q8—112no—
243C2×C22⋊Q8—112no—
244C2×C22⋊Q8C2×D1112yes—
245C2×C4×Q8C2×D1111yescharacteristic
246C2×C4×D4C2×D1111yescharacteristic
247#467—228no—
248#462—224no—
249C8×D4—224no—
250C2×#107—112no—
251C2×C4⋊C8—111no—
252C2×#103—111no—
253C2×#103—111no—
254C2×#103—112no—
255C2×#103—112no—
256C2×#103—112no—
257C2×C22⋊C8—112no—
258C2×C4×C8—111no—
259#399—222no—
260#396—22no—
261#390—21no—
262#390—221no—
263#389—21no—
264#384—221no—
265#384C2×D1111yescharacteristic
266#380C2×D1112yes—
267C4×C4⋊C4—111no—
268#340—111no—
269#340—112no—
270#340—111no—
271C22×C11—24no—
272C22×C11—24no—
273C22×C11—24no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11C2×#12111yescharacteristic
279C22×C11D4211yescharacteristic
280C22×C11#54611yescharacteristic
281C22×C11C22×Q1611yescharacteristic
282C22×C11C2×#13511yescharacteristic
283C22×C11#57711yescharacteristic
284C22×C11#57811yescharacteristic
285C4×C11—22no—
286C4×C11—42no—
287C4×C11—42no—
288C4×C11—82no—
289C4×C11—81no—
290C4×C11#46714yescomplemented
291C4×C11#53211yescharacteristic
292C4×C11#54011yescharacteristic
293C4×C11D4211yescharacteristic
294C4×C11#55011yescharacteristic
295Dic11—42no—
296Dic11—42no—
297Dic11—82no—
298C22×Q8—112no—
299C22×Q8C22×D1111yescharacteristic
300C22×D4C22⋊D1111yescharacteristic
301C23×C4C22×D1112yes—
302C2×Q16—224no—
303C2×Q16—224no—
304C2×Q16—442no—
305C22×C8—111no—
306C22×C8—112no—
307C22×C8—111no—
308C22×C8—224no—
309C22×C8—224no—
310C22×C8—442no—
311C4⋊Q8—222no—
312C4⋊Q8—222no—
313C22⋊Q8—24no—
314C22⋊Q8—42no—
315C22⋊Q8—224no—
316C22⋊Q8—224no—
317C22⋊Q8—442no—
318C22⋊Q8—442no—
319C4×Q8—22no—
320C4×Q8—22no—
321C4×D4—22no—
322C4×D4—22no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—111no—
328C2×C4⋊C4—111no—
329C2×C4⋊C4—222no—
330C2×C4⋊C4—222no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4C22⋊D1111yescharacteristic
334C2×C4⋊C4C22×D1111yescharacteristic
335C2×C4⋊C4C22×D1112yes—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—222no—
339C2×C22⋊C4—222no—
340C2×C22⋊C4C22⋊D1112yes—
341C2×C42—21no—
342C2×C42—221no—
343C2×C42C22×D1111yescharacteristic
344#107—224no—
345C4⋊C8—114no—
346#103—114no—
347#103—224no—
348#103—224no—
349#103—222no—
350#103—442no—
351C22⋊C8—224no—
352C4×C8—222no—
353#95—22no—
354#95—221no—
355C2×C11—44no—
356C2×C11#242811yescharacteristic
357C2×C11C2×#46711yescharacteristic
358C2×C11#306311yescharacteristic
359C2×C11#328411yescharacteristic
360C2×C11D4×Q1611yescharacteristic
361C2×C11#329911yescharacteristic
362C2×C11#330211yescharacteristic
363C24C2×C22⋊D1112yes—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—222no—
370C2×Q8—222no—
371C2×Q8—222no—
372C2×Q8—222no—
373C2×Q8—222no—
374C2×Q8—222no—
375C2×Q8D4×D1112yes—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4#432614yescomplemented
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—221no—
389C22×C4—221no—
390C22×C4—222no—
391C22×C4C2×C22⋊D1112yes—
392C22×C4C2×C22⋊D1111yescharacteristic
393C22×C4C2×C22⋊D1111yescharacteristic
394C22×C4C23×D1111yescharacteristic
395Q16—448no—
396C2×C8—114no—
397C2×C8—112no—
398C2×C8—221no—
399C2×C8—222no—
400C2×C8—221no—
401C2×C8—222no—
402C2×C8—221no—
403C2×C8—221no—
404C2×C8—221no—
405C2×C8—448no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—44no—
412C4⋊C4—42no—
413C4⋊C4—42no—
414C4⋊C4—81no—
415C4⋊C4—112no—
416C4⋊C4—112no—
417C4⋊C4—221no—
418C4⋊C4—221no—
419C4⋊C4—444no—
420C4⋊C4—444no—
421C4⋊C4—442no—
422C4⋊C4—442no—
423C22⋊C4—24no—
424C22⋊C4—44no—
425C22⋊C4—82no—
426C22⋊C4—444no—
427C22⋊C4—444no—
428C42—42no—
429C42—442no—
430C42D4×D1112yes—
431C42#434112yes—
432C11#2538611yescharacteristic, complemented, Sylow
433C23—22no—
434C23—22no—
435C23—22no—
436C23—22no—
437C23—22no—
438C23—22no—
439C23C2×#432614yes—
440C23C22×C22⋊D1111yescharacteristic
441Q8—22no—
442Q8—22no—
443Q8—41no—
444Q8—41no—
445Q8—442no—
446Q8—442no—
447Q8—442no—
448Q8—442no—
449D4—28no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—41no—
466C2×C4—42no—
467C2×C4—41no—
468C2×C4—222no—
469C2×C4—222no—
470C2×C4—441no—
471C2×C4—441no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4—442no—
477C2×C4#6699212yes—
478C2×C4#6699212yes—
479C2×C4C2×#432612yes—
480C2×C4#6700312yes—
481C2×C4C2×D4×D1111yescharacteristic
482C2×C4C2×D4×D1111yescharacteristic
483C2×C4C2×#434111yescharacteristic
484C2×C4#6703711yescharacteristic
485C2×C4#41×D1111yescharacteristic
486C2×C4#6704211yescharacteristic
487C8—222no—
488C8—224no—
489C8—441no—
490C22—24no—
491C22—24no—
492C22—24no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22D4×C22⋊D1111yescharacteristic
498C22C2×#6699211yescharacteristic
499C22C22×#432611yescharacteristic
500C22C2×#6700311yescharacteristic
501C22#1062336011yescharacteristic
502C22#1062336711yescharacteristic
503C22#1062336911yescharacteristic
504C4—22no—
505C4—42no—
506C4—42no—
507C4—82no—
508C4—81no—
509C4—442no—
510C4—442no—
511C4—882no—
512C4#1062266414yescomplemented
513C4#1062312711yescharacteristic
514C4#1062313011yescharacteristic
515C4#1062314011yescharacteristic
516C4#1062315011yescharacteristic
517C2—44no—
518C2#1307220611yescharacteristic
519C2C2×#1062266411yescharacteristic
520C2#1307830911yescharacteristic
521C2#1308034611yescharacteristic
522C2D4×#432611yescharacteristic
523C2#1308048611yescharacteristic
524C2#1308052711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2538C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#2538D11
hypocenterC11#25386
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2538

Complements

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

NH ≅ G/Ntype
1. C2×#10622664C2semidirect
2. C2×#10622644C2semidirect
5. #13069819C2semidirect
6. #13069624C2semidirect
7. #13069417C2semidirect
8. #13069372C2semidirect
9. #13069037C2semidirect
10. C4×#66899C2semidirect
92. #66899D4semidirect
111. C2×D4×C11Q16semidirect
290. C4×C11#467semidirect
378. C2×D4#4326semidirect
432. C11#25386semidirect
512. C4#10622664semidirect

Maximal subgroups

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

subgroupindex
C2×#106226642
C2×#106226442
C2×D4×C11⋊C82
#130735692
#130698192
#130696242
#130694172
#130693722
#130690372
C4×#668992
C11×#25382
#2538611