Finite Group Databasebeta

← #14803305

Subgroups — #14803305

Order 2816.

886 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622461C211yesmaximal, characteristic
2C2×#10622443C211yesmaximal, characteristic, complemented
3#13073989C211yesmaximal, characteristic, complemented
4#13073618C211yesmaximal, characteristic
5#13069985C212yesmaximal, complemented
6#13069935C212yesmaximal, complemented
7#13069468C212yesmaximal, complemented
8#13069421C211yesmaximal, characteristic
9#13069300C212yesmaximal, complemented
10C4×#66874C211yesmaximal, characteristic, complemented
11C11×#1948C211yesmaximal, characteristic, complemented
12C22×#4314C2212yes—
13C2×#66928—21no—
14C2×#66927C2211yescharacteristic
15C2×C4×Dic22C2211yescharacteristic
16C2×C4×Dic22C2211yescharacteristic
17C2×C11×#106C2212yes—
18C2×C11×C4⋊C8C2211yescharacteristic
19C11×#384C2211yescharacteristic
20C4×C11×C4⋊C4C2211yescharacteristic
21C2×#66885C2212yes—
22C2×Dic11⋊C8C2212yes—
23C2×C8×Dic11C2212yes—
24#10622601C2212yes—
25#10622601C2212yes—
26#10622598—21no—
27#10622598C2212yes—
28#10622596—22no—
29#10622587—21no—
30#10622587C2212yes—
31C2×#66874C2211yescharacteristic
32C2×#66874C2211yescharacteristic
33C2×#66873C2212yes—
34C2×#66873C2212yes—
35#10622552—21no—
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622461—24no—
38#10622443—24no—
39#10622285—22no—
40C11×#340C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×D44—21no—
44C22×D44—21no—
45C22×D44C2312yes—
46C22×Dic22D411yescharacteristic
47C22×Dic22C2311yescharacteristic
48C22×C8×C11C2312yes—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C42×C11—21no—
55C2×C42×C11C2311yescharacteristic
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11D411yescharacteristic
62C2×C4⋊Dic11C2311yescharacteristic
63C2×Dic11⋊C4—21no—
64C2×Dic11⋊C4D412yes—
65C2×C4×Dic11—21no—
66C2×C4×Dic11C2312yes—
67C22×C11⋊C8C2311yescharacteristic
68C22×C11⋊C8C2311yescharacteristic
69C2×#4314—24no—
70C2×#4314—24no—
71C2×#4314—42no—
72#66928—44no—
73#66927—22no—
74#66927—22no—
75C4×Dic22—22no—
76C4×Dic22—22no—
77C4×Dic22—22no—
78C4×Dic22—22no—
79C11×#106—42no—
80C11×C4⋊C8D414yes—
81C11×#95—21no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85#66885—24no—
86Dic11⋊C8—24no—
87C8×Dic11—24no—
88#66874—22no—
89#66874—22no—
90#66873—24no—
91#66873—42no—
92C4×C11⋊C8—22no—
93#25295—111nomaximal, Sylow
94C23×D11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11C2×D412yes—
104C22×Dic11C2×D412yes—
105C2×D44—22no—
106C2×D44—22no—
107C2×D44—22no—
108C2×D44—22no—
109C2×D44—22no—
110C2×D44—22no—
111C2×D44—42no—
112C2×D44—42no—
113C2×D44—42no—
114C2×D44—42no—
115C2×D44—81no—
116C2×D44—81no—
117C2×Dic22—22no—
118C2×Dic22—22no—
119C2×Dic22—21no—
120C2×Dic22—21no—
121C2×Dic22—21no—
122C2×Dic22—21no—
123C2×Dic22—21no—
124C2×Dic22SD1614yescomplemented
125C2×Dic22#4112yes—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11C2×D414yes—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—42no—
136C11×C4⋊C4—81no—
137C42×C11—42no—
138C42×C11C2×D412yes—
139C42×C11#4112yes—
140(C2×D11)⋊C4—44no—
141(C2×D11)⋊C4—44no—
142(C2×D11)⋊C4—82no—
143(C2×D11)⋊C4—82no—
144C4⋊Dic11—22no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—82no—
148Dic11⋊C4—24no—
149Dic11⋊C4—42no—
150C4×Dic11—22no—
151C4×Dic11—22no—
152C4×Dic11—42no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8#4112yes—
159#4314—48no—
160C2×#460—111no—
161C2×C8×Q8—111no—
162#2582—111no—
163#2548—111no—
164#2065—112no—
165#2055—112no—
166#1968—112no—
167#1957—111no—
168#1948D1111yescharacteristic, complemented
169#1934—112no—
170C4×#103—111no—
171C23×C11C22×D411yescharacteristic
172C22×D11—42no—
173C22×D11—42no—
174C22×D11—42no—
175C22×D11—42no—
176C22×D11—42no—
177C22×D11—42no—
178C22×D11—42no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—41no—
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×C11#13512yes—
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—22no—
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11C2×SD1614yes—
212D44—42no—
213D44—42no—
214D44—42no—
215D44—42no—
216D44—84no—
217D44—84no—
218Dic22—28no—
219Dic22—22no—
220Dic22—22no—
221Dic22—41no—
222Dic22—41no—
223C8×C11—24no—
224C11⋊C8—22no—
225C11⋊C8—41no—
226C22×SD16—112no—
227C2×#127—111no—
228C2×#124—221no—
229C2×C4×Q8—111no—
230C2×C4×Q8—111no—
231#460—224no—
232C8×Q8—224no—
233C2×#106C2×D1112yes—
234C2×C4⋊C8—112no—
235C2×C4⋊C8C2×D1111yescharacteristic
236C2×#103—111no—
237C2×#103—111no—
238C2×#102—112no—
239C2×#102—112no—
240C2×#102—112no—
241C2×C4×C8—112no—
242C2×C4×C8—111no—
243#398—222no—
244#394—222no—
245#391—112no—
246#391—221no—
247#390—112no—
248#390—112no—
249#390—221no—
250#389—112no—
251#389—221no—
252#384C2×D1111yescharacteristic
253C4×C4⋊C4C2×D1111yescharacteristic
254#340—111no—
255#340—111no—
256#340C2×D1112yes—
257C22×C11C2×#12111yescharacteristic
258C22×C11#54811yescharacteristic
259C22×C11#55011yescharacteristic
260C22×C11C22×SD1611yescharacteristic
261C22×C11C2×#13511yescharacteristic
262C22×C11#57611yescharacteristic
263C22×C11#57711yescharacteristic
264C2×D11—82no—
265C2×D11—82no—
266C2×D11—82no—
267C2×D11—82no—
268C2×D11—82no—
269C2×D11—82no—
270C2×D11—82no—
271C4×C11—22no—
272C4×C11—81no—
273C4×C11—81no—
274C4×C11—82no—
275C4×C11#46514yes—
276C4×C11#52911yescharacteristic
277C4×C11#54211yescharacteristic
278C4×C11#54611yescharacteristic
279C4×C11#54811yescharacteristic
280Dic11—24no—
281Dic11—42no—
282Dic11—42no—
283Dic11—81no—
284C22×Q8—111no—
285C22×Q8—111no—
286C22×D4—112no—
287C22×D4—221no—
288C22×D4—221no—
289C2×SD16—224no—
290C2×SD16—224no—
291C2×SD16—442no—
292C22×C8—111no—
293C22×C8—111no—
294C22×C8C22×D1112yes—
295#127—222no—
296#127—222no—
297#124—444no—
298C4×Q8—222no—
299C4×Q8—222no—
300C4×Q8—222no—
301C4×Q8—222no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—111no—
305C2×C4⋊C4—112no—
306C2×C4⋊C4—111no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—222no—
309C2×C4⋊C4C22×D1111yescharacteristic
310C2×C4⋊C4C22×D1111yescharacteristic
311C2×C4⋊C4C22×D1112yes—
312C2×C22⋊C4—222no—
313C2×C22⋊C4—222no—
314C2×C22⋊C4—222no—
315C2×C22⋊C4—222no—
316C2×C42—21no—
317C2×C42—112no—
318C2×C42—221no—
319C2×C42C22×D1111yescharacteristic
320#106—42no—
321C4⋊C8—224no—
322C4⋊C8D4414yes—
323#103—222no—
324#103—222no—
325#102—224no—
326#102—224no—
327#102—442no—
328C4×C8—224no—
329C4×C8—222no—
330#95—21no—
331#95—222no—
332#95—222no—
333#95—222no—
334C2×C11#242611yescharacteristic
335C2×C11C2×#46511yescharacteristic
336C2×C11#306211yescharacteristic
337C2×C11#336211yescharacteristic
338C2×C11#336511yescharacteristic
339C2×C11#339211yescharacteristic
340C2×C11#339611yescharacteristic
341D11—162no—
342C24—222no—
343C2×Q8—114no—
344C2×Q8—112no—
345C2×Q8—222no—
346C2×Q8—222no—
347C2×Q8—221no—
348C2×Q8—221no—
349C2×Q8—221no—
350C2×Q8—221no—
351C2×Q8—221no—
352C2×D4—222no—
353C2×D4—222no—
354C2×D4—222no—
355C2×D4—222no—
356C2×D4—222no—
357C2×D4—222no—
358C2×D4—442no—
359C2×D4—442no—
360C2×D4—442no—
361C2×D4—442no—
362C2×D4—881no—
363C2×D4—881no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—112no—
368C22×C4—112no—
369C22×C4—221no—
370C22×C4—221no—
371C22×C4D4×D1111yescharacteristic
372C22×C4D4×D1111yescharacteristic
373C22×C4C23×D1111yescharacteristic
374SD16—448no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—112no—
378C2×C8—221no—
379C2×C8—221no—
380C2×C8—221no—
381C2×C8—221no—
382C2×C8—221no—
383C2×C8C2×D4414yes—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—42no—
391C4⋊C4—81no—
392C4⋊C4—224no—
393C4⋊C4—222no—
394C4⋊C4—221no—
395C4⋊C4—221no—
396C4⋊C4—442no—
397C4⋊C4—882no—
398C22⋊C4—444no—
399C22⋊C4—444no—
400C22⋊C4—882no—
401C22⋊C4—882no—
402C42—42no—
403C42—222no—
404C42—222no—
405C42—442no—
406C42C2×D4412yes—
407C42#434312yes—
408C11#2529511yescharacteristic, complemented, Sylow
409C23—442no—
410C23—442no—
411C23—442no—
412C23—442no—
413C23—442no—
414C23—442no—
415C23—442no—
416C23C2×D4×D1111yescharacteristic
417Q8—228no—
418Q8—222no—
419Q8—222no—
420Q8—441no—
421Q8—441no—
422D4—442no—
423D4—442no—
424D4—442no—
425D4—442no—
426D4—884no—
427D4—884no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—114no—
440C2×C4—222no—
441C2×C4—222no—
442C2×C4—222no—
443C2×C4—222no—
444C2×C4—222no—
445C2×C4—222no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4—441no—
451C2×C4#6694812yes—
452C2×C4#6694812yes—
453C2×C4SD16×D1112yes—
454C2×C4#6696912yes—
455C2×C4C22×D4411yescharacteristic
456C2×C4#6703711yescharacteristic
457C2×C4C2×#434311yescharacteristic
458C2×C4#6704011yescharacteristic
459C2×C4#41×D1111yescharacteristic
460C2×C4#41×D1111yescharacteristic
461C8—24no—
462C8—222no—
463C8—441no—
464C22—882no—
465C22—882no—
466C22—882no—
467C22—882no—
468C22—882no—
469C22—882no—
470C22—882no—
471C22C2×#6694811yescharacteristic
472C22#1062313011yescharacteristic
473C22#1062316411yescharacteristic
474C22C2×SD16×D1111yescharacteristic
475C22C2×#6696911yescharacteristic
476C22#1062330511yescharacteristic
477C22#1062330911yescharacteristic
478C4—22no—
479C4—82no—
480C4—81no—
481C4—81no—
482C4—224no—
483C4—442no—
484C4—442no—
485C4—881no—
486C4#1062247714yes—
487C4#1062308511yescharacteristic
488C4#1062310711yescharacteristic
489C4#1062322211yescharacteristic
490C4#1062326411yescharacteristic
491C2—1762no—
492C2#1307218011yescharacteristic
493C2C2×#1062247711yescharacteristic
494C2#1307829711yescharacteristic
495C2#1308128611yescharacteristic
496C2#1308131111yescharacteristic
497C2#1308159211yescharacteristic
498C2#1308162711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1948C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenter#1948D11
hypocenterC11#25295
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
2. C2×#10622443C2semidirect
3. #13073989C2semidirect
5. #13069985C2semidirect
6. #13069935C2semidirect
7. #13069468C2semidirect
9. #13069300C2semidirect
10. C4×#66874C2semidirect
11. C11×#1948C2semidirect
124. C2×Dic22SD16semidirect
168. #1948D11semidirect
408. C11#25295semidirect

Maximal subgroups

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

subgroupindex
C2×#106224612
C2×#106224432
#130739892
#130736182
#130699852
#130699352
#130694682
#130694212
#130693002
C4×#668742
C11×#19482
#2529511