Finite Group Databasebeta

← #14649680

Subgroups — #14649680

Order 2816.

566 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078413C211yesmaximal, characteristic
2#13067179C211yesmaximal, characteristic, complemented
3#13067114C211yesmaximal, characteristic, complemented
4#13067007C211yesmaximal, characteristic
5#13066519C211yesmaximal, characteristic, complemented
6#13066474C211yesmaximal, characteristic, complemented
7C11×#2349C211yesmaximal, characteristic
8C2×C4×D4×C11—21no—
9C2×C4×D4×C11C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#389—21no—
12C11×#385—22no—
13C11×#382C2211yescharacteristic
14C11×#380—21no—
15C4×C11×C4⋊C4C2211yescharacteristic
16C2×C11×#95—21no—
17#10622828—21no—
18#10622622—22no—
19#10622621C412yescomplemented
20#10622620C412yescomplemented
21#10622577—21no—
22#10622538C2211yescharacteristic
23#10622538C2211yescharacteristic
24#10622537C2211yescharacteristic
25D4⋊(C11⋊C8)—22no—
26#10622090—21no—
27#10622090—21no—
28#10622090—22no—
29C22×D4×C11D411yescharacteristic
30C23×C4×C11—21no—
31C23×C4×C11—22no—
32C4×D4×C11—21no—
33C4×D4×C11—21no—
34C4×D4×C11—42no—
35C4×D4×C11—42no—
36C4×D4×C11C2×C412yes—
37C4×D4×C11D412yes—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—22no—
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—22no—
44C2×C42×C11—21no—
45C2×C42×C11C2311yescharacteristic
46#66979—21no—
47#66977—21no—
48#66977—21no—
49C2×#4318—21no—
50#66923—21no—
51#66922C2×C411yescharacteristic, complemented
52#66922C2×C411yescharacteristic, complemented
53C4×Dic22—21no—
54C4×Dic22—21no—
55C11×#95—22no—
56C11×#95—21no—
57C11×#95D411yescharacteristic
58C11×#95D411yescharacteristic
59C11×#95D412yes—
60#66896—22no—
61#66896—22no—
62C22⋊(C11⋊C8)—21no—
63C22⋊(C11⋊C8)—21no—
64#66872—22no—
65#66871—22no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)C2×C412yescomplemented
70C4×C11⋊C8—21no—
71C4×C11⋊C8—21no—
72#9175—111nomaximal, Sylow
73C24×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11C22⋊C412yes—
78C2×D4×C11SD1612yes—
79C2×D4×C11Q1612yes—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—21no—
86C22×C4×C11—44no—
87C22×C4×C11—44no—
88C22×C4×C11—82no—
89C22×C4×C11—82no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C2×Dic22—21no—
94C2×Dic22—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—42no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—82no—
100C11×C4⋊C4C22⋊C412yes—
101C11×C22⋊C4—22no—
102C11×C22⋊C4—22no—
103C11×C22⋊C4—44no—
104C42×C11—41no—
105C42×C11—41no—
106C42×C11C22×C411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11#4111yescharacteristic
109C42×C11#4111yescharacteristic
110C22⋊Dic11—41no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115Dic11⋊C4—41no—
116Dic11⋊C4—41no—
117C4×Dic11—41no—
118#4318—41no—
119#4318—41no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123#3077—111no—
124#2349D1111yescharacteristic
125#1518—111no—
126#1503—111no—
127#1478—111no—
128#1303—111no—
129#1286—111no—
130C23×C11—22no—
131C23×C11—22no—
132C23×C11—22no—
133C23×C11—42no—
134C23×C11—42no—
135C23×C11#12011yescharacteristic
136D4×C11—22no—
137D4×C11—22no—
138D4×C11—22no—
139D4×C11#10314yes—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—42no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—82no—
154C2×C4×C11—82no—
155C2×C4×C11—88no—
156C2×C4×C11C2×C22⋊C411yescharacteristic
157C2×C4×C11C4×D411yescharacteristic
158C2×C4×C11C4×D411yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12311yescharacteristic
162C2×C4×C11C2×SD1611yescharacteristic
163C2×C4×C11C2×Q1611yescharacteristic
164C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C11#13711yescharacteristic
166C2×Dic11—41no—
167C2×Dic11—41no—
168Dic22—81no—
169Dic22—81no—
170C11⋊C8—42no—
171C11⋊C8—81no—
172C11⋊C8—81no—
173#533—111no—
174C2×C4×D4—21no—
175C2×C4×D4C2×D1111yescharacteristic
176#478—222no—
177#476—112no—
178#474—112no—
179#431—111no—
180#431—111no—
181#428—221no—
182#423—111no—
183#418—221no—
184#389—21no—
185#385—22no—
186#382C2×D1111yescharacteristic
187#380—21no—
188C4×C4⋊C4C2×D1111yescharacteristic
189C2×#95—21no—
190#328—221no—
191#328—221no—
192#328—222no—
193D4⋊C8—222no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—24no—
197C22×C11—44no—
198C22×C11—44no—
199C22×C11—42no—
200C22×C11—42no—
201C22×C11#38611yescharacteristic
202C22×C11#45011yescharacteristic
203C22×C11#45111yescharacteristic
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—42no—
209C4×C11—42no—
210C4×C11—81no—
211C4×C11—82no—
212C4×C11C2×#10311yescharacteristic
213C4×C11#41711yescharacteristic
214C4×C11#48311yescharacteristic
215C4×C11#48411yescharacteristic
216Dic11—81no—
217Dic11—81no—
218C22×D4C22⋊D1111yescharacteristic
219C23×C4—21no—
220C23×C4—22no—
221C2×M16—221no—
222C4⋊Q8—111no—
223C4⋊Q8—111no—
224#125—221no—
225C22⋊Q8—221no—
226C22⋊Q8—221no—
227C4×Q8—221no—
228C4×Q8—221no—
229C4×D4—21no—
230C4×D4—21no—
231C4×D4—42no—
232C4×D4—42no—
233C4×D4C4×D1112yes—
234C4×D4D4412yes—
235#117—221no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4C22⋊D1111yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—22no—
242C2×C42—21no—
243C2×C42C22×D1111yescharacteristic
244#107—222no—
245#106—222no—
246C4⋊C8—112no—
247C4⋊C8—221no—
248C4⋊C8—221no—
249C4⋊C8—221no—
250#102—222no—
251#102—222no—
252C22⋊C8—221no—
253C22⋊C8—221no—
254C4×C8—221no—
255C4×C8—221no—
256#95—22no—
257#95—21no—
258#95C22⋊D1111yescharacteristic
259#95C22⋊D1111yescharacteristic
260#95C22⋊D1112yes—
261C2×C11—21no—
262C2×C11—21no—
263C2×C11—44no—
264C2×C11#187211yescharacteristic
265C2×C11#190411yescharacteristic
266C2×C11#190611yescharacteristic
267C24—21no—
268C2×Q8—221no—
269C2×Q8—221no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4(C2×D11)⋊C412yes—
274C2×D4#432412yes—
275C2×D4#432612yes—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—21no—
282C22×C4—44no—
283C22×C4—44no—
284C22×C4—82no—
285C22×C4—82no—
286C22×C4C2×C22⋊D1111yescharacteristic
287C22×C4C2×C22⋊D1111yescharacteristic
288C22×C4C2×C22⋊D1111yescharacteristic
289M16—441no—
290M16—441no—
291C2×C8—222no—
292C2×C8—441no—
293C2×C8—441no—
294C4⋊C4—21no—
295C4⋊C4—42no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—82no—
299C4⋊C4—221no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C4⋊C4—441no—
304C4⋊C4—441no—
305C4⋊C4(C2×D11)⋊C412yes—
306C22⋊C4—22no—
307C22⋊C4—22no—
308C22⋊C4—44no—
309C22⋊C4—441no—
310C42—41no—
311C42—41no—
312C42—441no—
313C42C2×C4×D1111yescharacteristic
314C42C2×D4411yescharacteristic
315C42#433911yescharacteristic
316C42#433911yescharacteristic
317C11#917511yescharacteristic, complemented, Sylow
318C23—22no—
319C23—22no—
320C23—22no—
321C23—42no—
322C23—42no—
323C23#6700611yescharacteristic
324Q8—881no—
325Q8—881no—
326D4—22no—
327D4—22no—
328D4—22no—
329D4#6687414yes—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—88no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4C2×(C2×D11)⋊C411yescharacteristic
349C2×C4C4×C22⋊D1111yescharacteristic
350C2×C4C4×C22⋊D1111yescharacteristic
351C2×C4#6698211yescharacteristic
352C2×C4#6698311yescharacteristic
353C2×C4#6698311yescharacteristic
354C2×C4#6698511yescharacteristic
355C2×C4C2×#432411yescharacteristic
356C2×C4#6699511yescharacteristic
357C2×C4C2×#432611yescharacteristic
358C8—442no—
359C8—881no—
360C8—881no—
361C22—21no—
362C22—21no—
363C22—24no—
364C22—44no—
365C22—44no—
366C22—42no—
367C22—42no—
368C22#1062282611yescharacteristic
369C22#1062283111yescharacteristic
370C22#1062284111yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—42no—
377C4—82no—
378C4—81no—
379C4—881no—
380C4—881no—
381C4#1062257911yescharacteristic
382C4C2×#6687411yescharacteristic
383C4#1062258311yescharacteristic
384C4#1062258411yescharacteristic
385C2—21no—
386C2—21no—
387C2—44no—
388C2#1306892311yescharacteristic
389C2#1306910311yescharacteristic
390C2#1306911711yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2349C2
socleC22×C11#386
prime radicalC22×D4×C11D4
cosocleC2×C42×C11C23
hypercenter#2349D11
hypocenterC11#9175
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2349

Complements

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

NH ≅ G/Ntype
2. #13067179C2semidirect
3. #13067114C2semidirect
5. #13066519C2semidirect
6. #13066474C2semidirect
19. #10622621C4semidirect
20. #10622620C4semidirect
51. #66922C2×C4semidirect
52. #66922C2×C4semidirect
69. C4⋊(C11⋊C8)C2×C4semidirect
317. C11#9175semidirect

Maximal subgroups

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

subgroupindex
#130784132
#130671792
#130671142
#130670072
#130665192
#130664742
C11×#23492
#917511