Finite Group Databasebeta

← #14673154

Subgroups — #14673154

Order 2816.

540 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 97 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×#10622308C211yesmaximal, characteristic
2C2×#10622154C212yesmaximal, complemented
3#13070333C212yesmaximal, complemented
4#13069364C211yesmaximal, characteristic, complemented
5C11×#1376C211yesmaximal, characteristic, complemented
6C22×D88—21no—
7C22×D88C2212yes—
8C2×#66927—21no—
9C2×C11×M32C2212yes—
10C2×C4×C8×C11C2211yescharacteristic
11C2×#66883C2211yescharacteristic
12#10622719C2211yescharacteristic
13#10622715—21no—
14#10622308—24no—
15#10622161—21no—
16#10622154—24no—
17#10622147—24no—
18C22×D44—22no—
19C22×D44—42no—
20C22×C8×C11D411yescharacteristic
21C22×C8×C11C2311yescharacteristic
22C2×C42×C11D411yescharacteristic
23#66979—21no—
24C2×#4318—21no—
25C2×D88—22no—
26C2×D88—22no—
27C2×D88—22no—
28C2×D88—22no—
29C2×D88—24no—
30C2×D88—22no—
31C2×D88—42no—
32C2×D88—42no—
33C2×D88D414yes—
34#66927—24no—
35#66927—42no—
36C11×M32—22no—
37C11×M32—22no—
38C2×C11×C16—22no—
39C4×C8×C11—22no—
40#66883—22no—
41#66882D412yescomplemented
42#66881—21no—
43Dic11⋊C8—42no—
44#13413—111nomaximal, Sylow
45C23×D11—42no—
46C22×C4×C11—21no—
47C22×C4×C11C2×D411yescharacteristic
48C2×D44—24no—
49C2×D44—48no—
50C2×D44—42no—
51C2×D44—42no—
52C2×D44—42no—
53C2×D44—42no—
54C2×D44—42no—
55C2×D44—88no—
56C2×C8×C11—21no—
57C2×C8×C11—21no—
58C2×C8×C11D812yes—
59C2×C8×C11C2×D412yes—
60C2×C8×C11C2×D411yescharacteristic
61C2×C8×C11#4111yescharacteristic
62C2×C8×C11#4112yes—
63C42×C11—21no—
64C42×C11SD1612yes—
65C22⋊Dic11—41no—
66C4⋊Dic11—22no—
67C4×Dic11—41no—
68#4318—41no—
69#4318—41no—
70C2×C11⋊C8—41no—
71D88—24no—
72D88—24no—
73D88—48no—
74D88—42no—
75D88—42no—
76C11×C16—42no—
77C2×#493—111no—
78C2×#361—112no—
79#2140—112no—
80#1945—111no—
81#1376D1111yescharacteristic, complemented
82C23×C11AGL(1,ℤ/8)11yescharacteristic
83C22×D11—44no—
84C22×D11—88no—
85C22×D11—82no—
86C22×D11—82no—
87C2×C4×C11—24no—
88C2×C4×C11—22no—
89C2×C4×C11#12011yescharacteristic
90C2×C4×C11#12111yescharacteristic
91C2×C4×C11#12411yescharacteristic
92C2×C4×C11C2×D811yescharacteristic
93C2×C4×C11C2×SD1611yescharacteristic
94C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
95C2×Dic11—42no—
96D44—44no—
97D44—44no—
98D44—816no—
99D44—82no—
100D44—82no—
101C8×C11—22no—
102C8×C11#12112yes—
103C8×C11#12312yes—
104C11⋊C8—81no—
105C22×D8—112no—
106C22×D8—221no—
107C2×#127—221no—
108C2×M32C2×D1112yes—
109#493—224no—
110C2×#108—111no—
111#427—111no—
112#424—221no—
113C2×C4×C8C2×D1111yescharacteristic
114#361—224no—
115#357—224no—
116#339—221no—
117C22×C11—22no—
118C22×C11#45011yescharacteristic
119C22×C11#45911yescharacteristic
120C22×C11#49011yescharacteristic
121C2×D11—88no—
122C2×D11—84no—
123C2×D11—164no—
124C2×D11—164no—
125C4×C11—24no—
126C4×C11#39411yescharacteristic
127C4×C11#44711yescharacteristic
128C4×C11#46011yescharacteristic
129C4×C11#48611yescharacteristic
130Dic11—82no—
131C22×D4—222no—
132C22×D4—442no—
133C2×D8—114no—
134C2×D8—224no—
135C2×D8—222no—
136C2×D8—222no—
137C2×D8—222no—
138C2×D8—222no—
139C2×D8—222no—
140C2×D8—442no—
141C2×D8—442no—
142C2×M16—221no—
143C22×C8D4411yescharacteristic
144C22×C8C22×D1111yescharacteristic
145#127—224no—
146#127—442no—
147#117—221no—
148C2×C42D4411yescharacteristic
149M32—22no—
150M32—22no—
151C2×C16—22no—
152#108—222no—
153#107—112no—
154#106—221no—
155C4⋊C8—442no—
156C4×C8—22no—
157C2×C11—21no—
158C2×C11—21no—
159C2×C11#204111yescharacteristic
160C2×C11#221312yes—
161D11—164no—
162C24—442no—
163C2×D4—224no—
164C2×D4—448no—
165C2×D4—442no—
166C2×D4—442no—
167C2×D4—442no—
168C2×D4—442no—
169C2×D4—442no—
170C2×D4—888no—
171C22×C4—21no—
172C22×C4C2×D4411yescharacteristic
173D8—224no—
174D8—224no—
175D8—448no—
176D8—442no—
177D8—442no—
178M16—441no—
179M16—441no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—441no—
183C2×C8D8812yes—
184C2×C8#433912yes—
185C2×C8D4×D1111yescharacteristic
186C2×C8D4×D1112yes—
187C2×C8#434311yescharacteristic
188C4⋊C4—222no—
189C22⋊C4—441no—
190C42—21no—
191C42—441no—
192C42#431412yes—
193C16—42no—
194C11#1341311yescharacteristic, complemented, Sylow
195C23—444no—
196C23—888no—
197C23—882no—
198C23—882no—
199C23#6696111yescharacteristic
200D4—444no—
201D4—444no—
202D4—8816no—
203D4—882no—
204D4—882no—
205C2×C4—24no—
206C2×C4—22no—
207C2×C4—442no—
208C2×C4#6692811yescharacteristic
209C2×C4#6693511yescharacteristic
210C2×C4#6694811yescharacteristic
211C2×C4C2×#431411yescharacteristic
212C2×C4C2×D8811yescharacteristic
213C2×C4#6696111yescharacteristic
214C8—22no—
215C8—881no—
216C8#6693712yes—
217C8#6694712yes—
218C22—22no—
219C22—888no—
220C22—884no—
221C22—1764no—
222C22—1764no—
223C22#1062232611yescharacteristic
224C22#1062234411yescharacteristic
225C22#1062245611yescharacteristic
226C4—24no—
227C4—882no—
228C4#1062228511yescharacteristic
229C4#1062230711yescharacteristic
230C4#1062234511yescharacteristic
231C4#1062246111yescharacteristic
232C2—21no—
233C2—21no—
234C2—1764no—
235C2#1306985111yescharacteristic
236C2#1307069312yes—
subgroupG/H
centerC22#10622456
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1376C2
socleC22×C11#459
prime radicalC2×#10622308C2
hypercenter#1376D11
hypocenterC11#13413
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×#10622154C2semidirect
3. #13070333C2semidirect
4. #13069364C2semidirect
5. C11×#1376C2semidirect
41. #66882D4semidirect
81. #1376D11semidirect
194. C11#13413semidirect

Maximal subgroups

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

subgroupindex
C2×#106223082
C2×#106221542
#130703332
#130693642
C11×#13762
#1341311