Finite Group Databasebeta

← #14656277

Subgroups — #14656277

Order 2816.

794 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 794 conjugacy classes of subgroups — too many to draw. Only its 139 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×#10622685C212yesmaximal, complemented
2#13069410C211yesmaximal, characteristic, complemented
3C2×#10622182C212yesmaximal, complemented
4#13066451C211yesmaximal, characteristic, complemented
5C2×C11×#493C211yesmaximal, characteristic, complemented
6C22×C11×D8—22no—
7C2×C11×#127C2212yes—
8C22×#4323—22no—
9C2×C4×D44C2211yescharacteristic
10C11×#493—24no—
11C2×C4×C8×C11C2211yescharacteristic
12C2×#66896—22no—
13C2×(C2×D11)⋊C8—22no—
14#10622685—24no—
15#10622685—24no—
16C2×C4⋊(C11⋊C8)C2211yescharacteristic
17C2×C4⋊(C11⋊C8)C2212yes—
18#10622182—24no—
19C22×D4×C11—22no—
20C22×D4×C11—22no—
21C22×D4×C11—22no—
22C22×D44D411yescharacteristic
23C22×C4×D11—21no—
24C2×C11×D8—28no—
25C2×C11×D8—44no—
26C2×C11×D8—44no—
27C22×C8×C11D412yes—
28C11×#127—22no—
29C11×#127—22no—
30C11×#127—22no—
31C11×#127D414yes—
32C2×C42×C11C2311yescharacteristic
33C2×#4323—28no—
34C2×#4323—44no—
35C2×#4323—44no—
36C2×(C2×D11)⋊C4—21no—
37C2×C4⋊Dic11D411yescharacteristic
38C22×C11⋊C8—22no—
39C22×C11⋊C8—21no—
40C4×D44—22no—
41C4×D44—22no—
42C4×C8×C11—22no—
43#66896—28no—
44(C2×D11)⋊C8—44no—
45C4⋊(C11⋊C8)—22no—
46C4⋊(C11⋊C8)—22no—
47C4⋊(C11⋊C8)D414yes—
48#10260—111nomaximal, Sylow
49C24×C11—42no—
50C23×D11—21no—
51C2×D4×C11—24no—
52C2×D4×C11—24no—
53C2×D4×C11—24no—
54C2×D4×C11—42no—
55C2×D4×C11—42no—
56C2×D4×C11—42no—
57C2×D4×C11—42no—
58C2×D4×C11—44no—
59C2×D4×C11—42no—
60C2×D4×C11—42no—
61C2×D4×C11—44no—
62C2×D4×C11—42no—
63C2×D4×C11—84no—
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11#4111yescharacteristic
67C22×Dic11—21no—
68C2×D44—22no—
69C2×D44—21no—
70C2×D44—22no—
71C2×D44D812yescomplemented
72C2×C4×D11—41no—
73C2×C4×D11—41no—
74C2×C4×D11—42no—
75C2×C4×D11—42no—
76C11×D8—416no—
77C2×C8×C11—22no—
78C2×C8×C11—22no—
79C2×C8×C11D814yescomplemented
80C42×C11C2×D412yes—
81C42×C11C2×D412yes—
82#4323—416no—
83(C2×D11)⋊C4—42no—
84C4⋊Dic11—22no—
85C2×C11⋊C8—24no—
86C2×C11⋊C8—41no—
87C2×C11⋊C8—42no—
88C2×C11⋊C8—42no—
89C2×C11⋊C8—42no—
90C2×#493D1111yescharacteristic, complemented
91C2×#459—112no—
92#1954—111no—
93C2×#331—112no—
94#1277—111no—
95C23×C11—44no—
96C23×C11—84no—
97C23×C11—82no—
98C23×C11—82no—
99C23×C11—84no—
100C23×C11#12111yescharacteristic
101C22×D11—22no—
102C22×D11—41no—
103C22×D11—42no—
104C22×D11—41no—
105C22×D11—42no—
106D4×C11—44no—
107D4×C11—48no—
108D4×C11—44no—
109D4×C11—84no—
110D4×C11—84no—
111D4×C11—82no—
112D4×C11—82no—
113D4×C11—82no—
114D4×C11—82no—
115C2×C4×C11—22no—
116C2×C4×C11#12012yes—
117C2×C4×C11#12011yescharacteristic
118C2×C4×C11#12112yes—
119C2×C4×C11#12711yescharacteristic
120C2×C4×C11C2×D811yescharacteristic
121C2×C4×C11C2×D812yes—
122C2×C4×C11#13511yescharacteristic
123C2×C4×C11AGL(1,ℤ/8)12yes—
124C2×C4×C11AGL(1,ℤ/8)12yes—
125C2×Dic11—41no—
126C2×Dic11—42no—
127D44—24no—
128D44—42no—
129C4×D11—82no—
130C4×D11—81no—
131C4×D11—81no—
132C8×C11—24no—
133C11⋊C8—44no—
134C11⋊C8—81no—
135C22×D8—22no—
136C22×D8—222no—
137C2×#127C2×D1112yes—
138C2×C4×D4—111no—
139#493—24no—
140#459—224no—
141#459—224no—
142C2×C4⋊C8—112no—
143C2×C4⋊C8—111no—
144C2×#102—222no—
145C2×C22⋊C8—222no—
146C2×C4×C8C2×D1111yescharacteristic
147#331—224no—
148C22×C11—84no—
149C22×C11—84no—
150C22×C11—84no—
151C22×C11—164no—
152C22×C11—164no—
153C22×C11#39211yescharacteristic
154C22×C11#45912yes—
155C22×C11#46611yescharacteristic
156C22×C11#46911yescharacteristic
157C22×C11#47212yes—
158C2×D11—44no—
159C2×D11—42no—
160C2×D11—82no—
161C2×D11—81no—
162C2×D11—81no—
163C4×C11—22no—
164C4×C11#44712yes—
165C4×C11#44712yes—
166C4×C11#44912yes—
167C4×C11#49311yescharacteristic
168C4×C11#49611yescharacteristic
169Dic11—81no—
170C22×D4—22no—
171C22×D4—22no—
172C22×D4—22no—
173C22×D4—111no—
174C23×C4—221no—
175C2×D8—28no—
176C2×D8—44no—
177C2×D8—44no—
178C2×D8—228no—
179C2×D8—444no—
180C2×D8—444no—
181C22×C8—222no—
182C22×C8—221no—
183C22×C8C22⋊D1112yes—
184#127—22no—
185#127—22no—
186#127—22no—
187#127C22⋊D1114yes—
188C4×D4—222no—
189C4×D4—222no—
190C2×C4⋊C4—111no—
191C2×C22⋊C4—221no—
192C2×C42C22×D1111yescharacteristic
193C4⋊C8—114no—
194C4⋊C8—222no—
195C4⋊C8—222no—
196#102—228no—
197C22⋊C8—444no—
198C4×C8—22no—
199C2×C11—164no—
200C2×C11#166712yes—
201C2×C11#168712yes—
202C2×C11#199911yescharacteristic
203C2×C11#201111yescharacteristic
204C2×C11#201811yescharacteristic
205D11—82no—
206C24—42no—
207C24—221no—
208C2×D4—24no—
209C2×D4—24no—
210C2×D4—24no—
211C2×D4—42no—
212C2×D4—42no—
213C2×D4—42no—
214C2×D4—42no—
215C2×D4—44no—
216C2×D4—44no—
217C2×D4—42no—
218C2×D4—42no—
219C2×D4—42no—
220C2×D4—84no—
221C2×D4—112no—
222C2×D4—222no—
223C2×D4—221no—
224C2×D4—222no—
225C22×C4—221no—
226C22×C4—442no—
227C22×C4—442no—
228C22×C4—441no—
229C22×C4—441no—
230C22×C4D4×D1111yescharacteristic
231C22×C4#434111yescharacteristic
232C22×C4C2×C22⋊D1111yescharacteristic
233D8—416no—
234D8—4416no—
235C2×C8—22no—
236C2×C8—22no—
237C2×C8—224no—
238C2×C8—442no—
239C2×C8—442no—
240C2×C8—442no—
241C2×C8—441no—
242C2×C8#432314yescomplemented
243C4⋊C4—222no—
244C22⋊C4—442no—
245C42D4×D1112yes—
246C42C2×C22⋊D1112yes—
247C11#1026011yescharacteristic, complemented, Sylow
248C23—44no—
249C23—82no—
250C23—82no—
251C23—84no—
252C23—84no—
253C23—222no—
254C23—441no—
255C23—442no—
256C23—441no—
257C23—442no—
258C23#6699111yescharacteristic
259D4—44no—
260D4—44no—
261D4—48no—
262D4—84no—
263D4—84no—
264D4—82no—
265D4—82no—
266D4—82no—
267D4—82no—
268D4—224no—
269D4—442no—
270C2×C4—22no—
271C2×C4—441no—
272C2×C4—442no—
273C2×C4—882no—
274C2×C4—881no—
275C2×C4—881no—
276C2×C4D8×D1111yescharacteristic
277C2×C4#6696412yes—
278C2×C4#6696511yescharacteristic
279C2×C4C2×#432312yes—
280C2×C4#6698512yes—
281C2×C4#6699012yes—
282C2×C4#6699212yes—
283C2×C4#6699311yescharacteristic
284C2×C4#6700611yescharacteristic
285C8—24no—
286C8—444no—
287C8—881no—
288C22—84no—
289C22—84no—
290C22—84no—
291C22—164no—
292C22—164no—
293C22—442no—
294C22—444no—
295C22—882no—
296C22—881no—
297C22—881no—
298C22#1062268512yes—
299C22#1062277011yescharacteristic
300C22#1062277211yescharacteristic
301C22#1062277312yes—
302C22#1062283611yescharacteristic
303C4—22no—
304C4—881no—
305C4#1062268611yescharacteristic
306C4#1062268711yescharacteristic
307C4#1062276912yes—
308C4#1062277112yes—
309C4#1062283012yes—
310C2—164no—
311C2—882no—
312C2#1306796812yes—
313C2#1306809212yes—
314C2#1306961111yescharacteristic
315C2#1306968711yescharacteristic
316C2#1306972311yescharacteristic
subgroupG/H
centerC23#66991
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#493C2
socleC23×C11#121
hypercenterC2×#493D11
hypocenterC11#10260
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#493

Complements

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

NH ≅ G/Ntype
1. C2×#10622685C2semidirect
2. #13069410C2semidirect
3. C2×#10622182C2semidirect
4. #13066451C2semidirect
5. C2×C11×#493C2semidirect
71. C2×D44D8semidirect
79. C2×C8×C11D8semidirect
90. C2×#493D11semidirect
242. C2×C8#4323semidirect
247. C11#10260semidirect

Maximal subgroups

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

subgroupindex
C2×#106226852
#130694102
C2×#106221822
#130664512
C2×C11×#4932
#1026011