Finite Group Databasebeta

← #14803636

Subgroups — #14803636

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×#10622294C211yesmaximal, characteristic, complemented
2C2×#10622454C211yesmaximal, characteristic
3#13073565C211yesmaximal, characteristic
4#13071672C211yesmaximal, characteristic, complemented
5#13070026C212yesmaximal, complemented
6#13069934C212yesmaximal
7#13069567C211yesmaximal, characteristic, complemented
8#13068970C212yesmaximal
9#13068622C212yesmaximal, complemented
10C4×#66885C211yesmaximal, characteristic
11C11×#1939C211yesmaximal, characteristic, complemented
12C22×#4314C2212yes—
13C2×#66950—21no—
14C2×#66950—21no—
15C2×C4×D44C2211yescharacteristic
16C2×#66922C2211yescharacteristic
17C2×#66922C2211yescharacteristic
18C2×C4×Dic22C2212yes—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C4⋊C8C2212yes—
21C2×C4×C8×C11C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×#66885C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66880C2212yes—
26C2×#66880C2212yes—
27C2×#66880C2212yes—
28C4⋊C4×Dic11—21no—
29#10622586—21no—
30#10622552C2212yes—
31#10622548C2212yes—
32C4×C4⋊Dic11C2211yescharacteristic
33#10622542C2212yes—
34#10622454—24no—
35#10622294—24no—
36#10622290—22no—
37#10622267—22no—
38C11×#336C2212yes—
39#10622189C2211yescharacteristic
40#10622189C2212yes—
41#10622189C2212yes—
42#10622189C2211yescharacteristic
43C22×D44C2311yescharacteristic
44C22×C4×D11—21no—
45C22×Dic22—21no—
46C22×Dic22C2312yes—
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2312yes—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C42×C11C2312yes—
53C2×C42×C11C2311yescharacteristic
54C2×(C2×D11)⋊C4—21no—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11C2311yescharacteristic
63C2×C4⋊Dic11C2312yes—
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66C2×Dic11⋊C4—22no—
67C2×C4×Dic11—22no—
68C2×C4×Dic11—21no—
69C2×#4314—24no—
70C2×#4314—24no—
71C2×#4314—42no—
72#66950—44no—
73#66950—44no—
74C4×D44—22no—
75C4×D44—22no—
76#66922—22no—
77#66922—22no—
78#66922—22no—
79#66922D414yes—
80C4×Dic22—24no—
81C4×Dic22—42no—
82C11×C4⋊C8—22no—
83C11×C4⋊C8—42no—
84C4×C8×C11—22no—
85C11×#95D412yes—
86C11⋊#95—21no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89#66885—22no—
90#66885—22no—
91#66880—24no—
92#66880—24no—
93#66880—24no—
94#25320—111nomaximal, Sylow
95C23×D11—21no—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—22no—
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—22no—
106C2×D44—21no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44#4112yes—
112C2×C4×D11—42no—
113C2×C4×D11—42no—
114C2×C4×D11—42no—
115C2×Dic22—22no—
116C2×Dic22—22no—
117C2×Dic22—22no—
118C2×Dic22—22no—
119C2×Dic22—22no—
120C2×Dic22—42no—
121C2×Dic22—42no—
122C2×Dic22—42no—
123C2×Dic22C2×D414yes—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—22no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11—22no—
130C2×C8×C11—21no—
131C2×C8×C11—22no—
132C2×C8×C11—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4SD1614yescomplemented
135C42×C11—22no—
136C42×C11—22no—
137C42×C11C2×D412yes—
138C42×C11#4112yes—
139(C2×D11)⋊C4—44no—
140(C2×D11)⋊C4—42no—
141(C2×D11)⋊C4—44no—
142C4⋊Dic11—24no—
143C4⋊Dic11—24no—
144C4⋊Dic11—22no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—22no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—44no—
152C4⋊Dic11—42no—
153C4⋊Dic11—44no—
154C4⋊Dic11#4112yes—
155Dic11⋊C4—44no—
156C4×Dic11—44no—
157C4×Dic11—42no—
158#4314—48no—
159C2×#487—111no—
160C2×#461—111no—
161#2542—111no—
162#2365—111no—
163#2072—112no—
164#2055—112no—
165#1988—111no—
166#1939D1111yescharacteristic, complemented
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—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11#12112yes—
186C2×C4×C11#12112yes—
187C2×C4×C11C2×SD1614yes—
188C2×C4×C11C2×SD1612yes—
189C2×C4×C11AGL(1,ℤ/8)12yes—
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C11H(5,𝔽2)11yescharacteristic
195C2×C4×C112−1+411yescharacteristic
196C2×Dic11—24no—
197C2×Dic11—22no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—42no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—42no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—42no—
210C2×Dic11—41no—
211D44—22no—
212D44—22no—
213D44—41no—
214D44—41no—
215C4×D11—84no—
216Dic22—24no—
217Dic22—24no—
218Dic22—42no—
219Dic22—42no—
220Dic22—84no—
221C8×C11—42no—
222C8×C11—41no—
223C8×C11—41no—
224C22×SD16—112no—
225C2×C4⋊Q8—111no—
226C2×C4⋊Q8—111no—
227C2×C22⋊Q8—221no—
228C2×C22⋊Q8—221no—
229C2×C4×Q8—112no—
230C2×C4×D4—111no—
231#487—224no—
232#461—224no—
233C2×C4⋊C8C2×D1111yescharacteristic
234C2×C4⋊C8C2×D1112yes—
235C2×#103—112no—
236C2×#103—112no—
237C2×#103—112no—
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—221no—
249C4×C4⋊C4C2×D1111yescharacteristic
250#340—112no—
251#340—111no—
252#340—112no—
253#340—111no—
254#336C2×D1112yes—
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—24no—
270C4×C11—22no—
271C4×C11—42no—
272C4×C11#46014yes—
273C4×C11#52911yescharacteristic
274C4×C11#54211yescharacteristic
275C4×C11#54611yescharacteristic
276C4×C11#54711yescharacteristic
277Dic11—42no—
278Dic11—44no—
279Dic11—81no—
280Dic11—82no—
281Dic11—81no—
282C22×Q8—112no—
283C22×Q8—221no—
284C22×D4—111no—
285C23×C4—221no—
286C2×SD16—224no—
287C2×SD16—224no—
288C2×SD16—442no—
289C22×C8C22×D1112yes—
290C22×C8C22×D1111yescharacteristic
291C22×C8C22×D1111yescharacteristic
292C4⋊Q8—114no—
293C4⋊Q8—222no—
294C4⋊Q8—222no—
295C4⋊Q8—222no—
296C22⋊Q8—444no—
297C22⋊Q8—444no—
298C4×Q8—224no—
299C4×Q8—442no—
300C4×D4—222no—
301C4×D4—222no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—111no—
304C2×C4⋊C4—112no—
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⋊C4—221no—
312C2×C4⋊C4D4411yescharacteristic
313C2×C4⋊C4D4411yescharacteristic
314C2×C22⋊C4—221no—
315C2×C22⋊C4—222no—
316C2×C22⋊C4—222no—
317C2×C42—222no—
318C2×C42—221no—
319C2×C42C22×D1112yes—
320C2×C42C22×D1111yescharacteristic
321C4⋊C8—22no—
322C4⋊C8—42no—
323#103—224no—
324#103—224no—
325#103—224no—
326#102—222no—
327#102—222no—
328C4×C8—22no—
329#95—221no—
330#95—222no—
331#95—222no—
332#95D4412yes—
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—114no—
343C2×Q8—222no—
344C2×Q8—222no—
345C2×Q8—222no—
346C2×Q8—222no—
347C2×Q8—222no—
348C2×Q8—442no—
349C2×Q8—442no—
350C2×Q8—442no—
351C2×D4—112no—
352C2×D4—221no—
353C2×D4—221no—
354C2×D4—221no—
355C2×D4—221no—
356C2×D4—221no—
357C22×C4—222no—
358C22×C4—221no—
359C22×C4—221no—
360C22×C4—222no—
361C22×C4—221no—
362C22×C4—442no—
363C22×C4—442no—
364C22×C4—442no—
365C22×C4C2×D4412yes—
366C22×C4C2×D4411yescharacteristic
367C22×C4C2×D4412yes—
368C22×C4C2×D4411yescharacteristic
369C22×C4C23×D1111yescharacteristic
370SD16—448no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—22no—
374C2×C8—21no—
375C2×C8—22no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—21no—
379C2×C8—22no—
380C4⋊C4—22no—
381C4⋊C4—112no—
382C4⋊C4—224no—
383C4⋊C4—224no—
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—222no—
387C4⋊C4—221no—
388C4⋊C4—222no—
389C4⋊C4—221no—
390C4⋊C4—221no—
391C4⋊C4—444no—
392C4⋊C4—444no—
393C4⋊C4—442no—
394C4⋊C4—444no—
395C4⋊C4#431414yescomplemented
396C22⋊C4—444no—
397C22⋊C4—442no—
398C22⋊C4—444no—
399C42—22no—
400C42—22no—
401C42—444no—
402C42—442no—
403C42D4×D1112yes—
404C42#434312yes—
405C11#2532011yescharacteristic, complemented, Sylow
406C23—222no—
407C23—441no—
408C23—441no—
409C23—441no—
410C23—441no—
411C23—441no—
412C23—441no—
413C23C22×D4411yescharacteristic
414Q8—224no—
415Q8—224no—
416Q8—442no—
417Q8—442no—
418Q8—884no—
419D4—222no—
420D4—222no—
421D4—441no—
422D4—441no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—224no—
431C2×C4—222no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—442no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—442no—
444C2×C4—441no—
445C2×C4—884no—
446C2×C4#6694812yes—
447C2×C4#6694812yes—
448C2×C4C2×#431414yes—
449C2×C4C2×#431412yes—
450C2×C4#6696112yes—
451C2×C4C2×D4×D1111yescharacteristic
452C2×C4#6703711yescharacteristic
453C2×C4C2×#434311yescharacteristic
454C2×C4#6704011yescharacteristic
455C2×C4#41×D1111yescharacteristic
456C2×C4#41×D1111yescharacteristic
457C8—42no—
458C8—41no—
459C8—41no—
460C22—442no—
461C22—442no—
462C22—442no—
463C22—881no—
464C22—881no—
465C22—881no—
466C22—881no—
467C22C2×#6694811yescharacteristic
468C22#1062308511yescharacteristic
469C22#1062310711yescharacteristic
470C22C22×#431411yescharacteristic
471C22C2×#6696111yescharacteristic
472C22#1062328411yescharacteristic
473C22#1062328411yescharacteristic
474C4—22no—
475C4—24no—
476C4—42no—
477C4—444no—
478C4—442no—
479C4—881no—
480C4—882no—
481C4—881no—
482C4#1062246114yes—
483C4#1062314311yescharacteristic
484C4#1062316211yescharacteristic
485C4#1062322211yescharacteristic
486C4#1062326411yescharacteristic
487C2—882no—
488C2#1307219111yescharacteristic
489C2C2×#1062246111yescharacteristic
490C2#1307814711yescharacteristic
491C2#1308048211yescharacteristic
492C2#1308092211yescharacteristic
493C2#1308125911yescharacteristic
494C2#1308133611yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1939C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1939D11
hypocenterC11#25320
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1939

Complements

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

NH ≅ G/Ntype
1. C2×#10622294C2semidirect
4. #13071672C2semidirect
5. #13070026C2semidirect
7. #13069567C2semidirect
9. #13068622C2semidirect
11. C11×#1939C2semidirect
134. C11×C4⋊C4SD16semidirect
166. #1939D11semidirect
395. C4⋊C4#4314semidirect
405. C11#25320semidirect

Maximal subgroups

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

subgroupindex
C2×#106222942
C2×#106224542
#130735652
#130716722
#130700262
#130699342
#130695672
#130689702
#130686222
C4×#668852
C11×#19392
#2532011