Finite Group Databasebeta

← #14735808

Subgroups — #14735808

Order 2816.

996 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 179 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079069C211yesmaximal, characteristic
2#13078992C212yesmaximal, complemented
3#13067914C218yesmaximal, complemented
4#13067211C212yesmaximal, complemented
5#13067208C211yesmaximal, characteristic, complemented
6C11×#3550C211yesmaximal, characteristic, complemented
7C11×#563C2214yescomplemented
8C11×#559—21no—
9Q82×C11—21no—
10C11×#556—22no—
11D4×Q8×C11—22no—
12C11×#542—24no—
13C11×#536—22no—
14C11×#533C2212yes—
15C11×#532C2211yescharacteristic
16C2×#67002—22no—
17C2×#66927C2211yescharacteristic
18#10622701—22no—
19#10622701—22no—
20#10622698—21no—
21#10622686—21no—
22#10622680C2218yes—
23#10622671C2214yes—
24#10622614—24no—
25C4×#4318C2211yescharacteristic
26C4×#4318C2212yes—
27#10622181C2218yescomplemented
28#10622178C2214yescomplemented
29C2×C11×#41D412yes—
30C22×Q8×C11—22no—
31C22×D44—21no—
32C22×D44—22no—
33C11×C4⋊Q8—24no—
34C11×C4⋊Q8—24no—
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D412yes—
37C11×C4⋊Q8D412yes—
38C11×#127D411yescharacteristic
39C11×#126—28no—
40C11×#125C2314yes—
41C11×#124—24no—
42C11×#124—24no—
43C11×#124C2312yes—
44C11×#123—24no—
45C11×#123—24no—
46C11×C22⋊Q8—24no—
47C11×C22⋊Q8—22no—
48C11×C22⋊Q8—22no—
49C11×C22⋊Q8—28no—
50C11×#121—22no—
51C4×Q8×C11—24no—
52C4×Q8×C11—22no—
53C4×Q8×C11—22no—
54C4×D4×C11—24no—
55C4×D4×C11—22no—
56C11×#117—22no—
57C11×#117D414yes—
58C2×C42×C11C2311yescharacteristic
59#67002—48no—
60C2×#4325—24no—
61C2×#4323—24no—
62C2×#4318—21no—
63C2×#4318—22no—
64#66927—21no—
65#66927—22no—
66#66927C2312yes—
67#66873—28no—
68#66873—28no—
69#66867C2312yes—
70#66867C2314yes—
71C4×C11⋊C8—21no—
72C4×C11⋊C8—22no—
73#19077—111nomaximal, Sylow
74C23×D11—41no—
75C11×#41—44no—
76C2×Q8×C11—24no—
77C2×Q8×C11—22no—
78C2×Q8×C11—22no—
79C2×Q8×C11—84no—
80C2×Q8×C11C2×D412yes—
81C2×D4×C11—22no—
82C2×D4×C11—22no—
83C2×D4×C11C2×D412yes—
84C22×C4×C11—24no—
85C22×C4×C11—22no—
86C22×C4×C11C2×D412yes—
87C22×C4×C11C2×D411yescharacteristic
88C2×D44—24no—
89C2×D44—22no—
90C2×D44—44no—
91C2×D44—48no—
92C2×D44—41no—
93C2×D44—42no—
94C11×C4⋊C4—28no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—24no—
99C11×C4⋊C4—24no—
100C11×C4⋊C4C2×D414yes—
101C11×C4⋊C4C2×D414yes—
102C11×C22⋊C4—24no—
103C11×C22⋊C4—28no—
104C11×C22⋊C4—24no—
105C11×C22⋊C4—24no—
106C42×C11—24no—
107C42×C11—24no—
108C42×C11C2×D412yes—
109C42×C11C2×D411yescharacteristic
110C42×C11C2411yescharacteristic
111#4325—48no—
112#4323—48no—
113#4318—24no—
114#4318—44no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—24no—
117#3550D1111yescharacteristic, complemented
118#3151—111no—
119#3138—112no—
120#1657—118no—
121#1526—112no—
122#1525—111no—
123C23×C11—22no—
124C23×C11#12011yescharacteristic
125C22×D11—42no—
126C22×D11—82no—
127C22×D11—84no—
128Q8×C11—42no—
129Q8×C11—44no—
130Q8×C11—44no—
131Q8×C11—84no—
132D4×C11—42no—
133D4×C11—44no—
134D4×C11—82no—
135C2×C4×C11—22no—
136C2×C4×C11—24no—
137C2×C4×C11—24no—
138C2×C4×C11—22no—
139C2×C4×C11—24no—
140C2×C4×C11—44no—
141C2×C4×C11—84no—
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12012yes—
144C2×C4×C11C22×D412yes—
145C2×C4×C11C22×D411yescharacteristic
146D44—44no—
147D44—48no—
148D44—82no—
149D44—84no—
150C11⋊C8—24no—
151C11⋊C8—44no—
152C2×AGL(1,ℤ/8)—222no—
153#563C2×D1114yescomplemented
154#559—21no—
155Q82—21no—
156#556—22no—
157D4×Q8—22no—
158#542—24no—
159#536—22no—
160#533C2×D1112yes—
161#532C2×D1111yescharacteristic
162C2×#127—111no—
163#496—114no—
164#493—221no—
165#492—221no—
166#490—118no—
167#486—222no—
168#486—222no—
169#418—224no—
170C4×M16—112no—
171C4×M16—111no—
172#330—118no—
173#329—114no—
174C22×C11—21no—
175C22×C11—22no—
176C22×C11—42no—
177C22×C11—44no—
178C22×C11C2×#12011yescharacteristic
179C2×D11—82no—
180C2×D11—84no—
181C2×D11—164no—
182C4×C11—21no—
183C4×C11—22no—
184C4×C11—42no—
185C4×C11—44no—
186C4×C11—44no—
187C4×C11#45312yes—
188C4×C11#45414yes—
189C2×#41C22⋊D1112yes—
190C22×Q8—22no—
191C22×D4—221no—
192C22×D4—222no—
193AGL(1,ℤ/8)—448no—
194C2×SD16—224no—
195C2×D8—224no—
196C2×M16—221no—
197C2×M16—222no—
198C4⋊Q8—24no—
199C4⋊Q8—24no—
200C4⋊Q8C22⋊D1111yescharacteristic
201C4⋊Q8C22⋊D1112yes—
202C4⋊Q8C22⋊D1112yes—
203#127—112no—
204#127—222no—
205#127—221no—
206#127C22⋊D1111yescharacteristic
207#126—28no—
208#125C22×D1114yes—
209#124—24no—
210#124—24no—
211#124C22×D1112yes—
212#123—24no—
213#123—24no—
214C22⋊Q8—24no—
215C22⋊Q8—22no—
216C22⋊Q8—22no—
217C22⋊Q8—28no—
218#121—22no—
219C4×Q8—24no—
220C4×Q8—22no—
221C4×Q8—22no—
222C4×D4—24no—
223C4×D4—22no—
224#117—22no—
225#117C22⋊D1114yes—
226C2×C42C22×D1111yescharacteristic
227#102—228no—
228#102—228no—
229#97—114no—
230#97—112no—
231C4×C8—222no—
232C4×C8—221no—
233C2×C11—41no—
234C2×C11—82no—
235C2×C11C2×#45311yescharacteristic
236C2×C11C2×#45412yes—
237D11—162no—
238C24—441no—
239#41—44no—
240C2×Q8—24no—
241C2×Q8—22no—
242C2×Q8—22no—
243C2×Q8—84no—
244C2×Q8C2×C22⋊D1112yes—
245C2×D4—22no—
246C2×D4—22no—
247C2×D4—224no—
248C2×D4—222no—
249C2×D4—444no—
250C2×D4—448no—
251C2×D4—441no—
252C2×D4—442no—
253C2×D4C2×C22⋊D1112yes—
254C22×C4—24no—
255C22×C4—22no—
256C22×C4C2×C22⋊D1112yes—
257C22×C4C2×C22⋊D1111yescharacteristic
258SD16—448no—
259D8—448no—
260M16—224no—
261M16—444no—
262C2×C8—222no—
263C2×C8—224no—
264C4⋊C4—28no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—24no—
269C4⋊C4—24no—
270C4⋊C4C2×C22⋊D1114yes—
271C4⋊C4C2×C22⋊D1114yes—
272C22⋊C4—24no—
273C22⋊C4—28no—
274C22⋊C4—24no—
275C22⋊C4—24no—
276C42—24no—
277C42—24no—
278C42C2×C22⋊D1112yes—
279C42C2×C22⋊D1111yescharacteristic
280C42C23×D1111yescharacteristic
281C11#1907711yescharacteristic, complemented, Sylow
282C23—22no—
283C23—442no—
284C23—882no—
285C23—884no—
286C23#6700611yescharacteristic
287Q8—42no—
288Q8—44no—
289Q8—44no—
290Q8—84no—
291D4—42no—
292D4—44no—
293D4—82no—
294D4—444no—
295D4—448no—
296D4—882no—
297D4—884no—
298C2×C4—22no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—22no—
302C2×C4—24no—
303C2×C4—44no—
304C2×C4—84no—
305C2×C4#6700611yescharacteristic
306C2×C4#6700612yes—
307C2×C4C22×C22⋊D1112yes—
308C2×C4C22×C22⋊D1111yescharacteristic
309C8—224no—
310C8—444no—
311C22—21no—
312C22—22no—
313C22—42no—
314C22—44no—
315C22—882no—
316C22—884no—
317C22—1764no—
318C22C2×#6700611yescharacteristic
319C4—21no—
320C4—22no—
321C4—42no—
322C4—44no—
323C4—44no—
324C4#1062285412yes—
325C4#1062285814yes—
326C2—41no—
327C2—82no—
328C2—1762no—
329C2C2×#1062285411yescharacteristic
330C2C2×#1062285812yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3550C2
socleC22×C11C2×#120
prime radical#13079069C2
hypercenter#3550D11
hypocenterC11#19077
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3550

Complements

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

NH ≅ G/Ntype
2. #13078992C2semidirect
3. #13067914C2semidirect
4. #13067211C2semidirect
5. #13067208C2semidirect
6. C11×#3550C2semidirect
7. C11×#563C22semidirect
27. #10622181C22semidirect
28. #10622178C22semidirect
117. #3550D11semidirect
153. #563C2×D11semidirect
281. C11#19077semidirect

Maximal subgroups

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

subgroupindex
#130790692
#130789922
#130679142
#130672112
#130672082
C11×#35502
#1907711