Finite Group Databasebeta

← #14642017

Subgroups — #14642017

Order 2816.

730 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 730 conjugacy classes of subgroups — too many to draw. Only its 131 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#13068310C212yesmaximal, complemented
2#13066442C212yesmaximal, complemented
3#13066437C212yesmaximal, complemented
4C11×#2297C211yesmaximal, characteristic
5C22×C11×#41C411yescharacteristic
6C2×C11×#117C411yescharacteristic
7C22×C42×C11C2211yescharacteristic
8C22×#4318—22no—
9C11×#391C411yescharacteristic
10C11×#391C2211yescharacteristic
11C11×#390C411yescharacteristic
12C11×#390C2211yescharacteristic
13C11×#386—22no—
14C4×C11×C22⋊C4—22no—
15#10622162—22no—
16#10622162C2214yes—
17C2×C11×#41—22no—
18C2×C11×#41—22no—
19C2×C11×#41—42no—
20C2×C11×#41—42no—
21C22×Q8×C11C2×C411yescharacteristic
22C22×D4×C11—21no—
23C22×D4×C11C2×C411yescharacteristic
24C23×C4×C11—21no—
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11D412yes—
27C11×#117—42no—
28C2×C11×C4⋊C4C2×C411yescharacteristic
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C22⋊C4—21no—
31C2×C11×C22⋊C4—22no—
32C2×C11×C22⋊C4—22no—
33C2×C42×C11—21no—
34C2×C42×C11—42no—
35C2×C42×C11C2×C411yescharacteristic
36C2×C42×C11D412yes—
37C2×C42×C11C2311yescharacteristic
38C2×#4318—28no—
39C2×#4318—44no—
40C2×#4318—44no—
41C22×C11⋊C8—24no—
42C11×#95—22no—
43C11×#95—22no—
44#7631—111nomaximal, Sylow
45C24×C11—21no—
46C24×C11C22⋊C411yescharacteristic
47C11×#41—48no—
48C11×#41—48no—
49C2×Q8×C11—21no—
50C2×Q8×C11—41no—
51C2×Q8×C11—41no—
52C2×Q8×C11M1612yescomplemented
53C2×D4×C11—24no—
54C2×D4×C11—21no—
55C2×D4×C11—41no—
56C2×D4×C11—41no—
57C2×D4×C11—42no—
58C2×D4×C11—42no—
59C2×D4×C11M1612yescomplemented
60C22×C4×C11—24no—
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—24no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—24no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—42no—
73C22×C4×C11—42no—
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C412yes—
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C2×D412yes—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C22⋊C4—42no—
81C11×C22⋊C4—44no—
82C11×C22⋊C4—42no—
83C11×C22⋊C4—42no—
84C42×C11—41no—
85C42×C11—42no—
86C42×C11—41no—
87C42×C11—42no—
88#4318—416no—
89C2×C11⋊C8—28no—
90C2×C11⋊C8—44no—
91C2×C11⋊C8—44no—
92#2297D1111yescharacteristic
93#1728—112no—
94#1272—112no—
95#1270—112no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11—22no—
99C23×C11—22no—
100C23×C11—22no—
101C23×C11—41no—
102C23×C11—41no—
103C23×C11—42no—
104C23×C11—42no—
105C23×C11#9912yes—
106C23×C11C2×C22⋊C411yescharacteristic
107Q8×C11—42no—
108Q8×C11—42no—
109D4×C11—42no—
110D4×C11—42no—
111D4×C11—48no—
112C2×C4×C11—28no—
113C2×C4×C11—28no—
114C2×C4×C11—24no—
115C2×C4×C11—24no—
116C2×C4×C11—21no—
117C2×C4×C11—22no—
118C2×C4×C11—21no—
119C2×C4×C11—22no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—48no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11#10012yes—
133C2×C4×C11#10414yes—
134C2×C4×C11C2×M1611yescharacteristic
135C2×C4×C11C2×M1611yescharacteristic
136C2×C4×C11AGL(1,ℤ/8)12yes—
137C2×C4×C11#13712yes—
138C11⋊C8—48no—
139C22×#41Dic1111yescharacteristic
140C22×M16—222no—
141C2×#117Dic1111yescharacteristic
142C22×C42C2×D1111yescharacteristic
143#391Dic1111yescharacteristic
144#391C2×D1111yescharacteristic
145#390Dic1111yescharacteristic
146#390C2×D1111yescharacteristic
147#386—22no—
148C4×C22⋊C4—22no—
149#336—114no—
150#336—222no—
151C22×C11—22no—
152C22×C11—24no—
153C22×C11—41no—
154C22×C11—42no—
155C22×C11—41no—
156C22×C11—42no—
157C22×C11—44no—
158C22×C11—81no—
159C22×C11—82no—
160C22×C11—81no—
161C22×C11#40711yescharacteristic
162C22×C11C2×#9911yescharacteristic
163C22×C11C2×#10011yescharacteristic
164C22×C11#41712yes—
165C22×C11C2×#10412yes—
166C4×C11—22no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—24no—
170C4×C11—22no—
171C4×C11—22no—
172C4×C11—42no—
173C4×C11—81no—
174C4×C11—81no—
175C2×#41—22no—
176C2×#41—22no—
177C2×#41—42no—
178C2×#41—42no—
179C22×Q8C2×Dic1111yescharacteristic
180C22×D4—21no—
181C22×D4C2×Dic1111yescharacteristic
182C23×C4—21no—
183C23×C4C2×Dic1111yescharacteristic
184C23×C4C22⋊D1112yes—
185C2×M16—228no—
186C2×M16—444no—
187C2×M16—444no—
188C22×C8—224no—
189#117—42no—
190C2×C4⋊C4C2×Dic1111yescharacteristic
191C2×C4⋊C4C2×Dic1111yescharacteristic
192C2×C22⋊C4—21no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C42—21no—
196C2×C42—42no—
197C2×C42C2×Dic1111yescharacteristic
198C2×C42C22⋊D1112yes—
199C2×C42C22×D1111yescharacteristic
200#95—22no—
201#95—22no—
202C2×C11—42no—
203C2×C11—82no—
204C2×C11#146211yescharacteristic
205C2×C11#148912yes—
206C2×C11#150412yes—
207C2×C11#152511yescharacteristic
208C2×C11#156011yescharacteristic
209C24—21no—
210C24C22⋊Dic1111yescharacteristic
211#41—48no—
212#41—48no—
213C2×Q8—21no—
214C2×Q8—41no—
215C2×Q8—41no—
216C2×Q8#431812yescomplemented
217C2×D4—24no—
218C2×D4—21no—
219C2×D4—41no—
220C2×D4—41no—
221C2×D4—42no—
222C2×D4—42no—
223C2×D4#431812yescomplemented
224C22×C4—24no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—24no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—24no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4C22⋊Dic1111yescharacteristic
239C22×C4C22⋊Dic1112yes—
240C22×C4C22×Dic1111yescharacteristic
241C22×C4C2×C22⋊D1112yes—
242M16—4416no—
243C2×C8—228no—
244C2×C8—444no—
245C2×C8—444no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C22⋊C4—42no—
249C22⋊C4—44no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C42—41no—
253C42—41no—
254C42—42no—
255C42—42no—
256C11#763111yescharacteristic, complemented, Sylow
257C23—21no—
258C23—21no—
259C23—22no—
260C23—22no—
261C23—22no—
262C23—41no—
263C23—41no—
264C23—42no—
265C23—42no—
266C23#6689812yes—
267C23C2×C22⋊Dic1111yescharacteristic
268Q8—42no—
269Q8—42no—
270D4—42no—
271D4—42no—
272D4—48no—
273C2×C4—28no—
274C2×C4—28no—
275C2×C4—24no—
276C2×C4—24no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—48no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4#6689712yes—
294C2×C4#6690114yes—
295C2×C4C2×#431811yescharacteristic
296C2×C4C2×#431811yescharacteristic
297C2×C4#6700212yes—
298C2×C4#6700412yes—
299C8—448no—
300C22—24no—
301C22—22no—
302C22—42no—
303C22—41no—
304C22—41no—
305C22—44no—
306C22—42no—
307C22—81no—
308C22—82no—
309C22—81no—
310C22#1062282011yescharacteristic
311C22C2×#6689711yescharacteristic
312C22C2×#6689811yescharacteristic
313C22#1062284512yes—
314C22C2×#6690112yes—
315C4—22no—
316C4—24no—
317C4—22no—
318C4—22no—
319C4—21no—
320C4—21no—
321C4—42no—
322C4—81no—
323C4—81no—
324C2—42no—
325C2—82no—
326C2#1306694311yescharacteristic
327C2#1306705512yes—
328C2#1306712012yes—
329C2#1306720811yescharacteristic
330C2#1306735111yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2297C2
socleC23×C11C2×C22⋊C4
prime radicalC22×C11×#41C4
cosocleC2×C42×C11C23
hypercenter#2297D11
hypocenterC11#7631
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2297

Complements

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

NH ≅ G/Ntype
1. #13068310C2semidirect
2. #13066442C2semidirect
3. #13066437C2semidirect
52. C2×Q8×C11M16semidirect
59. C2×D4×C11M16semidirect
216. C2×Q8#4318semidirect
223. C2×D4#4318semidirect
256. C11#7631semidirect

Maximal subgroups

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

subgroupindex
#130683102
#130664422
#130664372
C11×#22972
#763111