Finite Group Databasebeta

← #14814868

Subgroups — #14814868

Order 2816.

934 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×#10622584C212yesmaximal, complemented
2#13073569C211yesmaximal, characteristic
3#13069812C212yesmaximal, complemented
4#13069812C212yesmaximal, complemented
5#13069539C211yesmaximal, characteristic, complemented
6#13069417C211yesmaximal, characteristic, complemented
7#13069411C211yesmaximal, characteristic
8#13069377C211yesmaximal, characteristic, complemented
9#13068923C212yesmaximal, complemented
10C4×#66872C211yesmaximal, characteristic, complemented
11D4×C11×C4⋊C4C211yesmaximal, characteristic
12C2×C4×D4×C11—21no—
13C2×C4×D4×C11C2211yescharacteristic
14C22×C11×C4⋊C4C2212yes—
15C2×#66977C2212yes—
16C2×#66977C2212yes—
17C2×#66922C2211yescharacteristic
18C11×#389—21no—
19C11×#385—22no—
20C11×#384C2211yescharacteristic
21C11×#380C2212yes—
22C4×C11×C4⋊C4C2211yescharacteristic
23#10622834—21no—
24C2×C22⋊(C11⋊C8)C2212yes—
25C2×C22⋊(C11⋊C8)C2212yes—
26#10622589—21no—
27#10622584—28no—
28C2×#66874C2212yes—
29C2×#66874C2212yes—
30C2×#66874C2212yes—
31C2×#66874C2212yes—
32C2×#66872C2212yes—
33C2×#66872C2211yescharacteristic
34C2×#66872C2211yescharacteristic
35#10622562—22no—
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4×C11⋊C8C2211yescharacteristic
39#10622167C2212yes—
40#10622167C2211yescharacteristic
41#10622167C2211yescharacteristic
42C22×D4×C11D411yescharacteristic
43C23×C4×C11—22no—
44C23×C4×C11C2312yes—
45C22×Dic22C2312yes—
46C4×D4×C11—22no—
47C4×D4×C11—22no—
48C4×D4×C11—44no—
49C2×C11×C4⋊C4—24no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—42no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4D412yes—
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62C2×C22⋊Dic11—22no—
63C2×C22⋊Dic11—22no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68#66977—24no—
69#66977—24no—
70#66977—42no—
71#66977—42no—
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4—22no—
74C2×C4×Dic11—21no—
75C22×C11⋊C8C2311yescharacteristic
76C22×C11⋊C8C2312yes—
77C22×C11⋊C8C2311yescharacteristic
78#66922—22no—
79#66922—22no—
80C11×#95—21no—
81C11×#95—22no—
82C11⋊#95—21no—
83C22⋊(C11⋊C8)—24no—
84C22⋊(C11⋊C8)—42no—
85#66874—24no—
86#66874—24no—
87#66874—42no—
88#66874—42no—
89#66872—24no—
90#66872—22no—
91#66872D414yescomplemented
92C4⋊(C11⋊C8)—22no—
93C4×C11⋊C8—22no—
94#26234—111nomaximal, Sylow
95C24×C11C2×D412yes—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11SD1614yes—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—44no—
109C22×C4×C11—44no—
110C22×C4×C11—82no—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2411yescharacteristic
115C22×Dic11—21no—
116C22×Dic11—21no—
117C22×Dic11—22no—
118C2×Dic22—22no—
119C2×Dic22—22no—
120C2×Dic22—22no—
121C2×Dic22—22no—
122C2×Dic22—22no—
123C2×Dic22—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—44no—
131C11×C4⋊C4—42no—
132C11×C4⋊C4—81no—
133C11×C4⋊C4C2×D412yes—
134C11×C22⋊C4—24no—
135C11×C22⋊C4—44no—
136C42×C11—42no—
137C42×C11#4112yes—
138C42×C11#4112yes—
139C22⋊Dic11—44no—
140C22⋊Dic11—44no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11—42no—
144C4⋊Dic11—42no—
145C4⋊Dic11C2×D412yes—
146C4⋊Dic11#4112yes—
147Dic11⋊C4—44no—
148Dic11⋊C4—44no—
149C4×Dic11—42no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8C2×D412yes—
159C2×#483—112no—
160#2542—111no—
161D4×C4⋊C4D1111yescharacteristic
162#2035—112no—
163#2035—112no—
164#1981—111no—
165#1956—111no—
166#1954—111no—
167#1948—111no—
168#1872—112no—
169C4×#106—111no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11C2×SD1614yes—
177C23×C11C22×D411yescharacteristic
178D4×C11—28no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—41no—
197C2×C4×C11—88no—
198C2×C4×C11#12312yes—
199C2×C4×C11#12312yes—
200C2×C4×C11C2×SD1612yes—
201C2×C4×C11#13712yes—
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11H(5,𝔽2)11yescharacteristic
207C2×C4×C11H(5,𝔽2)11yescharacteristic
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217Dic22—42no—
218Dic22—42no—
219Dic22—42no—
220Dic22—42no—
221C11⋊C8—22no—
222C11⋊C8—41no—
223C11⋊C8—42no—
224C2×C4⋊Q8—111no—
225C2×C22⋊Q8—112no—
226C2×C22⋊Q8—112no—
227C2×C4×D4—21no—
228C2×C4×D4C2×D1111yescharacteristic
229C22×C4⋊C4C2×D1112yes—
230#483—228no—
231C2×#106—111no—
232C2×#106—112no—
233C2×#106—111no—
234C2×C4⋊C8—111no—
235C2×#103—112no—
236C2×#103—112no—
237C2×#103—112no—
238C2×#103—112no—
239C2×C22⋊C8—112no—
240C2×C22⋊C8—112no—
241C2×C4×C8—111no—
242#399—222no—
243#390—221no—
244#389—21no—
245#385—22no—
246#384—221no—
247#384C2×D1111yescharacteristic
248#380C2×D1112yes—
249C4×C4⋊C4—111no—
250C4×C4⋊C4C2×D1111yescharacteristic
251#340—111no—
252#340—112no—
253#340—111no—
254C22×C11—24no—
255C22×C11—24no—
256C22×C11—24no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11C2×#12311yescharacteristic
262C22×C11D4211yescharacteristic
263C22×C11#54611yescharacteristic
264C22×C11C22×SD1611yescharacteristic
265C22×C11C2×#13711yescharacteristic
266C22×C11#57711yescharacteristic
267C22×C11#57811yescharacteristic
268C4×C11—22no—
269C4×C11—42no—
270C4×C11—42no—
271C4×C11—82no—
272C4×C11—81no—
273C4×C11#48314yescomplemented
274C4×C11#53211yescharacteristic
275C4×C11#54011yescharacteristic
276C4×C11#55011yescharacteristic
277C4×C11#55911yescharacteristic
278Dic11—42no—
279Dic11—42no—
280Dic11—82no—
281C22×Q8—112no—
282C22×D4C22⋊D1111yescharacteristic
283C23×C4—22no—
284C23×C4C22×D1112yes—
285C22×C8—111no—
286C22×C8—111no—
287C22×C8—112no—
288C4⋊Q8—222no—
289C4⋊Q8—222no—
290C22⋊Q8—224no—
291C22⋊Q8—224no—
292C22⋊Q8—442no—
293C22⋊Q8—442no—
294C4×D4—22no—
295C4×D4—22no—
296C4×D4—44no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—111no—
304C2×C4⋊C4—222no—
305C2×C4⋊C4—222no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4C22⋊D1111yescharacteristic
309C2×C4⋊C4C22×D1112yes—
310C2×C4⋊C4C22×D1111yescharacteristic
311C2×C4⋊C4C22×D1111yescharacteristic
312C2×C22⋊C4—22no—
313C2×C22⋊C4—222no—
314C2×C22⋊C4—222no—
315C2×C22⋊C4C22⋊D1112yes—
316C2×C42—21no—
317C2×C42—221no—
318C2×C42C22×D1111yescharacteristic
319#106—114no—
320#106—222no—
321#106—224no—
322C4⋊C8—222no—
323#103—224no—
324#103—224no—
325#103—442no—
326#103—442no—
327C22⋊C8—224no—
328C22⋊C8—442no—
329C4×C8—222no—
330#95—21no—
331#95—22no—
332#95—221no—
333C2×C11—44no—
334C2×C11#244511yescharacteristic
335C2×C11C2×#48311yescharacteristic
336C2×C11#309711yescharacteristic
337C2×C11#327611yescharacteristic
338C2×C11D4×SD1611yescharacteristic
339C2×C11#329811yescharacteristic
340C2×C11#333111yescharacteristic
341C24C2×C22⋊D1112yes—
342C2×Q8—222no—
343C2×Q8—222no—
344C2×Q8—222no—
345C2×Q8—222no—
346C2×Q8—222no—
347C2×Q8—222no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4#432414yes—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—21no—
359C22×C4—22no—
360C22×C4—44no—
361C22×C4—44no—
362C22×C4—82no—
363C22×C4—221no—
364C22×C4—221no—
365C22×C4—222no—
366C22×C4C2×C22⋊D1112yes—
367C22×C4C2×C22⋊D1111yescharacteristic
368C22×C4C2×C22⋊D1111yescharacteristic
369C22×C4C23×D1111yescharacteristic
370C2×C8—112no—
371C2×C8—221no—
372C2×C8—221no—
373C2×C8—221no—
374C2×C8—222no—
375C2×C8—222no—
376C2×C8—221no—
377C2×C8—221no—
378C2×C8—222no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—44no—
386C4⋊C4—42no—
387C4⋊C4—81no—
388C4⋊C4—112no—
389C4⋊C4—112no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C4⋊C4—444no—
393C4⋊C4—444no—
394C4⋊C4—442no—
395C4⋊C4—442no—
396C4⋊C4D4×D1112yes—
397C22⋊C4—24no—
398C22⋊C4—44no—
399C22⋊C4—444no—
400C22⋊C4—444no—
401C42—42no—
402C42—442no—
403C42#433912yes—
404C42#433912yes—
405C11#2623411yescharacteristic, complemented, Sylow
406C23—22no—
407C23—22no—
408C23—22no—
409C23—22no—
410C23—22no—
411C23—22no—
412C23C2×#432414yes—
413C23C22×C22⋊D1111yescharacteristic
414Q8—442no—
415Q8—442no—
416Q8—442no—
417Q8—442no—
418D4—28no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—88no—
438C2×C4—222no—
439C2×C4—222no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4#6698212yes—
448C2×C4#6698212yes—
449C2×C4C2×#432412yes—
450C2×C4#6699512yes—
451C2×C4C2×#433911yescharacteristic
452C2×C4C2×#433911yescharacteristic
453C2×C4C2×D4×D1111yescharacteristic
454C2×C4#6703711yescharacteristic
455C2×C4#41×D1111yescharacteristic
456C2×C4#6704211yescharacteristic
457C8—222no—
458C8—442no—
459C8—441no—
460C22—24no—
461C22—24no—
462C22—24no—
463C22—42no—
464C22—42no—
465C22—42no—
466C22—42no—
467C22C2×#6698211yescharacteristic
468C22C22×#432411yescharacteristic
469C22D4×C22⋊D1111yescharacteristic
470C22C2×#6699511yescharacteristic
471C22#1062336011yescharacteristic
472C22#1062336711yescharacteristic
473C22#1062336911yescharacteristic
474C4—22no—
475C4—42no—
476C4—42no—
477C4—81no—
478C4—82no—
479C4—442no—
480C4—442no—
481C4—882no—
482C4#1062258414yescomplemented
483C4#1062307911yescharacteristic
484C4#1062308411yescharacteristic
485C4#1062309011yescharacteristic
486C4#1062309311yescharacteristic
487C2—44no—
488C2#1307237511yescharacteristic
489C2C2×#1062258411yescharacteristic
490C2#1307858511yescharacteristic
491C2#1308026211yescharacteristic
492C2D4×#432411yescharacteristic
493C2#1308047511yescharacteristic
494C2#1308092611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingD4×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenterD4×C4⋊C4D11
hypocenterC11#26234
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622584C2semidirect
3. #13069812C2semidirect
4. #13069812C2semidirect
5. #13069539C2semidirect
6. #13069417C2semidirect
8. #13069377C2semidirect
9. #13068923C2semidirect
10. C4×#66872C2semidirect
91. #66872D4semidirect
273. C4×C11#483semidirect
405. C11#26234semidirect
482. C4#10622584semidirect

Maximal subgroups

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

subgroupindex
C2×#106225842
#130735692
#130698122
#130695392
#130694172
#130694112
#130693772
#130689232
C4×#668722
D4×C11×C4⋊C42
#2623411