Finite Group Databasebeta

← #14672652

Subgroups — #14672652

Order 2816.

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

normal subgroups only

This group has 546 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
1C2×#10622522C212yesmaximal
2C2×#10622312C211yesmaximal, characteristic, complemented
3C2×#10622155C212yesmaximal, complemented
4#13069504C211yesmaximal, characteristic
5C11×#1376C211yesmaximal, characteristic, complemented
6C22×Dic44—21no—
7C22×Dic44C2212yes—
8C2×#66957C2211yescharacteristic
9C2×#66922—21no—
10C2×C11×M32C2212yes—
11C2×C4×C8×C11C2211yescharacteristic
12#10622723—21no—
13C2×#66883C2211yescharacteristic
14C2×#66869—21no—
15#10622522—24no—
16#10622522—24no—
17C2×Dic88—22no—
18C2×#66864—22no—
19#10622312—24no—
20#10622155—24no—
21C2×#4339—21no—
22C22×Dic22—22no—
23C22×C8×C11D411yescharacteristic
24C22×C8×C11C2311yescharacteristic
25C2×C42×C11D411yescharacteristic
26C2×C4⋊Dic11—42no—
27C2×#4318—21no—
28C2×Dic44—22no—
29C2×Dic44—22no—
30C2×Dic44—22no—
31C2×Dic44—22no—
32C2×Dic44—24no—
33C2×Dic44—22no—
34C2×Dic44—42no—
35C2×Dic44—42no—
36C2×Dic44D411yescharacteristic
37C2×Dic44D414yes—
38#66957—22no—
39#66957—22no—
40C2×D88D411yescharacteristic
41C2×#4314—21no—
42#66922—24no—
43#66922—42no—
44C11×M32—22no—
45C11×M32D414yes—
46C2×C11×C16—22no—
47C4×C8×C11—22no—
48(C2×D11)⋊C8—42no—
49#66883—22no—
50#66869—42no—
51Dic88—28no—
52#66864—28no—
53#13333—111nomaximal, Sylow
54C22×C4×C11—21no—
55C22×C4×C11C2×D411yescharacteristic
56C2×C22⋊D11—41no—
57C22×Dic11—42no—
58#4339—41no—
59#4339—41no—
60#4339—41no—
61#4339—41no—
62C2×D44—21no—
63C2×C4×D11—41no—
64C2×Dic22—24no—
65C2×Dic22—21no—
66C2×Dic22—42no—
67C2×Dic22—42no—
68C2×Dic22—42no—
69C2×Dic22—42no—
70C2×Dic22—42no—
71C2×C8×C11—21no—
72C2×C8×C11—21no—
73C2×C8×C11D812yes—
74C2×C8×C11C2×D412yes—
75C2×C8×C11C2×D411yescharacteristic
76C2×C8×C11C2×D412yes—
77C2×C8×C11#4111yescharacteristic
78C42×C11—21no—
79C42×C11D812yes—
80C4⋊Dic11—48no—
81#4318—41no—
82#4318—41no—
83C2×C11⋊C8—41no—
84Dic44—24no—
85Dic44—22no—
86Dic44—24no—
87Dic44—48no—
88Dic44—42no—
89Dic44—42no—
90D88—22no—
91#4314—42no—
92C11×C16—24no—
93C2×#510—112no—
94C2×#494—111no—
95C2×#362—112no—
96#1974—111no—
97#1376D1111yescharacteristic, complemented
98C23×C11AGL(1,ℤ/8)11yescharacteristic
99C22×D11—41no—
100C2×C4×C11—24no—
101C2×C4×C11—22no—
102C2×C4×C11#12011yescharacteristic
103C2×C4×C11#12111yescharacteristic
104C2×C4×C11#12711yescharacteristic
105C2×C4×C11C2×D811yescharacteristic
106C2×C4×C11C2×D811yescharacteristic
107C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
108C22⋊D11—81no—
109C22⋊D11—81no—
110C2×Dic11—44no—
111C2×Dic11—41no—
112C2×Dic11—82no—
113C2×Dic11—82no—
114D44—41no—
115D44—41no—
116C4×D11—81no—
117C4×D11—81no—
118Dic22—41no—
119Dic22—44no—
120Dic22—44no—
121Dic22—41no—
122Dic22—82no—
123Dic22—82no—
124C8×C11—22no—
125C8×C11#12012yes—
126C8×C11#12112yes—
127C11⋊C8—81no—
128C2×#135—111no—
129C22×Q16—112no—
130C22×Q16—221no—
131C2×C4⋊Q8—221no—
132#510—224no—
133#510—224no—
134C2×Q32—222no—
135C2×SD32—222no—
136C2×M32C2×D1112yes—
137#494—224no—
138C2×#108—111no—
139C2×#104—221no—
140#408—221no—
141C2×C4×C8C2×D1111yescharacteristic
142#362—224no—
143C22×C11—22no—
144C22×C11#44711yescharacteristic
145C22×C11#45911yescharacteristic
146C22×C11#49611yescharacteristic
147C2×D11—82no—
148C2×D11—81no—
149C4×C11—24no—
150C4×C11#39211yescharacteristic
151C4×C11#44711yescharacteristic
152C4×C11#45911yescharacteristic
153C4×C11#49311yescharacteristic
154Dic11—84no—
155Dic11—81no—
156C2×#41—221no—
157C22×Q8—222no—
158#135—222no—
159#135—222no—
160C2×Q16—114no—
161C2×Q16—111no—
162C2×Q16—224no—
163C2×Q16—222no—
164C2×Q16—222no—
165C2×Q16—222no—
166C2×Q16—222no—
167C2×Q16—222no—
168C2×Q16—442no—
169C2×Q16—442no—
170C2×SD16—221no—
171C2×D8—111no—
172C2×M16—221no—
173C22×C8D4411yescharacteristic
174C22×C8C22×D1111yescharacteristic
175C4⋊Q8—224no—
176C4⋊Q8—442no—
177C2×C4⋊C4—442no—
178C2×C42D4411yescharacteristic
179Q32—228no—
180SD32—228no—
181M32—22no—
182M32D4414yes—
183C2×C16—22no—
184#108—222no—
185#104—442no—
186C22⋊C8—442no—
187C4×C8—22no—
188C2×C11—21no—
189C2×C11—21no—
190C2×C11#201111yescharacteristic
191C2×C11#221412yes—
192D11—161no—
193#41—441no—
194#41—441no—
195#41—441no—
196#41—441no—
197C2×Q8—224no—
198C2×Q8—221no—
199C2×Q8—442no—
200C2×Q8—442no—
201C2×Q8—442no—
202C2×Q8—442no—
203C2×Q8—442no—
204C2×D4—221no—
205C2×D4—441no—
206C22×C4—21no—
207C22×C4—442no—
208C22×C4—441no—
209C22×C4C2×D4411yescharacteristic
210Q16—224no—
211Q16—222no—
212Q16—224no—
213Q16—448no—
214Q16—442no—
215Q16—442no—
216SD16—442no—
217D8—222no—
218M16—441no—
219M16—441no—
220C2×C8—21no—
221C2×C8—21no—
222C2×C8—441no—
223C2×C8D8812yes—
224C2×C8C2×D4412yes—
225C2×C8D4×D1111yescharacteristic
226C2×C8D4×D1112yes—
227C2×C8#434311yescharacteristic
228C4⋊C4—448no—
229C42—21no—
230C42D8812yes—
231C16—24no—
232C11#1333311yescharacteristic, complemented, Sylow
233C23—441no—
234C23#6696111yescharacteristic
235Q8—441no—
236Q8—444no—
237Q8—444no—
238Q8—441no—
239Q8—882no—
240Q8—882no—
241D4—441no—
242D4—441no—
243D4—881no—
244D4—881no—
245C2×C4—24no—
246C2×C4—22no—
247C2×C4—444no—
248C2×C4—441no—
249C2×C4—882no—
250C2×C4—882no—
251C2×C4—881no—
252C2×C4—881no—
253C2×C4#6692711yescharacteristic
254C2×C4#6693511yescharacteristic
255C2×C4#6694811yescharacteristic
256C2×C4C2×D8811yescharacteristic
257C2×C4C2×D8811yescharacteristic
258C2×C4#6696111yescharacteristic
259C8—22no—
260C8—881no—
261C8#6693512yes—
262C8#6694812yes—
263C22—22no—
264C22—882no—
265C22—881no—
266C22#1062232511yescharacteristic
267C22#1062234511yescharacteristic
268C22#1062245611yescharacteristic
269C4—24no—
270C4—881no—
271C4—884no—
272C4#1062228411yescharacteristic
273C4#1062230811yescharacteristic
274C4#1062234511yescharacteristic
275C4#1062245611yescharacteristic
276C2—21no—
277C2—21no—
278C2—1761no—
279C2#1306968911yescharacteristic
280C2#1307069812yes—
subgroupG/H
centerC22#10622456
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1376C2
socleC22×C11#459
prime radicalC2×#66957C22
hypercenter#1376D11
hypocenterC11#13333
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1376

Complements

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

NH ≅ G/Ntype
2. C2×#10622312C2semidirect
3. C2×#10622155C2semidirect
5. C11×#1376C2semidirect
97. #1376D11semidirect
232. C11#13333semidirect

Maximal subgroups

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

subgroupindex
C2×#106225222
C2×#106223122
C2×#106221552
#130695042
C11×#13762
#1333311