Finite Group Databasebeta

← #14667656

Subgroups — #14667656

Order 2816.

294 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 67 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
1#13081605C211yesmaximal, characteristic
2#13070845C211yesmaximal, characteristic, complemented
3#13070750C211yesmaximal, characteristic
4#13066664C211yesmaximal, characteristic, complemented
5Q8⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
6#13066576C211yesmaximal, characteristic
7C11×#1674C211yesmaximal, characteristic, complemented
8#10623115—21no—
9C11×#500C2211yescharacteristic
10C11×#462—21no—
11C8×Q8×C11C2211yescharacteristic
12#10622458—22no—
13#10622454—21no—
14#10622312C2211yescharacteristic
15C4×Dic44—21no—
16#10622309—21no—
17C4×D88C2211yescharacteristic
18C11×#335C2211yescharacteristic
19C11×#332—21no—
20#10622130—22no—
21#10622129—21no—
22#10622127—21no—
23C4⋊(C11⋊C16)C2211yescharacteristic
24C4×C11⋊C16C2211yescharacteristic
25C2×C11×Q16—41no—
26C11×C4⋊Q8—21no—
27C4×Q8×C11D411yescharacteristic
28#66999—41no—
29C2×Dic44—21no—
30C2×Dic44D412yes—
31C2×D88D411yescharacteristic
32C2×#4314—22no—
33#66951—42no—
34#66945—41no—
35#66928—22no—
36C4×D44—21no—
37#66922—21no—
38C4×Dic22—22no—
39C11×#107—21no—
40C11×#107—21no—
41C11×C4⋊C8—21no—
42C11×C4⋊C8—21no—
43C11×C4⋊C8D411yescharacteristic
44C11×#103—41no—
45C4×C8×C11—21no—
46C4×C8×C11C2311yescharacteristic
47#66885—21no—
48#66882D411yescharacteristic
49#66880—22no—
50C2×C11⋊C16—21no—
51C2×C11⋊C16—21no—
52#12383—111nomaximal, Sylow
53C2×Q8×C11—41no—
54C2×Q8×C11D811yescharacteristic
55C2×D44—21no—
56C2×C4×D11—41no—
57C2×Dic22—22no—
58C11×Q16—82no—
59C2×C8×C11—21no—
60C2×C8×C11—41no—
61C2×C8×C11C2×D411yescharacteristic
62C2×C8×C11C2×D411yescharacteristic
63C11×C4⋊C4—21no—
64C11×C4⋊C4—41no—
65C11×C4⋊C4—41no—
66C11×C4⋊C4D811yescharacteristic
67C42×C11—21no—
68C42×C11C2×D411yescharacteristic
69(C2×D11)⋊C4—42no—
70(C2×D11)⋊C4—42no—
71(C2×D11)⋊C4—41no—
72C4⋊Dic11—21no—
73C4⋊Dic11—41no—
74C4⋊Dic11—41no—
75Dic11⋊C4—42no—
76C4×Dic11—42no—
77Dic44—42no—
78Dic44—41no—
79Dic44—41no—
80D88—21no—
81D88—21no—
82#4314—82no—
83C11⋊C16—41no—
84C11⋊C16—41no—
85#3393—111no—
86#2241—111no—
87#2224—111no—
88#1674D1111yescharacteristic, complemented
89#1362—111no—
90Q8⋊C16—111no—
91#1331—111no—
92C22×D11—41no—
93Q8×C11—21no—
94Q8×C11—21no—
95Q8×C11—81no—
96Q8×C11—81no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—81no—
100C2×C4×C11#12011yescharacteristic
101C2×C4×C11C2×D811yescharacteristic
102C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
103C2×Dic11—41no—
104C2×Dic11—42no—
105D44—41no—
106D44—41no—
107C4×D11—81no—
108C4×D11—81no—
109Dic22—42no—
110Dic22—42no—
111C8×C11—21no—
112C8×C11—41no—
113C8×C11—81no—
114C8×C11#13511yescharacteristic
115C8×C11#13711yescharacteristic
116#556—221no—
117#500C2×D1111yescharacteristic
118#495—221no—
119#494—111no—
120#464—222no—
121#462—21no—
122#461—221no—
123C8×Q8C2×D1111yescharacteristic
124C4×Q16—221no—
125C4×D8—111no—
126#366—221no—
127C4⋊C16—111no—
128#358—222no—
129#357—221no—
130C4×C16—111no—
131#335C2×D1111yescharacteristic
132#332—21no—
133C22×C11#44711yescharacteristic
134C2×D11—81no—
135C2×D11—81no—
136C2×D11—81no—
137C4×C11—21no—
138C4×C11—41no—
139C4×C11—41no—
140C4×C11—161no—
141C4×C11#45211yescharacteristic
142C4×C11#45511yescharacteristic
143C4×C11#50811yescharacteristic
144C4×C11#50911yescharacteristic
145Dic11—82no—
146Dic11—81no—
147C2×Q16—41no—
148C2×Q16—112no—
149C2×Q16—221no—
150C2×SD16—222no—
151C2×D8—111no—
152C4⋊Q8—21no—
153C4⋊Q8—221no—
154#126—442no—
155#124—222no—
156C22⋊Q8—441no—
157C4×Q8—222no—
158C4×Q8C22⋊D1111yescharacteristic
159C4×D4—221no—
160#117—441no—
161C2×C16—221no—
162C2×C16—221no—
163#107—21no—
164#107—21no—
165#107—111no—
166C4⋊C8—21no—
167C4⋊C8—21no—
168C4⋊C8C22⋊D1111yescharacteristic
169#103—41no—
170#103—222no—
171#102—221no—
172C4×C8—21no—
173C4×C8C22×D1111yescharacteristic
174C2×C11#164111yescharacteristic
175C2×C11#218611yescharacteristic
176C2×C11#219511yescharacteristic
177D11—161no—
178C2×Q8—41no—
179C2×Q8—222no—
180C2×Q8#432311yescharacteristic
181C2×D4—221no—
182C22×C4—441no—
183Q16—82no—
184Q16—442no—
185Q16—441no—
186Q16—441no—
187SD16—882no—
188D8—221no—
189D8—221no—
190C2×C8—21no—
191C2×C8—41no—
192C2×C8D4×D1111yescharacteristic
193C2×C8D4×D1111yescharacteristic
194C4⋊C4—21no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—221no—
198C4⋊C4—442no—
199C4⋊C4—441no—
200C4⋊C4—441no—
201C4⋊C4#432311yescharacteristic
202C22⋊C4—442no—
203C22⋊C4—442no—
204C22⋊C4—441no—
205C42—21no—
206C42—442no—
207C42C2×C22⋊D1111yescharacteristic
208C16—441no—
209C16—441no—
210C11#1238311yescharacteristic, complemented, Sylow
211C23—441no—
212Q8—21no—
213Q8—21no—
214Q8—81no—
215Q8—81no—
216Q8—442no—
217Q8—442no—
218D4—441no—
219D4—441no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—81no—
223C2×C4—441no—
224C2×C4—442no—
225C2×C4—881no—
226C2×C4—881no—
227C2×C4C2×#432311yescharacteristic
228C2×C4#6699011yescharacteristic
229C2×C4#6700211yescharacteristic
230C8—21no—
231C8—41no—
232C8—81no—
233C8#6697111yescharacteristic
234C8#6697211yescharacteristic
235C22—881no—
236C22—881no—
237C22—881no—
238C22#1062264911yescharacteristic
239C4—21no—
240C4—41no—
241C4—41no—
242C4—161no—
243C4—882no—
244C4—881no—
245C4#1062276011yescharacteristic
246C4#1062280011yescharacteristic
247C4#1062280711yescharacteristic
248C4#1062281511yescharacteristic
249C2—1761no—
250C2#1306780711yescharacteristic
251C2#1307053711yescharacteristic
252C2#1307059211yescharacteristic
subgroupG/H
centerC22#10622649
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1674C2
socleC22×C11#447
prime radicalC2×D88D4
hypercenter#1674D11
hypocenterC11#12383
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #1674

Complements

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

NH ≅ G/Ntype
2. #13070845C2semidirect
4. #13066664C2semidirect
5. Q8⋊(C11⋊C16)C2semidirect
7. C11×#1674C2semidirect
88. #1674D11semidirect
210. C11#12383semidirect

Maximal subgroups

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

subgroupindex
#130816052
#130708452
#130707502
#130666642
Q8⋊(C11⋊C16)2
#130665762
C11×#16742
#1238311