Finite Group Databasebeta

← #14649462

Subgroups — #14649462

Order 2816.

568 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622448C211yesmaximal, characteristic
2#13076969C211yesmaximal, characteristic
3#13068593C211yesmaximal, characteristic
4C2×#10622120C211yesmaximal, characteristic, complemented
5C2×#10622124C211yesmaximal, characteristic, complemented
6#13066499C211yesmaximal, characteristic, complemented
7C11×#1296C211yesmaximal, characteristic, complemented
8C2×#66950—21no—
9C2×C42×D11C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C11×#384C2211yescharacteristic
14C2×(C2×D11)⋊C8—21no—
15C2×(C2×D11)⋊C8—21no—
16C2×#66879—21no—
17#10622600—21no—
18#10622600C412yes—
19#10622598—21no—
20#10622598C412yes—
21#10622587—21no—
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622448—22no—
25#10622448—22no—
26#10622188—21no—
27#10622124—22no—
28#10622120—22no—
29C22×C4×D11C2×C411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C22×C4×D11D411yescharacteristic
32C22×Dic22—21no—
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4C2×C412yes—
38C2×C42×C11C2311yescharacteristic
39C2×(C2×D11)⋊C4—22no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—22no—
42C2×C4⋊Dic11C2×C412yes—
43C2×C4×Dic11C2×C411yescharacteristic
44C2×C4×Dic11D411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46C22×C11⋊C8—21no—
47C22×C11⋊C8—21no—
48#66950—42no—
49#66950—42no—
50C42×D11—21no—
51C42×D11—21no—
52C42×D11—21no—
53C42×D11—21no—
54#66922—21no—
55#66922—21no—
56#66922—21no—
57#66922—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8D412yes—
62C11⋊#95—22no—
63C11⋊#95—22no—
64(C2×D11)⋊C8—24no—
65(C2×D11)⋊C8—42no—
66#66879—24no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)D412yes—
71#9138—111nomaximal, Sylow
72C23×D11C22⋊C411yescharacteristic
73C22×C4×C11—22no—
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×Dic11—22no—
78C22×Dic11C22⋊C411yescharacteristic
79C22×Dic11C22⋊C411yescharacteristic
80C22×Dic11C22⋊C411yescharacteristic
81C2×C4×D11—22no—
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—21no—
92C2×C4×D11—21no—
93C2×C4×D11—21no—
94C2×C4×D11—21no—
95C2×C4×D11—21no—
96C2×C4×D11—41no—
97C2×Dic22—41no—
98C2×Dic22—41no—
99C2×Dic22—41no—
100C2×Dic22—41no—
101C2×Dic22—41no—
102C2×Dic22—41no—
103C2×C8×C11—22no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C2×C8×C11—41no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C11×C4⋊C4—42no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11#4111yescharacteristic
117C42×C11#4111yescharacteristic
118(C2×D11)⋊C4—44no—
119C4⋊Dic11—22no—
120C4⋊Dic11—22no—
121C4⋊Dic11—44no—
122C4⋊Dic11—41no—
123C4⋊Dic11—41no—
124C4×Dic11—21no—
125C4×Dic11—21no—
126C4×Dic11—21no—
127C4×Dic11—21no—
128C4×Dic11—21no—
129C4×Dic11—21no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—41no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8—41no—
135C2×C11⋊C8—41no—
136C2×#432—111no—
137#2857—111no—
138#1797—111no—
139C2×#332—111no—
140C2×#332—111no—
141#1296—111no—
142#1296D1111yescharacteristic, complemented
143C23×C11C2×C22⋊C411yescharacteristic
144C22×D11—21no—
145C22×D11—21no—
146C22×D11—21no—
147C22×D11—21no—
148C22×D11—21no—
149C22×D11—21no—
150C22×D11#10112yes—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11C4×D411yescharacteristic
157C2×C4×C11C4×D411yescharacteristic
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12311yescharacteristic
162C2×C4×C11#13511yescharacteristic
163C2×C4×C11#13511yescharacteristic
164C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C11#13711yescharacteristic
168C2×C4×C11#13711yescharacteristic
169C2×C4×C11#13711yescharacteristic
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182C4×D11—42no—
183C4×D11—42no—
184C4×D11—41no—
185C4×D11—41no—
186C4×D11—41no—
187C4×D11—41no—
188C4×D11—41no—
189C4×D11—41no—
190C4×D11—41no—
191C4×D11—41no—
192Dic22—81no—
193Dic22—81no—
194Dic22—81no—
195Dic22—81no—
196C8×C11—42no—
197C8×C11—81no—
198C11⋊C8—42no—
199C11⋊C8—81no—
200C2×C4⋊Q8—111no—
201C2×C22⋊Q8—221no—
202C22×C42—111no—
203#432—222no—
204#432—222no—
205C2×C4⋊C8—111no—
206C2×C4⋊C8—111no—
207C2×C4⋊C8C2×D1111yescharacteristic
208C2×C4⋊C8C2×D1111yescharacteristic
209C2×C22⋊C8—221no—
210C2×C22⋊C8—221no—
211C2×#97—221no—
212#391—221no—
213#389—112no—
214#389—221no—
215#384C2×D1111yescharacteristic
216#380—112no—
217#380—221no—
218#336—221no—
219#332—222no—
220#332—222no—
221C22×C11#38611yescharacteristic
222C22×C11C2×#10111yescharacteristic
223C22×C11#41311yescharacteristic
224C22×C11#41611yescharacteristic
225C22×C11#41711yescharacteristic
226C22×C11#41811yescharacteristic
227C22×C11#41911yescharacteristic
228C2×D11—22no—
229C2×D11—22no—
230C2×D11—22no—
231C2×D11—41no—
232C2×D11—41no—
233C2×D11—41no—
234C2×D11—41no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—82no—
238C4×C11#45211yescharacteristic
239C4×C11#45211yescharacteristic
240C4×C11#46811yescharacteristic
241C4×C11#46811yescharacteristic
242C4×C11#46911yescharacteristic
243C4×C11#46911yescharacteristic
244C4×C11#48511yescharacteristic
245C4×C11#48511yescharacteristic
246Dic11—41no—
247Dic11—41no—
248Dic11—41no—
249Dic11—82no—
250C22×Q8—221no—
251C23×C4—111no—
252C23×C4—111no—
253C23×C4—111no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—221no—
257C22×C8—221no—
258C4⋊Q8—221no—
259C4⋊Q8—221no—
260C4⋊Q8—221no—
261C4⋊Q8—221no—
262C22⋊Q8—442no—
263C22⋊Q8—442no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—112no—
267C2×C4⋊C4—222no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4C4×D1112yes—
270C2×C22⋊C4—222no—
271C2×C42—111no—
272C2×C42—111no—
273C2×C42—111no—
274C2×C42—221no—
275C2×C42—221no—
276C2×C42—221no—
277C2×C42—221no—
278C2×C42C22×D1111yescharacteristic
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—112no—
283C4⋊C8—221no—
284C4⋊C8—221no—
285C4⋊C8—221no—
286C4⋊C8D4412yes—
287C22⋊C8—224no—
288C22⋊C8—442no—
289#97—224no—
290#95—222no—
291#95—222no—
292C2×C11#155211yescharacteristic
293C2×C11#155311yescharacteristic
294C2×C11#155611yescharacteristic
295C2×C11#155911yescharacteristic
296C2×C11#187311yescharacteristic
297C2×C11#189511yescharacteristic
298C2×C11#190111yescharacteristic
299D11—42no—
300C24—111no—
301C2×Q8—441no—
302C2×Q8—441no—
303C2×Q8—441no—
304C2×Q8—441no—
305C2×Q8—441no—
306C2×Q8—441no—
307C22×C4—22no—
308C22×C4—111no—
309C22×C4—111no—
310C22×C4—111no—
311C22×C4—222no—
312C22×C4—221no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—221no—
321C22×C4—221no—
322C22×C4—221no—
323C22×C4—221no—
324C22×C4—221no—
325C22×C4—221no—
326C22×C4—222no—
327C22×C4—441no—
328C22×C4C2×C4×D1111yescharacteristic
329C22×C4D4×D1111yescharacteristic
330C22×C4D4×D1111yescharacteristic
331C2×C8—22no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—222no—
338C2×C8—441no—
339C2×C8—441no—
340C2×C8—441no—
341C2×C8—441no—
342C2×C8—441no—
343C4⋊C4—42no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—222no—
349C4⋊C4—222no—
350C4⋊C4—444no—
351C4⋊C4—441no—
352C4⋊C4—441no—
353C22⋊C4—444no—
354C42—221no—
355C42—221no—
356C42—221no—
357C42—221no—
358C42—221no—
359C42—221no—
360C42C2×D4411yescharacteristic
361C42#433911yescharacteristic
362C42D4×D1111yescharacteristic
363C42#434311yescharacteristic
364C11#913811yescharacteristic, complemented, Sylow
365C23—112no—
366C23—221no—
367C23—221no—
368C23—221no—
369C23—221no—
370C23—221no—
371C23—221no—
372C23C22⋊C4×D1111yescharacteristic
373Q8—881no—
374Q8—881no—
375Q8—881no—
376Q8—881no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—221no—
383C2×C4—221no—
384C2×C4—221no—
385C2×C4—221no—
386C2×C4—221no—
387C2×C4—221no—
388C2×C4—221no—
389C2×C4—221no—
390C2×C4—221no—
391C2×C4—442no—
392C2×C4—442no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—442no—
402C2×C4—442no—
403C2×C4—442no—
404C2×C4C4×D4411yescharacteristic
405C2×C4#6693511yescharacteristic
406C2×C4#6693711yescharacteristic
407C2×C4#6694611yescharacteristic
408C2×C4#6694711yescharacteristic
409C2×C4#6694811yescharacteristic
410C2×C4#6696411yescharacteristic
411C2×C4#6696511yescharacteristic
412C2×C4#6696711yescharacteristic
413C2×C4#6696711yescharacteristic
414C2×C4#6696811yescharacteristic
415C2×C4#6696911yescharacteristic
416C2×C4#6697111yescharacteristic
417C2×C4#6697111yescharacteristic
418C8—42no—
419C8—81no—
420C8—442no—
421C8—881no—
422C22—222no—
423C22—222no—
424C22—222no—
425C22—441no—
426C22—441no—
427C22—441no—
428C22—441no—
429C22#1062227811yescharacteristic
430C22#1062235811yescharacteristic
431C22D11×#10111yescharacteristic
432C22#1062238311yescharacteristic
433C22#1062238511yescharacteristic
434C22#1062241511yescharacteristic
435C22#1062241611yescharacteristic
436C4—21no—
437C4—21no—
438C4—82no—
439C4—441no—
440C4—441no—
441C4—441no—
442C4—882no—
443C4#1062239511yescharacteristic
444C4#1062239611yescharacteristic
445C4#1062242311yescharacteristic
446C4#1062242511yescharacteristic
447C4#1062247811yescharacteristic
448C4#1062248011yescharacteristic
449C4#1062249911yescharacteristic
450C4#1062250111yescharacteristic
451C2—442no—
452C2#1306731311yescharacteristic
453C2#1306731811yescharacteristic
454C2#1306733111yescharacteristic
455C2#1306734311yescharacteristic
456C2#1306892711yescharacteristic
457C2#1306905311yescharacteristic
458C2#1306908311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1296D11
hypocenterC11#9138
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
4. C2×#10622120C2semidirect
5. C2×#10622124C2semidirect
6. #13066499C2semidirect
7. C11×#1296C2semidirect
142. #1296D11semidirect
364. C11#9138semidirect

Maximal subgroups

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

subgroupindex
C2×#106224482
#130769692
#130685932
C2×#106221202
C2×#106221242
#130664992
C11×#12962
#913811