Finite Group Databasebeta

← #14656280

Subgroups — #14656280

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×#10622308C211yesmaximal, characteristic, complemented
2C2×#10622456C212yesmaximal, complemented
3#13069410C211yesmaximal, characteristic, complemented
4C2×#10622123C212yesmaximal, complemented
5C11×#1277C211yesmaximal, characteristic, complemented
6C22×D88—22no—
7C22×D88—22no—
8C2×#66927C2212yes—
9C2×C4×D44C2211yescharacteristic
10C2×C11×C4⋊C8C2212yes—
11C2×C4×C8×C11C2211yescharacteristic
12C2×#66885—22no—
13C2×(C2×D11)⋊C8—22no—
14C2×C4⋊(C11⋊C8)C2211yescharacteristic
15#10622456—24no—
16#10622456—24no—
17#10622308—24no—
18#10622123—24no—
19C22×D44—22no—
20C22×D44—22no—
21C22×D44—22no—
22C22×D44D411yescharacteristic
23C22×C4×D11—21no—
24C22×C8×C11—22no—
25C22×C8×C11D412yes—
26C2×C42×C11C2311yescharacteristic
27C2×(C2×D11)⋊C4—21no—
28C2×C4⋊Dic11D411yescharacteristic
29C22×C11⋊C8—21no—
30C2×D88—28no—
31C2×D88—28no—
32C2×D88—44no—
33C2×D88—44no—
34C2×D88—44no—
35C2×D88—44no—
36#66927—22no—
37#66927—22no—
38#66927—22no—
39#66927D414yes—
40C4×D44—22no—
41C4×D44—22no—
42C11×C4⋊C8—22no—
43C11×C4⋊C8D414yes—
44C4×C8×C11—22no—
45#66885—28no—
46(C2×D11)⋊C8—44no—
47C4⋊(C11⋊C8)—22no—
48#10260—111nomaximal, Sylow
49C23×D11—21no—
50C23×D11—42no—
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11C2×D411yescharacteristic
53C22×C4×C11#4111yescharacteristic
54C22×Dic11—21no—
55C2×D44—22no—
56C2×D44—24no—
57C2×D44—24no—
58C2×D44—24no—
59C2×D44—21no—
60C2×D44—22no—
61C2×D44—42no—
62C2×D44—42no—
63C2×D44—42no—
64C2×D44—44no—
65C2×D44—42no—
66C2×D44—42no—
67C2×D44—44no—
68C2×D44—42no—
69C2×D44—42no—
70C2×D44—84no—
71C2×D44D812yescomplemented
72C2×C4×D11—41no—
73C2×C4×D11—41no—
74C2×C4×D11—42no—
75C2×C4×D11—42no—
76C2×C8×C11—22no—
77C2×C8×C11—24no—
78C2×C8×C11—22no—
79C2×C8×C11—42no—
80C2×C8×C11—42no—
81C2×C8×C11D814yescomplemented
82C42×C11C2×D412yes—
83C42×C11C2×D412yes—
84(C2×D11)⋊C4—42no—
85C4⋊Dic11—22no—
86C2×C11⋊C8—41no—
87C2×C11⋊C8—42no—
88D88—416no—
89D88—416no—
90C2×#493—111no—
91C2×#459—112no—
92#1954—111no—
93C2×#331—112no—
94#1277D1111yescharacteristic, complemented
95C23×C11#12111yescharacteristic
96C22×D11—22no—
97C22×D11—41no—
98C22×D11—42no—
99C22×D11—41no—
100C22×D11—42no—
101C22×D11—44no—
102C22×D11—84no—
103C22×D11—82no—
104C22×D11—82no—
105C22×D11—84no—
106C2×C4×C11—22no—
107C2×C4×C11#12011yescharacteristic
108C2×C4×C11#12012yes—
109C2×C4×C11#12112yes—
110C2×C4×C11#12711yescharacteristic
111C2×C4×C11C2×D812yes—
112C2×C4×C11C2×D811yescharacteristic
113C2×C4×C11#13511yescharacteristic
114C2×C4×C11AGL(1,ℤ/8)12yes—
115C2×C4×C11AGL(1,ℤ/8)12yes—
116C2×Dic11—41no—
117C2×Dic11—42no—
118D44—24no—
119D44—48no—
120D44—44no—
121D44—42no—
122D44—44no—
123D44—84no—
124D44—84no—
125D44—82no—
126D44—82no—
127D44—82no—
128D44—82no—
129C4×D11—82no—
130C4×D11—81no—
131C4×D11—81no—
132C8×C11—24no—
133C8×C11—44no—
134C11⋊C8—81no—
135C22×D8—222no—
136C22×D8—222no—
137C2×#127—112no—
138C2×C4×D4—111no—
139#493—224no—
140#459—224no—
141#459—224no—
142C2×C4⋊C8—111no—
143C2×C4⋊C8C2×D1112yes—
144C2×#102—222no—
145C2×C22⋊C8—222no—
146C2×C4×C8C2×D1111yescharacteristic
147#331—224no—
148C22×C11#39211yescharacteristic
149C22×C11#45912yes—
150C22×C11#46611yescharacteristic
151C22×C11#46911yescharacteristic
152C22×C11#47212yes—
153C2×D11—44no—
154C2×D11—42no—
155C2×D11—82no—
156C2×D11—81no—
157C2×D11—81no—
158C2×D11—84no—
159C2×D11—84no—
160C2×D11—84no—
161C2×D11—164no—
162C2×D11—164no—
163C4×C11—22no—
164C4×C11#44712yes—
165C4×C11#44712yes—
166C4×C11#44912yes—
167C4×C11#49311yescharacteristic
168C4×C11#49611yescharacteristic
169Dic11—81no—
170C22×D4—111no—
171C22×D4—222no—
172C22×D4—222no—
173C22×D4—222no—
174C23×C4—221no—
175C2×D8—228no—
176C2×D8—228no—
177C2×D8—444no—
178C2×D8—444no—
179C2×D8—444no—
180C2×D8—444no—
181C22×C8—22no—
182C22×C8—221no—
183C22×C8D4412yes—
184#127—114no—
185#127—222no—
186#127—222no—
187#127—222no—
188C4×D4—222no—
189C4×D4—222no—
190C2×C4⋊C4—111no—
191C2×C22⋊C4—221no—
192C2×C42C22×D1111yescharacteristic
193C4⋊C8—22no—
194C4⋊C8—222no—
195C4⋊C8D4414yes—
196#102—228no—
197C22⋊C8—444no—
198C4×C8—22no—
199C2×C11#166712yes—
200C2×C11#168712yes—
201C2×C11#199911yescharacteristic
202C2×C11#201111yescharacteristic
203C2×C11#201811yescharacteristic
204D11—82no—
205D11—164no—
206C24—221no—
207C24—442no—
208C2×D4—112no—
209C2×D4—222no—
210C2×D4—224no—
211C2×D4—224no—
212C2×D4—224no—
213C2×D4—222no—
214C2×D4—221no—
215C2×D4—442no—
216C2×D4—442no—
217C2×D4—442no—
218C2×D4—444no—
219C2×D4—444no—
220C2×D4—442no—
221C2×D4—442no—
222C2×D4—442no—
223C2×D4—442no—
224C2×D4—884no—
225C22×C4—221no—
226C22×C4—441no—
227C22×C4—441no—
228C22×C4—442no—
229C22×C4—442no—
230C22×C4C2×D4411yescharacteristic
231C22×C4D4×D1111yescharacteristic
232C22×C4#434311yescharacteristic
233D8—4416no—
234D8—4416no—
235C2×C8—22no—
236C2×C8—22no—
237C2×C8—24no—
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—441no—
241C2×C8—442no—
242C2×C8D8814yescomplemented
243C4⋊C4—222no—
244C22⋊C4—442no—
245C42C2×D4412yes—
246C42D4×D1112yes—
247C11#1026011yescharacteristic, complemented, Sylow
248C23—222no—
249C23—441no—
250C23—442no—
251C23—441no—
252C23—442no—
253C23—444no—
254C23—882no—
255C23—882no—
256C23—884no—
257C23—884no—
258C23#6694811yescharacteristic
259D4—224no—
260D4—448no—
261D4—444no—
262D4—442no—
263D4—444no—
264D4—884no—
265D4—884no—
266D4—882no—
267D4—882no—
268D4—882no—
269D4—882no—
270C2×C4—22no—
271C2×C4—441no—
272C2×C4—442no—
273C2×C4—881no—
274C2×C4—881no—
275C2×C4—882no—
276C2×C4#6692711yescharacteristic
277C2×C4#6693511yescharacteristic
278C2×C4#6693512yes—
279C2×C4#6694812yes—
280C2×C4C2×D8812yes—
281C2×C4#6696112yes—
282C2×C4D8×D1111yescharacteristic
283C2×C4#6696712yes—
284C2×C4#6697211yescharacteristic
285C8—24no—
286C8—44no—
287C8—881no—
288C22—442no—
289C22—444no—
290C22—882no—
291C22—881no—
292C22—881no—
293C22—884no—
294C22—884no—
295C22—884no—
296C22—1764no—
297C22—1764no—
298C22#1062228411yescharacteristic
299C22#1062245612yes—
300C22#1062247811yescharacteristic
301C22#1062249611yescharacteristic
302C22#1062251012yes—
303C4—22no—
304C4—881no—
305C4#1062230811yescharacteristic
306C4#1062232511yescharacteristic
307C4#1062234512yes—
308C4#1062238612yes—
309C4#1062242412yes—
310C2—882no—
311C2—1764no—
312C2#1306797212yes—
313C2#1306809612yes—
314C2#1306961511yescharacteristic
315C2#1306968911yescharacteristic
316C2#1306972611yescharacteristic
subgroupG/H
centerC23#66948
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1277C2
socleC23×C11#121
hypercenter#1277D11
hypocenterC11#10260
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
1. C2×#10622308C2semidirect
2. C2×#10622456C2semidirect
3. #13069410C2semidirect
4. C2×#10622123C2semidirect
5. C11×#1277C2semidirect
71. C2×D44D8semidirect
81. C2×C8×C11D8semidirect
94. #1277D11semidirect
242. C2×C8D88semidirect
247. C11#10260semidirect

Maximal subgroups

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

subgroupindex
C2×#106223082
C2×#106224562
#130694102
C2×#106221232
C11×#12772
#1026011