Finite Group Databasebeta

← #14770573

Subgroups — #14770573

Order 2816.

1074 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×#10623073C211yesmaximal, characteristic
2C2×#10622443C211yesmaximal, characteristic, complemented
3#13071575C211yesmaximal, characteristic, complemented
4#13069547C212yesmaximal
5#13069538C211yesmaximal, characteristic, complemented
6#13069426C212yesmaximal
7#13069417C211yesmaximal, characteristic, complemented
8#13068630C212yesmaximal, complemented
9#13068435C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic
11C11×#1802C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66989C2212yes—
14C2×#66979—21no—
15C2×#66977—21no—
16#10623073—24no—
17#10623073C418yescomplemented
18C2×#66940C2212yes—
19C2×#66932—22no—
20C2×#66922C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#102C2212yes—
24C11×#384C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27C2×#66880C2212yes—
28C2×#66880C2212yes—
29C2×Dic11⋊C8C2212yes—
30C2×C8×Dic11C2212yes—
31#10622591—22no—
32#10622590C2212yes—
33C4⋊C4×Dic11—21no—
34C4⋊C4×Dic11C2212yes—
35#10622587—21no—
36C2×#66874C2212yes—
37C2×#66874C2212yes—
38C4×C4⋊Dic11C2211yescharacteristic
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622443—24no—
41C11×#340C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C22×Dic22D411yescharacteristic
47C22×Dic22C2312yes—
48C22×C8×C11C2312yes—
49C4×D4×C11—22no—
50C4×D4×C11C2×C414yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C22⋊C4—21no—
56C2×C42×C11C2311yescharacteristic
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—22no—
59#66989—24no—
60#66989C2×C418yes—
61#66979—28no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11D411yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67#66977—28no—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4D412yes—
70C2×C4×Dic11—22no—
71C2×C4×Dic11—21no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11C2312yes—
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2311yescharacteristic
76#66940—24no—
77#66940C2×C418yes—
78#66932—216no—
79#66922—22no—
80#66922C2×C414yes—
81C4×Dic22C2×C414yes—
82C4×Dic22D414yes—
83C11×C4⋊C8—22no—
84C11×#102—42no—
85#66896—22no—
86#66896—22no—
87C11⋊#95—21no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91#66880—24no—
92#66880—42no—
93Dic11⋊C8—24no—
94C8×Dic11—24no—
95#66874—24no—
96#66874—42no—
97C4×C11⋊C8—22no—
98#22541—111nomaximal, Sylow
99C24×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11C22×C412yes—
106C22×C4×C11—21no—
107C22×C4×C11—24no—
108C22×C4×C11—22no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2411yescharacteristic
114C22×Dic11—21no—
115C22×Dic11—22no—
116C22×Dic11—21no—
117C22×Dic11C2×D412yes—
118C22×Dic11C2×D412yes—
119C2×Dic22—22no—
120C2×Dic22—22no—
121C2×Dic22—22no—
122C2×Dic22—22no—
123C2×Dic22—22no—
124C2×Dic22—22no—
125C2×Dic22—22no—
126C2×Dic22C22⋊C414yes—
127C2×Dic22C22×C414yes—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—42no—
135C11×C4⋊C4—81no—
136C11×C4⋊C4C22×C412yes—
137C11×C22⋊C4—24no—
138C42×C11C22×C412yes—
139C42×C11C2×D412yes—
140C22⋊Dic11—28no—
141C22⋊Dic11—28no—
142C4⋊Dic11—24no—
143C4⋊Dic11—24no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11C22⋊C414yes—
148C4⋊Dic11#4112yes—
149Dic11⋊C4—28no—
150Dic11⋊C4C22⋊C418yes—
151C4×Dic11—28no—
152C4×Dic11—42no—
153C4×Dic11—82no—
154C4×Dic11C22×C414yes—
155C4×Dic11C2×D414yes—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8#4112yes—
162C2×#556—111no—
163C2×C8×Q8—111no—
164#2355—111no—
165#1983—112no—
166#1981—111no—
167#1958—112no—
168#1956—111no—
169#1805—112no—
170#1802D1111yescharacteristic
171C4×#103—112no—
172C4×#102—111no—
173C23×C11—22no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11C22×D411yescharacteristic
181D4×C11—22no—
182D4×C11—22no—
183D4×C11—41no—
184D4×C11—41no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—22no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—48no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11C2×C22⋊C412yes—
195C2×C4×C11C2×C22⋊C412yes—
196C2×C4×C11#13512yes—
197C2×C4×C11#13512yes—
198C2×C4×C11C23×C411yescharacteristic
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11H(5,𝔽2)11yescharacteristic
203C2×C4×C112−1+411yescharacteristic
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—24no—
209C2×Dic11—22no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11C2×C22⋊C414yes—
218C2×Dic11C2×C22⋊C414yes—
219Dic22—28no—
220Dic22—24no—
221Dic22—24no—
222Dic22—42no—
223Dic22—42no—
224C8×C11—42no—
225C11⋊C8—22no—
226C11⋊C8—41no—
227#556—118no—
228#556—224no—
229C2×C4⋊Q8—111no—
230C2×#126—222no—
231C2×#124—112no—
232C2×C22⋊Q8—221no—
233C2×C4×Q8—111no—
234C2×C4×Q8—112no—
235C2×C4×D4C2×D1111yescharacteristic
236C2×#117—221no—
237C8×Q8—224no—
238C2×C4⋊C8—112no—
239C2×C4⋊C8C2×D1111yescharacteristic
240C2×#103—112no—
241C2×#103—112no—
242C2×#103—112no—
243C2×#103—112no—
244C2×#102—111no—
245C2×#102—111no—
246C2×#102C2×D1112yes—
247C2×C4×C8—112no—
248C2×C4×C8—111no—
249#391—221no—
250#387—222no—
251#384C2×D1111yescharacteristic
252#382—112no—
253C4×C4⋊C4—112no—
254C4×C4⋊C4—111no—
255C4×C4⋊C4—221no—
256#340—111no—
257#340—111no—
258#340C2×D1112yes—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—81no—
263C22×C11—81no—
264C22×C11—81no—
265C22×C11—81no—
266C22×C11C22×C22⋊C411yescharacteristic
267C22×C11#54811yescharacteristic
268C22×C11#55011yescharacteristic
269C22×C11C2×#13511yescharacteristic
270C22×C11C2×#13511yescharacteristic
271C22×C11#57711yescharacteristic
272C22×C11#57811yescharacteristic
273C4×C11—22no—
274C4×C11—42no—
275C4×C11—82no—
276C4×C11#41614yes—
277C4×C11C4×#4111yescharacteristic
278C4×C11#52011yescharacteristic
279C4×C11#54811yescharacteristic
280C4×C11#55011yescharacteristic
281Dic11—24no—
282Dic11—24no—
283Dic11—42no—
284Dic11—44no—
285Dic11—81no—
286C22×Q8—111no—
287C22×Q8—112no—
288C22×D4C22×D1111yescharacteristic
289C23×C4—21no—
290C22×C8—111no—
291C22×C8—111no—
292C22×C8C22×D1112yes—
293C4⋊Q8—114no—
294C4⋊Q8—222no—
295#126—2216no—
296#124—118no—
297#124—224no—
298C22⋊Q8—228no—
299C4×Q8—114no—
300C4×Q8—114no—
301C4×Q8—118no—
302C4×Q8—224no—
303C4×D4—22no—
304C4×D4C4×D1114yes—
305#117—228no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—111no—
309C2×C4⋊C4—112no—
310C2×C4⋊C4—111no—
311C2×C4⋊C4—111no—
312C2×C4⋊C4—222no—
313C2×C4⋊C4—221no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4C22×D1112yes—
316C2×C4⋊C4C22×D1111yescharacteristic
317C2×C22⋊C4—21no—
318C2×C22⋊C4—222no—
319C2×C22⋊C4—222no—
320C2×C42—112no—
321C2×C42—222no—
322C2×C42—221no—
323C2×C42—222no—
324C2×C42C22×D1111yescharacteristic
325C4⋊C8—22no—
326C4⋊C8—224no—
327#103—224no—
328#103—224no—
329#103—442no—
330#103—442no—
331#102—42no—
332#102—222no—
333#102—222no—
334C4×C8—224no—
335C4×C8—222no—
336#95—222no—
337#95—222no—
338#95—222no—
339#95—221no—
340C2×C11—82no—
341C2×C11#234111yescharacteristic
342C2×C11C2×#41611yescharacteristic
343C2×C11#289811yescharacteristic
344C2×C11#336011yescharacteristic
345C2×C11#336411yescharacteristic
346C2×C11#339311yescharacteristic
347C2×C11#339411yescharacteristic
348C24—21no—
349C2×Q8—114no—
350C2×Q8—114no—
351C2×Q8—222no—
352C2×Q8—222no—
353C2×Q8—222no—
354C2×Q8—222no—
355C2×Q8—222no—
356C2×Q8—222no—
357C2×Q8—222no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4C2×C4×D1112yes—
364C22×C4—21no—
365C22×C4—24no—
366C22×C4—22no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—112no—
370C22×C4—112no—
371C22×C4—221no—
372C22×C4—222no—
373C22×C4—221no—
374C22×C4D4×D1111yescharacteristic
375C22×C4D4×D1111yescharacteristic
376C22×C4C23×D1111yescharacteristic
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—112no—
381C2×C8—221no—
382C2×C8—221no—
383C2×C8—221no—
384C2×C8—221no—
385C2×C8—221no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—42no—
390C4⋊C4—81no—
391C4⋊C4—114no—
392C4⋊C4—118no—
393C4⋊C4—112no—
394C4⋊C4—228no—
395C4⋊C4—224no—
396C4⋊C4—224no—
397C4⋊C4—221no—
398C4⋊C4—221no—
399C4⋊C4—221no—
400C4⋊C4C2×C4×D1112yes—
401C22⋊C4—24no—
402C22⋊C4—228no—
403C22⋊C4—228no—
404C42—114no—
405C42—114no—
406C42—228no—
407C42—442no—
408C42—882no—
409C42C2×C4×D1112yes—
410C42D4×D1112yes—
411C11#2254111yescharacteristic, complemented, Sylow
412C23—22no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23C2×D4×D1111yescharacteristic
420Q8—228no—
421Q8—224no—
422Q8—224no—
423Q8—442no—
424Q8—442no—
425D4—22no—
426D4—22no—
427D4—41no—
428D4—41no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—22no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—48no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—114no—
439C2×C4—114no—
440C2×C4—222no—
441C2×C4—222no—
442C2×C4—222no—
443C2×C4—222no—
444C2×C4—224no—
445C2×C4—222no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4C22⋊C4×D1112yes—
454C2×C4C22⋊C4×D1112yes—
455C2×C4#6696512yes—
456C2×C4#6696912yes—
457C2×C4C22×C4×D1111yescharacteristic
458C2×C4C2×D4×D1111yescharacteristic
459C2×C4#6703711yescharacteristic
460C2×C4#6704011yescharacteristic
461C2×C4#41×D1111yescharacteristic
462C2×C4#41×D1111yescharacteristic
463C8—42no—
464C8—222no—
465C8—441no—
466C22—42no—
467C22—42no—
468C22—42no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22C2×C22⋊C4×D1111yescharacteristic
474C22#1062313011yescharacteristic
475C22#1062316411yescharacteristic
476C22C2×#6696511yescharacteristic
477C22C2×#6696911yescharacteristic
478C22#1062330611yescharacteristic
479C22#1062331011yescharacteristic
480C4—22no—
481C4—42no—
482C4—82no—
483C4—224no—
484C4—224no—
485C4—444no—
486C4—442no—
487C4—881no—
488C4#1062238514yes—
489C4#1062303511yescharacteristic
490C4#1062305311yescharacteristic
491C4#1062313011yescharacteristic
492C4#1062316411yescharacteristic
493C2—82no—
494C2#1307145311yescharacteristic
495C2C2×#1062238511yescharacteristic
496C2#1307714711yescharacteristic
497C2#1308126411yescharacteristic
498C2#1308130011yescharacteristic
499C2#1308160311yescharacteristic
500C2#1308161611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1802C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#1802D11
hypocenterC11#22541
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. C2×#10622443C2semidirect
3. #13071575C2semidirect
5. #13069538C2semidirect
7. #13069417C2semidirect
8. #13068630C2semidirect
9. #13068435C2semidirect
17. #10623073C4semidirect
411. C11#22541semidirect

Maximal subgroups

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

subgroupindex
C2×#106230732
C2×#106224432
#130715752
#130695472
#130695382
#130694262
#130694172
#130686302
#130684352
C4×#668962
C11×#18022
#2254111