Finite Group Databasebeta

← #14803907

Subgroups — #14803907

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622704C211yesmaximal, characteristic, complemented
2C2×C8×D44C211yesmaximal, characteristic
3#13073790C211yesmaximal, characteristic
4#13073539C211yesmaximal, characteristic
5#13070048C212yesmaximal, complemented
6#13069822C212yesmaximal, complemented
7#13069372C211yesmaximal, characteristic, complemented
8#13069038C212yesmaximal, complemented
9#13068644C212yesmaximal, complemented
10C4×#66880C211yesmaximal, characteristic, complemented
11C11×#1990C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C22×C8×D11C2212yes—
14C2×#66950C2212yes—
15C2×C4×D44C2211yescharacteristic
16C2×C4×Dic22C2211yescharacteristic
17C2×C4×C8×C11C2211yescharacteristic
18C11×#384C2211yescharacteristic
19#10622844—22no—
20C2×(C2×D11)⋊C8C2212yes—
21C2×#66880C2211yescharacteristic
22C2×#66880C2211yescharacteristic
23#10622704—24no—
24#10622607—22no—
25#10622601—21no—
26#10622601—21no—
27#10622600C2212yes—
28#10622600C2212yes—
29#10622600C2212yes—
30#10622598—21no—
31#10622590—21no—
32C2×#66874C2212yes—
33C2×#66871C2212yes—
34C2×#66871C2212yes—
35C4×C4⋊Dic11C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C8×D44—24no—
38C11×#340C2212yes—
39C11×#340C2212yes—
40#10622189C2211yescharacteristic
41#10622189C2211yescharacteristic
42#10622167C2212yes—
43C22×Q8×C11—21no—
44C22×D44D411yescharacteristic
45C22×C4×D11C2312yes—
46C22×Dic22C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8—22no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C4⋊C4C2312yes—
56C2×C42×C11C2311yescharacteristic
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4D412yes—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11D411yescharacteristic
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×Dic11⋊C4—21no—
68C2×C4×Dic11—21no—
69C2×C4×Dic11—21no—
70C22×C11⋊C8C2312yes—
71C2×C8×D11—24no—
72C2×C8×D11—24no—
73C2×C8×D11—42no—
74#66950—24no—
75#66950—42no—
76C4×D44—22no—
77C4×D44—22no—
78C4×Dic22—22no—
79C4×Dic22—22no—
80C4×C8×C11—22no—
81C11⋊#95—21no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85(C2×D11)⋊C8—24no—
86#66880—22no—
87#66880—22no—
88#66874—24no—
89#66871—24no—
90#66871—42no—
91C4⋊(C11⋊C8)D414yes—
92#25340—111nomaximal, Sylow
93C23×D11C2×D412yes—
94C2×Q8×C11—42no—
95C2×Q8×C11—81no—
96C2×Q8×C11—81no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2411yescharacteristic
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—21no—
106C22×Dic11C2×D412yes—
107C2×D44—22no—
108C2×D44—22no—
109C2×D44Q1614yes—
110C2×C4×D11—22no—
111C2×C4×D11—22no—
112C2×C4×D11—22no—
113C2×C4×D11—22no—
114C2×C4×D11—22no—
115C2×C4×D11—22no—
116C2×Dic22—21no—
117C2×Dic22—21no—
118C2×Dic22—21no—
119C2×Dic22—21no—
120C2×Dic22—21no—
121C2×Dic22#4112yes—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11#4112yes—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—42no—
133C11×C4⋊C4—42no—
134C11×C4⋊C4—81no—
135C42×C11C2×D412yes—
136C42×C11#4112yes—
137(C2×D11)⋊C4—24no—
138(C2×D11)⋊C4—44no—
139(C2×D11)⋊C4—82no—
140(C2×D11)⋊C4—82no—
141(C2×D11)⋊C4—82no—
142C4⋊Dic11—22no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—44no—
150Dic11⋊C4—42no—
151C4×Dic11—42no—
152C4×Dic11—42no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8C2×D414yes—
156C8×D11—48no—
157C2×#477—111no—
158C2×C8×D4—111no—
159#2563—111no—
160#2538—111no—
161#2076—112no—
162#2036—112no—
163#1990D1111yescharacteristic, complemented
164#1947—111no—
165#1892—112no—
166#1808—112no—
167C4×#103—111no—
168C23×C11C22×D411yescharacteristic
169C22×D11—22no—
170C22×D11—22no—
171C22×D11—22no—
172C22×D11—22no—
173C22×D11—22no—
174C22×D11—22no—
175C22×D11C2×Q1614yes—
176Q8×C11—84no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11#12112yes—
186C2×C4×C11#12112yes—
187C2×C4×C11C2×Q1612yes—
188C2×C4×C11#13512yes—
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C2×#4111yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11H(5,𝔽2)11yescharacteristic
194C2×C4×C112−1+411yescharacteristic
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210D44—28no—
211C4×D11—42no—
212C4×D11—42no—
213C4×D11—42no—
214C4×D11—42no—
215Dic22—22no—
216Dic22—22no—
217Dic22—41no—
218Dic22—41no—
219C8×C11—22no—
220C8×C11—41no—
221C11⋊C8—24no—
222C23×C8—112no—
223C2×C4⋊Q8C2×D1111yescharacteristic
224C2×C22⋊Q8—112no—
225C2×C4×Q8—111no—
226C2×C4×D4—111no—
227#477—224no—
228C8×D4—224no—
229C2×#107—112no—
230C2×#107—112no—
231C2×C4⋊C8—111no—
232C2×#103—111no—
233C2×#103—111no—
234C2×#103—112no—
235C2×C22⋊C8—112no—
236C2×C4×C8C2×D1111yescharacteristic
237#396—222no—
238#393—222no—
239#390—221no—
240#390—221no—
241#389—221no—
242#384C2×D1111yescharacteristic
243#382—221no—
244#380—112no—
245#380—112no—
246#380—112no—
247C4×C4⋊C4—111no—
248#340—111no—
249#340—111no—
250#340—112no—
251#340C2×D1112yes—
252#340C2×D1112yes—
253C22×C11C2×#12111yescharacteristic
254C22×C11#54611yescharacteristic
255C22×C11#54711yescharacteristic
256C22×C11C22×Q1611yescharacteristic
257C22×C11C2×#13511yescharacteristic
258C22×C11#57611yescharacteristic
259C22×C11#57711yescharacteristic
260C2×D11—24no—
261C2×D11—24no—
262C2×D11—24no—
263C2×D11—42no—
264C2×D11—42no—
265C2×D11—42no—
266C2×D11—42no—
267C4×C11—22no—
268C4×C11—82no—
269C4×C11—82no—
270C4×C11#46714yes—
271C4×C11#52911yescharacteristic
272C4×C11#54211yescharacteristic
273C4×C11#54611yescharacteristic
274C4×C11#54811yescharacteristic
275Dic11—42no—
276Dic11—42no—
277Dic11—81no—
278Dic11—81no—
279Dic11—81no—
280C22×Q8—21no—
281C22×Q8—111no—
282C22×D4—111no—
283C23×C4—112no—
284C22×C8—112no—
285C22×C8—224no—
286C22×C8—224no—
287C22×C8—442no—
288C22×C8C22×D1111yescharacteristic
289C22×C8C22×D1111yescharacteristic
290C4⋊Q8—22no—
291C4⋊Q8—22no—
292C22⋊Q8—224no—
293C22⋊Q8—442no—
294C4×Q8—222no—
295C4×Q8—222no—
296C4×D4—222no—
297C4×D4—222no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—111no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—111no—
304C2×C4⋊C4—111no—
305C2×C4⋊C4—222no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4C22×D1112yes—
308C2×C4⋊C4C22×D1112yes—
309C2×C22⋊C4—112no—
310C2×C22⋊C4—222no—
311C2×C22⋊C4—222no—
312C2×C22⋊C4—222no—
313C2×C22⋊C4—222no—
314C2×C42—221no—
315C2×C42—221no—
316C2×C42C22×D1111yescharacteristic
317#107—224no—
318#107—442no—
319C4⋊C8—114no—
320#103—224no—
321#103—222no—
322#103—222no—
323C22⋊C8—224no—
324C4×C8—22no—
325#95—222no—
326#95—222no—
327#95—222no—
328#95—221no—
329C2×C11#242711yescharacteristic
330C2×C11C2×#46711yescharacteristic
331C2×C11#306211yescharacteristic
332C2×C11#329911yescharacteristic
333C2×C11#330511yescharacteristic
334C2×C11#333811yescharacteristic
335C2×C11#334011yescharacteristic
336D11—44no—
337C24—112no—
338C2×Q8—42no—
339C2×Q8—81no—
340C2×Q8—81no—
341C2×Q8—112no—
342C2×Q8—221no—
343C2×Q8—221no—
344C2×Q8—221no—
345C2×Q8—221no—
346C2×Q8—221no—
347C2×D4—114no—
348C2×D4—222no—
349C2×D4—222no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—112no—
353C22×C4—221no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—221no—
361C22×C4—221no—
362C22×C4—221no—
363C22×C4D4×D1111yescharacteristic
364C22×C4D4×D1111yescharacteristic
365C22×C4C23×D1111yescharacteristic
366C2×C8—21no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—114no—
372C2×C8—222no—
373C2×C8—222no—
374C2×C8—448no—
375C2×C8#434312yes—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—42no—
381C4⋊C4—42no—
382C4⋊C4—81no—
383C4⋊C4—222no—
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—221no—
387C4⋊C4—221no—
388C4⋊C4—221no—
389C4⋊C4—221no—
390C4⋊C4—444no—
391C4⋊C4—442no—
392C22⋊C4—224no—
393C22⋊C4—444no—
394C22⋊C4—882no—
395C22⋊C4—882no—
396C22⋊C4—882no—
397C42—442no—
398C42—442no—
399C42#433912yes—
400C42D4×D1112yes—
401C11#2534011yescharacteristic, complemented, Sylow
402C23—114no—
403C23—222no—
404C23—222no—
405C23—222no—
406C23—222no—
407C23—222no—
408C23—222no—
409C23C2×D4×D1111yescharacteristic
410Q8—84no—
411Q8—222no—
412Q8—222no—
413Q8—441no—
414Q8—441no—
415D4—228no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—222no—
425C2×C4—222no—
426C2×C4—222no—
427C2×C4—222no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4—442no—
431C2×C4—442no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4#6693712yes—
444C2×C4#6693712yes—
445C2×C4#6696912yes—
446C2×C4Q16×D1112yes—
447C2×C4C2×#433911yescharacteristic
448C2×C4C2×D4×D1111yescharacteristic
449C2×C4C2×#434311yescharacteristic
450C2×C4#6704011yescharacteristic
451C2×C4#41×D1111yescharacteristic
452C2×C4#6704211yescharacteristic
453C8—22no—
454C8—41no—
455C8—224no—
456C22—224no—
457C22—224no—
458C22—224no—
459C22—442no—
460C22—442no—
461C22—442no—
462C22—442no—
463C22C2×#6693711yescharacteristic
464C22#1062320711yescharacteristic
465C22#1062325711yescharacteristic
466C22#1062328811yescharacteristic
467C22C2×#6696911yescharacteristic
468C22#1062329311yescharacteristic
469C22C2×Q16×D1111yescharacteristic
470C4—22no—
471C4—82no—
472C4—82no—
473C4—442no—
474C4—442no—
475C4—881no—
476C4—881no—
477C4—881no—
478C4#1062242614yes—
479C4#1062311111yescharacteristic
480C4#1062311311yescharacteristic
481C4#1062316111yescharacteristic
482C4#1062316411yescharacteristic
483C2—444no—
484C2#1307219411yescharacteristic
485C2C2×#1062242611yescharacteristic
486C2#1307829411yescharacteristic
487C2#1308049111yescharacteristic
488C2#1308056511yescharacteristic
489C2#1308100811yescharacteristic
490C2#1308102811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1990C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenter#1990D11
hypocenterC11#25340
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
1. C2×#10622704C2semidirect
5. #13070048C2semidirect
6. #13069822C2semidirect
7. #13069372C2semidirect
8. #13069038C2semidirect
9. #13068644C2semidirect
10. C4×#66880C2semidirect
11. C11×#1990C2semidirect
163. #1990D11semidirect
401. C11#25340semidirect

Maximal subgroups

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

subgroupindex
C2×#106227042
C2×C8×D442
#130737902
#130735392
#130700482
#130698222
#130693722
#130690382
#130686442
C4×#668802
C11×#19902
#2534011