Finite Group Databasebeta

← #14642016

Subgroups — #14642016

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#13071105C211yesmaximal, characteristic
2#13068308C212yesmaximal, complemented
3#13066442C211yesmaximal, characteristic, complemented
4#13066436C212yesmaximal, complemented
5C11×#1272C211yesmaximal, characteristic, complemented
6C22×#4343C411yescharacteristic
7C22×#4313—22no—
8C2×#66945C411yescharacteristic
9C2×C42×D11C2211yescharacteristic
10C11×#391C2211yescharacteristic
11#10622843C411yescharacteristic
12#10622601C411yescharacteristic
13#10622552C2211yescharacteristic
14#10622279—22no—
15#10622278—22no—
16C11×#336C2212yes—
17#10622188—22no—
18#10622162C2212yes—
19C22×Q8×C11C2×C411yescharacteristic
20C2×#4343—22no—
21C2×#4343—22no—
22C2×#4343—42no—
23C2×#4343—42no—
24C22×D44—21no—
25C22×D44C2×C411yescharacteristic
26C22×C4×D11—21no—
27C22×C4×D11C2×C411yescharacteristic
28C22×C4×D11D412yes—
29C22×C8×C11—22no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C42×C11C2311yescharacteristic
32C2×(C2×D11)⋊C4—21no—
33C2×(C2×D11)⋊C4—22no—
34C2×(C2×D11)⋊C4—22no—
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
48C23×D11—21no—
49C23×D11C22⋊C411yescharacteristic
50C2×Q8×C11—21no—
51C2×Q8×C11—41no—
52C2×Q8×C11—41no—
53C2×Q8×C11M1612yescomplemented
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11C22×C411yescharacteristic
57C22×C4×C11C2×D412yes—
58C22×Dic11—21no—
59C22×Dic11C22⋊C411yescharacteristic
60C22×Dic11C22⋊C412yes—
61#4343—48no—
62#4343—48no—
63C2×D44—24no—
64C2×D44—21no—
65C2×D44—41no—
66C2×D44—41no—
67C2×D44—42no—
68C2×D44—42no—
69C2×D44M1612yescomplemented
70C2×C4×D11—22no—
71C2×C4×D11—24no—
72C2×C4×D11—24no—
73C2×C4×D11—24no—
74C2×C4×D11—22no—
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11—22no—
78C2×C4×D11—22no—
79C2×C4×D11—42no—
80C2×C4×D11—42no—
81C2×C8×C11—24no—
82C2×C8×C11—42no—
83C2×C8×C11—42no—
84C11×C4⋊C4—41no—
85C42×C11—41no—
86(C2×D11)⋊C4—42no—
87(C2×D11)⋊C4—44no—
88(C2×D11)⋊C4—42no—
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—111no—
101#1272D1111yescharacteristic, complemented
102#1270—112no—
103C23×C11C2×C22⋊C411yescharacteristic
104C22×D11—21no—
105C22×D11—21no—
106C22×D11—22no—
107C22×D11—22no—
108C22×D11—22no—
109C22×D11—41no—
110C22×D11—41no—
111C22×D11—42no—
112C22×D11—42no—
113C22×D11#9912yes—
114Q8×C11—42no—
115Q8×C11—42no—
116C2×C4×C11—22no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—42no—
125C2×C4×C11C2×M1611yescharacteristic
126C2×C4×C11C2×M1611yescharacteristic
127C2×C4×C11AGL(1,ℤ/8)12yes—
128C2×C4×C11#13712yes—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—22no—
132C2×Dic11—22no—
133C2×Dic11—41no—
134C2×Dic11—42no—
135C2×Dic11#10012yes—
136C2×Dic11#10414yes—
137D44—42no—
138D44—42no—
139D44—48no—
140C4×D11—28no—
141C4×D11—28no—
142C4×D11—24no—
143C4×D11—24no—
144C4×D11—48no—
145C8×C11—44no—
146C11⋊C8—44no—
147C22×#41—111no—
148C22×M16—222no—
149C2×#117—111no—
150C22×C42—111no—
151#391—111no—
152#391C2×D1111yescharacteristic
153#390—111no—
154#390—111no—
155#386—222no—
156C4×C22⋊C4—222no—
157#336—112no—
158#336—222no—
159#336C2×D1112yes—
160C22×C11#40711yescharacteristic
161C22×C11C2×#9911yescharacteristic
162C22×C11C2×#10011yescharacteristic
163C22×C11#41712yes—
164C22×C11C2×#10412yes—
165C2×D11—22no—
166C2×D11—24no—
167C2×D11—41no—
168C2×D11—42no—
169C2×D11—41no—
170C2×D11—42no—
171C2×D11—44no—
172C2×D11—81no—
173C2×D11—82no—
174C2×D11—81no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—22no—
178C4×C11—22no—
179C4×C11—42no—
180C4×C11—81no—
181Dic11—22no—
182Dic11—24no—
183Dic11—81no—
184C2×#41—222no—
185C2×#41—222no—
186C2×#41—442no—
187C2×#41—442no—
188C22×Q8C4×D1111yescharacteristic
189C22×D4—111no—
190C22×D4—221no—
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—222no—
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—22no—
211#95—222no—
212C2×C11#146211yescharacteristic
213C2×C11#148912yes—
214C2×C11#150412yes—
215C2×C11#152511yescharacteristic
216C2×C11#156011yescharacteristic
217D11—42no—
218D11—82no—
219C24—111no—
220C24—221no—
221#41—448no—
222#41—448no—
223C2×Q8—21no—
224C2×Q8—41no—
225C2×Q8—41no—
226C2×Q8#431312yescomplemented
227C2×D4—112no—
228C2×D4—224no—
229C2×D4—221no—
230C2×D4—441no—
231C2×D4—441no—
232C2×D4—442no—
233C2×D4—442no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—112no—
237C22×C4—111no—
238C22×C4—222no—
239C22×C4—224no—
240C22×C4—224no—
241C22×C4—222no—
242C22×C4—224no—
243C22×C4—221no—
244C22×C4—221no—
245C22×C4—222no—
246C22×C4—222no—
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—444no—
262C22⋊C4—442no—
263C22⋊C4—442no—
264C22⋊C4—442no—
265C42—41no—
266C42—442no—
267C42—441no—
268C42—442no—
269C11#763111yescharacteristic, complemented, Sylow
270C23—112no—
271C23—221no—
272C23—221no—
273C23—222no—
274C23—222no—
275C23—222no—
276C23—441no—
277C23—441no—
278C23—442no—
279C23—442no—
280C23C22⋊C4×D1111yescharacteristic
281Q8—42no—
282Q8—42no—
283D4—442no—
284D4—442no—
285D4—448no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—112no—
296C2×C4—114no—
297C2×C4—228no—
298C2×C4—224no—
299C2×C4—224no—
300C2×C4—228no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—222no—
304C2×C4—222no—
305C2×C4—448no—
306C2×C4—441no—
307C2×C4—442no—
308C2×C4C2×#431311yescharacteristic
309C2×C4M16×D1111yescharacteristic
310C2×C4#6696712yes—
311C2×C4#6697112yes—
312C8—44no—
313C8—444no—
314C22—224no—
315C22—222no—
316C22—442no—
317C22—441no—
318C22—441no—
319C22—444no—
320C22—442no—
321C22—881no—
322C22—882no—
323C22—881no—
324C22#1062233911yescharacteristic
325C22D11×#9911yescharacteristic
326C22D11×#10011yescharacteristic
327C22#1062241612yes—
328C22D11×#10412yes—
329C4—22no—
330C4—22no—
331C4—21no—
332C4—21no—
333C4—42no—
334C4—81no—
335C4—224no—
336C4—222no—
337C4—881no—
338C2—442no—
339C2—882no—
340C2#1306694111yescharacteristic
341C2#1306705412yes—
342C2#1306711912yes—
343C2#1306720611yescharacteristic
344C2#1306735011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1272C2
socleC23×C11C2×C22⋊C4
prime radicalC22×#4343C4
cosocleC2×C42×C11C23
hypercenter#1272D11
hypocenterC11#7631
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
2. #13068308C2semidirect
3. #13066442C2semidirect
4. #13066436C2semidirect
5. C11×#1272C2semidirect
53. C2×Q8×C11M16semidirect
69. C2×D44M16semidirect
101. #1272D11semidirect
226. C2×Q8#4313semidirect
269. C11#7631semidirect

Maximal subgroups

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

subgroupindex
#130711052
#130683082
#130664422
#130664362
C11×#12722
#763111