Finite Group Databasebeta

← #14803639

Subgroups — #14803639

Order 2816.

894 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622706C211yesmaximal, characteristic, complemented
2C2×#10622454C211yesmaximal, characteristic
3#13073570C211yesmaximal, characteristic
4#13071674C211yesmaximal, characteristic, complemented
5#13070028C212yesmaximal, complemented
6#13069935C212yesmaximal
7#13069332C211yesmaximal, characteristic, complemented
8#13068972C212yesmaximal
9#13068620C212yesmaximal, complemented
10C4×#66873C211yesmaximal, characteristic
11C11×#1988C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#66999—21no—
14C2×#66999—21no—
15C22×#4314C2212yes—
16C2×#66940C2212yes—
17C2×C4×D44C2211yescharacteristic
18C2×#66922C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C4×C11×C4⋊C4C2211yescharacteristic
21C2×#66880C2212yes—
22C2×Dic11⋊C8C2212yes—
23#10622706—24no—
24#10622605—22no—
25#10622601C2212yes—
26#10622589C2212yes—
27#10622587C2212yes—
28C2×#66874C2212yes—
29C2×#66874C2212yes—
30C2×#66873C2211yescharacteristic
31C2×#66873C2211yescharacteristic
32C4×C4⋊Dic11—21no—
33C4×C4⋊Dic11C2211yescharacteristic
34#10622541—21no—
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622454—24no—
37#10622266—22no—
38C11×#340C2212yes—
39C11×#340C2212yes—
40#10622188C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×Q8×C11—21no—
44C22×D44C2311yescharacteristic
45C22×C4×D11—21no—
46C22×Dic22C2312yes—
47C22×C8×C11C2312yes—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8—22no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C42×C11—21no—
55C2×C42×C11C2311yescharacteristic
56#66999—44no—
57#66999—44no—
58C2×(C2×D11)⋊C4—21no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11D411yescharacteristic
64C2×C4⋊Dic11D411yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—22no—
69C2×C4×Dic11—22no—
70C2×C4×Dic11C2312yes—
71C22×C11⋊C8C2311yescharacteristic
72C22×C11⋊C8C2311yescharacteristic
73C2×#4314—24no—
74C2×#4314—24no—
75C2×#4314—42no—
76#66940—24no—
77#66940—42no—
78C4×D44—22no—
79C4×D44—22no—
80#66922—22no—
81#66922D414yes—
82C11×C4⋊C8—22no—
83C11×#95—21no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95D412yes—
87#66880—24no—
88Dic11⋊C8—42no—
89#66874—24no—
90#66874—24no—
91#66873—22no—
92#66873—22no—
93C4×C11⋊C8—22no—
94#25320—111nomaximal, Sylow
95C23×D11—21no—
96C2×Q8×C11—42no—
97C2×Q8×C11—42no—
98C2×Q8×C11—42no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—22no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2411yescharacteristic
105C22×Dic11—22no—
106C22×Dic11—21no—
107C22×Dic11C2×D412yes—
108C22×Dic11C2×D412yes—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44—21no—
112C2×D44—21no—
113C2×D44—21no—
114C2×D44#4112yes—
115C2×C4×D11—42no—
116C2×C4×D11—42no—
117C2×C4×D11—42no—
118C2×Dic22—22no—
119C2×Dic22—22no—
120C2×Dic22—22no—
121C2×Dic22—22no—
122C2×Dic22—22no—
123C2×Dic22C2×D414yes—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—42no—
133C11×C4⋊C4#4112yes—
134C42×C11—42no—
135C42×C11C2×D412yes—
136C42×C11#4112yes—
137(C2×D11)⋊C4—44no—
138(C2×D11)⋊C4—44no—
139(C2×D11)⋊C4—42no—
140C4⋊Dic11—24no—
141C4⋊Dic11—24no—
142C4⋊Dic11—22no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11SD1614yescomplemented
146Dic11⋊C4—44no—
147Dic11⋊C4—44no—
148Dic11⋊C4—44no—
149C4×Dic11—22no—
150C4×Dic11—22no—
151C4×Dic11—44no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158#4314—48no—
159C2×#487—111no—
160C2×#461—111no—
161#2542—111no—
162#2365—111no—
163#2072—112no—
164#2055—112no—
165#1988D1111yescharacteristic, complemented
166#1939—111no—
167#1880—112no—
168#1803—112no—
169C4×#102—111no—
170C23×C11C22×D411yescharacteristic
171C22×D11—22no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175C22×D11—41no—
176C22×D11—41no—
177C22×D11—41no—
178Q8×C11—84no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—22no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—41no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11#12112yes—
191C2×C4×C11#12112yes—
192C2×C4×C11C2×SD1612yes—
193C2×C4×C11AGL(1,ℤ/8)12yes—
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C11H(5,𝔽2)11yescharacteristic
199C2×C4×C112−1+411yescharacteristic
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—24no—
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11C2×SD1614yes—
212D44—22no—
213D44—22no—
214D44—41no—
215D44—41no—
216C4×D11—84no—
217Dic22—24no—
218Dic22—24no—
219Dic22—42no—
220Dic22—42no—
221C8×C11—42no—
222C11⋊C8—41no—
223C11⋊C8—41no—
224C22×SD16—112no—
225C2×C4⋊Q8—111no—
226C2×C4⋊Q8C2×D1111yescharacteristic
227C2×C22⋊Q8—221no—
228C2×C22⋊Q8—221no—
229C2×C4×Q8—112no—
230C2×C4×D4—111no—
231#487—224no—
232#461—224no—
233C2×C4⋊C8—112no—
234C2×C4⋊C8C2×D1111yescharacteristic
235C2×#103—112no—
236C2×#103—112no—
237C2×#103—112no—
238C2×#102—111no—
239C2×#102—111no—
240C2×C4×C8—111no—
241#399—222no—
242#391—112no—
243#390—112no—
244#389—221no—
245#387—222no—
246#384—112no—
247C4×C4⋊C4—111no—
248C4×C4⋊C4—221no—
249C4×C4⋊C4C2×D1111yescharacteristic
250#340—111no—
251#340—111no—
252#340C2×D1112yes—
253#340C2×D1112yes—
254#336—112no—
255C22×C11C2×#12111yescharacteristic
256C22×C11#54611yescharacteristic
257C22×C11#54811yescharacteristic
258C22×C11C22×SD1611yescharacteristic
259C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
260C22×C11#57811yescharacteristic
261C22×C11#57811yescharacteristic
262C2×D11—42no—
263C2×D11—42no—
264C2×D11—42no—
265C2×D11—81no—
266C2×D11—81no—
267C2×D11—81no—
268C2×D11—81no—
269C4×C11—22no—
270C4×C11—42no—
271C4×C11—81no—
272C4×C11—82no—
273C4×C11#46014yes—
274C4×C11#52911yescharacteristic
275C4×C11#54211yescharacteristic
276C4×C11#54611yescharacteristic
277C4×C11#54711yescharacteristic
278Dic11—24no—
279Dic11—42no—
280Dic11—44no—
281Dic11—81no—
282C22×Q8—21no—
283C22×Q8—112no—
284C22×D4—111no—
285C23×C4—221no—
286C2×SD16—224no—
287C2×SD16—224no—
288C2×SD16—442no—
289C22×C8—111no—
290C22×C8—111no—
291C22×C8C22×D1112yes—
292C4⋊Q8—22no—
293C4⋊Q8—22no—
294C4⋊Q8—114no—
295C4⋊Q8—222no—
296C22⋊Q8—444no—
297C22⋊Q8—444no—
298C4×Q8—224no—
299C4×Q8—442no—
300C4×D4—222no—
301C4×D4—222no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—111no—
304C2×C4⋊C4—111no—
305C2×C4⋊C4—111no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—222no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4—222no—
311C2×C4⋊C4C22×D1112yes—
312C2×C4⋊C4C22×D1111yescharacteristic
313C2×C4⋊C4C22×D1111yescharacteristic
314C2×C22⋊C4—222no—
315C2×C22⋊C4—222no—
316C2×C22⋊C4—221no—
317C2×C42—21no—
318C2×C42—112no—
319C2×C42—222no—
320C2×C42C22×D1111yescharacteristic
321C4⋊C8—22no—
322C4⋊C8—442no—
323#103—224no—
324#103—224no—
325#103—224no—
326#102—222no—
327#102—222no—
328C4×C8—222no—
329#95—21no—
330#95—112no—
331#95—222no—
332#95—222no—
333C2×C11#242711yescharacteristic
334C2×C11C2×#46011yescharacteristic
335C2×C11#304411yescharacteristic
336C2×C11#329811yescharacteristic
337C2×C11#333011yescharacteristic
338C2×C11#335911yescharacteristic
339C2×C11#336711yescharacteristic
340D11—82no—
341C24—221no—
342C2×Q8—42no—
343C2×Q8—42no—
344C2×Q8—42no—
345C2×Q8—114no—
346C2×Q8—222no—
347C2×Q8—222no—
348C2×Q8—222no—
349C2×Q8—222no—
350C2×Q8—222no—
351C2×D4—112no—
352C2×D4—221no—
353C2×D4—221no—
354C2×D4—221no—
355C2×D4—221no—
356C2×D4—221no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—22no—
360C22×C4—112no—
361C22×C4—112no—
362C22×C4—222no—
363C22×C4—221no—
364C22×C4—442no—
365C22×C4—442no—
366C22×C4—442no—
367C22×C4D4×D1111yescharacteristic
368C22×C4D4×D1111yescharacteristic
369C22×C4C23×D1111yescharacteristic
370SD16—448no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—221no—
375C2×C8—221no—
376C2×C8—221no—
377C2×C8—221no—
378C2×C8—221no—
379C2×C8—221no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—42no—
386C4⋊C4—114no—
387C4⋊C4—224no—
388C4⋊C4—224no—
389C4⋊C4—222no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C4⋊C4—444no—
393C4⋊C4—444no—
394C4⋊C4—444no—
395C4⋊C4#434312yes—
396C22⋊C4—444no—
397C22⋊C4—444no—
398C22⋊C4—442no—
399C42—42no—
400C42—222no—
401C42—222no—
402C42—444no—
403C42#433912yes—
404C42D4×D1112yes—
405C11#2532011yescharacteristic, complemented, Sylow
406C23—222no—
407C23—441no—
408C23—441no—
409C23—441no—
410C23—441no—
411C23—441no—
412C23—441no—
413C23C2×D4×D1111yescharacteristic
414Q8—84no—
415Q8—224no—
416Q8—224no—
417Q8—442no—
418Q8—442no—
419D4—222no—
420D4—222no—
421D4—441no—
422D4—441no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—22no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—114no—
435C2×C4—222no—
436C2×C4—222no—
437C2×C4—224no—
438C2×C4—222no—
439C2×C4—222no—
440C2×C4—222no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—884no—
447C2×C4#6693712yes—
448C2×C4#6693712yes—
449C2×C4#6696412yes—
450C2×C4SD16×D1112yes—
451C2×C4C2×#433911yescharacteristic
452C2×C4C2×D4×D1111yescharacteristic
453C2×C4C2×#434311yescharacteristic
454C2×C4#6704011yescharacteristic
455C2×C4#41×D1111yescharacteristic
456C2×C4#6704211yescharacteristic
457C8—42no—
458C8—441no—
459C8—441no—
460C22—442no—
461C22—442no—
462C22—442no—
463C22—881no—
464C22—881no—
465C22—881no—
466C22—881no—
467C22C2×#6693711yescharacteristic
468C22#1062316111yescharacteristic
469C22#1062316411yescharacteristic
470C22C2×#6696411yescharacteristic
471C22C2×SD16×D1111yescharacteristic
472C22#1062331011yescharacteristic
473C22#1062331011yescharacteristic
474C4—22no—
475C4—42no—
476C4—82no—
477C4—81no—
478C4—224no—
479C4—444no—
480C4—442no—
481C4—881no—
482C4#1062237514yes—
483C4#1062311111yescharacteristic
484C4#1062311311yescharacteristic
485C4#1062320711yescharacteristic
486C4#1062325711yescharacteristic
487C2—882no—
488C2#1307219411yescharacteristic
489C2C2×#1062237511yescharacteristic
490C2#1307814511yescharacteristic
491C2#1308047811yescharacteristic
492C2#1308091811yescharacteristic
493C2#1308125711yescharacteristic
494C2#1308133311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1988C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1988D11
hypocenterC11#25320
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
1. C2×#10622706C2semidirect
4. #13071674C2semidirect
5. #13070028C2semidirect
7. #13069332C2semidirect
9. #13068620C2semidirect
11. C11×#1988C2semidirect
145. C4⋊Dic11SD16semidirect
165. #1988D11semidirect
405. C11#25320semidirect

Maximal subgroups

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

subgroupindex
C2×#106227062
C2×#106224542
#130735702
#130716742
#130700282
#130699352
#130693322
#130689722
#130686202
C4×#668732
C11×#19882
#2532011