Finite Group Databasebeta

← #14674436

Subgroups — #14674436

Order 2816.

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

normal subgroups only

This group has 284 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
1C22×Dic88C211yesmaximal, characteristic
2C2×Dic176C212yesmaximal, complemented
3#13070707C211yesmaximal, characteristic
4#13066798C212yesmaximal, complemented
5C11×C22⋊C32C211yesmaximal, characteristic
6C22×Dic44—21no—
7C22×C11×C16C2211yescharacteristic
8#10622729—21no—
9C2×Dic88—21no—
10C2×Dic88—24no—
11C2×Dic88C2211yescharacteristic
12C2×Dic88C2212yes—
13C2×C11×C32C2212yes—
14#10622142C2211yescharacteristic
15#10622141—21no—
16Dic176—24no—
17C22×Dic22—41no—
18C22×C8×C11D411yescharacteristic
19#66977—41no—
20C2×Dic44—24no—
21C2×Dic44—22no—
22C2×Dic44—21no—
23C2×Dic44—42no—
24C2×Dic44—41no—
25C2×C11×C16—22no—
26C2×C11×C16D411yescharacteristic
27C2×C11×C16C2311yescharacteristic
28#66882—21no—
29#66880—41no—
30Dic88—24no—
31Dic88—22no—
32Dic88—22no—
33Dic88D414yes—
34C11×C32—22no—
35#13665—111nomaximal, Sylow
36C22×C4×C11D811yescharacteristic
37C22×Dic11—81no—
38C2×Dic22—44no—
39C2×Dic22—42no—
40C2×Dic22—41no—
41C2×Dic22—82no—
42C2×Dic22—81no—
43C2×C8×C11—21no—
44C2×C8×C11—21no—
45C2×C8×C11D811yescharacteristic
46C2×C8×C11C2×D411yescharacteristic
47C22⋊Dic11—81no—
48C4⋊Dic11—41no—
49Dic11⋊C4—81no—
50Dic44—24no—
51Dic44—44no—
52Dic44—41no—
53Dic44—42no—
54Dic44—41no—
55C11×C16—21no—
56C11×C16C2×D412yes—
57C22×Q32—111no—
58C2×Q64—112no—
59#2216—111no—
60#1416—112no—
61C22⋊C32D1111yescharacteristic
62C23×C11D1611yescharacteristic
63C2×C4×C11—21no—
64C2×C4×C11—21no—
65C2×C4×C11D1611yescharacteristic
66C2×C4×C11C2×D811yescharacteristic
67C2×Dic11—84no—
68C2×Dic11—82no—
69C2×Dic11—81no—
70C2×Dic11—81no—
71Dic22—44no—
72Dic22—84no—
73Dic22—82no—
74Dic22—81no—
75Dic22—81no—
76C8×C11—21no—
77C8×C11#12011yescharacteristic
78C8×C11AGL(1,ℤ/8)11yescharacteristic
79C22×Q16—221no—
80C2×Q32—112no—
81C2×Q32—111no—
82C2×Q32—224no—
83C2×Q32—221no—
84C22×C16C2×D1111yescharacteristic
85#467—221no—
86Q64—224no—
87C2×C32C2×D1112yes—
88#366—111no—
89#358—221no—
90C22×C11—21no—
91C22×C11—21no—
92C22×C11Q6412yescomplemented
93C22×C11C2×D1611yescharacteristic
94C4×C11—21no—
95C4×C11#44711yescharacteristic
96C4×C11#50911yescharacteristic
97Dic11—84no—
98Dic11—161no—
99Dic11—161no—
100C22×Q8—441no—
101C2×Q16—224no—
102C2×Q16—222no—
103C2×Q16—221no—
104C2×Q16—442no—
105C2×Q16—441no—
106C22×C8D4411yescharacteristic
107C22⋊Q8—441no—
108Q32—114no—
109Q32—224no—
110Q32—222no—
111Q32—222no—
112C2×C16—22no—
113C2×C16D4411yescharacteristic
114C2×C16C22×D1111yescharacteristic
115#107—221no—
116#103—441no—
117C32—22no—
118C2×C11—22no—
119C2×C11#218411yescharacteristic
120C2×C11C2×Q6411yescharacteristic
121C2×C11#226411yescharacteristic
122C2×Q8—444no—
123C2×Q8—442no—
124C2×Q8—441no—
125C2×Q8—882no—
126C2×Q8—881no—
127C22×C4—881no—
128C22×C4D8811yescharacteristic
129Q16—224no—
130Q16—444no—
131Q16—441no—
132Q16—442no—
133Q16—441no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8D8811yescharacteristic
137C2×C8C2×D4411yescharacteristic
138C4⋊C4—441no—
139C4⋊C4—881no—
140C22⋊C4—881no—
141C16—21no—
142C16D4×D1112yes—
143C11#1366511yescharacteristic, complemented, Sylow
144C23D17611yescharacteristic
145Q8—444no—
146Q8—884no—
147Q8—882no—
148Q8—881no—
149Q8—881no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—884no—
153C2×C4—882no—
154C2×C4—881no—
155C2×C4—881no—
156C2×C4D17611yescharacteristic
157C2×C4C2×D8811yescharacteristic
158C8—21no—
159C8#6693511yescharacteristic
160C8#6696111yescharacteristic
161C22—21no—
162C22—21no—
163C22Dic17612yescomplemented
164C22C2×D17611yescharacteristic
165C4—21no—
166C4—884no—
167C4—1761no—
168C4—1761no—
169C4#1062234511yescharacteristic
170C4#1062252111yescharacteristic
171C2—22no—
172C2#1307053011yescharacteristic
173C2C2×Dic17611yescharacteristic
174C2#1307093611yescharacteristic
subgroupG/H
centerC22C2×D176
commutator, cosocleC2×C11×C16C23
FrattiniC2×C16C22×D11
FittingC11×C22⋊C32C2
socleC22×C11C2×D16
prime radicalC23×C11D16
hypercenterC22⋊C32D11
hypocenterC11#13665
LCSG ▷ C2×C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C22⋊C32

Complements

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

NH ≅ G/Ntype
2. C2×Dic176C2semidirect
4. #13066798C2semidirect
92. C22×C11Q64semidirect
143. C11#13665semidirect
163. C22Dic176semidirect

Maximal subgroups

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

subgroupindex
C22×Dic882
C2×Dic1762
#130707072
#130667982
C11×C22⋊C322
#1366511