Finite Group Databasebeta

← #14642014

Subgroups — #14642014

Order 2816.

730 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 730 conjugacy classes of subgroups — too many to draw. Only its 105 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#13071103C211yesmaximal, characteristic
2#13068308C212yesmaximal, complemented
3#13066441C212yesmaximal, complemented
4#13066437C211yesmaximal, characteristic, complemented
5C11×#1270C211yesmaximal, characteristic, complemented
6C22×#4341C411yescharacteristic
7C22×#4313—22no—
8C2×#66945C411yescharacteristic
9C2×C42×D11C2211yescharacteristic
10C11×#390C2211yescharacteristic
11#10622834C411yescharacteristic
12#10622587C411yescharacteristic
13#10622569—22no—
14C22⋊C4×Dic11—22no—
15#10622542C2211yescharacteristic
16C11×#336C2212yes—
17#10622188—22no—
18#10622162C2212yes—
19C22×D4×C11C2×C411yescharacteristic
20C22×C22⋊D11—21no—
21C23×Dic11—21no—
22C2×#4341—22no—
23C2×#4341—22no—
24C2×#4341—42no—
25C2×#4341—42no—
26C22×C4×D11C2×C411yescharacteristic
27C22×C4×D11D412yes—
28C22×Dic22C2×C411yescharacteristic
29C22×C8×C11—22no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C22⋊C4—22no—
32C2×C42×C11C2311yescharacteristic
33C2×C22⋊Dic11—22no—
34C2×(C2×D11)⋊C4—21no—
35C2×C4⋊Dic11C2×C411yescharacteristic
36C2×C4×Dic11—21no—
37C2×C4×Dic11C2×C411yescharacteristic
38C2×C4×Dic11D412yes—
39C22×C11⋊C8—22no—
40C2×#4313—28no—
41C2×#4313—44no—
42C2×#4313—44no—
43#66945—42no—
44C42×D11—42no—
45C11⋊#95—22no—
46C11⋊#95—22no—
47#7631—111nomaximal, Sylow
48C24×C11—21no—
49C23×D11C22⋊C411yescharacteristic
50C2×D4×C11—21no—
51C2×D4×C11—41no—
52C2×D4×C11—41no—
53C2×D4×C11M1612yescomplemented
54C22×C4×C11—21no—
55C22×C4×C11C22×C411yescharacteristic
56C22×C4×C11C2×D412yes—
57C2×C22⋊D11—24no—
58C2×C22⋊D11—42no—
59C2×C22⋊D11—42no—
60C22×Dic11—24no—
61C22×Dic11—21no—
62C22×Dic11—21no—
63C22×Dic11—42no—
64C22×Dic11—42no—
65C22×Dic11C22⋊C411yescharacteristic
66C22×Dic11C22⋊C412yes—
67#4341—48no—
68#4341—48no—
69C2×C4×D11—22no—
70C2×C4×D11—24no—
71C2×C4×D11—24no—
72C2×C4×D11—22no—
73C2×C4×D11—21no—
74C2×C4×D11—21no—
75C2×C4×D11—22no—
76C2×C4×D11—22no—
77C2×Dic22—21no—
78C2×Dic22—41no—
79C2×Dic22—41no—
80C2×Dic22M1612yescomplemented
81C2×C8×C11—24no—
82C2×C8×C11—42no—
83C2×C8×C11—42no—
84C11×C4⋊C4—41no—
85C11×C22⋊C4—42no—
86C11×C22⋊C4—42no—
87C42×C11—41no—
88C22⋊Dic11—44no—
89(C2×D11)⋊C4—42no—
90C4⋊Dic11—41no—
91C4×Dic11—41no—
92C4×Dic11—42no—
93C4×Dic11—42no—
94C2×C11⋊C8—24no—
95C2×C11⋊C8—42no—
96C2×C11⋊C8—42no—
97#4313—416no—
98#2297—111no—
99#1728—112no—
100#1272—112no—
101#1270—111no—
102#1270D1111yescharacteristic, complemented
103C23×C11—22no—
104C23×C11—41no—
105C23×C11—41no—
106C23×C11—42no—
107C23×C11—42no—
108C23×C11C2×C22⋊C411yescharacteristic
109C22×D11—21no—
110C22×D11—21no—
111C22×D11—22no—
112C22×D11—22no—
113C22×D11#9912yes—
114D4×C11—42no—
115D4×C11—42no—
116C2×C4×C11—22no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—22no—
120C2×C4×C11—41no—
121C2×C4×C11—42no—
122C2×C4×C11C2×M1611yescharacteristic
123C2×C4×C11C2×M1611yescharacteristic
124C2×C4×C11AGL(1,ℤ/8)12yes—
125C2×C4×C11#13712yes—
126C22⋊D11—48no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—22no—
130C2×Dic11—22no—
131C2×Dic11—22no—
132C2×Dic11—48no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—42no—
137C2×Dic11#10012yes—
138C2×Dic11#10414yes—
139C4×D11—28no—
140C4×D11—28no—
141C4×D11—24no—
142C4×D11—24no—
143Dic22—42no—
144Dic22—42no—
145C8×C11—44no—
146C11⋊C8—44no—
147C22×#41—111no—
148C22×M16—222no—
149C2×#117—111no—
150C22×C42—111no—
151#391—111no—
152#391—111no—
153#390—111no—
154#390C2×D1111yescharacteristic
155#386—222no—
156C4×C22⋊C4—222no—
157#336—112no—
158#336—222no—
159#336C2×D1112yes—
160C22×C11—42no—
161C22×C11—44no—
162C22×C11—81no—
163C22×C11—82no—
164C22×C11—81no—
165C22×C11#40711yescharacteristic
166C22×C11C2×#9911yescharacteristic
167C22×C11C2×#10011yescharacteristic
168C22×C11#41712yes—
169C22×C11C2×#10412yes—
170C2×D11—22no—
171C2×D11—24no—
172C2×D11—41no—
173C2×D11—42no—
174C2×D11—41no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—22no—
178C4×C11—22no—
179C4×C11—81no—
180Dic11—22no—
181Dic11—24no—
182Dic11—42no—
183Dic11—81no—
184C2×#41—222no—
185C2×#41—222no—
186C2×#41—442no—
187C2×#41—442no—
188C22×Q8—111no—
189C22×D4—221no—
190C22×D4C4×D1111yescharacteristic
191C23×C4—111no—
192C23×C4—112no—
193C23×C4—221no—
194C2×M16—228no—
195C2×M16—444no—
196C2×M16—444no—
197C22×C8—22no—
198C22×C8—222no—
199#117—442no—
200C2×C4⋊C4—111no—
201C2×C4⋊C4C4×D1111yescharacteristic
202C2×C22⋊C4—22no—
203C2×C22⋊C4—221no—
204C2×C22⋊C4—222no—
205C2×C42—111no—
206C2×C42—112no—
207C2×C42—221no—
208C2×C42—442no—
209C2×C42C22×D1111yescharacteristic
210#95—222no—
211#95—222no—
212C2×C11—82no—
213C2×C11#146211yescharacteristic
214C2×C11#148912yes—
215C2×C11#150412yes—
216C2×C11#152511yescharacteristic
217C2×C11#156011yescharacteristic
218D11—42no—
219C24—21no—
220C24—111no—
221#41—448no—
222#41—448no—
223C2×Q8—112no—
224C2×Q8—221no—
225C2×Q8—441no—
226C2×Q8—441no—
227C2×D4—21no—
228C2×D4—41no—
229C2×D4—41no—
230C2×D4—224no—
231C2×D4—442no—
232C2×D4—442no—
233C2×D4#431312yescomplemented
234C22×C4—21no—
235C22×C4—112no—
236C22×C4—111no—
237C22×C4—222no—
238C22×C4—224no—
239C22×C4—224no—
240C22×C4—222no—
241C22×C4—221no—
242C22×C4—221no—
243C22×C4—222no—
244C22×C4—222no—
245C22×C4—224no—
246C22×C4—221no—
247C22×C4—221no—
248C22×C4—442no—
249C22×C4—442no—
250C22×C4C2×C4×D1111yescharacteristic
251C22×C4D4×D1112yes—
252M16—4416no—
253C2×C8—24no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—224no—
257C2×C8—442no—
258C2×C8—442no—
259C4⋊C4—41no—
260C4⋊C4—441no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C22⋊C4—442no—
264C22⋊C4—444no—
265C42—41no—
266C42—442no—
267C42—441no—
268C42—442no—
269C11#763111yescharacteristic, complemented, Sylow
270C23—22no—
271C23—41no—
272C23—41no—
273C23—42no—
274C23—42no—
275C23—112no—
276C23—221no—
277C23—221no—
278C23—222no—
279C23—222no—
280C23C22⋊C4×D1111yescharacteristic
281Q8—442no—
282Q8—442no—
283D4—42no—
284D4—42no—
285D4—448no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—112no—
293C2×C4—114no—
294C2×C4—228no—
295C2×C4—224no—
296C2×C4—224no—
297C2×C4—228no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—222no—
301C2×C4—222no—
302C2×C4—222no—
303C2×C4—448no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—442no—
308C2×C4C2×#431311yescharacteristic
309C2×C4M16×D1111yescharacteristic
310C2×C4#6696412yes—
311C2×C4#6696812yes—
312C8—44no—
313C8—444no—
314C22—44no—
315C22—42no—
316C22—81no—
317C22—82no—
318C22—81no—
319C22—224no—
320C22—222no—
321C22—442no—
322C22—441no—
323C22—441no—
324C22#1062233911yescharacteristic
325C22D11×#9911yescharacteristic
326C22D11×#10011yescharacteristic
327C22#1062238412yes—
328C22D11×#10412yes—
329C4—22no—
330C4—22no—
331C4—21no—
332C4—21no—
333C4—81no—
334C4—224no—
335C4—222no—
336C4—442no—
337C4—881no—
338C2—82no—
339C2—442no—
340C2#1306694111yescharacteristic
341C2#1306705212yes—
342C2#1306711712yes—
343C2#1306720611yescharacteristic
344C2#1306734811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1270C2
socleC23×C11C2×C22⋊C4
prime radicalC22×#4341C4
cosocleC2×C42×C11C23
hypercenter#1270D11
hypocenterC11#7631
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #13068308C2semidirect
3. #13066441C2semidirect
4. #13066437C2semidirect
5. C11×#1270C2semidirect
53. C2×D4×C11M16semidirect
80. C2×Dic22M16semidirect
102. #1270D11semidirect
233. C2×D4#4313semidirect
269. C11#7631semidirect

Maximal subgroups

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

subgroupindex
#130711032
#130683082
#130664412
#130664372
C11×#12702
#763111