Finite Group Databasebeta

← #14814896

Subgroups — #14814896

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×#10622497C212yesmaximal, complemented
2#13073565C211yesmaximal, characteristic
3C4⋊C4×D44C211yesmaximal, characteristic
4#13069822C212yesmaximal, complemented
5#13069821C212yesmaximal, complemented
6#13069539C211yesmaximal, characteristic, complemented
7#13069418C211yesmaximal, characteristic, complemented
8#13069410C211yesmaximal, characteristic
9#13069374C211yesmaximal, characteristic, complemented
10#13068922C212yesmaximal, complemented
11C4×C11×#107C211yesmaximal, characteristic, complemented
12C2×#66950C2212yes—
13C2×#66950C2212yes—
14C2×C4⋊C4×D11C2212yes—
15C2×C4×D44—21no—
16C2×C4×D44C2211yescharacteristic
17C2×#66922C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×(C2×D11)⋊C8C2212yes—
24C2×(C2×D11)⋊C8C2212yes—
25C2×#66880C2212yes—
26C2×#66880C2212yes—
27#10622600C2212yes—
28C2×#66874C2212yes—
29C2×#66874C2212yes—
30C2×#66871C2212yes—
31#10622552—21no—
32#10622548—21no—
33#10622548C2211yescharacteristic
34#10622541—21no—
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622497—28no—
37#10622290—22no—
38#10622281—22no—
39C11×#340C2211yescharacteristic
40C11×#340C2211yescharacteristic
41#10622167C2212yes—
42C22×D44D411yescharacteristic
43C22×C4×D11—22no—
44C22×C4×D11C2312yes—
45C22×Dic22C2312yes—
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C2×C11×C4⋊C4C2311yescharacteristic
49C2×C11×C4⋊C4C2311yescharacteristic
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C42×C11—21no—
53C2×C42×C11—21no—
54C2×C42×C11C2311yescharacteristic
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4D412yes—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11D411yescharacteristic
66C2×C4⋊Dic11C2312yes—
67C2×Dic11⋊C4—22no—
68C22×C11⋊C8C2312yes—
69#66950—24no—
70#66950—24no—
71#66950—42no—
72#66950—42no—
73C4⋊C4×D11—24no—
74C4⋊C4×D11—42no—
75C4×D44—22no—
76C4×D44—22no—
77C4×D44—44no—
78#66922—22no—
79#66922—22no—
80C11×#107—22no—
81C11×#107D414yescomplemented
82C4×C8×C11—22no—
83C11×#95—21no—
84C11×#95—21no—
85C11⋊#95—22no—
86(C2×D11)⋊C8—24no—
87(C2×D11)⋊C8—42no—
88#66880—24no—
89#66880—42no—
90#66874—24no—
91#66874—42no—
92#66871—24no—
93C4⋊(C11⋊C8)—22no—
94#26236—111nomaximal, Sylow
95C23×D11C2×D412yes—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2411yescharacteristic
103C22×Dic11—22no—
104C22×Dic11—22no—
105C22×Dic11C2×D412yes—
106C2×D44—22no—
107C2×D44—22no—
108C2×D44Q1614yes—
109C2×C4×D11—22no—
110C2×C4×D11—22no—
111C2×C4×D11—22no—
112C2×C4×D11—22no—
113C2×C4×D11—22no—
114C2×C4×D11—22no—
115C2×C4×D11—44no—
116C2×C4×D11—44no—
117C2×C4×D11—82no—
118C2×Dic22—22no—
119C2×Dic22—22no—
120C2×Dic22—22no—
121C2×Dic22—22no—
122C2×Dic22—22no—
123C2×Dic22—22no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11C2×D412yes—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4C2×D412yes—
136C11×C4⋊C4C2×D412yes—
137C11×C4⋊C4#4112yes—
138C42×C11—42no—
139C42×C11—42no—
140C42×C11#4112yes—
141C42×C11#4112yes—
142(C2×D11)⋊C4—24no—
143(C2×D11)⋊C4—44no—
144(C2×D11)⋊C4—44no—
145(C2×D11)⋊C4—44no—
146C4⋊Dic11—22no—
147C4⋊Dic11—22no—
148C4⋊Dic11—22no—
149C4⋊Dic11—44no—
150C4⋊Dic11—44no—
151C4⋊Dic11—42no—
152C4⋊Dic11—42no—
153C4⋊Dic11—42no—
154C4⋊Dic11—81no—
155Dic11⋊C4—44no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×#484—112no—
160#2542—111no—
161D4×C4⋊C4—111no—
162#2036—112no—
163#2036—112no—
164#1981—111no—
165#1956—111no—
166#1954—111no—
167#1947—111no—
168#1872—112no—
169C4×#107D1111yescharacteristic, complemented
170C23×C11C22×D411yescharacteristic
171C22×D11—22no—
172C22×D11—22no—
173C22×D11—22no—
174C22×D11—22no—
175C22×D11—22no—
176C22×D11—22no—
177C22×D11C2×Q1614yes—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11#12312yes—
193C2×C4×C11#12312yes—
194C2×C4×C11C2×Q1612yes—
195C2×C4×C11AGL(1,ℤ/8)12yes—
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11H(5,𝔽2)11yescharacteristic
201C2×C4×C11H(5,𝔽2)11yescharacteristic
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211D44—28no—
212C4×D11—42no—
213C4×D11—42no—
214C4×D11—42no—
215C4×D11—42no—
216C4×D11—88no—
217Dic22—42no—
218Dic22—42no—
219Dic22—42no—
220Dic22—42no—
221C8×C11—22no—
222C8×C11—41no—
223C11⋊C8—42no—
224C2×C4⋊Q8—111no—
225C2×C22⋊Q8—112no—
226C2×C22⋊Q8—112no—
227C2×C4×D4—111no—
228C2×C4×D4—221no—
229C22×C4⋊C4—112no—
230#484—228no—
231C2×#107—112no—
232C2×#107C2×D1111yescharacteristic
233C2×#107C2×D1111yescharacteristic
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×C8C2×D1111yescharacteristic
242#399—222no—
243#390—221no—
244#389—221no—
245#385—222no—
246#384—111no—
247#384—221no—
248#380—112no—
249C4×C4⋊C4C2×D1111yescharacteristic
250C4×C4⋊C4C2×D1111yescharacteristic
251#340—112no—
252#340C2×D1111yescharacteristic
253#340C2×D1111yescharacteristic
254C22×C11C2×#12311yescharacteristic
255C22×C11D4211yescharacteristic
256C22×C11#54611yescharacteristic
257C22×C11C22×Q1611yescharacteristic
258C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
259C22×C11#57711yescharacteristic
260C22×C11#57811yescharacteristic
261C2×D11—24no—
262C2×D11—24no—
263C2×D11—24no—
264C2×D11—42no—
265C2×D11—42no—
266C2×D11—42no—
267C2×D11—42no—
268C4×C11—22no—
269C4×C11—42no—
270C4×C11—42no—
271C4×C11—42no—
272C4×C11—81no—
273C4×C11#48414yescomplemented
274C4×C11#53211yescharacteristic
275C4×C11#54011yescharacteristic
276C4×C11#55011yescharacteristic
277C4×C11#55911yescharacteristic
278Dic11—42no—
279Dic11—82no—
280Dic11—82no—
281C22×Q8—112no—
282C22×D4—111no—
283C23×C4—112no—
284C23×C4—222no—
285C22×C8—112no—
286C22×C8C22×D1111yescharacteristic
287C22×C8C22×D1111yescharacteristic
288C4⋊Q8—222no—
289C4⋊Q8—222no—
290C22⋊Q8—224no—
291C22⋊Q8—224no—
292C22⋊Q8—442no—
293C22⋊Q8—442no—
294C4×D4—222no—
295C4×D4—222no—
296C4×D4—444no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—112no—
299C2×C4⋊C4—224no—
300C2×C4⋊C4—222no—
301C2×C4⋊C4—222no—
302C2×C4⋊C4—222no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—442no—
308C2×C4⋊C4C22×D1111yescharacteristic
309C2×C4⋊C4C22×D1111yescharacteristic
310C2×C4⋊C4C22×D1111yescharacteristic
311C2×C4⋊C4C22×D1111yescharacteristic
312C2×C22⋊C4—112no—
313C2×C22⋊C4—222no—
314C2×C22⋊C4—222no—
315C2×C22⋊C4—222no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42C22×D1111yescharacteristic
319#107—22no—
320#107—224no—
321#107D4414yescomplemented
322C4⋊C8—222no—
323#103—224no—
324#103—224no—
325#103—442no—
326#103—442no—
327C22⋊C8—224no—
328C22⋊C8—442no—
329C4×C8—22no—
330#95—21no—
331#95—21no—
332#95—222no—
333C2×C11#244511yescharacteristic
334C2×C11C2×#48411yescharacteristic
335C2×C11#309711yescharacteristic
336C2×C11#327211yescharacteristic
337C2×C11D4×Q1611yescharacteristic
338C2×C11#329911yescharacteristic
339C2×C11#333011yescharacteristic
340D11—44no—
341C24—112no—
342C2×Q8—222no—
343C2×Q8—222no—
344C2×Q8—222no—
345C2×Q8—222no—
346C2×Q8—222no—
347C2×Q8—222no—
348C2×D4—114no—
349C2×D4—222no—
350C2×D4—222no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—112no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4—444no—
365C22×C4—444no—
366C22×C4—882no—
367C22×C4D4×D1111yescharacteristic
368C22×C4D4×D1111yescharacteristic
369C22×C4C23×D1111yescharacteristic
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—222no—
376C2×C8—222no—
377C2×C8—222no—
378C2×C8C2×D4412yes—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—222no—
385C4⋊C4—222no—
386C4⋊C4—222no—
387C4⋊C4—444no—
388C4⋊C4—444no—
389C4⋊C4—444no—
390C4⋊C4—442no—
391C4⋊C4—442no—
392C4⋊C4—442no—
393C4⋊C4—881no—
394C4⋊C4C2×D4412yes—
395C4⋊C4C2×D4412yes—
396C4⋊C4#433912yes—
397C22⋊C4—224no—
398C22⋊C4—444no—
399C22⋊C4—444no—
400C22⋊C4—444no—
401C42—42no—
402C42—42no—
403C42#433912yes—
404C42#434312yes—
405C11#2623611yescharacteristic, complemented, Sylow
406C23—114no—
407C23—222no—
408C23—222no—
409C23—222no—
410C23—222no—
411C23—222no—
412C23—222no—
413C23C2×D4×D1111yescharacteristic
414Q8—442no—
415Q8—442no—
416Q8—442no—
417Q8—442no—
418D4—228no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—222no—
434C2×C4—222no—
435C2×C4—222no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4—442no—
439C2×C4—442no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—888no—
447C2×C4#6694712yes—
448C2×C4#6694712yes—
449C2×C4#6696412yes—
450C2×C4Q16×D1112yes—
451C2×C4C22×D4411yescharacteristic
452C2×C4C2×#433911yescharacteristic
453C2×C4C2×#433911yescharacteristic
454C2×C4C2×#434311yescharacteristic
455C2×C4#6704211yescharacteristic
456C2×C4#6704211yescharacteristic
457C8—22no—
458C8—41no—
459C8—442no—
460C22—224no—
461C22—224no—
462C22—224no—
463C22—442no—
464C22—442no—
465C22—442no—
466C22—442no—
467C22C2×#6694711yescharacteristic
468C22D4×D4411yescharacteristic
469C22#1062308111yescharacteristic
470C22C2×#6696411yescharacteristic
471C22C2×Q16×D1111yescharacteristic
472C22#1062330111yescharacteristic
473C22#1062330211yescharacteristic
474C4—22no—
475C4—42no—
476C4—42no—
477C4—42no—
478C4—81no—
479C4—442no—
480C4—882no—
481C4—882no—
482C4#1062249714yescomplemented
483C4#1062300811yescharacteristic
484C4#1062306611yescharacteristic
485C4#1062310811yescharacteristic
486C4#1062311611yescharacteristic
487C2—444no—
488C2#1307238111yescharacteristic
489C2C2×#1062249711yescharacteristic
490C2#1307858811yescharacteristic
491C2#1308021711yescharacteristic
492C2Q16×D4411yescharacteristic
493C2#1308049411yescharacteristic
494C2#1308092311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#107C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenterC4×#107D11
hypocenterC11#26236
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#107

Complements

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

NH ≅ G/Ntype
1. C2×#10622497C2semidirect
4. #13069822C2semidirect
5. #13069821C2semidirect
6. #13069539C2semidirect
7. #13069418C2semidirect
9. #13069374C2semidirect
10. #13068922C2semidirect
11. C4×C11×#107C2semidirect
81. C11×#107D4semidirect
169. C4×#107D11semidirect
273. C4×C11#484semidirect
321. #107D44semidirect
405. C11#26236semidirect
482. C4#10622497semidirect

Maximal subgroups

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

subgroupindex
C2×#106224972
#130735652
C4⋊C4×D442
#130698222
#130698212
#130695392
#130694182
#130694102
#130693742
#130689222
C4×C11×#1072
#2623611