Finite Group Databasebeta

← #14667451

Subgroups — #14667451

Order 2816.

338 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 73 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
1Q8×D88C211yesmaximal, characteristic, complemented
2#13070840C211yesmaximal, characteristic, complemented
3#13070652C211yesmaximal, characteristic
4#13067976C211yesmaximal, characteristic, complemented
5#13066670C211yesmaximal, characteristic, complemented
6#13066578C211yesmaximal, characteristic, complemented
7C11×Q8⋊C16C211yesmaximal, characteristic, complemented
8Q8×D44—21no—
9C8×Q8×C11C2211yescharacteristic
10#10622640—21no—
11C2×D176—21no—
12#10622459—21no—
13#10622459—22no—
14#10622308C2211yescharacteristic
15C4×D88—21no—
16C4×D88C2211yescharacteristic
17#10622295—21no—
18#10622295C2211yescharacteristic
19C11×C4⋊C16C2211yescharacteristic
20C4×C11×C16C2211yescharacteristic
21#10622147—21no—
22#10622147—22no—
23#10622123—21no—
24#10622096C2211yescharacteristic
25C2×Q8×D11—41no—
26C4×Q8×C11D411yescharacteristic
27C2×#4325—41no—
28C2×D88—21no—
29C2×D88—21no—
30C2×D88D411yescharacteristic
31#66950—42no—
32#66950—41no—
33#66927—21no—
34C4×D44—22no—
35C4×D44—21no—
36#66922—22no—
37#66922—21no—
38C2×C11×C16—21no—
39C2×C11×C16—21no—
40C11×C4⋊C8—21no—
41C11×C4⋊C8D411yescharacteristic
42C4×C8×C11—21no—
43C4×C8×C11C2311yescharacteristic
44#66885—22no—
45#66885—21no—
46#66882—22no—
47#66882—21no—
48#66882D411yescharacteristic
49#66882D412yes—
50#66873—41no—
51C4⋊(C11⋊C8)—21no—
52D176—42no—
53#12352—111nomaximal, Sylow
54C2×Q8×C11D811yescharacteristic
55Q8×D11—82no—
56Q8×D11—82no—
57C2×D44—21no—
58C2×D44—41no—
59C2×D44—41no—
60C2×D44—41no—
61C2×C4×D11—42no—
62C2×C4×D11—41no—
63C2×Dic22—42no—
64C2×Dic22—41no—
65C2×C8×C11—21no—
66C2×C8×C11C2×D411yescharacteristic
67C2×C8×C11C2×D411yescharacteristic
68C11×C4⋊C4—21no—
69C11×C4⋊C4D811yescharacteristic
70C42×C11—21no—
71C42×C11C2×D411yescharacteristic
72#4325—82no—
73(C2×D11)⋊C4—42no—
74(C2×D11)⋊C4—41no—
75C4⋊Dic11—21no—
76C4⋊Dic11—22no—
77C4⋊Dic11—42no—
78C4⋊Dic11—41no—
79C2×C11⋊C8—41no—
80D88—21no—
81D88—42no—
82D88—41no—
83D88—41no—
84D88SD1612yescomplemented
85C11×C16—41no—
86C11×C16—41no—
87Q8×D8—111no—
88#2240—111no—
89#2206—111no—
90#1668—111no—
91#1364—111no—
92Q8⋊C16D1111yescharacteristic, complemented
93#1331—111no—
94C22×D11—41no—
95C22×D11—81no—
96Q8×C11—21no—
97Q8×C11D1612yescomplemented
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11#12011yescharacteristic
101C2×C4×C11C2×D811yescharacteristic
102C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
103C2×Dic11—41no—
104C2×Dic11—42no—
105D44—22no—
106D44—41no—
107D44—81no—
108D44—81no—
109D44—81no—
110D44—81no—
111D44—161no—
112C4×D11—84no—
113C4×D11—81no—
114C4×D11—81no—
115Dic22—84no—
116Dic22—81no—
117Dic22—81no—
118C8×C11—21no—
119C8×C11—41no—
120C8×C11C2×SD1611yescharacteristic
121C8×C11#13711yescharacteristic
122C11⋊C8—81no—
123D4×Q8—221no—
124C2×D16—221no—
125#500—111no—
126#500—221no—
127#493—111no—
128#474—222no—
129#474—221no—
130#460—221no—
131C8×Q8C2×D1111yescharacteristic
132C4×D8—111no—
133C4×D8—221no—
134C4⋊C16C2×D1111yescharacteristic
135#357—221no—
136#357—222no—
137C4×C16C2×D1111yescharacteristic
138#335—111no—
139#331—221no—
140C22×C11#44711yescharacteristic
141C2×D11—42no—
142C2×D11—81no—
143C2×D11—81no—
144C2×D11—161no—
145C2×D11—161no—
146C2×D11—161no—
147C4×C11—22no—
148C4×C11—21no—
149C4×C11—41no—
150C4×C11#44811yescharacteristic
151C4×C11#45411yescharacteristic
152C4×C11C2×D1611yescharacteristic
153C4×C11#50911yescharacteristic
154Dic11—81no—
155Dic11—82no—
156C22×Q8—441no—
157C2×SD16—441no—
158C2×D8—111no—
159C2×D8—221no—
160C2×D8—221no—
161C4⋊Q8—222no—
162C4⋊Q8—221no—
163#127—221no—
164C22⋊Q8—442no—
165C22⋊Q8—441no—
166C4×Q8D4411yescharacteristic
167C4×D4—222no—
168C4×D4—221no—
169D16—442no—
170C2×C16—21no—
171C2×C16—21no—
172#107—111no—
173#107—112no—
174#107—222no—
175#107—221no—
176C4⋊C8—21no—
177C4⋊C8—221no—
178C4⋊C8D4411yescharacteristic
179#102—222no—
180#102—221no—
181#102—441no—
182C4×C8—21no—
183C4×C8C22×D1111yescharacteristic
184C2×C11#162711yescharacteristic
185C2×C11#218411yescharacteristic
186C2×C11#219311yescharacteristic
187D11—82no—
188D11—321no—
189C2×Q8—442no—
190C2×Q8—441no—
191C2×Q8—882no—
192C2×Q8—882no—
193C2×Q8D8811yescharacteristic
194C2×D4—221no—
195C2×D4—441no—
196C2×D4—441no—
197C2×D4—441no—
198C22×C4—442no—
199C22×C4—441no—
200SD16—882no—
201D8—112no—
202D8—221no—
203D8—442no—
204D8—441no—
205D8—441no—
206C2×C8—21no—
207C2×C8—441no—
208C2×C8D4×D1111yescharacteristic
209C2×C8D4×D1111yescharacteristic
210C4⋊C4—21no—
211C4⋊C4—222no—
212C4⋊C4—221no—
213C4⋊C4—442no—
214C4⋊C4—441no—
215C4⋊C4D8811yescharacteristic
216C22⋊C4—442no—
217C22⋊C4—441no—
218C42—21no—
219C42C2×D4411yescharacteristic
220C16—41no—
221C16—41no—
222C11#1235211yescharacteristic, complemented, Sylow
223C23—441no—
224C23—881no—
225Q8—21no—
226Q8—884no—
227Q8—881no—
228Q8—881no—
229Q8D17612yescomplemented
230D4—222no—
231D4—441no—
232D4—881no—
233D4—881no—
234D4—881no—
235D4—881no—
236D4—1761no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—442no—
240C2×C4—441no—
241C2×C4—884no—
242C2×C4—881no—
243C2×C4—881no—
244C2×C4#6693511yescharacteristic
245C2×C4C2×D8811yescharacteristic
246C2×C4#6696111yescharacteristic
247C8—21no—
248C8—41no—
249C8—881no—
250C8SD16×D1111yescharacteristic
251C8#6697111yescharacteristic
252C22—442no—
253C22—881no—
254C22—881no—
255C22—1761no—
256C22—1761no—
257C22—1761no—
258C22#1062234511yescharacteristic
259C4—22no—
260C4—21no—
261C4—41no—
262C4—882no—
263C4—881no—
264C4#1062241911yescharacteristic
265C4#1062244011yescharacteristic
266C4C2×D17611yescharacteristic
267C4#1062252111yescharacteristic
268C2—882no—
269C2—3521no—
270C2#1306772111yescharacteristic
271C2#1307053011yescharacteristic
272C2#1307058211yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×Q8⋊C16C2
socleC22×C11#447
prime radical#13070652C2
hypercenterQ8⋊C16D11
hypocenterC11#12352
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ Q8⋊C16

Complements

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

NH ≅ G/Ntype
1. Q8×D88C2semidirect
2. #13070840C2semidirect
4. #13067976C2semidirect
5. #13066670C2semidirect
6. #13066578C2semidirect
7. C11×Q8⋊C16C2semidirect
84. D88SD16semidirect
92. Q8⋊C16D11semidirect
97. Q8×C11D16semidirect
222. C11#12352semidirect
229. Q8D176semidirect

Maximal subgroups

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

subgroupindex
Q8×D882
#130708402
#130706522
#130679762
#130666702
#130665782
C11×Q8⋊C162
#1235211