Finite Group Databasebeta

← #14656082

Subgroups — #14656082

Order 2816.

676 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C2×#10622640C212yesmaximal
2#13069421C211yesmaximal, characteristic
3C2×Q8⋊(C11⋊C8)C212yesmaximal, complemented
4#13066499C211yesmaximal, characteristic, complemented
5C11×#2582C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C11C2212yes—
7C22×#4325—22no—
8C2×#66927C2211yescharacteristic
9C11×#398—22no—
10C11×#391—22no—
11C11×#389—22no—
12C11×#384C2211yescharacteristic
13#10622640—24no—
14#10622640—24no—
15C2×#66873—22no—
16C2×#66873—22no—
17C2×C4⋊(C11⋊C8)C2212yes—
18C2×C4×C11⋊C8C2211yescharacteristic
19Q8⋊(C11⋊C8)—24no—
20C22×Q8×C11D412yes—
21C22×D44—22no—
22C22×D44—21no—
23C4×Q8×C11—22no—
24C4×Q8×C11—22no—
25C4×Q8×C11—22no—
26C4×Q8×C11—22no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4D412yes—
31C2×C11×C4⋊C4D412yes—
32C2×C42×C11—22no—
33C2×C42×C11C2311yescharacteristic
34C2×#4325—28no—
35C2×#4325—44no—
36C2×#4325—44no—
37C22×C11⋊C8—21no—
38C22×C11⋊C8—22no—
39#66927—22no—
40#66927—21no—
41#66927D412yes—
42C11×#95—24no—
43C11×#95—22no—
44#66873—28no—
45#66873—44no—
46C4⋊(C11⋊C8)—22no—
47C4⋊(C11⋊C8)D414yes—
48C4×C11⋊C8—22no—
49#10230—111nomaximal, Sylow
50C23×D11—41no—
51C2×Q8×C11—22no—
52C2×Q8×C11—22no—
53C2×Q8×C11—22no—
54C2×Q8×C11—22no—
55C2×Q8×C11—22no—
56C2×Q8×C11SD1614yescomplemented
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D412yes—
62C2×D44—24no—
63C2×D44—22no—
64C2×D44—42no—
65C2×D44—42no—
66C2×D44—42no—
67C2×D44—41no—
68C2×D44—42no—
69C2×D44—42no—
70C2×D44—42no—
71C2×D44—42no—
72C11×C4⋊C4—22no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—42no—
75C11×C4⋊C4—42no—
76C11×C4⋊C4—42no—
77C11×C4⋊C4—42no—
78C11×C4⋊C4—42no—
79C11×C4⋊C4—82no—
80C42×C11—42no—
81C42×C11—42no—
82C42×C11C2×D411yescharacteristic
83C42×C11C2×D412yes—
84C42×C11#4111yescharacteristic
85#4325—416no—
86C2×C11⋊C8—22no—
87C2×C11⋊C8—24no—
88C2×C11⋊C8—41no—
89C2×C11⋊C8—41no—
90C2×C11⋊C8—42no—
91C2×C11⋊C8—42no—
92C2×#460—112no—
93#2582D1111yescharacteristic, complemented
94#1957—111no—
95C2×Q8⋊C8—112no—
96#1296—111no—
97C23×C11#12011yescharacteristic
98C22×D11—42no—
99C22×D11—82no—
100C22×D11—82no—
101C22×D11—81no—
102C22×D11—81no—
103Q8×C11—24no—
104Q8×C11—24no—
105Q8×C11—42no—
106Q8×C11—42no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—24no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—44no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11#12012yes—
118C2×C4×C11#12111yescharacteristic
119C2×C4×C11#12112yes—
120C2×C4×C11#12711yescharacteristic
121C2×C4×C11C2×SD1612yes—
122C2×C4×C11#13512yes—
123C2×C4×C11AGL(1,ℤ/8)12yes—
124C2×C4×C11#13712yes—
125D44—44no—
126D44—44no—
127D44—44no—
128D44—82no—
129D44—82no—
130D44—82no—
131C11⋊C8—42no—
132C11⋊C8—44no—
133C22×SD16—222no—
134C2×#127—111no—
135C2×C4×Q8C2×D1112yes—
136#460—224no—
137#460—224no—
138C2×C4⋊C8—112no—
139C2×#102—222no—
140C2×#102—222no—
141C2×C4×C8—111no—
142#398—22no—
143#391—22no—
144#389—22no—
145#384C2×D1111yescharacteristic
146Q8⋊C8—224no—
147C22×C11#39211yescharacteristic
148C22×C11#44812yes—
149C22×C11#44912yes—
150C22×C11#45311yescharacteristic
151C22×C11#45411yescharacteristic
152C2×D11—84no—
153C2×D11—82no—
154C2×D11—161no—
155C2×D11—161no—
156C2×D11—162no—
157C4×C11—21no—
158C4×C11—21no—
159C4×C11—44no—
160C4×C11—82no—
161C4×C11—82no—
162C4×C11#45012yes—
163C4×C11#45212yes—
164C4×C11#46512yes—
165C4×C11#46812yes—
166C22×Q8C22⋊D1112yes—
167C22×D4—222no—
168C22×D4—221no—
169C2×SD16—228no—
170C2×SD16—444no—
171C2×SD16—444no—
172C22×C8—222no—
173C22×C8—221no—
174#127—112no—
175#127—222no—
176#127—221no—
177C4×Q8—22no—
178C4×Q8—22no—
179C4×Q8—22no—
180C4×Q8—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4C22⋊D1112yes—
185C2×C4⋊C4C22⋊D1112yes—
186C2×C42—22no—
187C2×C42C22×D1111yescharacteristic
188C4⋊C8—114no—
189C4⋊C8—222no—
190#102—228no—
191#102—444no—
192C4×C8—222no—
193#95—24no—
194#95—22no—
195C2×C11#162011yescharacteristic
196C2×C11#162311yescharacteristic
197C2×C11#162612yes—
198C2×C11#200012yes—
199C2×C11#200611yescharacteristic
200D11—162no—
201C24—441no—
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8—22no—
206C2×Q8—22no—
207C2×Q8#432514yescomplemented
208C2×D4—224no—
209C2×D4—222no—
210C2×D4—442no—
211C2×D4—442no—
212C2×D4—442no—
213C2×D4—441no—
214C2×D4—442no—
215C2×D4—442no—
216C2×D4—442no—
217C2×D4—442no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4C2×C22⋊D1111yescharacteristic
222C22×C4C2×C22⋊D1112yes—
223SD16—4416no—
224C2×C8—222no—
225C2×C8—224no—
226C2×C8—441no—
227C2×C8—441no—
228C2×C8—442no—
229C2×C8—442no—
230C4⋊C4—22no—
231C4⋊C4—22no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C4⋊C4—82no—
238C42—42no—
239C42—42no—
240C42D4×D1111yescharacteristic
241C42D4×D1112yes—
242C42#434111yescharacteristic
243C11#1023011yescharacteristic, complemented, Sylow
244C23—442no—
245C23—882no—
246C23—882no—
247C23—881no—
248C23—881no—
249C23#6700611yescharacteristic
250Q8—24no—
251Q8—24no—
252Q8—42no—
253Q8—42no—
254D4—444no—
255D4—444no—
256D4—444no—
257D4—882no—
258D4—882no—
259D4—882no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—24no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—44no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4#6699012yes—
271C2×C4#6699111yescharacteristic
272C2×C4#6699212yes—
273C2×C4#6699311yescharacteristic
274C2×C4C2×#432512yes—
275C2×C4#6699512yes—
276C2×C4#6700212yes—
277C2×C4#6700312yes—
278C8—442no—
279C8—444no—
280C22—884no—
281C22—882no—
282C22—1761no—
283C22—1761no—
284C22—1762no—
285C22#1062283611yescharacteristic
286C22#1062284012yes—
287C22#1062285112yes—
288C22#1062285411yescharacteristic
289C22#1062285811yescharacteristic
290C4—21no—
291C4—21no—
292C4—44no—
293C4—82no—
294C4—82no—
295C4#1062265912yes—
296C4#1062266012yes—
297C4#1062266112yes—
298C4#1062266212yes—
299C2—1762no—
300C2#1306767511yescharacteristic
301C2#1306769411yescharacteristic
302C2#1306771212yes—
303C2#1306961712yes—
304C2#1306965811yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2582C2
socleC23×C11#120
prime radicalC2×#66927C22
hypercenter#2582D11
hypocenterC11#10230
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2582

Complements

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

NH ≅ G/Ntype
3. C2×Q8⋊(C11⋊C8)C2semidirect
4. #13066499C2semidirect
5. C11×#2582C2semidirect
56. C2×Q8×C11SD16semidirect
93. #2582D11semidirect
207. C2×Q8#4325semidirect
243. C11#10230semidirect

Maximal subgroups

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

subgroupindex
C2×#106226402
#130694212
C2×Q8⋊(C11⋊C8)2
#130664992
C11×#25822
#1023011