Finite Group Databasebeta

← #14803641

Subgroups — #14803641

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×#10622696C211yesmaximal, characteristic
2#13073570C211yesmaximal, characteristic
3#13071676C211yesmaximal, characteristic, complemented
4#13070027C212yesmaximal, complemented
5#13069930C212yesmaximal
6#13069569C211yesmaximal, characteristic, complemented
7#13069334C211yesmaximal, characteristic, complemented
8#13068969C212yesmaximal
9#13068619C212yesmaximal, complemented
10C4×#66885C211yesmaximal, characteristic
11C2×C11×#487C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#66999—21no—
15C2×#66999—21no—
16C2×Q8×Dic11C2212yes—
17C22×#4325C2212yes—
18C2×C4×D44C2211yescharacteristic
19C11×#487—24no—
20C2×C11×#103C2212yes—
21C2×C11×#103C2212yes—
22C2×C4×C8×C11C2211yescharacteristic
23#10622843C2212yes—
24C2×#66899C2212yes—
25C2×#66885C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×Dic11⋊C8C2212yes—
28#10622696—24no—
29#10622605—22no—
30#10622601C2212yes—
31#10622598—21no—
32#10622594—22no—
33#10622589C2212yes—
34C4⋊C4×Dic11—21no—
35C4×C4⋊Dic11C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622189C2211yescharacteristic
39#10622189C2211yescharacteristic
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43C22×Q8×C11—21no—
44C22×Q8×C11C2312yes—
45C22×D44C2311yescharacteristic
46C22×C4×D11—21no—
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8D414yes—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2312yes—
57C2×C42×C11C2311yescharacteristic
58#66999—44no—
59#66999—44no—
60Q8×Dic11—24no—
61Q8×Dic11—42no—
62C2×#4325—24no—
63C2×#4325—24no—
64C2×#4325—42no—
65C2×(C2×D11)⋊C4—21no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—22no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11D411yescharacteristic
70C2×C4⋊Dic11D411yescharacteristic
71C2×C4⋊Dic11C2311yescharacteristic
72C2×C4⋊Dic11C2311yescharacteristic
73C2×C4⋊Dic11C2311yescharacteristic
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—22no—
76C2×C4×Dic11—21no—
77C2×C4×Dic11—22no—
78C2×C4×Dic11C2312yes—
79C22×C11⋊C8C2312yes—
80C4×D44—22no—
81C4×D44—22no—
82C11×#103—24no—
83C11×#103—24no—
84C4×C8×C11—22no—
85#66899—24no—
86C11⋊#95—21no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89C11⋊#95D412yes—
90#66885—22no—
91#66885—22no—
92Dic11⋊C8—42no—
93C4⋊(C11⋊C8)—22no—
94#25320—111nomaximal, Sylow
95C23×D11—21no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11—42no—
102C2×Q8×C11—42no—
103C2×Q8×C11—42no—
104C2×Q8×C11C2×D414yes—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2411yescharacteristic
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11C2×D412yes—
114C22×Dic11C2×D412yes—
115C2×D44—21no—
116C2×D44—21no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44—21no—
120C2×D44#4112yes—
121C2×C4×D11—42no—
122C2×C4×D11—42no—
123C2×C4×D11—42no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—42no—
135C42×C11C2×D412yes—
136C42×C11#4112yes—
137#4325—48no—
138(C2×D11)⋊C4—44no—
139(C2×D11)⋊C4—44no—
140(C2×D11)⋊C4—42no—
141C4⋊Dic11—22no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—44no—
148C4⋊Dic11SD1614yescomplemented
149C4⋊Dic11#4112yes—
150Dic11⋊C4—44no—
151Dic11⋊C4—44no—
152C4×Dic11—22no—
153C4×Dic11—22no—
154C4×Dic11—44no—
155C4×Dic11—42no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×#487D1111yescharacteristic, complemented
160C2×#461—111no—
161#2542—111no—
162#2365—111no—
163#2072—112no—
164#2055—112no—
165#1988—111no—
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—24no—
179Q8×C11—24no—
180Q8×C11—42no—
181Q8×C11—42no—
182Q8×C11—84no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—24no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11#12112yes—
192C2×C4×C11#12112yes—
193C2×C4×C11C2×SD1612yes—
194C2×C4×C11AGL(1,ℤ/8)12yes—
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11H(5,𝔽2)11yescharacteristic
200C2×C4×C112−1+411yescharacteristic
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—22no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11C2×SD1614yes—
216D44—22no—
217D44—22no—
218D44—41no—
219D44—41no—
220C4×D11—84no—
221C8×C11—41no—
222C8×C11—41no—
223C11⋊C8—42no—
224C22×SD16—112no—
225C2×C4⋊Q8C2×D1111yescharacteristic
226C2×C4⋊Q8C2×D1111yescharacteristic
227C2×C22⋊Q8—221no—
228C2×C22⋊Q8—221no—
229C2×C4×Q8—112no—
230C2×C4×D4—111no—
231#487—24no—
232#461—224no—
233C2×C4⋊C8—111no—
234C2×C4⋊C8—112no—
235C2×#103—112no—
236C2×#103C2×D1112yes—
237C2×#103C2×D1112yes—
238C2×#102—111no—
239C2×#102—111no—
240C2×C4×C8C2×D1111yescharacteristic
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—111no—
249C4×C4⋊C4—221no—
250#340—111no—
251#340—111no—
252#340—112no—
253#340—112no—
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—44no—
271C4×C11—82no—
272C4×C11#46014yes—
273C4×C11#52911yescharacteristic
274C4×C11#54211yescharacteristic
275C4×C11#54611yescharacteristic
276C4×C11#54711yescharacteristic
277Dic11—24no—
278Dic11—42no—
279Dic11—42no—
280Dic11—81no—
281Dic11—81no—
282C22×Q8—21no—
283C22×Q8C22×D1112yes—
284C22×D4—111no—
285C23×C4—221no—
286C2×SD16—224no—
287C2×SD16—224no—
288C2×SD16—442no—
289C22×C8—112no—
290C22×C8C22×D1111yescharacteristic
291C22×C8C22×D1111yescharacteristic
292C4⋊Q8—22no—
293C4⋊Q8—22no—
294C4⋊Q8—22no—
295C4⋊Q8C22⋊D1114yes—
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—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—111no—
306C2×C4⋊C4—111no—
307C2×C4⋊C4—111no—
308C2×C4⋊C4—111no—
309C2×C4⋊C4—111no—
310C2×C4⋊C4—222no—
311C2×C4⋊C4—222no—
312C2×C4⋊C4—222no—
313C2×C4⋊C4C22×D1112yes—
314C2×C22⋊C4—222no—
315C2×C22⋊C4—222no—
316C2×C22⋊C4—221no—
317C2×C42—112no—
318C2×C42—222no—
319C2×C42—221no—
320C2×C42C22×D1111yescharacteristic
321C4⋊C8—222no—
322C4⋊C8—442no—
323#103—24no—
324#103—24no—
325#103—224no—
326#102—222no—
327#102—222no—
328C4×C8—22no—
329#95—112no—
330#95—222no—
331#95—222no—
332#95—221no—
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—22no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—42no—
348C2×Q8—42no—
349C2×Q8—42no—
350C2×Q8C2×C22⋊D1114yes—
351C2×D4—112no—
352C2×D4—221no—
353C2×D4—221no—
354C2×D4—221no—
355C2×D4—221no—
356C2×D4—221no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—112no—
360C22×C4—112no—
361C22×C4—221no—
362C22×C4—221no—
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—21no—
372C2×C8—21no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8—222no—
378C2×C8—222no—
379C2×C8—222no—
380C4⋊C4—24no—
381C4⋊C4—24no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—42no—
385C4⋊C4—114no—
386C4⋊C4—112no—
387C4⋊C4—222no—
388C4⋊C4—221no—
389C4⋊C4—221no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C4⋊C4—221no—
393C4⋊C4—444no—
394C4⋊C4—444no—
395C4⋊C4—444no—
396C22⋊C4—444no—
397C22⋊C4—444no—
398C22⋊C4—442no—
399C42—222no—
400C42—222no—
401C42—444no—
402C42—442no—
403C42#434112yes—
404C42C2×C22⋊D1112yes—
405C11#2532011yescharacteristic, complemented, Sylow
406C23—222no—
407C23—441no—
408C23—441no—
409C23—441no—
410C23—441no—
411C23—441no—
412C23—441no—
413C23C2×D4×D1111yescharacteristic
414Q8—24no—
415Q8—24no—
416Q8—42no—
417Q8—42no—
418Q8—84no—
419D4—222no—
420D4—222no—
421D4—441no—
422D4—441no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—24no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—114no—
432C2×C4—222no—
433C2×C4—222no—
434C2×C4—222no—
435C2×C4—222no—
436C2×C4—222no—
437C2×C4—222no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—884no—
447C2×C4SD16×D1112yes—
448C2×C4#6696712yes—
449C2×C4#6699212yes—
450C2×C4#6699212yes—
451C2×C4C2×#434111yescharacteristic
452C2×C4#41×D1111yescharacteristic
453C2×C4#41×D1111yescharacteristic
454C2×C4#6704211yescharacteristic
455C2×C4#6704311yescharacteristic
456C2×C4C22×C22⋊D1111yescharacteristic
457C8—41no—
458C8—41no—
459C8—442no—
460C22—442no—
461C22—442no—
462C22—442no—
463C22—881no—
464C22—881no—
465C22—881no—
466C22—881no—
467C22#1062320711yescharacteristic
468C22#1062320811yescharacteristic
469C22C2×SD16×D1111yescharacteristic
470C22C2×#6696711yescharacteristic
471C22#1062329711yescharacteristic
472C22#1062329711yescharacteristic
473C22C2×#6699211yescharacteristic
474C4—22no—
475C4—44no—
476C4—82no—
477C4—224no—
478C4—442no—
479C4—442no—
480C4—881no—
481C4—881no—
482C4#1062277614yes—
483C4#1062321111yescharacteristic
484C4#1062321311yescharacteristic
485C4#1062335511yescharacteristic
486C4#1062336011yescharacteristic
487C2—882no—
488C2#1307219611yescharacteristic
489C2C2×#1062277611yescharacteristic
490C2#1307814311yescharacteristic
491C2#1308048011yescharacteristic
492C2#1308092011yescharacteristic
493C2#1308125511yescharacteristic
494C2#1308133911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#487C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×#487D11
hypocenterC11#25320
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
3. #13071676C2semidirect
4. #13070027C2semidirect
6. #13069569C2semidirect
7. #13069334C2semidirect
9. #13068619C2semidirect
11. C2×C11×#487C2semidirect
148. C4⋊Dic11SD16semidirect
159. C2×#487D11semidirect
405. C11#25320semidirect

Maximal subgroups

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

subgroupindex
C2×#106226962
#130735702
#130716762
#130700272
#130699302
#130695692
#130693342
#130689692
#130686192
C4×#668852
C2×C11×#4872
#2532011