Finite Group Databasebeta

← #14770407

Subgroups — #14770407

Order 2816.

1250 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic22C211yesmaximal, characteristic
2C2×#10622292C211yesmaximal, characteristic, complemented
3#13071571C211yesmaximal, characteristic, complemented
4#13069587C212yesmaximal, complemented
5#13069577C211yesmaximal, characteristic, complemented
6#13069568C211yesmaximal, characteristic, complemented
7#13069562C212yesmaximal, complemented
8#13068624C212yesmaximal
9#13068616C211yesmaximal, characteristic
10#13068443C212yesmaximal
11C4×C11×#102C211yesmaximal, characteristic
12C23×Dic22—21no—
13C2×C4×D4×C11C2211yescharacteristic
14C2×D4×Dic11C2212yes—
15C2×#66977—21no—
16D4×Dic22—24no—
17D4×Dic22C418yescomplemented
18C2×#66941C2212yes—
19C2×#66931—22no—
20C2×#66922C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C2×#66896C2212yes—
27C2×#66879C2212yes—
28C2×Dic11⋊C8C2212yes—
29#10622590C2212yes—
30C4⋊C4×Dic11C2212yes—
31#10622548C2211yescharacteristic
32C4×C4⋊Dic11—21no—
33#10622542—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35#10622292—24no—
36#10622268—22no—
37C11×#340C2211yescharacteristic
38C11×#340C2211yescharacteristic
39#10622189C2212yes—
40#10622189C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C23×Dic11—22no—
47C22×Dic22—21no—
48C22×Dic22—22no—
49C22×Dic22—28no—
50C22×Dic22—44no—
51C22×Dic22—44no—
52C22×Dic22D411yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C4×D4×C11—22no—
56C4×D4×C11C2×C414yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C22⋊C4—21no—
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63C2×C22⋊Dic11—22no—
64D4×Dic11—24no—
65D4×Dic11C2×C418yes—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11D411yescharacteristic
70C2×C4⋊Dic11C2312yes—
71C2×C4⋊Dic11C2312yes—
72#66977—28no—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4D412yes—
75C2×C4×Dic11—22no—
76C2×C4×Dic11C2312yes—
77C22×C11⋊C8C2312yes—
78#66941—24no—
79#66941C2×C418yes—
80#66931—216no—
81#66922—22no—
82#66922C2×C414yes—
83C4×Dic22C2×C414yes—
84C4×Dic22D414yes—
85C11×#102—22no—
86C11×#102Q814yescomplemented
87C4×C8×C11—22no—
88C11×#95—21no—
89#66896—24no—
90C11⋊#95—22no—
91C11⋊#95—22no—
92C11⋊#95—22no—
93#66879—24no—
94Dic11⋊C8—24no—
95C4⋊(C11⋊C8)—22no—
96#22523—111nomaximal, Sylow
97C24×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11C22×C412yes—
102C2×D4×C11C2×Q812yes—
103C2×D4×C11#4112yes—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—24no—
107C22×C4×C11—21no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2411yescharacteristic
113C22×Dic11—28no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—44no—
117C22×Dic11—44no—
118C22×Dic11C2×D412yes—
119C22×Dic11C2×D412yes—
120C2×Dic22—28no—
121C2×Dic22—24no—
122C2×Dic22—22no—
123C2×Dic22—22no—
124C2×Dic22—432no—
125C2×Dic22—44no—
126C2×Dic22—44no—
127C2×Dic22—42no—
128C2×Dic22—42no—
129C2×Dic22C22⋊C414yes—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11C2×Q812yescomplemented
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4C22×C412yes—
141C11×C4⋊C4C2×Q812yescomplemented
142C11×C22⋊C4—24no—
143C42×C11—42no—
144C42×C11C22×C412yes—
145C42×C11C2×D412yes—
146C22⋊Dic11—28no—
147C4⋊Dic11—24no—
148C4⋊Dic11—22no—
149C4⋊Dic11—22no—
150C4⋊Dic11—22no—
151C4⋊Dic11—42no—
152C4⋊Dic11—81no—
153C4⋊Dic11C22⋊C414yes—
154C4⋊Dic11C22×C414yes—
155Dic11⋊C4—28no—
156Dic11⋊C4C22⋊C418yes—
157C4×Dic11—82no—
158C4×Dic11C22×C414yes—
159C4×Dic11C2×D414yes—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×D4×Q8—111no—
164C2×#446—111no—
165#2355—111no—
166#1993—112no—
167#1990—111no—
168#1988—111no—
169#1987—112no—
170#1804—112no—
171#1802—111no—
172#1762—112no—
173C4×#102D1111yescharacteristic
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11C22×D411yescharacteristic
182D4×C11—22no—
183D4×C11—22no—
184D4×C11—22no—
185D4×C11C4×Q814yes—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—48no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11C2×C22⋊C412yes—
199C2×C4×C11C2×C22⋊C412yes—
200C2×C4×C11AGL(1,ℤ/8)12yes—
201C2×C4×C11AGL(1,ℤ/8)12yes—
202C2×C4×C11C23×C411yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C22×Q811yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C112−1+411yescharacteristic
207C2×C4×C112−1+411yescharacteristic
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—24no—
213C2×Dic11—416no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11C2×C22⋊C414yes—
220C2×Dic11C2×C22⋊C414yes—
221Dic22—28no—
222Dic22—416no—
223Dic22—48no—
224C8×C11—22no—
225C8×C11—41no—
226C11⋊C8—42no—
227C23×Q8—221no—
228D4×Q8—118no—
229D4×Q8—224no—
230C2×C4⋊Q8—112no—
231C2×C4⋊Q8—111no—
232C2×C22⋊Q8—222no—
233C2×C22⋊Q8—221no—
234C2×C4×Q8—111no—
235C2×C4×D4—112no—
236C2×C4×D4C2×D1111yescharacteristic
237#446—224no—
238C2×C4⋊C8—112no—
239C2×C4⋊C8—111no—
240C2×#102—112no—
241C2×#102C2×D1111yescharacteristic
242C2×#102C2×D1111yescharacteristic
243C2×#97—112no—
244C2×C4×C8C2×D1111yescharacteristic
245#391—221no—
246#387—222no—
247#384—111no—
248#382—112no—
249C4×C4⋊C4—112no—
250C4×C4⋊C4—221no—
251C4×C4⋊C4C2×D1111yescharacteristic
252#340—112no—
253#340—112no—
254#340—112no—
255#340—112no—
256#340—112no—
257#340C2×D1111yescharacteristic
258#340C2×D1111yescharacteristic
259C22×C11—24no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11C22×C22⋊C411yescharacteristic
267C22×C11#54811yescharacteristic
268C22×C11D4×Q811yescharacteristic
269C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
271C22×C11#57711yescharacteristic
272C22×C11#57811yescharacteristic
273C4×C11—22no—
274C4×C11—42no—
275C4×C11—42no—
276C4×C11—81no—
277C4×C11#41814yes—
278C4×C11C2×C4×Q811yescharacteristic
279C4×C11#51911yescharacteristic
280C4×C11#54811yescharacteristic
281C4×C11D4×Q811yescharacteristic
282Dic11—24no—
283Dic11—24no—
284Dic11—44no—
285Dic11—82no—
286C22×Q8—111no—
287C22×Q8—222no—
288C22×Q8—228no—
289C22×Q8—221no—
290C22×Q8—444no—
291C22×Q8—444no—
292C22×D4C22×D1111yescharacteristic
293C23×C4—21no—
294C23×C4—222no—
295C22×C8—112no—
296C22×C8C22×D1111yescharacteristic
297C22×C8C22×D1111yescharacteristic
298C4⋊Q8—118no—
299C4⋊Q8—114no—
300C4⋊Q8—224no—
301C4⋊Q8—222no—
302C22⋊Q8—2216no—
303C22⋊Q8—228no—
304C4×Q8—114no—
305C4×Q8—114no—
306C4×D4—22no—
307C4×D4—118no—
308C4×D4—224no—
309C4×D4C4×D1114yes—
310C2×C4⋊C4—111no—
311C2×C4⋊C4—112no—
312C2×C4⋊C4—112no—
313C2×C4⋊C4—112no—
314C2×C4⋊C4—222no—
315C2×C4⋊C4—221no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4C22×D1111yescharacteristic
319C2×C4⋊C4C22×D1111yescharacteristic
320C2×C4⋊C4C22×D1111yescharacteristic
321C2×C22⋊C4—21no—
322C2×C22⋊C4—222no—
323C2×C42—21no—
324C2×C42—112no—
325C2×C42—222no—
326C2×C42C22×D1111yescharacteristic
327C4⋊C8—224no—
328C4⋊C8—222no—
329#102—22no—
330#102—224no—
331#102Dic2214yescomplemented
332#97—224no—
333C4×C8—22no—
334#95—21no—
335#95—222no—
336#95—222no—
337#95—222no—
338C2×C11—44no—
339C2×C11Q8×C22⋊C411yescharacteristic
340C2×C11C2×#41811yescharacteristic
341C2×C11#289811yescharacteristic
342C2×C11#336711yescharacteristic
343C2×C11#337311yescharacteristic
344C2×C11#338411yescharacteristic
345C2×C11#338611yescharacteristic
346C24—21no—
347C2×Q8—114no—
348C2×Q8—228no—
349C2×Q8—224no—
350C2×Q8—222no—
351C2×Q8—222no—
352C2×Q8—444no—
353C2×Q8—444no—
354C2×Q8—4432no—
355C2×Q8—442no—
356C2×Q8—442no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4C2×Dic2212yes—
361C2×D4C2×C4×D1112yes—
362C2×D4#433912yes—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—24no—
366C22×C4—21no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—112no—
370C22×C4—112no—
371C22×C4—228no—
372C22×C4—222no—
373C22×C4—222no—
374C22×C4—444no—
375C22×C4—444no—
376C22×C4D4×D1111yescharacteristic
377C22×C4D4×D1111yescharacteristic
378C22×C4C23×D1111yescharacteristic
379C2×C8—21no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—222no—
385C2×C8—222no—
386C2×C8—222no—
387C2×C8C2×Dic2212yescomplemented
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—118no—
393C4⋊C4—114no—
394C4⋊C4—114no—
395C4⋊C4—228no—
396C4⋊C4—224no—
397C4⋊C4—222no—
398C4⋊C4—222no—
399C4⋊C4—222no—
400C4⋊C4—442no—
401C4⋊C4—881no—
402C4⋊C4C2×Dic2212yescomplemented
403C4⋊C4C2×C4×D1112yes—
404C22⋊C4—24no—
405C22⋊C4—228no—
406C42—42no—
407C42—114no—
408C42—114no—
409C42—882no—
410C42C2×C4×D1112yes—
411C42D4×D1112yes—
412C11#2252311yescharacteristic, complemented, Sylow
413C23—22no—
414C23—22no—
415C23—22no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23C2×D4×D1111yescharacteristic
421Q8—228no—
422Q8—4416no—
423Q8—448no—
424D4—22no—
425D4—22no—
426D4—22no—
427D4C4×Dic2214yes—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—48no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—114no—
441C2×C4—114no—
442C2×C4—222no—
443C2×C4—222no—
444C2×C4—222no—
445C2×C4—222no—
446C2×C4—224no—
447C2×C4—4416no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4C22⋊C4×D1112yes—
454C2×C4C22⋊C4×D1112yes—
455C2×C4#6696412yes—
456C2×C4#6696712yes—
457C2×C4C22×Dic2211yescharacteristic
458C2×C4C22×C4×D1111yescharacteristic
459C2×C4C2×#433911yescharacteristic
460C2×C4C2×D4×D1111yescharacteristic
461C2×C4#6704311yescharacteristic
462C2×C4#6704311yescharacteristic
463C8—22no—
464C8—41no—
465C8—442no—
466C22—24no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22C2×C22⋊C4×D1111yescharacteristic
474C22D4×Dic2211yescharacteristic
475C22#1062308311yescharacteristic
476C22C2×#6696411yescharacteristic
477C22C2×#6696711yescharacteristic
478C22#1062330111yescharacteristic
479C22#1062330211yescharacteristic
480C4—22no—
481C4—42no—
482C4—42no—
483C4—81no—
484C4—224no—
485C4—224no—
486C4—444no—
487C4—882no—
488C4#1062238314yes—
489C4C2×C4×Dic2211yescharacteristic
490C4#1062304711yescharacteristic
491C4D4×Dic2211yescharacteristic
492C4#1062308311yescharacteristic
493C2—44no—
494C2C22⋊C4×Dic2211yescharacteristic
495C2C2×#1062238311yescharacteristic
496C2#1307714511yescharacteristic
497C2#1308133211yescharacteristic
498C2#1308140611yescharacteristic
499C2#1308151311yescharacteristic
500C2#1308153511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterC4×#102D11
hypocenterC11#22523
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C2×#10622292C2semidirect
3. #13071571C2semidirect
4. #13069587C2semidirect
5. #13069577C2semidirect
6. #13069568C2semidirect
7. #13069562C2semidirect
17. D4×Dic22C4semidirect
86. C11×#102Q8semidirect
135. C2×C8×C11C2×Q8semidirect
141. C11×C4⋊C4C2×Q8semidirect
331. #102Dic22semidirect
387. C2×C8C2×Dic22semidirect
402. C4⋊C4C2×Dic22semidirect
412. C11#22523semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic222
C2×#106222922
#130715712
#130695872
#130695772
#130695682
#130695622
#130686242
#130686162
#130684432
C4×C11×#1022
#2252311