Finite Group Databasebeta

← #14667465

Subgroups — #14667465

Order 2816.

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

normal subgroups only

This group has 304 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×Dic44C211yesmaximal, characteristic, complemented
2#13070840C211yesmaximal, characteristic
3#13070657C211yesmaximal, characteristic
4#13067976C211yesmaximal, characteristic
5#13066673C211yesmaximal, characteristic, complemented
6#13066581C211yesmaximal, characteristic, complemented
7C11×Q8⋊C16C211yesmaximal, characteristic, complemented
8Q8×Dic22—21no—
9C8×Q8×C11C2211yescharacteristic
10#10622640—21no—
11C2×#66864—21no—
12#10622463—21no—
13#10622463—22no—
14C4×Dic44—21no—
15C4×Dic44C2211yescharacteristic
16#10622308C2211yescharacteristic
17#10622295—21no—
18#10622295C2211yescharacteristic
19C11×C4⋊C16C2211yescharacteristic
20C4×C11×C16C2211yescharacteristic
21#10622147—21no—
22#10622147—22no—
23#10622123—21no—
24#10622096C2211yescharacteristic
25C4×Q8×C11D411yescharacteristic
26Q8×Dic11—41no—
27C2×#4325—41no—
28C2×Dic44D411yescharacteristic
29C2×D88—21no—
30C2×D88—21no—
31#66941—42no—
32#66941—41no—
33#66927—21no—
34#66922—22no—
35#66922—21no—
36C4×Dic22—22no—
37C4×Dic22—21no—
38C2×C11×C16—21no—
39C2×C11×C16—21no—
40C11×C4⋊C8—21no—
41C11×C4⋊C8D411yescharacteristic
42C4×C8×C11—21no—
43C4×C8×C11C2311yescharacteristic
44#66882—22no—
45#66882—21no—
46#66882D411yescharacteristic
47#66882D412yes—
48#66880—22no—
49#66880—21no—
50#66873—41no—
51C4⋊(C11⋊C8)—21no—
52#66864—42no—
53#12354—111nomaximal, Sylow
54C2×Q8×C11D811yescharacteristic
55C2×D44—41no—
56C2×D44—41no—
57C2×D44—41no—
58C2×Dic22—21no—
59C2×Dic22—42no—
60C2×Dic22—41no—
61C2×C8×C11—21no—
62C2×C8×C11C2×D411yescharacteristic
63C2×C8×C11C2×D411yescharacteristic
64C11×C4⋊C4—21no—
65C11×C4⋊C4D811yescharacteristic
66C42×C11—21no—
67C42×C11C2×D411yescharacteristic
68#4325—82no—
69C4⋊Dic11—22no—
70C4⋊Dic11—21no—
71C4⋊Dic11—42no—
72C4⋊Dic11—41no—
73Dic11⋊C4—42no—
74Dic11⋊C4—41no—
75C4×Dic11—42no—
76C4×Dic11—41no—
77C2×C11⋊C8—41no—
78Dic44—21no—
79Dic44SD1612yescomplemented
80D88—42no—
81D88—41no—
82D88—41no—
83C11×C16—41no—
84C11×C16—41no—
85Q8×Q16—111no—
86#2240—111no—
87#2207—111no—
88#1668—111no—
89#1365—111no—
90Q8⋊C16D1111yescharacteristic, complemented
91#1332—111no—
92C22×D11—81no—
93Q8×C11—21no—
94Q8×C11SD3212yescomplemented
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11#12011yescharacteristic
98C2×C4×C11C2×D811yescharacteristic
99C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
100C2×Dic11—41no—
101C2×Dic11—42no—
102C2×Dic11—41no—
103D44—81no—
104D44—81no—
105D44—81no—
106D44—81no—
107D44—161no—
108Dic22—22no—
109Dic22—41no—
110Dic22—161no—
111Dic22—162no—
112C8×C11—21no—
113C8×C11—41no—
114C8×C11C2×SD1611yescharacteristic
115C8×C11#13711yescharacteristic
116C11⋊C8—81no—
117Q82—221no—
118C2×SD32—221no—
119#500—111no—
120#500—221no—
121#493—111no—
122#477—222no—
123#477—221no—
124#460—221no—
125C8×Q8C2×D1111yescharacteristic
126C4×Q16—111no—
127C4×Q16—221no—
128C4⋊C16C2×D1111yescharacteristic
129#357—221no—
130#357—222no—
131C4×C16C2×D1111yescharacteristic
132#335—111no—
133#331—221no—
134C22×C11#44711yescharacteristic
135C2×D11—161no—
136C2×D11—161no—
137C2×D11—161no—
138C4×C11—22no—
139C4×C11—21no—
140C4×C11—41no—
141C4×C11#44811yescharacteristic
142C4×C11#45411yescharacteristic
143C4×C11C2×SD3211yescharacteristic
144C4×C11#51011yescharacteristic
145Dic11—42no—
146Dic11—82no—
147Dic11—81no—
148C2×Q16—111no—
149C2×SD16—441no—
150C2×D8—221no—
151C2×D8—221no—
152C4⋊Q8—222no—
153C4⋊Q8—221no—
154C4⋊Q8—442no—
155C4⋊Q8—441no—
156#127—221no—
157C4×Q8—222no—
158C4×Q8—221no—
159C4×Q8—441no—
160C4×Q8D4411yescharacteristic
161SD32—442no—
162C2×C16—21no—
163C2×C16—21no—
164#107—111no—
165#107—112no—
166#107—222no—
167#107—221no—
168C4⋊C8—21no—
169C4⋊C8—221no—
170C4⋊C8D4411yescharacteristic
171#103—222no—
172#103—221no—
173#102—441no—
174C4×C8—21no—
175C4×C8C22×D1111yescharacteristic
176C2×C11#162711yescharacteristic
177C2×C11#218511yescharacteristic
178C2×C11#219211yescharacteristic
179D11—321no—
180C2×Q8—221no—
181C2×Q8—442no—
182C2×Q8—441no—
183C2×Q8D8811yescharacteristic
184C2×D4—441no—
185C2×D4—441no—
186C2×D4—441no—
187Q16—112no—
188Q16—221no—
189SD16—882no—
190D8—442no—
191D8—441no—
192D8—441no—
193C2×C8—21no—
194C2×C8—441no—
195C2×C8D4×D1111yescharacteristic
196C2×C8D4×D1111yescharacteristic
197C4⋊C4—21no—
198C4⋊C4—222no—
199C4⋊C4—221no—
200C4⋊C4—442no—
201C4⋊C4—442no—
202C4⋊C4—441no—
203C4⋊C4—441no—
204C4⋊C4D8811yescharacteristic
205C42—21no—
206C42—442no—
207C42—441no—
208C42C2×D4411yescharacteristic
209C16—41no—
210C16—41no—
211C11#1235411yescharacteristic, complemented, Sylow
212C23—881no—
213Q8—21no—
214Q8—222no—
215Q8—441no—
216Q8—1761no—
217Q8—1762no—
218Q8#6686412yescomplemented
219D4—881no—
220D4—881no—
221D4—881no—
222D4—881no—
223D4—1761no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—441no—
227C2×C4—442no—
228C2×C4—441no—
229C2×C4#6693511yescharacteristic
230C2×C4C2×D8811yescharacteristic
231C2×C4#6696111yescharacteristic
232C8—21no—
233C8—41no—
234C8—881no—
235C8SD16×D1111yescharacteristic
236C8#6697111yescharacteristic
237C22—1761no—
238C22—1761no—
239C22—1761no—
240C22#1062234511yescharacteristic
241C4—22no—
242C4—21no—
243C4—41no—
244C4—442no—
245C4—882no—
246C4—881no—
247C4#1062241911yescharacteristic
248C4#1062244011yescharacteristic
249C4C2×#6686411yescharacteristic
250C4#1062252211yescharacteristic
251C2—3521no—
252C2#1306772111yescharacteristic
253C2#1307053511yescharacteristic
254C2#1307057511yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×Q8⋊C16C2
socleC22×C11#447
prime radical#10622308C22
hypercenterQ8⋊C16D11
hypocenterC11#12354
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×Dic44C2semidirect
5. #13066673C2semidirect
6. #13066581C2semidirect
7. C11×Q8⋊C16C2semidirect
79. Dic44SD16semidirect
90. Q8⋊C16D11semidirect
94. Q8×C11SD32semidirect
211. C11#12354semidirect
218. Q8#66864semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic442
#130708402
#130706572
#130679762
#130666732
#130665812
C11×Q8⋊C162
#1235411