Finite Group Databasebeta

← #14808033

Subgroups — #14808033

Order 2816.

1374 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622692C211yesmaximal, characteristic, complemented
2C2×#10622683C211yesmaximal, characteristic, complemented
3#13076968C211yesmaximal, characteristic, complemented
4#13069802C214yesmaximal, complemented
5#13069578C211yesmaximal, characteristic, complemented
6#13069423C211yesmaximal, characteristic, complemented
7#13068877C214yesmaximal, complemented
8C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
9C2×C11×#532C211yesmaximal, characteristic
10C22×C11×#41—21no—
11C11×#532—24no—
12C11×#532—24no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×#127C2211yescharacteristic
15C2×C11×#124—21no—
16C2×C11×#121—21no—
17C2×C11×#121C2212yes—
18C2×C4×D4×C11—21no—
19C2×C4×D4×C11C2212yes—
20C22×C42×C11C2211yescharacteristic
21C2×#66977—21no—
22C2×#66922C2211yescharacteristic
23C2×#66896C2214yes—
24C2×#66896C2214yes—
25#10622825—21no—
26#10622825C2212yes—
27C2×C22⋊(C11⋊C8)C2212yes—
28#10622692—24no—
29#10622683—24no—
30C2×#66872C2214yes—
31#10622548C2211yescharacteristic
32#10622542—21no—
33#10622541—21no—
34#10622541C2212yes—
35C2×C4×C11⋊C8C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622167C2214yes—
38#10622162C2212yes—
39C2×C11×#41—28no—
40C2×C11×#41—44no—
41C2×C11×#41—44no—
42C22×Q8×C11—21no—
43C22×D4×C11—22no—
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11C2312yes—
47C23×C4×C11—22no—
48C23×C4×C11D411yescharacteristic
49C23×C4×C11D411yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C22×Dic22—21no—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8D414yes—
54C11×#127—22no—
55C11×#127D414yes—
56C11×#124—28no—
57C11×#121—28no—
58C11×#121—24no—
59C11×#121—24no—
60C4×D4×C11—28no—
61C4×D4×C11—24no—
62C4×D4×C11—24no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C42×C11—22no—
68C2×C42×C11—22no—
69C2×C42×C11D411yescharacteristic
70C2×C42×C11D411yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C22⋊Dic11—22no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2312yes—
78C2×C4⋊Dic11C2312yes—
79#66977—44no—
80C2×Dic11⋊C4—22no—
81C22×C11⋊C8C2312yes—
82C22×C11⋊C8C2312yes—
83#66922—22no—
84#66922—22no—
85#66896—28no—
86#66896—28no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89C22⋊(C11⋊C8)—24no—
90#66872—28no—
91C4×C11⋊C8—22no—
92C4×C11⋊C8—22no—
93#25671—111nomaximal, Sylow
94C24×C11—22no—
95C24×C11C2×D411yescharacteristic
96C11×#41—432no—
97C2×Q8×C11—24no—
98C2×Q8×C11—42no—
99C2×Q8×C11—42no—
100C2×D4×C11—28no—
101C2×D4×C11—24no—
102C2×D4×C11—24no—
103C2×D4×C11—22no—
104C2×D4×C11—24no—
105C2×D4×C11—24no—
106C2×D4×C11—44no—
107C2×D4×C11—44no—
108C2×D4×C11—42no—
109C2×D4×C11—42no—
110C2×D4×C11—42no—
111C2×D4×C11—42no—
112C2×D4×C11C2×D414yes—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—28no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—44no—
125C22×C4×C11—44no—
126C22×C4×C11SD1614yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C22×Dic11—22no—
134C22×Dic11—22no—
135C2×Dic22—42no—
136C2×Dic22—42no—
137C2×Dic22—42no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4C2×D414yes—
141C11×C22⋊C4—28no—
142C11×C22⋊C4—28no—
143C42×C11—22no—
144C42×C11—22no—
145C42×C11—21no—
146C42×C11—21no—
147C42×C11C2×D412yes—
148C42×C11C2×D412yes—
149C22⋊Dic11—44no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C4⋊Dic11—24no—
153C4⋊Dic11—42no—
154C4⋊Dic11—42no—
155C4⋊Dic11—42no—
156Dic11⋊C4—44no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8#4114yescomplemented
163C2×#532D1111yescharacteristic
164C2×#498—111no—
165C2×#486—111no—
166#2857—111no—
167#2034—114no—
168#1990—111no—
169#1957—111no—
170#1864—114no—
171C4×C22⋊C8—111no—
172C23×C11—21no—
173C23×C11—21no—
174C23×C11—21no—
175C23×C11—21no—
176C23×C11—21no—
177C23×C11—21no—
178C23×C11—24no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11C2×SD1612yes—
186C23×C11C22×D411yescharacteristic
187Q8×C11—48no—
188D4×C11—28no—
189D4×C11—416no—
190D4×C11—44no—
191D4×C11—48no—
192D4×C11—48no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—28no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—24no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—416no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—44no—
209C2×C4×C11#12012yes—
210C2×C4×C11#12012yes—
211C2×C4×C11C2×SD1612yes—
212C2×C4×C11C2×SD1612yes—
213C2×C4×C11#13512yes—
214C2×C4×C11AGL(1,ℤ/8)12yes—
215C2×C4×C11AGL(1,ℤ/8)12yes—
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C2×#4112yes—
219C2×C4×C112−1+412yes—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226Dic22—84no—
227C11⋊C8—24no—
228C11⋊C8—42no—
229C22×#41—21no—
230#532—24no—
231#532—24no—
232C2×C4⋊Q8—111no—
233C2×C4⋊Q8C2×D1111yescharacteristic
234C2×#127C2×D1111yescharacteristic
235C2×#124—21no—
236C2×C22⋊Q8—221no—
237C2×#121—21no—
238C2×#121C2×D1112yes—
239C2×C4×D4—21no—
240C2×C4×D4C2×D1112yes—
241C22×C42C2×D1111yescharacteristic
242#498—224no—
243#486—224no—
244C2×#106—114no—
245C2×#102—114no—
246C2×#102—114no—
247C2×C22⋊C8—112no—
248C2×C4×C8—111no—
249C2×C4×C8—111no—
250#391—221no—
251#389—112no—
252#389—221no—
253#384—111no—
254#380—112no—
255#380—221no—
256#340—114no—
257#336—112no—
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—22no—
261C22×C11—41no—
262C22×C11—41no—
263C22×C11—41no—
264C22×C11—41no—
265C22×C11—44no—
266C22×C11—44no—
267C22×C11—44no—
268C22×C11—82no—
269C22×C11—82no—
270C22×C11—82no—
271C22×C11—82no—
272C22×C11C2×#12011yescharacteristic
273C22×C11#53211yescharacteristic
274C22×C11#53611yescharacteristic
275C22×C11C22×SD1611yescharacteristic
276C22×C11C2×#13511yescharacteristic
277C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
278C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
279C4×C11—22no—
280C4×C11—41no—
281C4×C11—44no—
282C4×C11—41no—
283C4×C11#44914yes—
284C4×C11#45014yes—
285C4×C11#54712yes—
286C4×C11#54812yes—
287Dic11—82no—
288Dic11—82no—
289C2×#41—28no—
290C2×#41—44no—
291C2×#41—44no—
292C22×Q8—21no—
293C22×Q8—221no—
294C22×D4—22no—
295C22×D4—21no—
296C22×D4—21no—
297C22×D4C22×D1112yes—
298C23×C4—22no—
299C23×C4C22⋊D1111yescharacteristic
300C23×C4C22⋊D1111yescharacteristic
301C23×C4C22×D1111yescharacteristic
302C22×C8—112no—
303C22×C8—112no—
304C4⋊Q8—22no—
305C4⋊Q8—222no—
306C4⋊Q8—222no—
307C4⋊Q8C22⋊D1114yes—
308#127—22no—
309#127C22⋊D1114yes—
310#124—28no—
311C22⋊Q8—444no—
312#121—28no—
313#121—24no—
314#121—24no—
315C4×D4—28no—
316C4×D4—24no—
317C4×D4—24no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—112no—
320C2×C4⋊C4—112no—
321C2×C4⋊C4—221no—
322C2×C4⋊C4—222no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4C22×D1112yes—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—222no—
329C2×C42—22no—
330C2×C42—22no—
331C2×C42C22⋊D1111yescharacteristic
332C2×C42C22⋊D1111yescharacteristic
333C2×C42C22×D1111yescharacteristic
334C2×C42C22×D1111yescharacteristic
335#106—228no—
336#102—228no—
337#102—228no—
338C22⋊C8—224no—
339C4×C8—222no—
340C4×C8—222no—
341#95—222no—
342#95—222no—
343C2×C11—42no—
344C2×C11—84no—
345C2×C11#243211yescharacteristic
346C2×C11C2×#45011yescharacteristic
347C2×C11C2×#44911yescharacteristic
348C2×C11#316711yescharacteristic
349C2×C11#318411yescharacteristic
350C2×C11#322711yescharacteristic
351C2×C11#322811yescharacteristic
352C24—22no—
353C24C2×C22⋊D1111yescharacteristic
354#41—432no—
355C2×Q8—24no—
356C2×Q8—42no—
357C2×Q8—42no—
358C2×Q8—442no—
359C2×Q8—442no—
360C2×Q8—442no—
361C2×D4—28no—
362C2×D4—24no—
363C2×D4—24no—
364C2×D4—24no—
365C2×D4—24no—
366C2×D4—22no—
367C2×D4—44no—
368C2×D4—44no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4—42no—
372C2×D4—42no—
373C2×D4C2×C22⋊D1114yes—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—28no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—44no—
386C22×C4—44no—
387C22×C4—222no—
388C22×C4—222no—
389C22×C4#432414yes—
390C22×C4C2×C22⋊D1111yescharacteristic
391C22×C4C2×C22⋊D1111yescharacteristic
392C22×C4C2×C22⋊D1111yescharacteristic
393C22×C4C2×C22⋊D1111yescharacteristic
394C22×C4C2×C22⋊D1111yescharacteristic
395C22×C4C23×D1111yescharacteristic
396C2×C8—114no—
397C2×C8—222no—
398C2×C8—222no—
399C2×C8—222no—
400C2×C8—222no—
401C2×C8—222no—
402C4⋊C4—24no—
403C4⋊C4—22no—
404C4⋊C4—224no—
405C4⋊C4—222no—
406C4⋊C4—222no—
407C4⋊C4—444no—
408C4⋊C4—442no—
409C4⋊C4—442no—
410C4⋊C4—442no—
411C4⋊C4C2×C22⋊D1114yes—
412C22⋊C4—28no—
413C22⋊C4—28no—
414C22⋊C4—444no—
415C42—22no—
416C42—22no—
417C42—21no—
418C42—21no—
419C42C2×C22⋊D1112yes—
420C42C2×C22⋊D1112yes—
421C11#2567111yescharacteristic, complemented, Sylow
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23—24no—
429C23—42no—
430C23—42no—
431C23—42no—
432C23—42no—
433C23—42no—
434C23—42no—
435C23C2×#432412yes—
436C23C22×C22⋊D1111yescharacteristic
437Q8—48no—
438Q8—884no—
439D4—28no—
440D4—416no—
441D4—48no—
442D4—44no—
443D4—48no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—28no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—24no—
454C2×C4—416no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—44no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4#6698512yes—
467C2×C4C2×#432412yes—
468C2×C4C2×#432412yes—
469C2×C4#6700212yes—
470C2×C4#6700312yes—
471C2×C4#6700612yes—
472C2×C4#6700612yes—
473C2×C4#41×D1112yes—
474C2×C4#6704312yes—
475C2×C4C22×C22⋊D1111yescharacteristic
476C2×C4C22×C22⋊D1111yescharacteristic
477C8—224no—
478C8—442no—
479C22—22no—
480C22—22no—
481C22—22no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—44no—
487C22—44no—
488C22—44no—
489C22—82no—
490C22—82no—
491C22—82no—
492C22—82no—
493C22C2×#6698511yescharacteristic
494C22C22×#432411yescharacteristic
495C22C2×#6700211yescharacteristic
496C22C2×#6700311yescharacteristic
497C22#1062335611yescharacteristic
498C22#1062336311yescharacteristic
499C22C2×#6700611yescharacteristic
500C4—22no—
501C4—44no—
502C4—41no—
503C4—41no—
504C4—882no—
505C4—882no—
506C4#1062283114yes—
507C4#1062285114yes—
508C4#1062335512yes—
509C4#1062336212yes—
510C2—42no—
511C2—84no—
512C2#1307224011yescharacteristic
513C2C2×#1062283111yescharacteristic
514C2C2×#1062285111yescharacteristic
515C2#1307917111yescharacteristic
516C2#1307935011yescharacteristic
517C2#1307974111yescharacteristic
518C2#1307974811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#532C2
socleC23×C11C22×D4
hypercenterC2×#532D11
hypocenterC11#25671
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. C2×#10622692C2semidirect
2. C2×#10622683C2semidirect
3. #13076968C2semidirect
4. #13069802C2semidirect
5. #13069578C2semidirect
6. #13069423C2semidirect
7. #13068877C2semidirect
8. C4×C22⋊(C11⋊C8)C2semidirect
162. C2×C11⋊C8#41semidirect
421. C11#25671semidirect

Maximal subgroups

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

subgroupindex
C2×#106226922
C2×#106226832
#130769682
#130698022
#130695782
#130694232
#130688772
C4×C22⋊(C11⋊C8)2
C2×C11×#5322
#2567111