Finite Group Databasebeta

← #14667737

Subgroups — #14667737

Order 2816.

292 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 71 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#13081009C211yesmaximal, characteristic
2#13070898C211yesmaximal, characteristic, complemented
3#13070759C211yesmaximal, characteristic, complemented
4#13068005C211yesmaximal, characteristic
5#13066673C211yesmaximal, characteristic, complemented
6#13066581C211yesmaximal, characteristic, complemented
7C11×D4⋊C16C211yesmaximal, characteristic
8#10623074—21no—
9C8×D4×C11C2211yescharacteristic
10#10622729—21no—
11C2×#66882—21no—
12#10622632—21no—
13#10622463—21no—
14#10622335—22no—
15C4×Dic44C2211yescharacteristic
16#10622295C2211yescharacteristic
17#10622295C2211yescharacteristic
18C11×C4⋊C16C2211yescharacteristic
19C4×C11×C16C2211yescharacteristic
20#10622143—22no—
21#10622143—21no—
22#10622141—21no—
23#10622124—21no—
24#10622096C2211yescharacteristic
25C22×C8×C11—21no—
26C4×D4×C11D411yescharacteristic
27D4×Dic11—41no—
28C2×#4324—41no—
29C2×C4⋊Dic11—22no—
30#66977—22no—
31C2×Dic44D411yescharacteristic
32#66943—41no—
33#66931—42no—
34#66922—21no—
35#66922—21no—
36C4×Dic22—21no—
37C2×C11×C16—21no—
38C2×C11×C16—21no—
39C11×C4⋊C8D411yescharacteristic
40C11×C22⋊C8—21no—
41C4×C8×C11C2311yescharacteristic
42#66882—22no—
43#66882—21no—
44#66882—21no—
45#66882—21no—
46#66882D412yes—
47#66882D411yescharacteristic
48#66880—22no—
49#66880—21no—
50#66874—41no—
51C4⋊(C11⋊C8)—21no—
52#12394—111nomaximal, Sylow
53C2×D4×C11D811yescharacteristic
54C22×C4×C11—21no—
55C22×Dic11—42no—
56C2×Dic22—21no—
57C2×Dic22—41no—
58C2×Dic22—41no—
59C2×C8×C11—21no—
60C2×C8×C11—41no—
61C2×C8×C11—41no—
62C2×C8×C11C2×D411yescharacteristic
63C2×C8×C11C2×D411yescharacteristic
64C11×C4⋊C4D811yescharacteristic
65C11×C22⋊C4—21no—
66C42×C11C2×D411yescharacteristic
67C22⋊Dic11—42no—
68#4324—82no—
69C4⋊Dic11—21no—
70C4⋊Dic11—22no—
71C4⋊Dic11—42no—
72C4⋊Dic11—41no—
73C4⋊Dic11—41no—
74C4⋊Dic11—41no—
75Dic11⋊C4—42no—
76Dic11⋊C4—41no—
77C4×Dic11—41no—
78C2×C11⋊C8—41no—
79Dic44—21no—
80Dic44—21no—
81C11×C16—22no—
82C11×C16—41no—
83#3338—111no—
84#2254—111no—
85#2225—111no—
86#1673—111no—
87#1365—111no—
88#1332—111no—
89D4⋊C16D1111yescharacteristic
90C23×C11—21no—
91D4×C11—21no—
92D4×C11SD3212yes—
93C2×C4×C11—21no—
94C2×C4×C11—41no—
95C2×C4×C11—41no—
96C2×C4×C11#12011yescharacteristic
97C2×C4×C11C2×D811yescharacteristic
98C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
99C2×Dic11—41no—
100C2×Dic11—41no—
101C2×Dic11—42no—
102C2×Dic11—81no—
103C2×Dic11—162no—
104Dic22—41no—
105Dic22—41no—
106Dic22—81no—
107Dic22—81no—
108Dic22—161no—
109C8×C11—21no—
110C8×C11—41no—
111C8×C11#13511yescharacteristic
112C8×C11#13711yescharacteristic
113C11⋊C8—81no—
114#554—221no—
115#500—111no—
116#500—111no—
117#484—222no—
118#477—221no—
119#467—221no—
120#461—221no—
121C4×Q16—111no—
122C8×D4C2×D1111yescharacteristic
123C2×#107—221no—
124#367—221no—
125#367—222no—
126C4⋊C16C2×D1111yescharacteristic
127#358—221no—
128C4×C16C2×D1111yescharacteristic
129#335—111no—
130#332—221no—
131C22×C11—22no—
132C22×C11—41no—
133C22×C11—41no—
134C22×C11#44711yescharacteristic
135C4×C11—21no—
136C4×C11—41no—
137C4×C11#45211yescharacteristic
138C4×C11#45611yescharacteristic
139C4×C11C2×SD3211yescharacteristic
140C4×C11#51011yescharacteristic
141Dic11—81no—
142Dic11—82no—
143Dic11—81no—
144Dic11—161no—
145C2×Q16—111no—
146C2×SD16—441no—
147C22×C8—21no—
148C4⋊Q8—221no—
149C4⋊Q8—221no—
150#125—441no—
151C22⋊Q8—222no—
152C22⋊Q8—442no—
153C4×Q8—221no—
154C4×D4—441no—
155C4×D4D4411yescharacteristic
156C2×C4⋊C4—222no—
157C2×C16—21no—
158C2×C16—21no—
159#107—111no—
160#107—112no—
161#107—222no—
162#107—221no—
163#107—221no—
164#107—221no—
165C4⋊C8—221no—
166C4⋊C8D4411yescharacteristic
167#103—222no—
168#103—221no—
169#103—441no—
170C22⋊C8—21no—
171C4×C8C22×D1111yescharacteristic
172C2×C11—42no—
173C2×C11#164711yescharacteristic
174C2×C11#218511yescharacteristic
175C2×C11#219411yescharacteristic
176C2×Q8—221no—
177C2×Q8—441no—
178C2×Q8—441no—
179C2×D4D8811yescharacteristic
180C22×C4—21no—
181C22×C4—442no—
182Q16—221no—
183Q16—221no—
184SD16—882no—
185C2×C8—21no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—441no—
189C2×C8D4×D1111yescharacteristic
190C2×C8D4×D1111yescharacteristic
191C4⋊C4—221no—
192C4⋊C4—222no—
193C4⋊C4—442no—
194C4⋊C4—442no—
195C4⋊C4—441no—
196C4⋊C4—441no—
197C4⋊C4—441no—
198C4⋊C4—441no—
199C4⋊C4D8811yescharacteristic
200C22⋊C4—21no—
201C22⋊C4—442no—
202C42—441no—
203C42C2×D4411yescharacteristic
204C16—22no—
205C16—41no—
206C11#1239411yescharacteristic, complemented, Sylow
207C23—21no—
208Q8—441no—
209Q8—441no—
210Q8—881no—
211Q8—881no—
212Q8—1761no—
213D4—21no—
214D4#6686412yes—
215C2×C4—21no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—441no—
219C2×C4—441no—
220C2×C4—442no—
221C2×C4—881no—
222C2×C4—1762no—
223C2×C4#6693511yescharacteristic
224C2×C4C2×D8811yescharacteristic
225C2×C4#6696111yescharacteristic
226C8—21no—
227C8—41no—
228C8—881no—
229C8#6696511yescharacteristic
230C8#6696811yescharacteristic
231C22—22no—
232C22—41no—
233C22—41no—
234C22#1062234511yescharacteristic
235C4—21no—
236C4—41no—
237C4—881no—
238C4—881no—
239C4—882no—
240C4—1761no—
241C4#1062239611yescharacteristic
242C4#1062243911yescharacteristic
243C4C2×#6686411yescharacteristic
244C4#1062252211yescharacteristic
245C2—42no—
246C2#1306785311yescharacteristic
247C2#1307053511yescharacteristic
248C2#1307058911yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×D4⋊C16C2
socleC22×C11#447
prime radicalC2×D4×C11D8
hypercenterD4⋊C16D11
hypocenterC11#12394
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ D4⋊C16

Complements

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

NH ≅ G/Ntype
2. #13070898C2semidirect
3. #13070759C2semidirect
5. #13066673C2semidirect
6. #13066581C2semidirect
206. C11#12394semidirect

Maximal subgroups

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

subgroupindex
#130810092
#130708982
#130707592
#130680052
#130666732
#130665812
C11×D4⋊C162
#1239411